UNIVERSITI TUNKU ABDUL RAHMAN FACULTY OF ENGINEERING AND SCIENCE DEPARTMENT OF ARCHITECTURE AND SUSTAINABLE DEVELOPMENT
UEBA2823 BUILDING STRUCTURE SYSTEM SEMESTER MAY 2019
ASSIGNMENT : A REPORT OF ANALYSIS OF EACH STRUCTURAL MEMBERS OF A BUILDING
GROUP MEMBERS :
LECTURER NAME
LAU CHI YING LIM CHEN HEE NY TZE WAY OW KAR YONG SHERLYNNA LIANG JING XIN
: IR. DR. LOW KAW SAI
SUBMISSION DATE : 7 AUGUST 2019
1703203 1804671 1803893 1703503 1703522
Table of contents 1.0 Abstract 2.0 Acknowledgement 3.0 Introduction 4.0 Truss 4.1 Application 4.1.1 Use of Trusses 4.1.1.1 Roof of Factory Shade 4.1.1.2 Ware House 4.1.1.3 Railway Platform 4.1.1.4 Garage Shed 4.1.1.5 Transmission Towers 4.1.1.6 Crane Truss 4.1.1.7 Bridge Truss 4.1.1.8 Sport Stadium Truss 4.2 Role 4.2.1 Types of Trusses 4.2.1.1 Pratt Truss 4.2.1.2 K-Truss 4.2.1.3 Howe Truss 4.2.1.4 Warren Truss 4.2.1.5 Bowstring Truss 4.2.1.6 King Post Truss 4.2.1.7 Queen Post Truss 4.3Function 4.4 Main possible modes of failure 4.4.1 Long span 4.4.2 Broken Connections 4.4.3 Wind load 4.4.4 Material 4.4.5 Buckling 4.4.6 Fatigue Cracking 4.4.7 Seismic Forces 4.4.8 Torsion 4.5 Suggestions for remedial measure 4.5.1 Determinacy 4.5.2 Member forces 4.5.2.1 Method of Joints 4.5.2.2 Method of Sections 4.5.2.3 Method of Force Resolutions 4.6 Case Study: Truss Pedestrian Bridge, Greece 4.6.1 Variations in Truss Member Forces 4.6.2 Truss Lateral Buckling 4.6.3 Methods of Providing Resistance to Truss Lateral Buckling
5.0 Cable and Pulley system 5.1 Application 5.1.1 Cable Net Structure 5.1.2 Suspension Bridge 5.1.3 Cable-stayed Bridge 5.1.4 Cable Truss 5.1.5 Pretensioned Cable Beam 5.1.6 Tensioned Straight Cable 5.1.7 Tensegric Shell 5.1.8 Elevator 5.1.9 Crane 5.2 Role and Function 5.2.1 Suspension Bridge 5.2.2 Cable-stayed Bridge 5.2.3 Cable Net Structure 5.2.4 Pretensioned Cable Beam 5.2.5 Tensegic Shell 5.2.6 Elevator 5.2.7 Crane 5.3 Main Possible Modes of Failure 5.3.1 Chose Wrong Cable Diameter 5.3.2 Chose Wrong Cable Class 5.3.3 Failure of Connector 5.3.4 Lack of Information 5.3.5 Damage of Cable 5.4 Suggestions for Remedial Measure 5.4.1 Choose the Cable Dimension Wisely 5.4.2 Maintenance and Checking Frequently on Cable 5.4.3 Communicate to The Manufacture Clearly 5.4.4 Choose High Quality of Cables and Connectors 5.4.5 ​Choose The Right Type of Cables 5.4.6 Maintenance and Check The Pulley System 5.4.7 Decrease The Speed of The Pulley System
6.0 Beam 6.1 Application 6.1.1 Based on Geometry a) Straight beam b) Curved beam c) Tapered beam 6.1.2 Based on Support Conditions 6.1.2.1 Simply Supported Beam 6.1.2.2 Fixed Support 6.1.2.3 Overhanging Beam 6.1.2.4 Continuous Beam
6.1.2.5 Cantilever Beam 6.1.2.6 Trussed Beam 6.2 Role 6.2.1 Based on Construction Materials and Cross-Section Shapes 6.2.2 Type of beams a) I Beam b) T Beam c) C Beam d) L Beam e) Rectangle Beam 6.2.3 Wood Beam 6.2.3.1 Glulam As Structural Element 6.2.4 Concrete Beam 6.2.5 Based on Method of Construction (a) Cast In-situ Concrete Beam (b) Precast Concrete Beam (c) Prestressed Concrete Beam 6.3 Function 6.3.1 One Way Beam System 6.3.2 Two Way Beam System 6.3.3 Three Way Beam System 6.4 Main possible modes of failure 6.4.1 ​Shear failure and flexural (bending) failure 6.5 Suggestions for remedial measure 6.5.1 Shear force diagram and bending moment diagram 6.5.2 Bending stresses in beams 7.0 Column 7.1 Application 7.1.1 Used of Column 7.1.1.1 Tower 7.1.1.2 High Rise Building 7.1.1.3 Bridge 7.1.1.4 Historical Buildings 7.1.1.5 Residential Houses 7.2 Role 7.2.1 Types of Columns 7.2.1.1 ​By Types of Reinforcement 1) Tied Column 2) Spiral Column 3) Composite Column 7.2.1.2 By Types of Loading 1) Axially Loaded Column 2) Column with Uniaxial Eccentric Loading 3) Column with Biaxial Eccentric Loading 7.2.1.3 By Slenderness Ratio 1) Short Column
2) Long Column 7.2.1.4 By Shape 1) Square or Rectangular Column 2) Circular Column 3) L-Shape Column 4) T-shape Column 5) Shape of Steel Column 6) Shape of Composite Column 7.2.1.5 By Construction Materials 1) Reinforced Concrete Column 2) Steel Column 3) Timber Column 4) Brick Column 1) Block Column 7.3 Function 7.3.1 Orientation of Columns 7.3.2 Design of Column 7.4 Main possible modes of failure 7.4.1 Column Capacity 7.4.2 Axial Loading 7.4.3 Strain Distribution In The Main Reinforcement 7.4.4 Crack Pattern 7.4.5 Short Column Behavior 7.5 Suggestions for remedial measure 7.5.1 Ways to Eliminate Short Column Effect 1) Separate The Infill Wall 2) Reduce Shear Force 7.6 Case Study - ShangHai World Financial Center 8.0 Conclusion 9.0 References
1.0 ABSTRACT In a building construction, structure is a body or assemblage of bodies in space to form a system that able to support the loads safely to the ground without exceeding the stress allowed in the members. It is a system or subsystem which was holding the components of a certain system and transfers the load through the members of a structure to provide stability and durability of a building. The project is an integrated component and involves structural theory, force calculation and basic structural proposal, designed to allow the demonstration of knowledge and understanding of building structure. The aim is to analyse the application, role and functions of structural members in a building. In this project, we will discuss for each of the following structural members of a building. They are: Truss, Cable and Pulley system, Beam , and Column. Moreover, the emphasis on our discussion will be on the application, role and functions, an assessment on the main possible modes of failure and suggestions for remedial measures to prevent failures applicable to each of these structural members in a building.
2.0 ACKNOWLEDGEMENT The success and final outcome of this assignment required a lot of guidance and assistance from many people and we are extremely fortunate to have got this all along the completion of our assignment work. Whatever we have done is only due to such guidance and assistance and we would not forget to thank them. I respect and thank Ir Dr Low for giving us an opportunity to do this assignment work and providing us all support and guidance which made us complete the assignment on time. We are extremely grateful to him for providing such a nice support and guidance. We are really grateful because we managed to complete this assignment within the time given by Ir Dr Low. This assignment cannot be completed without the effort and co-operation from our group members. Group member’s Chen Hee, Chi Ying, Sherlynna, Kar Yong and Tze Way. Last but not least, we would like to extend our gratitude to each individual that has helped and assisted us to complete this research report which without your involvement, this report would be insufficient and unsatisfactory.
3.0 INTRODUCTION Structural engineering is the science and art of planning, designing, and constructing safe and economical structures that will serve their intended purposes. Structural analysis is an integral part of any structural engineering project, its function being the prediction of the performance of the proposed structure. The functions of structure systems are including: 1. Carries the load of a building The loads acting on the structure consists of dead and live loads. Dead loads are the load that cannot change over the time in structure and their values are certain and constant. For instance, the weights of the building materials and components of the structure (floor material and material of roof); and the weights of fixed service equipment (HVAC and plumbing). Live loads are the loads that are movable and their values are uncertain. For example, things that permanently attached (Furniture and tables) and environmental loads that are created naturally by the environment (wind, snow, seismic and lateral soil pressure). 2. Superposition principle This principle is about keeping the structure in static and dynamic equilibrium. 3. Transfers the load to contiguous structural components Transfer the load safely to the ground and to the foundation of a building. This is to ensure and maintain the strength of a building. In structural analysis, the values of the loads are used to carry out an analysis of the structure in order to determine the stresses or stress resultants in the members and the deflections at various points of the structure. The results of the analysis are used to determine whether or not the structure satisfies the safety and serviceability requirements of the design codes. If these requirements are satisfied, then the design drawings and construction specifications are prepared, and the construction phase begins.
4.0 TRUSS A truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints or nodes, resulting in either a compression or tension force. They are commonly used as bridge designs and roof truss for supporting roof, given their ability to efficiently span long distances.
Figure 4.1 : Members under axial forces in a simple truss 1 - Compression axial force2 tension axial force. (Source: https://www.steelconstruction.info/Trusses)
Figure 4.2: Standard roof truss glossary (Source: https://www.bestwaytoframe.com/roof-trusses)
4.1 APPLICATION Trusses are also used to carry heavy loads and are sometimes used as transfer structures. The most common use of trusses is in range of buildings and bridges, where there is a requirement for quite a long spans, such as in stadium cover, airport terminals and other leisure buildings. Trusses are used to support the roof, the floor and internal loading such as services and suspended ceilings, are easily provided. The main reasons for using trusses are: 1. LONG SPAN
Figure 4.3: AT & T Stadium built up by using large span steel truss (Source: http://stadiumdb.com/stadiums/usa/cowboys_stadium) ● ● ●
Trusses can support heavy loads due to it creates unobstructed, column-free spaces greater than 30 metres (100 feet) for a variety of functions. For example, the largest covered stadium can span about 204 metres which is 670 feet; A long span truss is considered when spanning more than 60 feet
2. LIGHT WEIGHT
Figure 4.4: Lightweight steel roof truss (Source: https://janesroofs.co.za/portfolio-posts/light-weight-steel-roof-trusses/) ● ● ● ●
Steel truss is lighter than wood truss and widely used in industry. It can be transported to site easily and less energy consumption. Minimum cost to meet building industrial demand. Termite-proof and rust-resistant
3. REDUCED DEFLECTION
Figure 4.5: To show the eigenfrequencies and eigenmodes of bridge when trucks passing over it。 (Source: https://www.comsol.com/blogs/modeling-a-pratt-truss-bridge/) ●
Truss’s dimensions design consideration, dimensions or materials can affect its ability to support loads
4. OPPORTUNITY TO SUPPORT CONSIDERABLE LOADS
Figure 4.6: Simplified representation of wind pressures acting on building (Source: https://www.researchgate.net/figure/Simplified-representation-of-wind-pressures-actin g-on-building_fig13_303880357) ●
Truss can support dead load, live load, wind load.
4.1.1 USED OF TRUSSES 4.1.1.1 ROOF OF FACTORY SHADE
Figure 4.7 (Source: https://www.indiamart.com/proddetail/factory-shade-12746762112.html)
4.1.1.2 WARE HOUSE
Figure 4.8 (Source: https://singularityhub.com/2018/10/14/this-robotic-warehouse-fills-orders-in-five-minut es-and-fits-in-city-centers/)
4.1.3 RAILWAY PLATFORM
Figure 4.9 (Source: https://en.wikipedia.org/wiki/Brighton_railway_station)
4.1.4 GARAGE SHED
Figure 4.10 (Source: https://www.pinterest.com/pin/140456082098173879/?lp=true)
4.1.5 TRANSMISSION TOWERS
Figure 4.11 (Source: https://www.abc.net.au/news/2017-09-06/aemo-forecast-mixed-blackout-risk-for-sout h-australia-victoria/8875798 )
4.1.6 CRANE TRUSS
Figure 4.12 (Source: http://haiphongport.com.vn/596/print-article.html )
4.1.7 BRIDGE TRUSS
Figure 4.13 (Source: https://www.canambridges.com/products/steel-bridges/steel-standard-truss-bridges/)
4.1.8 SPORT STADIUM TRUSS
Figure 4.14 (Source: https://www.pinterest.com/pin/471611392211299321/?lp=true)
4.2 ROLE Trusses derive their strength from the triangle. The simplest of plane polygons, a triangle is unique in that it is defined by the length of its sides. That is, one and only one triangle can be drawn if the length of all three sides is given. Unique properties of a triangular object allow trusses to span across longer distances and a perfect trusses mean a structure that is made of members just adequate to keep it in equilibrium, when loaded without changing its shape. There are three types of trusses which are: 1. Perfect trusses (m=2j-3) 2. Deficient trusses (m<2j-3) 3. Redundant trusses (m>2j-3) Which m=members, j=joints 4.2.1 TYPES OF TRUSSES There are various types of truss are used in the industry and different of them have their identical characteristics such as function and load transfer. Below are examples of different types of truss:
Figure 4.15 : Some examples of roof trusses (Source: https://www.swedishwood.com/about_wood/choosing-wood/wood-and-wood-based-products /structural-elements/â&#x20AC;&#x2039;)
BRIDGE 4.2.1.1 PRATT TRUSS ● ● ● ● ●
Pratt truss is a very common type but has many variations The fundamental recognizing features are the diagonal web members which form a V-shape as contrast to howe truss bridge has an A-shape. It is regularly utilised for resisting railways. It is verticals functioned as compression members and diagonals functioned as tension members. The Pratt truss required more iron than Howe truss which is expensive.
Figure 4.16: Gatton Railway Bridge, Queensland, Australia
Figure 4.17: Forces in Pratt truss 4.2.1.2 K-TRUSS ● ● ● ●
The length of members undergoing compression is reduced. This reduction in length enables components of bridges to endure the compressional force. The design is complicated and it is considered to be one of the hardest bridges to build. The subdivided beams going outwards away from the centre of the span, generating a rhombus shape in the middle point of the span/ The subdivided beams going inward which towards the centre of the span and creating the letter ‘X’.
Figure 4.18 : Compressive members are shown as green and tension as red. （Source: https://shaancivilsimplified.blogspot.com/2017/02/k-truss-designs-bridge-structures.html)
4.2.1.3 HOWE TRUSS ● ● ●
Howe truss became very popular and was considered one of the best designs for railroad bridges back in the day Wooden beams for the diagonal members, which were in compression. It used iron and later steel for the vertical members, which were in tension.
Figure 4.19; Compressive members are shown as green and tension as red. (Source: https://www.quora.com/Which-bridge-is-stronger-the-Howe-truss-or-the-Warren-truss -1) 4.2.1.4 WARREN TRUSS ● ● ●
It uses equilateral triangles to spread out the loads on the bridges. The equilateral triangles minimize the forces to only compression and tension. The bridges are often used with verticals to reduce the panel size.
Figure 4.20: Compressive members are shown as green and tension as red. (Source:https://www.garrettsbridges.com/design/warren-truss/)
BUILDING 4.2.1.6 BOWSTRING TRUSS ● ●
First used for arched truss bridges known as tied-arch bridges It can be used to hold up the curved roofs and other military buildings. Many variations exist in the arrangements of the members connecting the nodes of the upper arc with those of the lower, straight sequence of members, from nearly isosceles triangles to variant of Pratt truss
Figure 4.21: Compressive members are shown as yellow and tension as purple. (Source: https://www.slideshare.net/gertrudeleeys/building-structure-project-1)
4.2.1.7 KING POST TRUSS ● ●
It is used for simple short-span bridges. Fewest number of truss members, two diagonal members, kingpost braces, that meet at the apex of the truss, one horizontal beam and the king post which connect the apex to the horizontal beam below.
Figure 4.22: Compressive members are shown as blue and tension as red. (Source: https://commons.wikimedia.org/wiki/File:King_post_truss.svg)
4.2.1.8 QUEEN POST TRUSS ● ● ●
It is similar to a king post truss in that outer supports are angled towards the center of the structure. It is simpler, lighter and requires less wood It can span longer openings than a king post truss
● As compared to king post truss uses one central supporting post, while queen post truss uses two.
Figure 4.23: Traditional Queen Post Truss (Source: https://www.homestratosphere.com/parts-of-roof-truss/)
4.3 FUNCTION The main two functions what trusses are widely used are to carry the roof load and to provide horizontal stability. â&#x20AC;&#x2039;Trusses. (n.d.) TYPICAL TRUSS BUILDING ARRANGEMENT
Lateral stability provided by portal trusses
Building braced in both directions.
Longitudinal stability provided by transverse wind girder and vertical cross bracing in blue color.
Lateral stability provided by longitudinal wind girder and vertical bracings in the gables in blue color.
No longitudinal wind girder.
Longitudinal stability provided by transverse wind girder and vertical bracings in green color.
At the left side, a series of portal trusses provide the lateral stability of the structure while the connections between the truss and the columns provide resistance to a global bending moment. Also the loads are applied to the column structure by purlins and side rails. At the right side, each truss and two columns between which it spans, constitute a simple structure;but does not resist the global bending moment at the connection between the truss and a column, and the bases of two columns are pinned. It is necessary bracing in both directions at the top level of the simple structure; It is achieved by means of a longitudinal wind girder which supports the transverse forces because of the wind on the side walls to the vertical bracing in the gable walls. A wind girder in the roof and vertical bracing in the elevations also provide longitudinal stability.
4.4 MAIN POSSIBLE MODES OF FAILURE Since the truss are all straight and in the same plane thus the force system acting at each joint is coplanar and concurrent. The stability of truss is not be contingent on whether it is statically determinate or indeterminate. The failure of truss structure can be defined as it is unstable structure which can be concluded as follows: 1. Unstable (b+r<2j) 2. Unstable (b+r>2j) 3. Stable (b+r=2j) BUILDING 4.4.1 LONG SPANS Long span trusses are 60' or greater in length. A long span truss can represent a greater risk to installers because the dimensions and weight of the truss itself can create instability, buckling and collapse of the truss if it is not handled, installed and braced properly. Long span trusses can be installed safely and efficiently but they require more detailed safety and handling measures than short span trusses. Avoid potential long span truss collapses and accidents by hiring a professional engineer to provide the temporary bracing plan and to supervise the erection process. 4.4.2 BROKEN CONNECTIONS
Figure 4.23: A set of parallel-chord wood trusses supporting a plywood floor deck. (Source: https://www.fireengineering.com/articles/2008/12/construction-concerns-truss-failure.htmlâ&#x20AC;&#x2039;) It used two pieces of lumber spliced together with gusset-plates to make the bottom chord. The bottom chord of the truss is in tension unless it is cantilever. The connector of the trusss will splice loosens because of the fire, corrosion, rot, or improper installation. As a result, the truss will become unstable and crumble due to the live and dead loads it supports.
4.4.3 WIND LOAD The primary mode of failure was at the truss connector plates caused by wind uplift forces which means wind flow pressures that create a strong lifting effect, much like the effect on airplane wings. Especially in the absence of other damage like torn shingles, broken tree limbs and detached siding that caused by strong winds.
Figure 4.24: Truss uplift illustration (Source: https://donan.com/article/what-goes-up-must-come-down-right-a-truss-uplift-discussion/â&#x20AC;&#x2039;)
4.4.4 MATERIAL Although timber trusses is cheaper than steel trusses, but timber trusses cannot stand up to the elements as well as steel trusses. It is because timber trusses are exposed to warping and bowing problems which can cause structural damage to the rest of the building and wood is also easily to rot and insect infestation which may cause lots of maintenance fee. Furthermore, wood trusses will get damaged in extreme weather conditions than steel trusses.
BRIDGE 4.4.5 BUCKLING Buckling is an unstably caused by the application of a force that cause failure of the member. Should an exceeding compressive force overcomes the resistance of the structure, it balances the bridge's strength so that the vertical members are weakened and collapsed as buckling occurs. Stressed further, the horizontal members may stretch to the point where they snap.
Figure 4.25: Buckling Bridge (Source: â&#x20AC;&#x2039;https://www.karamba3d.com/examples/moderate/buckling-bridge/â&#x20AC;&#x2039;) 4.4.6 FATIGUE CRACKING Resonance sets up standing waves that travel back and forth through the truss causing horizontal members to bend up and down. Friction weaken, crack and stretch until they break by heat. Because of the redundancy built into the truss design, one failed member will not cause a failure of the whole structure due to the remaining components withstand the stress; however, it does undermine the bridge structure. As repeated bending occurs at the nodes where the members meet, the gusset plates may crack, causing failure at the truss joints.
Figure 4.26: Example of fatigue crack (Source: https://www.researchgate.net/figure/Fatigue-cracking-in-the-floor-beam-web-caused-by-the-t ransverse-bending-deformation_fig20_290727498â&#x20AC;&#x2039;) 4.4.7 SEISMIC FORCES Truss bridge construction provide little resistance to seismic waves resulting from earthquakes or volcanic eruptions as they race through the ground, resulting in movement in three directions which are horizontal, vertical and side to side. Transportation engineers retrofit many older truss bridges in an attempt to make them more stable when seismic occur. This is a challenging task because the age of the bridges, and the construction methods applied at the period of their building varied for individual bridges. Rather than destroy structures and rebuild at a prohibitive cost, engineers must estimate each bridge on an individual basis.
4.4.8 TORSION Although truss bridge designs allow the wind to blow through the structure by offering little resistance due to the open areas between the members, high storm winds and hurricanes can produce torsion forces that twist the structure. Torsion is a deformation of the structure caused by the twisting of one end while the other remains motionless.
4.5 SUGGESTIONS FOR REMEDIAL MEASURE The first step is to calculate the failure load of the truss by using Eulerâ&#x20AC;&#x2122;s buckling equation which to estimate the bar forces at which each member will buckle (f_buckle. f_buckle. The formula is
In the real situation when calculate the load of the truss, we must consider that a member can buckle both in the plane of the truss(in-plane buckling) and out of the plane of the truss (out-of-plane buckling). F_buckle can be calculated for both in-plane buckling (f_buckle_in) and for out of plane buckling (f_buckle_out).
The member coordinate system used by RISA is shown at the right. The buckling forces for member 4 are:
4.5.1 DETERMINACY a) EXTERNAL ● ● ● ● ● ●
There will be 6 unknown values: 3 internal member forces and 3 reactions m + R → m + 3 in a simple truss And for every joint, 2 equilibriums can be written (Fx = 0 and Fy =0) – no rotation or moment at joint 2 j By comparing the total unknowns with total number of available equations, we can check the determinacy The determinacy of truss should be checked internally and externally The external determinacy is given by: R = 3 (provided that the support reactions have no lines of action that are either concurrent or parallel) If R > 3 Statically indeterminate (external) R = 3 Statically determinate (external) R < 3 Unstable truss system
b) INTERNAL ● ●
The internal determinacy is given by m = 2j – 3 (provided that the components of the truss do not form a collapsible mechanism) If m > 2j – 3 Statically indeterminate (internal) m = 2j – 3 Statically determinate (internal) m < 2j – 3 Unstable truss system
4.5.2 MEMBER FORCES There are some methods of calculating the member forces for the truss which are method of joints, method of sections and method of force resolution 4.5.2.1 METHOD OF JOINTS ● ● ● ●
Suitable to be used to determine all the member forces in the truss In this method, every joint will be analysed by drawing the Free Body Diagram, limiting the unknown values to TWO only. The selected joints must only consisted concurrent and coplanar forces Using the equilibrium of Fx = 0 and Fy =0, we can start and solve the problems
4.5.2.2 METHOD OF SECTIONS ● ● ● ●
When only some of the member forces need to be calculated, it is suitable to use this method. However, it can also be used to determine all the member forces in truss. The method of sections consists of cutting through the truss into two parts, provided that the unknown values are not more than three The unknown forces will be assumed to be either in tension or compression Three equilibriums (Fx = 0, Fy = 0, M = 0) will be used to solve the problems.
4.5.2.3 METHOD OF FORCE RESOLUTIONS ● ● ●
This is an extended version from the method of joints Every single joint is carefully analysed by considering not more than two unknowns at each joint. In this method, we do not have to write all the equations and calculations. All member forces are solved directly on the diagram.
4.5.3 LONG SPAN In order to prevent long span trusses buckling and collapse, there are some ways to solve this problem such as shorten the trusses as well as the distance between each truss. It can resists more dead and live load and is quite stable than long span. However, the technologies nowadays are becoming more and more advanced that can help to achieve long span trusses while keeping stable. For instance, portal frames are a type of structure frame that are characterised by a beam supported at either end by column. However, the joints between the beam and columns are ‘rigid’ so that the bending moment in the beam is transferred to the columns. The advantages of this truss is to reduce in sectional size and span large distance. 4.5.4 BROKEN CONNECTIONS The sagging of one truss will affect the progressive collapse of the adjacent trusses because of the eccentric load transferred to them by bracing and bridging. This bracing and bridging is installed as part of a truss-deck system for lateral stability, to transfer loads from one truss to another, and to keep the trusses from buckling and overturning under load. It is the way to solve this problem and sometimes this will not give firefighters much warning. The period between the first sign of impending collapse and collapse of building may not be long enough for evacuation even if the signs are recognized and action is taken.
4.5.5 WIND LOAD Sometimes the wind load impact to the roof is unable to avoid. However â&#x20AC;&#x2039;architects and engineers need to ensure a safe, sustainable, and cost-efficient design by utilizing wind engineering studies and taking into account â&#x20AC;&#x2039;building aerodynamics, especiallyâ&#x20AC;&#x2039; for the high rise building. There are numerous methods and softwares to calculate the wind load implications for building design in order to reduce the load impact on the structural system. 4.5.6 MATERIAL Long span trusses can be prefabricated in from various number of materials, such as steel, aluminium alloy, timber, reinforcement concrete and prestressed concrete. However, steel is often preferred because of its high strength and also it will not spread fire over its surface.
4.6 CASE STUDY: TRUSS PEDESTRIAN BRIDGE, GREECE
Figure 4.27 Truss Pedestrian Bridge, Greece (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.28: Truss with long top chord members (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.29:Force distribution for truss in (a) (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4. 30: Truss with tension members typically longer than compression members (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.31: Truss with tension members typically longer than compression members. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.32: Member symmetrical about the x and y axes (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf) a) Possible directions of member buckling when top chord is braced at each panel point. Use of a symmetrical member with equal stiffness about the x and y axes is appropriate.
Figure 4.33: Member stiffer about one axis than the other (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf) b) Possible directions of member buckling when top chord members may be made stiffer about one axis than the other to mitigate out-of-plane buckling tendencies.
Figure 4.34: Theoretical zero force members that provide buckling resistance to top chord. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.35 Steel Truss. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.36 Steel Truss. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
4.6.1 VARIATIONS IN TRUSS MEMBER FORCES
Figure 4.37 Tension and compression force on truss. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf) ● ● ● ●
Truss with all diagonals in compression and all interior verticals in tension. Use of cables in the truss shown in (a) Force distribution for new loading condition Instability in truss because vertical cannot provide required compressive force.
4.6.2 TRUSS LATERAL BUCKLING
Figure 4. 38: Truss before lateral buckling. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.39: Lateral buckling of truss. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
4.6.3 METHODS OF PROVIDING RESISTANCE TO TRUSS LATERAL BUCKLING
Figure 4.40: Planar truss with stiffened top chord to provide resistance to lateral buckling. (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.41: Three-dimensional truss: width of top plane provides resistance to lateral buckling (Source: https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdf)
Figure 4.42: Three-dimensional truss: sloped side members provide resistance to lateral buckling. (Source: â&#x20AC;&#x2039;https://www.sefindia.org/forum/files/truss_design_considerations_slides_108.pdfâ&#x20AC;&#x2039;)
5.0 Cable and Pulley System A pulley consists of a rope and a hub or "drum" in which there is a grooved wheel mounted with an axle. The pulley has been used in a wide range of applications in many circumstances and can be used to make a moving and lifting tasks easier. There are three basic types of pulleys, one that changes the direction of the force, one that changes the magnitude, and one that changes both the magnitude and direction.
a.) FIXED PULLEY ● ● ●
A fixed pulley is one in which the drum is stay at a single spot. While the force needed to move an object, there is no different than if you were lifting it by hand. The fixed pulley allows you to change the direction of the force needed to make more convenient while lifting or moving the object.
Figure 5.1: A fixed pulley changes the direction of the force required to move an object, (Source: https://www.groovylabinabox.com/groovy-pulleys/) b.) MOVABLE PULLEY ● ●
A movable pulley is one in which drum moves while u lift or move an object. There is no change in the direction of force needed, but the less force is needed to lift or move an object.
Figure 5.2: A movable pulley has a moveable axle and offers a mechanical advantage, requiring less force to move an object. (Source: https://www.groovylabinabox.com/groovy-pulleys/) c.) COMPOUND SYSTEM ● ● ●
Combination of moveable pulley and fixed pulley. Not only reduce the force needed to lift or move an object, it also changes the direction of the force applied. This type of pulley system makes it possible to move heavy loads very easily, the tradeoff is that considerably more motion is required to do the work.
Figure 5.3: A complex pulley system uses multiple blocks, each with multiple wheels. (Source:https://www.groovylabinabox.com/groovy-pulleys/)
5.1 APPLICATION 5.1.1 CABLE NET STRUCTURE ● ●
A cable net structure is an example of a tensile structure which a structure that is stabilised by tension rather than compression such as a piece of fabric pulled in opposite directions. The behavior of cable net is thus similar to that of a cable beam, with one set of a curved cable resisting the downward force and another set of oppositely curving cable resisting the upward lift.
Figure 5.4: Munich Olympic Stadium, (Source: https://www.archilovers.com/projects/151385/roofing-for-main-sports-facilities-in-the-municholympic-park.html)
5.1.2 SUSPENSION BRIDGE ●
Suspension bridge is a type of bridge which has cables between towers and from them vertical “suspender cables” (or hangers”) that hold the deck. Suspension cables are anchored at each end of the bridge and they carry the majority of the load.
Figure 5.5: Kurushima-Kaikyō Bridge, (Source:https://en.wikipedia.org/wiki/Kurushima-Kaiky%C5%8D_Bridge)
5.1.3 CABLE-STAYED BRIDGE ●
Cable-stayed bridge is a bridge similar to suspended bridge in that it has towers and a deck that is held by cables, but its cables connect to the deck directly to the towers instead via suspender cables.
Figure 5.6: Yuri Bridge, (Source:https://www.ihi.co.jp/iis/en/products/bridge/syacyou/index.html)
5.1.4 CABLE TRUSS ● ●
Cable truss bring toward to the system about the transparency and the dematerialization of the structure. Cable trusses rely on the introduction of prestress forces into the tensile elements of the truss to provide stability.
Figure 5.7: The Corso, Queensland Australia, (Source:http://www.strudyna.com/projects/the-corso-queensland-australia)
5.1.5 PRETENSIONED CABLE BEAM ●
Cable beam is simply suspended cable system. It is formed by adding a second set of cables with reverse curvature, to the existing suspension cables. This second set of cables can be added in various manners forming three possible combinations convex, concave and convex-concave beams.
Figure 5.8: David L. Lawrence Convention Center, (Source:http://abpcx.com/2012/04/pittsburgh-convention-center/|)
5.1.6 TENSIONED STRAIGHT CABLE
Figure 5.9: Millennium Dome, (Source: http://www.insightcruises.com/events/sa26/pdf/Ressler/A_Field_Guide_to_Great_Structures .pdf)
5.1.7 TENSEGRIC SHELL ● ● ●
Tensegric shell is a hybrid shell which is made up of cable net and compression bars. The structure of the tensegric net is derived from the tensegrity system, which was first discovered by Buckminister Fuller in the 1962. This system is defined as a state when a set of discontinuous compressive components interacts with a set of continuous tensile components to define a stable volume in space.
-
Figure 5.10: The Gymnastic Arena for the Korean Olympic, (Source: https://www.tensinet.com/index.php/projects-database/literature?view=project&id=4013)
5.1.8 ELEVATOR â&#x2014;? â&#x2014;?
An electric motor that hoists the cars up and down, including a braking system. A system of strong metal cables and pulleys running between the cars and the motors.
Figure 5.11: Elevator pulley system, (Sources: https://www.nationaltenders.com/site/singleproduct/liftstructureelevation_1063)
5.1.9 CRANE â&#x2014;? â&#x2014;?
Crane is a machine that is equipped with pulleys and cables that can be used to lift and lower materials upwards and also shift them horizontally. They are commonly employed in the construction industry and in the manufacture of heavy equipment.
Figure 5.12: Crane Pulley System, (Sources: https://en.wikibooks.org/wiki/Wikijunior:How_Things_Work/Pulley)
5.2 ROLE AND FUNCTION ● ●
Cable in flexible structural component that offers no resistance when compressed or bent in a curved shape. It helps to support tensile loading. Cables are often used in engineering structure for support and to transmitted load from one point to another when used to support suspension roof bridges and trolley wheels, cables form the main load carrying element in the structure.
5.2.1 SUSPENSION BRIDGE ●
● ●
The cable support systems in such a way that most of the weight of the bridge is supported by the two towers, which in turn dissipate the compression forces from the cables directly into the ground. smaller cables called suspenders, It run vertically from the bridge deck up to the main supporting cables. The suspenders transfer the bridge deck's compression forces to the towers via the main supporting cables, which create graceful arcs between the towers and down to the anchorages on each end.
Figure 5.13: Diagram of suspended bridge
Figure 5.14: Tensile force transmitted by the cable and compression force
5.2.2 CABLE - STAYED BRIDGE ● ● ●
● ●
The towers are the primary load-bearing structures which transmit the bridges to the ground. A cantilever is often used to support the bridge deck near the towers, but lengths further from them are supported by cables running directly to the towers. The deck of the bridge must be stronger to resist the horizontal compression loads than the suspended bridge because the cables pull to the sides as opposed to directly up. It does not require firm anchorage to resist the horizontal pull of the main cables of the suspension bridge. The cable are fixed to either side of each tower, this mean the weight of each side are balances the opposite side.
Figure 5.15: Flow of tensile force and compression force, (Source:http://www.technologystudent.com/forcmom/dkforce2.htm)
Figure 5.16: The cables carrying the same weight of bridge to achieve the balancing, (Source:http://www.technologystudent.com/struct1/cable1.htm)
5.2.3 CABLE NET STRUCTURE ● ●
●
Cable net is obtained when the suspension and pretension cables of the cable beams are laid in space to form a single surface. The behavior of cable net is thus similar to that of a cable beam, with one set of a curved cable resisting the downward force and another set of oppositely curving cable resisting the upward lift. The supports of the cable net can be provided in the form of a central mast and edge cables.
Figure 5.17: Cable net with edge cables and a center mast 5.2.4 PRETENSIONED CABLE BEAM ● ● ●
Straight cables are preferred since they can be more easily tensioned between two abutments. Such a section can not economically designed because of conflicting requirements of the midspan and section. At the maximum moment section generally occurring at mid span, it is best to place the cable as near to the bottom as possible.
Figure 5.18: Cable installed inside the beam, (Source: https://www.quora.com/What-is-the-difference-between-pretension-and-post-tension-in-struct ural-members) 5.2.5 TENSEGIC SHELL ● ● ●
In a tensegeric system, the structure is self equilibrating, with the "pull" in the compressive structures balancing the "push" from the tensile elements. the system is stable on its own, to support loads, the members of a tensegeric shell needs to be pre-stressed against each other. the bars are arranged such that they join the cables at the nodes and that they are not connected to each other.
5.2.6 ELEVATOR ●
● ●
The elevator car is balanced by a heavy counterweight that weighs roughly the same amount as the car when it's loaded half-full. the counterweight is keeping roughly equal tension on both sides of the pulley which holds up the elevator. When the counterweight moving up, the elevator car will be drag by the gravitational force and moving downward.
Figure 5.19: Force flow of elevator, (Source: https://www.transtutors.com/questions/elevator-and-counterweight-atwood-machi ne-a-system-of-two-objects-suspended-over-a-p-714874.htm#answer)
5.2.7 CRANE ● Similar to the principle of the fulcrum of a lever which is the center of balance between the input and output force in a class one lever. ● The pulley helps make it possible for the crane to lift heavy loads without having to put additional stress on the arm by forcing it to do all of the work, the cables between the motor and the object being lifted is run through a series of cables and pulleys to minimize the amount of work needed to lift the object off the ground.
Figure 5.20: A tower crane uses many different mechanisms, (Source: http://www.mstworkbooks.co.za/technology/gr7/gr7-technology-15.html) 5.3 MAIN POSSIBLE MODES OF FAILURE 5.3.1 CHOSE WRONG CABLE DIAMETER ●
Using the wrong method to measure the cable diameter.
Figure 5.21: The right and wrong way to measure cable diameter, (Source: https://www.usbr.gov/ssle/safety/RSHS/appD.pdf) 5.3.2 CHOSE WRONG CABLE CLASS ●
●
Cable is designed with many classes such as 6x7 (6 strands, 7 wires); 6x19 (6 strands, 19 main wires per strand); 6x37 (6 strands, nominally 37 wires per strand). When normally cable class use is the number of wires per strand may vary significantly (i.e., 6x19 nominal may have from 9 to 26 wires per strand).
5.3.3 FAILURE OF CONNECTOR ● ●
Issues of material quality and dimensional accuracy of components manufactured by casting (defects and lack of toughness), compounded by inadequate or misleading records. This will cause the connector not strong enough to bear the tensile force and break or spoil afterward.
Figure 5.22: Failed connector, (Source: https://www.designingbuildings.co.uk/wiki/Tension_cable_and_rod_connectors)
5.3.4 LACK OF INFORMATION ● ●
●
●
A lack of understanding of the behaviour of pinned joints in service. End connectors for tension rods are relatively specialist products so it may be necessary in part to rely on the manufacturer's specialist knowledge and some procedures. It is expected that manufacturers will wish to protect their specialist 'know-how' but their products should be subject to reasonable independent scrutiny prior to acceptance. Manufacturers may be follow the advise on defining specification requirements and acceptance criteria.
5.3.5 Deterioration OF CABLE ●
●
The damage of cable may be caused by an external factor such as it always dragged along a hard surface, this will create a great amount of mechanical wear. If did not change the damaged cable immediately, it will break and cause a big problem to the environment.
Figure 5.23:Cable Deterioration Types, (Source: https://www.maintworld.com/HSE/Steel-Wire-Rope-Failures-Who-Is-Accountable)
5.4 SUGGESTIONS FOR REMEDIAL MEASURE ●
●
Provided these loadings are coplanar (i.e. on same/one plane) with the cables, the requirements for equilibrium are formulated in an identical manner as in the case of truss. The tension force is always directed in the direction of the cable (For a frictionless pulley in static equilibrium, the tension in the cable is the same on both sides of the pulley).
Figure 5.24: Tension force applied on both sides of the pulley, (Souce: http://web.aeromech.usyd.edu.au/statics/doc/staticequilibrium.PDF)
● ● ● ●
A particle is in equilibrium if the resultant of all forces acting on the particle is equal to zero. Newton’s first law is a body at rest is not effect to any unbalanced forces. If the negative result force is greater than the reverse, meaning that the system is not equilibrium. Below are three equations of equilibrium:
5.4.1 Choose the cable dimension wisely ● Using the right way to choose the dimension of the cable. ● Measure the larger dimension of the cable 5.4.2 Maintenance and checking frequently on cable ● Checking the cable to avoid defect of the cable, such as core protrusion. ● if found out, need to repair or change the cable immediately.
Figure 5.25: Three type of defect of cable, (Source: https://twitter.com/awrf/status/892472260287758337) 5.4.3 Communicate to the manufacture clearly ● Tell the special need or requirement to the manufacture while ordering the cables or the connectors. ● Investigate with the manufacture to ensure both sides getting the clear information. ● Check the status of the cables and connectors, if found out the defective cables or connectors, must solve it immediately. 5.4.4 Choose high quality of cables and connectors ● Using the stainless steel cable and connectors to increase the toughness and the resistance of corrosion.
Figure 5.26: Stainless steel cable, (Source:https://www.kisspng.com/png-wire-rope-marine-grade-stainless-stainless-steel-r-116 2891/)
5.4.5 Choose the right type of cables
5.4.6 Maintenance and check the pulley system ● Stay the pulley clean to ensure the system function well. ● Ensure the status of the cable. 5.4.7 Decrease the speed of the pulley system ● The high speed operation of pulley system will generate frictional heat, which may lead to the formation of martensite structure on the surface of steel wires and early cracks of steel wires.
6.0 BEAM Beams are generally horizontal structural members which carry loads horizontally along their length to the supports where the loads are usually resolved into vertical forces. Beams are used for resisting vertical loads, shear forces and bending. Different types of beams can be classified based on the kind of support.
6.1 APPLICATION Beam as a structural support can be designed in many ways with different methods of application based on the form and condition of the building in order to ensure the building is safe from both internal force and internal force. 6.1.1 BASED ON GEOMETRY
(a) Straight Beam
(b) Curved Beam
Look
Number of nodes
2
3
Degree of freedom per node
Translations X, Y (2D) Translations X,Y,Z (3D) Rotations RZ (2D) Rotations RX, RY, RZ (3D)
For modelling
Axial, bending, transverse shear and torsional stresses
Shape
Only model linear variation
Can model quadratic variation due to the introduction of a mid-side node
Description
-
A beam with straight profile.
-
A beam with curved profile. Neutral axis does not
-
-
Benefits
Neutral axis of the cross-section passes through the centroid of the section. The variation of bending stress is linear, magnitude being proportional to the distance of a fiber from the neutral axis.
-Saving storage spaces. - Load exert to the structure of a building can be easily calculated by engineer.
-
coincide with the cross-section, but is shifted towards the centre of curvature of the beam. The stress distribution in case of curved beam is nonlinear(Hyper- bolic) because of the neutral axis is initially curved.
-More efficient than straight beams. -More complex due to the presence of bending stretching coupling. -The effects of shear deformation and rotatory inertia also increase the complexity.
(c) TAPERED BEAM (WEDGE BEAMS OR SLANT BEAMS) ● ● ● ●
Consisting of straight columns and tapered beam rafters. The primary frame or main support structure for a building. built up I-beam that is wider at one end than the other, giving a tapered appearance to the member. withstand a certain amount of torsional or rotational pressure
Figure 6.1: Welded Tapered Beam and its diagram. (Source: http://www.steelconbuilders.com/buildingtypes.html)
SHAPE:
Figure 6.2: Welded Tapered Beam and its diagram. (Source: http://www.steelconbuilders.com/buildingtypes.html) ● ● ● ●
Consisting of straight columns and tapered beam rafters. Typically used for single-story buildings spanning 30 feet to 60 feet. Tapered beam framing for multi-span construction of buildings up to 300 feet wide or more. can be either single slope or gabled and tend to have low slopes of 1:12 at the most. BENEFITS:
● ● ● ●
provide maximum floor space allow interior finishes to be installed quickly and easily made of high-strength steel less steel is required to manufacture tapered beams, this type of framing is more cost-effective than using all straight members
6.1.2 BASED ON SUPPORT CONDITIONS 6.1.2.1 SIMPLY SUPPORTED BEAM i) A beam supported on the ends which have no moment resistance and free to rotate. ii) One end is having roller support and other end is hinged supported. iii) Reaction: Vertical
Figure 6.3: Line diagram of simply supported beam. (Source: https://www.quora.com/What-is-a-simply-supported-beam) EXAMPLE
Figure 6.4: Stonehenge. (Source: https://www.slideshare.net/GOPALAKRISHNANGOMATH/deflection-in-simply-supported-be am)
Figure 6.5: the Coronado Bridge in San Diego. (Source: https://www.ck12.org/section/Proving-Lines-Parallel-::of::-Parallel-and-Perpendicular-Lines/) 6.1.2.2 FIXED SUPPORT i) resistance to vertical and horizontal forces as well as a moment ii) restrain both rotation and translation, known as rigid supports iii) only needs one fixed support in order to be stable iv) Reactions: Vertical, Horizontal, Moments
Figure 6.6: Fixed support diagram. (Source: https://skyciv.com/education/types-of-supports-in-structural-analysis/)
EXAMPLE
Figure 6.7: Fixed Support – Beam Fixed in Wall. (Source: https://theconstructor.org/structural-engg/types-of-supports-reactions-uses-structures /16974/) 6.1.2.3 OVERHANGING BEAM An overhanging beam is defined as a beam, which is freely supported at two points and having one or both ends extending beyond these supports. Mostly in the overhanging beam one support is hinge support while is roller support having one end as free as cantilever. There are two types of overhanging beam: ● ●
Single overhanging beam Double overhanging beam
(a) SINGLE OVERHANGING BEAM ● ● ●
It has two supports, hinged at one end, roller at the other end. Overhanging portion at any one of the supports. Loads can be applied on overhanging portion and can be converted to equivalent moment at the support. Moment and Reactions are same as that of Simply Supported Beam.
(b) DOUBLE OVERHANGING BEAM ●
This type of Beams will have over hangs at both the support.
●
Both the Overhanging beams will have rotation at supports.
Figure 6.8: Overhanging Beam diagram. (Source: http://mech-engineeringbd.blogspot.com/2016/06/overhanging-beam.html)
EXAMPLE
Figure 6.9: Old colonial overhanging balcony in Havana Vieja, the Old Town. (Source: https://www.alamy.com/stock-photo-old-colonial-overhanging-balcony-in-havana-vieja-th e-old-town-23677024.html) 6.1.2.4 CONTINUOUS BEAM i) Beams are made continuous over the supports to increase structural integrity. ii) Providing an alternate load path in the case of failure at a section. iii) A statically indeterminate structure. iv) Deflection of the mid-span can be reduced.
6.1.2.5 CANTILEVER BEAM i) A beam that is rigidly supported only at one end and carries a load at the other or open end ii) Resisted by the shear stress and a moment at the point of attachment to the support. iii) With axial loading, the beam experiences a shear stress parallel to the z-axis (vertical) and a moment. This moment consists of a force and an instantaneous axis of rotation about which the force is applied. iv) Reactions: Vertical, Moments
Figure 6.10: Cantilever Beam diagram. (Source: https://mechanicalc.com/reference/beam-analysis) EXAMPLE
Figure 6.11: West- link Bridge. (Source: http://www.bridgesofdublin.ie/bridge-building/types/cantilever)
Figure 6.12: Forth Railway Bridge, Scotland. (Source: http://www.bridgesofdublin.ie/bridge-building/famous-bridges/forth-railway-bridge-1890) 6.1.2.7 TRUSSED BEAM i) Trussed beam composed of steel section and strut ii) consists of steel sections (or wooden beams) and struts of steel rods. iii) used when there is great weight to be supported across wide space without support from beneath.
Figure 6.13: Trussed beam diagram. (Source: https://www.cs.princeton.edu/courses/archive/fall09/cos323/assign/truss/truss.html)
EXAMPLE
Figure 6.14: Trussed beam composed of steel section and strut. (Source: https://theconstructor.org/structural-engg/trussed-beams-design-principles-erection/396/)
Figure 6.15: Calhoun Street Bridge, Trenton NJ. (Source: https://www.cs.princeton.edu/courses/archive/fall09/cos323/assign/truss/truss.html
6.2 ROLE 6.2.1 Based on Construction Materials and Cross-Section Shapes The effect of deformation of a beam is highly depends on the cross section of the beam. In addition, the reaction of the beam to the load is determined by the cross-section and the materials of the beam. Choosing the right material is important as it will provide its ability properties to withstand load. Beam can be created and molded or fabricated into many shapes and materials. For example, most common beams are I-beam, T- beam, C-beam and L-beam.
6.2.2 TYPE OF BEAMS Concrete
Steel
(a) I-beam
Advantages -very efficient form for carrying both bending and shear loads in the plane of the web. -The cross-section has a reduced capacity in the transverse direction -inefficient in carrying torsion
Figure 6.16: I concrete beam (Source: https://bit.ly/31hjFzz)
Figure 6.17: I steel beam (Source: https://bit.ly/2ZtoIwr) Figure 6.18: web resists most of the shear force (Source: https://bit.ly/2Kn77Qj)
(b)T-beam
Figure 6.19: T concrete beam (Souce: https://bit.ly/2GIroik)
Figure 6.20: (Source: https://bit.ly/2YjGDZT)
-using part of slab as a beam -Can reduce beam height -longer span -behaves as singly reinforced beam -very efficient - slab portion carries the compressive load and web portion carries the tension. -When T-shaped sections are subjected to negative bending moments, the flange is located in the tension zone. -When sections are subjected to positive bending moments, the flange is located in the compression zone and the section is treated as a T-section.(higher resistance)
Figure 6.21: Stress distribution diagram (Source:https://www.dailycivil.co m/r-c-c-t-beam/) (c)C-beam
-
Figure 6. 22: (Source: )
-used in corners or where do not require complete flange width -usually used as purlins because c-beam (channel) have members spaced away from the neutral axis. -higher inertia moment than L-beam -offers a clean and flat surface for the full depth -can form an I-beam with two c-beam.
(d)L-beam
Figure 6.23: L concrete beam (Source: https://bit.ly/2T44UNr)
Figure 6.24: L steel beam (Source: http://www.krimherbarera ma.com/l-steel-beam/)
(e)Rectangle beam
Figure 6.25: Rectangle beam (Source: https://www.indiamart.co m/proddetail/concrete-be am-11395269188.html)
-used for axial members -typical floor beams because of the reduced overall structural depth -The beams are in prestressed or reinforced concrete. -subjected to bending moment, shear force and torsional moment because the beam receive their load from one side only.
-most commonly used beam and has cross section in the shape of a rectangle of specific breadth (b) and depth(d). -depends on the reinforcement location to yield the flexural capacity. Figure 6.26: Hollow rectangular beam (Source:https://www.quora .com/What-is-the-differenc e-between-an-I-section-an d-rectangular-beams)
(Shear stress is distributed parabolically over the rectangular cross-section.It is maximum at y=0 at the extreme end)
6.2.3 WOOD BEAM A larger section beam must be used to resist shear stresses. Steel and wood beam are usually made and designed safe for shear and bending.
Figure 6.27: Different orientation of wood in beam. (Source:http://www.learneasy.info/MDME/MEMmods/MEM30006A/Area_Moment/Area_Mo ment.html) Above the figure, 1 and 2 both show two different orientation of beam with same area even the same shape. Beam 1 is placed with breadth (b) x height (h) where arrangement of Beam 2 is the opposite of Beam 1. A human (load) is standing above both beams where Beam 2 create bending but the shape of Beam 1 almost remain unchanged. This can be discussed with the moment of inertia of a beam shape, also known as the second moment of area. The second moment of area is a measure of the 'efficiency' of a cross-sectional shape to resist bending caused by loading. Symbol is I. Units are mm4.
For a rectangle,
Where b is the breadth (horizontal) and h is height (vertical) if the load is vertical - e.g. gravity load.
This can be concluded that Beam 1 has a higher second moment of area (I) as the h value is bigger. Thus, Beam 1 is stronger than Beam 2.
6.2.3.1 GLULAM AS STRUCTURAL ELEMENT
Figure 6.28: Glulam structure (Source: https://www.glenfort.com/glulam-beams/) Basically wherever a steel or concrete structure is needed for a building, glulam could also be used. The beam sizes and layout did have a significant effect on the beam strength properties. Increasing layers of the beam will indirectly improve its bending strength. (a) ● ● ● ● ●
ADVANTAGES OF GLULAM Wider, deeper, and longer members can be produced Cambered, curved, and tapered configurations can be easily fabricated Lower-grade lumber can be used in lower-stressed zones of the member, lead to more efficient use and, therefore, conservation of the timber resource Pre Drying the laminations causes less member deformation and, therefore, less distress in the structure Naturally occurring, strength-reducing defects (e.g., knots) are randomized throughout the beam volume
(b) DIMENSION DESIGNATIONS GLULAM CROSS-SECTION
Figure 6.29: Dimension designations glulam cross-section (Source: https://www.swedishwood.com/about_wood/choosing-wood/wood-and-wood-based-p roducts/structural-elements/â&#x20AC;&#x2039;)
(c) THE LAMINATION EFFECT The solid plank strength can be significantly worsened by a single knot. However, only a very small defects risk occuring in the same section of large knots in several laminates.
Figure 6.30: A single lamination and a several lamination. (Source: https://www.swedishwood.com/about_wood/choosing-wood/wood-and-wood-based-p roducts/structural-elements/â&#x20AC;&#x2039;)
Laminating Effect DEFINITION
a strength increase of lamination lumber as a result of being bonded into a glulam beam
FORMULA
DESCRIPTION
Determining the ratio of the ultimate bending strength of a population of glulam beams (exhibiting wood failure) to the tensile strength of a population of lamination lumber
The factor kvar considers different test data COV for the glulam tested in bending and laminating lumber tested in tension. Vb.gl values for most glulam are typically range from about 0.15 to 0.20. Lamination lumber tensile strength is usually more variable, with Vt,lam = 0.25.As a result, a kvar that ranges between approximately 1.15 and 1.30, implying that lamination effects at the 5th percentile level are 15-30% higher than at the mean strength level. Examination of lamination and beam test results suggests that the apparent strength increase due to the lamination effect is a summation of separate, though interrelated, physical effects, some of which are a result of the testing procedure and others the effect of the bonding process. where, = mean bending strength of a population of glulam beams; and = mean tensile strength of a population of lamination lumber.
= Coefficient of variation (COV) of glulam beam bending strength; and = Coefficient of variation (COV) of lamination lumber tensile strength
6.2.4 CONCRETE BEAM However, reinforced concrete beams are generally designed for bending and almost unacceptable for shear. Production of a diagonal tension within the beam once the bending stresses combine with shear stresses together.
Figure 6.31: Compression and Tension in a beam. (Source:â&#x20AC;&#x2039;https://concretecountertopinstitute.com/free-training/compression-tension-concretecountertops-are-beams/â&#x20AC;&#x2039;) When a load is placed on the top of the beam, the above of the beam experience a maximum compression (fibres shorter) while at the bottom is maximum tension (fibres longer). The middle of the beam act as neutral axis which do not experience both compression and tension. Since concrete is weak in tension, excessive shear would lead to catastrophic failure. Increasing in the cross section size could not reduce and resist all diagonal tension stresses on the point where the concrete beam receive load. Thus, shear reinforcement should be done at the tension side where the shear stress exceeds the capacity of the concrete.
REINFORCEMENT IN CONCRETE BEAM
Singly reinforced beam
Doubly reinforced beam
(Source: https://www.quora.com/What-is-the-differen ce-between-singly-reinforced-and-doubly-re inforced-beams)
(Source: https://www.quora.com/What-is-the-differen ce-between-singly-reinforced-and-doubly-re inforced-beams)
-upper portion: subjected to compression
-Reinforcement in both tension and compression zone
-lower portion: reinforcements are provided to resist tension
-concrete is less depth -save cost
-Depth of concrete is greater
6.2.6 BASED ON METHOD OF CONSTRUCTION (a) CAST-IN-SITU CONCRETE BEAM ● ● ●
A construction of beam which is carried out at the building site Within the formwork filled with fresh concrete is placed with reinforcement steel bars Plastic bar chairs or plastic tipped metal
Figure 6.31: Cast In-situ Concrete Beam (Source: https://theconstructor.org/structural-engg/types-beams-construction/24684/)
(b) PRECAST CONCRETE BEAM ● ● ●
The beam is manufactured in factories, construction condition are more controllable than on-site construction. Good quality concrete Various cross sectional shapes can be manufactured (eg: Double T-beam, T-beam, inverted T-beam etc)
Figure 6.32: Precast concrete beam (Source: https://theconstructor.org/structural-engg/types-beams-construction/24684/)
(c) PRESTRESSED CONCRETE BEAM - the tendons are tensioned prior to the concrete being cast. The concrete bonds to the tendons as it cures, following which the end-anchoring of the tendons is released, and the tendon tension forces are transferred to the concrete as compression by static friction. -Two kind of forces in the beam:
1. Internal prestressing force 2. External forces (Dead load, Live load etc.)
Figure 6.33: Prestressed concrete. (Source: â&#x20AC;&#x2039;https://en.wikipedia.org/wiki/Prestressed_concreteâ&#x20AC;&#x2039;)
6.3 FUNCTION 6.3.1 ONE WAY BEAM SYSTEM
Each pair of external columns supports a long-spanning beam or girders. This form of construction is suitable for long, narrow buildings, especially when a column-free space is desired. The absence of columns in the interior is an advantage in structures such as car parks, as freedom from obstruction makes for greater and safer maneuverability, besides allowing the layout of the parking spaces to be altered at any time.
Figure 6.34: One way beam system (Source: â&#x20AC;&#x2039;https://slideplayer.com/slide/14842680/â&#x20AC;&#x2039;)
6.3.2 TWO-WAY BEAM SYSTEM
A two-layer system, where beams frame into girders, increases floor depth considerably and provides more space for mechanical systems. Steel girders span the short axis of a building bay thus contributing to the lateral stability of the structure.
Figure 6.35: Two way beam system (Source: https://slideplayer.com/slide/14842680/) 6.3.3 THREE-WAY BEAM SYSTEM
It is used when a large column-free space is required, where long-spanning plate girders or trusses can be used to carry the primary beam, which in turn supports a layer of secondary beams.
6.4 MAIN POSSIBLE MODES OF FAILURE 6.4.1 SHEAR FAILURE AND FLEXURAL (BENDING) FAILURE There are two principle ways of possible to cause a beam to fail its function. Both principles are shear failure and flexural (bending) failure respectively. Occurrence of shear failure in beam is because of the exceeding of the internal shear stresses of material capacity. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. In the simple word, diagonal crack due to shear failure occurs at the end of the beam (beam connected to column) where the shear stress exceeds the maximum in the cross section of beam of 45 degrees.
Figure 6.36: Shear failure of beam at the column (Source: https://www.quora.com/What-type-of-failure-happen-in-beam)
Most commonly shear failure can be seen is in concrete due to its weak tension strength. The most serious type of failure in concrete is due to the shortage in shear resistance. The concrete will give advance warning by showing cracking or deflections when a weight is placed on top of it. However, shear force diagrams is a method to show where the external force and moments are applied.
High tensile stresses in the web causes shear failure in the beam web or “shear flexure failure”, (Figure 6.36)
Bend strength, also known as flexural strength, modulus of rupture, or fracture strength, defined as the stress in the beam material just before it yields in a flexure test. The bend strength is the ability to resist the highest stress experienced within the material at its moment of rupture. This type of failure can be overcomed by providing main steel at bottom or on top of the beam. Beam mid span is the part of beam where occurs flexural failure. There are many causes that may lead to flexural failure.
Figure 6.37: Flexural failure happen in a building (Source: https://www.quora.com/What-type-of-failure-happen-in-beam)
Figure 6.38: Development of cracking in beams (Source: https://civildigital.com/failure-modes-beams/)
FAILURE IN BENDING FOR WOODEN BEAMS : ● ●
● ●
●
It may fail in direct compression at the concave compression surface ○ usually occurs in green timbers It may break in tension on the convex tension surface, because the tensile strength of wood parallel to the grain is usually greater than its compressive strength ○ usually occurs in well-seasoned timbers It may fail by lateral deflection of the compression fibers acting as a column It may fail in horizontal shear along the grain near the neutral axis ○ occurs suddenly and is more common in well-seasoned timbers of structural sizes than in green timbers or in small beams It may fail in compression perpendicular to the grain at points of concentrated load.
Figure 6.39: Cracking in wood due to bending failure. (Source: â&#x20AC;&#x2039;https://classes.mst.edu/civeng120/lessons/failure/bending/index.htmlâ&#x20AC;&#x2039;)
6.5 SUGGESTIONS FOR REMEDIAL MEASURE 6.5.1 SHEAR FORCE DIAGRAM AND BENDING MOMENT DIAGRAM
Figure 6.40: Shear force and bending moment diagram (Source: https://bit.ly/2YdzSsA)
General rules for drawing shear-moment diagrams :
External load, P as a point load exert at the middle of the length of beam, L where the resultantant force of the left portion, Fs= P/2 while the second diagram of figure 6.40 is the forming of (P/2 - P)- - P/2. It may be observed that the diagram shows the maximum shear at the left and right whereas zero shear at the point where load is applied. However, a maximum in bending moment is observed at the point of application of load.
6.5.2 BENDING STRESSES IN BEAMS The bending moment diagram is a method of determining the bending moment, M, along the length of the beam. Bending stress over the cross section of the beam at any location can be calculated by using the bending moment at that location along the
beam. The bending moment varies over the height of the cross section according to the flexure formula below:
where,
M = bending moment at the location of interest along the beam's length Ic = the centroidal moment of inertia of the beam's cross section y = the distance from the beam's neutral axis to the point of interest along the height of the cross section The negative sign indicates that a positive moment will result in a compressive stress above the neutral axis.
The bending stress is zero at the neutral axis of the beam, which is coincident with the centroid of the beam's cross section.The bending stress increases linearly away from the neutral axis until the maximum values at the extreme fibers at the top and bottom of the beam.
The maximum bending stress can be determined by:
where, c = the centroidal distance of the cross section (the distance from the centroid to the extreme fiber)
If the beam is asymmetric about the neutral axis such that the distances from the neutral axis to the top and the bottom of the beam are not equal, the maximum stress will occur at the farthest location from the neutral axis. Below the diagram, showing the tensile stress at the top of the beam is larger than the compressive stress at the bottom.
Figure 6.41: Tensile strength and compression in beam. (Source: https://mechanicalc.com/reference/beam-analysis)
The section modulus of a cross section combines the centroidal moment of inertia, Ic , and the centroidal distance, c:
The section modulus can characterizes the bending resistance of a cross section in a single term. The section modulus can be substituted into the flexure formula to calculate the maximum bending stress in a cross section:
6.5.3 SHEAR STRESSES IN BEAMS Shear diagram is a method to determine the shear force, V along the length of the beam. The average shear stress over the cross section of the beam can be calculated by:
The shear stress varies over the height of the cross section, as shown in the figure below:
The shear stress is zero at the free surfaces (the top and bottom of the beam), and it is maximum at the centroid. The equation for shear stress at any point located a distance y1 from the centroid of the cross section is given by:
where, V = the shear force acting at the location of the cross section Ic = the centroidal moment of inertia of the cross section b = the width of the cross section (above are all constants)
Q = the first moment of the area bounded by the point of interest and the extreme fiber of the cross section
7.0 COLUMN A column is a structural element that transmits the weight of the structure above to below through compression. In other words, a column is a compression member. Columns are frequently used to support beams or arches on which the upper parts of walls or ceilings rest. In architecture, column refers to such a structural element that also has certain proportional and decorative features such as column in greek era. Therefore, a column might also be a decorative element not needed for structural purposes and it also may be in a part of a wall. 7.1 APPLICATION Column is an element which support building in vertical way. Compared to beam which support building in horizontal line, column carry weight in vertical and it sends those weight to earth. This is why columns are designed like an “I” shape; so that it can be compressed, support and transfer weight from top to the ground.
Figure 7.1: An isometric view of a structure showing how loads transfer from top to ground. (Source: http://www.engineersdaily.com/2014/05/how-loads-flow-through-building.html)
7.1.1 USED OF COLUMN There are many places where columns are important to act as a main support, below shows that example of where can find the columns.
7.1.1.1 TOWER
Figure 7.2: Changi’s Smart Digital Tower (Source:https://www.straitstimes.com/singapore/transport/116-cameras-for-changis-smart-di gital-tower-trial) 7.1.1.2 HIGH RISE BUILDING
Figure 7.3: London High Rise Building (Source: https://www.cp24.com/news/toronto-building-codes-inspections-will-prevent-infernos-like-lon don-high-rise-officials-1.3459783) 7.1.1.3 BRIDGE
Figure 7.4: Cordova’s Bridge
(Source:https://www.cfcsl.com/en/cfcsl-proyectara-nuevo-puente-atirantado-cebu-cordova-fili pinas/) 7.1.1.4 HISTORICAL BUILDING
Figure 7.5: The Temple in Greek (Source: http://www.documentarytube.com/articles/greek-architecture-that-changed-history) 7.1.1.5 RESIDENTIAL HOUSE
Figure 7.6: Columns in Residential House (Source:https://www.lamudi.com.ph/house/buy/)
7.2 ROLE To be simple, Column has two main functions in architecture: 1. AS A SUPPORTIVE STRUCTURE As mentioned above, Column transfer weight load in vertical line; from top to ground. It might transfer loads from a ceiling, floor slab, roof slab, or from a beam, to a floor or foundations. Therefore without column, architecture cannot design a high spaces and eventually, a building.
Figure 7.7: Vertical Load Transfer (Source:http://engineeringfeed.com/5-steps-load-pathway) 2. AS A NON-SUPPORTIVE STRUCTURE- A DECORATIVE ELEMENT In the history of architecture, columns are widely applied to boost up the beauty of the building. This is where proportion and golden ratio were studied in ancient times especially in Greek and Roman era. Therefore in these era, columns are designed according to orders, which is:
Figure 7.8: Greek and Romen Columns Order (Source:https://buffaloah.com/a/DCTNRY/c/corinthorder.html)
7.2.1 TYPES OF COLUMNS There are several types of columns which are used in different parts of structures. Here are some categories to classify types of columns: 1. 2. 3. 4. 5.
By Types of Reinforcement By Types of Loading By Slenderness Ratio By Shape By Construction Materials
7.2.1.1. BY TYPES OF REINFORCEMENT 1. TIED COLUMN This type of column is commonly construction from reinforced concrete. Longitudinal reinforcement are confined within closely spaced tie reinforcement. It is estimated that 95% of all columns in buildings are tied.
Figure 7.9: Tied Column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/) 2. SPIRAL COLUMN Spiral column is also construction from reinforced concrete. In this type of column, longitudinal bars are also confined within closely spaced and continuously wound spiral reinforcement. Spiral reinforcement provide lateral restraint (Poisson’s effect) and delays axial load failure.
Figure 7.10: Spiral Column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
3. COMPOSITE COLUMN When the longitudinal reinforcement is in the form of structural steel section or pipe with or without longitudinal bars, it is called as a composite column. This type of column have high strength with fairly small cross section, in addition to exhibit good fibre performance.
Figure 7.11: Composite Column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
7.2.1.2. BY TYPES OF LOADING 1. AXIALLY LOADED COLUMN If vertical axial loads act on the center of gravity of the cross-section of the column, then it is termed as axially loaded column. Axially loaded column is rare in construction since coinciding vertical loads on the center of gravity of column cross section is not practical. Interior column of multi-storey buildings with symmetrical loads from floor slabs from all sides is an example of this type of column.
Figure 7.12: Axially Loaded Column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
2. COLUMN WITH UNIAXIAL ECCENTRIC LOADING When vertical loads do not coincide with the center of gravity of column cross section, but rather act eccentrically either on X or Y axis of the column cross section, then it is called uniaxially eccentric loading column. Column with uniaxial loading are generally encountered in the case of columns rigidly connected beam from one side only such as edge columns.
FIGURE 7.13: Column with uniaxial eccentric loading (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
3. COLUMN WITH BIAXIAL ECCENTRIC LOADING When vertical on the column is not coincide with the center of gravity of column cross section and does not act on either axis (X and Y axis), then the column is called biaxially eccentric loaded column. Columns with biaxial loading is common in corner columns with beams rigidly connected at right angles at the top of columns.
Figure 7.14: Column with biaxial eccentric loading (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
7.2.1.3. BY SLENDERNESS RATIO Based on slenderness ratio, (effective length/ least lateral dimension), columns are categorized as follow: 1. SHORT COLUMN If the ratio effective length of the column to the least lateral dimension is less than 12, the column is called as the short column. A short column fails by crushing (pure compression failure).
Figure 7.15: Short column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
2. LONG COLUMN If the ratio effective length of the column to the least lateral dimension exceeds 12, it is called as long column. A long column fails by bending or buckling.
Figure 7.16: Long column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
7.2.1.44. BY SHAPE 1. SQUARE OR RECTANGULAR COLUMN They are generally used in the construction of buildings. It is much easier to construct and cast rectangular or square columns than circular ones because of ease of shuttering and to support it from collapsing due to pressure while the concrete is still in flowable form.
Figure 7.17: Square column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
2. CIRCULAR COLUMN They are specially designed columns, which are mostly used in piling and elevation of the buildings.
Figure 7.18: Circular column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
3. L-SHAPE COLUMN Commonly, L-shaped column is utilized in the corners of the boundary wall and has similar characteristics of a rectangular or square column.
Figure 7.19: L-shaped column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
4. T-SHAPE COLUMN It is utilized based on design requirements of a structure. T-Shaped column is widely used in the construction of bridges.
Figure 7.20: T-shaped column (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
5. SHAPE OF STEEL COLUMN There are different standards and built up shape of steel columns which are shown in Fig. and Fig. Common shapes of steel columns include I, channel, equal angle, and a T-shape.
Figure 7.21: Steel column cross section shape (Standard) (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
Figure 7.22: Steel column cross section shape (built up) (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/)
6. SHAPE OF COMPOSITE COLUMN The usual shape of composite columns are shown as below:
Figure 7.23: Composite column shape (Source:https://theconstructor.org/tips/types-columns-building-construction/24764/) 7.2.1.5. BY CONSTRUCTIONN MATERIALS Types of columns based on construction materials include 1. REINFORCED CONCRETE COLUMN
Figure 7.24: Reinforce Concrete Column (Source:https://images.app.goo.gl/LHDpFi5Amuwk8Ds89)
2. STEEL COLUMN
Figure 7.25: Steel Column (Source:https://images.app.goo.gl/d27noeMvRckzCs2eA) 3. TIMBER COLUMN
Figure 7.26: Timber Column (Source:https://images.app.goo.gl/5rHZtepjeekcuJVe7) 4. BRICK COLUMN
Figure 7.27: Brick Column (Source:https://images.app.goo.gl/Ew8E2Wz8ZzPve6pK6)
5. BLOCK COLUMN
Figure 7.28: Block Column (Source:https://images.app.goo.gl/dasAXk1YUo3m3RMVA) 6. STONE COLUMN
Figure 7.29: Stone Column (Source:https://images.app.goo.gl/oZrPfbztmmbdcM58A)
7.3 FUNCTION As mentioned, column transfer weight from roof to ground. Therefore to build a building, the positioning and orientation of the column should also be considered into structural planning. Below are principles which helps in decides columns position. 1. Columns should preferably be located near the corners of a building, and at the intersection of beams or walls. 2. Select the position of column so as to reduce bending moments in beams. 3. Avoid larger spans of beams 4. Avoid larger center-to-center distance between columns. 5. Columns on property line.
7.3.1 ORIENTATION OF COLUMNS 1. Avoid projection of Columns The projection of columns outside the wall in the room should be avoided as they not only give bad appearance but also abstract the use of floor space, creating problems in placing furniture flush with the wall. The width of the column is required to be kept not less than 200mm to prevent the column from being slender.
Figure 7.30: Example of Projection of Column. (Source:https://images.app.goo.gl/ypySZqbvt8ryCwUHA) The spacing of the column should be considerably reduced so that the load on column on each floor is less and the necessity of large sections for columns does not arise. 2. Orient the column so that the depth of the column is contained in the major plane of bending or is perpendicular to the major axis of bending. This is provided to increase moment of inertia and hence greater moment resisting capacity. It also reduce Leff/d ratio resulting in an increase in the load carrying capacity of the column.
Figure 7.31: Columns in Major Bending Axis. (Source:https://images.app.goo.gl/kG3GP4eJtFkMYL4V9)
7.3.2 DESIGN OF COLUMN The load bearing capacity of a column is given by the expression below:
Where σc and σ3 represent the working stresses in concrete and steel. The stress allowed in steel is about 1.5 to 2 times the value of mσc. It has been observed that when the column is gradually loaded, the stresses in steel and concrete will be in the proportion of their modulus of elasticity as long as the stresses are within the elastic limits. The ultimate load carrying capacity of a column is given by the factor below:
Where σsy represents the yield point compressive stress in steel, σvu is the ultimate compressive strength of concrete cubes and σ is a factor less than unity.
Figure 32: Column Layout Plan of the Multi-story Building (Source:https://www.researchgate.net/publication/301784674_Design_Calculation_Analysis _of_Foundation_Columns_of_Buildings_A_Case_Study_at_Gwalior)
7.4 MAIN POSSIBLE MODES OF FAILURE Failure of the column can lead to the collapse of the entire structure. In a framed structure, where the columns are rigidly connected to other structural elements, besides the direct loads large bending moments are imposed on the columns. Reinforced columns are reinforced with the help of longitudinal bars are meant to carry the tensile stresses besides sharing the compressive forces with the concrete. Any bending moment taking place due to the accidental eccentricity of load on the column can be counterbalanced by providing adequate reinforcement. The columns can be reinforced with longitudinal bards and closely wound spiral reinforcement round the vertical bars. The spiral being wound closely has a confining effect on concrete within it. It is brought in tension and has got the ability to check the expanding tendency of concrete under loading.
7.4.1 COLUMN CAPACITY Failure of a column depends on its overall strength. Since the column could fail in either shear, bond splitting or flexure, the lateral force capacities according to the various failure modes were determined. The shear capacity 2 2250 of columns was calculated by the strength equation given in the design code of the Architectural Institute of Japan: Qsu = Qsut + Qsua = bjtpwσwycotφ + tanθ(1-β)bDνσB/2 (Eq1) The bond splitting capacity of columns is mainly dependent on the bond strength of the main reinforcement. In the derivation of the bond splitting capacity, the truss and arch model was also made as the basis of the shear resisting mechanism. The calculated bond strength using the proposed equations was used as the controlling parameter in the derivation of the bond splitting capacity. Accordingly, the bond splitting capacity is given by: Qbu = Qbut + Qbua = τbu(Σψh)jt + tanθ(1-β)bDνσB/2 (Eq2) The calculation of the flexural capacity was based on the ultimate strength concept wherein the shape of the concrete compression zone is represented by the stress-strain curve based on the e-function model and the stress-strain relationship for the main reinforcement is based on a bilinear elastic-perfectly plastic model. Considering the stress-strain conditions along the column cross section, an iterative procedure was done wherein at increasing values of the strain at the extreme compression fiber, locations of the neutral axis were determined and the corresponding values of the lateral load can be calculated by moment equilibrium. The flexural capacity, Qmu, of the column corresponds to the maximum calculated value obtained from the above procedure. 7.4.2 AXIAL LOADING In the aforementioned discussion of the column capacity based on the truss and arch model, the loading condition on a regular beam, where axial loading is not applied, is considered.
Figure 7.33: Effect of Axial Loading (Source:https://www.iitk.ac.in/nicee/wcee/article/2250.pdf) Figure above shows that a concrete arch will be formed along the diagonal of the column that would partly resist the axial load applied and the remaining of which would be carried by the main reinforcement. From equilibrium, it was derived that the lateral force due to the applied axial load, Qaxial, is resisted solely by the concrete arch and is given by:
Qaxial = σaxialbx’cosθ’sinθ’ For cases in the column behavior due to the arch mechanism, the lateral force, Qarch, is also resisted solely by the concrete arch as shown: Qarch = σarchbxcosθsinθ In order to maximize the lateral force contribution due to the arch mechanism and the axial load, both axial action and arch action are combined wherein he stress in the concrete arch is given by σarch+σaxial and the resulting lateral force is Qarch+Qaxial. From the figure, the depth and angle of the concrete arch for both the axial and arch actions are assumed to be identical. By a similar procedure as in the arch mechanism, the lateral force due to both actions is shown by: Qarch+Qaxial = (σarch+σaxial)bDtanθ/2 However, the stress in the concrete arch can be equated to the remaining concrete capacity after considering the stress carried by the truss mechanism (σarch+σaxial = νσB-σtruss). Therefore, the equation below shows that total lateral force due to the arch mechanism and the axial load is equivalent to the lateral force contribution due to pure arch action given in Eq1 and Eq2 for shear and bond splitting types, respectively. Qarch+Qaxial = (νσB-σtruss)bDtanθ/2
7.4.3 STRAIN DISTRIBUTION IN THE MAIN REINFORCEMENT In the truss mechanism, the value of the strain is determined using the calculated force on the main bar based on the equilibrium of the infinitesimal stringer elements. Since the column is loaded under double bending, it is considered as point symmetric at the center of the column. Hence, from the free body diagram shown below,
Figure 7.34: Equilibrium Conditions (Source:https://www.iitk.ac.in/nicee/wcee/article/2250.pdf) Since there is no vertical load for the truss mechanism (F1+F2=0) and that the stress condition at both points in the main reinforcement lying on a plane inclined as an angle φ passing through the center of the column is the same (F1=F2), it can be shown that the
strain is zero (F1=F2=0) at those same points in the main reinforcement. Since the force on the main bar is associated with stresses due to bond, it is directly dependent on the distance from the point of zero strain. Therefore, the resulting bond forces on the main bars for both the shear and bond splitting failure modes are represented by Equation: bond force = pwσwybcotφlx By converting the force to strain, the strain distribution due to the truss action in terms of the calculated capacity, Qtruss, is given by: εtruss = Qtrusslx/[jt(ag/2)E]
Figure 7.35: Truss Mechanism (Source:https://www.iitk.ac.in/nicee/wcee/article/2250.pdf) Next, the effect of axial loading will be incorporated into the derivation of the strain distribution in the main reinforcement due to the arch mechanism.
Figure 7.36: Arch Mechanism and Axial Loading (Source:https://www.iitk.ac.in/nicee/wcee/article/2250.pdf) By simple equilibrium of forces, the axial load is resisted by both the concrete arch and the main reinforcement. Using the remaining compressive stress of the concrete for the
arch mechanism with axial action, σarch+axial, the compressive force in the concrete arch is given by compressive force = σarch+axialbD/2cosθ
Figure 7.37: Main Bar Strain Distribution
7.4.4 CRACK PATTERN
Figure 7.38: Typical Crack Patterns (Source:https://www.iitk.ac.in/nicee/wcee/article/2250.pdf) Figure a, b, c and d: Typical shear failure Figure e and f: Flexural failure Figure g and h: Bond splitting failure 7.4.5 SHORT COLUMN BEHAVIOR
Figure 7.39: Short Column Behavior (Source:https://www.researchgate.net/publication/264150838_Investigation_of_short_colum n_effect_of_RC_buildings_Failure_and_prevention)
Consider the partially infilled frame with connected infill walls to the columns shown in Figure above. The shear force, V, of the short column can be calculated from equilibrium as follows:
where Mt and Mb are the bending moments at the top and bottom of the short column, respectively, and ls is the length of the short column.
7.5 SUGGESTIONS FOR REMEDIAL MEASURE Selecting good position for columns and walls during building architectural planning is the substantially effective technique of restrain-cracks prevention. Below are steps on designing columns, which follow Plain and Reinforced Concrete-Code of Practice, 2000: 1. Geometrical properties of column
2. Slenderness ratio
3. Evaluate the strength of column
Strength of column, Pcu can be calculated using the expression,
4. Calculation of longitudinal reinforcement
5. Calculation of transverse reinforcement
Pitch of the lateral ties can be any one of the following depending upon the conditions: ● Least dimension of the column ● 16 times the diameter of the longitudinal bar ● 48 times the diameter of the lateral ties Pitch of the spiral can be taken as 1/6th of the core diameter or smaller than or equal to 75mm, whichever holds a lesser value. 7.5.1 WAYS TO ELIMINATE SHORT COLUMN EFFECT 1. SEPARATE THE INFILL WALL One of the best ways to eliminate the short column effect is to separate the infill wall from the bounding structural frame with an adequate gap that would allow the column to freely bend. However, in this case, another problem occurs where the wall can easily fail in the out-of-plane direction due to inefficiency of its rigidity along the axis perpendicular to the wall plane. Cagatay (2005) proposed a suitable method which consists of locating a steel beam with a U-shaped section between the infill wall and the RC frame.
Figure 7.40: Steel Beam embedded in Column. (Source:https://images.app.goo.gl/9m29Xnzv33rtaRRf9) Hence, the RC column is free to bend along its entire height due to earthquake or lateral loads and the added steel beam with a U-shaped section prevents the infill wall from failing in the out-of-plane direction. 2. REDUCE SHEAR FORCE One of the other effective methods to eliminate the short column effect is to reduce the shear force acting on the short column. Pineda (1994) recommended a solution by adding infill wall segments that would slightly reduce the opening width next to the short column. He performed experimental tests on 1:3 scale models of two-dimensional frames. He recommended adding infill wall with a width of twice the required gap opening height. Alternatively, the requirements of the seismic-resistant codes, must also be satisfied to completely prevent the short column effect. In the following sections, the effect of adding infill wall segments surrounding the short column on the shear force demand are examined in 2D and three-dimensional (3D) computational models.
7.6 CASE STUDY- SHANGHAI WORLD FINANCIAL CENTER
Figure 7.41: Shanghai World Financial Center (Source:https://images.app.goo.gl/wJqa51TnmVfijDjD8) The columns of the mega-structure are of mixed structural steel and reinforced concrete. At the connection of the mega-diagonals to the columns,
Figure 7.42: Finite Element Analysis of a Mega-column to Mega-diagonal Connection. (Source:http://global.ctbuh.org/resources/papers/download/14-case-study-shanghai-world-fin ancial-center.pdf) The steel columns must be of a size capable of fully transferring the vertical component of the load in the diagonals to the composite columns. Above and below this connection, the size of the steel column is reduced. Away from the era where the steel columns transfer loads to the surrounding concrete, the steel columns need only be strong
enough to carry the construction load of the steelwork above and to meet specific requirements the building codes that govern and guide tall building design in China.
Figure 7.43: Plan of a Corner Mega-column (Source:â&#x20AC;&#x2039;http://global.ctbuh.org/resources/papers/download/14-case-study-shanghai-world-fin ancial-center.pdfâ&#x20AC;&#x2039;) Figure above shown in the lower reaches of the building the composite columns are of impressive size. Reinforcing steel must necessarily be 50mm (2inches) in diameter, the largest size available, and bundled into sets of four bars each.
8.0 CONCLUSION In a nutshell, the significant main components of each structural system of the building and correlate with architectural design were being identified and explained in this assignment. The character of a multi-storey building structure is to transmit the applied loads to the foundations. The structural frame transfers the load from their point of application to the foundations. In our point of view, it should combine the structural efficiency with least effect on the economy and the purpose of the other elements of the building. Hence, when selecting the structural grid, it explains the column positions and it is very essential to the decision for design. From this assignment, we learnt that structural analysis is very crucial and important as it will affect the stability and durability of a whole building. The structural grid is being defined mainly by the positions of column and the spanning of major beams between them. The formation of this kind of structural grid is very critical in making design evaluation and the following points should be considered: ● A column should be usually placed at every intersection of two grid lines. ● A main beam has to be positioned along every grid line. ● Ideally grid lines should be orthogonal. It means the two sets of parallel lines forming a rectangular grid, and the spacing between grid lines should be regular for circular buildings radial and circumferential grids are often used. ● In practice the shape of the building or the site may require some variation, irregular spacing or skewed grid lines which cannot be avoided. However, these can generally be concentrated in small areas, and allow the main part of the building to be set out in accordance with a regular orthogonal grid. The safe performance of a structure must be assessing cautiously as if there is collapse or failure on a structure, the entire building will be unserviceable. This means that the particular building is unsafe due to unexpected design scenario, or we can judge it as an unwise design. Structural engineering is the science and art of planning, designing, and constructing safe and economical structures which that will serve their intended functions and purposes. After this assignment, as architecture students, we will be more considerate of the structural system that needed in our architectural design in the future so that we are able to build a building not only based on the aesthetic but also be mindful of the structural system.
9.0 REFERENCES TRUSS Trusses. (n.d.). Retrieved from â&#x20AC;&#x2039;https://www.steelconstruction.info/Trusses Uplift Values On Truss Design Drawings. (n.d.). Retrieved from https://www.sbcindustry.com/content/1/uplift-values-truss-design-drawings What Goes Up Must Come Down...Right? A Truss Uplift Discussion - Donan - Forensic Engineering Experts. (n.d.). Retrieved from https://donan.com/article/what-goes-up-must-come-down-right-a-truss-uplift-discussio n/ CABLE AND PULLY More causes of wire rope damage. (n.d.). Retrieved from http://www.cranestodaymagazine.com/features/more-causes-of-wire-rope-damage How Does a Suspension Bridge Work? (n.d.). Retrieved from https://www.wonderopolis.org/wonder/how-does-a-suspension-bridge-work Alam, T. (2014, January 24). Cable Layout, Continuous Beam & Load Balancing Method. Retrieved from https://www.slideshare.net/tanviralam31337/cable-layout-continouous-beam-load-bal ancing-method BEAM A., Paul. (2017, March 16). Failure modes in beams: Types of Failure in Reinforced Concrete Beams: CivilDigital |. Retrieved from https://civildigital.com/failure-modes-beams/ S., Rusinkiewicz. (2009, December 15). The Pratt Truss Bridge. Retrieved from https://www.cs.princeton.edu/courses/archive/fall09/cos323/assign/truss/truss.html Stresses & Deflections in Beams. (2019). Retrieved from https://mechanicalc.com/reference/beam-analysis COLUMN Beklen. C. (2010). Investigation of Short Column Effect of RC buildings: Failure and Prevention. Retrieved from https://www.researchgate.net/publication/264150838_Investigation_of_short_column _effect_of_RC_buildings_Failure_and_prevention The Constructor Civil Engineering Home. (2019). Types of Columns in Building Construction. Retrieved from https://theconstructor.org/tips/types-columns-building-construction/24764/ The Constructor Civil Engineering Home. (2019). Types of Structural Design and its Processes. Retrieved from
https://theconstructor.org/structural-engg/types-structural-design-process/1673/ Nandy. A. (2016). Design Calculation and Analysis of Foundation and Columns of Buildings: A Case Study at Gwalior. Retrieved from https://www.researchgate.net/publication/301784674_Design_Calculation_Analysis_ of_Foundation_Columns_of_Buildings_A_Case_Study_at_Gwalior
Katz. P, Leslie. E. (2008). Case Study: Shanghai World Financial Center. Retrieved from http://global.ctbuh.org/resources/papers/download/14-case-study-shanghai-world-fina ncial-center.pdf