Metal building roof systems by IMCA

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER METAL BUILDING FRAMING

METAL BUILDING ROOF SYSTEMS Presented by Thomas M. Murray, Ph.D., P.E. Department of Civil and Environmental Engineering Virginia Tech, Blacksburg, Virginia thmurray@vt.edu X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER 06 March 2008 1

ROOF PANELS

METAL BUILDING FRAMING

Sheet to sheet fastener

Purlin

Sheet to structural fastener

Eave strut Roof panel

Girt Ridge

Wall panel

Anti-roll clip

Z - purlin

(a) Through-fastened panel

Standing seam clip

Clip fastener

Rigid frame

Z - purlin 3

(b) Standing seam panel

Presented by Thomas M. Murray, PhD1, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

ROOF PANELS

STANDING SEAM CLIPS

Pan Type Panel Profile

Rib Type Panel Profile

(a) Fixed Clip

(b) Sliding or Two-Piece Clip

ANTI-ROLL CLIPS

LECTURE OUTLINE • • • •

Presented by Thomas M. Murray, PhD2, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

Structural Behavior of C - and Z - Purlins Specific AISI Design Methods for Purlins Continuous Purlin Design System Anchorage Requirements

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

C – Purlins STRUCTURAL BEHAVIOR OF C – and Z – PURLINS

Building rafter

An Overview 9

C – Purlins

C – Purlins Resultant Applied Force

Resultant Applied Force

Anchorage Force

+ Shear Center

Shear Center

e C-purlins tend to twist because applied force does not act through the shear center. 11

Presented by Thomas M. Murray, PhD3, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

Resulting Torque = Force x e An anchorage system must be provided to resist this torque. 12

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Z - Purlins

Z - Purlins y

Resultant Applied Force b x2

Building rafter θ θp p

S.C.

Principal Axes

Z - Purlins

Torque is induced because load does not pass through the search center.

b x2

θp x

d y2

S.C. t

Location of resultant force, e, is not easily determined.

Presented by Thomas M. Murray, PhD4, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

b x2

θ θp p

d y2

Unless restrained, the Z – Purlin deflects in the principal axes directions, e.g. x2 and y2 -directions.

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Z - Purlins W

Z - Purlins

W(Ixy/Ix) (1) twisting of the Z-purlin

For constrained bending and the load acting through the shear center, there is a force W(Ixy/Ix) which must be resisted.

The combined effects of applied force eccentricity and non-principal axes bending cause

y x

W(Ixy/Ix)

(2) need for an anchorage system

Attachment to roof panels causes partially constrained bending and a system effect.

Z - Purlins W

C- and Z – Purlins

Ixy = product of inertia

Industry Practice •Constrained Bending is Assumed for Calculation of Stresses.

= Σ Ixy + Σ Adxdy y x

Ix = moment of inertia about x-axis

• Stresses are Calculated for Bending About the X-axis using fb = Mx y / Ix

W(Ixy/Ix)

• AISI Specification Provisions are used to Determine LRFD Strength or ASD Capacity 19

Presented by Thomas M. Murray, PhD5, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Definitions

Negative Moment w

Moment which causes compression in the bottom flange of a purlin.

M M

Positive Moment Moment which causes tension in the bottom flange of a purlin.

M(+)

M(-)

Note: Moment diagram is drawn on the tension side. 21

AISI Specification and Commentary

SPECIFIC AISI DESIGN METHODS FOR C – and Z – PURLINS

A Brief Overview

Presented by Thomas M. Murray, PhD6, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Combined LRFD and ASD

Sheathing and Purlin Provisions

LRFD Design Flexural Strength:

• Through Fastened Panels

φbRn = 0.9 Rn

• Standing Seam Panels

ASD Allowable Flexural Strength

• Gravity Loading

Ra = Rn/Ω Ω = Rn/1.67

• Uplift Loading

where Rn = Nominal Strength 25

Through Fastened Panels

Through Fastened Panels Gravity Loading

Sheet to sheet fastener

• Constrained Bending

Sheet to structural fastener

• AISI Provisions for Yielding, Local Buckling, and Lateral-Torsional Buckling.

Z - purlin

Presented by Thomas M. Murray, PhD7, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Through Fastened Panels

Through Fastened Panels Uplift Loading R-Factor Method

Uplift Loading

Nominal Strength:

• Constrained Bending

Mn = R Se Fy

• AISI Provisions for Yielding and Local Buckling

where Se = effective section modulus

• AISI R-Factor Method for flexuraltorsional and nonlinear distortional behavior.

Fy = material yield stress R = reduction factor 29

Through Fastened Panels

Uplift Loading R-Factor Method

R = reduction factor

TABLE C3.1.3-1 Simple Span C- or Z-Section R Values

= 0.6 for continuous C-purlins

Depth Range, in. (mm) d < 6.5 (165) 6.5 (165) < d < 8.5 (216) 8.5 (216) < d < 11.5 (292) 8.5 (216) < d < 11.5 (292)

= 0.7 for continuous Z-purlins Values determined experimentally. 31

Presented by Thomas M. Murray, PhD8, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

Profile C or Z C or Z Z C

R 0.70 0.65 0.50 0.40 32

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Through Fastened Panels

Uplift Loading R-Factor Method

• R-values were determined from tests of purlin systems without intermediate lateral restraints.

LRFD Design Strength:

• Reduction factors apply only to systems within limits of testing matrix, which is included in the Specification.

ASD Allowable Strength

φbMn = 0.9 Mn = 0.9 RSeFy

Ma = Mn/Ω Ω = RSeFy/1.67 where Se = effective section modulus 33

Through Fastened Panels

Standing Seam Panels

Uplift Loading R-Factor Method Limitations: Does NOT apply to (1) to a negative moment region between an inflection point and a support

Applies

Standing seam clip

Clip fastener Z - purlin

Does not apply

(2) to cantilevers. 35

Presented by Thomas M. Murray, PhD9, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

(a) Fixed clamp

(b) Sliding or two piece clip

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Standing Seam Panels

• Panel drape and clip friction provide some lateral restraint. • Degree of restraint depends on details of standing seam system. • Restraint varies from ~40% to near 100% of through-fastened systems.

Sheathing

• Mathematical procedures are not available for determining degree of restraint. 37

Standing Seam Panels

AISI Permitted Design Procedures:

A. Design purlins as unbraced between lateral restraints using lateral-torsional and distortional buckling provisions.

B. AISI TS-8-02 Base Test Method for Purlins Supporting a Standing Seam Roof System

Method ignores clip friction and hugging or drape effects of the standing seam panel. This approach is very conservative for systems without intermediate lateral restraints. 39

Presented by Thomas M. Murray, PhD10, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

The Base Test Method uses the results from two purlin line, simple span tests to determine the gravity loading positive moment strength or the uplift loading negative moment strength of continuous systems. 40

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

The Base Test Method

AISI Base Test Procedure

a) Conduct six single span, two purlin line tests.

A set of six tests is required for each combination of panel profile, purlin depth, and clip type.

b) Three tests are to use the thinnest purlin and three tests to use the thickest purlin in the inventory. c) Develop the R-factor relationship from the test results.

A procedure is available to significantly reduce the number of tests when several clip heights or types are used by the manufacturer. The tests are conducted in a vacuum chamber.

The Base Test Method

Standing seam panels Support beam

Eave angle

Ridge angle

Purlins

Vacuum Chamber 43

Presented by Thomas M. Murray, PhD11, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

The Base Test Method

AISI Test Procedure Procedure

AISI Procedure Procedure 100

M ts Rt = Mnt

Moment reduction factor R (%)

The Reduction Factor for each test is ≤ 1.0

where Mts = maximum moment from test Mnt = fully constrained flexural strength using measured dimensions and yield stress

90 80

Thinnest

Thickest

70 60 50

R-Factor Relationship

40 30 20 10 0 50

The Base Test Method

110 130 150 170 190 210 Nominal moment strength (K - in)

230

250 46

The Base Test Method

AISI Procedure Procedure

AISI Base Test Procedure

Moment reduction factor R (%)

100

The R-Factor relationship is a straight line, one standard deviation below the mean of the test results.

90 80 70 60 50

Possible Slope

R=(

R t ,max − R t ,min )( M n − M nt ,min ) + R t ,min M nt ,max - M nt ,min

20 10 0 50

110 130 150 170 190 210 Nominal moment strength (K - in)

230

250

Presented by Thomas M. Murray, PhD12, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

The Base Test Method

AISI Base Test Procedure

R=(

AISI Base Test Procedure The gravity loading positive moment region or uplift loading negative moment region nominal strength is then

R t ,max − R t ,min )(M n − M nt ,min ) + R t ,min M nt ,max - M nt ,min

Rt,max and Rt,min = mean minus one standard deviation of the three test results

Mn =RSeFy For LRFD φ = 0.90

Mn = SeFy= for the section for which R is being determined Mnt,min and Mnt,max = average tested flexural strengths

For ASD Ω = 1.67

The Base Test Method

The Base Test Method Example Results

Note: R can be greater for uplift loading.

Sheathing

(a) Gravity loading

Sheathing

(b) U plift loading

Gravity loading tends to increase rotation. Uplift loading tends to decrease rotation. Also, for uplift, torsional restraint is provided by the clip. 51

Presented by Thomas M. Murray, PhD13, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

Moment reduction factor R (%)

100 90 80 70 60 50 40 30

Nominal Strength Range

20 10 0 50

110 130 150 170 190 210 Nominal moment strength (K - in)

230

250 52

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design ww

CONTINUOUS PURLIN LINE DESIGN M(+)

M(-)

Lapped Purlins B u ild in g ra fte r

Continuous Purlin Line Design

Typical Design and Analysis Assumptions

• Constrained Bending

• An Inflection Point is a Brace Location

• Full Lateral Support Provided by Through Fastened Panels

• Use of Vertical Slotted Holes in Laps does not Effect Strength

• Partial Lateral Restraint Provided by Standing Seam Roof Panels

• Critical Location for Checking Combined Bending and Shear is Immediately Outside the Lap

• Continuous Purlin Line is Considered Prismatic or Non-Prismatic

Are these assumptions valid? 55

Presented by Thomas M. Murray, PhD14, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design • Constrained Bending Constrained bending implies that the purlin will deflect only in the plane parallel to the web. Obviously, not true, but universally used. Even implied in the AISI Specification Section C3.1.2 “Z-section bent about the centroidal axis perpendicular to the web …”

Continuous Purlin Line Design • Full Lateral Support Provided by Through Fastened Panels This assumption implies that there will be no lateral movement of the purlin. Again, obviously not true, but universally accepted. Sheathing

Continuous Purlin Line Design

• Partial Lateral Support Provided by Standing Seam Panels

• Partial Lateral Support Provided by Standing Seam Panels Cont.

This assumption implies that there will be some lateral movement of the purlin.

Use of lateral-torsional/distortional buckling equations is very conservative for roof systems without intermediate braces.

Lateral restraint comes from clip friction or panel drape/hugging. AISI Specification allows use of lateraltorsional/distorsional buckling equations or the Base Test Method 59

Presented by Thomas M. Murray, PhD15, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

R-values are 0.12 - 0.20 from L-T-B analyses, whereas the Base Test Method gives R-values of 0.40 - 0.95. 60

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design

• Continuous Purlin Line is Considered Prismatic or Non-Prismatic

• Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont.

One of two assumptions are commonly used for design:

For Gravity Loading:

1) The purlin line is prismatic, that is, a constant moment of inertia is assumed. 2) The purlin line is non-prismatic, that is, the moment of inertia within the lap is taken as the sum of the moments of inertia of the two 61 purlins.

Continuous Purlin Line Design

The Prismatic assumption results in larger positive moments and smaller negative moments. w

M(+)

M(-)

Continuous Purlin Line Design

• Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont.

For Gravity Loading:

The Non- Prismatic assumption results in larger negative moments and smaller positive moments. w

The Prismatic assumption is more conservative if the positive moment region controls The Non-Prismatic assumption is more conservative if the negative moment region controls

M(+)

M(-)

Presented by Thomas M. Murray, PhD16, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design

• Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont.

For Uplift Loading:

Two studies have shown that the Non-Prismatic assumption is more correct.

The reverse of gravity loading occurs. Fact: Purlins are not continuously connected in the lap and full continuity is not achieved. Therefore, which assumption is correct???????

Study 1: 24 Through-Fastened Tests (3 two-span and 21 three-span; 10 organizations) Analyzed using the non-prismatic assumption.

Continuous Purlin Line Design • Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont.

R = experimental / predicted

Conclusion from Study 1:

Combined Bending and Shear Failures Avg. R = 0.93 Range 0.81 – 1.06

Prismatic assumption decreases calculated moment for combined bending & shear, thus results become more unconservative.

Positive Moment Failures R = 0.93 and 0.94

(⇓ ⇓ R = experimental/predicted ⇑)

Note: R < 1.0 is unconservative 67

Presented by Thomas M. Murray, PhD17, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

For positive moment failures, the R-values 68 become closer to 1.0.

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design • Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont.

Continuous Purlin Line Design • Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont. I. P. 6" 6"

Study 2: 6"

7 Two- and Three-Span Tests 3 Through-Fastened 4 Standing Seam Analyzed using the non-prismatic assumption. Strain gages installed on the tension flange at and near the theoretical inflection point of an exterior 69 span.

Continuous Purlin Line Design

Inflection Point

FAR PURLIN 6

7 8 9 10

STRAIN GAGE POSITIONS

2 3 4

STRAIN GAGE POSITIONS

NEAR PURLIN 6" 6" INTERIOR SUPPORT

EXTERIOR SUPPORT

TEST BAY

Continuous Purlin Line Design

Theoretical inflection point 300

Load (lb/ft)

250

6 Position

• Continuous Purlin Line is Considered Prismatic or Non-Prismatic Cont.

200

CONCLUSION

150 100

Continuous purlin lines should be analyzed using the non-prismatic assumption.

50 0 -300

-200

-100

100 200 Strain (µε)

300

400

500 71

Presented by Thomas M. Murray, PhD18, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design • An Inflection Point is a Brace Point Location

Continuous Purlin Line Design • An Inflection Point is a Brace Location Traditionally considered a brace point. AISC says not so for H-Shapes (both lateral and torsional braces may be required at an I.P.) 2007 AISI Specification is silent but uses Cb from AISC Specification which follows AISC.

I.P.

End of Lap 73

Continuous Purlin Line Design

Center for Cold-Formed Steel Structures, Bulletin, Vol. 1, No. 2, August 1992, says I.P. is a 74 brace point and Cb =1.75.

Continuous Purlin Line Design

• An Inflection Point is a Brace Location

AISI Design Guide says I.P. is not a brace point. Design examples assume a cantilever from the end of the lap to the I.P. with Cb= 1.0.

Purlin movement at an I.P. was measured at Virginia Tech:

Three span setup with instrumentation in exterior bay.

Which is correct??????? 75

Presented by Thomas M. Murray, PhD19, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

I.P. 76

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design •An Inflection Point is a Brace Location

Continuous Purlin Line Design •An Inflection Point is a Brace Location 350

Through Fastened Panel

300

Load (plf)

250

Potentiometers

200 150 100 50

Positive Spread Outward

0 -0.100

-0.050

0.000 Spread (in.)

0.050

Continuous Purlin Line Design • An Inflection Point is a Brace Location

Results from Testing at VT:

Strength Comparisons of 7 test results assuming:

a) Lateral movement occurs at an I.P. b) I.P. movement is much less than other locations.

a) I.P. is not a brace point.

c) Movement on both sides in same direction.

c) Fully braced between end of lap and I.P.

b) I.P. is a brace point.

d) Double curvature did not occur. e) C-purlins move more than Z-purlins.

Presented by Thomas M. Murray, PhD20, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design

• An Inflection Point is a Brace Location

a) I.P. is not a brace point.

Can fully braced between end of lap and I.P. be justified within the AISI Specification?

Avg. Exp./Predicted = 1.056 Conservative

Probably “yes”, since Specification is silent on the issue.

(b) I.P. is a brace point. Avg. Exp./Predicted = 1.037 Conservative (c)Fully braced between end of lap and I.P. Avg. Exp./Predicted = 1.033

Conservative 81

Continuous Purlin Line Design

Note: Section 3.1.3 Beams Having One Flange Through-Fastened to Deck or Sheathing does not apply to “a continuous beam for the region between inflection points adjacent to a 82 support”.

Continuous Purlin Line Design

• Use of Vertical Slotted Holes in Laps does not Effect Strength

Vertical slotted holes in purlin webs at the ends of lap splices are used to facilitate erection.

The data from over 50 multiple span continuous purlin line test results does not show any effect. Vertical slotted holes are permitted in Specification with some limitations.

Presented by Thomas M. Murray, PhD21, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Continuous Purlin Line Design • Critical Location for Checking Combined Bending and Shear is Immediately Outside the Lap

Where should combined bending and shear be checked in a lapped purlin line? Within the lap? At the bolt line? Outside the lap? 85

System Anchorage SYSTEM ANCHORAGE REQUIREMENTS

PL • Z - Purlins

• Roof deck provides full or partial lateral restraint.

• An anchorage device removes force, PL, from the diaphragm. 87

Presented by Thomas M. Murray, PhD22, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

System Anchorage

Gravity Loading on Z-Purlins

Z-Purlins y

θp x

Initial position

xp θ

(a) Axes

(b) Unrestrained movement

System Anchorage

Providing Anchorage • Lateral Restraint at Discrete Points

Z-Purlins Wcosθ Wsinθ

Lateral Discrete Braces Remove Force from System

Sheathing Supports Purlin

(d) Panel and anchorage restraints 91

Presented by Thomas M. Murray, PhD23, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Providing Anchorage

• External Restraints

• Bracing Details that are not Recommended

pB rac e

Str ap

a Str

Br ace

– Must Anchor Interior Restraints Externally

C10x15.3 Horizontal

System Effect

2007 AISI Provisions

• A System of Purlins has Inherent Stiffness • Which is Called the “System Effect” ” • The System Effect Complicates Analysis of Roof Systems

2007 AISI Specification D6 Metal Roof and Wall Systems D6.3 Roof System Bracing and Anchorage • D6.3.1 Anchorage of Bracing • D6.3.2 Alternate Lateral and Stability Bracing – Torsional Braces

Presented by Thomas M. Murray, PhD24, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

Experimental Verification

AISI Analysis Methods

Testing Conducted at Virginia Tech

• Stiffness Models – Shell Finite Element Model – Frame Element Stiffness Model

• Computational Solutions – – – –

Component Stiffness Method Matrix Solution Method Manual Specification Method Simplified Solution Method

AISI Analysis Methods

AISI Manual Calculation Method Four Computational Steps Required:

Stiffness Models

– Determine Stiffness of the System – Determine Force Introduced into System by Each Purlin, Pi – Distribute Forces According to Stiffness – Evaluate Anchor Effectiveness

Shell Finite Element Model

Frame Element Model 99

Presented by Thomas M. Murray, PhD25, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

100

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

AISI Manual Calculation Method • Stiffness Model used to determine anchorage forces

AISI Manual Calculation Method Step 1 – Stiffness of the System – Anchor Stiffness, Ka – Inherent Stiffness of System • Connection of Purlin to Frame Line • Connection of Purlin to Sheathing ∆

∆

K sys =

C5 ELt 2 ⋅ Np 1000 d2

K total (i ) =

∑ (K

eff i , j

)+ K

sys

j =1 101

AISI Manual Calculation Method Step 2 - Force Introduced to System, Pi

– Portion of Force Absorbed by System – Forces Distributed to Anchors

• Down Slope Force • Eccentrically Applied Load (normal component) • Load Oblique to Principal Axes wLcosθ

Pi = C1 ⋅ W pi

 C 2 I xy L  (m + 0.25 b )t  α ⋅ cos θ − C 4 ⋅ sin θ  ⋅  ⋅ + C3 ⋅  d2   1000 I x d 

wLsinθ

AISI Manual Calculation Method Step 3 – Distribute Forces According to Stiffness

– Combined Effects

102

x2 y 2

103

Presented by Thomas M. Murray, PhD26, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

Purlin “i” Anchor “j”

 d pi, j  1  K eff (i , j ) =  +  K a C 6 ⋅ LAp E    Anchor Panel Flexibility Flexibility

−1

Inverse Yields Stiffness

104

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

AISI Manual Calculation Method Step 4 – Evaluate Anchor Effectiveness

• Simplified Solution Procedure

– Stiffness of System for Stability

– Simplified Form of Main Specification Procedure – Conservatively Neglects System Effect – Conservative Stiffness Check – Assumes Forces Evenly Distributed

• Stiffness (displacement) at Line of Anchorage • Diaphragm Displacement Between Lines of Anchorage Np

20 ⋅ K req =

1 φ

AISI Simplified Method

∑P

i=1

≤ K total

105

AISI Simplified Method

106

AISI Simplified Method

• Simplified Solution Procedure

– Find Anchorage Force

– Check Minimum Stiffness – Compare to Ka

 C 2 I xy L W (m + 0.25b)t   cosθ − C 4 ⋅ sinθ  s PL − s = C1 ⋅  ⋅ + C3 ⋅  d2  1000 I x d  N a 

107

Presented by Thomas M. Murray, PhD27, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

K a _ req=

20 ⋅ C6 ⋅ LA pEPL − s φC6 ⋅ LA pEd − 20PL − s S(Np − Na )

108

METAL BUILDING ROOF SYSTEMS

X SIMPOSIO-INTERNACIONAL DE ESTRUCTURASDE ACER

New AISI Design Guide Table of Contents • • • •

Introduction Design Methods for Purlins Continuous Purlin Line Design System Anchorage Requirements

Thank You!!

• References

To be Published by AISI Late 2009. 109

Presented by Thomas M. Murray, PhD28, P.E. Virginia Tech, Blacksburg, VA 06 March 2009

110