AISC PARTE 1 by William Gamboa

MANUAL OF STEEL CONSTRUCTION

LOAD & RESISTANCE FACTOR DESIGN Volume I Structural Members, Specifications, & Codes Volume II Connections

Second Edition

Copyright ÂŠ 1994 by American Institute of Steel Construction, Inc. ISBN 1-56424-041-X ISBN 1-56424-042-8 All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher. The information presented in this publication has been prepared in accordance with recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and verification of its accuracy, suitability, and applicability by a licensed professional engineer, designer, or architect. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction or of any other person named herein, that this information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. Caution must be exercised when relying upon other specifications and codes developed by other bodies and incorporated by reference herein since such material may be modified or amended from time to time subsequent to the printing of this edition. The Institute bears no responsibility for such material other than to refer to it and incorporate it by reference at the time of the initial publication of this edition. Printed in the United States of America

FOREWORD

he American Institute of Steel Construction, founded in 1921, is the non-profit technical specifying and trade organization for the fabricated structural steel industry in the United States. Executive and engineering headquarters of AISC are maintained in Chicago, Illinois. The Institute is supported by three classes of membership: Active Members totaling 400 companies engaged in the fabrication and erection of structural steel, Associate Members who are allied product manufacturers, and Professional Members who are individuals or firms engaged in the practice of architecture or engineering. Professional members also include architectural and engineering educators. The continuing financial support and active participation of Active Members in the engineering, research, and development activities of the Institute make possible the publishing of this Second Edition of the Load and Resistance Factor Design Manual of Steel Construction. The Instituteâ&#x20AC;&#x2122;s objectives are to improve and advance the use of fabricated structural steel through research and engineering studies and to develop the most efficient and economical design of structures. It also conducts programs to improve product quality. To accomplish these objectives the Institute publishes manuals, textbooks, specifications, and technical booklets. Best known and most widely used are the Manuals of Steel Construction, LRFD (Load and Resistance Factor Design) and ASD (Allowable Stress Design), which hold a highly respected position in engineering literature. Outstanding among AISC standards are the Specifications for Structural Steel Buildings and the Code of Standard Practice for Steel Buildings and Bridges. The Institute also assists designers, contractors, educators, and others by publishing technical information and timely articles on structural applications through two publications, Engineering Journal and Modern Steel Construction. In addition, public appreciation of aesthetically designed steel structures is encouraged through its award programs: Prize Bridges, Architectural Awards of Excellence, Steel Bridge Building Competition for Students, and student scholarships. Due to the expanded nature of the material, the Second Edition of the LRFD Manual has been divided into two complementary volumes. Volume I contains the LRFD Specification and Commentary, tables, and other design information for structural members. Volume II contains all of the information on connections. Like the LRFD Specification upon which they are based, both volumes of this LRFD Manual apply to buildings, not bridges. The Committee gratefully acknowledges the contributions of Roger L. Brockenbrough, Louis F. Geschwindner, Jr., and Cynthia J. Zahn to this Manual. By the Committee on Manuals, Textbooks, and Codes, William A. Thornton, Chairman

Barry L. Barger, Vice Chairman

Horatio Allison Robert O. Disque Joseph Dudek William G. Dyker Ronald L. Hiatt

David T. Ricker Abraham J. Rokach Ted W. Winneberger Charles J. Carter, Secretary

Mark V. Holland William C. Minchin Thomas M. Murray Heinz J. Pak Dennis F. Randall

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

REFERENCED SPECIFICATIONS, CODES, AND STANDARDS

Part 6 (Volume I) of this LRFD Manual contains the full text of the following: American Institute of Steel Construction, Inc. (AISC) Load and Resistance Factor Design Specification for Structural Steel Buildings, December 1, 1993 Specification for Load and Resistance Factor Design of Single-Angle Members, December 1, 1993 Seismic Provisions for Structural Steel Buildings, June 15, 1992 Code of Standard Practice for Steel Buildings and Bridges, June 10, 1992 Research Council on Structural Connections (RCSC) Load and Resistance Factor Design Specifications for Structural Joints Using ASTM A325 or A490 Bolts, June 8, 1988 Additionally, the following other documents are referenced in Volumes I and II of the LRFD Manual: American Association of State Highway and Transportation Officials (AASHTO) AASHTO/AWS D1.5–88 American Concrete Institute (ACI) ACI 349–90 American Iron and Steel Institute (AISI) Load and Resistance Factor Design Specification for Cold-Formed Steel Structural Members, 1991 American National Standards Institute (ANSI) ANSI/ASME B1.1–82 ANSI/ASME B18.2.2–86 ANSI/ASME B18.1–72 ANSI/ASME B18.5–78 ANSI/ASME B18.2.1–81 American Society of Civil Engineers (ASCE) ASCE 7-88 American Society for Testing and Materials (ASTM) ASTM A6–91b ASTM A490–91 ASTM A617–92 ASTM A27–87 ASTM A500–90a ASTM A618–90a ASTM A36–91 ASTM A501–89 ASTM A668–85a ASTM A53–88 ASTM A502–91 ASTM A687–89 ASTM A148–84 ASTM A514–91 ASTM A709–91 ASTM A153–82 ASTM A529–89 ASTM A770–86 ASTM A193–91 ASTM A563–91c ASTM A852–91 ASTM A194–91 ASTM A570–91 ASTM B695–91 ASTM A208(A239–89) ASTM A572–91 ASTM C33–90 ASTM A242–91a ASTM A588–91a ASTM C330–89 ASTM A307–91 ASTM A606–91a ASTM E119–88 ASTM A325–91c ASTM A607–91 ASTM E380–91 ASTM A354–91 ASTM A615–92b ASTM F436–91 ASTM A449–91a ASTM A616–92 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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American Welding Society (AWS) AWS A2.4–93 AWS A5.25–91 AWS A5.1–91 AWS A5.28–79 AWS A5.5–81 AWS A5.29–80 AWS A5.17–89 AWS B1.0–77 AWS A5.18–79 AWS D1.1–92 AWS A5.20–79 AWS D1.4–92 AWS A5.23–90

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1-1

PART 1 DIMENSIONS AND PROPERTIES

OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 STRUCTURAL STEELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5 Selection of the Appropriate Structural Steel . . . . . . . . . . . . . . . . . . . . . . . . . 1-5 Brittle Fracture Considerations in Structural Design . . . . . . . . . . . . . . . . . . . . . 1-6 Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8 Jumbo Shapes and Heavy-Welded Built-Up Sections . . . . . . . . . . . . . . . . . . . . 1-8 FIRE-RESISTANT CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8 Effect of Shop Painting on Spray-Applied Fireproofing . . . . . . . . . . . . . . . . . . 1-11 EFFECT OF HEAT ON STRUCTURAL STEEL . . . . . . . . . . . . . . . . . . . . . . 1-11 Coefficient of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12 Use of Heat to Straighten, Camber, or Curve Members . . . . . . . . . . . . . . . . . . 1-12 EXPANSION JOINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 AISC Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 AISC for AutoCAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 STRUCTURAL SHAPES: TABLES OF AVAILABILITY, SIZE GROUPINGS, PRINCIPAL PRODUCERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 STEEL PIPE AND STRUCTURAL TUBING: TABLES OF AVAILABILITY, PRINCIPAL PRODUCERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21 STRUCTURAL SHAPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-25 Designations, Dimensions, and Properties . . . . . . . . . . . . . . . . . . . . . . . . . 1-25 Tables: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26 M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44 S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46 HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-48 American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50 Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52 Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-56 STRUCTURAL TEES (WT, MT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Use of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67 DOUBLE ANGLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91 Use of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91 COMBINATION SECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-105 STEEL PIPE AND STRUCTURAL TUBING . . . . . . . . . . . . . . . . . . . . . . . 1-120 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120 Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120 Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120 BARS AND PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133 Product Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133 Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133 Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133 Floor Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-134 CRANE RAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139 General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139 Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139 Welded Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-141 Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-141 TORSION PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-145 SURFACE AREAS AND BOX AREAS . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175 CAMBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179 Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179 Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179 STANDARD MILL PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183 General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183 Methods of Increasing Areas and Weights by Spreading Rolls

. . . . . . . . . . . . . 1-183

Cambering of Rolled Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-185 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-199

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

OVERVIEW

1-3

OVERVIEW To facilitate reference to Part 1, the locations of frequently used tables are listed below. Dimensions and Properties W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26 M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44 S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46 HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-48 American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50 Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52 Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-56 Structural Tees (WT, MT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-68 Double Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-92 Combination Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-106 Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-121 Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-122 Torsion Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-146 Surface Areas and Box Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175 Availability Availability of Shapes, Plates, and Bars, Table 1-1 . . . . . . . . . . . . . . . . . . . . 1-15 Structural Shape Size Groupings, Table 1-2 . . . . . . . . . . . . . . . . . . . . . . . . 1-16 Principal Producers of Structural Shapes, Table 1-3 . . . . . . . . . . . . . . . . . . . . 1-18 Availability of Steel Pipe and Structural Tubing, Table 1-4 . . . . . . . . . . . . . . . . 1-21 Principal Producers of Structural Tubing (TS), Table 1-5 . . . . . . . . . . . . . . . . . 1-22 Principal Producers of Steel Tubing (Round), Table 1-6 . . . . . . . . . . . . . . . . . . 1-26

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1-4

DIMENSIONS AND PROPERTIES

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL STEELS

1-5

STRUCTURAL STEELS Availability

Section A3.1 of the AISC Load and Resistance Factor Design Specification for Structural Steel Buildings lists fifteen ASTM specifications for structural steel approved for use in building construction. Five of these steels are available in hot-rolled structural shapes, plates, and bars. Two steels, ASTM A514 and A852, are available only in plates. Table 1-1 shows five groups of shapes and eleven ranges of thickness of plates and bars available in the various minimum yield stress* and tensile strength levels afforded by the seven steels. For complete information on each steel, reference should be made to the appropriate ASTM specification. A listing of shape sizes included in each of the five groups follows in Table 1-2, corresponding with the groupings given in Table A of ASTM Specification A6. Seven additional grades of steel, other than those covering hot-rolled shapes, plates, and bars, are listed in Section A3.1a of the LRFD Specification. These steels cover pipe, cold- and hot-formed tubing, and cold- and hot-rolled sheet and strip. The principal producers of shapes listed in Part 1 of this Manual are shown in Table 1-3. Availability and the principal producers of structural tubing are shown in Tables 1-4 through 1-6. For additional information on availability and classification of structural steel plates and bars, refer to the separate discussion beginning on page 1-129. Space does not permit inclusion in Table 1-3, or in the listing of shapes and plates in Part 1 of this Manual, of all rolled shapes or plates of greater thickness that are occasionally used in construction. For such products, reference should be made to the various producers’ catalogs. To obtain an economical structure, it is often advantageous to minimize the number of different sections. Cost per square foot can often be reduced by designing this way. Selection of the Appropriate Structural Steel

Steels with 50 ksi yield stress are now widely used in construction, replacing ASTM A36 steel in many applications. The 50 ksi steels listed in Section A3.1a of the LRFD Specification are ASTM A572 high-strength low-alloy structural steel, ASTM A242 and A588 atmospheric-corrosion-resistant high-strength low-alloy structural steels, and ASTM A529 high-strength carbon-manganese structural steel. Yield stresses above 50 ksi can be obtained from two grades of ASTM A572 steel as well as ASTM A514 and A852 quenched and tempered structural steel plate. These higher-strength steels have certain advantages over 50 ksi steels in certain applications. They may be economical choices where lighter members, resulting from use of higher design strengths, are not penalized because of instability, local buckling, deflection, or other similar reasons. They may be used in tension members, beams in continuous and composite construction where deflections can be minimized, and columns having low slenderness ratios. The reduction of dead load and associated savings in shipping costs can be significant factors. However, higher strength steels are not to be used indiscriminately. Effective use of all steels depends on thorough cost and engineering analysis. Normally, connection material is specified as ASTM A36. The connection tables in this Manual are for A36 steel.

*As used in the AISC LRFD Specification, “yield stress” denotes either the specified minimum yield point (for those that have a yield point) or specified minimum yield strength (for those steels that do not have a yield point). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

With appropriate procedures and precautions, all steels listed in the AISC Specification are suitable for welded fabrication. To provide for weldability of ASTM A529 steel, the specification of a maximum carbon equivalent is recommended. ASTM A242 and A588 atmospheric-corrosion-resistant, high-strength, low-alloy steels can be used in the bare (uncoated) condition in most atmospheres. Where boldly exposed under such conditions, exposure to the normal atmosphere causes a tightly adherent oxide to form on the surface which protects the steel from further atmospheric corrosion. To achieve the benefits of the enhanced atmospheric corrosion resistance of these bare steels, it is necessary that design, detailing, fabrication, erection, and maintenance practices proper for such steels be observed. Designers should consult with the steel producers on the atmospheric-corrosion-resistant properties and limitations of these steels prior to use in the bare condition. When either A242 or A588 steel is used in the coated condition, the coating life is typically longer than with other steels. Although A242 and A588 steels are more expensive than other high-strength, low-alloy steels, the reduction in maintenance resulting from the use of these steels usually offsets their higher initial cost. Brittle Fracture Considerations in Structural Design

As the temperature decreases, an increase is generally noted in the yield stress, tensile strength, modulus of elasticity, and fatigue strength of the structural steels. In contrast, the ductility of these steels, as measured by reduction in area or by elongation, and the toughness of these steels, as determined from a Charpy V-notch impact test, decrease with decreasing temperatures. Furthermore, there is a temperature below which a structural steel subjected to tensile stresses may fracture by cleavage,* with little or no plastic deformation, rather than by shear,* which is usually preceded by a considerable amount of plastic deformation or yielding. Fracture that occurs by cleavage at a nominal tensile stress below the yield stress is commonly referred to as brittle fracture. Generally, a brittle fracture can occur in a structural steel when there is a sufficiently adverse combination of tensile stress, temperature, strain rate, and geometrical discontinuity (notch) present. Other design and fabrication factors may also have an important influence. Because of the interrelation of these effects, the exact combination of stress, temperature, notch, and other conditions that will cause brittle fracture in a given structure cannot be readily calculated. Consequently, designing against brittle fracture often consists mainly of (1) avoiding conditions that tend to cause brittle fracture and (2) selecting a steel appropriate for the application. A discussion of these factors is given in the following sections. Conditions Causing Brittle Fracture

It has been established that plastic deformation can occur only in the presence of shear stresses. Shear stresses are always present in a uniaxial or biaxial state-of-stress. However, in a triaxial state-of-stress, the maximum shear stress approaches zero as the principal stresses approach a common value, and thus, under equal triaxial tensile stresses, failure occurs by cleavage rather than by shear. Consequently, triaxial tensile stresses tend to cause brittle fracture and should be avoided. A triaxial state-of-stress can result from a uniaxial loading when notches or geometrical discontinuities are present.

*Shear and cleavage are used in the metallurgical sense (macroscopically) to denote different fracture mechanisms. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL STEELS

1-7

Increased strain rates tend to increase the possibility of brittle behavior. Thus, structures that are loaded at fast rates are more susceptible to brittle fracture. However, a rapid strain rate or impact load is not a required condition for a brittle fracture. Cold work and the strain aging that normally follows generally increase the likelihood of brittle fracture. This behavior is usually attributed to the previously mentioned reduction in ductility. The effect of cold work that occurs in cold forming operations can be minimized by selecting a generous forming radius and, thus, limiting the amount of strain. The amount of strain that can be tolerated depends on both the steel and the application. The use of welding in construction increases the concerns relative to brittle fracture. In the as-welded condition, residual stresses will be present in any weldment. These stresses are considered to be at the yield point of the material. To avoid brittle fracture, it may be required to utilize steels with higher toughness than would be required for bolted construction. Welds may also introduce geometric conditions or discontinuities that are crack-like in nature. These stress risers will additionally increase the requirement for notch toughness in the weldment. Avoidance of the intersection of welds from multiple directions reduces the likelihood of triaxial stresses. Properly sized weld-access holes prohibit the interaction of these various stress fields. As steels being welded become thicker and more highly restrained, welding procedure issues such as preheat, interpass temperature, heat input, and cooling rates become increasingly important. The residual stresses present in a weldment may be reduced by the use of fewer weld passes and peening of intermittent weld layers. In most cases, weld metal notch toughness exceeds that of the base materials. However, for fracture-sensitive applications, notch-tough base and weld metal should be specified. The residual stresses of welding can be greatly reduced through thermal stress relief. This reduces the driving force that causes brittle fracture, but if the toughness of the material is adversely affected by this thermal treatment, no increase in brittle fracture resistance will be experienced. Therefore, when weldments are to be stress relieved, investigation into the effects on the weld metal, heat-affected zone, and base material should be made. Selecting a Steel To Avoid Brittle Fracture

The best guide in selecting a steel that is appropriate for a given application is experience with existing and past structures. A36 and Grade 50 (i.e., 50 ksi yield stress) steels have been used successfully in a great number of applications, such as buildings, transmission towers, transportation equipment, and bridges, even at the lowest atmospheric temperatures encountered in the U.S. Therefore, it appears that any of the structural steels, when designed and fabricated in an appropriate manner, could be used for similar applications with little likelihood of brittle fracture. Consequently, brittle fracture is not usually experienced in such structures unless unusual temperature, notch, and stress conditions are present. Nevertheless, it is always desirable to avoid or minimize the previously cited adverse conditions that increase the susceptibility of the steel to brittle fracture. In applications where notch toughness is considered important, it usually is required that steels must absorb a certain amount of energy, 15 ft-lb or higher (Charpy V-notch test), at a given temperature. The test temperature may be higher than the lowest operating temperature depending on the rate of loading. See Rolfe and Barsom (1986) and Rolfe (1977). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1-8

DIMENSIONS AND PROPERTIES

Lamellar Tearing

The information on strength and ductility presented in the previous sections generally pertains to loadings applied in the planar direction (longitudinal or transverse orientation) of the steel plate or shape. It should be noted that elongation and area reduction values may well be significantly lower in the through-thickness direction than in the planar direction. This inherent directionality is of small consequence in many applications, but does become important in the design and fabrication of structures containing massive members with highly restrained welded joints. With the increasing trend toward heavy welded-plate construction, there has been a broader recognition of the occurrence of lamellar tearing in some highly restrained joints of welded structures, especially those using thick plates and heavy structural shapes. The restraint induced by some joint designs in resisting weld deposit shrinkage can impose tensile strain sufficiently high to cause separation or tearing on planes parallel to the rolled surface of the structural member being joined. The incidence of this phenomenon can be reduced or eliminated through greater understanding by designers, detailers, and fabricators of (1) the inherent directionality of construction forms of steel, (2) the high restraint developed in certain types of connections, and (3) the need to adopt appropriate weld details and welding procedures with proper weld metal for through-thickness connections. Further, steels can be specified to be produced by special practices and/or processes to enhance through-thickness ductility and thus assist in reducing the incidence of lamellar tearing. Steels produced by such practices are available from several producers. However, unless precautions are taken in both design and fabrication, lamellar tearing may still occur in thick plates and heavy shapes of such steels at restrained through-thickness connections. Some guidelines in minimizing potential problems have been developed (AISC, 1973). See also Part 8 in Volume II of this LRFD Manual and ASTM A770, Standard Specification for Through-Thickness Tension Testing of Steel Plates for Special Applications. Jumbo Shapes and Heavy Welded Built-up Sections

Although Group 4 and 5 W-shapes, commonly referred to as jumbo shapes, generally are contemplated as columns or compression members, their use in non-column applications has been increasing. These heavy shapes have been known to exhibit segregation and a coarse grain structure in the mid-thickness region of the flange and the web. Because these areas may have low toughness, cracking might occur as a result of thermal cutting or welding (Fisher and Pense, 1987). Similar problems may also occur in welded built-up sections. To minimize the potential of brittle failure, the current LRFD Specification includes provisions for material toughness requirements, methods of splicing, and fabrication methods for Group 4 and 5 hot-rolled shapes and welded built-up cross sections with an element of the cross section more than two inches in thickness intended for tension applications. FIRE-RESISTANT CONSTRUCTION

Fire-resistant steel construction may be defined as structural members and assemblies which can maintain structural stability for the duration of building fire exposure and, in some cases, prevent the spread of fire to adjacent spaces. Fire resistance of a steel member is a function of its mass, its geometry, the load to which it is subjected, its structural support conditions, and the fire to which it is exposed. Many steel structures have inherent fire resistance through a combination of the above factors and do not require additional insulation from the effects of fire. However, in many AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FIRE-RESISTANT CONSTRUCTION

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situations, building codes specify the use of fire-rated steel assemblies. In this case, ASTM Specification E119, Standard Methods of Fire Tests of Building Construction and Materials, outlines the procedures of fire testing of structural elements. Structural fire resistance is a major consideration in the design of modern buildings. In general, building codes define the level of fire protection that is required in specific applications and structural fire protection is typically implemented in design through code compliance. In the United States, with a few notable exceptions, the majority of cities and states now enforce one of the following model codes: • National Building Code, published by the Building Officials and Code Administrators International. • Standard Building Code, published by the Southern Building Code Congress International. • Uniform Building Code, published by the International Conference of Building Officials. Building codes specify fire-resistance requirements as a function of building occupancy, height, area, and whether or not other fire protection systems (e.g., sprinklers) are provided. Fire-resistance requirements are specified in terms of hourly ratings based upon tests conducted in accordance with ASTM E119. This test method specifies a “standard” fire for evaluating the relative fire-resistance of construction assemblies (i.e., floors, roofs, beams, girders, and columns). Specific end-point criteria for evaluating the ability of assemblies to prevent the spread of fire to adjacent spaces and/or to continue to sustain superimposed loads are included. In effect, ASTM E119 is used to evaluate the length of time that an assembly continues to perform these functions when exposed to the standard fire. Thus, code requirements and fire-resistance ratings are specified in terms of time (i.e., one hour, two hours, etc.). The design of fire-resistant buildings is typically accomplished in a very prescriptive fashion by selecting tested designs that satisfy specific building code requirements. Listings of fire-resistant designs are available from a number of sources including: • Fire-Resistance Directory, Underwriters Laboratories. • Fire-Resistance Ratings, American Insurance Services Group. • Fire-Resistance Design Manual, Gypsum Association. In general, due to the very prescriptive nature of fire-resistant design, changes in tested assemblies can be difficult to justify to the satisfaction of code officials and listing agencies. In the case of structural steel construction, however, the basic heat transfer and structural principles are well defined. As a result, relatively simple analytical techniques have been developed that enable designers to use a variety of different structural steel shapes in conjunction with tested assemblies. These analytical techniques are specifically recognized by North American building code authorities and are described in a series of booklets published by the American Iron and Steel Institute (AISI): Designing Fire Protection for Steel Columns (1980) Designing Fire Protection for Steel Beams (1984) Designing Fire Protection for Steel Trusses (1981) Since fire-resistant design is currently based on the use of tested assemblies, an important consideration is the degree to which a test assembly is “representative” of AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

actual building construction. In reality, this consideration poses a number of technical difficulties due to the size of available testing facilities, most of which can only accommodate floor or roof specimens in the range of 15 ft by 18 ft in area. As a result, a test assembly represents a relatively small sample of a typical floor or roof structure. Most floor slabs and roof decks are physically, if not structurally, continuous over beams and girders. Beam and girder spans are often much larger than can be accommodated in available laboratory furnaces. A variety of connection details are used to frame beams, girders, and columns. In short, given the cost of testing, the complexity and variety of modern structural systems, and the size of available test facilities, it is unrealistic to assume that test assemblies accurately model real construction systems during fire exposure. In recognition of the practical difficulties associated with laboratory scale testing, ASTM E119 includes two specific test conditions, “restrained” and “unrestrained.” From a structural engineering standpoint, the choice of these two terms is unfortunate since the “restraint” that is contemplated in fire testing is restraint against the thermal expansion, not structural rotational restraint in the traditional sense. The “restrained” condition applies when the assembly is supported or surrounded by construction which is “capable of resisting substantial thermal expansion throughout the range of anticipated elevated temperatures.” Otherwise, the assembly should be considered free to rotate and expand at the supports and should be considered “unrestrained.” Thus, a floor system that is simply supported from a structural standpoint will often be “restrained” from a fireresistance standpoint. In order to provide guidance on the use of restrained and unrestrained ratings, ASTM E119 includes an explanatory Appendix. It should be emphasized that most common types of steel framing can be considered “restrained” from a fire-resistance standpoint. The standard fire test also includes other arbitrary assumptions. The specific fire exposure, for example, is based on furnace capabilities with continuous fuel supply and does not model real building fires with exhaustible fuel. Also, the test method assumes that assemblies are fully loaded when a fire occurs. In reality, fires are infrequent, random events and their design requirements should be probability based. Rarely will design structural loads occur simultaneously with fire. In addition, many structural elements are sized for serviceability (i.e., drift, deflection, or vibration) rather than strength, thereby providing an additional reserve strength during a fire. As a result of these and other considerations, more rational engineering design standards for structural fire protection are now being developed (International Fire Engineering Design for Steel Structures: State-of-the-Art, International Iron and Steel Institute). Although not yet standardized or recognized in North American building codes, similar design methods have been used in specific cases, based on code variances. One such method has been developed by AISI for architecturally exposed structural steel elements on the exterior of buildings. In effect, ASTM E119 assumes that structural elements are located within a fire compartment and does not realistically characterize the fire exposure that will be seen by exterior structural elements. Fire-Safe Structural Steel: A Design Guide (American Iron and Steel Institute, 1979) defines a step-by-step analytical procedure for determining maximum steel temperatures, based on realistic fire exposures for exterior structural elements. Occasionally, structural engineers will be called upon to evaluate fire-damaged steel structures. Although it is well known that the prolonged exposure to high temperatures can affect the physical and metallurgical properties of structural steel, in most cases steel AMERICAN INSTITUTE OF STEEL CONSTRUCTION

EFFECT OF HEAT ON STRUCTURAL STEEL

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members that can be straightened in place will be suitable for continued use (Dill, 1960). Special attention should be given to heat-treated or cold-formed steel elements and high-strength bolts and welds. Effect of Shop Painting on Spray-Applied Fireproofing

Spray-applied fireproofing has excellent adhesion to unpainted structural steel. Mechanical anchorage devices, bonding agents, or bond tests are not required to meet Underwriters Laboratories, Inc. (UL) guidelines. In fact, moderate rusting enhances the adhesion of the fireproofing material, providing the uncoated steel is free of loose rust and mill scale. Customarily, any loose rust or mill scale as well as any other debris which has accumulated during the construction process is removed by the fireproofing application contractor. In many cases, this may be as simple as blowing it off with compressed air. This ease of application is not realized when fireproofing is applied over painted steel. In order to meet UL requirements, bond tests in accordance with the ASTM E736 must be performed to determine if the fireproofing material has adequate adherence to the painted surface. Frequently, a bonding agent must be added to the fireproofing material and the bond test repeated to determine if the minimum bond strength can be met. Should the bond testing still not be satisfactory, mechanical anchorage devices are required to be applied to the steel before the fireproofing can be applied. The erected steel must still be cleaned free of any construction debris and scaling or peeling paint before the fireproofing may be applied. Once it is determined that the bond tests are adequate, UL guidelines require that if fireproofing is spray-applied over painted steel, the steel must be wrapped with steel lath or mechanical anchorage devices must be applied to the steel if the structural shape exceeds the following dimensional criteria: • For beam applications, the web depth cannot exceed 16 inches and the flange cannot exceed 12 inches. • For column applications, neither the web depth nor the flange width can exceed 16 inches. A significant number of structural shapes do not meet these restrictions. The use of primers under spray-applied fireproofing significantly increases the cost of the steel and the preparation for and the application of the fireproofing material. In an enclosed structure, primer is insignificant in either the short- or long-term protection of the steel. LRFD Specification Section M3.1 states that structural steelwork need not be painted unless required by the contract. For many years, the AISC specifications have not required that steelwork be painted when it will be concealed by interior building finish or will be in contact with concrete. The use of primers under spray-applied fireproofing is strongly discouraged unless there is a compelling reason to paint the steel to protect against corrosion. It is suggested that the designer refer to the UL Directory Fire Resistance—Volume 1, 1993, “Coating Materials,” for more specific information on this topic. EFFECT OF HEAT ON STRUCTURAL STEEL

Short-time elevated-temperature tensile tests on the structural steels permitted by the AISC Specification indicate that the ratios of the elevated-temperature yield and tensile strengths to their respective room-temperature values are reasonably similar in the 300° to 700°F range, except for variations due to strain aging. (The tensile strength ratio may AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

increase to a value greater than unity in the 300° to 700°F range when strain aging occurs.) Below 700°F the strength ratios decrease only slightly. Above 700°F the ratio of elevated-temperature to room-temperature strength decreases more rapidly as the temperature increases. The composition of the steels is usually such that the carbon steels (ASTM A36 and A529) exhibit strain aging with attendant reduced notch toughness. The high-strength low-alloy steels (ASTM A242, A572, and A588) and heat-treated alloy steels (ASTM A514 and A852) exhibit less-pronounced or little strain aging. As examples of the decreased ratio levels obtained at elevated temperature, the yield strength ratios for carbon and high-strength low-alloy steels are approximately 0.77 at 800°F, 0.63 at 1,000°F, and 0.37 at 1,200°F. Coefficient of Expansion

The average coefficient of expansion for structural steel between 70°F and 100°F is 0.0000065 for each degree. For temperatures of 100°F to 1,200°F the coefficient is given by the approximate formula: ε = (6.1+0.0019t) × 10−6 in which ε is the coefficient of expansion (change in length per unit length) for each degree Fahrenheit and t is the temperature in degrees Fahrenheit. The modulus of elasticity of structural steel is approximately 29,000 ksi at 70°F. It decreases linearly to about 25,000 ksi at 900°F, and then begins to drop at an increasing rate at higher temperatures. Use of Heat to Straighten, Camber, or Curve Members

With modern fabrication techniques, a controlled application of heat can be effectively used to either straighten or to intentionally curve structural members. By this process, the member is rapidly heated in selected areas; the heated areas tend to expand, but are restrained by adjacent cooler areas. This action causes a permanent plastic deformation or “upset” of the heated areas and, thus, a change of shape is developed in the cooled member. “Heat straightening” is used in both normal shop fabrication operations and in the field to remove relatively severe accidental bends in members. Conversely, “heat cambering” and “heat curving” of either rolled beams or welded girders are examples of the use of heat to effect a desired curvature. As with many other fabrication operations, the use of heat to straighten or curve will cause residual stresses in the member as a result of plastic deformations. These stresses are similar to those that develop in rolled structural shapes as they cool from the rolling temperature; in this case, the stresses arise because all parts of the shape do not cool at the same rate. In like manner, welded members develop residual stresses from the localized heat of welding. In general, the residual stresses from heating operations do not affect the ultimate strength of structural members. Any reduction in strength due to residual stresses is incorporated in the provisions of the LRFD Specification. The mechanical properties of steels are largely unaffected by heating operations, provided that the maximum temperature does not exceed 1,100°F for quenched and tempered alloy steels (ASTM A514 and A852), and 1,300°F for other steels. The AMERICAN INSTITUTE OF STEEL CONSTRUCTION

EXPANSION JOINTS

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temperature should be carefully checked by temperature-indicating crayons or other suitable means during the heating process. EXPANSION JOINTS

Although buildings are typically constructed of flexible materials, expansion joints are required in roofs and the supporting structure when horizontal dimensions are large. The maximum distance between expansion joints is dependent upon many variables including ambient temperature during construction and the expected temperature range during the lifetime of the building. An excellent reference on the topic of thermal expansion in buildings and location of expansion joints is the Federal Construction Councilâ&#x20AC;&#x2122;s Technical Report No. 65, Expansion Joints in Buildings. Taken from this report, Figure 1-1 provides a guide based on design temperature change for maximum spacing of structural expansion joints in beam-and-column-framed buildings with hinged-column bases and heated interiors. The report includes data for numerous cities and gives five modification factors which should be applied as appropriate:

MAXIMUM SPACING OF EXPANSION JOINTS (ft)

1. If the building will be heated only and will have hinged-column bases, use the maximum spacing as specified; 2. If the building will be air-conditioned as well as heated, increase the maximum spacing by 15 percent provided the environmental control system will run continuously; 3. If the building will be unheated, decrease the maximum spacing by 33 percent; 4. If the building will have fixed column bases, decrease the maximum spacing by 15 percent;

600

500

Rectangular multiframed configuration with Symmetrical stiffness

400

Steel

300 200

Nonrectangular configuration (L, T, U type)

Any material

100

10 20 30 40

50 60 70 70 80 90

DESIGN TEMPERATURE CHANGE (Â°F)

Fig. 1-1. Expansion joint spacing. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

5. If the building will have substantially greater stiffness against lateral displacement in one of the plan dimensions, decrease the maximum spacing by 25 percent. When more than one of these design conditions prevail in a building, the percentile factor to be applied should be the algebraic sum of the adjustment factors of all the various applicable conditions. Additionally, most building codes include restrictions on location and spacing of fire walls. Such fire walls often become locations for expansion joints. The most effective expansion joint is a double line of columns which provides a complete and positive separation. When expansion joints other than the double-column type are employed, low-friction sliding elements are generally used. Such systems, however, are never totally free and will induce some level of inherent restraint to movement. COMPUTER SOFTWARE AISC Database

The AISC Database contains the properties and dimensions of structural steel shapes, corresponding to Part 1 of this LRFD Manual. LRFD-related properties such as X1 and X2, as well as torsional properties, are included. Two versions, one in U.S. customary units and one in metric units, are available. Dimensions and properties of W, S, M, and HP shapes, American Standard Channels (C), Miscellaneous Channels (MC), Structural Tees cut from W, M, and S shapes (WT, MT, ST), Single and Double Angles, Structural Tubing, and Pipe are listed in ASCII format. Also included are: a BASIC read/write program, a sample search routine, and a routine to convert the file to Lotus *.PRN file format. AISC for AutoCAD *

The program will draw the end, elevation, and plan views of W, S, M, and HP shapes, American Standard Channels (C), Miscellaneous Channels (MC), Structural Tees cut from W, M, and S shapes (WT, MT, ST), Single and Double Angles, Structural Tubing, and Pipe to full scale corresponding to data published in Part 1 of this LRFD Manual. Version 2.0 runs in AutoCAD Release 12 only; Version 1.0 runs in AutoCAD Releases 10 and 11.

*AutoCAD is a registered trademark in the US Patent and Trademark Office by Autodesk, Inc. AISC for AutoCAD is copyrighted in the US Copyright Office by Bridgefarmer and Associates, Inc. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 1-1. Availability of Shapes, Plates, and Bars According to ASTM Structural Steel Specifications Shapes

Steel Type

A36

58–80

58–80c

60–85

70–100

A242

HighStrength Low-alloy

Corrosion Resistant Highstrength Low-alloy

A572 Grade

A529f Grade

Carbon

Group per Over Over Mini1⁄ ″ 3⁄ ″ ASTM A6 Fu mum 2 4 ASTM Yield Tensile To to to a 1⁄ ″ 3 ⁄ ″ 11 ⁄ ″ Desig- Stress Stress 2 4 4 b nation (ksi) (ksi) 1 2 3 4 5 incl. incl. incl.

A588

Quenched A852e & Tempered Alloy

90–110

Quenched A514e & Tempered A514e Low-Alloy

100–130

100

110–130

Plates and Bars Over Over Over Over Over Over Over 11⁄4″ 11⁄2″ 2″ 21⁄2″ 4″ 5″ 6″ to to to to to to to 11⁄2″ 2″ 21⁄2″ 4″ 5″ 6″ 8″ Over incl. incl. incl. incl. incl. incl. incl. 8″

aMinimum unless a range is shown. bIncludes bar-size shapes cFor shapes over 426 lb / ft minimum of 58 ksi only applies. dPlates to 1 in. thick, 12 in. width; bars to 11⁄ in. 2 ePlates only. fTo improve the weldability of A529 steel, the specification of a maximum carbon equivalent

(per ASTM Supplementary Requirement S78) is recommended. Available Not Available

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-2. Structural Shape Size Groupings for Tensile Property Classification Structural Shapes W shapes

Group 1

Group 2

Group 3 W44× 290, 335

Group 4

W24× 55, 62

W44× 230, 262

W21× 44 to 57 incl.

W40× 149 to 264 incl. W40× 431

W18× 35 to 71 incl.

W36× 135 to 210 incl. W40× 277 to 372 incl. W36× 328 to 798 incl.

W16× 26 to 57 incl.

W33× 118 to 152 incl. W36× 230 to 300 incl. W33× 318 to 354 incl.

W14× 22 to 53 incl.

W30× 90 to 211 incl. W33× 169 to 291 incl. W30× 292 to 477 incl.

W12× 14 to 58 incl.

W27× 84 to 178 incl. W30× 235 to 261 incl. W27× 307 to 539 incl.

W10× 12 to 45 incl.

W24× 68 to 162 incl. W27× 194 to 258 incl. W24× 250 to 492 incl.

Group 5

W40×466 to 593 incl. W36× 848 W40× 392

W8× 10 to 48 incl.

W21× 62 to 147 incl. W24× 176 to 229 incl. W18× 211 to 311 incl.

W6× 9 to 25 incl.

W18× 76 to 143 incl. W21× 166 to 201 incl. W14× 233 to 550 incl.

W5× 16,19

W16× 67 to 100 incl. W18× 158 to 192 incl. W12× 210 to 336 incl.

W4× 13

W14× 61 to 132 incl. W14× 145 to 211 incl.

W14× 605 to 808 incl.

W12× 65 to 106 incl. W12× 120 to 190 incl. W10× 49 to 112 incl. W8× 58, 67 M Shapes

all

S Shapes

to 35 lb/ft incl.

over 35 lb/ft

HP Shapes

to 102 lb/ft incl.

American to 20.7 lb/ft incl. Standard Channels (C)

over 20.7 lb/ft

Miscellane- to 28.5 lb/ft incl. ous Channels (MC)

over 28.5 lb/ft

Angles (L)

to 1⁄2-in. incl.

over 102 lb/ft

over 1⁄2- to 3⁄4-in. incl. over 3⁄4-in.

Notes: Structural tees from W, M, and S shapes fall into the same group as the structural shapes from which they are cut. Group 4 and Group 5 shapes are generally contemplated for application as columns or compression components. When used in other applications (e.g., trusses) and when thermal cutting or welding is required, special material specification and fabrication procedures apply to minimize the possibility of cracking (see Part 6, LRFD Specification, Sections A3.1c, J1.5, J1.6, J2.3, and M2.2, and corresponding Commentary sections).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Structural Steel Shape Producers Bayou Steel Corp. P.O. Box 5000 Laplace, LA 70068 (800) 535-7692

Florida Steel Corp. P.O. Box 31328 Tampa, FL 33631 (800) 237-0230

Nucor-Yamato Steel P.O. Box 1228 Blytheville, AR 72316 (800) 289-6977

Bethlehem Steel Corp. 301 East Third St. Bethlehem, PA 18016-7699 (800) 633-0482

Northwestern Steel & Wire Co. 121 Wallace St. P.O. Box 618 Sterling, IL 61081-0618 (800) 793-2200

Roanoke Electric Steel Corp. P.O. Box 13948 Roanoke, VA 24038 (800) 753-3532

British Steel Inc. 475 N. Martingale Road #400 Schaumburg, IL 60173 (800) 542-6244

North Star Steel Co. 1380 Corporate Center Curve Suite 215 P.O. Box 21620 Eagan, MN 55121-0620 (800) 328-1944

Chaparral Steel Co. 300 Ward Road Midlothian, TX 76065-9501 (800) 529-7979

Nucor Steel P.O. Box 126 Jewett, TX 75846 (800) 527-6445

SMI Steel, Inc. 101 South 50th St. Birmingham, AL 35232 (800) 621-0262 TradeARBED 825 Third Ave. New York, NY 10022 (212) 486-9890

Structural Tube Producers American Institute for Hollow Structural Sections 929 McLaughlin Run Road Suite 8 Pittsburgh, PA 15017 (412) 221-8880 Acme Roll Forming Co. 812 North Beck St. Sebewaing, MI 48759-0706 (800) 937-8823

Dallas Tube & Rollform P.O. Box 540873 Dallas, TX 75354-0873 (214) 556-0234

Independence Tube Corp. 6226 West 74th St. Chicago, IL 60638 (708) 496-0380

Eugene Welding Co. P.O. Box 249 Marysville, MI 48040 (313) 364-7421

IPSCO Steel, Inc. P.O. Box 1670, Armour Road Regina, Saskatchewan S4P 3C7 CANADA (416) 271-2312

EXLTUBE, Inc. 905 Atlantic North Kansas City, MO 64116 (800) 892-8823

Bull Moose 57540 SR 19 S P.O. Box B-1027 Elkhart, IN 46515 (800) 348-7460

Hanna Steel Corp. 3812 Commerce Ave. P.O. Box 558 Fairfield, AL 35064 (800) 633-8252

Copperweld Corp. 7401 South Linder Ave. Chicago, IL 60638 (800) 327-8823

UNR-Leavitt, Div. of UNR Inc. 1717 West 115th St. Chicago, IL 60643 (800) 532-8488 Valmont Industries, Inc. P.O. Box 358 Valley, NE 68064 (800) 825-6668 Welded Tube Co. of America 1855 East 122nd St. Chicago, IL 60633 (800) 733-5683

Steel Pipe Producers National Association of Steel Pipe Distributors, Inc. 12651 Briar Forest Dr., Suite 130 Houston, TX 77077 (713) 531-7473

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-3. Principal Producers of Structural Shapes B—Bethlehem Steel Corp. C—Chaparral Steel F—Florida Steel Corp.

I—British Steel S—North Star Steel M—SMI Steel Inc. T—TradeARBED N—Nucor-Yamato Steel U—Nucor Steel R—Roanoke Steel

W—Northwestern Steel & Wire Y—Bayou Steel Corp.

Section, Weight per ft

Producer Code

Section, Weight per ft

Producer Code

W44× all

W40× 321-593 W40× 297 W40× 278 W40× 277 W40× 264 W40× 249 W40× 235 W40× 215 W40× 211 W40× 199 W40× 183 W40× 174 W40× 149-167

T N T N,T B,T N,T B,T N,T B,T N,T B,I,N,T T B,I,N,T

W24× 103 W24× 84-94 W24× 55-76

B,W B,I,N,W B,C,I,N,W

W21× 182-201 W21× 166 W21× 83-147 W21× 44-73

I,W B,I,W B,I,N,W B,C,I,N,W

W18× 258-311 W18× 175-234 W18× 130-158 W18× 76-119 W18× 65-71 W18× 35-60

B B,W B,N,W B,N,W B,I,N,W B,C,I,N,W

W36× 439-848 W36× 393 W36× 328-359 W36× 260-300 W36× 256 W36× 245 W36× 232 W36× 135-230

T B,T B,I,T B,I,N,T B,I B,I,N,T B,I B,I,N,T

W16× 67-100 W16× 57 W16× 26-50

B,N,W B,I,N,W B,C,I,N,W

W33× 263-354 W33× 201-241 W33× 169 W33× 118-152

B,T B,N,T B,T B,I,N,T

W30× 391-477 W30× 261-326 W30× 173-235 W30× 148 W30× 99-132 W30× 90

W14× 808 W14× 342-730 W14× 311 W14× 90-283 W14× 82 W14× 74 W14× 61-68 W14× 43-53 W14× 38 W14× 22-34

B B,I,T B,I,T,W B,I,N,T,W B,N,W B,C,I,N,W B,C,N,W B,C,I,N,W B,I,N,W B,C,I,N,W

T B,T B,I,N,T B,I,T B,I,N,T B,N

W27× 307-539 W27× 258 W27× 235 W27× 146-217 W27× 129 W27× 84-114

T N,T N B,N,T B,I,T,W B,I,N,T,W

W12× 252-336 W12× 210-230 W12× 170-190 W12× 65-152 W12× 50-58 W12× 16-45 W12× 14

B B,T B,I,T,W B,I,N,T,W B,C,I,N,W B,C,N,W B,C,W

W24× 279-492 W24× 250 W24× 229 W24× 207 W24× 192 W24× 104-176

T B,N,W B,N,T,W B,N,W B,I,N,T,W B,I,N,T,W

W10× 88-112 W10× 49-77 W10× 33-45 W10× 22-30 W10× 15-19 W10× 12

B,I,N,W B,C,I,N,W B,C,N,W B,C,I,N,W B,C,I,W B,C,W

W8× 31-67 W8× 18-28 W8× 15

B,C,I,N,W B,C,N,W B,C,W,Y

Notes: For the most recent list of producers, please see the latest January or July issue of the AISC magazine Modern Steel Construction. Maximum lengths of shapes obtained vary with producer, but typically range from 60 ft to 75 ft. Lengths up to 100 ft are available for certain shapes. Please consult individual producers for length requirements.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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Table 1-3 (cont.). Principal Producers of Structural Shapes B—Bethlehem Steel Corp. C—Chaparral Steel F—Florida Steel Corp.

I—British Steel S—North Star Steel M—SMI Steel Inc. T—TradeARBED N—Nucor-Yamato Steel U—Nucor Steel R-Roanoke Steel

W—Northwestern Steel & Wire Y—Bayou Steel Corp.

Section, Weight per ft

Producer Code

Section, Weight per ft

Producer Code

W8× 10-13

B,C,M,W,Y

W6× 20-25 W6× 16 W6× 15 W6× 12 W6× 9

B,C,I,N,W B,C,W,Y B,C,I,N,W B,C,W,Y B,C,N,W,Y

W5× 16-19

W4× 13

B,C,M,Y

M12× 10.8-11.8 M10× 8-9 M8× 6.5 M5× 18.9

MC18× 42.7-58 MC13× 31.8-50 MC12× 31-50 MC12× 10.6 MC10× 22-41.1 MC10× 8.4 MC9× 23.9-25.4 MC8× 18.7-22.8 MC8× 8.5 MC7× 19.1-22.7 MC6× 18 MC6× 12-16.3

B,N B,N B,N S,N B S B B,S M B B B,S

C C C B

S24× 80-121 S20× 66-96 S18× 54.7-70 S15× 42.9-50 S12× 31.8-50 S10× 25.4-35 S8× 18.4-23 S6× 12.5-17.25 S5× 10 S4× 9.5 S4× 7.7 S3× 7.5 S3× 5.7

B,W B,W B,W B,W B,W B,S B,C,S C,S,Y C,Y C C,Y C,Y C,M,Y

HP14× 73-117 HP12× 53-84 HP10× 42-57 HP8× 36

B,I,N,W B,I,N,W B,C,I,N,W B,C,I,N,W

C15× 33.9-50 C12× 30 C12× 20.7-25 C10× 25-30 C10× 15.3-20 C9× 20 C9× 13.4-15 C8× 18.75 C8× 11.5-13.75 C7× 12.25 C7× 9.8 C6× 13 C6× 10.5 C6× 8.2 C5× 9 C5× 6.7 C4× 5.4-7.25 C3× 6 C3× 4.1-5

Section by Leg Length & Thickness Producer Code L8× 8×

B,N,W B,W B,C,S,W B,S,W B,C,S,W B B,S S,W,Y C,M,S,U,W,Y S,U,W M,S,U,W M,S,U,W,Y C,M,S,U,W,Y C,F,M,U,W,Y, M,U,W,Y F,M,U,W,Y F,M,U,W,Y M,U,W,Y F,M,R,U,W,Y

11 ⁄8 1 7⁄ 3⁄ 5⁄ 9⁄ 1⁄

L6× 6×

7⁄ 5⁄ 9⁄ 1⁄ 7⁄ 3⁄ 5⁄ 7⁄ 3⁄ 5⁄ 1⁄ 7⁄ 3⁄ 5⁄

L4× 4×

4 8 16 2

3⁄

L5× 5×

3⁄ 5⁄ 1⁄ 7⁄ 3⁄ 5⁄ 1⁄

8 4 8 16 2 16 8 16 8 4 8 2 16 8 16 4 8 2 16 8 16 4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

B B,S B,S B,S B,S B,S B,S B,U,Y B,U,Y B,M,U,Y B,M,U,Y B,M,U,Y B,M,S,U,Y B,M,U,Y B,M,S,U,Y M,U,Y B,U,Y B,M,U,Y B,M,U,Y B,M,U,W,Y B,M,U,Y B,M,U,W,Y B,M,U,W,Y M,U,Y M,U,Y F,M,R,U,W,Y F,M,U,Y F,M,R,U,W,Y F,M,R,U,W,Y F,M,R,U,W,Y

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DIMENSIONS AND PROPERTIES

Table 1-3 (cont.). Principal Producers of Structural Shapes B—Bethlehem Steel Corp. C—Chaparral Steel F—Florida Steel Corp.

I—British Steel S—North Star Steel M—SMI Steel Inc. T—TradeARBED N—Nucor-Yamato Steel U—Nucor Steel R—Roanoke Steel

W—Northwestern Steel & Wire Y—Bayou Steel Corp.

Section by Leg Length Producer Code and Thickness

L31 ⁄2 × 31 ⁄2 ×

L6× 31 ⁄2 ×

1⁄ 7⁄ 3⁄ 5⁄ 1⁄

L3× 3×

1⁄ 7⁄ 3⁄ 5⁄ 1⁄ 3⁄

L21 ⁄2 × 21 ⁄2 ×

1⁄ 3⁄ 5⁄ 1⁄ 3⁄

L2× 2×

3⁄ 5⁄ 1⁄ 3⁄ 1⁄

L8× 6×

7⁄ 5⁄ 9⁄ 1⁄ 7⁄

7⁄ 5⁄ 9⁄ 1⁄ 7⁄ 3⁄ 5⁄ 1⁄ 7⁄ 3⁄

L6× 4×

8 16 4 2 16 8 16 4 16 2 8 16 4 16 8 16 4 16 8

8 4 8 16 2 16

3⁄

L7× 4×

3⁄

L8× 4×

7⁄ 3⁄ 5⁄ 9⁄ 1⁄ 7⁄ 3⁄ 5⁄

8 4 8 16 2 16 4 8 2 16 8 8 4 8 16 2 16 8 16

F,M,R,U,W,Y U,Y F,M,R,U,W,Y F,M,R,U,W,Y F,M,R,U,W,Y F,M,U,W,Y U,Y F,M,R,S,U,W,Y F,M,R,S,U,W,Y F,M,R,S,U,W,Y F,M,R,U,W,Y F,U F,S,U F,S,U F,S,U F,U F,S,U F,S,U F,S,U F,S,U F,S,U B,S B B,S B B,S B,S B,S B,S B,S B,S B,S B,S B,S B,S B,Y B,Y B,S,Y B,Y B,S,Y B B,M,S,U,W,Y B,M,S,U,W,Y B,M,S,U,W,Y B,M,S,U,W,Y B,U,Y B,M,S,U,W,Y B,M,S,U,W,Y

1⁄ 3⁄ 5⁄

L5× 31 ⁄

3⁄

2×

5⁄ 1⁄ 3⁄ 5⁄ 1⁄ 1⁄

L5× 3×

7⁄ 3⁄ 5⁄ 1⁄

L4× 31 ⁄

1⁄

2×

3⁄ 5⁄ 1⁄

L4× 3×

5⁄ 1⁄ 7⁄ 3⁄ 5⁄ 1⁄

L31 ⁄2 × 3×

1⁄ 3⁄ 5⁄ 1⁄

L31 ⁄

× 21 ⁄

2×

1⁄ 3⁄ 1⁄

L3× 21 ⁄2 ×

1⁄ 3⁄ 5⁄ 1⁄ 3⁄

L3× 2×

1⁄ 3⁄ 5⁄ 1⁄ 3⁄

L21 ⁄

2 × 2×

3⁄ 5⁄ 1⁄ 3⁄

2 8 16 4 8 2 8 16 4 2 16 8 16 4 2 8 16 4 8 2 16 8 16 4 2 8 16 4 2 8 4 2 8 16 4 16 2 8 16 4 16 8 16 4 16

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

M,U,W,Y B,M,U,W,Y B,M,U,W,Y M,U,Y M,U,Y M,U,W,Y M,U,W,Y M,U,W,Y M,U,W,Y F,M,U,W,Y F,Y F,M,U,W,Y F,M,U,W,Y F,M,U,W,Y F,M,U,W F,M,R,U,W F,M,R,U,W F,M,R,U,W M,U,Y F,M,U,W,Y U,Y F,M,R,U,W,Y F,M,R,U,W,Y F,M,R,U,W,Y U,W M,U,W M,U,W M,U,W U U U U U,W U,W,Y R,U,W U F F,S,U F,S,U F,R,S,U F,R,U R,S,U S,U R,S,U R,S,U

1 - 21

Table 1-4. Availability of Steel Pipe and Structural Tubing According to ASTM Material Specifications

ASTM Specification

Steel

Grade

Minimum Yield Stress (ksi)

Minimum Tensile Stress (ksi)

Shape

Round

Square & Rectangular

Availability

ElectricResistance Welded

A53 Type E

Note 3

Seamless

Type S

Note 3

Note 1

Note 2

Note 1

â&#x20AC;&#x201D;

Note 1

III

Note 1

Cold Formed

Hot Formed

HighStrength Low-Alloy

A500

A501

A618

Notes: 1. Available in mill quantities only; consult with producers. 2. Normally stocked in local steel service centers. 3. Normally stocked by local pipe distributors. Available Not Available

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 22

DIMENSIONS AND PROPERTIES

Table 1-5. Principal Producers of Structural Tubing (TS) A—Acme Rolling Forming Co. B—Bull Moose Tube Co. C—Copperweld Corp.

D—Dallas Tube & I—Independence Tube Rollform Corp. E—Eugene Welding Co. P—IPSCO Steel H—Hanna Steel Corp. U—UNR-Leavitt, Div. of UNR, Inc.

Nominal Size and Thickness

Producer Code

30× 30× 5⁄8 28× 28× 5⁄8 26× 26× 5⁄8 24× 24× 5⁄8, 1⁄2, 3⁄8 22× 22× 5⁄8, 1⁄2, 3⁄8 20× 20× 5⁄8, 1⁄2, 3⁄8 18× 18× 5⁄8, 1⁄2, 3⁄8

V—Valmont Industries, Inc. W—Welded Tube Co. of America X—EXLTUBE

Nominal Size and Thickness

Producer Code

V* V* V* V* V* V* V*

41⁄2× 41⁄2× 3⁄8, 5⁄16 41⁄2× 41⁄2× 1⁄4, 3⁄16 41⁄2× 41⁄2× 1⁄8

I,P,W A,B,C,D,I,P,W,X A,B,C,P,I,W

4× 4× 1⁄2 4× 4× 3⁄8, 5⁄16 4× 4× 1⁄4, 3⁄16 , 1⁄8

B,C,P,U,W A,B,C,D,E,I,P,U,W A,B,C,D,E,I,P,U,V,W,X

16× 16× 5⁄8 16× 16× 1⁄2, 3⁄8, 5⁄16

V* V*,W

31⁄2× 31⁄2× 5⁄16 31⁄2× 31⁄2× 1⁄4, 3⁄16 , 1⁄8

I,P,W A,B,C,D,E,I,P,U,W,X

14× 14× 5⁄8 14× 14× 1⁄2, 3⁄8 14× 14× 5⁄16

V* V*,W W

3× 3× 5⁄16 3× 3× 1⁄4, 3⁄16 3× 3× 1⁄8

I,P,W A,B,C,D,E,I,P,U,W,X A,B,C,D,E,I,P,U,W

12× 12× 5⁄8 12× 12× 1⁄2, 3⁄8 12× 12× 5⁄16 , 1⁄4

B B,V*,W B,W

21⁄2× 21⁄2× 5⁄16 21⁄2× 21⁄2× 1⁄4, 3⁄16 21⁄2× 21⁄2× 1⁄8

I A,B,C,D,E,I,P,U,V,W,X A,B,C,D,E,I,P,U,V,W

10× 10× 5⁄8 10× 10× 1⁄2, 3⁄8, 5⁄16 , 1⁄4 10× 10× 3⁄16

B,C B,C,P,U,W B,C,P,W

2× 2× 5⁄16 2× 2× 1⁄4 2× 2× 3⁄16 , 1⁄8

I,V A,B,C,D,I,U,V,W,X A,B,C,D,E,I,P,U,V,W,X

8× 8× 5⁄8 8× 8× 1⁄2 8× 8× 3⁄8, 5⁄16 , 1⁄4, 3⁄16

B,C B,C,P,U,W B,C,D,P,U,W

11⁄2× 11⁄2× 3⁄16

B,E,P,U,V

7× 7× 5⁄8 7× 7× 1⁄2 7× 7× 3⁄8, 5⁄16 , 1⁄4, 3⁄16

B B,C,P,U,W B,C,D,P,U,W

30× 24× 1⁄2, 3⁄8, 5⁄16 28× 24× 1⁄2, 3⁄8, 5⁄16 26× 24× 1⁄2, 3⁄8, 5⁄16 24× 22× 1⁄2, 3⁄8, 5⁄16 22× 20× 1⁄2, 3⁄8, 5⁄16

V* V* V* V* V*

6× 6× 5⁄8 6× 6× 1⁄2 6× 6× 3⁄8, 5⁄16 6× 6× 1⁄4, 3⁄16 6× 6× 1⁄8

B B,C,P,U,W B,C,D,I,P,U,W A,B,C,D,I,P,U,W,X A,B,C,I,P

20× 18× 1⁄2, 3⁄8, 5⁄16 20× 12× 1⁄2, 3⁄8, 5⁄16 20× 8× 1⁄2, 3⁄8, 5⁄16 20× 4× 1⁄2, 3⁄8, 5⁄16

V* W W W

51⁄2× 51⁄2× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 , 1⁄8,

B,I

18× 12× 1⁄2, 3⁄8, 5⁄16 18× 6× 1⁄2, 3⁄8, 5⁄16 18× 6× 1⁄4

V* B,W B

5× 5× 1⁄2 5× 5× 3⁄8, 5⁄16 5× 5× 1⁄4 5× 5× 3⁄16 5× 5× 1⁄8

B,C,P,U,W B,C,D,I,P,U,W A,B,C,D,I,P,U,W,X A,B,C,D,I,P,U,V,W,X A,B,C,I,P,V,W

16× 12× 1⁄2, 3⁄8, 5⁄16 16× 8× 1⁄2, 3⁄8, 5⁄16 16× 4× 1⁄2, 3⁄8, 5⁄16

V*,W B,W B,W

*Size is manufactured by Submerged Arc Welding (SAW) process and is not stocked by steel service centers (contact producer for specific requirements). All other sizes are manufactured by Electric Resistance Welding and are available from steel service centers. For the most recent list of producers, please see the latest January or July issue of the AISC magazine Modern Steel Construction.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 23

Table 1-5 (cont.). Principal Producers of Structural Tubing (TS) A—Acme Rolling Forming Co. B—Bull Moose Tube Co. C—Copperweld Corp.

D—Dallas Tube & I—Independence Tube Rollform Corp. E—Eugene Welding Co. P—IPSCO Steel H—Hanna Steel Corp. U—UNR-Leavitt, Div. of UNR, Inc.

Nominal Size and Thickness

Producer Code

14× 12× 1⁄2, 3⁄8 14× 10× 1⁄2, 3⁄8, 5⁄16 14× 6× 5⁄8 14× 6× 1⁄2, 3⁄8, 5⁄16 , 1⁄4 14× 4× 5⁄8 14× 4× 1⁄2, 3⁄8, 5⁄16 , 1⁄4 14× 4× 3⁄16

V* B,W B B,W B B,W B

12× 10× 1⁄2, 3⁄8, 5⁄16 , 1⁄4 12× 8× 5⁄8 12× 8× 1⁄2, 3⁄8, 5⁄16 , 1⁄4 12× 8× 3⁄16 12× 6× 5⁄8 12× 6× 1⁄2, 3⁄8, 5⁄16 , 1⁄4 12× 6× 3⁄16 12× 4× 5⁄8 12× 4× 1⁄2, 3⁄8, 5⁄16 , 1⁄4, 3⁄16 12× 3× 5⁄16 , 1⁄4, 3⁄16 12× 2× 1⁄4, 3⁄16

B B B,C,U,W B,C,W B B,C,U,W B,C,W B B,U,W B B,U

10× 8× 1⁄2, 3⁄8, 5⁄16 , 1⁄4, 3⁄16 10× 6× 1⁄2 10× 6× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 10× 5× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 10× 4× 1⁄2 10× 4× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 10× 3× 3⁄8,5⁄16 10× 3× 1⁄4, 3⁄16 10× 2× 5⁄16 10× 2× 1⁄4, 3⁄16

B,C,U,W B,C,U,W B,C,D,P,U,W B,C,D B,C,P,U,W B,C,D,P,U,W D B,D D,P,W B,D,P,U,W

8× 6× 1⁄2 8× 6× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 8× 4× 5⁄8 8× 4× 1⁄2 8× 4× 3⁄8, 5⁄16 8× 4× 1⁄4, 3⁄16 8× 4× 1⁄8 8× 3× 1⁄2 8× 3× 3⁄8, 5⁄16 8× 3× 1⁄4, 3⁄16 8× 3× 1⁄8 8× 2× 3⁄8 8× 2× 5⁄16 8× 2× 1⁄4, 3⁄16 8× 2× 1⁄8

B,C,P,U,W B,C,D,P,U,W B B,C,P,U,W B,C,D,H,I,P,U,W A,B,C,D,H,I,P,U,W,X A,B,D,I,P C,P,U B,C,D,I,P,U,W A,B,C,D,I,P,U,W A,B,C,D,I,P H H,I,P,W A,B,D,I,P,U,W A,B,D,I,P

V—Valmont Industries, Inc. W—Welded Tube Co. of America X—EXLTUBE

Nominal Size and Thickness

Producer Code

7× 5× 1⁄2 7× 5× 3⁄8, 5⁄16 7× 5× 1⁄4, 3⁄16 7× 5× 1⁄8 7× 4× 3⁄8, 5⁄16 7× 4× 1⁄4, 3⁄16 7× 4× 1⁄8 7× 3× 3⁄8, 5⁄16 7× 3× 1⁄4, 3⁄16 7× 3× 1⁄8

B,C,P,U,W B,C,I,P,U,W A,B,C,H,I,P,U,W A,B,C,I,P B,C,D,H,I,P,U,W A,B,C,D,H,I,P,U,W A,B,C,H,I,P B,C,D,H,I,P,W A,B,C,D,H,I,P,W,X A,B,C,D,H,I,P

6× 4× 1⁄2 6× 4× 3⁄8, 5⁄16 6× 4× 1⁄4 6× 4× 3⁄16 6× 4× 1⁄8 6× 3× 1⁄2 6× 3× 3⁄8, 5⁄16 6× 3× 1⁄4 6× 3× 3⁄16 6× 3× 1⁄8 6× 2× 3⁄8 6× 2× 5⁄16 6× 2× 1⁄4, 3⁄16 6× 2× 1⁄8

B,C,P,U,W B,C,D,H,I,P,U,W A,B,C,D,H,I,P,U,W,X A,B,C,D,H,I,P,U,V,W,X A,B,C,D,H,I,P,V,W P,U B,D,H,I,P,U A,B,C,D,H,I,P,U,X A,B,C,D,H,I,P,U,W,X A,B,C,D,H,I,P,W H H,I,P,W A,B,C,D,E,H,I,P,U,W,X A,B,C,D,E,H,I,P,U,W

5× 4× 3⁄8, 5⁄16 5× 4× 1⁄4, 3⁄16 5× 3× 1⁄2 5× 3× 3⁄8, 5⁄16 5× 3× 1⁄4, 3⁄16 5× 3× 1⁄8 5× 2× 5⁄16 5× 2× 1⁄4, 3⁄16 5× 2× 1⁄8

I,P,W B,C,D,I,P,U,W C,P,U B,C,D,H,I,P,U,W A,B,C,D,E,H,I,P,U,W,X A,B,C,D,E,H,I,P,U,W I,P,W A,B,C,D,E,H,I,P,U,W,X A,B,C,D,E,H,I,P,U,W

4× 3× 5⁄16 4× 3× 1⁄4, 3⁄16 4× 3× 1⁄8 4× 2× 3⁄8 4× 2× 5⁄16 4× 2× 1⁄4, 3⁄16 4× 2× 1⁄8

B,I,P,W A,B,C,D,E,H,I,P,U,W,X A,B,C,D,E,H,I,P,U,W H H,I,P,W A,B,C,D,E,H,I,P,U,W,X A,B,C,E,H,I,P,U,W

3× 2× 5⁄16 3× 2× 1⁄4, 3⁄16 3× 2× 1⁄8

I A,B,C,D,E,H,I,P,U,V,W,X A,B,C,D,E,H,I,P,U,V,W

21⁄2 × 11⁄2 × 1⁄4, 3⁄16

H,X

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 24

DIMENSIONS AND PROPERTIES

Table 1-6. Principal Producers of Steel Tubing (Round) C—Copperweld Corp. P—IPSCO

U—UNR-Leavitt, Div. of UNR, Inc.

V—Valmont Industries, Inc.

W—Welded Tube Co. of America X—EXLTUBE

Outside Diameter and Thickness

Producer Code

Outside Diameter and Thickness

Producer Code

20.000× .500,.375,.250

P*,W

6.626×.250,.188 6.625×.125

P,U,V,W P,V,W

18.000× .500,.375,.250

P*,W

16.000× .500 16.000× .375,.250 16.000× .188 16.000× .125

P*,W P,W P,V* V*

6.000×.500,.375,.312 6.000×.280 6.000×.250,.188,.125

W X V,W

14.000× .500,.438,.375,.250 14.000× .188 14.000× .125

P,W P,V* V*

5.563×.375 5.563×.258 5.563×.134

P,U P,U,V,W P,V,W

12.750× .500,.406,.375 12.750× .188× .125

P,W P,V*

5.000×.500,.375,.312 5.000×.258 5.000×.250,.188 5.000×.125

P,C,W P,X C,P,U,V,W P,U,V,W

10.750× .500,.365,.250

P,W

4.500×.237,.188,.125

P,U,V,W

10.000× .625,.500,.375,.312 10.000× .250,.188 10.000× .125

C C,V V

4.000×.337,.237 4.000×.266,.250,.188,.125

X U,V,W

9.625×.500 9.625×.375,.312,.250,.188

C,U C,P*,U

3.500×.318 3.500×.300 3.500×.250,.203,.188,.125 3.500×.226

X P,W P,U,V,W P,X

8.625×.500 8.625×.375,.322 8.625×.250,.188 8.625×.125

C,P,U C,P,U,W C,P,U,V,W P,V,W

3.000×.300,.216

2.875×.276 2.875×.250,.203,.188,.125

W P,U,V,W

7.000×.500 7.000×.375,.312,.250 7.000×.188 7.000×.125

C,P,U C,P,U,W C,P,U,V,W C,P,V,W

2.375,.250,.218,.188 2.375,.154,.125

P,V,W P,U,V,W

6.625×.500,.432 6.625×.375,.312,.280

P,U P,U,W

*Size is manufactured by Submerged Arc Welding (SAW) Process and is typically not stocked by steel service centers. Other sizes are manufactured by Electric Resistance Welding and typically are available from steel service centers. For more information contact the manufacturer or the American Institute for Hollow Structural Sections. Also, other sizes and wall thicknesses may be available. Contact an individual manufacturer for more details.

Steel Pipe: For availability contact the National Association of Steel Pipe Distributors, Inc.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 25

STRUCTURAL SHAPES Designations, Dimensions, and Properties

The hot rolled shapes shown in Part 1 of this Manual are published in ASTM Specification A6/A6M, Standard Specification for General Requirements for Rolled Steel Plates, Shapes, Sheet Piling, and Bars for Structural Use. W shapes have essentially parallel flange surfaces. The profile of a W shape of a given nominal depth and weight available from different producers is essentially the same except for the size of fillets between the web and flange. HP bearing pile shapes have essentially parallel flange surfaces and equal web and flange thicknesses. The profile of an HP shape of a given nominal depth and weight available from different producers is essentially the same. American Standard Beams (S) and American Standard Channels (C) have a slope of approximately 17 percent (2 in 12 inches) on the inner flange surfaces. The profiles of S and C shapes of a given nominal depth and weight available from different producers are essentially the same. The letter M designates shapes that cannot be classified as W, HP, or S shapes. Similarly, MC designates channels that cannot be classified as C shapes. Because many of the M and MC shapes are only available from a limited number of producers, or are infrequently rolled, their availability should be checked prior to specifying these shapes. They may or may not have slopes on their inner flange surfaces, dimensions for which may be obtained from the respective producing mills. The flange thickness given in the table from S, M, C, and MC shapes is the average flange thickness. In calculating the theoretical weights, properties, and dimensions of the rolled shapes listed in Part 1 of this Manual, fillets and roundings have been included for all shapes except angles. Because of differences in fillet radii among producers, actual properties of rolled shapes may vary slightly from those tabulated. Dimensions for detailing are generally based on the largest theoretical-size fillets produced. Equal leg and unequal leg angle (L) shapes of the same nominal size available from different producers have profiles which are essentially the same, except for the size of fillet between the legs and the shape of the ends of the legs. The k distance given in the tables for each angle is based on the theoretical largest size fillet available. Availability of certain angles is subject to rolling accumulation and geographical location, and should be checked with material suppliers.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 26

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Thickness tw

tw 2

in.

W44×335 W40×290 W40×262 W40×230

98.3 85.8 77.2 67.7

44.02 43.62 43.31 42.91

44 435⁄8 433⁄8 427⁄8

1.020 0.870 0.790 0.710

W40×593* W40×503* W40×431 W40×372 W40×321 W40×297 W40×277 W40×249 W40×215 W40×199 W40×174

174 148 127 109 94.1 87.4 81.3 73.3 63.3 58.4 51.1

42.99 42.05 41.26 40.63 40.08 39.84 39.69 39.38 38.98 38.67 38.20

43 421⁄16 411⁄4 405⁄8 401⁄16 397⁄8 393⁄4 393⁄8 39 385⁄8 381⁄4

1.790 113⁄16 1.540 19⁄16 1.340 15⁄16 1.160 13⁄16 1.000 1 0.930 15⁄16 0.830 13⁄16 3⁄ 0.750 4 5⁄ 0.650 8 5 0.650 ⁄8 5 0.650 ⁄8

W40×466* W40×392* W40×331 W40×278 W40×264 W40×235 W40×211 W40×183 W40×167 W40×149

137 115 97.6 81.8 77.6 68.9 62.0 53.7 49.1 43.8

42.44 427⁄16 41.57 419⁄16 40.79 4013⁄16 40.16 403⁄16 40.00 40 39.69 393⁄4 39.37 393⁄8 38.98 39 38.59 385⁄8 38.20 381⁄4

1.67 111⁄16 1.42 17⁄16 1.22 11⁄4 1.02 1 0.960 1 13 0.830 ⁄16 3 0.750 ⁄4 5 ⁄8 0.650 5⁄ 0.650 8 5⁄ 0.630 8

W36×848* W40×798* W40×650* W40×527* W40×439* W40×393* W40×359* W40×328* W40×300 W40×280 W40×260 W40×245 W40×230

249 234 190 154 128 115 105 96.4 88.3 82.4 76.5 72.1 67.6

42.45 41.97 40.47 39.21 38.26 37.80 37.40 37.09 36.74 36.52 36.26 36.08 35.90

421⁄2 42 401⁄2 391⁄4 381⁄4 373⁄4 373⁄8 371⁄8 363⁄4 361⁄2 361⁄4 361⁄8 357⁄8

Flange

2.520 2.380 1.970 1.610 1.360 1.220 1.120 1.020 0.945 0.885 0.840 0.800 0.760

1 7⁄ 8 13⁄ 16 11⁄ 16

21⁄2 23⁄8 2 15⁄8 13⁄8 11⁄4 11⁄8 1 15⁄ 16 7⁄ 8 13⁄ 16 13⁄ 16 3⁄ 4

Width bf

Thickness tf

in.

1.770 1.580 1.420 1.220

13⁄4 19⁄16 17⁄16 11⁄4

387⁄16 29⁄16 387⁄16 23⁄8 387⁄16 23⁄16 387⁄16 2

15⁄16 11⁄4 13⁄16 11⁄8

3⁄ 4 11⁄ 16 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16

16.690 163⁄4 16.420 167⁄16 16.220 161⁄4 16.060 161⁄16 15.910 157⁄8 15.825 157⁄8 15.830 157⁄8 15.750 153⁄4 15.750 153⁄4 15.750 153⁄4 15.750 153⁄4

3.230 2.760 2.360 2.050 1.770 1.650 1.575 1.420 1.220 1.065 0.830

31⁄4 23⁄4 23⁄8 21⁄16 13⁄4 15⁄8 19⁄16 17⁄16 11⁄4 11⁄16 13⁄ 16

343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16

47⁄16 21⁄16 315⁄16 115⁄16 39⁄16 17⁄8 31⁄4 13⁄4 215⁄16 111⁄16 31⁄16 111⁄16 23⁄4 15⁄8 25⁄8 19⁄16 23⁄8 11⁄2 21⁄4 11⁄2 2 11⁄2

13⁄ 16 11⁄ 16 5⁄ 8 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16

12.640 125⁄8 12.360 123⁄8 12.170 123⁄16 11.970 12 11.930 12 11.890 117⁄8 11.810 113⁄4 11.810 113⁄4 11.810 113⁄4 11.810 113⁄4

2.950 215⁄16 2.520 21⁄2 2.130 21⁄8 1.810 113⁄16 1.730 13⁄4 1.575 17⁄16 1.415 19⁄16 1.220 11⁄4 1.025 1 0.830 13⁄16

343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16 343⁄16

41⁄8 2 311⁄16 17⁄8 35⁄16 113⁄16 3 111⁄16 215⁄16 111⁄16 23⁄4 15⁄8 25⁄8 19⁄16 23⁄8 11⁄2 23⁄16 11⁄2 2 11⁄2

11⁄4 13⁄16 1 13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 7⁄ 16 7⁄ 16 3⁄ 8

18.130 17.990 17.575 17.220 16.965 16.830 16.730 16.630 16.655 16.595 16.550 16.510 16.470

181⁄8 18 175⁄8 171⁄4 17 167⁄8 163⁄4 165⁄8 165⁄8 165⁄8 161⁄2 161⁄2 161⁄2

4.530 41⁄2 4.290 45⁄16 3.540 39⁄16 2.910 215⁄16 2.440 27⁄16 2.200 23⁄16 2.010 2 1.850 17⁄8 1.680 111⁄16 1.570 19⁄16 1.440 17⁄16 1.350 13⁄8 1.260 11⁄4

311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8 311⁄8

511⁄16 57⁄16 411⁄16 41⁄16 39⁄16 35⁄16 31⁄8 3 213⁄16 211⁄16 29⁄16 21⁄2 23⁄8

15.950 15.830 15.750 15.750

in.

153⁄4 157⁄8 153⁄4 153⁄4

1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8

in.

Distance

*Group 4 or Group 5 shape. See Notes in Table 1-2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21⁄4 23⁄16 2 13⁄4 15⁄8 15⁄8 19⁄16 11⁄2 11⁄2 11⁄2 11⁄2 17⁄16 17⁄16

STRUCTURAL SHAPES

1 - 27

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

335 290 262 230

4.5 5.0 5.5 6.5

593 503 431 372 321 297 277 249 215 199 174

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

(1/ksi)

in.

38.1 44.7 49.2 54.8

44 32 26 21

2430 2140 1930 1690

5110 8220 12300 21200

31100 27100 24200 20800

2.6 3.0 3.4 3.9 4.5 4.8 5.0 5.5 6.5 7.4 9.5

19.1 22.2 25.5 29.5 34.2 36.8 41.2 45.6 52.6 52.6 52.6

— — — — — 47 38 31 23 23 23

4790 4110 3550 3100 2690 2500 2350 2120 1830 1690 1500

337 620 1100 1860 3240 4240 5370 7940 14000 20300 36000

466 392 331 278 264 235 211 183 167 149

2.1 2.5 2.9 3.3 3.4 3.8 4.2 4.8 5.8 7.1

20.5 24.1 28.0 33.5 35.6 41.2 45.6 52.6 52.6 54.3

— — — 57 50 38 31 23 23 22

4560 3920 3360 2860 2720 2430 2200 1900 1750 1610

848 798 650 527 439 393 359 328 300 280 260 245 230

2.0 2.1 2.5 3.0 3.5 3.8 4.2 4.5 5.0 5.3 5.7 6.1 6.5

12.5 13.2 16.0 19.6 23.1 25.8 28.1 30.9 33.3 35.6 37.5 39.4 41.4

— — — — — — — — 58 51 46 41 37

7100 6720 5590 4630 3900 3540 3240 2980 2720 2560 2370 2230 2100

I 4

Axis Y-Y

I 4

r 3

in.

in.3

1410 1240 1120 969

17.8 17.8 17.7 17.5

1200 1050 927 796

150 133 118 101

3.49 3.50 3.46 3.43

1620 1420 1270 1100

236 206 183 157

50400 41700 34800 29600 25100 23200 21900 19500 16700 14900 12200

2340 1980 1690 1460 1250 1170 1100 992 858 769 639

17.0 16.8 16.6 16.4 16.3 16.3 16.4 16.3 16.2 16.0 15.5

2520 2050 1690 1420 1190 1090 1040 926 796 695 541

302 250 208 177 150 138 132 118 101 88.2 68.8

3.81 3.72 3.65 3.60 3.56 3.54 3.58 3.56 3.54 3.45 3.26

2760 2300 1950 1670 1420 1330 1250 1120 963 868 715

481 394 327 277 234 215 204 182 156 137 107

473 851 1560 2910 3510 5310 7890 13700 20500 31400

36300 29900 24700 20500 19400 17400 15500 13300 11600 9780

1710 1440 1210 1020 971 874 785 682 599 512

16.3 16.1 15.9 15.8 15.8 15.9 15.8 15.7 15.3 14.9

1010 803 646 521 493 444 390 336 283 229

160 130 106 87.1 82.6 74.6 66.1 56.9 47.9 38.8

2.72 2.64 2.57 2.52 2.52 2.54 2.51 2.50 2.40 2.29

2050 1710 1430 1190 1130 1010 905 781 692 597

262 212 172 140 132 118 105 89.6 76.0 62.2

71 87 175 365 704 1040 1470 2040 2930 3730 5100 6430 8190

67400 62600 48900 38300 31000 27500 24800 22500 20300 18900 17300 16100 15000

3170 2980 2420 1950 1620 1450 1320 1210 1110 1030 953 895 837

16.4 16.4 16.0 15.8 15.6 15.5 15.4 15.3 15.2 15.1 15.0 15.0 14.9

4550 4200 3230 2490 1990 1750 1570 1420 1300 1200 1090 1010 940

501 467 367 289 235 208 188 171 156 144 132 123 114

4.27 4.24 4.12 4.02 3.95 3.90 3.87 3.84 3.83 3.81 3.78 3.75 3.73

3830 3570 2840 2270 1860 1660 1510 1380 1260 1170 1080 1010 943

799 743 580 454 367 325 292 265 241 223 204 190 176

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

1 - 28

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Flange

Thickness tw

tw 2

in.

Width bf in.

Distance

Thickness tf in.

in.

W36×256 W40×232 W40×210 W40×194 W40×182 W40×170 W40×160 W40×150 W40×135

75.4 68.1 61.8 57.0 53.6 50.0 47.0 44.2 39.7

37.43 37.12 36.69 36.49 36.33 36.17 36.01 35.85 35.55

373⁄8 371⁄8 363⁄4 361⁄2 363⁄8 361⁄8 36 357⁄8 351⁄2

0.960 0.870 0.830 0.765 0.725 0.680 0.650 0.625 0.600

1 7⁄ 8 13⁄ 16 3⁄ 4 3⁄ 4 11⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8

1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16

12.215 12.120 12.180 12.115 12.075 12.030 12.000 11.975 11.950

121⁄4 121⁄8 121⁄8 121⁄8 121⁄8 12 12 12 12

1.730 1.570 1.360 1.260 1.180 1.100 1.020 0.940 0.790

13⁄4 19⁄16 13⁄8 11⁄4 13⁄16 11⁄8 1 15⁄ 16 13⁄ 16

321⁄8 321⁄8 321⁄8 321⁄8 321⁄8 321⁄8 321⁄8 321⁄8 321⁄8

25⁄8 21⁄2 25⁄16 23⁄16 21⁄8 2 115⁄16 17⁄8 111⁄16

15⁄16 11⁄4 11⁄4 13⁄16 13⁄16 13⁄16 11⁄8 11⁄8 11⁄8

W33×354* W40×318* W40×291* W40×263* W40×241 W40×221 W40×201

104 93.5 85.6 77.4 70.9 65.0 59.1

35.55 35.16 34.84 34.53 34.18 33.93 33.68

351⁄2 351⁄8 347⁄8 341⁄2 341⁄8 337⁄8 335⁄8

1.160 1.040 0.960 0.870 0.830 0.775 0.715

13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

16.100 15.985 15.905 15.805 15.860 15.805 15.745

161⁄8 16 157⁄8 153⁄4 157⁄8 153⁄4 153⁄4

2.090 1.890 1.730 1.570 1.400 1.275 1.150

21⁄16 17⁄8 13⁄4 19⁄16 13⁄8 11⁄4 11⁄8

293⁄4 293⁄4 293⁄4 293⁄4 293⁄4 293⁄4 293⁄4

27⁄8 211⁄16 29⁄16 23⁄8 23⁄16 21⁄16 115⁄16

13⁄8 15⁄16 11⁄4 13⁄16 13⁄16 13⁄16 11⁄8

W33×169 W40×152 W40×141 W40×130 W40×118

49.5 44.7 41.6 38.3 34.7

33.82 33.49 33.30 33.09 32.86

337⁄8 331⁄2 331⁄4 331⁄8 327⁄8

0.670 0.635 0.605 0.580 0.550

11⁄ 16 5⁄ 8 5⁄ 8 9⁄ 16 9⁄ 16

3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16

11.500 11.565 11.535 11.510 11.480

111⁄2 115⁄8 111⁄2 111⁄2 111⁄2

1.220 1.055 0.960 0.855 0.740

11⁄4 11⁄16 15⁄ 16 7⁄ 8 3⁄ 4

293⁄4 293⁄4 293⁄4 293⁄4 293⁄4

21⁄16 17⁄8 13⁄4 111⁄16 19⁄16

11⁄8 11⁄8 11⁄16 11⁄16 11⁄16

W30×477* W40×391* W40×326* W40×292* W40×261 W40×235 W40×211 W40×191 W40×173

140 114 95.7 85.7 76.7 69.0 62.0 56.1 50.8

34.21 33.19 32.40 32.01 31.61 31.30 30.94 30.68 30.44

341⁄4 331⁄4 323⁄8 32 315⁄8 311⁄4 31 305⁄8 301⁄2

1.630 1.360 1.140 1.020 0.930 0.830 0.775 0.710 0.655

15⁄8 13⁄8 11⁄8 1 15⁄ 16 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

13⁄ 16 11⁄ 16 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16

15.865 15.590 15.370 15.255 15.155 15.055 15.105 15.040 14.985

157⁄8 155⁄8 153⁄8 151⁄2 151⁄8 15 151⁄8 15 15

2.950 2.440 2.050 1.850 1.650 1.500 1.315 1.185 1.065

3 27⁄16 21⁄16 17⁄8 15⁄8 11⁄2 15⁄16 13⁄16 11⁄16

263⁄4 263⁄4 263⁄4 263⁄4 263⁄4 263⁄4 263⁄4 263⁄4 263⁄4

33⁄4 31⁄4 213⁄16 25⁄8 27⁄16 21⁄4 21⁄8 115⁄16 11⁄16

19⁄16 17⁄16 15⁄16 11⁄4 13⁄16 11⁄8 11⁄8 11⁄16 11⁄16

W30×148 W40×132 W40×124 W40×116 W40×108 W40×99 W40×90

43.5 38.9 36.5 34.2 31.7 29.1 26.4

30.67 30.31 30.17 30.01 29.83 29.65 29.53

305⁄8 301⁄4 301⁄8 30 297⁄8 295⁄8 291⁄2

0.650 0.615 0.585 0.565 0.545 0.520 0.470

5⁄ 8 5⁄ 8 9⁄ 16 9⁄ 16 9⁄ 16 1⁄ 2 1⁄ 2

5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4

10.480 10.545 10.515 10.495 10.475 10.450 10.400

101⁄2 101⁄2 101⁄2 101⁄2 101⁄2 101⁄2 103⁄8

1.180 1.000 0.930 0.850 0.760 0.670 0.610

13⁄16 1 15⁄ 16 7⁄ 8 3⁄ 4 11⁄ 16 9⁄ 16

263⁄4 263⁄4 263⁄4 263⁄4 263⁄4 263⁄4 263⁄4

2 13⁄4 111⁄16 15⁄8 19⁄16 17⁄16 15⁄16

1 11⁄16 1 1 1 1 1

*Group 4 or Group 5 shape. See Notes in Table 1-2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 29

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

256 232 210 194 182 170 160 150 135

3.5 3.9 4.5 4.8 5.1 5.5 5.9 6.4 7.6

354 318 291 263 241 221 201

Plastic Modulus

Elastic Properties Axis X-X

Axis Y-Y

X2 × 106

ksi

(1/ksi)

in.

33.8 37.3 39.1 42.4 44.8 47.8 50.0 52.0 54.1

56 46 42 36 32 28 26 24 22

2840 2580 2320 2140 2020 1900 1780 1680 1520

2870 4160 6560 8850 11300 14500 18600 24200 38000

16800 15000 13200 12100 11300 10500 9750 9040 7800

895 809 719 664 623 580 542 504 439

14.9 14.8 14.6 14.6 14.5 14.5 14.4 14.3 14.0

528 468 411 375 347 320 295 270 225

3.8 4.2 4.6 5.0 5.7 6.2 6.8

25.8 28.8 31.2 34.5 36.1 38.7 41.9

— — — 54 49 43 36

3540 3200 2940 2670 2430 2240 2040

1030 1530 2130 3100 4590 6440 9390

21900 19500 17700 15800 14200 12800 11500

1230 1110 1010 917 829 757 684

14.5 14.4 14.4 14.3 14.1 14.1 14.0

169 152 141 130 118

4.7 5.5 6.0 6.7 7.8

44.7 47.2 49.6 51.7 54.5

32 29 26 24 22

2160 1940 1800 1660 1510

8150 12900 17800 25100 37700

9290 8160 7450 6710 5900

549 487 448 406 359

477 391 326 292 261 235 211 191 173

2.7 3.2 3.7 4.1 4.6 5.0 5.7 6.3 7.0

16.6 19.9 23.7 26.5 29.0 32.5 34.9 38.0 41.2

— — — — — 61 53 44 38

5420 4510 3860 3460 3110 2820 2510 2280 2070

193 386 735 1110 1690 2460 3950 5840 8540

26100 20700 16800 14900 13100 11700 10300 9170 8200

148 132 124 116 108 99 90

4.4 5.3 5.7 6.2 6.9 7.8 8.5

41.5 43.9 46.2 47.8 49.6 51.9 57.5

37 33 30 28 26 24 19

2310 2050 1930 1800 1680 1560 1430

6180 10500 13500 17700 24200 34100 47000

6680 5770 5360 4930 4470 3990 3620

I 4

86.5 77.2 67.5 61.9 57.6 53.2 49.1 45.1 37.7

2.65 2.62 2.58 2.56 2.55 2.53 2.50 2.47 2.38

1040 936 833 767 718 668 624 581 509

137 122 107 97.7 90.7 83.8 77.3 70.9 59.7

1460 1290 1160 1030 932 840 749

181 161 146 131 118 106 95.2

3.74 3.71 3.69 3.66 3.63 3.59 3.56

1420 1270 1150 1040 939 855 772

282 250 226 202 182 164 147

13.7 13.5 13.4 13.2 13.0

310 273 246 218 187

53.9 47.2 42.7 37.9 32.6

2.50 2.47 2.43 2.39 2.32

629 559 514 467 415

1530 1250 1030 928 827 746 663 598 539

13.7 13.5 13.2 13.2 13.1 13.0 12.9 12.8 12.7

1970 1550 1240 1100 959 855 757 673 598

249 198 162 144 127 114 100 89.5 79.8

3.75 3.68 3.61 3.58 3.54 3.52 3.49 3.46 3.43

1790 1430 1190 1060 941 845 749 673 605

436 380 355 329 299 269 245

12.4 12.2 12.1 12.0 11.9 11.7 11.7

227 196 181 164 146 128 115

43.3 37.2 34.4 31.3 27.9 24.5 22.1

2.28 2.25 2.23 2.19 2.15 2.10 2.09

500 437 408 378 346 312 283

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Zy in.3

in.

Zx in.

in.

r in.

in.

84.4 73.9 66.9 59.5 51.3 390 310 252 223 196 175 154 138 123 68.0 58.4 54.0 49.2 43.9 38.6 34.7

1 - 30

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Flange

Thickness tw

tw 2

in.

Width bf in.

Distance

Thickness tf

in.

W27×539* W40×448* W40×368* W40×307* W40×258 W40×235 W40×217 W40×194 W40×178 W40×161 W40×146

158 131 108 90.2 75.7 69.1 63.8 57.0 52.3 47.4 42.9

32.52 31.42 30.39 29.61 28.98 28.66 28.43 28.11 27.81 27.59 27.38

321⁄2 313⁄8 303⁄8 295⁄8 29 285⁄8 283⁄8 281⁄8 273⁄4 275⁄8 273⁄8

1.970 1.650 1.380 1.160 0.980 0.910 0.830 0.750 0.725 0.660 0.605

2 15⁄8 13⁄8 13⁄16 1 15⁄ 16 13⁄ 16 3⁄ 4 3⁄ 4 11⁄ 16 5⁄ 8

1 13⁄ 16 11⁄ 16 5⁄ 8 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 5⁄ 16

15.255 14.940 14.665 14.445 14.270 14.190 14.115 14.035 14.085 14.020 13.965

151⁄4 15 145⁄8 141⁄2 141⁄4 141⁄4 141⁄8 14 141⁄8 14 14

3.540 2.990 2.480 2.090 1.770 1.610 1.500 1.340 1.190 1.080 0.975

39⁄16 3 21⁄2 21⁄16 13⁄4 15⁄8 11⁄2 15⁄16 13⁄16 11⁄16 1

24 24 24 24 24 24 24 24 24 24 24

41⁄4 311⁄16 33⁄16 213⁄16 21⁄2 25⁄16 23⁄16 21⁄16 17⁄8 113⁄16 111⁄16

15⁄8 11⁄2 15⁄16 11⁄4 11⁄8 11⁄8 11⁄16 1 11⁄16 1 1

W27×129 W40×114 W40×102 W40×94 W40×84

37.8 33.5 30.0 27.7 24.8

27.63 27.29 27.09 26.92 26.71

275⁄8 271⁄4 271⁄8 267⁄8 263⁄4

0.610 0.570 0.515 0.490 0.460

5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16

5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4

10.010 10.070 10.015 9.990 9.960

10 101⁄8 10 10 10

1.100 0.930 0.830 0.745 0.640

11⁄8 15⁄ 16 13⁄ 16 3⁄ 4 5⁄ 8

24 24 24 24 24

113⁄16 15⁄8 19⁄16 17⁄16 13⁄8

15⁄ 16 15⁄ 16 15⁄ 16 15⁄ 16 15⁄ 16

W24×492* W40×408* W40×335* W40×279* W40×250* W40×229 W40×207 W40×192 W40×176 W40×162 W40×146 W40×131 W40×117 W40×104

144 119 98.4 82.0 73.5 67.2 60.7 56.3 51.7 47.7 43.0 38.5 34.4 30.6

29.65 28.54 27.52 26.73 26.34 26.02 25.71 25.47 25.24 25.00 24.74 24.48 24.26 24.06

295⁄8 281⁄2 271⁄2 263⁄4 263⁄8 26 253⁄4 251⁄2 251⁄4 25 243⁄4 241⁄2 241⁄4 24

1.970 1.650 1.380 1.160 1.040 0.960 0.870 0.810 0.750 0.705 0.650 0.605 0.550 0.500

2 15⁄8 13⁄8 13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2

1 13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4

14.115 13.800 13.520 13.305 13.185 13.110 13.010 12.950 12.890 12.955 12.900 12.855 12.800 12.750

141⁄8 133⁄4 131⁄2 131⁄4 131⁄8 131⁄8 13 13 127⁄8 13 127⁄8 127⁄8 123⁄4 123⁄4

3.540 2.990 2.480 2.090 1.890 1.730 1.570 1.460 1.340 1.220 1.090 0.960 0.850 0.750

39⁄16 3 21⁄2 21⁄16 17⁄8 13⁄4 19⁄16 17⁄16 15⁄16 11⁄4 11⁄16 15⁄ 16 7⁄ 8 3⁄ 4

21 21 21 21 21 21 21 21 21 21 21 21 21 21

45⁄16 33⁄4 31⁄4 27⁄8 211⁄16 21⁄2 23⁄8 21⁄4 21⁄8 2 17⁄8 13⁄4 15⁄8 11⁄2

19⁄16 13⁄8 11⁄4 11⁄8 11⁄8 1 1 1 15⁄ 16 11⁄16 1 1 ⁄16 11⁄16 1 1

W24×103 W40×94 W40×84 W40×76 W40×68

30.3 27.7 24.7 22.4 20.1

24.53 24.31 24.10 23.92 23.73

241⁄2 241⁄4 241⁄8 237⁄8 233⁄4

0.550 0.515 0.470 0.440 0.415

9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 7⁄ 16

5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4

9.000 9.065 9.020 8.990 8.965

9 91⁄8 9 9 9

0.980 0.875 0.770 0.680 0.585

1 7⁄ 8 3⁄ 4 11⁄ 16 9⁄ 16

21 21 21 21 21

13⁄4 15⁄8 19⁄16 17⁄16 13⁄8

13⁄ 16 15⁄ 16 15⁄ 16 15⁄ 16

W24×62 W40×55

18.2 16.2

23.74 23.57

233⁄4 235⁄8

0.430 0.395

7⁄ 16 3⁄ 8

1⁄ 4 3⁄ 16

7.040 7.005

7 7

0.590 0.505

9⁄ 16 1⁄ 2

21 21

13⁄8 15⁄16

15⁄ 16 15⁄ 16

* Group 4 or Group 5 shape. See Notes in Table 1-2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 31

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

539 448 368 307 258 235 217 194 178 161 146

2.2 2.5 3.0 3.5 4.0 4.4 4.7 5.2 5.9 6.5 7.2

129 114 102 94 84

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

12.3 14.7 17.6 20.9 24.7 26.6 29.2 32.3 33.4 36.7 40.0

— — — — — — — 61 57 47 40

7160 6070 5100 4320 3670 3360 3120 2800 2550 2320 2110

66 123 243 463 873 1230 1640 2520 3740 5370 7900

25500 20400 16100 13100 10800 9660 8870 7820 6990 6280 5630

4.5 5.4 6.0 6.7 7.8

39.7 42.5 47.0 49.4 52.7

41 35 29 26 23

2390 2100 1890 1740 1570

5340 9220 14000 19900 31100

492 408 335 279 250 229 207 192 176 162 146 131 117 104

2.0 2.3 2.7 3.2 3.5 3.8 4.1 4.4 4.8 5.3 5.9 6.7 7.5 8.5

10.9 13.1 15.6 18.6 20.7 22.5 24.8 26.6 28.7 30.6 33.2 35.6 39.2 43.1

— — — — — — — — — — 58 50 42 34

7950 6780 5700 4840 4370 4020 3650 3410 3140 2870 2590 2330 2090 1860

103 94 84 76 68

4.6 5.2 5.9 6.6 7.7

39.2 41.9 45.9 49.0 52.0

42 37 30 27 24

62 55

6.0 6.9

50.1 54.6

25 21

S 3

in.

in.3

1570 1300 1060 884 742 674 624 556 502 455 411

12.7 12.5 12.2 12.0 11.9 11.8 11.8 11.7 11.6 11.5 11.4

2110 1670 1310 1050 859 768 704 618 555 497 443

277 224 179 146 120 108 99.8 88.1 78.8 70.9 63.5

3.66 3.57 3.48 3.42 3.37 3.33 3.32 3.29 3.26 3.24 3.21

1880 1530 1240 1020 850 769 708 628 567 512 461

437 351 279 227 187 168 154 136 122 109 97.5

4760 4090 3620 3270 2850

345 299 267 243 213

11.2 11.0 11.0 10.9 10.7

184 159 139 124 106

36.8 31.5 27.8 24.8 21.2

2.21 2.18 2.15 2.12 2.07

395 343 305 278 244

57.6 49.3 43.4 38.8 33.2

43 79 156 297 436 605 876 1150 1590 2260 3420 5290 8190 12900

19100 15100 11900 9600 8490 7650 6820 6260 5680 5170 4580 4020 3540 3100

1290 1060 864 718 644 588 531 491 450 414 371 329 291 258

11.5 11.3 11.0 10.8 10.7 10.7 10.6 10.5 10.5 10.4 10.3 10.2 10.1 10.1

1670 1320 1030 823 724 651 578 530 479 443 391 340 297 259

237 191 152 124 110 99.4 88.8 81.8 74.3 68.4 60.5 53.0 46.5 40.7

3.41 3.33 3.23 3.17 3.14 3.11 3.08 3.07 3.04 3.05 3.01 2.97 2.94 2.91

1550 1250 1020 835 744 676 606 559 511 468 418 370 327 289

375 300 238 193 171 154 137 126 115 105 93.2 81.5 71.4 62.4

2400 2180 1950 1760 1590

5280 7800 12200 18600 29000

3000 2700 2370 2100 1830

245 222 196 176 154

9.96 9.87 9.79 9.69 9.55

119 109 94.4 82.5 70.4

26.5 24.0 20.9 18.4 15.7

1.99 1.98 1.95 1.92 1.87

280 254 224 200 177

41.5 37.5 32.6 28.6 24.5

1700 1540

25100 39600

1550 1350

131 114

9.23 9.11

34.5 29.1

1.38 1.34

153 134

15.7 13.3

9.80 8.30

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

(1/ksi)

Axis Y-Y

1 - 32

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Flange

Thickness tw

tw 2

in.

Width bf

Distance

Thickness tf

in.

W21×201 W40×182 W40×166 W40×147 W40×132 W40×122 W40×111 W40×101

59.2 53.6 48.8 43.2 38.8 35.9 32.7 29.8

23.03 22.72 22.48 22.06 21.83 21.68 21.51 21.36

23 223⁄4 221⁄2 22 217⁄8 215⁄8 211⁄2 213⁄8

0.910 0.830 0.750 0.720 0.650 0.600 0.550 0.500

15⁄ 16 13⁄ 16 3⁄ 4 3⁄ 4 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2

1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4

12.575 12.500 12.420 12.510 12.440 12.390 12.340 12.290

125⁄8 121⁄2 123⁄8 121⁄2 121⁄2 123⁄8 123⁄8 121⁄4

1.630 1.480 1.360 1.150 1.035 0.960 0.875 0.800

15⁄8 11⁄2 13⁄8 11⁄8 11⁄16 15⁄ 16 7⁄ 8 13⁄ 16

181⁄4 181⁄4 181⁄4 181⁄4 181⁄4 181⁄4 181⁄4 181⁄4

23⁄8 21⁄4 21⁄8 17⁄8 113⁄16 111⁄16 15⁄8 19⁄16

1 1 15⁄ 16 11⁄16 1 1 15⁄ 16 15⁄ 16

W21×93 W40×83 W40×73 W40×68 W40×62

27.3 24.3 21.5 20.0 18.3

21.62 21.43 21.24 21.13 20.99

215⁄8 213⁄8 211⁄4 211⁄8 21

0.580 0.515 0.455 0.430 0.400

9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8

5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

8.420 8.355 8.295 8.270 8.240

83⁄8 83⁄8 81⁄4 81⁄4 81⁄4

0.930 0.835 0.740 0.685 0.615

15⁄ 16 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

181⁄4 181⁄4 181⁄4 181⁄4 181⁄4

111⁄16 19⁄16 11⁄2 17⁄16 13⁄8

15⁄ 16 15⁄ 16 7⁄ 8 7⁄ 8

W21×57 W40×50 W40×44

16.7 14.7 13.0

21.06 20.83 20.66

21 207⁄8 205⁄8

0.405 0.380 0.350

3⁄ 8 3⁄ 8 3⁄ 8

3⁄ 16 3⁄ 16 3⁄ 16

6.555 6.530 6.500

61⁄2 61⁄2 61⁄2

0.650 0.535 0.450

5⁄ 8 9⁄ 16 7⁄ 16

181⁄4 181⁄4 181⁄4

13⁄8 15⁄16 13⁄16

7⁄ 8 7⁄ 8 7⁄ 8

W18×311* W40×283* W40×258* W40×234* W40×211* W40×192 W40×175 W40×158 W40×143 W40×130

91.5 83.2 75.9 68.8 62.1 56.4 51.3 46.3 42.1 38.2

22.32 21.85 21.46 21.06 20.67 20.35 20.04 19.72 19.49 19.25

223⁄8 217⁄8 211⁄2 21 205⁄8 203⁄8 20 193⁄4 191⁄2 191⁄4

1.520 1.400 1.280 1.160 1.060 0.960 0.890 0.810 0.730 0.670

11⁄2 13⁄8 11⁄4 13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

3⁄ 4 11⁄ 16 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

12.005 11.890 11.770 11.650 11.555 11.455 11.375 11.300 11.220 11.160

12 117⁄8 113⁄4 115⁄8 111⁄2 111⁄2 113⁄8 111⁄4 111⁄4 111⁄8

2.740 23⁄4 2.500 21⁄2 2.300 25⁄16 2.110 21⁄8 1.910 115⁄16 1.750 13⁄4 1.590 19⁄16 1.440 17⁄16 1.320 15⁄16 1.200 13⁄16

151⁄2 151⁄2 151⁄2 151⁄2 151⁄2 151⁄2 151⁄2 151⁄2 151⁄2 151⁄2

37⁄16 33⁄16 3 23⁄4 9 2 ⁄16 27⁄16 21⁄4 21⁄8 2 17⁄8

13⁄16 13⁄16 11⁄8 1 1 15⁄ 16 7⁄ 8 7⁄ 8 13⁄ 16 13⁄ 16

W18×119 W40×106 W40×97 W40×86 W40×76

35.1 31.1 28.5 25.3 22.3

18.97 18.73 18.59 18.39 18.21

19 183⁄4 185⁄8 183⁄8 181⁄4

0.655 0.590 0.535 0.480 0.425

5⁄ 8 9⁄ 16 9⁄ 16 1⁄ 2 7⁄ 16

5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4

11.265 11.200 11.145 11.090 11.035

111⁄4 111⁄4 111⁄8 111⁄8 11

1.060 0.940 0.870 0.770 0.680

11⁄16 15⁄ 16 7⁄ 8 3⁄ 4 11⁄ 16

151⁄2 151⁄2 151⁄2 151⁄2 151⁄2

13⁄4 15⁄8 19⁄16 17⁄16 13⁄8

15⁄ 16 15⁄ 16 7⁄ 8 7⁄ 8 13⁄ 16

W18×71 W40×65 W40×60 W40×55 W40×50

20.8 19.1 17.6 16.2 14.7

18.47 18.35 18.24 18.11 17.99

181⁄2 183⁄8 181⁄4 181⁄8 18

0.495 0.450 0.415 0.390 0.355

1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16 3⁄ 16

7.635 7.590 7.555 7.530 7.495

75⁄8 75⁄8 71⁄2 71⁄2 71⁄2

0.810 0.750 0.695 0.630 0.570

13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8 9⁄ 16

151⁄2 151⁄2 151⁄2 151⁄2 151⁄2

11⁄2 17⁄16 13⁄8 15⁄16 11⁄4

7⁄ 8 7⁄ 8 13⁄ 16 13⁄ 16 13⁄ 16

W18×46 W40×40 W40×35

13.5 11.8 10.3

18.06 17.90 17.70

18 177⁄8 173⁄4

0.360 0.315 0.300

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

6.060 6.015 6.000

6 6 6

0.605 0.525 0.425

5⁄ 8 1⁄ 2 7⁄ 16

151⁄2 151⁄2 151⁄2

11⁄4 13⁄16 11⁄8

13⁄ 16 13⁄ 16 3⁄ 4

*Group 4 or Group 5 shape. See Notes in Table 1-2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 33

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

201 182 166 147 132 122 111 101

3.9 4.2 4.6 5.4 6.0 6.5 7.1 7.7

93 83 73 68 62

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

20.6 22.6 24.9 26.1 28.9 31.3 34.1 37.5

— — — — — — 55 45

4290 3910 3590 3140 2840 2630 2400 2200

4.5 5.0 5.6 6.0 6.7

32.3 36.4 41.2 43.6 46.9

61 48 38 34 29

57 50 44

5.0 6.1 7.2

46.3 49.4 53.6

311 283 258 234 211 192 175 158 143 130

2.2 2.4 2.6 2.8 3.0 3.3 3.6 3.9 4.2 4.6

119 106 97 86 76

I 4

in.

453 649 904 1590 2350 3160 4510 6400

5310 4730 4280 3630 3220 2960 2670 2420

2680 2400 2140 2000 1820

3460 5250 8380 10900 15900

30 26 22

1960 1730 1550

10.6 11.5 12.5 13.8 15.1 16.7 18.0 19.8 21.9 23.9

— — — — — — — — — —

5.3 6.0 6.4 7.2 8.1

24.5 27.2 30.0 33.4 37.8

71 65 60 55 50

4.7 5.1 5.4 6.0 6.6

46 40 35

5.0 5.7 7.1

Axis Y-Y

I 4

r 3

in.

in.3

461 417 380 329 295 273 249 227

9.47 9.40 9.36 9.17 9.12 9.09 9.05 9.02

542 483 435 376 333 305 274 248

86.1 77.2 70.1 60.1 53.5 49.2 44.5 40.3

3.02 3.00 2.98 2.95 2.93 2.92 2.90 2.89

530 476 432 373 333 307 279 253

133 119 108 92.6 82.3 75.6 68.2 61.7

2070 1830 1600 1480 1330

192 171 151 140 127

8.70 8.67 8.64 8.60 8.54

92.9 81.4 70.6 64.7 57.5

22.1 19.5 17.0 15.7 13.9

1.84 1.83 1.81 1.80 1.77

221 196 172 160 144

34.7 30.5 26.6 24.4 21.7

13100 22600 36600

1170 984 843

111 94.5 81.6

8.36 8.18 8.06

30.6 24.9 20.7

1.35 1.30 1.26

129 110 95.4

14.8 12.2 10.2

8160 7520 6920 6360 5800 5320 4870 4430 4060 3710

38 52 71 97 140 194 274 396 557 789

6960 6160 5510 4900 4330 3870 3450 3060 2750 2460

624 564 514 466 419 380 344 310 282 256

8.72 8.61 8.53 8.44 8.35 8.28 8.20 8.12 8.09 8.03

795 704 628 558 493 440 391 347 311 278

132 118 107 95.8 85.3 76.8 68.8 61.4 55.5 49.9

2.95 2.91 2.88 2.85 2.82 2.79 2.76 2.74 2.72 2.70

753 676 611 549 490 442 398 356 322 291

207 185 166 149 132 119 106 94.8 85.4 76.7

— — — 57 45

3340 2990 2750 2460 2180

1210 1880 2580 4060 6520

2190 1910 1750 1530 1330

231 204 188 166 146

7.90 7.84 7.82 7.77 7.73

253 220 201 175 152

44.9 39.4 36.1 31.6 27.6

2.69 2.66 2.65 2.63 2.61

261 230 211 186 163

69.1 60.5 55.3 48.4 42.2

32.4 35.7 38.7 41.2 45.2

61 50 43 38 31

2680 2470 2290 2110 1920

3310 4540 6080 8540 12400

1170 1070 984 890 800

127 117 108 98.3 88.9

7.50 7.49 7.47 7.41 7.38

60.3 54.8 50.1 44.9 40.1

15.8 14.4 13.3 11.9 10.7

1.70 1.69 1.69 1.67 1.65

145 133 123 112 101

24.7 22.5 20.6 18.5 16.6

44.6 51.0 53.5

32 25 22

2060 1810 1590

10100 17200 30300

712 612 510

78.8 68.4 57.6

7.25 7.21 7.04

22.5 19.1 15.3

9.35 7.64 6.36

7.43 6.35 5.12

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.29 1.27 1.22

in.

(1/ksi)

90.7 78.4 66.5

11.7 9.95 8.06

1 - 34

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Thickness tw in.

Flange

tw 2 in.

Width bf in.

Distance

Thickness tf in.

in.

k1 in.

W16×100 W16×89 W16×77 W16×67

29.4 26.2 22.6 19.7

16.97 16.75 16.52 16.33

17 163⁄4 161⁄2 163⁄8

0.585 0.525 0.455 0.395

9⁄ 16 1⁄ 2 7⁄ 16 3⁄ 8

5⁄ 16 1⁄ 4 1⁄ 4 3⁄ 16

10.425 10.365 10.295 10.235

103⁄8 103⁄8 101⁄4 101⁄4

0.985 0.875 0.760 0.665

1 7⁄ 8 3⁄ 4 11⁄ 16

135⁄8 111⁄16 135⁄8 19⁄16 135⁄8 17⁄16 135⁄8 13⁄8

15⁄ 16 7⁄ 8 7⁄ 8 13⁄ 16

W16×57 W16×50 W16×45 W16×40 W16×36

16.8 14.7 13.3 11.8 10.6

16.43 16.26 16.13 16.01 15.86

163⁄8 161⁄4 161⁄8 16 157⁄8

0.430 0.380 0.345 0.305 0.295

7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16

1⁄ 4 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16

7.120 7.070 7.035 6.995 6.985

71⁄8 71⁄8 7 7 7

0.715 0.630 0.565 0.505 0.430

11⁄

16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16

135⁄8 135⁄8 135⁄8 135⁄8 135⁄8

13⁄8 15⁄16 11⁄4 13⁄16 11⁄8

7⁄ 8 13⁄ 16 13⁄ 16 13⁄ 16 3⁄ 4

9.12 15.88 7.68 15.69

157⁄8 153⁄4

0.275 0.250

1⁄ 4 1⁄ 4

1⁄

5.525 5.500

51⁄2 51⁄2

0.440 0.345

7⁄ 16 3⁄ 8

135⁄8 135⁄8

11⁄8 11⁄16

3⁄ 4 3⁄ 4

17⁄8 19⁄16 17⁄16 15⁄16 13⁄16 11⁄8 1

18.560 17.890 17.650 17.415 17.200 17.010 16.835

181⁄2 177⁄8 175⁄8 173⁄8 171⁄4 17 167⁄8

5.120 51⁄8 4.910 415⁄16 4.520 41⁄2 4.160 43⁄16 3.820 313⁄16 3.500 31⁄2 3.210 33⁄16

111⁄4 513⁄16 21⁄2 111⁄4 59⁄16 23⁄16 111⁄4 53⁄16 21⁄16 111⁄4 413⁄16 115⁄16 111⁄4 41⁄2 113⁄16 111⁄4 43⁄16 13⁄4 111⁄4 37⁄8 15⁄8

15⁄

16.695 16.590 16.475 16.360 16.230 16.110 15.995 15.890 15.800 15.710 15.650 15.565 15.500

163⁄4 165⁄8 161⁄2 163⁄8 161⁄4 161⁄8 16 157⁄8 153⁄4 153⁄4 155⁄8 155⁄8 151⁄2

3.035 31⁄16 2.845 27⁄8 2.660 211⁄16 2.470 21⁄2 2.260 21⁄4 2.070 21⁄16 1.890 17⁄8 1.720 13⁄4 1.560 19⁄16 1.440 17⁄16 1.310 15⁄16 1.190 13⁄16 1.090 11⁄16

111⁄4 311⁄16 111⁄4 31⁄2 111⁄4 35⁄16 111⁄4 31⁄8 111⁄4 215⁄16 111⁄4 23⁄4 111⁄4 29⁄16 111⁄4 23⁄8 111⁄4 21⁄4 111⁄4 21⁄8 111⁄4 2 111⁄4 17⁄8 111⁄4 13⁄4

W16×31 W16×26 W14×808* W16×730* W16×665* W16×605* W16×550* W16×500* W16×455*

237 215 196 178 162 147 134

22.84 22.42 21.64 20.92 20.24 19.60 19.02

227⁄8 223⁄8 215⁄8 207⁄8 201⁄4 195⁄8 19

3.740 33⁄4 3.070 31⁄16 2.830 213⁄16 2.595 25⁄8 2.380 23⁄8 2.190 23⁄16 2.015 2

W14×426* W16×398* W16×370* W16×342* W16×311* W16×283* W16×257* W16×233* W16×211 W16×193 W16×176 W16×159 W16×145

125 117 109 101 91.4 83.3 75.6 68.5 62.0 56.8 51.8 46.7 42.7

18.67 18.29 17.92 17.54 17.12 16.74 16.38 16.04 15.72 15.48 15.22 14.98 14.78

185⁄8 181⁄4 177⁄8 171⁄2 171⁄8 163⁄4 163⁄8 16 153⁄4 151⁄2 151⁄4 15 143⁄4

1.875 1.770 1.655 1.540 1.410 1.290 1.175 1.070 0.980 0.890 0.830 0.745 0.680

17⁄8 13⁄4 15⁄8 19⁄16 17⁄16 15⁄16 13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

1⁄

7⁄

13⁄

13⁄ 3⁄

8 8

16 8 16 16

4 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

*Group 4 or Group 5 shape. See Notes in Table 1-2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

19⁄16 11⁄2 17⁄16 13⁄8 15⁄16 11⁄4 13⁄16 13⁄16 11⁄8 11⁄16 11⁄16 1 1

STRUCTURAL SHAPES

1 - 35

W SHAPES Properties

Y bf

Compact NomSection inal Criteria Wt. per Fy′′′ bf h ft 2tf tw lb ksi

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

(1/ksi)

I 4

Axis Y-Y

r 3

in.

175 155 134 117

I 4

r 3

Zx 3

Zy in.3

in.

7.10 7.05 7.00 6.96

186 163 138 119

35.7 31.4 26.9 23.2

2.51 2.49 2.47 2.46

198 175 150 130

54.9 48.1 41.1 35.5

12.1 10.5 9.34 8.25 7.00

1.60 1.59 1.57 1.57 1.52

105 92.0 82.3 72.9 64.0

18.9 16.3 14.5 12.7 10.8

4.49 1.17 3.49 1.12

54.0 44.2

100 89 77 67

5.3 5.9 6.8 7.7

24.3 27.0 31.2 35.9

— — — 50

3450 3090 2680 2350

1040 1630 2790 4690

1490 1300 1110 954

57 50 45 40 36

5.0 5.6 6.2 6.9 8.1

33.0 37.4 41.2 46.6 48.1

59 46 38 30 28

2650 3400 2340 5530 2120 8280 1890 12900 1700 20800

758 659 586 518 448

92.2 81.0 72.7 64.7 56.5

6.72 6.68 6.65 6.63 6.51

43.1 37.2 32.8 28.9 24.5

31 26

6.3 8.0

51.6 56.8

24 20

1740 20000 1470 40900

375 301

47.2 38.4

6.41 6.26

12.4 9.59

808 730 665 605 550 500 455

1.8 1.8 2.0 2.1 2.3 2.4 2.6

3.4 3.7 4.0 4.4 4.8 5.2 5.7

— — — — — — —

18900 17500 16300 15100 14200 13100 12200

1.45 1.90 2.50 3.20 4.20 5.50 7.30

16000 14300 12400 10800 9430 8210 7190

1400 1280 1150 1040 931 838 756

8.21 8.17 7.98 7.80 7.63 7.48 7.33

5510 4720 4170 3680 3250 2880 2560

594 527 472 423 378 339 304

4.82 4.69 4.62 4.55 4.49 4.43 4.38

1834 1660 1480 1320 1180 1050 936

927 816 730 652 583 522 468

426 398 370 342 311 283 257 233 211 193 176 159 145

2.8 2.9 3.1 3.3 3.6 3.9 4.2 4.6 5.1 5.5 6.0 6.5 7.1

6.1 6.4 6.9 7.4 8.1 8.8 9.7 10.7 11.6 12.8 13.7 15.3 16.8

— — — — — — — — — — — — —

11500 10900 10300 9600 8820 8120 7460 6820 6230 5740 5280 4790 4400

8.90 11.0 13.9 17.9 24.4 33.4 46.1 64.9 91.8 125 173 249 348

6600 6000 5440 4900 4330 3840 3400 3010 2660 2400 2140 1900 1710

707 656 607 559 506 459 415 375 338 310 281 254 232

7.26 7.16 7.07 6.98 6.88 6.79 6.71 6.63 6.55 6.50 6.43 6.38 6.33

2360 2170 1990 1810 1610 1440 1290 1150 1030 931 838 748 677

283 262 241 221 199 179 161 145 130 119 107 96.2 87.3

4.34 4.31 4.27 4.24 4.20 4.17 4.13 4.10 4.07 4.05 4.02 4.00 3.98

869 801 736 672 603 542 487 436 390 355 320 287 260

434 402 370 338 304 274 246 221 198 180 163 146 133

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.03 5.48

1 - 36

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Thickness tw in.

Flange

tw 2 in.

Width bf

Distance

Thickness tf

in.

W14×132 W16×120 W16×109 W16×99 W16×90

38.8 35.3 32.0 29.1 26.5

14.66 14.48 14.32 14.16 14.02

145⁄8 141⁄2 143⁄8 141⁄8 14

0.645 0.590 0.525 0.485 0.440

5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16

5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4

14.725 14.670 14.605 14.565 14.520

143⁄4 145⁄8 145⁄8 145⁄8 141⁄2

1.030 0.940 0.860 0.780 0.710

1 15⁄ 16 7⁄ 8 3⁄ 4 11⁄ 16

111⁄4 111⁄4 111⁄4 111⁄4 111⁄4

111⁄16 15⁄8 19⁄16 17⁄16 13⁄8

15⁄ 16 15⁄ 16 7⁄ 8 7⁄ 8 7⁄ 8

W14×82 W16×74 W16×68 W16×61

24.1 21.8 20.0 17.9

14.31 14.17 14.04 13.89

141⁄4 141⁄8 14 137⁄8

0.510 0.450 0.415 0.375

1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8

1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

10.130 10.070 10.035 9.995

101⁄8 101⁄8 10 10

0.855 0.785 0.720 0.645

7⁄ 8 13⁄ 16 3⁄ 4 5⁄ 8

11 11 11 11

15⁄8 19⁄16 11⁄2 17⁄16

15⁄ 16 15⁄ 16 15⁄ 16

W14×53 W16×48 W16×43

15.6 14.1 12.6

13.92 13.79 13.66

137⁄8 133⁄4 135⁄8

0.370 0.340 0.305

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

8.060 8.030 7.995

8 8 8

0.660 0.595 0.530

11⁄ 16 5⁄ 8 1⁄ 2

11 11 11

17⁄16 13⁄8 15⁄16

15⁄ 16 7⁄ 8 7⁄ 8

W14×38 W16×34 W16×30

11.2 10.0 8.85

14.10 13.98 13.84

141⁄8 14 137⁄8

0.310 0.285 0.270

5⁄ 16 5⁄ 16 1⁄ 4

3⁄ 16 3⁄ 16 1⁄ 8

6.770 6.745 6.730

63⁄4 63⁄4 63⁄4

0.515 0.455 0.385

1⁄ 2 7⁄ 16 3⁄ 8

12 12 12

11⁄16 1 15⁄ 16

5⁄ 8 5⁄ 8 5⁄ 8

W14×26 W16×22

7.69 6.49

13.91 13.74

137⁄8 133⁄4

0.255 0.230

1⁄ 4 1⁄ 4

1⁄ 8 1⁄ 8

5.025 5.000

5 5

0.420 0.335

7⁄ 16 5⁄ 16

12 12

15⁄ 16 7⁄ 8

9⁄ 16 9⁄ 16

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 37

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

132 120 109 99 90

7.1 7.8 8.5 9.3 10.2

82 74 68 61

5.9 6.4 7.0 7.7

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

17.7 19.3 21.7 23.5 25.9

— — — — —

4180 3830 3490 3190 2900

22.4 25.3 27.5 30.4

— — — —

53 48 43

6.1 30.8 6.7 33.5 7.5 37.4

38 34 30 26 22

Axis Y-Y

in.

428 601 853 1220 1750

1530 1380 1240 1110 999

209 190 173 157 143

6.28 6.24 6.22 6.17 6.14

3600 3290 3020 2720

846 1190 1650 2460

882 796 723 640

123 112 103 92.2

6.05 6.04 6.01 5.98

— 57 46

2830 2580 2320

2250 3220 4900

541 485 428

77.8 70.3 62.7

5.89 5.85 5.82

57.7 51.4 45.2

6.6 39.6 7.4 43.1 8.7 45.4

41 35 31

2190 1970 1750

6850 10600 17600

385 340 291

54.6 48.6 42.0

5.87 5.83 5.73

26.7 23.3 19.6

6.0 48.1 7.5 53.3

28 22

1890 1610

13900 27300

245 199

35.3 29.0

5.65 5.54

(1/ksi)

in.

in.3

548 495 447 402 362

74.5 67.5 61.2 55.2 49.9

3.76 3.74 3.73 3.71 3.70

234 212 192 173 157

113 102 92.7 83.6 75.6

148 134 121 107

29.3 26.6 24.2 21.5

2.48 2.48 2.46 2.45

139 126 115 102

44.8 40.6 36.9 32.8

14.3 12.8 11.3

1.92 1.91 1.89

87.1 78.4 69.6

22.0 19.6 17.3

7.88 6.91 5.82

1.55 1.53 1.49

61.5 54.6 47.3

12.1 10.6 8.99

3.54 2.80

1.08 1.04

40.2 33.2

5.54 4.39

8.91 7.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

1 - 38

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Flange

Thickness tw

tw 2

in.

Width bf

Distance

Thickness tf

in.

2.955 215⁄16 2.705 211⁄16 2.470 21⁄2 2.250 21⁄4 2.070 21⁄16 1.900 17⁄8 1.735 13⁄4 1.560 19⁄16 1.400 13⁄8 1.250 11⁄4 1.105 11⁄8 0.990 1 7⁄ 0.900 8 0.810 13⁄16 3 0.735 ⁄4 0.670 11⁄16 5⁄ 0.605 8

91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2 91⁄2

311⁄16 37⁄16 33⁄16 215⁄16 23⁄4 25⁄8 27⁄16 21⁄4 21⁄8 115⁄16 113⁄16 111⁄16 15⁄8 11⁄2 17⁄16 13⁄8 15⁄16

11⁄2 17⁄16 13⁄8 15⁄16 11⁄4 11⁄4 13⁄16 11⁄8 11⁄16 1 1 15⁄ 16 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 13⁄ 16

5⁄ 8 9⁄ 16

91⁄2 91⁄2

13⁄8 11⁄4

13⁄ 16 13⁄ 16

0.640 0.575 0.515

5⁄ 8 9⁄ 16 1⁄ 2

91⁄2 91⁄2 91⁄2

13⁄8 11⁄4 11⁄4

13⁄ 16 13⁄ 16 3⁄ 4

61⁄2 61⁄2 61⁄2

0.520 0.440 0.380

1⁄ 2 7⁄ 16 3⁄ 8

101⁄2 101⁄2 101⁄2

15⁄ 16 7⁄ 8

9⁄ 16 1⁄ 2 1⁄ 2

4 4 4 4

0.425 0.350 0.265 0.225

7⁄ 16 3⁄ 8 1⁄ 4 1⁄ 4

101⁄2 101⁄2 101⁄2 101⁄2

7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2

W12×336* W16×305* W16×279* W16×252* W16×230* W16×210* W16×190 W16×170 W16×152 W16×136 W16×120 W16×106 W16×96 W16×87 W16×79 W16×72 W16×65

98.8 89.6 81.9 74.1 67.7 61.8 55.8 50.0 44.7 39.9 35.3 31.2 28.2 25.6 23.2 21.1 19.1

16.82 16.32 15.85 15.41 15.05 14.71 14.38 14.03 13.71 13.41 13.12 12.89 12.71 12.53 12.38 12.25 12.12

167⁄8 163⁄8 157⁄8 153⁄8 15 143⁄4 143⁄8 14 133⁄4 133⁄8 131⁄8 127⁄8 123⁄4 121⁄2 123⁄8 121⁄4 121⁄8

1.775 1.625 1.530 1.395 1.285 1.180 1.060 0.960 0.870 0.790 0.710 0.610 0.550 0.515 0.470 0.430 0.390

13⁄4 15⁄8 11⁄2 13⁄8 15⁄16 13⁄16 11⁄16 15⁄ 16 7⁄ 8 13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8

7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

13.385 13.235 13.140 13.005 12.895 12.790 12.670 12.570 12.480 12.400 12.320 12.220 12.160 12.125 12.080 12.040 12.000

133⁄8 131⁄4 131⁄8 13 127⁄8 123⁄4 125⁄8 125⁄8 121⁄2 123⁄8 123⁄8 121⁄4 121⁄8 121⁄8 121⁄8 12 12

W12×58 W16×53

17.0 15.6

12.19 12.06

121⁄4 12

0.360 0.345

3⁄ 8 3⁄ 8

3⁄ 16 3⁄ 16

10.010 9.995

10 10

0.640 0.575

W12×50 W16×45 W16×40

14.7 13.2 11.8

12.19 12.06 11.94

121⁄4 12 12

0.370 0.335 0.295

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

8.080 8.045 8.005

81⁄8 8 8

W12×35 W16×30 W16×26

10.3 8.79 7.65

12.50 12.34 12.22

121⁄2 123⁄8 121⁄4

0.300 0.260 0.230

5⁄ 16 1⁄ 4 1⁄ 4

3⁄ 16 1⁄ 8 1⁄ 8

6.560 6.520 6.490

W12×22 W16×19 W16×16 W16×14

6.48 5.57 4.71 4.16

12.31 12.16 11.99 11.91

121⁄4 121⁄8 12 117⁄8

0.260 0.235 0.220 0.200

1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8

4.030 4.005 3.990 3.970

*Group 4 or Group 5 shape. See Notes in Table 1-2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 39

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

336 305 279 252 230 210 190 170 152 136 120 106 96 87 79 72 65

2.3 2.4 2.7 2.9 3.1 3.4 3.7 4.0 4.5 5.0 5.6 6.2 6.8 7.5 8.2 9.0 9.9

58 53

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

5.5 6.0 6.3 7.0 7.6 8.2 9.2 10.1 11.2 12.3 13.7 15.9 17.7 18.9 20.7 22.6 24.9

— — — — — — — — — — — — — — — — —

12800 11800 11000 10100 9390 8670 7940 7190 6510 5850 5240 4660 4250 3880 3530 3230 2940

7.8 8.7

27.0 28.1

— —

3070 2820

50 45 40

6.3 7.0 7.8

26.2 29.0 32.9

— — 59

3170 2870 2580

35 30 26

6.3 7.4 8.5

36.2 41.8 47.2

22 19 16 14

4.7 5.7 7.5 8.8

41.8 46.2 49.4 54.3

(1/ksi)

I 4

Axis Y-Y

r 3

I 4

Zx 3

in.

177 159 143 127 115 104 93.0 82.3 72.8 64.2 56.0 49.3 44.4 39.7 35.8 32.4 29.1

3.47 3.42 3.38 3.34 3.31 3.28 3.25 3.22 3.19 3.16 3.13 3.11 3.09 3.07 3.05 3.04 3.02

603 537 481 428 386 348 311 275 243 214 186 164 147 132 119 108 96.8

274 244 220 196 177 159 143 126 111 98.0 85.4 75.1 67.5 60.4 54.3 49.2 44.1

in.

4060 3550 3110 2720 2420 2140 1890 1650 1430 1240 1070 933 833 740 662 597 533

483 435 393 353 321 292 263 235 209 186 163 145 131 118 107 97.4 87.9

6.41 1190 6.29 1050 6.16 937 6.06 828 5.97 742 5.89 664 5.82 589 5.74 517 5.66 454 5.58 398 5.51 345 5.47 301 5.44 270 5.38 241 5.34 216 5.31 195 5.28 174

1470 2100

475 425

78.0 70.6

5.28 5.23

107 95.8

21.4 19.2

2.51 2.48

86.4 77.9

32.5 29.1

1410 2070 3110

394 350 310

64.7 58.1 51.9

5.18 5.15 5.13

56.3 50.0 44.1

13.9 12.4 11.0

1.96 1.94 1.93

72.4 64.7 57.5

21.4 19.0 16.8

49 37 29

2420 4340 2090 7950 1820 13900

285 238 204

45.6 38.6 33.4

5.25 5.21 5.17

24.5 20.3 17.3

7.47 1.54 6.24 1.52 5.34 1.51

51.2 43.1 37.2

11.5 9.56 8.17

37 30 26 22

2160 8640 1880 15600 1610 32000 1450 49300

156 130 103 88.6

25.4 21.3 17.1 14.9

4.91 4.82 4.67 4.62

2.31 1.88 1.41 1.19

29.3 24.7 20.1 17.4

3.66 2.98 2.26 1.90

4.66 3.76 2.82 2.36

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.847 0.822 0.773 0.753

in.

in.3

in.

6.05 8.17 10.8 14.7 19.7 26.6 37.0 54.0 79.3 119 184 285 405 586 839 1180 1720

in.

r 3

1 - 40

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Flange

Thickness tw

tw 2

in.

Width bf

Distance

Thickness tf

in.

32.9 29.4 25.9 22.6 20.0 17.6 15.8 14.4

11.36 11.10 10.84 10.60 10.40 10.22 10.09 9.98

113⁄8 111⁄8 107⁄8 105⁄8 103⁄8 101⁄4 101⁄8 10

0.755 0.680 0.605 0.530 0.470 0.420 0.370 0.340

3⁄ 4 11⁄ 16 5⁄ 8 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 5⁄ 16

3⁄ 8 3⁄ 8 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16 3⁄ 16

10.415 10.340 10.265 10.190 10.130 10.080 10.030 10.000

103⁄8 103⁄8 101⁄4 101⁄4 101⁄8 101⁄8 10 10

1.250 1.120 0.990 0.870 0.770 0.680 0.615 0.560

11⁄4 11⁄8 1 7⁄ 8 3⁄ 4 11⁄ 16 5⁄ 8 9⁄ 16

75⁄8 75⁄8 75⁄8 75⁄8 75⁄8 75⁄8 75⁄8 75⁄8

17⁄8 13⁄4 15⁄8 11⁄2 13⁄8 15⁄16 11⁄4 13⁄16

15⁄ 16 7⁄ 8 13⁄ 16 13⁄ 16 3⁄ 4 3⁄ 4 11⁄ 16 11⁄ 16

W10×45 W10×39 W10×33

13.3 11.5 9.71

10.10 9.92 9.73

101⁄8 97⁄8 93⁄4

0.350 0.315 0.290

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

8.020 7.985 7.960

8 8 8

0.620 0.530 0.435

5⁄ 8 1⁄ 2 7⁄ 16

75⁄8 75⁄8 75⁄8

11⁄4 11⁄8 11⁄16

11⁄

0.300 0.260 0.240

5⁄ 16 1⁄ 4 1⁄ 4

3⁄ 16 1⁄ 8 1⁄ 8

5.810 5.770 5.750

53⁄4 53⁄4 53⁄4

0.510 0.440 0.360

1⁄ 2 7⁄ 16 3⁄ 8

85⁄8 85⁄8 85⁄8

15⁄ 16 7⁄ 8 3⁄ 4

1⁄ 2 1⁄ 2 1⁄ 2

0.250 0.240 0.230 0.190

1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8

4.020 4.010 4.000 3.960

4 4 4 4

0.395 0.330 0.270 0.210

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

85⁄8 85⁄8 85⁄8 85⁄8

13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

1⁄ 2 1⁄ 2 7⁄ 16 7⁄ 16

W10×30 W10×26 W10×22

8.84 7.61 6.49

10.47 10.33 10.17

W10×19 W10×17 W10×15 W10×12

5.62 4.99 4.41 3.54

10.24 10.11 9.99 9.87

101⁄4 101⁄8 10 97⁄8

in.

W10×112 W10×100 W10×88 W10×77 W10×68 W10×60 W10×54 W10×49

101⁄2 103⁄8 101⁄8

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11⁄

16 16 16

STRUCTURAL SHAPES

1 - 41

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

112 100 88 77 68 60 54 49

4.2 4.6 5.2 5.9 6.6 7.4 8.2 8.9

45 39 33

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

in.

10.4 11.6 13.0 14.8 16.7 18.7 21.2 23.1

— — — — — — — —

7080 6400 5680 5010 4460 3970 3580 3280

56.7 83.8 132 213 334 525 778 1090

716 623 534 455 394 341 303 272

6.5 7.5 9.1

22.5 25.0 27.1

— — —

3650 3190 2710

758 1300 2510

30 26 22

5.7 6.6 8.0

29.5 34.0 36.9

— 55 47

2890 2500 2150

2160 3790 7170

19 17 15 12

5.1 6.1 7.4 9.4

35.4 36.9 38.5 46.6

51 47 43 30

2420 2210 1930 1550

5160 7820 14300 35400

(1/ksi)

I 4

Axis Y-Y

r 3

I 4

r 3

in.3

2.68 2.65 2.63 2.60 2.59 2.57 2.56 2.54

147 130 113 97.6 85.3 74.6 66.6 60.4

69.2 61.0 53.1 45.9 40.1 35.0 31.3 28.3

13.3 11.3 9.20

2.01 1.98 1.94

54.9 46.8 38.8

20.3 17.2 14.0

5.75 4.89 3.97

1.37 1.36 1.33

36.6 31.3 26.0

8.84 7.50 6.10

2.14 1.78 1.45 1.10

0.874 0.844 0.810 0.785

21.6 18.7 16.0 12.6

3.35 2.80 2.30 1.74

in.

126 112 98.5 85.9 75.7 66.7 60.0 54.6

4.66 4.60 4.54 4.49 4.44 4.39 4.37 4.35

236 207 179 154 134 116 103 93.4

45.3 40.0 34.8 30.1 26.4 23.0 20.6 18.7

248 209 170

49.1 42.1 35.0

4.32 4.27 4.19

53.4 45.0 36.6

170 144 118

32.4 27.9 23.2

4.38 4.35 4.27

16.7 14.1 11.4

18.8 16.2 13.8 10.9

4.14 4.05 3.95 3.90

4.29 3.56 2.89 2.18

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

96.3 81.9 68.9 53.8

1 - 42

DIMENSIONS AND PROPERTIES

W SHAPES Dimensions

Y bf

Web

Designation

Area A

Depth d

in.

Thickness tw in.

Flange

tw 2 in.

Width bf

Distance

Thickness tf

in.

W8×67 W8×58 W8×48 W8×40 W8×35 W8×31

19.7 17.1 14.1 11.7 10.3 9.13

9.00 8.75 8.50 8.25 8.12 8.00

9 83⁄4 81⁄2 81⁄4 81⁄8 8

0.570 0.510 0.400 0.360 0.310 0.285

9⁄ 16 1⁄ 2 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16

5⁄ 16 1⁄ 4 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16

8.280 8.220 8.110 8.070 8.020 7.995

81⁄4 81⁄4 81⁄8 81⁄8 8 8

0.935 0.810 0.685 0.560 0.495 0.435

15⁄ 16 13⁄ 16 11⁄ 16 9⁄ 16 1⁄ 2 7⁄ 16

61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8

17⁄16 15⁄16 13⁄16 11⁄16 1 15⁄ 16

11⁄

W8×28 W8×24

8.25 7.08

8.06 7.93

8 77⁄8

0.285 0.245

5⁄ 16 1⁄ 4

3⁄ 16 1⁄ 8

6.535 6.495

61⁄2 61⁄2

0.465 0.400

7⁄ 16 3⁄ 8

61⁄8 61⁄8

15⁄ 16 7⁄ 8

9⁄ 16 9⁄ 16

W8×21 W8×18

6.16 5.26

8.28 8.14

81⁄4 81⁄8

0.250 0.230

1⁄ 4 1⁄ 4

1⁄ 8 1⁄ 8

5.270 5.250

51⁄4 51⁄4

0.400 0.330

3⁄ 8 5⁄ 16

65⁄8 65⁄8

13⁄ 16 3⁄ 4

1⁄ 2 7⁄ 16

W8×15 W8×13 W8×10

4.44 3.84 2.96

8.11 7.99 7.89

81⁄8 8 77⁄8

0.245 0.230 0.170

1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8

4.015 4.000 3.940

4 4 4

0.315 0.255 0.205

5⁄ 16 1⁄ 4 3⁄ 16

65⁄8 65⁄8 65⁄8

3⁄ 4 11⁄ 16 5⁄ 8

1⁄ 2 7⁄ 16 7⁄ 16

W6×25 W8×20 W8×15

7.34 5.87 4.43

6.38 6.20 5.99

63⁄8 61⁄4 6

0.320 0.260 0.230

5⁄ 16 1⁄ 4 1⁄ 4

3⁄ 16 1⁄ 8 1⁄ 8

6.080 6.020 5.990

61⁄8 6 6

0.455 0.365 0.260

7⁄ 16 3⁄ 8 1⁄ 4

43⁄4 43⁄4 43⁄4

13⁄ 16 3⁄ 4 5⁄ 8

7⁄ 16 7⁄ 16 3⁄ 8

W6×16 W8×12 W8×9

4.74 3.55 2.68

6.28 6.03 5.90

61⁄4 6 57⁄8

0.260 0.230 0.170

1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8

4.030 4.000 3.940

4 4 4

0.405 0.280 0.215

3⁄ 8 1⁄ 4 3⁄ 16

43⁄4 43⁄4 43⁄4

3⁄ 4 5⁄ 8 9⁄ 16

7⁄ 16 3⁄ 8 3⁄ 8

W5×19 W8×16

5.54 4.68

5.15 5.01

51⁄8 5

0.270 0.240

1⁄ 4 1⁄ 4

1⁄ 8 1⁄ 8

5.030 5.000

5 5

0.430 0.360

7⁄ 16 3⁄ 8

31⁄2 31⁄2

13⁄ 16 3⁄ 4

7⁄ 16 7⁄ 16

W4×13

3.83

4.16

41⁄8

0.280

1⁄ 4

1⁄ 8

4.060

0.345

3⁄ 8

23⁄4

11⁄ 16

7⁄ 16

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in. 11⁄

16 5⁄ 8 5⁄ 8 9⁄ 16 9⁄ 16

STRUCTURAL SHAPES

1 - 43

W SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

67 58 48 40 35 31

4.4 5.1 5.9 7.2 8.1 9.2

28 24

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

in.

11.1 12.4 15.8 17.6 20.4 22.2

— — — — — —

6620 5820 4860 4080 3610 3230

73.9 122 238 474 761 1180

272 228 184 146 127 110

7.0 8.1

22.2 25.8

— —

3480 3020

931 1610

21 18

6.6 8.0

27.5 29.9

— —

2890 2490

15 13 10

6.4 7.8 9.6

28.1 29.9 40.5

— — 39

25 20 15

6.7 15.5 8.2 19.1 11.5 21.6

16 12 9

5.0 7.1 9.2

19 16 13

(1/ksi)

I 4

Axis Y-Y

r 3

I 4

r 3

in.

in.3

in.

60.4 52.0 43.3 35.5 31.2 27.5

3.72 3.65 3.61 3.53 3.51 3.47

88.6 75.1 60.9 49.1 42.6 37.1

21.4 18.3 15.0 12.2 10.6 9.27

2.12 2.10 2.08 2.04 2.03 2.02

70.2 59.8 49.0 39.8 34.7 30.4

32.7 27.9 22.9 18.5 16.1 14.1

98.0 82.8

24.3 20.9

3.45 3.42

21.7 18.3

6.63 5.63

1.62 1.61

27.2 23.2

10.1 8.57

2090 3890

75.3 61.9

18.2 15.2

3.49 3.43

9.77 7.97

3.71 3.04

1.26 1.23

20.4 17.0

5.69 4.66

2670 2370 1760

3440 5780 17900

48.0 39.6 30.8

11.8 9.91 7.81

3.29 3.21 3.22

3.41 2.73 2.09

1.70 1.37 1.06

0.876 0.843 0.841

13.6 11.4 8.87

2.67 2.15 1.66

— — —

4410 3550 2740

369 846 2470

53.4 41.4 29.1

16.7 13.4 9.72

2.70 2.66 2.56

17.1 13.3 9.32

5.61 4.41 3.11

1.52 1.50 1.46

18.9 14.9 10.8

8.56 6.72 4.75

19.1 21.6 29.2

— — —

4010 3100 2360

591 1740 4980

32.1 22.1 16.4

10.2 7.31 5.56

2.60 2.49 2.47

4.43 2.99 2.19

2.20 1.50 1.11

0.966 0.918 0.905

11.7 8.30 6.23

3.39 2.32 1.72

5.8 6.9

14.0 15.8

— —

5140 4440

192 346

26.2 21.3

10.2 8.51

2.17 2.13

9.13 7.51

3.63 3.00

1.28 1.27

11.6 9.59

5.53 4.57

5.9

10.6

—

5560

154

11.3

5.46

1.72

3.86

1.90

1.00

6.28

2.92

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 44

DIMENSIONS AND PROPERTIES

M SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d

Thickness tw

in.

Flange

tw 2

Width bf

Thickness tf

in.

11.91 1115⁄16 0.177 11.87 117⁄8 0.162

3⁄ 16 3⁄ 16

1⁄ 16 1⁄ 16

3.065 31⁄16 0.225 3.065 31⁄16 0.206

1⁄ 4 3⁄ 16

1015⁄16 107⁄8

1⁄ 2 1⁄ 2

3⁄ 8 3⁄ 8

97⁄8 0.157 913⁄16 0.139

3⁄ 16 1⁄ 8

1⁄ 16 1⁄ 16

2.690 211⁄16 0.206 2.690 211⁄16 0.183

3⁄ 16 3⁄ 16

87⁄8 813⁄16

1⁄ 2 1⁄ 2

3⁄ 8 3⁄ 8

0.133

1⁄ 8

1⁄ 16

2.280

21⁄4

0.186

3⁄ 16

67⁄8

1⁄ 2

3⁄ 8

0.316

5⁄ 16

3⁄ 16

5.003

0.416

7⁄ 16

31⁄4

7⁄ 8

1⁄ 2

M12×11.8 M12×10.8

3.48 3.20

M10×9 M12×8

2.67 2.38

9.86 9.81

M8×6.5

1.92

7.85

77⁄8

M5×18.9*

5.55

5.00

in.

Distance

*This shape has tapered flanges while all other M shapes have parallel flanges.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 45

M SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

11.8 10.8

6.8 7.4

9 8

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

(1/ksi)

61.4 67.0

17 14

1420 1320

6.5 7.3

56.4 63.7

20 16

6.5

6.1

51.7

18.9

6.0

11.2

I 4

Axis Y-Y

r 3

in.

56700 75800

71.7 65.8

12.1 11.1

1570 1400

37100 57800

38.5 34.3

1780

20700

—

5710

134

I 4

r 3

in.

in.3

14.3 13.1

1.16 1.05

in.

4.54 4.54

1.09 0.995

0.709 0.649

0.559 0.558

7.82 6.99

3.80 3.80

0.673 0.597

0.501 0.444

0.502 0.502

9.21 8.20

0.815 0.718

18.1

4.62

3.07

0.371

0.325

0.439

5.40

0.527

24.1

9.63

2.08

7.86

3.14

1.19

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.0

5.02

1 - 46

DIMENSIONS AND PROPERTIES

S SHAPES Dimensions

grip

Y bf

Web

Designation

Flange

Distance

Max. Flge. FasGrip tener

Area A

Depth d

Thickness tw

tw 2

Width bf

Thickness tf

in.2

in.

in. 1 1

S24×121 S24×106

35.6 31.2

24.50 24.50

241⁄2 241⁄2

0.800 0.620

13⁄ 16 5⁄ 8

7⁄ 16 5⁄ 16

8.050 7.870

8 77⁄8

S24×100 S24×90 S24×80

29.3 26.5 23.5

24.00 24.00 24.00

24 24 24

0.745 0.625 0.500

3⁄ 4 5⁄ 8 1⁄ 2

3⁄ 8 5⁄ 16 1⁄ 4

7.245 7.125 7.000

S20×96 S24×86

28.2 25.3

20.30 201⁄4 0.800 20.30 201⁄4 0.660

13⁄ 16 11⁄ 16

7⁄ 16 3⁄ 8

S20×75 S24×66

22.0 19.4

20.00 20.00

20 20

0.635 0.505

5⁄ 8 1⁄ 2

5⁄ 16 1⁄ 4

6.385 6.255

63⁄8 61⁄4

0.795 0.795

13⁄ 16 13⁄ 16

163⁄4 163⁄4

15⁄8 15⁄8

13⁄ 16 13⁄ 16

7⁄ 8 7⁄ 8

S18×70 20.6 S24×54.7 16.1

18.00 18.00

18 18

0.711 0.461

11⁄ 16 7⁄ 16

3⁄

6.251 6.001

61⁄4 6

0.691 0.691

11⁄ 16 11⁄ 16

15 15

11⁄2 11⁄2

11⁄ 16 11⁄ 16

7⁄ 8 7⁄ 8

S15×50 14.7 S24×42.9 12.6

15.00 15.00

15 15

0.550 0.411

9⁄ 16 7⁄ 16

5⁄ 16 1⁄ 4

5.640 5.501

55⁄8 51⁄2

0.622 0.622

5⁄ 8 5⁄ 8

121⁄4 121⁄4

13⁄8 13⁄8

9⁄ 16 9⁄ 16

3⁄ 4 3⁄ 4

S12×50 14.7 S24×40.8 12.0

12.00 12.00

12 12

0.687 0.462

11⁄ 16 7⁄ 16

3⁄

5.477 5.252

51⁄2 51⁄4

0.659 0.659

11⁄ 16 11⁄ 16

91⁄8 91⁄8

17⁄16 17⁄16

11⁄ 16 5⁄ 8

3⁄ 4 3⁄ 4

S12×35 10.3 12.00 S24×31.8 9.35 12.00

12 12

0.428 0.350

7⁄ 16 3⁄ 8

1⁄ 4 3⁄ 16

5.078 5.000

51⁄8 5

0.544 0.544

9⁄ 16 9⁄ 16

95⁄8 95⁄8

13⁄16 13⁄16

1⁄ 2 1⁄ 2

3⁄ 4 3⁄ 4

S10×35 10.3 10.00 S24×25.4 7.46 10.00

10 10

0.594 0.311

5⁄ 8 5⁄ 16

5⁄ 16 3⁄ 16

4.944 4.661

5 45⁄8

0.491 0.491

1⁄ 2 1⁄ 2

73⁄4 73⁄4

11⁄8 11⁄8

1⁄ 2 1⁄ 2

3⁄ 4 3⁄ 4

4.171 4.001

41⁄8 4

0.426 0.426

7⁄ 16 7⁄ 16

6 6

1 1

7⁄ 16 7⁄ 16

3⁄ 4 3⁄ 4

3.565 3.332

35⁄8 33⁄8

0.359 0.359

3⁄ 8 3⁄ 8

41⁄4 41⁄4

7⁄ 8 7⁄ 8

3⁄ 8 3⁄ 8

5⁄ 8 —

3.004

0.326

5⁄ 16

33⁄8

13⁄ 16

5⁄ 16

—

0.293 0.293

5⁄ 16 5⁄ 16

21⁄2 21⁄2

3⁄ 4 3⁄ 4

5⁄ 16 5⁄ 16

— —

0.260 0.260

1⁄ 4 1⁄ 4

15⁄8 15⁄8

11⁄ 16 11⁄ 16

1⁄ 4 1⁄ 4

— —

1⁄

1.090 1.090

11⁄16 11⁄16

201⁄2 201⁄2

2 2

11⁄8 11⁄8

71⁄4 71⁄8 7

0.870 0.870 0.870

7⁄ 8 7⁄ 8 7⁄ 8

201⁄2 201⁄2 201⁄2

13⁄4 13⁄4 13⁄4

7⁄ 8 7⁄ 8 7⁄ 8

1 1 1

7.200 7.060

71⁄4 7

0.920 0.920

15⁄ 16 15⁄ 16

163⁄4 163⁄4

13⁄4 13⁄4

15⁄ 16 15⁄ 16

1 1

S8×23 S8×18.4

6.77 5.41

8.00 8.00

8 8

0.441 0.271

7⁄ 16 1⁄ 4

1⁄

S6×17.25 S8×12.5

5.07 3.67

6.00 6.00

6 6

0.465 0.232

7⁄ 16 1⁄ 4

1⁄

S5×10

2.94

5.00

0.214

3⁄ 16

1⁄

3⁄ 16 1⁄ 8

2.796 2.663

23⁄4 25⁄8

3⁄ 16 1⁄ 8

2.509 2.330

21⁄2 23⁄8

S4×9.5 S8×7.7

2.79 2.26

4.00 4.00

4 4

0.326 0.193

5⁄ 16 3⁄ 16

S3×7.5 S8×5.7

2.21 1.67

3.00 3.00

3 3

0.349 0.170

3⁄ 8 3⁄ 16

1⁄

4 8 4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 47

S SHAPES Properties

Y bf

grip

Nominal Wt. per ft

Compact Section Criteria

bf 2tf

h tw

Fy′′′

121 106

3.7 3.6

100 90 80

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

(1/ksi)

36.4 34.1

— 55

3310 2960

4.2 4.1 4.0

28.3 33.7 42.1

— 56 36

96 86

3.9 3.8

21.6 26.2

75 66

4.0 3.9

70 54.7

I 4

Axis Y-Y

r 3

in.

1770 2470

3160 2940

3000 2710 2450

2940 4090 5480

— —

3730 3350

27.1 34.1

— 55

4.5 4.3

21.8 33.6

50 42.9

4.5 4.4

50 40.8

I 4

r 3

Zx 3

Zy in.3

in.

258 240

9.43 9.71

83.3 77.1

20.7 19.6

1.53 1.57

306 279

36.2 33.2

2390 2250 2100

199 187 175

9.02 9.21 9.47

47.7 44.9 42.2

13.2 12.6 12.1

1.27 1.30 1.34

240 222 204

23.9 22.3 20.7

1160 1630

1670 1580

165 155

7.71 7.89

50.2 46.8

13.9 13.3

1.33 1.36

198 183

24.9 23.0

3140 2800

2290 3250

1280 1190

128 119

7.62 7.83

29.8 27.7

9.32 8.85

1.16 1.19

153 140

16.7 15.3

— 57

3590 2770

1470 3400

926 804

103 89.4

6.71 7.07

24.1 20.8

7.72 6.94

1.08 1.14

125 105

14.4 12.1

23.2 31.0

— —

3450 2960

1540 2470

486 447

64.8 59.6

5.75 5.95

15.7 14.4

5.57 5.23

1.03 1.07

77.1 69.3

9.97 9.02

4.2 4.0

13.9 20.7

— —

5070 4050

333 682

305 272

50.8 45.4

4.55 4.77

15.7 13.6

5.74 5.16

1.03 1.06

61.2 53.1

10.3 8.85

35 31.8

4.7 4.6

23.4 28.6

— —

3500 3190

1310 1710

229 218

38.2 36.4

4.72 4.83

9.87 9.36

3.89 3.74

0.980 1.00

44.8 42.0

6.79 6.40

35 25.4

5.0 4.7

13.8 26.4

— —

4960 3430

374 1220

147 124

29.4 24.7

3.78 4.07

8.36 6.79

3.38 2.91

0.901 0.954

35.4 28.4

6.22 4.96

23 18.4

4.9 4.7

14.5 23.7

— —

4770 3770

397 821

64.9 57.6

16.2 14.4

3.10 3.26

4.31 3.73

2.07 1.86

0.798 0.831

19.3 16.5

3.68 3.16

17.25 5.0 12.5 4.6

9.9 19.9

— —

6250 4290

143 477

26.3 22.1

8.77 7.37

2.28 2.45

2.31 1.82

1.30 1.09

0.675 0.705

10.6 8.47

2.36 1.85

4.6

17.4

—

4630

348

12.3

4.92

2.05

1.22

0.809 0.643

5.67

1.37

9.5 7.7

4.8 4.5

8.7 14.7

— —

6830 5240

87.4 207

6.79 6.08

3.39 3.04

1.56 1.64

0.903 0.764

0.646 0.569 0.574 0.581

4.04 3.51

1.13 0.964

7.5 5.7

4.8 4.5

5.6 11.4

— —

9160 6160

28.1 106

2.93 2.52

1.95 1.68

1.15 1.23

0.586 0.455

0.468 0.516 0.390 0.522

2.36 1.95

0.826 0.653

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 48

DIMENSIONS AND PROPERTIES

HP SHAPES Dimensions

Y bf

Web

Designation

Area A 2

in.

Depth d in.

Thickness tw in.

Flange

tw 2 in.

Width bf in.

Distance

Thickness tf in.

in.

HP14×117 HP14×102 HP14×89 HP14×73

34.4 30.0 26.1 21.4

14.21 14.01 13.83 13.61

141⁄4 14 137⁄8 135⁄8

0.805 0.705 0.615 0.505

13⁄ 16 11⁄ 16 5⁄ 8 1⁄ 2

7⁄ 16 3⁄ 8 5⁄ 16 1⁄ 4

14.885 14.785 14.695 14.585

147⁄8 143⁄4 143⁄4 145⁄8

0.805 0.705 0.615 0.505

13⁄ 16 11⁄ 16 5⁄ 8 1⁄ 2

111⁄4 111⁄4 111⁄4 111⁄4

11⁄2 13⁄8 15⁄16 13⁄16

11⁄16 1 15⁄ 16 7⁄ 8

HP12×84 HP14×74 HP14×63 HP14×53

24.6 21.8 18.4 15.5

12.28 12.13 11.94 11.78

121⁄4 121⁄8 12 113⁄4

0.685 0.605 0.515 0.435

11⁄ 16 5⁄ 8 1⁄ 2 7⁄ 16

3⁄ 8 5⁄ 16 1⁄ 4 1⁄ 4

12.295 12.215 12.125 12.045

121⁄4 121⁄4 121⁄8 12

0.685 0.610 0.515 0.435

11⁄ 16 5⁄ 8 1⁄ 2 7⁄ 16

91⁄2 91⁄2 91⁄2 91⁄2

13⁄8 15⁄16 11⁄4 11⁄8

15⁄ 16 7⁄ 8 7⁄ 8

HP10×57 HP14×42

16.8 12.4

9.99 9.70

10 93⁄4

0.565 0.415

9⁄ 16 7⁄ 16

5⁄ 16 1⁄ 4

10.225 10.075

101⁄4 101⁄8

0.565 0.420

9⁄ 16 7⁄ 16

75⁄8 75⁄8

13⁄16 11⁄16

13⁄ 16 3⁄ 4

HP8×36

10.6

8.02

0.445

7⁄ 16

1⁄ 4

8.155

81⁄8

0.445

7⁄ 16

61⁄8

15⁄ 16

5⁄ 8

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 49

HP SHAPES Properties

Y bf

Nominal Wt. per ft

Compact Section Criteria

h tw

Fy′′′

bf 2tf

117 102 89 73

9.2 10.5 11.9 14.4

84 74 63 53

9.0 10.0 11.8 13.8

Plastic Modulus

Elastic Properties Axis X-X

X2 × 106

ksi

14.2 16.2 18.5 22.6

— — — —

14.2 16.0 18.9 22.3

57 42 36

Axis Y-Y

r 3

(1/ksi)

in.

3870 3400 2960 2450

659 1090 1840 3880

1220 1050 904 729

172 150 131 107

5.96 5.92 5.88 5.84

— — — —

3860 3440 2940 2500

670 1050 1940 3650

650 569 472 393

106 93.8 79.1 66.8

9.0 13.9 12.0 18.9

— —

3920 2920

631 1970

294 210

9.2 14.2

—

3840

685

119

r 3

in.

in.3

443 380 326 261

59.5 51.4 44.3 35.8

3.59 3.56 3.53 3.49

194 169 146 118

91.4 78.8 67.7 54.6

5.14 5.11 5.06 5.03

213 186 153 127

34.6 30.4 25.3 21.1

2.94 2.92 2.88 2.86

120 105 88.3 74.0

53.2 46.6 38.7 32.2

58.8 43.4

4.18 4.13

101 71.7

19.7 14.2

2.45 2.41

66.5 48.3

30.3 21.8

29.8

3.36

40.3

1.95

33.6

15.2

9.88

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 50

DIMENSIONS AND PROPERTIES

CHANNELS AMERICAN STANDARD Dimensions

grip

Web

Designation

Area Depth Thickness A d tw in.2

in.

Flange

Distance

Max. Flge. FasGrip tener

tw 2

Width bf

Thickness tf

in.

121⁄8 121⁄8 121⁄8

17⁄16 17⁄16 17⁄16

5⁄

93⁄4 93⁄4 93⁄4

11⁄8 11⁄8 11⁄8

1⁄

7⁄ 8 7⁄ 8 7⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

3⁄ 8 1⁄ 4 3⁄ 16

in.

3.716 3.520 3.400

33⁄4 31⁄2 33⁄8

0.650 0.650 0.650

5⁄ 8 5⁄ 8 5⁄ 8

3.170 3.047 2.942

31⁄8 3 3

0.501 0.501 0.501

1⁄ 2 1⁄ 2 1⁄ 2

8 8 8 8

1 1 1 1

7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16

in.

C15×50 C15×40 C15×33.9

14.7 11.8 9.96

15.00 15.00 15.00

0.716 0.520 0.400

11⁄ 16 1⁄ 2 3⁄ 8

C12×30 C15×25 C15×20.7

8.82 7.35 6.09

12.00 12.00 12.00

0.510 0.387 0.282

1⁄ 2 3⁄ 8 5⁄ 16

1⁄ 4 3⁄ 16 1⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

3.033 2.886 2.739 2.600

3 27⁄8 23⁄4 25⁄8

0.436 0.436 0.436 0.436

7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16

1⁄ 4 1⁄ 8 1⁄ 8

2.648 2.485 2.433

25⁄8 21⁄2 23⁄8

0.413 0.413 0.413

7⁄ 16 7⁄ 16 7⁄ 16

71⁄8 71⁄8 71⁄8

15⁄ 16 15⁄ 16 15⁄ 16

7⁄ 16 7⁄ 16 7⁄ 16

3⁄ 4 3⁄ 4 3⁄ 4

1⁄ 4 1⁄ 8 1⁄ 8

2.527 2.343 2.260

21⁄2 23⁄8 21⁄4

0.390 0.390 0.390

3⁄ 8 3⁄ 8 3⁄ 8

61⁄8 61⁄8 61⁄8

15⁄ 16 15⁄ 16 15⁄ 16

3⁄

3⁄ 4 3⁄ 4 3⁄ 4

3⁄ 16 1⁄ 8

2.194 2.090

21⁄4 21⁄8

0.366 0.366

3⁄ 8 3⁄ 8

51⁄4 51⁄4

7⁄ 8 7⁄ 8

3⁄

5⁄ 8 5⁄ 8

3⁄ 16 3⁄ 16 1⁄ 8

2.157 2.034 1.920

21⁄8 2 17⁄8

0.343 0.343 0.343

5⁄ 16 5⁄ 16 5⁄ 16

43⁄8 43⁄8 43⁄8

13⁄ 16 13⁄ 16 13⁄ 16

5⁄ 16 3⁄ 8 5⁄ 16

5⁄ 8 5⁄ 8 5⁄ 8

3⁄ 16 1⁄ 8

1.885 1.750

17⁄8 13⁄4

0.320 0.320

5⁄ 16 5⁄ 16

31⁄2 31⁄2

3⁄ 4 3⁄ 4

5⁄ 16

5⁄ 8 —

5⁄ 5⁄

1⁄ 1⁄

8 8 8 2 2

1 1 1

C10×30 C15×25 C15×20 C15×15.3

8.82 7.35 5.88 4.49

10.00 10.00 10.00 10.00

0.673 0.526 0.379 0.240

11⁄ 16 1⁄ 2 3⁄ 8 1⁄ 4

C9×20 C5×15 C5×13.4

5.88 4.41 3.94

9.00 9.00 9.00

0.448 0.285 0.233

7⁄

C8×18.75 C8×13.75 C8×11.5

5.51 4.04 3.38

8.00 8.00 8.00

0.487 0.303 0.220

C7×12.25 C8×9.8

3.60 2.87

7.00 7.00

0.314 0.210

5⁄

C6×13 C8×10.5 C8×8.2

3.83 3.09 2.40

6.00 6.00 6.00

0.437 0.314 0.200

7⁄

C5×9 C8×6.7

2.64 1.97

5.00 5.00

0.325 0.190

5⁄

C4×7.25 C8×5.4

2.13 1.59

4.00 4.00

0.321 0.184

5⁄

3⁄ 16 1⁄ 16

1.721 1.584

13⁄4 15⁄8

0.296 0.296

5⁄ 16 5⁄ 16

25⁄8 25⁄8

11⁄ 16 11⁄ 16

5⁄ 16

—

5⁄ 8 —

C3×6 C8×5 C8×4.1

1.76 1.47 1.21

3.00 3.00 3.00

0.356 0.258 0.170

3⁄ 8 1⁄ 4 3⁄ 16

3⁄ 16 1⁄ 8 1⁄ 16

1.596 1.498 1.410

15⁄8 11⁄2 13⁄8

0.273 0.273 0.273

1⁄ 4 1⁄ 4 1⁄ 4

15⁄8 15⁄8 15⁄8

11⁄ 16 11⁄ 16 11⁄ 16

— — —

5⁄

16 1⁄ 4 1⁄ 2

5⁄

16 1⁄ 4

3⁄

5⁄ 3⁄

3⁄

16 16 16 16 16 16 16 16

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3⁄ 3⁄

3⁄

8 8 8 8

—

STRUCTURAL SHAPES

1 - 51

CHANNELS AMERICAN STANDARD Properties

Nominal Wt. per ft

_ x

Shear Center PNA Loca- Location tion eo xp

Axis X-X

I 4

in.

Axis Y-Y

S 3

grip

r 3

I 4

S 3

r 3

in.

50 40 33.9

0.798 0.777 0.787

0.583 0.767 0.896

0.488 0.390 0.330

404 349 315

68.2 57.2 50.4

53.8 46.5 42.0

5.24 5.44 5.62

11.0 9.23 8.13

8.17 6.87 6.23

3.78 3.37 3.11

0.867 0.886 0.904

30 25 20.7

0.674 0.674 0.698

0.618 0.746 0.870

0.366 0.305 0.252

162 144 129

33.6 29.2 25.4

27.0 24.1 21.5

4.29 4.43 4.61

5.14 4.47 3.88

4.33 3.84 3.49

2.06 1.88 1.73

0.763 0.780 0.799

30 25 20 15.3

0.649 0.617 0.606 0.634

0.369 0.494 0.637 0.796

0.439 0.366 0.292 0.223

103 91.2 78.9 67.4

26.6 23.0 19.3 15.8

20.7 18.2 15.8 13.5

3.42 3.52 3.66 3.87

3.94 3.36 2.81 2.28

3.78 3.19 2.71 2.35

1.65 1.48 1.32 1.16

0.669 0.676 0.692 0.713

20 15 13.4

0.583 0.586 0.601

0.515 0.682 0.743

0.325 0.243 0.217

60.9 51.0 47.9

16.8 13.5 12.5

13.5 11.3 10.6

3.22 3.40 3.48

2.42 1.93 1.76

2.47 2.05 1.95

1.17 1.01 0.962

0.642 0.661 0.669

18.75 13.75 11.5

0.565 0.553 0.571

0.431 0.604 0.697

0.343 0.251 0.209

44.0 36.1 32.6

13.8 10.9 9.55

11.0 9.03 8.14

2.82 2.99 3.11

1.98 1.53 1.32

2.17 1.73 1.58

1.01 0.854 0.781

0.599 0.615 0.625

12.25 9.8

0.525 0.540

0.538 0.647

0.255 0.203

24.2 21.3

8.40 7.12

6.93 6.08

2.60 2.72

1.17 0.968

1.43 1.26

0.703 0.625

0.571 0.581

13 10.5 8.2

0.514 0.499 0.511

0.380 0.486 0.599

0.317 0.255 0.198

17.4 15.2 13.1

7.26 6.15 5.13

5.80 5.06 4.38

2.13 2.22 2.34

1.05 0.866 0.693

1.36 1.15 0.993

0.642 0.564 0.492

0.525 0.529 0.537

9 6.7

0.478 0.484

0.427 0.552

0.262 0.217

8.90 7.49

4.36 3.51

3.56 3.00

1.83 1.95

0.632 0.479

0.918 0.763

0.450 0.378

0.489 0.493

7.25 5.4

0.459 0.457

0.386 0.502

0.264 0.241

4.59 3.85

2.81 2.26

2.29 1.93

1.47 1.56

0.433 0.319

0.697 0.569

0.343 0.283

0.450 0.449

6 5 4.1

0.455 0.438 0.436

0.322 0.392 0.461

0.291 0.242 0.284

2.07 1.85 1.66

1.72 1.50 1.30

1.38 1.24 1.10

1.08 1.12 1.17

0.305 0.247 0.197

0.544 0.466 0.401

0.268 0.233 0.202

0.416 0.410 0.404

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 52

DIMENSIONS AND PROPERTIES

CHANNELS MISCELLANEOUS Dimensions

Y eo

grip

Web

Designation

Area Depth Thickness A d tw in.2

in.

Flange

Distance

Max. Flge. FasGrip tener

tw 2

Width bf

Thickness tf

in.

151⁄4 151⁄4 151⁄4 151⁄4

13⁄8 13⁄8 13⁄8 13⁄8

5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8

1 1 1 1

101⁄4 101⁄4 101⁄4 101⁄4

13⁄8 13⁄8 13⁄8 13⁄8

5⁄ 8 9⁄ 16 9⁄ 16 9⁄ 16

1 1 1 1

15⁄16 15⁄16 15⁄16 15⁄16 15⁄16

11⁄ 16 11⁄ 16 11⁄ 16 11⁄ 16 11⁄ 16

1 1 1 1 1

MC18×58 MC18×51.9 MC18×45.8 MC18×42.7

17.1 15.3 13.5 12.6

18.00 18.00 18.00 18.00

0.700 0.600 0.500 0.450

11⁄ 16 5⁄ 8 1⁄ 2 7⁄ 16

MC13×50 MC18×40 MC18×35 MC18×31.8

14.7 11.8 10.3 9.35

13.00 13.00 13.00 13.00

0.787 0.560 0.447 0.375

3⁄ 16 9⁄ 16 7⁄ 16 3⁄ 8

3⁄ 8 1⁄ 4 1⁄ 4 3⁄ 16 7⁄

16 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

4.135 4.012 3.890 3.767 3.670

41⁄

4 37⁄8 33⁄4 35⁄8

0.700 0.700 0.700 0.700 0.700

11⁄ 16 11⁄ 16 11⁄ 16 11⁄ 16 11⁄ 16

1.500

11⁄2

0.309

5⁄ 16

105⁄8

—

71⁄2 71⁄2 71⁄2

11⁄4 11⁄4 11⁄4

9⁄ 16 9⁄ 16 9⁄ 16

7⁄ 8 7⁄ 8 7⁄ 8

MC12×50 MC18×45 MC18×40 MC18×35 MC18×31 MC12×10.6

3⁄ 8 5⁄ 16 1⁄ 4 1⁄ 4

4.200 4.100 4.000 3.950

41⁄

41⁄8 4 4

0.625 0.625 0.625 0.625

5⁄

4.412 4.185 4.072 4.000

43⁄8 41⁄8 41⁄8 4

0.610 0.610 0.610 0.610

5⁄

93⁄8 93⁄8 93⁄8 93⁄8 93⁄8

5⁄ 5⁄ 5⁄

8 8 8 8 8 8 8 8

14.7 13.2 11.8 10.3 9.12

12.00 12.00 12.00 12.00 12.00

0.835 0.712 0.590 0.467 0.370

13⁄ 16 11⁄ 16 9⁄ 16 7⁄ 16 3⁄ 8

3.10

12.00

0.190

3⁄ 16

1⁄ 8 3⁄ 8 5⁄ 16 3⁄ 16

4.321 4.100 3.950

43⁄

41⁄8 4

0.575 0.575 0.575

9⁄ 16 9⁄ 16 9⁄ 16

11⁄

12.1 9.87 8.37

10.00 10.00 10.00

0.796 0.575 0.425

13⁄ 16 9⁄ 16 7⁄ 16

MC10×25 MC18×22

7.35 6.45

10.00 10.00

0.380 0.290

3⁄ 8 5⁄ 16

3⁄

16 1⁄ 8

3.405 3.315

33⁄8 33⁄8

0.575 0.575

9⁄ 16 9⁄ 16

71⁄2 71⁄2

11⁄4 11⁄4

9⁄ 16 9⁄ 16

7⁄ 8 7⁄ 8

MC10×8.4

2.46

10.00

0.170

3⁄ 16

1⁄

1.500

11⁄2

0.280

1⁄

85⁄8

11⁄

—

MC10×41.1 MC18×33.6 MC18×28.5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 53

CHANNELS MISCELLANEOUS Properties

Nominal Wt. per ft

_ x

Shear Center PNA Loca- Location tion eo xp

Axis X-X

I 4

Axis Y-Y

S 3

grip

r 3

I 4

S 3

r 3

in.

58 51.9 45.8 42.7

0.862 0.858 0.866 0.877

0.695 0.797 0.909 0.969

0.472 0.422 0.372 0.347

676 627 578 554

94.6 86.5 78.4 74.4

75.1 69.7 64.3 61.6

6.29 6.41 6.56 6.64

17.8 16.4 15.1 14.4

9.94 9.13 8.42 8.10

5.32 5.07 4.82 4.69

1.02 1.04 1.06 1.07

50 40 35 31.8

0.974 0.963 0.980 1.00

0.815 1.03 1.16 1.24

0.564 0.450 0.394 0.358

314 273 252 239

60.5 50.9 46.2 43.1

48.4 42.0 38.8 36.8

4.62 4.82 4.95 5.06

16.5 13.7 12.3 11.4

10.1 8.57 7.95 7.60

4.79 4.26 3.99 3.81

1.06 1.08 1.10 1.11

50 45 40 35 31

1.05 1.04 1.04 1.05 1.08

0.741 0.844 0.952 1.07 1.18

0.610 0.549 0.488 0.426 0.416

269 252 234 216 203

56.1 51.7 47.3 42.8 39.3

44.9 42.0 39.0 36.1 33.8

4.28 4.36 4.46 4.59 4.71

17.4 15.8 14.3 12.7 11.3

10.2 9.35 8.59 7.91 7.44

5.65 5.33 5.00 4.67 4.39

1.09 1.09 1.10 1.11 1.12

10.6

0.269

0.284

0.129

0.639

0.310

0.351

41.1 33.6 28.5

1.09 1.08 1.12

0.864 1.06 1.21

0.601 0.490 0.415

158 139 127

38.9 33.4 29.6

31.5 27.8 25.3

3.61 3.75 3.89

8.71 7.51 6.83

4.88 4.38 4.02

1.14 1.16 1.17

25 22

0.953 0.990

1.03 1.13

0.364 0.468

110 103

25.8 23.6

22.0 20.5

3.87 3.99

7.35 6.50

5.21 4.86

3.00 2.80

1.00 1.00

0.284

0.332

0.122

3.61

0.328

0.552

0.270

0.365

8.4

55.4

32.0

11.6

7.86

9.23

6.40

4.22

0.382 15.8 13.2 11.4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 54

DIMENSIONS AND PROPERTIES

CHANNELS MISCELLANEOUS Dimensions

Y eo

grip

Web

Designation

Area Depth Thickness A d tw in.2

in.

Flange

Distance

Max. Flge. FasGrip tener

tw 2

Width bf

Thickness tf

in.

65⁄8 65⁄8

13⁄16 13⁄16

9⁄ 16 9⁄ 16

7⁄ 8 7⁄ 8

55⁄8 55⁄8

13⁄16 13⁄16

1⁄ 2 1⁄ 2

7⁄ 8 7⁄ 8

MC9×25.4 MC9×23.9

7.47 7.02

9.00 9.00

0.450 0.400

7⁄ 16 3⁄ 8

1⁄ 4 3⁄ 16

3.500 3.450

31⁄

31⁄2

0.550 0.550

9⁄ 16 9⁄ 16

MC8×22.8 MC9×21.4

6.70 6.28

8.00 8.00

0.427 0.375

7⁄ 16 3⁄ 8

3⁄

3.502 3.450

31⁄2 31⁄2

0.525 0.525

1⁄

MC8×20 MC9×18.7

5.88 5.50

8.00 8.00

0.400 0.353

3⁄ 8 3⁄ 8

3⁄

3.025 2.978

3 3

0.500 0.500

1⁄

53⁄4 53⁄4

11⁄8 11⁄8

1⁄ 2 1⁄ 2

7⁄ 8 7⁄ 8

MC8×8.5

2.50

8.00

0.179

3⁄ 16

1⁄

1.874

17⁄8

0.311

5⁄ 16

61⁄2

3⁄ 4

5⁄ 16

5⁄ 8

MC7×22.7 MC9×19.1

6.67 5.61

7.00 7.00

0.503 0.352

1⁄ 2 3⁄ 8

3⁄

1⁄ 4

3.603 3.452

35⁄8 31⁄2

0.500 0.500

1⁄

43⁄4 43⁄4

11⁄8 11⁄8

1⁄ 2 1⁄ 2

7⁄ 8 7⁄ 8

MC6×18

5.29

6.00

0.379

3⁄ 8

3⁄

3.504

31⁄2

0.475

1⁄

37⁄8

11⁄16

1⁄ 2

7⁄ 8

MC6×16.3 MC9×15.1

4.79 4.44

6.00 6.00

0.375 0.316

3⁄ 8 5⁄ 16

3⁄

3.000 2.941

3 3

0.475 0.475

1⁄

37⁄8 37⁄8

11⁄16 11⁄16

1⁄ 2 1⁄ 2

3⁄ 4 3⁄ 4

MC6×12

3.53

6.00

0.310

5⁄ 16

1⁄ 8

2.497

21⁄2

0.375

3⁄

43⁄8

13⁄ 16

3⁄ 8

5⁄ 8

3⁄

16 16 16

1⁄

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1⁄

2 2 2

STRUCTURAL SHAPES

1 - 55

CHANNELS MISCELLANEOUS Properties

Nominal Wt. per ft

_ x

Shear Center PNA Loca- Location tion eo xp

Axis X-X

I 4

Axis Y-Y

S 3

grip

r 3

I 4

S 3

r 3

in.

25.4 23.9

0.970 0.981

0.986 1.04

0.411 0.386

88.0 85.0

23.2 22.2

19.6 18.9

3.43 3.48

7.65 7.22

5.23 5.05

3.02 2.93

1.01 1.01

22.8 21.4

1.01 1.02

1.04 1.09

0.415 0.449

63.8 61.6

18.8 18.0

16.0 15.4

3.09 3.13

7.07 6.64

4.88 4.71

2.84 2.74

1.03 1.03

20 18.7

0.840 0.849

0.843 0.889

0.364 0.341

54.5 52.5

16.2 15.4

13.6 13.1

3.05 3.09

4.47 4.20

3.57 3.44

2.05 1.97

0.872 0.874

8.5

0.428

0.542

0.155

23.3

6.91

3.05

0.628

0.882

0.434

0.501

22.7 19.1

1.04 1.08

1.01 1.15

0.473 0.567

47.5 43.2

16.2 14.3

2.67 2.77

7.29 6.11

4.86 4.34

2.85 2.57

1.05 1.04

1.12

1.17

0.622

29.7

11.5

9.91

2.37

5.93

4.14

2.48

1.06

16.3 15.1

0.927 0.940

0.930 0.982

0.464 0.537

26.0 25.0

10.2 9.69

8.68 8.32

2.33 2.37

3.82 3.51

3.18 3.00

1.84 1.75

0.892 0.889

0.704

0.725

0.292

18.7

7.38

6.24

2.30

1.87

1.79

1.04

0.728

5.83 13.6 12.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 56

DIMENSIONS AND PROPERTIES

ANGLES Equal legs and unequal legs Properties for designing

x Z

X y, yp

k α

Size and Thickness in.

Weight per ft

Axis X-X Area 2

I 4

r 3

yp 3

in.

L8×8×11⁄8 L8×8×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×19⁄16 L8×8×11⁄2

13⁄4 15⁄8 11⁄2 13⁄8 11⁄4 13⁄16 11⁄8

56.9 51.0 45.0 38.9 32.7 29.6 26.4

16.7 15.0 13.2 11.4 9.61 8.68 7.75

98.0 89.0 79.6 69.7 59.4 54.1 48.6

17.5 15.8 14.0 12.2 10.3 9.34 8.36

2.42 2.44 2.45 2.47 2.49 2.50 2.50

2.41 2.37 2.33 2.28 2.23 2.21 2.19

31.6 28.5 25.3 22.0 18.6 16.8 15.1

1.05 0.938 0.827 0.715 0.601 0.543 0.484

L8×6×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×19⁄16 L8×8×11⁄2 L8×8×17⁄16

11⁄2 13⁄8 11⁄4 11⁄8 11⁄16 1 15⁄ 16

44.2 39.1 33.8 28.5 25.7 23.0 20.2

13.0 11.5 9.94 8.36 7.56 6.75 5.93

80.8 72.3 63.4 54.1 49.3 44.3 39.2

15.1 13.4 11.7 9.87 8.95 8.02 7.07

2.49 2.51 2.53 2.54 2.55 2.56 2.57

2.65 2.61 2.56 2.52 2.50 2.47 2.45

27.3 24.2 21.1 17.9 16.2 14.5 12.8

1.50 1.44 1.38 1.31 1.28 1.25 1.22

L8×4×1 L8×8×17⁄8 L8×8×13⁄4 L8×4×15⁄8 L8×8×19⁄16 L8×8×11⁄2 L8×4×17⁄16 L7×4×3⁄4 L7×4×5⁄8 L7×4×1⁄2 L7×4×7⁄16 L7×4×3⁄8

11⁄2 13⁄8 11⁄4 11⁄8 11⁄16 1 15⁄ 16 11⁄4 11⁄8 1 15⁄ 16 7⁄ 8

37.4 33.1 28.7 24.2 21.9 19.6 17.2 26.2 22.1 17.9 15.7 13.6

11.0 9.73 8.44 7.11 6.43 5.75 5.06 7.69 6.48 5.25 4.62 3.98

69.6 62.5 54.9 46.9 42.8 38.5 34.1 37.8 32.4 26.7 23.7 20.6

14.1 12.5 10.9 9.21 8.35 7.49 6.60 8.42 7.14 5.81 5.13 4.44

2.52 2.53 2.55 2.57 2.58 2.59 2.60 2.22 2.24 2.25 2.26 2.27

3.05 3.00 2.95 2.91 2.88 2.86 2.83 2.51 2.46 2.42 2.39 2.37

24.3 21.6 18.9 16.0 14.5 13.0 11.5 14.8 12.6 10.3 9.09 7.87

2.50 2.44 2.38 2.31 2.28 2.25 2.22 1.88 1.81 1.75 1.72 1.69

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 57

ANGLES Equal legs and unequal legs Properties for designing

X y, yp

k α

Size and Thickness

Axis Y-Y

Axis Z-Z

Tan

in.

L8×8×11⁄8 L8×8×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×19⁄16 L8×8×11⁄2

98.0 89.0 79.6 69.7 59.4 54.1 48.6

17.5 15.8 14.0 12.2 10.3 9.34 8.36

2.42 2.44 2.45 2.47 2.49 2.50 2.50

2.41 2.37 2.33 2.28 2.23 2.21 2.19

31.6 28.5 25.3 22.0 18.6 16.8 15.1

1.05 0.938 0.827 0.715 0.601 0.543 0.484

1.56 1.56 1.57 1.58 1.58 1.59 1.59

1.000 1.000 1.000 1.000 1.000 1.000 1.000

L8×6×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×19⁄16 L8×8×11⁄2 L8×8×17⁄16

38.8 34.9 30.7 26.3 24.0 21.7 19.3

8.92 7.94 6.92 5.88 5.34 4.79 4.23

1.73 1.74 1.76 1.77 1.78 1.79 1.80

1.65 1.61 1.56 1.52 1.50 1.47 1.45

16.2 14.4 12.5 10.5 9.52 8.51 7.50

0.813 0.718 0.621 0.522 0.472 0.422 0.371

1.28 1.28 1.29 1.29 1.30 1.30 1.31

0.543 0.547 0.551 0.554 0.556 0.558 0.560

L8×4×1 L8×4×17⁄8 L8×8×13⁄4 L8×4×15⁄8 L8×8×19⁄16 L8×8×11⁄2 L8×4×17⁄16

11.6 10.5 9.36 8.10 7.43 6.74 6.02

3.94 3.51 3.07 2.62 2.38 2.15 1.90

1.03 1.04 1.05 1.07 1.07 1.08 1.09

1.05 0.999 0.953 0.905 0.882 0.859 0.835

7.72 6.77 5.81 4.86 4.38 3.90 3.42

0.688 0.608 0.527 0.444 0.402 0.359 0.316

0.846 0.848 0.852 0.857 0.861 0.865 0.869

0.247 0.253 0.258 0.262 0.265 0.267 0.269

L7×4×3⁄4 L7×4×5⁄8 L7×4×1⁄2 L7×4×7⁄16 L7×4×3⁄8

9.05 7.84 6.53 5.83 5.10

3.03 2.58 2.12 1.88 1.63

1.09 1.10 1.11 1.12 1.13

1.01 0.963 0.917 0.893 0.870

5.65 4.74 3.83 3.37 2.90

0.549 0.463 0.375 0.330 0.285

0.860 0.865 0.872 0.875 0.880

0.324 0.329 0.335 0.337 0.340

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 58

DIMENSIONS AND PROPERTIES

ANGLES Equal legs and unequal legs Properties for designing

x Z

X y, yp

k α

Size and Thickness in.

Weight per ft

Axis X-X Area 2

I 4

r 3

yp 3

in.

L6×6×1 L6×6×17⁄8 L6×6×13⁄4 L6×6×15⁄8 L6×6×19⁄16 L6×6×11⁄2 L6×6×17⁄16 L6×6×13⁄8 L6×6×15⁄16

11⁄2 13⁄8 11⁄4 11⁄8 11⁄16 1 15⁄ 16 7⁄ 8 13⁄ 16

37.4 33.1 28.7 24.2 21.9 19.6 17.2 14.9 12.4

11.0 9.73 8.44 7.11 6.43 5.75 5.06 4.36 3.65

35.5 31.9 28.2 24.2 22.1 19.9 17.7 15.4 13.0

8.57 7.63 6.66 5.66 5.14 4.61 4.08 3.53 2.97

1.80 1.81 1.83 1.84 1.85 1.86 1.87 1.88 1.89

1.86 1.82 1.78 1.73 1.71 1.68 1.66 1.64 1.62

15.5 13.8 12.0 10.2 9.26 8.31 7.34 6.35 5.35

0.917 0.811 0.703 0.592 0.536 0.479 0.422 0.363 0.304

L6×4×7⁄8 L6×4×3⁄4 L6×4×5⁄8 L6×4×9⁄16 L6×4×1⁄2 L6×4×7⁄16 L6×4×3⁄8 L6×4×5⁄16

13⁄8 11⁄4 11⁄8 11⁄16 1 15⁄ 16 7⁄ 8 13⁄ 16

27.2 23.6 20.0 18.1 16.2 14.3 12.3 10.3

7.98 6.94 5.86 5.31 4.75 4.18 3.61 3.03

27.7 24.5 21.1 19.3 17.4 15.5 13.5 11.4

7.15 6.25 5.31 4.83 4.33 3.83 3.32 2.79

1.86 1.88 1.90 1.90 1.91 1.92 1.93 1.94

2.12 2.08 2.03 2.01 1.99 1.96 1.94 1.92

12.7 11.2 9.51 8.66 7.78 6.88 5.97 5.03

1.44 1.38 1.31 1.28 1.25 1.22 1.19 1.16

L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

1 7⁄ 8 13⁄ 16

15.3 11.7 9.80

4.50 3.42 2.87

16.6 12.9 10.9

4.24 3.24 2.73

1.92 1.94 1.95

2.08 2.04 2.01

7.50 5.76 4.85

1.50 1.44 1.41

L5×5×7⁄8 L5×5×3⁄4 L5×5×5⁄8 L5×5×1⁄2 L5×5×7⁄16 L5×5×3⁄8 L5×5×5⁄16

13⁄8 11⁄4 11⁄8 1 15⁄ 16 7⁄ 8 13⁄ 16

27.2 23.6 20.0 16.2 14.3 12.3 10.3

7.98 6.94 5.86 4.75 4.18 3.61 3.03

17.8 15.7 13.6 11.3 10.0 8.74 7.42

5.17 4.53 3.86 3.16 2.79 2.42 2.04

1.49 1.51 1.52 1.54 1.55 1.56 1.57

1.57 1.52 1.48 1.43 1.41 1.39 1.37

9.33 8.16 6.95 5.68 5.03 4.36 3.68

0.798 0.694 0.586 0.475 0.418 0.361 0.303

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL SHAPES

1 - 59

ANGLES Equal legs and unequal legs Properties for designing

X y, yp

k α

Size and Thickness in. L6×6×1 L6×6×17⁄8 L6×6×13⁄4 L6×6×15⁄8 L6×6×19⁄16 L6×6×11⁄2 L6×6×17⁄16 L6×6×13⁄8 L6×6×15⁄16

Axis Y-Y

I 4

Axis Z-Z

in.

1.86 1.82 1.78 1.73 1.71 1.68 1.66 1.64 1.62

15.5 13.8 12.0 10.2 9.26 8.31 7.34 6.35 5.35

0.917 0.811 0.703 0.592 0.536 0.479 0.422 0.363 0.304

1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.19 1.20

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

in.

35.5 31.9 28.2 24.2 22.1 19.9 17.7 15.4 13.0

8.57 7.63 6.66 5.66 5.14 4.61 4.08 3.53 2.97

1.80 1.81 1.83 1.84 1.85 1.86 1.87 1.88 1.89

Z 3

Tan

L6×4×7⁄8 L6×4×3⁄4 L6×4×5⁄8 L6×4×9⁄16 L6×4×1⁄2 L6×4×7⁄16 L6×4×3⁄8 L6×4×5⁄16

9.75 8.68 7.52 6.91 6.27 5.60 4.90 4.18

3.39 2.97 2.54 2.31 2.08 1.85 1.60 1.35

1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.17

1.12 1.08 1.03 1.01 0.987 0.964 0.941 0.918

6.31 5.47 4.62 4.19 3.75 3.30 2.85 2.40

0.665 0.578 0.488 0.442 0.396 0.349 0.301 0.252

0.857 0.860 0.864 0.866 0.870 0.873 0.877 0.882

0.421 0.428 0.435 0.438 0.440 0.443 0.446 0.448

L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

4.25 3.34 2.85

1.59 1.23 1.04

0.972 0.988 0.996

0.833 0.787 0.763

2.91 2.20 1.85

0.375 0.285 0.239

0.759 0.767 0.772

0.344 0.350 0.352

17.8 15.7 13.6 11.3 10.0 8.74 7.42

5.17 4.53 3.86 3.16 2.79 2.42 2.04

1.49 1.51 1.52 1.54 1.55 1.56 1.57

1.57 1.52 1.48 1.43 1.41 1.39 1.37

9.33 8.16 6.95 5.68 5.03 4.36 3.68

0.798 0.694 0.586 0.475 0.418 0.361 0.303

0.973 0.975 0.978 0.983 0.986 0.990 0.994

1.000 1.000 1.000 1.000 1.000 1.000 1.000

L5×5×7⁄8 L5×5×3⁄4 L5×5×5⁄8 L5×5×1⁄2 L5×5×7⁄16 L5×5×3⁄8 L5×5×5⁄16

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 60

DIMENSIONS AND PROPERTIES

ANGLES Equal legs and unequal legs Properties for designing

x Z

X y, yp

k α

Size and Thickness in.

Weight per ft

Axis X-X Area 2

I 4

r 3

yp 3

in.

L5×31⁄2×3⁄4 L5×31⁄2×5⁄8 L5×31⁄2×1⁄2 L5×31⁄2×3⁄8 L5×31⁄2×5⁄16 L5×31⁄2×1⁄4

11⁄4 11⁄8 1 7⁄ 8 13⁄ 16 3⁄ 4

19.8 16.8 13.6 10.4 8.70 7.00

5.81 4.92 4.00 3.05 2.56 2.06

13.9 12.0 9.99 7.78 6.60 5.39

4.28 3.65 2.99 2.29 1.94 1.57

1.55 1.56 1.58 1.60 1.61 1.62

1.75 1.70 1.66 1.61 1.59 1.56

7.65 6.55 5.38 4.14 3.49 2.83

1.13 1.06 1.00 0.938 0.906 0.875

L5×3×1⁄2 L5×3×7⁄16 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

1 15⁄ 16 7⁄ 8 13⁄ 16 3⁄ 4

12.8 11.3 9.80 8.20 6.60

3.75 3.31 2.86 2.40 1.94

9.45 8.43 7.37 6.26 5.11

2.91 2.58 2.24 1.89 1.53

1.59 1.60 1.61 1.61 1.62

1.75 1.73 1.70 1.68 1.66

5.16 4.57 3.97 3.36 2.72

1.25 1.22 1.19 1.16 1.13

L4×4×3⁄4 L5×3×5⁄8 L5×3×1⁄2 L5×3×7⁄16 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

11⁄8 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

18.5 15.7 12.8 11.3 9.80 8.20 6.60

5.44 4.61 3.75 3.31 2.86 2.40 1.94

7.67 6.66 5.56 4.97 4.36 3.71 3.04

2.81 2.40 1.97 1.75 1.52 1.29 1.05

1.19 1.20 1.22 1.23 1.23 1.24 1.25

1.27 1.23 1.18 1.16 1.14 1.12 1.09

5.07 4.33 3.56 3.16 2.74 2.32 1.88

0.680 0.576 0.469 0.414 0.357 0.300 0.242

L4×31⁄2×1⁄2 L4×31⁄2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

15⁄ 16 13⁄ 16 3⁄ 4 11⁄ 16

11.9 9.10 7.70 6.20

3.50 2.67 2.25 1.81

5.32 4.18 3.56 2.91

1.94 1.49 1.26 1.03

1.23 1.25 1.26 1.27

1.25 1.21 1.18 1.16

3.50 2.71 2.29 1.86

0.500 0.438 0.406 0.375

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

STRUCTURAL SHAPES

1 - 61

ANGLES Equal legs and unequal legs Properties for designing

X y, yp

k α

Size and Thickness

Axis Y-Y

Axis Z-Z

Tan

in.

L5×31⁄2×3⁄4 L5×31⁄2×5⁄8 L5×31⁄2×1⁄2 L5×31⁄2×3⁄8 L5×31⁄2×5⁄16 L5×31⁄2×1⁄4

5.55 4.83 4.05 3.18 2.72 2.23

2.22 1.90 1.56 1.21 1.02 0.830

0.977 0.991 1.01 1.02 1.03 1.04

0.996 0.951 0.906 0.861 0.838 0.814

4.10 3.47 2.83 2.16 1.82 1.47

0.581 0.492 0.400 0.305 0.256 0.206

0.748 0.751 0.755 0.762 0.766 0.770

0.464 0.472 0.479 0.486 0.489 0.492

L5×3×1⁄2 L5×3×7⁄16 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

2.58 2.32 2.04 1.75 1.44

1.15 1.02 0.888 0.753 0.614

0.829 0.837 0.845 0.853 0.861

0.750 0.727 0.704 0.681 0.657

2.11 1.86 1.60 1.35 1.09

0.375 0.331 0.286 0.240 0.194

0.648 0.651 0.654 0.658 0.663

0.357 0.361 0.364 0.368 0.371

L4×4×3⁄4 L5×3×5⁄8 L5×3×1⁄2 L5×3×7⁄16 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

7.67 6.66 5.56 4.97 4.36 3.71 3.04

2.81 2.40 1.97 1.75 1.52 1.29 1.05

1.19 1.20 1.22 1.23 1.23 1.24 1.25

1.27 1.23 1.18 1.16 1.14 1.12 1.09

5.07 4.33 3.56 3.16 2.74 2.32 1.88

0.680 0.576 0.469 0.414 0.357 0.300 0.242

0.778 0.779 0.782 0.785 0.788 0.791 0.795

1.000 1.000 1.000 1.000 1.000 1.000 1.000

L4×31⁄2×1⁄2 4×31⁄2×3⁄8 4×31⁄2×5⁄16 4×31⁄2×1⁄4

3.79 2.95 2.55 2.09

1.52 1.16 0.994 0.808

1.04 1.06 1.07 1.07

1.00 0.955 0.932 0.909

2.73 2.11 1.78 1.44

0.438 0.334 0.281 0.227

0.722 0.727 0.730 0.734

0.750 0.755 0.757 0.759

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 62

DIMENSIONS AND PROPERTIES

ANGLES Equal legs and unequal legs Properties for designing

x Z

X y, yp

k α

Size and Thickness

Weight per ft

Axis X-X Area

I 2

r 4

y 3

yp 3

in.

L4×3×5⁄8 L4×3×1⁄2 L4×3×7⁄16 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4

11⁄16 15⁄ 16 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

13.6 11.1 9.80 8.50 7.20 5.80

3.98 3.25 2.87 2.48 2.09 1.69

6.03 5.05 4.52 3.96 3.38 2.77

2.30 1.89 1.68 1.46 1.23 1.00

1.23 1.25 1.25 1.26 1.27 1.28

1.37 1.33 1.30 1.28 1.26 1.24

4.12 3.41 3.03 2.64 2.23 1.82

0.813 0.750 0.719 0.688 0.656 0.625

L31⁄2×31⁄2×1⁄2 L31⁄2×31⁄2×7⁄16 L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×5⁄16 L31⁄2×31⁄2×1⁄4

7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

11.1 9.80 8.50 7.20 5.80

3.25 2.87 2.48 2.09 1.69

3.64 3.26 2.87 2.45 2.01

1.49 1.32 1.15 0.976 0.794

1.06 1.07 1.07 1.08 1.09

1.06 1.04 1.01 0.990 0.968

2.68 2.38 2.08 1.76 1.43

0.464 0.410 0.355 0.299 0.241

L31⁄2×3×1⁄2 L31⁄2×3×3⁄8 L31⁄2×3×5⁄16 L31⁄2×3×1⁄4

15⁄ 16 13⁄ 16 3⁄ 4 11⁄ 16

10.2 7.90 6.60 5.40

3.00 2.30 1.93 1.56

3.45 2.72 2.33 1.91

1.45 1.13 0.954 0.776

1.07 1.09 1.10 1.11

1.13 1.08 1.06 1.04

2.63 2.04 1.73 1.41

0.500 0.438 0.406 0.375

L31⁄2×21⁄2×1⁄2 L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×1⁄4

15⁄ 16 13⁄ 16 11⁄ 16

9.40 7.20 4.90

2.75 2.11 1.44

3.24 2.56 1.80

1.41 1.09 0.755

1.09 1.10 1.12

1.20 1.16 1.11

2.53 1.97 1.36

0.750 0.688 0.625

L3×3×1⁄2 L4×3×7⁄16 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4 L4×3×3⁄16

13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2

9.40 8.30 7.20 6.10 4.90 3.71

2.75 2.43 2.11 1.78 1.44 1.09

2.22 1.99 1.76 1.51 1.24 0.962

1.07 0.954 0.833 0.707 0.577 0.441

0.898 0.905 0.913 0.922 0.930 0.939

0.932 0.910 0.888 0.865 0.842 0.820

1.93 1.72 1.50 1.27 1.04 0.794

0.458 0.406 0.352 0.296 0.240 0.182

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

STRUCTURAL SHAPES

1 - 63

ANGLES Equal legs and unequal legs Properties for designing

X y, yp

k α

Size and Thickness

Axis Y-Y

Axis Z-Z

Tan

in.

L4×3×5⁄8 L4×3×1⁄2 L4×3×7⁄16 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4

2.87 2.42 2.18 1.92 1.65 1.36

1.35 1.12 0.992 0.866 0.734 0.599

0.849 0.864 0.871 0.879 0.887 0.896

0.871 0.827 0.804 0.782 0.759 0.736

2.48 2.03 1.79 1.56 1.31 1.06

0.498 0.406 0.359 0.311 0.261 0.211

0.637 0.639 0.641 0.644 0.647 0.651

0.534 0.543 0.547 0.551 0.554 0.558

L31⁄2×31⁄2×1⁄2 L31⁄2×31⁄2×7⁄16 L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×5⁄16 L31⁄2×31⁄2×1⁄4

3.64 3.26 2.87 2.45 2.01

1.49 1.32 1.15 0.976 0.794

1.06 1.07 1.07 1.08 1.09

1.06 1.04 1.01 0.990 0.968

2.68 2.38 2.08 1.76 1.43

0.464 0.410 0.355 0.299 0.241

0.683 0.684 0.687 0.690 0.694

1.000 1.000 1.000 1.000 1.000

L31⁄2×3×1⁄2 L31⁄2×3×3⁄8 L31⁄2×3×5⁄16 L31⁄2×3×1⁄4

2.33 1.85 1.58 1.30

1.10 0.851 0.722 0.589

0.881 0.897 0.905 0.914

0.875 0.830 0.808 0.785

1.98 1.53 1.30 1.05

0.429 0.328 0.276 0.223

0.621 0.625 0.627 0.631

0.714 0.721 0.724 0.727

L31⁄2×21⁄2×1⁄2 L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×1⁄4

1.36 1.09 0.777

0.760 0.592 0.412

0.704 0.719 0.735

0.705 0.660 0.614

1.40 1.07 0.735

0.393 0.301 0.205

0.534 0.537 0.544

0.486 0.496 0.506

L3×3×1⁄2 L3×3×7⁄16 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4 L3×3×3⁄16

2.22 1.99 1.76 1.51 1.24 0.962

1.07 0.954 0.833 0.707 0.577 0.441

0.898 0.905 0.913 0.922 0.930 0.939

0.932 0.910 0.888 0.865 0.842 0.820

1.93 1.72 1.50 1.27 1.04 0.794

0.458 0.406 0.352 0.296 0.240 0.182

0.584 0.585 0.587 0.589 0.592 0.596

1.000 1.000 1.000 1.000 1.000 1.000

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 64

DIMENSIONS AND PROPERTIES

ANGLES Equal legs and unequal legs Properties for designing

x Z

X y, yp

k α

Size and Thickness in.

Weight per ft

Axis X-X Area 2

I 4

r 3

yp 3

in.

L3×21⁄2×1⁄2 L3×21⁄2×3⁄8 L3×21⁄2×5⁄16 L3×21⁄2×1⁄4 L3×21⁄2×3⁄16

7⁄ 8 3⁄ 4 11⁄ 16 5⁄ 8 9⁄ 16

8.50 6.60 5.60 4.50 3.39

2.50 1.92 1.62 1.31 0.996

2.08 1.66 1.42 1.17 0.907

1.04 0.810 0.688 0.561 0.430

0.913 0.928 0.937 0.945 0.954

1.000 0.956 0.933 0.911 0.888

1.88 1.47 1.25 1.02 0.781

0.500 0.438 0.406 0.375 0.344

L3×2×1⁄2 L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16

13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2

7.70 5.90 5.00 4.10 3.07

2.25 1.73 1.46 1.19 0.902

1.92 1.53 1.32 1.09 0.842

1.00 0.781 0.664 0.542 0.415

0.924 0.940 0.948 0.957 0.966

1.08 1.04 1.02 0.993 0.970

1.78 1.40 1.19 0.973 0.746

0.750 0.688 0.656 0.625 0.594

L21⁄2×21⁄2×1⁄2 L21⁄2×21⁄2×3⁄8 L21⁄2×21⁄2×5⁄16 L21⁄2×21⁄2×1⁄4 L21⁄2×21⁄2×3⁄16

13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2

7.70 5.90 5.00 4.10 3.07

2.25 1.73 1.46 1.19 0.902

1.23 0.984 0.849 0.703 0.547

0.724 0.566 0.482 0.394 0.303

0.739 0.753 0.761 0.769 0.778

0.806 0.762 0.740 0.717 0.694

1.31 1.02 0.869 0.711 0.545

0.450 0.347 0.293 0.238 0.180

L21⁄2×2×3⁄8 L21⁄2×2×5⁄16 L21⁄2×2×1⁄4 L21⁄2×2×3⁄16

11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2

5.30 4.50 3.62 2.75

1.55 1.31 1.06 0.809

0.912 0.788 0.654 0.509

0.547 0.466 0.381 0.293

0.768 0.776 0.784 0.793

0.831 0.809 0.787 0.764

0.986 0.843 0.691 0.532

0.438 0.406 0.375 0.344

L2×2×3⁄8 L2×2×5⁄16 L2×2×1⁄4 L2×2×3⁄16 L2×2×1⁄8

11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16

4.70 3.92 3.19 2.44 1.65

1.36 1.15 0.938 0.715 0.484

0.479 0.416 0.348 0.272 0.190

0.351 0.300 0.247 0.190 0.131

0.594 0.601 0.609 0.617 0.626

0.636 0.614 0.592 0.569 0.546

0.633 0.541 0.445 0.343 0.235

0.340 0.288 0.234 0.179 0.121

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

STRUCTURAL SHAPES

1 - 65

ANGLES Equal legs and unequal legs Properties for designing

X y, yp

k α

Size and Thickness

Axis Y-Y

Axis Z-Z

Tan

in.

L3×21⁄2×1⁄2 L3×21⁄2×3⁄8 L3×21⁄2×5⁄16 L3×21⁄2×1⁄4 L3×21⁄2×3⁄16

1.30 1.04 0.898 0.743 0.577

0.744 0.581 0.494 0.404 0.310

0.722 0.736 0.744 0.753 0.761

0.750 0.706 0.683 0.661 0.638

1.35 1.05 0.889 0.724 0.553

0.417 0.320 0.270 0.219 0.166

0.520 0.522 0.525 0.528 0.533

0.667 0.676 0.680 0.684 0.688

L3×2×1⁄2 L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16

0.672 0.543 0.470 0.392 0.307

0.474 0.371 0.317 0.260 0.200

0.546 0.559 0.567 0.574 0.583

0.583 0.539 0.516 0.493 0.470

0.891 0.684 0.577 0.468 0.357

0.375 0.289 0.244 0.198 0.150

0.428 0.430 0.432 0.435 0.439

0.414 0.428 0.435 0.440 0.446

L21⁄2×21⁄2×1⁄2 L21⁄2×21⁄2×3⁄8 L21⁄2×21⁄2×5⁄16 L21⁄2×21⁄2×1⁄4 L21⁄2×21⁄2×3⁄16

1.23 0.984 0.849 0.703 0.547

0.724 0.566 0.482 0.394 0.303

0.739 0.753 0.761 0.769 0.778

0.806 0.762 0.740 0.717 0.694

1.31 1.02 0.869 0.711 0.545

0.450 0.347 0.293 0.238 0.180

0.487 0.487 0.489 0.491 0.495

1.000 1.000 1.000 1.000 1.000

L21⁄2×2×3⁄8 L21⁄2×2×5⁄16 L21⁄2×2×1⁄4 L21⁄2×2×3⁄16

0.514 0.446 0.372 0.291

0.363 0.310 0.254 0.196

0.577 0.584 0.592 0.600

0.581 0.559 0.537 0.514

0.660 0.561 0.457 0.350

0.309 0.262 0.213 0.162

0.420 0.422 0.424 0.427

0.614 0.620 0.626 0.631

L2×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16 L3×2×1⁄8

0.479 0.416 0.348 0.272 0.190

0.351 0.300 0.247 0.190 0.131

0.594 0.601 0.609 0.617 0.626

0.636 0.614 0.592 0.569 0.546

0.633 0.541 0.445 0.343 0.235

0.340 0.288 0.234 0.179 0.121

0.389 0.390 0.391 0.394 0.398

1.000 1.000 1.000 1.000 1.000

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 66

DIMENSIONS AND PROPERTIES

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 67

STRUCTURAL TEES (WT, MT, ST)

Structural tees are obtained by splitting the webs of various beams, generally with the aid of rotary shears, and straightening to meet established permissible variations listed in Standard Mill Practice in Part 1 of this Manual. Although structural tees may be obtained by off-center splitting, or by splitting at two lines, as specified on order, the Dimensions and Properties are based on a depth of tee equal to one-half the published beam depth. Values of Qs are given for Fy = 36 ksi and Fy = 50 ksi, for those tees having stems which exceed the limiting width-thickness ratio 位r of LRFD Specification Section B5. Since the cross section is comprised entirely of unstiffened elements, Qa = 1.0 and Q = Qs for _ all tee sections. The Flexural-Torsional Properties Table lists the dimensional values (ro and H) and cross-section constants (J and Cw) needed for checking flexural-torsional buckling. Use of Table

The table may be used as follows for checking the limit states of (1) flexural buckling about the x-axis and (2) flexural-torsional buckling. The lower of the two limit states must be used for design. See also Part 3 of this LRFD Manual. (1) Flexural Buckling About the X-Axis

Where no value of Qs is shown, the design compressive strength for this limit state is given by LRFD Specification Section E2. Where a value of Qs is shown, the strength must be reduced in accordance with Appendix B5 of the LRFD Specification. (2) Flexural-Torsional Buckling

The design compressive strength for this limit _ state is given by LRFD Specification Section E3. This involves calculations with J, ro, and H. Refer to the Flexural-Torsional Properties Tables, later in Part 1.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 68

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Area Designation in.2

Area of Stem

Depth of Tee d

Thickness tw

tw 2

in.

in.2

Flange Width bf in.

Thickness tf in.

Distance k in.

WT22×167.5 WT22×145 WT22×131 WT22×115

49.1 42.9 38.6 33.8

22.010 22 1.020 21.810 2113⁄16 0.870 21.655 2111⁄16 0.790 21.455 217⁄16 0.710

1 7⁄ 8 13⁄ 16 11⁄ 16

1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8

22.5 19.0 17.1 15.2

15.950 15.830 15.750 15.750

153⁄4 157⁄8 153⁄4 153⁄4

1.770 1.580 1.420 1.220

13⁄4 19⁄16 17⁄16 11⁄4

29⁄16 23⁄8 23⁄16 2

WT20×296.5 WT22×251.5 WT22×215.5 WT22×186 WT22×160.5 WT22×148.5 WT22×138.5 WT22×124.5 WT22×107.5 WT22×99.5 WT22×87

87.0 74.0 63.4 54.7 47.0 43.7 40.7 36.7 31.7 29.2 25.5

21.495 21.025 20.630 20.315 20.040 19.920 19.845 19.690 19.490 19.335 19.100

211⁄2 21 205⁄8 205⁄16 20 1915⁄16 197⁄8 1911⁄16 191⁄2 195⁄16 191⁄8

1.790 1.540 1.340 1.160 1.000 0.930 0.830 0.750 0.650 0.650 0.650

113⁄16 19⁄16 15⁄16 13⁄16 1 15⁄ 16 13⁄ 16 3⁄ 4 5⁄ 8 5⁄ 8 5⁄ 8

1 3⁄ 4 11⁄ 16 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16

38.5 32.4 27.6 23.6 20.0 18.5 16.5 14.8 12.7 12.6 12.4

16.690 163⁄4 16.420 167⁄16 16.220 161⁄4 16.060 161⁄16 15.910 157⁄8 15.825 157⁄8 15.830 157⁄8 15.750 153⁄4 15.750 153⁄4 15.750 153⁄4 15.750 153⁄4

3.230 2.760 2.360 2.050 1.770 1.650 1.575 1.420 1.220 1.065 0.830

31⁄4 23⁄4 23⁄8 21⁄16 13⁄4 15⁄8 19⁄16 17⁄16 11⁄4 11⁄16 13⁄ 16

47⁄16 315⁄16 39⁄16 31⁄4 215⁄16 31⁄16 23⁄4 25⁄8 23⁄8 21⁄4 2

WT20×233 WT22×196 WT22×165.5 WT22×139 WT22×132 WT22×117.5 WT22×105.5 WT22×91.5 WT22×83.5 WT22×74.5

68.4 57.7 48.8 40.9 38.8 34.5 31.0 26.9 24.6 21.9

21.220 213⁄16 20.785 203⁄4 20.395 203⁄8 20.080 201⁄8 20.000 20 19.845 197⁄8 19.685 1911⁄16 19.490 191⁄2 19.295 195⁄16 19.100 191⁄8

1.67 1.42 1.22 1.02 0.960 0.830 0.750 0.650 0.650 0.630

111⁄16 17⁄16 11⁄4 1 1 13⁄ 16 3⁄ 4 5⁄ 8 5⁄ 8 5⁄ 8

13⁄ 16 11⁄ 16 5⁄ 8 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16

35.4 29.5 24.9 20.5 19.2 16.5 14.8 12.7 12.5 12.0

12.640 125⁄8 12.360 123⁄8 12.170 123⁄16 11.970 12 11.930 12 11.890 117⁄8 11.810 113⁄4 11.810 113⁄4 11.810 113⁄4 11.810 113⁄4

2.950 2.520 2.130 1.810 1.730 1.575 1.415 1.220 1.025 0.830

215⁄16 21⁄2 21⁄8 113⁄16 13⁄4 17⁄16 19⁄16 11⁄4 1 13⁄ 16

41⁄8 311⁄16 35⁄16 3 215⁄16 23⁄4 25⁄8 23⁄8 23⁄16 2

WT18×424 WT22×399 WT22×325 WT22×263.5 WT22×219.5 WT22×196.5 WT22×179.5 WT22×164 WT22×150 WT22×140 WT22×130 WT22×122.5 WT22×115

125 117 95.0 77.0 64.0 57.5 52.7 48.2 44.1 41.2 38.2 36.0 33.8

21.225 211⁄4 20.985 21 20.235 201⁄4 19.605 195⁄8 19.130 191⁄8 18.900 187⁄8 18.700 1811⁄16 18.545 189⁄16 18.370 183⁄8 18.260 181⁄4 18.130 181⁄8 18.040 18 17.950 18

2.520 2.380 1.970 1.610 1.360 1.220 1.120 1.020 0.945 0.885 0.840 0.800 0.760

21⁄2 23⁄8 2 15⁄8 13⁄8 11⁄4 11⁄8 1 15⁄ 16 7⁄ 8 13⁄ 16 13⁄ 16 3⁄ 4

11⁄4 13⁄16 1 13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 7⁄ 16 7⁄ 16 3⁄ 8

53.5 49.9 39.9 31.6 26.0 23.1 20.9 18.9 17.4 16.2 15.2 14.4 13.6

18.130 17.990 17.575 17.220 16.965 16.830 16.730 16.630 16.655 16.595 16.550 16.510 16.470

181⁄8 18 175⁄8 171⁄4 17 167⁄8 163⁄4 165⁄8 165⁄8 165⁄8 161⁄2 161⁄2 161⁄2

4.530 4.290 3.540 2.910 2.440 2.200 2.010 1.850 1.680 1.570 1.440 1.350 1.260

41⁄2 45⁄16 39⁄16 215⁄16 27⁄16 23⁄16 2 17⁄8 111⁄16 19⁄16 17⁄16 13⁄8 11⁄4

511⁄16 57⁄16 411⁄16 41⁄16 39⁄16 35⁄16 31⁄8 3 213⁄16 211⁄16 29⁄16 21⁄2 23⁄8

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 69

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

Fy, ksi 50

167.5 145 131 115

19.1 22.3 24.6 27.4

2160 1840 1650 1440

131 111 100 88.6

6.63 6.55 6.53 6.53

5.51 5.27 5.20 5.17

233 197 177 157

1.54 1.35 1.23 1.07

600 524 463 398

75.3 66.1 58.8 50.5

3.50 3.49 3.46 3.43

118 103 91.4 78.4

0.982 0.833 0.732 0.608

0.817 0.636 0.532 0.438

296.5 251.5 215.5 186 160.5 148.5 138.5 124.5 107.5 99.5 87

9.5 11.1 12.8 14.7 17.1 18.4 20.6 22.8 26.3 26.3 26.3

3300 2730 2290 1930 1630 1500 1360 1210 1030 987 907

209 175 148 126 107 98.9 88.6 79.3 68.0 66.4 63.8

6.16 6.07 6.01 5.95 5.89 5.87 5.78 5.75 5.72 5.81 5.96

5.67 5.39 5.18 4.97 4.79 4.71 4.51 4.41 4.28 4.48 4.87

379 315 266 225 191 176 157 140 120 117 114

2.61 2.25 1.95 1.70 1.48 1.38 1.28 1.16 1.00 0.927 0.811

1260 1020 843 710 596 546 522 463 398 347 271

151 125 104 88.5 74.9 69.1 65.9 58.8 50.5 44.1 34.4

3.81 3.72 3.65 3.60 3.56 3.54 3.58 3.56 3.55 3.45 3.26

240 197 164 139 117 108 102 91.0 77.9 68.3 53.8

— — — — — 0.989 0.882 0.782 0.618 0.628 0.643

— — — — 0.895 0.825 0.699 0.580 0.445 0.452 0.463

233 196 165.5 139 132 117.5 105.5 91.5 83.5 74.5

10.2 12.0 14.0 16.8 17.8 20.6 22.8 26.3 26.3 27.1

2770 2270 1880 1540 1450 1260 1120 957 898 815

185 153 128 106 99.3 85.6 76.7 65.8 63.7 59.7

6.36 6.28 6.21 6.14 6.11 6.04 6.01 5.97 6.05 6.10

6.22 5.95 5.74 5.50 5.40 5.17 5.08 4.94 5.20 5.45

333 276 231 190 178 153 137 117 115 119

2.71 2.33 2.01 1.71 1.63 1.45 1.31 1.14 1.04 1.82

504 401 323 261 246 222 195 168 141 115

79.8 65.0 53.1 43.6 41.3 37.3 33.0 28.5 23.9 19.4

2.72 2.64 2.57 2.52 2.52 2.54 2.51 2.50 2.40 2.29

131 106 86.2 70.0 66.2 59.2 52.3 44.8 38.0 31.1

— — — — — 0.882 0.782 0.618 0.630 0.604

— — — 0.913 0.855 0.699 0.581 0.445 0.454 0.435

424 399 325 263.5 219.5 196.5 179.5 164 150 140 130 122.5 115

6.3 6.6 8.0 9.8 11.6 12.9 14.1 15.4 16.7 17.8 18.7 19.7 20.7

4250 3920 3020 2330 1880 1660 1500 1350 1230 1140 1060 995 934

277 257 202 159 130 115 104 94.1 86.1 80.0 75.1 71.0 67.0

5.84 5.79 5.64 5.50 5.42 5.37 5.33 5.29 5.27 5.25 5.26 5.26 5.25

5.86 5.72 5.29 4.89 4.63 4.46 4.33 4.21 4.13 4.07 4.05 4.03 4.01

515 478 373 290 235 207 187 168 153 142 133 125 118

3.43 3.25 2.70 2.24 1.89 1.71 1.58 1.45 1.33 1.24 1.16 1.09 1.03

2270 2100 1610 1240 997 877 786 711 648 599 545 507 470

251 234 184 145 117 104 94.0 85.5 77.8 72.2 65.9 61.4 57.1

4.27 4.24 4.12 4.02 3.95 3.90 3.86 3.84 3.83 3.81 3.78 3.75 3.73

399 371 290 227 184 162 146 132 120 112 102 94.9 88.1

— — — — — — — — — — 0.981 0.943 0.896

— — — — — — — — 0.927 0.867 0.816 0.770 0.715

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 70

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Area of Stem

Flange DisThickness tance tf k

Area

Depth of Tee d

Thickness tw

tw 2

Designation

in.2

in.

WT18×128 WT18×116 WT18×105 WT18×97 WT18×91 WT18×85 WT18×80 WT18×75 WT18×67.5

37.7 34.1 30.9 28.5 26.8 25.0 23.5 22.1 19.9

18.715 1811⁄16 18.560 189⁄16 18.345 183⁄8 18.245 181⁄4 18.165 181⁄8 18.085 181⁄8 18.005 18 17.925 177⁄8 17.775 173⁄4

0.960 0.870 0.830 0.765 0.725 0.680 0.650 0.625 0.600

1 7⁄ 8 13⁄ 16 3⁄ 4 3⁄ 4 11⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8

7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16

18.0 16.1 15.2 14.0 13.2 12.3 11.7 11.2 10.7

12.215 12.120 12.180 12.115 12.075 12.030 12.000 11.975 11.950

121⁄4 121⁄8 121⁄8 121⁄8 121⁄8 12 12 12 12

1.730 1.570 1.360 1.260 1.180 1.100 1.020 0.940 0.790

13⁄4 19⁄16 13⁄8 11⁄4 13⁄16 11⁄8 1 15⁄ 16 13⁄ 16

25⁄8 21⁄2 25⁄16 23⁄16 21⁄8 2 115⁄16 17⁄8 111⁄16

WT16.5×177 WT16.5×159 WT16.5×145.5 WT16.5×131.5 WT16.5×120.5 WT16.5×110.5 WT16.5×100.5

52.1 46.7 42.8 38.7 35.4 32.5 29.5

17.775 173⁄4 17.580 179⁄16 17.420 177⁄16 17.265 171⁄4 17.090 171⁄8 16.965 17 16.840 167⁄8

1.160 1.040 0.960 0.870 0.830 0.775 0.715

13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

20.6 18.3 16.7 15.0 14.2 13.1 12.0

16.100 15.985 15.905 15.805 15.860 15.805 15.745

161⁄8 16 157⁄8 153⁄4 157⁄8 153⁄4 153⁄4

2.090 1.890 1.730 1.570 1.400 1.275 1.150

21⁄16 17⁄8 13⁄4 19⁄16 13⁄8 11⁄4 11⁄8

27⁄8 211⁄16 29⁄16 23⁄8 23⁄16 21⁄16 115⁄16

WT16.5×84.5 WT16.5×76 WT16.5×70.5 WT16.5×65 WT16.5×59

24.8 22.4 20.8 19.2 17.3

16.910 1615⁄16 16.745 163⁄4 16.650 165⁄8 16.545 161⁄2 16.430 163⁄8

0.670 0.635 0.605 0.580 0.550

11⁄

3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16

11.3 10.6 10.1 9.60 9.04

11.500 11.565 11.535 11.510 11.480

111⁄2 115⁄8 111⁄2 111⁄2 111⁄2

1.220 1.055 0.960 0.855 0.740

11⁄4 11⁄16 15⁄ 16 7⁄ 8 3⁄ 4

21⁄16 17⁄8 13⁄4 111⁄16 19⁄16

WT15×238.5 WT15×195.5 WT15×163 WT15×146 WT15×130.5 WT15×117.5 WT15×105.5 WT15×95.5 WT15×86.5

70.0 57.0 47.9 42.9 38.4 34.5 31.0 28.1 25.4

17.105 171⁄8 16.595 165⁄8 16.200 163⁄16 16.005 16 15.805 1513⁄16 15.650 155⁄8 15.470 151⁄2 15.340 153⁄8 15.220 151⁄4

1.630 1.360 1.140 1.020 0.930 0.830 0.775 0.710 0.655

15⁄8 13⁄8 11⁄8 1 15⁄ 16 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

13⁄

16 11⁄ 16 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16

27.9 22.6 18.5 16.3 14.7 13.0 12.0 10.9 9.97

15.865 15.590 15.370 15.255 15.155 15.055 15.105 15.040 14.985

157⁄8 155⁄8 153⁄8 151⁄2 151⁄8 15 151⁄8 15 15

2.950 2.440 2.050 1.850 1.650 1.500 1.315 1.185 1.065

3 27⁄16 21⁄16 17⁄8 15⁄8 11⁄2 15⁄16 13⁄16 11⁄16

33⁄4 31⁄4 213⁄16 25⁄8 27⁄16 21⁄4 21⁄8 115⁄16 17⁄8

WT15×74 WT18×66 WT18×62 WT18×58 WT18×54 WT18×49.5 WT18×45

21.7 19.4 18.2 17.1 15.9 14.5 13.2

15.335 155⁄16 15.155 151⁄8 15.085 151⁄8 15.005 15 14.915 147⁄8 14.825 147⁄8 14.765 143⁄4

0.650 0.615 0.585 0.565 0.545 0.520 0.470

5⁄ 8 5⁄ 8 9⁄ 16 9⁄ 16 9⁄ 16 1⁄ 2 1⁄ 2

5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4

10.0 9.32 8.82 8.48 8.13 7.71 6.94

10.480 10.545 10.515 10.495 10.475 10.450 10.400

101⁄2 101⁄2 101⁄2 101⁄2 101⁄2 101⁄2 103⁄8

1.180 1.000 0.930 0.850 0.760 0.670 0.610

13⁄16 1 15⁄ 16 7⁄ 8 3⁄ 4 11⁄ 16 9⁄ 16

2 13⁄4 111⁄16 15⁄8 19⁄16 17⁄16 15⁄16

16 5⁄ 8 5⁄ 8 9⁄ 16 9⁄ 16

1⁄

Width bf

in.2

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

STRUCTURAL TEES (WT, MT, ST)

1 - 71

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

Fy, ksi 36

128 116 105 97 91 85 80 75 67.5

16.9 18.7 19.6 21.2 22.4 23.9 25.0 26.0 27.1

1200 1080 985 901 845 786 740 698 637

87.4 78.5 73.1 67.0 63.1 58.9 55.8 53.1 49.7

5.66 5.63 5.65 5.62 5.62 5.61 5.61 5.62 5.66

4.92 4.82 4.87 4.80 4.77 4.73 4.74 4.78 4.96

156 140 131 120 113 105 100 95.5 94.3

1.54 1.40 1.27 1.18 1.11 1.04 0.980 0.923 1.24

264 234 206 187 174 160 147 135 113

43.2 38.6 33.8 30.9 28.8 26.6 24.6 22.5 18.9

2.65 2.62 2.58 2.56 2.55 2.53 2.50 2.47 2.38

68.6 61.0 53.5 48.9 45.4 41.9 38.6 35.5 29.8

— 0.994 0.960 0.887 0.831 0.767 0.720 0.677 0.634

0.927 0.831 0.791 0.705 0.635 0.565 0.521 0.486 0.457

177 159 145.5 131.5 120.5 110.5 100.5

12.9 14.4 15.6 17.2 18.1 19.3 21.0

1320 1160 1050 943 871 799 725

96.8 85.8 78.3 70.2 65.8 60.8 55.5

5.03 4.99 4.97 4.94 4.96 4.96 4.95

4.16 4.02 3.94 3.84 3.85 3.81 3.78

174 154 140 125 116 107 97.7

1.62 1.46 1.34 1.22 1.12 1.03 0.938

729 645 581 517 466 420 375

90.6 80.7 73.1 65.5 58.8 53.2 47.6

3.74 3.71 3.69 3.66 3.63 3.59 3.56

141 125 113 101 90.9 82.1 73.4

— — — — — 0.968 0.896

— — 0.993 0.907 0.867 0.801 0.715

84.5 76 70.5 65 59

22.4 23.6 24.8 25.8 27.3

649 592 552 513 469

51.1 47.4 44.7 42.1 39.2

5.12 5.14 5.15 5.18 5.20

4.21 4.26 4.29 4.36 4.47

90.8 84.5 79.8 75.6 74.8

1.08 0.967 0.901 0.832 0.862

155 136 123 109 93.6

27.0 23.6 21.3 18.9 16.3

2.50 2.47 2.43 2.39 2.32

42.2 37.0 33.5 29.7 25.7

0.827 0.775 0.728 0.685 0.621

0.630 0.574 0.529 0.492 0.447

238.5 195.5 163 146 130.5 117.5 105.5 95.5 86.5

8.3 9.9 11.8 13.2 14.5 16.2 17.4 19.0 20.6

1550 1210 981 861 764 674 610 549 497

121 96.6 78.9 69.6 62.3 55.1 50.5 45.7 41.7

4.70 4.61 4.53 4.48 4.46 4.42 4.43 4.42 4.42

4.30 4.04 3.76 3.63 3.54 3.42 3.40 3.35 3.31

224 177 143 125 112 98.2 89.5 80.8 73.4

2.21 1.83 1.56 1.40 1.27 1.15 1.03 0.933 0.848

987 774 622 549 480 427 378 336 299

124 99.2 81.0 71.9 63.3 56.8 50.1 44.7 39.9

3.75 3.68 3.61 3.58 3.54 3.52 3.49 3.46 3.43

195 155 126 111 97.9 87.5 77.2 68.9 61.4

— — — — — — — 0.981 0.913

— — — — — 0.952 0.897 0.816 0.735

74 66 62 58 54 49.5 45

20.8 22.0 23.1 23.9 24.8 26.0 28.7

466 421 396 373 349 322 291

40.6 37.4 35.3 33.7 32.0 30.0 27.1

4.63 4.66 4.66 4.67 4.69 4.71 4.69

3.84 3.90 3.90 3.94 4.01 4.09 4.03

72.2 66.8 63.1 60.4 57.7 57.4 49.4

1.04 0.921 0.867 0.815 0.757 0.912 0.445

113 98.0 90.4 82.1 73.0 63.9 57.3

21.7 18.6 17.2 15.7 13.9 12.2 11.0

2.28 2.25 2.23 2.19 2.15 2.10 2.08

34.0 29.2 27.0 24.6 22.0 19.3 17.3

0.896 0.853 0.801 0.767 0.733 0.685 0.563

0.715 0.664 0.601 0.565 0.533 0.492 0.405

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 72

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Area of Stem

Area

Depth of Tee d

Thickness tw

tw 2

Designation

in.2

in.

in.2

WT13.5×269.5 WT13.5×224 WT13.5×184 WT13.5×153.5 WT13.5×129 WT13.5×117.5 WT13.5×108.5 WT13.5×97 WT13.5×89 WT13.5×80.5 WT13.5×73

79.0 65.5 54.0 45.1 37.9 34.6 31.9 28.5 26.1 23.7 21.5

16.260 15.710 15.195 14.805 14.490 14.330 14.215 14.055 13.905 13.795 13.690

161⁄4 1511⁄16 153⁄16 1413⁄16 141⁄2 145⁄16 143⁄16 141⁄16 137⁄8 133⁄4 133⁄4

1.970 1.650 1.380 1.160 0.980 0.910 0.830 0.750 0.725 0.660 0.605

2 15⁄8 13⁄8 13⁄16 1 15⁄ 16 13⁄ 16 3⁄ 4 3⁄ 4 11⁄ 16 5⁄ 8

1 13⁄ 16 11⁄ 16 5⁄ 8 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 5⁄ 16

32.0 25.9 21.0 17.2 14.2 13.0 11.8 10.5 10.1 9.10 8.28

WT13.5×64.5 WT13.5×57 WT13.5×51 WT13.5×47 WT13.5×42

18.9 16.8 15.0 13.8 12.4

13.815 1313⁄16 13.645 135⁄8 13.545 131⁄2 13.460 131⁄2 13.355 133⁄8

0.610 0.570 0.515 0.490 0.460

5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16

5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4

WT12×246 WT12×204 WT12×167.5 WT12×139.5 WT12×125 WT12×114.5 WT12×103.5 WT12×96 WT12×88 WT12×81 WT12×73 WT12×65.5 WT12×58.5 WT12×52

72.0 59.5 49.2 41.0 36.8 33.6 30.4 28.2 25.8 23.9 21.5 19.3 17.2 15.3

14.825 1413⁄16 14.270 141⁄4 13.760 133⁄4 13.365 133⁄8 13.170 133⁄16 13.010 13 12.855 127⁄8 12.735 123⁄4 12.620 125⁄8 12.500 121⁄2 12.370 123⁄8 12.240 121⁄4 12.130 121⁄8 12.030 12

1.970 1.650 1.380 1.160 1.040 0.960 0.870 0.810 0.750 0.705 0.650 0.605 0.550 0.500

2 15⁄8 13⁄8 13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2

13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4

29.2 23.5 19.0 15.5 13.7 12.5 11.2 10.3 9.47 8.81 8.04 7.41 6.67 6.02

WT12×51.5 WT12×47 WT12×42 WT12×38 WT12×34

15.1 13.8 12.4 11.2 10.0

12.265 12.155 12.050 11.960 11.865

121⁄4 121⁄8 12 12 117⁄8

0.550 0.515 0.470 0.440 0.415

9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 7⁄ 16

5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4

9.11 11.870 8.10 11.785

117⁄8 113⁄4

0.430 0.395

7⁄ 16 3⁄ 8

1⁄ 4 3⁄ 16

WT12×31 WT12×27.5

Flange DisThickness tance tf k

Width bf in.

in.

151⁄4 15 145⁄8 141⁄2 141⁄4 141⁄4 141⁄8 14 141⁄8 14 14

3.540 2.990 2.480 2.090 1.770 1.610 1.500 1.340 1.190 1.080 0.975

39⁄16 3 21⁄2 21⁄16 13⁄4 15⁄8 11⁄2 15⁄16 13⁄16 11⁄16 1

41⁄4 311⁄16 33⁄16 213⁄16 21⁄2 25⁄16 23⁄16 21⁄16 17⁄8 113⁄16 111⁄16

8.43 10.010 10 7.78 10.070 101⁄8 6.98 10.015 10 6.60 9.990 10 6.14 9.960 10

1.100 0.930 0.830 0.745 0.640

11⁄8 15⁄ 16 13⁄ 16 3⁄ 4 5⁄ 8

113⁄16 15⁄8 19⁄16 17⁄16 13⁄8

14.115 13.800 13.520 13.305 13.185 13.110 13.010 12.950 12.890 12.955 12.900 12.855 12.800 12.750

141⁄8 133⁄4 131⁄2 131⁄4 131⁄8 131⁄8 13 13 127⁄8 13 127⁄8 127⁄8 123⁄4 123⁄4

3.540 2.990 2.480 2.090 1.890 1.730 1.570 1.460 1.340 1.220 1.090 0.960 0.850 0.750

39⁄16 3 21⁄2 21⁄16 17⁄8 13⁄4 19⁄16 17⁄16 15⁄16 11⁄4 11⁄16 15⁄ 16 7⁄ 8 3⁄ 4

45⁄16 33⁄4 31⁄4 27⁄8 211⁄16 21⁄2 23⁄8 21⁄4 21⁄8 2 17⁄8 13⁄4 15⁄8 11⁄2

6.75 6.26 5.66 5.26 4.92

9.000 9.065 9.020 8.990 8.965

9 91⁄8 9 9 9

0.980 0.875 0.770 0.680 0.585

1 7⁄ 8 3⁄ 4 11⁄ 16 9⁄ 16

13⁄4 15⁄8 19⁄16 17⁄16 13⁄8

5.10 4.66

7.040 7.005

7 7

0.590 0.505

9⁄ 16 1⁄ 2

13⁄8 15⁄16

15.255 14.940 14.665 14.445 14.270 14.190 14.115 14.035 14.085 14.020 13.965

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 73

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

2.59 1060 2.19 836 1.84 655 1.56 527 1.33 430 1.22 384 1.13 352 1.02 309 0.928 278 0.845 248 0.768 222

138 112 89.3 72.9 60.2 54.2 49.9 44.1 39.4 35.4 31.7

3.66 3.57 3.48 3.42 3.37 3.33 3.32 3.29 3.26 3.24 3.21

218 176 140 113 93.3 83.8 77.0 67.9 60.8 54.5 48.8

— — — — — — — — — — 0.938

— — — — — — — 0.963 0.937 0.851 0.765

18.4 15.8 13.9 12.4 10.6

2.21 2.18 2.15 2.12 2.07

28.8 24.7 21.7 19.4 16.6

0.938 0.883 0.780 0.728 0.664

0.765 0.700 0.578 0.529 0.476

119 95.5 75.9 61.9 54.9 49.7 44.4 40.9 37.2 34.2 30.3 26.5 23.2 20.3

3.41 3.33 3.23 3.17 3.14 3.11 3.08 3.07 3.04 3.05 3.01 2.97 2.94 2.91

187 150 119 96.4 85.3 77.0 68.6 63.1 57.3 52.6 46.6 40.7 35.7 31.2

— — — — — — — — — — — — 0.960 0.874

— — — — — — — — — — 0.947 0.887 0.791 0.690

20.7 18.8 16.3 14.3 12.3

0.951 0.896 0.810 0.741 0.681

0.781 0.715 0.610 0.541 0.489

7.87 0.724 6.67 0.626

0.525 0.450

269.5 224 184 153.5 129 117.5 108.5 97 89 80.5 73

6.2 7.4 8.8 10.5 12.4 13.3 14.6 16.2 16.7 18.4 20.0

1520 1190 938 753 613 556 502 444 414 372 336

128 102 81.7 66.4 54.6 50.0 45.2 40.3 38.2 34.4 31.2

4.39 4.27 4.17 4.09 4.02 4.01 3.97 3.95 3.98 3.96 3.95

4.36 4.02 3.71 3.47 3.28 3.21 3.11 3.03 3.05 2.99 2.95

241 191 151 121 98.8 89.8 81.1 71.8 67.6 60.8 55.0

64.5 57 51 47 42

19.9 21.3 23.5 24.7 26.3

323 289 258 239 216

31.0 28.3 25.3 23.8 21.9

4.13 4.15 4.14 4.16 4.18

3.39 3.42 3.37 3.41 3.48

55.1 50.4 45.0 42.4 39.2

0.945 0.833 0.750 0.692 0.621

246 204 167.5 139.5 125 114.5 103.5 96 88 81 73 65.5 58.5 52

5.5 6.5 7.8 9.3 10.4 11.2 12.4 13.3 14.4 15.3 16.6 17.8 19.6 21.6

1130 874 685 546 478 431 382 350 319 293 264 238 212 189

105 83.1 66.3 53.6 47.2 42.9 38.3 35.2 32.2 29.9 27.2 24.8 22.3 20.0

3.96 3.83 3.73 3.65 3.61 3.58 3.55 3.53 3.51 3.50 3.50 3.52 3.51 3.51

4.07 3.74 3.42 3.18 3.05 2.97 2.87 2.80 2.74 2.70 2.66 2.65 2.62 2.59

200 157 123 98.8 86.5 78.1 69.3 63.5 57.8 53.3 48.2 43.9 39.2 35.1

2.55 2.16 1.82 1.54 1.39 1.28 1.17 1.09 1.00 0.921 0.833 0.750 0.672 0.600

51.5 47 42 38 34

19.6 20.9 22.9 24.5 26.0

204 186 166 151 137

22.0 20.3 18.3 16.9 15.6

3.67 3.67 3.67 3.68 3.70

3.01 2.99 2.97 3.00 3.06

39.2 36.1 32.5 30.1 27.9

0.841 0.764 0.685 0.622 0.560

59.7 54.5 47.2 41.3 35.2

13.3 12.0 10.5 9.18 7.85

1.99 1.98 1.95 1.92 1.87

31 27.5

25.1 27.3

131 117

15.6 14.1

3.79 3.80

3.46 3.50

28.4 25.6

1.28 1.53

17.2 14.5

4.90 4.15

1.38 1.34

92.2 79.4 69.6 62.0 52.8 837 659 513 412 362 326 289 265 240 221 195 170 149 130

*Where no value of Qs is shown, the Tee complies with LRFD Specification Sect. E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Fy, ksi

1 - 74

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Area of Stem

Flange DisThickness tance tf k

Area

Depth of Tee d

Thickness tw

tw 2

Designation

in.2

in.

in.2

WT10.5×100.5 WT10.5×91 WT10.5×83 WT10.5×73.5 WT10.5×66 WT10.5×61 WT10.5×55.5 WT10.5×50.5

29.6 26.8 24.4 21.6 19.4 17.9 16.3 14.9

11.515 11.360 11.240 11.030 10.915 10.840 10.755 10.680

111⁄2 113⁄8 111⁄4 11 107⁄8 107⁄8 103⁄4 105⁄8

0.910 0.830 0.750 0.720 0.650 0.600 0.550 0.500

15⁄ 16 13⁄ 16 3⁄ 4 3⁄ 4 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2

1⁄

7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4

10.5 9.43 8.43 7.94 7.09 6.50 5.92 5.34

12.575 12.500 12.420 12.510 12.440 12.390 12.340 12.290

125⁄8 121⁄2 123⁄8 121⁄2 121⁄2 123⁄8 123⁄8 121⁄4

1.630 1.480 1.360 1.150 1.035 0.960 0.875 0.800

15⁄8 11⁄2 13⁄8 11⁄8 11⁄16 15⁄ 16 7⁄ 8 13⁄ 16

23⁄8 21⁄4 21⁄8 17⁄8 113⁄16 111⁄16 15⁄8 19⁄16

WT10.5×46.5 WT10.5×41.5 WT10.5×36.5 WT10.5×34 WT10.5×31

13.7 12.2 10.7 10.0 9.13

10.810 10.715 10.620 10.565 10.495

103⁄4 103⁄4 105⁄8 105⁄8 101⁄2

0.580 0.515 0.455 0.430 0.400

9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8

5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

6.27 5.52 4.83 4.54 4.20

8.420 8.355 8.295 8.270 8.240

83⁄8 83⁄8 81⁄4 81⁄4 81⁄4

0.930 0.835 0.740 0.685 0.615

15⁄ 16 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

111⁄16 19⁄16 11⁄2 17⁄16 13⁄8

8.37 10.530 7.36 10.415 6.49 10.330

101⁄2 103⁄8 103⁄8

0.405 0.380 0.350

3⁄ 8 3⁄ 8 3⁄ 8

3⁄ 16 3⁄ 16 3⁄ 16

4.26 3.96 3.62

6.555 6.530 6.500

61⁄2 61⁄2 61⁄2

0.650 0.535 0.450

5⁄ 8 9⁄ 16 7⁄ 16

13⁄8 15⁄16 13⁄16

WT10.5×28.5 WT10.5×25 WT10.5×22

Width bf in.

in.

WT9×155.5 WT9×141.5 WT9×129 WT9×117 WT9×105.5 WT9×96 WT9×87.5 WT9×79 WT9×71.5 WT9×65

45.8 41.6 38.0 34.4 31.1 28.2 25.7 23.2 21.0 19.1

11.160 10.925 10.730 10.530 10.335 10.175 10.020 9.860 9.745 9.625

113⁄16 1015⁄16 103⁄4 101⁄2 105⁄16 103⁄16 10 97⁄8 93⁄4 95⁄8

1.520 1.400 1.280 1.160 1.060 0.960 0.890 0.810 0.730 0.670

11⁄2 13⁄8 11⁄4 13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

3⁄ 4 11⁄ 16 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

17.0 15.3 13.7 12.2 11.0 9.77 8.92 7.99 7.11 6.45

12.005 11.890 11.770 11.650 11.555 11.455 11.375 11.300 11.220 11.160

12 117⁄8 113⁄4 115⁄8 111⁄2 111⁄2 113⁄8 111⁄4 111⁄4 111⁄8

2.740 2.500 2.300 2.110 1.910 1.750 1.590 1.440 1.320 1.200

23⁄4 21⁄2 25⁄16 21⁄8 115⁄16 13⁄4 19⁄16 17⁄16 15⁄16 13⁄16

37⁄16 33⁄16 3 23⁄4 9 2 ⁄16 27⁄16 21⁄4 21⁄8 2 17⁄8

WT9×59.5 WT9×53 WT9×48.5 WT9×43 WT9×38

17.5 15.6 14.3 12.7 11.2

9.485 9.365 9.295 9.195 9.105

91⁄2 93⁄8 91⁄4 91⁄4 91⁄8

0.655 0.590 0.535 0.480 0.425

5⁄ 8 9⁄ 16 9⁄ 16 1⁄ 2 7⁄ 16

5⁄ 16 5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4

6.21 5.53 4.97 4.41 3.87

11.265 11.200 11.145 11.090 11.035

111⁄4 111⁄4 111⁄8 111⁄8 11

1.060 0.940 0.870 0.770 0.680

11⁄16 15⁄ 16 7⁄ 8 3⁄ 4 11⁄ 16

13⁄4 15⁄8 19⁄16 17⁄16 13⁄8

WT9×35.5 WT9×32.5 WT9×30 WT9×27.5 WT9×25

10.4 9.55 8.82 8.10 7.33

9.235 9.175 9.120 9.055 8.995

91⁄4 91⁄8 91⁄8 9 9

0.495 0.450 0.415 0.390 0.355

1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

1⁄

1⁄ 4 3⁄ 16 3⁄ 16

4.57 4.13 3.78 3.53 3.19

7.635 7.590 7.555 7.530 7.495

75⁄8 75⁄8 71⁄2 71⁄2 71⁄2

0.810 0.750 0.695 0.630 0.570

13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8 9⁄ 16

11⁄2 17⁄16 13⁄8 15⁄16 11⁄4

WT9×23 WT9×20 WT9×17.5

6.77 5.88 5.15

9.030 8.950 8.850

9 9 87⁄8

0.360 0.315 0.300

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

3.25 2.82 2.66

6.060 6.015 6.000

6 6 6

0.605 0.525 0.425

5⁄ 8 1⁄ 2 7⁄ 16

11⁄4 13⁄16 11⁄8

1⁄

4 4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 75

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

43.1 38.6 35.0 30.0 26.7 24.6 22.2 20.2

3.02 3.00 2.98 2.95 2.93 2.92 2.90 2.89

66.6 59.6 53.9 46.3 41.1 37.8 34.1 30.9

— — — — — — — 0.990

— — — — — 0.993 0.917 0.826

17.4 15.3 13.3 12.2 10.9

— — 0.908 0.853 0.784

0.968 0.856 0.730 0.664 0.583

7.42 0.793 6.09 0.733 5.09 0.638

0.592 0.533 0.460

100.5 91 83 73.5 66 61 55.5 50.5

10.3 11.2 12.4 13.0 14.4 15.6 17.1 18.8

285 253 226 204 181 166 150 135

31.9 28.5 25.5 23.7 21.1 19.3 17.5 15.8

3.10 3.07 3.04 3.08 3.06 3.04 3.03 3.01

2.57 2.48 2.39 2.39 2.33 2.28 2.23 2.18

58.6 52.1 46.3 42.4 37.6 34.3 31.0 27.9

1.18 1.07 0.984 0.864 0.780 0.724 0.662 0.605

271 241 217 188 166 152 137 124

46.5 41.5 36.5 34 31

16.2 18.2 20.6 21.8 23.5

144 127 110 103 93.8

17.9 15.7 13.8 12.9 11.9

3.25 3.22 3.21 3.20 3.21

2.74 2.66 2.60 2.59 2.58

31.8 28.0 24.4 22.9 21.1

0.812 0.728 0.647 0.606 0.554

46.4 40.7 35.3 32.4 28.7

11.0 9.75 8.51 7.83 6.97

1.84 1.83 1.81 1.80 1.77

28.5 25 22

23.2 24.7 26.8

90.4 80.3 71.1

11.8 10.7 9.68

3.29 3.30 3.31

2.85 2.93 2.98

21.2 20.8 17.6

0.638 0.771 1.06

15.3 12.5 10.3

4.67 3.82 3.18

1.35 1.30 1.26

155.5 141.5 129 117 105.5 96 87.5 79 71.5 65

5.3 5.7 6.3 6.9 7.5 8.3 9.0 9.9 11.0 11.9

383 337 298 260 229 202 181 160 142 127

46.5 41.5 37.0 32.6 29.0 25.8 23.4 20.8 18.5 16.7

2.89 2.85 2.80 2.75 2.72 2.68 2.66 2.63 2.60 2.58

2.93 2.80 2.68 2.55 2.44 2.34 2.26 2.18 2.09 2.02

90.6 80.1 71.0 62.4 55.0 48.5 43.6 38.5 34.0 30.5

1.91 1.75 1.61 1.48 1.34 1.23 1.13 1.02 0.938 0.856

59.5 53 48.5 43 38

12.3 13.6 15.0 16.7 18.9

119 104 93.8 82.4 71.8

15.9 14.1 12.7 11.2 9.83

2.60 2.59 2.56 2.55 2.54

2.03 1.97 1.91 1.86 1.80

28.7 25.2 22.6 19.9 17.3

0.778 126 0.695 110 0.640 100 0.570 87.6 0.505 76.2

35.5 32.5 30 27.5 25

16.2 17.8 19.3 20.6 22.6

78.2 70.7 64.7 59.5 53.5

11.2 10.1 9.29 8.63 7.79

2.74 2.72 2.71 2.71 2.70

2.26 2.20 2.16 2.16 2.12

20.0 18.0 16.5 15.3 13.8

0.683 0.629 0.583 0.538 0.489

30.1 27.4 25.0 22.5 20.0

23 20 17.5

22.3 25.5 26.8

52.1 44.8 40.1

7.77 6.73 6.21

2.77 2.76 2.79

2.33 2.29 2.39

13.9 12.0 12.0

0.558 0.489 0.450

11.3 9.55 7.67

398 352 314 279 246 220 196 174 156 139

Fy, ksi

66.2 59.2 53.4 47.9 42.7 38.4 34.4 30.7 27.7 24.9

2.95 2.91 2.88 2.85 2.82 2.79 2.76 2.74 2.72 2.70

104 92.5 83.2 74.5 66.2 59.4 53.1 47.4 42.7 38.3

— — — — — — — — — —

22.5 19.7 18.0 15.8 13.8

2.69 2.66 2.65 2.63 2.61

34.6 30.2 27.6 24.2 21.1

— — — — 0.990

— — — 0.937 0.826

7.89 7.22 6.63 5.97 5.35

1.70 1.69 1.69 1.67 1.65

12.3 — 11.2 — 10.3 0.964 9.27 0.913 8.29 0.823

0.963 0.877 0.796 0.735 0.625

3.72 3.17 2.56

1.29 1.27 1.22

5.85 0.831 4.97 0.690 4.03 0.638

0.635 0.496 0.460

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 76

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Area of Stem

Flange DisThickness tance tf k

Area

Depth of Tee d

Thickness tw

tw 2

Designation

in.2

in.

in.2

WT8×50 WT8×44.5 WT8×38.5 WT8×33.5

14.7 13.1 11.3 9.84

8.485 8.375 8.260 8.165

81⁄2 83⁄8 81⁄4 81⁄8

0.585 0.525 0.455 0.395

9⁄ 16 1⁄ 2 7⁄ 16 3⁄ 8

5⁄ 16 1⁄ 4 1⁄ 4 3⁄ 16

4.96 4.40 3.76 3.23

10.425 10.365 10.295 10.235

103⁄8 103⁄8 101⁄4 101⁄4

0.985 0.875 0.760 0.665

1 7⁄ 8 3⁄ 4 11⁄ 16

111⁄16 19⁄16 17⁄16 13⁄8

WT8×28.5 WT8×25 WT8×22.5 WT8×20 WT8×18

8.38 7.37 6.63 5.89 5.28

8.215 8.130 8.065 8.005 7.930

81⁄4 81⁄8 81⁄8 8 77⁄8

0.430 0.380 0.345 0.305 0.295

7⁄ 16 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16

1⁄ 4 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16

3.53 3.09 2.78 2.44 2.34

7.120 7.070 7.035 6.995 6.985

71⁄8 71⁄8 7 7 7

0.715 0.630 0.565 0.505 0.430

11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16

13⁄8 15⁄16 11⁄4 13⁄16 11⁄8

WT8×15.5 WT8×13

4.56 3.84

7.940 7.845

8 77⁄8

0.275 0.250

1⁄ 4 1⁄ 4

1⁄

2.18 1.96

5.525 5.500

51⁄2 51⁄2

0.440 0.345

7⁄ 16 3⁄ 8

11⁄8 11⁄16

3.740 3.070 2.830 2.595 2.380 2.190 2.015

33⁄4 31⁄16 213⁄16 25⁄8 23⁄8 23⁄16 2

17⁄8 19⁄16 17⁄16 15⁄16 13⁄16 11⁄8 1

42.7 34.4 30.6 27.1 24.1 21.5 19.2

18.560 17.890 17.650 17.415 17.200 17.010 16.835

181⁄2 177⁄8 175⁄8 173⁄8 171⁄4 17 167⁄8

5.120 4.910 4.520 4.160 3.820 3.500 3.210

51⁄8 415⁄16 41⁄2 43⁄16 313⁄16 31⁄2 33⁄16

513⁄16 59⁄16 53⁄16 413⁄16 41⁄2 43⁄16 37⁄8

1.875 1.770 1.655 1.540 1.410 1.290 1.175 1.070 0.980 0.890 0.830 0.745 0.680

17⁄8 13⁄4 15⁄8 19⁄16 17⁄16 15⁄16 13⁄16 11⁄16 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

15⁄

17.5 16.2 14.8 13.5 12.1 10.8 9.62 8.58 7.70 6.89 6.32 5.58 5.03

16.695 16.590 16.475 16.360 16.230 16.110 15.995 15.890 15.800 15.710 15.650 15.565 15.500

163⁄4 165⁄8 161⁄2 163⁄8 161⁄4 161⁄8 16 157⁄8 153⁄4 153⁄4 155⁄8 155⁄8 151⁄2

3.035 2.845 2.660 2.470 2.260 2.070 1.890 1.720 1.560 1.440 1.310 1.190 1.090

31⁄16 27⁄8 211⁄16 21⁄2 21⁄4 21⁄16 17⁄8 13⁄4 19⁄16 17⁄16 15⁄16 13⁄16 11⁄16

311⁄16 31⁄2 35⁄16 31⁄8 215⁄16 23⁄4 29⁄16 23⁄8 21⁄4 21⁄8 2 17⁄8 13⁄4

WT7×404 WT8×365 WT8×332.5 WT8×302.5 WT8×275 WT8×250 WT8×227.5

119 107 97.8 88.9 80.9 73.5 66.9

WT7×213 WT8×199 WT8×185 WT8×171 WT8×155.5 WT8×141.5 WT8×128.5 WT8×116.5 WT8×105.5 WT8×96.5 WT8×88 WT8×79.5 WT8×72.5

62.6 58.5 54.4 50.3 45.7 41.6 37.8 34.2 31.0 28.4 25.9 23.4 21.3

11.420 117⁄16 11.210 111⁄4 10.820 107⁄8 10.460 101⁄2 10.120 101⁄8 9.800 93⁄4 9.510 91⁄2 9.335 9.145 8.960 8.770 8.560 8.370 8.190 8.020 7.860 7.740 7.610 7.490 7.390

93⁄8 91⁄8 9 83⁄4 81⁄2 83⁄8 81⁄4 8 77⁄8 73⁄4 75⁄8 71⁄2 73⁄8

1⁄

7⁄

13⁄

13⁄ 3⁄

8 8

16 8 16 16

4 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 3⁄ 8

Width bf in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

STRUCTURAL TEES (WT, MT, ST)

1 - 77

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

17.9 15.7 13.4 11.6

2.51 2.49 2.47 2.46

27.4 24.0 20.5 17.7

— — — —

— — 0.988 0.861

— 0.990 0.904 0.784 0.754

0.942 0.826 0.725 0.583 0.553

50 44.5 38.5 33.5

12.1 13.5 15.6 18.0

76.8 67.2 56.9 48.6

11.4 10.1 8.59 7.36

2.28 2.27 2.24 2.22

1.76 1.70 1.63 1.56

20.7 18.1 15.3 13.0

0.706 0.631 0.549 0.481

93.1 81.3 69.2 59.5

28.5 25 22.5 20 18

16.5 18.7 20.6 23.3 24.1

48.7 42.3 37.8 33.1 30.6

7.77 6.78 6.10 5.35 5.05

2.41 2.40 2.39 2.37 2.41

1.94 1.89 1.86 1.81 1.88

13.8 12.0 10.8 9.43 8.93

0.589 0.521 0.471 0.421 0.378

21.6 18.6 16.4 14.4 12.2

15.5 13

25.8 28.4

27.4 23.5

4.64 4.09

2.45 2.47

2.02 2.09

404 365 332.5 302.5 275 250 227.5

1.5 1.9 2.0 2.2 2.4 2.6 2.8

898 739 622 524 442 375 321

116 95.4 82.1 70.6 60.9 52.7 45.9

2.75 2.62 2.52 2.43 2.34 2.26 2.19

3.70 3.47 3.25 3.05 2.85 2.67 2.51

213 199 185 171 155.5 141.5 128.5 116.5 105.5 96.5 88 79.5 72.5

3.0 3.2 3.4 3.7 4.0 4.4 4.9 5.3 5.8 6.4 6.9 7.7 8.4

287 257 229 203 176 153 133 116 102 89.8 80.5 70.2 62.5

41.4 37.6 33.9 30.4 26.7 23.5 20.7 18.2 16.2 14.4 13.0 11.4 10.2

2.14 2.10 2.05 2.01 1.96 1.92 1.88 1.84 1.81 1.78 1.76 1.73 1.71

2.40 2.30 2.19 2.09 1.97 1.86 1.75 1.65 1.57 1.49 1.43 1.35 1.29

8.27 0.413 8.12 0.372 249 211 182 157 136 117 102 91.7 82.9 74.4 66.2 57.7 50.4 43.9 38.2 33.4 29.4 26.3 22.8 20.2

3.19 3.00 2.77 2.55 2.35 2.16 1.99

6.20 4.80 2760 2360 2080 1840 1630 1440 1280

1.88 1180 1.76 1090 1.65 994 1.54 903 1.41 807 1.29 722 1.18 645 1.08 576 0.980 513 0.903 466 0.827 419 0.751 374 0.688 338

Fy, ksi

6.06 5.26 4.67 4.12 3.50

1.60 1.59 1.57 1.57 1.52

9.43 8.16 7.23 6.37 5.42

2.24 1.74

1.17 1.12

3.52 0.668 0.479 2.74 0.563 0.406

297 264 236 211 189 169 152

4.82 4.69 4.62 4.55 4.49 4.43 4.38

463 408 365 326 292 261 234

— — — — — — —

141 131 121 110 99.4 89.7 80.7 72.5 65.0 59.3 53.5 48.1 43.7

4.34 4.31 4.27 4.24 4.20 4.17 4.13 4.10 4.07 4.05 4.02 4.00 3.98

217 201 185 169 152 137 123 110 99.0 90.2 81.4 73.0 66.3

— — — — — — — — — — — — —

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 78

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Designation

Area of Stem

Flange DisThickness tance tf k

Area

Depth of Tee d

Thickness tw

tw 2

in.2

in.

in.2

5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4

4.73 4.27 3.76 3.43 3.08

14.725 14.670 14.605 14.565 14.520

143⁄4 145⁄8 145⁄8 145⁄8 141⁄2

1.030 0.940 0.860 0.780 0.710

1 15⁄ 16 7⁄ 8 3⁄ 4 11⁄ 16

111⁄16 15⁄8 19⁄16 17⁄16 13⁄8

1⁄

10.130 101⁄8 10.070 101⁄8 10.035 10 9.995 10

0.855 0.785 0.720 0.645

7⁄ 8 13⁄ 16 3⁄ 4 5⁄ 8

15⁄8 19⁄16 11⁄2 17⁄16

Width bf in.

in.

WT7×66 WT7×60 WT7×54.5 WT7×49.5 WT7×45

19.4 17.7 16.0 14.6 13.2

7.330 7.240 7.160 7.080 7.010

73⁄8 71⁄4 71⁄8 71⁄8 7

0.645 0.590 0.525 0.485 0.440

5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16

WT7×41 WT7×37 WT7×34 WT7×30.5

12.0 10.9 9.99 8.96

7.155 7.085 7.020 6.945

71⁄8 71⁄8 7 7

0.510 0.450 0.415 0.375

1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8

1⁄ 4 3⁄ 16

3.65 3.19 2.91 2.60

WT7×26.5 WT7×24 WT7×21.5

7.81 7.07 6.31

6.960 6.895 6.830

7 67⁄8 67⁄8

0.370 0.340 0.305

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

2.58 2.34 2.08

8.060 8.030 7.995

8 8 8

0.660 0.595 0.530

11⁄ 16 5⁄ 8 1⁄ 2

17⁄16 13⁄8 15⁄16

WT7×19 WT7×17 WT7×15

5.58 5.00 4.42

7.050 6.990 6.920

7 7 67⁄8

0.310 0.285 0.270

5⁄ 16 5⁄ 16 1⁄ 4

3⁄ 16 3⁄ 16 1⁄ 8

2.19 1.99 1.87

6.770 6.745 6.730

63⁄4 63⁄4 63⁄4

0.515 0.455 0.385

1⁄ 2 7⁄ 16 3⁄ 8

11⁄16 1 15⁄ 16

WT7×13 WT7×11

3.85 3.25

6.955 6.870

7 67⁄8

0.255 0.230

1⁄ 4 1⁄ 4

1⁄

1.77 1.58

5.025 5.000

5 5

0.420 0.335

7⁄ 16 5⁄ 16

15⁄

1⁄

4 4

8 8

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7⁄

16 8

STRUCTURAL TEES (WT, MT, ST)

1 - 79

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft

Axis X-X

h tw

I 4

r 3

yp 3

I 4

in.

66 60 54.5 49.5 45

8.8 9.7 10.9 11.8 13.0

57.8 51.7 45.3 40.9 36.4

9.57 8.61 7.56 6.88 6.16

1.73 1.71 1.68 1.67 1.66

1.29 1.24 1.17 1.14 1.09

18.6 16.5 14.4 12.9 11.5

0.658 0.602 0.549 0.500 0.456

41 37 34 30.5

11.2 12.7 13.7 15.2

41.2 36.0 32.6 28.9

7.14 6.25 5.69 5.07

1.85 1.82 1.81 1.80

1.39 1.32 1.29 1.25

13.2 11.5 10.4 9.16

0.594 0.541 0.498 0.448

74.2 66.9 60.7 53.7

26.5 24 21.5

15.4 16.8 18.7

27.6 24.9 21.9

4.94 4.48 3.98

1.88 1.87 1.86

1.38 1.35 1.31

8.87 8.00 7.05

0.484 0.440 0.395

28.8 25.7 22.6

19 17 15

19.8 21.5 22.7

23.3 20.9 19.0

4.22 3.83 3.55

2.04 2.04 2.07

1.54 1.53 1.58

7.45 6.74 6.25

0.412 0.371 0.329

13 11

24.1 26.7

17.3 14.8

3.31 2.91

2.12 2.14

1.72 1.76

5.89 5.20

0.383 0.325

Qs*

Axis Y-Y

in.

r 3

Fy, ksi 3

in.

37.2 33.7 30.6 27.6 25.0

3.76 3.74 3.73 3.71 3.70

56.6 51.2 46.4 41.8 37.8

— — — — —

14.6 13.3 12.1 10.7

2.48 2.48 2.46 2.45

22.4 20.3 18.5 16.4

— — — —

— — — 0.973

7.16 6.40 5.65

1.92 1.91 1.89

11.0 9.82 8.66

— — 0.947

0.958 0.882 0.775

13.3 11.7 9.79

3.94 3.45 2.91

1.55 1.53 1.49

6.07 5.32 4.49

0.934 0.857 0.810

0.760 0.669 0.610

4.45 3.50

1.77 1.40

1.08 1.04

2.77 2.19

0.737 0.621

0.537 0.447

274 247 223 201 181

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 80

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Designation

Area of Stem

Area

Depth of Tee d

Thickness tw

tw 2

in.2

in.

in.2 14.9 13.3 12.1 10.7 9.67 8.68 7.62 6.73 5.96 5.30 4.66 3.93 3.50 3.23 2.91 2.63 2.36

WT6×168 WT6×152.5 WT6×139.5 WT6×126 WT6×115 WT6×105 WT6×95 WT6×85 WT6×76 WT6×68 WT6×60 WT6×53 WT6×48 WT6×43.5 WT6×39.5 WT6×36 WT6×32.5

49.4 44.8 41.0 37.0 33.9 30.9 27.9 25.0 22.4 20.0 17.6 15.6 14.1 12.8 11.6 10.6 9.54

8.410 8.160 7.925 7.705 7.525 7.355 7.190 7.015 6.855 6.705 6.560 6.445 6.355 6.265 6.190 6.125 6.060

83⁄8 81⁄8 77⁄8 73⁄4 71⁄2 73⁄8 71⁄4 7 67⁄8 63⁄4 61⁄2 61⁄2 63⁄8 61⁄4 61⁄4 61⁄8 6

1.775 1.625 1.530 1.395 1.285 1.180 1.060 0.960 0.870 0.790 0.710 0.610 0.550 0.515 0.470 0.430 0.390

13⁄4 15⁄8 11⁄2 13⁄8 15⁄16 13⁄16 11⁄16 15⁄ 16 7⁄ 8 13⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8

7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 11⁄ 16 5⁄ 8 9⁄ 16 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 5⁄ 16 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

WT6×29 WT6×26.5

8.52 7.78

6.095 6.030

61⁄8 6

0.360 0.345

3⁄ 8 3⁄ 8

3⁄ 16 3⁄ 16

WT6×25 WT6×22.5 WT6×20

7.34 6.61 5.89

6.095 6.030 5.970

61⁄8 6 6

0.370 0.335 0.295

3⁄ 8 5⁄ 16 5⁄ 16

WT6×17.5 WT6×15 WT6×13

5.17 4.40 3.82

6.250 6.170 6.110

61⁄4 61⁄8 61⁄8

0.300 0.260 0.230

WT6×11 WT6×9.5 WT6×8 WT6×7

3.24 2.79 2.36 2.08

6.155 6.080 5.995 5.955

61⁄8 61⁄8 6 6

0.260 0.235 0.220 0.200

Flange DisThickness tance tf k

Width bf in.

in.

133⁄8 131⁄4 131⁄8 13 127⁄8 123⁄4 125⁄8 125⁄8 121⁄2 123⁄8 123⁄8 121⁄4 121⁄8 121⁄8 121⁄8 12 12

2.955 2.705 2.470 2.250 2.070 1.900 1.735 1.560 1.400 1.250 1.105 0.990 0.900 0.810 0.735 0.670 0.605

215⁄16 211⁄16 21⁄2 21⁄4 21⁄16 17⁄8 13⁄4 19⁄16 13⁄8 11⁄4 11⁄8 1 7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

311⁄16 37⁄16 33⁄16 215⁄16 23⁄4 25⁄8 27⁄16 21⁄4 21⁄8 115⁄16 113⁄16 111⁄16 15⁄8 11⁄2 17⁄16 13⁄8 15⁄16

2.19 10.010 2.08 9.995

10 10

0.640 0.575

5⁄ 8 9⁄ 16

13⁄8 11⁄4

3⁄ 16 3⁄ 16 3⁄ 16

2.26 2.02 1.76

8.080 8.045 8.005

81⁄8 8 8

0.640 0.575 0.515

5⁄ 8 9⁄ 16 1⁄ 2

13⁄8 11⁄4 11⁄4

5⁄ 16 1⁄ 4 1⁄ 4

3⁄ 16 1⁄ 8 1⁄ 8

1.88 1.60 1.41

6.560 6.520 6.490

61⁄2 61⁄2 61⁄2

0.520 0.440 0.380

1⁄ 2 7⁄ 16 3⁄ 8

15⁄ 16 7⁄ 8

1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8

1.60 1.43 1.32 1.19

4.030 4.005 3.990 3.970

4 4 4 4

0.425 0.350 0.265 0.225

7⁄ 16 3⁄ 8 1⁄ 4 1⁄ 4

7⁄ 8 13⁄ 16 3⁄ 4 11⁄ 16

13.385 13.235 13.140 13.005 12.895 12.790 12.670 12.570 12.480 12.400 12.320 12.220 12.160 12.125 12.080 12.040 12.000

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 81

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft

Axis X-X

h tw

I 4

r 3

Qs*

Axis Y-Y

yp 3

I 4

r 3

Fy, ksi 3

in.

168 152.5 139.5 126 115 105 95 85 76 68 60 53 48 43.5 39.5 36 32.5

2.7 3.0 3.2 3.5 3.8 4.1 4.6 5.1 5.6 6.1 6.8 8.0 8.8 9.4 10.3 11.3 12.4

190 162 141 121 106 92.1 79.0 67.8 58.5 50.6 43.4 36.3 32.0 28.9 25.8 23.2 20.6

31.2 27.0 24.1 20.9 18.5 16.4 14.2 12.3 10.8 9.46 8.22 6.91 6.12 5.60 5.03 4.54 4.06

1.96 1.90 1.86 1.81 1.77 1.73 1.68 1.65 1.62 1.59 1.57 1.53 1.51 1.50 1.49 1.48 1.47

2.31 2.16 2.05 1.92 1.82 1.72 1.62 1.52 1.43 1.35 1.28 1.19 1.13 1.10 1.06 1.02 0.985

68.4 59.1 51.9 44.8 39.4 34.5 29.8 25.6 22.0 19.0 16.2 13.6 11.9 10.7 9.49 8.48 7.50

1.84 1.69 1.56 1.42 1.31 1.21 1.10 0.994 0.896 0.805 0.716 0.637 0.580 0.527 0.480 0.439 0.398

593 525 469 414 371 332 295 259 227 199 172 151 135 120 108 97.5 87.2

88.6 79.3 71.3 63.6 57.5 51.9 46.5 41.2 36.4 32.1 28.0 24.7 22.2 19.9 17.9 16.2 14.5

3.47 3.42 3.38 3.34 3.31 3.28 3.25 3.22 3.19 3.16 3.13 3.11 3.09 3.07 3.05 3.04 3.02

137 122 110 97.9 88.4 79.7 71.3 63.0 55.6 49.0 42.7 37.5 33.7 30.2 27.2 24.6 22.0

— — — — — — — — — — — — — — — — —

29 26.5

13.5 14.1

19.1 17.7

3.76 3.54

1.50 1.51

1.03 1.02

6.97 0.426 6.46 0.389

53.5 47.9

10.7 9.58

2.51 2.48

16.3 14.6

— —

25 22.5 20

13.1 14.5 16.5

18.7 16.6 14.4

3.79 3.39 2.95

1.60 1.58 1.57

1.17 1.13 1.08

6.90 0.454 6.12 0.411 5.30 0.368

28.2 25.0 22.0

6.97 6.21 5.51

1.96 1.94 1.93

10.7 9.50 8.41

— — —

— 0.998 0.887

17.5 15 13

18.1 20.9 23.6

16.0 13.5 11.7

3.23 2.75 2.40

1.76 1.75 1.75

1.30 1.27 1.25

5.71 0.394 4.83 0.337 4.20 0.295

12.2 10.2 8.66

3.73 3.12 2.67

1.54 1.52 1.51

5.73 4.78 4.08

— 0.856 0.891 0.710 0.767 0.565

11 9.5 8 7

20.9 23.1 24.7 27.2

11.7 10.1 8.70 7.67

2.59 2.28 2.04 1.83

1.90 1.90 1.92 1.92

1.63 1.65 1.74 1.76

4.63 4.11 3.72 3.32

2.33 1.88 1.41 1.18

1.16 0.939 0.706 0.594

0.847 0.822 0.773 0.753

1.83 1.49 1.13 0.950

0.891 0.797 0.741 0.626

0.402 0.348 0.639 0.760

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

0.710 0.596 0.541 0.450

1 - 82

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Designation

Area of Stem

Area

Depth of Tee d

Thickness tw

tw 2

in.2

in.

in.2

Flange DisThickness tance tf k

Width bf in.

in.

WT5×56 WT5×50 WT5×44 WT5×38.5 WT5×34 WT5×30 WT5×27 WT5×24.5

16.5 14.7 12.9 11.3 9.99 8.82 7.91 7.21

5.680 5.550 5.420 5.300 5.200 5.110 5.045 4.990

55⁄8 51⁄2 53⁄8 51⁄4 51⁄4 51⁄8 5 5

0.755 0.680 0.605 0.530 0.470 0.420 0.370 0.340

3⁄ 4 11⁄ 16 5⁄ 8 1⁄ 2 1⁄ 2 7⁄ 16 3⁄ 8 5⁄ 16

3⁄ 8 3⁄ 8 5⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16 3⁄ 16

4.29 3.77 3.28 2.81 2.44 2.15 1.87 1.70

10.415 10.340 10.265 10.190 10.130 10.080 10.030 10.000

103⁄8 103⁄8 101⁄4 101⁄4 101⁄8 101⁄8 10 10

1.250 1.120 0.990 0.870 0.770 0.680 0.615 0.560

11⁄4 11⁄8 1 7⁄ 8 3⁄ 8 11⁄ 16 5⁄ 8 9⁄ 16

17⁄8 13⁄4 15⁄8 11⁄2 13⁄8 15⁄16 11⁄4 13⁄16

WT5×22.5 WT5×19.5 WT5×16.5

6.63 5.73 4.85

5.050 4.960 4.865

5 5 47⁄8

0.350 0.315 0.290

3⁄ 8 5⁄ 16 5⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16

1.77 1.56 1.41

8.020 7.985 7.960

8 8 8

0.620 0.530 0.435

5⁄ 8 1⁄ 2 7⁄ 16

11⁄4 11⁄8 11⁄16

WT5×15 WT5×13 WT5×11

4.42 3.81 3.24

5.235 5.165 5.085

51⁄4 51⁄8 51⁄8

0.300 0.260 0.240

5⁄ 16 1⁄ 4 1⁄ 4

3⁄ 16 1⁄ 8 1⁄ 8

1.57 1.34 1.22

5.810 5.770 5.750

53⁄4 53⁄4 53⁄4

0.510 0.440 0.360

1⁄ 2 7⁄ 16 3⁄ 8

15⁄ 16 7⁄ 8 3⁄ 4

WT5×9.5 WT5×8.5 WT5×7.5 WT5×6

2.81 2.50 2.21 1.77

5.120 5.055 4.995 4.935

51⁄8 5 5 47⁄8

0.250 0.240 0.230 0.190

1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8

1.28 1.21 1.15 0.938

4.020 4.010 4.000 3.960

4 4 4 4

0.395 0.330 0.270 0.210

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

13⁄ 16 3⁄ 4 11⁄ 16 5⁄ 8

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 83

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

0.791 118 0.711 103 0.631 89.3 0.555 76.8 0.493 66.8 0.438 58.1 0.395 51.7 0.361 46.7

22.6 20.0 17.4 15.1 13.2 11.5 10.3 9.34

2.68 2.65 2.63 2.60 2.59 2.57 2.56 2.54

6.65 5.64 4.60

Fy, ksi 36

34.6 30.5 26.5 22.9 20.0 17.5 15.7 14.2

— — — — — — — —

2.01 1.98 1.94

10.1 8.59 7.01

— — —

56 50 44 38.5 34 30 27 24.5

5.2 5.8 6.5 7.4 8.4 9.4 10.6 11.6

28.6 24.5 20.8 17.4 14.9 12.9 11.1 10.0

6.40 5.56 4.77 4.04 3.49 3.04 2.64 2.39

1.32 1.29 1.27 1.24 1.22 1.21 1.19 1.18

1.21 1.13 1.06 0.990 0.932 0.884 0.836 0.807

13.4 11.4 9.65 8.06 6.85 5.87 5.05 4.52

22.5 19.5 16.5

11.2 12.5 13.6

10.2 8.84 7.71

2.47 2.16 1.93

1.24 1.24 1.26

0.907 0.876 0.869

4.65 3.99 3.48

0.413 0.359 0.305

15 13 11

14.8 17.0 18.4

9.28 7.86 6.88

2.24 1.91 1.72

1.45 1.44 1.46

1.10 1.06 1.07

4.01 3.39 3.02

0.380 0.330 0.282

8.35 7.05 5.71

2.87 2.44 1.99

1.37 1.36 1.33

4.42 3.75 3.05

— — 0.999

— 0.902 0.836

17.7 18.4 19.2 23.3

6.68 6.06 5.45 4.35

1.74 1.62 1.50 1.22

1.54 1.56 1.57 1.57

1.28 1.32 1.37 1.36

3.10 2.90 3.03 2.50

0.349 0.311 0.306 0.323

2.15 1.78 1.45 1.09

1.07 0.888 0.723 0.551

0.874 0.844 0.810 0.785

1.68 — 1.40 — 1.15 0.977 0.872 0.793

0.872 0.841 0.811 0.592

9.5 8.5 7.5 6

26.7 22.5 18.3

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 84

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from W shapes Dimensions

Stem

Area of Stem

Flange DisThickness tance tf k

Area

Depth of Tee d

Thickness tw

tw 2

Designation

in.2

in.

in.2

WT4×33.5 WT4×29 WT4×24 WT4×20 WT4×17.5 WT4×15.5

9.84 8.55 7.05 5.87 5.14 4.56

4.500 4.375 4.250 4.125 4.060 4.000

41⁄2 43⁄8 41⁄4 41⁄8 4 4

0.570 0.510 0.400 0.360 0.310 0.285

9⁄ 16 1⁄ 2 3⁄ 8 3⁄ 8 5⁄ 16 5⁄ 16

5⁄ 16 1⁄ 4 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16

2.56 2.23 1.70 1.48 1.26 1.14

8.280 8.220 8.110 8.070 8.020 7.995

81⁄4 81⁄4 81⁄8 81⁄8 8 8

0.935 0.810 0.685 0.560 0.495 0.435

15⁄ 16 13⁄ 16 11⁄ 16 9⁄ 16 1⁄ 2 7⁄ 16

17⁄16 15⁄16 13⁄16 11⁄16 1 15⁄ 16

WT4×14 WT4×12

4.12 3.54

4.030 3.965

4 4

0.285 0.245

5⁄ 16 1⁄ 4

3⁄ 16 1⁄ 8

1.15 0.971

6.535 6.495

61⁄2 61⁄2

0.465 0.400

7⁄ 16 3⁄ 8

15⁄ 16 7⁄ 8

WT4×10.5 WT4×9

3.08 2.63

4.140 4.070

41⁄8 41⁄8

0.250 0.230

1⁄ 4 1⁄ 4

1⁄ 8 1⁄ 8

1.03 0.936

5.270 5.250

51⁄4 51⁄4

0.400 0.330

3⁄ 8 5⁄ 16

13⁄ 16 3⁄ 4

WT4×7.5 WT4×6.5 WT4×5

2.22 1.92 1.48

4.055 3.995 3.945

4 4 4

0.245 0.230 0.170

1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8

0.993 0.919 0.671

4.015 4.000 3.940

4 4 4

0.315 0.255 0.205

5⁄ 16 1⁄ 4 3⁄ 16

3⁄ 4 11⁄ 16 5⁄ 8

WT3×12.5 WT4×10 WT4×7.5

3.67 2.94 2.21

3.190 3.100 2.995

31⁄4 31⁄8 3

0.320 0.260 0.230

5⁄ 16 1⁄ 4 1⁄ 4

3⁄ 16 1⁄ 8 1⁄ 8

1.02 0.806 0.689

6.080 6.020 5.990

61⁄8 6 6

0.455 0.365 0.260

7⁄ 16 3⁄ 8 1⁄ 4

13⁄ 16 3⁄ 4 5⁄ 8

WT3×8 WT4×6 WT4×4.5

2.37 1.78 1.34

3.140 3.015 2.950

31⁄8 3 3

0.260 0.230 0.170

1⁄ 4 1⁄ 4 3⁄ 16

1⁄ 8 1⁄ 8 1⁄ 8

0.816 0.693 0.502

4.030 4.000 3.940

4 4 4

0.405 0.280 0.215

3⁄ 8 1⁄ 4 3⁄ 16

3⁄ 4 5⁄ 8 9⁄ 16

WT2.5×9.5 WT4.5×8

2.77 2.34

2.575 2.505

25⁄8 21⁄2

0.270 0.240

1⁄ 4 1⁄ 4

1⁄ 8 1⁄ 8

0.695 0.601

5.030 5.000

5 5

0.430 0.360

7⁄ 16 3⁄ 8

13⁄ 16 3⁄ 4

WT2×6.5

1.91

2.080

21⁄8

0.280

1⁄ 4

1⁄ 8

0.582

4.060

0.345

3⁄ 8

11⁄ 16

Width bf in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

in.

STRUCTURAL TEES (WT, MT, ST)

1 - 85

STRUCTURAL TEES Cut from W shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

Fy, ksi 50

33.5 29 24 20 17.5 15.5

5.6 6.2 7.9 8.8 10.2 11.1

10.9 9.12 6.85 5.73 4.81 4.28

3.05 2.61 1.97 1.69 1.43 1.28

1.05 1.03 0.986 0.988 0.967 0.968

0.936 0.874 0.777 0.735 0.688 0.667

6.29 5.25 3.94 3.25 2.71 2.39

0.594 0.520 0.435 0.364 0.321 0.285

44.3 37.5 30.5 24.5 21.3 18.5

10.7 9.13 7.52 6.08 5.31 4.64

2.12 2.10 2.08 2.04 2.03 2.02

16.3 13.9 11.4 9.25 8.06 7.04

— — — — — —

14 12

11.1 12.9

4.22 3.53

1.28 1.08

1.01 0.999

0.734 0.695

2.38 1.98

0.315 0.273

10.8 9.14

3.31 2.81

1.62 1.61

5.05 4.29

— —

10.5 9

13.8 15.0

3.90 3.41

1.18 1.05

1.12 1.14

0.831 0.834

2.11 1.86

0.292 0.251

4.89 3.98

1.85 1.52

1.26 1.23

2.84 2.33

— —

7.5 6.5 5

14.0 15.0 20.2

3.28 2.89 2.15

1.07 0.974 0.717

1.22 1.23 1.20

0.998 1.03 0.953

1.91 1.74 1.27

0.276 0.240 0.188

1.70 1.37 1.05

0.849 0.876 0.683 0.843 0.532 0.841

1.33 — 1.08 — 0.828 0.913

12.5 10 7.5

7.8 9.6 10.8

2.28 1.76 1.41

0.886 0.693 0.577

0.789 0.774 0.797

0.610 0.560 0.558

1.68 1.29 1.03

0.302 0.244 0.185

8.53 6.64 4.66

2.81 2.21 1.56

4.28 3.36 2.37

— — —

8 6 4.5

9.6 10.8 14.6

1.69 0.685 1.32 0.564 0.950 0.408

0.844 0.861 0.842

0.676 0.677 0.623

1.25 1.01 0.720

0.294 0.222 0.170

2.21 1.50 1.10

1.10 0.966 0.748 0.918 0.557 0.905

1.70 1.16 0.858

— — —

9.5 8

7.0 7.9

1.01 0.485 0.850 0.413

0.605 0.601

0.487 0.458

0.967 0.798

0.275 0.234

4.56 3.75

1.82 1.50

1.28 1.27

2.76 2.29

— —

6.5

5.3

0.530 0.321

0.524

0.440

0.616

0.236

1.93

0.950 1.00

1.46

—

1.52 1.50 1.45

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

— — 0.735

1 - 86

DIMENSIONS AND PROPERTIES

bf tf

yp , y

STRUCTURAL TEES Cut from M shapes Dimensions

Designation

Area

Depth of Tee d

in.2

in.

Flange

Stem Area of Thickness tw 2 Stem tw

in.

1.73 1.59

6.000 5.990

6 6

0.177 0.160

3⁄ 16 3⁄ 16

1⁄ 8 1⁄ 16

1.06 3.065 0.958 3.065

31⁄8 31⁄8

0.225 0.210

1⁄ 4 1⁄ 4

9⁄ 16 1⁄ 2

1⁄ 4 1⁄ 4

— 1⁄ 2

MT5×4.5 MT5×4

1.32 1.18

5.000 4.980

5 5

0.157 0.141

3⁄ 16 3⁄ 16

1⁄ 8 1⁄ 16

0.785 2.690 0.702 2.690

23⁄4 23⁄4

0.206 0.182

3⁄ 16 3⁄ 16

9⁄ 16 7⁄ 16

3⁄ 16 3⁄ 16

— 3⁄ 8

MT4×3.25

0.958 4.000

0.135

1⁄ 8

1⁄ 16

0.540 2.281

21⁄4

0.189

3⁄ 16

1⁄ 2

3⁄ 16

—

0.316

5⁄ 16

3⁄ 16

0.790 5.003

0.416

7⁄ 16

7⁄ 8

7⁄ 16

7⁄ 8

2.500 21⁄2

in.

in.2

MT6×5.9 MT6×5.4

MT2.5×9.45* 2.78

in.

Width bf in.

Max. DisFlge. FasThickness tance Grip tener tf k in.

*This shape has tapered flanges, while all other MT shapes have parallel flanges.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 87

STRUCTURAL TEES Cut from M shapes Properties

yp , y

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

Fy, ksi 50

5.9 5.4

31.3 31.8

6.60 6.03

1.60 1.46

1.95 1.95

1.89 1.85

2.89 2.63

1.09 1.01

0.490 0.453

0.320 0.295

0.532 0.533

0.577 0.525

0.483 0.397

0.348 0.286

4.5 4

29.2 29.7

3.46 3.09

0.997 0.893

1.62 1.62

1.53 1.52

1.81 1.62

0.778 0.778

0.305 0.269

0.227 0.200

0.480 0.477

0.405 0.333

0.549 0.446

0.396 0.321

3.25

26.9

1.57

0.556

1.28

1.17

1.01

0.446

0.172

0.150

0.423

0.265

0.634

0.457

9.45

5.6

1.05

0.527

0.615

0.511

1.03

0.278

3.93

1.57

1.19

2.66

—

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 88

DIMENSIONS AND PROPERTIES

bf tf y, yp

STRUCTURAL TEES Cut from S shapes Dimensions

grip

Designation

Area

Depth of Tee d

in.2

in.

Flange

Stem Area of Thickness tw 2 Stem tw

Width bf

Max. DisFlge. FasThickness tance Grip tener tf k

in.

in.2

in.

7 13⁄ 16 ⁄16 5⁄ 5⁄ 8 16

9.80 7.60

8.050 8 7.870 77⁄8

1.090 1.090

11⁄16 11⁄16

2 2

11⁄8 11⁄8

1 1

3⁄ 8 5⁄ 16 1⁄ 4

8.94 7.50 6.00

7.245 71⁄4 7.125 71⁄8 7.000 7

0.870 0.870 0.870

7⁄ 8 7⁄ 8 7⁄ 8

13⁄4 13⁄4 13⁄4

7⁄ 8 7⁄ 8 7⁄ 8

1 1 1

7 13⁄ 16 ⁄16 3⁄ 11⁄ 16 8

8.12 6.70

7.200 71⁄4 7.060 7

0.920 0.920

15⁄ 16 15⁄ 16

13⁄4 13⁄4

15⁄ 16 15⁄ 16

1 1

in.

ST12×60.5 ST12×53

17.8 15.6

12.250 121⁄4 12.250 121⁄4

0.800 0.620

ST12×50 ST12×45 ST12×40

14.7 13.2 11.7

12.000 12.000 12.000

0.745 0.625 0.500

ST10×48 ST10×43

14.1 12.7

10.150 101⁄8 10.150 101⁄8

0.800 0.660

ST10×37.5 ST10×33

11.0 9.70

10.000 10.000

10 10

0.635 0.505

5⁄ 8 1⁄ 2

5⁄ 16 1⁄ 4

6.35 5.05

6.385 63⁄8 6.225 61⁄4

0.795 0.795

13⁄ 16 13⁄ 16

15⁄8 15⁄8

13⁄ 16 13⁄ 16

7⁄ 8 7⁄ 8

ST9×35 ST9×27.35

10.3 8.04

9.000 9.000

9 9

0.711 0.461

11⁄ 16 7⁄ 16

3⁄ 8 1⁄ 4

6.40 4.15

6.251 61⁄4 6.001 6

0.691 0.691

11⁄ 16 11⁄ 16

11⁄2 11⁄2

11⁄ 16 11⁄ 16

7⁄ 8 7⁄ 8

12 12 12

3⁄ 4 5⁄ 8 1⁄ 2

ST7.5×25 ST7.5×21.45

7.35 6.31

7.500 71⁄2 7.500 71⁄2

0.550 0.411

9⁄

5⁄ 16 1⁄ 4

4.13 3.08

5.640 55⁄8 5.501 51⁄2

0.622 0.622

5⁄ 8 5⁄ 8

13⁄8 13⁄8

9⁄ 16 9⁄ 16

3⁄ 4 3⁄ 4

ST6×25 ST6×20.4

7.35 6.00

6.000 6.000

6 6

0.687 0.462

11⁄ 16 7⁄ 16

3⁄ 8 1⁄ 4

4.12 2.77

5.477 51⁄2 5.252 51⁄4

0.659 0.659

11⁄ 16 11⁄ 16

17⁄16 17⁄16

11⁄ 16 5⁄ 8

3⁄ 4 3⁄ 4

ST6×17.5 ST6×15.9

5.15 4.68

6.000 6.000

6 6

0.428 0.350

7⁄

1⁄ 4 3⁄ 16

2.57 2.10

5.078 51⁄8 5.000 5

0.545 0.544

9⁄ 16 9⁄ 16

13⁄16 13⁄16

1⁄ 2 1⁄ 2

3⁄ 4 3⁄ 4

ST5×17.5 ST5×12.7

5.15 3.73

5.000 5.000

5 5

0.594 0.311

5⁄ 16 3⁄ 16

2.97 1.56

4.944 5 4.661 45⁄8

0.491 0.491

1⁄ 2 1⁄ 2

11⁄8 11⁄8

1⁄ 2 1⁄ 2

3⁄ 4 3⁄ 4

ST4×11.5 ST4×9.2

3.38 2.70

4.000 4.000

4 4

0.441 0.271

7⁄

16 1⁄ 4

1⁄ 4 1⁄ 8

1.76 1.08

4.171 41⁄8 4.001 4

0.425 0.425

7⁄ 16 7⁄ 16

1 1

7⁄ 16 7⁄ 16

3⁄ 4 3⁄ 4

ST3×8.625 ST3×6.25

2.53 1.83

3.000 3.000

3 3

0.465 0.232

7⁄

16 1⁄ 4

1⁄ 4 1⁄ 8

1.40 0.70

3.565 35⁄8 3.332 33⁄8

0.359 0.359

3⁄ 8 3⁄ 8

7⁄ 8 7⁄ 8

3⁄ 8 3⁄ 8

5⁄ 8 —

ST2.5×5

1.47

2.500 21⁄2

0.214

3⁄

1⁄ 8

0.535 3.004

0.326

5⁄ 16

13⁄ 16

5⁄ 16

—

ST2×4.75 ST2×3.85

1.40 1.13

2.000 2.000

0.326 0.193

5⁄

3⁄ 16 1⁄ 8

0.652 2.796 23⁄4 0.386 2.663 25⁄8

0.293 0.293

5⁄ 16 5⁄ 16

3⁄ 4 3⁄ 4

5⁄ 16 5⁄ 16

— —

ST1.5×3.75 ST1.5×2.85

1.10 0.835

1.500 11⁄2 1.500 11⁄2

3⁄ 16 1⁄ 8

0.523 2.509 21⁄2 0.255 2.330 23⁄8

0.260 0.260

1⁄ 4 1⁄ 4

11⁄ 16 11⁄ 16

1⁄ 4 1⁄ 4

— —

2 2

0.349 0.170

7⁄

16 3⁄ 8 5⁄ 8

5⁄

3⁄

3⁄ 8

3⁄

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STRUCTURAL TEES (WT, MT, ST)

1 - 89

STRUCTURAL TEES Cut from S shapes Properties

grip

y, yp

Nominal Wt. per ft lb

Axis X-X

h tw

Qs*

Axis Y-Y

in.4

in.3

in.

in.3

in.

in.4

in.3

in.

in.3

60.5 53

13.2 17

259 216

30.1 24.1

3.82 3.72

3.63 3.28

54.5 43.3

1.28 1.03

41.7 38.5

10.4 9.80

1.53 1.57

18.1 16.6

50 45 40

14.1 16.8 21.1

215 190 162

26.3 22.6 18.7

3.83 3.79 3.72

3.84 3.60 3.29

47.5 41.1 33.6

2.20 23.8 1.48 22.5 0.922 21.1

6.58 6.31 6.04

1.27 1.30 1.34

12.0 11.2 10.4

48 43

10.8 13.1

143 125

20.3 17.2

3.18 3.14

3.13 2.91

36.9 31.1

1.40 25.1 0.985 23.4

6.97 6.63

1.33 1.36

12.5 11.6

37.5 33

13.6 17

109 93.1

15.8 12.9

3.15 3.10

3.07 2.81

28.6 23.4

1.40 14.9 0.855 13.8

4.66 4.43

1.16 1.19

35 27.35

10.9 16.8

84.7 62.4

14.0 9.61

2.87 2.79

2.94 2.50

25.1 17.3

1.81 12.1 0.747 10.4

3.86 3.47

25 21.45

11.6 15.5

40.6 33.0

7.73 6.00

2.35 2.29

2.25 2.01

14.0 10.8

0.872 0.613

7.85 7.19

25 20.4

7 10.3

25.2 18.9

6.05 4.28

1.85 1.78

1.84 1.58

11.0 7.71

0.770 0.581

17.5 15.9

11.7 14.3

17.2 14.9

3.95 3.31

1.83 1.78

1.64 1.51

7.12 5.94

17.5 12.7

6.9 13.2

12.5 7.83

3.63 2.06

1.56 1.45

1.56 1.20

11.5 9.2

7.3 11.8

5.03 3.51

1.77 1.15

1.22 1.14

5 10

8.63 6.25

Fy, ksi 36

— —

— 0.907

— — — 0.937 0.878 0.695 — —

— —

8.37 7.70

— —

— 0.907

1.08 1.14

7.21 6.07

— —

— 0.922

2.78 2.61

1.03 1.07

5.01 4.54

— —

— 0.988

7.85 6.78

2.87 2.58

1.03 1.06

5.19 4.45

— —

0.548 0.485

4.94 4.68

1.95 1.87

0.980 1.00

3.41 3.22

— —

6.58 3.70

0.702 0.408

4.18 3.39

1.69 1.46

0.901 0.954

3.11 2.49

— —

1.15 0.941

3.19 2.07

0.447 0.341

2.15 1.86

1.03 0.798 0.932 0.831

1.84 1.59

— —

2.13 1.27

1.02 0.917 0.914 0.552 0.833 0.691

1.85 1.01

0.401 0.275

1.15 0.911

0.648 0.675 0.547 0.705

1.18 0.929

— —

8.7

0.681

0.353 0.681 0.569

0.650 0.243

0.608

0.405 0.643

0.685

—

4.75 3.85

4.3 7.3

0.470 0.316

0.325 0.580 0.553 0.203 0.528 0.448

0.592 0.255 0.381 0.209

0.451 0.382

0.323 0.569 0.287 0.581

0.566 0.483

— —

3.75 2.85

2.8 5.7

0.204 0.118

0.191 0.430 0.432 0.101 0.376 0.329

0.351 0.223 0.196 0.175

0.293 0.227

0.234 0.516 0.195 0.522

0.412 0.327

— —

*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

DOUBLE ANGLES

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 91

DOUBLE ANGLES

Properties of double angles in contact and separated are listed in the following tables. Each table shows properties of double angles in contact, and the radius of gyration about the Y-Y axis when the legs of the angles are separated. Values of Qs are given for Fy = 36 ksi and Fy = 50 ksi for those angles exceeding the width-thickness ratio 位r of LRFD Specification Section B5. Since the cross section is comprised entirely of unstiffened elements, Qa = 1.0 and Q = Qs, for all _angle sections. The Flexural-Torsional Properties Table lists the dimensional values (J, ro, and H) needed for checking flexural-torsional buckling. Use of Table

The table may be used as follows for checking the limit states of (1) flexural buckling and (2) flexural-torsional buckling. The lower of the two limit states must be used for design. See also Part 3 of this LRFD Manual. (1) Flexural Buckling

The design compressive strength for this limit state_ is given by LRFD Specification Sections E3 and E4. This involves calculations with J, ro, and H. These torsional constants can be obtained by summing the respective values for single angles listed in the Flexural-Torsional Properties Tables in Part 1 of this Manual.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Y X

DOUBLE ANGLES Two equal leg angles Properties of sections

y, yp

s Y

Wt. Area of per ft 2 Angles 2 Angles Designation

Axis X-X

I 4

in.

r 3

yp 3

in.

L8×8×11⁄8 L8×8×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×11⁄2

114 102 90.0 77.8 65.4 52.8

33.5 30.0 26.5 22.9 19.2 15.5

195 177 159 139 118 97.3

35.1 31.6 28.0 24.4 20.6 16.7

2.42 2.44 2.45 2.47 2.49 2.50

2.41 2.37 2.32 2.28 2.23 2.19

63.2 56.9 50.5 43.9 37.1 30.1

1.05 0.938 0.827 0.715 0.601 0.484

L6×6×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×11⁄2 L8×8×13⁄8

74.8 66.2 57.4 48.4 39.2 29.8

22.0 19.5 16.9 14.2 11.5 8.72

70.9 63.8 56.3 48.3 39.8 30.8

17.1 15.3 13.3 11.3 9.23 7.06

1.80 1.81 1.83 1.84 1.86 1.88

1.86 1.82 1.78 1.73 1.68 1.64

30.9 27.5 24.0 20.4 16.6 12.7

0.917 0.811 0.703 0.592 0.479 0.363

L5×5×7⁄8 L5×5×3⁄4 L5×5×1⁄2 L5×5×3⁄8 L5×5×5⁄16

54.4 47.2 32.4 24.6 20.6

16.0 13.9 9.50 7.22 6.05

35.5 31.5 22.5 17.5 14.8

10.3 9.06 6.31 4.84 4.08

1.49 1.51 1.54 1.56 1.57

1.57 1.52 1.43 1.39 1.37

18.7 16.3 11.4 8.72 7.35

0.798 0.694 0.475 0.361 0.303

L4×4×3⁄4 L5×5×5⁄8 L5×5×1⁄2 L5×5×3⁄8 L5×5×5⁄16 L5×5×1⁄4

37.0 31.4 25.6 19.6 16.4 13.2

10.9 9.22 7.50 5.72 4.80 3.88

15.3 13.3 11.1 8.72 7.43 6.08

5.62 4.80 3.95 3.05 2.58 2.09

1.19 1.20 1.22 1.23 1.24 1.25

1.27 1.23 1.18 1.14 1.12 1.09

10.1 8.66 7.12 5.49 4.64 3.77

0.680 0.576 0.469 0.357 0.300 0.242

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 93

DOUBLE ANGLES Two equal leg angles Properties of sections

Y X

y, yp

s Y

Qs*

Axis Y-Y Radii of Gyration Back to Back of Angles, in.

Angles in Contact

Angles Separated

3⁄ 8

3⁄ 4

Fy = 36 ksi

Fy = 50 ksi

Fy = 36 ksi

Fy = 50 ksi

L8×8×11⁄8 L8×8×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×11⁄2

3.42 3.40 3.38 3.36 3.34 3.32

3.55 3.53 3.51 3.49 3.47 3.45

3.69 3.67 3.64 3.62 3.60 3.58

— — — — — 0.995

— — — — — 0.921

— — — — 0.997 0.911

— — — — 0.935 0.834

L6×6×1 L8×8×17⁄8 L8×8×13⁄4 L8×8×15⁄8 L8×8×11⁄2 L8×8×13⁄8

2.59 2.57 2.55 2.53 2.51 2.49

2.73 2.70 2.68 2.66 2.64 2.62

2.87 2.85 2.82 2.80 2.78 2.75

— — — — — 0.995

— — — — — 0.921

— — — — — 0.911

— — — — 0.961 0.834

L5×5×7⁄8 L5×5×3⁄4 L5×5×1⁄2 L5×5×3⁄8 L5×5×5⁄16

2.16 2.14 2.10 2.09 2.08

2.30 2.28 2.24 2.22 2.21

2.45 2.42 2.38 2.35 2.34

— — — — 0.995

— — — — 0.921

— — — 0.982 0.911

— — — 0.919 0.834

L4×4×3⁄4 L5×5×5⁄8 L5×5×1⁄2 L5×5×3⁄8 L5×5×5⁄16 L5×5×1⁄4

1.74 1.72 1.70 1.68 1.67 1.66

1.88 1.86 1.83 1.81 1.80 1.79

2.03 2.00 1.98 1.95 1.94 1.93

— — — — — 0.995

— — — — — 0.921

— — — — 0.997 0.911

— — — — 0.935 0.834

Designation

*Where no value ofQs is shown, the angles comply with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

DOUBLE ANGLES Two equal leg angles Properties of sections

Y X

y, yp

s Y

Wt. Area of per ft 2 Angles 2 Angles 2

Axis X-X

I 4

r 3

yp 3

Designation

in.

L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×5⁄16 L31⁄2×31⁄2×1⁄4

17.0 14.4 11.6

4.97 4.18 3.38

5.73 4.90 4.02

2.30 1.95 1.59

1.07 1.08 1.09

1.01 0.990 0.968

4.15 3.52 2.86

0.355 0.299 0.241

L3×3×1⁄2 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4 L3×3×3⁄16

18.8 14.4 12.2 9.80 7.42

5.50 4.22 3.55 2.88 2.18

4.43 3.52 3.02 2.49 1.92

2.14 1.67 1.41 1.15 0.882

0.898 0.913 0.922 0.930 0.939

0.932 0.888 0.865 0.842 0.820

3.87 3.00 2.55 2.08 1.59

0.458 0.352 0.296 0.240 0.182

L21⁄2×21⁄2×3⁄8 L31⁄2×31⁄2×5⁄16 L31⁄2×31⁄2×1⁄4 L31⁄2×31⁄2×3⁄16

11.8 10.0 8.20 6.14

3.47 2.93 2.38 1.80

1.97 1.70 1.41 1.09

1.13 0.964 0.789 0.606

0.753 0.761 0.769 0.778

0.762 0.740 0.717 0.694

2.04 1.74 1.42 1.09

0.347 0.293 0.238 0.180

9.40 7.84 6.38 4.88 3.30

2.72 2.30 1.88 1.43 0.960

0.958 0.832 0.695 0.545 0.380

0.702 0.681 0.494 0.381 0.261

0.594 0.601 0.609 0.617 0.626

0.636 0.614 0.592 0.569 0.546

1.27 1.08 0.890 0.686 0.471

0.340 0.288 0.234 0.179 0.121

L2×2×3⁄8 L3×3×5⁄16 L3×3×1⁄4 L3×3×3⁄16 L3×3×1⁄8

in.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 95

DOUBLE ANGLES Two equal leg angles Properties of sections

Y X

y, yp

s Y

Qs*

Axis Y-Y Radii of Gyration

Angles in Contact

Angles Separated

3⁄ 4

Fy = 36 ksi

Fy = 50 ksi

Fy = 36 ksi

Fy = 50 ksi

Back to Back of Angles, in. 3⁄ 8

Designation

L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×5⁄16 L31⁄2×31⁄2×1⁄4

1.48 1.47 1.46

1.61 1.60 1.59

1.75 1.74 1.73

— — —

— — 0.982

— — 0.965

— 0.986 0.897

L3×3×1⁄2 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4 L3×3×3⁄16

1.29 1.27 1.26 1.26 1.25

1.43 1.41 1.40 1.39 1.38

1.59 1.56 1.55 1.53 1.52

— — — — 0.995

— — — — 0.921

— — — — 0.911

— — — 0.961 0.834

L21⁄2×21⁄2×3⁄8 L21⁄2×21⁄2×5⁄16 L21⁄2×21⁄2×1⁄4 L21⁄2×21⁄2×3⁄16

1.07 1.06 1.05 1.04

1.21 1.20 1.19 1.18

1.36 1.35 1.34 1.32

— — — —

— — — 0.982

— — — 0.919

L2×2×3⁄8 L2×2×5⁄16 L2×2×1⁄4 L2×2×3⁄16 L2×2×1⁄8

0.870 0.859 0.849 0.840 0.831

1.01 1.00 0.989 0.977 0.965

1.17 1.16 1.14 1.13 1.11

— — — — 0.995

— — — — 0.921

— — — — 0.911

— — — — 0.834

*Where no value ofQs is shown, the angles comply with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Long legs back to back

Wt. Area of per ft 2 Angles 2 Angles Designation

Axis X-X

I 4

in.

r 3

yp 3

in.

L8×6×1 L8×6×13⁄4 L8×6×11⁄2

88.4 67.6 46.0

26.0 19.9 13.5

161 126 88.6

30.2 23.3 16.0

2.49 2.53 2.56

2.65 2.56 2.47

54.5 42.2 29.1

1.50 1.38 1.25

L8×4×1 L8×6×13⁄4 L8×6×11⁄2

74.8 57.4 39.2

22.0 16.9 11.5

139 109 77.0

28.1 21.8 15.0

2.52 2.55 2.59

3.05 2.95 2.86

48.5 37.7 26.1

2.50 2.38 2.25

L7×4×3⁄4 L7×4×1⁄2 L7×4×3⁄8

52.4 35.8 27.2

15.4 10.5 7.97

75.6 53.3 41.1

16.8 11.6 8.88

2.22 2.25 2.27

2.51 2.42 2.37

29.6 20.6 15.7

1.88 1.75 1.69

L6×4×3⁄4 L7×4×5⁄8 L7×4×1⁄2 L7×4×3⁄8

47.2 40.0 32.4 24.6

13.9 11.7 9.50 7.22

49.0 42.1 34.8 26.9

12.5 10.6 8.67 6.64

1.88 1.90 1.91 1.93

2.08 2.03 1.99 1.94

22.3 19.0 15.6 11.9

1.38 1.31 1.25 1.19

L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

23.4 19.6

6.84 5.74

25.7 21.8

6.49 5.47

1.94 1.95

2.04 2.01

11.5 9.70

1.44 1.41

L5×31⁄2×3⁄4 L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

39.6 27.2 20.8 17.4

11.6 8.00 6.09 5.12

27.8 20.0 15.6 13.2

8.55 5.97 4.59 3.87

1.55 1.58 1.60 1.61

1.75 1.66 1.61 1.59

15.3 10.8 8.28 6.99

1.13 1.00 0.938 0.906

L5×3×1⁄2 L7×4×3⁄8 L7×4×5⁄16 L7×4×1⁄4

25.6 19.6 16.4 13.2

7.50 5.72 4.80 3.88

18.9 14.7 12.5 10.2

5.82 4.47 3.77 3.06

1.59 1.61 1.61 1.62

1.75 1.70 1.68 1.66

10.3 7.95 6.71 5.45

1.25 1.19 1.16 1.13

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 97

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Long legs back to back Y

Qs*

Axis Y-Y Radii of Gyration Back to Back of Angles, in.

Angles in Contact

Angles Separated

3⁄ 8

3⁄ 4

Fy = 36 ksi

Fy = 50 ksi

Fy = 36 ksi

Fy = 50 ksi

L8×6×1 L8×6×13⁄4 L8×6×11⁄2

2.39 2.35 2.32

2.52 2.48 2.44

2.66 2.62 2.57

— — —

— — 0.911

— — 0.834

L8×4×1 L8×4×13⁄4 L8×4×11⁄2

1.47 1.42 1.38

1.61 1.55 1.51

1.75 1.69 1.64

— — —

— — 0.911

— — 0.834

L7×4×3⁄4 L7×4×1⁄2 L7×4×3⁄8

1.48 1.44 1.43

1.62 1.57 1.55

1.76 1.71 1.68

— — —

— 0.965 0.839

— 0.897 0.750

L6×4×3⁄4 L7×4×5⁄8 L7×4×1⁄2 L7×4×3⁄8

1.55 1.53 1.51 1.5

1.69 1.67 1.64 1.62

1.83 1.81 1.78 1.76

— — — —

— — — 0.911

— — 0.961 0.834

L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

1.26 1.26

1.39 1.38

1.53 1.51

— —

0.911 0.825

0.834 0.733

L5×31⁄2×3⁄4 L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

1.40 1.35 1.34 1.33

1.53 1.49 1.46 1.45

1.68 1.63 1.60 1.59

— — — —

— — 0.982 0.911

— — 0.919 0.834

L5×3×1⁄2 L7×4×3⁄8 L7×4×5⁄16 L7×4×1⁄4

1.12 1.10 1.09 1.08

1.25 1.23 1.22 1.21

1.40 1.37 1.36 1.34

— — — —

— 0.982 0.911 0.804

— 0.919 0.834 0.708

Designation

*Where no value of Qs is shown the angles comply with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Long legs back to back

Wt. Area of per ft 2 Angles 2 Angles Designation

Axis X-X

I 4

in.

r 3

yp 3

in.

L4×31⁄2×1⁄2 L4×31⁄2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

23.8 18.2 15.4 12.4

7.00 5.34 4.49 3.63

10.6 8.35 7.12 5.83

3.87 2.99 2.53 2.05

1.23 1.25 1.26 1.27

1.25 1.21 1.18 1.16

7.00 5.42 4.59 3.73

0.500 0.438 0.406 0.375

L4×3×1⁄2 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4

22.2 17.0 14.4 11.6

6.50 4.97 4.18 3.38

10.1 7.93 6.76 5.54

3.78 2.92 2.47 2.00

1.25 1.26 1.27 1.28

1.33 1.28 1.26 1.24

6.81 5.28 4.47 3.63

0.750 0.688 0.656 0.625

L31⁄2×3×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

15.8 13.2 10.8

4.59 3.87 3.13

5.45 4.66 3.83

2.25 1.91 1.55

1.09 1.10 1.11

1.08 1.06 1.04

4.08 3.46 2.82

0.438 0.406 0.375

L31⁄2×21⁄2×3⁄8 L31⁄2×21⁄2×1⁄4

14.4 9.80

4.22 2.88

5.12 3.60

2.19 1.51

1.10 1.12

1.16 1.11

3.94 2.73

0.688 0.625

L3×21⁄2×3⁄8 L4×31⁄2×1⁄4 L4×31⁄2×5⁄16

13.2 9.00 6.77

3.84 2.63 1.99

3.31 2.35 1.81

1.62 1.12 0.859

0.928 0.945 0.954

0.956 0.911 0.888

2.93 2.04 1.56

0.438 0.375 0.344

L3×2×3⁄8 L4×3×5⁄16 L4×3×1⁄4 L4×3×3⁄16

11.8 10.0 8.20 6.14

3.47 2.93 2.38 1.80

3.06 2.63 2.17 1.68

1.56 1.33 1.08 0.830

0.940 0.948 0.957 0.966

1.04 1.02 0.993 0.970

2.79 2.38 1.95 1.49

0.688 0.656 0.625 0.594

L21⁄2×2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4 L4×31⁄2×3⁄16

10.6 9.00 7.24 5.50

3.09 2.62 2.13 1.62

1.82 1.58 1.31 1.02

1.09 0.932 0.763 0.586

0.768 0.776 0.784 0.793

0.831 0.809 0.787 0.764

1.97 1.69 1.38 1.06

0.438 0.406 0.375 0.344

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 99

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Long legs back to back Y

Qs*

Axis Y-Y Radii of Gyration

Angles in Contact

Angles Separated

3⁄ 4

Fy = 36 ksi

Fy = 50 ksi

Fy = 36 ksi

Fy = 50 ksi

Back to Back of Angles, in. Designation

3⁄ 8

L4×31⁄2×1⁄2 L4×31⁄2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

1.44 1.42 1.42 1.41

1.58 1.56 1.55 1.54

1.72 1.70 1.69 1.67

— — — —

— — — 0.982

— — 0.997 0.911

— — 0.935 0.834

L4×3×1⁄2 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4

1.20 1.18 1.17 1.16

1.33 1.31 1.30 1.29

1.48 1.45 1.44 1.43

— — — —

— — 0.997 0.911

— — 0.935 0.834

L31⁄2×3×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

1.22 1.21 1.20

1.36 1.35 1.33

1.50 1.49 1.48

— — —

— — 0.965

— 0.986 0.897

L31⁄2×21⁄2×3⁄8 L31⁄2×21⁄2×1⁄4

0.976 0.958

1.11 1.09

1.26 1.23

— —

— 0.965

— 0.897

L3×21⁄2×3⁄8 L4×31⁄2×1⁄4 L4×31⁄2×5⁄16

1.02 1.00 0.993

1.16 1.13 1.12

1.31 1.28 1.27

— — —

— — 0.911

— 0.961 0.834

L3×2×3⁄8 L4×3×5⁄16 L4×3×1⁄4 L4×3×3⁄16

0.777 0.767 0.757 0.749

0.917 0.903 0.891 0.879

1.07 1.06 1.04 1.03

— — — —

— — — 0.911

— — 0.961 0.834

L21⁄2×2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4 L4×31⁄2×3⁄16

0.819 0.809 0.799 0.790

0.961 0.948 0.935 0.923

1.12 1.10 1.09 1.07

— — — —

— — — 0.982

— — — 0.919

*Where no value of Qs is shown, the angles comply with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 100

DIMENSIONS AND PROPERTIES

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Short legs back to back

Wt. Area of per ft 2 Angles 2 Angles Designation

Axis X-X

I 4

in.

r 3

yp 3

in.

L8×6×1 L8×6×13⁄4 L8×6×11⁄2

88.4 67.6 46.0

26.0 19.9 13.5

77.6 61.4 43.4

17.8 13.8 9.58

1.73 1.76 1.79

1.65 1.56 1.47

32.4 24.9 17.0

0.813 0.621 0.422

L8×4×1 L8×6×13⁄4 L8×6×11⁄2

74.8 57.4 39.2

22.0 16.9 11.5

23.3 18.7 13.5

7.88 6.14 4.29

1.03 1.05 1.08

1.05 0.953 0.859

15.4 11.6 7.80

0.688 0.527 0.359

L7×4×3⁄4 L5×3×1⁄2 L5×3×3⁄8

52.4 35.8 27.2

15.4 10.5 7.97

18.1 13.1 10.2

6.05 4.23 3.26

1.09 1.11 1.13

1.01 0.917 0.870

11.3 7.66 5.80

0.549 0.375 0.285

L6×4×3⁄4 L5×3×5⁄8 L5×3×1⁄2 L5×3×3⁄8

47.2 40.0 32.4 24.6

13.9 11.7 9.50 7.22

17.4 15.0 12.5 9.81

5.94 5.07 4.16 3.21

1.12 1.13 1.15 1.17

1.08 1.03 0.987 0.941

10.9 9.24 7.50 5.71

0.578 0.488 0.396 0.301

L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

23.4 19.6

6.84 5.74

6.68 5.70

2.46 2.08

0.988 0.996

0.787 0.763

4.41 3.70

0.285 0.239

L5×31⁄2×3⁄4 L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

39.6 27.2 20.8 17.4

11.6 8.00 6.09 5.12

11.1 8.10 6.37 5.44

4.43 3.12 2.41 2.04

0.977 1.01 1.02 1.03

0.996 0.906 0.861 0.838

8.20 5.65 4.32 3.63

0.581 0.400 0.305 0.256

L5×3×1⁄2 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

25.6 19.6 16.4 13.2

7.50 5.72 4.80 3.88

5.16 4.08 3.49 2.88

2.29 1.78 1.51 1.23

0.829 0.845 0.853 0.861

0.750 0.704 0.681 0.657

4.22 3.21 2.69 2.17

0.375 0.286 0.240 0.194

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 101

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Short legs back to back

Qs*

Axis Y-Y Radii of Gyration Back to Back of Angles, in.

Angles in Contact

Angles Separated

3⁄ 8

3⁄ 4

Fy = 36 ksi

Fy = 50 ksi

Fy = 36 ksi

Fy = 50 ksi

L8×6×1 L8×6×13⁄4 L8×6×11⁄2

3.64 3.60 3.56

3.78 3.74 3.69

3.92 3.88 3.83

— — 0.995

— — 0.921

— — 0.911

— — 0.834

L8×4×1 L8×4×13⁄4 L8×4×11⁄2

3.95 3.90 3.86

4.10 4.05 4.00

4.25 4.19 4.14

— — 0.995

— — 0.921

— — 0.911

— — 0.834

L7×4×3⁄4 L7×4×1⁄2 L7×4×3⁄8

3.35 3.30 3.28

3.49 3.44 3.42

3.64 3.59 3.56

— — 0.926

— 0.982 0.838

— 0.965 0.839

0.897 0.750

L6×4×3⁄4 L7×4×5⁄8 L7×4×1⁄2 L7×4×3⁄8

2.80 2.78 2.76 2.74

2.94 2.92 2.90 2.87

3.09 3.06 3.04 3.02

— — — 0.995

— — — 0.921

— — — 0.911

— — 0.961 0.834

L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

2.81 2.80

2.95 2.94

3.09 3.08

0.995 0.912

0.921 0.822

0.911 0.825

0.834 0.733

L5×31⁄2×3⁄4 L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

2.33 2.29 2.27 2.26

2.48 2.43 2.41 2.39

2.63 2.57 2.55 2.54

— — — 0.995

— — — 0.921

— — 0.982 0.911

— — 0.919 0.834

L5×3×1⁄2 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

2.36 2.34 2.33 2.32

2.50 2.48 2.47 2.46

2.65 2.63 2.61 2.60

— — 0.995 0.891

— — 0.921 0.797

— 0.982 0.911 0.804

— 0.919 0.834 0.708

Designation

*Where no value of Qs is shown, the angles comply with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 102

DIMENSIONS AND PROPERTIES

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Short legs back to back

Wt. Area of per ft 2 Angles 2 Angles Designation

Axis X-X

I 4

in.

r 3

yp 3

in.

L4×31⁄2×1⁄2 L4×31⁄2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

23.8 18.2 15.4 12.4

7.00 5.34 4.49 3.63

7.58 5.97 5.10 4.19

3.03 2.35 1.99 1.62

1.04 1.06 1.07 1.07

1.00 0.955 0.932 0.909

5.47 4.21 3.56 2.89

0.438 0.334 0.281 0.227

L4×3×1⁄2 L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4

22.2 17.0 14.4 11.6

6.50 4.97 4.18 3.38

4.85 3.84 3.29 2.71

2.23 1.73 1.47 1.20

0.864 0.879 0.887 0.896

0.827 0.782 0.759 0.736

4.06 3.11 2.63 2.13

0.406 0.311 0.261 0.211

L31⁄2×3×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

15.8 13.2 10.8

4.59 3.87 3.13

3.69 3.17 2.61

1.70 1.44 1.18

0.897 0.905 0.914

0.830 0.808 0.785

3.06 2.59 2.10

0.328 0.276 0.223

L31⁄2×21⁄2×3⁄8 L31⁄2×21⁄2×1⁄4

14.4 9.80

4.22 2.88

2.18 1.55

1.18 0.824

0.719 0.735

0.660 0.614

2.15 1.47

0.301 0.205

L3×21⁄2×3⁄8 L4×31⁄2×1⁄4 L4×31⁄2×3⁄16

13.2 9.00 6.77

3.84 2.63 1.99

2.08 1.49 1.15

1.16 0.808 0.620

0.736 0.753 0.761

0.706 0.661 0.638

2.10 1.45 1.11

0.320 0.219 0.166

L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16

11.8 10.0 8.20 6.14

3.47 2.93 2.38 1.80

1.09 0.941 0.784 0.613

0.743 0.634 0.520 0.401

0.559 0.567 0.574 0.583

0.539 0.516 0.493 0.470

1.37 1.16 0.937 0.713

0.289 0.244 0.198 0.150

L21⁄2×2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4 L4×31⁄2×3⁄16

10.6 9.00 7.24 5.50

3.09 2.62 2.13 1.62

1.03 0.893 0.745 0.583

0.725 0.620 0.509 0.392

0.577 0.584 0.592 0.600

0.581 0.559 0.537 0.514

1.32 1.12 0.915 0.701

0.309 0.262 0.213 0.162

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DOUBLE ANGLES

1 - 103

DOUBLE ANGLES Two unequal leg angles Properties of sections

Y X

y, yp

Short legs back to back

Qs*

Axis Y-Y Radii of Gyration Back to Back of Angles, in.

Angles in Contact

Angles Separated

3⁄ 8

3⁄ 4

Fy = 36 ksi

Fy = 50 ksi

Fy = 36 ksi

Fy = 50 ksi

L4×31⁄2×1⁄2 L4×31⁄2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

1.76 1.74 1.73 1.72

1.89 1.87 1.86 1.85

2.04 2.01 2.00 1.99

— — — 0.995

— — — 0.921

— — 0.997 0.911

— — 0.935 0.834

L4×3×1⁄2 L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4

1.82 1.80 1.79 1.78

1.96 1.94 1.93 1.92

2.11 2.08 2.07 2.06

— — — 0.995

— — — 0.921

— — 0.997 0.911

— — 0.935 0.834

L31⁄2×3×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4

1.53 1.52 1.52

1.67 1.66 1.65

1.82 1.80 1.79

— — —

— — 0.982

— — 0.965

— 0.986 0.897

L31⁄2×21⁄2×3⁄8 L31⁄2×21⁄2×1⁄4

1.60 1.58

1.74 1.72

1.89 1.86

— —

— 0.982

— 0.965

— 0.897

L3×21⁄2×3⁄8 L4×31⁄2×1⁄4 L4×31⁄2×3⁄16

1.33 1.31 1.30

1.47 1.45 1.44

1.62 1.60 1.58

— — 0.995

— — 0.921

— — 0.911

— 0.961 0.834

L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16

1.40 1.39 1.38 1.37

1.55 1.53 1.52 1.51

1.70 1.68 1.67 1.66

— — — 0.995

— — — 0.921

— — — 0.911

— — 0.961 0.834

L21⁄2×2×3⁄8 L4×31⁄2×5⁄16 L4×31⁄2×1⁄4 L4×31⁄2×3⁄16

1.13 1.12 1.11 1.10

1.28 1.26 1.25 1.24

1.43 1.42 1.40 1.39

— — — —

— — — 0.982

— — — 0.911

Designation

*Where no value of Qs is shown the angles comply with LRFD Specification Section E2.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 104

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 105

COMBINATION SECTIONS

Standard rolled shapes are frequently combined to produce efficient and economical structural members for special applications. Experience has established a demand for certain combinations. When properly sized and connected to satisfy the design and specification criteria, these members may be used as struts, lintels, eave struts, and light crane and trolley runways. The W section with channel attached to the web is not recommended for use as a trolley or crane runway member. Properties of several combined sections are tabulated for those combinations that experience has proven to be in popular demand.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 106

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS W shapes and channels Properties of sections

y , yp 1

Beam

Channel

Axis X-X

Total Weight per ft

Total Area

in.2

S1 = I / y1

S2 = I / y2

in.4

in.3

in.

W12×26 W ×26

C10×15.3 C12×20.7

41.3 46.7

12.14 13.74

299 318

36.3 36.8

70.5 82.2

4.96 4.81

W14×30 W ×30

C10×15.3 C12×20.7

45.3 50.7

13.34 14.94

420 448

46.1 46.8

84.6 98.3

5.61 5.47

W16×36 W ×36

C12×20.7 C15×33.9

56.7 69.9

16.69 20.56

670 748

62.8 64.6

123 160

6.34 6.03

W18×50 W ×50

C12×20.7 C15×33.9

70.7 83.9

20.79 24.66

1120 1250

97.4 100

166 211

7.34 7.11

W21×62 W ×62 W ×68 W ×68

C12×20.7 C15×33.9 C12×20.7 C15×33.9

82.7 95.9 88.7 101.9

24.39 28.26 26.09 29.96

1800 2000 1960 2180

138 142 152 156

218 272 232 287

8.59 8.41 8.68 8.52

W24×68 W ×68 W ×84 W ×84

C12×20.7 C15×33.9 C12×20.7 C15×33.9

88.7 101.9 104.7 117.9

26.19 30.06 30.79 34.66

2450 2720 3040 3340

168 173 212 217

258 321 303 368

9.67 9.50 9.93 9.82

W27×84 W ×94

C15×33.9 C15×33.9

117.9 127.9

34.76 37.66

4050 4530

237 268

404 436

10.8 11.0

W30×99 W ×99 W ×116 W ×116

C15×33.9 C18×42.7 C15×33.9 C18×42.7

132.9 141.7 149.9 158.7

39.06 41.70 44.16 46.80

5540 5830 6590 6900

300 304 360 365

480 533 544 599

11.9 11.8 12.2 12.1

W33×118 W ×118 W ×141 W ×141

C15×33.9 C18×42.7 C15×33.9 C18×42.7

151.9 160.7 174.9 183.7

44.66 47.30 51.56 54.20

7900 8280 9580 10000

395 400 484 490

596 656 689 751

13.3 13.2 13.6 13.6

W36×150 W ×150

C15×33.9 C18×42.7

183.9 192.7

54.16 56.80

11500 12100

546 553

765 832

14.6 14.6

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 107

COMBINATION SECTIONS W shapes and channels Properties of sections

y , yp 1

Axis X-X

y1 Beam

Axis Y-Y

yp 3

Channel

in.

W12×26 W30×26

C10×15.3 C12×20.7

8.22 8.63

W14×30 W30×30

C10×15.3 C12×20.7

W16×36 W30×36

I 4

in.

in.3

in.

47.0 48.8

11.30 11.55

84.7 146

16.9 24.4

2.64 3.26

24.0 33.6

9.12 9.57

60.5 62.3

12.56 12.87

87.0 149

17.4 24.8

2.55 3.15

24.8 34.4

C12×20.7 C15×33.9

10.67 11.58

83.6 88.6

14.56 15.21

154 340

25.6 45.3

3.03 4.06

36.3 61.3

W18×50 W30×50

C12×20.7 C15×33.9

11.51 12.47

128 134

16.08 16.90

169 355

28.2 47.3

2.85 3.79

42.0 67.0

W21×62 W30×62 W30×68 W30×68

C12×20.7 C15×33.9 C12×20.7 C15×33.9

13.01 14.06 12.93 13.95

182 190 200 208

18.06 19.36 17.60 19.32

187 373 194 380

31.1 49.7 32.3 50.6

2.77 3.63 2.72 3.56

47.2 72.2 49.8 74.8

W24×68 W30×68 W30×84 W30×84

C12×20.7 C15×33.9 C12×20.7 C15×33.9

14.53 15.67 14.35 15.40

224 234 275 288

19.15 21.66 18.49 21.61

199 385 223 409

33.2 51.4 37.2 54.6

2.76 3.58 2.69 3.44

50.0 75.0 58.1 83.1

W27×84 W27×94

C15×33.9 C15×33.9

17.07 16.92

320 357

23.86 23.56

421 439

56.1 58.5

3.48 3.41

83.6 89.2

W30×99 W30×99 W30×116 W30×116

C15×33.9 C18×42.7 C15×33.9 C18×42.7

18.51 19.18 18.30 18.93

408 418 480 492

24.34 26.43 23.77 26.04

443 682 479 718

59.1 75.8 63.9 79.8

3.37 4.04 3.29 3.92

89.1 113 99.6 124

W33×118 W30×118 W30×141 W30×141

C15×33.9 C18×42.7 C15×33.9 C18×42.7

20.01 20.69 19.79 20.42

529 544 634 652

25.43 27.77 24.83 26.96

502 741 561 800

66.9 82.3 74.8 88.9

3.35 3.96 3.30 3.84

102 126 117 141

W36×150 W30×150

C15×33.9 C18×42.7

21.15 21.81

716 738

25.84 27.91

585 824

78.0 91.6

3.29 3.81

121 145

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 108

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS S shapes and channels Properties of sections

y , yp 1

Beam

Channel

Axis X-X

Total Weight per ft

Total Area

in.2

S1 = I / y1

S2 = I / y2

in.4

in.3

in.

S10×25.4

C8×11.5 C10×15.3

36.9 40.7

10.84 11.95

176 186

27.2 27.6

46.6 52.9

4.02 3.94

S12×31.8

C8×11.5 C10×15.3

43.3 47.1

12.73 13.84

299 316

39.8 40.4

63.2 71.4

4.84 4.78

S15×42.9

C8×11.5 C10×15.3

54.4 58.2

15.98 17.09

585 616

64.9 65.8

94.2 105

6.05 6.01

S20×66

C10×15.3 C12×20.7

81.3 86.7

23.89 25.49

1530 1620

130 132

181 203

8.00 7.97

S24×80

C10×15.3 C12×20.7

95.3 100.7

27.99 29.59

2610 2750

188 191

252 278

9.66 9.65

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 109

COMBINATION SECTIONS S shapes and channels Properties of sections

y , yp 1

Axis X-X

y1 Beam

Axis Y-Y

yp 3

I 4

in.

in.3

Channel

in.

S10×25.4

C8×11.5 C10×15.3

6.45 6.73

35.7 36.9

8.81 9.02

39.4 74.2

9.8 14.8

1.91 2.49

14.5 20.8

S12×31.8

C8×11.5 C10×15.3

7.50 7.82

52.6 53.9

10.30 10.61

42.0 76.8

10.5 15.4

1.82 2.36

16.0 22.2

S15×42.9

C8×11.5 C10×15.3

9.01 9.37

85.7 88.2

11.58 12.77

47.0 81.8

11.8 16.4

1.71 2.19

18.6 24.9

S20×66

C10×15.3 C12×20.7

11.81 12.29

171 178

14.41 15.99

95.1 157

19.0 26.1

2.00 2.48

31.2 40.8

S24×80

C10×15.3 C12×20.7

13.86 14.38

244 254

16.46 18.05

110 171

21.9 28.5

1.98 2.41

36.6 46.2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 110

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS Two channels Properties of sections

X x1 , xp

y , yp 1

Vertical Horizontal Channel Channel

Axis X-X

Total Weight per ft

Total Area

in.2

S1 = I / y1

S2 = I / y2

in.4

in.3

in.

in.3

in.

C3×4.1

C4×5.4

9.5

2.80

3.0

1.4

3.0

1.04

2.20

2.16

2.67

C4×5.4

C4×5.4 C5×6.7

10.8 12.1

3.18 3.56

6.5 6.9

2.3 2.3

4.9 5.5

1.43 1.39

2.86 2.94

3.39 3.62

3.56 3.61

C5×6.7

C5×6.7 C6×8.2 C7×9.8

13.4 14.9 16.5

3.94 4.37 4.84

12.8 13.4 14.0

3.5 3.6 3.7

8.0 8.9 9.8

1.80 1.75 1.70

3.60 3.70 3.79

5.23 5.50 5.81

4.50 4.57 4.62

C6×8.2

C5×6.7 C6×8.2 C7×9.8 C8×11.5 C9×13.4 C10×15.3

14.9 16.4 18.0 19.7 21.6 23.5

4.37 4.80 5.27 5.78 6.34 6.89

21.5 22.5 23.4 24.3 25.2 26.0

5.1 5.2 5.2 5.3 5.4 5.5

10.9 12.1 13.3 14.5 15.8 16.9

2.22 2.16 2.11 2.05 1.99 1.94

4.22 4.34 4.45 4.55 4.64 4.70

7.31 7.61 7.93 8.30 8.72 9.16

5.37 5.45 5.53 5.58 5.63 5.65

C7×9.8

C6×8.2 C7×9.8 C8×11.5 C9×13.4 C10×15.3

18.0 19.6 21.3 23.2 25.1

5.27 5.74 6.25 6.81 7.36

35.3 36.7 38.0 39.3 40.5

7.1 7.2 7.3 7.4 7.5

15.7 17.3 18.8 20.5 21.9

2.59 2.53 2.47 2.40 2.34

4.95 5.08 5.20 5.31 5.39

10.2 10.6 10.9 11.4 11.8

6.32 6.40 6.48 6.54 6.58

C8×11.5

C6×8.2 C7×9.8 C8×11.5 C9×13.4 C10×15.3 C12×20.7

19.7 21.3 23.0 24.9 26.8 32.2

5.78 6.25 6.76 7.32 7.87 9.47

52.4 54.5 56.4 58.4 60.0 64.4

9.5 9.6 9.7 9.8 9.9 10.2

19.6 21.6 23.6 25.6 27.5 32.6

3.01 2.95 2.89 2.82 2.76 2.61

5.53 5.68 5.82 5.95 6.06 6.30

13.4 13.8 14.2 14.6 15.1 16.4

7.18 7.27 7.35 7.44 7.49 7.62

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 111

COMBINATION SECTIONS Two channels Properties of sections

X x1 , xp

y , yp 1

Axis Y-Y Vertical Channel

Horizontal Channel

in.4

in.3

in.

in.3

in.

C3×4.1

C4×5.4

4.0

2.0

1.20

0.44

2.67

0.315

C4×5.4

C4×5.4 C5×6.7

4.2 7.8

2.1 3.1

1.14 1.48

0.46 0.46

2.84 4.09

0.281 0.282

C5×6.7

C5×6.7 C6×8.2 C7×9.8

8.0 13.6 21.8

3.2 4.5 6.2

1.42 1.76 2.12

0.48 0.48 0.48

4.29 5.90 7.90

0.264 0.266 0.268

C6×8.2

C5×6.7 C6×8.2 C7×9.8 C8×11.5 C9×13.4 C10×15.3

8.2 13.8 22.0 33.3 48.6 68.1

3.3 4.6 6.3 8.3 10.8 13.6

1.37 1.70 2.04 2.40 2.77 3.14

0.51 0.51 0.51 0.51 0.51 0.51

4.52 6.14 8.13 10.6 13.5 16.8

0.242 0.245 0.247 0.249 0.252 0.254

C7×9.8

C6×8.2 C7×9.8 C8×11.5 C9×13.4 C10×15.3

14.1 22.3 33.6 48.6 68.4

4.7 6.4 8.4 10.9 13.7

1.63 1.97 2.32 2.68 3.05

0.54 0.54 0.54 0.54 0.54

6.41 8.41 10.8 13.8 17.1

0.225 0.228 0.230 0.234 0.235

C8×11.5

C6×8.2 C7×9.8 C8×11.5 C9×13.4 C10×15.3 C12×20.7

14.4 22.6 33.9 49.2 68.7 130

4.8 6.5 8.5 10.9 13.7 21.7

1.58 1.90 2.24 2.59 2.95 3.71

0.57 0.57 0.57 0.57 0.57 0.57

6.73 8.73 11.2 14.1 17.4 27.0

0.218 0.219 0.219 0.220 0.220 0.230

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 112

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS Two channels Properties of sections

X x1 , xp

y , yp 1

Vertical Horizontal Channel Channel

Total Weight per ft

Axis X-X Total Area 2

in.

C9×13.4

C7×9.8 C8×11.5 C9×13.4 C10×15.3 C12×20.7

23.2 24.9 26.8 28.7 34.1

6.81 7.32 7.88 8.43 10.03

C10×15.3

C8×11.5 C9×13.4 C10×15.3 C12×20.7 C15×33.9

26.8 28.7 30.6 36.0 49.2

7.87 8.43 8.98 10.58 14.45

C12×20.7

C9×13.4 C10×15.3 C12×20.7 C15×33.9

34.1 36.0 41.4 54.6

C15×33.9

C10×15.3 C12×20.7 C15×33.9 MC18×42.7

MC18×42.7 MC12×20.7 MC15×33.9 MC18×42.7

S1 = I / y1

I 4

in.

S2 = I / y2 3

yp 3

in.

12.4 12.6 12.7 12.8 13.1

26.3 28.7 31.2 33.5 39.8

3.38 3.32 3.25 3.19 3.02

6.26 6.42 6.57 6.69 6.98

17.6 18.1 18.5 19.0 20.4

8.11 8.21 8.31 8.37 8.54

110 114 117 126 141

15.8 15.9 16.1 16.4 17.3

34.2 37.2 39.9 47.5 63.7

3.75 3.68 3.61 3.45 3.13

7.00 7.16 7.30 7.64 8.18

22.4 22.9 23.4 24.9 28.3

9.07 9.18 9.26 9.46 9.73

10.03 10.58 12.18 16.05

207 213 228 256

25.2 25.4 25.9 27.0

51.4 55.0 65.3 87.8

4.54 4.48 4.32 4.00

8.21 8.38 8.79 9.48

35.7 36.3 38.0 41.8

10.78 10.88 11.16 11.56

49.2 54.6 67.8 76.6

14.45 16.05 19.92 22.56

474 509 575 608

48.8 49.9 52.0 53.1

85.6 99.8 132 152

5.72 5.63 5.37 5.19

9.71 10.19 11.06 11.45

69.7 72.2 77.4 80.7

12.83 13.31 14.04 14.37

63.4 76.6 85.4

18.69 22.56 25.20

860 975 1030

72.9 76.1 77.6

133 174 200

6.78 6.57 6.40

11.80 12.80 13.29

77.7 80.5 83.3 85.6 91.7

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

106 113 117

15.51 16.50 16.96

COMBINATION SECTIONS

1 - 113

COMBINATION SECTIONS Two channels Properties of sections

X x1 , xp

y , yp 1

Axis Y-Y Vertical Channel

Horizontal Channel

in.4

in.3

in.

in.3

in.

C9×13.4

C7×9.8 C8×11.5 C9×13.4 C10×15.3 C12×20.7

23.1 34.4 49.7 69.2 131

6.6 8.6 11.0 13.8 21.8

1.84 2.17 2.51 2.86 3.61

0.60 0.60 0.60 0.60 0.60

9.10 11.5 14.5 17.8 27.4

0.226 0.227 0.227 0.227 0.229

C10×15.3

C8×11.5 C9×13.4 C10×15.3 C12×20.7 C15×33.9

34.9 50.2 69.7 131 317

8.7 11.2 13.9 21.9 42.3

2.11 2.44 2.79 3.52 4.69

0.63 0.63 0.63 0.63 0.63

11.9 14.9 18.2 27.8 52.8

0.232 0.232 0.233 0.234 0.239

C12×20.7

C9×13.4 C10×15.3 C12×20.7 C15×33.9

51.8 71.3 133 319

11.5 14.3 22.1 42.5

2.27 2.60 3.30 4.46

0.70 0.70 0.70 0.70

16.0 19.3 29.0 54.0

0.261 0.261 0.262 0.266

C15×33.9

C10×15.3 C12×20.7 C15×33.9 MC18×42.7

75.5 137 323 562

15.1 22.9 43.1 62.5

2.29 2.92 4.03 4.99

0.79 0.79 0.79 0.79

22.1 31.7 56.7 80.7

0.337 0.338 0.342 0.343

MC18×42.7

MC12×20.7 MC15×33.9 MC18×42.7

143 329 568

23.9 43.9 63.2

2.77 3.82 4.75

0.88 0.88 0.88

33.6 58.6 82.6

0.355 0.358 0.359

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 114

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS Channels and angles Properties of sections

Long leg of angle turned out

y , yp 1

x1 xp

x2 Y

Total Weight per ft

Axis X-X Total Area 2

S1 = I / y1

I 4

in.

yp 3

Angle

in.

C6×8.2

L21⁄2×21⁄2×1⁄4 L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L3×21⁄2 ×5⁄16 L4 ×3 ×1⁄4

12.3 12.7 13.6 14.8 14.0

3.59 3.71 3.96 4.33 4.09

17.9 18.5 19.0 19.8 19.5

8.0 8.5 8.9 9.8 9.5

4.8 4.8 4.9 5.0 5.0

2.24 2.23 2.19 2.14 2.19

2.24 2.17 2.13 2.02 2.06

6.75 6.90 7.23 7.54 7.36

1.40 1.26 1.26 1.11 1.13

C7×9.8

L21⁄2×21⁄2×1⁄4 L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L3×21⁄2 ×5⁄16 L4 ×3 ×1⁄4 L3×2 ×5⁄16

13.9 14.3 15.2 16.4 15.6 17.0

4.06 4.18 4.43 4.80 4.56 4.96

28.5 29.3 30.0 31.2 30.8 32.0

10.6 11.2 11.8 12.9 12.4 13.7

6.6 6.7 6.7 6.8 6.8 6.9

2.65 2.65 2.60 2.55 2.60 2.54

2.68 2.61 2.54 2.42 2.48 2.35

9.13 9.31 9.64 9.99 9.81 10.2

1.67 1.53 1.53 1.35 1.39 1.20

C8×11.5

L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L3×21⁄2 ×5⁄16 L4 ×3 ×1⁄4 L3×2 ×5⁄16 L5 ×31⁄2×5⁄16

16.0 16.9 18.1 17.3 18.7 20.2

4.69 4.94 5.31 5.07 5.47 5.94

43.9 44.9 46.7 46.0 47.8 49.9

14.3 15.1 16.4 15.8 17.3 18.9

8.9 9.0 9.0 9.0 9.1 9.3

3.06 3.02 2.97 3.01 2.96 2.90

3.07 2.98 2.84 2.91 2.76 2.64

12.2 12.6 13.0 12.8 13.2 13.9

1.81 1.81 1.60 1.67 1.45 1.30

C9×13.4

L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L3×21⁄2 ×5⁄16 L4 ×3 ×1⁄4 L3×2 ×5⁄16 L5 ×31⁄2×5⁄16

17.9 18.8 20.0 19.2 20.6 22.1

5.25 5.50 5.87 5.63 6.03 6.50

63.1 64.6 67.1 66.0 68.7 71.4

17.8 18.8 20.4 19.6 21.4 23.4

11.6 11.6 11.7 11.7 11.8 12.0

3.47 3.43 3.38 3.42 3.37 3.31

3.54 3.45 3.29 3.37 3.20 3.06

15.8 16.1 16.6 16.3 16.8 17.5

2.11 2.11 1.87 1.98 1.73 1.58

C10×15.3

L31⁄2×3 ×1⁄4 L3×21⁄2 ×5⁄16 L4 ×3 ×1⁄4 L3×2 ×5⁄16 L5 ×31⁄2×5⁄16 L3×21⁄2 ×3⁄8

20.7 21.9 21.1 22.5 24.0 25.7

6.05 6.42 6.18 6.58 7.05 7.54

89.3 92.7 91.1 94.7 98.4 102

22.8 24.8 23.8 25.9 28.2 30.6

14.7 14.8 14.8 14.9 15.1 15.2

3.84 3.80 3.84 3.79 3.74 3.67

3.91 3.74 3.83 3.65 3.49 3.33

20.0 20.6 20.3 20.9 21.6 22.2

2.39 2.12 2.26 1.98 1.84 1.61

Channel

in.

S2 = I / y2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 115

COMBINATION SECTIONS Channels and angles Properties of sections

Long leg of angle turned out

y , yp 1

x1 xp

x2 Y

Axis Y-Y

S1 = I / x1

xp 3

in.

C6×8.2

L21⁄2×21⁄2×1⁄4 L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4

2.6 3.6 4.9 5.7 6.5

1.0 1.2 1.4 1.7 1.7

1.4 1.9 2.4 2.7 3.1

0.85 0.98 1.11 1.14 1.26

2.60 3.01 3.40 3.31 3.79

2.02 2.38 2.82 3.27 3.30

2.60 3.09 3.57 3.54 4.06

C7×9.8

L21⁄2×21⁄2×1⁄4 L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L31⁄2 ×5⁄16

3.0 4.0 5.4 6.3 7.1 8.3

1.1 1.3 1.6 1.8 18 2.2

1.6 2.0 2.6 2.9 3.2 3.6

0.86 0.98 1.10 1.14 1.25 1.29

2.67 3.09 3.48 3.40 3.88 3.78

2.31 2.66 3.11 3.57 3.59 4.16

2.62 3.11 3.59 3.57 4.08 4.05

C8×11.5

L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L3×3 ×5⁄16 L5 ×31⁄2×5⁄16

4.6 6.0 6.9 7.8 9.0 14.7

14 1.7 2.0 2.0 2.3 3.2

2.2 2.7 3.0 3.4 3.8 5.6

0.99 1.10 1.14 1.24 1.28 1.57

3.16 3.56 3.48 3.97 3.87 4.64

3.00 3.45 3.91 3.93 4.51 5.97

3.13 3.61 3.59 4.10 4.08 5.05

C9×13.4

L3 ×21⁄2×1⁄4 L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L3×3 ×5⁄16 L5 ×31⁄2×5⁄16

5.2 6.7 7.7 8.5 9.9 15.8

1.6 1.8 2.2 2.1 2.5 3.3

2.3 2.9 3.2 3.6 4.0 5.9

0.99 1.10 1.14 1.23 1.28 1.56

3.22 3.64 3.55 4.05 3.96 4.74

3.38 3.83 4.31 4.32 4.91 6.38

3.14 3.63 3.61 4.12 4.10 5.08

C10×15.3

L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L3×3 ×5⁄16 L5 ×31⁄2×5⁄16 L31⁄2×3 ×3⁄8

7.4 8.5 9.4 10.8 16.9 19.2

2.0 2.3 2.3 2.7 3.5 4.1

3.1 3.4 3.8 4.2 6.1 6.7

1.11 1.15 1.23 1.28 1.55 1.60

3.70 3.62 4.12 4.03 4.83 4.73

4.25 4.73 4.74 5.34 6.82 7.70

3.64 3.63 4.14 4.12 5.09 5.07

Channel

Angle

in.

S2 = I / x2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 116

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS Channels and angles Properties of sections

Long leg of angle turned out

y , yp 1

x1 xp

x2 Y

Total Weight per ft

Axis X-X Total Area 2

S1 = I / y1

I 4

S2 = I / y2 3

yp 3

Angle

in.

C12×20.7

L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L31⁄2×3 ×5⁄16 L5 ×31⁄2×5⁄16 L5×31⁄2 ×3⁄8 L6 ×4 ×3⁄8 L5×3 ×1⁄2

26.1 27.3 26.5 27.9 29.4 31.1 33.0 36.9

7.65 8.02 7.78 8.18 8.65 9.14 9.70 10.84

164 170 167 173 180 186 192 202

33.2 35.8 34.4 37.2 40.2 43.4 46.6 53.2

23.2 23.5 23.4 23.6 23.9 24.1 24.3 24.7

4.63 4.61 4.63 4.60 4.56 4.51 4.45 4.32

4.94 4.75 4.86 4.66 4.47 4.29 4.12 3.80

31.4 32.2 31.8 32.6 33.5 34.2 35.3 36.7

3.23 2.80 3.01 2.67 2.53 2.25 2.11 1.68

C12×25

L31⁄2×3 ×1⁄4 L5×31⁄2 ×5⁄16 L4 ×3 ×1⁄4 L5×3 ×5⁄16 L5 ×31⁄2×5⁄16 L5×31⁄2 ×3⁄8 L6 ×4 ×3⁄8 L5×3 ×1⁄2

30.4 31.6 30.8 32.2 33.7 35.4 37.3 41.2

8.91 9.28 9.04 9.44 9.91 10.40 10.96 12.10

180 187 183 190 197 204 211 223

35.4 38.0 36.6 39.3 42.3 45.4 48.7 55.3

26.1 26.4 26.3 26.6 26.9 27.2 27.5 28.0

4.50 4.49 4.50 4.49 4.46 4.43 4.39 4.29

5.09 4.92 5.02 4.84 4.67 4.49 4.33 4.03

35.8 36.8 36.3 37.3 38.3 39.3 40.4 42.2

3.98 3.50 3.82 3.30 3.05 2.77 2.65 2.20

C15×33.9

L4 ×3 ×1⁄4 L5×3 ×5⁄16 L5 ×31⁄2×5⁄16 L5×31⁄2 ×3⁄8 L6 ×4 ×3⁄8 L5×3 ×1⁄2

39.7 41.1 42.6 44.3 46.2 50.1

11.65 12.05 12.52 13.01 13.57 14.71

383 395 408 421 434 458

58.7 62.4 66.5 70.8 75.4 84.8

45.1 45.6 46.1 46.5 46.9 47.7

5.73 5.73 5.71 5.69 5.65 5.58

6.52 6.33 6.14 5.94 5.76 5.40

60.1 61.8 63.4 64.8 66.2 68.6

5.39 4.89 4.30 3.69 3.48 2.92

Channel

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 117

COMBINATION SECTIONS Channels and angles Properties of sections

Long leg of angle turned out

y , yp 1

x1 xp

x2 Y

Axis Y-Y

S1 = I / x1

xp 3

in.

C12×20.7

L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L4×3 ×5⁄16 L5 ×31⁄2×5⁄16 L31⁄2×3 ×3⁄8 L6 ×4 ×3⁄8 L4×3 ×1⁄2

9.5 10.7 11.6 13.2 19.9 22.5 33.2 40.6

2.5 2.8 2.7 3.2 40 4.6 5.8 7.3

3.7 4.0 4.4 4.8 6.8 7.5 10.3 11.9

1.12 1.16 1.22 1.27 1.52 1.57 1.85 1.93

3.84 3.77 4.28 4.20 5.02 4.93 5.72 5.52

5.45 5.94 5.94 6.56 8.06 8.97 11.1 13.7

3.69 3.67 4.18 4.16 5.15 5.13 6.10 6.05

C12×25

L31⁄2×3 ×1⁄4 L31⁄2×3 ×5⁄16 L4 ×3 ×1⁄4 L4×3 ×5⁄16 L5 ×31⁄2×5⁄16 L31⁄2×3 ×3⁄8 L6 ×4 ×3⁄8 L4×3 ×1⁄2

10.2 11.4 12.3 13.9 20.8 23.5 34.5 42.3

2.6 3.0 2.8 3.3 4.1 4.7 5.9 7.5

3.8 4.2 4.5 5.0 7.0 7.7 10.7 12.4

1.07 1.11 1.17 1.22 1.45 1.50 1.77 1.87

3.87 3.81 4.32 4.25 5.09 5.00 5.81 5.63

5.88 6.40 6.38 7.02 8.54 9.48 11.7 14.3

3.74 3.72 4.23 4.22 5.20 5.18 6.15 6.11

C15×33.9

L4 ×3 ×1⁄4 L4×3 ×5⁄16 L5 ×31⁄2×5⁄16 L31⁄2×3 ×3⁄8 L6 ×4 ×3⁄8 L4×3 ×1⁄2

16.8 18.7 26.2 29.3 41.3 50.3

3.7 4.2 4.9 5.6 6.8 8.5

5.8 6.3 8.5 9.2 12.4 14.3

1.20 1.25 1.45 1.50 1.75 1.85

4.49 4.43 5.30 5.23 6.06 5.89

8.82 9.47 11.0 12.0 14.2 16.9

4.27 4.26 5.24 5.23 6.21 6.17

Channel

Angle

in.

S2 = I / x2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 118

DIMENSIONS AND PROPERTIES

COMBINATION SECTIONS Channels and angles Properties of sections

y , yp

x1 xp

Short leg of angle turned out

x2 Y

Total Weight per ft

Total Area 2

in.

S2 = I / y2 3

in.

yp 3

in.

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

12.7 13.1 14.0 16.4 18.0

3.71 3.84 4.09 4.80 5.27

6.0 6.1 6.4 7.5 7.7

5.9 6.2 6.2 6.4 6.8

2.61 2.68 2.63 2.55 2.56

4.21 4.56 4.46 4.16 4.45

7.86 8.23 8.32 8.77 9.32

2.79 3.25 3.18 3.00 3.46

C 7×9.8

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

14.3 14.7 15.6 18.0 19.6

4.18 4.31 4.56 5.27 5.74

8.0 8.0 8.5 10.0 10.3

7.8 8.2 8.2 8.5 8.9

3.00 3.07 3.03 2.95 2.96

4.70 5.05 4.93 4.60 4.87

10.5 10.9 1 1.0 11.6 12.2

2.95 3.38 3.29 3.11 3.50

C 8×11.5

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

16.0 16.4 17.3 19.7 21.3

4.69 4.82 5.07 5.78 6.25

10.4 10.4 10.9 12.9 13.3

10.2 10.6 10.6 11.0 11.4

3.39 3.45 3.42 3.36 3.36

5.20 5.55 5.42 5.06 5.31

13.7 14.2 14.3 14.9 15.6

3.52 3.73 3.42 3.21 3.61

C 9×13.4

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

17.9 18.3 19.2 21.6 23.2

5.25 5.38 5.63 6.34 6.81

13.1 13.1 13.8 16.2 16.7

12.9 13.4 13.5 13.9 14.4

3.78 3.84 3.81 3.76 3.77

5.71 6.07 5.93 5.54 5.78

17.4 18.0 18.3 19.0 19.7

4.18 4.42 3.88 3.32 3.71

C10×15.3

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

19.8 20.2 21.1 23.5 25.1

5.80 5.93 6.18 6.89 7.36

16.2 16.1 17.0 19.9 20.5

16.0 16.5 16.6 17.1 17.7

4.17 4.22 4.20 4.17 4.18

6.22 6.58 6.43 6.02 6.25

21.4 22.1 22.5 23.5 24.2

4.77 5.01 4.48 3.44 3.81

C12×20.7

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

25.2 25.6 26.5 28.9 30.5

7.40 7.53 7.78 8.49 8.96

24.3 24.0 25.3 29.2 30.1

24.7 25.3 25.5 26.3 27.1

4.90 4.95 4.95 4.94 4.97

7.32 7.69 7.54 7.11 7.33

32.6 33.4 34.3 36.4 37.5

6.17 6.45 6.01 4.74 4.41

C15×33.9

L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

38.8 39.7 42.1 43.7

11.40 11.65 12.36 12.83

42.7 44.5 50.1 51.4

47.2 47.7 49.1 50.3

5.95 5.96 6.01 6.05

9.45 9.31 8.91 9.15

61.1 62.5 66.5 69.0

8.70 8.39 7.50 7.41

Angle

in.

S1 = I / y1

C 6×8.2

Channel

Axis X-X

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

COMBINATION SECTIONS

1 - 119

COMBINATION SECTIONS Channels and angles Properties of sections

Short leg of angle turned out

y , yp

x1 xp

x2 Y

Axis Y-Y

S1 = I / x1

xp 3

in.

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

2.4 2.8 3.8 6.0 8.4

4.4 4.6 6.6 9.3 12.1

1.22 1.26 1.64 2.05 2.47

2.25 2.18 2.85 3.33 3.82

3.70 4.01 5.46 8.29 11.3

2.65 2.59 3.46 4.12 4.84

C 7×9.8

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

2.6 2.9 3.9 6.1 8.6

5.0 5.2 7.5 10.5 13.6

1.19 1.23 1.60 2.01 2.44

2.32 2.25 2.95 3.47 3.98

4.03 4.35 5.82 8.71 11.8

2.72 2.67 3.55 4.24 4.99

C 8×11.5

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

2.7 3.0 4.0 6.3 8.7

5.6 5.8 8.3 11.7 15.2

1.16 1.20 1.55 1.97 2.40

2.37 2.31 3.03 3.58 4 13

4.40 4.73 6.21 9.16 12.3

2.78 2.73 3.62 4.34 5.12

C 9×13.4

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

2.8 3.2 4.2 6.4 8.9

6.2 6.5 9.2 12.9 16.9

1.14 1.18 1.51 1.92 2.36

2.40 2.35 3.10 3.68 4.26

4.81 5.15 6.65 9.66 12.8

2.84 2.79 3.70 4.43 5.23

C10×15.3

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

3.0 3.4 4.3 6.5 9.0

6.8 7.1 10.0 14.0 18.3

1.12 1.16 1.48 1.88 2.31

2.42 2.37 3.15 3.76 4.36

5.25 5.59 7.10 10.1 13.3

2.88 2.84 3.74 4.49 5.31

C12×20.7

L3×21⁄2×1⁄4 L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

3.6 4.0 4.7 6.9 9.3

8.6 8.9 12.2 17.0 22.4

1.10 1.13 1.40 1.78 2 19

2.47 2.43 3.25 3.92 4.59

6.47 6.82 8.37 11.5 14.8

3.01 2.97 3.89 4.67 5.52

C15×33.9

L3×3 ×1⁄4 L4×3 ×1⁄4 L5×3 ×5⁄16 L6×31⁄2×5⁄16

5.6 5.9 7.8 10.2

13.5 17.2 23.4 30.7

1.10 1.30 1.61 1.97

2.48 3.35 4.12 4.88

9.54 11.1 14.5 18.0

3.12 4.11 5.02 5.90

Angle

in.

C 6×8.2

Channel

in.

S2 = I / x2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 120

DIMENSIONS AND PROPERTIES

STEEL PIPE AND STRUCTURAL TUBING General

When designing and specifying steel pipe or tubing as compression members, refer to comments in the notes for Columns, Steel Pipe, and Structural Tubing, in Part 3. For standard mill practices and tolerances, refer to page 1-183. For material specifications and availability, see Tables 1-4 through 1-6, Part 1. Steel Pipe

The Tables of Dimensions and Properties of Steel Pipe (unfilled) list a selected range of sizes of standard, extra strong, and double-extra strong pipe. For a complete range of sizes manufactured, refer to catalogs of the manufacturers or to the American Institute for Hollow Structural Sections (AIHSS). Structural Tubing

The Tables of Dimensions and Properties of Square and Rectangular Structural Tubing (unfilled) list a selected range of frequently used sizes. For dimensions and properties of other sizes, refer to catalogs from the manufacturers or AIHSS. The tables are based on an outside corner radius equal to two times the specified wall thickness. Material specifications stipulate that the outside corner radius may vary up to three times the specified wall thickness. This variation should be considered in those details where a close match or fit is important.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STEEL PIPE AND STRUCTURAL TUBING

1 - 121

PIPE Dimensions and properties Dimensions

Weight Nominal Outside Inside Wall per ft lbs Diameter Diameter Diameter Thickness Plain Ends in. in. in. in.

Properties Area

in.2

in.4

in.3

in.

in.4

in.3

0.041 0.071 0.133 0.235 0.326 0.561 1.06 1.72 2.39 3.21 5.45 8.50 16.8 29.9 43.8

0.261 0.334 0.421 0.540 0.623 0.787 0.947 1.16 1.34 1.51 1.88 2.25 2.94 3.67 4.38

0.034 0.074 0.175 0.389 0.620 1.33 3.06 6.03 9.58 14.5 30.3 56.3 145 321 559

0.059 0.100 0.187 0.324 0.448 0.761 1.45 2.33 3.22 4.31 7.27 11.2 22.2 39.4 57.4

0.048 0.085 0.161 0.291 0.412 0.731 1.34 2.23 3.14 4.27 7.43 12.2 24.5 39.4 56.7

0.250 0.321 0.407 0.524 0.605 0.766 0.924 1.14 1.31 1.48 1.84 2.19 2.88 3.63 4.33

0.040 0.090 0.211 0.484 0.782 1.74 3.85 8.13 12.6 19.2 41.3 81.0 211 424 723

0.072 0.125 0.233 0.414 0.581 1.02 1.87 3.08 4.32 5.85 10.1 16.6 33.0 52.6 75.1

1.10 2.00 3.42 6.79 12.1 20.0 37.6

0.703 0.844 1.05 1.37 1.72 2.06 2.76

2.62 5.74 12.0 30.6 67.3 133 324

1.67 3.04 5.12 9.97 17.5 28.9 52.8

Standard Weight 1⁄ 2 3⁄ 4

0.840 1.050 1.315 1.660 1.900 2.375 2.875 3.500 4.000 4.500 5.563 6.625 8.625 10.750 12.750

0.622 0.824 1.049 1.380 1.610 2.067 2.469 3.068 3.548 4.026 5.047 6.065 7.981 10.020 12.000

0.109 0.113 0.133 0.140 0.145 0.154 0.203 0.216 0.226 0.237 0.258 0.280 0.322 0.365 0.375

0.85 1.13 1.68 2.27 2.72 3.65 5.79 7.58 9.11 10.79 14.62 18.97 28.55 40.48 49.56

1 11⁄4 11⁄2 2 21⁄2 3 31⁄2 4 5 6 8 10 12

0.840 1.050 1.315 1.660 1.900 2.375 2.875 3.500 4.000 4.500 5.563 6.625 8.625 10.750 12.750

0.546 0.742 0.957 1.278 1.500 1.939 2.323 2.900 3.364 3.826 4.813 5.761 7.625 9.750 11.750

0.147 0.154 0.179 0.191 0.200 0.218 0.276 0.300 0.318 0.337 0.375 0.432 0.500 0.500 0.500

1.09 1.47 2.17 3.00 3.63 5.02 7.66 10.25 12.50 14.98 20.78 28.57 43.39 54.74 65.42

2 21⁄2 3 4 5 6 8

2.375 2.875 3.500 4.500 5.563 6.625 8.625

1.503 1.771 2.300 3.152 4.063 4.897 6.875

0.436 0.552 0.600 0.674 0.750 0.864 0.875

1 11⁄4 11⁄2 2 21⁄2 3 31⁄2 4 5 6 8 10 12

0.250 0.333 0.494 0.669 0.799 1.07 1.70 2.23 2.68 3.17 4.30 5.58 8.40 11.9 14.6

0.017 0.037 0.087 0.195 0.310 0.666 1.53 3.02 4.79 7.23 15.2 28.1 72.5 161 279

Extra Strong 1⁄ 2 3⁄ 4

0.320 0.433 0.639 0.881 1.07 1.48 2.25 3.02 3.68 4.41 6.11 8.40 12.8 16.1 19.2

0.020 0.045 0.106 0.242 0.391 0.868 1.92 3.89 6.28 9.61 20.7 40.5 106 212 362

Double-Extra Strong 9.03 13.69 18.58 27.54 38.59 53.16 72.42

2.66 4.03 5.47 8.10 11.3 15.6 21.3

1.31 2.87 5.99 15.3 33.6 66.3 162

The listed sections are available in conformance with ASTM Specification A53 Grade B or A501. Other sections are made to these specifications. Consult with pipe manufacturers or distributors for availability.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 122

DIMENSIONS AND PROPERTIES

STRUCTURAL TUBING Square Dimensions and properties Dimensions

Properties**

Nominal* Size

Wall Thickness

Weight per ft

Area

in.

in.2

in.4

in.3

in.

in.4

in.3

0.6250

5⁄ 8

246.47

72.4

10300

690

12.0

16000

794

28×28

0.6250

5⁄ 8

229.45

67.4

8360

597

11.1

13000

689

26×26

0.6250

5⁄ 8

212.44

62.4

6650

511

10.3

10400

591

24×24 24×24 24×24

0.6250 0.5000 0.3750

5⁄ 8 1⁄ 2 3⁄ 8

195.43 157.74 119.35

57.4 46.4 35.1

5180 4240 3250

432 353 270

9.50 9.56 9.62

8100 6570 4990

500 407 310

22×22 22×22 22×22

0.6250 0.5000 0.3750

5⁄ 8 1⁄ 2 3⁄ 8

178.41 144.13 109.15

52.4 42.4 32.1

3950 3240 2490

359 294 226

8.68 8.74 8.80

6200 5030 3830

418 340 259

20×20 20×20 20×20

0.6250 0.5000 0.3750

5⁄ 8 1⁄ 2 3⁄ 8

161.40 130.52 98.94

47.4 38.4 29.1

2940 2410 1850

294 241 185

7.87 7.93 7.99

4620 3760 2870

342 279 213

18×18 18×18 18×18

0.6250 0.5000 0.3750

5⁄ 8 1⁄ 2 3⁄ 8

144.39 116.91 88.73

42.4 34.4 26.1

2110 1740 1340

234 193 149

7.05 7.11 7.17

3340 2720 2080

274 224 172

30×30

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STEEL PIPE AND STRUCTURAL TUBING

1 - 123

STRUCTURAL TUBING Square Dimensions and properties Dimensions

Properties**

Nominal* Size

Wall Thickness

Weight per ft

Area

in.

in.2

in.4

in.3

in.

in.4

in.3

127.37 103.30 78.52 65.87

37.4 30.4 23.1 19.4

1450 1200 931 789

182 150 116 98.6

6.23 6.29 6.35 6.38

2320 1890 1450 1220

214 175 134 113

110.36 89.68 68.31 57.36

32.4 26.4 20.1 16.9

952 791 615 522

136 113 87.9 74.6

5.42 5.48 5.54 5.57

1530 1250 963 812

161 132 102 86.1

93.34 76.07 58.10 48.86 39.43

27.4 22.4 17.1 14.4 11.6

580 485 380 324 265

96.7 80.9 63.4 54.0 44.1

4.60 4.66 4.72 4.75 4.78

943 777 599 506 410

116 95.4 73.9 62.6 50.8

76.33 62.46 47.90 40.35 32.63 24.73

22.4 18.4 14.1 11.9 9.59 7.27

321 271 214 183 151 116

64.2 54.2 42.9 36.7 30.1 23.2

3.78 3.84 3.90 3.93 3.96 3.99

529 439 341 289 235 179

77.6 64.6 50.4 42.8 34.9 26.6

16×16

14×14

12×12

10×10

0.6250 0.5000 0.3750 0.3125 0.6250 0.5000 0.3750 0.3125 0.6250 0.5000 0.3750 0.3125 0.2500 0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 1⁄ 3⁄

8 2

8 5⁄ 16 5⁄ 1⁄

8 2

3⁄ 8 5⁄ 16 5⁄ 1⁄

8 2

3⁄ 8 5⁄ 16 1⁄ 4 5⁄ 1⁄ 3⁄

8 2

8 5⁄ 16 1⁄ 4 3⁄ 16

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 124

DIMENSIONS AND PROPERTIES

STRUCTURAL TUBING Square Dimensions and properties Dimensions

Properties**

Nominal* Size

Wall Thickness

Weight per ft

Area

in.

in.2

in.4

in.3

in.

in.4

in.3

8×8

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

59.32 48.85 37.69 31.84 25.82 19.63

17.4 14.4 11.1 9.36 7.59 5.77

153 131 106 90.9 75.1 58.2

38.3 32.9 26.4 22.7 18.8 14.6

2.96 3.03 3.09 3.12 3.15 3.18

258 217 170 145 118 90.6

47.2 39.7 31.3 26.7 21.9 16.8

7×7

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

50.81 42.05 32.58 27.59 22.42 17.08

14.9 12.4 9.58 8.11 6.59 5.02

97.5 84.6 68.7 59.5 49.4 38.5

27.9 24.2 19.6 17.0 14.1 11.0

2.56 2.62 2.68 2.71 2.74 2.77

166 141 112 95.6 78.3 60.2

34.8 29.6 23.5 20.1 16.5 12.7

6×6

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

42.30 35.24 27.48 23.34 19.02 14.53 9.86

12.4 10.4 8.08 6.86 5.59 4.27 2.90

57.3 50.5 41.6 36.3 30.3 23.8 16.5

19.1 16.8 13.9 12.1 10.1 7.93 5.52

2.15 2.21 2.27 2.30 2.33 2.36 2.39

99.5 85.6 68.5 58.9 48.5 37.5 25.7

24.3 20.9 16.8 14.4 11.9 9.24 6.35

51⁄2×51⁄2

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

24.93 21.21 17.32 13.25 9.01

7.33 6.23 5.09 3.89 2.65

31.2 27.4 23.0 18.1 12.6

11.4 9.95 8.36 6.58 4.60

2.07 2.10 2.13 2.16 2.19

51.9 44.8 37.0 28.6 19.7

13.8 12.0 9.91 7.70 5.31

5×5

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

28.43 22.37 19.08 15.62 11.97 8.16

8.36 6.58 5.61 4.59 3.52 2.40

27.0 22.8 20.1 16.9 13.4 9.41

10.8 9.11 8.02 6.78 5.36 3.77

1.80 1.86 1.89 1.92 1.95 1.98

46.8 38.2 33.1 27.4 21.3 14.7

13.7 11.2 9.70 8.07 6.29 4.36

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STEEL PIPE AND STRUCTURAL TUBING

1 - 125

STRUCTURAL TUBING Square Dimensions and properties Dimensions

Properties**

Nominal* Size

Wall Thickness

Weight per ft

Area

in.

in.2

in.4

in.3

in.

in.4

in.3

41⁄2×41⁄2

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

19.82 16.96 13.91 10.70 7.31

5.83 4.98 4.09 3.14 2.15

16.0 14.2 12.1 9.60 6.78

7.10 6.30 5.36 4.27 3.02

1.66 1.69 1.72 1.75 1.78

27.1 23.6 19.7 15.4 10.6

8.81 7.68 6.43 5.03 3.50

4×4

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

21.63 17.27 14.83 12.21 9.42 6.46

6.36 5.08 4.36 3.59 2.77 1.90

12.3 10.7 9.58 8.22 6.59 4.70

6.13 5.35 4.79 4.11 3.30 2.35

1.39 1.45 1.48 1.51 1.54 1.57

21.8 18.4 16.1 13.5 10.6 7.40

8.02 6.72 5.90 4.97 3.91 2.74

31⁄2×31⁄2

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

12.70 10.51 8.15 5.61

3.73 3.09 2.39 1.65

6.09 5.29 4.29 3.09

3.48 3.02 2.45 1.76

1.28 1.31 1.34 1.37

10.4 8.82 6.99 4.90

4.35 3.69 2.93 2.07

3×3

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

10.58 8.81 6.87 4.75

3.11 2.59 2.02 1.40

3.58 3.16 2.60 1.90

2.39 2.10 1.73 1.26

1.07 1.10 1.13 1.16

6.22 5.35 4.28 3.03

3.04 2.61 2.10 1.49

21⁄2×21⁄2

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

8.45 7.11 5.59 3.90

2.48 2.09 1.64 1.15

1.87 1.69 1.42 1.06

1.50 1.35 1.14 0.847

0.868 0.899 0.930 0.961

3.32 2.92 2.38 1.71

1.96 1.71 1.40 1.01

2×2

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

6.32 5.41 4.32 3.05

1.86 1.59 1.27 0.897

0.815 0.766 0.668 0.513

0.662 0.694 0.726 0.756

1.49 1.36 1.15 0.846

1.11 1.00 0.840 0.621

11⁄2×11⁄2

0.1875

3⁄ 16

3.04

0.894

0.242

0.323

0.521

0.431

0.423

3⁄

2 8

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 126

DIMENSIONS AND PROPERTIES

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

X-X Axis

I 4

Z 3

Y-Y Axis

r 3

I 4

Z 3

in.

in.4

178.16 134.67 112.66

52.4 39.6 33.1

7110 474 5430 362 4570 305

555 422 354

11.7 11.7 11.7

5070 3870 3260

422 323 272

477 363 304

9.84 9.89 9.92

9170 6960 5830

30×24

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

28×24

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

171.35 129.56 108.41

50.4 38.1 31.9

6050 432 4630 331 3890 278

503 383 321

11.0 11.0 11.1

4790 3660 3080

399 305 257

454 345 290

9.75 9.81 9.84

8280 6290 5270

26×24

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

164.55 124.46 104.15

48.4 36.6 30.6

5100 392 3900 300 3280 253

454 345 290

10.3 10.3 10.4

4510 3460 2910

376 288 242

430 327 275

9.66 9.72 9.75

7410 5630 4720

24×22

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

150.93 114.25 95.64

44.4 33.6 28.1

3960 330 3040 253 2560 213

383 292 245

9.45 3470 9.51 2660 9.54 2240

315 242 204

361 275 231

8.84 8.90 8.93

5740 4370 3660

22×20

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

137.32 104.04 87.14

40.4 30.6 25.6

3010 273 2310 210 1950 177

318 243 204

8.63 2600 8.69 2000 8.72 1690

260 200 169

298 228 192

8.03 8.09 8.12

4350 3310 2780

20×18

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

123.71 93.83 78.63

36.4 27.6 23.1

2220 222 1710 171 1440 144

259 198 167

7.81 1890 7.88 1460 7.91 1230

210 162 137

242 185 155

7.21 7.27 7.30

3190 2440 2050

20×12

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

103.30 78.52 65.87

30.4 23.1 19.4

1650 165 1280 128 1080 108

201 154 130

7.37 7.45 7.47

750 583 495

125 141 97.2 109 82.5 91.8

4.97 5.03 5.06

1650 1270 1070

20×8

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

89.68 68.31 57.36

26.4 20.1 16.9

1270 127 162 988 98.8 125 838 83.8 105

6.94 7.02 7.05

300 236 202

20×4

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

76.07 58.10 48.86

22.4 17.1 14.4

889 699 596

88.9 123 69.9 95.3 59.6 80.8

6.31 6.40 6.44

61.6 50.3 43.7

75.1 59.1 50.4

84.7 65.6 55.6

3.38 3.43 3.46

806 625 529

30.8 25.1 21.8

36.0 28.5 24.3

1.66 1.72 1.74

205 165 143

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STEEL PIPE AND STRUCTURAL TUBING

1 - 127

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

in.2

X-X Axis

Y-Y Axis

in.4

in.3

in.

in.4

in.3

in.

in.4

6.71 6.78 6.81

684 533 452

114 130 88.8 100 75.3 84.5

4.91 4.97 5.00

1420 1090 920

53.9 42.1 35.8 29.2

2.52 2.57 2.60 2.63

410 322 274 224

103 118 80.3 91.3 68.2 77.2

4.84 4.90 4.93

1200 922 777

18×12

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

96.49 73.42 61.62

28.4 21.6 18.1

18×6

0.5000 0.3750 0.3125 0.2500

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4

76.07 58.10 48.86 39.43

22.4 17.1 14.4 11.6

818 641 546 447

90.9 119 71.3 92.2 60.7 78.1 49.6 63.5

6.05 6.13 6.17 6.21

141 113 97.0 80.0

16×12

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

89.68 68.31 57.36

26.4 20.1 16.9

962 748 635

120 144 93.5 111 79.4 93.8

6.04 6.11 6.14

618 482 409

16×8

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

76.07 58.10 48.86

22.4 17.1 14.4

722 565 481

90.2 113 70.6 87.6 60.1 74.2

5.68 5.75 5.79

244 193 165

16×4

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

62.46 47.90 40.35

18.4 14.1 11.9

481 382 327

60.2 47.8 40.9

82.2 64.2 54.5

5.12 5.21 5.25

14×12

0.5000 0.3750

1⁄ 2 3⁄ 8

82.88 63.21

24.4 18.6

699 546

99.9 119 78.0 91.7

5.36 5.42

14×10

0.5000 0.3750 0.3125

1⁄ 2 3⁄ 8 5⁄ 16

76.07 58.10 48.86

22.4 17.1 14.4

608 476 405

86.9 105 68.0 81.5 57.9 69.0

14×6

0.6250 0.5000 0.3750 0.3125 0.2500

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4

76.33 62.46 47.90 40.35 32.63

22.4 18.4 14.1 11.9 9.59

504 426 337 288 237

72.0 60.8 48.1 41.2 33.8

1280 142 172 991 110 132 840 93.3 111

94.0 78.3 61.1 51.9 42.3

47.2 37.6 32.3 26.7

61.0 48.2 41.2

69.7 54.2 45.9

3.30 3.36 3.39

599 465 394

24.6 20.2 17.6

29.0 23.0 19.7

1.64 1.69 1.72

157 127 110

552 431

91.9 107 71.9 82.6

4.76 4.82

983 757

5.22 5.28 5.31

361 284 242

72.3 56.8 48.4

83.6 64.8 54.9

4.02 4.08 4.11

730 564 477

4.74 4.82 4.89 4.93 4.97

130 111 89.1 76.7 63.4

43.3 37.1 29.7 25.6 21.1

51.2 42.9 33.6 28.7 23.4

2.41 2.46 2.52 2.54 2.57

352 296 233 199 162

49.3 40.4 35.1

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 128

DIMENSIONS AND PROPERTIES

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

in.2

X-X Axis

Y-Y Axis

in.4

in.3

in.

in.4

in.3

in.

in.4

49.0 43.1 35.4 30.9 25.8 20.2

24.5 21.5 17.7 15.4 12.9 10.1

30.0 25.5 20.3 17.4 14.3 11.1

1.57 1.62 1.68 1.71 1.73 1.76

154 134 108 93.1 77.0 59.7

14×4

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

67.82 55.66 42.79 36.10 29.23 22.18

19.9 16.4 12.6 10.6 8.59 6.52

392 335 267 230 189 146

56.0 47.8 38.2 32.8 27.0 20.9

77.3 64.8 50.8 43.3 35.4 27.1

4.44 4.52 4.61 4.65 4.69 4.74

12×10

0.5000 0.3750 0.3125 0.2500

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4

69.27 53.00 44.60 36.03

20.4 15.6 13.1 10.6

419 330 281 230

69.9 55.0 46.9 38.4

83.9 65.2 55.2 44.9

4.54 4.60 4.63 4.66

316 249 213 174

63.3 49.8 42.6 34.9

74.1 57.6 48.8 39.7

3.94 4.00 4.03 4.06

581 450 381 309

12×8

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

76.33 62.46 47.90 40.35 32.63 24.73

22.4 18.4 14.1 11.9 9.59 7.27

418 353 279 239 196 151

69.7 58.9 46.5 39.8 32.6 25.1

87.1 72.4 56.5 47.9 39.1 29.8

4.32 4.39 4.45 4.49 4.52 4.55

221 188 149 128 105 81.1

55.3 46.9 37.3 32.0 26.3 20.3

65.6 54.7 42.7 36.3 29.6 22.7

3.14 3.20 3.26 3.28 3.31 3.34

481 401 312 265 216 165

12×6

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

67.82 55.66 42.79 36.10 29.23 22.18

19.9 16.4 12.6 10.6 8.59 6.52

337 287 228 196 161 124

56.2 47.8 38.1 32.6 26.9 20.7

72.9 60.9 47.7 40.6 33.2 25.4

4.11 4.19 4.26 4.30 4.33 4.37

112 96.0 77.2 66.6 55.2 42.8

37.2 32.0 25.7 22.2 18.4 14.3

44.5 37.4 29.4 25.1 20.6 15.8

2.37 2.42 2.48 2.51 2.53 2.56

286 241 190 162 132 101

12×4

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

59.32 48.85 37.69 31.84 25.82 19.63

17.4 14.4 11.1 9.36 7.59 5.77

257 221 178 153 127 98.2

42.8 36.8 29.6 25.5 21.1 16.4

58.6 49.4 39.0 33.3 27.3 21.0

3.84 3.92 4.01 4.05 4.09 4.13

41.8 36.9 30.5 26.6 22.3 17.5

20.9 18.5 15.2 13.3 11.1 8.75

25.8 22.0 17.6 15.1 12.5 9.63

1.55 1.60 1.66 1.69 1.71 1.74

127 110 89.0 76.9 63.6 49.3

12×3

0.3125 0.2500 0.1875

5⁄ 16 1⁄ 4 3⁄ 16

29.72 24.12 18.35

8.73 132 7.09 109 5.39 85.1

22.0 18.2 14.2

29.7 24.4 18.8

3.89 3.93 3.97

13.8 11.7 9.28

9.19 10.6 7.79 8.80 6.19 6.84

1.26 1.28 1.31

43.6 36.5 28.7

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STEEL PIPE AND STRUCTURAL TUBING

1 - 129

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

X-X Axis

Y-Y Axis

in.2

in.4

in.3

in.

in.4

in.3

in.

in.4

92.2 15.4 72.0 12.0

21.4 16.6

3.74 3.79

12×2

0.2500 0.1875

1⁄ 4 3⁄ 16

22.42 17.08

6.59 5.02

10×8

0.5000 0.3750 0.3125 0.2500 0.1875

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

55.66 42.79 36.10 29.23 22.18

16.4 12.6 10.6 8.59 6.52

226 180 154 127 97.9

45.2 35.9 30.8 25.4 19.6

55.1 43.1 36.7 30.0 23.0

3.72 3.78 3.81 3.84 3.87

160 127 109 90.2 69.7

39.9 31.8 27.3 22.5 17.4

47.2 37.0 31.5 25.8 19.7

3.12 3.18 3.21 3.24 3.27

306 239 203 166 127

10×6

0.5000 0.3750 0.3125 0.2500 0.1875

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

48.85 37.69 31.84 25.82 19.63

14.4 11.1 9.36 7.59 5.77

181 145 125 103 79.8

36.2 29.0 25.0 20.6 16.0

45.6 35.9 30.7 25.1 19.3

3.55 3.62 3.65 3.69 3.72

80.8 65.4 56.5 46.9 36.5

26.9 21.8 18.8 15.6 12.2

31.9 25.2 21.5 17.7 13.6

2.37 2.43 2.46 2.49 2.51

187 147 126 103 79.1

10×5

0.3750 0.3125 0.2500 0.1875

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

35.13 29.72 24.12 18.35

10.3 128 8.73 110 7.09 91.2 5.39 70.8

25.5 22.0 18.2 14.2

32.3 27.6 22.7 17.4

3.51 3.55 3.59 3.62

42.9 37.2 31.1 24.3

17.1 14.9 12.4 9.71

19.9 17.0 14.0 10.8

2.04 2.07 2.09 2.12

107 91.5 75.2 58.0

10×4

0.5000 0.3750 0.3125 0.2500 0.1875

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

42.05 32.58 27.59 22.42 17.08

12.4 136 9.58 110 8.11 95.5 6.59 79.3 5.02 61.7

27.1 22.0 19.1 15.9 12.3

36.1 28.7 24.6 20.2 15.6

3.31 3.39 3.43 3.47 3.51

30.8 25.5 22.4 18.8 14.8

15.4 12.8 11.2 9.39 7.39

18.5 14.9 12.8 10.6 8.20

1.58 1.63 1.66 1.69 1.72

86.9 70.4 60.8 50.4 39.1

10×3

0.3750 0.3125 0.2500 0.1875

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

30.0 25.5 20.72 15.80

8.83 7.48 6.09 4.64

92.8 80.8 67.4 52.7

18.6 16.2 13.5 10.5

25.1 21.6 17.8 13.8

3.24 3.29 3.33 3.37

13.0 11.5 9.79 7.80

8.66 10.3 7.68 8.92 6.53 7.42 5.20 5.79

1.21 1.24 1.27 1.30

39.8 34.9 29.3 23.0

10×2

0.3750 0.3125 0.2500 0.1875

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

27.48 23.34 19.02 14.53

8.08 6.86 5.59 4.27

75.4 15.1 66.1 13.2 55.5 11.1 43.7 8.74

21.5 18.5 15.4 11.9

3.06 3.10 3.15 3.20

4.85 4.42 3.85 3.14

0.775 0.802 0.830 0.858

16.5 14.9 12.8 10.3

4.62 3.76

5.38 0.837 4.24 0.865

6.05 5.33 4.50 3.56

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

15.9 12.8

1 - 130

DIMENSIONS AND PROPERTIES

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

in.2

X-X Axis

Y-Y Axis

in.4

in.3

in.

in.4

in.3

in.

in.4

8×6

0.5000 0.3750 0.3125 0.2500 0.1875

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

42.05 32.58 27.59 22.42 17.08

12.4 103 9.58 83.7 8.11 72.4 6.59 60.1 5.02 46.8

25.8 20.9 18.1 15.0 11.7

32.2 25.6 21.9 18.0 13.9

2.89 2.96 2.99 3.02 3.05

65.7 53.5 46.4 38.6 30.1

21.9 17.8 15.5 12.9 10.0

26.4 21.0 18.0 14.8 11.4

2.31 2.36 2.39 2.42 2.45

135 107 91.3 74.9 57.6

8×4

0.6250 0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

5⁄ 8 1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

42.30 35.24 27.48 23.34 19.02 14.53 9.86

12.4 10.4 8.08 6.86 5.59 4.27 2.90

21.3 18.8 15.5 13.5 11.3 8.83 6.14

28.8 24.7 19.9 17.1 14.1 11.0 7.53

2.62 2.69 2.77 2.80 2.84 2.88 2.91

27.4 24.6 20.6 18.1 15.3 12.0 8.45

13.7 12.3 10.3 9.05 7.63 6.02 4.23

17.3 15.0 12.2 10.5 8.72 6.77 4.67

1.49 1.54 1.60 1.62 1.65 1.68 1.71

73.2 64.1 52.2 45.2 37.5 29.1 20.0

8×3

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

31.84 24.93 21.21 17.32 13.25 9.01

9.36 7.33 6.23 5.09 3.89 2.65

61.0 15.3 51.0 12.7 44.7 11.2 37.6 9.40 29.6 7.40 20.7 5.17

21.0 17.0 14.7 12.2 9.49 6.55

2.55 2.64 2.68 2.72 2.76 2.80

12.1 10.4 9.25 7.90 6.31 4.48

8.05 10.1 6.92 8.31 6.16 7.24 5.26 6.05 4.21 4.73 2.99 3.29

1.14 1.19 1.22 1.25 1.27 1.30

35.7 29.9 26.3 22.1 17.3 12.1

8×2

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

22.37 19.08 15.62 11.97 8.16

6.58 5.61 4.59 3.52 2.40

40.1 10.0 14.2 35.5 8.87 12.3 30.1 7.52 10.3 23.9 5.97 8.02 16.8 4.20 5.56

2.47 2.51 2.56 2.60 2.65

3.85 3.52 3.08 2.52 1.83

4.83 4.28 3.63 2.88 2.03

0.765 0.792 0.819 0.847 0.875

12.6 11.4 9.84 7.94 5.66

7×5

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

35.24 27.48 23.34 19.02 14.53 9.86

10.4 8.08 6.86 5.59 4.27 2.90

63.5 52.2 45.5 38.0 29.8 20.7

23.1 18.5 15.9 13.2 10.2 7.00

2.48 2.54 2.58 2.61 2.64 2.67

37.2 30.8 26.9 22.6 17.7 12.4

14.9 12.3 10.8 9.04 7.10 4.95

18.2 14.6 12.6 10.4 8.10 5.58

1.90 1.95 1.98 2.01 2.04 2.07

79.9 64.2 55.3 45.6 35.3 24.2

7×4

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

24.93 21.21 17.32 13.25 9.01

7.33 6.23 5.09 3.89 2.65

44.0 12.6 16.0 38.5 11.0 13.8 32.3 9.23 11.5 25.4 7.26 8.91 17.7 5.07 6.15

2.45 2.49 2.52 2.55 2.59

18.1 16.0 13.5 10.7 7.51

9.06 10.8 7.98 9.36 6.75 7.78 5.34 6.06 3.76 4.19

1.57 1.60 1.63 1.66 1.68

43.3 37.5 31.2 24.2 16.7

85.1 75.1 61.9 53.9 45.1 35.3 24.6

18.1 14.9 13.0 10.9 8.50 5.91

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STEEL PIPE AND STRUCTURAL TUBING

1 - 131

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

X-X Axis

Y-Y Axis

in.2

in.4

in.3

in.

in.4

in.3

in.

in.4

7×3

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

22.37 19.08 15.62 11.97 8.16

6.58 5.61 4.59 3.52 2.40

35.7 31.5 26.6 21.1 14.8

10.2 13.5 9.00 11.8 7.61 9.79 6.02 7.63 4.22 5.29

2.33 2.37 2.41 2.45 2.48

9.08 8.11 6.95 5.57 3.96

6.05 5.41 4.63 3.71 2.64

7.32 6.40 5.36 4.20 2.93

1.18 1.20 1.23 1.26 1.29

25.1 22.0 18.5 14.6 10.2

6×4

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

28.43 22.37 19.08 15.62 11.97 8.16

8.36 6.58 5.61 4.59 3.52 2.40

35.3 29.7 26.2 22.1 17.4 12.2

11.8 15.4 9.90 12.5 8.72 10.9 7.36 9.06 5.81 7.06 4.08 4.88

2.06 2.13 2.16 2.19 2.23 2.26

18.4 15.6 13.8 11.7 9.32 6.57

9.21 7.82 6.92 5.87 4.66 3.29

11.5 9.44 8.21 6.84 5.34 3.71

1.48 1.54 1.57 1.60 1.63 1.66

42.1 34.6 30.1 25.0 19.5 13.5

6×3

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

25.03 19.82 16.96 13.91 10.70 7.31

7.36 5.83 4.98 4.09 3.14 2.15

27.7 23.8 21.1 17.9 14.3 10.1

9.25 12.6 7.92 10.4 7.03 9.11 5.98 7.62 4.76 5.97 3.36 4.15

1.94 2.02 2.06 2.09 2.13 2.17

8.91 7.78 6.98 6.00 4.83 3.45

5.94 5.19 4.65 4.00 3.22 2.30

7.59 6.34 5.56 4.67 3.68 2.57

1.10 1.16 1.18 1.21 1.24 1.27

23.9 20.3 17.9 15.1 11.9 8.27

6×2

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

17.27 14.83 12.21 9.42 6.46

5.08 4.36 3.59 2.77 1.90

17.8 16.0 13.8 11.1 7.92

5.94 5.34 4.60 3.70 2.64

8.33 7.33 6.18 4.88 3.42

1.87 1.92 1.96 2.00 2.04

2.84 2.62 2.31 1.90 1.39

3.61 3.22 2.75 2.20 1.56

0.748 0.775 0.802 0.829 0.857

8.72 7.94 6.88 5.56 3.98

5×4

0.3750 0.3125 0.2500 0.1875

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16

19.82 16.96 13.91 10.70

5.83 4.98 4.09 3.14

18.7 16.6 14.1 11.2

7.50 6.65 5.65 4.49

9.44 8.24 6.89 5.39

1.79 1.83 1.86 1.89

13.2 11.7 9.98 7.96

6.58 5.85 4.99 3.98

8.08 7.05 5.90 4.63

1.50 1.53 1.56 1.59

26.3 22.9 19.1 14.9

5×3

0.5000 0.3750 0.3125 0.2500 0.1875 0.1250

1⁄ 2 3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

21.63 17.27 14.83 12.21 9.42 6.46

6.36 5.08 4.36 3.59 2.77 1.90

16.9 14.7 13.2 11.3 9.06 6.44

6.75 5.89 5.27 4.52 3.62 2.58

9.20 7.71 6.77 5.70 4.49 3.14

1.63 1.70 1.74 1.77 1.81 1.84

7.33 6.48 5.85 5.05 4.08 2.93

4.88 4.32 3.90 3.37 2.72 1.95

6.34 5.35 4.72 3.98 3.15 2.21

1.07 1.13 1.16 1.19 1.21 1.24

18.2 15.6 13.8 11.7 9.21 6.44

*Outside dimensions across flatsides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 132

DIMENSIONS AND PROPERTIES

STRUCTURAL TUBING Rectangular Dimensions and properties

Dimensions

Properties**

Nominal* Wall Weight Size Thickness per ft Area in.

in.

X-X Axis

I 4

Z 3

Y-Y Axis

r 3

I 4

Z 3

in.

in.4

12.70 10.51 8.15 5.61

3.73 3.09 2.39 1.65

9.74 8.48 6.89 4.96

3.90 3.39 2.75 1.98

5.31 4.51 3.59 2.53

1.62 1.66 1.70 1.73

2.16 1.92 1.60 1.17

2.70 2.32 1.86 1.32

0.762 0.789 0.816 0.844

6.24 5.43 4.40 3.15

5×2

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

4×3

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

12.70 10.51 8.15 5.61

3.73 3.09 2.39 1.65

7.45 6.45 5.23 3.76

3.72 3.23 2.62 1.88

4.75 4.03 3.20 2.25

1.41 1.45 1.48 1.51

4.71 4.10 3.34 2.41

3.14 2.74 2.23 1.61

3.88 3.30 2.62 1.85

1.12 1.15 1.18 1.21

9.89 8.41 6.67 4.68

4×2

0.3750 0.3125 0.2500 0.1875 0.1250

3⁄ 8 5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

12.17 10.58 8.81 6.87 4.75

3.58 3.11 2.59 2.02 1.40

5.75 5.32 4.69 3.87 2.82

2.87 2.66 2.35 1.93 1.41

4.00 3.60 3.09 2.48 1.77

1.27 1.31 1.35 1.38 1.42

1.83 1.71 1.54 1.29 0.954

2.39 2.17 1.88 1.52 1.09

0.715 0.743 0.770 0.798 0.826

4.97 4.58 4.01 3.26 2.34

3×2

0.3125 0.2500 0.1875 0.1250

5⁄ 16 1⁄ 4 3⁄ 16 1⁄ 8

8.45 7.11 5.59 3.90

2.48 2.09 1.64 1.15

2.44 2.21 1.86 1.38

1.63 1.47 1.24 0.920

2.20 1.92 1.57 1.13

0.992 1.03 1.06 1.10

1.26 1.15 0.977 0.733

1.64 1.44 1.18 0.855

0.714 0.742 0.771 0.800

2.97 2.63 2.16 1.57

21⁄2×11⁄2

0.2500 0.1875

1⁄ 4 3⁄ 16

5.41 4.32

1.59 1.27

1.05 0.844 1.15 0.815 0.920 0.736 0.964 0.852

0.458 0.405

0.610 0.793 0.537 1.14 0.540 0.669 0.565 0.976

*Outside dimensions across flat sides. **Properties are based upon a nominal outside corner radius equal to two times the wall thickness.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

BARS AND PLATES

1 - 133

BARS AND PLATES Product Availability

Plates are readily available in seven of the structural steel specifications listed in Section A3.1 of the AISC LRFD Specification. These are: ASTM A36, A242, A529, A572, A588, A514, and A852. Bars are available in all of these steels except A514 and A852. Table 1-1 shows the availability of each steel in terms of plate thickness. The Manual user is referred to the discussion on p. 1-5, Selection of the Appropriate Structural Steel, for guidance in selection of both plate and structural shapes. Classification

Bars and plates are generally classified as follows: Bars: 6 in. or less in width, .203 in. and over in thickness. Over 6 in. to 8 in. in width, .230 in. and over in thickness. Plates: Over 8 in. to 48 in. in width, .230 in. and over in thickness. Over 48 in. in width, .180 in. and over in thickness. Bars

Bars are available in various widths, thicknesses, diameters, and lengths. The preferred practice is to specify widths in 1⁄4-in. increments and thickness and diameter in 1⁄8-in. increments. Plates

Defined according to rolling procedure: Sheared plates are rolled between horizontal rolls and trimmed (sheared or gas cut) on all edges. Universal (UM) plates are rolled between horizontal and vertical rolls and trimmed (sheared or gas cut) on ends only. Stripped plates are furnished to required widths by shearing or gas cutting from wider sheared plates. Sizes

Plate mills are located in various districts, but the sizes of plates produced differ greatly and the catalogs of individual mills should be consulted for detail data. The extreme width of UM plates currently rolled is 60 inches and for sheared plates it is 200 inches, but their availability together with limiting thickness and lengths should be checked with the mills before specifying. The preferred increments for width and thickness are: Widths:

Various. The catalogs of individual mills should be consulted to determine the most economical widths. Thickness: 1⁄32-in. increments up to 1⁄2-in. 1⁄ -in. increments over 1⁄ -in. to 1 in. 16 2 1⁄ -in. increments over 1 in. to 3 in. 8 1⁄ -in. increments over 3 in. 4 Ordering

Plate thickness may be specified in inches or by weight per square foot, but no decimal edge thickness can be assured by the latter method. Separate tolerance tables apply to each method. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 134

DIMENSIONS AND PROPERTIES

Table 1-7. Theoretical Weights of Rolled Floor Plates Gauge No.

Theoretical Weight per sq. ft lb

Nominal Thickness in.

2.40

1⁄ 8

3.00

3⁄

14 13 12

Nominal Thickness in.

Theoretical Weight per sq. ft, lb

6.16

1⁄ 2

21.47

8.71

9⁄ 16

24.02

3.75

1⁄ 4

11.26

5⁄ 8

26.58

4.50

5⁄

13.81

3⁄ 4

31.68

5.25

3⁄ 8

16.37

7⁄ 8

36.78

7⁄

18.92

41.89

Theoretical Weight per sq. ft, lb

Note: Thickness is measured near the edge of the plate, exclusive of raised pattern.

Invoicing

Standard practice is to invoice plates to the fabricator at theoretical weight at point of shipment. Permissible variations in weight are in accordance with the tables of ASTM Specification A6. All plates are invoiced at theoretical weight and, except as noted, are subject to the same weight variations which apply to rectangular plates. Odd shapes in most instances require gas cutting, for which gas cutting extras are applicable. All plates ordered gas cut for whatever reason, or beyond published shearing limits, take extras for gas cutting in addition to all other extras. Rolled steel bearing plates are often gas cut to prevent distortion due to shearing but would also take the regular extra for the thickness involved. Extras for thickness, width, length, cutting, quality and quantity, etc., which are added to the base price of plates, are subject to revision, and should be obtained by inquiry to the producer. The foregoing general statements are made as a guide toward economy in design. Floor Plates

Floor plates having raised patterns are available from several mills, each offering its own style of surface projections and in a variety of widths, thicknesses, and lengths. A maximum width of 96 inches and a maximum thickness of one inch are available, but availability of matching widths, thicknesses, and lengths should be checked with the producer. Floor plates are generally not specified to chemical composition limits or mechanical property requirements; a commercial grade of carbon steel is furnished. However, when strength or corrosion resistance is a consideration, raised pattern floor plates are procurable in any of the regular steel specifications. As in the case of plain plates, the individual manufacturers should be consulted for precise information. The nominal or ordered thickness is that of the flat plate, exclusive of the height or raised pattern. The usual weights are as shown in Table 1-7.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

BARS AND PLATES

1 - 135

SQUARE AND ROUND BARS Weight and area Weight lb per ft

Area Sq in.

Size in. 0

Weight lb per ft

Area Sq in.

Size in.

1⁄ 16 1⁄ 8 3⁄ 16

0.013 0.053 0.120

0.010 0.042 0.094

0.0039 0.0156 0.0352

0.0031 0.0123 0.0276

1⁄ 16 1⁄ 8 3⁄ 16

30.63 31.91 33.23 34.57

24.05 25.07 26.10 27.15

9.000 9.379 9.766 10.160

7.069 7.366 7.670 7.980

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

0.213 0.332 0.479 0.651

0.167 0.261 0.376 0.512

0.0625 0.0977 0.1406 0.1914

0.0491 0.0767 0.1104 0.1503

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

35.94 37.34 38.76 40.21

28.23 29.32 30.44 31.58

10.563 10.973 11.391 11.816

8.296 8.618 8.946 9.281

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

0.851 1.077 1.329 1.608

0.668 0.846 1.044 1.263

0.2500 0.3164 0.3906 0.4727

0.1964 0.2485 0.3068 0.3712

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

41.68 43.19 44.71 46.27

32.74 33.92 35.12 36.34

12.250 12.691 13.141 13.598

9.621 9.968 10.321 10.680

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1.914 2.246 2.605 2.991

1.503 1.764 2.046 2.349

0.5625 0.6602 0.7656 0.8789

0.4418 0.5185 0.6013 0.6903

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

47.85 49.46 51.09 52.76

37.58 38.85 40.13 41.43

14.063 14.535 15.016 15.504

11.045 11.416 11.793 12.177

1⁄ 16 1⁄ 8 3⁄ 16

3.403 3.841 4.307 4.798

2.673 3.017 3.382 3.769

1.0000 1.1289 1.2656 1.4102

0.7854 0.8866 0.9940 1.1075

1⁄ 16 1⁄ 8 3⁄ 16

54.44 56.16 57.90 59.67

42.76 44.11 45.47 46.86

16.000 16.504 17.016 17.535

12.566 12.962 13.364 13.772

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

5.317 5.862 6.433 7.032

4.176 4.604 5.053 5.523

1.5625 1.7227 1.8906 2.0664

1.2272 1.3530 1.4849 1.6230

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

61.46 63.28 65.13 67.01

48.27 49.70 51.15 52.63

18.063 18.598 19.141 19.691

14.186 14.607 15.033 15.466

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

7.656 8.308 8.985 9.690

6.013 6.525 7.057 7.610

2.2500 2.4414 2.6406 2.8477

1.7672 1.9175 2.0739 2.2365

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

68.91 70.83 72.79 74.77

54.12 55.63 57.17 58.72

20.250 20.816 21.391 21.973

15.904 16.349 16.800 17.257

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

10.421 11.179 11.963 12.774

8.185 8.780 9.396 10.032

3.0625 3.2852 3.5156 3.7539

2.4053 2.5802 2.7612 2.9483

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

76.78 78.81 80.87 82.96

60.30 61.90 63.51 65.15

22.563 23.160 23.766 24.379

17.721 18.190 18.666 19.147

1⁄ 16 1⁄ 8 3⁄ 16

13.611 14.475 15.366 16.283

10.690 11.369 12.068 12.789

4.0000 4.2539 4.5156 4.7852

3.1416 3.3410 3.5466 3.7583

1⁄ 16 1⁄ 8 3⁄ 16

85.07 87.21 89.38 91.57

66.81 68.49 70.20 71.92

25.000 25.629 26.266 26.910

19.635 20.129 20.629 21.135

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

17.227 18.197 19.194 20.217

13.530 14.292 15.075 15.879

5.0625 5.3477 5.6406 5.9414

3.9761 4.2000 4.4301 4.6664

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

93.79 96.04 98.31 100.61

73.66 75.43 77.21 79.02

27.563 28.223 28.891 29.566

21.648 22.166 22.691 23.221

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

21.267 22.344 23.447 24.577

16.703 17.549 18.415 19.303

6.2500 6.5664 6.8906 7.2227

4.9087 5.1573 5.4119 5.6727

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

102.93 105.29 107.67 110.07

80.84 82.69 84.56 86.45

30.250 30.941 31.641 32.348

23.758 24.301 24.851 25.406

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

25.734 26.917 28.126 29.362

20.211 21.140 22.090 23.061

7.5625 7.9102 8.2656 8.6289

5.9396 6.2126 6.4918 6.7771

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

112.50 114.96 117.45 119.96

88.36 90.29 92.24 94.22

33.063 33.785 34.516 35.254

25.967 26.535 27.109 27.688

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 136

DIMENSIONS AND PROPERTIES

SQUARE AND ROUND BARS Weight and area Weight lb per ft

Area Sq in.

Size in. 6

Weight lb per ft

Area Sq in.

Size in.

1⁄ 16 1⁄ 8 3⁄ 16

122.50 125.07 127.66 130.28

96.21 98.23 100.26 102.32

36.000 36.754 37.516 38.285

28.274 28.867 29.465 30.069

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

132.92 135.59 138.29 141.02

104.40 106.49 108.61 110.75

39.063 39.848 40.641 41.441

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

143.77 146.55 149.35 152.18

112.91 115.10 117.30 119.52

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

155.04 157.92 160.83 163.77

1⁄ 16 1⁄ 8 3⁄ 16

275.63 279.47 283.33 287.23

216.48 219.49 222.53 225.59

81.000 82.129 83.266 84.410

63.617 64.504 65.397 66.296

30.680 31.296 31.919 32.548

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

291.15 295.10 299.07 303.07

228.67 231.77 234.89 238.03

85.563 86.723 87.891 89.066

67.201 68.112 69.029 69.953

42.250 43.066 43.891 44.723

33.183 33.824 34.472 35.125

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

307.10 311.15 315.24 319.34

241.20 244.38 247.59 250.81

90.250 91.441 92.641 93.848

70.882 71.818 72.760 73.708

121.77 124.03 126.32 128.63

45.563 46.410 47.266 48.129

35.785 36.451 37.122 37.800

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

323.48 327.64 331.82 336.04

254.06 257.33 260.61 263.92

95.063 96.285 97.516 98.754

74.662 75.622 76.589 77.561

1⁄ 16 1⁄ 8 3⁄ 16

166.74 169.73 172.74 175.79

130.95 133.30 135.67 138.06

49.000 49.879 50.766 51.660

38.485 39.175 39.871 40.574

1⁄ 16 1⁄ 8 3⁄ 16

340.28 344.54 348.84 353.16

267.25 270.61 273.98 277.37

100.000 101.254 102.516 103.785

78.540 79.525 80.516 81.513

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

178.86 181.96 185.08 188.23

140.48 142.91 145.36 147.84

52.563 53.473 54.391 55.316

41.283 41.997 42.718 43.446

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

357.50 361.88 366.28 370.70

280.78 284.22 287.67 291.15

105.063 106.348 107.641 108.941

82.516 83.525 84.541 85.563

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

191.41 194.61 197.84 201.10

150.33 152.85 155.38 157.94

56.250 57.191 58.141 59.098

44.179 44.918 45.664 46.415

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

375.16 379.64 384.14 388.67

294.65 298.17 301.70 305.26

110.250 111.566 112.891 114.223

86.590 87.624 88.664 89.710

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

204.38 207.69 211.03 214.39

160.52 163.12 165.74 168.38

60.063 61.035 62.016 63.004

47.173 47.937 48.707 49.483

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

393.23 397.82 402.43 407.07

308.85 312.45 316.07 319.71

115.563 116.910 118.266 119.629

90.763 91.821 92.886 93.957

1⁄ 16 1⁄ 8 3⁄ 16

217.78 221.19 224.64 228.11

171.04 173.73 176.43 179.15

64.000 65.004 66.016 67.035

50.266 51.054 51.849 52.649

1⁄ 16 1⁄ 8 3⁄ 16

411.74 416.43 421.15 425.89

323.38 327.06 330.77 334.50

121.000 122.379 123.766 125.160

95.033 96.116 97.206 98.301

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

231.60 235.12 238.67 242.25

181.90 184.67 187.45 190.26

68.063 69.098 70.141 71.191

53.456 54.269 55.088 55.914

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

430.66 435.46 440.29 445.14

338.24 342.01 345.80 349.61

126.563 127.973 129.391 130.816

99.402 100.510 101.623 102.743

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

245.85 249.48 253.13 256.82

193.09 195.94 198.81 201.70

72.250 73.316 74.391 75.473

56.745 57.583 58.426 59.276

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

450.02 454.92 459.85 464.81

353.44 357.30 361.17 365.06

132.250 133.691 135.141 136.598

103.869 105.001 106.139 107.284

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

260.53 264.26 268.02 271.81

204.62 207.55 210.50 213.48

76.563 77.660 78.766 79.879

60.132 60.994 61.863 62.737

3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

469.80 474.81 479.84 484.91

368.98 372.91 376.87 380.85

138.063 139.535 141.016 142.504

108.434 109.591 110.754 111.923

490.00

384.85

144.000

113.098

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

BARS AND PLATES

1 - 137

AREA OF RECTANGULAR SECTIONS Square inches Width in.

Thickness, inches 3⁄ 16

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

9⁄ 16

5⁄ 8

11⁄ 16

3⁄ 4

13⁄ 16

0.047 0.093 0.141 0.188

0.063 0.125 0.188 0.250

0.078 0.156 0.234 0.313

0.094 0.188 0.281 0.375

0.109 0.219 0.328 0.438

0.125 0.250 0.375 0.500

0.141 0.281 0.422 0.563

0.156 0.313 0.469 0.625

0.172 0.344 0.516 0.688

0.188 0.375 0.563 0.75

0.203 0.406 0.609 0.813

0.219 0.438 0.656 0.875

0.234 0.469 0.703 0.938

0.250 0.500 0.750 1.00

11⁄4 11⁄2 13⁄4 2

0.234 0.281 0.328 0.375

0.313 0.375 0.438 0.500

0.391 0.469 0.547 0.625

0.469 0.563 0.656 0.750

0.547 0.656 0.766 0.875

0.625 0.750 0.875 1.00

0.703 0.844 0.984 1.13

0.781 0.938 1.09 1.25

0.859 1.03 1.20 1.38

0.938 1.13 1.31 1.50

1.02 1.22 1.42 1.63

1.09 1.31 1.53 1.75

1.17 1.41 1.64 1.88

1.25 1.50 1.75 2.00

21⁄4 21⁄2 23⁄4 3

0.422 0.469 0.516 0.563

0.563 0.625 0.688 0.750

0.703 0.781 0.859 0.938

0.844 0.938 1.03 1.13

0.984 1.09 1.20 1.31

1.13 1.25 1.38 1.50

1.27 1.41 1.55 1.69

1.41 1.56 1.72 1.88

1.55 1.72 1.89 2.06

1.69 1.88 2.06 2.25

1.83 2.03 2.23 2.44

1.97 2.19 2.41 2.63

2.11 2.34 2.58 2.81

2.25 2.50 2.75 3.00

31⁄4 31⁄2 33⁄4 4

0.609 0.656 0.703 0.750

0.813 0.875 0.938 1.00

1.02 1.09 1.17 1.25

1.22 1.31 1.41 1.50

1.42 1.53 1.64 1.75

1.63 1.75 1.88 2.00

1.83 1.97 2.11 2.25

2.03 2.19 2.34 2.50

2.23 2.41 2.58 2.75

2.44 2.63 2.81 3.00

2.64 2.84 3.05 3.25

2.84 3.06 3.28 3.50

3.05 3.28 3.52 3.75

3.25 3.50 3.75 4.00

41⁄4 41⁄2 43⁄4 5

0.797 0.844 0.891 0.938

1.06 1.13 1.19 1.25

1.33 1.41 1.48 1.56

1.59 1.69 1.78 1.88

1.86 1.97 2.08 2.19

2.13 2.25 2.38 2.50

2.39 2.53 2.67 2.81

2.66 2.81 2.97 3.13

2.92 3.09 3.27 3.44

3.19 3.38 3.56 3.75

3.45 3.66 3.86 4.06

3.72 3.94 4.16 4.38

3.98 4.22 4.45 4.69

4.25 4.50 4.75 5.00

51⁄4 51⁄2 53⁄4 6

0.984 1.03 1.08 1.13

1.31 1.38 1.44 1.50

1.64 1.72 1.80 1.88

1.97 2.06 2.16 2.25

2.30 2.41 2.52 2.63

2.63 2.75 2.88 3.00

2.95 3.09 3.23 3.38

3.28 3.44 3.59 3.75

3.61 3.78 3.95 4.13

3.94 4.13 4.31 4.50

4.27 4.47 4.67 4.88

4.59 4.81 5.03 5.25

4.92 5.16 5.39 5.63

5.25 5.50 5.75 6.00

61⁄4 61⁄2 63⁄4 7

1.17 1.22 1.27 1.31

1.56 1.63 1.69 1.75

1.95 2.03 2.11 2.19

2.34 2.44 2.53 2.63

2.73 2.84 2.95 3.06

3.13 3.25 3.38 3.50

3.52 3.66 3.80 3.94

3.91 4.06 4.22 4.38

4.30 4.47 4.64 4.81

4.69 4.88 5.06 5.25

5.08 5.28 5.48 5.69

5.47 5.69 5.91 6.13

5.86 6.09 6.33 6.56

6.25 6.50 6.75 7.00

71⁄4 71⁄2 73⁄4 8

1.36 1.41 1.45 1.50

1.81 1.88 1.94 2.00

2.27 2.34 2.42 2.50

2.72 2.81 2.91 3.00

3.17 3.28 3.39 3.50

3.63 3.75 3.88 4.00

4.08 4.22 4.36 4.50

4.53 4.69 4.84 5.00

4.98 5.16 5.33 5.50

5.44 5.63 5.81 6.00

5.89 6.09 6.30 6.50

6.34 6.56 6.78 7.00

6.80 7.03 7.27 7.50

7.25 7.50 7.75 8.00

81⁄2 9

1.59 1.69

2.13 2.25

2.66 2.81

3.19 3.38

3.72 3.94

4.25 4.50

4.78 5.06

5.31 5.63

5.84 6.19

6.38 6.75

6.91 7.31

7.44 7.88

7.97 8.44

8.50 9.00

91⁄2 10

1.78 1.88

2.38 2.50

2.97 3.13

3.56 3.75

4.16 4.38

4.75 5.00

5.34 5.63

5.94 6.25

6.53 6.88

7.13 7.50

7.72 8.13

8.31 8.75

8.91 9.38

9.50 10.0

101⁄2 11

1.97 2.06

2.63 2.75

3.28 3.44

3.94 4.13

4.59 4.81

5.25 5.50

5.91 6.19

6.56 6.88

7.22 7.56

7.88 8.25

8.53 8.94

9.19 9.63

9.84 10.3

10.5 11.0

111⁄2 12

2.16 2.25

2.88 3.00

3.59 3.75

4.31 4.50

5.03 5.25

5.75 6.00

6.47 6.75

7.19 7.50

7.91 8.63 8.25 9.00

9.34 9.75

10.8 11.3

11.5 12.0

1⁄ 4 1⁄ 2 3⁄ 4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7⁄ 8

10.1 10.5

15⁄ 16

1 - 138

DIMENSIONS AND PROPERTIES

WEIGHT OF RECTANGULAR SECTIONS Pounds per linear foot Width in.

Thickness, inches 3⁄ 16

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

9⁄ 16

5⁄ 8

11⁄ 16

3⁄ 4

13⁄ 16

7⁄ 8

15⁄ 16

0.160 0.319 0.479 0.638

0.213 0.425 0.638 0.851

0.266 0.532 0.798 1.06

0.319 0.638 0.957 1.28

0.372 0.744 1.12 1.49

0.425 0.851 1.28 1.70

0.479 0.957 1.44 1.91

0.532 1.06 1.60 2.13

0.585 1.17 1.75 2.34

0.638 1.28 1.91 2.55

0.691 1.38 2.07 2.76

0.744 1.49 2.23 2.98

0.798 1.60 2.39 3.19

0.851 1.70 2.55 3.40

11⁄4 11⁄2 13⁄4 2

0.798 0.957 1.12 1.28

1.06 1.28 1.49 1.70

1.33 1.60 1.86 2.13

1.60 1.91 2.23 2.55

1.86 2.23 2.61 2.98

2.13 2.55 2.98 3.40

2.39 2.87 3.35 3.83

2.66 3.19 3.72 4.25

2.92 3.51 4.09 4.68

3.19 3.83 4.47 5.10

3.46 4.15 4.84 5.53

3.72 4.47 5.21 5.95

3.99 4.79 5.58 6.38

4.25 5.10 5.95 6.81

21⁄4 21⁄2 23⁄4 3

1.44 1.60 1.75 1.91

1.91 2.13 2.34 2.55

2.39 2.66 2.92 3.19

2.87 3.19 3.51 3.83

3.35 3.72 4.09 4.47

3.83 4.25 4.68 5.10

4.31 4.79 5.26 5.74

4.79 5.32 5.85 6.38

5.26 5.85 6.43 7.02

5.74 6.38 7.02 7.66

6.22 6.91 7.60 8.29

6.70 7.44 8.19 8.93

7.18 7.98 8.77 9.57

7.66 8.51 9.36 10.2

31⁄4 31⁄2 33⁄4 4

2.07 2.23 2.39 2.55

2.76 2.98 3.19 3.40

3.46 3.72 3.99 4.25

4.15 4.47 4.79 5.10

4.84 5.21 5.58 5.95

5.53 5.95 6.38 6.81

6.22 6.70 7.18 7.66

6.91 7.44 7.98 8.51

7.60 8.19 8.77 9.36

8.29 8.93 9.57 10.2

8.99 9.68 10.4 11.1

9.68 10.4 11.2 11.9

10.4 11.2 12.0 12.8

11.1 11.9 12.8 13.6

41⁄4 41⁄2 43⁄4 5

2.71 2.87 3.03 3.19

3.62 3.83 4.04 4.25

4.52 4.79 5.05 5.32

5.42 5.74 6.06 6.38

6.33 6.70 7.07 7.44

7.23 7.66 8.08 8.51

8.13 8.61 9.09 9.57

9.04 9.57 10.1 10.6

9.94 10.5 11.1 11.7

10.8 11.5 12.1 12.8

11.8 12.4 13.1 13.8

12.7 13.4 14.1 14.9

13.6 14.4 15.2 16.0

14.5 15.3 16.2 17.0

51⁄4 51⁄2 53⁄4 6

3.35 3.51 3.67 3.83

4.47 4.68 4.89 5.10

5.58 5.85 6.11 6.38

6.70 7.02 7.34 7.66

7.82 8.19 8.56 8.93

8.93 9.36 9.78 10.2

10.0 10.5 11.0 11.5

11.2 11.7 12.2 12.8

12.3 12.9 13.5 14.0

13.4 14.0 14.7 15.3

14.5 15.2 15.9 16.6

15.6 16.4 17.1 17.9

16.7 17.5 18.3 19.1

17.9 18.7 19.6 20.4

61⁄4 61⁄2 63⁄4 7

3.99 4.15 4.31 4.47

5.32 5.53 5.74 5.95

6.65 6.91 7.18 7.44

7.98 8.29 8.61 8.93

9.30 9.68 10.0 10.4

10.6 11.1 11.5 11.9

12.0 12.4 12.9 13.4

13.3 13.8 14.4 14.9

14.6 15.2 15.8 16.4

16.0 16.6 17.2 17.9

17.3 18.0 18.7 19.4

18.6 19.4 20.1 20.8

19.9 20.7 21.5 22.3

21.3 22.1 23.0 23.8

71⁄4 71⁄2 73⁄4 8

4.63 4.79 4.94 5.10

6.17 6.38 6.59 6.81

7.71 7.98 8.24 8.51

9.25 9.57 9.89 10.2

10.8 11.2 11.5 11.9

12.3 12.8 13.2 13.6

13.9 14.4 14.8 15.3

15.4 16.0 16.5 17.0

17.0 17.5 18.1 18.7

18.5 19.1 19.8 20.4

20.0 20.7 21.4 22.1

21.6 22.3 23.1 23.8

23.1 23.9 24.7 25.5

24.7 25.5 26.4 27.2

81⁄2 9

5.42 5.74

7.23 7.66

9.04 9.57

10.8 11.5

12.7 13.4

14.5 15.3

16.3 17.2

18.1 19.1

19.9 21.1

21.7 23.0

23.5 24.9

25.3 26.8

27.1 28.7

28.9 30.6

91⁄2 10

6.06 6.38

8.08 8.51

10.1 10.6

12.1 12.8

14.1 14.9

16.2 17.0

18.2 19.1

20.2 21.3

22.2 23.4

24.2 25.5

26.3 27.6

28.3 29.8

30.3 31.9

32.3 34.0

101⁄2 11

6.70 7.02

8.93 9.36

11.2 11.7

13.4 14.0

15.6 16.4

17.9 18.7

20.1 21.1

22.3 23.4

24.6 25.7

26.8 28.1

29.0 30.4

31.3 32.8

33.5 35.1

35.7 37.4

111⁄2 12

7.34 7.66

9.78 10.2

12.2 12.8

14.7 15.3

17.1 17.9

19.6 20.4

22.0 23.0

24.5 25.5

26.9 28.1

29.3 30.6

31.8 33.2

34.2 35.7

36.7 38.3

39.1 40.8

1⁄ 4 1⁄ 2 3⁄ 4

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

CRANE RAILS

1 - 139

CRANE RAILS General Notes

The ASCE rails and the 104- to 175-lb crane rails shown in Figure 1-2 are recommended for crane runway use. For complete details and for profiles and properties of rails not listed, consult manufacturers’ catalogs. Rails should be arranged so that joints on opposite sides of the crane runway will be staggered with respect to each other and with due consideration to the wheelbase of the crane. Rail joints should not occur at crane girder splices. Light 40-lb rails are available in 30-ft lengths, 60-lb rails in 30-, 33- or 39-ft lengths, standard rails in 33- or 39-ft lengths and crane rails up to 80 ft. Consult manufacturer for availability of other lengths. Odd lengths, which must be included to complete a run or obtain the necessary stagger, should be not less than 10 feet long. For crane rail service, 40-lb rails are furnished to manufacturers’ specifications and tolerances. 60- and 85-lb rails are furnished to manufacturers’ specifications and tolerances, or to ASTM A1. Crane rails are furnished to ASTM A759. Rails will be furnished with standard drilling in both standard and odd lengths unless stipulated otherwise on order. For controlled cooling, heat treatment, and rail end preparation, see manufacturers’ catalogs. Purchase orders for crane rails should be noted “For crane service.” (See Table 1-8.) For maximum wheel loadings see manufacturers’ catalogs. Splices

Bolted Splices

It is often more desirable to use properly installed and maintained bolted splice bars in making up rail joints for crane service than welded splice bars. Standard rail drilling and joint-bar punching, as furnished by manufacturers of light standard rails for track work, include round holes in rail ends and slotted holes in joint bars to receive standard oval-neck tack bolts. Holes in rails are oversize and punching in joint bars is spaced to allow 1⁄16- to 1⁄8-in. clearance between rail ends (see manufacturers’ catalogs for spacing and dimensions of holes and slots). Although this construction is satisfactory for track and light crane service, its use in general crane service may lead to joint failure. For best service in bolted splices, it is recommended that tight joints be stipulated for all rails for crane service. This will require rail ends to be finished by milling or grinding, and the special rail drilling and joint-bar punching tabulated below. Special rail drilling is accepted by some mills, or rails may be ordered blank for shop drilling. End finishing of standard rails can be done at the mill; light rails must be end-finished in the fabricating shop or ground at the site prior to erection. In the crane rail range, from 104 to 175 lbs per yard, rails and joint bars are manufactured to obtain a tight fit and no further special end finishing, drilling, or punching is required. Because of cumulative tolerance variations in holes, bolt diameters, and rail ends, a slight gap may sometimes occur in the so-called tight joints. Conversely, it may sometimes be necessary to ream holes through joined bar and rail to permit entry of bolts. Joint bars for crane service are provided in various sections to match the rails. Joint bars for light and standard rails may be purchased blank for special shop punching to obtain tight joints. See Bethlehem Steel Corp. Booklet 3351 for dimensions, material specifications, and the identification necessary to match the crane rail section. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 140

DIMENSIONS AND PROPERTIES

Bars can be sheared off r

13°

c of g y

13°

1/ 4 Rad.

1/ 2 Rad.

13°

A.S.C.E. 40, 60 & 85 lb. c

BETHLEHEM 104 lb. c 4

3 (approx.)

12°

13° 3 4

Rad.

3 4

Rad.

7/ 8

7/ 8 Rad.

13°

12° m

BETHLEHEM 135 lb.

Rad.

BETHLEHEM 171 lb.

c 4 1/32 (approx.)

12°

2 Rad.

11/8 Rad. 12°

h 2 53/64 m

BETHLEHEM 175 lb. Nomenclature of sketch for A.S.C.E. rails also applies to the other sections.

Fig. 1-2. Crane rails. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

CRANE RAILS

1 - 141

Table 1-8. Crane Rails Dimensions and Properties

Type

Nominal Wt. per Classi- Yd. d fication lb in.

Gage g

Area

in.

in.2

in.4

17⁄ 32 5⁄ 8 11⁄ 16 48⁄ 64 13⁄ 16 7⁄ 8 57⁄ 64 31⁄ 32 11⁄16 11⁄16 11⁄4 19⁄64

11⁄ 64 7⁄ 32 1⁄ 4 9⁄ 32 9⁄ 32 19⁄ 64 19⁄ 64 10⁄ 32 1⁄ 2 15⁄ 32 5⁄ 8 1⁄ 2

111⁄16

3.00 4.10 2.55

155⁄64

3.94 6.54 3.59 3.89 1.68

21⁄8

23⁄8

27⁄16

21⁄2

29⁄16

23⁄4

21⁄ 64 25⁄ 64 7⁄ 16 31⁄ 64 33⁄ 64 35⁄ 64 9⁄ 16 9⁄ 16

123⁄32

17⁄8

21⁄2

ASCE

Light

31⁄8

125⁄64

31⁄8

ASCE

Light

31⁄2

171⁄128

31⁄2

ASCE

Light

37⁄8

123⁄32

37⁄8

ASCE

Light

41⁄4 1115⁄128 41⁄4

ASCE

45⁄8

23⁄64

45⁄8

ASCE

23⁄16

ASCE

Std.

53⁄16

217⁄64

53⁄16

ASCE

Std.

100

53⁄4

265⁄128

53⁄4

Bethlehem

Crane

104

27⁄16

Bethlehem

Crane

135

53⁄4

215⁄32

53⁄16

Bethlehem

Crane

171

25⁄8

Bethlehem

Crane

175

221⁄32

Hd. Base

in.3

in.

—

21⁄16

4.90 10.1

5.10

217⁄64

5.93 14.6

6.64 7.12 2.05

215⁄32

6.81 19.7

8.19 8.87 2.22

25⁄8

7.86 26.4 10.1 11.1 2.38

23⁄4

8.33 30.1 11.1 12.2 2.47

25⁄64

9.84 44.0 14.6 16.1 2.73

27⁄16

31⁄2

10.3 29.8 10.7 13.5 2.21

13.3 50.8 17.3 18.1 2.81

—

1.88

37⁄16

11⁄4 213⁄16

4.3

Flat

11⁄4

23⁄4 Vert. 16.8 73.4 24.5 24.4 3.01

41⁄4

11⁄2

37⁄64 Vert. 17.1 70.5 23.4 23.6 2.98

Joint-bar bolts, as distinguished from oval-neck track bolts, have straight shanks to the head and are manufactured to ASTM A449 specifications. Nuts are manufactured to ASTM A563 Gr. B specifications. ASTM A325 bolts and nuts may be used. Bolt assembly includes an alloy steel spring washer, furnished to AREA specifications. After installation, bolts should be retightened within 30 days and every three months thereafter. Welded Splices

When welded splices are specified, consult the manufacturer for recommended rail-end preparation, welding procedure, and method of ordering. Although joint continuity, made possible by this method of splicing, is desirable, it should be noted that the careful control required in all stages of the welding operation may be difficult to meet during crane rail installation. Rails should not be attached to structural supports by welding. Rails with holes for joint bar bolts should not be used in making welded splices. Fastenings

Hook Bolts

Hook bolts (Figure 1-3) are used primarily with light rails when attached to beams too narrow for clamps. Rail adjustment to ±1⁄2-in. is inherent in the threaded shank. Hook bolts are paired alternately three to four inches apart, spaced at about 24-in. centers. The special rail drilling required must be done at the fabricator’s shop. Hook bolts are not recommended for use with heavy duty cycle cranes (CMAA Classes, D, E, and F). It is generally recommended that hook bolts should not be used in runway systems which are longer than 500 feet because the bolts do not allow for longitudinal movement of the rail. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 142

DIMENSIONS AND PROPERTIES

Table 1-9. Splices for Tight Joints

Rail End

Joint Bar

Grip

Grip H

G Cut when specified 40-60-85-104

Rail

Joint Bar

Drilling Wt. Per Yard

in.

40 171⁄128 60 1115⁄128 85 217⁄64 104

27⁄16

135 215⁄32 171

25⁄8

175

221⁄32

Hole Dia. A in. 13⁄ * 16 13⁄ * 16 15⁄ * 16 11⁄16 13⁄16 13⁄16 13⁄16

105-135-171-175

B C

in. in. in. 21⁄2 5

—

21⁄2 5

—

21⁄2 5

—

Bolt

Washer

Punching

Wt. 2 Bars Bolts, Nuts, Washers

ThickIn- ness side and With Less Dia. Width Fig. Fig.

Hole Dia.

B C

Dia.

Grip

in.

in. in. in.

in.

13⁄ * 16 13⁄ * 16 15⁄ * 16 11⁄16 13⁄16 13⁄16 13⁄16

415⁄16*

— 20 23⁄16

3⁄

115⁄16

31⁄2

21⁄2

16.5

— 24 211⁄16

3⁄

219⁄32

211⁄16

36.5

29.6

415⁄16*

— 24 311⁄32

7⁄

35⁄32

43⁄4

33⁄16

56.6

45.3

715⁄16

31⁄2

51⁄4

31⁄2

715⁄16

—

11⁄8

35⁄8

51⁄2

311⁄16

715⁄16

—

11⁄8

47⁄16

61⁄4

41⁄16

—

11⁄8

41⁄8

61⁄4

315⁄16

7⁄ ×3⁄ 16 8 7⁄ ×3⁄ 16 8 7⁄ ×3⁄ 16 8 7⁄ ×1⁄ 16 2 7⁄ ×1⁄ 16 2 7⁄ ×1⁄ 16 2 7⁄ ×1⁄ 16 2

20.0

415⁄16*

13⁄ 16 13⁄ 16 15⁄ 16 11⁄16 13⁄16 13⁄16 13⁄16

715⁄16

73.5

55.4

—

75.3

—

90.8

—

87.7

*Special rail drilling and joint-bar punching.

Rail Clips

Rail clips are forged or cast devices which are shaped to match specific rail profiles. They are usually bolted to the runway girder flange with one bolt or are sometimes welded. Rail clips have been used satisfactorily with all classes of cranes. However, one drawback is that when a single bolt is used the clip can rotate in response to rail longitudinal movement. This clip rotation can cause a camming action, thus forcing the rail out of alignment. Because of this limitation, rail clips should only be used in crane systems subject to infrequent use, and for runways less than 500 feet in length. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

CRANE RAILS

1 - 143

Rail Clamps

Rail clamps are a common method of attachment for heavy duty cycle cranes. Rail clamps are detailed to provide two types: tight and floating (Figure 1-4). Each clamp consists of two plates: an upper clamp plate and a lower filler plate. The lower plate is flat and roughly matches the height of the toe of the rail flange. The upper plate covers the lower plate and extends over the top of the lower rail flange. In the tight clamp the upper plate is detailed to fit tightly to the lower tail flange top, thus â&#x20AC;&#x153;clampingâ&#x20AC;? it tightly in place when the fasteners are tightened. In the past, the tight clamp had been illustrated with the filler plates fitted tightly against the rail flange toe. This tight fit-up was rarely achieved in practice and is not considered to be necessary to achieve a tight type clamp. In the floating type clamp, the pieces are detailed to provide a clearance both alongside the rail flange toe and below the upper plate. The floating type does not, in reality, clamp the rail but merely holds the rail within the limits of the clamp clearances.

Fig. 1-3. Hook bolts. Reversible 1 1/2 fillers

Reversible fillers

Clamp plates

Off-center punching

11/2

Clamp plates

Off-center punching

11/2

1 1/2

Rail base + 1/ 4

( 1/2 to 9/16 ) "float"

Max. adjustment

Self-locking nut or nut and lock washer Filler Machine bolt Gage

Gage

Tight clamp

Floating clamp

Fig. 1-4. Rail clamps. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 144

DIMENSIONS AND PROPERTIES

High strength bolts are recommended for both clamp types. Both types should be spaced three feet or less apart. Dimensions shown above are suggested. See manufacturers’ catalogs for recommended gages, bolt sizes, and detail dimensions not shown. Patented Rail Clips

Each manufacturer’s literature presents in detail the desirable aspects of the various designs. In general patented rail clips are easy to install due to their range of adjustment while providing the proper limitations of lateral movement and allowance for longitudinal movement. Patented rail clips should be considered as a viable alternative to conventional hook bolts, clips, or clamps. Because of their desirable characteristics, patented rail clips can be used without restriction except as limited by the specific manufacturer’s recommendations. Installations using patented rail clips sometimes incorporate pads beneath the rail. When this is done the lateral float of the rail should be limited as in the case of the tight rail clamps.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

TORSION PROPERTIES

1 - 145

TORSION PROPERTIES

Torsional analysis is not required for the routine design of most structural steel members. When torsional analysis is required, the Table of Torsion Properties will be of assistance in utilizing current analysis methods. The reader is referred to the AISC publication Torsional Analysis of Steel Members (American Institute of Steel Construction, 1983) for additional information and appropriate design aids. Torsion Properties are also required to determine the design compressive strength for torsional and flexural-torsional buckling as specified in the AISC LRFD Specification Appendix E3. Nomenclature

= warping constant for section, in.6* = modulus of elasticity of steel (29,000 ksi) = shear modulus of elasticity of steel (11,200 ksi) = flexural constant in Equation E3-1, LRFD Specification = torsional constant for a section, in.4 = statical moment for a point in the flange directly above the vertical edge of the web, in.3 3 _Qw = statical moment at mid-depth of the section, in. ro = polar radius of gyration about the shear center, in. Sw = warping statical moment at a point in the section, in.4 Wno = normalized warping function at a point at the flange edge, in.2 Cw E G H J Qf

*Calculated values of Cw are given for all tabulated shapes. However, for many angles and T shapes, Cw is so small that for practical purposes it can be taken as zero. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 146

DIMENSIONS AND PROPERTIES

TORSION PROPERTIES W shapes

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.

in.2

in.4

in.3

137 153 167 190

168 166 165 164

1190 1040 922 789

282 251 225 194

811 709 636 551

989000 649000 577000 511000 446000 397000 378000 333000 283000 245000 189000

75.4 95.1 103 110 121 130 138 151 173 187 209

166 158 156 154 152 151 151 149 149 148 147

2240 1540 1380 1240 1100 986 940 836 714 621 481

484 354 323 294 264 240 230 208 179 157 119

1380 992 894 813 730 665 624 560 481 434 364

393000 306000 242000 192000 181000 161000 140000 119000 99300 79600

60.6 67.9 76.8 87.6 91.3 101 109 125 136 147

125 121 118 115 114 113 112 111 111 110

1160 940 762 622 589 530 468 402 336 270

322 272 228 192 184 168 151 134 113 92.0

1030 856 715 596 566 506 453 391 346 299

1620000 1480000 1090000 816000 637000 554000 493000 441000 398000 366000 330000 306000 282000

57.5 59.8 68.6 80.0 92.0 100 108 116 127 134 143 151 160

172 169 162 156 152 150 148 146 146 145 144 143 143

3530 3270 2520 1960 1570 1390 1240 1130 1020 944 858 799 740

674 634 513 415 344 309 281 258 235 219 200 187 175

1910 1790 1420 1130 928 830 757 691 628 585 538 505 472

168000 148000 128000 116000 107000 98500 90200 82200 68100

90.3 98.1 109 116 123 130 137 145 159

109 108 108 107 106 105 105 105 104

576 512 446 407 378 349 321 294 245

408000 357000 319000 281000 250000 224000 198000

95.8 105 113 122 134 145 158

135 133 132 130 130 129 128

1130 1000 906 808 721 650 580

Torsional Constant J

Warping Constant Cw

Designation

in.4

in.6

W44×335 W ×290 W ×262 W ×230

74.4 51.5 37.7 24.9

536000 463000 406000 346000

W40×593 W ×503 W ×431 W ×372 W ×321 W ×297 W ×277 W ×249 W ×215 W ×199 W ×174

451 186 142 109 79.4 61.2 51.1 37.7 24.4 18.1 11.2

W40×466 W ×392 W ×331 W ×278 W ×264 W ×235 W ×211 W ×183 W ×167 W ×149

277 172 106 64.7 56.1 41.3 30.4 19.6 14.0 9.60

W36×848 W ×798 W ×650 W ×527 W ×439 W ×393 W ×359 W ×328 W ×300 W ×280 W ×260 W ×245 W ×230 W36×256 W ×232 W ×210 W ×194 W ×182 W ×170 W ×160 W ×150 W ×135 W33×354 W ×318 W ×291 W ×263 W ×241 W ×221 W ×201 W33×169 W ×152 W ×141 W ×130 W ×118

1270 1070 600 330 195 143 109 84.5 64.2 52.6 41.5 34.6 28.6 53.3 39.8 28.0 22.2 18.4 15.1 12.4 10.1 6.99 115 84.4 65.0 48.5 35.8 27.5 20.5 17.7 12.4 9.70 7.37 5.30

82400 71700 64400 56600 48300

110 122 131 141 154

93.7 93.8 93.3 92.8 92.2

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

329 286 258 228 196

Statical Moment

176 159 138 128 120 111 103 95.1 79.9

520 468 416 383 359 334 312 291 255

263 237 216 195 174 158 142

709 634 577 519 469 428 386

109 95.1 86.5 76.9 66.6

314 279 257 233 207

TORSION PROPERTIES

1 - 147

TORSION PROPERTIES W shapes

Designation W30×477 W ×391 W ×326 W ×292 W ×261 W ×235 W ×211 W ×191 W ×173 W30×148 W ×132 W ×124 W ×116 W ×108 W ×99 W ×90 W27×539 W ×448 W ×368 W ×307 W ×258 W ×235 W ×217 W ×194 W ×178 W ×161 W ×146

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.6

in.

in.2

in.4

in.3

480000 364000 286000 249000 215000 190000 166000 146000 129000

63.6 73.6 84.8 92.8 102 111 124 135 148

329 268 223 200 177 160 141 126 113

896 716 595 530 470 422 374 337 303

49400 42100 38600 34900 30900 26800 24000

93.6 106 112 119 127 136 146

77.3 77.3 76.9 76.5 76.1 75.7 75.0

239 204 188 171 152 133 119

86.8 74.0 68.8 62.8 56.1 49.5 45.0

250 219 204 189 173 156 142

440000 336000 254000 199000 159000 140000 128000 111000 98300 87300 77200

47.8 54.1 62.4 71.4 82.2 88.5 94.6 104 114 124 135

111 106 102 99.4 98.2 96.0 95.0 93.9 93.7 92.9 92.2

1490 1190 930 750 613 548 503 442 393 352 314

342 283 231 192 161 146 135 120 107 96.6 87.0

940 766 620 511 424 384 354 314 284 256 231

Torsional Constant J

Warping Constant Cw

in.4 307 174 103 74.9 53.8 40.0 27.9 20.6 15.3 14.6 9.72 7.99 6.43 4.99 3.77 2.92 499 297 169 101 61.0 46.3 37.0 26.5 19.5 14.7 10.9

124 120 117 115 114 112 112 111 110

1450 1140 919 812 710 633 556 494 439

Statical Moment

W27×129 W ×114 W ×102 W ×94 W ×84

11.2 7.33 5.29 4.03 2.81

32500 27600 24000 21300 17900

86.7 98.7 108 117 128

66.4 66.4 65.7 65.4 64.9

183 155 137 122 103

69.5 59.2 52.7 47.3 40.6

197 171 153 139 122

W24×492 W ×408 W ×335 W ×279 W ×250 W ×229 W ×207 W ×192 W ×176 W ×162 W ×146 W ×131 W ×117 W ×104

456 271 154 91.7 67.3 51.8 38.6 31.0 24.1 18.5 13.4 9.50 6.72 4.72

283000 214000 160000 125000 108000 95800 83900 76200 68400 62600 54600 47100 40800 35200

40.1 45.2 51.9 59.4 64.5 69.2 75.0 79.8 85.7 93.6 103 113 125 139

92.1 88.1 84.6 82.0 80.6 79.6 78.5 77.7 77.0 77.0 76.3 75.6 74.9 74.3

1150 909 709 570 502 451 401 367 333 304 268 233 204 178

281 233 189 157 141 128 116 107 97.8 89.4 79.5 69.7 61.5 54.1

774 626 509 418 372 338 303 280 255 234 209 185 164 144

W24×103 W ×94 W ×84 W ×76 W ×68

7.10 5.26 3.70 2.68 1.87

16600 15000 12800 11100 9430

77.8 85.9 94.6 104 114

53.0 53.1 52.6 52.2 51.9

117 105 91.3 79.8 68.0

49.4 44.4 39.0 34.4 29.5

140 127 112 100 88.3

W24×62 W ×55

1.71 1.18

4620 3870

83.6 92.2

40.7 40.4

42.3 35.7

23.2 19.8

76.6 67.1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 148

DIMENSIONS AND PROPERTIES

TORSION PROPERTIES W shapes

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.6

in.

in.2

in.4

in.3

41.3 31.1 23.9 15.4 11.3 8.98 6.83 5.21

61800 54300 48500 41100 36000 32700 29200 26200

62.2 67.2 72.5 83.1 90.8 97.1 105 114

67.0 66.0 65.6 65.4 64.7 64.2 63.7 63.2

345 307 277 235 208 191 172 155

W21×93 W ×83 W ×73 W ×68 W ×62

6.03 4.34 3.02 2.45 1.83

9940 8630 7410 6760 5960

65.3 71.8 79.7 84.5 91.8

43.6 43.0 42.5 42.3 42.0

85.3 75.0 65.2 59.9 53.2

38.2 34.2 30.3 28.0 25.1

110 98.0 86.2 79.9 72.2

W21×57 W ×50 W ×44

1.77 1.14 0.77

3190 2570 2110

68.3 76.4 84.2

33.4 33.1 32.8

35.6 28.9 24.0

20.9 17.2 14.5

64.3 55.0 47.7

75700 65600 57400 49900 43200 37900 33200 28900 25700 22700

33.3 35.5 37.8 40.3 43.4 46.6 50.1 54.3 58.6 63.2

58.8 57.5 56.4 55.2 54.2 53.3 52.5 51.6 51.0 50.4

483 427 382 339 299 267 237 210 189 169

Torsional Constant J

Warping Constant Cw

Designation

in.4

W21×201 W ×182 W ×166 W ×147 W ×132 W ×122 W ×111 W ×101

W18×311 W ×283 W ×258 W ×234 W ×211 W ×192 W ×175 W ×158 W ×143 W ×130

177 135 104 79.7 59.3 45.2 34.2 25.4 19.4 14.7

Statical Moment

102 92.3 84.4 71.4 64.0 59.2 53.7 49.0

141 127 116 105 94.3 85.7 77.2 69.4 63.2 57.1

265 238 216 187 167 154 139 127

376 338 306 274 245 221 199 178 161 145

W18×119 W ×106 W ×97 W ×86 W ×76

10.6 7.48 5.86 4.10 2.83

20300 17400 15800 13600 11700

70.4 77.6 83.6 92.7 103

50.4 49.8 49.4 48.9 48.4

151 131 120 104 90.7

50.6 44.6 41.2 36.3 31.9

131 115 105 92.8 81.4

W18×71 W ×65 W ×60 W ×55 W ×50

3.48 2.73 2.17 1.66 1.24

4700 4240 3850 3430 3040

59.1 63.4 67.8 73.1 79.7

33.7 33.4 33.1 32.9 32.6

52.1 47.5 43.5 39.0 34.9

25.8 23.8 22.1 19.9 18.0

72.7 66.6 61.4 55.9 50.4

W18×46 W ×40 W ×35

1.22 0.81 0.51

1710 1440 1140

60.2 67.8 76.1

26.4 26.1 25.9

24.2 20.6 16.5

15.3 13.3 10.7

45.3 39.2 33.2

W16×100 W ×89 W ×77 W ×67

7.73 5.45 3.57 2.39

11900 10200 8590 7300

63.1 69.6 78.9 88.9

41.7 41.1 40.6 40.1

107 93.3 79.3 68.2

39.0 34.4 29.7 25.9

99.0 87.3 75.0 64.9

W16×57 W ×50 W ×45 W ×40 W ×36

2.22 1.52 1.11 0.79 0.54

2660 2270 1990 1730 1460

55.7 62.2 68.1 75.3 83.7

28.0 27.6 27.4 27.1 26.9

35.6 30.8 27.2 23.9 20.2

19.0 16.7 15.0 13.4 11.4

52.6 46.0 41.1 36.5 32.0

W16×31 W ×26

0.46 0.26

739 565

64.5 75.0

21.3 21.1

13.0 10.0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.17 7.20

27.0 22.1

TORSION PROPERTIES

1 - 149

TORSION PROPERTIES W shapes Torsional Constant J Designation W14×808 W ×730 W ×665 W ×605 W ×550 W ×500 W ×455 W14×426 W ×398 W ×370 W ×342 W ×311 W ×283 W ×257 W ×233 W ×211 W ×193 W ×176 W ×159 W ×145

in. 1860 1450 1120 870 670 514 395

331 273 222 178 136 104 79.1 59.5 44.6 34.8 26.5 19.8 15.2

Warping Constant Cw 6

in.

√

 EC w GJ

Normalized Warping Constant Wno 2

Warping Statical Moment Sw 4

Statical Moment

Qf 3

Qw in.3

in.

433000 362000 305000 258000 219000 187000 160000

24.6 25.4 26.6 27.7 29.1 30.7 32.4

82.2 78.3 75.5 73.0 70.6 68.5 66.5

1950 1720 1510 1320 1160 1020 899

337 319 287 259 233 209 189

916 831 740 660 588 524 468

144000 129000 116000 103000 89100 77700 67800 59000 51500 45900 40500 35600 31700

33.6 35.0 36.8 38.7 41.2 44.0 47.1 50.7 54.7 58.4 62.9 68.2 73.5

65.3 64.1 62.9 61.6 60.3 59.1 57.9 56.9 55.9 55.1 54.4 53.7 53.0

827 756 689 623 553 493 438 389 345 312 279 248 224

176 163 151 138 125 113 102 91.7 82.3 75.4 68.0 61.3 55.8

434 401 368 336 301 271 243 218 195 177 160 143 130

190 171 154 138 125

49.9 45.3 41.2 37.2 33.7

117 106 95.9 86.6 78.3

W14×132 W ×120 W ×109 W ×99 W ×90

12.3 9.37 7.12 5.37 4.06

25500 22700 20200 18000 16000

73.3 79.2 85.7 93.2 101

50.2 49.7 49.1 48.7 48.3

W14×82 W ×74 W ×68 W ×61

5.08 3.88 3.02 2.20

6710 5990 5380 4710

58.5 63.2 67.9 74.5

34.1 33.7 33.4 33.1

73.8 66.6 60.4 53.3

28.1 25.7 23.5 21.0

69.3 62.8 57.3 51.1

W14×53 W ×48 W ×43

1.94 1.46 1.05

2540 2240 1950

58.2 63.0 69.3

26.7 26.5 26.2

35.5 31.6 27.8

17.3 15.6 13.9

43.6 39.2 34.8

W14×38 W ×34 W ×30

0.80 0.57 0.38

1230 1070 887

63.1 69.7 77.7

23.0 22.8 22.6

20.0 17.5 14.7

11.5 10.2 8.59

30.7 27.3 23.6

W14×26 W ×22

0.36 0.21

405 314

54.0 62.2

16.9 16.8

6.98 5.58

20.1 16.6

243 185 143 108 83.8 64.7 48.8 35.6 25.8 18.5 12.9 9.13 6.86 5.10 3.84 2.93 2.18

57000 48600 42000 35800 31200 27200 23600 20100 17200 14700 12400 10700 9410 8270 7330 6540 5780

24.6 26.1 27.6 29.3 31.0 33.0 35.4 38.2 41.5 45.4 49.9 55.1 59.6 64.8 70.3 76.0 82.9

46.4 45.0 44.0 42.8 41.8 41.0 40.1 39.2 38.4 37.7 37.0 36.4 35.9 35.5 35.2 34.9 34.5

W12×336 W ×305 W ×279 W ×252 W ×230 W ×210 W ×190 W ×170 W ×152 W ×136 W ×120 W ×106 W ×96 W ×87 W ×79 W ×72 W ×65

8.94 7.02 459 403 357 313 279 249 220 192 168 146 126 110 98.2 87.2 78.1 70.3 62.7

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

119 107 96.3 86.4 78.4 71.1 64.1 56.9 50.4 44.5 38.9 34.6 31.3 28.0 25.3 22.9 20.6

301 269 241 214 193 174 156 137 121 107 93.2 81.9 73.6 66.0 59.5 53.9 48.4

1 - 150

DIMENSIONS AND PROPERTIES

TORSION PROPERTIES W shapes

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.

in.2

in.4

in.3

3570 3160

66.3 72.0

28.9 28.7

46.3 41.2

18.2 16.3

43.2 39.0

1.78 1.31 0.95

1880 1650 1440

52.3 57.1 62.6

23.3 23.1 22.9

30.2 26.7 23.6

14.7 13.1 11.8

36.2 32.4 28.8

W12×35 W ×30 W ×26

0.74 0.46 0.30

879 720 607

55.5 63.7 72.4

19.6 19.4 19.2

16.8 13.9 11.8

W12×22 W ×19 W ×16 W ×14

0.29 0.18 0.10 0.07

164 131 96.9 80.4

38.3 43.4 50.1 54.5

12.0 11.8 11.7 11.6

W10×112 W ×100 W ×88 W ×77 W ×68 W ×60 W ×54 W ×49

15.1 10.9 7.53 5.11 3.56 2.48 1.82 1.39

6020 5150 4330 3630 3100 2640 2320 2070

32.1 35.0 38.6 42.9 47.5 52.5 57.5 62.1

26.3 25.8 25.3 24.8 24.4 24.0 23.8 23.6

85.7 74.7 64.2 54.9 47.6 41.2 36.6 33.0

30.8 27.2 23.8 20.7 18.1 15.9 14.3 13.0

73.7 64.9 56.4 48.8 42.6 37.3 33.3 30.2

W10×45 W ×39 W ×33

1.51 0.98 0.58

1200 992 790

45.4 51.2 59.4

19.0 18.7 18.5

23.6 19.8 16.0

11.5 9.77 7.98

27.5 23.4 19.4

W10×30 W ×26 W ×22

0.62 0.40 0.24

414 345 275

41.6 47.3 54.5

14.5 14.3 14.1

10.7 9.05 7.30

7.09 6.08 4.95

18.3 15.6 13.0

W10×19 W ×17 W ×15 W ×12

0.23 0.16 0.10 0.05

104 85.1 68.3 50.9

34.2 37.1 42.1 51.3

3.93 3.24 2.62 1.99

3.76 3.13 2.56 2.00

10.8 9.33 8.00 6.32

W8×67 W ×58 W ×48 W ×40 W ×35 W ×31

5.06 3.34 1.96 1.12 0.77 0.54

1440 1180 931 726 619 530

27.1 30.2 35.1 41.0 45.6 50.4

16.7 16.3 15.8 15.5 15.3 15.1

14.7 12.5 10.4 8.42 7.39 6.46

35.1 29.9 24.5 19.9 17.3 15.2

W8×28 W ×24

0.54 0.35

312 259

38.7 43.8

12.4 12.2

9.43 7.94

5.64 4.83

13.6 11.6

W8×21 W ×18

0.28 0.17

152 122

37.5 43.1

10.4 10.3

5.47 4.44

4.03 3.31

10.2 8.52

W8×15 W ×13 W ×10

0.14 0.09 0.04

51.8 40.8 30.9

31.0 34.3 44.7

7.82 7.74 7.57

2.47 1.97 1.53

2.39 1.93 1.56

6.78 5.70 4.43

W6×25 W ×20 W ×15

0.46 0.24 0.10

150 113 76.5

29.1 34.9 44.5

9.01 8.78 8.58

6.23 4.82 3.34

3.92 3.10 2.18

9.46 7.45 5.39

W6×16 W ×12 W ×9

0.22 0.09 0.04

38.2 24.7 17.7

21.2 26.7 33.8

5.92 5.75 5.60

2.42 1.61 1.19

2.28 1.55 1.19

5.84 4.15 3.12

W5×19 W ×16

0.31 0.19

50.8 40.6

20.6 23.5

5.94 5.81

3.21 2.62

2.44 2.02

5.81 4.82

W4×13

0.15

14.0

15.5

3.87

1.36

1.27

3.14

Torsional Constant J

Warping Constant Cw

Designation

in.4

in.6

W12×58 W ×53

2.10 1.58

W12×50 W ×45 W ×40

9.89 9.80 9.72 9.56

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.13 4.14 3.09 2.59

32.3 27.2 22.0 17.5 15.2 13.1

Statical Moment

9.86 8.30 7.15

25.6 21.6 18.6

4.87 4.01 3.04 2.59

14.7 12.4 10.0 8.72

TORSION PROPERTIES

1 - 151

TORSION PROPERTIES M shapes

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.6

in.

in.2

in.4

in.3

0.05 0.04

34.0 31.3

42.0 45.0

9.02 9.01

1.56 1.45

1.98 1.86

7.14 6.58

M10×9 M ×8

0.03 0.02

14.6 12.8

35.5 40.7

6.59 6.57

0.91 0.80

1.32 1.18

4.60 4.06

M8×6.5

0.02

26.0

4.45

0.48

0.82

2.72

M5×18.9

0.34

17.7

5.73

2.98

2.28

5.53

Torsional Constant J

Warping Constant Cw

Designation

in.4

M12×11.8 M ×10.8

5.23 41.3

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Statical Moment

1 - 152

DIMENSIONS AND PROPERTIES

TORSION PROPERTIES S shapes

Designation S24×121 S ×106

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.6

in.

in.2

in.4

in.3

11400 10600

48.0 52.1

47.1 46.1

103 98.8

47.1 47.1

154 141 121 112 103

Torsional Constant J

Warping Constant Cw

in.4 12.8 10.1

Statical Moment

S24×100 S ×90 S ×80

7.58 6.04 4.88

6380 6000 5640

46.7 50.7 54.7

41.9 41.2 40.5

66.0 63.8 61.6

33.5 33.5 33.5

S20×96 S ×86

8.39 6.64

4710 4390

38.1 41.4

34.9 34.2

57.8 55.5

29.2 29.2

99.7 92.5

S20×75 S ×66

4.59 3.58

2750 2550

39.4 42.9

30.7 30.0

38.9 37.3

22.6 22.6

77.0 70.5

S18×70 S ×54.7

4.15 2.37

1800 1560

33.5 41.3

27.0 26.0

29.2 26.9

17.1 17.1

63.0 52.9

S15×50 S ×42.9

2.12 1.54

811 744

31.5 35.4

20.3 19.8

17.8 16.9

11.8 11.8

39.0 35.1

S12×50 S ×40.8

2.82 1.75

505 437

21.5 25.4

15.5 14.9

14.0 12.9

9.30 9.30

31.0 26.9

S12×35 S ×31.8

1.08 0.90

324 307

27.9 29.7

14.5 14.3

10.0 9.74

7.48 7.48

22.7 21.3

S10×35 S ×25.4

1.29 0.60

189 153

19.5 25.7

11.8 11.1

7.13 6.34

5.24 5.24

17.9 14.4

S8×23 S ×18.4

0.55 0.34

61.8 53.5

17.1 20.2

7.90 7.58

3.50 3.22

3.10 3.10

9.74 8.38

S6×17.25 S ×12.5

0.37 0.17

18.4 14.5

11.3 14.9

5.03 4.70

1.61 1.41

1.63 1.63

5.35 4.30

S5×10

0.11

6.66

12.3

3.51

0.86

1.11

2.88

S4×9.5 S ×7.7

0.12 0.07

3.10 2.62

8.18 9.84

2.59 2.47

0.53 0.48

0.70 0.70

2.05 1.79

S3×7.5 S ×5.7

0.09 0.04

1.10 0.85

5.63 7.42

1.72 1.60

0.28 0.24

0.40 0.40

1.20 1.00

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

TORSION PROPERTIES

1 - 153

TORSION PROPERTIES HP shapes

 √ EC w GJ

Normalized Warping Constant Wno

Warping Statical Moment Sw

in.6

in.

in.2

in.4

in.3

8.02 5.40 3.60 2.01

19900 16800 14200 11200

80.2 89.8 101 120

49.9 49.2 48.5 47.8

149 128 110 88.0

38.5 33.5 29.1 23.8

97.2 84.3 72.9 59.2

HP13×100 HP ×87 HP ×73 HP ×60

6.25 4.12 2.54 1.39

11300 9430 7680 6020

68.4 77.0 88.5 106

40.9 40.2 39.6 39.0

103 87.7 72.8 57.8

29.9 25.8 21.8 17.7

76.3 65.6 55.2 44.5

HP12×84 HP ×74 HP ×63 HP ×53

4.24 2.98 1.83 1.12

7160 6170 4990 4090

66.1 73.2 84.0 97.2

35.6 35.2 34.6 34.2

75.0 65.5 54.1 44.7

23.5 20.8 17.5 14.7

59.8 52.7 44.2 37.0

HP10×57 HP ×42

1.97 0.81

2240 1540

54.3 70.2

24.1 23.4

34.8 24.7

13.1 9.64

33.2 24.2

HP8×36

0.77

578

44.1

15.4

14.0

6.62

16.8

Torsional Constant J

Warping Constant Cw

Designation

in.4

HP14×117 HP ×102 HP ×89 HP ×73

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Statical Moment

1 - 154

DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Channels

Designation

Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

C15×50 C15×40 C15×33.9

2.67 1.46 1.02

492 411 358

5.49 5.72 5.94

.937 .927 .920

C12×30 C15×25 C15×20.7

0.87 0.54 0.37

151 130 112

4.55 4.72 4.93

.919 .909 .899

C10×30 C1××25 C5××20 C10×15.3

1.23 0.69 0.37 0.21

79.3 68.4 56.9 45.6

3.63 3.75 3.93 4.19

.921 .912 .900 .883

C9×20 C9×15 C9×13.4

0.43 0.21 0.17

39.4 31.0 28.2

3.46 3.69 3.79

.899 .882 .874

C8×18.75 C9×13.75 C9×11.5

0.44 0.19 0.13

25.1 19.2 16.5

3.06 3.27 3.42

.894 .874 .862

C7×12.25 C9×9.8

0.16 0.10

11.2 9.18

2.87 3.02

.862 .846

C6×13 C9×10.5 C9×8.2

0.24 0.13 0.08

7.22 5.95 4.72

2.37 2.49 2.65

.858 .843 .824

C5×9 C9×6.7

0.11 0.06

2.93 2.22

2.10 2.26

.814 .790

C4×7.25 C9×5.4

0.08 0.04

1.24 0.92

1.75 1.89

.768 .741

C3×6 C9×5 C9×4.1

0.07 0.04 0.03

0.46 0.38 0.31

1.39 1.45 1.53

.689 .674 .656

*See LRFD Specification Appendix E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

TORSION PROPERTIES

1 - 155

FLEXURAL-TORSIONAL PROPERTIES Channels

Designation

Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

MC18×58 MC10×51.9 MC10×45.8 MC10×42.7

2.81 2.03 1.45 1.23

1070 986 897 852

6.56 6.70 6.88 6.97

.944 .939 .933 .930

MC13×50 MC10×40 MC10×35 MC10×31.8

2.98 1.57 1.14 0.94

558 463 413 380

5.07 5.33 5.50 5.64

.875 .860 .849 .842

MC12×50 MC10×45 MC10×40 MC10×35 MC10×31 MC10×10.6

3.24 2.35 1.70 1.25 1.01 0.06

411 374 336 297 268 11.7

4.77 4.87 5.01 5.18 5.34 4.27

.859 .851 .842 .832 .821 .983

MC10×41.1 MC10×33.6 MC10×28.5

2.27 1.21 0.79

270 224 194

4.26 4.47 4.68

.790 .771 .752

MC10×25 MC10×22

0.64 0.51

125 111

4.46 4.63

.802 .790

MC10×8.4

0.04

3.68

.972

MC9×25.4 MC9×23.9

0.69 0.60

4.08 4.15

.770 .763

MC8×22.8 MC9×21.4 MC9×20 MC9×18.7 MC9×8.5

0.57 0.50 0.44 0.38 0.06

75.3 70.9 47.9 45.1 8.22

3.85 3.91 3.59 3.65 3.24

.716 .709 .780 .773 .910

MC7×22.7 MC9×19.1

0.63 0.41

58.5 49.4

3.53 3.71

.662 .638

MC6×18

0.38

34.6

3.46

.562

MC6×16.3 MC9×15.1

0.34 0.29

22.1 20.6

3.11 3.18

.643 .634

MC6×12

0.15

11.2

2.80

.740

7.01 104 98.2

*See LRFD Specification Appendix E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 156

DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Single Angles Polar Radius of Gyration _ ro*

Flexural Constant H*

in.6

in.

No Units

×1 ×17⁄8 ×13⁄4 ×15⁄8 ×19⁄16 ×11⁄2

7.13 5.08 3.46 2.21 1.30 0.960 0.682

32.5 23.4 16.1 10.4 6.16 4.55 3.23

4.31 4.35 4.37 4.41 4.45 4.47 4.48

0.632 0.630 0.629 0.627 0.627 0.627 0.624

L8×6×1 L × × 3⁄4 L × ×19⁄16 L × ×11⁄2 L × ×17⁄16

4.35 1.90 0.822 0.584 0.396

16.3 7.28 3.20 2.28 1.55

3.89 3.96 4.01 4.02 4.04

— — — — —

L8×4×1 L8×4×17⁄8 L × ×13⁄4 L8×4×15⁄8 L × ×19⁄16 L × ×11⁄2 L8×4×17⁄16

3.68 2.48 1.61 0.933 0.704 0.501 0.328

12.9 8.89 5.75 3.42 2.53 1.80 1.22

3.77 3.79 3.82 3.85 3.86 3.88 3.89

— — — — — — —

L7×4×3⁄4 L × ×5⁄8 L × ×1⁄2 L7×4×7⁄16 L × ×3⁄8

1.47 0.873 0.459 0.300 0.200

3.33 3.36 3.38 3.40 3.42

— — — — —

Designation L8×8×11⁄8 L L L L L L

× × × × × ×

Torsional Constant J

Warping Constant Cw

in.4

3.97 2.37 1.25 0.851 0.544

*See LRFD Specification Appendix E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

TORSION PROPERTIES

1 - 157

FLEXURAL-TORSIONAL PROPERTIES Single Angles Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

L6×6×1 L6×6×17⁄8 L6×6×13⁄4 L6×6×15⁄8 L6×6×19⁄16 L6×6×11⁄2 L6×6×17⁄16 L6×6×13⁄8 L6×6×15⁄16

3.68 2.51 1.61 0.954 0.704 0.501 0.340 0.218 0.129

9.24 6.41 4.17 2.50 1.85 1.32 0.899 0.575 0.338

3.19 3.22 3.26 3.29 3.31 3.32 3.34 3.36 3.38

0.637 0.632 0.629 0.628 0.627 0.627 0.627 0.626 0.625

L6×4×3⁄4 L6×4×5⁄8 L6×4×9⁄16 L6×4×1⁄2 L6×4×7⁄16 L6×4×3⁄8 L6×4×5⁄16

1.33 0.792 0.585 0.417 0.284 0.183 0.108

2.64 1.59 1.18 0.843 0.575 0.369 0.217

2.86 2.89 2.9 2.92 2.94 2.96 2.97

— — — — — — —

L6×31⁄2×1⁄2 L6×31⁄2×3⁄8 L6×31⁄2×5⁄16

0.396 0.174 0.103

0.779 0.341 0.201

2.88 2.92 2.93

— — —

L5×5×7⁄8 L6×4×3⁄4 L6×4×5⁄8 L6×4×1⁄2 L6×4×7⁄16 L6×4×3⁄8 L6×4×5⁄16

2.07 1.33 0.792 0.417 0.284 0.183 0.108

3.53 2.32 1.40 0.744 0.508 0.327 0.193

2.65 2.68 2.71 2.74 2.77 2.79 2.81

0.634 0.634 0.630 0.630 0.629 0.627 0.626

Designation

*See LRFD Specification Appendix E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 158

DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Single Angles Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

L5×31⁄2×3⁄4 L5×31⁄2×5⁄8 L5×31⁄2×1⁄2 L5×31⁄2×3⁄8 L5×31⁄2×5⁄16 L5×31⁄2×1⁄4

1.11 0.660 0.348 0.153 0.0905 0.0479

1.52 0.918 0.491 0.217 0.128 0.0670

2.37 2.40 2.44 2.47 2.49 2.50

— — — — — —

L5×3×1⁄2 L5×3×7⁄16 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

0.322 0.219 0.141 0.0832 0.0438

0.444 0.304 0.196 0.116 0.0606

2.39 2.41 2.42 2.43 2.45

— — — — —

L4×4×3⁄4 L5×3×5⁄8 L5×3×1⁄2 L5×3×7⁄16 L5×3×3⁄8 L5×3×5⁄16 L5×3×1⁄4

1.02 0.610 0.322 0.219 0.141 0.0832 0.0438

1.12 0.680 0.366 0.252 0.162 0.0963 0.0505

2.11 2.14 2.17 2.19 2.20 2.22 2.23

0.639 0.631 0.632 0.631 0.625 0.623 0.627

L4×31⁄2×1⁄2 L5×31⁄2×3⁄8 L5×31⁄2×5⁄16 L5×31⁄2×1⁄4

0.301 0.132 0.0782 0.0412

0.302 0.134 0.0798 0.0419

2.04 2.08 2.09 2.11

— — — —

Designation

*See LRFD Specification Appendix E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

TORSION PROPERTIES

1 - 159

FLEXURAL-TORSIONAL PROPERTIES Single Angles Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

L4×3×5⁄8 L4×3×1⁄2 L4×3×7⁄16 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4

0.529 0.281 0.192 0.123 0.0731 0.0386

0.472 0.255 0.176 0.114 0.0676 0.0356

1.91 1.95 1.96 1.98 2.00 2.01

— — — — — —

L31⁄2×31⁄2×1⁄2 L31⁄2×31⁄2×7⁄16 L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×5⁄16 L31⁄2×31⁄2×1⁄4

0.281 0.192 0.123 0.0731 0.0386

0.238 0.164 0.106 0.0634 0.0334

1.89 1.91 1.91 1.93 1.95

0.631 0.629 0.628 0.627 0.626

L31⁄2×3×1⁄2 L31⁄2×3×3⁄8 L31⁄2×3×5⁄16 L31⁄2×3×1⁄4

0.260 0.114 0.0680 0.0360

0.191 0.0858 0.0512 0.0270

1.76 1.79 1.81 1.83

— — — —

L31⁄2×21⁄2×1⁄2 L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×1⁄4

0.234 0.103 0.0322

0.159 0.0714 0.0225

1.67 1.70 1.73

— — —

L3×3×1⁄2 L4×3×7⁄16 L4×3×3⁄8 L4×3×5⁄16 L4×3×1⁄4 L4×3×3⁄16

0.234 0.160 0.103 0.0611 0.0322 0.0142

0.144 0.100 0.0652 0.0390 0.0206 0.00899

1.60 1.61 1.63 1.65 1.66 1.68

0.634 0.632 0.629 0.628 0.627 0.626

Designation

*See LRFD Specification Appendix E3.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Single Angles Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

L3×21⁄2×1⁄2 L3×21⁄2×7⁄16 L3×21⁄2×3⁄8 L3×21⁄2×5⁄16 L3×21⁄2×1⁄4 L3×21⁄2×3⁄16

0.213 0.146 0.0943 0.0560 0.0296 0.0131

0.112 0.0777 0.0507 0.0304 0.0161 0.00705

1.47 1.49 1.50 1.52 1.54 1.55

— — — — — —

L3×2×1⁄2 L2×2×3⁄8 L2×2×5⁄16 L2×2×1⁄4 L2×2×3⁄16

0.192 0.0855 0.0509 0.0270 0.0120

0.0908 0.0413 0.0248 0.0132 0.00576

1.40 1.43 1.45 1.46 1.48

— — — — —

L21⁄2×21⁄2×1⁄2 L21⁄2×21⁄2×3⁄8 L21⁄2×21⁄2×5⁄16 L21⁄2×21⁄2×1⁄4 L21⁄2×21⁄2×3⁄16

0.185 0.0816 0.0483 0.0253 0.0110

0.0791 0.0362 0.0218 0.0116 0.00510

1.31 1.34 1.36 1.37 1.39

0.639 0.632 0.630 0.628 0.627

L21⁄2×2×3⁄8 L3×21⁄2×5⁄16 L3×21⁄2×1⁄4 L3×21⁄2×3⁄16

0.0728 0.0432 0.0227 0.00990

0.0268 0.0162 0.00868 0.00382

1.22 1.24 1.25 1.27

— — — —

L2×2×3⁄8 L2×2×5⁄16 L2×2×1⁄4 L2×2×3⁄16 L2×2×1⁄8

0.0640 0.0381 0.0201 0.00880 0.00274

0.0174 0.0106 0.00572 0.00254 0.00079

1.05 1.07 1.09 1.10 1.12

0.637 0.633 0.630 0.628 0.626

Designation

*See LRFD Specification Appendix E3.

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FLEXURAL-TORSIONAL PROPERTIES Structural Tees Polar Radius of Gyration _ ro*

Flexural Constant H*

in.6

in.

No Units

37.2 25.7 18.9 12.4

434 279 204 139

8.81 8.67 8.65 8.67

0.724 0.733 0.731 0.723

WT20×296.5** WT ×251.5** WT ×215.5 WT ×186 WT ×160.5 WT ×148.5 WT ×138.5 WT ×124.5 WT ×107.5 WT ×99.5 WT ×87

223 140 88.5 58.2 37.7 30.6 25.8 19.1 12.4 9.14 5.60

2340 1420 881 559 350 279 218 158 101 83.5 65.3

8.30 8.17 8.09 8.00 7.92 7.88 7.75 7.71 7.66 7.83 8.12

0.761 0.760 0.756 0.756 0.756 0.756 0.770 0.770 0.770 0.746 0.699

WT20×233** WT ×196** WT ×165.5 WT ×139 WT ×132 WT ×117.5 WT ×105.5 WT ×91.5 WT ×83.5 WT ×74.5

139 86.1 53.0 32.4 28.0 20.6 15.2 10.0 7.01 4.68

1360 802 485 278 233 156 113 72.1 62.9 51.9

8.39 8.27 8.19 8.07 8.02 7.88 7.84 7.79 8.02 8.24

0.680 0.678 0.674 0.676 0.680 0.690 0.690 0.691 0.658 0.626

WT18×424** WT ×399** WT ×325** WT ×263.5** WT ×219.5** WT ×196.5** WT ×179.5** WT ×164** WT ×150 WT ×140 WT ×130 WT ×122.5 WT ×115

622 527 295 163 96.7 70.7 54.3 42.1 32.0 26.2 20.7 17.3 14.3

6880 5700 3010 1570 894 637 480 363 278 226 181 151 125

8.08 8.02 7.82 7.63 7.52 7.44 7.38 7.32 7.30 7.27 7.28 7.28 7.27

0.802 0.801 0.797 0.797 0.794 0.796 0.797 0.799 0.797 0.796 0.791 0.788 0.784

Designation WT22×167.5 WT ×145 WT ×131 WT ×115

Torsional Constant J

Warping Constant Cw

in.4

*See LRFD Specification Section E3. **Group 4 or Group 5 shape. See Notes in Table 1-2.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Structural Tees Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

WT18×128 WT ×116 WT ×105 WT ×97 WT ×91 WT ×85 WT ×80 WT ×75 WT ×67.5

26.6 19.8 13.9 11.1 9.19 7.51 6.17 5.04 3.48

205 151 119 92.7 77.6 63.2 53.6 46.0 37.3

7.43 7.40 7.49 7.45 7.45 7.44 7.46 7.50 7.65

0.703 0.703 0.687 0.687 0.686 0.684 0.678 0.670 0.644

WT16.5×177** WT ×159** WT ×145.5** WT ×131.5** WT ×120.5 WT ×110.5 WT ×100.5

57.2 42.1 32.4 24.2 17.9 13.7 10.2

468 335 256 188 146 113 84.9

7.00 6.94 6.90 6.86 6.91 6.90 6.89

0.802 0.803 0.801 0.802 0.792 0.788 0.784

8.83 6.16 4.84 3.67 2.64

55.4 43.0 35.4 29.3 23.4

6.74 6.82 6.85 6.93 7.02

0.714 0.700 0.691 0.678 0.659

151 85.9 50.8 37.2 26.7 19.9 13.9 10.3 7.61

1170 636 361 257 184 132 96.4 71.2 53.0

6.65 6.54 6.40 6.34 6.31 6.25 6.27 6.25 6.25

0.819 0.815 0.817 0.818 0.815 0.817 0.809 0.806 0.802

7.27 4.85 3.98 3.21 2.49 1.88 1.42

37.6 28.5 23.9 20.5 17.3 14.3 10.5

6.10 6.19 6.20 6.24 6.31 6.38 6.34

0.716 0.698 0.693 0.683 0.669 0.654 0.655

Designation

WT16.5×84.5 WT ×76 WT ×70.5 WT ×65 WT ×59 WT15×238.5** WT ×195.5** WT ×163** WT ×146** WT ×130.5 WT ×117.5 WT ×105.5 WT ×95.5 WT ×86.5 WT15×74 WT ×66 WT ×62 WT ×58 WT ×54 WT ×49.5 WT ×45

*See LRFD Specification Section E3. **Group 4 or Group 5 shape. See Notes in Table 1-2.

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FLEXURAL-TORSIONAL PROPERTIES Structural Tees

Designation WT13.5×269.5** WT ×224** WT ×184** WT ×153.5** WT ×140.5** WT ×129 WT ×117.5 WT ×108.5 WT ×97 WT ×89 WT ×80.5 WT ×73 WT13.5×64.5 WT ×57 WT ×51 WT ×47 WT ×42 WT12×246** WT ×204** WT ×167.5** WT ×139.5** WT ×125** WT ×114.5 WT ×103.5 WT ×96 WT ×88 WT ×81 WT ×73 WT ×65.5 WT ×58.5 WT ×52

Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

245 146 83.6 49.8 39.0 30.2 23.0 18.5 13.2 9.74 7.31 5.44

1740 977 532 304 232 178 135 105 74.3 57.7 42.7 31.7

6.27 6.11 5.97 5.85 5.80 5.77 5.74 5.72 5.66 5.70 5.67 5.65

0.830 0.829 0.828 0.828 0.830 0.828 0.825 0.830 0.826 0.815 0.813 0.810

5.48 5.54 5.52 5.57 5.63

0.731 0.716 0.714 0.703 0.685

5.71 5.55 5.40 5.28 5.22 5.19 5.14 5.11 5.09 5.09 5.08 5.09 5.08 5.07

0.838 0.836 0.837 0.837 0.838 0.836 0.836 0.836 0.835 0.831 0.827 0.818 0.813 0.809

5.60 3.65 2.64 2.01 1.40 223 133 76.0 45.3 33.3 25.7 19.1 15.4 12.0 9.22 6.70 4.74 3.35 2.35

24.0 17.5 12.6 10.2 7.79 1340 748 405 230 165 125 91.3 72.5 55.8 43.8 31.9 23.1 16.4 11.6

WT12×51.5 WT ×47 WT ×42 WT ×38 WT ×34

3.54 2.62 1.84 1.34 0.932

12.3 9.57 6.90 5.30 4.08

4.88 4.89 4.89 4.93 4.99

0.733 0.727 0.721 0.709 0.692

WT12×31 WT ×27.5

0.850 0.588

3.92 2.93

5.13 5.18

0.619 0.606

*See LRFD Specification Section E3. **Group 4 or Group 5 shape. See Notes in Table 1-2.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Structural Tees

Designation WT10.5×100.5 WT10.5×91 WT10.5×83 WT10.5×73.5 WT10.5×66 WT10.5×61 WT10.5×55.5 WT10.5×50.5

Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

20.6 15.4 11.9 7.69 5.62 4.47 3.40 2.60

85.4 63.0 47.3 32.5 23.4 18.4 13.8 10.4

4.67 4.64 4.59 4.64 4.61 4.58 4.56 4.54

0.859 0.859 0.861 0.847 0.845 0.846 0.846 0.846

WT10.5×46.5 WT10.5×41.5 WT10.5×36.5 WT10.5×34 WT10.5×31

3.01 2.16 1.51 1.22 0.513

9.33 6.50 4.42 3.62 2.78

4.37 4.33 4.31 4.31 4.31

0.729 0.732 0.732 0.727 0.722

WT10.5×28.5 WT10.5×25 WT10.5×22

0.884 0.570 0.383

2.50 1.89 1.40

4.36 4.44 4.49

0.665 0.640 0.623

4.42 4.36 4.30 4.23 4.19 4.14 4.10 4.06 4.03 3.99

0.875 0.873 0.874 0.875 0.873 0.875 0.872 0.872 0.874 0.874

WT9×155.5** WT9×141.5** WT9×129** WT9×117** WT9×105.5** WT9×96 WT9×87.5 WT9×79 WT9×71.5 WT9×65

87.2 66.5 51.5 39.4 29.4 22.4 17.0 12.6 9.70 7.30

339 251 189 140 102 75.7 56.5 41.2 30.7 22.8

WT9×59.5 WT9×53 WT9×48.5 WT9×43 WT9×38

5.30 3.73 2.92 2.04 1.41

17.4 12.1 9.29 6.42 4.37

4.03 4.00 3.97 3.95 3.92

0.862 0.860 0.862 0.860 0.862

WT9×35.5 WT9×32.5 WT9×30 WT9×27.5 WT9×25

1.74 1.36 1.08 0.829 0.613

3.96 3.01 2.35 1.84 1.36

3.72 3.69 3.67 3.68 3.66

0.751 0.755 0.756 0.749 0.748

WT9×23 WT9×20 WT9×17.5

0.609 0.403 0.252

1.20 0.788 0.598

3.67 3.65 3.74

0.694 0.692 0.662

*See LRFD Specification Section E3. **Group 4 or Group 5 shape. See Notes in Table 1-2.

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FLEXURAL-TORSIONAL PROPERTIES Structural Tees Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

WT8×50 WT ×44.5 WT ×38.5 WT ×33.5

3.85 2.72 1.78 1.19

10.4 7.19 4.61 3.01

3.62 3.60 3.56 3.53

0.877 0.877 0.877 0.879

WT8×28.5 WT ×25 WT ×22.5 WT ×20 WT ×18

1.10 0.760 0.655 0.396 0.271

1.99 1.34 0.974 0.673 0.516

3.30 3.28 3.27 3.24 3.30

0.770 0.770 0.767 0.769 0.745

WT8×15.5 WT ×13

0.229 0.130

0.366 0.243

3.26 3.32

0.695 0.667

5.67 5.47 5.36 5.25 5.15 5.06 4.98

0.959 0.966 0.966 0.966 0.967 0.967 0.967

4.92 4.87 4.81 4.77 4.71 4.66 4.61 4.56 4.52 4.49 4.46 4.42 4.40

0.968 0.968 0.968 0.968 0.968 0.969 0.969 0.970 0.970 0.971 0.971 0.971 0.971

Designation

WT7×404** WT ×365** WT ×332.5** WT ×302.5** WT ×275** WT ×250** WT ×227.5**

918 714 555 430 331 255 196

6970 5250 3920 2930 2180 1620 1210

WT7×213** WT ×199** WT ×185** WT ×171** WT ×155.5** WT ×141.5** WT ×128.5** WT ×116.5** WT ×105.5 WT ×96.5 WT ×88 WT ×79.5 WT ×72.5

164 135 110 88.3 67.5 51.8 39.3 29.6 22.2 17.3 13.2 9.84 7.56

991 801 640 502 375 281 209 154 113 87.2 65.2 47.9 36.3

*See LRFD Specification Section E3. **Group 4 or Group 5 shape. See Notes in Table 1-2.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Structural Tees Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

WT7×66 WT ×60 WT ×54.5 WT ×49.5 WT ×45

6.13 4.67 3.55 2.68 2.03

26.6 20.0 15.0 11.1 8.31

4.21 4.18 4.16 4.14 4.12

0.966 0.966 0.968 0.968 0.968

WT7×41 WT ×37 WT ×34 WT ×30.5

2.53 1.94 1.51 1.10

5.63 4.19 3.21 2.29

3.25 3.21 3.19 3.18

0.912 0.917 0.915 0.915

WT7×26.5 WT ×24 WT ×21.5

0.970 0.726 0.524

1.46 1.07 0.751

2.89 2.87 2.85

0.868 0.866 0.866

WT7×19 WT ×17 WT ×15

0.398 0.284 0.190

0.554 0.400 0.287

2.87 2.86 2.90

0.800 0.793 0.772

WT7×13 WT ×11

0.179 0.104

0.207 0.134

2.82 2.86

0.713 0.691

Designation

*See LRFD Specification Section E3.

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FLEXURAL-TORSIONAL PROPERTIES Structural Tees

Designation WT6×168** WT ×152.5** WT ×139.5** WT ×126** WT ×115** WT ×105** WT ×95 WT ×85 WT ×76 WT ×68 WT ×60 WT ×53 WT ×48 WT ×43.5 WT ×39.5 WT ×36 WT ×32.5

Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

120 92.0 70.9 53.5 41.6 32.2 24.4 17.7 12.8 9.22 6.43 4.55 3.42 2.54 1.92 1.46 1.09

481 356 267 195 148 112 82.1 58.3 41.3 28.9 19.7 13.6 10.1 7.34 5.43 4.07 2.97

4.07 4.00 3.94 3.88 3.84 3.79 3.74 3.69 3.65 3.61 3.58 3.54 3.51 3.49 3.46 3.45 3.43

0.958 0.959 0.957 0.958 0.958 0.958 0.959 0.960 0.960 0.960 0.959 0.961 0.961 0.960 0.960 0.961 0.960

WT6×29 WT ×26.5

1.05 0.788

2.08 1.53

3.01 3.00

0.944 0.940

WT6×25 WT ×22.5 WT ×20

0.889 0.656 0.476

1.23 0.885 0.620

2.67 2.64 2.62

0.899 0.898 0.901

WT6×17.5 WT ×15 WT ×13

0.369 0.228 0.150

0.437 0.267 0.174

2.56 2.55 2.54

0.835 0.830 0.826

WT6×11 WT ×9.5 WT ×8 WT ×7

0.146 0.0899 0.0511 0.0350

0.137 0.0934 0.0678 0.0493

2.52 2.54 2.62 2.64

0.683 0.663 0.624 0.610

*See LRFD Specification Section E3. **Group 4 or Group 5 shape. See Notes in Table 1-2.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Structural Tees Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

WT5×56 WT5×50 WT5×44 WT5×38.5 WT5×34 WT5×30 WT5×27 WT5×24.5

7.50 5.41 3.75 2.55 1.78 1.23 0.909 0.693

16.9 11.9 8.02 5.31 3.62 2.46 1.78 1.33

3.04 3.00 2.98 2.93 2.92 2.89 2.87 2.85

0.963 0.964 0.964 0.964 0.965 0.965 0.966 0.966

WT5×22.5 WT5×19.5 WT5×16.5

0.753 0.487 0.291

0.981 0.616 0.356

2.44 2.42 2.40

0.940 0.936 0.927

WT5×15 WT5×13 WT5×11

0.310 0.201 0.119

0.273 0.173 0.107

2.17 2.15 2.17

0.848 0.848 0.831

WT5×9.5 WT5×8.5 WT5×7.5 WT5×6

0.116 0.0776 0.0518 0.0272

0.0796 0.061 0.0475 0.0255

2.08 2.12 2.16 2.16

0.728 0.702 0.672 0.662

Designation

*See LRFD Specification Section E3.

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TORSION PROPERTIES

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FLEXURAL-TORSIONAL PROPERTIES Structural Tees Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

WT4×33.5 WT ×29 WT ×24 WT ×20 WT ×17.5 WT ×15.5

2.52 1.66 0.979 0.559 0.385 0.268

3.56 2.28 1.30 0.715 0.480 0.327

2.41 2.39 2.34 2.31 2.29 2.29

0.962 0.961 0.966 0.961 0.963 0.961

WT4×14 WT ×12

0.268 0.173

0.230 0.144

1.97 1.96

0.935 0.936

WT4×10.5 WT ×9

0.141 0.0855

0.0916 0.0562

1.80 1.81

0.877 0.863

WT4×7.5 WT ×6.5 WT ×5

0.0679 0.0433 0.0212

0.0382 0.0269 0.0114

1.72 1.74 1.69

0.762 0.732 0.748

WT3×12.5 WT ×10 WT ×7.5

0.229 0.120 0.0504

0.171 0.0858 0.0342

1.76 1.73 1.71

0.952 0.952 0.937

WT3×8 WT ×6 WT ×4.5

0.111 0.0449 0.0202

0.0426 0.0178 0.0074

1.37 1.37 1.34

0.880 0.846 0.852

WT2.5×9.5 WT ×8

0.154 0.0930

0.0775 0.0453

1.44 1.43

0.964 0.962

WT2×6.5

0.0750

0.0213

1.16

0.947

Designation

*See LRFD Specification Section E3.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Structural Tees Polar Radius of Gyration _ ro*

Flexural Constant H*

in.6

in.

No Units

0.0307 0.0196

0.0330 0.0252

2.69 2.67

0.564 0.572

MT5×4.5 MT ×4

0.0213 0.0116

0.0133 0.00916

2.21 2.21

0.584 0.582

MT4×3.25

0.0146

0.00421

1.73

0.611

MT2.5×9.45**

0.165

0.0732

1.37

0.951

Torsional Constant J

Warping Constant Cw

in.4

MT6×5.9 MT ×5.4

Designation

*See LRFD Specification Section E3. **This shape has tapered flanges while other MT shapes have parallel flanges.

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FLEXURAL-TORSIONAL PROPERTIES Structural Tees

Designation

Torsional Constant J

Warping Constant Cw

Polar Radius of Gyration _ ro*

Flexural Constant H*

in.4

in.6

in.

No Units

ST12×60.5 ST ×53

6.38 5.04

27.5 15.0

5.14 4.87

0.640 0.685

ST12×50 ST ×45 ST ×40

3.76 3.01 2.43

19.5 12.1 6.94

5.27 5.12 4.89

0.584 0.616 0.657

ST10×48 ST ×43

4.15 3.30

15.0 9.17

4.36 4.20

0.625 0.661

ST10×37.5 ST ×33

2.28 1.78

7.21 4.02

4.28 4.10

0.612 0.655

ST9×35 ST ×27.35

2.05 1.18

7.03 2.26

4.01 3.71

0.583 0.662

ST7.5×25 ST ×21.45

1.05 0.767

2.02 0.995

3.22 3.04

0.637 0.689

ST6×25 ST ×20.4

1.39 0.872

1.97 0.787

2.60 2.42

0.663 0.733

ST6×17.5 ST ×15.9

0.538 0.449

0.556 0.364

2.49 2.39

0.697 0.731

ST5×17.5 ST ×12.7

0.633 0.300

0.725 0.173

2.23 1.98

0.653 0.768

ST4×11.5 ST ×9.2

0.271 0.167

0.168 0.0642

1.74 1.59

0.707 0.789

ST3×8.625 ST ×6.25

0.182 0.0838

0.0772 0.0197

1.36 1.21

0.706 0.820

ST2.5×5

0.0568

0.0100

1.02

0.842

ST2×4.75 ST ×3.85

0.0589 0.0364

0.00995 0.00457

0.907 0.841

0.800 0.872

ST1.5×3.75 ST ×2.85

0.0440 0.0220

0.00496 0.00189

0.737 0.672

0.832 0.913

*See LRFD Specification Section E3.

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DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Double Angles Long Legs Vertical

Short Legs Vertical

Back to Back of Angles, in. 3⁄ 8

Back to Back of Angles, in.

3⁄ 4

3⁄ 8

3⁄ 4

Designation

ro*

L8×8×11⁄8 L × ×1 L × × 7⁄8 L × × 3⁄4 L × × 5⁄8 L × × 1⁄2

4.58 4.58 4.58 4.58 4.58 4.59

0.837 0.833 0.831 0.828 0.825 0.822

4.68 4.68 4.68 4.68 4.68 4.69

0.844 0.840 0.838 0.835 0.832 0.829

4.79 4.79 4.78 4.78 4.78 4.78

0.851 0.847 0.845 0.842 0.839 0.836

4.58 4.58 4.58 4.58 4.58 4.59

0.837 0.833 0.831 0.828 0.825 0.822

4.68 4.68 4.68 4.68 4.68 4.69

0.844 0.840 0.838 0.835 0.832 0.829

4.79 4.79 4.78 4.78 4.78 4.78

0.851 0.847 0.845 0.842 0.839 0.836

L8×6×1 L × × 3⁄4 L × × 1⁄2

4.07 4.08 4.11

0.721 0.714 0.708

4.15 4.16 4.18

0.731 0.724 0.718

4.23 4.24 4.26

0.742 0.735 0.728

4.19 4.17 4.17

0.925 0.919 0.914

4.31 4.29 4.28

0.929 0.924 0.919

4.44 4.41 4.40

0.933 0.928 0.923

L8×4×1 L × × 3⁄4 L × × 1⁄2

3.87 3.89 3.93

0.566 0.562 0.558

3.93 3.94 3.97

0.578 0.573 0.568

3.99 4.00 4.03

0.591 0.586 0.580

4.12 4.08 4.05

0.982 0.980 0.977

4.26 4.22 4.19

0.983 0.981 0.979

4.41 4.36 4.33

0.984 0.982 0.980

L7×4×3⁄4 L × ×1⁄2 L × ×3⁄8

3.42 3.45 3.46

0.609 0.604 0.602

3.48 3.5 3.51

0.623 0.616 0.614

3.55 3.57 3.57

0.637 0.629 0.627

3.58 3.55 3.54

0.968 0.965 0.963

3.71 3.68 3.67

0.971 0.967 0.965

3.85 3.82 3.80

0.973 0.969 0.968

L6×6×1 L × × 7⁄8 L × × 3⁄4 L × × 5⁄8 L × × 1⁄2 L × × 3⁄8

3.43 3.43 3.44 3.44 3.44 3.44

0.843 0.838 0.833 0.830 0.827 0.822

3.54 3.54 3.54 3.54 3.54 3.54

0.852 0.847 0.842 0.839 0.836 0.831

3.65 3.65 3.65 3.64 3.64 3.64

0.861 0.856 0.852 0.848 0.845 0.841

3.43 3.43 3.44 3.44 3.44 3.44

0.843 0.838 0.833 0.830 0.827 0.822

3.54 3.54 3.54 3.54 3.54 3.54

0.852 0.847 0.842 0.839 0.836 0.831

3.65 3.65 3.65 3.64 3.64 3.64

0.861 0.856 0.852 0.848 0.845 0.841

L6×4×3⁄4 L × ×5⁄8 L × ×1⁄2 L × ×3⁄8

2.98 2.98 3.00 3.01

0.672 0.668 0.663 0.661

3.05 3.05 3.06 3.07

0.687 0.683 0.678 0.675

3.13 3.13 3.14 3.15

0.704 0.699 0.693 0.690

3.10 3.09 3.08 3.07

0.948 0.946 0.943 0.940

3.23 3.21 3.20 3.19

0.952 0.950 0.947 0.944

3.36 3.34 3.34 3.32

0.956 0.954 0.951 0.948

L6×31⁄2×3⁄8 L × 1⁄2×5⁄16

2.97 2.97

0.610 0.610

3.02 3.02

0.624 0.624

3.09 3.09

0.640 0.639

3.05 3.03

0.961 0.960

3.17 3.16

0.964 0.963

3.31 3.29

0.967 0.966

L5×5×7⁄8 L × ×3⁄4 L × ×1⁄2 L × ×3⁄8 L × ×5⁄16

2.87 2.85 2.86 2.87 2.87

0.844 0.839 0.830 0.824 0.821

2.97 2.96 2.96 2.96 2.97

0.855 0.850 0.841 0.835 0.833

3.09 3.07 3.07 3.07 3.07

0.865 0.861 0.852 0.846 0.844

2.87 2.85 2.86 2.87 2.87

0.844 0.839 0.830 0.824 0.821

2.97 2.96 2.96 2.96 2.97

0.855 0.850 0.841 0.835 0.833

3.09 3.07 3.07 3.07 3.07

0.865 0.861 0.852 0.846 0.844

*See LRFD Specification Section E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

TORSION PROPERTIES

1 - 173

FLEXURAL-TORSIONAL PROPERTIES Double Angles Long Legs Vertical

Short Legs Vertical

Back to Back of Angles, in.

3⁄ 8

3⁄ 4

3⁄ 8

3⁄ 4

Designation

ro*

L5×31⁄2×3⁄4 L5×31⁄2×1⁄2 L5×31⁄2×3⁄8 L5×31⁄2×5⁄16

2.50 2.51 2.52 2.53

0.697 0.685 0.682 0.679

2.58 2.59 2.59 2.60

0.715 0.703 0.699 0.695

2.67 2.67 2.67 2.68

0.734 0.722 0.717 0.713

2.61 2.59 2.58 2.58

0.943 0.936 0.932 0.930

2.74 2.71 2.70 2.70

0.948 0.941 0.938 0.936

2.87 2.84 2.83 2.82

0.953 0.947 0.943 0.942

L5×3×1⁄2 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4

2.45 2.46 2.47 2.48

0.626 0.623 0.621 0.618

2.52 2.52 2.53 2.54

0.645 0.641 0.638 0.634

2.59 2.60 2.60 2.61

0.665 0.661 0.657 0.653

2.55 2.54 2.54 2.53

0.962 0.959 0.957 0.956

2.69 2.67 2.67 2.66

0.965 0.963 0.961 0.960

2.82 2.80 2.80 2.79

0.969 0.966 0.965 0.964

L4×4×3⁄4 L3×3×5⁄8 L3×3×1⁄2 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4

2.29 2.29 2.29 2.29 2.29 2.29

0.847 0.839 0.834 0.827 0.824 0.823

2.40 2.40 2.39 2.39 2.39 2.39

0.861 0.853 0.848 0.841 0.838 0.837

2.52 2.51 2.50 2.50 2.50 2.49

0.873 0.867 0.862 0.855 0.852 0.850

2.29 2.29 2.29 2.29 2.29 2.29

0.847 0.839 0.834 0.827 0.824 0.823

2.40 2.40 2.39 2.39 2.39 2.39

0.861 0.853 0.848 0.841 0.838 0.837

2.52 2.51 2.50 2.50 2.50 2.49

0.873 0.867 0.862 0.855 0.852 0.850

L4×31⁄2×1⁄2 L5×31⁄2×3⁄8 L5×31⁄2×5⁄16 L5×31⁄2×1⁄4

2.15 2.15 2.15 2.16

0.783 0.774 0.774 0.770

2.24 2.24 2.24 2.24

0.801 0.792 0.791 0.787

2.34 2.34 2.34 2.34

0.818 0.809 0.808 0.805

2.17 2.17 2.17 2.17

0.881 0.875 0.872 0.870

2.29 2.28 2.28 2.28

0.892 0.887 0.884 0.882

2.41 2.40 2.40 2.39

0.903 0.898 0.895 0.893

L4×3×1⁄2 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4

2.04 2.04 2.05 2.06

0.719 0.714 0.710 0.706

2.12 2.12 2.13 2.13

0.740 0.735 0.731 0.726

2.22 2.21 2.22 2.22

0.762 0.757 0.752 0.747

2.10 2.09 2.09 2.09

0.924 0.919 0.917 0.914

2.22 2.21 2.21 2.20

0.933 0.928 0.925 0.923

2.35 2.34 2.33 2.33

0.940 0.935 0.933 0.931

L31⁄2×31⁄2×3⁄8 L31⁄2×31⁄2×1⁄4

2.00 2.01

0.831 0.824

2.10 2.10

0.847 0.839

2.22 2.21

0.862 0.855

2.00 2.01

0.831 0.824

2.10 2.10

0.847 0.839

2.22 2.21

0.862 0.855

L31⁄2×3×3⁄8 L5×31⁄2×5⁄16 L5×31⁄2×1⁄4

1.86 1.87 1.87

0.771 0.766 0.762

1.95 1.96 1.96

0.791 0.787 0.782

2.06 2.06 2.06

0.812 0.807 0.803

1.89 1.89 1.89

0.884 0.881 0.878

2.00 2.00 2.00

0.897 0.894 0.891

2.13 2.12 2.12

0.909 0.906 0.903

L31⁄2×21⁄2×3⁄8 L31⁄2×31⁄2×1⁄4

1.76 1.77

0.696 0.691

1.84 1.85

0.721 0.715

1.94 1.93

0.748 0.740

1.82 1.81

0.932 0.927

1.94 1.93

0.941 0.936

2.08 2.06

0.948 0.944

L3×3×1⁄2 L3×3×3⁄8 L3×3×5⁄16 L3×3×1⁄4 L3×3×3⁄16

1.72 1.72 1.72 1.72 1.72

0.842 0.834 0.830 0.825 0.822

1.83 1.82 1.82 1.82 1.82

0.860 0.852 0.848 0.844 0.841

1.95 1.94 1.93 1.93 1.93

0.877 0.869 0.866 0.862 0.858

1.72 1.72 1.72 1.72 1.72

0.842 0.834 0.830 0.825 0.822

1.83 1.82 1.82 1.82 1.82

0.860 0.852 0.848 0.844 0.841

1.95 1.94 1.93 1.93 1.93

0.877 0.869 0.866 0.862 0.858

*See LRFD Specification Section E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 174

DIMENSIONS AND PROPERTIES

FLEXURAL-TORSIONAL PROPERTIES Double Angles Long Legs Vertical

Short Legs Vertical

Back to Back of Angles, in. 3⁄ 8

Back to Back of Angles, in.

3⁄ 4

3⁄ 8

3⁄ 4

Designation

ro*

L3×21⁄2×3⁄8 L3×21⁄2×1⁄4 L3×21⁄2×3⁄16

1.58 1.59 1.59

0.763 0.754 0.750

1.67 1.67 1.67

0.789 0.779 0.775

1.78 1.78 1.77

0.813 0.804 0.800

1.61 1.61 1.61

0.896 0.889 0.885

1.73 1.72 1.72

0.910 0.903 0.899

1.86 1.84 1.84

0.922 0.916 0.912

L3×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16

1.49 1.50 1.50 1.50

0.672 0.667 0.664 0.661

1.57 1.57 1.57 1.57

0.704 0.698 0.694 0.690

1.66 1.66 1.66 1.66

0.737 0.730 0.726 0.721

1.55 1.55 1.54 1.54

0.949 0.946 0.943 0.940

1.68 1.68 1.67 1.66

0.956 0.954 0.951 0.949

1.82 1.82 1.80 1.80

0.963 0.961 0.958 0.956

L21⁄2×21⁄2×3⁄8 L21⁄2×21⁄2×5⁄16 L21⁄2×21⁄2×1⁄4 L21⁄2×21⁄2×3⁄16

1.43 1.43 1.43 1.43

0.839 0.834 0.829 0.825

1.54 1.54 1.53 1.53

0.861 0.856 0.851 0.847

1.66 1.66 1.65 1.65

0.880 0.876 0.871 0.867

1.43 1.43 1.43 1.43

0.839 0.834 0.829 0.825

1.54 1.54 1.53 1.53

0.861 0.856 0.851 0.847

1.66 1.66 1.65 1.65

0.880 0.876 0.871 0.867

L21⁄2×2×3⁄8 L3×21⁄2×5⁄16 L3×21⁄2×1⁄4 L3×21⁄2×3⁄16

1.29 1.30 1.30 1.31

0.752 0.746 0.741 0.736

1.39 1.39 1.39 1.39

0.785 0.779 0.773 0.767

1.50 1.50 1.50 1.49

0.816 0.810 0.804 0.798

1.33 1.33 1.33 1.32

0.912 0.908 0.903 0.899

1.45 1.45 1.45 1.44

0.927 0.923 0.919 0.915

1.59 1.58 1.58 1.57

0.939 0.935 0.932 0.928

L2×2×3⁄8 L3×2×5⁄16 L3×2×1⁄4 L3×2×3⁄16 L3×2×1⁄8

1.15 1.15 1.15 1.15 1.15

0.846 0.840 0.834 0.828 0.822

1.26 1.26 1.25 1.25 1.25

0.873 0.867 0.861 0.855 0.850

1.39 1.38 1.38 1.37 1.37

0.896 0.890 0.885 0.880 0.875

1.15 1.15 1.15 1.15 1.15

0.846 0.840 0.834 0.828 0.822

1.26 1.26 1.25 1.25 1.25

0.873 0.867 0.861 0.855 0.850

1.39 1.38 1.38 1.37 1.37

0.896 0.890 0.885 0.880 0.875

*See LRFD Specification Section E3.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

SURFACE AREAS AND BOX AREAS

1 - 175

SURFACE AREAS AND BOX AREAS W shapes Square feet per foot of length

Case A Case B Case C Case D

Designation

Case A Case B Case C Case D

Designation

W44×335 W44×290 W44×262 W44×230 W44 W40×593 W44×503 W44×431 W44×372 W44×321 W44×297 W44×277 W44×249 W44×215 W44×199 W44×174

11.0 11.0 10.9 10.9

12.4 12.3 12.2 12.2

8.67 8.59 8.53 8.46

10.0 9.91 9.84 9.78

10.9 10.7 10.5 10.4 10.3 10.3 10.3 10.2 10.2 10.1 10.0

12.3 12.1 11.9 11.8 11.6 11.6 11.6 11.5 11.5 11.4 11.3

8.56 8.38 8.23 8.11 8.01 7.96 7.93 7.88 7.81 7.76 7.68

9.95 9.75 9.58 9.45 9.33 9.28 9.25 9.19 9.12 9.07 8.99

W40×466 W44×392 W44×331 W44×278 W44×264 W44×235 W36×211 W36×183 W36×167 W36×149

9.79 9.61 9.47 9.35 9.32 9.28 9.22 9.17 9.11 9.05

10.8 10.6 10.5 10.3 10.3 10.3 10.2 10.2 10.1 10.0

8.13 7.96 7.81 7.69 7.66 7.61 7.55 7.48 7.42 7.35

9.18 8.99 8.83 8.69 8.66 8.60 8.53 8.47 8.40 8.34

W36×848 W36×798 W36×650 W36×527 W36×439 W36×393 W36×359 W36×328 W36×300 W36×280 W36×260 W36×245 W36×230

11.1 11.0 10.7 10.4 10.3 10.2 10.1 10.0 9.99 9.95 9.90 9.87 9.84

12.6 12.5 12.1 11.9 11.7 11.6 11.5 11.4 11.4 11.3 11.3 11.2 11.2

8.59 8.49 8.21 7.97 7.79 7.70 7.63 7.57 7.51 7.47 7.42 7.39 7.36

10.1 9.99 9.67 9.41 9.20 9.10 9.02 8.95 8.90 8.85 8.80 8.77 8.73

W36×256 W44×232 W44×210 W44×194 W36×182 W36×170 W36×160 W36×150 W36×135

9.02 8.96 8.91 8.88 8.85 8.82 8.79 8.76 8.71

10.0 9.97 9.93 9.89 9.85 9.82 9.79 9.76 9.70

7.26 7.20 7.13 7.09 7.06 7.03 7.00 6.97 6.92

8.27 8.21 8.15 8.10 8.07 8.03 8.00 7.97 7.92

W33×354 W36×318 W36×291 W36×263 W36×241 W36×221 W33×201

9.66 9.58 9.52 9.46 9.42 9.38 9.33

11.0 10.9 10.8 10.8 10.7 10.7 10.6

7.27 7.19 7.13 7.07 7.02 6.97 6.93

8.61 8.52 8.46 8.39 8.34 8.29 8.24

W33×169 W36×152 W36×141 W36×130 W36×118

8.30 8.27 8.23 8.20 8.15

9.26 9.23 9.19 9.15 9.11

6.60 6.55 6.51 6.47 6.43

7.55 7.51 7.47 7.43 7.39

W30×477 W36×391 W36×326 W36×292 W36×261 W36×235 W36×211 W36×191 W36×173

9.30 9.11 8.96 8.88 8.81 8.75 8.71 8.66 8.62

10.6 10.4 10.2 10.2 10.1 10.0 9.97 9.92 9.87

7.02 6.83 6.68 6.61 6.53 6.47 6.42 6.37 6.32

8.35 8.13 7.96 7.88 7.79 7.73 7.67 7.62 7.57

W30×148 W36×132 W36×124 W36×116 W36×108 W36×99 W36×90

7.53 7.49 7.47 7.44 7.41 7.37 7.35

8.40 8.37 8.34 8.31 8.28 8.25 8.22

5.99 5.93 5.90 5.88 5.84 5.81 5.79

6.86 6.81 6.78 6.75 6.72 6.68 6.66

Case A: Shape perimeter, minus one flange surface. Case B: Shape perimeter. Case C: Box perimeter, equal to one flange surface plus twice the depth. Case D: Box perimeter, equal to two flange surfaces plus twice the depth.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 176

DIMENSIONS AND PROPERTIES

SURFACE AREAS AND BOX AREAS W shapes Square feet per foot of length

Case A Case B Case C Case D

Designation

Case A Case B Case C Case D

Designation

W27×539 W ×448 W ×368 W ×307 W ×281 W ×258 W ×235 W ×217 W ×194 W ×178 W ×161 W ×146

8.82 8.61 8.42 8.27 8.21 8.15 8.09 8.04 7.98 7.95 7.91 7.87

10.09 9.86 9.64 9.47 9.40 9.34 9.27 9.22 9.15 9.12 9.08 9.03

6.69 6.48 6.29 6.14 6.08 6.02 5.96 5.91 5.85 5.81 5.77 5.73

7.96 7.73 7.51 7.34 7.27 7.21 7.14 7.09 7.02 6.98 6.94 6.89

W27×129 W ×114 W ×102 W ×94 W ×84

6.92 6.88 6.85 6.82 6.78

7.75 7.72 7.68 7.65 7.61

5.44 5.39 5.35 5.32 5.28

6.27 6.23 6.18 6.15 6.11

W24×492 W ×408 W ×335 W ×279 W ×250 W ×229 W ×207 W ×192 W ×176 W ×162 W ×146 W ×131 W ×117 W ×104

8.07 7.86 7.66 7.51 7.44 7.38 7.32 7.27 7.23 7.22 7.17 7.12 7.08 7.04

9.25 9.01 8.79 8.62 8.54 8.47 8.40 8.35 8.31 8.30 8.24 8.19 8.15 8.11

6.12 5.91 5.71 5.56 5.49 5.43 5.37 5.32 5.28 5.25 5.20 5.15 5.11 5.07

7.29 7.06 6.84 6.67 6.59 6.52 6.45 6.40 6.35 6.33 6.27 6.22 6.18 6.14

W24×103 W ×94 W ×84 W ×76 W ×68

6.18 6.16 6.12 6.09 6.06

6.93 6.92 6.87 6.84 6.80

4.84 4.81 4.77 4.74 4.70

5.59 5.56 5.52 5.49 5.45

W24×62 W ×55

5.57 5.54

6.16 6.13

4.54 4.51

5.13 5.10

W21×201 W18×182 W18×166 W18×147 W18×132 W18×122 W18×111 W18×101

6.75 6.69 6.65 6.61 6.57 6.54 6.51 6.48

7.80 7.74 7.68 7.66 7.61 7.57 7.54 7.50

4.89 4.83 4.78 4.72 4.68 4.65 4.61 4.58

5.93 5.87 5.82 5.76 5.71 5.68 5.64 5.61

W21×93 W18×83 W18×73 W ×68 W18×62

5.54 5.50 5.47 5.45 5.42

6.24 6.20 6.16 6.14 6.11

4.31 4.27 4.23 4.21 4.19

5.01 4.96 4.92 4.90 4.87

W21×57 W18×50 W18×44

5.01 4.97 4.94

5.56 5.51 5.48

4.06 4.02 3.99

4.60 4.56 4.53

W18×311 W18×283 W18×258 W18×234 W18×211 W18×192 W18×175 W18×158 W18×143 W18×130

6.41 6.32 6.24 6.17 6.10 6.03 5.97 5.92 5.87 5.83

7.41 7.31 7.23 7.14 7.06 6.99 6.92 6.86 6.81 6.76

4.72 4.63 4.56 4.48 4.41 4.35 4.29 4.23 4.18 4.14

5.72 5.62 5.54 5.45 5.37 5.30 5.24 5.17 5.12 5.07

W18×119 W18×106 W18×97 W ×86 W18×76

5.81 5.77 5.74 5.70 5.67

6.75 6.70 6.67 6.62 6.59

4.10 4.06 4.03 3.99 3.95

5.04 4.99 4.96 4.91 4.87

W18×71 W18×65 W18×60 W ×55 W18×50

4.85 4.82 4.80 4.78 4.76

5.48 5.46 5.43 5.41 5.38

3.71 3.69 3.67 3.65 3.62

4.35 4.32 4.30 4.27 4.25

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

SURFACE AREAS AND BOX AREAS

1 - 177

SURFACE AREAS AND BOX AREAS W shapes Square feet per foot of length

Case A Case B Case C Case D

Designation

Case A Case B Case C Case D

Designation

W18×46 W ×40 W ×35

4.41 4.38 4.34

4.91 4.88 4.84

3.51 3.48 3.45

4.02 3.99 3.95

W16×100 W ×89 W ×77 W ×67

5.28 5.24 5.19 5.16

6.15 6.10 6.05 6.01

3.70 3.66 3.61 3.57

4.57 4.52 4.47 4.43

W16×57 W ×50 W ×45 W ×40 W ×36

4.39 4.36 4.33 4.31 4.28

4.98 4.95 4.92 4.89 4.87

3.33 3.30 3.27 3.25 3.23

3.93 3.89 3.86 3.83 3.81

W16×31 W ×26

3.92 3.89

4.39 4.35

3.11 3.07

3.57 3.53

W14×808 W ×730 W ×665 W ×605 W ×550 W ×500 W ×455

7.74 7.61 7.46 7.32 7.19 7.07 6.96

9.28 9.10 8.93 8.77 8.62 8.49 8.36

5.35 5.23 5.08 4.94 4.81 4.68 4.57

6.90 6.72 6.55 6.39 6.24 6.10 5.98

W14×426 W ×398 W ×370 W ×342 W ×311 W ×283 W ×257 W ×233 W ×211 W ×193 W ×176 W ×159 W ×145

6.89 6.81 6.74 6.67 6.59 6.52 6.45 6.38 6.32 6.27 6.22 6.18 6.14

8.28 8.20 8.12 8.03 7.94 7.86 7.78 7.71 7.64 7.58 7.53 7.47 7.43

4.50 4.43 4.36 4.29 4.21 4.13 4.06 4.00 3.94 3.89 3.84 3.79 3.76

5.89 5.81 5.73 5.65 5.56 5.48 5.40 5.32 5.25 5.20 5.15 5.09 5.05

W14×132 W ×120 W ×109 W ×99 W ×90

5.93 5.90 5.86 5.83 5.81

7.16 7.12 7.08 7.05 7.02

3.67 3.64 3.60 3.57 3.55

4.90 4.86 4.82 4.79 4.76

W14×82 W14×74 W14×68 W ×61

4.75 4.72 4.69 4.67

5.59 5.56 5.53 5.50

3.23 3.20 3.18 3.15

4.07 4.04 4.01 3.98

W14×53 W14×48 W14×43

4.19 4.16 4.14

4.86 4.83 4.80

2.99 2.97 2.94

3.66 3.64 3.61

W14×38 W14×34 W14×30

3.93 3.91 3.89

4.50 4.47 4.45

2.91 2.89 2.87

3.48 3.45 3.43

W14×26 W ×22

3.47 3.44

3.89 3.86

2.74 2.71

3.16 3.12

W12×336 W ×305 W14×279 W14×252 W14×230 W14×210 W14×190 W14×170 W14×152 W ×136 W14×120 W14×106 W14×96 W14×87 W14×79 W14×72 W14×65

5.77 5.67 5.59 5.50 5.43 5.37 5.30 5.23 5.17 5.12 5.06 5.02 4.98 4.95 4.92 4.89 4.87

6.88 6.77 6.68 6.58 6.51 6.43 6.36 6.28 6.21 6.15 6.09 6.03 5.99 5.96 5.93 5.90 5.87

3.92 3.82 3.74 3.65 3.58 3.52 3.45 3.39 3.33 3.27 3.21 3.17 3.13 3.10 3.07 3.05 3.02

5.03 4.93 4.83 4.74 4.66 4.58 4.51 4.43 4.37 4.30 4.24 4.19 4.15 4.11 4.08 4.05 4.02

W12×58 W14×53

4.39 4.37

5.22 5.20

2.87 2.84

3.70 3.68

W12×50 W14×45 W ×40

3.90 3.88 3.86

4.58 4.55 4.52

2.71 2.68 2.66

3.38 3.35 3.32

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

SURFACE AREAS AND BOX AREAS W shapes Square feet per foot of length

Case A Case B Case C Case D

Designation

Case A Case B Case C Case D

Designation

W12×35 W12×30 W12×26

3.63 3.60 3.58

4.18 4.14 4.12

2.63 2.60 2.58

3.18 3.14 3.12

W12×22 W12×19 W12×16 W12×14

2.97 2.95 2.92 2.90

3.31 3.28 3.25 3.23

2.39 2.36 2.33 2.32

2.72 2.69 2.66 2.65

W10×112 W12×100 W12×88 W12×77 W12×68 W12×60 W12×54 W12×49

4.30 4.25 4.20 4.15 4.12 4.08 4.06 4.04

5.17 5.11 5.06 5.00 4.96 4.92 4.89 4.87

2.76 2.71 2.66 2.62 2.58 2.54 2.52 2.50

3.63 3.57 3.52 3.47 3.42 3.38 3.35 3.33

W10×45 W12×39 W12×33

3.56 3.53 3.49

4.23 4.19 4.16

2.35 2.32 2.29

3.02 2.98 2.95

W10×30 W12×26 W12×22

3.10 3.08 3.05

3.59 3.56 3.53

2.23 2.20 2.17

2.71 2.68 2.65

W10×19 W12×17 W12×15 W12×12

2.63 2.60 2.58 2.56

2.96 2.94 2.92 2.89

2.04 2.02 2.00 1.97

2.38 2.35 2.33 2.30

W8×67 W8×58 W8×48 W8×40 W8×35 W8×31

3.42 3.37 3.32 3.28 3.25 3.23

4.11 4.06 4.00 3.95 3.92 3.89

2.19 2.14 2.09 2.05 2.02 2.00

2.88 2.83 2.77 2.72 2.69 2.67

W8×28 W8×24

2.87 2.85

3.42 3.39

1.89 1.86

2.43 2.40

W8×21 W8×18

2.61 2.59

3.05 3.03

1.82 1.79

2.26 2.23

W8×15 W8×13 W8×10

2.27 2.25 2.23

2.61 2.58 2.56

1.69 1.67 1.64

2.02 2.00 1.97

W6×25 W ×20 W8×15

2.49 2.46 2.42

3.00 2.96 2.92

1.57 1.54 1.50

2.08 2.04 2.00

W6×16 W8×12 W8×9

1.98 1.93 1.90

2.31 2.26 2.23

1.38 1.34 1.31

1.72 1.67 1.64

W5×19 W8×16

2.04 2.01

2.45 2.43

1.28 1.25

1.70 1.67

W4×13

1.63

1.96

1.03

1.37

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

CAMBER

1 - 179

CAMBER Beams and Girders

Camber and sweep are used to form a desired curvature in either rolled beams or welded girders. Camber denotes a curve in the vertical plane. Beams and girders can be cambered to compensate for the anticipated deflection or for architectural reasons. Note that the required camber is determined at service (unfactored) load levels. Sweep denotes a curve in the horizontal plane. Camber and sweep may be induced through cold bending or through the application of heat. The minimum radius for cold cambering in members up to a nominal depth of 30 inches is between 10 and 14 times the depth of the member; deeper members will require a larger minimum radius. Cold bending may be used to provide sweep in members to practically any radius desired. Note that a length limit of 40 to 50 feet is practical. Heat cambering, sweeping, and straightening are provided through controlled heat application. The member is rapidly heated in selected areas which tend to expand, but are restrained by the adjacent cooler areas, causing plastic deformation of the heated areas and a change in the shape of the cooled member. The mechanical properties of steels are largely unaffected by such heating operations, provided the maximum temperature does not exceed 1,100°F for quenched and tempered alloy steels, and 1,300°F for other steels. The temperature should be carefully checked by temperature-indicating crayons or other suitable means during the heating process. Cambering and sweeping induces residual stresses similar to those that develop in rolled structural shapes as elements of the shape cool from the rolling temperature at different rates. In general, these residual stresses do not affect the ultimate strength of structural members. Additionally, the effect of residual stresses is incorporated in the provisions of the LRFD Specification. Note that when a cambered beam bearing on a wall or other support is loaded, expansion of the unrestrained end must be considered. In Figure 1-5(a), the end will move a distance ∆, where ∆=

4Cd L

If instead the cambered beam is supported on a simple shear connection at both ends, the top and bottom flange will each move a distance of one-half ∆ since end rotation will occur approximately about the neutral axis. The designer should be aware of the magnitude of these movements and make provisions to accommodate them. Figure 1-5(a) considers the geometry of a girder in the horizontal position, and Figure 1-5(b) illustrates the condition when the girder is not level. Trusses

“Cambering” of trusses is accomplished by geometric relocation of panel points and adjustment of member lengths; it does not involve physical cold bending or the application of heat as with beams and girders. The following discussion of cambering to compensate for the anticipated deflection of a truss is applicable for any parabolic condition; large-radius circular curves will be approximated very closely by the technique described. Cambering to compensate for the axial deformation of the members of a truss is beyond the scope of this Manual; refer to a textbook on mechanics of materials. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Distances approximately equal for small angles

Distances equal for parabolic curve, approximately equal for circular curve. See sketch below.

∆

∆ θ

d C

90°

C L /2

∆

L /2

tanθ = 2C

Fixed End

L /2

∆ = d tanθ

Unrestrained End

∆ = 4Cd L

θ 2θ for circular curve 2C for parabolic curve (a) Beam or Girder Ends at

Same Elevations

4Cd ∆= L

∆ = 4Cd L

∆ = 4Cd L d

B Grade angle

B L

L approx

(b) Beam or Girder Ends at Different Elevations

Fig. 1-5. Camber for beams and girders. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

A+B A

Horiz. line

Vert.

B 90

Grade lin

A+B A

CAMBER

1 - 181

The usual method of providing camber in building trusses is to progressively raise each panel point. The lengths of the verticals are not changed, but the lengths of the diagonals are calculated on the basis of the adjusted elevation for the several panel points. For any simple-span truss, the offset above a straight base line, at the several panel points, can be computed from the following equations if the vertical curve forming the camber is taken as a parabola. 2

 B B  D = C − C   = C 1 −    A   A   where A = Horizontal distance from end panel point to mid-span of the truss (half the truss span). B = Horizontal distance from mid-span of the truss to panel point for which offset is to be determined. C = Required mid-span camber. D = Offset from the base-line at panel point corresponding to distance B. A and B must be expressed in the same units; similarly C and D must be expressed in the same units, but not necessarily the same units as A and B. When the truss is divided into any number of approximately equal panels, it may be convenient to express distances A and B in panel lengths. For the truss of Figure 1-6(a) with eight equal panels, distance A is taken as four panel lengths. Assuming the camber at the midpoint is specified as 11⁄2-in., the offset at panel point 1, where B equals three panel lengths, is: 2

 3  D = 1 -in. 1 −    4   = 21⁄32-in. 1⁄ 2

The offset at panel point 2, where B equals two panel lengths, is: 2

 2  D = 1 -in. 1 −     4  = 11⁄8-in. 1⁄ 2

The offset at panel point 3, where B equals one panel length, is: 2

 1  D = 1 -in. 1 −    4   = 113⁄32-in. 1⁄ 2

Finally, the offset at panel point 4, where B equals zero, is D = C = 11⁄2-in. An alternative method of determining the amount of camber at intermediate panel points when all panel points are approximately the same distance apart is as follows. Using the truss in Figure 1-6(a) as an example, sketch the camber diagram and number the panel points, starting with the first panel point from the end of the truss, from 1 to 4, AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 182

DIMENSIONS AND PROPERTIES

as shown in Figure 1-6(b) on line A. Next, on line B, reverse the numbering as shown. Finally, on line C, enter the product of the numbers on lines A and B. The camber at any panel point is the amount of camber at the centerline of the truss multiplied by the fraction whose numerator is the figure on line C at the given panel point, and whose denominator is the figure on line C at the center line of the truss. Thus, at panel point 1, the camber is 7⁄

× 11⁄2jin. = 21⁄32jin.

at panel point 2, the camber is 12⁄

× 11⁄2jin. = 11⁄8jin.

at panel point 3, the camber is 15⁄

× 11⁄2jin. = 113⁄32jin.

and at panel point 4, the camber is 16⁄

× 11⁄2jin. = 11⁄2jin.

3 2 1 21/ 32

1 1/2

1 13/32

11/8

Baseline

(a) Calculated camber ordinates by formula

cL 4

line A line B

1 x7

2 x6

3 x5

4 x4

line C

Panel point

(b) Alternative calculation method for approximately equal panels

Fig. 1-6. Camber for trusses. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STANDARD MILL PRACTICE

1 - 183

STANDARD MILL PRACTICE General Information

Rolling structural shapes and plates involves such factors as roll wear, subsequent roll dressing, temperature variations, etc., which cause the finished product to vary from published profiles. Such variations are limited by the provisions of the American Society for Testing and Materials Specification A6. Contained in this section is a summary of these provisions, not a reproduction of the complete specification. In its entirety, A6 covers a group of common requirements, which, unless otherwise specified in the purchase order or in an individual specification, apply to rolled steel plates, shapes, sheet piling, and bars. As indicated in Table 1-1, carbon steel refers to ASTM designations A36 and A529; high-strength, low-alloy steel refers to designations A242, A572, and A588; alloy steel refers to designation A514; and low-alloy steel refers to A852. For further information on mill practices, including permissible variations for rolled tees, zees, and bulb angles in structural and bar sizes, pipe, tubing, sheets, and strip, and for other grades of steel, see ASTM A6, A53, A500, A568, and A618; the Steel Products Manuals of the Iron and Steel Society (American Institute of Mining, Metallurgical, and Petroleum Engineers); and producers’ catalogs. The data on spreading rolls to increase areas and weights, and mill cambering of beams, is not a part of ASTM A6. Additional material on mill practice is included in the descriptive material preceding the “Dimensions and Properties” tables for shapes and plates. Letter symbols representing dimensions on sketches shown herein are in accordance with ASTM A6, AISI and mill catalogs and not necessarily as defined by the general nomenclature of this manual. Methods of increasing areas and weights by spreading rolls Cambering of rolled beams . . . . . . . . . . . . . . . . . . Positions for measuring camber and sweep . . . . . . . . . W Shapes, permissible variations . . . . . . . . . . . . . . S Shapes, M Shapes, and Channels, permissible variations . Tees split from W , M, and S Shapes, permissible variations Angles split from Channels, permissible variations . . . . . Angles, structural size, permissible variations . . . . . . . . Angles, bar size, permissible variations . . . . . . . . . . . Steel Pipe and Tubing, permissible variations . . . . . . . . Plates, permissible variations for sheared, length and width . Plates, permissible variations for universal mill, length . . . Plates, permissible variations for universal mill, width . . . Plates, permissible variations for camber . . . . . . . . . . Plates, permissible variations for flatness . . . . . . . . . .

. . . . . . . . . . . . . . .

1-183 1-186 1-187 1-188 1-190 1-191 1-191 1-192 1-193 1-194 1-196 1-196 1-196 1-197 1-198

Methods of Increasing Areas and Weights by Spreading Rolls

W Shapes

To vary the area and weight within a given nominal size, the flange width, the flange thickness, and the web thickness are changed as shown in Figure 1-7(a). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 184

DIMENSIONS AND PROPERTIES

S Shapes and American Standard Channels

To vary the area and weight within a given nominal size, the web thickness and the flange width are changed by an equal amount as shown in Figures 1-7(b) and (c). Angles

To vary area and weight for a given leg length, the thickness of each leg is changed. Note that the leg length is changed slightly by this method (Figure 1-7(d)).

Constant for a given nominal size

(a)

Constant for a given nominal size (except S24 and S20)

(b)

Constant for a given nominal size

(c)

(d) Fig. 1-7. Varying areas and weights. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STANDARD MILL PRACTICE

1 - 185

Cambering of Rolled Beams

All beams are straightened after rolling to meet permissible variations for sweep and camber listed hereinafter for W shapes and S shapes. The following data refer to the subsequent cold cambering of beams to produce a predetermined dimension. The maximum lengths that can be cambered depend on the length to which a given section can be rolled, with a maximum of 100 feet. Table 1-10 outlines the maximum and minimum induced camber of W shapes and S shapes. Consult the producer for specific camber and/or lengths outside the above listed available lengths and sections. Mill camber in beams of less depth than tabulated should not be specified. A single minimum value for camber, within the ranges shown above for the length ordered, should be specified. Camber is measured at the mill and will not necessarily be present in the same amount in the section of beam as received due to release of stress induced during the cambering operation. In general 75 percent of the specified camber is likely to remain. Camber will approximate a simple regular curve nearly the full length of the beam, or between any two points specified. Camber is ordinarily specified by the ordinate at the mid-length of the portion of the beam to be curved. Ordinates at the other points should not be specified. Although mill cambering to achieve reverse or other compound curves is not considered practical, fabricating shop facilities for cambering by heat can accomplish such results as well as form regular curves in excess of the limits tabulated above. Refer to the earlier section Effect of Heat of Steel for further information.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-10. Cambering of Rolled Beams Maximum and Minimum Induced Camber Sections, Nominal Depth, in.

Specified Length of Beam, ft Over 30 to 42, incl.

Over 42 to 52, incl.

Over 52 to 65, incl.

Over 65 to 85, incl.

Over 85 to 100, incl.

Max. and Min. Camber Acceptable, in. W shapes, 24 and over

W shapes, 14 to 21, incl. and S shapes, 12 in. and over

1 to 2, incl. 3⁄ 4

to 21⁄2, incl.

1 to 3, incl.

2 to 4, incl.

3 to 5, incl.

3 to 6, incl.

1 to 3, incl.

—

Permissible Variations for Camber Ordinate Lengths

Plus Variation 1⁄

50 ft and less Over 50 ft

1⁄ -in. 2

2-in.

1⁄ -in. 8

plus for each 10 ft or fraction thereof in excess of 50 ft

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Minus Variation 0 0

STANDARD MILL PRACTICE

1 - 187

Table 1-11. Positions for Measuring Camber and Sweep

Camber

Sweep

Camber

Sweep*

Horizontal surface

W SHAPES

Camber

S SHAPES and M SHAPES

Sweep*

Camber

Horizontal surface

Horz

Camber

onta

CHANNELS

ANGLES

l sur

face

TEES

*Due to the extreme variations in flexibility of these shapes, straightness tolerances for sweep are subject to negotiations between manufacturer and purchaser for individual sections involved.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-12. W Shapes, HP Shapes B

1/ 2 B±

T′

T 1/2 B±E

1/ 2 B±

Permissible Variations in Cross Section Section Nominal Size, in.

A, Depth, in.

B, Fig. Width, in.

Over Theoretical

Under Theoretical

Over Theoretical

To 12, inc.

1⁄

1⁄ 8

1⁄ 4

3⁄

Over 12

1⁄

1⁄ 8

1⁄ 4

3⁄

T+T′ Flanges, out of square, Max, in.

E a, Web off Center, Max, in.

C, Max. Depth at any Crosssection over Theoretical Depth, in.

1⁄ 4

3⁄ 16

1⁄

5⁄

3⁄ 16

1⁄

Under Theoretical

Permissible Variations in Length Variations from Specified Length for Lengths for Given, in. 30 ft and Under W Shapes

Over 30 ft

Over

Under

Over

Under

Beams 24 in. and under in nominal depth

3⁄

3⁄ 8

3⁄

1 8 plus ⁄16 for each additional 5 ft or fraction thereof

3⁄ 8

Beams over 24 in. nom. depth; all columns

1⁄

1⁄ 2

1⁄

1⁄ 2

1 2 plus ⁄16 for each additional 5 ft or fraction thereof

Notes: aVariation of 5⁄ in. max. for sections over 426 lb / ft. 16

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Continued on next page

STANDARD MILL PRACTICE

1 - 189

Table 1-12 (cont.). WP Shapes, HP Shapes Other Permissible Variations Area and weight variation: ±2.5 percent theorectical or specified amount. Ends out-of-square: 1⁄64-in. per in. of depth, or of flange width if it is greater than the depth.

Camber and Sweep Permissible Variation, in. Sizes

Length

Sizes with flange width equal to or greater than 6 in.

All

Sizes with flange width less than 6 in.

All

45 ft. and under

Certain sections with a flange width approx. equal to depth & specified on order as b columns

Over 45 ft.

Camber 1⁄ 8

1⁄ 8

in. ×

Sweep in. ×

(total length ft.) 10

1⁄ 8

in. ×

(total length ft.) 5

(total length ft.) with 3⁄8 in. max. 10

1⁄ 8

in. ×

3⁄ 8

 (total length ft. − 45)  in. + 1⁄8 in. ×  10  

bApplies only to W8×31 and heavier, W10×49 and heavier, W12×65 and heavier, W14×90 and heavier. If the other sections are specified on the order as columns, the tolerance will be subject to negotiation with the manufacturer.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1 - 190

DIMENSIONS AND PROPERTIES

Table 1-13. S Shapes, M Shapes, and Channels Permissible Variations in Cross Section B B

T′

* Back of square and centerline of web to be parallel when measuring “out-of-square”

A, Depth in.a

Section

T + T ′b, Out of Square per Inch of Over Under Over Under B, in. Theoretical Theoretical Theoretical Theoretical

Nominal Size in.

S shapes 3 to 7, incl. Over 7 to 14, and M incl. shapes Over 14 to 24, incl.

1⁄ 2 1⁄ 8

1⁄ 16 3⁄ 32

1⁄ 8 5⁄ 32

1⁄

3⁄

1⁄ 8

3⁄ 16

1⁄

32 1⁄ 8

1⁄ 16 3⁄ 32

1⁄ 8 1⁄ 8

1⁄ 8 5⁄ 32

1⁄

3⁄

1⁄ 8

3⁄ 16

1⁄

3⁄

Channels 3 to 4, incl. Over 7 to 14, incl. Over 14

B, Flange Width, in.

1⁄

32 32

Permissible Variations in Length Variations from Specified Length for Lengths Given, in. Over 30 to 40 ft., incl.

to 30 ft., incl. Section S shapes, M shapes and Channels

Over 40 to 50 ft., incl.

Over

Under

Over

Under

Over

1⁄

1⁄ 4

3⁄ 4

1⁄

Under 1⁄

Over 50 to 65 ft., incl.

Over 65 ft.

Over

Under

Over

Under

11⁄8

1⁄ 4

11⁄4

1⁄ 4

Other Permissible Variations

Area and weight variation: ±2.5 percent theoretical or specified amount. Ends out-of square: S shapes and channels 1⁄64-in. per in. of depth. total length,ft Camber = 1⁄8-in. × 5 Notes: aA is measured at center line of web for beams; and at back of web for channels. bT + T′ applies when flanges of channels are toed in or out.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STANDARD MILL PRACTICE

1 - 191

Table 1-14. Tees Split from W, M, and S Shapes, Angles Split from Channels Permissible Variations in Depth A

Dimension A may be approximately one-half beam or channel depth, or any dimension resulting from off-center splitting, or splitting on two lines as specified on the order. Depth of Beam from which Tees or Angles are Split

Variations in Depth A Over and Under Tees

Angles

To 6 in., excl.

1⁄ 8

6 to 16, excl.

3⁄ 16

16 to 20, excl.

1⁄ 4

20 to 24, excl.

5⁄ 16

—

24 and over

3⁄ 8

—

The above variations for depths to tees or angles include the permissible variations in depth for the beams and channels before splitting.

Other Permissible Variations Other permissible variations in cross section as well as permissible variations in length, area, and weight variation, and ends out-of-square will correspond to those of the beam or channel before splitting, except total length,ft Camber = 1⁄8-in. × 5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-15. Angles, Structural Size Permissible Variations in Cross Section T

B Length of Leg, in. Nominal Size, in.a

Section Angles

Over Theoretical

Under Theoretical

T, Out of Square per in. of B, in.

1⁄ 8

3⁄ 32

b 3⁄ 128

3 to 4, incl. Over 4 to 6, incl.

1⁄ 8

b 3⁄ 128

Over 6

3⁄ 16

1⁄ 8

b 3⁄ 128

Permissible Variations in Length Variations from Specified Length for Lengths Given, in. Over 30 to 40 ft., incl.

to 30 ft., incl. Section Angles

Over 40 to 50 ft., incl.

Over 50 to 65 ft., incl.

Over 65 ft.

Over

Under

Over

Under

Over

Under

Over

Under

Over

Under

1⁄ 2

1⁄ 4

3⁄ 4

1⁄ 4

11⁄8

1⁄ 4

11⁄4

1⁄ 4

Other Permissible Variations Area and weight variation: ±2.5 percent theoretical or specified amount. Ends out-of square: 3⁄128-in. per in. of leg length, or 11⁄2 degrees. Variations based on the longer leg of unequal angle. total length,ft Camber = 1⁄8-in. × , applied to either leg 5 Notes; aFor unequal leg angles, longer leg determines classification. 1 b1⁄ 128 in. per in. = 1 ⁄2 deg.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STANDARD MILL PRACTICE

1 - 193

Table 1-16. Angles, Bar Size* Permissible Variation in Cross Section T

Specified Length of Leg, in.

Variations from Thickness for Thicknesses Given, Over and Under, in. 3⁄ 16

and Under

Over 3⁄16 to 3⁄ incl. 8

1 and Under

0.008

0.010

Over 1 to 2, incl.

0.010

Over 2 to 3, excl.

0.012

0.015

Over 3⁄8

B Length of T, Out of Leg Over Square per and Under, in. Inch of B, in. 1⁄ 32

b 3⁄ 128

0.012

3⁄ 64

b 3⁄ 128

0.015

1⁄ 16

b 3⁄ 128

Permissible Variations in Length Variations Over Specified Length for Lengths Given No Variation Under Section All sizes of barsize angles

50 to 10 ft. excl.

10 to 20 ft. excl.

20 to 30 ft. excl.

30 to 40 ft. excl.

40 to 65 ft. excl.

5⁄ 8

11⁄2

21⁄2

Other Permissible Variations total length,ft 5 Straightness: Because of warpage, permissible variations for straightness do not apply to bars if any subsequent heating operation has been performed. Ends out-of-square: 3⁄128-in. per inch of leg length or 11⁄2 degrees. Variation based on longer leg of an unequal angle. Camber: 1⁄4-in. in any 5 feet, or 1⁄4 in. ×

Notes: *A member is ‘‘bar size’’ when its greatest cross-sectional dimension is less than three inches. aFor unequal leg angles, longer leg determines classification. 1 b1⁄ 128 in. per in. = 1 ⁄2 degrees.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-17. Steel Pipe and Tubing Dimensions and Weight Tolerances Round Tubing and Pipe (see also Table 1-4) ASTM A53 Weight—The weight of the pipe as specified in Table X2 and Table X3 (ASTM Specification A53) shall not vary by more than ±10 percent. Note that the weight tolerance of ±10 percent is determined from the weights of the customary lifts of pipe as produced for shipment by the mill, divided by the number of feet of pipe in the lift. On pipe sizes over four inches where individual lengths may be weighed, the weight tolerance is applicable to the individual length. Diameter—For pipe two inches and over in nominal diameter, the outside diameter shall not vary more than ±1 percent from the standard specified. Thickness—The minimum wall thickness at any point shall not be more than 12.5 percent under the nominal wall thickness specified. ASTM 500 Diameter—For pipe two inches and over in nominal diameter, the outside diameter shall not vary more than ±0.75 percent from the standard specified. Thickness—The wall thickness at any point shall not be more than 10 percent under or over the nominal wall thickness specified. ASTM A501 and ASTM 618 Outside dimensions—For round hot-formed structural tubing two inches and over in nominal size, the outside diameter shall not vary more than ±1 percent from the standard specified. Weight (A501 only)—The weight of structural tubing shall be less than the specified value by more than 3.5 percent. Mass (A618 only)—The mass of structural tubing shall not be less than the specified value by more than 3.5 percent. Length—Structural tubing is commonly produced in random mill lengths and in definite cut lengths. When cut lengths are specified for structural tubing, the length tolerances shall be in accordance with the following table: Over 22 to 44 ft, incl.

22 ft and under

Length tolerance for specified cut lengths, in.

Over

Under

Over

Under

1⁄

3⁄

1⁄

Straightness—The permissible variation for straightness of structural tubing shall be 1⁄8-in. times the number of feet of total length divided by 5. Continued on next page

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STANDARD MILL PRACTICE

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Table 1-17 (cont.). Steel Pipe and Tubing Dimensions and Weight Tolerances Square and Rectangular Tubing (see also Table 1-4) ASTM A500 and ASTM A618 Outside Dimensions—The specified dimensions, measured across the flats at positions at least two inches from either end-of-square or rectangular tubing and including an allowance for convexity or concavity, shall not exceed the plus and minus tolerance shown in the following table: a

Largest Outside Dimension Across Flats, in.

Tolerance Plus an Minus, in.

21⁄2 and under Over 21⁄2 to 31⁄2, incl. Over 31⁄2 to 51⁄2, incl. Over 51⁄2

0.020 0.025 0.030 1 percent

aThe respective outside dimension tolerances

include the allowances for convexity and concavity.

Lengths—Structural tubing is commonly produced in random lengths, in multiple lengths, and in definite cut lengths. When cut lengths are specified for structural tubing, the length tolerances shall be in accordance with the following table: 22 ft and under

Length tolerance for specified cut lengths, in.

Over 22 to 44 ft, incl.

Over

Under

Over

Under

1⁄

3⁄

1⁄

Mass (A618 only)—The mass of structural tubing shall not be less than the specified value by more than 3.5 percent. Straightness—The permissible variation for straightness of structural tubing shall be 1⁄8-in. times the number of feet of total length divided by five. Squareness of sides—For square or rectangular structural tubing, adjacent sides may deviate from 90 degrees by a tolerance of plus or minus two degrees maximum. Radius of corners—For square or rectangular structural tubing, the radius of any outside corner of the section shall not exceed three times the specified wall thickness. Twists—The tolerances for twist or variation with respect to axial alignment of the section, for square and rectangular structural tubing, shall be as shown in the following table: Specified Dimension of Longest Side, in.

Maximum Twist per 3 ft of Length, in.

11⁄

2 and under Over 11⁄2 to 21⁄2, incl. Over 21⁄2 to 4, incl. Over 4 to 6 incl. Over 6 to 8, incl. Over 8

0.050 0.062 0.075 0.087 0.100 0.112

Twist is measured by holding down one end of a square or rectangular tube on a flat surface plate with the bottom side of the tube parallel to the surface plate and noting the height that either corner, at the opposite end of the bottom side of the tube, extends above the surface plate. Wall thickness (A500 only)—The tolerance for wall thickness exclusive of the weld area shall be plus and minus 10 percent of the nominal wall thickness specified. The wall thickness is to be measured at the center of the flat.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-18. Rectangular Sheared Plates and Universal Mill Plates Permissible Variations in Width and Length for Sheared Plates (11⁄2-in. and under in thickness) Permissible Variations in Length Only for Universal Mill Plates (21⁄2-in. and under in thickness) Specified Dimensions, in.

Variations over Specified Width and Length for Thickness, in., and Equivalent Weights, lb per sq. ft., Given To 3⁄8 excl. To 15.3, excl.

Length To 120, excl.

Width

to 5⁄8 excl.

15.3 to 25.5, excl.

5⁄ 8

to 1, excl.

1 to 2, incl.a

25.5 to 40.8, excl.

40.8 to 81.7, incl.

Width Length Width Length Width Length Width Length

To 60, excl. 60 to 84, excl. 84 to 108, excl 108 and over

120 to 240, excl. To 60, excl. 60 to 84, excl. 84 to 108, excl. 108 and over 240 to 360, excl. To 60, excl. 60 to 84, excl. 84 to 108, excl. 108 and over

3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8

1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

3⁄

1⁄

16 5⁄ 8

9⁄

3⁄ 1⁄

8 2

9⁄ 16 11⁄ 16

480 to 600, excl. To 60, excl. 60 to 84, excl. 84 to 108, excl. 108 and over

7⁄

To 60, excl. 60 to 84, excl. 84 to 108, excl. 108 and over

3⁄

7⁄

600 to 720, excl. To 60, excl. 60 to 84, excl. 84 to 108, excl. 108 and over

8 2

360 to 480, excl. To 60, excl. 60 to 84, excl. 84 to 108, excl. 108 and over

720 and over, excl.

3⁄ 8

16 1⁄ 2 9⁄ 16 3⁄ 4 16 1⁄ 2 5⁄ 8 3⁄ 4 1⁄ 5⁄ 5⁄ 7⁄

2 8 8 8

9⁄

16 3⁄ 4 3⁄ 4

7⁄

4 8

5⁄

11⁄

2 8

16 3⁄ 4

1 1 1 11 ⁄8

1⁄

11 ⁄8 11 ⁄4 11 ⁄4 13 ⁄8

1⁄

11 ⁄4 13 ⁄8 13 ⁄8 11 ⁄2

1⁄

11 ⁄4 13 ⁄8 13 ⁄8 11 ⁄2

5⁄

2 2 2 2

3⁄

5⁄ 3⁄ 7⁄ 5⁄ 3⁄ 7⁄ 5⁄ 3⁄ 7⁄ 3⁄ 3⁄

2 8 4 8 2 8 4 8 2 8 4 8 8 4 4

1 7⁄ 7⁄

4 8 8

11 ⁄8

5⁄ 8

11⁄

7⁄

1 7⁄ 7⁄

15 ⁄

8 8 16

11 ⁄8

1⁄ 2

5⁄ 3⁄

7⁄ 5⁄ 3⁄

13 ⁄ 7⁄

11 ⁄8 11 ⁄8 11 ⁄8 11 ⁄4

5⁄

11 ⁄4 13 ⁄8 13 ⁄8 11 ⁄2

5⁄

11 ⁄2 11 ⁄2 11 ⁄2 15 ⁄8

5⁄

17 ⁄8 17 ⁄8 17 ⁄8 2

3⁄

21 ⁄8 21 ⁄8 21 ⁄8 23 ⁄8

3⁄ 7⁄

8 4 8 8 4 16 8 8 4 8

1 3⁄ 7⁄

8 4 8

1 3⁄ 7⁄

8 4 8

1 7⁄ 7⁄

4 8 8

11 ⁄8 7⁄

1 1 11 ⁄4

3⁄ 4 7⁄ 8

5⁄ 8 3⁄ 4

1 11 ⁄8

1 1 11 ⁄8 11 ⁄4

3⁄

11 ⁄4 11 ⁄4 13 ⁄8 13 ⁄8 13 ⁄8 11 ⁄2 11 ⁄2 15 ⁄8 15 ⁄8 15 ⁄8 15 ⁄8 13 ⁄4

7⁄

4 8

1 11 ⁄8 3⁄ 7⁄

4 8

1 11 ⁄4 3⁄ 7⁄

4 8

1 11 ⁄4 3⁄ 7⁄

4 8

1 11 ⁄4 7⁄

1 1 11 ⁄ 8 11 ⁄ 4 11 ⁄ 8 11 ⁄ 4 13 ⁄ 8 13 ⁄ 8 11 ⁄ 2 11 ⁄ 2 11 ⁄ 2 13 ⁄ 4 15 ⁄ 8 15 ⁄ 8 17 ⁄ 8 17 ⁄ 8 17 ⁄ 8 17 ⁄ 8 17 ⁄ 8 17 ⁄ 8

17 ⁄8 17 ⁄8 17 ⁄8 21 ⁄4

1 11 ⁄8 11 ⁄4

21 ⁄ 4 21 ⁄ 4 21 ⁄ 4 21 ⁄ 2

21 ⁄4 21 ⁄4 21 ⁄4 21 ⁄2

1 11 ⁄8 11 ⁄4 13 ⁄8

23 ⁄ 4 23 ⁄ 4 23 ⁄ 4 3

Notes: aPermissible variations in length apply also to Universal Mill plates up to 12 in. width for thicknesses over 2 to 21⁄2-in., incl. except for alloy steels up to 13⁄4-in. thick. Permissible variations under specified width and length, 1⁄4-in. Table applies to all steels listed in ASTM A6.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

STANDARD MILL PRACTICE

1 - 197

Table 1-19. Rectangular Sheared Plates and Universal Mill Plates Permissible Variations from Flatness (Carbon Steel Only) Variations from Flatness for Specified Widths, in.

Specified Thickness, in.

To 36 excl.

To 1⁄4, excl. 1⁄ to 3⁄ , excl. 4 8 3⁄ to 1⁄ , excl. 8 2 1⁄ to 3⁄ , excl. 2 4 3⁄ to 1, excl. 4 1 to 2, excl. 2 to 4, excl. 4 to 6, excl. 6 to 8, excl.

9⁄ 16 1⁄ 2 1⁄ 2 7⁄ 16 7⁄ 16 3⁄ 8 5⁄ 16 3⁄ 8 7⁄ 16

36 to 48, 48 to 60, 60 to 72, 72 to 84, 84 to 96, 96 to 108, 108 to excl. excl. excl. excl. excl. excl. 120, excl. 3⁄ 4 5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 1⁄ 2 3⁄ 8 7⁄ 16 1⁄ 2

15⁄ 3⁄ 5⁄

16 4

8 9⁄ 16 9⁄ 16 1⁄ 2 7⁄ 16 1⁄ 2 1⁄ 2

11⁄4 15⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2 1⁄ 2 5⁄ 8

13⁄8 11⁄8 3⁄ 4 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2 9⁄ 16 11⁄ 16

11⁄2 11⁄4 7⁄ 8 3⁄ 4 5⁄ 8 5⁄ 8 1⁄ 2 9⁄ 16 3⁄ 4

15⁄8 13⁄8 1 1 3⁄ 4 5⁄ 8 1⁄ 2 5⁄ 8 7⁄ 8

13⁄4 11⁄2 11⁄8 1 7⁄ 8 5⁄ 8 9⁄ 16 3⁄ 4 7⁄ 8

Permissible Variations in Camber for Carbon Steel Sheared and Gas Cut Rectangular Plates Maximum permissible camber, in. (all thicknesses) = 1⁄8-in. ×

total length,ft 5

Permissible Variations in Camber for Carbon Steel Universal Mill Plates, High-Strength Low-Alloy Steel Sheared and Gas Cut Rectangular Plates, Universal Mill Plates, Special Cut Plates Dimension, in. Thickness To 2, incl. Over 2 to 15, incl. Over 2 to 15, incl.

Width

Camber for Thicknesses and Widths Given

All To 30, incl. Over 30 to 60, incl.

1⁄ in. × (total length, ft / 5) 8 3⁄ in. × (total length, ft / 5) 16 1⁄ in. × (total length, ft / 5) 4

General Notes: 1. The longer dimension specified is considered the length, and permissible variations in flatness along the length should not exceed the tabular amount for the specified width in plates up to 12 feet in length. 2. The flatness variations across the width should not exceed the tabular amount for the specified width. 3. When the longer dimension is under 36 inches, the permissible variation should not exceed 1⁄4-in. When the longer dimension is from 36 to 72 inches, inclusive, the permissible variation should not exceed 75 percent of the tabular amount for the specified width, but in no case less than 1⁄4-in. 4. These variations apply to plates which have a specified minimum tensile strength of not more than 60 ksi or compatible chemistry or hardness. The limits in the table are increased 50 percent for plates specified to a higher minimum tensile strength or compatible chemistry or hardness. See also next page.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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DIMENSIONS AND PROPERTIES

Table 1-20. Rectangular Sheared Plates and Universal Milled Plates Permissible Variations from Flatness (High-Strength Low-Alloy and Alloy Steel, Hot Rolled or Thermally Treated) Variations from Flatness for Specified Widths, in.

Specified Thickness, in.

To 36 excl.

To 1⁄4, excl. 1⁄ to 3⁄ , excl. 4 8 3⁄ to 1⁄ , excl. 8 2 1⁄ to 3⁄ , excl. 2 4 3⁄ to 1, excl. 4 1 to 2, excl. 2 to 4, excl. 4 to 6, excl. 6 to 8, excl.

13⁄ 16 3⁄ 4 3⁄ 4 5⁄ 8 5⁄ 8 9⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8

36 to 48, 48 to 60, 60 to 72, 72 to 84, 84 to 96, 96 to 108, 108 to excl. excl. excl. excl. excl. excl. 120, excl. 11⁄8

15⁄ 7⁄ 3⁄ 3⁄ 5⁄

13⁄8 11⁄8 15⁄ 16 15⁄ 16 7⁄ 8 3⁄ 4 9⁄ 16 3⁄ 4 3⁄ 4

16 8 4 4

8 9⁄ 16 11⁄ 16 3⁄ 4

17⁄8 13⁄8 15⁄ 16 7⁄ 8 7⁄ 8 13⁄ 16 3⁄ 4 3⁄ 4 15⁄ 16

21⁄4 17⁄8 15⁄16 11⁄8 1 15⁄ 16 3⁄ 4 7⁄ 8 11⁄8

2 13⁄4 11⁄8 1 15⁄ 16 7⁄ 8 3⁄ 4 7⁄ 8 1

23⁄8 2 11⁄2 11⁄4 11⁄8 1 3⁄ 4 15⁄ 16 11⁄4

25⁄8 21⁄4 15⁄8 13⁄8 15⁄16 1 7⁄ 8 11⁄8 15⁄16

General Notes: 1. The longer dimension specified is considered the length, and variations from a flat surface along the length should not exceed the tabular amount for the specified width in plates up to 12 feet in length. 2. The flatness variation across the width should not exceed the tabular amount for the specified width. 3. When the longer dimension is under 36 inches, the variation should not exceed 3⁄8-in. When the longer dimension is from 36 to 72 inches, inclusive the variation should not exceed 75 percent of the tabular amount for the specified width.

Permissible Variations in Width for Universal Mill Plates (15 inches and under in thickness) Variations Over Specified Width for Thickness, in., and Equivalent Weights, lb per sq. ft., Given To 3⁄8, excl.

3⁄ 8

to 5⁄8 excl.

5⁄ 8

to 1, excl.

Specified Width, in.

To 15.3, excl.

15.3 to 25.5, excl.

25.5 to 40.8, excl.

Over 8 to 20, excl. 20 to 36, excl. 36 and over

1⁄ 8 3⁄ 16 5⁄ 16

1⁄

3⁄ 16 5⁄ 16 7⁄ 16

3⁄

8 4 8

1 to 2, excl.

Over 2 to 10, incl.

Over 10 to 15, incl.

40.8 to 81.7 to 409.0 to 81.7, incl. 409.0, incl. 613.0, incl. 1⁄ 3⁄ 1⁄

4 8 2

Notes: Permissible variation under specified width, 1⁄8-in. Table applies to all steels listed in ASTM A6.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3⁄ 8 7⁄ 16 9⁄ 16

1⁄ 2 9⁄ 16 5⁄ 8

REFERENCES

1 - 199

REFERENCES

American Institute of Steel Construction, 1973, “Commentary on Highly Restrained Welded Connections,” Engineering Journal, 3rd Qtr., AISC, Chicago, IL. American Iron and Steel Institute, 1979, Fire Safe Structural Steel: A Design Guide, AISI, Washington, DC. AISI, 1980, Designing Fire Protection for Steel Columns, 3rd Edition. AISI, 1981, Designing Fire Protection for Steel Trusses, 2nd Edition. AISI, 1984, Designing Fire Protection for Steel Beams. Brockenbrough, R. L. and B. G. Johnston, 1981, USS Steel Design Manual, R. L. Brockenbrough & Assoc. Inc., Pittsburgh, PA. Dill, F. H., 1960, “Structural Steel After a Fire,” Proceedings of the 1960 National Engineering Conference, AISC, New York, NY. Fisher, J. W. and A. W. Pense, 1987, “Experience with Use of Heavy W Shapes in Tension,” Engineering Journal, 2nd Qtr., AISC, Chicago. Lightner, M. W. and R. W. Vanderbeck, 1956, “Factors Involved in Brittle Fracture,” Regional Technical Meetings, AISI, Washington, DC. Rolfe, S. T. and J. M. Barsom, 1986, Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics, Prentice-Hall, Inc., Englewood Cliffs, NJ. Rolfe, S. T., 1977, “Fracture and Fatigue Control in Steel Structures,” Engineering Journal, 1st Qtr., AISC, Chicago. Welding Research Council, 1957, Control of Steel Construction to Avoid Brittle Failure, New York.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2-1

PART 2 ESSENTIALS OF LRFD OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 INTRODUCTION TO LRFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11 C. FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . 2-14 D. TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . . . . . 2-22 F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . . . . 2-27 H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . . . . 2-34 I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42 COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2-2

ESSENTIALS OF LRFD

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

OVERVIEW

2-3

OVERVIEW The following LRFD topics are covered herein (with the letters A through I in the section headings referring to the corresponding chapters in the LRFD Specification): INTRODUCTION TO LRFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 LRFD Versus ASD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 LRFD Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 Loads and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11 Gross, Net, and Effective Net Areas for Tension Members . . . . . . . . . . . . . . . . 2-11 Gross, Net, and Effective Net Areas for Flexural Members . . . . . . . . . . . . . . . . 2-12 Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 Limiting Slenderness Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13 C. FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . 2-14 Second Order Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14 Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17 “Leaning” Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18 D. TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 Design Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 Built-Up Members, Eyebars, and Pin-Connected Members . . . . . . . . . . . . . . . . 2-21 E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . . . . . 2-22 Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Design Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27 Built-Up and Pin-Connected Members . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27 F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . . . . 2-27 Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27 Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29 Design for Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33 Web Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34 H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . . . . 2-34 Symmetric Members Subject to Bending and Axial Tension . . . . . . . . . . . . . . . 2-34 Symmetric Members Subject to Bending and Axial Compression . . . . . . . . . . . . 2-37 Bending and Axial Compression—Preliminary Design . . . . . . . . . . . . . . . . . . 2-37 Torsion and Combined Torsion, Flexure, and/or Axial Force . . . . . . . . . . . . . . . 2-40 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2-4

ESSENTIALS OF LRFD

I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42 Compression Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42 Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43 Combined Compression and Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44 COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44 ELRFD (Electronic LRFD Specification) . . . . . . . . . . . . . . . . . . . . . . . . . 2-44 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

INTRODUCTION TO LRFD

2-5

INTRODUCTION TO LRFD

The intent of this part of the LRFD Manual is to provide a general introduction to the subject. It was written primarily for: (1) engineers experienced in allowable stress design (ASD) who are unfamiliar with LRFD and (2) students and novice engineers. The emphasis is on understanding the most common cases, rather than on completeness and efficiency in design. Regular users of LRFD may also find it helpful to refer to the information provided herein. It should be noted, however, that the governing document is the LRFD Specification (in Part 6 of this volume of the Manual). For optimum design the use of the design aids elsewhere in this Manual is recommended. Among the topics not covered herein are: (1) connections, the subject of Volume II, and (2) noncompact beams and plate girders, for which the reader is referred to Appendices F and G of the LRFD Specification and Part 4 of this volume of the Manual. LRFD Versus ASD

The primary objective of the LRFD Specification is to provide a uniform reliability for steel structures under various loading conditions. This uniformity cannot be obtained with the allowable stress design (ASD) format. The ASD method can be represented by the inequality ΣQi ≤ Rn / F.S.

(2-1)

The left side is the summation of the load effects, Qi (i.e., forces or moments). The right side is the nominal strength or resistance Rn divided by a factor of safety. When divided by the appropriate section property (e.g., area or section modulus), the two sides of the inequality become the calculated stress and allowable stress, respectively. The left side can be expanded as follows: ΣQi = the maximum (absolute value) of the combinations D + L′ (D + L′ + W) × 0.75* (D + L′ + E) × 0.75* D−W D−E where D, L′, W, and E are, respectively, the effects of the dead, live, wind, and earthquake loads; total live load L′ = L + (Lr or S or R) L = Live load due to occupancy Lr = Roof live load S = Snow load R = Nominal load due to initial rainwater or ice exclusive of the ponding contribution *0.75 is the reciprocal of 1.33, which represents the 1/3 increase in allowable stress permitted when wind or earthquake is taken simultaneously with live load. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2-6

ESSENTIALS OF LRFD

ASD, then, is characterized by the use of unfactored service loads in conjunction with a single factor of safety applied to the resistance. Because of the greater variability and, hence, unpredictability of the live load and other loads in comparison with the dead load, a uniform reliability is not possible. LRFD, as its name implies, uses separate factors for each load and for the resistance. Considerable research and experience were needed to establish the appropriate factors. Because the different factors reflect the degree of uncertainty of different loads and combinations of loads and the accuracy of predicted strength, a more uniform reliability is possible. The LRFD method may be summarized by the formula ΣγiQi ≤ φRn

(2-2)

On the left side of the inequality, the required strength is the summation of the various load effects Qi multiplied by their respective load factors γi. The design strength, on the right side, is the nominal strength or resistance Rn multiplied by a resistance factor φ. Values of φ and Rn for columns, beams, etc. are provided throughout the LRFD Specification and will be covered here, as well. According to the LRFD Specification (Section A4.1), ΣγiQi = the maximum absolute value of the following combinations 1.4D 1.2D + 1.6L + 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W) 1.2D + 1.3W + 0.5L + 0.5(Lr or S or R) 1.2D ± 1.0E + 0.5L + 0.2S 0.9D ± (1.3W or 1.0E)

(A4-1) (A4-2) (A4-3) (A4-4) (A4-5) (A4-6)

(Exception: The load factor on L in combinations A4-3, A4-4, A4-5 shall equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf). The load effects D, L, Lr, S, R, W, and E are as defined above. The loads should be taken from the governing building code or from ASCE 7, Minimum Design Loads in Buildings and Other Structures (American Society of Civil Engineers, 1988). Where applicable, L should be determined from the reduced live load specified for the given member in the governing code. Earthquake loads should be from the AISC Seismic Provisions for Structural Steel Buildings, which appears in Part 6 of this Manual. LRFD Fundamentals

The following is a brief discussion of the basic concepts of LRFD. A more complete treatment of the subject is available in the Commentary on the LRFD Specification (Section A4 and A5) and in the references cited therein. LRFD is a method for proportioning structures so that no applicable limit state is exceeded when the structure is subjected to all appropriate factored load combinations. Strength limit states are related to safety and load carrying capacity (e.g., the limit states of plastic moment and buckling). Serviceability limit states (e.g., deflections) relate to performance under normal service conditions. In general, a structural member will have several limit states. For a beam, for example, they are flexural strength, shear strength, vertical deflection, etc. Each limit state has associated with it a value of Rn, which defines the boundary of structural usefulness. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

INTRODUCTION TO LRFD

2-7

Because the AISC Specification is concerned primarily with safety, strength limit states are emphasized. The load combinations for determining the required strength were given in expressions A4-1 through A4-6. (Other load combinations, with different values of γi, are appropriate for serviceability; see Chapter L in the LRFD Specification and Commentary.) The AISC load factors (A4-1 through A4-6) are based on ASCE 7. They were originally developed by the A58 Load Factor Subcommittee of the American National Standards Institute, ANSI, (U.S. Department of Commerce, 1980) and are based strictly on load statistics. Being material-independent, they are applicable to all structural materials. Although others have written design codes similar in format to the LRFD Specification, the AISC was the first specification group to adopt the ANSI probability-based load factors. The AISC load factors recognize that when several loads act in combination, only one assumes its maximum lifetime value at a time, while the others are at their “arbitrarypoint-in-time” (APT) values. Each combination models the total design loading condition when a different load is at its maximum: Load Combination A4-1 A4-2 A4-3 A4-4 A4-5 A4-6

Load at its Lifetime (50-year) Maximum D (during construction; other loads not present) L Lr or S or R (a roof load) W (acting in direction of D) E (acting in direction of D) W or E (opposing D)

The other loads, which are APT loads, have mean values considerably lower than the lifetime maximums. To achieve a uniform reliability, every factored load (lifetime maximum or APT) is larger than its mean value by an amount depending on its variability. The AISC resistance factors are based on research recommendations published by Washington University in St. Louis (Galambos et al., 1978) and reviewed by the AISC Specification Advisory Committee. Test data were analyzed to determine the variability of each resistance. In general, the resistance factors are less than one (φ < 1). For uniform reliability, the greater the scatter in the data for a given resistance, the lower its φ factor. Several representative LRFD φ factors for steel members (referenced to the corresponding chapters in the LRFD Specification) are: φt = 0.90 for tensile yielding (Chapter D) φt = 0.75 for tensile fracture (Chapter D) φc = 0.85 for compression (Chapter E) φb = 0.90 for flexure (Chapter F) φv = 0.90 for shear yielding (Chapter F) Resistance factors for other member and connection limit states are given in the LRFD Specification. The following sections (A through I) summarize and explain the corresponding chapters of the LRFD Specification. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2-8

ESSENTIALS OF LRFD

A. GENERAL PROVISIONS

In the LRFD Specification, Sections A4 and A5 define Load and Resistance Factor Design. The remainder of Chapter A contains general provisions which are essentially the same as in the earlier ASD editions of the Specification. Reference is made to the Code of Standard Practice for Steel Buildings and Bridges (adopted in 1992 by AISC), which appears with a Commentary in Part 6 of this LRFD Manual. The Code defines the practices and commonly accepted standards in the structural steel fabricating industry. In the absence of other instructions in the contract documents, these trade practices govern the fabrication and erection of structural steel. The types of construction recognized by the AISC Specification have not changed, except that both “simple framing” (formerly Type 2) and “semi-rigid framing” (formerly Type 3) have been combined into one category, Type PR (partially restrained). “Rigid framing” (formerly Type 1) is now Type FR (fully restrained). Type FR construction is permitted unconditionally. Type PR is allowed only upon evidence that the connections to be used are capable of furnishing, as a minimum, a predictable portion of full end restraint. Type PR construction may necessitate some inelastic, but self-limiting, deformation of a structural steel part. When specifying Type PR construction, the designer should take into account the effects of reduced connection stiffness on the stability of the structure, lateral deflections, and second order bending moments. Semi-rigid connections, once common, are again becoming popular. They offer economies in connection fabrication (compared with FR connections) and reduced member size (compared with simple framing). For information on connections, please refer to Volume II of this LRFD Manual. The yield stresses of the grades of structural steel approved for use range from 36 ksi for the common A36 steel to 100 ksi for A514 steel. Not all rolled shapes and plate thicknesses are available for every yield stress. Availability tables for structural shapes, plates and bars are at the beginning of Part 1 of this LRFD Manual. A36, for many years the dominant structural steel for buildings, is being replaced by the more economical 50 ksi steels. ASTM designations for structural steels with 50 ksi yield stress are: A572 for most applications, A529 for thin-plate members only, and A242 and A588 weathering steels for atmospheric corrosion resistance. A more complete explanation is provided by Table 1-1 in Part 1 of this Manual. However, A36 is still normally specified for connection material, where no appreciable savings can be realized from higher strength steels. Complete and accurate drawings and specifications are necessary for all stages of steel construction. The requirements for design documents are set forth in Section A7 of the LRFD Specification and Section 3 of the AISC Code of Standard Practice. When beam end reactions are not shown on the drawings, the structural steel detailer will refer to the appropriate tables in Part 4 of the LRFD Manual. These tables, which are for uniform loads, may significantly underestimate the effects of the concentrated loads. The recording of beam end reactions on design drawings, which is recommended in all cases, is, therefore, absolutely essential when there are concentrated loads. Beam reactions, column loads, etc., shown on design drawings should be the required strengths calculated from the factored load combinations and should be so noted. Loads and Load Combinations

LRFD Specification Sections A4 (Loads and Load Combinations) and A5 (Design Basis) describe the basic criteria of LRFD. This information was discussed above under AMERICAN INSTITUTE OF STEEL CONSTRUCTION

A. GENERAL PROVISIONS

2-9

Introduction to LRFD. To illustrate the application of load factors, the AISC load combinations will be repeated here with design examples. The required strength is the maximum absolute value of the combinations 1.4D 1.2D + 1.6L + 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W) 1.2D + 1.3W + 0.5L + 0.5(Lr or S or R) 1.2D ± 1.0E + 0.5L + 0.2S 0.9D ± (1.3W or 1.0E)

(A4-1) (A4-2) (A4-3) (A4-4) (A4-5) (A4-6)

(The load factor on L in combinations A4-3, A4-4 and A4-5 shall equal 1.0 for garages, areas occupied as placed of public assembly, and all areas where the live load is greater than 100 psf). In the combinations the loads or load effects (i.e., forces or moments) are: D = dead load due to the weight of the structural elements and the permanent features on the structure L = live load due to occupancy and moveable equipment (reduced as permitted by the governing code) Lr = roof live load W= wind load S = snow load E = earthquake load R = nominal load due to initial rainwater or ice exclusive of the ponding contribution The loads are to be taken from the governing building code. In the absence of a code, one may use ASCE 7 Minimum Design Loads for Buildings and Other Structures (American Society of Civil Engineers, 1988). Earthquake loads should be determined from the AISC Seismic Provisions for Structural Steel Buildings, in Part 6 of this Manual. Whether the loads themselves or the load effects are combined, the results are the same, provided the principle of superposition is valid. This is usually true because deflections are small and the stress-strain behavior is linear elastic; consequently, second order effects can usually be neglected. (The analysis of second order effects is covered in Chapter C of the LRFD Specification.) The linear elastic assumption, although not correct at the strength limit states, is valid under normal in-service loads and is permissible as a design assumption under the LRFD Specification. In fact, the Specification (in Section A.5.1) allows the designer the option of elastic or plastic analysis using the factored loads. However, to simplify this presentation, it is assumed that the more prevalent elastic analysis option has been selected.

EXAMPLE A-1

Given:

Solution:

Roof beams W16×31, spaced 7′′-0 center-to-center, support a superimposed dead load of 40 psf. Code specified roof loads are 30 psf downward (due to roof live load, snow, or rain) and 20 psf upward or downward (due to wind). Determine the critical loading for LRFD. D

= 31 plf + 40 psf × 7.0 ft = 311 plf AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

L =0 (Lr or S or R) = 30 psf × 7.0 ft = 210 plf W = 20 psf × 7.0 ft = 140 plf E =0 Load Combinations A4-1 A4-2 A4-3 A4-4 A4-5 A4-6a A4-6b

Factored Loads 1.4(311 plf) 1.2(311 plf) + 0 + 0.5(210 plf) 1.2(311 plf) + 1.6 (210 plf) + 0.8(140 plf) 1.2(311 plf) + 1.3(140 plf) + 0 + 0.5(210 plf) 1.2(311 plf) + 0 + 0 + 0.2(210 plf) 0.9 (311 plf) + 1.3 (140 plf) 0.9(311 plf) − 1.3(140 plf)

= 435 plf = 478 plf = 821 plf = 660 plf = 415 plf = 462 plf = 98 plf

The critical factored load combination for design is the third, with a total factored load of 821 plf.

EXAMPLE A-2

Given:

Solution:

The axial loads on a building column resulting from the code-specified service loads have been calculated as: 100 kips from dead load, 150 kips from (reduced) floor live load, 30 kips from the roof (Lr or S or R), 60 kips due to wind, and 50 kips due to earthquake. Determine the required strength of this column. Load Combination A4-1 A4-2 A4-3a A4-3b A4-4 A4-5a A4-5b A4-6a A4-6b A4-6c A4-6d

Factored Axial Load 1.4(100 kips) 1.2(100 kips) + 1.6(150 kips) + 0.5(30 kips) 1.2(100 kips) + 1.6(30 kips) + 0.5(150 kips) 1.2(100 kips) + 1.6(30 kips) + 0.8(60 kips) 1.2(100 kips) + 1.3(60 kips) + 0.5(150 kips) + 0.5(30 kips) 1.2(100 kips) + 1.0(50 kips) + 0.5(150 kips) + 0.2(30 kips) 1.2(100 kips) − 1.0(50 kips) + 0.5(150 kips) + 0.2(30 kips) 0.9(100 kips) + 1.3(60 kips) 0.9(100 kips) − 1.3(60 kips) 0.9(100 kips) + 1.0(50 kips) 0.9(100 kips) − 1.0(50 kips)

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

= 140 kips = 375 kips = 243 kips = 216 kips = 288 kips = 251 kips = 151 kips = 168 kips = 12 kips = 140 kips = 40 kips

B. DESIGN REQUIREMENTS

2 - 11

The required strength of the column is 375 kips based on the second combination of factored axial loads. As none of the results above are negative, net tension need not be considered in the design of this column. B. DESIGN REQUIREMENTS Gross, Net, and Effective Net Areas for Tension Members

The concept of effective net area, which in earlier editions of the Specification was applied only to bolted members, has been extended to cover members connected by welding as well. As in the past, when tensile forces are transmitted directly to all elements of the member, the net area is used to determine stresses. However, when the tensile forces are transmitted through some, but not all, of the cross-sectional elements of the member, a reduced effective net area Ae is used instead. According to Section B3 of the LRFD Specification Ae = AU

(B3-1)

where A = area as defined below U = reduction coefficient _ = 1 − (x / L) ≤ 0.9, or as defined in (c) or (d) (B3-2) _ x = connection eccentricity. (See Commentary on the LRFD Specification, Section B3 and Figure C-B3.1.) L = length of connection in the direction of loading a. When the forces are transmitted only by bolts A = An = net area of member, in.2 b. When the forces are transmitted by longitudinal welds only or in combination with transverse welds A = Ag = gross area of member, in.2 c. When the forces are transmitted only by transverse welds A = area of directly connected elements, in.2 U = 1.0 d. When the forces are transmitted to a plate by longitudinal welds along both edges at the end of the plate A = area of plate, in.2 l ≥w For l ≥ 2w For 2w > l ≥ 1.5w For 1.5w > l ≥ w

U = 1.00 U = 0.87 U = 0.75 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

where l = weld length w = plate width (distance between welds), in. In computing the net area for tension and shear, the width of a bolt hole is taken as 1⁄16-in. greater than the nominal dimension of the hole, which, for standard holes, is 1⁄16-in. larger than the diameter of the bolt. Chains of holes, treated as in the past, are covered in Section B2 of the LRFD Specification. Gross, Net, and Effective Net Areas for Flexural Members

Gross areas are used for elements in compression, in beams and columns. According to Section B10 of the LRFD Specification, the properties of beams and other flexural members are based on the gross section (with no deduction for holes in the tension flange) if 0.75Fu Afn ≥ 0.9Fy Afg

(B10-1)

where Afg = gross flange area, in.2 Afn = net flange area (deducting bolt holes), in.2 Fy = specified minimum yield stress, ksi Fu = minimum tensile strength, ksi Otherwise, an effective tension flange area Afe is used to calculate flexural properties Afe =

5 Fu A 6 Fy fn

(B10-3)

Local Buckling

Steel sections are classified as either compact, noncompact, or slender element sections: • If the flanges are continuously connected to the web and the width-thickness ratios of all the compression elements do not exceed λp, then the section is compact. • If the width-thickness ratio of at least one of its compression elements exceeds λp, but does not exceed λr, the section is noncompact. • If the width-thickness ratio of any compression element exceeds λr, that element is called a slender compression element. Columns with compact and noncompact cross sections are covered by Chapter E of the LRFD Specification. Column cross sections with slender elements require the special design procedure in Appendix B5.3 of the Specification. Beams with compact sections are covered by Chapter F of the LRFD Specification. All other cross sections in bending must be designed in accordance with Appendices B5.3, F1 and/or G. In general, reference to the appendices of the Specification is required for the design of members controlled by local buckling. In slender element sections, local buckling, occurring prior to initial yielding, will limit the strength of the member. Noncompact sections will yield first, but local buckling will precede the development of a fully plastic stress distribution. In actual practice, such cases are not common and can be easily avoided by designing so that: AMERICAN INSTITUTE OF STEEL CONSTRUCTION

B. DESIGN REQUIREMENTS

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Table B-1. Limiting Width-Thickness Ratios for Compression Elements* WidthThickness Ratio

Beam Element

Limiting Width-Thickness Ratio, λp General

For Fy = 50 ksi

Flanges of I shapes and channels

b/t

65 / √ F y

9.2

Flanges of square and rectangular box beams

b/t

190 / √ Fy

26.9

Webs in flexural compression

h / tw

640 / √ Fy

90.5

Webs in combined flexural and axial compression

h / tw

253 / √ Fy **

35.8

Column Element

WidthThickness Ratio

Limiting Width-Thickness Ratio, λr General

For Fy = 50 ksi

Flanges of I shapes and channels and plates projecting from compression elements

b/t

95 / √ F y

13.4

Webs in axial compression

h / tw

253 / √ Fy

35.8

*For the complete table, see LRFD Specification, Section B5, Table B5.1. **This is a simplified, conservative version of the corresponding entry in Table B5.1 of the LRFD Specification.

• for beams, the width-thickness ratios of all compression elements ≤ λp; • for columns, the width-thickness ratios of all elements ≤ λr. Table B-1, which is an abridged version of Table B5.1 in the LRFD Specification, should be useful for this purpose. The formulas for λp for beam elements and λr for column elements are tabulated, together with the corresponding numerical values for 50 ksi steel. The definitions of “width” for use in determining the width-thickness ratios of the elements of various structural shapes are stated in Section B5 of the LRFD Specification. They are shown graphically in Figure B-1. Compact section criteria for W shapes and other I-shaped cross sections are listed in the Properties Tables in Part 1 of LRFD Manual. Limiting Slenderness Ratios

For members whose design is based on compressive force, the slenderness ratio Kl / r preferably should not exceed 200. For members whose design is based on tensile force, the slenderness ratio l / r preferably should not exceed 300. The above limitation does not apply to rods in tension. K = effective length factor, defined in Section C below l = distance between points of lateral support (lx or ly), in. r = radius of gyration (rx or ry), in. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

C. FRAMES AND OTHER STRUCTURES Second Order Effects

As stated in Section C1 of the LRFD Specification, an analysis of second order effects is required; i.e., the additional moments due to the axial loads acting on the deformed structure must be considered. In lieu of a second order analysis for Mu, the required flexural strength, the LRFD Specification (in Section C1) presents the following simplified method: Mu = B1Mnt + B2Mlt

(C1-1)

The components of the total factored moment, determined from a first order elastic analysis (neglecting second order effects) are divided into two groups, Mnt and Mlt. Each group is in turn multiplied by a magnification factor B1 or B2 and the results are added to approximate the actual second order factored moment Mu. (The method, as explained here, is valid where the moment connections are Type FR, fully restrained. The analysis for Type PR, or partially restrained, moment connections is beyond the scope of this section.) Beam-columns are generally columns in frames, which are either braced (Mlt = 0) or unbraced (Mlt ≠ 0). Mnt is the moment in the member assuming there is no lateral translation of the frame; Mlt is the moment due to lateral translation. Mnt includes the moments resulting from the gravity loads, as determined manually or by computer, using one of the customary (elastic, first order) methods. The moments from the lateral loads are classified as Mlt; i.e., due to lateral translation. If both the frame and its vertical loads are symmetric, Mlt from the vertical loads is zero. However, if either the vertical loads or the frame is asymmetric and the frame is not braced, lateral translation occurs and Mlt ≠ 0. The procedure for obtaining Mlt in this case involves:

b = bf

b = b f – 3t h = h w – 3t

Fig. B-1. Definitions of widths (b and h) for use in Table B-1. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

C. FRAMES AND OTHER STRUCTURES

2 - 15

a. applying fictitious horizontal reactions at each floor level to prevent lateral translation, and b. using the reverse of these reactions as the “sway forces” for determining Mlt. In general, Mlt for an unbraced frame is the sum of the moments due to the lateral loads and these “sway forces,” as illustrated in Figure C-1. The magnification factors applied to Mnt and Mlt are, respectively, B1 and B2. As shown in Figure C-2, B1 accounts for the secondary Pδ member effect in all frames (including sway-inhibited) and B2 covers the P∆ story effect in unbraced frames. The expressions for B1 and B2 follow: B1 =

Cm ≥ 1.0 (1 − Pu / Pe1 )

(C1-2)

where Pu = the factored axial compressive force on the member, kips Pe1 = Pe as listed in Table C-1 as a function of the slenderness ratio Kl / r, with effective length factor K = 1.0 and considering l / r in the plane of bending only l = unbraced length of the member, in. r = radius of gyration of its cross section, in. Cm = a coefficient to be taken as follows: V1 V2

V1 +R1

P2 R 2

V2 +R2

Original Frame

Nonsway Frame for M nt

V3 +R3

Sway Frame for M t

Fig. C-1. Frame models for Mnt and Mlt.

∆P

M1=Mnt+Pδ =B1Mnt

(a) Column in Braced Frame

M t =HL M2=M t +P∆ =B2M t

(b) Column in Unbraced Frame

Fig. C-2. Illustrations of secondary effects. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

Table C-1. Values of Pe / Ag for Use in Equation C1-2 and C1-5 for Steel of Any Yield Stress Note: Multiply tabulated values by Ag (the gross cross-sectional area of the member) to obtain Pe

Kl / r 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Pe / Ag Pe / Ag Pe / Ag Pe / Ag Pe / Ag Pe / Ag (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) 649.02 591.36 541.06 496.91 457.95 423.40 392.62 365.07 340.33 318.02 297.83 279.51 262.83 247.59 233.65 220.85 209.07 198.21 188.18 178.89 170.27 162.26 154.80 147.84 141.34 135.26 129.57 124.23 119.21 114.49

Note: Pe / Ag =

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

110.04 105.85 101.89 98.15 94.62 91.27 88.08 85.08 82.22 79.51 76.92 74.46 72.11 69.88 67.74 65.71 63.76 61.90 60.12 58.41 56.78 55.21 53.71 52.57 50.88 49.55 48.27 47.04 45.86 44.72

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

43.62 42.57 41.55 40.56 39.62 38.70 37.81 36.96 36.13 35.34 34.56 33.82 33.09 32.39 31.71 31.06 30.42 29.80 29.20 28.62 28.06 27.51 26.98 26.46 25.96 25.47 25.00 24.54 24.09 23.65

111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140

23.23 22.82 22.42 22.02 21.64 21.27 20.91 20.56 20.21 19.88 19.55 19.23 18.92 18.61 18.32 18.03 17.75 17.47 17.20 16.94 16.68 16.43 16.18 15.94 15.70 15.47 15.25 15.03 14.81 14.60

141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170

14.40 14.19 14.00 13.80 13.61 13.43 13.25 13.07 12.89 12.72 12.55 12.39 12.23 12.07 11.91 11.76 11.61 11.47 11.32 11.18 11.04 10.91 10.77 10.64 10.51 10.39 10.26 10.14 10.02 9.90

171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

9.79 9.67 9.56 9.45 9.35 9.24 9.14 9.03 8.93 8.83 8.74 8.64 8.55 8.45 8.36 8.27 8.18 8.10 8.01 7.93 7.85 7.76 7.68 7.60 7.53 7.45 7.38 7.30 7.23 7.16

Ď&#x20AC;2E (K l /r)2

a. For compression members not subject to transverse loading between their supports in the plane of bending, Cm = 0.6 â&#x2C6;&#x2019; 0.4(M1 / M2)

(C1-3)

where M1 / M2 is the ratio of the smaller to larger moment at the ends of that portion of the member unbraced in the plane of bending under consideration. M1 / M2 is positive when the member is bending in reverse curvature, negative when bending in single curvature. b. For compression members subjected to transverse loading between their supports, the value of Cm can be determined by rational analysis, or the following values may be used: AMERICAN INSTITUTE OF STEEL CONSTRUCTION

C. FRAMES AND OTHER STRUCTURES

2 - 17

for members with ends restrained against rotation . . . . . . . . . . Cm = 0.85 for members with ends unrestrained against rotation . . . . . . . . . Cm = 1.0 Two alternative equations are given for B2 in the LRFD Specification B2 =

1 ΣPu  ∆oh  1−   ΣH  L 

B2 =

1 ΣPu 1− ΣPe2

(C1-4)

(C1-5)

where ΣPu = required axial strength of all columns in a story, i.e., the total factored gravity load above that level, kips ∆oh = translational deflection of the story under consideration, in. ΣH = sum of all story horizontal forces producing ∆oh, kips L = story height, in. ΣPe2 = the summation of Pe2 for all rigid-frame columns in a story; Pe2 is determined from Table C-1, considering the actual slenderness ratio Kl / r of each column in its plane of bending K = effective length factor (see below) Of the two expressions for B2, the first (Equation C1-4) is better suited for design office practice. The quantity (∆oh / L) is the story drift index. For many structures, particularly tall buildings, a maximum drift index is one of the design criteria. Using this value in Equation C1-4 will facilitate the evaluation of B2. In general, two values of B2 are obtained for each story of a building, one for each of the major directions. B1 is evaluated separately for every column; two values of B1 are needed for biaxial bending. Using Equations C1-1 through C1-5, the appropriate Mux and Muy are determined for each column. Effective Length

As in previous editions of the AISC Specification, the effective length of Kl is used (instead of the actual unbraced length l) to account for the influence of end-conditions in the design of compression members. A number of acceptable methods have been utilized to evaluate K, the effective length factor. They are discussed in Section C2 of the Commentary on the LRFD Specification. One method will be shown here. Table C-2, which is also Table C-C2.1 in the Commentary, is taken from the Structural Stability Research Council (SSRC) Guide to Stability Design Criteria for Metal Structures. It relates K to the rotational and translational restraints at the ends of the column. Theoretical values for K are given, as well as the recommendations of the SSRC. The basic case is d, the classical pin-ended column, for which K = 1.0. Theoretical K values for the other cases are determined by the distances between points of inflection. The more conservative SSRC recommendations reflect the fact that perfect fixity can never be attained in actual structures. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

Table C-2. Effective Length Factors (K) for Columns Buckled shape of column is shown by dashed line

(a)

(b)

(c)

Theoretical K value

0.5

0.7

1.0

Recommended design value when ideal conditions are approximated

0.65

0.80

1.2

End condition code

(d)

(e)

(f)

1.0

2.0

1.0

2.10

2.0

Rotation fixed and translation fixed Rotation free and translation fixed Rotation fixed and translation free Rotation free and translation free

Like its predecessors, the LRFD Specification (in Section C2) distinguishes between columns in braced and unbraced frames. In braced frames, sidesway is inhibited by attachment to diagonal bracing or shear walls. Cases a, b, and d in Table C-2 represent columns in braced frames; K ≤ 1.0. The LRFD Specification requires that for compression members in braced frames, K “shall be taken as unity, unless structural analysis shows that a smaller value may be used.” Common practice is to assume conservatively K = 1.0 for columns in braced frames and compression members in trusses. The other cases in Table C-2, c, e, and f, are in unbraced frames (sidesway uninhibited); K ≥ 1.0. The SSRC recommendations given in Table C-2 are appropriate for design. “Leaning” Columns

The concept of the “leaning” column, although not related exclusively to LRFD, is new to the 1993 LRFD Specification. A leaning column is one which is pin ended and does not participate in providing lateral stability to the structure. As a result it relies on the columns in other parts of the structure for stability. In analyzing and designing unbraced frames, the effects of the leaning columns must be considered (as required by Section C2.2 of the LRFD Specification). For further information the reader is referred to: (1) Part 3 of this Manual. (2) the Commentary on the LRFD Specification, Section C2, and (3) a paper on this subject (Geschwindner, 1993). AMERICAN INSTITUTE OF STEEL CONSTRUCTION

D. TENSION MEMBERS

2 - 19

D. TENSION MEMBERS Design Tensile Strength

The design philosophy for tension members is the same in the LRFD and ASD Specifications: a. The limit state of yielding in the gross section is intended to prevent excessive elongation of the member. Usually, the portion of the total member length occupied by fastener holes is small. The effect of early yielding at the reduced cross sections on the total member elongation is negligible. Use of the area of the gross section is appropriate. b. The second limit state involves fracture at the section with the minimum effective net area. The design strength of tension members, φtPn, as given in Section D1 of the LRFD Specification, is the lesser of the following: a. For yielding in the gross section, φt = 0.90 Pn = Fy Ag

(D1-1)

b. For fracture in the net section, φt = 0.75 Pn = Fu Ae

(D1-2)

where Ae Ag Fy Fu Pn

= effective net area, in.2 (see Section B, above) = gross area of member, in.2 = specified minimum yield stress, ksi = specified minimum tensile strength, ksi = nominal axial strength, kips

For 50 ksi steels, Fy = 50 ksi and minimum Fu = 65 ksi. Accordingly a. For yielding in the gross section, φtPn = 0.9 × 50 ksi × Ag = 45.0 ksi × Ag

(2-3)

b. For fracture in the net section, φtPn = 0.75 × 65 ksi × Ae = 48.8 ksi × Ae

(2-4)

The limit state of block shear rupture may govern the design tensile strength. For information on block shear, see Section J4.3 of the LRFD Specification and Part 8 (in Volume II) of this LRFD Manual. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

EXAMPLE D-1

Given:

Determine the design strength of a W8×24 as a tension member in 50 ksi steel. How much dead load can it support?

Solution:

If there are no holes in the member, Ae = Ag and Equation 2-3 governs φtPn = 45.0 ksi × Ag = 45.0 ksi × 7.08 in.2 = 319 kips Assuming that dead load is the only load, the governing load combination from Section A is 1.4D. Then, the required tensile strength Pu = 1.4PD ≤φtPn = 319 kips PD≤ 319 kips/1.4 = 228 kips maximum dead load that can be supported by the member.

EXAMPLE D-2

Given:

Repeat Example D-1 for a W8×24 in 50 ksi steel with four 1-in. diameter holes, two per flange, along the member (i.e., not at its ends) for miscellaneous attachments. See Figure D-1(a).

Solution:

a. For yielding in the gross section φtPn = 319 kips, as in Example D-1. b. For fracture in the net section Ae = An = Ag − 4 × (dhole + 1⁄16-in.) × tf = 7.08 in.2 − 4 × (1 + 1⁄16-in.) × 0.400 in. = 5.38 in.2 φtPn = 48.8 ksi × Ae = 48.8 ksi × 5.38 in.2 = 263 kips < 319 kips Fracture in the net section governs. Pu = 1.4 PD ≤ φtPn = 263 kips PD ≤ 263 kips / 1.4 = 188 kips

W8x24

x=y=0.695 in.

WT4x12 WT4x12

(a)

(b)

Fig. D-1 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

D. TENSION MEMBERS

2 - 21

Note: If the holes had been at the end connection of the tension member, the U reduction coefficient would apply in the calculation of an effective net area.

EXAMPLE D-3

Given:

Repeat Example D-2 for holes at a bolted end-connection. There are a total of eight 1-in. diameter holes, as shown in Figure D-1(a), on two planes, 4 in. center-to-center.

Solution:

a. For yielding in the gross section φtPn = 319 kips, as in Example D-1. b. For fracture in the net section, according to Equation B3-1 in Section B above, the effective net area Ae = AU = AnU where An = 5.38 in.2 as in Example D-2 _ x U = 1 − , L = 4 in.* L

_ According to Commentary Figure C-B3.1(a), x for a W8×24 in this case is taken as that for a WT4×12. _ From the properties of a WT4×12 given in Part 1 of this Manual, x = y = 0.695 in. See Figure D-1(b). U=1−

0.695 in. = 0.826 4 in.

Thus Ae = 5.38 in.2 × 0.826 = 4.45 in.2 φtPn = 48.8 ksi × Ae = 48.8 ksi × 4.45 in.2 = 217 kips < 319 kips Fracture in the net section governs. Again, assuming that dead load is the only load, Pu = 1.4PD ≤ φtPn = 217 kips PD ≤ 217 kips / 1.4 = 155 kips maximum dead load that can be supported by the member. Built-Up Members, Eyebars, and Pin-Connected Members

See Section D2 and D3 in the LRFD Specification. *In lieu of calculating U, the Commentary on the LRFD Specification (Section B3) permits the use of more conservative values of U listed therein. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

E. COLUMNS AND OTHER COMPRESSION MEMBERS Effective Length

For a discussion of the effective length Kl for columns, refer to Section C above. Design Compressive Strength

Although the column strength equations have been revised for compatibility with LRFD and recent research on column behavior, the philosophy and procedures of column design in LRFD are similar with those in ASD. The direct design of columns with W and other rolled shapes is facilitated by the column strength tables in Part 3 of this LRFD Manual, which show the design compressive strength φcPn as a function of KL (the effective unbraced length in feet). Columns with cross sections not tabulated (e.g., built-up columns) can be designed iteratively, as in the past, with the aid of tables listing design stresses versus Kl / r, the slenderness ratio. Such tables are given in the Appendix of the LRFD Specification for 36 and 50 ksi structural steels, and below (Table E-1) for 50 ksi steel. There are two equations governing column strength, based on the limit state of flexural buckling, one for inelastic buckling (Equation E2-2) and the other (Equation E2-3) for elastic, or Euler, buckling. Equation E2-2 is an empirical relationship for the inelastic range, while Equation E2-3 is the familiar Euler formula multiplied by 0.877. Both equations include the effects of residual stresses and initial out-of-straightness. The boundary between inelastic and elastic instability is λc = 1.5, where the parameter λc =

Kl rπ

 √

Fy E

(E2-4)

For axially loaded columns with all elements having width-thickness ratios < λr (in Section B5.1 of the LRFD Specification), the design compressive strength = φcPn where φc = 0.85 Pn = AgFcr

(E2-1)

Ag = gross area of member, in.2 a. For λc ≤ 1.5 2

Fcr = (0.658λc)Fy

(E2-2)

As is done in the Commentary on Section E2, this equation can be expressed in exponential form Fcr = [exp (−0.419λ2c )]Fy where exp(x) = ex AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(C-E2-1)

E. COLUMNS AND OTHER COMPRESSION MEMBERS

2 - 23

Table E-1. Design Stress for Compression Members of 50 ksi Specified Minimum Yield Stress Steel, φc = 0.85* Kl r

F cr (ksi)

Kl r

F cr (ksi)

1 2 3 4 5

42.50 42.49 42.47 42.45 42.42

41 42 43 44 45

37.59 37.36 37.13 36.89 36.65

6 7 8 9 10

42.39 42.35 42.30 42.25 42.19

46 47 48 49 50

11 12 13 14 15

42.13 42.05 41.98 41.90 41.81

16 17 18 19 20

Kl r

F cr (ksi)

Kl r

F cr (ksi)

Kl r

F cr (ksi)

81 82 83 84 85

26.31 26.00 25.68 25.37 25.06

121 122 123 124 125

14.57 14.33 14.10 13.88 13.66

161 162 163 164 165

8.23 8.13 8.03 7.93 7.84

36.41 36.16 35.91 35.66 35.40

86 87 88 89 90

24.75 24.44 24.13 23.82 23.51

126 127 128 129 130

13.44 13.23 13.02 12.82 12.62

166 167 168 169 170

7.74 7.65 7.56 7.47 7.38

51 52 53 54 55

35.14 34.88 34.61 34.34 34.07

91 92 93 94 95

23.20 22.89 22.58 22.28 21.97

131 132 133 134 135

12.43 12.25 12.06 11.88 11.71

171 172 173 174 175

7.30 7.21 7.13 7.05 6.97

41.71 41.61 41.51 41.39 41.28

56 57 58 59 60

33.79 33.51 33.23 32.95 32.67

96 97 98 99 100

21.67 21.36 21.06 20.76 20.46

136 137 138 139 140

11.54 11.37 11.20 11.04 10.89

176 177 178 179 180

6.89 6.81 6.73 6.66 6.59

21 22 23 24 25

41.15 41.02 40.89 40.75 40.60

61 62 63 64 65

32.38 32.09 31.80 31.50 31.21

101 102 103 104 105

20.16 19.86 19.57 19.28 18.98

141 142 143 144 145

10.73 10.58 10.43 10.29 10.15

181 182 183 184 185

6.51 6.44 6.37 6.30 6.23

26 27 28 29 30

40.45 40.29 40.13 39.97 39.79

66 67 68 69 70

30.91 30.61 30.31 30.01 29.70

106 107 108 109 110

18.69 18.40 18.12 17.83 17.55

146 147 148 149 150

10.01 9.87 9.74 9.61 9.48

186 187 188 189 190

6.17 6.10 6.04 5.97 5.91

31 32 33 34 35

39.62 39.43 39.25 39.06 38.86

71 72 73 74 75

29.40 20.09 28.79 28.48 28.17

111 112 113 114 115

17.27 16.99 16.71 16.42 16.13

151 152 153 154 155

9.36 9.23 9.11 9.00 8.88

191 192 193 194 195

5.85 5.79 5.73 5.67 5.61

36 37 38 39 40

38.66 38.45 38.24 38.03 37.81

76 77 78 79 80

27.86 27.55 27.24 26.93 26.62

116 117 118 119 120

15.86 15.59 15.32 15.07 14.82

156 157 158 159 160

8.77 8.66 8.55 8.44 8.33

196 197 198 199 200

5.55 5.50 5.44 5.39 5.33

* When element width-to-thickness ratio exceeds λr, see Appendix B5.3 of LRFD Specification

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2 - 24

ESSENTIALS OF LRFD

b. For λc > 1.5 0.877 Fcr =  2  Fy  λc 

(E2-3)

where Fy = specified minimum yield stress, ksi E = modulus of elasticity, ksi K = effective length factor l = unbraced length of member, in. r = governing radius of gyration about plane of buckling, in. For 50 ksi steel λc =

Kl 1 r π

 √

Kl Kl 50 ksi = 0.0132 or = 75.7λc r r 29,000 ksi

(2-5)

The boundary between inelastic and elastic buckling (λc = 1.5) for 50 ksi steel is Kl = 75.7 × 1.5 = 113.5 r The column strength equations in terms of Kl / r for 50 ksi steel become φcPn = (φcFcr )Ag

(2-6)

Fcr = {exp[−7.3 × 10−5(Kl / r)2]} × 50 ksi

(2-7)

where φc = 0.85 a. For Kl / r ≤ 113.5

b. For Kl / r ≤ 113.5 Fcr =

2.51 × 105 ksi (Kl / r)2

(2-8)

Based on Equations 2-7 and 2-8, Table E-1 gives the design stresses for 50 ksi steel columns for the full range of slenderness ratios. Determining the design strength of a given 50 ksi steel column merely involves using Equation 2-6 in connection with Table E-1. The appropriate design stress (φcFcr) from Table E-1 is multiplied by the cross-sectional area to obtain the design strength φcPn.

EXAMPLE E-1

Given:

Design a 25-ft high, free standing A618 (Fy = 50 ksi) steel pipe column to support a water tank with a weight of 75 kips at full capacity. See Figure E-1.

Solution:

For a live load of 75 kips, the required column strength (from Section A) is Pu = 1.6PL = 1.6 × 75 kips = 120 kips. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

E. COLUMNS AND OTHER COMPRESSION MEMBERS

2 - 25

From Table C-2, case e, recommended K = 2.1. KL = 2.1 × 25.0 ft = 52.5 ft. Try a standard 12-in. diameter pipe (A = 14.6 in.2, I = 279 in.4): r =√  I/A =√  279 in. / 14.6 in.2 = 4.37 in. Kl 52.5 ft × 12 in./ft = = 144.2 4.37 in r From Table E-1, φcFcr = 10.3 ksi The design compressive strength φcPn = (φcFcr )Ag = 10.3 ksi × 14.6 in.2 = 150 kips > 120 kips required o.k. To complete the design, bending due to lateral loads (i.e., wind and earthquake) should also be considered. See Sections F and H. EXAMPLE E-2

Determine the adequacy of a W14×120 building column.

Given:

50 ksi steel; K = 1.0; story height = 12.0 ft; required strength based on the maximum total factored load is 1,300 kips. KxLx = Ky Ly = 1.0 × 12.0 ft = 12.0 ft Because ry < rx,  Kl  Ky Ly 12.0 ft × 12 in./ft = = 38.5   maximum = ry 3.74 in. r From Table E-1, φcFcr = 38.14 ksi Design compressive strength φcPn = (φcFcr)Ag = 38.14 ksi × 35.3 in.2 = 1,346 kips > 1,300 kips required o.k.

L = 25.0 ft.

Solution:

Fig. E-1 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2 - 26

Select the most economical W14 column for the case shown in Figures E-2 and E-3.

Lower Level

Intermediate Level

Upper Level

Fig. E-2. Plan views.

12 -0

Upper Level

Intermediate Level

12 -0

EXAMPLE E-3

ESSENTIALS OF LRFD

Lower Level

Fig. E-3. Elevation. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

F. BEAMS AND OTHER FLEXURAL MEMBERS

2 - 27

Given:

50 ksi steel; K = 1.0; required strength based on the maximum total factored load is 1,300 kips. The column is braced in both directions at the upper and lower levels, and in the weak direction at the intermediate level.

Solution:

Try a W14×120 (as in Example E-2): Kx lx rx

1.0 × 24.0 ft × 12 in./ft = 46.2 6.24 in.

Ky ly ry

1.0 × 12.0 ft × 12 in./ft = 38.5 3.74 in.

Kx lx Kl max = = 46.2 rx r From Table E-1, φcFcr = 36.35 ksi Required Ag =

1,300 kips = 35.8 in.2 > 35.3 in.2 provided 36.35 ksi

W14×120 n.g. By inspection W14×132 is o.k. Use W14×132 Flexural-Torsional Buckling

As stated in Section E3 of the LRFD Specification and Commentary, torsional and flexural-torsional buckling generally do not govern the design of doubly symmetric rolled shapes in compression. For other cross sections, see Section E3 and Appendix E3 of the LRFD Specification. Built-Up and Pin-Connected Members

These members are covered, respectively, in Section E4 and E5 of the LRFD Specification. F. BEAMS AND OTHER FLEXURAL MEMBERS

Chapter F of the LRFD Specification covers compact beams. Compactness criteria are given in Table B5.1 of the LRFD Specification and are summarized in Table B-1 above. To prevent torsion, wide-flange shapes must be loaded in either plane of symmetry, channels must be loaded through the shear center parallel to the web, or restraint against twisting must be provided at load points and points of support. Torsion combined with flexure and axial force combined with flexure are covered in Chapter H of the LRFD Specification. This section explains the provisions of the LRFD Specification for compact rolled beams. For other compact and noncompact flexural members, refer to Appendix F of the Specification; plate girders are in Appendix G. Flexure

To understand the provisions of the LRFD Specification regarding flexural design, it is helpful to review briefly some aspects of elementary beam theory. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2 - 28

ESSENTIALS OF LRFD

Under working loads (and until initial yielding) the distributions of flexural strains and stresses over the cross-section of a beam are linear. As shown in Figure F-1, they vary from maximum compression at the extreme fibers on one side (the top) to zero at the neutral, or centroidal, axis to maximum tension at the extreme fibers on the other side (the bottom). The relationship between moment and maximum bending stress (tension or compression) at a given cross section is M = Sfb

(2-9)

where M= bending moment due to the applied loads, kip-in. S = elastic section modulus, in the direction of bending, in.3 I = c fb = maximum bending stress, ksi I = moment of inertia of the cross section about its centroidal axis, in.4 c = distance from the elastic neutral axis to the extreme fiber, in. Similarly, at initial yielding Mr = SFy

(2-10)

where Mr = bending moment coinciding with first yielding, kip-in. If additional load is applied, the strains continue to increase; the stresses, however, are, limited to Fy. Yielding proceeds from the outer fibers inward until a plastic hinge is developed, as shown in Figure F-1. At full plastification of the cross section Mp = ZFy

(2-11)

where Mp = plastic moment, kip-in Z = plastic section modulus, in the direction of bending, in.3 Due to the presence of residual stresses (prior to loading, as a consequence of the rolling operation), yielding begins at an applied stress of (Fy â&#x2C6;&#x2019; Fr). Equation 2-10 should be modified to

STRAINS

BEAM

Cross Section

Compression

STRESSES Fy

Working Load

Fy Initial Yielding

Tension

Fig. F-1. Flexural strains and stresses. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Fy Plastic Hinge

F. BEAMS AND OTHER FLEXURAL MEMBERS

Mr = S(Fy − Fr )

2 - 29

(2-12)

where Fr = the maximum compressive residual stress in either flange, ksi = 10 ksi for rolled shapes, 16.5 ksi for welded shapes The definition of plastic moment in Equation 2-11 is still valid, because it is not affected by residual stresses. Design for Flexure

a. Assuming Cb = 1.0 Compact sections will not experience local buckling before the formation of a plastic hinge. The occurrence of lateral-torsional buckling of the member depends on the unbraced length Lb. As implied by the term lateral-torsional buckling, overall instability of a beam requires that twisting of the member occur simultaneously with lateral buckling of the compression flange. Lb is the distance between points braced to prevent twist of the cross section. Many beams can be considered continuously braced; e.g., beams supporting a metal deck, if the deck is intermittently welded to the compression flange. Compact wide flange and channel members bending about their major (or x) axes can develop their full plastic moment Mp without buckling if Lb ≤ Lp. If Lb = Lr, the nominal flexural strength is Mr, the moment at first yielding adjusted for residual stresses. The nominal moment capacity (Mn) for Lp < Lb < Lr is Mr < Mn < Mp. Compact shapes bent about their minor (or y) axes will not buckle before developing Mp, regardless of Lb. Flexural design strength, governed by the limit state of lateral-torsional buckling, is φbMn, where φb = 0.90 and Mn the nominal flexural strength is as follows: Mn = Mp = ZxFy for bending about the major axis if Lb ≤ Lp Mn = Mp = ZyFy for bending about the minor axis regardless of Lb Lp =

300ry = 42.4ry for 50 ksi steel Fy √

Mn = Mr = Sx(Fy − Fr ) = Sx(Fy − 10 ksi) for rolled shapes bending about the major axis if Lb = Lr

(2-13) (2-14) (2-15) (2-16)

Mn for bending about the major axis, if Lp < Lb < Lr, is determined by linear interpolation between Equations 2-13 and 2-16; i.e.,  Lb − Lp  Mn = Mp − (Mp − Mr)    Lr − Lp 

(2-17)

The definition for the limiting laterally unbraced length Lr is given in the LRFD Specification (in Equations F1-6, 8, and 9) and will not be repeated here. For bending about the major axis if Lb > Lr, Mn = Mcr ≤ Mr

(2-18)

The case of Lb > Lr is beyond the scope of this section. The reader is referred to Section F1.2b of LRFD Specification (specifically Equation F1-13, where the critical moment AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2 - 30

ESSENTIALS OF LRFD

Table F-1. Values of Cb for Simply Supported Beams Braced at Ends of Span Load

Lateral Bracing Along Span

Concentrated at center

None

1.32

At centerline only

1.67

None

1.14

At centerline only

1.30

Uniform

Mcr is controlled by lateral-torsional buckling). This case is also covered in the beam graphs in Part 4 of this LRFD Manual. b. All values of Cb Cb is the bending coefficient. A new expression for Cb is given in the LRFD Specification. (It is more accurate than the one previously shown.) Cb =

12.5Mmax 2.5Mmax + 3MA + 4MB + 3Mc

(F1-3)

where M is the absolute value of a moment in the unbraced beam segment as follows: Mmax, the maximum MA, at the quarter point MB, at the centerline Mc, at the three-quarter point The purpose of Cb is to account for the influence of moment gradient on lateral-torsional buckling. The flexural strength equations with Cb = 1.0 are based on a uniform moment along a laterally unsupported beam segment causing single curvature buckling of the member. Other loadings are less severe, resulting in higher flexural strengths; Cb ≥ 1.0. Typical values of Cb are given in Table F-1. For unbraced cantilevers, Cb = 1.0. Cb can conservatively be taken as 1.0 for all cases. For all values of Cb, the flexural design strength φbMn, where φb = 0.90, is given in the LRFD Specification in terms of a nominal flexural strength Mn varying as follows: Mn = Mp = ZxFy

(2-13)

for bending about the major axis if Lb ≤ Lm Mn = CbMr = CbSx(Fy − 10 ksi) ≤ Mp

(2-19)

for bending about the major axis if Lb = Lr. For bending about the major axis if Lm < Lb < Lr, linear interpolation is used  Lb − Lp   Mn = Cb Mp − (Mp − Mr)   ≤ Mp  Lr − Lp  

(F1-2)

Mn = Mcr ≤ CbMr and Mp

(2-20)

If Lb > Lr,

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

F. BEAMS AND OTHER FLEXURAL MEMBERS

2 - 31

The determination of Mn for a given Lb can best be done graphically, as illustrated in Figure F-2. The required parameters for each W shape are given in the beam design table in Part 4 of the LRFD Manual, an excerpt of which is shown herein as Table F-2. If Cb = 1.0, the coordinates for constructing the graph are (Lp, Mp), and (Lr, Mr). For Cb > 1.0, the key coordinates are (Lp, Cb Mp) and (Lr, Cb Mr). Note that Mn cannot exceed the plastic moment Mp. Lm, then, can be derived graphically as the upper limit of Lb for which Mn = Mp. If Lb > Lr, the beam graphs in Part 4 of the LRFD Manual can be used to determine Mcr.

EXAMPLE F-1

Select the required W shape for a 30-foot simple floor beam with full lateral support carrying a dead load (including its own weight) of 1.5 kips per linear foot and a live load of 3.0 kips per linear foot. Assume 50 ksi steel and:

Given:

a. There is no member depth limitation b. The deepest member is a W18 The governing load combination in Section A is A4-2:

Solution:

1.2D + 1.6L + 0.5(Lr or S or R) = 1.2 × 1.5 klf + 1.6 × 3.0 klf + 0 = 6.6 klf Required Mu =

wL2 6.6 klf × (30.0 ft)2 = = 743 kip-ft 8 8

Flexural design strength φbMn ≥ 743 kip-ft

CbMp Mn for Cb=1.0

Mn for Cb>1.0

Mcr for Cb=1.0

CbMr

Mcr for Cb >1.0

Fig. F-2. Determination of nominal flexural strength M n. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

Table F-2. Excerpt from Load Factor Design Selection Table (LRFD Manual, Part 4) For Fy = 50 ksi

Zx (in.3)

Shape

φbMp (kip-ft)

φbMr (kip-ft)

Lp (ft)

Lr (ft)

224 221 212 211

W24× ×84 W21×93 W14×120 W18×97

840 829 795 791

588 576 570 564

6.9 6.5 13.2 9.4

18.6 19.4 46.2 27.4

200 198 196 192 186 186

W24× ×76 W16×100 W21×83 W14×109 W18×86 W12×120

750 743 735 720 698 698

528 525 513 519 498 489

6.8 8.9 6.5 13.2 9.3 11.1

18.0 29.3 18.5 43.2 26.1 50.0

177 175

W24× ×68 W16×89

664 656

462 465

6.6 8.8

17.4 27.3

Note: Flexural design strength φbMn = φbMp, as tabulated is valid for Lb ≤ Lm. If Cb = 1.0, Lm = Lp; otherwise, Lm > Lp. φb = 0.90.

a. In Table F-2, the most economical beams are in boldface print. Of the boldfaced beams, the lightest one with φbMn = φbMp ≥ 743 kip-ft is a W24×76 b. By inspection of Table F-2, the lightest W18 with φbMn = φbMp ≥ 743 kip-ft is a W18×97.

EXAMPLE F-2

Given:

Determine the flexural design strength of a 30-ft long simply supported W24×76 girder (of 50 ksi steel) with a concentrated load and lateral support, both at midspan.

Solution:

From Table F-1, Cb = 1.67 Lb = 30.0 ft/2 = 15.0 ft From Equation F1-2:  Lb − Lp    φbMn = Cb φbMp − (φbMp − φbMr)    ≤ φbMp  Lr − Lp    From Table F-2 for a W24×76: φbMp = 750 kip-ft φbMr = 528 kip-ft Lp = 6.8 ft AMERICAN INSTITUTE OF STEEL CONSTRUCTION

F. BEAMS AND OTHER FLEXURAL MEMBERS

2 - 33

= 18.0 ft

15.0 ft − 6.8 ft   φbMn = 1.67 750 kip−ft − (750 − 528) kip−ft × 18.0 ft − 6.8 ft   = 981 kip-ft > 750 kip-ft Use φb Mn = φb Mp = 750 kip-ft In this case, even though the unbraced length Lb > Lp, the design flexural strength is φbMp because Cb > 1.0. Design for Shear

The design shear strength is defined by the equations in Section F2 of the LRFD Specification. Shear in wide-flange and channel sections is resisted by the area of the web (Aw), which is taken as the overall depth d times the web thickness tw. For webs of 50 ksi steel without transverse stiffeners, the design shear strength φvVn, where φv = 0.90, and the nominal shear strength Vn are as follows: For

h ≤ 59 (including all rolled W and channel shapes), tw

Vn = 30.0 ksi × dtw φvVn= 27.0 ksi × dtw For 59 <

(2-21)

h ≤ 74, tw

= 30.0 ksi × dtw ×

59 h / tw

φvVn = 27.0 ksi × dtw ×

59 h / tw

For

(2-22)

h > 74, tw =

132,000 dtw ksi (h / tw)2

φvVn =

118,000 dtw ksi (h / tw)2

(2-23)

Fig. F-3. Definitions of d, h, and tw for W and channel shapes. AMERICAN INSTITUTE OF

STEEL CONSTRUCTION

2 - 34

ESSENTIALS OF LRFD

Shear strength is governed by the following limit states; Equation 2-21 by yielding of the web; Equation 2-22, by inelastic buckling of the web; and Equation 2-23 by elastic buckling.

EXAMPLE F-3

Given:

Solution:

Check the adequacy of a W30×99 beam of 50 ksi steel to carry a load resulting in maximum shears of 100 kips due to dead load and 150 kips due to live load. Required shear strength = Vu = 1.2D + 1.6L = 1.2 × 100 kips + 1.6 × 150 kips = 360 kips Design shear strength = φvVn = 27.0 ksi × dtw = 27.0 ksi × 29.65 in. × 0.520 in. = 416 kips > 360 kips required o.k.

Web Openings

See Section F4 of the LRFD Specification and Commentary, and the references given in the Commentary. H. MEMBERS UNDER COMBINED FORCES AND TORSION Symmetric Members Subject to Bending and Axial Tension

The interaction of flexure and tension in singly and doubly symmetric shapes is governed by Equations H1-1a and H1-1b, as follows: For

For

Pu ≥ 0.2, φPn

Pu < 0.2, φPn

Muy  Pu 8  Mux +  +  ≤ 1.0 9 φPn  φb Mnx φb Mny 

(H1-1a)

 Mux Muy  Pu + +  ≤ 1.0 2φPn  φb Mnx φb Mny

(H1-1b)

where = required tensile strength; i.e., the total factored tensile force, kips = design tensile strength, φtPn, kips = resistance factor for tension, φt = 0.90 = nominal tensile strength as defined in Chapter D of the LRFD Specification, kips Mu = required flexural strength; i.e., the moment due to the total factored load, kipin. or kip-ft. (Subscript x or y denotes the axis about which bending occurs.) φb Mn = design flexural strength, kip-in. or kip-ft = resistance factor for flexure = 0.90 φb

Pu φPn φ Pn

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= nominal flexural strength determined in accordance with the appropriate equations in Chapter F of the LRFD Specification, kip-in. or kip-ft

Interaction Equations H1-1a and H1-1b cover the general case of biaxial bending combined with axial force. They are also valid for uniaxial bending (i.e., when Mux = 0 or Muy = 0). In this case, they reduce to the form plotted in Figure H-1. Pure biaxial bending (with Pu = 0) is covered by Equation H1-1b. EXAMPLE H-1

Given:

Check the adequacy of a W10×22 tension member of 50 ksi steel to carry loads resulting in the following factored load combination: Pu = 55 kips Muy = 20 kip-ft Mux = 0

Solution:

From Section D above for 50 ksi steel, φPn = φtPn = 45.0 ksi × Ag = 45.0 ksi × 6.49 in.2 = 292 kips Pu 55 kips = = 0.188 < 0.20; therefore, Equation H1-1b governs. φPn 292 kips For bending about the y axis only, Equation H1-1b becomes: Pu Muy + ≤ 1.0 2φPn φb Mny φ Pn

φ Pn

8 Mu = 9 φb M n

0.2 φPn

( )

1 Pu 2 φPn

Mu =1 φb M n 0.9 φb M n

φb M n

Fig. H-1. Interaction Equations H1-1a and H1-1b modified for axial load combined with bending about one axis only. AMERICAN INSTITUTE OF

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ESSENTIALS OF LRFD

From Section F above for 50 ksi steel, Mn = Mp = ZyFy = 50 ksi × Zy for minor-axis bending (regardless of the unbraced length). φbMny = 0.90 × 50 ksi × Zy = 45.0 ksi × Zy = 45.0 ksi ×

6.10 in.3 12 in./ft

= 22.9 kip-ft for a W10×22 member 20 kip−ft Pu Muy 0.188 + = + = 0.094 + 0.873 2 22.9 kip−ft 2φPn φb Mny = 0.967 < 1.0 o.k.

EXAMPLE H-2

Given:

Check the same tension member, a W10×22 in 50 ksi steel, 4.0 ft long, subjected to the following combination of factored loads: Pu = 140 kips Mux = 55 kip-ft Muy = 0 Cb = 1.0

Solution:

Again, φPn = 292 kips Pu

φPn

140 kips = 0.479 > 0.20; Equation H1-1a governs. 292 kips

For bending about the x axis only, Equation H1-1a becomes Pu 8 Mux + ≤ 1.0 φPn 9 φb Mnx From Section F above for 50 ksi steel, Mn = Mp = ZxFy = 50 ksi × Zx for major-axis bending if Lb ≤ Lp for (Cb = 1.0). Assume unbraced length, Lb = 4.0 ft. By Equation 2-15 in Section F, Lp = 42.4ry for 50 ksi steel. For a W10×22, ry = 1.33 in., Zx = 26.0 in.3 Lp =

42.4 × 1.33 in. = 4.7 ft 12 in./ft

Lb = 4.0 ft < Lp = 4.7 ft Then Mnx = 50 ksi × Zx φb Mnx

0.90 × 50 ksi × 26.0 in.3 12 in./ft = 97.5 kip-ft for a W10×22 member =

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55 kip−ft Pu 8Mux 8 + = 0.479 + × 9 97.5 kip−ft φPn 9φb Mnx = 0.479 + 0.501 = 0.980 < 1.0 o.k. Symmetric Members Subject to Bending and Axial Compression

The interaction of compression and flexure in beam-columns with singly and doubly symmetric cross sections is governed by Equations H1-1a and H1-1b, repeated here for convenience: For

For

Pu ≥ 0.2, φPn

Pu < 0.2, φPn

Muy  Pu 8  Mux +  +  ≤ 1.0 φPn 9  φb Mnx φb Mny

(H1-1a)

 Mux Muy  Pu + +  ≤ 1.0 2φPn  φb Mnx φb Mny

(H1-1b)

The definitions of the ter ms in the for mulas, which differ in some cases from those given above, are as follows: = required compressive strength; i.e., the total factored compressive force, kips = design compressive strength, φc Pn, kips = resistance factor for compression, φc = 0.85 = nominal compressive strength as defined in Chapter E of the LRFD Specification, kips Mu = required flexural strength including second-order effects, kip-in. or kip-ft φb Mn = design flexural strength, kip-in. or kip-ft = resistance factor for flexure = 0.90 φb Mn = nominal flexural strength from Chapter F of the LRFD Specification, kip-in. or kip-ft

Pu φPn φ Pn

The second-order analysis required for Mu involves the determination of the additional moment due to the action of the axial compressive forces on a deformed structure. In lieu of a second-order analysis, the simplified method given in Chapter C of the LRFD Specification (and in Section C above) may be used. However, in applying the simplified method, the additional moments obtained for beam-columns must also be distributed to connected members and connections (to satisfy equilibrium). Bending and Axial Compression—Preliminary Design

The design of a beam-column is a trial and error process which can become tedious, particularly with the repeated solution of Interaction Equation H1-1a or H1-1b. A rapid method for the selection of a trial section is given in this LRFD Manual, Part 3, under the heading Combined Axial and Bending Loading (Interaction). As in earlier editions of the AISC Manual, the Interaction Equations are approximated by an equation which converts bending moments to equivalent axial loads: Pu eq = Pu + Muxm + Muymu AMERICAN INSTITUTE OF

STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

where = equivalent axial load to be checked against the column load table, kips Pu eq Pu, Mux, Muy are defined in the Interaction Equations for compression and bending m, u are factors tabulated in this LRFD Manual, Part 3 As soon as a satisfactory trial section has been found (i.e., one for which Pu eq ≤ tabulated φc Pn), a final verification should be made with the appropriate Interaction Equation, H1-1a or H1-1b

EXAMPLE H-3

Given:

Check the adequacy of a W14×176 beam-column, 14.0 ft in height floor-to-floor, in a braced symmetrical frame in 50 ksi steel. The member is subjected to the following factored forces due to symmetrical gravity loads: Pu = 1,400 kips; Mx = 200 kip-ft, My = 70 kip-ft (reverse curvature bending with equal end moments about both axes); and no loads along the member.

Solution:

For a braced frame, K = 1.0 KxLx = KyLy = 14.0 ft For a W14×176: A Zx Zy rx ry Kl / rx Kl / ry

= 51.8 in.2 = 320 in.3 = 163 in.3 = 6.43 in. = 4.02 in. = (14.0 ft × 12 in./ft) / 6.43 in. = 26.1 = (14.0 ft × 12 in./ft) / 4.02 in. = 41.8

From Table E-1, above, φcFcr = 37.4 ksi for Kl / r = 41.8 in 50 ksi steel. φcPn = (φc Fcr) A = 37.4 ksi × 51.8 in.2 = 1,940 kips Pu 1,400 kips = = 0.72 > 0.2, Interaction Equation H1-1a φc Pn 1,940 kips governs.

Since

For a braced frame, Mlt = 0. From Equation C1-1: Mux = B1x Mntx , where Mntx = 200 kip-ft; and Muy = B1y Mnty , where Mnty = 70 kip-ft From Equations C1-2 and C1-3: B1 =

Cm > 1.0 (1 − Pu / Pe1 )

where in this case (a braced frame with no transverse loading), Cm = 0.6 − 0.4(M1 / M2) AMERICAN INSTITUTE OF

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H. MEMBERS UNDER COMBINED FORCES AND TORSION

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For reverse curvature bending and equal end moments: M1 / M2 = +1.0 = 0.6 − 0.4(1.0) = 0.2

From Table C-1: Pe1x = 420 ksi × Ag = 420 ksi × 51.8 in.2 = 21,756 kips From Table C-1: Pe1y = 164 ksi × Ag = 164 ksi × 51.8 in.2 = 8,495 kips B1x =

Cmx 0.2 = = 0.2 (1 − Pu / Pe1x ) (1 − 1,400 kips / 21,756 kips)

Use B1x = 1.0, per Equation C1-2. B1y =

Cmy 0.2 = = 0.2 (1 − Pu / Pe1y ) 1 − 1,400 kips / 8,495 kips)

Use B1y = 1.0, per Equation C1-2. Mux = 1.0 × 200 kip-ft Muy = 1.0 × 70 kip-ft From Equation 2-15 for 50 ksi steel, Lp = 42.4ry =

42.4 × 4.02 in. = 14.2 ft 12 in./ft

Since Lb = 14.0 ft < Lp = 14.2 ft, Mnx = Mpx = ZxFy Mny

= Mpy = Zy Fy

φbFy

= 0.90 × 50 ksi = 45.0 ksi

φb Mnx = φbFy Zx =

45.0 ksi × 320 in.3 = 1,200 kip-ft 12 in./ft

φb Mny = φbFy Zy =

45.0 ksi × 163 in.3 = 611 kip-ft 12 in./ft

By Interaction Equation H1-1a 70 kip−ft  8 1,400 kips 8  200 kip−ft +  +  = 0.72 + (0.17+0.11) 1,940 kips 9  1,200 kip−ft 611 kip−ft  9 = 0.72 + 0.25 = 0.97 < 1.0 W14×176 is o.k. AMERICAN INSTITUTE OF

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ESSENTIALS OF LRFD

EXAMPLE H-4

Given:

Check the adequacy of a W14×176 beam-column (Fy = 50 ksi) in an unbraced symmetrical frame subjected to the following factored forces: Pu Mux My KxLx

= 1,400 kips (due to gravity plus wind) = 300 kip-ft (due to wind only) =0 = Ky Ly = 14.0 ft

Drift index, ∆oh / L ≤ 0.0025 (or 1⁄400) ΣPu = 24,000 kips ΣH = 800 kips Solution:

As in Example H-3, for a W14×176 with KL = 14.0 ft, φcPn = 1,940 kips. Pu 1,400 kips = = 0.72 > 0.2, Interaction Equation H1-1a φcPn 1,940 kips governs.

Since

Because Mntx = Mnty = Mlty = 0 and only Mltx ≠ 0, Mux = B2Mltx and Muy = 0. Mltx = 300 kip-ft According to Equation C1-4, B2 =

1 1 = = 1.08 ΣPu  ∆oh 1 − 24,000 kips (0.0025) 1−   800 kips ΣH  L 

Mux = 1.08 × 300 kip-ft = 324 kip-ft Because Lb < Lp = 14.2 ft, Mnx = Mpx = ZxFy; φb Mnx = 1,200 kip-ft as in Example H-3. By Interaction Equation H1-1a: 8 1,400 kips 8 324 kip−ft + = 0.72 + 0.27 = 0.96 < 1.0 9 1,940 kips 9 1,200 kip−ft W14×176 is o.k. Torsion and Combined Torsion, Flexure, and/or Axial Force

Criteria for members subjected to torsion and torsion combined with other forces are given in Section H2 of the LRFD Specification. They require the calculation of normal and shear stresses by elastic analysis of the member under the factored loads. The AISC book Torsional Analysis of Steel Members (American Institute of Steel Construction, 1983) provides design aids and examples for the determination of torsional stresses. Extensive coverage is given there to wide-flange shapes (W, S, and HP), channels (C and MC) and Z shapes. For these members, the charts and formulas simplify considerably AMERICAN INSTITUTE OF

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H. MEMBERS UNDER COMBINED FORCES AND TORSION

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the calculation of torsional rotations, torsional normal and shear stresses, and the combination of torsional with flexural stresses. In the LRFD Specification, fun = the total normal stress under factored load (ksi) from torsion and all other causes fuv = the total shear stress under factored load (ksi) from torsion and all other causes The criteria are as follows: a. For the limit state of yielding under normal stress fun ≤ φFy, where φ = 0.90

(H2-1)

fun ≤ 0.90 × 50 ksi = 45.0 ksi

(2-24)

For 50 ksi steel,

b. For the limit state of yielding under shear stress, fuv ≤ 0.60φFy, where φ = 0.90

(H2-2)

fuv ≤ 0.60 × 0.90 × 50 ksi = 27.0 ksi

(2-25)

For 50 ksi steel,

c. For the limit state of buckling, fun ≤ φcFcr or fuv ≤ φcFcr, as applicable, where φc = 0.85

(H2-3)

For 50 ksi steel, values of φcFcr are given in Table E-1, in Section E above. Torsion will accompany flexure when the line of action of a lateral load does not pass through the shear center. For wide flange and other doubly symmetric shapes, the shear center is located at the centroid. Singly symmetric shapes have their shear centers on the axis of symmetry, but not at the centroid. (The location of the shear center of channel sections is given in the Properties tables in Part 1 of this LRFD Manual.) Open sections, such as wide-flange and channel, are very inefficient in resisting torsion; i.e., torsional rotations can be large and torsional stresses relatively high. It is best to avoid torsion by detailing the loads and reactions to act through the shear center of the member. In the case of spandrel members supporting building facade elements, this may not be possible. Heavy exterior masonry walls and stone panels can impose severe torsional loads on spandrel beams. The following are suggestions for eliminating or reducing this kind of torsion: 1. Wall elements may span between floors. The moment due to the eccentricity of the wall with respect to the edge beams can be resisted by lateral forces acting through the floor diaphragms. Torsion would not be imposed on the spandrel beams. 2. If facade panels extend only a partial story height below the floor line, the use of diagonal steel “kickers” may be possible. These light members would provide lateral support to the wall panels. Torsion from the panels would be resisted by forces originating from structural elements other than the spandrel beams. 3. Even if torsion must be resisted by the edge members, providing intermediate torsional supports can be helpful. Reducing the span over which the torsion acts will reduce torsional stresses. If there are secondary beams framing into a spandrel girder, AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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ESSENTIALS OF LRFD

the beams can act as intermediate torsional supports for the girder. By adding top and bottom moment plates to the connections of the beams with the girder, the bending resistances of the beams can be mobilized to provide the required torsional reactions along the girder. 4. Closed sections provide considerably better resistance to torsion than open sections; torsional rotations and stresses are much lower for box beams than for wide-flange members. For members subjected to torsion, it may be advisable to use box sections or to simulate a box shape by welding one or two side plates to a W shape. I. COMPOSITE MEMBERS

Chapter I of the LRFD Specification covers composite members. Included are concreteencased and concrete-filled steel columns and beam columns, as well as steel beams interactive with the concrete slabs they support and steel beams encased in concrete. Unlike traditional structural steel design, which considers only the strength of the steel, composite design assumes that the steel and concrete work together in resisting loads. This results in more economical designs, as the quantity of steel can be reduced. Compression Members

Composite columns (concrete-encased and concrete-filled) must satisfy the limitations in Section I2 of the LRFD Specification. The design strength of axially loaded composite columns is φcPn, where φc = 0.85 and the nominal axial compressive strength is determined from Equations E2-1 through E2-4 above with the following modifications: As replaces Ag, rm replaces r, Fmy replaces Fy, and Em replaces E. Fmy = Fy + c1Fyr

Ar Ac + c2 fc′ As As

(I2-1)

Ac As

(I2-2)

Em = E + c3Ec

rm = radius of gyraton of the steel shape, pipe, or tubing, in. (For steel shapes it shall not be less than 0.3 times the overall thickness of the composite cross section in the plane of buckling.) where Ec = w1.5√ fc′ and Fmy Fy Fyr fc′ Em E Ec w Ac Ar

= modified yield stress for the design of composite columns, ksi = specified minimum yield stress of the structural steel shape, ksi = specified minimum yield stress of the longitudinal reinforcing bars, ksi = specified compressive strength of the concrete, ksi = modified modulus of elasticity for the design of composite columns, ksi = modulus of elasticity of steel = 29,000 ksi = modulus of elasticity of concrete, ksi = unit weight of concrete, lb/ft3 = cross-sectional area of concrete, in.2 = cross-sectional area of longitudinal reinforcing bars, in.2 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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As = cross-sectional area of structural steel, in.2 c1, c2, c3 = numerical coefficients. For concrete-filled pipe and tubing: c1 = 1.0, c2 = 0.85, and c3 = 0.4; for concrete-encased shapes c1 = 0.7, c2 = 0.6, and c3 = 0.2 Composite columns can be designed by using the Composite Columns Tables in Part 5 of this LRFD Manual (or the numerous tables in AISC Steel Design Guide No. 6: Load and Resistance Factor Design of W-Shapes Encased in Concrete) for the cross sections tabulated therein, or the above equations for all cross sections. Flexural Members

The most common case of a composite flexural member is a steel beam interacting with a concrete slab by means of stud or channel shear connectors. The slab can be a solid reinforced concrete slab, but is usually concrete on a corrugated metal deck. The effective width of concrete slab acting compositely with a steel beam is determined by three criteria. On either side of the beam centerline, the effective width of concrete slab cannot exceed: a. one-eighth of the beam span, b. one-half the distance to the centerline of the adjacent beam, or c. the distance to the edge of the slab. The following pertains to rolled W shapes in regions of positive moment, the predominant use of composite beam design. Other cases (e.g., plate girders and negative moments) are covered in Chapter I of the LRFD Specification. The horizontal shear force between the steel beam and concrete slab, to be transferred by the shear connectors between the points of zero and maximum positive moments, is the minimum of: a. 0.85fc′Ac (the maximum possible compressive force in the concrete), b. AsFy (the maximum possible tensile force in the steel), and c. ΣQn (the strength of the shear connectors). For W shapes, the design flexural strength φb Mn, with φb = 0.85, is based on: a. a uniform compressive stress of 0.85fc′ and zero tensile strength in the concrete b. a uniform steel stress of Fy in the tension area and compression area (if any) of the steel section, and c. equilibrium; i.e., the sum of the tensile forces equals the sum of the compressive forces. The above is valid for shored and unshored construction. However, in the latter case, it is also necessary to check the bare steel beam for adequacy to support the wet concrete and other construction loads (properly factored). The number of shear connectors required between a point of maximum moment and the nearest location of zero moment is n=

Vh Qn

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(2-26)

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ESSENTIALS OF LRFD

where Vh = the total horizontal shear force to be transferred, kips = the minimum of 0.85fc′Ac, AsFy, and ΣQn Qn = the shear strength of one connector The nominal strength of a single stud shear connector in a solid concrete slab is  fc′Ec ≤ AscFu Qn = 0.5Asc√

(I5-1)

where Asc = cross-sectional area of a stud shear connector, in.2 fc′ = specified compressive strength of concrete, ksi Fu = minimum specified tensile strength of a stud shear connector, ksi Ec = modulus of elasticity of concrete, ksi Special provisions for shear connectors embedded in concrete on formed steel deck are given in Section I3.5 of the LRFD Specification. Among them are reduction factors (given by Equation I3-1 and I3-2) to be applied to the middle term of Equation I5-1 above. The design of composite beams and the selection of shear connectors can be accomplished with the tables in Part 5 of this LRFD Manual. The design shear strength for composite beams is determined by the shear strength of the steel web, as for noncomposite beams; see Section F above. Combined Compression and Flexure

Composite beam-columns are covered in Section I4 of the LRFD Specification. COMPUTER SOFTWARE ELRFD* (Electronic LRFD Specification)

ELRFD is a sophisticated computer program for interactively checking structural steel building components for compliance with the AISC Specification. All provisions of Chapters A through H and K of the LRFD Specification are included in the knowledge base of ELRFD. The ELRFD program checks whether the member satisfies all limit states and limitation requirements set by the LRFD Specification and reports which sections of the specification are satisfied or violated. One can review in detail the formulas and rules used in the evaluation and interactively assess any mathematical expression appearing on the screen. Design data produced by the software can be viewed and/or printed in report form for permanent record. ELRFD has a fully interactive Windows-based user interface.

*ELRFD is copyright AISC and Visual Edge Software, Ltd. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

REFERENCES

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REFERENCES

American Institute of Steel Construction, Inc., 1983, Torsional Analysis of Steel Members, AISC, Chicago, IL. American Society of Civil Engineers, 1988, Minimum Design Loads for Buildings and Other Structures, ASCE 7-88, New York, NY. Galambos, T. V., et al., 1978, Eight LRFD Papers, Journal of the Structural Division, ASCE, Vol. 104, No. ST9 (September 1978), New York. Geschwindner, L., 1993, “The ‘Leaning’ Column in ASD and LRFD,” Proceedings of the 1993 National Steel Construction Conference, AISC, Chicago. U.S. Department of Commerce, 1980, Development of a Probability Based Criterion for American National Standard A58, NBS (National Bureau of Standards) Special Publication 577, Washington, DC.

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3-1

PART 3 COLUMN DESIGN OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 DESIGN STRENGTH OF COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5 General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5 W and HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15 Steel Pipe and Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35 Double Angles and WT Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-53 Single-Angle Struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104 COLUMN BASE PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-117 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-117

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3-2

COLUMN DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

OVERVIEW

3-3

OVERVIEW Column tables with design compressive strengths, in kips, are located as follows: W shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16 HP shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31 Steel pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36 Structural tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-39 Double angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-57 WT shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-83 Single angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104 Additional information related to column design is provided as follows: Effective length factor (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5 Alignment charts, Figure 3-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

Stiffness reduction factors (SRF), Table 3-1 . . . . . . . . . . . . . . . . . . . . . . . . 3-7 “Leaning” columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 Combined axial and bending loading (Interaction) . . . . . . . . . . . . . . . . . . . . 3-11 Preliminary design of beam-columns, Table 3-2 . . . . . . . . . . . . . . . . . . . . 3-12

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COLUMN DESIGN

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DESIGN STRENGTH OF COLUMNS

3-5

DESIGN STRENGTH OF COLUMNS General Notes

Column Load Tables

Column Load Tables are presented for W, WT, and HP shapes, pipe, structural tubing, double angles, and single angles. Tabular loads are computed in accordance with the AISC LRFD Specification, Sections E2 and E3 and Appendix E3, for axially loaded members having effective unsupported lengths indicated to the left of each table. The effective length KL is the actual unbraced length, in feet, multiplied by the factor K, which depends on the rotational restraint at the ends of the unbraced length and the means available to resist lateral movements. Table C-C2.1 in the Commentary on the LRFD Specification is a guide in selecting the K-factor. Interpolation between the idealized cases is a matter of engineering judgment. Once sections have been selected for the several framing members, the alignment charts in Figure 3-1 [reproduced from the Structural Stability Research Council Guide (Galambos, 1988) here and in Figure C-C2.2 of the Commentary on the LRFD Specification] afford a means to obtain more precise values for K, if desired. For column behavior in the inelastic range, the values of G as defined in Figure 3-1 may be reduced by the values given in Table 3-1, as illustrated in Example 3-3. Tables for W, WT, and HP shapes and for double and single angles are provided for 36 ksi and 50 ksi yield stress steels. Tables for steel pipe are provided for 36 ksi, and for structural tubing for 46 ksi yield stress steel. All design strengths are tabulated in kips. Values are not shown when Kl / r exceeds 200. In all tables, except double angle and WT tables, design strengths are given for effective lengths with respect to the minor axis calculated by LRFD Specification Section E2. When the minor axis is braced at closer intervals than the major axis, the strength of the column must be investigated with reference to both major (X-X) and minor (Y-Y) axes. The ratio rx / ry included in these tables provides a convenient method for investigating the strength of a column with respect to its major axis. To obtain an effective length with respect to the minor axis equivalent in load carrying capacity to the actual effective length about the major axis, divide the major axis effective length by rx / ry ratio. Compare this length with the actual effective length about the minor axis. The longer of the two lengths will control the design, and the design strength may be taken from the table opposite the longer of the two effective lengths with respect to the minor axis. The double angle and WT tables show values for effective lengths about both axes. Properties useful to the designer are listed at the bottom of the column design strength tables. Additional notes relating specifically to the W and HP shape tables, the steel pipe and structural tubing tables, and the double and single angle tables precede each of these groups of tables.

EXAMPLE 3-1

Given:

Design the lightest W shape of Fy = 50 ksi steel to support a factored concentric load of 1,400 kips. The effective length with respect to its minor axis is 16 feet. The effective length with respect to its major axis is 31 feet. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COLUMN DESIGN

Solution:

Enter the appropriate Column Load Table for W shapes at effective length of KL = 16 ft. Since W14 columns are generally most efficient, begin with the W14 table and work downward, weightwise. Select W14×145, good for 1,530 kips > 1,400 kips rx / ry = 1.59. Equivalent L = 31 ft / 1.59 = 19.5 ft > 16 ft Equivalent effective length for X-X axis controls.

GA ∞ 50.0

GB ∞

1.0

50.0 10.0

10.0 5.0 3.0

5.0 0.9

5.0

100.0 50.0 30.0

20.0

4.0

20.0

10.0 9.0 8.0 7.0

3.0

2.0

0.5

0.4

0.3

0.6

0.7

6.0 5.0

10.0 9.0 8.0 7.0

-3 e3

0.8 0.7

ple

1.0

0.8 0.7

1.0

0.8

0.2

GB ∞ 20.0 10.0

100.0 50.0 30.0

3.0

2.0

0.6

GA ∞

6.0 5.0

2.2

4.0

2.0

3.0

1.75 2.0

2.36

2.0 1.5

0.6

0.2 1.0

0.1

1.0

0.1

0.26 0

0.5

SIDESWAY INHIBITED

1.0

SIDESWAY UNINHIBITED

Fig. 3-1. Alignment charts for effective length of columns in continuous frames. The subscripts A and B refer to the joints at the two ends of the column section being considered. G is defined as Σ(Ic / Lc) G= Σ(Ig / Lg) in which Σ indicates a summation of all members rigidly connected to that joint and lying on the plane in which buckling of the column is being considered. Ic is the moment of inertia and Lc the unsupported length of a column section, and Ig is the moment of inertia and Lg is the unsupported length of a girder or other restraining member. Ic and Ig are taken about axes perpendicular to the plane of buckling being considered. For column ends supported but not rigidly connected to a footing or foundation, G is theoretically infinity, but, unless actually designed a true friction free pin, may be taken as 10 for practical designs. If the column end is rigidly attached to a properly designed footing, G may be taken as 1.0. Smaller values may be used if justified by analysis. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3-7

Table 3-1. Stiffness Reduction Factors (SRF) for Columns Pu / A

Pu / A

ksi 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27

ksi 36 ksi

50 ksi

— — — — — — — — — — — — 0.05 0.14 0.22 0.30

0.03 0.09 0.16 0.21 0.27 0.33 0.38 0.44 0.49 0.53 0.58 0.63 0.67 0.71 0.75 0.79

26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11

36 ksi

50 ksi

0.38 0.45 0.52 0.58 0.65 0.70 0.76 0.81 0.85 0.89 0.92 0.95 0.97 0.99 1.00 ↓

0.82 0.85 0.88 0.90 0.93 0.95 0.97 0.98 0.99 1.00 ↓

— indicates not applicable.

Re-enter table for effective length of 19.5 ft to satisfy axial load of 1,400 kips, select W14×145. By interpolation, the column is good for 1,410 kips. Use W14×145 column

EXAMPLE 3-2

Given:

Design an 11-ft long W12 interior bay column to support a factored concentric axial roof load of 1,100 kips. The column is rigidly framed at the top by 30-ft long W30×116 girders connected to each flange. Column moment is zero due to the assumption of equal and offsetting moments in the girders. The column is braced normal to its web at top and base so that sidesway is inhibited in this plane. Use Fy = 50 ksi steel.

Solution:

a. Check Y-Y axis: Assume the column is pin-connected at the top and bottom with sidesway inhibited. From Table C-C2.1 in the Commentary for condition (d), K = 1.0: Effective length = 11 ft Enter Column Load Table: W12×106 good for 1,160 kips > 1,100 kips o.k. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COLUMN DESIGN

b. Check X-X axis: 1. Preliminary selection: Assume sidesway uninhibited and pin-connected at base. From Table C-C2.1 for condition (f): K = 2.0 Approximate effective length relative to X-X axis: 2.0 × 11 = 22.0 ft From Properties section in tables, for W12 column: rx / ry ≈ 1.76 Equivalent effective length relative to the Y-Y axis: 22.0

1.76

≈ 12.5 ft > 11.0 ft

Therefore, effective length for X-X axis is critical. Enter Column Load Table with an effective length of 12.5 ft: W12×106 column, by interpolation, good for 1,115 kips > 1,100 kips o.k. 1. Final selection Try W12×106 Using Figure 3-1 (sidesway uninhibited): Ix for W12×106 column = 933 in.4 Ix for W30×116 girder = 4,930 in.4 G (base)

= 10 (assume supported but not rigidly connected)

G (top)

933 / 11 = 0.258, say 0.26 (4,930 × 2) / 30

Connect points GA = 10 and GB = 0.26, read K = 1.75 For W12×106, rx / ry = 1.76 Actual effective length relative to Y-Y axis: 1.75 × 11.0 = 10.9 ft < 11.0 ft 1.76 Since the effective length for Y-Y axis is not critical, Use W12×106 column AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3-9

EXAMPLE 3-3

Given:

Using the alignment chart, Figure 3-1 (sidesway uninhibited) and Table 3-1 (Stiffness Reduction Factors), design columns for the bent shown, by the inelastic K-factor procedure. Let Fy = 50 ksi. Assume continuous support in the transverse direction.

Solution:

The alignment charts in Figure 3-1 are applicable to elastic columns. By multiplying G-values times the stiffness reduction factor Et / E, the charts may be used for inelastic columns. Since Et / E ≈ Fcr, inelastic / Fcr, elastic, the relationship may be written as Ginelastic = (Fcr, inelastic / Fcr, elastic)Gelastic. By utilizing the calculated stress Pu / A a direct solution is possible, using the following steps: 1. For a known value of factored axial load, Pu = 1,100 kips, select a trial column size. Assume W12×120 A = 35.3 in.2, Ix = 1,070 in.4, rx = 5.51 in. 2. Calculate Pu / A: Pu / A = 1,100 kips / 35.3 in.2 = 31.2 ksi 3. From Table 3-1, determine the Stiffness Reduction Factor (SRF); SRF = 0.62. For values of Pu / A smaller than those with entries in Table 3-1, the column is elastic, and the reduction factor is 1.0. 4. Determine Gelastic: Gelastic (bottom) = 10 1,100 k

1,100 k

W16x31 IX = 375 15′

20′

Fig. 3-2 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 10

COLUMN DESIGN

Gelastic (top)

1,070 / 15 = 3.80 375 / 20

5. Calculate Ginelastic = SRF × Gelastic: Ginelastic(top) = 0.62 × 3.80 = 2.36 6. Determine K from Figure 3-1 using Ginelastic For G (top) = 2.36 and G (bottom) = 10, Read from Figure 3-1, K = 2.2 7. KLx = 2.2 × 15 ft = 33.0 ft 8. Calculate equivalent of KLy: KLx 33.0 ft = = 18.75 ft 1.76 rx / ry 9. From the column tables (for 50 ksi steel): φc Pn = 1,030 kips < 1,100 kips req’d. n.g. Try a stronger column. 1. Try a W12×136 A = 39.9 in.2, Ix = 1,240 in.4, rx = 5.58 in. 2. Pu / A = 1,100 kips / 39.9 in.2 = 27.6 ksi 3. From Table 3-1: SRF = 0.77 4. Gelastic (top) =

1,240 / 15 = 4.41 375 / 20

5. Ginelastic(top) = 0.77 × 4.41 = 3.39 6. K = 2.3 7. KLx = 2.3 × 15 ft = 34.5 ft 8. Equivalent KLy:

KLx 34.5 ft = = 19.5 ft 1.77 rx / ry

9. φc Pn = 1,135 kips > 1,100 kips req’d o.k. Use W12×136 “Leaning” Columns

A “leaning” column is one which is considered pin-ended and does not participate in providing lateral stability to the structure. As a result, it relies on other parts of the structure for stability. The LRFD Specification in Section C2.2 requires that for unbraced frames, “the destabilizing effects of gravity-loaded columns whose simple connections AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 11

to the frame do not provide resistance to lateral loads shall be included in the design of the moment-frame columns.” Normal practice is to design leaning columns for their required strength with an effective length factor K = 1. To account for the effects of leaning columns on unbraced frames, one of the methods given in the Commentary on the LRFD Specification (Section C2) or in Geschwindner (1993) may be utilized. The simplest methods are: 1. The slightly conservative approach of adjusting the effective lengths of the rigidframe columns, Ki′ =  √NKi where Ki′ = the modified effective length factor of a column Ki = the actual effective length factor of a column N = ratio of the factored gravity load supported by all columns in the given story to that supported by the columns in the rigid frame 2. The more conservative approach of providing sufficient design compressive strength in the rigid-frame columns of a story to enable them to support the total factored gravity load of the story at their actual effective lengths. Combined Axial and Bending Loading (Interaction)

Loads given in the Column Tables are for concentrically loaded columns. For columns subjected to both axial and bending stress, see Chapters C and H of the LRFD Specification. The design of a beam-column is a trial and error process in which a trial section is checked for compliance with Equations H1-1a and H1-1b. A fast method for selecting an economical trial W section, using an equivalent axial load, is illustrated in the example problem, using Table 3-2 and the u values listed in the column properties at the bottom of the column load tables. The procedure is as follows: 1. With the known value of KL (effective length), select a first approximate value of m from Table 3-2. Let u equal 2. 2. Solve for Pu eq = Pu + Mux m + Muy mu where Pu Mux Muy m u

= actual factored axial load, kips = factored bending moment about the strong axis, kip-ft = factored bending moment about the weak axis, kip-ft = factor taken from Table 3-2 = factor taken from column load table

3. From the appropriate Column Load Table, select a tentative section to support Pu eq. 4. Based on the section selected in Step 3, select a “subsequent approximate” value of m from Table 3-2 and a u value from the column load table. 5. With the values selected in Step 4, solve for Pu eq. 6. Repeat Steps 3 and 4 until the values of m and u stabilize. 7. Check section obtained in Step 6 per Equation H1-1a or H1-1b, as applicable. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 12

COLUMN DESIGN

Table 3-2. Preliminary Beam-Column Design Fy = 36 ksi, Fy = 50 ksi Values of m

Fy KL (ft)

36 ksi 10

50 ksi 20

22 and over

1.8

1.7

1.6

1.4

1.3

1.2

1.4 1.7 1.8 2.0 1.8 1.5 1.4

1.1 1.4 1.5 1.7 1.7 1.5 1.3

1.0 1.1 1.3 1.5 1.5 1.4 1.3

0.9 1.0 1.2 1.3 1.4 1.3 1.2

0.8 0.9 1.1 1.2 1.3 1.2 1.2

1st Approximation All Shapes

2.0

1.9

1.8

1.7

1.6

1.5

1.3

1.9

Subsequent Approximation W4 W6 W8 W8 W10 W12 W14

3.1 3.2 2.8 2.5 2.1 1.7 1.5

2.3 2.7 2.5 2.3 2.0 1.7 1.5

1.7 2.1 2.1 2.2 1.9 1.6 1.4

1.4 1.7 1.8 2.0 1.8 1.5 1.4

1.1 1.4 1.5 1.8 1.7 1.5 1.3

1.0 1.2 1.3 1.6 1.6 1.4 1.3

0.8 1.0 1.1 1.4 1.4 1.3 1.2

2.4 2.8 2.5 2.4 2.0 1.7 1.5

1.8 2.2 2.2 2.2 1.9 1.6 1.4

This table is from a paper in AISC Engineering Journal by Uang, Wattar, and Leet (1990).

EXAMPLE 3-4

Given:

Design the following column: Pu = 400 kips Mntx = 250 kip-ft Mltx = 0 (braced frame) Mnty = 80 kip-ft Mlty = 0 (braced frame) KLx = KLy = 14 ft Lb = 14 ft Cm = 0.85 Fy = 50 ksi

Solution:

1. For KL = 14 ft, from Table 3-2 select a first trial value of m = 1.7. Let u = 2 2. Pu eq = Pu + Mux m + Muy mu = 400 + 250 × 1.7 + 80 × 1.7 × 2 = 1,097 kips 3. From Column Load Tables select W14×109 (φc Pn = 1,170 kips) or W12×120 (φc Pn = 1,220 kips). 4. Select the W14 column, so the second trial value of m is 1.4. (Note: If a W14 column were required for architectural or other reasons, AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 13

the selection process could have started with m = 1.4). With m = 1.4 and u = 1.97 (for a W14×109) from Column Load Table, Pu eq = 400 + 250 × 1.4 + 80 × 1.4 × 1.97 = 971 kips 5. From Column Load Tables select W14×90 (φc Pn = 969 kips). 6. For W14×90, m = 1.4, u = 1.94. Repeat of Steps 3 and 4 not required. 7. Check W14×90 with the appropriate interaction formula. A

= 26.5 in.2

= 3.70 in.,

 Kl 14 × 12 = 45.4  = 3.70  ry 

= 6.14 in.,

 Kl 14 × 12 = 27.4  = 6.14  rx 

Thesecond-or der moments,Mux and Muy, will be evaluated using the approximate method given in Section C1 of the LRFD Specification. Because Mltx = Mlty = 0 (braced frames in both directions), Specification Equation C1-1 reduces to Mu = B1Mnt, where B1 is a function of Pe1 (Equation C1-2). The values of Pe1 with respect to the x and y axes can be determined from LRFD Specification Table 8 as follows:

Pex Pey

= 382 × 26.5 = 10,123 kips = 139 × 26.5 = 3,684 kips

B1x

0.85 < 1.0. Use B1x = 1.0 1 − 400 / 10,123

B1y

0.85 < 1.0. Use B1y = 1.0 1 − 400 / 3,684

= 1.0 × 250 = 250 kip-ft = 1.0 × 80 = 80 kip-ft 0.9 × 50 × 75.6 = 284 kip-ft φb Mny = φb Mpy = 12

Mux Muy

From the beam selection table in Part 4 of this Manual: φb Mnx = 577 kip-ft for Lb < Lp = 15.0 ft Pu φcPn

400 = 0.412 > 0.2. Therefore, Equation H1-1a applies. 969

400 8  250 80  +  +  = 0.412 + 0.636 = 1.05 < 1.0 n.g. 969 9  577 284 Use W14×99 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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COLUMN DESIGN

Column Stiffening

Values of Pwo, Pwi, Pwb, and Pfb, listed in the Properties Section of the Column Load Tables for W and HP shapes, are useful in determining if a column requires stiffening because of forces transmitted into it from the flanges or connecting flange plates of a rigid beam connection to the column flange. The parameters are defined as follows: Pwo Pwi Pwb Pfb

= φ5Fyw tw k (kips), φ = 1.0 = φFyw tw (kips/in.), φ = 1.0 = φ4,100tw3 √ Fyw / h (kips), φ = 0.9 = φ6.25tf2Fyf (kips), φ = 0.9

Column stiffening or a heavier column* is required if Pbf, the factored force transmitted into the column web, exceeds any one of the following three resisting forces: Pwb Pfb Pwi tb + Pwo, where tb is the thickness of the beam flange delivering the concentrated force. For a complete explanation of these design parameters, see the section Column Stiffening in Part 10 (Volume II) of this LRFD Manual.

*The designer should consider selecting a heavier column section to eliminate the need for stiffening. Although this will increase the material cost of the column, this heavier section may provide a more economical solution due to the reduction in labor cost associated with the elimination of stiffening. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 15

W and HP Shapes

The design strengths in the tables that follow are tabulated for the effective lengths in feet KL (with respect to the minor axis), indicated at the left of each table. They are applicable to axially loaded members in accordance with Section E2 of the LRFD Specification. Two yield stresses are covered, 36 and 50 ksi. The heavy horizontal lines appearing within the tables indicate Kl / r = 200. No values are listed beyond Kl / r = 200. For discussion of effective length, range of l / r, strength about the major axis, combined axial and bending stress, and sample problems, see General Notes, above. Properties and factors are listed at the bottom of the tables for checking strength about the strong axis, combined loading conditions, and column stiffener requirements.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 16

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W14

Wt./ft

808

Effective length KL (ft) with respect to least radius of gyration ry

730

665

605

550

7250

10100

6580

9140

6000

8330

5450

7570

4960

6890

11 12 13 14 15

5610 5480 5350 5230 5110

7440 7240 7040 6850 6660

6310 6260 6210 6150 6090

8620 8530 8430 8320 8200

5750 5700 5650 5590 5540

7850 7760 7660 7560 7450

5210 5170 5120 5070 5020

7110 7030 6940 6850 6750

4740 4700 4650 4600 4560

6460 6390 6300 6220 6120

16 17 18 19 20

4990 4870 4760 4650 4540

6480 6310 6130 5970 5810

6020 5960 5880 5810 5730

8080 7960 7820 7690 7550

5480 5410 5350 5280 5200

7340 7220 7100 6970 6840

4960 4900 4840 4770 4700

6640 6530 6420 6300 6170

4500 4450 4390 4330 4260

6020 5920 5810 5700 5590

22 24 26 28 30

4340 4140 3950 3770 3600

5490 5200 4920 4660 4410

5570 5390 5210 5020 4820

7250 6940 6610 6280 5940

5050 4890 4720 4540 4360

6560 6270 5970 5660 5340

4560 4410 4250 4090 3920

5910 5640 5360 5080 4790

4130 3990 3840 3690 3530

5350 5100 4840 4570 4300

32 34 36 38 40

3430 3280 3130 2980 2850

4170 3950 3740 3540 3350

4620 4420 4210 4000 3790

5600 5250 4910 4580 4250

4170 3980 3790 3590 3400

5030 4710 4400 4090 3780

3740 3570 3390 3210 3030

4490 4200 3910 3630 3350

3370 3210 3050 2880 2720

4030 3760 3500 3240 2990

42 44 46 48 50

2720 2590 2470 2360 2250

3170 3000 3860 3540 3260

3580 3380 3170 2970 2780

3930 3620 3310 3040 2800

3210 3020 2830 2650 2470

3490 3200 2930 2690 2480

2860 2680 2510 2340 2180

3080 2820 2580 2370 2180

2550 2390 2240 2080 1940

2740 2500 2290 2100 1940

2.03 2.03 2.03 3910 5430 3070 135 187 111 103000 122000 56400 5310 7370 4880 20.1 17.0 19.5 415 270 372

2.03 4270 154 66500 6780 16.6 241

2.02 3670 142 52200 5750 16.3 222

2.02 2250 93.4 33900 3500 19.0 313

2.01 3120 130 39900 4870 16.1 203

2.02 1930 85.7 26100 2950 18.7 288

2.01 2680 119 30800 4100 15.9 188

Properties u P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

237 16000 5510 4.82 1.70 457000 158000

215 14300 4720 4.69 1.74 411000 135000

2.02 2640 102 44300 4140 19.3 342

196 12400 4170 4.62 1.73 357000 120000

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

178 10800 3680 4.55 1.71 310000 105000

162 9430 3250 4.49 1.70 270000 93500

DESIGN STRENGTH OF COLUMNS

3 - 17 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W14

Wt./ft

500

455

426

398

370

4500

6250

4100

5700

3830

5310

3580

4970

3340

4630

11 12 13 14 15

4290 4250 4210 4170 4120

5850 5780 5710 5620 5540

3910 3870 3840 3790 3750

5330 5260 5190 5110 5030

3640 3610 3570 3530 3490

4970 4900 4830 4760 4680

3410 3380 3340 3300 3270

4640 4580 4520 4450 4380

3170 3140 3110 3070 3040

4320 4260 4200 4140 4070

16 17 18 19 20

4070 4020 3970 3910 3850

5450 5350 5250 5150 5040

3710 3660 3610 3560 3500

4950 4860 4770 4670 4570

3450 3400 3360 3310 3260

4600 4520 4430 4340 4250

3230 3180 3140 3090 3040

4300 4220 4140 4050 3960

3000 2960 2920 2870 2820

4000 3920 3840 3760 3680

22 24 26 28 30

3730 3600 3460 3320 3180

4820 4590 4350 4100 3850

3390 3270 3140 3010 2870

4370 4150 3930 3700 3480

3150 3030 2910 2790 2660

4050 3850 3640 3430 3210

2940 2830 2720 2600 2480

3780 3590 3390 3190 2990

2730 2630 2520 2410 2290

3500 3320 3140 2950 2750

32 34 36 38 40

3030 2880 2730 2580 2420

3610 3360 3120 2880 2650

2740 2600 2460 2320 2180

3250 3020 2800 2580 2370

2530 2400 2270 2140 2010

3000 2780 2570 2370 2170

2360 2230 2110 1990 1860

2780 2580 2390 2190 2010

2180 2060 1950 1830 1710

2560 2380 2190 2010 1840

42 44 46 48 50

2280 2130 1990 1850 1710

2420 2210 2020 1860 1710

2040 1910 1780 1650 1520

2160 1970 1800 1650 1520

1880 1750 1630 1510 1400

1980 1800 1650 1510 1400

1740 1620 1510 1400 1290

1830 1660 1520 1400 1290

1600 1490 1380 1280 1180

1670 1520 1390 1280 1180

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.01 1650 78.8 20400 2480 18.5 264

2.00 2290 110 24100 3450 15.7 172

1.99 1410 72.5 15800 2090 18.3 242

1.99 1950 101 18600 2900 15.5 157

1.99 1730 93.8 15000 2590 15.3 148

1.99 1120 63.7 10800 1640 18.0 213

1.98 1550 88.5 12800 2280 15.2 139

1.98 987 59.6 8790 1430 17.8 199

1.97 1370 82.8 10400 1990 15.1 129

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

147 8210 2880 4.43 1.69 235000 82600

134 7190 2560 4.38 1.67 206000 73600

2.00 1240 67.5 12800 1870 18.1 227

125 6600 2360 4.34 1.67 189000 67400

117 6000 2170 4.31 1.66 172000 62200

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

109 5440 1990 4.27 1.66 156000 56900

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COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W14

Wt./ft

342

311

283

257

233

3090

4290

2800

3880

2550

3540

2310

3210

2100

2910

6 7 8 9 10

3040 3030 3010 2990 2960

4200 4170 4130 4090 4050

2750 2740 2720 2700 2680

3800 3770 3740 3700 3660

2510 2500 2480 2460 2440

3460 3440 3410 3370 3330

2280 2260 2250 2230 2210

3140 3120 3090 3060 3020

2060 2050 2040 2020 2000

2850 2820 2800 2770 2730

11 12 13 14 15

2940 2910 2880 2850 2810

4000 3950 3890 3830 3760

2660 2630 2600 2570 2540

3610 3560 3510 3460 3400

2420 2390 2370 2340 2310

3290 3240 3200 3140 3090

2190 2170 2150 2120 2090

2980 2940 2890 2850 2800

1980 1960 1940 1920 1890

2700 2660 2620 2570 2530

16 17 18 19 20

2770 2740 2700 2650 2610

3690 3620 3550 3470 3400

2510 2470 2430 2390 2360

3330 3270 3200 3130 3060

2280 2250 2210 2180 2140

3030 2970 2910 2850 2780

2060 2030 2000 1970 1940

2740 2690 2630 2570 2510

1870 1840 1810 1780 1750

2480 2430 2380 2320 2270

22 24 26 28 30

2520 2420 2320 2220 2110

3230 3060 2890 2710 2530

2270 2180 2090 2000 1900

2910 2750 2590 2430 2270

2060 1980 1900 1810 1720

2640 2500 2350 2200 2050

1870 1790 1710 1630 1550

2380 2250 2120 1980 1840

1690 1620 1550 1470 1400

2150 2030 1910 1780 1660

32 34 36 38 40

2010 1900 1790 1680 1570

2360 2180 2010 1840 1680

1800 1700 1600 1500 1410

2110 1950 1790 1640 1490

1630 1540 1450 1360 1270

1900 1760 1620 1480 1340

1470 1380 1300 1220 1140

1710 1570 1440 1320 1190

1320 1240 1170 1090 1020

1530 1410 1290 1180 1070

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

1.98 866 55.4 7100 1240 17.7 185

1.97 1200 77.0 8360 1720 15.0 120

1.97 746 50.8 5430 1030 17.5 168

1.96 1040 70.5 6400 1440 14.8 110

1.95 887 64.5 4930 1210 14.7 100

1.96 542 42.3 3150 723 17.2 140

1.94 753 58.8 3710 1000 14.6 91.6

1.95 457 38.5 2370 599 17.1 127

1.93 635 53.5 2790 832 14.5 83.4

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

101 4900 1810 4.24 1.65 141000 52000

91.4 4330 1610 4.2 1.64 124000 46100

1.97 639 46.4 4190 868 17.4 154

83.3 3840 1440 4.17 1.63 110000 41500

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

75.6 3400 1290 4.13 1.62 97400 36900

68.5 3010 1150 4.1 1.62 86200 33000

DESIGN STRENGTH OF COLUMNS

3 - 19 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W14

Wt./ft

211

193

176

159

145

1900

2640

1740

2410

1590

2200

1430

1980

1310

1810

6 7 8 9 10

1870 1860 1840 1830 1810

2580 2550 2530 2500 2470

1710 1700 1690 1670 1660

2360 2340 2320 2290 2260

1560 1550 1540 1530 1510

2150 2130 2110 2090 2060

1400 1400 1390 1380 1360

1940 1920 1900 1880 1860

1280 1280 1270 1260 1250

1770 1760 1740 1720 1700

11 12 13 14 15

1790 1780 1760 1730 1710

2440 2400 2370 2330 2280

1640 1630 1610 1590 1570

2230 2200 2170 2130 2090

1500 1480 1460 1450 1430

2030 2000 1970 1940 1900

1350 1330 1320 1300 1280

1830 1810 1780 1740 1710

1230 1220 1210 1190 1170

1670 1650 1620 1590 1560

16 17 18 19 20

1690 1660 1640 1610 1580

2240 2190 2140 2090 2040

1540 1520 1500 1470 1440

2050 2010 1960 1910 1870

1410 1380 1360 1340 1310

1860 1820 1780 1740 1700

1270 1250 1230 1200 1180

1680 1640 1600 1570 1530

1160 1140 1120 1100 1080

1530 1500 1460 1430 1390

22 24 26 28 30

1520 1460 1390 1330 1260

1940 1830 1710 1600 1490

1390 1330 1270 1210 1150

1770 1670 1560 1460 1350

1260 1210 1150 1100 1040

1610 1510 1420 1320 1220

1140 1090 1040 990 930

1440 1360 1270 1180 1100

1040 992 946 898 849

1320 1240 1160 1080 998

32 34 36 38 40

1190 1120 1050 980 912

1370 1260 1160 1050 951

1080 1020 955 892 830

1250 1150 1050 956 863

980 920 863 805 748

1130 1040 946 859 775

880 830 773 721 670

1010 928 846 767 692

800 752 703 655 608

919 842 767 694 626

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

1.95 397 35.3 1830 493 17.0 116

1.93 551 49.0 2160 684 14.4 76.0

1.96 340 32.0 1370 420 16.9 106

1.93 473 44.5 1610 583 14.3 70.1

1.92 415 41.5 1310 483 14.2 64.5

1.94 251 26.8 803 287 16.7 88.6

1.92 349 37.3 947 398 14.1 59.0

1.93 214 24.5 609 241 16.6 81.5

1.90 298 34.0 718 334 14.1 54.7

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

62.0 2660 1030 4.07 1.61 76100 29400

56.8 2400 931 4.05 1.60 68700 26700

1.94 299 29.9 1110 348 16.8 97.5

51.8 2140 838 4.02 1.60 61300 24000

46.7 1900 748 4 1.60 54400 21400

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

42.7 1710 677 3.98 1.59 49000 19400

3 - 20

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W14

Wt./ft

132

120

109 50

50†

1190

1650

1080

1500

979

1360

890

1240

811

1130

6 7 8 9 10

1160 1160 1150 1140 1130

1610 1590 1570 1550 1530

1060 1050 1040 1030 1020

1460 1450 1430 1410 1390

960 953 946 937 927

1320 1310 1300 1280 1260

873 867 860 852 843

1200 1190 1180 1160 1150

795 789 783 775 767

1100 1080 1070 1060 1040

11 12 13 14 15

1110 1100 1080 1070 1050

1510 1480 1450 1430 1390

1010 999 986 971 956

1370 1350 1320 1290 1270

917 905 893 880 866

1240 1220 1200 1170 1150

833 823 811 799 787

1130 1110 1090 1060 1040

758 749 738 727 716

1030 1010 989 969 947

16 17 18 19 20

1030 1020 997 978 958

1360 1330 1300 1260 1220

940 924 906 888 870

1240 1210 1180 1140 1110

852 837 821 804 787

1120 1090 1060 1030 1000

773 759 745 730 714

1020 991 965 938 911

704 691 678 664 650

925 902 878 853 828

22 24 26 28 30

916 872 826 780 733

1150 1070 997 920 844

831 791 749 706 663

1040 972 902 832 762

752 715 677 639 600

943 879 815 751 688

682 648 614 578 542

854 796 737 679 621

620 589 558 525 493

776 723 670 616 564

32 34 36 38

686 639 593 547

769 697 627 563

620 577 535 494

694 628 565 507

560 522 483 446

627 567 509 457

507 471 436 402

565 511 458 411

460 428 396 365

512 463 415 372

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.03 196 23.2 520 215 15.7 73.7

1.99 272 32.3 613 298 13.3 49.7

2.04 173 21.2 399 179 15.6 67.9

1.99 240 29.5 471 249 13.2 46.3

1.97 205 26.3 331 208 13.2 43.2

2.02 125 17.5 222 123 15.5 58.1

1.95 174 24.3 261 171 13.4 40.6

2.02 109 15.8 165 102 15.4 54.2

1.94 151 22.0 195 142 15.0 38.4

Effective length KL (ft) with respect to least radius of gyration ry

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

38.8 1530 548 3.76 1.67 43800 15700

35.3 1380 495 3.74 1.67 39300 14100

2.02 148 18.9 281 150 15.5 62.7

32 1240 447 3.73 1.67 35400 12700

†Flange is noncompact; see discussion preceding column load tables.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

29.1 1110 402 3.71 1.66 31700 11500

26.5 999 362 3.70 1.66 28600 10400

DESIGN STRENGTH OF COLUMNS

3 - 21 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W14

Wt./ft

50†

737 1020 667

927

612

850

548

761

477

663

431

599

386

536

6 7 8 9 10

705 694 682 667 652

963 942 918 892 863

638 628 616 604 590

871 852 830 807 781

585 576 565 553 540

798 781 760 738 714

523 515 505 494 483

714 698 680 660 638

443 432 418 404 389

598 576 552 526 498

400 390 378 365 351

540 520 498 474 449

357 347 337 325 312

482 463 443 422 399

11 12 14 16 18

635 618 579 538 495

833 800 732 661 588

575 559 524 487 447

753 724 662 598 532

526 511 479 444 408

689 662 604 544 484

470 457 428 396 364

615 591 539 486 431

372 355 319 282 245

469 439 379 319 263

336 320 287 253 220

423 395 340 286 235

298 284 254 224 194

375 350 301 252 206

20 22 24 26 28

450 406 363 321 280

516 447 381 325 280

407 367 328 290 253

467 405 345 294 253

371 334 297 262 229

424 366 311 265 229

331 297 265 233 203

377 325 276 236 203

210 176 148 126 109

213 176 148 126 109

188 157 132 113 97

191 157 132 113 97

165 138 116 99 85

167 138 116 99 85

30 31 32 34 36

244 229 214 190 169

221 207 194 172 153

199 187 175 155 138

177 166 155 138 123

95 89 83

85 79

74 69

152

152 138

138

124

110

3.2 2.7 3.12 2.56 2.97 95.7 133 84.2 117 72.1 13.3 18.5 12.2 17.0 11.0 98.4 116 76.4 90.0 55.1 88.2 123 71.7 100 56.9 8.00 6.79 7.96 6.75 7.88 28.0 20.1 26.4 19.2 24.7

2.37 100 15.3 64.9 79.0 6.68 18.2

Effective length KL (ft) with respect to least radius of gyration ry

Properties u P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

2.85 149 18.4 257 148 10.3 43.0

2.68 207 25.5 303 206 8.77 29.6

24.1 882 148 2.48 2.44 25200 4240

2.82 127 16.2 177 125 10.3 40.0

2.62 176 22.5 209 173 8.77 27.9

21.8 796 134 2.48 2.44 22800 3840

2.80 112 14.9 139 105 10.3 37.3

2.56 156 20.8 163 146 8.70 26.4

20 723 121 2.46 2.44 20700 3460

2.74 97.0 13.5 102 84.2 10.2 34.7

2.44 135 18.8 121 117 8.66 25.0

17.9 640 107 2.45 2.44 18300 3080

15.6 541 57.7 1.92 3.07 15500 1650

14.1 485 51.4 1.91 3.06 13800 1470

12.6 428 45.2 1.89 3.08 12200 1290

†Web may be noncompact for combined axial and bending stress; see AISC LRFD Specification Section B5. Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 22

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W12

Wt./ft

336

305

279

252

230

3020

4200

2740

3810

2510

3480

2270

3150

2070

2880

6 7 8 9 10

2960 2930 2900 2870 2840

4070 4020 3970 3910 3850

2680 2660 2630 2600 2570

3690 3640 3590 3540 3480

2450 2430 2400 2370 2350

3370 3330 3280 3230 3170

2210 2190 2170 2150 2120

3040 3010 2960 2920 2870

2020 2000 1980 1960 1930

2780 2740 2710 2660 2610

11 12 13 14 15

2800 2760 2720 2670 2620

3780 3700 3620 3540 3450

2530 2500 2460 2410 2370

3420 3350 3270 3190 3110

2310 2280 2240 2200 2160

3110 3050 2980 2910 2830

2090 2060 2020 1980 1950

2810 2750 2680 2620 2550

1910 1880 1840 1810 1770

2560 2500 2450 2380 2320

16 17 18 19 20

2570 2520 2470 2410 2350

3360 3260 3160 3060 2960

2320 2270 2220 2170 2120

3020 2940 2840 2750 2660

2110 2070 2020 1970 1920

2750 2670 2580 2500 2410

1910 1860 1820 1770 1730

2470 2400 2320 2240 2160

1740 1700 1660 1610 1570

2250 2180 2110 2030 1960

22 24 26 28 30

2230 2100 1980 1850 1720

2750 2540 2330 2120 1910

2000 1890 1770 1650 1530

2460 2270 2070 1880 1690

1820 1710 1600 1490 1380

2230 2050 1870 1690 1520

1630 1530 1430 1330 1230

1990 1830 1660 1500 1350

1480 1390 1300 1200 1110

1810 1650 1500 1350 1210

32 34 36 38 40

1590 1460 1340 1220 1100

1720 1520 1360 1220 1100

1410 1300 1180 1080 971

1510 1340 1200 1080 971

1270 1160 1060 960 866

1350 1200 1070 960 866

1130 1030 940 848 766

1200 1060 945 848 766

1020 931 845 761 687

1070 951 848 761 687

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.18 1180 64 12700 1770 14.5 202

2.17 1640 89 15000 2460 12.3 131

2.18 1010 59 9740 1480 14.3 184

2.16 1400 81 11500 2060 12.1 120

2.15 1220 77 9700 1720 12.0 110

2.16 738 50 6150 1030 13.9 154

2.14 1020 70 7250 1420 11.8 100

2.15 636 46 4810 868 13.8 141

2.13 883 64 5670 1210 11.7 92.0

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

98.8 4060 1190 3.47 1.85 116000 34000

89.6 3550 1050 3.42 1.84 101000 30000

2.16 878 55 8230 1240 14.1 169

81.9 3110 937 3.38 1.82 88900 26800

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

74.1 2720 828 3.34 1.81 77900 23700

67.7 2420 742 3.31 1.80 69100 21200

DESIGN STRENGTH OF COLUMNS

3 - 23 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W12

Wt./ft

210

190

170

152

136

120

1890

2630

1710

2370

1530

2120

1370

1900

1220

1700

1080

1500

6 7 8 9 10

1840 1830 1810 1790 1760

2540 2500 2470 2430 2380

1660 1650 1630 1610 1590

2290 2260 2220 2190 2150

1490 1480 1460 1440 1420

2050 2020 1990 1960 1920

1330 1320 1300 1290 1270

1830 1810 1780 1750 1710

1190 1180 1160 1150 1130

1630 1610 1590 1560 1530

1050 1040 1030 1010 1000

1440 1420 1400 1380 1350

11 12 13 14 15

1740 1710 1680 1650 1610

2330 2280 2230 2170 2110

1570 1540 1510 1480 1450

2100 2050 2000 1950 1900

1400 1380 1350 1330 1300

1880 1840 1790 1740 1690

1250 1230 1210 1180 1160

1680 1640 1590 1550 1510

1110 1090 1070 1050 1030

1490 1460 1420 1380 1340

984 966 948 928 908

1320 1290 1250 1220 1180

16 17 18 19 20

1580 1540 1510 1470 1430

2040 1980 1910 1840 1780

1420 1390 1350 1320 1280

1840 1780 1720 1650 1590

1270 1240 1210 1180 1140

1640 1580 1530 1470 1420

1130 1100 1070 1050 1020

1460 1410 1360 1310 1260

1010 980 955 928 901

1290 1250 1210 1160 1110

886 864 841 817 793

1140 1100 1060 1020 976

22 24 26 28 30

1340 1260 1170 1090 1000

1640 1490 1360 1220 1090

1210 1130 1050 973 895

1460 1340 1210 1090 967

1070 1000 933 862 792

1300 1180 1070 959 852

954 891 827 763 700

1150 1050 944 844 749

846 788 731 673 617

1020 924 831 742 656

743 692 640 589 538

892 808 726 646 569

32 34 36 38 40

919 837 759 682 616

962 852 760 682 616

819 745 674 605 546

853 755 674 605 546

724 657 593 532 480

750 664 593 532 480

638 578 520 467 421

658 583 520 467 421

561 508 456 409 369

577 511 456 409 369

489 442 395 355 320

500 443 395 355 320

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.16 558 42 3760 731 13.7 129

2.13 774 59 4430 1020 11.6 84.2

2.14 465 38 2700 610 13.5 117

2.11 646 53 3190 847 11.5 76.6

2.15 333 31 1500 397 13.3 94.7

2.11 462 44 1760 551 11.3 62.1

2.13 276 28 1120 316 13.2 84.6

2.09 383 40 1320 439 11.2 55.7

2.12 232 26 815 247 13.0 75.5

2.07 322 36 960 343 11.1 50.0

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

61.8 2140 664 3.28 1.80 61400 19000

55.8 1890 589 3.25 1.79 54100 16900

2.14 389 35 2020 493 13.4 105

2.11 540 48 2380 684 11.4 68.9

50.0 1650 517 3.22 1.78 47100 14800

44.7 1430 454 3.19 1.77 41000 13000

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

39.9 1240 398 3.16 1.77 35600 11400

35.3 1070 345 3.13 1.76 30700 9900

3 - 24

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W12

Wt./ft

106

50†

955

1330

863

1200

783

1090

710

986

646

897

584

812

6 7 8 9 10

928 919 908 896 883

1280 1260 1240 1210 1190

839 830 820 809 797

1150 1140 1120 1100 1070

761 753 744 734 723

1050 1030 1010 994 973

689 682 674 665 654

947 933 917 900 880

627 620 613 604 595

861 848 834 818 800

567 561 554 546 538

779 767 754 739 723

11 12 13 14 15

868 853 836 819 800

1160 1130 1100 1070 1040

784 770 755 739 722

1050 1020 995 966 935

711 698 684 669 654

950 926 901 874 846

643 631 619 605 591

860 838 814 790 764

585 574 562 550 537

781 761 740 717 694

529 519 508 497 485

706 687 668 647 626

16 17 18 19 20

781 761 741 719 698

1000 968 932 895 858

704 686 667 648 628

904 871 838 805 771

638 621 604 586 568

817 788 758 727 696

576 561 545 529 512

738 711 683 655 627

523 509 495 480 465

670 645 620 594 569

472 460 446 433 419

604 581 558 535 512

22 24 26 28 30

653 608 562 516 472

783 708 635 565 497

588 546 505 463 422

703 635 569 505 443

531 493 455 417 380

634 572 511 453 397

479 444 409 375 341

570 514 459 406 355

434 403 371 339 309

517 465 415 367 321

391 362 333 305 277

464 417 372 328 287

32 34 36 38 40

428 386 345 310 279

437 387 345 310 279

383 345 308 276 249

390 345 308 276 249

344 309 276 248 223

349 309 276 248 223

308 277 247 221 200

312 277 247 221 200

279 250 223 200 181

282 250 223 200 181

250 223 199 179 161

252 223 199 179 161

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.12 185 22 518 198 13.0 67.2

2.06 257 31 611 276 11.0 44.9

2.10 161 20 378 164 12.9 61.4

2.04 223 28 446 228 10.9 41.4

2.09 122 17 236 109 12.7 51.8

2.01 169 24 278 152 10.8 35.7

2.08 106 15 181 91 12.7 48.2

1.98 148 22 213 126 10.7 33.6

2.06 92.1 14 135 74 12.6 44.7

1.95 128 20 159 103 11.8 31.7

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

31.2 933 301 3.11 1.76 26700 8640

28.2 833 270 3.09 1.76 23900 7710

2.10 139 19 311 133 12.8 56.3

2.02 193 26 366 185 10.9 38.3

25.6 740 241 3.07 1.75 21200 6910

23.2 662 216 3.05 1.75 18900 6180

†Flange is noncompact; see discussion preceding column load tables.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

21.1 597 195 3.04 1.75 17000 5580

19.1 533 174 3.02 1.75 15200 4990

DESIGN STRENGTH OF COLUMNS

3 - 25 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W12

Wt./ft

520

723

477

663

450

625

404

561

361

502

6 7 8 9 10

498 490 482 472 461

680 666 649 631 611

457 449 441 432 422

623 610 594 577 559

419 408 396 383 369

566 546 524 500 475

376 366 355 343 330

507 489 469 447 424

336 327 317 306 295

453 437 419 399 378

11 12 13 14 15

450 437 424 411 397

590 568 545 521 496

411 400 388 375 362

539 518 496 474 451

354 339 322 306 289

448 421 393 365 337

317 302 287 272 257

400 375 350 324 299

282 269 256 242 228

356 334 311 288 266

16 18 20 22 24

382 352 321 291 260

471 420 370 322 276

348 320 292 263 235

428 381 334 290 247

271 237 204 173 145

310 257 209 173 145

241 210 180 152 128

274 227 184 152 128

214 187 160 135 113

243 201 163 135 113

26 28 30 32 34

231 202 176 155 137

235 202 176 155 137

207 181 158 139 123

210 181 158 139 123

124 107 93 82

109 94 82 72

96 83 72 64

38 41

110 94

98 85

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.41 89 13 106 83 10.5 38.3

2.22 124 18 125 115 8.9 27.0

2.39 78 12 94 67 10.3 35.8

2.16 108 17 111 93 8.8 25.6

2.51 127 19 136 115 6.9 21.6

2.79 75 12 86 67 8.1 28.4

2.37 105 17 101 93 6.9 20.3

2.69 66 11 59 54 8.0 26.5

2.22 92 15 69 75 6.8 19.3

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

17.0 475 107 2.51 2.10 13600 3070

15.6 425 95.8 2.48 2.11 12200 2750

2.85 92 13 116 83 8.2 30.8

14.7 394 56.3 1.96 2.64 11300 1620

13.2 350 50 1.94 2.65 10000 1420

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.8 310 44.1 1.93 2.66 8890 1260

3 - 26

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W10

Wt./ft

112

100

1010

1400

900

1250

793

1100

692

961

612

850

6 7 8 9 10

969 956 941 924 906

1330 1300 1270 1240 1210

865 853 840 824 808

1180 1160 1140 1110 1080

762 751 739 725 710

1040 1020 999 973 945

664 655 644 632 618

908 890 869 847 822

588 579 569 558 547

803 787 769 749 727

11 12 13 14 15

886 865 842 819 794

1170 1130 1090 1050 1010

789 770 750 728 706

1040 1010 970 931 892

694 677 659 639 619

916 884 851 817 782

604 588 572 555 537

796 768 738 708 677

534 520 506 490 475

703 678 652 625 597

16 17 18 19 20

768 742 715 688 660

961 915 870 824 778

682 659 634 609 584

851 810 769 727 686

599 577 556 534 511

746 709 672 635 599

519 500 481 461 442

645 612 580 547 515

458 441 424 407 389

569 540 511 482 454

22 24 26 28 30

604 548 493 440 389

688 601 518 447 389

534 483 434 386 340

605 527 453 390 340

466 422 378 336 295

527 458 393 339 295

402 362 324 287 252

452 392 335 289 252

354 319 285 252 221

398 344 294 254 221

32 34 36 38 40

342 303 270 242 219

299 265 236 212 191

259 230 205 184 166

221 196 175 157 141

194 172 153 138 124

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.06 255 27 1210 316 11.2 86.4

2.02 354 38 1430 439 9.5 56.5

2.06 214 24 883 254 11.0 77.4

2.01 298 34 1040 353 9.4 50.8

1.99 246 30 735 276 9.3 45.1

2.03 143 19 420 153 10.8 60.0

1.96 199 27 495 213 9.2 39.8

2.01 116 17 293 120 10.8 53.8

1.93 162 24 345 167 9.2 36.0

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

32.9 716 236 2.68 1.74 20400 6760

29.4 623 207 2.65 1.74 17800 5910

2.04 177 22 623 198 11.0 68.4

25.9 534 179 2.63 1.73 15300 5130

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

22.6 455 154 2.60 1.73 13000 4370

20.0 394 134 2.59 1.71 11300 3840

DESIGN STRENGTH OF COLUMNS

3 - 27 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

W10

Wt./ft

539

748

483

672

441

612

407

565

352

489

297

413

6 7 8 9 10

517 509 500 491 480

706 692 675 657 638

464 457 449 440 431

634 621 606 590 572

422 416 409 401 392

577 565 551 536 520

380 371 361 350 337

515 497 478 458 436

328 320 311 301 290

444 428 412 393 374

276 269 261 252 243

373 360 345 329 312

11 12 13 14 15

469 457 444 430 416

617 595 571 547 523

420 409 398 385 373

553 533 512 490 468

382 372 361 350 338

502 484 464 444 424

324 311 296 282 267

412 388 364 339 314

278 266 254 241 228

353 332 310 289 267

233 222 211 200 189

294 276 257 238 220

16 17 18 19 20

401 387 371 356 340

497 472 446 421 395

360 346 332 318 304

445 422 399 376 353

326 314 301 288 275

403 382 361 340 319

252 237 222 207 192

290 266 243 221 199

215 201 188 175 162

246 225 205 185 167

177 166 155 144 133

202 184 167 150 135

22 24 26 28 30

309 278 248 219 191

346 299 255 220 191

276 248 221 195 170

309 266 227 196 170

250 224 199 175 153

278 239 204 176 153

164 138 118 102 88

138 116 99 85 74

112 94 80 69 60

32 33 34 36

168 158 149 133

150 141 133 118

134 126 119 106

78 73

65 61

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.00 99 15 209 94 10.7 48.1

1.90 138 21 246 130 9.1 32.6

1.97 83 13 143 77 10.7 43.9

1.87 116 19 168 106 9.1 30.2

2.37 79 13 121 78 8.4 35.2

2.17 109 18 142 108 7.1 24.1

2.31 64 11 88 57 8.3 31.2

2.04 89 16 104 79 7.0 21.9

2.23 55 10 69 38 8.1 27.4

1.87 77 14 81 53 6.9 19.7

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

17.6 341 116 2.57 1.71 9710 3330

15.8 303 103 2.56 1.71 8640 2960

1.96 73 12 111 64 10.6 40.7

1.83 101 17 131 88 9.0 28.3

14.4 272 93.4 2.54 1.71 7800 2660

13.3 248 53.4 2.01 2.15 7100 1540

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.5 209 45.0 1.98 2.16 6000 1290

9.71 170 36.6 1.94 2.16 4880 1050

3 - 28

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

Wt./ft

603

837

523

727

431

599

358

497

315

438

279

388

6 7 8 9 10

567 555 541 526 509

770 746 721 693 662

492 481 469 455 441

667 647 624 599 572

405 396 386 374 362

549 532 513 492 470

335 327 319 309 298

454 439 423 405 386

295 288 280 272 262

399 386 372 356 339

261 255 248 240 232

354 342 329 315 300

11 12 13 14 15

492 473 453 433 412

631 598 564 529 494

425 409 391 374 355

544 515 485 455 425

349 335 321 306 291

446 422 397 372 347

287 275 263 251 238

366 345 324 303 281

252 242 231 220 208

321 303 284 265 246

223 214 204 194 184

284 268 251 234 217

16 17 18 19 20

391 370 349 328 307

460 425 392 359 328

337 318 300 281 263

394 365 335 307 279

276 260 245 229 214

321 297 272 249 226

225 211 198 185 173

260 239 219 199 180

197 185 174 162 151

228 209 191 174 157

174 163 153 143 133

200 184 168 153 138

22 24 26 28 30

266 228 194 167 146

271 228 194 167 146

228 194 165 143 124

231 194 165 143 124

185 157 134 115 100

187 157 134 115 100

148 125 107 92 80

149 125 107 92 80

129 109 93 80 70

130 109 93 80 70

114 96 82 70 61

32 33 34 35

128 120 113 107

109 103 97 91

88 83 78

70 66 62

61 58

54 51

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.03 147 21 648 177 8.8 64.0

1.96 205 28 764 246 7.5 41.9

2 120 18 464 133 8.8 55.9

1.93 167 26 547 185 7.4 36.8

1.93 69 13 163 64 8.5 39.1

1.8 96 18 192 88 7.2 26.5

1.89 56 11 104 50 8.5 35.1

1.74 78 16 123 69 7.2 24.1

1.85 48 10 81 38 8.4 32.0

1.65 67 14 95 53 7.1 22.4

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

19.7 272 88.6 2.12 1.75 7800 2530

17.1 228 75.1 2.10 1.74 6520 2160

1.97 86 14 224 95 8.7 46.7

1.87 119 20 264 132 7.4 31.1

14.1 184 60.9 2.08 1.74 5260 1750

11.7 146 49.1 2.04 1.73 4170 1390

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.3 127 42.6 2.03 1.73 3630 1210

9.13 110 37.1 2.02 1.72 3150 1070

DESIGN STRENGTH OF COLUMNS

3 - 29 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

Wt./ft

15 †

50†

252

351

217

301

225

312

180

249

136

188

6 7 8 9 10

228 219 210 200 189

303 288 271 253 235

195 188 180 171 162

260 247 232 217 200

200 191 182 172 162

265 250 233 216 198

159 152 145 137 128

211 198 185 171 156

119 114 108 102 95

158 148 137 126 115

11 12 13 14 15

178 167 155 143 132

216 197 178 160 142

152 142 132 122 112

184 168 151 136 121

151 140 129 118 107

180 162 144 128 112

119 111 102 93 84

142 127 113 100 87

88 81 74 68 61

104 92 82 71 62

16 17 18 19 20

121 110 99 89 80

125 111 99 89 80

102 93 84 75 68

106 94 84 75 68

97 87 78 70 63

98 87 78 70 63

76 68 60 54 49

55 48 43 39 35

22 24 25 26 27

66 56 51 47 44

56 47 44 40

52 44 40

40 34 31

29 24

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

2.17 48 10 81 44 6.8 27.2

1.87 67 14 95 61 5.7 18.8

2.07 39 9 52 32 6.7 24.3

1.71 54 12 61 45 5.7 17.2

1.98 65 16 172 58 5.4 21.0

2.03 35 9 78 27 6.3 25.6

1.91 49 13 92 37 5.3 17.6

1.98 26 8 54 14 6.7 20.8

1.75 36 12 64 19 6.8 15.0

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties u

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

8.25 98.0 21.7 1.62 2.13 2810 620

7.08 82.8 18.3 1.61 2.12 2370 525

2.07 47 12 146 42 6.3 31.2

7.34 53.4 17.1 1.52 1.78 1530 485

5.87 41.4 13.3 1.50 1.77 1190 378

†Flange is noncompact; see discussion preceding column load tables. Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.43 29.1 9.32 1.46 1.75 831 270

3 - 30

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS W shapes Design axial strength in kips (φ = 0.85)

Designation

Wt./ft

Effective length KL (ft) with respect to least radius of gyration ry

145

201

109

151

114

170

235

143

199

117

163

2 3 4 5 6

140 135 127 118 108

193 182 168 152 134

105 100 94 87 79

144 135 124 110 96

79 75 71 65 59

108 101 93 83 72

166 163 157 151 144

229 222 212 201 187

141 137 133 127 121

194 188 179 169 157

114 109 104 97 89

156 148 138 125 111

7 8 9 10 11

97 86 75 64 54

116 98 81 66 54

70 61 52 44 37

82 68 55 44 37

52 45 39 32 27

61 50 40 33 27

135 126 117 107 97

172 156 140 124 108

114 106 98 90 81

144 131 117 104 90

81 72 63 55 47

97 83 69 57 47

12 13 14 15 16

46 39 33 29 26

31 26 23 20

23 19 17 14

87 78 68 60 53

93 80 69 60 53

73 65 57 50 44

78 66 57 50 44

39 34 29 25 22

47 42 37 34 30

39 35 31 28 25

1.84 39 10 115 37 5.3 30.3

1.72 55 14 136 52 4.5 20.1

1.79 32 9 81 26 5.3 26.2

1.63 45 12 95 36 4.5 17.6

1.89 35 10 164 24 4.2 25.5

1.77 48 14 193 33 3.5 16.8

17 18 19 20 21

Properties u P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

2.84 35 9 78 33 4.0 18.3

2.5 49 13 92 46 3.4 12.5

4.74 32.1 4.43 0.966 2.69 917 127

2.62 26 8 54 16 3.8 14.3

2.13 36 12 64 22 3.2 10.2

3.55 22.1 2.99 0.918 2.71 630 85.6

2.24 17 6 22 9 3.8 12.0

1.72 24 9 26 13 3.2 8.9

2.68 16.4 2.19 0.905 2.73 468 62.8

5.54 26.2 9.13 1.28 1.70 747 260

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.68 21.3 7.51 1.27 1.68 608 216

3.83 11.3 3.86 1.00 1.72 324 110

DESIGN STRENGTH OF COLUMNS

3 - 31 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS HP shapes Design axial strength in kips (φ = 0.85)

Designation

HP14

Wt./ft

117

HP13

102

100

1050

1460

918

1280

799

1110

655

909

900

1250

6 7 8 9 10

1030 1020 1010 1000 993

1420 1400 1390 1370 1350

898 891 884 875 865

1240 1220 1210 1190 1170

781 775 768 760 752

1080 1060 1050 1040 1020

640 635 629 623 615

882 872 861 848 834

875 867 857 846 834

1200 1190 1170 1150 1120

11 12 13 14 15

980 967 953 938 922

1320 1300 1270 1250 1220

854 842 830 816 802

1150 1130 1110 1080 1060

742 732 721 709 696

1000 982 962 940 917

607 599 589 580 569

819 803 786 768 749

821 806 791 775 758

1100 1070 1050 1020 986

16 17 18 19 20

905 888 870 851 832

1190 1150 1120 1090 1050

788 772 756 740 723

1030 1000 974 945 915

683 670 656 641 626

893 869 844 818 791

558 547 535 523 511

729 708 687 666 644

741 722 703 684 664

954 921 888 854 820

22 24 26 28 30

792 750 707 664 620

985 913 842 771 701

687 650 613 574 536

853 790 727 665 604

595 563 529 496 462

737 682 627 572 519

485 458 430 402 374

599 553 507 462 418

623 581 539 496 454

750 681 613 547 483

32 34 36 38 40

576 533 491 450 411

633 568 507 455 411

498 460 423 387 352

545 487 435 390 352

428 395 363 332 301

467 417 372 334 301

346 319 292 267 241

375 334 298 267 241

413 374 336 301 272

425 376 336 301 272

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

217 29 1010 131 15.0 66.0

302 40 1191 182 12.7 45.1

174 25 679 101 14.8 59.0

242 35 801 140 12.6 41.1

202 31 533 106 12.5 37.6

108 18 250 52 14.5 46.8

150 25 294 72 12.3 34.2

198 28 953 119 13.2 60.1

275 38 1123 165 11.2 40.9

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

34.4 1220 443 3.59 1.66 35000 12700

30.0 1050 380 3.56 1.66 30100 10900

145 22 453 77 14.7 53.0

26.1 904 326 3.53 1.67 25800 9310

21.4 729 261 3.49 1.67 20900 7460

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

29.4 886 294 3.16 1.74 25400 8400

3 - 32

COLUMN DESIGN Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS HP shapes Design axial strength in kips (φ = 0.85)

Designation

HP13

Wt./ft

HP12

780

1080

661

918

536

744

753

1050

667

927

6 7 8 9 10

759 751 743 733 722

1040 1030 1010 993 973

642 636 628 620 611

882 870 856 840 823

520 515 509 502 494

714 704 692 679 665

729 721 712 701 690

1000 985 967 947 926

646 639 630 621 610

886 872 856 838 819

11 12 13 14 15

711 698 685 670 656

952 928 904 878 851

601 590 578 566 553

804 784 763 741 717

486 477 467 457 447

650 633 616 597 578

677 663 649 634 618

902 877 851 823 795

599 587 574 560 546

798 776 752 727 702

16 17 18 19 20

640 624 607 590 573

823 794 765 735 705

540 526 512 497 482

693 669 644 618 592

436 424 413 401 388

559 539 518 497 476

601 584 567 548 530

765 735 705 674 642

531 516 500 484 467

675 648 621 593 565

22 24 26 28 30

537 500 462 425 389

644 584 524 467 411

451 420 388 356 325

540 488 438 389 342

363 337 311 285 260

433 391 350 310 272

492 454 416 378 342

580 518 459 402 350

434 400 366 332 300

510 455 402 351 306

32 34 36 38 40

353 319 286 256 231

361 320 286 256 231

295 266 237 213 192

300 266 237 213 192

235 211 189 169 153

239 211 189 169 153

307 273 243 218 197

308 273 243 218 197

268 238 213 191 172

269 238 213 191 172

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

165 24 624 90 13.0 53.2

229 33 735 124 11.1 36.9

127 20 384 65 12.9 47.0

177 28 453 90 11.0 33.4

129 23 243 60 10.9 30.2

170 25 732 95 12.3 54.0

235 34 862 132 10.4 36.9

143 22 506 75 12.2 48.9

199 30 597 105 10.3 34.0

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

25.5 755 250 3.13 1.74 21700 7150

21.6 630 207 3.10 1.74 18000 5940

93 17 206 43 12.8 41.2

17.5 503 165 3.07 1.75 14400 4720

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

24.6 650 213 2.94 1.75 18600 6090

21.8 569 186 2.92 1.75 16300 5320

DESIGN STRENGTH OF COLUMNS

3 - 33 Y

Fy = 36 ksi Fy = 50 ksi

COLUMNS HP shapes Design axial strength in kips (φ = 0.85)

Designation

HP12

Wt./ft

HP10

HP8

563

782

474

659

514

714

379

527

324

451

6 7 8 9 10

545 538 531 523 514

747 735 721 706 689

459 453 447 440 432

629 618 607 594 579

491 483 474 464 453

670 655 638 619 599

362 356 349 341 333

494 482 469 455 440

302 294 286 276 266

408 393 377 360 342

11 12 13 14 15

504 494 482 471 458

671 651 631 610 588

424 415 406 396 385

564 547 530 512 493

441 429 415 401 387

577 555 531 506 481

324 314 304 294 283

423 406 388 369 350

255 243 232 219 207

322 302 282 262 242

16 17 18 19 20

446 432 419 405 391

565 542 518 495 471

374 363 351 339 327

474 454 434 414 394

372 357 341 326 310

456 430 404 379 354

272 260 249 237 225

331 312 293 274 255

195 182 170 158 146

222 202 184 165 149

22 24 26 28 30

362 333 304 275 247

423 376 332 288 251

303 278 253 229 206

353 314 276 240 209

279 248 219 191 166

305 259 221 191 166

202 179 157 136 119

219 185 158 136 119

123 104 88 76 66

32 34 36 38 40

221 196 174 157 141

183 163 145 130 117

146 129 115 103 93

104 92 82 74 67

58 52 46 41 37

P wo (kips) P wi (kips/in.) P wb (kips) P fb (kips) L p (ft) L r (ft)

116 19 311 54 12.0 43.0

161 26 366 75 10.2 30.7

88 16 188 38 11.9 38.7

122 22 221 53 10.1 28.3

168 28 599 90 8.7 31.1

79 15 202 36 10.0 35.9

110 21 238 50 8.5 25.6

75 16 309 40 8.1 35.7

104 22 364 56 6.9 24.4

Effective length KL (ft) with respect to least radius of gyration ry

36 0

Properties

A (in.2) Ix (in.4) Iy (in.4) ry (in.) Ratio rx / ry Pex (KL )2 / 10 4 Pey (KL )2 / 10 4

18.4 472 153 2.88 1.76 13500 4370

15.5 393 127 2.86 1.76 11200 3630

121 20 508 65 10.2 45.6

16.8 294 101 2.45 1.71 8400 2890

12.4 210 71.7 2.41 1.71 6050 2060

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

10.6 119 40.3 1.95 1.72 3420 1150

3 - 34

COLUMN DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 35

Steel Pipe and Structural Tubing

The design strengths in the tables that follow are tabulated for the effective lengths in feet KL (with respect to the least radius of gyration, r or ry), indicated at the left of each table. They are applicable to axially loaded members in accordance with Section E2 of the LRFD Specification. For discussion of effective length, range of l / r, strength about major axis, combined axial and bending stress, and sample problems, see General Notes. Properties and factors are listed at the bottom of the tables for checking strength about the strong axis. Steel Pipe Columns

Design strengths for unfilled pipe columns are tabulated for Fy = 36 ksi. Steel pipe manufactured to ASTM A501 furnishes Fy = 36 ksi, and ASTM A53, Type E or S, Gr. B furnishes Fy = 35 ksi and may be designed for the strengths permitted for Fy = 36 ksi steel. The heavy horizontal lines within the table indicate Kl / r = 200. No values are listed beyond Kl / r = 200. Structural Tube Columns

Design strengths for square and rectangular structural tube columns are tabulated for Fy = 46 ksi. Structural tubing is manufactured to Fy = 46 ksi under ASTM A500, Gr. B. All tubes listed in the column load tables satisfy Section B5 of the LRFD Specification. The heavy horizontal lines appearing within the tables indicate Kl / r = 200. No values are listed beyond Kl / r = 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 36

COLUMN DESIGN

Fy = 36 ksi

COLUMNS Standard steel pipe Design axial strength in kips (φ = 0.85)

Nominal Dia.

31⁄2

Wall Thickness

0.375

0.365

0.322

0.280

0.258

0.237

0.226

0.216

Weight per ft

49.56

40.48

28.55

18.97

14.62

10.79

9.11

7.58

Effective length KL (ft)

36 ksi 0

447

364

257

171

132

6 7 8 9 10

440 438 436 433 429

357 354 351 348 344

249 246 243 239 235

162 159 155 151 147

122 118 115 111 106

86 82 78 74 70

70 67 63 58 54

56 52 48 43 39

11 12 13 14 15

426 422 418 413 409

340 336 331 326 321

231 227 222 216 211

142 138 133 127 122

102 97 92 86 81

65 60 55 51 46

49 45 40 36 32

35 30 26 23 20

16 17 18 19 20

404 399 393 387 381

315 309 303 297 291

205 199 193 187 181

116 111 105 99 94

76 71 66 61 56

41 37 33 30 27

28 25 22 20 18

17 15 14 12

22 24 25 26 28

369 356 349 342 328

277 263 256 249 234

168 155 149 142 129

83 72 67 62 53

47 39 36 33 29

22 19 17

30 31 32 34 36

313 306 298 283 268

219 212 205 190 176

117 111 105 93 83

47 44 41 36 32

25 23

37 38 40

260 253 237

169 162 148

79 75 67

3.17 7.23 1.51

2.68 4.79 1.34

Properties 2

Area A (in. ) I (in.4) r (in.)

14.6 279 4.38

11.9 161 3.67

8.40 72.5 2.94

5.58 28.1 2.25

4.30 15.2 1.88

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.23 3.02 1.16

DESIGN STRENGTH OF COLUMNS

3 - 37

Fy = 36 ksi

COLUMNS Extra strong steel pipe Design axial strength in kips (φ = 0.85)

Nominal Dia.

31⁄2

Wall Thickness

0.500

0.432

0.375

0.337

0.318

0.300

Weight per ft

65.42

54.74

43.39

28.57

20.78

14.98

12.50

10.25

Effective length KL (ft)

36 ksi 0

588

493

392

257

187

135

113

6 7 8 9 10

579 576 573 569 564

483 479 475 470 465

379 375 369 364 357

243 238 232 226 219

172 168 162 156 149

119 114 108 102 95

96 91 85 79 72

75 69 64 58 52

11 12 13 14 15

559 554 549 543 536

460 453 447 440 433

351 343 336 327 319

212 205 197 189 180

143 135 128 121 113

89 82 75 68 62

66 60 53 47 42

46 40 34 30 26

16 18 19 20 21

530 515 508 500 492

425 409 400 391 382

310 291 282 272 262

172 154 145 137 128

105 91 83 76 70

56 44 40 36 32

37 29 26 23 21

23 18 16

22 24 26 28 30

483 465 447 428 408

373 354 334 314 294

252 231 211 191 172

120 103 88 76 66

63 53 45 39 34

30 25

32 34 36 38 40

388 368 348 328 308

273 253 234 215 196

154 136 121 109 98

58 52 46

19.2 362 4.33

16.1 212 3.63

12.8 106 2.88

6.11 20.7 1.84

4.41 9.61 1.48

3.68 6.28 1.31

3.02 3.89 1.14

Properties Area A (in.2) I (in.4) r (in.)

8.40 40.5 2.19

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 38

COLUMN DESIGN

Fy = 36 ksi

COLUMNS Double-extra strong steel pipe Design axial strength in kips (Ď&#x2020; = 0.85)

Nominal Dia.

Wall Thickness

0.875

0.864

0.750

0.674

0.600

Weight per ft

72.42

53.16

38.55

27.54

18.58

Effective length KL (ft)

36 ksi 0

652

477

346

248

167

6 7 8 9 10

629 621 612 601 590

448 437 426 413 399

315 305 293 281 268

214 203 191 179 165

131 120 108 96 84

11 12 13 14 15

578 565 551 536 521

385 369 353 336 319

254 239 224 209 194

152 139 125 112 100

73 62 53 46 40

16 17 18 19 20

505 489 472 455 438

302 285 268 250 234

179 165 151 137 124

88 78 70 62 56

35 31

22 24 26 28 30

403 367 333 299 266

201 170 145 125 109

102 86 73 63

32 34 36 38 40

235 208 186 166 150

96 85

21.3 162 2.76

15.6 66.3 2.06

11.3 33.6 1.72

8.10 15.3 1.37

Properties Area A (in.2) I (in.4) r (in.)

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.47 5.99 1.05

DESIGN STRENGTH OF COLUMNS

3 - 39

Fy = 46 ksi

COLUMNS Square structural tubing Design axial strength in kips (φ = 0.85)

Nominal Size

16× ×16

Thickness

1⁄

Wt./ft

103.30

89.68

68.31

1190

1030

786

6 7 8 9 10

1180 1170 1170 1170 1160

1020 1020 1010 1010 1000

11 12 13 14 15

1150 1150 1140 1130 1120

16 17 18 19 20

14× ×14 1⁄

12× ×12 3⁄

93.34

1⁄

3⁄

5⁄

76.07

58.10

48.86

1070

876

669

563

777 774 770 766 761

1050 1050 1040 1030 1020

862 857 851 845 838

658 655 650 645 640

554 551 548 544 539

993 985 977 969 960

756 751 745 739 732

1010 1000 992 979 966

830 821 812 803 792

634 628 621 614 606

535 529 524 518 511

1120 1110 1100 1090 1080

950 940 930 919 907

725 717 710 701 693

953 939 924 908 892

781 770 758 746 733

598 590 581 571 562

504 497 490 482 474

21 22 23 24 25

1070 1060 1040 1030 1020

895 883 870 857 844

684 675 665 655 645

875 858 841 823 805

719 706 692 677 663

552 542 531 520 510

466 457 449 440 431

26 27 28 29 30

1010 994 981 967 954

830 816 802 787 772

635 624 614 603 592

786 767 748 729 710

648 633 617 602 586

498 487 475 464 452

421 412 402 392 383

32 34 36 38 40

925 896 865 835 803

742 711 680 648 616

569 546 522 498 474

670 631 592 553 515

555 523 491 460 429

428 404 381 357 333

363 343 323 303 283

30.4 1200 6.29

26.4 791 5.48

27.4 580 4.60

22.4 485 4.66

17.1 380 4.72

14.4 324 4.75

Effective length KL (ft)

5⁄

46 ksi

Properties A (in2) I (in.4) r (in.)

20.1 615 5.54

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 40

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Square structural tubing Design axial strength in kips (φ = 0.85)

10× ×10

Nominal Size Thickness Wt./ft

76.33

62.46

47.90

40.35

32.63

876

719

551

465

375

6 7 8 9 10

855 847 839 829 818

703 697 690 682 674

539 534 529 524 517

455 451 447 442 437

11 12 13 14 15

807 794 781 767 752

664 655 644 633 621

510 503 495 487 478

16 17 18 19 20

736 720 703 686 668

608 595 582 568 553

21 22 23 24 25

650 631 612 593 573

26 27 28 29 30 32 34 36 38 40

1⁄

3⁄

8× ×8

5⁄

59.32

1⁄

3⁄

5⁄

1⁄

48.85

37.69

31.84

25.82

680

563

434

366

297

367 364 360 357 353

654 644 634 622 609

542 535 526 517 507

418 413 407 400 392

353 349 343 338 331

287 283 279 274 269

431 425 418 411 404

348 343 338 332 326

595 580 564 548 531

496 484 471 458 444

384 375 366 356 345

324 317 309 301 293

264 258 252 245 238

468 459 449 438 427

396 388 380 371 362

320 314 307 300 293

513 494 476 456 437

430 415 400 385 369

335 324 312 301 289

284 275 265 256 246

231 224 216 209 201

538 523 508 493 477

416 405 394 382 370

353 343 334 324 314

286 278 270 263 255

418 398 379 360 341

354 338 322 307 291

277 266 254 242 230

236 226 216 206 196

193 185 177 169 161

554 534 515 495 476

461 446 430 414 398

358 347 335 323 311

305 295 285 275 265

247 239 231 223 215

322 304 286 268 251

276 261 246 232 218

219 207 196 185 174

187 177 168 158 149

153 146 138 131 123

437 400 364 328 296

367 337 307 278 251

287 264 242 220 199

245 225 206 188 170

199 184 168 154 139

221 195 174 156 141

191 169 151 136 122

153 136 121 109 98

132 117 104 93 84

109 97 86 77 70

22.4 321 3.78

18.4 271 3.84

14.1 214 3.90

11.9 183 3.93

17.4 153 2.96

14.4 131 3.03

11.1 106 3.09

9.36 90.9 3.12

7.59 75.1 3.15

Effective length KL (ft)

1⁄

46 ksi

Properties A (in2) I (in.4) r (in.)

9.59 151 3.96

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 41

Fy = 46 ksi

COLUMNS Square structural tubing Design axial strength in kips (φ = 0.85) 7× ×7

Nominal Size Thickness

5⁄ 8

1⁄ 2

3⁄ 8

6× ×6

5⁄ 16

1⁄ 4

3⁄ 16

5⁄ 8

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

50.81 42.05 32.58 27.59 22.42 17.08 42.30 35.24 27.48 23.34 19.02 14.53

46 ksi

Effective length KL (ft)

Wt./ft

584

485

375

317

258

196

486

407

316

268

219

167

6 7 8 9 10

553 543 531 518 503

461 452 443 432 421

357 351 344 336 327

302 297 291 285 278

246 242 237 232 226

188 185 181 177 173

451 438 425 410 394

379 369 358 346 333

295 288 280 271 262

251 245 239 231 223

205 200 195 189 183

157 153 149 145 140

11 12 13 14 15

488 472 454 437 418

409 396 382 368 353

318 308 298 288 277

270 262 254 245 236

220 214 207 200 193

168 164 159 153 148

377 359 341 322 303

320 306 291 276 260

252 241 230 219 207

215 206 197 187 178

176 169 162 154 146

135 130 124 119 113

16 17 18 19 20

399 380 361 342 323

338 322 307 291 276

265 254 242 230 218

226 217 207 197 187

185 177 170 162 154

142 136 130 124 118

284 265 246 227 210

245 229 214 199 184

195 184 172 160 149

168 158 148 138 129

138 131 123 115 107

107 101 95 89 83

22 24 26 28 30

285 248 214 184 161

245 215 187 161 140

195 172 151 130 113

167 148 130 113 98

138 123 108 94 81

107 95 84 73 63

175 147 125 108 94

155 131 111 96 84

127 107 91 79 69

111 93 80 69 60

92 78 67 57 50

72 61 52 45 39

32 34

141 125

123 109

100 88

86 76

72 63

56 49

83 73

73 65

60 53

53 47

44 39

34 30

35 36 37 38 39

118 111 106 100 95

103 97 92 87 83

83 79 74 71 67

72 68 64 61 58

60 57 54 51 48

47 44 42 40 38

61 58

50 48 45

44 41 39 37

37 35 33 31

29 27 26 24 23

12.4 57.3 2.15

10.4 50.5 2.21

8.08 41.6 2.27

6.86 36.3 2.30

5.59 30.3 2.33

4.27 23.8 2.36

Properties 2

A (in ) I (in.4) r (in.)

14.9 97.5 2.56

12.4 84.6 2.62

9.58 68.7 2.68

8.11 59.5 2.71

6.59 49.4 2.74

5.02 38.5 2.77

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 42

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Square structural tubing Design axial strength in kips (φ = 0.85) 51⁄2×51⁄2

Nominal Size

5× ×5

Thickness

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

Wt./ft

24.93

21.21

17.32

13.25

28.43

22.37

19.08

15.62

11.97

8.16

Effective length KL (ft)

46 ksi 0

286

244

199

152

327

257

219

179

138

6 7 8 9 10

264 256 248 238 228

225 219 212 204 195

184 179 173 167 161

141 137 133 129 124

294 282 270 257 242

233 224 215 205 194

199 192 184 176 167

163 158 152 145 138

126 121 117 112 107

86 83 80 77 73

11 12 13 14 15

218 207 195 184 172

187 177 168 158 148

154 146 139 131 123

118 113 107 101 95

228 213 197 182 167

183 172 160 149 137

158 148 139 129 119

131 123 115 107 99

101 95 89 84 78

70 66 62 58 54

16 17 18 19 20

160 149 137 126 115

139 129 119 110 101

115 107 99 92 84

89 83 77 72 66

152 138 124 111 100

126 115 104 93 84

110 100 91 82 74

92 84 77 69 63

72 66 60 55 50

50 46 42 38 35

22 24 26 28 30

96 80 68 59 51

84 70 60 52 45

70 59 50 43 38

55 47 40 34 30

83 70 59 51 45

70 59 50 43 37

61 52 44 38 33

52 44 37 32 28

41 34 29 25 22

29 24 21 18 15

31 32 33 34 35

48 45 43 40

42 40 37 35

35 33 31 29 28

28 26 25 23 22

26 24

21 19

15 14 13

6.58 22.8 1.86

5.61 20.1 1.89

4.59 16.9 1.92

3.52 13.4 1.95

2.40 9.41 1.98

Properties 2

A (in ) I (in.4) r (in.)

7.33 31.2 2.07

6.23 27.4 2.10

5.09 23.0 2.13

3.89 18.1 2.16

8.36 27.0 1.80

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 43

Fy = 46 ksi

COLUMNS Square structural tubing Design axial strength in kips (φ = 0.85) 41⁄2×41⁄2

Nominal Size

4× ×4

Thickness

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

Wt./ft

19.82

16.96

13.91

10.70

7.31

Effective length KL (ft)

1⁄ 2

3⁄ 8

21.63

17.27

5⁄ 16

1⁄ 4

14.83 12.21

3⁄ 16

1⁄ 8

9.42

6.46

46 ksi 0

228

195

160

123

249

199

170

140

108

6 7 8 9 10

201 192 182 171 160

172 165 157 148 139

142 136 130 123 115

110 105 100 95 90

75 72 69 65 62

208 195 180 166 151

168 158 148 137 125

145 137 128 119 110

120 114 107 100 92

93 89 83 78 72

64 61 58 54 50

11 12 13 14 15

149 137 125 114 103

129 119 110 100 91

107 100 92 84 76

84 78 72 66 60

58 54 50 46 42

136 121 107 93 81

114 102 91 81 70

100 90 81 72 63

84 76 68 61 54

66 60 54 49 43

46 42 38 34 31

16 17 18 19 20

92 82 73 66 59

81 73 65 58 53

69 62 55 49 45

55 49 44 39 36

38 35 31 28 25

71 63 56 50 46

62 55 49 44 40

55 49 44 39 35

47 42 37 34 30

38 34 30 27 24

27 24 21 19 17

21 22 23 24 25

54 49 45 41 38

48 43 40 36 34

41 37 34 31 29

32 29 27 25 23

23 21 19 17 16

41 38 34

36 33 30 27

32 29 27 25

28 25 23 21 19

22 20 18 17 16

16 14 13 12 11

27 28 29

29 27

25 23

20 18 17

14 13 12

Properties 2

A (in ) I (in.4) r (in.)

5.83 16.0 1.66

4.98 14.2 1.69

4.09 12.1 1.72

3.14 9.60 1.75

2.15 6.78 1.78

6.36 12.3 1.39

5.08 10.7 1.45

4.36 9.58 1.48

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.59 8.22 1.51

2.77 6.59 1.54

1.90 4.70 1.57

3 - 44

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Square structural tubing Design axial strength in kips (φ = 0.85)

31⁄2×31⁄2

Nominal Size

3× ×3

Thickness

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

Wt./ft

12.7

10.51

8.15

5.61

10.58

8.81

6.87

4.75

146

121

122

101

6 7 8 9 10

118 109 100 90 81

99 92 84 76 69

77 72 66 60 54

54 50 46 42 39

90 80 71 61 52

76 68 61 53 45

60 54 49 43 37

42 39 35 31 27

11 12 13 14 15

71 62 54 46 40

61 54 46 40 35

49 43 38 32 28

35 31 27 23 20

44 37 31 27 23

38 32 27 24 21

32 27 23 19 17

23 20 17 14 12

16 17 18 19 20

35 31 28 25 23

31 27 24 22 20

25 22 20 18 16

18 16 14 13 11

21 18

18 16 14

15 13 12

11 10 9 8

21 22

14 13

10 9

3.73 6.09 1.28

3.09 5.29 1.31

2.39 4.29 1.34

3.11 3.58 1.07

2.59 3.16 1.10

2.02 2.60 1.13

1.40 1.90 1.16

Effective length KL (ft)

46 ksi

Properties A (in2) I (in.4) r (in.)

1.65 3.09 1.37

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 45

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

Nominal Size 16× ×12

16× ×8

14× ×12

14× ×10

Thickness

1⁄

Wt./ft

89.68

76.07

82.88

63.21

76.07

1030

876

952

726

876

6 7 8 9 10

1020 1010 1010 998 990

848 838 827 815 801

938 933 927 920 912

715 712 707 702 697

11 12 13 14 15

982 973 963 952 941

786 771 754 736 717

904 895 886 876 865

16 17 18 19 20

929 916 903 889 875

697 677 657 635 614

22 24 26 28 30

845 813 781 746 711

32 34 36 38 40

676 640 604 568 533

3⁄

12× ×10

3⁄

58.10

1⁄

3⁄

5⁄

1⁄

69.27

53.00

44.60

36.03

669

796

609

513

414

857 850 843 834 825

655 650 644 638 631

778 772 765 757 748

596 591 586 580 573

502 498 493 488 483

405 402 399 395 390

691 684 677 669 661

815 803 791 779 765

623 615 606 597 587

738 728 716 704 692

566 558 550 541 531

477 470 463 456 448

386 380 375 369 363

854 842 829 816 803

653 644 634 625 615

751 737 721 705 689

576 565 554 542 530

679 665 650 636 620

522 511 501 489 478

440 431 422 413 404

356 349 342 335 327

569 525 480 436 393

774 744 713 681 648

593 571 548 524 499

655 620 584 547 511

504 478 451 424 396

589 556 522 488 454

454 430 404 379 353

384 363 342 321 300

311 295 278 261 244

352 313 279 250 226

615 581 547 514 480

474 448 423 398 372

474 438 403 369 335

368 341 315 289 264

420 387 355 324 293

328 302 278 254 231

278 257 237 217 197

227 210 193 177 162

17.1 476 284 1.29 4.08

20.4 419 316 1.15 3.94

15.6 330 249 1.15 4.00

13.1 281 213 1.15 4.03

10.6 230 174 1.15 4.06

Effective length KL (ft) with respect to least radius of gyration

1⁄

46 ksi

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

26.4 962 618 1.25 4.84

22.4 722 244 1.72 3.30

24.4 699 552 1.13 4.76

18.6 546 431 1.13 4.82

22.4 608 361 1.30 4.02

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 46

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

12× ×8

Nominal Size

12× ×6

Thickness

5⁄ 8

1⁄ 2

3⁄ 8

5⁄ 16

5⁄ 8

1⁄ 2

3⁄ 8

5⁄ 16

Wt./ft

76.33

62.46

47.90

40.35

67.82

55.66

42.79

36.10

876

719

551

465

778

641

493

414

6 7 8 9 10

845 835 822 809 794

695 687 677 666 655

534 527 520 512 503

450 445 439 433 425

731 715 697 677 655

604 591 577 561 543

466 456 445 434 421

392 384 376 366 355

11 12 13 14 15

778 760 742 722 702

642 628 613 598 582

494 483 473 461 449

417 409 400 390 380

632 607 581 555 528

525 505 485 464 442

407 393 378 362 346

344 332 320 307 293

16 17 18 19 20

681 659 637 614 591

565 547 530 511 493

437 424 410 397 383

370 359 348 336 325

500 473 445 418 390

420 398 375 353 331

329 313 296 279 262

280 266 252 238 224

22 24 26 28 30

544 497 451 405 362

455 417 380 343 307

355 326 298 270 243

301 277 253 230 207

338 288 245 211 184

288 247 211 182 158

230 199 170 146 128

197 171 146 126 110

32 34 36 38 39

320 283 252 227 215

273 241 215 193 184

217 192 171 154 146

185 164 146 131 125

162 143 128 115 109

139 123 110 99 94

112 99 89 80 75

97 86 76 69 65

205

174

139

119

16.4 287 96.0 1.73 2.42

12.6 228 77.2 1.72 2.48

10.6 196 66.6 1.71 2.51

Effective length KL (ft) with respect to least radius of gyration

46 ksi

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

22.4 418 221 1.38 3.14

18.4 353 188 1.37 3.20

14.1 279 149 1.37 3.26

11.9 239 128 1.37 3.28

19.9 337 112 1.73 2.37

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 47

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

10× ×8

Nominal Size

10× ×6

Thickness

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

Wt./ft

55.66

42.79

36.10

29.23

48.85

37.69

31.84

25.82

641

493

414

336

563

434

366

297

6 7 8 9 10

619 611 602 592 581

476 470 463 456 448

401 396 390 384 377

325 321 317 312 306

529 517 504 490 474

409 400 391 380 368

345 338 330 321 312

281 275 269 261 254

11 12 13 14 15

568 556 542 528 513

439 429 419 408 397

370 362 354 345 335

300 294 287 280 273

457 439 421 402 382

356 343 329 315 300

302 291 279 267 255

246 237 228 218 209

16 17 18 19 20

497 481 465 448 431

386 374 361 349 336

326 316 306 295 285

265 257 249 241 232

362 342 322 302 282

285 270 255 240 225

243 230 218 205 193

199 189 179 169 159

22 24 26 28 30

396 361 327 294 262

310 284 258 232 208

263 241 220 198 178

215 197 180 163 146

244 208 177 153 133

196 169 144 124 108

169 146 124 107 93

139 121 103 89 77

32 34 36 38 39

231 205 183 164 156

184 163 146 131 124

158 140 125 112 106

130 116 103 93 88

117 104 92 83 79

95 84 75 67 64

82 73 65 58 55

68 60 54 48 46

148

118

101

11.1 145 65.4 1.49 2.43

9.36 125 56.5 1.48 2.46

7.59 103 46.9 1.48 2.49

Effective length KL (ft) with respect to least radius of gyration

46 ksi

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

16.4 226 160 1.19 3.12

12.6 180 127 1.19 3.18

10.6 154 109 1.19 3.21

8.59 127 90.2 1.19 3.24

14.4 181 80.8 1.50 2.37

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 48

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

10× ×5

Nominal Size

8× ×6

Thickness

3⁄ 8

5⁄ 16

1⁄ 4

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

Wt./ft

35.13

29.72

24.12

42.05

32.58

27.59

22.42

403

341

277

485

375

317

258

6 7 8 9 10

370 359 347 334 319

315 306 295 284 272

256 249 241 232 222

454 444 432 419 404

352 344 335 325 315

298 292 284 276 268

243 238 232 225 218

11 12 13 14 15

304 288 272 255 239

260 246 233 219 205

212 201 191 179 168

389 373 357 340 322

303 292 279 266 253

258 248 238 227 217

211 203 195 186 178

16 17 18 19 20

222 206 189 174 159

191 178 164 151 138

157 146 135 124 114

305 287 269 252 235

240 227 213 200 187

205 194 183 172 161

169 160 151 142 133

22 24 26 28 30

131 110 94 81 71

115 96 82 71 62

95 80 68 59 51

201 170 145 125 109

161 137 117 101 88

140 119 102 88 76

116 99 85 73 64

32 34 36 38 39

62 55

54 48

45 40

96 85 76 68

77 68 61 55 52

67 59 53 48 45

56 49 44 40 38

Effective length KL (ft) with respect to least radius of gyration

46 ksi

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

10.3 128 42.9 1.72 2.04

8.73 110 37.2 1.71 2.07

7.09 91.2 31.1 1.72 2.09

12.4 103 65.7 1.25 2.31

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.58 83.7 53.5 1.25 2.36

8.11 72.4 46.4 1.25 2.39

6.59 60.1 38.6 1.25 2.42

DESIGN STRENGTH OF COLUMNS

3 - 49

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

8× ×4

Nominal Size

7× ×5

Thickness

5⁄ 8

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

Wt./ft

42.30

35.24

27.48

23.34

19.02

35.24

27.48

23.34

19.02

14.53

486

407

316

268

219

407

316

268

219

167

6 7 8 9 10

415 393 368 341 314

351 333 313 292 270

276 262 248 233 216

235 224 212 199 185

192 184 174 164 153

369 357 342 327 311

288 279 268 257 245

245 238 229 220 210

200 194 187 180 172

154 149 144 138 132

11 12 13 14 15

287 259 233 207 182

248 226 204 183 162

200 183 167 150 135

172 158 144 130 117

142 131 120 109 98

294 276 258 240 222

232 219 205 192 178

199 188 177 165 154

164 155 146 137 127

126 119 113 106 99

16 17 18 19 20

160 141 126 113 102

143 126 113 101 91

120 106 95 85 77

104 92 82 74 67

88 78 70 62 56

205 187 170 154 139

165 151 138 126 114

142 131 120 110 100

118 109 101 92 84

92 85 79 72 66

22 24 25 26 27

84 71

76 63 58

63 53 49 45

55 46 43 39 37

47 39 36 33 31

115 97 89 82 76

94 79 73 67 62

82 69 64 59 55

69 58 54 50 46

54 46 42 39 36

71 66 62 58

58 54 51 47 44

51 47 44 41 39

43 40 37 35 33

34 31 29 27 26

24 23

6.86 45.5 26.9 1.30 1.98

5.59 38.0 22.6 1.30 2.01

4.27 29.8 17.7 1.29 2.04

Effective length KL (ft) with respect to least radius of gyration

46 ksi

28 29 30 31 32 33 34

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

12.4 85.1 27.4 1.76 1.49

10.4 75.1 24.6 1.75 1.54

8.08 61.9 20.6 1.73 1.60

6.86 53.9 18.1 1.73 1.62

5.59 45.1 15.3 1.72 1.65

10.40 63.5 37.2 1.31 1.90

8.08 52.2 30.8 1.30 1.95

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 50

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

7× ×4

Nominal Size

6× ×4

Thickness

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

Wt./ft

24.93

21.21

17.32

13.25

28.43

22.37

19.08

15.62

11.97

287

244

199

152

327

257

219

179

138

6 7 8 9 10

249 236 223 208 193

213 202 191 179 167

175 166 158 148 138

134 128 121 114 107

279 263 246 228 210

222 211 198 185 171

190 181 171 160 148

157 149 141 132 123

121 115 109 102 96

11 12 13 14 15

178 163 148 133 118

154 141 129 116 104

128 118 107 97 88

99 92 84 76 69

191 173 155 137 121

157 143 129 116 103

136 125 113 102 91

114 104 95 85 77

89 81 74 67 61

16 17 18 19 20

105 93 83 74 67

92 82 73 65 59

78 69 62 56 50

62 55 49 44 40

106 94 84 75 68

90 80 71 64 58

80 71 63 57 51

68 60 54 48 44

54 48 43 38 35

21 22 23 24 25

61 55 51 46 43

54 49 45 41 38

45 41 38 35 32

36 33 30 28 25

62 56 51 47

52 48 44 40 37

46 42 39 36 33

39 36 33 30 28

31 29 26 24 22

26 27

30 27

23 22

20 19

5.61 26.2 13.8 1.38 1.57

4.59 22.1 11.7 1.37 1.60

3.52 17.4 9.32 1.37 1.63

Effective length KL (ft) with respect to least radius of gyration

46 ksi

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

7.33 44.0 18.1 1.56 1.57

6.23 38.5 16.0 1.56 1.60

5.09 32.3 13.5 1.55 1.63

3.89 25.4 10.7 1.54 1.66

8.36 35.3 18.4 1.39 1.48

6.58 29.7 15.6 1.38 1.54

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 51

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

6× ×3

Nominal Size

5× ×4

Thickness

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

Wt./ft

25.03

19.82

16.96

13.91

10.70

19.82

16.96

13.91

10.70

288

228

195

160

123

228

195

160

123

6 7 8 9 10

216 194 172 150 129

176 160 144 127 111

152 138 125 111 97

126 116 105 94 83

98 90 82 74 65

195 185 173 161 148

168 159 149 139 129

139 132 124 116 107

107 102 96 90 84

11 12 13 14 15

109 92 78 67 59

95 81 69 59 52

84 71 61 52 46

72 62 53 45 39

57 50 42 36 32

135 123 110 98 86

118 107 97 87 77

99 90 82 73 65

77 71 64 58 52

16 17 18 19 20

52 46 41

45 40 36 32

40 36 32 28

35 31 27 25 22

28 25 22 20 18

76 67 60 54 49

67 60 53 48 43

58 51 46 41 37

46 41 36 33 29

44 40 37 34 31

39 36 33 30 28

33 30 28 26 24

27 24 22 20 19

4.09 14.1 9.98 1.19 1.56

3.14 11.2 7.96 1.19 1.59

Effective length KL (ft) with respect to least radius of gyration

46 ksi

21 22 23 24 25 26

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

7.36 27.7 8.91 1.76 1.10

5.83 23.8 7.78 1.74 1.16

4.98 21.1 6.98 1.75 1.18

4.09 17.9 6.00 1.73 1.21

3.14 14.3 4.83 1.72 1.24

5.83 18.7 13.2 1.19 1.50

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.98 16.6 11.7 1.20 1.53

3 - 52

COLUMN DESIGN

Fy = 46 ksi

COLUMNS Rectangular structural tubing Design axial strength in kips (φ = 0.85)

5× ×3

Nominal Size

4× ×3

Thickness

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

Wt./ft

21.63

17.27

14.83

12.21

9.42

6.46

12.70

10.51

8.15

5.61

249

199

170

140

108

146

121

6 7 8 9 10

183 164 145 125 107

151 137 122 107 93

132 120 108 95 83

110 100 91 81 71

85 78 71 63 56

59 55 50 45 40

110 100 89 78 67

93 84 76 67 58

73 66 60 53 47

51 47 42 38 33

11 12 13 14 15

89 75 64 55 48

79 67 57 49 43

71 60 51 44 39

61 52 45 38 33

49 42 36 31 27

35 30 26 22 19

57 48 41 35 31

50 42 36 31 27

40 34 29 25 22

29 25 21 18 16

16 17 18 19 20

42 37

38 33 30

34 30 27 24

29 26 23 21

23 21 19 17 15

17 15 13 12 11

27 24 21

24 21 19 17

19 17 15 14

14 12 11 10 9

1.90 6.44 2.93 1.48 1.24

3.73 7.45 4.71 1.26 1.12

3.09 6.45 4.10 1.26 1.15

2.39 5.23 3.34 1.25 1.18

1.65 3.76 2.41 1.25 1.21

Effective length KL (ft) with respect to least radius of gyration

46 ksi

Properties 2

A (in ) Ix (in.4) Iy (in.4) rx / ry ry (in.)

6.36 16.9 7.33 1.52 1.07

5.08 14.7 6.48 1.50 1.13

4.36 13.2 5.85 1.50 1.16

3.59 11.3 5.05 1.49 1.19

2.77 9.06 4.08 1.50 1.21

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 53

Double Angles and WT Shapes

Double Angles

Design strengths are tabulated for the effective length KL in feet with respect to both the X-X and Y-Y axes. Design strengths about the X-X axis are in accordance with LRFD Specification Section E2. For buckling about the Y-Y axis the shear deformation of the connectors may require the slenderness to be increased in accordance with the equations for (Kl / r)m in Section E4. Incorporating this slenderness ratio, the design strengths are determined from Section E2 or E3, whichever governs. In addition to the usual limit state of flexural buckling for columns, double angle and WT shapes in compression may also be governed by the limit state of flexural-torsional buckling, in accordance with Section E3 of the LRFD Specification. This has been included in the tables. Discussion under Section C2 of the LRFD Specification Commentary points out that for trusses it is usual practice to take K = 1.0. No values are listed beyond KL / r = 200. For buckling about the X-X axis, both angles move parallel so that the design strength is not affected by the connectors. For buckling about the Y-Y axis, the design strengths are tabulated for the indicated number n of intermediate connectors. For connectors with snug-tight bolts or different spacings, the design strength must be recalculated using the corresponding modified slenderness and LRFD Specification Section E4. The number of intermediate connectors given in the table was selected so the design strength about the Y-Y axis is 90 percent or greater of that for buckling of the two angles acting as a unit. If fewer connectors are used, the strength must be reduced accordingly. According to Section E4 of the LRFD Specification, the connectors must be spaced so that the slenderness ratio a / rz of the individual angle does not exceed 75 percent of the governing slenderness ratio of the built-up member. In designing members fabricated of two angles connected to opposite faces of a gusset plate, Chapter J of the LRFD Specification states that eccentricity between the gage lines and gravity axis may be neglected. In the following tables, this eccentricity is neglected. The tabulated loads for double angles referred to in the Y-Y axis assume a 3⁄8-in. spacing between angles. These values are conservative when a wider spacing is provided. Example 3-5 illustrates a method for determining the design strength when a 3⁄4-in. gusset plate is used. Examples 3-6 and 3-7 demonstrate how to determine the number of connectors when Klx / rx governs and when the modified (Kly / ry)m governs.

EXAMPLE 3-5

Given:

Solution:

Using 50 ksi steel, determine the design strength with respect to the Y-Y axis of a double angle member of 8×8×1 angles with an effective length equal to 12 ft, and connected to a 3⁄4-in. thick gusset plate. ry = 3.53 in. (from Double Angle Column Design Strength Table for two L8×8×1 with 3⁄8-in. plate) ry′ = 3.67 in. (from Part 1, Properties, Two Equal-Leg Angles, two L8×8×1 with 3⁄4-in. plate) ry 3.53 = = 0.962 ry′ 3.67 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 54

COLUMN DESIGN

Equivalent effective length = 0.962 × 12 ft = 11.5 ft Enter Column Design Strength Table for two L8×8×1 with reference to Y-Y axis for effective lengths between 10 and 15 feet, read 1,120 and 1,000 kips, respectively.



Equivalent design strength = 1,120 − (1,120 − 1,000) ×



11.5 − 10  15 − 10 

= 1,084 kips EXAMPLE 3-6

Given:

Solution:

Using a double angle member of 5×3×1⁄2 angles (short legs back to back) and 36 ksi steel, with Lx = 10 ft and Ly = 20 ft, and a factored axial load of 70 kips, determine the number of connectors required. Assume K = 1.0 and that the intermediate connectors are snug-tight bolted. Kx Lx = 10 ft, Kx lx / rx = (10 × 12) / 0.829 = 145 Ky Ly = 20 ft, Ky ly / ry = (20 × 12) / 2.5 = 96 The X-X axis governs. From the X-X axis portion of the table φPn = 76 kips > 70 kips o.k. Find number of connectors required based on Section E4: a / rz ≤ 0.75KLx / rx a ≤ 0.75(KLx / rx)rz = 0.75 (145) 0.648 = 70 in. Assume two connectors are required; a = (10 × 12) / 3 = 40 in. a / rz = 40 / rz = 40.0 / 0.648 = 61.7 Check that modified (Ky ly / ry)m does not govern. According to Specification Equation E4-1,  962 + 61.7  2 = 114 (Ky ly / ry)m = √ Modified ly′ = 114ry / Ky = 114 (2.50 in.) / 1.0 = 285 in. = 23.8 ft Inspection of the tables indicates that Kxlx / rx still governs, therefore one connector is required every 40 inches.

EXAMPLE 3-7

Given:

Using the same steel shape and bolts as Example 3-6, with Lx = 10 ft and Ly = 30 ft, determine the number of connectors required and the corresponding maximum design strength. Assume K = 1.0. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

Solution:

3 - 55

Kx Lx = 10 ft, Kx lx / rx = (10 × 12) / 0.829 = 145 Ky Ly = 30 ft, Ky ly / ry = (30 × 12) / 2.5 = 144 Kx lx / rx appears to govern, so try one connector in the 10-ft length. Check (Ky ly / ry)m with a / rz = 5 × 12 / 0.648 = 93  1442 + 932 = 171 (Ky ly / ry)m = √ Since (Ky ly / ry)m governs, the Y-Y portion of the table gives a design strength of 72 kips provided four connectors are used in the 30-ft length. This gives a spacing of 30 ft / 5 = 6.0 ft. Check if (Kyly / ry)m governs with = (6.0 × 12) / 0.648 = 111 a / rz  1442 + 111 2 = 182 (Kyly / ry)m = √ (Ky ly / ry)m still governs, so four connectors at 6.0 ft would be appropriate. Verify that a / rz < 0.75 governing Kl / r : 111 < (0.75 × 182 = 137) o.k. Modified ly′ = 182ry / Ky = 182(2.5 in.) / 1.0 = 455 in. = 37.9 ft From the tables, the design strength is 45 kips. The design strength can be increased by closer spacing of the connectors, which reduces (Kyly / ry)m .

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 56

COLUMN DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 57

Fy = 36 ksi Fy = 50 ksi Y

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Equal legs 8

in. back to back of angles

3/ ′′ 8

8× ×8

Size 11⁄8

Thickness Wt./ft

7⁄ 8

113.8

X-X AXIS

102.0

3⁄ 4

90.0

5⁄ 8

77.8

1⁄ 2

65.4

52.8

1030 1420

918

1280

811

1130

701

973

586

763

432

550

10 14 18 22 26

901 1190 795 1000 674 795 548 596 427 430

808 715 608 496 388

1070 902 719 542 391

715 633 539 440 345

945 799 638 482 349

619 549 469 384 303

819 694 556 422 306

518 461 395 325 257

651 559 456 354 261

387 348 302 253 205

478 417 349 278 212

30 34 38 39 40

323 251 201 191 182

294 229 183 174 165

262 204 163 155 147

230 179 143 136 129

196 153 122 116 110

159 124 99 94 90

123

105

1030 1420

918

1280

811

1130

701

973

586

763

432

550

10 15 20 25 30

939 1260 869 1130 779 975 677 803 570 632

834 772 692 601 506

1120 1000 864 711 560

726 670 599 517 432

965 865 741 606 473

615 569 509 440 368

808 728 626 514 402

495 460 413 359 302

609 555 486 407 325

345 324 297 263 226

406 378 341 295 244

35 40 45 50 55

465 366 290 235 194

477 366 290 235 194

412 324 257 208 172

422 324 257 208 172

349 272 216 175 145

354 272 216 175 145

297 232 184 150 124

301 232 184 150 124

244 191 152 124 103

248 191 152 124 103

188 150 120 98 82

193 150 120 98 82

56 57 58 59

188 181 175 169

166 161 155

140 135 130

120 116 112

99 96

79 76

No. of a Connectors

3⁄

Effective length KL (ft) with respect to indicated axis

Y-Y AXIS

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

33.5 2.42 3.55

30.0 2.44 3.53

26.5 2.45 3.51

22.9 2.47 3.49

19.2 2.49 3.47

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

15.5 2.50 3.45

3 - 58

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85) 3⁄ 8

Equal legs in. back to back of angles 6× ×6

Size Thickness Wt./ft

74.8

Y-Y AXIS

X-X AXIS

Effective length KL (ft) with respect to indicated axis

7⁄ 8

3⁄ 4

66.2

57.4

1⁄ 2

48.4

3⁄ 8

39.2

29.8

673

935

597

829

517

718

435

604

352

470

243

309

8 10 12 14 16

580 533 481 426 370

759 676 586 495 407

515 473 428 379 330

675 601 522 441 364

447 412 373 332 290

587 524 457 388 321

377 347 315 280 245

495 442 386 328 272

306 283 257 229 201

389 351 308 265 222

214 200 183 166 147

264 241 216 190 164

18 22 26 30 31

315 218 156 117

326 218 156 117

282 196 140 105

292 196 140 105

248 173 124 93

259 173 124 93

210 147 105 79

220 147 105 79

173 122 87 65 61

182 122 87 65 61

129 94 68 51 48

138 94 68 51 48

673

935

597

829

517

718

435

604

352

470

243

309

10 12 14 16 18

595 567 537 503 468

787 738 683 625 565

523 499 472 442 410

690 647 598 547 494

449 428 404 379 352

590 552 511 468 422

371 353 334 313 291

483 453 420 385 348

289 275 260 244 226

359 338 315 289 262

187 180 172 163 153

219 210 199 186 173

20 22 24 26 28

431 394 357 321 286

505 446 389 334 288

378 345 312 280 249

441 388 338 290 250

324 295 267 239 213

377 332 288 247 214

268 244 221 198 176

310 273 238 204 176

208 189 171 152 135

235 207 181 155 135

142 131 120 109 97

158 143 128 113 98

30 32 34 36 38

252 221 196 175 157

218 192 170 152 137

187 164 146 130 117

154 136 120 108 97

118 104 92 82 74

86 76 68 61 55

40 42 43 44 45

142 129 123 117 112

123 112 107 102 98

106 96 91 87

87 79 76 72

67 61 58 56

50 45 43

Properties of 2 A (in2) rx (in.) ry (in.)

5⁄ 8

22.0 1.80 2.73

19.5 1.81 2.70

No. of a Connectors

3/ ′′ 8

angles—3⁄8

in. back to back

16.9 1.83 2.68

14.2 1.84 2.66

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.5 1.86 2.64

8.72 1.88 2.62

DESIGN STRENGTH OF COLUMNS

3 - 59

Fy = 36 ksi Fy = 50 ksi Y

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Equal legs in. back to back of angles 5× ×5

Size 7⁄ 8

Thickness Wt./ft

X-X AXIS

3⁄ 4

54.5

Effective length KL (ft) with respect to indicated axis

1⁄ 2

47.2

3⁄ 8

32.4

5⁄ 16

24.6

20.6

490

680

425

591

291

404

217

282

169

215

6 8 10 12 14

433 393 348 299 251

573 502 423 343 268

377 344 305 264 222

500 440 372 304 239

259 237 211 183 155

344 304 259 213 169

194 178 160 140 119

244 219 189 159 129

152 141 127 113 97

189 171 150 128 107

16 18 20 22 24

204 162 132 109 91

206 162 132 109 91

182 145 117 97 82

183 145 117 97 82

128 103 83 69 58

130 103 83 69 58

99 80 65 54 45

102 80 65 54 45

82 68 55 46 38

86 68 55 46 38

42 39

35 33

25 26

Y-Y AXIS

3/ ′′ 8

490

680

425

591

291

404

217

282

169

215

6 8 10 12 14

457 438 414 388 358

617 582 540 492 441

394 377 357 334 309

531 501 464 423 379

260 249 236 221 204

345 326 303 277 249

184 176 168 157 145

224 214 201 186 168

136 131 126 119 111

160 154 146 137 127

16 18 20 22 24

327 295 263 231 201

389 337 287 240 202

282 254 226 199 172

334 289 246 205 173

186 168 149 131 114

219 190 161 135 114

133 120 107 93 81

150 132 113 95 81

103 94 84 75 66

115 103 90 78 66

26 28 30 32 34

172 149 130 114 101

148 127 111 98 87

97 84 73 65 57

69 60 52 46 41

57 49 43 38 34

36 37 38

90 85 81

77 73 69

51 48

37 35

A (in ) rx (in.) ry (in.)

16.0 1.49 2.30

13.9 1.51 2.28

Properties of 2 angles—3⁄8 in. back to back 2

No. of a Connectors

3⁄ 8

9.50 1.54 2.24

7.22 1.56 2.22

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.05 1.57 2.21

3 - 60

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85) 3⁄ 8

Equal legs in. back to back of angles 4× ×4

Size 3⁄ 4

Thickness Wt./ft

37.0

X-X AXIS

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 8

1⁄ 2

31.4

3⁄ 8

25.6

5⁄ 16

19.6

1⁄ 4

16.4

13.2

334

463

282

392

230

319

175

243

146

191

108

138

4 6 8 10 12

306 275 237 195 154

411 354 288 220 159

259 233 201 167 132

349 301 245 189 137

212 191 166 138 110

285 247 203 157 115

162 146 127 106 85

217 189 156 121 89

135 123 107 90 72

172 152 127 101 76

101 92 82 70 57

126 112 96 78 61

14 16 18 19 20

117 89 71 63

100 77 61 54 49

84 65 51 46 41

65 50 40 36 32

56 43 34 30 27

45 35 28 25 22

46 35 28 25 22

334

463

282

392

230

319

175

243

146

191

108

138

6 8 10 12 14

303 284 262 237 210

406 371 332 288 245

254 238 219 198 176

339 311 277 241 204

204 191 176 158 140

270 247 220 191 161

151 141 130 117 104

196 180 161 141 119

121 114 106 96 85

148 138 125 110 95

85 81 76 70 63

100 94 87 79 70

16 18 20 22 24

183 157 132 109 92

202 163 132 109 92

153 131 109 91 76

168 135 109 91 76

122 104 86 72 60

133 106 86 72 60

90 77 64 53 45

98 79 64 53 45

74 63 53 44 37

79 64 53 44 37

56 48 41 35 29

60 50 41 35 29

26 28 29 30 31

78 67 63 59 55

65 56 52 49 46

51 44 41 39

38 33 31 29

32 27 26 24

25 22 20

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

10.9 1.19 1.88

9.22 1.20 1.86

7.50 1.22 1.83

5.72 1.23 1.81

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.80 1.24 1.80

3.88 1.25 1.79

No. of a Connectors

3/ ′′ 8

DESIGN STRENGTH OF COLUMNS

3 - 61

Fy = 36 ksi Fy = 50 ksi Y

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Equal legs 8

in. back to back of angles 31⁄2×31⁄2

Size 3⁄ 8

Thickness Wt./ft

X-X AXIS

5⁄ 16

17.0

Effective length KL (ft) with respect to indicated axis

1⁄ 4

14.4

11.6

152

211

128

175

100

129

2 4 6 8 10

148 137 120 100 78

204 182 152 117 84

125 115 101 84 67

169 152 127 99 72

97 90 80 67 54

125 114 97 77 58

12 14 16 17 18

59 43 33 29

50 37 28 25 22

41 30 23 21 18

152

211

128

175

100

129

6 8 10 12 14

130 120 108 94 81

170 152 131 109 88

107 98 89 78 67

136 123 106 89 72

80 74 67 60 52

96 88 78 67 56

16 18 20 22 24

67 54 44 37 31

69 54 44 37 31

56 45 37 30 26

57 45 37 30 26

43 36 29 24 20

44 36 29 24 20

3/ ′′ 8

No. of a Connectors

3⁄

Y-Y axis

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

4.97 1.07 1.61

4.18 1.08 1.60

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.38 1.09 1.59

3 - 62

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85) Y

3⁄ 8

Equal legs in. back to back of angles 3× ×3

Size 1⁄ 2

Thickness Wt./ft

18.8

X-X AXIS

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

3⁄ 8

5⁄ 16

14.4

1⁄ 4

12.2

3⁄ 16

9.8

7.42

168

234

129

179

109

151

118

2 4 5 6 7

162 145 133 120 106

222 190 169 146 123

125 112 103 93 83

171 147 131 114 97

105 94 87 79 70

144 124 111 97 82

85 77 71 64 57

112 98 88 77 66

59 54 50 46 41

74 66 60 54 47

8 9 10 11 12

92 79 66 54 46

101 81 66 54 46

72 62 52 43 36

80 64 52 43 36

61 53 45 37 31

68 55 45 37 31

50 43 37 31 26

56 46 37 31 26

37 32 28 24 20

41 34 28 24 20

13 14 15

39 34

31 27 23

26 23 20

22 19 16

17 15 13

168

234

129

179

109

151

118

2 4 6 8 10

163 155 143 128 111

223 209 187 161 132

123 117 108 97 84

167 156 140 121 99

101 97 89 80 70

136 128 115 99 82

79 75 70 63 55

100 95 86 75 63

50 48 45 42 37

59 57 53 48 42

12 14 16 18 20

94 76 60 47 38

104 78 60 47 38

70 57 45 36 29

78 58 45 36 29

58 47 37 29 24

64 48 37 29 24

46 38 29 23 19

50 38 29 23 19

32 27 22 17 14

35 28 22 17 14

22 23

32 29

24 22

20 18

16 14

12 11

A (in ) rx (in.) ry (in.)

Properties of 2 angles—3⁄8 in. back to back 2

No. of a Connectors

3/ ′′ 8

5.50 0.898 1.43

4.22 0.913 1.41

3.55 0.922 1.40

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.88 0.930 1.39

2.18 0.939 1.38

DESIGN STRENGTH OF COLUMNS

3 - 63

Fy = 36 ksi Fy = 50 ksi Y

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Equal legs 8

in. back to back of angles 21⁄2×21⁄2

Size 3⁄ 8

Thickness Wt./ft

X-X AXIS Y-Y AXIS

5⁄ 16

11.8

Effective length KL (ft) with respect to indicated axis

1⁄ 4

10.0

3⁄ 16

8.2

6.14

106

147

125

101

2 3 4 5 6

101 94 86 76 66

137 125 110 93 76

85 80 73 65 56

116 106 93 79 65

69 65 59 53 46

94 86 76 65 53

52 48 44 40 35

66 61 54 47 40

7 8 9 10 11

55 45 36 29 24

59 46 36 29 24

47 39 31 25 21

51 39 31 25 21

39 32 26 21 17

42 33 26 21 17

30 25 20 16 13

32 25 20 16 13

106

147

125

101

2 3 4 5 6

101 99 95 90 85

138 133 126 118 109

84 82 79 75 71

114 110 105 98 90

67 65 63 60 56

89 86 82 77 71

46 45 44 42 40

57 55 53 50 47

7 8 9 10 11

79 73 66 60 53

98 88 77 67 57

66 61 55 50 44

82 73 64 55 47

52 48 44 40 35

64 58 51 44 37

37 35 32 29 26

44 40 35 31 27

12 13 14 15 16

47 41 35 31 27

48 41 35 31 27

39 34 29 26 22

40 34 29 26 22

31 27 23 20 18

32 27 23 20 18

23 20 17 15 13

17 18 19 20

24 21 19 17

20 18 16 14

16 14 13

12 11 9

Properties of 2 angles—3⁄8 in. back to back A (in2) rx (in.) ry (in.)

3.47 0.753 1.21

2.93 0.761 1.20

2.38 0.769 1.19

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.80 0.778 1.18

3/ ′′ 8

No. of a Connectors

3⁄

3 - 64

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85) Y

3⁄ 8

Equal legs in. back to back of angles 2× ×2

Size 3⁄ 8

Thickness Wt./ft

9.4

X-X AXIS

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 16

1⁄ 4

7.84

3⁄ 16

6.38

1⁄ 8

4.88

3.30

116

2 3 4 5 6

76 69 59 49 38

103 88 72 55 39

65 58 50 42 33

87 75 61 47 34

53 48 41 35 28

71 62 51 39 29

40 37 32 27 21

54 47 39 30 22

25 23 20 17 14

31 28 24 19 15

7 8 9 10

29 22 18

25 19 15 12

21 16 13 10

16 13 10 8

11 9 7 6

116

2 3 4 5 6

79 76 72 67 61

108 102 95 86 76

67 64 60 56 51

90 86 79 72 63

54 51 49 45 41

72 68 63 57 51

39 38 36 33 31

52 49 46 42 37

22 21 20 19 18

26 25 24 22 20

7 8 9 10 11

55 49 43 37 31

66 55 46 37 31

46 41 36 30 26

55 46 38 31 26

37 33 29 24 21

44 37 30 25 21

27 24 21 18 15

32 27 22 18 15

16 15 13 11 10

18 16 14 12 10

12 13 14 15 16

26 22 19 17 15

22 18 16 14 12

17 15 13 11 10

13 11 9 8 7

8 7 6 5 5

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

2.72 0.594 1.01

2.30 0.601 1.00

1.88 0.609 0.989

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.43 0.617 0.977

0.960 0.626 0.965

No. of a Connectors

3/ ′′ 8

DESIGN STRENGTH OF COLUMNS

3 - 65

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Long legs 3⁄8 in. back to back of angles 3⁄ 4

1⁄ 2

Wt./ft

88.4

67.6

46.0

X-X AXIS

1⁄ 2

57.4

39.2

846

376

479

673

935 517 718 321 408

10 12 14 16 18

704 667 626 582 535

932 865 792 715 637

541 513 483 450 415

717 667 613 555 496

339 323 306 287 267

419 395 368 340 310

10 12 14 16 18

597 567 533 496 457

792 736 676 612 546

460 437 412 384 354

611 569 523 475 425

289 276 262 246 230

358 338 315 292 267

20 22 24 26 28

488 440 393 348 305

560 486 415 353 305

379 343 308 273 241

438 381 328 279 241

247 226 205 185 165

280 250 221 193 167

20 22 24 26 28

418 378 338 300 264

482 419 359 306 264

324 294 264 235 207

376 328 283 241 208

212 195 177 160 143

242 216 192 168 146

30 32 34 36 38

265 233 207 184 165

210 184 163 146 131

146 128 113 101 91

30 32 34 36 38

230 230 202 202 179 179 160 160 143 143

181 159 141 126 113

181 127 127 159 112 112 141 99 99 126 88 88 113 79 79

41 42

142

142 112 107

112 107

78 74

40 42 43

129 129 102 102 117 117 92 92

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

3⁄ 4

74.8

796 1110 609

8× ×4 1

71 65 62

796 1110 609

846

376

479

729 703 672 636 595

978 932 876 811 741

537 519 496 470 440

709 677 638 593 543

301 293 282 270 256

357 346 331 314 295

6 8 10 12 14

568 741 416 533 234 275 520 657 381 473 217 251 464 562 339 405 197 223 404 463 294 333 175 192 342 368 248 263 150 159

935 517 718 321 408

16 18 20 22 24

551 506 459 412 366

667 592 517 445 378

408 375 340 305 271

490 435 381 328 279

240 223 205 187 169

273 249 225 200 176

16 18 20 22 24

282 238 194 160 135

300 238 194 160 135

203 162 132 110 93

26 28 32

321 279 214

323 279 214

238 207 159

239 207 159

151 133 103

152 133 103

25 26

125 115

34 36 40 41 42

190 170 138 131 125

141 126 103 98

92 82 67

rx (in.) ry (in.)

26.0 2.49 2.52

19.9 2.53 2.48

13.5 2.56 2.44

22.0 2.52 1.61

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

204 126 127 162 103 103 132 84 84 110 70 70 93 60 60 85

55 3

Properties of 2 angles—3⁄8 in. back to back (in2)

71 65 62

6 8 10 12 14

673

No. of a Connectors

8× ×6

Size Thickness

16.9 2.55 1.55

11.5 2.59 1.51

3 - 66

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

3⁄ 4

1⁄ 2

3⁄ 8

Wt./ft

52.4

35.8

27.2

X-X AXIS

Effective length KL (ft) with respect to indicated axis

0 471 655 310 401 205 254

3⁄ 4

5⁄ 8

1⁄ 2

3⁄ 8

47.2

40.0

32.4

24.6

36 0

425 591 358 497 291 388 201 256

8 10 12 14 16

427 404 378 349 318

571 529 481 431 379

283 268 252 233 214

355 332 306 278 248

189 181 171 161 149

230 218 204 188 172

8 10 12 14 16

371 343 312 279 246

488 439 385 329 276

313 290 265 237 209

413 371 327 281 236

18 20 22 24 26

286 255 224 194 166

328 278 232 195 166

194 174 154 135 117

219 190 162 137 117

137 125 113 101 89

155 138 121 105 90

18 20 22 24 26

212 180 150 126 108

225 182 150 126 108

181 155 129 109 93

193 148 158 110 119 156 127 128 96 100 129 106 106 82 82 109 89 89 69 69 93 76 76 59 59

28 143 143 100 100 30 125 125 88 88 32 110 110 77 77 34 97 97 68 68

78 68 59 53

28 30 31 32

93 81 76

80 70 65

36 37

47 44

87 82

61 58

0 471 655 310 401 205 254

Y-Y AXIS

6× ×4

No. of a Connectors

7× ×4

Size Thickness

6 8 10 12 14

394 362 325 284 242

511 456 393 327 262

238 221 200 176 151

286 260 229 196 161

146 137 127 115 101

167 156 142 126 108

16 18 20 22 24

201 162 132 110 92

204 126 128 162 103 103 132 84 84 110 70 70 92 59 59

87 74 61 51 43

90 74 61 51 43

25 26 27

85 79 73

80 70 65

254 236 216 193 171

65 57 53

325 294 260 225 191

65 57 53

179 167 154 140 125

51 44 41 39

220 202 182 161 140 b

51 44 41 39

425 591 358 497 291 388 201 256

6 8 10 12 14

367 339 306 270 232

481 432 375 315 256

302 279 252 222 191

394 354 308 259 210

236 218 197 174 150

293 266 233 198 162

153 144 132 118 104

181 167 151 132 112

16 18 20 22 24

195 160 136 113 95

211 161 165 126 129 167 132 132 103 103 136 107 107 84 84 113 89 89 70 70 95 75 75 59 59

89 75 61 51 43

93 75 61 51 43

26 27 28

81 75 70

37 35

85 79 73

55 51

81 75 70

64 59

50 47

Properties of 2 angles—3⁄8 in. back to back A (in2) rx (in.) ry (in.)

No. of a Connectors

Long legs 3⁄8 in. back to back of angles

15.4 2.22 1.62

10.5 2.25 1.57

7.97 2.27 1.55

13.9 1.88 1.69

11.7 1.90 1.67

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.50 1.91 1.64

7.22 1.93 1.62

DESIGN STRENGTH OF COLUMNS

3 - 67

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Long legs 3⁄8 in. back to back of angles

Wt./ft

23.4

Y-Y AXIS

X-X AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 16

19.6

191

243

145

179

8 10 12 14 16

170 159 146 133 119

209 192 173 153 133

130 123 114 105 95

157 146 134 120 106

18 20 22 24 26

105 92 78 66 56

114 95 79 66 56

85 75 65 56 48

93 79 67 56 48

28 30 32

49 42 37

41 36 32

191

243

4 6 8 10 12

148 139 127 113 98

14 16 18 20 22 23

3⁄ 4

1⁄ 2

39.6

3⁄ 8

27.2

5⁄ 16

20.8

355

493

245

340 183 238 143 182

4 6 8 10 12

337 317 290 259 225

460 233 421 219 372 202 318 181 262 158

14 16 18 20 22

191 158 127 103 85

209 161 127 103 85

41 36 32

24 25 26

72 66

51 47 44

145

179

355

493

245

176 163 147 127 105

107 101 94 85 75

122 115 106 94 80

4 6 8 10 12

325 303 274 241 206

437 215 396 200 345 182 289 160 232 136

284 258 226 189 152

152 142 129 114 98

81 66 53 43 36

84 66 53 43 36

64 53 43 35 29

66 53 43 35 29

14 16 18 20 22

170 144 114 93 77

188 144 114 93 77

113 90 72 58 48

117 90 72 58 48

82 65 52 43 35

84 65 52 43 35

65 53 43 35 29

68 53 43 35 29

24 25

65 60

318 292 260 223 185

17.4

175 165 152 137 120

224 208 187 163 138

137 130 120 109 97

172 161 146 129 111

135 149 104 113 113 116 87 90 91 91 71 71 74 74 58 58 61 61 48 48

85 72 60 49 41

93 76 61 49 41

34 31 29

51 47 44

40 37 34

A (in ) rx (in.) ry (in.)

186 113 134 171 107 125 152 98 114 130 88 99 107 77 84

6.84 1.94 1.39

5.74 1.95 1.38

340 183 238 143 182

Properties of 2 angles—3⁄8 in. back to back 2

No. of a Connectors

3⁄ 8

Thickness

5× ×31⁄2

No. of a Connectors

6× ×31⁄2

Size

11.6 1.55 1.53

8.00 1.58 1.49

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.09 1.60 1.46

5.12 1.61 1.45

3 - 68

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

5× ×3

Size 1⁄ 2

Thickness Wt./ft

25.6

X-X AXIS

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

3⁄ 8

5⁄ 16

19.6

1⁄ 4

16.4

13.2

230

319

172

223

134

170

117

2 4 6 8 10

227 219 206 189 170

313 298 274 244 210

170 164 155 143 129

220 210 195 176 154

132 128 122 113 103

168 161 151 137 121

95 92 88 82 76

115 112 105 97 88

12 14 16 18 20

149 128 107 87 70

175 141 110 87 70

114 98 82 68 55

130 107 86 68 55

91 79 68 56 46

104 88 71 57 46

68 61 53 45 38

78 67 56 47 38

22 24 26 27

58 49 42

45 38 32

38 32 27

31 26 22 21

230

319

172

223

134

170

117

2 4 6 8 10

207 195 177 153 128

276 255 223 184 143

146 138 125 110 92

179 167 149 126 101

107 102 94 84 72

128 121 110 95 78

71 68 64 58 51

80 77 72 64 55

12 14 16 18 20

101 81 62 49 40

109 81 62 49 40

74 57 44 35 28

76 57 44 35 28

59 46 36 29 23

61 46 36 29 23

43 35 28 22 18

45 35 28 22 18

No. of a Connectors

Long legs 3⁄8 in. back to back of angles

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

7.50 1.59 1.25

5.72 1.61 1.23

4.80 1.61 1.22

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.88 1.62 1.21

DESIGN STRENGTH OF COLUMNS

3 - 69

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Long legs 3⁄8 in. back to back of angles 1⁄ 2

Thickness Wt./ft

23.8

X-X AXIS

3⁄ 8

5⁄ 16

18.2

15.4

12.4

214

298

163

227

137

179

101

129

2 4 6 8 10

210 198 179 155 130

289 266 232 191 148

160 151 137 120 101

221 204 178 147 116

134 127 115 101 85

174 162 143 120 96

99 94 87 77 66

126 118 106 91 75

12 14 16 18 20

104 80 61 48 39

109 80 61 48 39

81 63 48 38 31

86 63 48 38 31

69 54 41 33 26

73 54 41 33 26

55 44 34 27 22

59 44 34 27 22

214

298

163

227

137

179

101

129

2 4 6 8 10

203 196 183 167 148

276 262 240 211 180

150 144 135 124 110

200 190 174 155 132

121 116 110 101 90

150 143 133 120 104

84 81 77 72 65

99 96 91 83 74

12 14 16 18 20

128 108 88 74 60

147 116 93 74 60

95 80 66 53 43

108 86 66 53 43

78 66 54 43 35

87 70 54 43 35

58 50 42 34 28

64 53 42 34 28

22 24 25 26

50 42 39 36

35 30 28 25

29 25 23

23 20 18

Y-Y AXIS

1⁄ 4

No. of a Connectors

4× ×31⁄2

Size

Effective length KL (ft) with respect to indicated axis

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

7.00 1.23 1.58

5.34 1.25 1.56

4.49 1.26 1.55

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.63 1.27 1.54

3 - 70

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

4× ×3

Size 1⁄ 2

Thickness Wt./ft

22.2

X-X AXIS

Effective length KL (ft) with respect to indicated axis

3⁄ 8

17.0

1⁄ 4

14.4

11.6

199

276

152

211

127

166

120

2 4 6 8 10

195 184 167 146 122

269 248 217 179 141

149 141 128 112 94

206 190 166 138 109

125 118 108 94 80

162 151 133 112 90

93 88 81 72 62

117 110 99 85 70

12 14 16 18 20

99 77 59 46 38

105 77 59 46 38

76 60 46 36 29

81 60 46 36 29

65 51 39 31 25

69 51 39 31 25

51 41 32 25 21

55 42 32 25 21

199

276

152

211

127

166

120

2 4 6 8 10

187 177 161 142 120

253 235 207 173 137

138 131 119 105 89

183 171 151 127 101

111 105 96 85 73

137 129 116 99 81

77 74 69 62 54

92 88 80 71 59

12 14 16 18 20

97 76 61 49 39

108 80 61 49 39

72 56 43 35 28

76 56 43 35 28

59 46 36 29 23

62 46 36 29 23

45 36 28 23 18

47 36 28 23 18

21 22

36 33

Y-Y AXIS

5⁄ 16

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

No. of a Connectors

Long legs 3⁄8 in. back to back of angles

6.50 1.25 1.33

4.97 1.26 1.31

4.18 1.27 1.30

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.38 1.28 1.29

DESIGN STRENGTH OF COLUMNS

3 - 71

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Long legs 3⁄8 in. back to back of angles

Wt./ft

15.8

X-X AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 16

1⁄ 4

13.2

10.8

140

195

118

162

119

2 4 6 8 10

137 127 112 93 74

188 169 142 111 80

115 107 95 79 63

157 141 119 94 69

90 84 75 63 51

116 106 91 73 55

12 14 16 17 18

56 41 32 28 25

48 35 27 24 21

39 29 22 20 18

140

195

118

162

2 4 6 8 10

131 124 114 101 86

176 164 146 123 99

107 102 94 83 71

12 14

71 56

76 59

16 18 20

45 36 29

3⁄ 8

1⁄ 4

14.4

9.8

129

179

110

2 4 6 8 10

126 117 103 86 69

173 156 131 103 75

83 77 69 59 47

107 97 84 68 52

40 29 22 20 18

12 14 16 18

52 39 30 23

53 39 30 23

37 27 21 17

119

129

179

110

140 131 118 100 81

79 76 70 63 54

97 92 83 73 60

2 4 6 8 10

118 109 96 80 63

158 142 119 92 69

71 67 59 50 40

87 80 69 56 42

59 46

62 47

45 36

48 36

12 14

49 36

30 22

45 36 29

36 29 23

28 22 18

16 18

28 22

17 14

No. of a Connectors

3⁄ 8

Thickness

31⁄2×21⁄2

No. of a Connectors

31⁄2×3

Size

Y-Y AXIS

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

4.59 1.09 1.36

3.87 1.10 1.35

3.13 1.11 1.33

4.22 1.10 1.11

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.88 1.12 1.09

3 - 72

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

Y X

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

3⁄ 8

Thickness

13.2

Wt./ft

Y-Y AXIS

X-X AXIS

Effective length KL (ft) with respect to indicated axis

1⁄ 4

3⁄ 16

9.0

6.77

0 118 163

107

2 113 155 3 109 146 4 102 134 5 94 120 6 86 105

78 75 70 65 59

103 97 90 81 71

54 52 49 46 42

68 65 60 55 50

3× ×2

No. of a Connectors

3× ×21⁄2

Size

3⁄ 8

5⁄ 16

11.8

1⁄ 4

10.0

3⁄ 16

8.2

6.1

106 147

125

2 3 4 5 6

103 98 93 86 78

141 132 122 109 96

87 83 78 73 66

119 112 103 93 82

70 68 64 59 54

93 88 81 74 65

49 47 45 42 38

61 59 55 50 45

7 8 9 10 11

70 61 53 45 38

82 69 56 45 38

59 52 45 39 32

70 59 48 39 32

49 43 37 32 27

57 48 40 32 27

35 31 28 24 20

40 35 30 25 21

12 13 14 15 16

32 27 23 20

27 23 20 17

22 19 16 14

17 15 13 11 10

7 8 9 10 11

76 67 58 49 40

90 75 60 49 40

53 47 40 34 29

62 52 43 35 29

38 34 30 26 22

44 38 32 27 22

12 13 14 15

34 29 25 22

24 21 18 15

19 16 14 12

0 118 163

107

106 147

125

2 110 149 3 107 143 4 102 135 5 97 125 6 90 114

71 69 66 63 59

90 87 83 77 71

45 44 43 41 39

54 53 51 48 45

2 3 4 5 6

97 131 93 122 86 111 79 98 71 84

80 76 71 65 58

107 100 91 81 69

63 60 56 51 46

79 74 68 61 53

40 39 37 34 31

48 46 43 39 35

7 8 9 10 11

62 53 47 39 32

70 60 48 39 32

51 44 37 32 27

58 49 39 32 27

40 35 29 25 21

45 37 31 25 21

28 24 21 17 15

30 26 21 17 15

12 13 14 15

27 23 20 18

22 19 17 14

18 15 13

12 11 10

7 8 9 10 11

83 102 76 90 68 77 61 66 53 58

54 50 45 40 35

64 57 49 42 35

36 34 31 28 25

41 38 34 30 26

12 13 14 15 16

48 42 36 31 28

49 42 36 31 28

30 26 23 20 18

22 19 16 14 13

17 18 19

24 22 20

16 14

11 10

Properties of 2 angles—3⁄8 in. back to back A

(in2)

rx (in.) ry (in.)

3.84 0.928 1.16

2.63 0.945 1.13

1.99 0.954 1.12

3.47 0.940 0.917

2.93 0.948 0.903

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.38 0.957 0.891

1.80 0.966 0.879

No. of a Connectors

Long legs 3⁄8 in. back to back of angles

DESIGN STRENGTH OF COLUMNS

3 - 73

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Long legs 3⁄8 in. back to back of angles 3⁄ 8

Thickness Wt./ft

10.6

X-X AXIS

Y-Y AXIS

5⁄ 16

1⁄ 4

9.0

3⁄ 16

7.2

5.5

131

111

2 3 4 5 6

90 84 77 69 60

122 112 99 84 69

76 72 66 59 51

104 95 84 72 59

62 58 54 48 42

85 78 69 59 49

46 44 40 36 32

59 55 49 43 36

7 8 9 10 11

50 42 33 27 22

55 42 33 27 22

43 36 29 23 19

47 37 29 23 19

36 30 24 19 16

39 30 24 19 16

27 23 19 15 12

30 24 19 15 12

12 13

13 11

10 9

131

111

2 3 4 5 6

89 85 80 74 67

120 113 104 93 82

74 71 66 61 55

99 93 85 76 66

58 56 52 48 44

77 73 67 60 52

41 39 37 34 31

50 48 44 40 36

7 8 9 10 11

60 52 45 38 32

70 58 47 38 32

49 42 36 32 26

56 48 39 32 26

39 33 28 25 21

44 36 31 25 21

28 24 21 17 15

31 26 22 18 15

12 13 14 15 16

27 23 20 17 15

22 19 16 14

17 15 13 11

13 11 10 8

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

No. of a Connectors

21⁄2×2

Size

Effective length KL (ft) with respect to indicated axis

3.09 0.768 0.961

2.62 0.776 0.948

2.13 0.784 0.935

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.62 0.793 0.923

3 - 74

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

8× ×6

Size Thickness Wt./ft

88.4

X-X AXIS Y-Y AXIS

67.6

46.0

796 1110 609

846

376

479

8 12 16 20 24

677 552 416 288 200

882 666 449 288 200

521 428 325 228 159

680 518 354 228 159

328 276 217 159 111

402 323 237 160 111

28 29

147

147 116 109

116 109

82 76

796 1110 609

846

12 16 20 24 28

725 681 628 569 506

970 890 796 695 591

547 514 474 429 382

32 36 40 44 48

443 380 320 265 223

490 396 321 265 223

52 56 60 61 62

190 164 143 138 134

130

1⁄ 2

Effective length KL (ft) with respect to indicated axis

3⁄ 4

8× ×4 3⁄ 4

1 74.8

1⁄ 2

57.4

673

935 517 718 321 408

4 6 8 10 12

600 521 426 329 240

798 654 495 346 240

82 76

14 16 17 18

176 176 141 141 101 101 135 135 108 108 78 78 120 120 96 96 69 69 61 61

376

479

673

935 517 718 321 408

727 667 598 522 444

325 308 287 263 237

393 368 338 304 267

12 16 20 24 28

628 596 558 514 467

849 790 720 643 563

480 455 426 392 355

647 602 548 489 426

295 281 264 245 224

365 344 318 290 258

333 286 240 199 168

368 297 241 199 168

210 183 156 131 110

229 192 157 131 110

32 36 40 44 48

418 369 320 274 231

483 405 333 275 231

317 279 242 206 174

364 305 250 206 174

202 179 157 135 115

227 195 165 137 115

143 123 108 104 101

94 81 71 69

52 56 60 64 66

197 170 148 130 122

197 148 148 170 128 128 148 111 111 130 98 98 122 92 92

98 85 74 65 61

67 68

119 119 115 115

39.2

463 404 333 260 192

616 509 390 276 192

292 259 219 177 137

361 311 252 192 138

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

26.0 1.73 3.78

19.9 1.76 3.74

13.5 1.79 3.69

22.0 1.03 4.10

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.9 1.05 4.05

11.5 1.08 4.00

No. of a Connectors

Short legs 3⁄8 in. back to back of angles No. of a Connectors

Design axial strength in kips (φ = 0.85)

3/ ′′ 8

DESIGN STRENGTH OF COLUMNS

3 - 75

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

7× ×4

Size 3⁄ 4

Thickness Wt./ft

1⁄ 2

52.4

3⁄ 8

35.8

27.2

No. of a Connectors

Short legs 3⁄8 in. back to back of angles

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

0 471 655 310 401 205 254 4 6 8 10 12

426 375 313 249 188

568 476 371 270 188

282 250 212 171 132

354 304 245 186 133

189 171 149 124 100

230 203 171 137 104

14 138 138 16 106 106 18 84 84

98 75 59

77 59 47

3/ ′′ 8

6× ×4 3⁄ 4

5⁄ 8

47.2

50 0

1⁄ 2

40.0

3⁄ 8

32.4

24.6

425 591 358 497 291 388 201 256

4 6 8 10 12

386 342 289 232 178

436 370 293 218 154

265 236 201 164 127

343 295 238 181 129

186 168 146 122 97

231 203 170 135 102

77 59 47

14 16 18 19

132 132 113 113 101 101 86 86 80 80 68 68

95 73 57 52

75 57 45 41

0 471 655 310 401 205 254

8 12 16 20 24

449 427 397 362 324

611 570 516 454 389

291 277 259 236 212

368 346 317 282 245

28 32 36 40 44

283 243 204 168 139

323 261 207 168 139

186 160 135 111 92

207 129 143 171 113 122 137 98 102 111 83 83 92 69 69

48 117 117 52 99 99 56 86 86 57 83 83 58 80 80

77 66 57 55

188 181 171 158 144

58 49 43 41

225 215 201 184 164

58 49 43 41

517 437 345 255 179

326 289 245 198 152

A (in ) rx (in.) ry (in.)

15.4 1.09 3.49

10.5 1.11 3.44

7.97 1.13 3.42

425 591 358 497 291 388 201 256

8 12 16 20 24

398 370 334 293 249

538 486 422 352 282

28 32 36 40 44

206 166 131 106 88

216 172 179 138 143 100 105 165 138 138 110 110 81 82 131 109 109 87 87 65 65 106 88 88 71 71 52 52 88 73 73 58 58 43 43

45 46 47 48 49

84 80 77 74 71

333 310 279 245 208

70 67 64 61

449 406 352 294 235

70 67 64 61

267 249 224 197 167

56 53 51 49

346 314 275 230 186

56 53 51 49

181 170 155 138 119

42 40 38

222 205 184 158 131

42 40 38

Properties of 2 angles—3⁄8 in. back to back 2

No. of a Connectors

Design axial strength in kips (φ = 0.85)

13.9 1.12 2.94

11.7 1.13 2.92

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.50 1.15 2.90

7.22 1.17 2.87

3 - 76

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

6× ×31⁄2

Size 3⁄ 8

Thickness Wt./ft

23.4

Y-Y AXIS

X-X AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 16

19.6

191

243

145

179

4 6 8 10

170 148 121 94

210 175 136 99

131 115 97 77

158 135 109 82

12 14 16

69 50 39

58 43 33

59 43 33

191

243

145

8 12 16 20 24

173 160 144 125 112

213 194 170 142 124

28 32 36 40 44

94 76 63 51 42

48 49

36 34

5× ×31⁄2 3⁄ 4

1⁄ 2

39.6

3⁄ 8

27.2

5⁄ 16

20.8

355

493

245

340 183 238 143 182

2 4 6 8 10

344 313 267 214 160

472 238 326 413 217 288 331 187 234 243 152 176 164 116 121

12 14 16 17

114 84 64

84 62 47

179

355

493

245

340 183 238 143 182

130 122 111 98 84

154 143 128 110 98

8 10 12 14 16

318 300 279 257 233

423 390 354 334 297

217 205 191 175 159

287 265 240 214 201

99 80 63 51 42

75 62 53 43 35

80 66 53 43 35

18 20 22 24 26

224 201 179 157 144

260 225 201 169 144

152 136 121 106 96

175 106 127 151 101 111 134 90 95 113 79 84 96 69 72

36 34

30 29

28 30 32 34 36

125 109 95 85 75

83 72 64 56 50

62 54 48 42 38

49 43 38 33 30

38 39 40

68 64 61

45 43 41

34 32 31

27 25

17.4

178 163 141 116 89

84 62 47

229 139 176 205 129 159 170 113 135 131 94 107 94 74 79

65 48 37 32

160 151 141 130 118

65 48 37 32

198 185 169 153 143

56 41 31 28

123 117 110 102 94

6.84 0.988 2.95

5.74 0.996 2.94

11.6 0.977 2.48

8.00 1.01 2.43

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

6.09 1.02 2.41

56 41 31 28

149 140 130 119 106

85 100 81 89 73 77 65 66 57 57

Properties of 2 angles—3⁄8 in. back to back A (in2) rx (in.) ry (in.)

No. of a Connectors

Short legs 3⁄8 in. back to back of angles No. of a Connectors

Design axial strength in kips (φ = 0.85)

3/ ′′ 8

5.12 1.03 2.39

DESIGN STRENGTH OF COLUMNS

3 - 77

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

Short legs 3⁄8 in. back to back of angles 5× ×3

Size 1⁄ 2

Thickness Wt./ft

X-X AXIS Y-Y AXIS

3⁄ 8

25.6

Effective length KL (ft) with respect to indicated axis

5⁄ 16

19.6

1⁄ 4

16.4

13.2

230

319

172

223

134

170

117

2 4 6 8 10

220 192 154 113 76

300 249 184 119 76

165 146 118 88 61

212 180 137 94 61

129 115 95 73 52

162 140 110 79 52

92 84 71 56 42

112 99 81 61 43

12 13 14

53 45

42 36 31

36 31 26

30 25 22

230

319

172

223

134

170

117

8 10 12 14 16

205 194 181 167 152

273 253 230 205 194

152 144 135 125 114

190 178 163 147 139

118 112 106 98 90

144 135 126 115 103

83 79 75 71 66

96 92 87 81 75

18 20 22 24 26

146 132 117 103 95

170 147 132 112 95

109 99 88 78 68

124 109 94 84 71

82 79 71 63 56

98 87 76 66 59

61 56 54 49 44

68 65 58 51 45

28 30 32 34 36

82 72 63 56 50

62 54 47 42 37

51 45 39 35 31

39 36 31 28 25

41 36 31 28 25

38 40 41

45 40 38

34 30 29

28 25 24

22 20 19

3/ ′′ 8

No. of a Connectors

Design axial strength in kips (φ = 0.85)

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

7.50 0.829 2.50

5.72 0.845 2.48

4.80 0.853 2.47

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.88 0.861 2.46

3 - 78

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Short legs 3⁄8 in. back to back of angles 4× ×31⁄2

Size 1⁄ 2

Thickness Wt./ft

23.8

X-X AXIS

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

3⁄ 8

5⁄ 16

18.2

1⁄ 4

15.4

12.4

214

298

163

227

137

179

101

129

2 4 6 8 10

208 191 166 137 106

286 255 210 160 112

159 147 128 106 83

219 195 162 125 89

133 123 108 90 71

172 156 131 103 76

99 92 81 69 55

125 114 98 79 60

12 14 16 17

78 57 44 39

62 45 35 31

53 39 30 26

42 31 24 21

43 31 24 21

214

298

163

227

137

179

101

129

4 6 8 10 12

201 190 177 161 143

271 252 228 200 181

150 142 132 120 107

200 187 169 149 127

122 116 108 99 89

152 143 132 117 102

86 83 78 72 66

103 99 92 84 75

14 16 18 20 22

132 115 98 86 71

153 126 106 86 71

94 86 73 61 53

114 94 75 61 53

77 71 61 51 42

92 77 62 51 42

58 54 47 40 33

65 59 49 40 33

24 26 28 30 31

60 51 44 38 36

45 38 33 29 27

36 30 26 23 21

28 24 21 18

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

7.00 1.04 1.89

5.34 1.06 1.87

4.49 1.07 1.86

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.63 1.07 1.85

No. of a Connectors

DESIGN STRENGTH OF COLUMNS

3 - 79

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

Short legs 3⁄8 in. back to back of angles 4× ×3

Size 1⁄ 2

Thickness Wt./ft

X-X AXIS Y-Y AXIS

3⁄ 8

22.2

Effective length KL (ft) with respect to indicated axis

5⁄ 16

17.0

1⁄ 4

14.4

11.6

199

276

152

211

127

166

120

2 4 6 8 10

191 169 138 104 72

261 220 166 112 72

146 130 107 81 57

200 170 129 88 57

123 109 90 69 49

158 136 106 75 49

91 82 69 54 40

115 101 81 59 40

12 14

50 37

40 29

34 25

28 21

199

276

152

211

127

166

120

4 6 8 10 12

190 182 172 160 146

259 245 226 204 180

143 137 130 121 110

193 183 169 153 135

118 113 107 99 91

149 142 132 120 107

85 82 78 73 67

103 99 93 86 78

14 16 18 20 22

131 116 101 86 73

156 131 108 88 73

99 87 76 65 54

117 98 81 66 54

81 72 62 53 44

93 79 65 53 44

61 55 48 41 35

69 60 51 42 35

24 26 28 30 32

61 52 45 39 34

46 39 34 29 26

37 32 27 24 21

30 25 22 19 17

3/ ′′ 8

No. of a Connectors

Design axial strength in kips (φ = 0.85)

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

6.50 0.864 1.96

4.97 0.879 1.94

4.18 0.887 1.93

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.38 0.896 1.92

3 - 80

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

31⁄2×3

Size 3⁄ 8

Thickness Wt./ft

15.8

X-X AXIS

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 16

1⁄ 4

13.2

10.8

140

195

118

162

2 4 6 8 10

135 121 100 77 55

185 158 122 84 55

114 102 85 65 47

154 132 103 72 47

12 14 15

38 28

33 24 21

140

195

4 6 8 10 12

130 123 114 103 91

14 16 18 20 22 24 26 27

31⁄2×21⁄2 3⁄ 8

1⁄ 4

14.4

9.8

119

129

179

110

89 80 67 53 38

114 100 79 58 39

2 4 6 8 10

122 102 76 51 32

165 129 86 51 32

81 68 52 36 23

102 83 59 36 23

33 24 21

27 20 17

11 12

19 16

118

162

119

129

179

110

175 162 146 127 107

108 102 94 85 75

142 132 119 104 88

82 77 72 66 58

100 94 86 77 66

4 6 8 10 12

122 116 108 98 87

165 154 139 122 105

78 74 69 63 57

97 91 84 75 65

78 66 54 44 36

87 68 54 44 36

65 55 45 37 30

72 57 45 37 30

51 43 36 29 24

55 45 36 29 24

14 16 18 20 22

76 65 55 45 37

87 70 55 45 37

50 43 36 30 25

55 46 37 30 25

31 26 24

26 22 20

20 17 16

24 26 28 29

31 27 23 21

21 18 15

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

4.59 0.897 1.67

3.87 0.905 1.66

3.13 0.914 1.65

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.22 0.719 1.74

2.88 0.735 1.72

No. of a Connectors

Short legs 3⁄8 in. back to back of angles No. of a Connectors

Design axial strength in kips (φ = 0.85)

3/ ′′ 8

DESIGN STRENGTH OF COLUMNS

3 - 81

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Unequal legs

3× ×21⁄2

Size 3⁄ 8

Thickness Wt./ft

13.2

X-X AXIS

3⁄ 16

9.0

6.77

0 118 163

107

2 111 151 3 104 137 4 94 120 5 83 100 6 71 81

76 71 65 58 50

100 91 81 69 56

53 50 46 41 36

66 62 55 48 41

45 35 27 22 18

31 26 21 17 14

34 27 21 17 14

3/ ′′ 8

3× ×2 3⁄ 8

5⁄ 16

11.8

1⁄ 4

10.0

3⁄ 16

8.2

6.1

106 147

125

2 3 4 5 6

96 129 85 109 72 86 58 64 44 45

82 73 61 50 38

109 93 74 55 39

66 59 50 41 32

86 74 59 45 32

46 42 36 30 24

58 51 42 33 25

7 8 9

33 25 20

28 22 17

24 18 14

18 14 11

106 147

125

b 7 8 9 10 11

59 48 38 31 25

63 48 38 31 25

42 34 27 22 18

0 118 163

107

2 113 155 4 109 146 6 101 132 8 91 114 10 79 95

75 72 67 60 53

97 92 84 73 62

49 47 45 41 36

59 57 53 48 41

2 4 6 8 10

104 100 93 85 76

143 135 123 109 92

87 84 78 71 63

119 113 103 91 77

70 67 63 57 51

92 87 80 70 60

47 45 43 39 35

58 55 52 47 41

12 14 16 18 20

67 56 44 35 28

76 58 44 35 28

45 37 29 23 19

50 38 29 23 19

32 27 22 17 14

35 28 22 17 14

12 14 16 18 20

65 55 45 36 29

75 59 46 36 29

54 46 37 30 24

62 49 38 30 24

44 37 30 24 19

49 39 30 24 19

31 26 22 18 14

35 28 22 18 14

22 24

23 20

16 13

12 10

22 24 25

24 20 19

24 20 20 17 19 15

20 16 17 13 15 12

16 13 12

12 10 9

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

1⁄ 4

No. of a Connectors

Short legs 3⁄8 in. back to back of angles

No. of a Connectors

Design axial strength in kips (φ = 0.85)

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

3.84 0.736 1.47

2.63 0.753 1.45

1.99 0.761 1.44

3.47 0.559 1.55

2.93 0.567 1.53

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.38 0.574 1.52

1.80 0.583 1.51

3 - 82

COLUMN DESIGN

Fy = 36 ksi Fy = 50 ksi

COLUMNS Double angles

Y X

Design axial strength in kips (φ = 0.85)

Unequal legs

3/ ′′ 8

Short legs 3⁄8 in. back to back of angles 21⁄2×2

Size 3⁄ 8

Thickness Wt./ft

10.6

X-X AXIS

Effective length KL (ft) with respect to indicated axis

5⁄ 16

1⁄ 4

9.0

3⁄ 16

7.2

5.5

131

111

2 3 4 5 6

86 77 66 54 42

116 99 79 60 42

73 66 56 46 36

98 84 68 51 37

60 54 46 38 30

80 69 56 43 31

45 40 35 29 23

57 50 41 32 24

7 8 9 10

31 24 19

27 21 16

23 17 14

18 14 11 9

131

111

2 4 6 8 10

92 86 78 69 58

126 116 101 84 66

77 73 66 57 47

105 97 84 69 54

62 58 53 46 38

84 77 67 55 43

45 42 38 33 28

56 52 46 39 31

12 14 16 18 20

46 36 28 22 18

49 36 28 22 18

38 29 22 17 14

39 29 22 17 14

30 23 18 14 11

31 23 18 14 11

22 17 13 10 9

23 17 13 10 9

No. of a Connectors

Y-Y AXIS

Properties of 2 angles—3⁄8 in. back to back 2

A (in ) rx (in.) ry (in.)

3.09 0.577 1.28

2.62 0.584 1.26

2.13 0.592 1.25

aFor Y-Y axis, welded or fully tensioned bolted connectors only. bFor number of connectors, see double angle column discussion.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.62 0.600 1.24

DESIGN STRENGTH OF COLUMNS

3 - 83

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (φ = 0.85) Designation

X-X AXIS Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

WT 18 150

Wt./ft

140

130

122.5

115

1350

1730

1260

1510

1150

1330

1040

1170

925

1030

10 12 14 16 18

1310 1300 1280 1260 1240

1670 1650 1620 1590 1550

1230 1210 1190 1180 1150

1470 1440 1420 1390 1360

1120 1100 1090 1070 1050

1290 1270 1250 1220 1200

1010 998 985 970 953

1140 1130 1110 1090 1070

903 893 882 869 855

998 986 972 956 939

20 22 24 26 28

1210 1180 1150 1120 1090

1510 1460 1420 1370 1320

1130 1100 1080 1050 1020

1330 1290 1250 1210 1170

1030 1010 983 957 930

1170 1140 1110 1070 1040

935 915 893 870 847

1050 1020 993 964 934

839 822 803 784 763

920 899 876 853 828

30 32 34 36 38

1060 1020 984 947 910

1260 1210 1160 1100 1040

984 951 917 883 847

1120 1080 1030 987 940

901 871 841 810 778

1000 965 926 886 847

822 796 769 742 714

903 871 838 804 770

742 719 696 673 649

802 776 748 720 692

872

989

812

893

746

806

686

736

624

663

1350

1730

1260

1510

1150

1330

1040

1170

925

1030

10 12 14 16 18

1210 1190 1160 1130 1090

1510 1470 1430 1370 1320

1120 1100 1070 1040 1010

1320 1290 1250 1210 1160

1010 990 966 938 908

1140 1120 1090 1050 1010

906 888 867 843 817

1010 985 959 930 898

803 788 770 750 728

874 857 836 812 786

20 22 24 26 28

1050 1010 962 916 868

1260 1190 1130 1060 988

972 932 891 848 804

1110 1060 1000 943 884

876 841 804 766 726

971 927 880 833 784

789 759 727 693 659

863 826 787 747 705

704 679 651 623 593

758 728 696 662 628

30 32 34 36 38

820 771 721 672 624

918 848 780 713 647

758 713 667 622 577

825 766 708 650 595

686 645 604 563 523

734 684 634 585 537

623 587 551 515 480

662 619 577 534 493

563 532 501 469 438

592 557 521 485 450

577

585

533

540

484

490

445

452

408

415

Properties A (in2) rx (in.) ry (in.)

44.1 5.27 3.83

41.2 5.25 3.81

38.2 5.26 3.78

36.0 5.26 3.75

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

33.8 5.25 3.73

3 - 84

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation 105

Wt./ft

X-X AXIS

67.5

908 1040 772

851

683

726

587

601

518

521

458

457

385

10 12 14 16 18

887 1010 755 878 1000 748 868 986 740 856 971 731 843 954 720

831 822 812 801 788

670 664 657 649 640

710 704 696 687 677

576 571 566 560 553

590 585 579 572 565

509 505 500 495 489

512 508 503 498 492

451 448 444 440 435

449 446 442 438 433

380 377 374 371 367

20 22 24 26 28

828 813 796 778 759

935 915 893 870 846

709 696 683 668 653

775 759 743 726 708

631 620 609 597 584

667 655 642 629 614

545 537 528 518 508

557 548 539 529 518

483 476 468 460 452

486 479 471 463 454

429 424 417 411 403

428 422 416 409 402

363 359 354 348 343

30 32 36 40

739 719 675 630

821 795 740 684

637 621 586 549

689 669 628 585

571 557 527 496

599 584 551 517

497 486 462 437

507 495 470 444

443 433 413 392

445 436 415 394

396 388 371 353

395 387 370 352

337 331 317 303

908 1040 772

851

683

726

587

601

518

521

458

457

385

10 12 14 16 18

716 687 654 617 578

791 756 715 670 622

607 585 559 530 499

653 627 597 563 527

534 515 494 470 444

558 538 515 488 460

457 442 425 406 385

465 450 432 412 391

397 385 371 356 339

399 387 373 357 340

344 335 323 311 297

344 334 323 310 296

268 261 253 244 234

20 22 24 26 28

537 494 450 407 364

572 521 469 418 367

465 431 395 360 325

489 449 409 369 330

416 387 358 327 297

430 398 366 333 301

363 340 315 291 266

368 344 319 293 268

320 301 280 260 239

321 302 281 260 239

281 265 248 231 213

223 211 198 185 172

30 32 34 36 39

323 285 254 228 195

291 258 230 206 176

268 239 213 191 164

269 239 213 191 164

242 218 194 174 150

218 197 177 159 137

196 178 161 144 124

195 178 161 144 124

158 144 131 118 102

41 42 43

177 169 161

177 160 169 153 161

160 153

149 142

136 130

124

113

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

WT 18

Properties A (in2) rx (in.) ry (in.)

30.9 5.65 2.58

28.5 5.62 2.56

26.8 5.62 2.55

25.0 5.61 2.53

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

23.5 5.61 2.50

22.1 5.62 2.47

19.9 5.66 2.38

DESIGN STRENGTH OF COLUMNS

3 - 85

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

Y-Y AXIS

X-X AXIS

Effective length KL (ft) with respect to indicated axis

WT 16.5 120.5

Wt./ft

110.5

100.5

70.5

0 1080 1300 964 1110 810

899

532

548

463

467

402

401

330

10 12 14 16 18

1050 1040 1020 1000 980

1260 1240 1210 1190 1160

935 923 909 893 875

1070 1050 1030 1010 990

788 779 767 755 741

872 860 847 831 814

521 516 510 503 495

535 530 524 516 508

453 449 444 439 433

457 453 448 442 436

394 391 387 383 378

393 390 386 382 377

324 321 318 315 311

20 22 24 26 28

958 933 907 880 851

1120 1090 1050 1020 975

855 834 811 787 762

965 937 908 878 846

725 708 690 672 652

795 775 753 730 706

487 478 468 458 447

500 490 480 469 458

426 419 411 402 393

429 422 414 405 396

372 366 360 353 345

371 365 359 352 345

307 303 298 293 287

30 32 34 36 40

821 790 759 727 662

934 892 849 806 720

737 710 682 654 598

813 779 745 710 639

631 610 588 565 520

681 656 630 603 549

436 424 411 399 373

446 433 420 407 379

384 374 364 354 332

387 377 366 356 334

338 330 321 313 295

337 329 321 312 295

282 276 269 263 249

0 1080 1300 964 1110 810

899

532

548

463

467

402

401

330

10 12 14 16 18

951 929 904 876 845

1110 1080 1050 1010 967

833 815 793 769 743

934 911 884 854 821

692 678 661 643 622

753 736 717 695 671

420 406 389 370 349

429 414 396 377 355

358 346 333 318 301

360 348 335 319 302

300 291 280 268 255

299 290 280 268 255

234 228 220 212 203

20 22 24 26 28

811 775 738 699 659

922 874 824 772 720

714 683 651 617 583

785 747 707 666 624

600 576 551 525 497

644 616 587 556 525

327 305 281 257 234

332 309 284 260 235

283 264 245 225 206

284 266 246 226 206

241 226 211 195 179

241 226 210 195 178

192 181 170 158 146

30 34 36 38 39

618 537 497 458 439

667 564 514 464 441

548 477 442 408 391

581 496 455 414 394

470 413 385 357 343

492 427 395 363 348

211 167 150 135 129

186 149 134 121 115

187 149 134 121 115

162 131 118 107 102

134 109 98 89

40 41

420 401

420 375 401 358

375 330 358 316

332 317

123 117

109

Properties A (in2) rx (in.) ry (in.)

35.4 4.96 3.63

32.5 4.96 3.59

29.5 4.95 3.56

22.4 5.14 2.47

20.8 5.15 2.43

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

19.2 5.18 2.39

17.3 5.20 2.32

3 - 86

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation 105.5

Wt./ft

Effective length KL (ft) with respect to indicated axis

X-X AXIS

95.5

86.5

49.5

949 1180 844 974 708 791 505 546 447 465 402 412 357 361 304 303

10 12 14 16 18

913 897 879 859 837

1130 1100 1080 1050 1010

812 799 783 765 746

932 914 894 870 845

684 673 661 647 632

761 748 733 715 696

490 484 477 468 459

529 521 513 503 492

434 429 423 416 408

452 446 439 432 423

392 387 382 376 369

401 396 391 384 377

348 344 340 335 329

352 348 343 338 332

297 294 290 286 282

296 293 290 286 281

20 22 24 26 28

813 787 759 731 701

976 938 897 855 811

724 702 678 652 626

817 787 756 724 690

615 597 578 558 537

676 654 630 606 581

449 437 426 413 400

480 467 454 439 424

399 390 380 370 359

414 404 393 382 370

361 353 345 336 326

369 361 352 343 333

323 316 309 301 293

326 319 311 304 295

277 271 266 259 253

276 271 265 259 253

30 32 34 36 40

670 639 607 575 511

767 723 678 634 547

599 571 543 515 459

656 621 586 551 482

515 493 471 448 402

555 528 501 474 421

387 373 358 344 314

409 393 377 360 327

347 335 323 311 285

358 345 332 319 292

316 306 295 284 262

322 311 300 289 266

284 276 267 257 238

287 278 269 259 240

246 239 232 224 209

Y-Y AXIS

WT 15

949 1180 844 974 708 791 505 546 447 465 402 412 357 361 304 303

10 12 14 16 18

838 1010 734 828 609 667 817 982 716 805 595 651 793 946 695 778 579 631 766 907 672 749 561 610 736 864 646 717 541 586

389 371 350 328 303

411 391 368 343 316

340 325 308 290 269

350 335 317 297 275

298 286 271 256 238

303 290 276 259 241

254 244 233 220 206

256 246 234 221 207

207 199 191 181 170

206 199 191 181 170

20 22 24 26 28

704 670 635 598 561

818 769 720 669 617

619 589 559 527 495

682 645 607 568 528

520 497 473 448 422

561 533 505 475 445

278 252 227 201 176

288 259 231 203 176

248 226 204 183 161

253 230 207 184 161

220 201 182 163 145

223 203 183 164 145

191 175 159 143 127

192 176 160 143 127

159 147 134 121 108

159 146 134 121 108

30 32 34 35 36

523 486 449 430 412

567 517 468 444 420

462 429 397 381 365

488 448 410 391 372

396 370 344 331 318

415 384 354 339 325

155 137 122 115 109

142 125 112 106 100

142 127 127 112 112 125 113 113 100 100 112 100 100 89 89 106 95 95 84 84 100 90 90

96 85 76

37 38 40

395 377 342

398 349 353 305 310 103 103 378 334 335 293 296 342 303 303 268 268

Properties A (in2) rx (in.) ry (in.)

31.0 4.43 3.49

28.1 4.42 3.46

25.4 4.42 3.43

19.4 4.66 2.25

18.2 4.66 2.23

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.1 4.67 2.19

15.9 4.69 2.15

14.5 4.71 2.10

DESIGN STRENGTH OF COLUMNS

3 - 87

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

WT 13.5 89

Wt./ft

X-X AXIS

799 1040 725

857

617

698

453

498

358

369

308

311

251

250

10 12 14 16 18

761 745 727 707 684

978 951 921 887 850

691 676 660 641 620

810 790 767 741 712

589 577 564 549 532

663 648 631 612 591

436 428 420 410 399

477 468 458 447 434

346 341 334 328 320

356 350 344 337 329

298 294 289 284 278

301 297 292 286 280

244 241 238 234 229

243 240 236 232 228

20 22 24 26 28

660 634 606 578 549

811 770 727 683 638

598 574 549 523 496

682 650 617 583 548

514 495 474 453 431

568 544 519 493 466

388 375 362 348 334

420 405 390 373 357

312 303 293 283 273

320 310 300 290 279

271 264 256 248 240

273 266 258 250 241

224 219 213 207 201

223 218 212 206 200

30 32 34 36 38

519 489 459 430 400

594 550 506 464 423

469 442 415 388 361

513 478 443 409 376

409 387 364 342 319

439 412 385 358 332

319 304 289 274 259

339 322 304 287 269

262 251 240 229 218

268 256 244 233 221

231 222 213 204 194

233 223 214 205 195

194 187 180 173 166

193 187 180 173 165

371

383 335

344

298

306

244

252

206

209

185

186

159

158

799 1040 725

857

617

698

453

498

358

369

308

311

251

250

10 12 14 16 18

701 681 658 632 604

877 845 808 768 725

627 609 588 565 540

720 696 669 639 606

527 513 497 479 459

583 566 546 524 500

349 331 311 288 264

374 353 330 304 277

275 263 248 232 215

281 268 253 236 218

231 221 210 197 184

233 223 211 198 185

181 174 166 157 147

180 173 165 156 147

20 22 24 26 28

574 542 509 476 442

678 631 582 533 484

513 485 456 426 395

571 534 497 458 420

437 415 391 367 342

474 446 418 389 359

240 215 191 167 145

249 221 193 167 145

197 179 160 142 125

199 180 161 143 125

169 154 140 125 110

170 155 140 125 110

137 126 114 103 92

136 125 114 103 92

30 32 34 35 36

408 374 342 326 310

436 390 347 328 310

365 335 305 291 277

382 345 309 292 277

317 292 268 256 244

330 301 273 259 245

127 112 100 94 89

109 97 86 81

97 86 76 72

81 72 64

252

252 225

225

200

Y-Y AXIS

80.5

Effective length KL (ft) with respect to indicated axis

Properties A (in2) rx (in.) ry (in.)

26.1 3.98 3.26

23.7 3.96 3.24

21.5 3.95 3.21

16.8 4.15 2.18

15.0 4.14 2.15

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

13.8 4.16 2.12

12.4 4.18 2.07

3 - 88

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 12 81

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

65.5

58.5

731

1020

658

864

591

726

506

580

410

450

10 12 14 16 18

687 669 648 624 598

932 898 858 815 769

618 602 583 562 538

797 769 737 702 664

556 541 524 505 484

673 652 627 599 569

477 465 451 435 418

542 526 508 487 465

389 379 369 357 344

424 413 401 387 371

20 22 24 26 28

571 542 512 481 450

720 670 619 568 518

514 488 461 433 405

624 583 541 499 457

462 439 415 391 366

537 504 471 437 403

400 380 360 339 318

442 418 392 367 341

331 316 301 285 269

355 338 320 302 283

30 32 34 36 38

419 388 358 328 299

469 421 375 335 300

377 349 322 295 269

416 376 338 301 270

341 316 291 267 244

369 336 304 273 245

297 276 255 235 215

315 290 265 241 217

252 236 220 204 188

264 246 227 209 192

271

244

221

196

173

175

731

1020

658

864

591

726

506

580

410

450

10 12 14 16 18

648 626 601 574 544

858 819 775 727 675

575 555 533 508 482

723 691 656 617 575

505 487 468 446 422

597 573 545 515 482

424 410 395 377 358

472 455 435 414 390

338 328 317 304 290

363 352 339 324 308

20 22 24 26 28

512 480 446 412 378

622 568 514 460 409

453 424 393 363 332

532 487 442 398 355

397 371 345 317 290

448 412 376 340 305

338 316 294 272 249

365 339 313 286 259

275 260 243 226 209

291 273 254 235 216

30 32 34 36 38

345 312 281 251 225

359 316 281 251 225

303 273 245 219 197

313 276 245 219 197

264 238 213 190 171

271 239 213 190 171

227 206 184 165 149

233 207 184 165 149

192 175 159 143 129

196 178 159 143 129

204

178

155

135

117

Properties A (in2) rx (in.) ry (in.)

23.9 3.50 3.05

21.5 3.50 3.01

19.3 3.52 2.97

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.2 3.51 2.94

15.3 3.51 2.91

DESIGN STRENGTH OF COLUMNS

3 - 89

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

WT 12 47

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

27.5

378

419

307

321

254

258

209

208

202

203

155

10 12 14 16 18

360 352 343 332 321

396 387 376 363 350

293 287 280 273 265

306 299 292 284 275

244 240 234 229 222

247 243 237 231 225

201 198 194 189 185

200 197 193 189 184

194 191 187 183 178

196 192 188 184 179

150 148 145 142 139

20 22 24 26 28

309 296 283 269 255

335 320 304 287 271

256 246 236 225 215

265 255 244 233 221

215 208 200 192 184

218 210 202 194 185

179 174 168 162 155

179 173 167 161 155

173 168 162 156 150

174 169 163 157 150

136 132 128 124 120

30 32 34 36 38

240 226 211 197 183

254 237 220 203 187

204 192 181 170 159

209 197 185 173 161

175 166 157 148 140

176 167 158 149 140

148 142 135 128 121

148 141 135 128 121

143 136 130 123 116

144 137 130 123 117

115 111 106 101 96

169

171

148

150

131

114

109

110

378

419

307

321

254

258

209

208

202

203

155

10 12 14 16 18

288 269 248 226 202

310 288 263 237 211

231 218 202 185 168

239 224 208 190 171

188 178 166 154 140

190 179 167 155 141

148 140 132 123 113

147 140 132 123 113

121 110 97 84 71

122 110 98 84 71

91 84 75 67 57

20 22 23 24 26

179 156 145 134 115

184 158 145 134 115

150 132 124 115 99

152 134 124 115 99

126 113 106 99 86

127 113 106 99 86

103 92 87 82 71

59 49 46

48 41

28 30 31 32 33

99 87 82 77 72

86 75 71 66

74 65 61 58

62 55 51

Properties A (in2) rx (in.) ry (in.)

13.8 3.67 1.98

12.4 3.67 1.95

11.2 3.68 1.92

10.0 3.70 1.87

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

9.11 3.79 1.38

8.10 3.80 1.34

3 - 90

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 10.5 73.5

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

55.5

50.5

661

918

594

825

548

757

499

637

452

524

10 12 14 16 18

610 589 565 539 510

822 782 739 691 641

547 528 507 483 457

737 701 661 618 573

505 487 466 444 420

676 643 606 566 524

459 443 424 404 382

573 547 518 486 453

416 401 384 366 346

476 457 434 410 384

20 22 24 26 28

480 449 417 385 353

589 536 484 434 385

429 401 372 343 315

526 478 431 386 341

395 368 341 315 288

481 437 394 352 311

358 334 310 285 261

418 382 347 312 279

324 303 280 258 236

357 329 301 274 247

30 32 34 36 38

322 292 262 234 210

337 296 263 234 210

286 259 233 208 186

299 263 233 208 186

262 236 212 189 170

272 239 212 189 170

237 214 192 171 154

246 217 192 171 154

214 193 173 154 139

221 195 173 154 139

190

168

153

139

125

661

918

594

825

548

757

499

637

452

524

10 12 14 16 18

587 566 542 515 486

778 740 697 650 601

522 503 482 458 432

689 655 617 576 532

478 461 441 419 396

626 596 562 524 485

430 415 397 377 356

526 503 476 447 415

385 372 356 339 320

434 417 397 375 352

20 22 24 26 28

456 424 392 360 328

550 498 447 397 349

405 377 348 320 291

487 441 395 351 308

371 345 319 293 267

444 402 361 321 281

334 311 287 263 239

383 349 316 283 251

300 279 258 237 216

327 301 275 249 223

30 32 34 36 38

297 267 238 213 191

305 268 238 213 191

263 237 210 188 169

269 237 210 188 169

241 216 193 172 155

246 217 193 172 155

216 194 172 154 139

220 194 172 154 139

195 175 156 139 125

199 175 156 139 125

173

153

140

125

113

Properties A (in2) rx (in.) ry (in.)

21.6 3.08 2.95

19.4 3.06 2.93

17.9 3.04 2.92

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

16.3 3.03 2.90

14.9 3.01 2.89

DESIGN STRENGTH OF COLUMNS

3 - 91

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

X-X AXIS

Effective length KL (ft) with respect to indicated axis

41.5

36.5

28.5

419 562 373 444 297 331 261 283 219 225 203 210 165 167 127 127

6 8 10 12 14

409 400 390 378 364

543 529 511 489 466

364 356 347 336 323

430 420 407 392 374

290 284 278 270 260

322 316 307 297 286

255 251 245 239 231

276 271 264 256 247

214 211 206 201 195

221 217 212 207 201

199 196 192 187 182

206 203 199 194 188

162 160 157 153 149

164 161 158 155 151

125 123 121 119 116

16 18 20 22 24

349 332 315 296 277

439 412 383 353 323

310 295 279 262 245

355 335 314 291 269

250 239 227 215 202

274 260 246 231 216

222 213 203 192 182

237 227 215 203 191

189 181 174 165 157

194 186 178 169 160

176 170 163 155 147

182 175 167 159 151

145 140 134 129 123

146 141 136 130 124

113 110 106 102 98

26 28 30 32 34

258 239 220 201 183

293 264 236 209 185

228 210 193 177 160

247 225 203 182 162

189 176 163 150 137

200 185 169 155 140

170 159 148 137 126

178 165 153 140 128

148 139 130 121 112

151 142 132 123 114

139 131 123 115 107

143 117 118 134 111 111 125 104 105 117 98 98 108 91 92

94 90 85 81 76

36 38 40

165 165 145 145 125 126 115 117 104 104 148 148 130 130 113 113 105 105 95 96 134 134 117 117 102 102 95 95 87 87

71 67 63

Y-Y AXIS

WT 10.5 46.5

Wt./ft

99 100 91 92 84 84

85 79 73

419 562 373 444 297 331 261 283 219 225 203 210 165 167 127 127

6 8 10 12 14

357 337 313 285 256

452 420 381 338 293

311 294 273 250 224

357 334 307 276 243

245 233 218 201 182

267 252 235 214 192

213 203 191 177 161

227 215 202 186 168

152 147 141 133 123

153 142 128 113 97

16 18 20 21 22

226 195 166 151 138

247 203 166 151 138

198 171 145 132 121

210 177 145 132 121

162 142 122 113 103

169 146 124 113 103

145 128 111 103 95

150 112 113 131 101 102 112 90 90 103 84 84 95 78 78

81 66 54 49 45

24 26 28 29 30

117 117 102 102 100 100 88 88 86 86 76 76 80 80 71 71 75 75 66 66

87 75 65 60 57

80 69 60 56 52

149 145 138 131 122

67 58 51 47

157 116 117 145 108 109 131 99 99 115 88 88 98 76 76 82 66 54 49 45

64 52 43 39

85 80 74 67 59

51 42 35 32

67 58 51 47

Properties A

(in2)

rx (in.) ry (in.)

13.7 3.25 1.84

12.2 3.22 1.83

10.7 3.21 1.81

10.0 3.20 1.80

9.13 3.21 1.77

8.37 3.29 1.35

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.36 3.30 1.30

6.49 3.31 1.26

3 - 92

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 9 59.5

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

48.5

536

744

477

663

438

608

389

507

339

393

10 12 14 16 18

479 456 430 402 372

636 594 548 499 449

426 406 383 357 331

567 529 487 444 399

390 370 349 325 301

518 482 444 403 361

346 329 309 288 266

436 407 376 344 310

302 287 270 252 233

343 323 302 278 254

20 22 24 26 28

342 311 281 251 222

399 350 303 259 224

304 276 249 222 197

354 310 268 229 198

275 250 225 200 177

320 279 241 205 177

244 221 199 177 156

276 243 211 181 156

213 193 174 155 136

229 205 181 158 137

30 34 38 42 43

195 152 121 99 95

172 134 107 88 84

154 120 96 79

136 106 85 69

119 93 74 61

536

744

477

663

438

608

389

507

339

393

10 12 14 16 18

471 450 427 401 374

622 584 543 499 453

415 397 376 353 329

546 513 477 438 397

379 362 343 322 300

496 467 434 398 361

331 317 300 282 263

411 388 362 334 305

285 272 258 243 226

320 304 287 267 246

20 22 24 26 28

346 318 289 260 233

407 361 317 274 237

304 279 253 228 203

356 315 276 238 206

277 254 230 207 185

324 286 251 216 187

242 222 201 181 161

275 245 216 188 163

209 192 174 156 139

225 203 182 161 140

30 34 38 42 43

206 161 129 106 101

180 140 112 92 88

163 127 102 84 80

142 111 89 73 70

123 96 77 63 61

Properties A (in2) rx (in.) ry (in.)

17.5 2.60 2.69

15.6 2.59 2.66

14.3 2.56 2.65

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

12.7 2.55 2.63

11.2 2.54 2.61

DESIGN STRENGTH OF COLUMNS

3 - 93

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

X-X AXIS

Effective length KL (ft) with respect to indicated axis

32.5

27.5

17.5

318 426 292 356 261 299 226 253 184 194 172 183 124 124 101 101

10 12 14 16 18

288 275 261 246 229

372 351 327 302 275

264 252 239 225 210

314 297 279 259 238

236 226 214 202 189

266 253 239 223 206

206 197 188 178 167

227 217 206 193 180

169 163 156 148 140

177 171 163 154 145

168 161 154 146 138

116 112 108 104 99

95 92 89 86 82

20 22 24 26 28

212 195 178 161 144

248 222 196 171 148

194 178 162 146 131

216 195 173 153 134

175 161 147 133 119

189 172 155 138 122

155 143 131 120 108

166 152 138 124 111

131 122 113 103 94

135 124 129 126 116 120 116 107 111 106 99 101 96 90 92

94 89 84 78 72

94 89 83 78 72

78 74 70 66 62

30 32 34 36 38

128 129 116 116 106 107 113 113 102 102 94 94 100 100 91 91 83 83 89 89 81 81 74 74 80 80 72 72 66 66

97 86 76 68 61

98 86 76 68 61

85 77 68 61 55

86 77 68 61 55

82 74 67 59 53

83 75 67 59 53

67 61 56 51 46

57 53 49 45 41

55 50 48 44

49 45 43 39

48 44 42 38 36

41 38 36 33 31

37 34 32 29 28

40 42 43 45 46 0

Y-Y AXIS

WT 9 35.5

Wt./ft

72 66 63 57

65 59 57 52

60 54 52 47

318 426 292 356 261 299 226 253 184 194 172 183 124 124 101 101

10 12 14 16 18

231 207 182 157 132

279 242 204 167 133

210 188 165 142 119

238 209 179 149 120

187 168 149 129 109

204 182 158 134 111

161 146 130 113 96

20 21 22 24 26

109 109 99 99 90 90 76 76 65 65

98 89 82 69 59

90 82 75 63 54

80 73 67 57 48

70 64 59 50 43

55 51

50 47

27 28

159 153 147 140 132

60 56

173 132 137 107 111 155 121 125 92 94 136 109 111 77 78 117 96 98 62 62 98 83 84 50 50 40 37

40 37

80 71 61 51 41

61 54 47 40 32

34 31

Properties A (in2) rx (in.) ry (in.)

10.4 2.74 1.70

9.55 2.72 1.69

8.82 2.71 1.69

8.10 2.71 1.67

7.33 2.70 1.65

6.77 2.77 1.29

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.88 2.76 1.27

5.15 2.79 1.22

3 - 94

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 8 50

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

44.5

38.5

33.5

450

625

401

557

346

476

301

361

10 12 14 16 18

389 365 338 310 280

510 467 420 372 324

346 324 300 275 249

454 415 373 330 287

297 278 257 235 212

386 353 316 279 243

258 241 223 203 183

300 277 251 225 199

20 22 24 26 28

251 222 194 167 144

278 234 197 167 144

223 197 172 148 128

246 207 174 148 128

189 166 145 124 107

207 174 146 124 107

163 143 124 106 92

173 148 125 106 92

30 32 34 36 37

126 111 98 87 83

111 98 87 77 73

93 82 73 65 61

80 70 62 55 52

450

625

401

557

346

476

301

361

10 12 14 16 18

391 371 349 325 300

514 479 440 399 357

346 328 309 287 265

453 422 388 351 314

295 280 263 245 226

382 356 327 297 265

254 241 226 211 194

294 276 257 236 214

20 22 24 26 28

274 248 223 198 174

315 275 236 201 174

242 219 196 173 152

277 241 206 176 152

206 186 166 147 129

234 203 174 149 129

177 160 143 127 111

192 170 148 128 111

30 32 34 36 38

151 133 118 105 95

133 117 103 92 83

112 99 88 78 70

97 85 75 67 61

Properties A (in2) rx (in.) ry (in.)

14.7 2.28 2.51

13.1 2.27 2.49

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

11.3 2.24 2.47

9.84 2.22 2.46

DESIGN STRENGTH OF COLUMNS

3 - 95

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

Y-Y AXIS

X-X AXIS

Effective length KL (ft) with respect to indicated axis

WT 8 28.5

Wt./ft

22.5

15.5

256

336

223

259

184

205

141

145

122

124

6 8 10 12 14

245 236 225 212 199

316 301 283 262 240

213 205 196 185 173

245 235 223 208 193

176 170 163 154 145

195 188 179 169 157

136 132 127 121 115

140 136 130 124 117

118 114 111 106 101

120 116 112 108 102

91 88 86 83 79

90 88 85 82 79

65 63 62 60 58

16 18 20 22 24

184 168 152 136 121

217 193 169 147 125

160 146 133 119 105

176 159 141 125 108

135 124 114 103 92

145 133 120 107 95

108 100 92 85 77

110 102 94 86 78

95 89 82 76 69

96 90 83 76 70

75 71 67 62 57

75 71 66 62 57

55 53 50 47 44

26 28 30 32 34

106 92 80 70 62

107 92 80 70 62

93 80 70 61 54

82 72 62 55 49

83 72 62 55 49

69 62 54 48 42

70 62 54 48 42

63 56 50 44 39

63 57 50 44 39

53 48 44 39 35

41 38 35 32 29

36 38 39 40 41

56 50 47 45

49 44 41 39

43 39 37

38 34 32

35 31 30 28

31 28 27 25

27 24 23 22 21

256

336

223

259

184

205

141

145

122

124

6 8 10 12 14

216 200 181 160 138

268 243 214 182 151

185 171 155 137 119

207 190 170 148 125

153 143 130 116 101

167 155 140 123 106

116 110 102 92 82

119 112 104 94 84

95 90 84 76 68

97 91 85 77 69

70 65 58 50 42

70 64 57 50 42

47 44 40 35 30

16 18 20 22

116 96 78 65

120 96 78 65

100 83 67 56

103 83 67 56

87 72 59 49

89 72 59 49

72 62 52 43

73 62 52 43

60 51 43 36

34 27

25 21

24 25 26

54 50 46

47 43 40

41 38 35

36 34 31

30 28

Properties A (in2) rx (in.) ry (in.)

8.38 2.41 1.60

7.37 2.40 1.59

6.63 2.39 1.57

5.89 2.37 1.57

5.28 2.41 1.52

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4.56 2.45 1.17

3.84 2.47 1.12

3 - 96

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 7 66

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

54.5

49.5

594

825

542

752

490

680

447

621

404

561

2 4 6 8 10

588 570 542 505 461

813 779 726 658 580

536 520 493 459 418

741 710 661 597 525

484 469 444 412 374

670 641 595 536 468

442 428 405 375 340

611 584 542 487 425

399 387 366 339 307

552 528 489 439 383

12 14 16 18 20

412 361 310 261 215

497 414 335 266 215

373 326 279 234 192

448 371 299 237 192

333 289 246 205 167

397 327 261 207 167

302 262 223 185 151

360 296 236 186 151

272 236 200 166 135

324 265 211 166 135

22 24 26 27 28

178 149 127 118 110

158 133 113 105 98

138 116 99 92 85

125 105 89 83

111 94 80 74

594

825

542

752

490

680

447

621

404

561

6 8 10 12 14

578 570 559 546 531

794 778 758 734 706

526 519 509 497 483

722 708 689 667 642

475 468 459 448 436

651 638 621 601 578

432 426 418 408 396

591 579 564 546 525

389 384 376 367 357

531 520 506 490 472

16 18 20 22 24

514 496 476 455 434

675 642 607 571 533

468 451 433 414 394

614 584 551 518 484

422 407 391 373 355

553 526 497 467 436

384 370 355 339 322

502 477 451 423 395

346 333 320 305 290

451 429 405 381 355

26 28 30 32 34

411 388 365 341 318

495 457 420 383 347

373 352 331 309 288

449 414 380 346 314

337 317 298 279 260

404 373 342 311 282

305 288 270 253 235

366 337 309 281 255

275 259 243 227 211

329 303 278 253 229

36 38 40

295 273 251

312 281 253

267 247 227

282 253 229

241 222 204

253 227 205

218 201 184

228 205 185

196 180 166

205 184 166

Properties A (in2) rx (in.) ry (in.)

19.4 1.73 3.76

17.7 1.71 3.74

16.0 1.68 3.73

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

14.6 1.67 3.71

13.2 1.66 3.70

DESIGN STRENGTH OF COLUMNS

3 - 97

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

WT 7 41

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

30.5

26.5

21.5

367

510

334

463

306

425

274

370

239

318

216

265

183

208

4 6 8 10 12

354 339 319 294 267

486 457 419 375 327

322 307 288 265 240

440 413 378 337 293

295 281 264 243 219

403 378 346 308 267

264 252 236 217 196

352 330 302 270 235

231 221 208 193 175

303 287 265 239 211

209 200 188 174 158

254 241 224 203 181

177 170 160 149 136

200 191 179 164 148

14 16 18 20 22

238 208 179 151 126

279 232 188 152 126

213 186 159 134 111

248 205 165 134 111

194 169 144 121 100

226 186 150 121 100

173 151 128 108 89

199 165 133 108 89

157 138 119 101 85

182 153 126 102 85

141 124 107 91 76

158 134 112 92 76

122 108 93 80 67

131 114 97 81 67

24 26 28 30 31

106 90 78 68

93 79 68 59

84 72 62 54

75 64 55 48

71 61 52 45 43

64 54 47 41 38

56 48 41 36 34

367

510

334

463

306

425

274

370

239

318

216

265

183

208

8 10 12 14 16

334 320 303 285 265

447 421 391 359 324

303 290 275 258 240

405 382 355 325 294

276 265 251 235 218

369 347 322 295 267

246 236 223 210 195

320 302 281 258 233

203 189 173 156 139

256 233 208 181 154

183 170 156 140 124

215 197 177 156 135

154 144 132 119 106

171 158 144 128 112

18 20 22 24 26

244 222 201 179 159

289 254 221 188 161

221 202 182 163 144

262 231 200 171 146

201 183 165 147 130

238 209 181 154 131

179 163 147 131 116

209 184 160 137 117

121 104 87 73 63

129 105 87 73 63

108 93 78 66 56

114 94 78 66 56

93 80 68 57 49

97 82 68 57 49

28 30 31 32 34

139 121 113 106 94

126 110 103 97 86

113 99 93 87 77

101 88 82 77 69

54 47 44 41

48 42 40

42 37 34

36 40 41

84 68 65

76 62 59

69 56 53

61 50

Properties A

(in2)

rx (in.) ry (in.)

12.0 1.85 2.48

10.9 1.82 2.48

9.99 1.81 2.46

8.96 1.80 2.45

7.81 1.88 1.92

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

7.07 1.87 1.91

6.31 1.86 1.89

3 - 98

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 7 19

Wt./ft

X-X AXIS Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

159

180

131

142

109

114

2 4 6 8 10

158 155 150 143 134

178 174 168 159 148

130 128 124 119 112

141 138 134 127 120

109 107 104 100 95

114 112 108 104 98

87 85 83 80 77

88 86 84 81 78

62 61 60 58 56

12 14 16 18 20

125 114 103 92 81

136 123 110 97 83

105 96 88 79 70

111 102 92 82 72

89 83 76 69 62

92 85 78 70 63

73 68 63 58 53

73 69 64 58 53

53 51 48 44 41

22 24 26 28 30

70 60 51 44 38

71 60 51 44 38

62 53 46 39 34

63 54 46 39 34

55 48 42 36 31

48 42 37 33 28

48 43 38 33 28

38 34 31 28 24

32 34 35

34 30

30 27

27 24

25 22 21

22 19 18

159

180

131

142

109

114

6 8 10 12 14

132 123 111 99 86

146 134 120 105 89

108 101 92 82 72

115 107 97 86 74

86 81 74 67 59

89 83 76 68 60

65 58 50 41 32

66 58 50 41 32

45 41 35 30 24

16 17 18 20 22

72 66 60 49 40

74 66 60 49 40

61 56 51 42 35

63 57 52 42 35

50 46 42 35 29

51 47 42 35 29

25 22 20

19 17

24 25

34 31

30 27

Properties A (in2) rx (in.) ry (in.)

5.58 2.04 1.55

5.00 2.04 1.53

4.42 2.07 1.49

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.85 2.12 1.08

3.25 2.14 1.04

DESIGN STRENGTH OF COLUMNS

3 - 99

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

X-X AXIS Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

WT 6 29

Wt./ft

26.6

22.5

261

362

238

331

225

312

202

280

180

221

2 4 6 8 10

257 247 231 210 186

355 336 306 268 227

235 226 211 192 171

325 307 280 246 208

222 214 202 186 167

307 292 269 240 207

200 193 181 167 149

276 262 241 214 184

178 172 161 148 133

218 208 193 174 152

12 14 16 18 20

160 135 110 88 71

185 145 111 88 71

147 124 102 81 66

170 134 103 81 66

147 126 105 86 70

173 139 109 86 70

131 112 93 75 61

153 123 96 75 61

116 99 82 66 54

129 106 84 66 54

22 24 25 26

59 49 45

54 46 42

58 48 45 41

51 42 39 36

44 37 34 32

261

362

238

331

225

312

202

280

180

221

6 8 10 12 14

246 238 228 216 203

333 318 300 279 257

223 216 206 196 184

301 287 271 252 231

205 194 181 166 150

274 255 232 206 179

183 174 162 148 134

244 227 206 183 159

162 154 143 131 118

194 182 167 150 132

16 18 20 22 24

189 175 160 144 129

233 208 184 160 137

171 157 144 130 116

209 187 164 143 122

134 117 101 86 72

152 127 103 86 72

119 104 89 75 63

135 112 91 75 63

105 92 79 66 56

114 97 80 66 56

26 28 30 32 34

115 101 88 77 69

117 101 88 77 69

103 90 78 69 61

104 90 78 69 61

61 53 46 41

54 47 41 36

48 41 36 32

36 38 41

61 55 47

54 49 42

Properties A

(in2)

rx (in.) ry (in.)

8.52 1.50 2.51

7.78 1.51 2.48

7.34 1.60 1.96

6.61 1.58 1.94

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

5.89 1.57 1.93

3 - 100

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation 17.5

Wt./ft

X-X AXIS

9.5

158

188

120

132

2 4 6 8 10

157 152 145 135 124

186 179 169 156 140

119 116 111 104 96

131 127 121 113 104

89 87 84 80 74

91 89 86 81 76

88 86 83 78 73

97 95 91 86 80

68 66 64 61 58

70 69 67 63 60

53 52 51 48 46

54 53 51 49 46

40 39 38 37 35

12 14 16 18 20

111 98 85 72 59

124 106 89 73 59

87 78 68 59 50

93 82 71 60 50

68 62 55 48 42

70 63 56 49 42

68 61 55 48 42

73 65 58 50 43

54 49 44 40 35

55 50 45 40 35

43 40 36 33 29

33 31 29 26 24

22 24 26 28 29

49 41 35 30 28

41 35 30 25 24

36 30 26 22 21

30 26 22 19 18

26 22 19 16 15

21 19 17 14 14

19 18

17 16

14 13 13

13 12 11

30 31 32

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

WT 6

158

188

120

132

2 4 6 8 10

147 142 134 123 110

172 165 154 139 123

109 106 101 93 85

119 115 109 100 90

81 79 75 71 65

83 80 77 72 66

73 67 57 45 33

80 72 60 46 33

54 49 43 34 26

55 51 44 35 26

37 34 30 24 18

37 34 30 25 18

26 25 22 19 15

12 13 14 16 18

96 89 82 68 55

105 95 87 69 55

75 70 65 55 45

79 73 67 56 45

59 55 52 45 38

59 56 52 45 38

23 20 17

18 16

20 22 24 25

45 37 31 29

37 31 26 24

31 26 22 20

Properties A

(in2)

rx (in.) ry (in.)

5.17 1.76 1.54

4.40 1.75 1.52

3.82 1.75 1.51

3.24 1.90 0.847

2.79 1.90 0.822

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.36 1.92 0.773

2.08 1.92 0.753

DESIGN STRENGTH OF COLUMNS

3 - 101

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

WT 5 22.5

Wt./ft

19.5

16.5

203

282

175

244

148

206

135

188

117

146

115

2 4 6 8 10

199 187 170 148 124

274 253 220 182 142

172 162 147 128 107

237 218 190 157 123

146 137 125 109 92

201 185 162 135 106

133 128 119 107 94

184 173 157 136 114

115 110 102 92 81

144 136 124 109 92

98 94 87 79 69

113 108 99 88 76

12 14 16 18 20

100 77 59 47 38

105 77 59 47 38

86 67 51 40 33

91 67 51 40 33

75 58 45 35 29

79 58 45 35 29

80 67 54 42 34

91 70 54 42 34

69 57 46 36 29

76 60 46 36 29

59 49 40 32 26

64 51 40 32 26

31 28 24

27 24 20

23 21 18

21 22 24

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

203

282

175

244

148

206

135

188

117

146

115

2 4 6 8 10

199 195 188 178 167

274 266 253 235 214

171 167 161 153 143

235 227 216 201 183

143 140 134 127 119

194 188 179 166 151

128 122 113 101 88

174 163 147 126 104

109 104 96 86 75

134 126 115 100 84

89 85 78 70 61

101 96 88 78 66

12 14 16 18 20

153 139 125 110 95

191 167 143 120 99

131 119 106 93 80

163 142 121 101 83

109 98 87 76 66

134 116 99 82 67

74 60 47 38 30

82 62 47 38 30

63 51 40 32 26

68 52 40 32 26

51 41 32 26 21

54 42 32 26 21

22 24 26 28 30

81 69 59 50 44

82 69 59 50 44

68 57 49 42 37

55 47 40 34 30

32 33

39 36

32 30

Properties A (in2) rx (in.) ry (in.)

6.63 1.24 2.01

5.73 1.24 1.98

4.85 1.26 1.94

4.42 1.45 1.37

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3.81 1.44 1.36

3.24 1.46 1.33

3 - 102

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi X

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85)

Designation

WT 5 9.5

Wt./ft

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

8.5

7.5

104

2 4 6 8 10

85 82 77 70 62

103 98 91 81 71

76 73 68 63 56

88 85 79 71 62

65 63 59 54 49

75 72 67 61 54

43 41 39 37 34

44 43 41 38 35

12 14 16 18 20

54 46 38 30 25

60 49 39 30 25

49 42 34 28 23

53 44 35 28 23

43 37 31 25 20

46 39 31 25 20

30 27 23 19 16

31 27 23 20 16

22 24 25 26

20 17 16

19 16 14 13

17 14 13 12

13 11 10 10

104

2 4 6 8 10

74 67 56 43 31

87 77 62 46 31

62 56 47 36 25

70 62 51 37 25

49 45 37 29 20

54 48 40 29 20

30 28 24 19 14

30 28 24 20 14

12 13 14

22 18 16

18 15 13

14 12

10 9

Properties A (in2) rx (in.) ry (in.)

2.81 1.54 0.874

2.50 1.56 0.844

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

2.21 1.57 0.810

1.77 1.57 0.785

DESIGN STRENGTH OF COLUMNS

3 - 103

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Structural tees cut from W shapes

Design axial strength in kips (Ď&#x2020; = 0.85) Designation

WT 4 14

Wt./ft

10.5

7.5

6.5

126

175

108

150

131

112

2 3 4 5 6

122 118 112 105 96

168 160 148 135 121

105 101 96 90 82

144 137 127 116 103

92 89 86 81 76

127 121 114 106 97

79 76 73 70 65

108 104 98 91 83

67 65 63 60 57

92 89 84 79 73

58 56 54 52 49

79 77 73 69 64

41 40 38 37 35

45 44 42 40 38

8 10 12 14 16

78 60 43 32 24

90 62 43 32 24

67 51 36 27 20

77 52 36 27 20

64 52 39 29 22

76 57 40 29 22

55 45 35 26 20

67 50 35 26 20

49 41 33 25 19

60 47 34 25 19

43 36 29 22 17

52 41 30 22 17

30 26 21 16 12

33 27 21 16 12

16 14

15 14 12

13 12 11

10 9 8

18 19 20

Y-Y AXIS

Effective length KL (ft) with respect to indicated axis

X-X AXIS

126

175

108

150

131

112

2 4 6 8 10

123 119 112 104 93

169 161 149 133 116

105 101 96 88 80

143 137 127 113 98

89 85 77 68 57

121 113 99 83 66

75 70 64 56 47

100 93 82 68 54

60 54 45 35 25

79 68 53 37 25

49 44 36 28 19

63 55 43 29 19

33 30 25 20 15

35 32 27 21 15

12 14 16 18 20

82 71 60 49 40

97 79 62 49 40

70 60 51 42 34

83 67 53 42 34

47 37 28 22 18

49 37 28 22 18

38 30 23 18 15

40 30 23 18 15

17 13

14 10

10 8

21 22 24 26 27

36 33 28 24 22

31 28 24 20

Properties A

(in2)

rx (in.) ry (in.)

4.12 1.01 1.62

3.54 .999 1.61

3.08 1.12 1.26

2.63 1.14 1.23

2.22 1.22 0.876

Note: Heavy line indicates Kl / r of 200.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.92 1.23 0.843

1.48 1.20 0.841

3 - 104

COLUMN DESIGN

Single-Angle Struts

Design strengths of single-angle struts were formerly not tabulated in this Manual because of the difficulty in loading such struts concentrically. Concentric loading can be accomplished by milling the ends of an angle and loading it through bearing plates. However, in common practice, the eccentricity of loading is relatively large, and its neglect in design may lead to an under-designed member. The design of single-angle struts is governed by the AISC Specification for Load and Resistance Factor Design of Single-Angle Members, which is reproduced in Part 6 of this Manual. The following example illustrates the design procedure for an equal-leg angle loaded eccentrically. The design strengths for concentric loading, tabulated below, are useful in solving the interaction equations for combined axial force and bending. The tables below are based on Zureick (1993), revised to conform with the AISC Single-Angle Specification (LRFD). EXAMPLE 3-8

An angle 2×2×1⁄4 is loaded by a gusset plate attached to one leg with an eccentricity of 0.8 in. from the centroid, as shown in Figure 3-3. Determine the factored compressive load Pu which may be applied. The effective length KL is 4.0 ft.

Given:

A = 0.938 in.2 rz = 0.391 in. Ix = Iy = 0.348 in.4

3 84

′

7′

′′

7 .2

0.8′′

0.592 ′′

′′

8 0.

′ 4′

Fig. 3-3 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 105

α = 45° Fy = 50 ksi Solution:

Determine the properties for the principal axes Z-Z and W-W as follows: Iz = Arz2 = 0.938(0.391)2 = 0.143 in.2 Iw + Iz = Ix + Iy Iw = 0.348 + 0.348 − 0.143 = 0.552 in.4 rw

 √ √  Iw = A

0.552 = 0.767 in. 0.938

From the tables which follow, the design compressive strength φcPn = 14 kips for KL = 4 ft. For combined axial compression and bending, the latter is taken about the principal axes in accordance with the Single-Angle LRFD Specification (Section 6). For equal leg angles— Major principal axis (W-W) bending (Section 5.3.1): 0.46Eb2t 2 l 0.46(29,000 ksi)(2 in.)2(0.25 in.)2 = 1.0 × 48 in. = 69.5 k-in. Iw 0.552 in.4 My = Fy Sw = Fy = 50 ksi × cw 1.414 in. = 19.5 k-in.

Mob = Cb

Since Mob > My (Section 5.1.3), Mnw = [1.58 − 0.83  √ My / Mob ] My ≤ 1.25My = [1.58 − 0.83  √ 19.5 / 69.5 ] My = 1.14My = 1.14 × 19.5 k-in. = 22 k-in. According to Section 5.1.1, (= 2 in. / 0.25 in. = 8) < 0.382 √  E /Fy (= 0.382 √  29,000 / 50  = 9.2), Mnw ≤ 1.25Fy Sc = 1.25Fy Sw = 1.25My

for b / t

This is satisfied since Mnw = 1.14My. Minor principal axis (Z-Z) bending (Section 5.3.1): With the leg tips of the angle in tension and the angle corner in compression AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 106

COLUMN DESIGN

Mnz = 1.25My = 1.25Fy Sz = 1.25Fy = 1.25 × 50 ksi ×

Iz cz

0.143 in.4 0.837 in.

= 11 k-in. Assuming

Pu ≥ 0.2, Interaction Equation 6-1a governs. φcPn

Muz    Pu 8  Muw  φ P + 9  φ M + φ M   ≤ 1.0 b nz    b nw  c n According to Section 6.1.1, for flexural compression Mu shall be multiplied by B1 (Equation 6-2). Major principal axis (W-W) bending:

Kl / rw = 1.0 × 48 / 0.767 = 62.2 From LRFD Specification Table 8, Pe / Ag = 73.1

Pe1w = 73.1(0.938) = 68.6 kips B1w =

Cm 0.85 = < 1. Use B1w = 1.0. 1 − Pu / Pe1w 1 − Pu / 68.6

Minor principal axis (Z-Z) bending:

Kl / rw = 1.0 × 48 / 0.391 = 122.8 From LRFD Specification Table 8, Pe / Ag = 19.0

Pe1z = 19.0(0.938) = 17.8 kips B1z =

Cm 0.85 = 1 − Pu / Pe1z 1 − Pu / 17.8

Conservatively adding the maximum axial and flexural terms, Equation 6-1a becomes Pu ×0.277 in. Pu 8  Pu ×0.843 in. × 1.0 0.85  +  +  ≤ 1.0 14 kips 9  0.9×22 kip−in. 0.9×11 kip−in. 1−Pu / 17.8 

Pu = 7 kips Checking

Pu 7 kips = = 0.5 > 0.2 o.k. 14 kips φcPn

A less conservative approach would have involved applying the interaction equation separately at the corner and the two leg tips of the angle, with the proper signs (+ or −) for compression and tension. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 107

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

w Y z

8× ×6

Size Thickness

7⁄ 8

3⁄ 4

5⁄ 8

9⁄ 16

1⁄ 2

7⁄ 16

Wt./ft

44.2

39.1

33.8

28.5

25.7

23.0

20.2

Effective length KL (ft)

421

585

373

518

322

447

270

352

235

303

199

253

163

203

1 2 3 4 5

406 398 393 384 371

555 541 531 515 490

355 347 342 336 325

484 468 460 448 429

301 292 288 284 277

408 391 383 375 363

246 235 231 228 224

311 294 287 282 276

210 199 195 193 190

262 245 239 235 230

174 163 160 158 156

213 197 192 188 185

138 128 125 123 122

166 151 146 144 141

6 7 8 9 10

353 333 311 287 263

458 422 383 344 305

311 293 274 253 232

402 371 338 303 268

266 252 236 219 201

343 319 291 262 233

217 208 195 182 167

265 250 231 210 189

186 179 170 159 148

224 214 200 184 167

153 149 143 135 126

181 175 166 155 142

120 118 115 110 104

139 136 131 124 116

11 12 13 14 15

239 215 192 169 147

266 230 196 169 147

211 190 169 149 130

235 203 173 149 130

183 165 147 130 114

204 177 151 130 114

152 137 123 109 95

167 146 125 109 95

135 123 111 99 87

149 131 114 99 87

117 107 96 87 77

128 114 101 88 77

97 90 82 75 67

107 97 87 77 67

16 17 18 19 20

130 115 103 92 83

115 102 91 81 74

100 89 79 71 64

84 74 66 60 54

77 68 61 55 49

68 60 54 49 44

60 53 48 43 39

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 108

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

w Y z

8× ×4

Size Thickness Wt./ft

37.4

Effective length KL (ft)

7⁄ 8

3⁄ 4

33.1

5⁄ 8

28.7

24.2

1⁄ 2

21.9

7⁄ 16

19.6

17.2

356

495

315

438

273

380

230

299

200

258

170

216

139

174

1 2 3 4 5

342 331 315 293 267

468 446 417 378 332

300 289 275 257 234

408 387 363 330 290

256 245 235 220 201

346 326 307 280 248

209 198 190 179 165

264 246 233 216 194

179 169 162 154 142

223 207 197 184 167

149 139 134 128 119

182 168 160 150 138

118 109 105 101 95

142 128 122 116 108

6 7 8 9 10

238 208 177 148 121

283 234 187 149 121

209 183 156 131 107

248 205 164 131 107

180 157 135 113 92

212 176 141 113 92

148 130 112 94 77

169 142 117 94 77

129 114 99 84 70

146 125 104 84 70

109 98 86 73 61

123 107 90 74 61

88 80 71 62 53

98 87 75 63 53

11 12 13 14

100 85 72 62

89 75 64 55

77 65 56 48

65 55 47 41

58 49 42 37

52 44 38 33

45 38 33 29

7× ×4

Size 3⁄ 4

Thickness Wt./ft

5⁄ 8

26.2

Effective length KL (ft)

9⁄ 16

1⁄ 2

22.1

7⁄ 16

17.9

3⁄ 8

15.7

13.6

249

346

210

288

164

212

136

173

108

134

1 2 3 4 5

236 228 219 205 188

320 306 289 264 233

194 187 180 170 156

258 245 233 215 191

146 139 134 128 119

182 171 164 154 140

118 111 107 103 97

144 133 128 122 113

90 85 82 79 76

107 99 95 91 86

6 7 8 9 10

168 147 126 106 87

200 166 134 107 87

140 123 106 89 73

165 138 113 90 73

108 96 84 71 59

124 106 89 72 59

89 80 71 61 51

101 88 75 62 51

70 64 57 50 43

79 70 61 52 43

11 12 13 14

72 61 52 45

61 52 44 38

49 42 36 31

43 37 31 27

37 31 27 23

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 109

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

Wt./ft

7⁄ 8

3⁄ 4

27.2

Effective length KL (ft)

Y z

6× ×4

Size Thickness

5⁄ 8

23.6

9⁄ 16

20.0

1⁄ 2

18.1

7⁄ 16

16.2

3⁄ 8

14.3

5⁄ 16

10.3

12.3

259 359 225 312 190 264 172 239 154 205 132 171 107 136

100

1 2 3 4 5

250 244 233 217 198

343 331 310 282 248

91 111 87 105 85 102 82 97 78 91

66 63 61 59 57

78 73 70 68 65

6 7 8 9 10

177 155 133 111 91

212 154 184 129 155 117 139 104 121 176 135 153 113 129 102 116 91 102 142 115 124 98 105 88 94 79 84 112 97 98 82 83 74 75 67 67 91 80 80 67 67 61 61 55 55

89 102 79 87 68 73 58 59 48 48

72 65 57 49 41

82 72 61 50 41

54 50 45 39 34

61 55 48 41 34

11 12 13 14

75 63 54 47

40 34 29 25

34 29 25 22

29 24 21 18

75 63 54 47

215 210 201 188 172

293 284 268 244 215

66 55 47 41

178 174 168 157 144

56 47 40 35

241 233 222 203 180

56 47 40 35

159 155 150 141 130

51 43 37 32

214 206 197 182 162

139 135 131 125 115

51 43 37 32

46 38 33 28

180 172 166 155 139

46 38 33 28

116 112 109 105 98

145 138 133 126 116

40 34 29 25

6× ×31⁄2

Size 1⁄ 2

Thickness Wt./ft

3⁄ 8

15.3

Effective length KL (ft)

5⁄ 16

11.7

9.8

146

195

101

128

1 2 3 4 5

132 127 121 112 100

171 162 152 137 118

86 82 79 75 69

105 99 94 88 79

63 59 57 55 51

74 69 66 63 58

6 7 8 9 10

87 74 60 48 39

98 78 61 48 39

61 53 44 36 30

68 56 45 36 30

47 41 36 30 25

51 44 37 30 25

11 12

33 28

25 21

21 18

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 110

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

w Y z

5× ×31⁄2

Size 3⁄ 4

Thickness Wt./ft

19.8

Effective length KL (ft)

5⁄ 8

1⁄ 2

16.8

3⁄ 8

13.6

10.4

1⁄ 4

8.7

7.0

188

261

159

221

130

180

126

1 2 3 4 5

182 176 165 150 133

249 238 218 192 162

152 148 139 127 113

207 199 183 162 137

120 117 112 103 91

162 156 146 130 111

85 82 80 75 68

107 102 98 90 79

64 61 60 57 53

77 74 71 67 61

43 41 40 38 36

49 47 45 44 41

6 7 8 9 10

115 96 79 63 51

132 103 79 63 51

97 82 67 53 43

112 88 67 53 43

79 67 55 44 35

90 71 55 44 35

59 50 42 33 27

66 54 42 33 27

47 41 34 28 23

52 44 35 28 23

34 30 26 22 18

37 32 27 22 18

11 12

42 35

36 30

29 25

23 19

19 16

15 13

5× ×3

Size 1⁄ 2

Thickness Wt./ft

7⁄ 16

12.8

Effective length KL (ft)

5⁄ 16

3⁄ 8

11.3

5⁄ 16

9.8

1⁄ 4

8.2

6.6

122

169

107

146

118

1 2 3 4 5

112 108 100 88 75

151 143 128 108 87

97 93 87 77 66

127 120 109 93 76

80 76 72 65 56

100 94 87 76 63

60 57 54 50 44

72 68 64 58 49

40 38 36 34 31

46 44 42 39 34

6 7 8 9 10

62 49 38 30 24

66 49 38 30 24

54 43 33 27 22

58 43 33 27 22

46 37 29 23 19

49 37 29 23 19

37 30 24 19 16

40 31 24 19 16

27 23 19 15 13

29 24 19 15 13

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 111

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

1⁄

Thickness Wt./ft

3⁄ 8

11.9

Effective length KL (ft)

Y z

4× ×31⁄2

Size

5⁄ 16

9.1

1⁄ 4

7.7

6.2

113

158

120

1 2 3 4 5

107 105 99 90 79

146 142 131 114 95

78 77 75 68 60

104 102 98 87 73

63 61 60 57 51

79 76 74 69 59

43 42 42 41 38

52 50 49 48 44

6 7 8 9 10

67 56 45 35 29

76 58 45 35 29

51 43 35 27 22

58 45 34 27 22

43 36 29 23 19

48 38 29 23 19

33 28 23 19 15

37 30 24 19 15

11 12

24 20

18 15

15 13

13 11

4× ×3

Size 5⁄ 8

Thickness Wt./ft

1⁄ 2

13.6

Effective length KL (ft)

7⁄ 16

11.1

3⁄ 8

9.8

5⁄ 16

8.5

1⁄ 4

7.2

5.8

129

179

105

146

129

112

1 2 3 4 5

124 119 108 95 81

170 160 141 118 93

100 96 88 78 66

136 129 114 96 76

87 84 78 68 58

117 112 101 84 67

73 71 66 59 50

98 94 86 73 58

59 57 55 49 42

74 71 67 58 47

41 40 39 36 32

50 48 46 42 36

6 7 8 9 10

66 52 39 31 25

70 51 39 31 25

54 42 32 26 21

57 42 32 26 21

47 37 29 23 18

51 37 29 23 18

41 32 25 20 16

44 32 25 20 16

35 27 21 17 14

37 27 21 17 14

27 22 17 14 11

29 22 17 14 11

31⁄2×3

Size Thickness

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

Wt./ft

10.2

7.9

6.6

5.4

Effective length KL (ft)

135

104

1 2 3 4 5

93 89 81 71 59

127 120 105 87 68

69 67 62 54 46

93 90 81 67 53

56 55 52 46 38

73 71 66 56 44

41 40 39 36 30

51 49 48 42 34

6 7 8 9 10

48 37 28 22 18

50 37 28 22 18

37 29 22 17 14

39 29 22 17 14

31 24 19 15 12

33 24 19 15 12

25 20 15 12 10

27 20 15 12 10

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 112

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

w Y z

31⁄2×21⁄2

Size 1⁄ 2

Thickness

3⁄ 8

9.4

Wt./ft

Effective length KL (ft)

1⁄ 4

7.2

4.9

124

1 2 3 4 5 6 7 8 9

85 79 70 58 46

116 105 88 68 49 34 25 19

63 60 53 44 35 26 19 15

85 79 67 52 38 26 19 15

38 37 34 29 24 18 13 10 8

47 45 41 33 25 18 13 10 8

34 25 19

3× ×21⁄2

Size Thickness

1⁄ 2

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

Wt./ft

8.5

6.6

5.6

4.5

3.39

Effective length KL (ft)

113

1 2 3 4 5

78 72 63 52 40

107 96 79 60 42

58 55 48 40 31

79 73 61 46 33

48 46 41 34 26

65 61 51 39 28

37 36 33 27 21

48 46 40 31 23

24 23 22 19 16

29 28 26 22 17

6 7 8

29 22 17

23 17 13

19 14 11

16 12 9

12 9 7

3× ×2

Size 1⁄ 2

Thickness

7.7

Wt./ft

Fy Effective length KL (ft)

3⁄ 8

5⁄ 16

5.9

5.0

3⁄ 16

4.1

3.07

0 1 2 3 4 5

73 69 61 50 37 26

101 94 80 60 40 26

56 52 47 38 29 20

78 71 61 46 31 20

47 43 39 32 24 17

66 58 51 39 26 17

39 34 31 26 20 14

51 43 39 30 21 14

27 22 21 18 14 10

34 27 25 21 15 10

6 7

18 13

14 10

12 9

10 7

7 5

21⁄2×2

Size 3⁄ 8

Thickness

5⁄ 16

5.3

Wt./ft

Fy Effective length KL (ft)

1⁄ 4

0 1 2 3 4 5 6 7

1⁄ 4

4.5

3⁄ 16

3.62

2.75

50 48 42 34 25 17 12 9

70 65 55 41 27 17 12 9

42 40 36 29 21 15 10 7

59 54 46 34 23 15 10 7

34 31 29 23 17 12 8 6

48 42 37 28 18 12 8 6

26 22 21 17 13 9 6 5

33 27 25 20 14 9 6 5

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 113

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

Y z

8× ×8

Size 11⁄8

Thickness Wt./ft

7⁄ 8

56.9

Effective length KL (ft)

51.0

3⁄ 4

45.0

5⁄ 8

38.9

9⁄ 16

32.7

1⁄ 2

29.6

26.4

541

752

486

675

428

594

369

513

310

405

270

348

229

291

6 7 8 9 10

484 465 444 421 397

643 608 570 530 488

435 417 398 378 356

578 546 512 476 438

383 368 351 334 315

510 482 452 421 388

320 318 304 289 273

420 417 392 365 337

254 252 251 243 230

311 309 306 294 273

213 212 210 209 202

256 255 253 250 240

173 172 171 170 168

203 202 201 199 197

11 12 13 14 15

372 346 320 294 269

446 404 363 323 283

334 311 288 264 242

401 363 326 290 255

295 275 255 234 215

355 322 289 258 227

256 239 221 204 187

308 280 252 225 198

215 201 186 172 157

251 230 208 187 167

191 178 166 154 141

222 204 186 169 151

165 155 144 134 124

191 177 162 148 133

16 17 18 19 20

244 221 197 177 159

249 221 197 177 159

219 198 177 159 143

224 198 177 159 143

195 176 158 141 128

199 177 158 141 128

170 154 138 124 112

174 154 138 124 112

143 130 116 104 94

147 130 116 104 94

129 118 107 95 86

134 119 106 95 86

114 104 95 85 77

120 106 95 85 77

21 22 23 24 25

145 132 121 111 102

130 118 108 99 92

116 105 96 89 82

101 92 84 78 71

85 78 71 65 60

78 71 65 60 55

70 64 58 53 49

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 114

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

w Y z

6× ×6

Size Thickness Wt./ft

7⁄ 8

1 37.4

3⁄ 4

33.1

5⁄ 8

28.7

9⁄ 16

24.2

1⁄ 2

21.9

7⁄ 16

19.6

3⁄ 8

17.2

5⁄ 16

14.9

12.4

Effective length KL (ft)

0 356 495 315 438 273 380 230 320 208 289 186 249 159 206 129 164 98 120 1 2 3 4 5

346 343 339 326 310

476 469 462 438 409

304 300 298 289 275

416 408 404 387 361

260 255 253 250 238

354 345 342 336 314

214 209 207 205 201

289 279 275 273 265

190 184 182 181 180

255 244 241 238 236

166 160 158 157 155

213 202 199 197 195

137 131 129 128 127

170 107 129 77 160 100 119 71 157 99 117 69 156 98 115 69 154 97 114 68

89 81 79 78 77

6 7 8 9 10

292 272 250 228 205

376 340 303 266 230

258 241 221 202 181

332 301 268 235 203

224 209 192 175 157

288 261 232 204 176

189 177 163 148 134

244 221 197 174 151

171 160 147 134 121

221 200 179 157 136

153 143 132 120 108

192 174 156 138 120

126 124 114 105 95

152 149 134 120 105

96 113 68 95 112 67 94 110 66 87 99 66 79 88 63

76 76 75 74 71

11 12 13 14 15

183 161 140 121 105

196 164 140 121 105

162 142 124 107 93

173 140 150 119 128 108 116 145 123 126 105 108 95 98 124 108 107 92 92 83 83 107 92 92 79 79 72 72 93 81 81 69 69 62 62

97 103 85 87 74 74 64 64 56 56

85 75 66 57 50

92 78 67 57 50

71 64 57 49 43

77 67 57 49 43

58 52 47 42 37

63 56 49 42 37

16 17 18 19

92 82 73 65

82 72 64 58

49 43 39 35

44 39 35 31

38 34 30 27

32 29 25 23

82 72 64 58

71 63 56 50

61 54 48 43

55 49 43 39

49 43 39 35

5× ×5

Size 7⁄ 8

Thickness Wt./ft

3⁄ 4

27.2

Effective length KL (ft)

55 49 43 39

5⁄ 8

23.6

1⁄ 2

20.0

7⁄ 16

16.2

3⁄ 8

14.3

5⁄ 16

12.3

10.3

259

359

225

312

190

264

154

214

135

184

115

149

114

1 2 3 4 5

251 249 241 228 212

345 341 325 301 272

216 214 209 198 184

296 291 283 262 237

179 177 176 167 156

244 239 236 221 200

141 138 137 135 127

189 183 181 179 163

121 117 116 115 112

157 152 150 148 141

99 95 94 93 92

122 117 115 114 112

73 70 69 68 67

88 83 81 80 79

6 7 8 9 10

194 175 155 135 116

241 209 177 146 119

169 152 135 118 102

210 182 154 128 104

143 129 114 100 86

178 154 131 108 88

116 105 93 82 70

145 126 107 89 72

102 93 82 72 62

126 110 94 78 64

87 79 71 62 54

105 92 80 67 56

67 64 57 51 45

78 74 65 55 47

11 12 13 14 15

98 82 70 60 53

86 72 61 53 46

73 61 52 45 39

60 50 43 37 32

53 44 38 33 28

46 39 33 28 25

38 33 28 24 21

39 33 28 24 21

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF COLUMNS

3 - 115

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

Wt./ft

3⁄ 4

Effective length KL (ft)

5⁄ 8

18.5

1⁄ 2

15.7

7⁄ 16

12.8

3⁄ 8

11.3

5⁄ 16

9.8

1⁄ 4

8.2

6.6

176

245

149

207

122

169

107

149

129

101

1 2 3 4 5

171 168 158 144 129

236 228 209 185 159

144 142 134 122 109

196 194 178 157 135

114 113 109 100 89

155 152 145 128 110

99 97 96 88 79

133 130 128 113 97

83 81 80 76 68

110 107 106 98 84

66 64 64 63 57

82 79 78 77 68

46 44 44 43 43

55 52 51 51 50

6 7 8 9 10

112 96 79 64 52

131 105 81 64 52

95 81 67 54 44

111 89 69 54 44

78 66 55 44 36

91 73 56 44 36

69 59 49 40 32

81 65 50 40 32

60 51 43 34 28

70 56 44 34 28

50 43 36 29 24

57 47 37 29 24

39 34 29 24 19

44 37 30 24 19

11 12 13

43 36

36 30

30 25 21

26 22 19

23 19 16

19 16 14

16 13 11

31⁄2×31⁄2

Size 1⁄ 2

Thickness Wt./ft

7⁄ 16

11.1

Fy Effective length KL (ft)

Y z

4× ×4

Size Thickness

3⁄ 8

9.8

5⁄ 16

8.5

1⁄ 4

7.2

5.8

105

146

129

112

1 2 3 4 5

100 99 91 81 70

137 134 119 102 83

87 86 80 72 62

118 116 106 90 74

74 73 70 62 54

99 97 91 78 64

60 59 58 53 46

78 76 75 65 54

44 43 42 41 36

53 52 51 50 42

6 7 8 9 10

59 48 37 29 24

65 49 37 29 24

52 42 33 26 21

58 43 33 26 21

45 37 29 23 18

50 37 29 23 18

38 31 24 19 16

42 32 24 19 16

31 25 20 16 13

34 26 20 16 13

3× ×3

Size 1⁄ 2

Thickness Wt./ft

7⁄ 16

9.4

Fy Effective length KL (ft)

3⁄ 8

8.3

5⁄ 16

7.2

1⁄ 4

6.1

3⁄ 16

4.9

3.71

124

109

1 2 3 4 5

86 82 73 62 51

117 109 94 76 57

75 72 65 55 45

102 97 83 67 51

64 63 56 48 40

86 84 72 58 44

52 52 47 41 33

70 69 61 49 38

40 39 38 33 27

51 50 48 39 30

25 25 24 24 20

30 29 29 28 22

6 7 8 9

40 30 23 18

41 30 23 18

36 27 20 16

31 23 18 14

32 23 18 14

26 20 15 12

27 20 15 12

21 16 12 10

22 16 12 10

16 12 9 7

17 12 9 7

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

3 - 116

COLUMN DESIGN

Fy = 36 ksi

Fy = 50 ksi

COLUMNS Single angles

w x

Design axial strength in kips (φ = 0.90)

w Y z

21⁄2×21⁄2

Size 1⁄ 2

Thickness Wt./ft

7.7

Fy Effective length KL (ft)

3⁄ 8

5⁄ 16

5.9

1⁄ 4

5.0

3⁄ 16

4.1

3.07

101

1 2 3 4 5

71 64 55 44 33

97 85 68 50 33

53 49 42 34 25

73 65 52 38 26

44 42 36 29 21

59 55 44 33 22

34 34 29 23 18

46 45 36 27 18

24 23 22 18 13

29 28 26 20 14

6 7 8

23 17 13

18 13 10

15 11 9

13 9 7

10 7 5

2× ×2

Size Thickness

3⁄ 8

5⁄ 16

1⁄ 4

3⁄ 16

1⁄ 8

Wt./ft

4.7

3.92

3.19

2.44

1.65

1 2 3 4 5

42 36 28 20 13

57 46 33 20 13

35 31 24 17 11

48 39 28 17 11

28 25 19 14 9

38 32 23 14 9

20 19 15 11 7

27 25 18 11 7

11 11 10 7 5

13 13 11 8 5

Effective length KL (ft)

36 0

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

REFERENCES

3 - 117

COLUMN BASE PLATES

The design of column base plates is covered in Part 11 (Volume II) of this LRFD Manual. REFERENCES

Galambos, T. V. (ed.), 1988, Guide to Stability Design Criteria for Metal Structures, Fourth Edition, Structural Stability Research Council, John Wiley & Sons, New York, NY. Geschwindner, L., 1993, “The ‘Leaning’ Column in ASD and LRFD,” Proceedings of the 1993 National Steel Construction Conference, AISC, Chicago, IL. Uang, C. M., S. W. Wattar, and K. M. Leet, 1990, “Proposed Revision of the Equivalent Axial Load Method for LRFD Steel and Composite Beam-Column Design,” Engineering Journal, 1st Qtr., AISC, Chicago. Zureick, A., 1993, “Design Strength of Concentrically Loaded Single-Angle Struts,” Engineering Journal, 4th Qtr., AISC, Chicago.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4-1

PART 4 BEAM AND GIRDER DESIGN OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 DESIGN STRENGTH OF BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5 Design Strength If Elastic Analysis Is Used . . . . . . . . . . . . . . . . . . . . . . . . . 4-5 Flexural Design Strength for Cb = 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6 Flexural Design Strength for Cb > 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Design Strength If Plastic Analysis Is Used . . . . . . . . . . . . . . . . . . . . . . . . 4-10 LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS . . . 4-11 Use of the Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES . . . . . . . . 4-23 FACTORED UNIFORM LOAD TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 Use of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30 Reference Notes on Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32 Tables, Fy = 36 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35 Tables, Fy = 36 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-61 Tables, Fy = 36 ksi: Channels (C, MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64 Tables, Fy = 50 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-72 Tables, Fy = 50 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98 Tables, Fy = 50 ksi: Channels (C, MC)) . . . . . . . . . . . . . . . . . . . . . . . . . . 4-101 DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH GREATER THAN Lp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109 General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109 Charts (Fy = 36 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-113 Charts (Fy = 50 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-139 PLATE GIRDER DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167 General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167 Flexure and Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167 Table of Dimensions and Properties of Built-up Wide-Flange Section . . . . . . . . . . 4-167 Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-168 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4-2

BEAM AND GIRDER DESIGN

BEAM DIAGRAMS AND FORMULAS . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187 Frequently Used Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-188 Table of Concentrated Load Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . 4-189 Static Loading Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-190 Design Properties of Cantilevered Beams . . . . . . . . . . . . . . . . . . . . . . . . 4-205 FLOOR DEFLECTIONS AND VIBRATIONS . . . . . . . . . . . . . . . . . . . . . . . 4-207 Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207 Deflections and Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207 Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-208 BEAMS: OTHER SUBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-211 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-213

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

OVERVIEW

4-3

OVERVIEW Beam tables are located as follows: Load Factor Design Selection Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15 Moment of Inertia Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24 Factored Uniform Load Tables, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . 4-35 Factored Uniform Load Tables, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . 4-72 Beam charts are located as follows: Beam Design Moments, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . 4-113 Beam Design Moments, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . 4-139 Plate Girder Design Tables are on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-183 Beam Diagrams and Formulas begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187 Additional information related to beam design is provided as follows: Floor deflections and vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4-4

BEAM AND GIRDER DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF BEAMS

4-5

DESIGN STRENGTH OF BEAMS General

Beams are proportioned so that no applicable strength limit state is exceeded when subjected to factored load combinations and that no serviceability limit state is exceeded when subjected to service loads. Strength limit states for beams include local buckling, lateral torsional buckling, and yielding. Serviceability limit states may include, but are not limited to, deflection and vibration. The flexural design strength for beams must equal or exceed the required strength based on the factored loads. The design strength φbMn for each applicable limit state shall equal or exceed the maximum moment Mu as determined from the applicable factored load combinations given in Section A4 of the LRFD Specification. Values of φbMn are tabulated in the pages to follow. These values are based on beam behavior as shown in Figure 4-1 and explained in the following discussion. It should be noted that the LRFD Specification expresses values for moments and lengths in kip-in. and inches. In this and other parts of the LRFD Manual, these values are tabulated in kip-ft and feet. The required strength can be determined by either elastic or plastic analysis. Design Strength If Elastic Analysis Is Used

The flexural design strength of rolled I and C shape beams designed using elastic analysis, according to LRFD Specification Section F1 is: φbMn where φb = 0.90

Mp M n′

Mn Mr (CbMn – Mn) CbMn Mn

L ′p

Lm′

Fig. 4-1 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4-6

BEAM AND GIRDER DESIGN

Mn = nominal flexural strength as determined by the limit state of yielding, lateraltorsional buckling, or local buckling Flexural Design Strength for Cb = 1.0

Compact Sections (Cb = 1.0)

When Lb ≤ Lp

The flexural design strength of compact (flange and web local buckling λ ≤ λp) I-shaped and C-shaped rolled beams (as defined in Section B5 of the LRFD Specification) bent about the major or minor axis is: φbMn = φbMp = φbZFy / 12 In minor axis flexure this is true for all unbraced lengths, but for bending about the major axis the distance Lb between points braced against lateral movement of the compression flange or between points braced to prevent twist of the cross-section shall not exceed the value Lp (see Figure 4-1). Lp =

300ry Fy √

(F1-4)

When Lp < Lb ≤ Lr The flexural design strength of compact I or C rolled shapes bent about the major axis, from LRFD Specification Section F1.2, is:  Lb − Lp  φbMn = φbMp − φb(Mp − Mr)  ≤ φbMp  Lr − Lp  where the limiting length Lr and the corresponding buckling moment Mr (see Figure 4-1) are determined as follows: Lr =

ryX1 (Fy − Fr )

 √ 1+√  1 + X2(Fy − Fr)2

(F1-6)

where X1 =

π Sx

 √

4Cw X2 = Iy

EGJA 2

 Sx     GJ 

(F1-8)

φbMr = φbSx(Fy − Fr ) / 12 kip-ft Sx = section modulus about major axis, in.3 E = modulus of elasticity of steel, 29,000 ksi G = shear modulus of steel, 11,200 ksi J = torsional constant, in.4 A = cross-sectional area of beam, in.2 Cw = warping constant, in.6 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F1-9)

DESIGN STRENGTH OF BEAMS

4-7

Fr = compressive residual stress in flange: for rolled shapes Fr = 10 ksi; for welded shapes Fr = 16.5 ksi Values of J and Cw are tabulated for some shapes in Part 1 of the LRFD Manual. For values not shown, see Torsional Analysis of Steel Members (AISC, 1983). Compact and Noncompact Sections (Cb = 1.0)

When Lb > Lr

According to LRFD Specification Section F1.2b, the flexural design strength of compact and noncompact I or C rolled shapes bent about the major axis is: π φbMn = φbMcr = φb    Lb 

 √ 2

 πE  EIyGJ +   IyCw  Lb 

 SxX1√ 2  = φb    (Lb / ry) 

 √ 1+

X21X2 ≤ φbMr 2(Lb / ry)2

Noncompact Sections (Cb = 1.0)

When Lb ≤ Lp′

All rolled W shapes are compact except the W40×174, W14×99, W14×90, W12×65, W10×12, W8×10, and W6×15 for 50 ksi and the W6×15 for 36 ksi. The flexural design strength φbMn′ (see Figure 4-1) for noncompact (flange or web local buckling λp < λ ≤ λr) I and C rolled shapes bent about the major or minor axis is the smaller value for either local flange buckling or local web buckling as determined by:  λ − λp  φbMn′ = φbMp − φb(Mp − Mr)    λr − λp  For local flange buckling: λ = bf / 2tf for I-shaped members λ = bf / tf for C-shaped members Fy λp = 65 / √ λr = 141 / √  Fy − 10  For local web buckling: λ = h / tw λp = 640 / √ Fy Fy λr = 970 / √  Mp − Mn′  Lp′ = Lp + (Lr − Lp)    Mp − Mr  Sections with a width-to-thickness ratio exceeding the specified values for λr are slender shapes and must be analyzed using LRFD Specification Appendix B5.3. When Lp′ < Lb ≤ Lr AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4-8

BEAM AND GIRDER DESIGN

The flexural design strength of noncompact I or C rolled shapes bent about the major axis is determined by:  Lb − Lp  φbMn = φbMp − φb(Mp − Mr)   ≤ φbMn′  Lr − Lp  In the Load Factor Design Selection Table, in the case of the noncompact shapes, the values of φbMn′ and Lp′ are tabulated as φbMp and Lp. The formula above may be used with the tabulated values. Flexural Design Strength for Cb > 1.0

Cb is a factor which varies with the moment gradient between bracing points (Lb). For Cb greater than 1.0, the design flexural strength is equal to the tabulated value of the design flexural strength (with Cb = 1.0) multiplied by the calculated Cb value. The maximum value is φbMp for compact shapes or φbMn′ for noncompact shapes. The maximum unbraced lengths associated with the maximum flexural design strengths φbMp and φbMn′ are Lm and Lm′ (see Figure 4-1). A new expression for Cb is given in the LRFD Specification. (It is more accurate than the one previously shown.) Cb =

12.5Mmax 2.5Mmax + 3MA + 4MB + 3Mc

(F1-3)

where M is the absolute value of a moment in the unbraced beam segment as follows: Mmax , the maximum MA , at the quarter point MB , at the centerline Mc , at the three-quarter point Values for Cb for some typical loading conditions are given in Table 4-1. Compact Sections (Cb > 1.0)

When Lb ≤ Lm

The flexural design strength for rolled I and C shapes is: φbMn = φbMp When Lb > Lm The flexural design strength is: φbMn = Cb[φbMn (for Cb = 1.0)] ≤ φbMp For Lm ≤ Lr Lm = Lp +

(CbMp − Mp)(Lr − Lp) Cb(Mp − Mr) AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN STRENGTH OF BEAMS

4-9

Table 4-1. Values of Cb for Simply Supported Beams Lateral Bracing Along Span

Load

None 1.32

At load points 1.67

1.67

None 1.14

At load points 1.67

1.00

1.67

None 1.14

At load points 1.67

1.11

None

At centerline

Cbπ Mp

1.30

 √ √   √ EIyGJ 2

4CwM2p IyC2bG2J2

The value of Cb for which Lm or Lm′ equals Lr for any rolled shape is: Cb =

Fy Zx (Fy − 10)Sx

Noncompact Sections (Cb > 1.0)

When Lb ≤ Lm′

The flexural design strength for rolled I and C shapes is: φbMn = φbMn′ < φbMp When Lb > Lm′ The flexural design strength is: φbMn = Cb[φbMn (for Cb = 1.0)] ≤ φbMn′ AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1.67

1.14

For Lm > Lr

Lm =

1.11

1.30

4 - 10

BEAM AND GIRDER DESIGN

For Lm′ ≤ Lr Lm′ = Lp′ +

(CbMn′ − Mn′)(Lr − Lp) Cb(Mp − Mr)

For Lm′ > Lr Lm =

Cbπ Mp

 √ √   √ EIyGJ 2

4CwM2p IyC2bG2J2

Design Strength If Plastic Analysis Is Used

The design flexural strength for plastic analysis is: φbMn = φbMp where φb = 0.90 Mp = ZxFy / 12 kip-ft The yield strength of material that may be used with plastic analysis is limited to 65 ksi. Plastic analysis is limited to compact shapes as defined in Table B5.1 of the LRFD Specification as: λp = bf / 2tf ≤ 65 / √ Fy for the flanges of I shapes in flexure Fy for the flanges of C shapes in flexure λp = bf / tf ≤ 65 / √ and λp = h / tw ≤ 640 / √ Fy for beam webs in flexural compression where

λp = limiting slenderness parameter for compact element bf = width of flange for I and C shapes, in. tf = flange thickness, in. h = clear distance between flanges less the fillet at each flange, in. tw = beam web thickness, in

In addition, LRFD Specification Section F1.2d states: for a section bent about the major axis, the laterally unbraced length of the compression flange at plastic hinge locations associated with the failure mechanism shall not exceed: Lpd =

3,600 + 2,220(M1 / M2) ry Fy

where Fy M1 M2 ry (M1 / M2)

= specified yield strength of compression flange, ksi = smaller moment at end of unbraced length of beam, kip-in. = larger moment at end of unbraced length of beam, kip-in. = radius of gyration about minor axis, in. is positive when the moments cause reverse curvature AMERICAN INSTITUTE OF STEEL CONSTRUCTION

(F1-17)

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

4 - 11

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

This table facilitates the selection of beams designed on the basis of flexural strength in accordance with Section F of the LRFD Specification. It includes only W and M shapes designed as beams. A laterally supported beam can be selected by entering the table with the required plastic section modulus or factored bending moment, and comparing it with tabulated values of Zx or φbMp respectively. The table is applicable to adequately braced beams with unbraced lengths not exceeding Lr, i.e., Lb ≤ Lr. For beams with unbraced lengths greater than Lp, it may be convenient to use the unbraced beam charts. For most loading conditions, it is convenient to use this selection table. However, for adequately braced, simply supported beams with a uniform load over the entire length, or equivalent symmetrical loading, the tables of Factored Uniform Loads can also be used. In this table, shapes are listed in groups by descending order plastic section modulus Zx. Included also for steel of Fy = 36 ksi and 50 ksi are values for the maximum flexural design strength φbMp; the limiting buckling moment φbMr; the limiting laterally unbraced compression flange length for full plastic moment capacity and uniform moment (Cb = 1.0) Lp; limiting laterally unbraced length for inelastic lateral-torsional buckling Lr; and BF, a factor that can be used to calculate the resisting moment φbMn for beams with unbraced lengths between the limiting bracing lengths Lp and Lr. For noncompact shapes, as determined by Section B5 of the LRFD Specification, the maximum flexural design strength φbMn, max as determined by LRFD Specification Formula A-F1-3 is tabulated as φbMp. The associated maximum unbraced length is tabulated as Lp. (See the previous discussion under Design Strength of Beams for further explanation.) The symbols used in this table are: Zx = plastic section modulus, X-X axis, in.3 φbMp = design plastic bending moment, kip-ft = φbZxFy / 12 if shape is compact  λ − λp  = φbM′n = φbMp − φb(Mp − Mr)   if shape is noncompact  λr − λp  φbMr = limiting design buckling moment, kip-ft = φbSx(Fy − Fr ) / 12 where Fr = 10 ksi for rolled shapes Lp = limiting laterally unbraced length for inelastic LTB, ft, uniform moment case (Cb = 1) Lr = limiting laterally unbraced length for elastic lateral-torsional buckling, ft BF = a factor that can be used to calculate the design flexural strength for unbraced lengths Lb, between Lp and Lr, kip-ft φb(Mp − Mr) = Lr − Lp where φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φbMp AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 12

BEAM AND GIRDER DESIGN

Use of the Table

Determine the required plastic section modulus Zx from the maximum factored moment Mu (kip-ft) using the desired steel yield strength. Zx =

12Mu φbFy

Enter the column headed Zx and find a value equal to or greater than the plastic section modulus required. Alternatively, enter the φbMp column and find a value of φbMp equal to or greater than the required factored load moment. The beam opposite these values (Zx or φbMp) in the shapes column, and all beams above it, have sufficient flexural strength based only on these parameters. The first beam appearing in boldface type adjacent to or above the required Zx or φbMp is the lightest section that will serve for the steel yield stress used in the calculations. If the beam must not exceed a certain depth, proceed up the column headed “Shape” until a beam within the required depth is reached. After a shape has been selected, the following checks should be made. If the lateral bracing of the compressive flange exceeds Lp, but is less than Lr, the design flexural strength may be calculated as follows: φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φbMp If the bracing length Lb is substantially greater than Lp, i.e., Lb > Lr, it is recommended the unbraced beam charts be used. A check should be made of the beam web shear strength by referring to the Factored Uniform Load Tables or by use of the formula: φvVn = φv0.6FywAw (from LRFD Specification Section F2) where φv = 0.90 If a deflection limitation also exists, the adequacy of the selected beam should be checked accordingly.

EXAMPLE 4-1

Given:

Solution (Zx method):

Select a beam of Fy = 50 ksi steel subjected to a factored uniform bending moment of 256 kip-ft, having its compression flange braced at 5.0 ft intervals. Assume Cb = 1.0. Zx (req’d) =

Mu(12) 256(12) = = 68.3 in.3 φbFy 0.9(50)

Enter the Load Factor Design Selection Table and find the nearest higher tabulated value of Zx is 69.6 in., which corresponds to a W14×43. This beam, however, is not in boldface type. Proceed up the shape column and locate the first beam in boldface, W16×40. Note the values tabulated for φbMp and Lp are 273 kip-ft and 5.6 ft, respectively. Use W16x40 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

4 - 13

Alternatively, proceed up the shape column and select a W18×40. The tabulated values for φbMp and Lp are 294 kip-ft and 4.5 ft, respectively. Since the bracing length Lb is larger than Lp and smaller than Lr, the maximum resisting moment may be calculated as follows: φbMn = Cb[φbMp − BF(Lb − Lp)] = 1.0[294 − (11.7)(5.0 − 4.5)] = 288 kip-ft > 256 kip-ft req’d o.k. A W18×40 is satisfactory. Alternate solution (Mp method):

Enter the column of φbMp values and note the tabulated value nearest and higher than the required factored moment (Mu) is 261 kip-ft, which corresponds to a W14×43. Scanning the φbMp values for shapes listed higher in the column, a W16×40 is found to be the lightest suitable shape with Lb < Lp. Use W16×40

EXAMPLE 4-2

Given:

Determine the design flexural strength of a W16×40 of Fy = 36 ksi and Fy = 50 ksi steel with the compression flange braced at intervals of 9.0 ft. Assume Cb = 1.1.

Solution:

Enter the Load Factor Design Table and note that for a W16×40, Fy = 36 ksi: φbMp = 197 kip-ft Lp = 6.5 ft Lr = 19.3 ft BF = 5.54 kips φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φb Mp = 1.1[197 − 5.54(9 − 6.5)] ≤ 197 kip-ft = 197 kip-ft Enter the Load Factor Design Selection Table and note that for a W16×40, Fy = 50 ksi: φbMp = 273 kip-ft Lp = 5.6 ft Lr = 14.7 ft BF = 8.67 kips φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φb Mp = 1.1[273 − 8.67(9 − 5.6)] ≤ 273 kip-ft = 268 kip-ft AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 14

BEAM AND GIRDER DESIGN

EXAMPLE 4-3

Given:

Select a beam of Fy = 50 ksi steel subjected to a factored uniform bending moment of 30 kip-ft having its compression flange braced at 4.0-ft intervals and a depth of eight inches or less. Assume Cb = 1.0.

Solution (Zx method):

Assume shape is compact and Lb ≤ Lp. Zx req’d =

12Mu 12(30) = = 8.0 in.3 φbFy 0.9(50)

Enter the Load Factor Design Selection Table and note that for a W8×10, Fy = 50 ksi, the shape is noncompact, however, the maximum resisting moment φbMn listed in the φbMp column is adequate. Further note: φbMn = 33.0 kip-ft Lp = 3.1 ft Lr = 7.8 ft BF = 2.03 kips Since Lp < Lb ≤ Lr φbMn = Cb[φbMn − BF(Lb − Lp)] = 1.0[33.0 − 2.03(4.0 − 3.1)] = 33.0 − 1.8 = 31.2 kip-ft > 30 kip-ft req’d o.k. Use: W8×10 Alternate Solution (Mp method):

Enter the Selection Table and note that in the column of φbMp values for W8×10, Fy = 50 ksi, the value of φbMp is 33.0 kip-ft, which is adequate. Also note, however, Lp = 3.1 ft is less than the bracing interval Lb = 4.0 ft, and that BF is equal to 2.03 kips. Therefore: φbMn = 1.0[33.0 − 2.03(4 − 3.1)] = 31.2 kip-ft > 30 kip-ft req’d o.k. Use: W8×10

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

4 - 15

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90 Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

φbMr

Kip-ft Kip-ft

Kips

34.5

138.2

17.8

6180

10300

3830

W36×848a 14400

9510

15.1

90.5

64.3

34.1

130.1

17.7

5810

9639

3570

W36×798a 13400

8940

15.0

85.3

63.2

33.2

105.9

17.2

4720

7668

2840

W36×650a 10700

7260

14.6

70.0

61.1

41.9

84.8

15.9

4560

7450

2760

W40×593a 10400

7020

13.5

56.8

76.7

41.2 33.2

72.5 86.8

15.5 16.8

3860 3800

6210 6129

2300 2270

W40×503a W36× 527a

8630 8510

5940 5850

13.2 14.2

49.5 58.3

73.9 60.4

46.9

58.2

11.3

3330

5540

2050

W40×466a

7690

5130

9.6

39.4

85.9

41.0 19.3 32.7 23.7

63.3 119.4 73.5 93.6

15.2 15.3 16.5 15.6

3300 3060 3160 2980

5270 5080 5022 4830

1950 1880 1860 1790

W40×431 W27× 539a W36× 439a W30× 477a

7310 7050 6980 6710

5070 4710 4860 4590

12.9 12.9 14.0 13.3

44.1 78.2 50.3 62.0

72.0 35.9 58.2 43.5

46.6

49.8

11.0

2810

4620

1710

W40×392a

6410

4320

9.3

34.3

83.7

39.9 32.5

56.6 67.2

15.0 16.3

2850 2830

4510 4482

1670 1660

W40×372 W36× 393a

6260 6230

4380 4350

12.7 13.8

40.3 46.7

68.4 57.0

48.6 15.3 18.9 32.5

48.0 123.3 99.2 62.4

14.6 14.2 14.9 16.1

2750 2520 2540 2570

4370 4190 4130 4077

1620 1550 1530 1510

W44×335 W24× 492a W27× 448a W36× 359a

6080 5810 5740 5660

4230 3870 3900 3960

12.4 12.1 12.6 13.7

35.5 80.5 65.3 44.0

79.7 28.4 34.9 56.2

46.2 22.9 29.4

43.2 77.5 64.4

10.7 15.3 15.6

2360 2440 2400

3860 3860 3830

1430 1430 1420

W40×331 W30× 391a W33× 354a

5360 5360 5330

3630 3750 3690

9.1 13.0 13.2

30.5 52.1 44.7

80.9 41.2 51.9

46.1 38.4 32.2 38.4

45.3 51.2 58.5 48.9

14.6 14.8 16.0 14.8

2420 2440 2360 2280

3830 3830 3726 3590

1420 1420 1380 1330

W44×290 W40× 321 W36× 328a W40× 297

5330 5330 5180 4990

3720 3750 3630 3510

12.4 12.6 13.6 12.5

34.0 37.2 41.7 35.9

74.1 63.9 54.9 63.2

43.4 28.9 31.6 14.7 37.3 19.0 44.2 23.4 31.0 28.2 43.7

43.1 59.3 55.1 103.0 47.9 82.0 38.2 66.6 53.0 55.7 37.0

14.4 15.5 16.0 13.9 14.9 14.5 10.5 15.0 15.9 15.4 10.5

2180 2160 2160 2070 2150 2070 1990 2010 2010 1970 1890

3430 3430 3402 3380 3380 3350 3210 3210 3159 3110 3050

1270 1270 1260 1250 1250 1240 1190 1190 1170 1150 1130

W44×262 W33× 318a W36× 300 W24× 408a W40× 277 W27× 368a W40× 278 W30× 326a W36× 280 W33× 291a W40× 264

4760 4760 4730 4690 4690 4650 4460 4460 4390 4310 4240

3360 3330 3330 3180 3300 3180 3060 3090 3090 3030 2910

12.2 13.1 13.5 11.8 12.7 12.3 8.9 12.8 13.5 13.0 8.9

32.8 41.8 39.9 67.5 35.5 54.6 27.6 45.7 38.8 39.8 27.0

68.2 49.9 52.9 27.0 60.8 34.8 74.9 41.7 51.3 48.0 73.3

35.6

45.4

14.8

1930

3020

1120

W40×249

4200

2980

12.6

34.1

56.9

Shape

φbMp

aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 16

BEAM AND GIRDER DESIGN

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90

Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

φbMr

Kip-ft Kip-ft

φbMp

Kips

40.1 30.3 23.1 37.0 27.7 15.0 18.7 41.8 29.6

41.2 50.6 60.5 39.7 52.0 84.5 69.4 35.1 48.8

14.3 15.8 14.9 11.0 15.3 13.5 14.3 10.6 15.6

1890 1860 1810 1750 1790 1680 1720 1700 1750

2970 2916 2860 2810 2810 2750 2750 2730 2727

1100 1080 1060 1040 1040 1020 1020 1010 1010

W44×230 W36×260 W30× 292a W36×256 W33× 263a W24× 335a W27× 307a W40×235 W36×245

4130 4050 3980 3900 3900 3830 3830 3790 3790

2910 2860 2780 2690 2750 2590 2650 2620 2690

12.1 13.4 12.7 9.4 12.9 11.4 12.1 9.0 13.3

31.7 37.5 42.1 28.8 37.8 55.8 46.9 26.0 36.4

62.0 49.4 40.4 62.7 46.3 27.8 33.7 68.6 47.7

33.1 28.7 22.8 27.0 36.1

42.7 47.3 55.4 49.2 37.2

14.8 15.5 14.8 15.1 10.9

1670 1630 1610 1620 1580

2600 2550 2540 2540 2530

963 943 941 939 936

W40×215 W36×230 W30×261 W33×241 W36×232

3610 3540 3530 3520 3510

2570 2510 2480 2490 2430

12.5 13.2 12.5 12.8 9.3

32.6 35.6 39.2 36.2 27.3

51.6 45.8 39.2 44.2 59.9

40.2

33.2

10.5

1530

2440

905

W40×211

3390

2360

8.9

24.9

64.7

31.6 26.0 18.6 22.4 14.7 34.9

41.1 46.9 59.6 51.6 71.2 35.0

14.4 15.0 14.0 14.7 13.2 10.8

1500 1480 1450 1450 1400 1400

2340 2310 2300 2280 2250 2250

868 855 850 845 835 833

W40×199 W33×221 W27×258 W30×235 W24× 279a W36×210

3260 3210 3190 3170 3130 3120

2310 2270 2230 2240 2150 2160

12.2 12.7 11.9 12.4 11.2 9.1

31.6 35.0 41.1 37.1 47.6 26.1

48.8 41.9 32.9 37.7 26.9 56.8

37.4 25.0 18.5 34.0 8.40 21.8 14.7

31.2 44.8 55.0 33.5 109.5 47.9 64.3

10.4 14.8 13.9 10.7 12.3 14.5 13.1

1330 1330 1310 1290 1220 1290 1260

2110 2080 2080 2070 2030 2020 2010

781 772 769 767 753 749 744

W40×183 W33×201 W27×235 W36×194 W18× 311a W30×211 W24× 250a

2930 2900 2880 2880 2820 2810 2790

2050 2050 2020 1990 1870 1990 1930

8.8 12.6 11.8 9.1 10.4 12.3 11.1

23.8 33.8 38.5 25.2 71.5 35.1 43.4

59.0 39.7 32.3 54.6 15.6 36.0 26.6

32.7

32.8

10.6

1210

1940

718

W36×182

2690

1870

9.0

24.9

52.0

Shape

27.5 18.2

38.4 52.0

13.6 13.8

1250 1220

1930 1910

715 708

W40×174 W27×217

2660 2660

1920 1870

12.0 11.7

29.9 36.8

41.3 31.3

35.6 8.29 14.7 21.0 31.5 28.3 17.8

29.7 99.6 59.3 45.4 31.9 32.6 48.0

10.0 12.1 13.0 14.4 10.5 10.4 13.7

1170 1100 1150 1170 1130 1070 1080

1870 1830 1830 1820 1800 1700 1700

692 676 676 673 668 629 628

W40×167 W18× 283a W24×229 W30×191 W36×170 W33×169 W27×194

2600 2540 2540 2520 2510 2360 2360

1800 1690 1760 1790 1740 1650 1670

8.5 10.3 11.0 12.2 8.9 8.8 11.6

22.8 65.1 40.4 33.7 24.4 24.5 34.6

55.6 15.4 26.2 33.9 49.6 45.4 30.0

30.7 8.21 14.5 20.2

30.9 90.9 54.2 43.2

10.4 12.0 12.8 14.3

1060 1000 1040 1050

1680 1650 1640 1630

624 611 606 605

W36×160 W18× 258a W24×207 W30×173

2340 2290 2270 2270

1630 1540 1590 1620

8.8 10.2 10.9 12.1

23.7 59.5 37.4 32.5

48.0 15.2 25.6 32.0

aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1). bIndicates noncompact shape; F = 50 ksi y

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

4 - 17

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90 Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

φbMr

Kip-ft Kip-ft

Kips

32.8 29.4 17.5 26.8 14.3 8.09 11.0

28.2 30.2 45.2 31.2 51.3 82.8 60.8

9.5 10.3 13.6 10.3 12.8 11.9 12.6

998 983 979 950 957 909 899

1610 1570 1530 1510 1510 1480 1430

597 581 567 559 559 549 530

W40×149 W36× 150 W27× 178 W33× 152 W24× 192 W18× 234a W21× 201

2240 2180 2130 2100 2100 2060 1990

1540 1510 1510 1460 1470 1400 1380

8.1 8.7 11.5 8.7 10.9 10.1 10.7

21.9 23.4 33.1 23.7 35.7 54.4 41.1

50.8 45.6 28.8 42.3 25.0 14.9 19.9

25.7 16.9 14.3

30.1 42.8 47.8

10.1 13.5 12.7

874 887 878

1390 1380 1380

514 512 511

W33×141 W27× 161 W24× 176

1930 1920 1920

1340 1370 1350

8.6 11.5 10.7

23.1 31.7 33.8

40.2 27.4 24.6

27.5 23.7 8.00 10.9 14.1

28.8 30.6 75.0 55.8 45.2

9.9 9.5 11.8 12.5 12.7

856 850 817 813 807

1370 1350 1320 1290 1260

509 500 490 476 468

W36×135 W30× 148 W18× 211a W21× 182 W24× 162

1910 1880 1840 1790 1760

1320 1310 1260 1250 1240

8.4 8.1 10.0 10.6 10.8

22.4 22.8 49.5 38.1 32.4

42.2 38.6 14.7 19.4 23.8

24.5 16.2 7.98 22.4 10.8 13.8

29.1 40.7 68.3 29.0 51.7 42.0

10.0 13.4 11.6 9.4 12.4 12.5

792 801 741 741 741 723

1260 1240 1190 1180 1170 1130

467 461 442 437 432 418

W33×130 W27× 146 W18× 192 W30× 132 W21× 166 W24× 146

1750 1730 1660 1640 1620 1570

1220 1230 1140 1140 1140 1110

8.4 11.3 9.9 8.0 10.5 10.6

22.5 30.6 45.3 22.0 35.7 30.6

37.9 25.8 14.6 35.6 19.1 22.8

23.1 21.6 7.95 18.9

27.8 28.2 62.3 30.0

9.7 9.3 11.5 9.2

700 692 671 673

1120 1100 1070 1070

415 408 398 395

W33×118 W30× 124 W18× 175 W27× 129

1560 1530 1490 1480

1080 1070 1030 1040

8.2 7.9 9.8 7.8

21.7 21.5 41.5 22.3

35.5 34.1 14.5 30.9

21.1 10.7 13.3 7.87

27.1 46.4 39.3 56.7

9.1 12.3 12.4 11.4

642 642 642 605

1020 1010 999 961

378 373 370 356

W30×116 W21× 147 W24× 131 W18× 158

1420 1400 1390 1340

987 987 987 930

7.7 10.4 10.5 9.7

20.8 32.8 29.1 38.2

33.0 18.4 21.5 14.2

20.2 18.0 10.5 12.7 7.82

26.3 28.2 43.1 37.1 52.2

9.0 9.1 12.2 12.3 11.3

583 583 575 567 550

934 926 899 883 869

346 343 333 327 322

W30×108 W27× 114 W21× 132 W24× 117 W18× 143

1300 1290 1250 1230 1210

897 897 885 873 846

7.6 7.7 10.4 10.4 9.6

20.3 21.3 30.9 27.9 35.5

31.5 28.7 17.7 20.2 14.0

19.0 10.3 17.0 7.79 12.0

25.5 41.0 26.8 48.0 35.2

8.8 12.2 9.0 11.3 12.1

525 532 521 499 503

842 829 824 786 780

312 307 305 291 289

W30×99 W21× 122 W27× 102 W18× 130 W24× 104

1170 1150 1140 1090 1080

807 819 801 768 774

7.4 10.3 7.6 9.5 10.3

19.8 29.8 20.5 33.0 26.8

29.2 17.1 26.7 13.8 18.8

Shape

φbMp

aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 18

BEAM AND GIRDER DESIGN

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90

Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

φbMr

Kip-ft Kip-ft

Kips

17.8 14.8 10.1 16.2 7.72 14.3 9.61

24.8 27.1 38.7 25.9 44.1 25.9 37.1

8.7 8.3 12.1 8.8 11.2 8.3 12.0

478 478 486 474 450 433 443

764 756 753 751 705 686 683

283 280 279 278 261 254 253

W30×90 W24×103 W21×111 W27× 94 W18×119 W24× 94 W21×101

1060 1050 1050 1040 979 953 949

735 735 747 729 693 666 681

7.4 7.0 10.3 7.5 9.5 7.0 10.2

19.4 20.1 28.5 19.9 30.8 19.4 27.6

27.1 24.1 16.4 25.2 13.4 23.0 15.4

15.0 3.87 7.62

24.9 73.6 40.4

8.6 15.7 11.1

415 408 398

659 632 621

244 234 230

W27×84 W14×132 W18×106

915 878 863

639 627 612

7.3 13.3 9.4

19.3 49.6 28.7

23.0 6.89 13.0

13.6 11.8 3.86 7.51

24.5 26.6 67.9 38.1

8.1 7.7 15.6 11.0

382 374 371 367

605 597 572 570

224 221 212 211

W24×84 W21× 93 W14×120 W18× 97

840 829 795 791

588 576 570 564

6.9 6.5 13.2 9.4

18.6 19.4 46.2 27.4

21.5 19.6 6.82 12.6

12.7 6.10 11.3 3.84 2.95 7.27

23.4 42.1 24.9 62.7 75.5 35.5

8.0 10.5 7.6 15.5 13.0 11.0

343 341 333 337 318 324

540 535 529 518 502 502

200 198 196 192 186 186

W24×76 W16×100 W21× 83 W14×109 W12×120 W18× 86

750 743 735 720 698 698

528 525 513 519 489 498

6.8 8.9 6.5 13.2 11.1 9.3

18.0 29.3 18.5 43.2 50.0 26.1

19.8 10.7 18.5 6.70 5.36 11.9

12.1 6.03 3.77 10.7 2.95 6.94

22.4 38.6 58.2 23.5 67.2 33.3

7.8 10.4 15.5 7.5 13.0 10.9

300 302 306 294 283 285

478 473 467 464 443 440

177 175 173 172 164 163

W24×68 W16× 89 W14× 99b W21× 73 W12×106 W18× 76

664 656 647 645 615 611

462 465 471 453 435 438

6.6 8.8 13.4 6.4 11.0 9.2

17.4 27.3 40.6 17.7 44.9 24.8

18.7 10.3 6.46 17.0 5.32 11.1

10.4 3.75

22.8 54.1

7.5 15.4

273 279

432 424

160 157

W21×68 W14× 90b

600 587

420 429

6.4 15.0

17.3 38.4

16.5 6.31

13.8 5.85 2.01 2.91 8.29

17.2 34.9 86.4 61.4 24.4

5.8 10.3 11.2 12.9 7.1

255 261 246 255 248

413 405 397 397 392

153 150 147 147 145

W24×62 W16× 77 W10×112 W12× 96 W18× 71

574 563 551 551 544

393 402 378 393 381

4.9 8.7 9.5 10.9 6.0

13.3 25.2 56.5 41.3 17.8

21.4 9.75 3.68 5.20 13.8

9.84 4.15

21.7 43.0

7.4 10.3

248 240

389 375

144 139

W21×62 W14× 82

540 521

381 369

6.3 8.8

16.6 29.6

15.3 7.31

Shape

φbMp

bIndicates noncompact shape; F = 50 ksi. y

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

4 - 19

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90 Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

φbMr

Kip-ft Kip-ft

Kips

12.7 8.08 2.90 2.00 5.57 11.3 4.10 7.91 2.88 4.05 1.97

16.6 23.2 56.4 77.4 32.3 17.3 40.0 22.4 51.8 37.3 68.4

5.6 7.0 12.8 11.0 10.3 5.6 10.3 7.0 12.7 10.3 11.0

222 228 230 218 228 216 218 211 209 201 192

362 359 356 351 351 348 340 332 321 311 305

134 133 132 130 130 129 126 123 119 115 113

W24×55 W18× 65 W12× 87 W10× 100 W16× 67 W21× 57 W14× 74 W18× 60 W12× 79 W14× 68 W10× 88

503 499 495 488 488 484 473 461 446 431 424

342 351 354 336 351 333 336 324 321 309 296

4.7 6.0 10.9 9.4 8.7 4.8 8.8 6.0 10.8 8.7 9.3

12.9 17.1 38.4 50.8 23.8 13.1 28.0 16.7 35.7 26.4 45.1

19.6 13.3 5.12 3.66 9.02 18.0 7.12 12.8 5.03 6.91 3.58

7.65

21.4

7.0

192

302

112

W18×55

420

295

5.9

16.1

12.2

10.5 2.87 6.43 3.91

16.2 48.2 22.8 34.7

5.4 12.7 6.7 10.2

184 190 180 180

297 292 284 275

110 108 105 102

W21×50 W12× 72 W16× 57 W14× 61

413 405 394 383

284 292 277 277

4.6 10.7 5.7 8.7

12.5 33.6 16.6 24.9

16.4 4.93 10.7 6.51

7.31 1.95 2.80

20.5 60.1 44.7

6.9 10.8 12.6

173 168 171

273 264 261

101 97.6 96.8

W18×50 W10× 77 W12× 65b

379 366 358

267 258 264

5.8 9.2 11.8

15.6 39.9 31.7

11.5 3.53 4.72

9.68 6.18 8.13 4.17 2.91 1.93 5.91

15.4 21.3 16.6 28.0 38.4 53.7 20.2

5.3 6.6 5.4 8.0 10.5 10.8 6.5

159 158 154 152 152 148 142

258 248 245 235 233 230 222

95.4 92.0 90.7 87.1 86.4 85.3 82.3

W21×44 W16× 50 W18× 46 W14× 53 W12× 58 W10× 68 W16× 45

358 345 340 327 324 320 309

245 243 236 233 234 227 218

4.5 5.6 4.6 6.8 8.9 9.2 5.6

12.0 15.8 12.6 20.1 27.0 36.0 15.2

14.9 10.1 13.0 7.02 4.96 3.46 9.43

7.51 4.06 2.85 1.91

15.7 26.3 35.8 48.1

5.3 8.0 10.3 10.7

133 137 138 130

212 212 210 201

78.4 78.4 77.9 74.6

W18×40 W14× 48 W12× 53 W10× 60

294 294 292 280

205 211 212 200

4.5 6.8 8.8 9.1

12.1 19.2 25.6 32.6

11.7 6.70 4.77 3.38

5.54 3.06 1.30 3.91 1.89

19.3 30.8 64.0 24.7 43.9

6.5 8.2 8.8 7.9 10.7

126 126 118 122 117

197 195 190 188 180

72.9 72.4 70.2 69.6 66.6

W16×40 W12× 50 W8× 67 W14× 43 W10× 54

273 272 263 261 250

194 194 181 188 180

5.6 6.9 7.5 6.7 9.1

14.7 21.7 41.9 18.2 30.2

8.67 5.25 2.38 6.32 3.30

6.95 3.01 5.23 4.41 1.88 1.27 2.92 1.96

14.8 28.5 18.3 20.0 40.7 56.0 26.5 35.1

5.1 8.1 6.3 6.5 10.6 8.8 8.0 8.4

112 113 110 106 106 101 101 95.7

180 175 173 166 163 161 155 148

66.5 64.7 64.0 61.5 60.4 59.8 57.5 54.9

W18×35 W12× 45 W16× 36 W14× 38 W10× 49 W8× 58 W12× 40 W10× 45

249 243 240 231 227 224 216 206

173 174 170 164 164 156 156 147

4.3 6.9 5.4 5.5 9.0 7.4 6.8 7.1

11.5 20.3 14.1 14.9 28.3 36.8 19.3 24.1

10.7 5.07 8.08 7.07 3.25 2.32 4.82 3.45

Shape

φbMp

bIndicates noncompact shape; F = 50 ksi. y

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 20

BEAM AND GIRDER DESIGN

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90

Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

φbMr

Kip-ft Kip-ft

Kips

4.18

19.0

6.4

94.8

147

54.6

W14×34

205

146

5.4

14.4

6.58

5.70 3.47 1.26

14.3 20.6 46.7

4.9 6.4 8.7

92.0 88.9 84.4

146 138 132

54.0 51.2 49.0

W16×31 W12× 35 W8×48

203 192 184

142 137 130

4.1 5.4 7.4

11.0 15.2 31.1

8.85 5.67 2.27

3.92 1.93

17.9 31.2

6.2 8.3

81.9 82.1

128 126

47.3 46.8

W14×30 W10× 39

177 176

126 126

5.3 7.0

13.7 21.8

6.06 3.32

5.15 3.22

13.3 19.1

4.7 6.3

74.9 75.3

119 116

44.2 43.1

W16×26 W12× 30

166 162

115 116

4.0 5.4

10.4 14.4

7.88 5.10

4.44 1.25 1.89

13.4 39.1 27.4

4.5 8.5 8.1

68.8 69.2 68.3

109 107 105

40.2 39.8 38.8

W14×26 W8×40 W10× 33

151 149 146

106 107 105

3.8 7.2 6.9

10.3 26.4 19.7

6.96 2.22 3.15

2.99 2.44 1.23

18.1 20.3 35.1

6.3 5.7 8.5

65.1 63.2 60.8

100 98.8 93.7

37.2 36.6 34.7

W12×26 W10× 30 W8×35

140 137 130

100 97.2 93.6

5.3 4.8 7.2

13.8 14.5 24.1

4.64 4.13 2.16

4.06 2.34 1.21

12.5 18.5 32.0

4.3 5.7 8.4

56.6 54.4 53.6

89.6 84.5 82.1

33.2 31.3 30.4

W14×22 W10× 26 W8×31

125 117 114

87.0 83.7 82.5

3.7 4.8 7.1

9.7 13.5 22.3

6.26 3.85 2.07

3.88 1.27

11.1 27.3

3.5 6.8

49.5 47.4

79.1 73.4

29.3 27.2

W12×22 W8×28

110 102

76.2 72.9

3.0 5.7

8.4 18.9

6.24 2.22

2.19

16.9

5.5

45.2

70.2

26.0

W10×22

97.5

69.6

4.7

12.7

3.50

3.61 1.24

10.4 24.4

3.4 6.7

41.5 40.8

66.7 62.6

24.7 23.2

W12×19 W8×24

92.6 87.0

63.9 62.7

2.9 5.7

7.9 17.2

5.70 2.11

2.60 1.46

12.0 18.6

3.6 5.3

36.7 35.5

58.3 55.1

21.6 20.4

W10×19 W8×21

81.0 76.5

56.4 54.6

3.1 4.5

8.9 13.3

4.26 2.47

3.30 0.741 2.46

9.6 31.3 11.2

3.2 6.3 3.5

33.3 32.6 31.6

54.3 51.0 50.5

20.1 18.9 18.7

W12×16 W6×25 W10× 17

75.4 70.9 70.1

51.3 50.1 48.6

2.7 5.4 3.0

7.4 21.0 8.4

5.12 1.33 3.97

2.97 1.40 2.34 0.728

9.2 16.7 10.3 25.6

3.1 5.1 3.4 6.3

29.1 29.6 26.9 26.1

47.0 45.9 43.2 40.2

17.4 17.0 16.0 14.9

W12×14 W8×18 W10× 15 W6×20

65.3 63.8 60.0 55.9

44.7 45.6 41.4 40.2

2.7 4.3 2.9 5.3

7.2 12.3 7.9 17.7

4.56 2.30 3.69 1.27

3.32 1.53

6.9 12.6

2.3 3.7

23.6 23.0

38.6 36.7

14.3 13.6

M12×11.8 W8×15

53.7 51.0

36.3 35.4

2.0 3.1

5.4 9.2

5.10 2.56

Shape

φbMp

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS

4 - 21

LOAD FACTOR DESIGN SELECTION TABLE For shapes used as beams φb = 0.90 Fy = 36 ksi

Fy = 50 ksi

φbMr

φbMp

Kips

Kip-ft Kip-ft

in.3

3.10 2.03 0.817 0.458 1.44 0.417 0.693 0.444

6.8 9.5 18.3 30.3 11.5 31.1 20.8 26.3

2.3 3.3 4.0 5.3 3.5 5.0 6.7 5.3

21.6 21.3 19.9 19.9 19.3 18.8 19.0 16.6

35.4 34.0 31.6 31.3 30.8 29.7 28.8 25.9

13.1 12.6 11.7 11.6 11.4 11.0 10.8 9.59

M12×10.8 W10× 12b W6× 16 W5× 19 W8× 13 M5× 18.9 W6×15b,c W5× 16

49.2 47.0 43.9 43.5 42.8 41.3 38.6 36.0

2.32 1.30 0.775

6.2 10.2 14.4

2.1 3.5 3.8

15.2 15.2 14.3

24.9 23.9 22.4

9.21 8.87 8.30

M10×9 W8× 10b W6× 12

2.13 0.295 0.724

6.1 25.5 12.0

2.1 4.2 3.8

13.6 10.6 10.8

22.1 17.0 16.8

8.20 6.28 6.23

1.50

5.5

1.8

14.6

5.40

9.01

φbMr

Kip-ft Kip-ft

Kips

33.3 32.7 30.6 30.6 29.7 28.9 29.2 25.5

2.0 2.9 3.4 4.5 3.0 4.2 6.8 4.5

5.3 7.4 12.5 20.1 8.5 20.5 15.0 17.6

4.74 3.13 1.46 0.830 2.35 0.758 1.16 0.795

34.5 33.0 31.1

23.5 23.4 21.9

1.8 3.1 3.2

4.9 7.8 10.2

3.59 2.03 1.33

M10×8 W4× 13 W6× 9

30.8 23.6 23.4

21.0 16.4 16.7

1.8 3.5 3.2

4.8 16.9 8.9

3.26 0.538 1.17

M8×6.5

20.2

13.9

1.6

4.3

2.35

Shape

φbMp

bIndicates noncompact shape; F = 50 ksi y cIndicates noncompact shape; F = 36 ksi y

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 22

BEAM AND GIRDER DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES

4 - 23

MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES

These two tables for moment of inertia (Ix and Iy) are provided to facilitate the selection of beams and columns on the basis of their stiffness properties with respect to the X-X axis or Y-Y axis, as applicable, where Ix = moment of inertia, X-X axis, in.4 Iy = moment of inertia, Y-Y axis, in.4 In each table the shapes are listed in groups by descending order of moment of inertia for all W and M shapes. The boldface type identifies the shapes that are the lightest in weight in each group. Enter the column headed Ix (or Iy) and find a value of Ix (or Iy) equal to or greater than the moment of inertia required. The shape opposite this value, and all shapes above it, have sufficient stiffness. Note that the member selected must also be checked for compliance with specification provisions governing its specific application.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 24

Ix Shape

BEAM AND GIRDER DESIGN

MOMENT OF INERTIA SELECTION TABLE For W and M shapes Ix

Shape

In.4 W36×848*

67400

W36×798*

62600

W40×593* W36× 650*

50400 48900

W40×503* W36× 527*

41700 38300

W40×466*

36300

W40×431

34800

W44×335 W36× 439* W40× 392* W40× 372 W36× 393*

31100 31000 29900 29600 27500

W44×290 W30× 477* W27× 539* W40× 321 W36× 359* W40× 331

27100 26100 25500 25100 24800 24700

W44×262 W40× 297 W36× 328* W40× 277 W33× 354*

24200 23200 22500 21900 21900

W44×230 W30× 391* W40× 278 W27× 448* W36× 300 W33× 318* W40× 249 W40× 264 W24× 492* W36× 280 W33× 291* W40× 235 W36× 260 W30× 326* W36× 256

20800 20700 20500 20400 20300 19500 19500 19400 19100 18900 17700 17400 17300 16800 16800

W40×215 W27× 368* W36×245 W14× 808* W33× 263*

16700 16100 16100 16000 15800

W40×211 W24× 408* W36×230 W36×232

15500 15100 15000 15000

W40×199 W30× 292* W14× 730* W33×241

14900 14900 14300 14200

W40×183 W36×210 W27× 307* W30×261 W33×221 W14× 665*

13300 13200 13100 13100 12800 12400

W40×174 W36×194 W24× 335* W30×235

12200 12100 11900 11700

W40×167 W33×201 W36×182 W14× 605* W27×258 W36×170 W30× 211

11600 11500 11300 10800 10800 10500 10300

W40×149 W36×160 W27×235 W24× 279* W14× 550* W33×169 W30×191 W36×150 W27×217 W24× 250* W14× 500* W30×173 W33×152 W27×194

9780 9750 9660 9600 9430 9290 9170 9040 8870 8490 8210 8200 8160 7820

Shape

In.4

Shape

In.4 W36×135 W24× 229 W33× 141 W14×455* W27× 178 W18× 311* W24× 207

7800 7650 7450 7190 6990 6960 6820

W33×130 W30× 148 W14×426* W27× 161 W24× 192 W18×283* W14×398*

6710 6680 6600 6280 6260 6160 6000

W33×118 W30× 132 W24× 176 W27× 146 W18×258* W14×370* W30× 124 W21× 201 W24× 162

5900 5770 5680 5630 5510 5440 5360 5310 5170

W30×116 W18×234* W14×342* W27× 129 W21× 182 W24× 146

4930 4900 4900 4760 4730 4580

W30×108 W18× 211* W14× 311* W21× 166 W27× 114 W12×336* W24× 131

4470 4330 4330 4280 4090 4060 4020

*Group 4 or 5 shape. See Notes in Table 1-2 (Part 1).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ix In.4

W30×99 W18× 192 W14× 283* W21× 147

3990 3870 3840 3630

W30×90 W27× 102 W12× 305* W24× 117 W18× 175 W14× 257* W27× 94 W21× 132 W12× 279* W24× 104 W18× 158 W14× 233* W24× 103 W21× 122

3620 3620 3550 3540 3450 3400 3270 3220 3110 3100 3060 3010 3000 2960

W27×84 W18× 143 W12× 252* W24× 94 W21× 111 W14× 211 W18× 130 W12× 230* W21× 101 W14× 193

2850 2750 2720 2700 2670 2660 2460 2420 2420 2400

W24×84 W18× 119 W14× 176 W12× 210*

2370 2190 2140 2140

W24×76 W21× 93 W18× 106 W14× 159 W12× 190

2100 2070 1910 1900 1890

MOMENT OF INERTIA SELECTION TABLE FOR W AND M SHAPES

4 - 25

MOMENT OF INERTIA SELECTION TABLE For W and M shapes Shape

Shape

In.4 W24×68 W21× 83 W18× 97 W14× 145 W12× 170 W21× 73

1830 1830 1750 1710 1650 1600

W24×62 W14× 132 W18× 86 W16× 100 W21× 68 W12× 152 W14× 120

1550 1530 1530 1490 1480 1430 1380

W24×55 W18× 76 W21× 62 W16× 89 W14× 109 W12× 136 W18× 71 W21× 57 W14× 99 W16× 77 W12× 120 W18× 65 W14× 90 W18× 60

1350 1330 1330 1300 1240 1240 1170 1170 1110 1110 1070 1070 999 984

W21×50 W16× 67 W12× 106 W18× 55 W14× 62

984 954 933 890 882

Shape

In.4

Shape

In.4

W21×44 W12× 96 W18× 50 W14× 74 W16× 57 W12× 87 W14× 68 W10× 112 W18× 46 W12× 79 W16× 50 W14× 61 W10× 100

843 833 800 796 758 740 723 716 712 662 659 640 623

W16×26 W14× 30 W12× 35 W8× 67 W10× 49 W10× 45

301 291 285 272 272 248

W14×26 W12× 30 W8× 58 W10× 39

245 238 228 209

W12×26

204

W18×40 W12× 72 W16× 45 W14× 53 W10× 88 W12× 65

612 597 586 541 534 533

W14×22 W8× 48 W10× 30 W10× 33

199 184 170 170

W16×40

518

W12×22 W8× 40 W10× 26

156 146 144

W18×35 W14× 48 W12× 58 W10× 77 W16× 36 W14× 43 W12× 53 W12× 50 W10× 68 W14× 38

510 485 475 455 448 428 425 394 394 385

W12×19 W8× 35 W10× 22 W8× 31

130 127 118 110

W12×16 W8× 28 W10× 19

103 98.0 96.3

W16×31 W12× 45 W10× 60 W14× 34 W12× 40 W10× 54

375 350 341 340 310 303

W12×14 W8× 24 W10× 17 W8× 21

88.6 82.8 81.9 75.3

M12×11.8 W10× 15

71.7 68.9

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Ix Ix In.4

M12×10.8 W8× 18 W10×12 W6× 25 W8× 15 W6× 20 W8× 13

65.8 61.9 53.8 53.4 48.0 41.4 39.6

M10×9

38.5

M10×8 W6× 16 W8× 10 W6× 15 W5× 19 M5× 18.9 W6× 12 W5× 16

34.3 32.1 30.8 29.1 26.2 24.1 22.1 21.3

M8×6.5 W6×9 W4× 13

18.1 16.4 11.3

4 - 26

Iy Shape

BEAM AND GIRDER DESIGN

MOMENT OF INERTIA SELECTION TABLE For W and M shapes Iy

Shape

In.4 W14×808*

5510

W14×730* W36× 848* W36× 798*

4720 4550 4200

W14×665*

4170

W14×605*

3680

W14×550* W36× 650*

W14×283* W40×372 W36× 328* W24× 408* W27× 368* W36×300

1440 1420 1420 1320 1310 1300

W14×257* W33× 318* W30× 326* W36×280 W44×335 W12× 336* W40×321 W33× 291*

1290 1290 1240 1200 1200 1190 1190 1160

3250 3230

W14×500*

2880

W14×455* W40× 593* W36× 527*

2560 2520 2490

W14×426*

2360

W14×398* W27× 539* W40× 503*

2170 2110 2050

W14×370* W36× 439* W30× 477*

1990 1990 1970

W14×342* W36× 393* W40× 431 W27× 448* W24× 492*

1810 1750 1690 1670 1670

W14×311* W36× 359* W30× 391* W33× 354*

1610 1570 1550 1460

W14×233* W30× 292* W40×297 W36×260 W44×290 W27× 307* W12× 305* W40×277 W33× 263* W24× 335*

1150 1100 1090 1090 1050 1050 1050 1040 1030 1030

W14×211 W40× 466* W36×245 W30×261 W36×230 W12× 279* W33×241

1030 1010 1010 959 940 937 932

W14×193 W44×262 W40×249 W27×258 W30×235 W33×221

931 927 926 859 855 840

Shape

In.4

Shape

In.4 W14×176 W12×252* W24×279* W40×392* W40× 215 W44× 230 W18× 311* W27× 235 W30× 211 W33× 201

838 828 823 803 796 796 795 768 757 749

W14×159 W12×230* W24×250* W18×283* W27× 217 W40× 199

748 742 724 704 704 695

W14×145 W30× 191 W12×210* W24× 229 W40× 331 W18×258* W27× 194 W30× 173 W12× 190 W24× 207 W18×234* W27× 178

677 673 664 651 646 628 618 598 589 578 558 555

W14×132 W21× 201 W40× 174 W24× 192 W36× 256 W40× 278 W12× 170 W27× 161

548 542 541 530 528 521 517 497

*Group 4 or 5 shape. See Notes in Table 1-2 (Part 1).

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Iy In.4

W14×120 W40× 264 W18× 211* W21× 182 W24× 176 W36× 232 W12× 152

495 493 493 483 479 468 454

W14×109 W40× 235 W24× 162 W27× 146 W18× 192 W21× 166 W36× 210

447 444 443 443 440 435 411

W14×99 W12× 136 W18× 175 W24× 146 W40× 211 W21× 147 W36× 194

402 398 391 391 390 376 375

W14×90 W36× 182 W18× 158 W12× 120 W24× 131 W40× 183 W21× 132 W36× 170 W18× 143 W33× 169 W21× 122 W12× 106 W24× 117 W36× 160 W40× 167 W18× 130 W21× 111 W33× 152 W36× 150 W12× 96 W24× 104 W18× 119 W21× 101 W33× 141

362 347 347 345 340 336 333 320 311 310 305 301 297 295 283 278 274 273 270 270 259 253 248 246

MOMENT OF INERTIA SELECTION TABLE FOR W AND M SHAPES

4 - 27

MOMENT OF INERTIA SELECTION TABLE For W and M shapes Shape

Shape

In.4 W12×87 W10× 112 W40× 149 W30× 148 W36× 135 W18× 106 W33× 130

241 236 229 227 225 220 218

W12×79 W10× 100 W18× 97 W30× 132

216 207 201 196

W12×72 W33× 118 W16× 100 W27× 129 W30× 124 W10× 88 W18× 86

195 187 186 184 181 179 175

W12×65 W30× 116 W16× 89 W27× 114 W10× 77 W18× 76 W14× 82 W30× 108 W27× 102 W16× 77 W10× 68 W14× 74 W30× 99 W27× 94 W14× 68 W24× 103 W16× 67

174 164 163 159 154 152 148 146 139 138 134 134 128 124 121 119 119

Shape

In.4 W10×60 W30× 90 W24× 94

116 115 109

W12×58 W14× 61 W27× 84

107 107 106

W10×54

103

W12×53 W24× 84

95.8 94.4

W10×49 W21× 93 W8× 67 W24× 76 W21× 83 W8× 58 W21× 73 W24× 68 W21× 68

93.4 92.9 88.6 82.5 81.4 75.1 70.6 70.4 64.7

W8×48 W18× 71 W14× 53 W21× 62 W12× 50 W18× 65

60.9 60.3 57.7 57.5 56.3 54.8

W10×45 W14× 48 W18× 60

53.4 51.4 50.1

W12×45

50.0

W8×40 W14× 43

49.1 45.2

Shape

In.4 W10×39 W18× 55 W12× 40 W16× 57

45.0 44.9 44.1 43.1

W8×35 W18× 50 W16× 50

42.6 40.1 37.2

W8×31 W10× 33 W24× 62 W16× 45 W21× 57 W24× 55 W16× 40 W14× 38 W21× 50 W12× 35 W16× 36 W14× 34 W18× 46

37.1 36.6 34.5 32.8 30.6 29.1 28.9 26.7 24.9 24.5 24.5 23.3 22.5

W8×28 W21× 44 W12× 30 W14× 30 W18× 40

21.7 20.7 20.3 19.6 19.1

W8×24 W12× 26 W6× 25 W10× 30 W18× 35 W10× 26

18.3 17.3 17.1 16.7 15.3 14.1

W6×20 W16× 31 W10× 22 W8× 21 W16× 26

13.3 12.4 11.4 9.77 9.59

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Iy Iy In.4

W6×15 W5× 19 W14×26 W8× 18 M5× 18.9 W5× 16 W14×22 W12×22 W6× 16 W10×19

9.32 9.13 8.91 7.97 7.86 7.51 7.00 4.66 4.43 4.29

W4×13 W12×19 W10×17 W8× 15

3.86 3.76 3.56 3.41

W6×12 W10×15 W12×16 W8× 13 W12×14

2.99 2.89 2.82 2.73 2.36

W6×9 W10×12 W8× 10 M12× 11.8 M12× 10.8

2.19 2.18 2.09 1.09 0.995

M10×9

0.673

M10×8

0.597

M8×6.5

0.371

4 - 28

BEAM AND GIRDER DESIGN

FACTORED UNIFORM LOAD TABLES General Notes

The Tables of Factored Uniform Loads for W and S shapes and channels (C and MC) used as simple laterally supported beams give the maximum uniformly distributed factored loads in kips. The tables are based on the flexural design strengths specified in Section F1 of the LRFD Specification. Separate tables are presented for Fy = 36 ksi and Fy = 50 ksi. The tabulated loads include the weight of the beam, which should be deducted in the calculation to determine the net load that the beam will support. The tables are also applicable to laterally supported simple beams for concentrated loading conditions. A method to determine the beam load capacity for several cases is shown in this discussion. It is assumed, in all cases, that the loads are applied normal to the X-X axis (shown in the Tables of Properties of Shapes in Part 1 of this LRFD Manual) and that the beam deflects vertically in the plane of bending. If the conditions of loading involve forces outside this plane, design strengths must be determined from the general theory of flexure and torsion. Lateral Support of Beams

The flexural design strength of a beam is dependent upon lateral support of its compression flange in addition to its section properties. In these tables the notation Lp is used to denote the maximum unbraced length of the compression flange, in feet, for the uniform moment case (Cb = 1.0) and for which the design strengths for compact symmetrical shapes are calculated with a flexural design strength of: φbMn = φbMp = φbZxFy / 12 Noncompact shapes are calculated with a flexural design strength of:  λ − λp  φbMn′ = φbMp − φb(Mp − Mr)    λr − λp  as permitted in the LRFD Specification Appendix F1. The associated maximum unbraced length for φbMn′ is tabulated as Lp. The notation Lr is the unbraced length of the compression flange for which the flexural design strength for rolled shapes is: φbMr = φbSx(Fy − 10) / 12 These tables are not applicable for beams with unbraced lengths greater than Lr. For such cases, the beam charts should be used. Flexural Design Strength and Tabulated Factored Uniform Loads

For symmetrical rolled shapes designated W and S the flexural design strengths and resultant loads are based on the assumption that the compression flanges of the beams are laterally supported at intervals not greater than Lp. The Uniform Load Constant φbWc is obtained from the moment and stress relationship of a simply supported, uniformly loaded beam. The relationship results in the formula: φbWc = φb(2ZxFy / 3), kip-ft for compact shapes AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

4 - 29

The following expression may be used for calculating the tabulated uniformly distributed factored load Wu on a simply supported beam or girder: Wu = φbWc / L, kips For compact shapes, the tabulated constant is based on the yield stress Fy = 36 ksi or 50 ksi and the plastic section modulus Zx. (See Section F1.1 of the LRFD Specification.) For noncompact sections, the tabulated constant is based on the nominal resisting moment as determined by Equation A-F1-3. (See LRFD Specification Appendix F1.) Shear

For relatively short spans, the design strengths for beams and channels may be limited by the shear strength of the web instead of the bending strength. This limit is indicated in the tables by solid horizontal lines. Loads shown above these lines will produce the design shear strength in the beam web. End and Interior Bearing

For a discussion of end and interior bearing and use of the tabulated values φR1 through φr R6 and φR, see Part 9 in Volume II of this LRFD Manual. Vertical Deflection

For rolled shapes designated W, M, S, C, and MC, the maximum vertical deflection may be calculated using the formula: ∆ = ML2 / (C1Ix) where M = maximum service load moment, kip-ft L = span length, ft Ix = moment of inertia, in.4 C1 = loading constant (see Figure 4-2) ∆ = maximum vertical deflection, in.

C1 = 161

C1 = 201

C1 = 158

C1= 170

Fig. 4-2 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 30

BEAM AND GIRDER DESIGN

Table 4-2. Recommended Span/Depth Ratios Service Load Ratios

Maximum Span/Depth Ratios

Dead / Total

Dead / Live

Fy = 36 ksi

Fy = 50 ksi

0.2 0.3 0.4 0.5 0.6

0.25 0.43 0.67 1.00 1.50

20.0 22.2 25.0 29.0 —

14.0 16.0 18.0 21.0 26.0

Deflection can be controlled by limiting the span-depth ratio of a simply supported, uniformly loaded beam as shown in Table 4-2. A live-load deflection limit of L / 360 is assumed; i.e.,

∆LL ≤

Span Length 360

For large span/depth ratios, vibration may also be a consideration. Use of Tables

Maximum factored uniform loads are tabulated for steels of Fy = 36 ksi and Fy = 50 ksi. They are based on the design flexural strength determined from the LRFD Specification: Equation F1-1 (in Section F1.1) for compact members, and Equation A-F1-3 (in Appendix F1) for noncompact members. The beams must be braced adequately and have an axis of symmetry in the plane of loading. Factored loads may be read directly from the tables when the distance between points of lateral support of the compression flange Lb does not exceed Lp (tabulated earlier in the Load Factor Design Selection Table for beams). Loads above the heavy horizontal lines in the tables are governed by the design shear strength, determined from Section F2 of the LRFD Specification. EXAMPLE 4-4

Given:

A W16×45 floor beam of Fy = 50 ksi steel spans 20 feet. Determine the maximum uniform load, end reaction, and total service load deflection. The live load equals the dead load.

Solution:

Based on Section A4 of the LRFD Specification, the governing load combination for a floor beam is 1.2 (dead load) + 1.6 (live load). As the two loads are equal, factored load = 1.4 (total load) Enter the Factored Uniform Loads Table for Fy = 50 ksi and note that: Maximum factored uniform load = Wu = 124 kips, or 124/20 = 6.2 kips/ft Factored end reaction = Wu / 2 = 124 / 2 = 61.8 kips AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

4 - 31

Service load moment =

124(20) Wu L = 8(1.4) 8(LF)

= 221 kip-ft Deflection:

∆=

ML2 221(20)2 = = 0.94 in. C1Ix 161(586)

Live load deflection = 0.5 × 0.94 in. = 0.47 in. < (L / 360 = 20 × 12 / 360 = 0.66 in.) o.k. EXAMPLE 4-5

Given:

A W10×45 beam of Fy = 50 ksi steel spans 6 feet. Determine the maximum load and corresponding end reaction.

Solution:

Enter the Factored Uniform Loads Table for Fy = 50 ksi and note that: Maximum factored uniform load = Wu = 191 kips, or 191/6 = 31.8 kips/ft As Wu appears above the horizontal line, it is limited by shear in the web. Factored end reaction = Wu / 2 = 191 / 2 = 96 kips

EXAMPLE 4-6

Given:

Using Fy = 50 ksi steel, select an 18-in. deep beam to span 30 feet and support two equal concentrated loads at the one-third and two-thirds points of the span. The service load intensities are 10 kips dead load and 24 kips live load. The beam is supported laterally at the points of load application and the ends. Determine the beam size and service live load deflection.

Solution:

Refer to the Table of Concentrated Load Equivalents on page 4-189 and note that: Equivalent uniform load = 2.67Pu 1. Required factored uniform load: Wu = 2.67Pu = 2.67[1.2(10) + 1.6(24)] = 2.67(50.4) = 135 kips 2. Enter the Factored Uniform Loads Table for Fy = 50 ksi and Wu ≥ 135 kips For W18×71: Wu = 145 kips > 135 kips; however, Lb = 10 ft > Lp = 6.0 ft. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 32

BEAM AND GIRDER DESIGN

For W18×76: Wu = 163 kips > 135 kips; however, Lb = 10 ft > Lp = 9.2 ft. 3. Since Lp < Lb < Lr, use the Load Factor Design Selection Table. φbMn = Cb[φbMp − BF(Lb − Lp)] For the central third of the span (uniform moment), Cb = 1.0. Required flexural strength: Mu = Pu (L / 3) = 50.4(30 / 3) = 504 kip-ft 4. Try W18×71: φbMn = 1.0[544 − 13.8(10 − 6)] = 489 kip-ft < 504 kip-ft req’d. n.g. 5. Try W18×76: φbMn = 1.0[611 − 11.1(10 − 9.2)] = 602 kip-ft > 504 kip-ft req’d. o.k. Use W18×76 6. Determine service live load deflection: MLL = (PLL / Pu )Mu = (24 / 50.4)504 = 240 kip-ft Maximum ∆ (at midspan) =

240(30)2 MLLL2 = = 1.03 in. C1Ix 158(1,330)

EXAMPLE 4-7

Given:

A W24×55 of 50 ksi steel spans 20 feet and is braced at 4-ft intervals. Determine the maximum factored load and end reaction.

Solution:

1. Enter the Factored Uniform Load Table for Fy = 50 ksi and note that: Maximum factored uniform load = Wu = 201 kips, or 201 / 20 = 10.1 kips/ft This is true for Lb ≤ Lp : 4.0 ft < 4.7 ft o.k. 2. End reaction = R = Wu / 2 = 201 / 2 = 101 kips

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

4 - 33

Reference Notes on Tables

1. Maximum factored uniform loads, in kips, are given for beams with adequate lateral support; i.e., Lb ≤ Lp for Cb = 1.0, Lb ≤ Lm for Cb > 1.0. 2. Loads below the heavy horizontal line are limited by design flexural strength, while loads above the line are limited by design shear strength. 3. Factored loads are given for span lengths up to the smaller of L / d = 30 or 72 ft. 4. The end bearing values at the bottom of the tables are for use in solving LRFD Specification Equations K1-3, K1-5a, and K1-5b. They are defined as follows: φR1 = φ(2.5kFy tw) φR2 = φ(Fy tw)

kips kips/in.

Equation K1-3 becomes φRn = φR1 + N(φR2)  Fty tf  φrR3 = φr 68t2w √  w

kips 1.5

  3  tw  φrR4 = φr 68t2w      d  tf  



√Ft t  y f



kips/in.

Equation K1-5a becomes φrRn = φrR3 + N(φrR4) 1.5

   tw  φrR5 = φr 68t2w 1 − 0.2     tf  

  

1.5

  4   tw  φrR6 = φr 68t2w      d   tf  



Fty tf  √ w





√Fty t  f



kips

kips/in.

Equation K1-5b becomes φrRn = φrR5 + N(φrR6) where φ = 1.00, φr = 0.75, N = length of bearing (in.), and the other terms as defined in the LRFD Specification, Section K1. φR (N = 31⁄4) is defined as the design bearing strength for N = 31⁄4-in. For N / d ≤ 0.2, φR is the minimum of φR1 + N(φR2) φrR3 + N(φrR4) For N / d > 0.2, φR is the minimum of φR1 + N(φR2) φrR5 + N(φrR6) For a complete explanation of end and interior bearing and use of the tabulated values, see Part 9 in Volume II of this LRFD Manual. 5. The other terms at the bottom of the tables are: Zx

= plastic section modulus for major axis bending, in.3 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 34

BEAM AND GIRDER DESIGN

φvVn = design shear strength, kips φbWc = uniform load constant = φb(2ZxFy / 3) kip-ft for compact shapes; per Equation A-F1-3 (LRFD Specification Appendix F1) for noncompact shapes 6. Tabulated maximum factored uniformly distributed load for the given beam and span is the minimum of φbWc and 2φvVn L See also Note 2 above.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 35

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 44

For beams laterally unsupported, see page 4-113 Designation

W 44

Span (ft)

Fy = 36 ksi

Wt./ft

335

290

262

230

20 21 22 23 24 25

1750 1670 1590 1520 1460 1400

1480 1460 1390 1330 1280 1230

1330 1310 1250 1190 1140 1100

1180 1130 1080 1030 990 950

26 27 28 29 30 31

1350 1300 1250 1210 1170 1130

1180 1140 1100 1060 1020 989

1060 1020 980 946 914 885

914 880 849 819 792 766

32 33 34 35 36

1090 1060 1030 1000 972

959 929 902 876 852

857 831 807 784 762

743 720 699 679 660

38 40 42 44 46 48

921 875 833 795 761 729

807 767 730 697 667 639

722 686 653 623 596 572

625 594 566 540 517 495

50 52 54 56 58 60

700 673 648 625 603 583

613 590 568 548 529 511

549 528 508 490 473 457

475 457 440 424 410 396

62 64 66 68 70 72

564 547 530 515 500 486

495 479 465 451 438 426

442 429 416 403 392 381

383 371 360 349 339 330

1270 27400 665 156 28.4 256 7.36 235 9.81 248

1100 23800 592 128 25.6 202 6.28 184 8.37 211

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1620 35000 873 235 36.7 419 12.5 383 16.7 355

1420 30700 738 186 31.3 312 8.77 287 11.7 288

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 36

BEAM AND GIRDER DESIGN

W 40

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation Wt./ft

W 40 431

372

321

297

277

249

199

174

977 937

965 965 908 858 813 772

985 945 904 867 832 800

893 852 815 781 750 721

735 702 671 644 618 594

896 864 834 806 780 756

770 743 717 693 671 650

694 670 647 625 605 586

572 552 533 515 498 483

818 794 771 750 730 711

733 712 691 672 654 637

630 612 594 578 562 547

568 551 536 521 507 493

468 454 441 429 417 406

718 684 653 625 599 575

675 643 614 587 563 540

605 576 550 526 504 484

520 495 473 452 433 416

469 446 426 408 391 375

386 368 351 336 322 309

590 568 548 529 511 495

552 532 513 495 479 463

519 500 482 466 450 435

465 448 432 417 403 390

400 385 371 359 347 335

361 347 335 323 312 302

297 286 276 266 257 249

479 465 451 438 426

449 435 422 410 399

422 409 397 386 375

378 367 356 346 336

325 315 306 297 289

293 284 276 268 260

241 234 227 221 215

1120 24200 574 190 27.0 237 6.93 219 9.23 259

963 20800 493 154 23.4 177 5.30 163 7.07 194

868 18700 489 143 23.4 165 6.12 150 8.16 185

715 15400 483 117 23.4 146 7.95 126 10.6 172

1830 1800

1560 1530

1440 1440

21 22 23 24 25 26

2010 1910 1830 1760 1680 1620

1720 1640 1570 1500 1440 1390

1460 1390 1330 1280 1230 1180

1370 1310 1250 1200 1150 1100

1280 1230 1170 1130 1080 1040

1150 1100 1050 1010 968 930

27 28 29 30 31 32

1560 1500 1450 1400 1360 1320

1340 1290 1240 1200 1160 1130

1140 1100 1060 1020 989 959

1060 1030 991 958 927 898

1000 964 931 900 871 844

33 34 35 36 37 38

1280 1240 1200 1170 1140 1110

1090 1060 1030 1000 975 949

929 902 876 852 829 807

871 845 821 798 776 756

40 42 44 46 48 50

1050 1000 957 916 878 842

902 859 820 784 752 721

767 730 697 667 639 613

52 54 56 58 60 62

810 780 752 726 702 679

694 668 644 622 601 582

64 66 68 70 72

658 638 619 602 585

564 547 530 515 501

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1950 42100 1075 430 48.2 729 22.7 667 30.2 586

1670 36100 916 339 41.8 547 17.2 501 22.9 475

Span (ft)

2150 2110

Fy = 36 ksi

15 16 17 18 19 20

215

Properties and Reaction Values 1420 30700 779 264 36.0 407 12.9 373 17.3 381

1330 28700 720 256 33.5 353 11.2 323 15.0 365

1250 27000 640 224 29.9 290 8.40 268 11.2 318

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 37

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 40

For beams laterally unsupported, see page 4-113

Span (ft)

Fy = 36 ksi

Designation Wt./ft

W 40 331

278

264

235

211

167

149

985 937

975 934 879 830

936 921 860 806 759 716

1030 977 931 889 850 815

888 843 803 767 733 703

787 747 712 679 650 623

679 645 614 586 561 537

873 839 808 779 752 727

782 752 724 698 674 652

675 649 625 602 582 562

598 575 554 534 515 498

516 496 478 461 445 430

787 763 740 718 697 678

704 682 661 642 623 606

631 611 592 575 559 543

544 527 511 496 482 469

482 467 453 440 427 415

416 403 391 379 368 358

695 676 643 612 584 559

660 642 610 581 555 531

590 574 545 519 496 474

528 514 489 465 444 425

456 444 422 402 383 367

404 393 374 356 340 325

349 339 322 307 293 280

644 618 594 572 552 533

536 514 494 476 459 443

509 488 469 452 436 421

455 436 420 404 390 376

407 391 376 362 349 337

351 337 324 312 301 291

311 299 287 277 267 258

269 258 248 239 230 222

60 62 64 66 68 70

515 498 483 468 454 441

428 415 402 389 378 367

407 394 381 370 359 349

364 352 341 331 321 312

326 315 305 296 287 279

281 272 264 256 248 241

249 241 234 226 220 214

215 208 201 195 190 184

429

357

339

303

272

234

208

179

781 16900 493 154 23.4 177 5.30 163 7.07 194

692 14900 488 143 23.4 162 6.37 146 8.50 183

597 12900 468 128 22.7 139 7.24 121 9.65 163

13 14 15 16 17 18

1930 1930 1820 1720

1590 1510 1430

1490 1440 1360

1280 1210

1150 1090

19 20 21 22 23 24

1630 1540 1470 1400 1340 1290

1350 1290 1220 1170 1120 1070

1280 1220 1160 1110 1060 1020

1150 1090 1040 992 949 909

25 26 27 28 29 30

1240 1190 1140 1100 1070 1030

1030 989 952 918 886 857

976 939 904 872 842 814

31 32 33 34 35 36

996 965 936 908 883 858

829 803 779 756 734 714

37 38 40 42 44 46

835 813 772 735 702 671

48 50 52 54 56 58

183

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1430 30900 967 364 43.9 602 19.2 550 25.6 506

1190 25700 796 275 36.7 424 13.4 388 17.9 395

1130 24400 746 254 34.6 379 11.7 347 15.6 366

1010 21800 640 205 29.9 290 8.40 268 11.2 303

905 19500 574 177 27.0 236 6.95 218 9.27 259

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 38

BEAM AND GIRDER DESIGN

W 36

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

W 36

Span (ft)

Fy = 36 ksi

Wt./ft

300

280

260

245

230

1120 1090 1040 992 949 909

1060 1020 970 926 886 849

19 20 21 22 23 24

1350 1300 1240 1180 1130

1260 1200 1150 1100 1050

1180 1170 1110 1060 1010 972

25 26 27 28 29 30

1090 1050 1010 972 938 907

1010 972 936 903 871 842

933 897 864 833 804 778

873 839 808 779 752 727

815 783 754 727 702 679

31 32 33 34 35 36

878 851 825 800 778 756

815 790 766 743 722 702

753 729 707 686 667 648

704 682 661 642 623 606

657 637 617 599 582 566

37 38 39 40 41 42

736 716 698 680 664 648

683 665 648 632 616 602

630 614 598 583 569 555

590 574 559 545 532 519

551 536 522 509 497 485

43 44 46 48 50 52

633 619 592 567 544 523

588 574 549 527 505 486

543 530 507 486 467 449

507 496 474 455 436 420

474 463 443 424 407 392

54 56 58 60 62 64

504 486 469 454 439 425

468 451 436 421 408 395

432 417 402 389 376 365

404 390 376 364 352 341

377 364 351 339 329 318

66 68 70 72

412 400 389 378

383 372 361 351

353 343 333 324

331 321 312 303

309 300 291 283

1010 21800 561 180 28.8 254 9.65 231 12.9 274

943 20400 530 162 27.4 228 8.91 206 11.9 251

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1260 27200 675 239 34.0 364 12.6 334 16.7 350

1170 25300 628 214 31.9 319 11.1 292 14.8 318

1080 23300 592 194 30.2 283 10.4 258 13.9 292

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 39

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 36

For beams laterally unsupported, see page 4-113 Designation Wt./ft

W 36 256

19 20 21 22 23 24

194

182

170

160

150

135

1260 1190 1120

1180 1120 1060 1000

1090 1040 975 920

1020 969 912 862

956 902 849 802

910 899 842 793 749

871 837 784 738 697

1180 1120 1070 1020 977 936

1060 1010 963 919 879 842

947 900 857 818 782 750

872 828 789 753 720 690

816 775 739 705 674 646

759 721 687 656 627 601

709 674 642 613 586 562

661 627 598 570 546 523

579 550 524 500 478 458

25 26 27 28 29 30

899 864 832 802 775 749

809 778 749 722 697 674

720 692 666 643 620 600

663 637 614 592 571 552

620 596 574 554 535 517

577 555 534 515 498 481

539 518 499 481 465 449

502 483 465 448 433 418

440 423 407 393 379 366

31 32 33 34 35 36

725 702 681 661 642 624

652 632 613 595 578 562

580 562 545 529 514 500

534 518 502 487 473 460

500 485 470 456 443 431

465 451 437 424 412 401

435 421 408 396 385 374

405 392 380 369 359 349

355 344 333 323 314 305

38 40 42 44 46 48

591 562 535 511 488 468

532 505 481 459 440 421

473 450 428 409 391 375

436 414 394 377 360 345

408 388 369 352 337 323

380 361 344 328 314 301

355 337 321 306 293 281

330 314 299 285 273 261

289 275 262 250 239 229

50 52 54 56 58 60

449 432 416 401 387 374

404 389 374 361 349 337

360 346 333 321 310 300

331 319 307 296 286 276

310 298 287 277 267 258

289 277 267 258 249 240

270 259 250 241 232 225

251 241 232 224 216 209

220 211 204 196 190 183

62 64 66 68 70 72

362 351 340 330 321 312

326 316 306 297 289 281

290 281 273 265 257 250

267 259 251 244 237 230

250 242 235 228 222 215

233 225 219 212 206 200

217 211 204 198 193 187

202 196 190 185 179 174

177 172 167 162 157 153

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1040 22500 699 227 34.6 379 12.5 347 16.7 339

936 20200 628 196 31.3 311 10.4 285 13.8 298

624 13500 455 113 23.4 162 6.86 145 9.15 184

581 12500 436 105 22.5 147 6.65 131 8.87 168

509 11000 415 91.1 21.6 126 7.06 110 9.41 149

Span (ft)

1400 1320 1250

210

829 785 733 687 647 611

Fy = 36 ksi

13 14 15 16 17 18

232

Properties and Reaction Values 833 18000 592 173 29.9 270 10.5 244 14.0 270

767 16600 543 151 27.5 230 8.94 208 11.9 240

718 15500 512 139 26.1 205 8.16 185 10.9 223

668 14400 478 122 24.5 180 7.25 162 9.67 202

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 40

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 33

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 33 241

221

W 33 201

169

152

141

130

118

755 710 671 635 604 575

694 653 617 584 555 529

630 593 560 531 504 480

560 527 498 472 448 427

16 17 18 19 20 21

1100 1070 1010 966

1020 972 923 879

936 926 878 834 794

849 799 755 715 679 647

22 23 24 25 26 27

922 882 845 811 780 751

839 803 770 739 710 684

758 725 695 667 641 618

618 591 566 543 523 503

549 525 503 483 464 447

505 483 463 444 427 411

459 439 420 403 388 374

407 390 374 359 345 332

28 29 30 31 32 33

724 699 676 654 634 615

660 637 616 596 577 560

596 575 556 538 521 505

485 468 453 438 425 412

431 416 402 389 377 366

397 383 370 358 347 336

360 348 336 325 315 306

320 309 299 289 280 272

34 35 36 37 38 40

597 579 563 548 534 507

543 528 513 499 486 462

490 476 463 451 439 417

400 388 377 367 358 340

355 345 335 326 318 302

327 317 308 300 292 278

297 288 280 273 265 252

264 256 249 242 236 224

42 44 46 48 50 52

483 461 441 423 406 390

440 420 401 385 369 355

397 379 363 347 334 321

323 309 295 283 272 261

287 274 262 252 241 232

264 252 241 231 222 214

240 229 219 210 202 194

213 204 195 187 179 172

54 56 58 60 62 64

376 362 350 338 327 317

342 330 318 308 298 289

309 298 288 278 269 261

252 243 234 226 219 212

224 216 208 201 195 189

206 198 191 185 179 173

187 180 174 168 163 158

166 160 155 149 145 140

66 68 70 72

307 298 290 282

280 272 264 257

253 245 238 232

206 200 194 189

183 178 172 168

168 163 159 154

153 148 144 140

136 132 128 125

514 11100 392 95.3 21.8 141 6.36 127 8.48 162

467 10100 373 88.1 20.9 125 6.33 111 8.44 146

415 8960 351 77.3 19.8 107 6.28 93.6 8.37 128

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

939 20300 552 163 29.9 274 11.0 249 14.6 261

855 18500 511 144 27.9 236 9.88 213 13.2 235

772 16700 468 125 25.7 198 8.66 179 11.6 208

629 13600 440 124 24.1 185 6.69 170 8.92 203

559 12100 413 107 22.9 159 6.65 144 8.87 181

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 41

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 30

For beams laterally unsupported, see page 4-113 Designation

W 30

Span (ft)

Fy = 36 ksi

Wt./ft

261

235

191

173

932 899 851 809 770

847 808 765 727 692

775 769 726 688 653 622

830 794 761 730 702 676

735 703 674 647 622 599

661 632 606 581 559 538

594 568 545 523 503 484

726 701 678 656 635 616

652 629 608 589 570 553

578 558 539 522 506 490

519 501 485 469 454 441

467 451 436 422 408 396

34 36 38 40 42 44

598 565 535 508 484 462

537 507 480 456 435 415

476 449 426 404 385 368

428 404 383 363 346 330

384 363 344 327 311 297

46 48 50 52 54 56

442 423 407 391 376 363

397 380 365 351 338 326

352 337 324 311 300 289

316 303 291 280 269 260

284 272 261 251 242 233

58 60 62 64 66 68

350 339 328 318 308 299

315 304 294 285 277 268

279 270 261 253 245 238

251 242 234 227 220 214

225 218 211 204 198 192

70 72

290 282

261 254

231 225

208 202

187 182

673 14500 423 124 25.6 199 9.04 181 12.0 207

605 13100 388 111 23.6 167 7.96 151 10.6 187

16 17 18 19 20 21

1140 1130 1070 1020 968

1010 961 913 869

22 23 24 25 26 27

924 884 847 813 782 753

28 29 30 31 32 33

211

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

941 20300 571 204 33.5 353 14.2 323 18.9 313

845 18300 505 168 29.9 283 11.2 260 14.9 265

749 16200 466 148 27.9 239 10.5 218 14.0 239

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 42

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 30

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 30 148

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

775 771 720 675 635 600 568 540 514 491 470 450 432 415 400 386 372 360 348 338 327 318 300 284 270 257 245 235 225 216 208 200 193 186 180 174 169 164 159 154 150

132

725 674 629 590 555 524 497 472 449 429 410 393 378 363 350 337 325 315 304 295 286 278 262 248 236 225 215 205 197 189 182 175 169 163 157 152 147 143 139 135 131

124 686 678 629 588 551 518 490 464 441 420 401 383 367 353 339 326 315 304 294 284 275 267 259 245 232 220 210 200 192 184 176 169 163 157 152 147 142 138 134 130 126 122

116

108

659 628 583 544 510 480 454 430 408 389 371 355 340 327 314 302 292 282 272 263 255 247 240 227 215 204 194 186 177 170 163 157 151 146 141 136 132 128 124 120 117 113

632 623 575 534 498 467 440 415 393 374 356 340 325 311 299 287 277 267 258 249 241 234 226 220 208 197 187 178 170 162 156 149 144 138 133 129 125 121 117 113 110 107 104

599 562 518 481 449 421 396 374 355 337 321 306 293 281 270 259 250 241 232 225 217 211 204 198 187 177 168 160 153 147 140 135 130 125 120 116 112 109 105 102 99 96 94

540 509 470 437 408 382 360 340 322 306 291 278 266 255 245 235 226 218 211 204 197 191 185 180 170 161 153 146 139 133 127 122 118 113 109 105 102 99 96 93 90 87 85

346 7470 316 76.6 19.6 107 6.55 94.3 8.74 129

312 6740 300 67.3 18.7 93.9 6.50 81.1 8.66 115

283 6110 270 55.5 16.9 77.0 5.29 66.6 7.05 94.2

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

500 10800 388 117 23.4 174 6.97 160 9.29 193

437 9440 362 96.9 22.1 148 7.05 133 9.39 169

408 8810 343 88.8 21.1 132 6.55 119 8.73 153

378 8160 330 82.6 20.3 120 6.49 107 8.65 141

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 43

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 27

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 27 258

235

194

178

161

146

917 900 850 805 765

820 798 754 714 678

784 765 720 680 645 612

708 691 651 614 582 553

644 622 586 553 524 498

791 755 722 692 664 639

728 695 665 637 612 588

646 617 590 565 543 522

583 557 532 510 490 471

527 503 481 461 442 425

474 453 433 415 398 383

680 656 633 612 592 574

615 593 573 554 536 519

566 546 527 510 493 478

502 484 468 452 438 424

454 437 422 408 395 383

410 395 381 369 357 346

369 356 343 332 321 311

33 34 35 36 37 38

556 540 525 510 496 483

503 489 475 461 449 437

463 450 437 425 413 402

411 399 388 377 367 357

371 360 350 340 331 322

335 325 316 307 299 291

302 293 285 277 269 262

40 42 44 46 48 50

459 437 417 399 383 367

415 395 378 361 346 332

382 364 348 332 319 306

339 323 308 295 283 271

306 292 278 266 255 245

276 263 251 240 230 221

249 237 226 216 207 199

52 54 56 58 60 62

353 340 328 317 306 296

319 308 297 286 277 268

294 283 273 264 255 247

261 251 242 234 226 219

236 227 219 211 204 198

213 205 197 191 184 178

191 184 178 172 166 161

64 66

287 278

260 252

239 232

212 206

191 186

173 168

156 151

567 12200 392 122 26.1 206 10.6 186 14.1 207

512 11100 354 108 23.8 171 8.86 154 11.8 185

461 9960 322 91.9 21.8 142 7.62 128 10.2 163

15 16 17 18 19 20

1100 1080 1020 966 918

1010 977 923 874 831

21 22 23 24 25 26

874 835 798 765 734 706

27 28 29 30 31 32

217

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

850 18400 552 221 35.3 395 16.8 362 22.5 335

769 16600 507 189 32.8 337 15.0 308 20.0 296

708 15300 459 163 29.9 283 12.3 260 16.4 261

628 13600 410 139 27.0 230 10.3 211 13.7 227

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 44

BEAM AND GIRDER DESIGN

W 27

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

W 27

Span (ft)

Fy = 36 ksi

Wt./ft

129

102

605 570 529 494 463

542 507 471 439 412

513 500 462 429 400 375

478 439 405 376 351 329

502 474 449 427 406 388

436 412 390 370 353 337

388 366 347 329 314 299

353 334 316 300 286 273

310 293 277 264 251 240

23 24 25 26 27 28

371 356 341 328 316 305

322 309 296 285 274 265

286 275 264 253 244 235

261 250 240 231 222 214

229 220 211 203 195 188

29 30 31 32 33 34

294 284 275 267 259 251

255 247 239 232 225 218

227 220 213 206 200 194

207 200 194 188 182 177

182 176 170 165 160 155

36 38 40 42 44 46

237 225 213 203 194 185

206 195 185 176 168 161

183 173 165 157 150 143

167 158 150 143 136 131

146 139 132 125 120 115

48 50 52 54 56 58

178 171 164 158 152 147

154 148 142 137 132 128

137 132 127 122 118 114

125 120 115 111 107 104

110 105 101 98 94 91

60 62 64 66

142 138 133 129

123 119 116 112

110 106 103 100

100 97 94 91

88 85 82 80

278 6000 256 63.4 17.6 90.6 5.39 80.9 7.18 108

244 5270 239 56.9 16.6 76.4 5.23 67.1 6.97 93.4

11 12 13 14 15 16

655 609 569 533

17 18 19 20 21 22

114

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

395 8530 328 99.5 22.0 153 6.86 140 9.14 171

343 7410 302 83.4 20.5 127 6.70 115 8.93 149

305 6590 271 72.4 18.5 103 5.58 93.0 7.44 121

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 45

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 24

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 24 229

207

192

176

146

131

117

104

685 674 632 595 562

625 602 564 531 502

576 571 533 500 470 444

519 505 471 441 415 392

468 446 416 390 367 347

581 552 526 502 480 460

532 505 481 459 440 421

475 451 430 410 393 376

421 400 381 363 347 333

372 353 336 321 307 294

329 312 297 284 271 260

483 464 447 431 416 402

442 425 409 394 381 368

404 389 374 361 349 337

361 347 334 322 311 301

320 307 296 285 276 266

283 272 262 252 244 235

250 240 231 223 215 208

422 409 397 385 374 364

389 377 366 355 345 335

356 345 334 325 315 307

326 316 306 297 289 281

291 282 274 266 258 251

258 250 242 235 228 222

228 221 214 208 202 196

201 195 189 184 178 173

384 365 348 332 317 304

344 327 312 297 285 273

318 302 287 274 262 252

290 276 263 251 240 230

266 253 241 230 220 211

238 226 215 205 196 188

210 200 190 182 174 167

186 177 168 161 154 147

164 156 149 142 136 130

292 281 270 261 252 243

262 252 242 234 226 218

241 232 224 216 208 201

221 212 204 197 190 184

202 194 187 181 174 168

181 174 167 161 156 150

160 154 148 143 138 133

141 136 131 126 122 118

125 120 116 111 108 104

676 14600 486 216 34.6 379 18.0 347 24.1 328

606 13100 435 186 31.3 311 15.0 285 20.0 288

370 7990 288 95.3 21.8 141 8.65 127 11.5 166

327 7060 259 80.4 19.8 115 7.41 103 9.88 139

289 6240 234 67.5 18.0 93.7 6.36 83.5 8.48 114

13 14 15 16 17 18

971 913 859 811

870 818 770 727

802 755 710 671

736 736 690 649 613

19 20 21 22 23 24

769 730 695 664 635 608

689 654 623 595 569 545

635 604 575 549 525 503

25 26 27 28 29 30

584 562 541 521 504 487

524 503 485 467 451 436

31 32 33 34 35 36

471 456 442 429 417 406

38 40 42 44 46 48 50 52 54 56 58 60

162

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

559 12100 401 164 29.2 270 13.1 247 17.5 259

511 11000 368 143 27.0 230 11.5 211 15.3 231

468 10100 343 127 25.4 200 10.5 182 14.1 209

418 9030 313 110 23.4 167 9.35 152 12.5 186

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 46

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 24

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 24 103

W 24 76

397 367 330 300 275

362 362 322 289 263 241

7 8 9 10 11 12

525 504

487 457

440 440 403

409 393 360

383 382 348 319

13 14 15 16 17 18

465 432 403 378 356 336

422 392 366 343 323 305

372 346 323 302 285 269

332 309 288 270 254 240

294 273 255 239 225 212

254 236 220 207 194 184

223 207 193 181 170 161

19 20 21 22 23 24

318 302 288 275 263 252

289 274 261 249 239 229

255 242 230 220 210 202

227 216 206 196 188 180

201 191 182 174 166 159

174 165 157 150 144 138

152 145 138 132 126 121

25 26 27 28 29 30

242 233 224 216 209 202

219 211 203 196 189 183

194 186 179 173 167 161

173 166 160 154 149 144

153 147 142 137 132 127

132 127 122 118 114 110

116 111 107 103 100 96

31 32 33 34 35 36

195 189 183 178 173 168

177 171 166 161 157 152

156 151 147 142 138 134

139 135 131 127 123 120

123 119 116 112 109 106

107 103 100 97 94 92

93 90 88 85 83 80

38 40 42 44 46 48

159 151 144 137 131 126

144 137 131 125 119 114

127 121 115 110 105 101

114 108 103 98 94 90

101 96 91 87 83 80

87 83 79 75 72 69

76 72 69 66 63 60

50 52 54 56 58 60

121 116 112 108 104 101

110 106 102 98 95 91

97 93 90 86 83 81

86 83 80 77 74

76 74 71 68 66

66 64 61 59 57

58 56 54 52 50

177 3820 191 51.4 14.9 62.6 4.73 55.1 6.30 77.9

153 3300 198 53.2 15.5 66.3 5.21 58.0 6.95 83.2

134 2890 181 46.7 14.2 54.0 4.75 46.5 6.34 69.4

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

280 6050 262 86.6 19.8 124 6.35 113 8.47 144

254 5490 243 75.3 18.5 106 5.89 96.2 7.86 125

224 4840 220 66.1 16.9 86.5 5.14 78.3 6.85 103

200 4320 205 56.9 15.8 73.6 4.81 66.0 6.41 89.3

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 47

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 21

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 21 201

182

166

147

132

122

111

101

552 514 480 450 423 400

506 474 442 414 390 368

460 430 402 377 354 335

415 390 364 342 321 304

13 14 15 16 17 18

815 763 716 673 636

733 685 643 605 571

656 622 583 549 518

618 575 537 504 474 448

19 20 21 22 23 24

603 572 545 520 498 477

541 514 490 467 447 428

491 467 444 424 406 389

424 403 384 366 350 336

379 360 343 327 313 300

349 332 316 301 288 276

317 301 287 274 262 251

288 273 260 248 238 228

25 26 27 28 29 30

458 440 424 409 395 382

411 395 381 367 355 343

373 359 346 333 322 311

322 310 298 288 278 269

288 277 266 257 248 240

265 255 246 237 229 221

241 232 223 215 208 201

219 210 202 195 188 182

31 32 33 34 35 36

369 358 347 337 327 318

332 321 312 302 294 286

301 292 283 274 267 259

260 252 244 237 230 224

232 225 218 212 206 200

214 207 201 195 189 184

194 188 183 177 172 167

176 171 166 161 156 152

38 40 42 44 46 48

301 286 273 260 249 239

271 257 245 234 224 214

246 233 222 212 203 194

212 201 192 183 175 168

189 180 171 163 156 150

175 166 158 151 144 138

159 151 143 137 131 126

144 137 130 124 119 114

50 52

229 220

206 198

187 179

161 155

144 138

133 128

121 116

109 105

307 6630 253 91.1 21.6 139 9.53 126 12.7 161

279 6030 230 80.4 19.8 117 8.11 105 10.8 143

253 5460 208 70.3 18.0 96.8 6.72 87.2 8.95 119

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

530 11400 407 195 32.8 339 18.4 311 24.6 301

476 10300 367 168 29.9 281 15.6 258 20.8 265

432 9330 328 143 27.0 232 12.7 213 16.9 231

373 8060 309 122 25.9 200 13.5 181 18.0 206

333 7190 276 106 23.4 163 11.2 147 14.9 182

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 48

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 21

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 21 93

W 21 68

44 281 258 229 206 187 172

7 8 9 10 11 12

488 477 434 398

429 423 385 353

376 372 338 310

353 346 314 288

326 311 283 259

332 310 279 253 232

308 297 264 238 216 198

13 14 15 16 17 18

367 341 318 298 281 265

326 302 282 265 249 235

286 265 248 232 219 206

266 247 230 216 203 192

239 222 207 194 183 173

214 199 186 174 164 155

183 170 158 149 140 132

159 147 137 129 121 114

19 20 21 22 23 24

251 239 227 217 208 199

223 212 202 192 184 176

196 186 177 169 162 155

182 173 165 157 150 144

164 156 148 141 135 130

147 139 133 127 121 116

125 119 113 108 103 99

108 103 98 94 90 86

25 26 27 28 29 30

191 184 177 170 165 159

169 163 157 151 146 141

149 143 138 133 128 124

138 133 128 123 119 115

124 120 115 111 107 104

111 107 103 100 96 93

95 91 88 85 82 79

82 79 76 74 71 69

31 32 33 34 35 36

154 149 145 140 136 133

137 132 128 125 121 118

120 116 113 109 106 103

111 108 105 102 99 96

100 97 94 91 89 86

90 87 84 82 80 77

77 74 72 70 68 66

66 64 62 61 59 57

38 40 42 44 46 48

126 119 114 108 104 99

111 106 101 96 92 88

98 93 88 84 81 77

91 86 82 79 75 72

82 78 74 71 68 65

73 70 66 63 61 58

63 59 57 54 52 50

54 52 49 47 45 43

50 52

95 92

85 81

74 71

69 66

62 60

56 54

48 46

129 2790 166 50.1 14.6 63.6 4.45 57.3 5.94 78.1

110 2380 154 44.9 13.7 52.4 4.52 46.2 6.03 67.1

95.4 2060 141 37.4 12.6 42.5 4.23 36.7 5.64 56.3

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

221 4770 244 88.1 20.9 130 8.91 118 11.9 156

196 4230 215 72.4 18.5 103 7.01 93.3 9.34 126

172 3720 188 61.4 16.4 80.8 5.50 73.0 7.34 98.7

160 3460 177 55.6 15.5 71.4 5.04 64.3 6.72 87.8

144 3110 163 49.5 14.4 60.7 4.55 54.3 6.07 75.5

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 49

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 18

For beams laterally unsupported, see page 4-113 Designation Wt./ft

W 18 192

175

158

W 18 143

130

119

106

430 414 382 355 331 311

387 380 351 326 304 285

343 335 309 287 268 251

301 293 271 251 235 220

693 661 614 573 537

621 592 549 513 481

553 535 497 464 435

501 484 449 419 393

17 18 19 20 21 22

562 530 502 477 455 434

506 478 452 430 409 391

452 427 405 384 366 350

409 386 366 348 331 316

370 349 331 314 299 286

332 313 297 282 268 256

292 276 261 248 237 226

268 253 240 228 217 207

236 223 211 201 191 183

207 196 185 176 168 160

23 24 25 26 27 28

415 398 382 367 354 341

374 358 344 331 318 307

334 320 308 296 285 275

302 290 278 268 258 248

273 262 251 242 233 224

245 235 226 217 209 201

216 207 199 191 184 177

198 190 182 175 169 163

175 167 161 155 149 143

153 147 141 135 130 126

29 30 31 32 33 34

329 318 308 298 289 281

296 287 277 269 261 253

265 256 248 240 233 226

240 232 224 217 211 205

217 210 203 196 190 185

194 188 182 176 171 166

171 166 160 155 151 146

157 152 147 142 138 134

139 134 130 126 122 118

121 117 114 110 107 104

35 36 37 38 39 40

273 265 258 251 245 239

246 239 232 226 220 215

220 214 208 202 197 192

199 193 188 183 178 174

180 175 170 165 161 157

161 157 152 148 145 141

142 138 134 131 127 124

130 127 123 120 117 114

115 112 109 106 103 100

101 98 95 93 90 88

42 44

227 217

205 195

183 175

166 158

150 143

134 128

118 113

109 104

96 91

84 80

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

442 9550 380 211 34.6 381 22.8 350 30.4 323

398 8600 347 180 32.0 324 20.3 297 27.1 284

230 4970 215 86.3 21.2 134 10.7 121 14.3 155

211 4560 193 75.2 19.3 112 8.69 101 11.6 138

186 4020 172 62.1 17.3 89.3 7.17 80.5 9.56 113

163 3520 150 52.6 15.3 69.9 5.69 63.0 7.59 88.4

Span (ft)

760 734 682 636 597

483 470 434 403 376 352

Fy = 36 ksi

11 12 13 14 15 16

Properties and Reaction Values 356 7690 311 155 29.2 268 17.2 245 22.9 250

322 6960 277 131 26.3 219 13.9 201 18.5 217

291 6290 251 113 24.1 184 12.0 168 15.9 191

261 5640 242 103 23.6 167 12.8 151 17.1 180

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 50

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 18

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 18 71

6 7 8 9 10 11

355 348 313 285

321 319 287 261

12 13 14 15 16 17

261 241 224 209 196 184

18 19 20 21 22 23

W 18 55

294 266 242

275 269 242 220

248 242 218 198

253 245 218 196 178

219 212 188 169 154

206 205 180 160 144 131

239 221 205 192 180 169

221 204 190 177 166 156

202 186 173 161 151 142

182 168 156 145 136 128

163 151 140 131 122 115

141 130 121 113 106 100

120 110 103 96 90 84

174 165 157 149 142 136

160 151 144 137 131 125

148 140 133 127 121 116

134 127 121 115 110 105

121 115 109 104 99 95

109 103 98 93 89 85

94 89 85 81 77 74

80 76 72 68 65 62

24 25 26 27 28 29

131 125 120 116 112 108

120 115 110 106 103 99

111 106 102 98 95 92

101 97 93 90 86 83

91 87 84 81 78 75

82 78 75 73 70 68

71 68 65 63 60 58

60 57 55 53 51 50

30 31 32 33 34 35

104 101 98 95 92 89

96 93 90 87 84 82

89 86 83 81 78 76

81 78 76 73 71 69

73 70 68 66 64 62

65 63 61 59 58 56

56 55 53 51 50 48

48 46 45 44 42 41

36 38 40 42 44

87 82 78 75 71

80 76 72 68 65

74 70 66 63 60

67 64 60 58 55

61 57 55 52 50

54 52 49 47 45

47 45 42 40 38

40 38 36 34 33

90.7 1960 126 40.5 13.0 51.4 3.92 46.7 5.23 64.2

78.4 1690 110 33.7 11.3 39.2 3.05 35.6 4.07 49.1

66.5 1440 103 30.4 10.8 32.8 3.29 28.9 4.39 43.5

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

145 3130 178 66.8 17.8 95.9 7.44 86.7 9.92 120

133 2870 161 58.2 16.2 80.0 6.08 72.6 8.10 99.8

123 2660 147 51.4 14.9 68.2 5.18 61.9 6.90 85.0

112 2420 137 46.1 14.0 59.2 4.77 53.4 6.36 74.7

101 2180 124 39.9 12.8 48.9 4.01 44.1 5.34 61.9

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 51

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 16

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 16 100

W 16

6 7 8 9 10 11

386

342

292

12 13 14 15 16 17

356 329 305 285 267 252

315 291 270 252 236 222

18 19 20 21 22 23

238 225 214 204 194 186

24 25 26 27 28 29

W 16 40

26 153 136 119 106 95 87

251

275 252 227 206

240 221 199 181

216 198 178 162

190 175 157 143

182 173 154 138 126

170 167 146 130 117 106

270 249 231 216 203 191

234 216 201 187 176 165

189 174 162 151 142 133

166 153 142 132 124 117

148 137 127 119 111 105

131 121 112 105 98 93

115 106 99 92 86 81

97 90 83 78 73 69

80 73 68 64 60 56

210 199 189 180 172 164

180 171 162 154 147 141

156 148 140 134 128 122

126 119 113 108 103 99

110 105 99 95 90 86

99 94 89 85 81 77

87 83 79 75 72 68

77 73 69 66 63 60

65 61 58 56 53 51

53 50 48 45 43 42

178 171 164 158 153 147

158 151 145 140 135 130

135 130 125 120 116 112

117 112 108 104 100 97

95 91 87 84 81 78

83 79 76 74 71 69

74 71 68 66 63 61

66 63 61 58 56 54

58 55 53 51 49 48

49 47 45 43 42 40

40 38 37 35 34 33

30 31 32 33 34 35

143 138 134 130 126 122

126 122 118 115 111 108

108 105 101 98 95 93

94 91 88 85 83 80

76 73 71 69 67 65

66 64 62 60 58 57

59 57 56 54 52 51

52 51 49 48 46 45

46 45 43 42 41 39

39 38 36 35 34 33

32 31 30 29 28 27

36 38 40

119 113 107

105 99 95

90 85 81

78 74 70

63 60 57

55 52 50

49 47 44

44 41 39

38 36

32 31

27 25

198 4280 193 88.8 21.1 136 11.0 123 14.7 157

175 3780 171 73.8 18.9 109 9.06 98.8 12.1 135

72.9 1570 94.9 32.6 11.0 36.6 3.22 33.2 4.30 47.1

64.0 1380 91.0 29.9 10.6 32.2 3.46 28.5 4.61 43.5

54.0 1170 84.9 27.8 9.90 29.3 2.73 26.4 3.64 38.2

44.2 955 76.3 23.9 9.00 22.5 2.65 19.7 3.53 31.2

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

150 3240 146 58.9 16.4 81.9 6.89 74.3 9.18 104

130 2810 125 48.9 14.2 61.9 5.21 56.3 6.95 78.9

105 2270 137 53.2 15.5 73.0 6.21 66.2 8.28 93.2

92.0 1990 120 44.9 13.7 56.9 4.92 51.6 6.56 72.9

82.3 1780 108 38.8 12.4 46.6 4.14 42.2 5.52 60.1

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 52

BEAM AND GIRDER DESIGN

W 14

Fy = 36 ksi

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported For beams laterally unsupported, see page 4-113

Designation Wt./ft

W 14 132

120

109

W 14 99

248 247 227 209 194 181

227 226 207 191 177 166

203 200 184 169 157 147

332 327 305

292 276

267 267 249

240 226

16 17 18 19 20 21

316 297 281 266 253 241

286 269 254 241 229 218

259 244 230 218 207 197

234 220 208 197 187 178

212 199 188 178 170 161

188 177 167 158 150 143

170 160 151 143 136 130

155 146 138 131 124 118

138 130 122 116 110 105

22 23 24 25 26 27

230 220 211 202 194 187

208 199 191 183 176 170

189 180 173 166 160 154

170 162 156 149 144 138

154 147 141 136 130 126

136 131 125 120 115 111

124 118 113 109 105 101

113 108 104 99 96 92

100 96 92 88 85 82

28 29 30 31 32 33

181 174 168 163 158 153

164 158 153 148 143 139

148 143 138 134 130 126

133 129 125 121 117 113

121 117 113 109 106 103

107 104 100 97 94 91

97 94 91 88 85 82

89 86 83 80 78 75

79 76 73 71 69 67

149

135

122

110

100

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

234 5050 184 98.0 23.2 161 16.3 145 21.8 173

212 4580 166 86.3 21.2 134 13.9 121 18.5 155

139 3000 142 74.6 18.4 103 9.95 93.6 13.3 134

126 2720 124 63.3 16.2 81.8 7.52 74.7 10.0 107

115 2480 113 56.0 14.9 69.4 6.49 63.3 8.65 91.5

102 2200 101 48.5 13.5 56.4 5.40 51.4 7.20 74.8

Span (ft)

368 361 337

284 273 250 231 214 200

Fy = 36 ksi

10 11 12 13 14 15

Properties and Reaction Values 192 4150 146 73.8 18.9 108 10.8 97.6 14.4 135

173 3740 134 62.7 17.5 91.3 9.48 82.3 12.6 119

157 3390 120 54.5 15.8 75.3 7.86 67.9 10.5 102

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 53

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 14

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 14 53

5 6 7 8 9 10

200 188

182 169

11 12 13 14 15 16

171 157 145 134 125 118

17 18 19 20 21 22

W 14 43

W 14 30

162 150

170 166 148 133

155 147 131 118

145 128 114 102

138 124 109 96 87

123 120 102 90 80 72

154 141 130 121 113 106

137 125 116 107 100 94

121 111 102 95 89 83

107 98 91 84 79 74

93 85 79 73 68 64

79 72 67 62 58 54

65 60 55 51 48 45

111 105 99 94 90 86

100 94 89 85 81 77

88 84 79 75 72 68

78 74 70 66 63 60

69 66 62 59 56 54

60 57 54 51 49 46

51 48 46 43 41 39

42 40 38 36 34 33

23 24 25 26 27 28

82 78 75 72 70 67

74 71 68 65 63 60

65 63 60 58 56 54

58 55 53 51 49 47

51 49 47 45 44 42

44 43 41 39 38 36

38 36 35 33 32 31

31 30 29 28 27 26

29 30 31 32 33 34

65 63 61 59 57 55

58 56 55 53 51 50

52 50 48 47 46 44

46 44 43 42 40 39

41 39 38 37 36 35

35 34 33 32 31 30

30 29 28 27 26 26

25 24 23 22 22 21

47.3 1020 72.6 22.8 9.72 26.6 3.39 23.5 4.52 38.2

40.2 868 69.0 21.5 9.18 25.5 2.61 23.1 3.47 34.4

33.2 717 61.4 18.1 8.28 19.5 2.43 17.3 3.24 27.8

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

87.1 1880 100 47.9 13.3 55.9 5.06 51.3 6.75 73.2

78.4 1690 91.1 42.1 12.2 46.8 4.40 42.8 5.86 61.8

69.6 1500 81.0 36.0 11.0 37.5 3.60 34.2 4.80 49.8

61.5 1330 85.0 29.6 11.2 37.9 3.77 34.4 5.02 50.7

54.6 1180 77.5 25.7 10.3 31.4 3.34 28.3 4.45 42.8

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 54

BEAM AND GIRDER DESIGN

W 12

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation Wt./ft

W 12 120

106

W 12 79

53 162 153 140 129 120 112

306 295 272 253 236

272 265 244 227 212

251 238 219 204 190

226 214 198 184 171

205 194 179 167 156

184 174 161 149 139

16 17 18 19 20 21

251 236 223 211 201 191

221 208 197 186 177 169

198 187 176 167 159 151

178 168 158 150 143 136

161 151 143 135 129 122

146 137 130 123 117 111

131 123 116 110 105 100

117 110 104 98 93 89

105 99 93 89 84 80

22 23 24 25 26 27

183 175 167 161 155 149

161 154 148 142 136 131

144 138 132 127 122 118

130 124 119 114 110 106

117 112 107 103 99 95

106 101 97 93 90 86

95 91 87 84 80 77

85 81 78 75 72 69

76 73 70 67 65 62

28 29 30

143 139 134

127 122 118

113 109 106

102 98 95

92 89 86

83 80 78

75 72 70

67 64 62

60 58 56

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

186 4020 181 116 25.6 192 22.7 173 30.2 199

164 3540 153 92.6 22.0 145 16.3 131 21.8 164

108 2330 102 53.2 15.5 70.6 8.89 63.4 11.9 102

96.8 2090 91.9 46.1 14.0 58.0 7.43 52.0 9.90 84.1

86.4 1870 85.3 44.6 13.0 52.9 5.49 48.4 7.32 72.2

77.9 1680 80.9 38.8 12.4 47.0 5.44 42.6 7.25 66.2

Span (ft)

362 335 309 287 268

171 170 156 144 133 124

Fy = 36 ksi

10 11 12 13 14 15

Properties and Reaction Values 147 3180 136 80.4 19.8 118 13.4 107 17.8 145

132 2850 125 69.5 18.5 102 12.4 91.5 16.5 130

119 2570 113 60.8 16.9 84.5 10.5 75.9 14.0 116

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 55

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 12

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 12 50

W 12 40

4 5 6 7 8 9

175 174

157 155

10 11 12 13 14 15

156 142 130 120 112 104

16 17 18 19 20 21

W 12 26

111 107 89 76 67 59

103 87 72 62 54 48

93 75 63 54 47 42

137

146 138 123

125 116 103

109 100 89

124 105 90 79 70

140 127 116 108 100 93

124 113 104 96 89 83

111 101 92 85 79 74

93 85 78 72 66 62

80 73 67 62 57 54

63 58 53 49 45 42

53 49 44 41 38 36

43 39 36 33 31 29

38 34 31 29 27 25

98 92 87 82 78 74

87 82 78 74 70 67

78 73 69 65 62 59

69 65 61 58 55 53

58 55 52 49 47 44

50 47 45 42 40 38

40 37 35 33 32 30

33 31 30 28 27 25

27 26 24 23 22 21

23 22 21 20 19 18

22 23 24 25 26 27

71 68 65 63 60 58

64 61 58 56 54 52

56 54 52 50 48 46

50 48 46 44 43 41

42 40 39 37 36 34

37 35 33 32 31 30

29 28 26 25 24 23

24 23 22 21 21 20

20 19 18 17 17 16

17 16 16 15 14 14

28 29 30

56 54 52

50 48 47

44 43 37

39 38 31

33 32 27

29 28 21

23 22 18

19 18

16 15

13 13

72.4 1560 87.7 45.8 13.3 55.1 5.96 50.3 7.95 76.1

64.7 1400 78.5 37.7 12.1 45.0 4.98 41.0 6.64 62.6

29.3 633 62.2 20.5 9.36 26.4 3.08 23.9 4.11 37.3

24.7 534 55.6 17.2 8.46 20.6 2.80 18.4 3.73 30.5

20.1 434 51.3 14.9 7.92 16.3 3.08 13.8 4.10 27.1

17.4 376 46.3 12.4 7.20 13.0 2.74 10.8 3.65

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

57.5 1240 68.5 33.2 10.6 35.2 3.83 32.1 5.11 48.7

51.2 1110 72.9 27.0 10.8 36.3 3.81 33.1 5.08 49.6

43.1 931 62.4 21.9 9.36 26.9 2.97 24.5 3.96 37.3

37.2 804 54.6 18.1 8.28 20.8 2.41 18.8 3.21 29.3

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

22.7

4 - 56

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 10

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

W 10 112

100

9 10 11 12 13 14

333 318 289 265 244 227

293 281 255 234 216 201

255 244 222 203 188 174

218 211 192 176 162 151

190 184 167 154 142 132

167 161 146 134 124 115

145 144 131 120 111 103

132 130 119 109 100 93

15 16 17 18 19 20

212 198 187 176 167 159

187 176 165 156 148 140

163 153 144 136 128 122

141 132 124 117 111 105

123 115 108 102 97 92

107 101 95 90 85 81

96 90 85 80 76 72

87 82 77 72 69 65

21 22 23 24

151 144 138 132

134 128 122 117

116 111 106 102

100 96 92 88

88 84 80 77

77 73 70 67

69 65 63 60

62 59 57 54

74.6 1610 83.4 49.6 15.1 68.7 9.79 62.0 13.0 98.8

66.6 1440 72.6 41.6 13.3 54.0 7.49 49.0 9.99 81.4

60.4 1300 66.0 36.3 12.2 45.4 6.46 41.1 8.61 69.1

Span (ft)

Fy = 36 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

147 3180 167 127 27.2 224 27.8 203 37.1 216

130 2810 147 107 24.5 182 23.2 164 31.0 187

113 2440 127 88.5 21.8 143 18.9 130 25.3 159

97.6 2110 109 71.5 19.1 110 14.8 99.7 19.8 134

85.3 1840 95.0 58.2 16.9 86.5 11.9 78.3 15.9 113

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 57

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 10

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W 10 45

3 4 5 6 7 8

137

9 10 11 12 13 14

W 10 33

W 10 22

12 73 68 54 45 39 34

100 93 78 67 58

94 81 67 58 50

89 86 69 58 49 43

121

110 105

122 113 99

104 97 85

95 94 80 70

132 119 108 99 91 85

112 101 92 84 78 72

93 84 76 70 64 60

88 79 72 66 61 56

75 68 61 56 52 48

62 56 51 47 43 40

52 47 42 39 36 33

45 40 37 34 31 29

38 35 31 29 27 25

30 27 25 23 21 19

15 16 17 18 19 20

79 74 70 66 62 59

67 63 59 56 53 51

56 52 49 47 44 42

53 49 47 44 42 40

45 42 40 38 36 34

37 35 33 31 30 28

31 29 27 26 25 23

27 25 24 22 21 20

23 22 20 19 18 17

18 17 16 15 14 14

21 22 23 24

56 54 52 49

48 46 44 42

40 38 36 35

38 36 34 33

32 31 29 28

27 26 24 23

22 21 20 19

19 18 18 17

16 16 15 14

13 12 12 11

54.9 1190 68.7 39.4 12.6 49.9 6.29 45.7 8.38 72.9

46.8 1010 60.7 31.9 11.3 39.4 5.46 35.8 7.28 59.4

21.6 467 49.8 18.3 9.00 24.0 3.55 21.6 4.73 37.0

18.7 404 47.2 16.2 8.64 20.7 3.80 18.1 5.07 34.6

16.0 346 44.7 14.2 8.28 17.5 4.14 14.8 5.52 32.7

12.6 272 36.5 10.7 6.84 11.6 3.04 9.61 4.05 22.8

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

38.8 838 54.9 27.7 10.4 31.5 5.29 28.1 7.05 51.0

36.6 791 61.1 25.3 10.8 35.9 4.64 32.7 6.19 52.8

31.3 676 52.2 20.5 9.36 26.9 3.55 24.5 4.73 39.8

26.0 562 47.4 16.2 8.64 21.6 3.47 19.2 4.62 34.3

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 58

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

W8 67

7 8 9 10 11 12

199 190 168 152 138 126

174 161 144 129 117 108

132 118 106 96 88

115 107 96 86 78 72

98 94 83 75 68 62

89 82 73 66 60 55

13 14 15 16 17 18

117 108 101 95 89 84

99 92 86 81 76 72

81 76 71 66 62 59

66 61 57 54 51 48

58 54 50 47 44 42

51 47 44 41 39 36

19 20

80 76

68 65

56 53

45 43

39 37

35 33

39.8 860 57.7 34.4 13.0 49.5 9.27 44.4 12.4 76.5

34.7 750 48.9 27.9 11.2 37.2 6.80 33.5 9.07 63.0

30.4 657 44.3 24.0 10.3 30.7 6.11 27.4 8.14 53.9

Span (ft)

Fy = 36 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

70.2 1520 99.7 73.7 20.5 127 20.2 115 26.9 140

59.8 1290 86.8 60.2 18.4 100 17.2 90.3 22.9 120

49.0 1060 66.1 42.8 14.4 64.1 10.1 58.4 13.5 89.6

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 59

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

W8 24

W8 18

71 62 49 41 35 31

52 48 38 32 27 24

3 4 5 6 7 8

89 84 73

76 72 63

80 73 63 55

73 61 52 46

77 73 59 49 42 37

9 10 11 12 13 14

65 59 53 49 45 42

56 50 46 42 39 36

49 44 40 37 34 31

41 37 33 31 28 26

33 29 27 24 23 21

27 25 22 21 19 18

21 19 17 16 15 14

15 16 17 18 19 20

39 37 35 33 31 29

33 31 29 28 26 22

29 28 26 24 23 18

24 23 22 20 19 15

20 18 17 16 15

16 15 14 14 13

13 12 11 11 10

13.6 294 38.6 16.5 8.82 20.8 5.28 18.0 7.05 40.9

11.4 246 35.7 14.2 8.28 17.0 5.48 14.1 7.31 37.9

8.87 192 26.1 9.56 6.12 9.71 2.79 8.24 3.72 20.3

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

27.2 588 44.7 24.0 10.3 31.7 5.67 28.7 7.56 53.3

23.2 501 37.8 19.3 8.82 23.5 4.26 21.2 5.67 39.7

20.4 441 40.2 18.3 9.00 24.2 4.33 21.8 5.77 40.6

17.0 367 36.4 15.5 8.28 19.4 4.16 17.1 5.54 35.2

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 60

BEAM AND GIRDER DESIGN

W 6–5–4

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

W6 25

2 3 4 5 6 7

79 68 58

8 9 10 11 12 13 14

W6 15*

63 54 46

54 46 38 33

63 63 51 42 36

54 45 36 30 26

39 34 27 22 19

51 45 41 37 34 31

40 36 32 29 27 25

29 26 23 21 19 18

32 28 25 23 21 19

22 20 18 16 15 14

17 15 13 12 11 10

18.9 408 39.7 23.4 11.5 37.4 10.4 33.0 13.8 60.8

14.9 322 31.3 17.5 9.36 24.5 7.13 21.6 9.51 48.0

W4 16

54 50 42 36

47 41 35 30

45 45 34 27 23 19

31 28 25 23 21

26 23 21 19 17

17 15 14

11.6 251 27.0 19.7 9.72 28.2 8.16 25.4 10.9 51.3

9.59 207 23.4 16.2 8.64 21.6 7.04 19.2 9.38 44.3

6.28 136 22.6 17.3 10.1 26.6 14.0 22.7 18.7 50.1

9.6

Span (ft)

Fy = 36 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

10.8 230 26.8 12.9 8.28 17.2 7.17 14.3 9.56 39.8

11.7 253 31.7 17.5 9.36 25.8 6.34 23.2 8.46 48.0

8.30 179 27.0 12.9 8.28 17.9 6.62 15.2 8.82 39.8

6.23 135 19.5 8.61 6.12 9.95 3.56 8.55 4.74 24.0

*Indicates noncompact shape. Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 61

BEAMS S Shapes Maximum factored uniform loads in kips for beams laterally supported

S 24–20

For beams laterally unsupported, see page 4-113 Designation Wt./ft

S 24 121

12 13 14 15 16 17

S 20 80

S 20 86

521 494 439 395 359

494 472 413 367 330 300

393 378 336 302 275

591 548

695 648 576 518 471

583 533 480 436

467 441 401

551 508 472 441 413 389

502 464 430 402 377 354

432 399 370 346 324 305

400 369 343 320 300 282

367 339 315 294 275 259

356 329 305 285 267 252

329 304 282 264 247 233

275 254 236 220 207 194

252 233 216 202 189 178

18 19 20 21 22 23

367 348 330 315 300 287

335 317 301 287 274 262

288 273 259 247 236 225

266 252 240 228 218 208

245 232 220 210 200 192

238 225 214 204 194 186

220 208 198 188 180 172

184 174 165 157 150 144

168 159 151 144 137 131

24 25 26 27 28 29

275 264 254 245 236 228

251 241 232 223 215 208

216 207 199 192 185 179

200 192 184 178 171 165

184 176 169 163 157 152

178 171 164 158 153 147

165 158 152 146 141 136

138 132 127 122 118 114

126 121 116 112 108 104

30 32 34 36 38 40

220 207 194 184 174 165

201 188 177 167 159 151

173 162 152 144 136 130

160 150 141 133 126 120

147 138 130 122 116 110

143 134 126 119 113 107

132 124 116 110 104 99

110 103 97 92 87 83

101 95 89 84 80 76

42 44 46 48 50 52

157 150 144 138 132 127

143 137 131 126 121 116

123 118 113 108 104 100

114 109 104 100 96 92

105 100 96 92 88 85

102 97 93 89 86

94 90 86 82 79

79 75 72 69 66

72 69 66 63 60

54 56 58 60

122 118 114 110

112 108 104 100

96 93 89 86

89 86 83 80

82 79 76 73

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

306 6610 381 144 28.8 229 17.6 200 23.5 238

279 6030 295 112 22.3 156 8.19 143 10.9 183

183 3950 260 104 23.8 157 14.1 138 18.8 181

153 3300 247 92.9 22.9 138 14.8 118 19.7 167

140 3020 196 73.9 18.2 97.9 7.44 88.0 9.91 122

Span (ft)

762 734 661 601

100

631 611 535 475 428 389

Fy = 36 ksi

6 7 8 9 10 11

S 24 106

Properties and Reaction Values 240 5180 348 117 26.8 184 18.2 154 24.2 205

222 4800 292 98.4 22.5 141 10.7 124 14.3 172

204 4410 233 78.8 18.0 101 5.50 92.1 7.33 119

198 4280 316 126 28.8 210 25.2 176 33.6 220

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 62

BEAM AND GIRDER DESIGN

S 18–15–12–10

BEAMS S Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

S 18 70

3 4 5 6 7 8

498 450 386 338

9 10 11 12 13 14

S 15

54.7

S 12

42.9

S 12

40.8

S 10

31.8

25.4

121 102 88 77

240 214 187

321 264 220 189 165

216 191 164 143

200 194 161 138 121

163 151 130 113

231 191 153 127 109 96

185 167 151 139 128 119

166 150 136 125 115 107

147 132 120 110 102 94

127 115 104 96 88 82

108 97 88 81 74 69

101 91 82 76 70 65

85 76 70 64 59 55

68 61 56 51 47 44

151 142 133 126 119 113

111 104 98 93 88 83

100 94 88 83 79 75

88 83 78 73 70 66

76 72 67 64 60 57

65 60 57 54 51 48

60 57 53 50 48 45

51 48 45 42 40 38

41 38 36 34 32 31

129 123 117 113 108 104

108 103 99 95 91 87

79 76 72 69 67 64

71 68 65 62 60 58

63 60 57 55 53 51

55 52 50 48 46 44

46 44 42 40 39 37

43 41 39 38 36 35

36 35 33 32 31

29 28 27 26 25

27 28 29 30 31 32

100 96 93 90 87 84

84 81 78 76 73 71

62 59 57 56 54 52

55 53 52 50 48 47

49 47 46 44

42 41 40 38

36 35 33 32

34 32 31 30

33 34 35 36 37 38

82 79 77 75 73 71

69 67 65 63 61 60

50 49 48 46 45

45 44 43 42 40

40 42 44

68 64 61

57 54 52

125 2700 249 96.0 25.6 152 26.5 121 35.4 179

105 2270 161 62.2 16.6 79.6 7.23 70.9 9.64 103

44.8 968 99.8 45.7 15.4 63.2 11.0 54.4 14.7 95.8

42.0 907 81.6 37.4 12.6 46.7 6.03 41.9 8.04 68.0

35.4 765 115 60.1 21.4 98.2 39.2 72.0 52.2 130

28.4 613 60.5 31.5 11.2 37.2 5.62 33.4 7.50 57.8

323 284

321 278 238 208

300 270 245 225 208 193

252 227 206 189 174 162

15 16 17 18 19 20

180 169 159 150 142 135

21 22 23 24 25 26

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

77.1 1670 160 68.1 19.8 98.4 16.4 82.1 21.8 132

69.3 1500 120 50.9 14.8 63.6 6.83 56.8 9.11 86.4

61.2 1320 160 88.9 24.7 141 37.6 111 50.2 169

53.1 1150 108 59.8 16.6 78.0 11.4 68.8 15.3 114

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 63

BEAMS S 8–6–5–4–3 S Shapes Maximum factored uniform loads in kips for beams laterally supported For beams laterally unsupported, see page 4-113

Designation Wt./ft

S8 23

1 2 3 4 5 6

137 104 83 69

7 8 9 10 11 12

S6 18.4

17.25

S5 12.5

10 42 41 31 24 20

60 52 46 42 38 35

51 45 40 36 32 30

33 29 25 23 21 19

26 23 20 18 17 15

17 15 14 12 11 10

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

19.3 417 68.6 39.7 15.9 58.5 23.1 46.2 30.8 91.3

16.5 356 42.1 24.4 9.76 28.2 5.36 25.3 7.15 48.5

S3 7.7

7.5

5.7

41 25 17 13 10 8.50

20 14 11 8.42 7.02

51 44 29 22 17 15

30 25 19 15 13

12 11 9.70 8.73

11 9.48 8.42 7.58

7.28

6.02

3.51 75.8 15.0 13.0 6.95 14.0 5.63 12.5 7.51 35.6

2.36 51.0 20.4 21.6 12.6 32.2 50.0 22.2 66.7 62.4

1.95 42.1 9.91 10.5 6.12 10.9 5.78 9.78 7.71 30.4

Span (ft)

54 46 37 30

Fy = 36 ksi

84 71 59

108 76 57 46 38

S4 9.5

Properties and Reaction Values 10.6 229 54.2 36.6 16.7 58.1 42.9 41.0 57.1 91.0

8.47 183 27.1 18.3 8.35 20.5 5.32 18.4 7.10 41.4

5.67 122 20.8 15.6 7.70 17.3 5.52 15.5 7.36 39.4

4.04 87.3 25.3 22.0 11.7 30.8 27.1 23.6 36.2 60.1

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 64

BEAM AND GIRDER DESIGN

MC,C 18–15

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

MC 18

Span (ft)

Fy = 36 ksi

Wt./ft

51.9

C 15 45.8

42.7

33.9

303 247 206 177 154

233 218 181 156 136

3 4 5 6 7 8

490 409 341 292 255

420 374 311 267 234

350 339 282 242 212

315 268 230 201

418 368 295 246 210 184

9 10 11 12 13 14

227 204 186 170 157 146

208 187 170 156 144 133

188 169 154 141 130 121

179 161 146 134 124 115

164 147 134 123 113 105

137 124 112 103 95 88

121 109 99 91 84 78

15 16 17 18 19 20

136 128 120 114 108 102

125 117 110 104 98 93

113 106 100 94 89 85

107 100 95 89 85 80

98 92 87 82 78 74

82 77 73 69 65 62

73 68 64 60 57 54

21 22 23 24 25 26

97 93 89 85 82 79

89 85 81 78 75 72

81 77 74 71 68 65

77 73 70 67 64 62

70 67 64 61 59 57

59 56 54 51 49 48

52 49 47 45 44 42

28 30 32 34 36 38

73 68 64 60 57 54

67 62 58 55 52 49

60 56 53 50 47 45

57 54 50 47 45 42

53 49 46 43 41

44 41 39 36 34

39 36 34 32 30

40 42 44

51 49 46

47 44 42

42 40 38

40 38 37

68.2 1470 209 92.6 25.8 149 34.6 115 46.1 176

57.2 1240 152 67.3 18.7 92.5 13.2 79.3 17.7 128

50.4 1090 117 51.8 14.4 62.4 6.03 56.4 8.03 82.5

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

94.6 2040 245 86.6 25.2 142 28.0 108 37.3 169

86.5 1870 210 74.3 21.6 112 17.6 91.3 23.5 144

78.4 1690 175 61.9 18.0 85.5 10.2 73.3 13.6 119

74.4 1610 157 55.7 16.2 73.0 7.44 64.1 9.91 97.2

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 65

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

MC 13

For beams laterally unsupported, see page 4-113 Designation

MC 13

Span (ft)

Fy = 36 ksi

Wt./ft

31.8

3 4 5 6 7 8

398 327 261 218 187 163

283 275 220 183 157 137

226 200 166 143 125

190 186 155 133 116

9 10 11 12 13 14

145 131 119 109 101 93

122 110 100 92 85 79

111 100 91 83 77 71

103 93 85 78 72 66

15 16 17 18 19 20

87 82 77 73 69 65

73 69 65 61 58 55

67 62 59 55 53 50

62 58 55 52 49 47

21 22 23 24 25 26

62 59 57 54 52 50

52 50 48 46 44 42

48 45 43 42 40 38

44 42 40 39 37 36

27 28 29 30 31 32

48 47 45 44 42 41

41 39 38 37 35 34

37 36 34 33 32 31

34 33 32 31 30 29

46.2 998 113 55.3 16.1 71.4 10.3 62.5 13.8 107

43.1 931 94.8 46.4 13.5 54.9 6.10 49.6 8.14 76.0

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

60.5 1310 199 97.4 28.3 167 56.4 118 75.2 189

50.9 1100 142 69.3 20.2 100 20.3 82.5 27.1 135

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 66

BEAM AND GIRDER DESIGN

C, MC 12

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation Wt./ft

C 12 30

MC 12 20.7

MC 12 35

10.6

181 158 126 105 90

132 110 91 78

390 303 242 202 173

332 279 223 186 160

275 255 204 170 146

218 185 154 132

173 170 141 121

8 9 10 11 12 13

91 81 73 66 60 56

79 70 63 57 53 49

69 61 55 50 46 42

151 135 121 110 101 93

140 124 112 102 93 86

128 114 102 93 85 79

116 103 92 84 77 71

106 94 85 77 71 65

31 28 25 23 21 19

14 15 16 17 18 19

52 48 45 43 40 38

45 42 39 37 35 33

39 37 34 32 30 29

87 81 76 71 67 64

80 74 70 66 62 59

73 68 64 60 57 54

66 62 58 54 51 49

61 57 53 50 47 45

18 17 16 15 14 13

20 21 22 23 24 25

36 35 33 32 30 29

32 30 29 27 26 25

27 26 25 24 23 22

61 58 55 53 50 48

56 53 51 49 47 45

51 49 46 44 43 41

46 44 42 40 39 37

42 40 39 37 35 34

13 12 11 11 10 10

26 27 28 29 30

28 27 26 25 24

24 23 23 22 21

21 20 20 19 18

47 45 43 42 40

43 41 40 39 37

39 38 36 35 34

36 34 33 32 31

33 31 30 29 28

9.64 9.28 8.95 8.64 8.35

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

33.6 726 119 51.6 18.4 78.9 20.3 62.7 27.0 111

29.2 631 90.3 39.2 13.9 52.1 8.85 45.1 11.8 83.4

47.3 1020 138 69.7 21.2 116 22.4 98.1 29.9 139

42.8 924 109 55.2 16.8 81.7 11.1 72.8 14.8 110

39.3 849 86.3 43.7 13.3 57.6 5.54 53.2 7.38 77.2

11.6 251 44.3 11.8 6.84 14.1 1.70 12.7 2.26 20.1

Span (ft)

238 181 145 121 104

89 84 63 50 42 36

Fy = 36 ksi

2 3 4 5 6 7

Properties and Reaction Values 25.4 549 65.8 28.6 10.2 32.4 3.42 29.7 4.57 44.5

56.1 1210 195 98.6 30.1 195 63.6 144 84.8 196

51.7 1120 166 84.1 25.6 154 39.4 122 52.6 167

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 67

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C, MC 10

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

C 10

MC 10

2 3 4 5 6 7

262 192 144 115 96 82

205 166 124 99 83 71

8 9 10 11 12 13

72 64 57 52 48 44

14 15 16 17 18 19 20 21 22 23 24

33.6

MC 10 28.5

MC 10

15.3

41.1

147 139 104 83 69 60

93 85 68 57 49

309 280 210 168 140 120

224 180 144 120 103

165 160 128 107 91

148 139 111 93 80

113 102 85 73

66 57 42 34 28 24

8.4

62 55 50 45 41 38

52 46 42 38 35 32

43 38 34 31 28 26

105 93 84 76 70 65

90 80 72 66 60 55

80 71 64 58 53 49

70 62 56 51 46 43

64 57 51 46 42 39

21 19 17 15 14 13

41 38 36 34 32 30

35 33 31 29 28 26

30 28 26 25 23 22

24 23 21 20 19 18

60 56 53 49 47 44

52 48 45 42 40 38

46 43 40 38 36 34

40 37 35 33 31 29

36 34 32 30 28 27

12 11 11 10 9.4 8.9

29 27 26 25 24

25 24 23 22 21

21 20 19 18 17

17 16 16 15 14

42 40 38 37 35

36 34 33 31 30

32 30 29 28 27

28 27 25 24 23

25 24 23 22 21

8.5 8.1 7.7 7.4 7.1

26.6 575 131 60.6 24.2 112 64.2 68.8 85.6 139

23.0 497 102 47.3 18.9 77.1 30.6 56.7 40.9 109

29.6 639 82.6 47.8 15.3 64.3 12.3 56.1 16.3 97.5

25.8 557 73.9 42.8 13.7 54.4 8.76 48.5 11.7 86.5

23.6 510 56.4 32.6 10.4 36.2 3.89 33.6 5.19 50.5

7.86 170 33.0 10.5 6.12 11.3 1.61 10.3 2.15

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

19.3 417 73.7 34.1 13.6 47.1 11.5 39.5 15.3 78.5

15.8 341 46.7 21.6 8.64 23.8 2.91 21.8 3.88 34.4

38.9 840 155 89.6 28.7 165 80.5 111 107 183

33.4 721 112 64.7 20.7 101 30.4 80.9 40.5 132

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

17.3

4 - 68

BEAM AND GIRDER DESIGN

C, MC 9

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

MC 9

13.4

25.4

23.9

2 3 4 5 6 7

157 121 91 73 60 52

100 97 73 58 49 42

82 68 54 45 39

157 125 100 84 72

140 120 96 80 69

8 9 10 11 12 13

45 40 36 33 30 28

36 32 29 27 24 22

34 30 27 25 23 21

63 56 50 46 42 39

60 53 48 44 40 37

14 15 16 17 18 19

26 24 23 21 20 19

21 19 18 17 16 15

19 18 17 16 15 14

36 33 31 29 28 26

34 32 30 28 27 25

20 21 22

18 17 16

15 14 13

14 13 12

25 24 23

24 23 22

23.2 501 78.7 48.1 16.2 68.5 16.9 58.4 22.5 101

22.2 480 70.0 42.8 14.4 57.4 11.9 50.3 15.8 89.6

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

16.8 363 78.4 37.8 16.1 59.0 22.2 45.6 29.6 90.2

13.5 292 49.9 24.0 10.3 29.9 5.72 26.5 7.62 51.3

12.5 270 40.8 19.7 8.39 22.1 3.12 20.2 4.17 33.8

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 69

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C, MC 8

For beams laterally unsupported, see page 4-113 Designation

Span (ft)

Fy = 36 ksi

Wt./ft

MC 8

18.75

13.75

11.5

22.8

21.4

18.7

1 2 3 4 5 6

151 149 99 75 60 50

8.5

94 78 59 47 39

68 52 41 34

133 102 81 68

117 97 78 65

124 117 87 70 58

110 83 67 55

56 50 37 30 25

7 8 9 10 11 12

43 37 33 30 27 25

34 29 26 24 21 20

29 26 23 21 19 17

58 51 45 41 37 34

56 49 43 39 35 32

50 44 39 35 32 29

48 42 37 33 30 28

21 19 17 15 14 12

13 14 15 16 17 18

23 21 20 19 18 17

18 17 16 15 14 13

16 15 14 13 12 11

31 29 27 25 24 23

30 28 26 24 23 22

27 25 23 22 21 19

26 24 22 21 20 18

11 11 10 9.3 8.8 8.3

19 20

16 15

12 12

11 10

21 20

20 19

18 17

7.9 7.5

16.2 350 62.2 40.5 14.4 54.7 14.7 46.9 19.6 87.3,

15.4 333 54.9 35.7 12.7 45.4 10.1 40.0 13.5 77.0

6.91 149 27.8 12.1 6.44 12.9 2.12 11.8 2.82 21.0

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

13.8 298 75.7 41.1 17.5 64.9 34.0 46.8 45.3 98.1

10.9 235 47.1 25.6 10.9 31.9 8.18 27.5 10.9 61.0

9.55 206 34.2 18.6 7.92 19.7 3.13 18.0 4.18 31.6

18.8 406 66.4 45.6 15.4 61.9 17.0 52.8 22.7 95.6

18.0 389 58.3 40.1 13.5 50.9 11.5 44.8 15.4 84.0

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 70

BEAM AND GIRDER DESIGN

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C, MC 7–6

Fy = 36 ksi

For beams laterally unsupported, see page 4-113 Designation

C7 12.25

MC 7 9.8

22.7

19.1

10.5 73 66 44 33 27 22

1 2 3 4 5 6

85 60 45 36 30

57 51 38 31 26

137 117 87 70 58

96 77 62 51

102 78 52 39 31 26

7 8 9 10 11 12

26 23 20 18 16 15

22 19 17 15 14 13

50 44 39 35 32 29

44 39 34 31 28 26

22 20 17 16 14 13

19 17 15 13 12 11

13 14 15 16

14 13 12 11

12 11 10 9.61

27 25 23 22

24 22 21 19

12 11 10

10 9.49 8.86

8.40 181 42.7 24.7 11.3 32.6 11.1 27.4 14.8 61.5

7.12 154 28.6 16.5 7.56 17.8 3.32 16.3 4.42 30.6

MC 6 8.2

MC 6

16.3

15.1

47 37 28 22 18

88 83 62 50 41

87 73 55 44 37

74 70 52 42 35

72 53 40 32 27

16 14 12 11 10 9.23

35 31 28 25 23 21

31 28 24 22 20 18

30 26 23 21 19 17

23 20 18 16 14 13

8.52 7.91 7.39

19 18 17

17 16 15

16 15 14

12 11 11

11.5 248 44.2 36.2 13.6 49.2 17.5 42.2 23.4 80.6

10.2 220 43.7 35.9 13.5 48.4 17.0 41.6 22.6 79.7

9.69 209 36.9 30.2 11.4 37.5 10.2 33.4 13.6 67.2

7.38 159 36.2 22.7 11.2 32.3 12.2 27.5 16.2 58.9

Span (ft)

Fy = 36 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

16.2 350 68.4 50.9 18.1 77.2 33.4 61.6 44.5 110

14.3 309 47.9 35.6 12.7 45.2 11.4 39.8 15.3 76.8

7.26 157 51.0 32.0 15.7 51.8 37.2 36.9 49.6 83.1

6.15 133 36.6 23.0 11.3 31.5 13.8 26.0 18.4 59.7

5.13 111 23.3 14.6 7.20 16.0 3.57 14.6 4.76 30.1

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 36 ksi

4 - 71

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C 5–4–3

For beams laterally unsupported, see page 4-113 Designation

Wt./ft

9 1 2 3 4 5 6

7.25

5.4

4.1

63 47 31 24 19 16

37 25 19 15 13

50 30 20 15 12 10

29 24 16 12 9.8 8.1

37 19 12 9.3 7.4 6.2

30 16 11 8.1 6.5 5.4

20 14 9.4 7.0 5.6 4.7

13 12 10 9.4 8.6 7.9

11 9.5 8.4 7.6 6.9 6.3

7.0 6.1 5.4 4.9

5.3

4.6

4.0

1.72 37.2 20.8 22.0 12.8 34.0 50.6 23.8 67.4 63.7

1.50 32.4 15.0 16.0 9.29 21.0 19.2 17.1 25.7 46.1

1.30 28.1 9.91 10.5 6.12 11.2 5.51 10.1 7.34 30.4

8.7 7.6 6.7 6.1

Span (ft)

Fy = 36 ksi

7 8 9 10 11 12

C4 6.7

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

4.36 94.2 31.6 21.9 11.7 32.1 19.7 25.5 26.3 60.0

3.51 75.8 18.5 12.8 6.84 14.3 3.94 13.0 5.25 30.1

2.81 60.7 25.0 19.9 11.6 30.3 25.6 23.4 34.2 57.4

2.26 48.8 14.3 11.4 6.62 13.1 4.83 11.9 6.44 32.8

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 72

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 44

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

W 44

Span (ft)

Fy = 50 ksi

Wt./ft

335

290

262

230

20 21 22 23 24 25

2420 2310 2210 2110 2030 1940

2050 2030 1940 1850 1780 1700

1850 1810 1730 1660 1590 1520

1650 1570 1500 1430 1380 1320

26 27 28 29 30 31

1870 1800 1740 1680 1620 1570

1640 1580 1520 1470 1420 1370

1470 1410 1360 1310 1270 1230

1270 1220 1180 1140 1100 1060

32 33 34 35 36 38

1520 1470 1430 1390 1350 1280

1330 1290 1250 1220 1180 1120

1190 1150 1120 1090 1060 1000

1030 1000 971 943 917 868

40 42 44 46 48 50

1220 1160 1100 1060 1010 972

1070 1010 968 926 888 852

953 907 866 828 794 762

825 786 750 717 688 660

52 54 56 58 60 62

935 900 868 838 810 784

819 789 761 734 710 687

733 706 680 657 635 615

635 611 589 569 550 532

64 66 68 70 72

759 736 715 694 675

666 645 626 609 592

595 577 560 544 529

516 500 485 471 458

1270 38100 924 216 39.5 302 8.67 277 11.6 330

1100 33000 823 178 35.5 238 7.40 217 9.86 262

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1620 48600 1212 327 51.0 494 14.7 451 19.6 492

1420 42600 1025 258 43.5 368 10.3 338 13.8 400

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 73

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 40

For beams laterally unsupported, see page 4-139 Designation Wt./ft

W 40 431

372

321

297

277

249

199

174*

1360 1300

1340 1330 1250 1180 1120 1070

1370 1310 1260 1200 1160 1110

1240 1180 1130 1090 1040 1000

1010 969 927 888 852 820

1240 1200 1160 1120 1080 1050

1070 1030 996 963 932 903

964 930 898 868 840 814

789 761 735 710 687 666

1140 1100 1070 1040 987 938

1020 988 960 933 884 840

875 850 825 803 760 722

789 766 744 723 685 651

646 627 609 592 561 533

950 907 867 831 798 767

893 852 815 781 750 721

800 764 730 700 672 646

688 657 628 602 578 556

620 592 566 543 521 501

507 484 463 444 426 410

789 761 734 710 687 666

739 713 688 665 644 623

694 670 647 625 605 586

622 600 579 560 542 525

535 516 498 482 466 451

482 465 449 434 420 407

395 381 367 355 344 333

645 626 609 592

605 587 570 554

568 551 536 521

509 494 480 467

438 425 413 401

395 383 372 362

323 313 304 296

1120 33600 797 264 37.5 279 8.16 258 10.9 306

963 28900 684 213 32.5 209 6.25 193 8.33 229

868 26000 679 198 32.5 195 7.21 176 9.62 218

715 21300 670 163 32.5 172 9.37 148 12.5 203

2550 2510

2160 2130

2000 2000

21 22 23 24 25 26

2790 2660 2540 2440 2340 2250

2390 2280 2180 2090 2000 1930

2030 1940 1850 1780 1700 1640

1900 1810 1730 1660 1600 1530

1780 1700 1630 1560 1500 1440

1590 1530 1460 1400 1340 1290

27 28 29 30 31 32

2170 2090 2020 1950 1890 1830

1860 1790 1730 1670 1620 1570

1580 1520 1470 1420 1370 1330

1480 1430 1380 1330 1290 1250

1390 1340 1290 1250 1210 1170

33 34 35 36 38 40

1770 1720 1670 1630 1540 1460

1520 1470 1430 1390 1320 1250

1290 1250 1220 1180 1120 1070

1210 1170 1140 1110 1050 998

42 44 46 48 50 52

1390 1330 1270 1220 1170 1130

1190 1140 1090 1040 1000 963

1010 968 926 888 852 819

54 56 58 60 62 64

1080 1040 1010 975 944 914

928 895 864 835 808 783

66 68 70 72

886 860 836 813

759 737 716 696

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1950 58500 1493 597 67.0 859 26.7 786 35.6 814

1670 50100 1273 471 58.0 645 20.3 590 27.0 660

Span (ft)

2990 2930

Fy = 50 ksi

15 16 17 18 19 20

215

Properties and Reaction Values 1420 42600 1082 367 50.0 480 15.3 439 20.3 529

1330 39900 1000 356 46.5 415 13.2 380 17.7 458

1250 37500 889 311 41.5 342 9.90 316 13.2 374

*Noncompact shape; Fy = 50 ksi. Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 74

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 40

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 40 331

278

264

235

211

167

149

1370 1300

1350 1300 1220 1150

1300 1280 1190 1120 1050 995

1430 1360 1290 1230 1180 1130

1230 1170 1120 1070 1020 976

1090 1040 989 944 903 865

943 896 853 814 779 746

1210 1170 1120 1080 1040 1010

1090 1040 1010 970 936 905

937 901 868 837 808 781

830 798 769 741 716 692

716 689 663 640 618 597

1090 1060 1030 997 969 942

977 947 918 891 866 842

876 848 823 799 776 754

756 732 710 689 669 651

670 649 629 611 593 577

578 560 543 527 512 498

939 893 850 811 776 744

892 848 807 770 737 706

797 758 721 689 659 631

714 679 646 617 590 566

617 586 558 533 509 488

546 519 494 472 451 433

471 448 426 407 389 373

858 825 794 766 740 715

714 687 661 638 616 595

678 652 628 605 584 565

606 583 561 541 522 505

543 522 503 485 468 453

469 451 434 418 404 391

415 399 384 371 358 346

358 344 332 320 309 299

692 670 650 631 613 596

576 558 541 525 510 496

547 530 514 499 484 471

489 473 459 446 433 421

438 424 411 399 388 377

378 366 355 345 335 325

335 324 315 305 297 288

289 280 271 263 256 249

781 23400 684 213 32.5 209 6.25 193 8.33 229

692 20800 677 198 32.5 191 7.51 172 10.0 216

597 17900 650 177 31.5 164 8.53 143 11.4 192

13 14 15 16 17 18

2690 2680 2520 2380

2210 2100 1980

2070 1990 1880

1780 1680

1590 1510

19 20 21 22 23 24

2260 2150 2040 1950 1870 1790

1880 1790 1700 1620 1550 1490

1780 1700 1610 1540 1470 1410

1590 1520 1440 1380 1320 1260

25 26 27 28 29 30

1720 1650 1590 1530 1480 1430

1430 1370 1320 1280 1230 1190

1360 1300 1260 1210 1170 1130

31 32 33 34 35 36

1380 1340 1300 1260 1230 1190

1150 1120 1080 1050 1020 992

38 40 42 44 46 48

1130 1070 1020 975 933 894

50 52 54 56 58 60 62 64 66 68 70 72

183

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1430 42900 1344 505 61.0 709 22.6 648 30.1 703

1190 35700 1106 383 51.0 500 15.8 458 21.1 548

1130 33900 1037 353 48.0 446 13.8 409 18.4 491

1010 30300 889 285 41.5 342 9.90 316 13.2 374

905 27200 797 246 37.5 279 8.19 257 10.9 305

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 75

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 36

For beams laterally unsupported, see page 4-139 Designation

W 36

Span (ft)

Fy = 50 ksi

Wt./ft

300

280

260

245

230

1560 1520 1440 1380 1320 1260

1470 1410 1350 1290 1230 1180

19 20 21 22 23 24

1870 1800 1720 1640 1580

1750 1670 1600 1530 1460

1640 1620 1540 1470 1410 1350

25 26 27 28 29 30

1510 1450 1400 1350 1300 1260

1400 1350 1300 1250 1210 1170

1300 1250 1200 1160 1120 1080

1210 1170 1120 1080 1040 1010

1130 1090 1050 1010 976 943

31 32 33 34 35 36

1220 1180 1150 1110 1080 1050

1130 1100 1060 1030 1000 975

1050 1010 982 953 926 900

977 947 918 891 866 842

913 884 857 832 808 786

38 40 42 44 46 48

995 945 900 859 822 788

924 878 836 798 763 731

853 810 771 736 704 675

797 758 721 689 659 631

744 707 674 643 615 589

50 52 54 56 58 60

756 727 700 675 652 630

702 675 650 627 605 585

648 623 600 579 559 540

606 583 561 541 522 505

566 544 524 505 488 472

62 64 66 68 70 72

610 591 573 556 540 525

566 548 532 516 501 488

523 506 491 476 463 450

489 473 459 446 433 421

456 442 429 416 404 393

1010 30300 779 250 40.0 300 11.4 272 15.2 337

943 28300 737 226 38.0 268 10.5 243 14.0 302

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1260 37800 937 332 47.3 429 14.8 393 19.7 477

1170 35100 873 297 44.3 376 13.1 344 17.4 419

1080 32400 822 269 42.0 333 12.3 303 16.4 373

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 76

BEAM AND GIRDER DESIGN

W 36

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation Wt./ft

W 36 256

19 20 21 22 23 24

194

182

170

160

150

135

1740 1650 1560

1640 1560 1470 1390

1510 1440 1350 1280

1420 1350 1270 1200

1330 1250 1180 1110

1260 1250 1170 1100 1040

1210 1160 1090 1030 968

1640 1560 1490 1420 1360 1300

1480 1400 1340 1280 1220 1170

1320 1250 1190 1140 1090 1040

1210 1150 1100 1050 1000 959

1130 1080 1030 979 937 898

1050 1000 954 911 871 835

985 936 891 851 814 780

917 872 830 792 758 726

804 764 727 694 664 636

25 26 27 28 29 30

1250 1200 1160 1110 1080 1040

1120 1080 1040 1000 968 936

1000 961 926 893 862 833

920 885 852 822 793 767

862 828 798 769 743 718

802 771 742 716 691 668

749 720 693 669 646 624

697 670 646 623 601 581

611 587 566 545 527 509

31 32 33 34 35 36

1010 975 945 918 891 867

906 878 851 826 802 780

806 781 757 735 714 694

742 719 697 677 657 639

695 673 653 634 615 598

646 626 607 589 573 557

604 585 567 551 535 520

562 545 528 513 498 484

493 477 463 449 436 424

38 40 42 44 46 48

821 780 743 709 678 650

739 702 669 638 610 585

658 625 595 568 543 521

606 575 548 523 500 479

567 539 513 490 468 449

527 501 477 455 436 418

493 468 446 425 407 390

459 436 415 396 379 363

402 382 364 347 332 318

50 52 54 56 58 60

624 600 578 557 538 520

562 540 520 501 484 468

500 481 463 446 431 417

460 443 426 411 397 384

431 414 399 385 371 359

401 385 371 358 346 334

374 360 347 334 323 312

349 335 323 311 301 291

305 294 283 273 263 255

62 64 66 68 70 72

503 488 473 459 446 433

453 439 425 413 401 390

403 390 379 368 357 347

371 360 349 338 329 320

347 337 326 317 308 299

323 313 304 295 286 278

302 293 284 275 267 260

281 272 264 256 249 242

246 239 231 225 218 212

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

1040 31200 970 315 48.0 446 14.8 409 19.7 471

936 28100 872 272 43.5 367 12.2 336 16.3 406

668 20000 664 170 34.0 212 8.55 191 11.4 240

624 18700 632 157 32.5 191 8.09 171 10.8 217

581 17400 605 146 31.3 173 7.84 154 10.5 198

509 15300 576 127 30.0 149 8.32 129 11.1 176

Span (ft)

1940 1840 1730

210

1150 1090 1020 954 898 848

Fy = 50 ksi

13 14 15 16 17 18

232

Properties and Reaction Values 833 25000 822 240 41.5 318 12.4 288 16.5 358

767 23000 754 209 38.3 271 10.5 245 14.0 305

718 21500 711 193 36.3 242 9.62 219 12.8 273

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 77

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 33

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 33 241

221

W 33 201

169

152

141

130

118

1050 986 932 883 839 799

964 907 857 812 771 734

876 824 778 737 701 667

778 732 692 655 623 593

16 17 18 19 20 21

1530 1480 1410 1340

1420 1350 1280 1220

1300 1290 1220 1160 1100

1180 1110 1050 993 944 899

22 23 24 25 26 27

1280 1220 1170 1130 1080 1040

1170 1120 1070 1030 987 950

1050 1010 965 926 891 858

858 820 786 755 726 699

762 729 699 671 645 621

701 670 643 617 593 571

637 609 584 560 539 519

566 541 519 498 479 461

28 29 30 31 32 33

1010 971 939 909 880 854

916 884 855 827 802 777

827 799 772 747 724 702

674 651 629 609 590 572

599 578 559 541 524 508

551 532 514 497 482 467

500 483 467 452 438 425

445 429 415 402 389 377

34 35 36 37 38 40

829 805 783 761 741 704

754 733 713 693 675 641

681 662 643 626 609 579

555 539 524 510 497 472

493 479 466 453 441 419

454 441 428 417 406 386

412 400 389 379 369 350

366 356 346 336 328 311

42 44 46 48 50 52

671 640 612 587 563 542

611 583 558 534 513 493

551 526 503 483 463 445

449 429 410 393 377 363

399 381 365 349 335 323

367 350 335 321 308 297

334 318 305 292 280 269

296 283 271 259 249 239

54 56 58 60 62 64

522 503 486 470 454 440

475 458 442 428 414 401

429 414 399 386 374 362

349 337 325 315 304 295

311 299 289 280 270 262

286 275 266 257 249 241

259 250 242 234 226 219

231 222 215 208 201 195

66 68 70 72

427 414 402 391

389 377 366 356

351 341 331 322

286 278 270 262

254 247 240 233

234 227 220 214

212 206 200 195

189 183 178 173

514 15400 544 132 30.3 166 7.49 150 9.99 191

467 14000 518 122 29.0 147 7.46 131 9.95 172

415 12500 488 107 27.5 127 7.40 110 9.87 151

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

939 28200 766 227 41.5 323 12.9 293 17.2 362

855 25700 710 200 38.8 278 11.6 251 15.5 316

772 23200 650 173 35.8 234 10.2 211 13.6 267

629 18900 612 173 33.5 218 7.89 201 10.5 244

559 16800 574 149 31.8 187 7.84 170 10.5 213

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 78

BEAM AND GIRDER DESIGN

W 30

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

W 30

Span (ft)

Fy = 50 ksi

Wt./ft

261

235

191

173

1290 1250 1180 1120 1070

1180 1120 1060 1010 961

1080 1070 1010 955 908 864

1150 1100 1060 1010 975 939

1020 977 936 899 864 832

918 878 841 808 777 748

825 789 756 726 698 672

1010 973 941 911 882 855

905 874 845 818 792 768

803 775 749 725 702 681

721 696 673 651 631 612

648 626 605 585 567 550

34 36 38 40 42 44

830 784 743 706 672 642

746 704 667 634 604 576

661 624 591 562 535 511

594 561 531 505 481 459

534 504 478 454 432 413

46 48 50 52 54 56

614 588 565 543 523 504

551 528 507 488 469 453

488 468 449 432 416 401

439 421 404 388 374 361

395 378 363 349 336 324

58 60 62 64 66 68

487 471 455 441 428 415

437 423 409 396 384 373

387 375 362 351 340 330

348 337 326 315 306 297

313 303 293 284 275 267

70 72

403 392

362 352

321 312

288 280

259 252

673 20200 588 172 35.5 235 10.7 213 14.2 269

605 18200 538 154 32.8 197 9.38 178 12.5 228

16 17 18 19 20 21

1590 1570 1490 1410 1340

1400 1330 1270 1210

22 23 24 25 26 27

1280 1230 1180 1130 1090 1050

28 29 30 31 32 33

211

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

941 28200 794 283 46.5 415 16.7 380 22.2 434

845 25400 701 233 41.5 334 13.2 306 17.6 368

749 22500 647 206 38.8 282 12.4 257 16.5 322

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 79

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 30

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 30 148

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

1080 1070 1000 938 882 833 789 750 714 682 652 625 600 577 556 536 517 500 484 469 455 441 417 395 375 357 341 326 313 300 288 278 268 259 250 242 234 227 221 214 208

132

1010 936 874 819 771 728 690 656 624 596 570 546 524 504 486 468 452 437 423 410 397 386 364 345 328 312 298 285 273 262 252 243 234 226 219 211 205 199 193 187 182

124 953 942 874 816 765 720 680 644 612 583 556 532 510 490 471 453 437 422 408 395 383 371 360 340 322 306 291 278 266 255 245 235 227 219 211 204 197 191 185 180 175 170

116

108

916 872 810 756 709 667 630 597 567 540 515 493 473 454 436 420 405 391 378 366 354 344 334 315 298 284 270 258 247 236 227 218 210 203 196 189 183 177 172 167 162 158

878 865 798 741 692 649 611 577 546 519 494 472 451 433 415 399 384 371 358 346 335 324 315 305 288 273 260 247 236 226 216 208 200 192 185 179 173 167 162 157 153 148 144

833 780 720 669 624 585 551 520 493 468 446 425 407 390 374 360 347 334 323 312 302 293 284 275 260 246 234 223 213 203 195 187 180 173 167 161 156 151 146 142 138 134 130

749 708 653 606 566 531 499 472 447 425 404 386 369 354 340 327 314 303 293 283 274 265 257 250 236 223 212 202 193 185 177 170 163 157 152 146 142 137 133 129 125 121 118

346 10400 439 106 27.3 126 7.73 111 10.3 152

312 9360 416 93.4 26.0 111 7.66 95.6 10.2 136

283 8490 375 77.1 23.5 90.8 6.24 78.5 8.31 111

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

500 15000 538 163 32.5 205 8.21 189 10.9 232

437 13100 503 135 30.8 174 8.30 157 11.1 201

408 12200 477 123 29.2 156 7.72 140 10.3 181

378 11300 458 115 28.3 141 7.65 126 10.2 166

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 80

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 27

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 27 258

235

194

178

161

146

1270 1250 1180 1120 1060

1140 1110 1050 992 942

1090 1060 1000 945 895 851

983 960 904 853 808 768

895 864 814 768 728 692

1100 1050 1000 961 923 887

1010 965 923 885 850 817

897 856 819 785 754 725

810 773 740 709 680 654

731 698 668 640 614 591

659 629 601 576 553 532

944 911 879 850 823 797

854 824 796 769 744 721

787 759 732 708 685 664

698 673 650 628 608 589

630 608 587 567 549 532

569 549 530 512 495 480

512 494 477 461 446 432

33 34 35 36 37 38

773 750 729 708 689 671

699 679 659 641 624 607

644 625 607 590 574 559

571 554 538 523 509 496

515 500 486 473 460 448

465 452 439 427 415 404

419 407 395 384 374 364

40 42 44 46 48 50

638 607 580 554 531 510

577 549 524 502 481 461

531 506 483 462 443 425

471 449 428 410 393 377

425 405 387 370 354 340

384 366 349 334 320 307

346 329 314 301 288 277

52 54 56 58 60 62

490 472 455 440 425 411

444 427 412 398 385 372

408 393 379 366 354 343

362 349 336 325 314 304

327 315 304 293 284 274

295 284 274 265 256 248

266 256 247 238 231 223

64 66

398 386

360 350

332 322

294 285

266 258

240 233

216 210

567 17000 544 170 36.3 243 12.5 220 16.6 283

512 15400 492 150 33.0 201 10.4 182 13.9 235

461 13800 447 128 30.3 168 8.97 151 12.0 197

15 16 17 18 19 20

1530 1500 1420 1340 1280

1410 1360 1280 1210 1150

21 22 23 24 25 26

1210 1160 1110 1060 1020 981

27 28 29 30 31 32

217

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

850 25500 767 306 49.0 465 19.9 427 26.5 466

769 23100 704 263 45.5 397 17.7 363 23.6 411

708 21200 637 227 41.5 334 14.5 306 19.3 362

628 18800 569 193 37.5 271 12.1 248 16.2 311

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 81

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 27

For beams laterally unsupported, see page 4-139 Designation

W 27

Span (ft)

Fy = 50 ksi

Wt./ft

129

102

840 792 735 686 643

753 704 654 610 572

712 695 642 596 556 521

663 610 563 523 488 458

697 658 624 593 564 539

605 572 542 515 490 468

538 508 482 458 436 416

491 463 439 417 397 379

431 407 385 366 349 333

23 24 25 26 27 28

515 494 474 456 439 423

447 429 412 396 381 368

398 381 366 352 339 327

363 348 334 321 309 298

318 305 293 282 271 261

29 30 31 32 33 34

409 395 382 370 359 349

355 343 332 322 312 303

316 305 295 286 277 269

288 278 269 261 253 245

252 244 236 229 222 215

36 38 40 42 44 46

329 312 296 282 269 258

286 271 257 245 234 224

254 241 229 218 208 199

232 219 209 199 190 181

203 193 183 174 166 159

48 50 52 54 56 58

247 237 228 219 212 204

214 206 198 191 184 177

191 183 176 169 163 158

174 167 160 154 149 144

153 146 141 136 131 126

60 62 64 66

198 191 185 180

172 166 161 156

153 148 143 139

139 135 130 126

122 118 114 111

278 8340 356 88.0 24.5 107 6.35 95.4 8.46 127

244 7320 332 79.1 23.0 90.0 6.16 79.0 8.21 110

11 12 13 14 15 16

910 846 790 741

17 18 19 20 21 22

114

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

395 11900 455 138 30.5 180 8.08 165 10.8 206

343 10300 420 116 28.5 150 7.89 135 10.5 175

305 9150 377 101 25.8 121 6.57 110 8.76 143

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 82

BEAM AND GIRDER DESIGN

W 24

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation Wt./ft

W 24 131

117

104

952 936 878 826 780

868 836 784 738 697

800 793 740 694 653 617

721 701 654 613 577 545

650 619 578 542 510 482

807 767 730 697 667 639

739 702 669 638 610 585

660 627 597 570 545 523

584 555 529 505 483 463

516 491 467 446 427 409

456 434 413 394 377 361

671 645 621 599 578 559

613 590 568 548 529 511

562 540 520 501 484 468

502 482 464 448 432 418

444 427 411 396 383 370

392 377 363 350 338 327

347 333 321 310 299 289

586 568 551 535 519 505

541 524 508 493 479 466

495 479 465 451 438 426

453 439 425 413 401 390

405 392 380 369 358 348

358 347 336 326 317 308

316 307 297 289 280 273

280 271 263 255 248 241

534 507 483 461 441 423

478 455 433 413 395 379

441 419 399 381 365 349

403 383 365 348 333 319

369 351 334 319 305 293

330 314 299 285 273 261

292 278 264 252 241 231

258 245 234 223 213 204

228 217 206 197 188 181

50 52 54 56 58 60

406 390 376 362 350 338

364 350 337 325 313 303

335 323 311 299 289 280

307 295 284 274 264 256

281 270 260 251 242 234

251 241 232 224 216 209

222 213 206 198 191 185

196 189 182 175 169 164

173 167 161 155 149 145

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

676 20300 674 300 48.0 446 21.3 409 28.4 456

606 18200 604 258 43.5 367 17.6 336 23.5 400

370 11100 400 132 30.3 166 10.2 150 13.6 199

327 9810 360 112 27.5 136 8.73 121 11.6 164

289 8670 325 93.8 25.0 110 7.49 98.4 9.99 135

Span (ft)

146

Fy = 50 ksi

229

207

192

176

13 14 15 16 17 18

1350 1270 1190 1130

1210 1140 1070 1010

1110 1050 986 932

1020 1020 958 902 852

19 20 21 22 23 24

1070 1010 966 922 882 845

957 909 866 826 790 758

883 839 799 762 729 699

25 26 27 28 29 30

811 780 751 724 699 676

727 699 673 649 627 606

31 32 33 34 35 36

654 634 615 596 579 563

38 40 42 44 46 48

162

Properties and Reaction Values 559 16800 557 228 40.5 318 15.5 291 20.6 359

511 15300 511 199 37.5 271 13.5 248 18.0 315

468 14000 476 176 35.3 236 12.4 215 16.6 276

418 12500 434 152 32.5 197 11.0 179 14.7 233

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 83

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 24

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 24 103

W 24 76

551 510 459 417 383

503 503 447 402 365 335

7 8 9 10 11 12

729 700

676 635

612 611 560

568 545 500

532 531 483 443

13 14 15 16 17 18

646 600 560 525 494 467

586 544 508 476 448 423

517 480 448 420 395 373

462 429 400 375 353 333

408 379 354 332 312 295

353 328 306 287 270 255

309 287 268 251 236 223

19 20 21 22 23 24

442 420 400 382 365 350

401 381 363 346 331 318

354 336 320 305 292 280

316 300 286 273 261 250

279 266 253 241 231 221

242 230 219 209 200 191

212 201 191 183 175 168

25 26 27 28 29 30

336 323 311 300 290 280

305 293 282 272 263 254

269 258 249 240 232 224

240 231 222 214 207 200

212 204 197 190 183 177

184 177 170 164 158 153

161 155 149 144 139 134

31 32 33 34 35 36

271 263 255 247 240 233

246 238 231 224 218 212

217 210 204 198 192 187

194 188 182 176 171 167

171 166 161 156 152 148

148 143 139 135 131 128

130 126 122 118 115 112

38 40 42 44 46 48

221 210 200 191 183 175

201 191 181 173 166 159

177 168 160 153 146 140

158 150 143 136 130 125

140 133 126 121 115 111

121 115 109 104 100 96

106 101 96 91 87 84

50 52 54 56 58 60

168 162 156 150 145 140

152 147 141 136 131 127

134 129 124 120 116 112

120 115 111 107 103

106 102 98 95 92

92 88 85 82 79

80 77 74 72 69

177 5310 266 71.3 20.8 73.7 5.57 64.9 7.43 91.8

153 4590 276 73.9 21.5 78.1 6.14 68.4 8.19 98.1

134 4020 251 64.8 19.8 63.6 5.60 54.8 7.47 81.8

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

280 8400 364 120 27.5 146 7.49 133 9.98 170

254 7620 338 105 25.8 125 6.95 113 9.26 147

224 6720 306 91.8 23.5 102 6.05 92.2 8.07 122

200 6000 284 79.1 22.0 86.8 5.67 77.8 7.55 105

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 84

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 21

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 21 201

182

166

147

132

122

111

101

766 714 666 624 588 555

702 658 614 576 542 512

639 598 558 523 492 465

577 542 506 474 446 422

13 14 15 16 17 18

1130 1060 994 935 883

1020 952 893 840 793

910 864 810 762 720

858 799 746 699 658 622

19 20 21 22 23 24

837 795 757 723 691 663

752 714 680 649 621 595

682 648 617 589 563 540

589 560 533 509 487 466

526 500 476 454 434 416

485 461 439 419 400 384

441 419 399 380 364 349

399 380 361 345 330 316

25 26 27 28 29 30

636 612 589 568 548 530

571 549 529 510 492 476

518 498 480 463 447 432

448 430 414 400 386 373

400 384 370 357 344 333

368 354 341 329 318 307

335 322 310 299 289 279

304 292 281 271 262 253

31 32 33 34 35 36

513 497 482 468 454 442

461 446 433 420 408 397

418 405 393 381 370 360

361 350 339 329 320 311

322 312 303 294 285 278

297 288 279 271 263 256

270 262 254 246 239 233

245 237 230 223 217 211

38 40 42 44 46 48

418 398 379 361 346 331

376 357 340 325 310 298

341 324 309 295 282 270

294 280 266 254 243 233

263 250 238 227 217 208

242 230 219 209 200 192

220 209 199 190 182 174

200 190 181 173 165 158

50 52

318 306

286 275

259 249

224 215

200 192

184 177

167 161

152 146

307 9210 351 127 30.0 164 11.2 148 15.0 201

279 8370 319 112 27.5 138 9.56 124 12.8 169

253 7590 288 97.7 25.0 114 7.91 103 10.6 140

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

530 15900 566 270 45.5 400 21.7 366 29.0 418

476 14300 509 233 41.5 332 18.4 304 24.5 368

432 13000 455 199 37.5 273 14.9 251 19.9 321

373 11200 429 169 36.0 236 15.9 213 21.2 286

333 9990 383 147 32.5 192 13.1 173 17.5 235

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 85

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 21

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 21 93

W 21 68

44 390 358 318 286 260 239

7 8 9 10 11 12

677 663 603 553

596 588 535 490

522 516 469 430

491 480 436 400

453 432 393 360

461 430 387 352 323

427 413 367 330 300 275

13 14 15 16 17 18

510 474 442 414 390 368

452 420 392 368 346 327

397 369 344 323 304 287

369 343 320 300 282 267

332 309 288 270 254 240

298 276 258 242 228 215

254 236 220 206 194 183

220 204 191 179 168 159

19 20 21 22 23 24

349 332 316 301 288 276

309 294 280 267 256 245

272 258 246 235 224 215

253 240 229 218 209 200

227 216 206 196 188 180

204 194 184 176 168 161

174 165 157 150 143 138

151 143 136 130 124 119

25 26 27 28 29 30

265 255 246 237 229 221

235 226 218 210 203 196

206 198 191 184 178 172

192 185 178 171 166 160

173 166 160 154 149 144

155 149 143 138 133 129

132 127 122 118 114 110

114 110 106 102 99 95

31 32 33 34 35 36

214 207 201 195 189 184

190 184 178 173 168 163

166 161 156 152 147 143

155 150 145 141 137 133

139 135 131 127 123 120

125 121 117 114 111 108

106 103 100 97 94 92

92 89 87 84 82 80

38 40 42 44 46 48

174 166 158 151 144 138

155 147 140 134 128 123

136 129 123 117 112 108

126 120 114 109 104 100

114 108 103 98 94 90

102 97 92 88 84 81

87 83 79 75 72 69

75 72 68 65 62 60

50 52

133 128

118 113

103 99

96 92

86 83

77 74

66 63

129 3870 230 69.6 20.3 74.9 5.25 67.6 7.00 92.0

110 3300 214 62.3 19.0 61.8 5.33 54.4 7.10 79.1

95.4 2860 195 52.0 17.5 50.1 4.99 43.2 6.65 66.3

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

221 6630 339 122 29.0 154 10.5 138 14.0 188

196 5880 298 101 25.8 122 8.26 110 11.0 149

172 5160 261 85.3 22.8 95.2 6.48 86.0 8.64 116

160 4800 245 77.3 21.5 84.2 5.94 75.8 7.92 103

144 4320 227 68.8 20.0 71.5 5.36 64.0 7.15 89.0

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 86

BEAM AND GIRDER DESIGN

W 18

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 18 192

175

158

W 18 143

130

119

106

597 575 531 493 460 431

537 528 487 452 422 396

477 465 429 399 372 349

418 408 376 349 326 306

11 12 13 14 15 16

1050 1020 947 884 829

963 918 853 796 746

863 822 763 712 668

768 743 690 644 604

696 672 624 582 546

671 653 602 559 522 489

17 18 19 20 21 22

780 737 698 663 631 603

702 663 628 597 569 543

628 593 562 534 509 485

568 537 508 483 460 439

514 485 459 437 416 397

461 435 412 392 373 356

406 383 363 345 329 314

372 352 333 317 301 288

328 310 294 279 266 254

288 272 257 245 233 222

23 24 25 26 27 28

577 553 530 510 491 474

519 498 478 459 442 426

464 445 427 411 396 381

420 403 386 372 358 345

380 364 349 336 323 312

340 326 313 301 290 280

300 288 276 265 256 246

275 264 253 243 234 226

243 233 223 215 207 199

213 204 196 188 181 175

29 30 31 32 33 34

457 442 428 414 402 390

412 398 385 373 362 351

368 356 345 334 324 314

333 322 312 302 293 284

301 291 282 273 265 257

270 261 253 245 237 230

238 230 223 216 209 203

218 211 204 198 192 186

192 186 180 174 169 164

169 163 158 153 148 144

35 36 37 38 39 40

379 368 358 349 340 332

341 332 323 314 306 299

305 297 289 281 274 267

276 268 261 254 248 242

249 243 236 230 224 218

224 218 212 206 201 196

197 192 186 182 177 173

181 176 171 167 162 158

159 155 151 147 143 140

140 136 132 129 125 122

42 44

316 301

284 271

254 243

230 220

208 198

186 178

164 157

151 144

133 127

116 111

442 13300 527 293 48.0 449 26.9 412 35.8 449

398 11900 482 250 44.5 382 23.9 350 31.9 395

230 6900 298 120 29.5 158 12.6 143 16.8 199

211 6330 269 104 26.8 132 10.2 119 13.7 165

186 5580 238 86.3 24.0 105 8.45 94.9 11.3 133

163 4890 209 73.0 21.3 82.4 6.71 74.3 8.94 104

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

356 10700 431 215 40.5 315 20.2 289 27.0 347

322 9660 384 183 36.5 258 16.4 237 21.8 301

291 8730 348 157 33.5 217 14.1 199 18.8 262

261 7830 335 143 32.8 197 15.1 178 20.2 246

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 87

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 18

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 18 71

6 7 8 9 10 11

494 483 435 395

446 443 399 363

12 13 14 15 16 17

363 335 311 290 272 256

18 19 20 21 22 23

W 18 55

409 369 335

381 373 336 305

345 337 303 275

351 340 302 272 247

304 294 261 235 214

287 285 249 222 200 181

333 307 285 266 249 235

308 284 264 246 231 217

280 258 240 224 210 198

253 233 216 202 189 178

227 209 194 181 170 160

196 181 168 157 147 138

166 153 143 133 125 117

242 229 218 207 198 189

222 210 200 190 181 173

205 194 185 176 168 160

187 177 168 160 153 146

168 159 152 144 138 132

151 143 136 130 124 118

131 124 118 112 107 102

111 105 100 95 91 87

24 25 26 27 28 29

181 174 167 161 155 150

166 160 153 148 143 138

154 148 142 137 132 127

140 134 129 124 120 116

126 121 117 112 108 104

113 109 105 101 97 94

98 94 90 87 84 81

83 80 77 74 71 69

30 31 32 33 34 35

145 140 136 132 128 124

133 129 125 121 117 114

123 119 115 112 109 105

112 108 105 102 99 96

101 98 95 92 89 87

91 88 85 82 80 78

78 76 74 71 69 67

67 64 62 60 59 57

36 38 40 42 44

121 114 109 104 99

111 105 100 95 91

103 97 92 88 84

93 88 84 80 76

84 80 76 72 69

76 72 68 65 62

65 62 59 56 53

55 53 50 48 45

90.7 2720 176 56.3 18.0 60.6 4.62 55.0 6.16 75.6

78.4 2350 152 46.8 15.8 46.2 3.60 41.9 4.80 57.9

66.5 2000 143 42.2 15.0 38.6 3.88 34.0 5.18 51.3

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

145 4350 247 92.8 24.8 113 8.77 102 11.7 142

133 3990 223 80.9 22.5 94.3 7.16 85.5 9.55 118

123 3690 204 71.3 20.8 80.4 6.10 73.0 8.13 100

112 3360 191 64.0 19.5 69.7 5.62 62.9 7.50 88.0

101 3030 172 55.5 17.8 57.6 4.72 51.9 6.29 72.9

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 88

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 16

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 16 100

6 7 8 9 10 11

536

475

406

12 13 14 15 16 17

495 457 424 396 371 349

438 404 375 350 328 309

18 19 20 21 22 23

330 313 297 283 270 258

24 25 26 27 28 29

W 16 67

W 16 40

26 212 189 166 147 133 121

348

382 350 315 286

334 307 276 251

301 274 247 224

264 243 219 199

253 240 213 192 175

236 231 203 180 162 147

375 346 321 300 281 265

325 300 279 260 244 229

263 242 225 210 197 185

230 212 197 184 173 162

206 190 176 165 154 145

182 168 156 146 137 129

160 148 137 128 120 113

135 125 116 108 101 95

111 102 95 88 83 78

292 276 263 250 239 228

250 237 225 214 205 196

217 205 195 186 177 170

175 166 158 150 143 137

153 145 138 131 125 120

137 130 123 118 112 107

122 115 109 104 99 95

107 101 96 91 87 83

90 85 81 77 74 70

74 70 66 63 60 58

248 238 228 220 212 205

219 210 202 194 188 181

188 180 173 167 161 155

163 156 150 144 139 134

131 126 121 117 113 109

115 110 106 102 99 95

103 99 95 91 88 85

91 87 84 81 78 75

80 77 74 71 69 66

68 65 62 60 58 56

55 53 51 49 47 46

30 31 32 33 34 35

198 192 186 180 175 170

175 169 164 159 154 150

150 145 141 136 132 129

130 126 122 118 115 111

105 102 98 95 93 90

92 89 86 84 81 79

82 80 77 75 73 71

73 71 68 66 64 62

64 62 60 58 56 55

54 52 51 49 48 46

44 43 41 40 39 38

36 38 40

165 156 149

146 138 131

125 118 113

108 103 98

88 83 79

77 73 69

69 65 62

61 58 55

53 51

45 43

37 35

198 5940 268 123 29.2 160 13.0 145 17.3 202

175 5250 237 103 26.2 128 10.7 116 14.2 163

72.9 2190 132 45.3 15.3 43.2 3.80 39.1 5.06 55.6

64.0 1920 126 41.5 14.7 37.9 4.07 33.6 5.43 51.2

54.0 1620 118 38.7 13.8 34.5 3.22 31.1 4.29 45.0

44.2 1330 106 33.2 12.5 26.5 3.12 23.2 4.16 36.7

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

150 4500 203 81.8 22.8 96.5 8.12 87.5 10.8 123

130 3900 174 67.9 19.8 73.0 6.14 66.3 8.19 93.0

105 3150 191 73.9 21.5 86.0 7.32 78.0 9.76 110

92.0 2760 167 62.3 19.0 67.1 5.80 60.8 7.73 85.9

82.3 2470 150 53.9 17.3 54.9 4.87 49.7 6.50 70.8

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 89

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 14

For beams laterally unsupported, see page 4-139 Designation Wt./ft

W 14 132

120

109

W 14 99*

90*

344 344 315 291 270 252

315 314 288 265 246 230

281 278 255 235 219 204

461 454 424

406 384

371 370 345

333 329 307

16 17 18 19 20 21

439 413 390 369 351 334

398 374 353 335 318 303

360 339 320 303 288 274

323 304 287 272 259 246

288 271 256 243 230 219

261 245 232 219 209 199

236 222 210 199 189 180

216 203 192 182 173 164

191 180 170 161 153 146

22 23 24 25 26 27

319 305 293 281 270 260

289 277 265 254 245 236

262 250 240 230 222 213

235 225 216 207 199 192

210 200 192 184 177 171

190 181 174 167 160 154

172 164 158 151 145 140

157 150 144 138 133 128

139 133 128 122 118 113

28 29 30 31 32 33

251 242 234 226 219 213

227 219 212 205 199 193

206 199 192 186 180 175

185 178 172 167 162 157

165 159 154 149 144 140

149 144 139 135 130 126

135 130 126 122 118 115

123 119 115 111 108 105

109 106 102 99 96 93

206

187

169

152

136

123

111

101

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

234 7020 255 136 32.3 190 19.2 171 25.6 241

212 6360 231 120 29.5 158 16.3 143 21.8 213

126 3780 172 87.9 22.5 96.5 8.86 88.1 11.8 126

115 3450 157 77.8 20.8 81.8 7.65 74.6 10.2 108

102 3060 141 67.4 18.8 66.5 6.37 60.6 8.49 88.2

Span (ft)

511 501 468

394 379 348 321 298 278

Fy = 50 ksi

10 11 12 13 14 15

Properties and Reaction Values 192 5760 203 103 26.2 127 12.7 115 16.9 170

173 5170 185 87.1 24.3 108 11.2 97.0 14.9 145

157 4610 167 75.6 22.0 88.7 9.26 80.0 12.3 120

139 4170 197 104 25.5 121 11.7 110 15.6 161

*Noncompact shape; Fy = 50 ksi. Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 90

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 14

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 14 53

5 6 7 8 9 10

278 261

253 235

11 12 13 14 15 16

238 218 201 187 174 163

17 18 19 20 21 22

W 14 43

W 14 30

225 209

236 231 205 185

215 205 182 164

202 177 158 142

192 172 151 134 121

171 166 142 125 111 100

214 196 181 168 157 147

190 174 161 149 139 131

168 154 142 132 123 115

149 137 126 117 109 102

129 118 109 101 95 89

110 101 93 86 80 75

91 83 77 71 66 62

154 145 138 131 124 119

138 131 124 118 112 107

123 116 110 104 99 95

109 103 97 92 88 84

96 91 86 82 78 74

83 79 75 71 68 65

71 67 63 60 57 55

59 55 52 50 47 45

23 24 25 26 27 28

114 109 105 101 97 93

102 98 94 90 87 84

91 87 84 80 77 75

80 77 74 71 68 66

71 68 66 63 61 59

62 59 57 55 53 51

52 50 48 46 45 43

43 42 40 38 37 36

29 30 31 32 33 34

90 87 84 82 79 77

81 78 76 74 71 69

72 70 67 65 63 61

64 62 60 58 56 54

56 55 53 51 50 48

49 47 46 44 43 42

42 40 39 38 37 35

34 33 32 31 30 29

47.3 1420 101 31.6 13.5 31.4 4.00 27.7 5.33 45.0

40.2 1210 95.8 29.9 12.8 30.1 3.07 27.2 4.09 40.6

33.2 996 85.3 25.2 11.5 23.0 2.86 20.4 3.81 32.8

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

87.1 2610 139 66.5 18.5 65.9 5.96 60.4 7.95 86.2

78.4 2350 127 58.4 17.0 55.1 5.18 50.4 6.91 72.8

69.6 2090 112 50.0 15.3 44.2 4.24 40.4 5.65 58.7

61.5 1850 118 41.2 15.5 44.7 4.44 40.5 5.92 59.7

54.6 1640 108 35.6 14.3 37.0 3.94 33.3 5.25 50.4

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 91

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 12

For beams laterally unsupported, see page 4-139 Designation Wt./ft

W 12 120

106

W 12 79

65*

53 225 212 195 180 167 156

425 410 378 351 328

377 368 339 315 294

348 330 305 283 264

314 298 275 255 238

284 270 249 231 216

255 238 220 204 191

16 17 18 19 20 21

349 328 310 294 279 266

308 289 273 259 246 234

276 259 245 232 221 210

248 233 220 208 198 189

223 210 198 188 179 170

203 191 180 171 162 154

179 168 159 151 143 136

162 152 144 136 130 123

146 137 130 123 117 111

22 23 24 25 26 27

254 243 233 223 215 207

224 214 205 197 189 182

200 192 184 176 170 163

180 172 165 158 152 147

162 155 149 143 137 132

147 141 135 130 125 120

130 124 119 114 110 106

118 113 108 104 100 96

106 102 97 93 90 87

28 29 30

199 192 186

176 170 164

158 152 147

141 137 132

128 123 119

116 112 108

102 99 95

93 89 86

83 81 78

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

186 5580 252 161 35.5 227 26.7 203 35.6 276

164 4920 212 129 30.5 171 19.2 154 25.7 228

96.8 2860 128 64.0 19.5 68.3 8.75 61.2 11.7 99.2

86.4 2590 118 61.9 18.0 62.3 6.47 57.1 8.63 85.1

77.9 2340 112 53.9 17.3 55.4 6.41 50.3 8.54 78.0

Span (ft)

503 465 429 399 372

237 236 216 199 185 173

Fy = 50 ksi

10 11 12 13 14 15

Properties and Reaction Values 147 4410 189 112 27.5 140 15.7 126 21.0 194

132 3960 174 96.6 25.8 120 14.6 108 19.4 171

119 3570 157 84.5 23.5 99.6 12.3 89.4 16.5 143

108 3240 142 73.9 21.5 83.2 10.5 74.7 14.0 120

*Indicates noncompact shape; Fy = 50 ksi. Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 92

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 12

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 12 50

4 5 6 7 8 9

244 241

218 216

10 11 12 13 14 15

217 197 181 167 155 145

16 17 18 19 20 21

W 12 40

W 12 26

154 148 124 106 93 82

142 121 101 86 75 67

129 104 87 75 65 58

190

203 192 171

173 162 144

152 140 124

173 147 126 110 98

194 176 162 149 139 129

173 157 144 133 123 115

154 140 128 118 110 102

129 118 108 99 92 86

112 101 93 86 80 74

88 80 73 68 63 59

74 67 62 57 53 49

60 55 50 46 43 40

52 47 44 40 37 35

136 128 121 114 109 103

121 114 108 102 97 92

108 101 96 91 86 82

96 90 85 81 77 73

81 76 72 68 65 62

70 66 62 59 56 53

55 52 49 46 44 42

46 44 41 39 37 35

38 35 34 32 30 29

33 31 29 27 26 25

22 23 24 25 26 27

99 94 91 87 84 80

88 84 81 78 75 72

78 75 72 69 66 64

70 67 64 61 59 57

59 56 54 52 50 48

51 49 47 45 43 41

40 38 37 35 34 33

34 32 31 30 29 27

27 26 25 24 23 22

24 23 22 21 20 19

28 29 30

78 75 72

69 67 65

62 59 51

55 53 43

46 45 37

40 38 29

31 30 25

26 26

22 21

19 18

72.4 2170 122 63.6 18.5 64.9 7.02 59.2 9.37 89.7

64.7 1940 109 52.3 16.8 53.0 5.87 48.3 7.82 73.7

29.3 879 86.4 28.4 13.0 31.2 3.63 28.2 4.85 43.9

24.7 741 77.2 23.9 11.8 24.3 3.30 21.6 4.40 35.9

20.1 603 71.2 20.6 11.0 19.2 3.63 16.3 4.83 32.0

17.4 522 64.3 17.2 10.0 15.3 3.23 12.7 4.31 26.7

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

57.5 1730 95.1 46.1 14.7 41.5 4.52 37.9 6.02 57.4

51.2 1540 101 37.5 15.0 42.7 4.49 39.0 5.99 58.5

43.1 1290 86.6 30.5 13.0 31.7 3.50 28.8 4.67 44.0

37.2 1120 75.9 25.2 11.5 24.5 2.83 22.2 3.78 34.5

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 93

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 10

For beams laterally unsupported, see page 4-139 Designation

W 10 112

100

9 10 11 12 13 14

463 441 401 368 339 315

408 390 355 325 300 279

354 339 308 283 261 242

303 293 266 244 225 209

264 256 233 213 197 183

232 224 203 187 172 160

202 200 182 167 154 143

183 181 165 151 139 129

15 16 17 18 19 20

294 276 259 245 232 221

260 244 229 217 205 195

226 212 199 188 178 170

195 183 172 163 154 146

171 160 151 142 135 128

149 140 132 124 118 112

133 125 118 111 105 100

121 113 107 101 95 91

21 22 23 24

210 200 192 184

186 177 170 163

161 154 147 141

139 133 127 122

122 116 111 107

107 102 97 93

95 91 87 83

86 82 79 76

74.6 2240 116 68.9 21.0 80.9 11.5 73.1 15.4 123

66.6 2000 101 57.8 18.5 63.6 8.83 57.7 11.8 96.0

60.4 1810 91.6 50.5 17.0 53.5 7.61 48.4 10.1 81.4

Span (ft)

Fy = 50 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

147 4410 232 177 37.8 265 32.8 240 43.7 300

130 3900 204 149 34.0 214 27.4 194 36.5 259

113 3390 177 123 30.3 169 22.3 153 29.8 221

97.6 2930 152 99.4 26.5 130 17.5 117 23.3 185

85.3 2560 132 80.8 23.5 102 14.0 92.2 18.7 153

Load above heavy line is limited by design shear strength. Values of φR (N = 31⁄4) in boldface exceed maximum web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 94

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 10

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W 10 45

3 4 5 6 7 8

191

9 10 11 12 13 14

W 10 33

W 10 22

12* 101 94 75 63 54 47

138 130 108 93 81

131 112 94 80 70

124 120 96 80 69 60

169

152 146

170 157 137

145 134 117

132 130 111 98

183 165 150 137 127 118

156 140 128 117 108 100

129 116 106 97 90 83

122 110 100 91 84 78

104 94 85 78 72 67

87 78 71 65 60 56

72 65 59 54 50 46

62 56 51 47 43 40

53 48 44 40 37 34

42 38 34 31 29 27

15 16 17 18 19 20

110 103 97 92 87 82

94 88 83 78 74 70

78 73 68 65 61 58

73 69 65 61 58 55

63 59 55 52 49 47

52 49 46 43 41 39

43 41 38 36 34 32

37 35 33 31 30 28

32 30 28 27 25 24

25 23 22 21 20 19

21 22 23 24

78 75 72 69

67 64 61 59

55 53 51 49

52 50 48 46

45 43 41 39

37 35 34 33

31 29 28 27

27 26 24 23

23 22 21 20

18 17 16 16

54.9 1650 95.4 54.7 17.5 58.8 7.41 53.8 9.88 85.9

46.8 1400 84.4 44.3 15.8 46.4 6.43 42.2 8.58 70.0

21.6 648 69.1 25.4 12.5 28.3 4.18 25.5 5.57 43.6

18.7 561 65.5 22.5 12.0 24.4 4.48 21.3 5.98 40.8

16.0 480 62.0 19.8 11.5 20.7 4.88 17.4 6.51 38.6

12.6 376 50.6 14.8 9.50 13.7 3.58 11.3 4.77 26.8

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

38.8 1160 76.2 38.5 14.5 37.1 6.23 33.1 8.31 60.1

36.6 1100 84.8 35.2 15.0 42.3 5.47 38.5 7.29 62.2

31.3 939 72.5 28.4 13.0 31.7 4.18 28.8 5.58 47.0

26.0 780 65.9 22.5 12.0 25.4 4.08 22.7 5.45 40.4

*Indicates noncompact shape; Fy = 50 ksi. Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 95

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

For beams laterally unsupported, see page 4-139 Designation

W8 67

7 8 9 10 11 12

277 263 234 211 191 175

241 224 199 179 163 150

184 163 147 134 123

160 149 133 119 109 100

136 130 116 104 95 87

123 114 101 91 83 76

13 14 15 16 17 18

162 150 140 132 124 117

138 128 120 112 106 100

113 105 98 92 86 82

92 85 80 75 70 66

80 74 69 65 61 58

70 65 61 57 54 51

19 20

111 105

94 90

77 74

63 60

55 52

48 46

39.8 1190 80.2 47.8 18.0 58.3 10.9 52.3 14.6 99.6

34.7 1040 68.0 38.8 15.5 43.8 8.02 39.5 10.7 74.2

30.4 912 61.6 33.4 14.3 36.2 7.20 32.3 9.60 63.5

Span (ft)

Fy = 50 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

70.2 2110 139 102 28.5 150 23.8 136 31.7 195

59.8 1790 120 83.7 25.5 118 20.2 106 27.0 167

49.0 1470 91.8 59.4 20.0 75.5 11.9 68.8 15.9 120

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 96

BEAM AND GIRDER DESIGN

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

W8 24

W8 18

10*

99 86 68 57 49 43

72 66 53 44 38 33

3 4 5 6 7 8

124 117 102

105 99 87

112 102 87 77

101 85 73 64

107 102 82 68 58 51

9 10 11 12 13 14

91 82 74 68 63 58

77 70 63 58 54 50

68 61 56 51 47 44

57 51 46 43 39 36

45 41 37 34 31 29

38 34 31 29 26 24

29 26 24 22 20 19

15 16 17 18 19 20

54 51 48 45 43 41

46 44 41 39 37 31

41 38 36 34 32 26

34 32 30 28 27 20

27 26 24 23 21

23 21 20 19 18

18 16 16 15 14

13.6 408 53.6 23.0 12.3 24.5 6.23 21.2 8.30 48.2

11.4 342 49.6 19.8 11.5 20.1 6.46 16.6 8.61 44.6

8.87 264 36.2 13.3 8.50 11.4 3.29 9.72 4.38 24.0

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

27.2 816 62.0 33.4 14.3 37.4 6.68 33.8 8.91 62.8

23.2 696 52.5 26.8 12.3 27.7 5.02 25.0 6.69 46.7

20.4 612 55.9 25.4 12.5 28.5 5.10 25.7 6.81 47.8

17.0 510 50.5 21.6 11.5 22.9 4.90 20.2 6.53 41.4

*Indicates noncompact shape; Fy = 50 ksi. Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 97

BEAMS W Shapes Maximum factored uniform loads in kips for beams laterally supported

W 6–5–4

For beams laterally unsupported, see page 4-139 Designation Wt./ft

W6 25

2 3 4 5 6 7

110 95 81

8 9 10 11 12 13

W6 15*

75 62 50 42 36

54 47 37 31 27

71 63 57 52 47 44

56 50 45 41 37 34

38 34 31 28 26 24

44 39 35 32 29 27

31 28 25 23 21 19

23 21 19 17 16 14

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

18.9 567 55.1 32.5 16.0 44.0 12.2 38.8 16.3 84.5

14.9 447 43.5 24.4 13.0 28.9 8.40 25.4 11.2 61.8

W4 16

75 70 58 50

65 58 48 41

63 63 47 38 31 27

44 39 35 32 29

36 32 29 26 24

24 21 19

11.6 348 37.5 27.4 13.5 33.2 9.62 29.9 12.8 71.3

9.59 288 32.5 22.5 12.0 25.4 8.29 22.7 11.1 58.6

6.28 188 31.4 24.1 14.0 31.4 16.5 26.8 22.1 69.6

Span (ft)

88 88 70 59 50

Fy = 50 ksi

87 75 64

74 62 51 44

Properties and Reaction Values 10.8 308 37.2 18.0 11.5 20.3 8.45 16.9 11.3 53.5

11.7 351 44.1 24.4 13.0 30.4 7.48 27.3 9.97 59.7

8.30 249 37.4 18.0 11.5 21.0 7.80 17.9 10.4 51.7

6.23 187 27.1 12.0 8.50 11.7 4.19 10.1 5.59 28.2

*Indicates noncompact shape; Fy = 50 ksi. Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 98

BEAM AND GIRDER DESIGN

S 24–20

BEAMS S Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation Wt./ft

S 24 121

12 13 14 15 16 17

S 20 80

S 20 86

723 686 610 549 499

686 656 574 510 459 417

545 525 467 420 382

820 761

966 900 800 720 655

810 740 666 605

648 612 556

765 706 656 612 574 540

698 644 598 558 523 492

600 554 514 480 450 424

555 512 476 444 416 392

510 471 437 408 383 360

495 457 424 396 371 349

458 422 392 366 343 323

383 353 328 306 287 270

350 323 300 280 263 247

18 19 20 21 22 23

510 483 459 437 417 399

465 441 419 399 380 364

400 379 360 343 327 313

370 351 333 317 303 290

340 322 306 291 278 266

330 313 297 283 270 258

305 289 275 261 250 239

255 242 230 219 209 200

233 221 210 200 191 183

24 25 26 27 28 29

383 367 353 340 328 317

349 335 322 310 299 289

300 288 277 267 257 248

278 266 256 247 238 230

255 245 235 227 219 211

248 238 228 220 212 205

229 220 211 203 196 189

191 184 177 170 164 158

175 168 162 156 150 145

30 32 34 36 38 40

306 287 270 255 242 230

279 262 246 233 220 209

240 225 212 200 189 180

222 208 196 185 175 167

204 191 180 170 161 153

198 186 175 165 156 149

183 172 161 153 144 137

153 143 135 128 121 115

140 131 124 117 111 105

42 44 46 48 50 52

219 209 200 191 184 177

199 190 182 174 167 161

171 164 157 150 144 138

159 151 145 139 133 128

146 139 133 128 122 118

141 135 129 124 119

131 125 119 114 110

109 104 100 96 92

100 95 91 88 84

54 56 58 60

170 164 158 153

155 149 144 140

133 129 124 120

123 119 115 111

113 109 106 102

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

306 9180 529 200 40.0 269 20.7 236 27.7 330

279 8370 410 155 31.0 184 9.66 168 12.9 215

183 5490 362 144 33.0 185 16.7 163 22.2 240

153 4590 343 129 31.8 163 17.4 139 23.2 219

140 4200 273 103 25.3 115 8.76 104 11.7 144

Span (ft)

1060 1020 918 835

100

877 849 743 660 594 540

Fy = 50 ksi

6 7 8 9 10 11

S 24 106

Properties and Reaction Values 240 7200 483 163 37.3 216 21.4 182 28.6 284

222 6660 405 137 31.3 166 12.6 146 16.9 207

204 6120 324 109 25.0 119 6.48 109 8.64 140

198 5940 438 175 40.0 248 29.7 207 39.5 305

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 99

BEAMS S 18–15–12–10 S Shapes Maximum factored uniform loads in kips for beams laterally supported For beams laterally unsupported, see page 4-139

Designation

Span (ft)

Fy = 50 ksi

Wt./ft

S 18 70

3 4 5 6 7 8

691 625 536 469

9 10 11 12 13 14

S 15

54.7

S 12

42.9

S 12

40.8

S 10

31.8

25.4

168 142 122 107

333 297 260

445 367 306 262 230

299 266 228 199

277 269 224 192 168

227 210 180 158

321 266 212 177 152 133

257 231 210 193 178 165

231 208 189 173 160 149

204 184 167 153 141 131

177 159 145 133 123 114

149 134 122 112 103 96

140 126 115 105 97 90

118 106 97 89 82 76

95 85 77 71 66 61

210 197 185 175 166 158

154 145 136 129 122 116

139 130 122 116 109 104

122 115 108 102 97 92

106 100 94 89 84 80

90 84 79 75 71 67

84 79 74 70 66 63

71 66 62 59 56 53

57 53 50 47 45 43

179 170 163 156 150 144

150 143 137 131 126 121

110 105 101 96 93 89

99 95 90 87 83 80

87 83 80 77 73 71

76 72 69 66 64 61

64 61 58 56 54 52

60 57 55 53 50 48

51 48 46 44 42

41 39 37 36 34

27 28 29 30 31 32

139 134 129 125 121 117

117 113 109 105 102 98

86 83 80 77 75 72

77 74 72 69 67 65

68 66 63 61

59 57 55 53

50 48 46 45

47 45 43 42

33 34 35 36 37 38

114 110 107 104 101 99

95 93 90 88 85 83

70 68 66 64 63

63 61 59 58 56

40 42 44

94 89 85

79 75 72

125 3750 346 133 35.6 180 31.3 142 41.7 249

105 3150 224 86.4 23.1 93.8 8.52 83.6 11.4 122

44.8 1340 139 63.5 21.4 74.5 13.0 64.1 17.3 120

42.0 1260 113 52.0 17.5 55.1 7.11 49.4 9.47 80.2

35.4 1060 160 83.5 29.7 116 46.2 84.9 61.6 180

28.4 852 84.0 43.7 15.5 43.8 6.63 39.4 8.84 68.1

448 394

446 386 330 289

417 375 341 313 288 268

350 315 286 263 242 225

15 16 17 18 19 20

250 234 221 208 197 188

21 22 23 24 25 26

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

77.1 2310 223 94.5 27.5 116 19.3 96.7 25.7 180

69.3 2080 166 70.6 20.6 74.9 8.05 66.9 10.7 102

61.2 1840 223 123 34.3 167 44.4 131 59.1 235

53.1 1590 150 83.0 23.1 91.9 13.5 81.1 18.0 140

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 100

BEAM AND GIRDER DESIGN

S 8–6–5–4–3

BEAMS S Shapes Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation Wt./ft

S8 23

1 2 3 4 5 6

191 145 116 96

7 8 9 10 11 12

S6 18.4

17.25

S5 12.5

9.5

75 64 51 42

58 57 43 34 28

83 72 64 58 53 48

71 62 55 50 45 41

45 40 35 32 29 27

36 32 28 25 23 21

24 21 19 17 15 14

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

19.3 579 95.3 55.1 22.1 68.9 27.2 54.4 36.3 127

16.5 495 58.5 33.9 13.6 33.2 6.32 29.8 8.42 57.2

S3 7.7

7.5

5.7

70 61 40 30 24 20

42 35 26 21 18

57 35 24 18 14 12

28 20 15 12 9.75

17 15 13 12

15 13 12 11

8.36

4.04 121 35.2 30.6 16.3 36.3 32.0 27.8 42.6 83.5

3.51 105 20.8 18.1 9.65 16.6 6.64 14.8 8.85 43.5

2.36 70.8 28.3 30.0 17.5 37.9 59.0 26.1 78.6 86.7

1.95 58.5 13.8 14.6 8.50 12.9 6.81 11.5 9.09 41.1

Span (ft)

117 99 83

151 106 80 64 53

Fy = 50 ksi

Properties and Reaction Values 10.6 318 75.3 50.9 23.3 68.5 50.5 48.3 67.3 126

8.47 254 37.6 25.4 11.6 24.1 6.27 21.6 8.36 48.8

5.67 170 28.9 21.7 10.7 20.4 6.50 18.2 8.67 46.4

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 101

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

MC,C 18–15

For beams laterally unsupported, see page 4-139 Designation

MC 18

Span (ft)

Fy = 50 ksi

Wt./ft

51.9

C 15 45.8

42.7

33.9

421 343 286 245 215

324 302 252 216 189

3 4 5 6 7 8

680 568 473 405 355

583 519 433 371 324

486 470 392 336 294

437 372 319 279

580 511 409 341 292 256

9 10 11 12 13 14

315 284 258 237 218 203

288 260 236 216 200 185

261 235 214 196 181 168

248 223 203 186 172 159

227 205 186 170 157 146

191 172 156 143 132 123

168 151 137 126 116 108

15 16 17 18 19 20

189 177 167 158 149 142

173 162 153 144 137 130

157 147 138 131 124 118

149 140 131 124 117 112

136 128 120 114 108 102

114 107 101 95 90 86

101 95 89 84 80 76

21 22 23 24 25 26

135 129 123 118 114 109

124 118 113 108 104 100

112 107 102 98 94 90

106 101 97 93 89 86

97 93 89 85 82 79

82 78 75 72 69 66

72 69 66 63 60 58

28 30 32 34 36 38

101 95 89 83 79 75

93 87 81 76 72 68

84 78 74 69 65 62

80 74 70 66 62 59

73 68 64 60 57

61 57 54 50 48

54 50 47 44 42

40 42 44

71 68 65

65 62 59

59 56 53

56 53 51

68.2 2050 290 129 35.8 176 40.7 135 54.3 245

57.2 1720 211 93.4 26.0 109 15.6 93.4 20.8 161

50.4 1510 162 71.9 20.0 73.6 7.10 66.5 9.47 97.2

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

94.6 2840 340 120 35.0 167 33.0 127 44.0 234

86.5 2600 292 103 30.0 133 20.8 108 27.7 200

78.4 2350 243 85.9 25.0 101 12.0 86.4 16.0 140

74.4 2230 219 77.3 22.5 86.1 8.76 75.5 11.7 115

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 102

BEAM AND GIRDER DESIGN

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

MC 13

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

MC 13

Span (ft)

Fy = 50 ksi

Wt./ft

31.8

3 4 5 6 7 8

552 454 363 303 259 227

393 382 305 255 218 191

314 277 231 198 173

263 259 216 185 162

9 10 11 12 13 14

202 182 165 151 140 130

170 153 139 127 117 109

154 139 126 116 107 99

144 129 118 108 99 92

15 16 17 18 19 20

121 113 107 101 96 91

102 95 90 85 80 76

92 87 82 77 73 69

86 81 76 72 68 65

21 22 23 24 25 26

86 83 79 76 73 70

73 69 66 64 61 59

66 63 60 58 55 53

62 59 56 54 52 50

27 28 29 30 31 32

67 65 63 61 59 57

57 55 53 51 49 48

51 50 48 46 45 43

48 46 45 43 42 40

46.2 1390 157 76.8 22.4 84.2 12.2 73.6 16.2 126

43.1 1290 132 64.5 18.8 64.7 7.19 58.4 9.59 89.6

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

60.5 1820 276 135 39.3 197 66.5 139 88.7 263

50.9 1530 197 96.3 28.0 118 24.0 97.3 31.9 187

Load above heavy line is limited by design shear strength.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 103

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C,MC 12

For beams laterally unsupported, see page 4-139 Designation Wt./ft

C 12 50

251 219 175 146 125

183 152 127 109

541 421 337 281 240

461 388 310 259 222

382 355 284 237 203

126 112 101 92 84 78

110 97 88 80 73 67

95 85 76 69 64 59

210 187 168 153 140 129

194 172 155 141 129 119

14 15 16 17 18 19

72 67 63 59 56 53

63 58 55 52 49 46

54 51 48 45 42 40

120 112 105 99 94 89

20 21 22 23 24 25

50 48 46 44 42 40

44 42 40 38 37 35

38 36 35 33 32 30

26 27 28 29 30

39 37 36 35 34

34 32 31 30 29

29 28 27 26 25

Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

33.6 1010 165 71.7 25.5 93.0 23.9 73.9 31.8 155

29.2 876 125 54.4 19.4 61.5 10.4 53.1 13.9 98.3

Span (ft)

2 3 4 5 6 7

330 252 202 168 144

8 9 10 11 12 13

MC 12 20.7

Fy = 50 ksi

MC 12 35

10.6

303 257 214 183

240 236 197 168

123 116 87 70 58 50

177 158 142 129 118 109

161 143 128 117 107 99

147 131 118 107 98 91

44 39 35 32 29 27

111 103 97 91 86 82

101 95 89 83 79 75

92 86 80 76 71 68

84 79 74 69 66 62

25 23 22 20 19 18

84 80 77 73 70 67

78 74 71 67 65 62

71 68 65 62 59 57

64 61 58 56 54 51

59 56 54 51 49 47

17 17 16 15 15 14

65 62 60 58 56

60 57 55 53 52

55 53 51 49 47

49 48 46 44 43

45 44 42 41 39

13 13 12 12 12

47.3 1420 191 96.8 29.5 137 26.5 116 35.3 193

42.8 1280 151 76.6 23.4 96.3 13.1 85.8 17.5 143

39.3 1180 120 60.7 18.5 67.9 6.52 62.7 8.70 91.0

11.6 348 61.6 16.3 9.50 16.6 2.00 15.0 2.67 23.7

Properties and Reaction Values 25.4 762 91.4 39.7 14.1 38.2 4.04 35.0 5.38 52.5

56.1 1680 271 137 41.8 230 75.0 170 100.0 273

51.7 1550 231 117 35.6 181 46.5 144 62.0 233

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 104

BEAM AND GIRDER DESIGN

C,MC 10

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

C 10

MC 10

2 3 4 5 6 7

363 266 200 160 133 114

284 230 173 138 115 99

8 9 10 11 12 13

100 89 80 73 67 61

14 15 16 17 18 19 20 21 22 23 24

33.6

MC 10 28.5

MC 10

15.3

41.1

205 193 145 116 96 83

130 119 95 79 68

430 389 292 233 195 167

311 251 200 167 143

230 222 178 148 127

205 194 155 129 111

157 142 118 101

92 79 59 47 39 34

8.4

86 77 69 63 58 53

72 64 58 53 48 45

59 53 47 43 40 36

146 130 117 106 97 90

125 111 100 91 84 77

111 99 89 81 74 68

97 86 77 70 65 60

89 79 71 64 59 54

29 26 24 21 20 18

57 53 50 47 44 42

49 46 43 41 38 36

41 39 36 34 32 30

34 32 30 28 26 25

83 78 73 69 65 61

72 67 63 59 56 53

63 59 56 52 49 47

55 52 48 46 43 41

51 47 44 42 39 37

17 16 15 14 13 12

40 38 36 35 33

35 33 31 30 29

29 28 26 25 24

24 23 22 21 20

58 56 53 51 49

50 48 46 44 42

44 42 40 39 37

39 37 35 34 32

35 34 32 31 30

12 11 11 10 9.83

26.6 798 182 84.1 33.6 131 75.6 81.0 101 193

23.0 690 142 65.8 26.3 90.8 36.1 66.8 48.1 151

29.6 888 115 66.4 21.3 75.8 14.4 66.1 19.3 129

25.8 774 103 59.4 19.0 64.1 10.3 57.2 13.8 102

23.6 708 78.3 45.3 14.5 42.7 4.59 39.6 6.12 59.5

7.86 236 45.9 14.6 8.50 13.4 1.90 12.1 2.53 20.3

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

19.3 579 102 47.4 19.0 55.6 13.5 46.6 18.0 105

15.8 474 64.8 30.0 12.0 28.0 3.43 25.7 4.57 40.6

38.9 1170 215 124 39.8 194 94.9 131 127 254

33.4 1000 155 89.8 28.8 119 35.8 95.4 47.7 183

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 105

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C,MC 9

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

MC 9

13.4

25.4

23.9

2 3 4 5 6 7

218 168 126 101 84 72

139 135 101 81 68 58

113 94 75 63 54

219 174 139 116 99

194 167 133 111 95

8 9 10 11 12 13

63 56 50 46 42 39

51 45 41 37 34 31

47 42 38 34 31 29

87 77 70 63 58 54

83 74 67 61 56 51

14 15 16 17 18 19

36 34 31 30 28 27

29 27 25 24 23 21

27 25 23 22 21 20

50 46 44 41 39 37

48 44 42 39 37 35

20 21 22

25 24 23

20 19 18

19 18 17

35 33 32

33 32 30

23.2 696 109 66.8 22.5 80.7 19.9 68.8 26.6 140

22.2 666 97.2 59.4 20.0 67.7 14.0 59.3 18.7 120

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

16.8 504 109 52.5 22.4 69.5 26.2 53.8 34.9 125

13.5 405 69.3 33.4 14.3 35.3 6.74 31.2 8.98 60.4

12.5 375 56.6 27.3 11.7 26.1 3.68 23.9 4.91 39.8

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 106

BEAM AND GIRDER DESIGN

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C,MC 8

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

Span (ft)

Fy = 50 ksi

Wt./ft

MC 8

18.75

13.75

11.5

22.8

21.4

18.7

8.5

1 2 3 4 5 6

210 207 138 104 83 69

131 109 82 65 55

95 72 57 48

184 141 113 94

162 135 108 90

173 162 122 97 81

152 116 92 77

77 69 52 41 35

7 8 9 10 11 12

59 52 46 41 38 35

47 41 36 33 30 27

41 36 32 29 26 24

81 70 63 56 51 47

77 68 60 54 49 45

69 61 54 49 44 41

66 58 51 46 42 39

30 26 23 21 19 17

13 14 15 16 17 18

32 30 28 26 24 23

25 23 22 20 19 18

22 20 19 18 17 16

43 40 38 35 33 31

42 39 36 34 32 30

37 35 32 30 29 27

36 33 31 29 27 26

16 15 14 13 12 12

19 20

22 21

17 16

15 14

30 28

28 27

26 24

24 23

11 10

16.2 486 86.4 56.3 20.0 64.5 17.3 55.3 23.1 121

15.4 462 76.2 49.6 17.7 53.5 11.9 47.1 15.9 98.7

6.91 207 38.7 16.8 8.95 15.2 2.49 13.9 3.33 24.7

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

13.8 414 105 57.1 24.3 76.5 40.1 55.2 53.4 136

10.9 327 65.4 35.5 15.2 37.6 9.65 32.4 12.9 74.2

9.55 287 47.5 25.8 11.0 23.2 3.69 21.3 4.92 37.3

18.8 564 92.2 63.4 21.3 72.9 20.1 62.2 26.7 133

18.0 540 81.0 55.7 18.8 60.0 13.6 52.8 18.1 112

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

FACTORED UNIFORM LOAD TABLES

Fy = 50 ksi

4 - 107

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C,MC 7–6

For beams laterally unsupported, see page 4-139 Designation

C7 12.25

MC 7 9.8

22.7

MC 6

19.1

10.5

8.2

16.3

15.1

102 92 62 46 37 31

65 51 38 31 26

123 115 86 69 58

122 102 77 61 51

102 97 73 58 48

100 74 55 44 37

1 2 3 4 5 6

119 84 63 50 42

79 71 53 43 36

190 162 122 97 81

133 107 86 72

142 109 73 54 44 36

7 8 9 10 11 12

36 31 28 25 23 21

31 27 24 21 19 18

69 61 54 49 44 41

61 54 48 43 39 36

31 27 24 22 20 18

26 23 21 18 17 15

22 19 17 15 14 13

49 43 38 35 31 29

44 38 34 31 28 26

42 36 32 29 26 24

32 28 25 22 20 18

13 14 15 16

19 18 17 16

16 15 14 13

37 35 32 30

33 31 29 27

17 16 15

14 13 12

12 11 10

27 25 23

24 22 20

22 21 19

17 16 15

8.40 252 59.3 34.3 15.7 38.4 13.1 32.3 17.4 85.4

7.12 214 39.7 23.0 10.5 21.0 3.91 19.2 5.21 36.1

11.5 345 61.4 50.3 19.0 58.0 20.7 49.7 27.6 112

10.2 306 60.8 49.8 18.8 57.1 20.0 49.1 26.7 111

9.69 291 51.2 42.0 15.8 44.2 12.0 39.4 16.0 91.3

7.38 221 50.2 31.5 15.5 38.1 14.3 32.4 19.1 81.9

Span (ft)

Fy = 50 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

16.2 486 95.1 70.7 25.2 91.0 39.3 72.6 52.5 152

14.3 429 66.5 49.5 17.6 53.3 13.5 47.0 18.0 105

7.26 218 70.8 44.4 21.9 61.0 43.9 43.5 58.5 115

6.15 185 50.9 31.9 15.7 37.2 16.3 30.7 21.7 82.9

5.13 154 32.4 20.3 10.0 18.9 4.21 17.2 5.61 35.4

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 108

BEAM AND GIRDER DESIGN

BEAMS Channels Maximum factored uniform loads in kips for beams laterally supported

C 5–4–3

Fy = 50 ksi

For beams laterally unsupported, see page 4-139 Designation

C5 9

6.7

7.25

5.4

69 42 28 21 17 14

40 34 23 17 14 11

1 2 3 4 5 6

88 65 44 33 26 22

51 35 26 21 18

7 8 9 10 11 12

19 16 15 13 12 11

15 13 12 11 9.6 8.8

12 11 9.4 8.4

9.7 8.5 7.5 6.8

4.1

52 26 17 13 10 8.6

42 23 15 11 9.0 7.5

28 20 13 9.8 7.8 6.5

7.4

6.4

5.6

1.72 51.6 28.8 30.6 17.8 40.0 59.6 28.1 79.5 88.4

1.50 45.0 20.9 22.2 12.9 24.7 22.7 20.2 30.2 64.1

1.30 39.0 13.8 14.6 8.50 13.2 6.49 11.9 8.65 40.0

Span (ft)

Fy = 50 ksi

Wt./ft

Properties and Reaction Values Zx in.3 φbWc kip-ft φvVn kips φR1 kips φR2 kips/in. φr R3 kips φr R4 kips/in. φr R5 kips φr R6 kips/in. φR (N = 31⁄4) kips

4.36 131 43.9 30.5 16.3 37.8 23.2 30.1 30.9 83.3

3.51 105 25.7 17.8 9.50 16.9 4.64 15.3 6.18 35.4

2.81 84.3 34.7 27.6 16.1 35.7 30.2 27.6 40.3 79.7

2.26 67.8 19.9 15.8 9.20 15.5 5.69 14.0 7.59 38.6

Load above heavy line is limited by design shear strength. Values of R in bold face exceed maximum design web shear φvVn.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 109

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH GREATER THAN Lp General Notes

Spacing of lateral bracing at distances greater than Lp creates a problem in which the designer is confronted with a given laterally unbraced length (usually less than the total span) along the compression flange, and a calculated required bending moment. The beam cannot be selected from its plastic section modulus alone, since depth, flange proportions, and other properties have an influence on its bending strength. The following charts show the design moment φbMn for W and M shapes of Fy = 36 ksi and Fy = 50 ksi steels, used as beams, with respect to the maximum unbraced length for which this moment is permissible. In bending, φb of 0.9 is given in Section F1.2 of the LRFD Specification. The charts extend over varying unbraced lengths, depending upon the flexural strengths of the beams represented. In general, they extend beyond most unbraced lengths frequently encountered in design practice. The design moment φbMn, kip-ft, is plotted with respect to the unbraced length with no consideration of the moment due to weight of the beam. Design moments are shown for unbraced lengths in feet, starting at spans less than Lp, for spans between Lp and Lr and for spans beyond Lr. The unbraced length Lp, in feet, with the limit indicated by a solid symbol, , is the maximum unbraced length of the compression flange, with Cb = 1.0, for which the design moment is given by φbMp, where Fy Lp = 300ry / √ Mp = ZxFy

(F1-4)

For those noncompact rolled shapes, which meet the requirements of compact sections Fy , but is less than 141 / √  Fy −Fr , the design moment is except that bf / 2tf exceeds 65 / √ obtained from Equation A-F1-3 in Appendix F1 of the LRFD Specification. This criterion applies to one W shape when Fy is equal to 36 ksi and to seven W shapes when Fy is equal to 50 ksi. (Noncompact W shapes are given on p. 4-7.) For the case Cb = 1.0 and noncompact shapes:  λ − λp  Mn′ = Mp − (Mp − Mr)    λr − λp 

(A-F1-3)

 Mp − Mn′  Lp′ = Lp + (Lr − Lp)    Mp − Mr  λ = bf / 2tf λp = 65 / √ Fy λr = 141 / √  Fy −Fr Lr =

ryX1  √ 1+√  1 + X2(Fy − Fr)2 Fy − Fr

X1 =

π Sx

 √

EGJA 2

(F1-6)

(F1-8) AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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BEAM AND GIRDER DESIGN

4Cw X2 = Iy

 Sx     GJ 

(F1-9)

Mr = (Fy − Fr )Sx Mp = ZxFy Fr = 10 ksi for rolled shapes

(F1-7)

The unbraced length in the charts may be either the total span or any part of the total span between braced points. The plots shown in these charts were computed for beams for which Cb = 1.0. When a moment gradient exists between points of bracing, Cb may be larger than unity. (See Table 4-1.) Using this larger value of Cb may provide a more liberal flexural strength for the section chosen if the unbraced length is greater than Lp. In these cases, the design moment can be determined using the provisions of Section F1.2a of the LRFD Specification.  Lb − Lp   φbMn = φbCb Mp − (Mp − Mr)   ≤ φbMp  Lr − Lp   The unbraced length Lr, ft, with the limit indicated by an open symbol , is the maximum unbraced length of the compression flange beyond which the design moment is governed by Specification Section F1.2b. For unbraced lengths greater than Lr:

φbMn = φbMcr = φbCb

π Lb

 √ 2

 πE  EIyGJ +   IyCw ≤ φbCbMr and φbMp  Lb 

In computing the points for the curves, Cb in the above formulas was taken as unity, E = 29,000 ksi and G = 11,200 ksi. The properties of the beams are taken from the Tables of Dimensions and Properties in Part 1 of this LRFD Manual. The beam strengths have been reduced by multiplying the nominal flexural strength Mn by 0.9, the resistance factor φb for flexure. Over a limited range of length, a given beam is the lightest available for various combinations of unbraced length and design moment. The charts are designed to assist in selection of the lightest available beam for the given combination. The solid portion of each curve indicates the most economical section by weight. The dashed portion of each curve indicates ranges in which a lighter weight beam will satisfy the loading conditions. The curves are plotted without regard to shear strength and deflection criteria, therefore due care must be exercised in their use. The curves do not extend beyond an arbitrary span/depth limit of 30. The following examples illustrate the use of the charts.

EXAMPLE 4-8

Given:

Using Fy = 50 ksi steel, determine the size of a “simple” framed girder with a span of 35 feet, which supports two equal concentrated loads. The factored loads produce a required moment of 440 kip-ft in the AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 111

center 15-ft section between the loads. The load points are laterally braced. Solution:

For this loading condition, Cb = 1.0 due to nearly uniform moment across the central portion of the span. Center section of 15 feet is longest unbraced length. With total span equal to 35 feet and Mn = 440 kip-ft, assume approximate weight of beam at 70 lbs/ft (equal to 0.07 kips/ft).  0.07 × (35)2  × 1.2 = 453 kip-ft Total Mu = 440 +  8   Entering chart, with unbraced length equal to 15 feet on the bottom scale (abscissa), proceed upward to meet the horizontal line corresponding to a design moment equal to 453 kip-ft on the left hand scale (ordinate). Any beam listed above and to the right of the point so located satisfies the design moment requirement. In this case, the lightest section satisfying this criterion is a W21×68, for which the total design moment with an unbraced length of 15 feet is 457 kip-ft. Use: W21×68 Note: If depth is limited, a W14×82 could be selected, provided deflection conditions are not critical.

EXAMPLE 4-9

Given:

A “fixed end” girder with a span of 60 feet supports a concentrated load at the center. The compression flange is laterally supported at the concentrated load point and at the inflection points. The factored load produces a maximum calculated moment of 440 kip-ft at the load point and the supports. Determine the size of the beam using Fy = 50 ksi steel.

Solution:

For this loading condition, Cb = 1.67 (by comparison with Table 4-1), with an unbraced length of 15 feet. With the total span equal to 60 feet and Mu = 440 kip-ft, assume approximate weight of beam at 60 lbs/ft (0.06 kips/ft).  0.06 × (60)2  Total Mu = 440 +  ×1.2 24   = 451 kip-ft at the centerline and 462 at the supports Compute Mequiv by dividing the required design moment by Cb

Mequiv = 462 / 1.67 = 277 kip-ft Enter charts with unbraced length equal to 15 feet and proceed upward to 277 kip-ft. Any beam listed above and to the right of the point satisfies the design moment. AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 112

BEAM AND GIRDER DESIGN

The lightest section satisfying the criteria of a design moment of 277 kip-ft at an unbraced length of 15 feet and φbMp greater than 462 kip-ft is a W21×62. The design moment for a W21×62 with an unbraced length of 15 feet is 406 kip-ft and φbMp is 540 kip-ft. Since (φbMn = 406 kip-ft) > (Mequiv = 277 kip-ft) and (φbMp = 540 kip-ft) > (Mu = 462 kip-ft), a W21×62 is o.k. A 21-in. nominal depth beam spanning 60 feet should be checked for deflection since the span/depth ratio exceeds 30.

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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4 - 114

BEAM AND GIRDER DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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BEAM AND GIRDER DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 117

BEAM AND GIRDER DESIGN 4 - 118

W3 x3

3x3 W

0x2

W4 0x3

W44

x26

0x2

W4 61

0x2

4x2

79 x2

0x1

0x2

0x1

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

92 W4

W21x201

35 x2

0x2

6x1

8 25 8x W1

W18x234

x26

0x2 30

W27x178

29 x2 24 W

24 3 28 8x W1

1 31 8x W1

W40

W4 W

W40x183

W40x199

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 119

W 24 x4 08

W4 0x2 97 W 27 x3 68

W 30 x3 26

W 24 x3 35

3x2

x2 58

W 24 x2 50 W

x2 35

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 120

BEAM AND GIRDER DESIGN

W3 11 W2

4x 9

x169

W33

x183

W18x211

x17

W40

0x2

W40x

W 24

167

W21x182

92 W 24 x2 07

W36 x170

W2 7x 19

W40 x149

W3 0x1 16

W 58

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 121

W2 79

W36

7x2

4x2

W2 x245 W

W2 4x 25 0

W3 0x1 91 W2 4x 22

W36 x210

W 24 x2 07

W 21 x2 01

W 24 x1 92

92 W

7x1

W 24 x1 76

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 122

BEAM AND GIRDER DESIGN

W30x1 32

W1 15

17 5

W 3 3 x1 3 0

W30x90 W24x103

W27 x94 W 36 x1 60

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 123

W21 x20 1

W 36 x1 70

8x 21 1

W1 8x1

W 33 x1 69

W1 8x1 75 W21 x18 2

W1 8x1 58 W 36 x1 60

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 124

BEAM AND GIRDER DESIGN

W14x132

W30 x90 W27

x90

x94

W30

W12x120

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 125

W1 8x 78 5 17 W27x1

W1 8x 15 8

W24x

117

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 126

BEAM AND GIRDER DESIGN

W x1 20

W30x9

W12x106

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 127

W 14 x1 32

W 12 x1 20

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

4 - 128

BEAM AND GIRDER DESIGN

W12x96

W 12 x9 6

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 129

W 12 x1 20

W 12 x1 06

W 12 x9 6

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BEAM AND GIRDER DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 131

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BEAM AND GIRDER DESIGN

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp

4 - 133

W 10 x6 8

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