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First Edition 2008MOHD.HANIM OSMAN 2008

All rights reserved. No part of this publication may be reproduced or transmittedin any form or by any means, electronic or mechanical including photocopy,recording, or any information storage and retrieval system, without permissionin writing from Universiti Teknologi Malaysia, Skudai, 81310 Johor DarulTak'zim, Malaysia.

Perpustakaan Negara Malaysia Cataloguing-in-Publication Data

Analysis, design and performance of steel section with trapezoid web / editor

Mohd. Hanim Osman.Includes indexISBN 978-983-52-0575-01. Structural engineering. 2. Structural design. I. Mohd. Hanim Osman.II. Universiti Teknologi Malaysia. Fakulti Kejuruteraan Sivil.624.1

Pereka Kulit: MOHD.NAZIR MD.BASRI

Diatur huruf oleh /Typeset byMOHD.HANIM OSMAN & RAKAN-RAKAN

Fakulti Kejuruteraan AwamUniversiti Teknologi Malaysia

81310 SkudaiJohor Darul Ta'zim, MALAYSIA

Diterbitkan di Malaysia oleh / Published in Malaysia byPENERBIT

UNIVERSITI TEKNOLOGI MALAYSIA

34 38, Jalan Kebudayaan 1, Taman Universiti,81300 Skudai,

Johor Darul Ta'zim, MALAYSIA.(PENERBIT UTM anggotaPERSATUAN PENERBIT BUKU MALAYSIA/

MALAYSIAN BOOK PUBLISHERS ASSOCIATION dengan no. keahlian 9101)

Dicetak di Malaysia oleh / Printed in Malaysia byUNIVISION PRESS

Lot 47 & 48, Jalan SR 1/9, Seksyen 9

Jln. Serdang Raya, Tmn Serdang Raya43300 Seri Kembangan, Selangor Darul Ehsan

MALAYSIA


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Contents

CONTENTS

Preface vi

Chapter 1 Buckling Analysis of Plate Girder withTrapezoid Web Subjected to Shear LoadingIzni Syahrizal Ibrahim, Mohd Hanim Osmanand Fathoni Usman

1

Chapter 2 Lateral Torsional Buckling of Beam withTrapezoid WebMohd. Hanim Osman, Sarifuddin Saad,Fatimah Denan and Abdul Karim Mirasa

12

Chapter 3 Analytical Study on Secondary Bendingmoment in Trapezoid Web Beam

Mohd Hanim Osman, Abd. Latif Saleh, A. AzizSaim and Fong Shiaw Ween

26

Chapter 4 Buckling Analysis of Column with TrapezoidWebMohd Hanim Osman, Tan Cher Siang and Abd.Latif Salleh

43

Chapter 5 Performance Test on Simply SupportedComposite Beam with TWP Steel SectionGoh Kee Keong and Mohd Hanim Osman

56

Chapter 6 Experimental Test on Steel Beam withPartial Strength Connections usingTrapezoid Web Profiled Steel Sections

Arizu Sulaiman, Mahmood Md Tahir and AnisSaggaff

68


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Contents

Chapter 7 Field Capacity of Steel Pile with CorrugatedWeb Surface

Mohd Hanim Osman, Fauziah Kasim and A.Aziz Saim

82

Chapter 8 Second Moment of Area about the MinorAxis of Trapezoid Web SectionMohd.Hanim Osman, Sarifuddin Saad, FatimahDenan and Tan Cher Siang

99

Chapter 9 Local Flange Buckling of Trapezoid WebProfileNg Zee Leong and Mohd Hanim Osman

121


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Preface

PREFACE

Built-up steel sections with trapezoid web have been used for yearsin some countries, particularly to increase the out of plane stiffnessand shear buckling strength without the use of vertical stiffeners.Steel plate with corrugated web is not a new idea and has for somany years been used in aircraft design, shipbuilding forcontainers, as cold-formed webs for long span roof beam and later

for civil engineering applications in buildings and bridges. The useof corrugated webs allows for the use of thin plates without theneed of stiffeners, therefore it considerably reduces the cost of thefabrication and improves their fatigue life. The sections arefabricated by welding the trapezoid web steel plate to two flangesand proved to be an alternative to the conventional hot rolled andwelded sections in respect to its strength/weight ratio.

Theoretical and experimental studies have been conductedto study the bending capacity, shear, local flange and lateral beambuckling and column buckling. Other structural behavioursstudied were secondary bending moment, torsional behaviour andflexural stiffness about major and minor axis. Finite elementanalysis is used to study the critical buckling by using the Eigenvalue analysis, and also to study the stress distribution in the weband around the web boundary.

Experimental work to study the performance of compositebeam using the trapezoid section as the steel component was alsocarried out. The purpose of the study is to utilise the section in the


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Preface

design of long span girders such bridges. Another scope of studywas the soil skin friction resistance of the section when used as

foundation pile.The results of the studies are used to develop a new design guidefor the section. This is to promote the use of the section inconstruction industries in this region.

Mohd. Hanim Osman

Faculty of Civil EngineeringUniversiti Teknologi Malaysia2008


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1BUCKLING ANALYSIS OF PLATEGIRDER WITH TRAPEZOID WEBSUBJ ECTED TO SHEAR LOADING

Izni Syahrizal Ibrahim, Mohd Hanim Osman and FathoniUsman

1.1 INTRODUCTION

Plate girder structure, which is constructed from welded steelplate, is well recognized. Economical design of girders and beamsnormally requires thin webs. But if the web is extremely thin theproblem of plate buckling may arise. Possible ways to reduce thisrisk consist of using thicker plates, web stiffeners or strengtheningthe web by making it corrugation. The conventional provision ofstiffeners to allow the use of thin webs has two disadvantages, i.e.high fabrication cost and a possible reduced life due to fatiguecracking that may initiate at them stiffener weld. The use ofcorrugated plates (Fig. 1.1) to replace the flat stiffened plates asthe web can eliminate both disadvantages.

The uses of corrugated webs have been increasingly used in manydiverse engineering structures from structural engineering toaerospace and marine engineering. The corrugation of the websacts as transverse stiffeners that allows for the use of thin plates.Because of the high slenderness ratio, web stability against shearbuckling is of prime importance.

Various formulas for shear buckling of corrugated section have

been proposed by previous researchers. However, they wereapplicable only to certain configuration for which they werederived. Experimental and analytical studies are being carried out


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2 Analysis, Design and Performance of Steel Section with Trapezoid Web

to develop formula that can be used for all types of webconfiguration. Part of the analytical study is presented herein.

Eigen-value buckling analysis in the finite element method wasemployed in this study to determine the elastic shear buckling ofvarious corrugation types. Analysis on normal web panel, inwhich the formula of shear buckling capacity has been wellestablished, was also carried out as a comparison.

Figure 1.1 Trapezoidally Web Plate Girder

1.2 THEORETICAL FORMULAS FOR SHEARCAPACITY

It has been reported that corrugated panels loaded in shear exhibitboth local and global buckling depending on the geometry of thecorrugations. Hamilton reported that differences in panelthickness, aspect ratio, and configuration of corrugation influencethe behavior of the panel [1]. Turner et.al. investigated that fromnumerical analysis results corrugation angle influenced thebuckling behavior of thin corrugated panel [2].

Elgaaly determined that in the local buckling mode, the corrugatedwebs acts as a series of flat subpanels that mutually support eachother along their vertical (longer) edges and are supported by the

flanges at their horizontal (shorter) edge [4]. These flat platesubpanels are subjected to shear, and the elastic buckling stress is


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Buckling Analysis of Plate Girder with Trapezoid Web Subjected to Shear Loading 3

given by:

2w

2

2

l)t/b)(1(12 Ek

=

(1.1)

wherek is a buckling coefficient, which is a function of the panelaspect ratio (b/hw) and the boundary support conditions. For thelonger edges simply supported and the shorter edges clamped, k =

5.34 + 2.31(b/hw) - 3.44(b/hw)

2

+ 8.39(b/hw)

3

, and in the casewhere all edges are clamped, k = 8.98 + 5.6(b/hw)2. The

geometrical nominations of the trapezoid web section are shown inFig. 1.2. The designed shear force:

Vd =l hwtw (1.2)

Figure 1.2Geometrical nomination of trapezoid web section

1.3 SHEAR BUCKLING ANALYSIS BY FINITEELEMENT METHOD

The objective of the finite element analysis is to study the criticalshear by using Eigenvalue-buckling analysis. Eigenvalue buckling

analysis is a linear analysis, which may be applied to relativelystiff structures to estimate the maximum load that can be supportedto structural instability or collapse [9]. Five series of model have

q

s

b d b d

hrtw


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been developed and the thickness of each model increased from 1to 5 mm.

Semiloof thin shell element (QSL8) in LUSAS structural analysissoftware was chosen for meshing the surface element of themodels. QSL8 is grouped as shell element [10]. Elastic-Isotropicmaterial is applied to each element. Other element attributes usedon the model include geometry of the model, support conditionsand loading. A series of finite element model of corrugated webwere carried out. The geometrical corrugation is shown in Table

1.1. For shear model support condition, AD is restrained in eachtranslation and rotational direction. BC is restrained in x and zdirections translation. Shear load is applied only on BC, as shownin Fig. 1.3.

Figure 1.3Finite element models

Table 1.1Dimension for finite element models

FEM E fy hw q s b d hr

Model kN/mm2 N/mm2 mm mm mm mm mm mm

Index

TWP 400 205 355 400 400 457 170 80 80 45

TWP 600 205 355 600 400 457 170 80 80 45

TWP 800 205 355 800 400 457 170 80 80 45

TWP 1200 205 355 1200 400 457 170 80 80 45

TWP 1600 205 355 1600 400 457 170 80 80 45

A

B

C

D

V


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The result of the Eigenvalue analysis as shown in Table 1.2 is usedto build the empirical equation. To obtain the contribution of the

corrugation to the critical shear capacity of the trapezoid webpanel, the equation proposed is based on three key parameter;hw/tw, b/tw, and b/hw. It is assumed that the web panels of themodels are simply supported at both top and bottom flanges. Fromthe analysis, a new equation for critical shear stress is proposed asfollows:

22

2

)/)(1(12

6.1

ww

creth

Ek

= (1.3)

where, k = 1.8/(b/hw)2-(b/hw)

3+ 8*(b/hw)+9

The dimensions of the experimental models and the comparisonbetween the value of Vcr derived from the proposed equation andthe experimental results that previously held in UTM [7, 8] are

shown in Table 1.3, where depth hw and thickness tw of the web issubjected to a vertical shear force V, constant in the x-direction.The Von Mises criterion is used, so the yield stress in shear is:

y

y

y f6.03

f=

(1.4)

In the case where ycre 8.0 > , inelastic buckling will occur and

the inelastic buckling stress cri can be calculated by [4]:

cri = yycre8.0 (1.5)

The results of critical shear capacity compared with experimentalresults shows that the proposed equation is sufficient and thefollowing equation could be used to calculate the critical shear


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capacity:

Vcr = cr * hw * tw (1.6)

Table 1.2FEA results as raw data

FEM tw hw b Vcr Model mm mm mm kN N/mm2Index

TWP 400-1 1 400 170 9.56 23.90TWP 400-2 2 400 170 75.54 94.42

TWP 400-3 3 400 170 249.11 207.59TWP 400-4 4 400 170 571.66 357.28TWP 400-5 5 400 170 1070.97 535.48

TWP 600-1 1 600 170 12.94 21.57TWP 600-2 2 600 170 102.46 85.39TWP 600-3 3 600 170 337.90 187.72TWP 600-4 4 600 170 767.79 319.91TWP 600-5 5 600 170 1409.00 469.67

TWP 800-1 1 800 170 16.50 20.62

TWP 800-2 2 800 170 130.73 81.71TWP 800-3 3 800 170 433.95 180.81TWP 800-4 4 800 170 1003.25 313.52TWP 800-5 5 800 170 1789.34 447.33

TWP 1200-1 1 1200 170 22.69 18.91TWP 1200-2 2 1200 170 180.20 75.08TWP 1200-3 3 1200 170 554.79 154.11TWP 1200-4 4 1200 170 1295.26 269.85TWP 1200-5 5 1200 170 2626.91 437.82

TWP 1600-1 1 1600 170 30.44 19.02TWP 1600-2 2 1600 170 241.60 75.50TWP 1600-3 3 1600 170 804.35 167.57TWP 1600-4 4 1600 170 1869.85 292.16


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Table 1.3Dimensions of experimental models and comparisonbetween proposed equation and experiment results

Specimen fy tw hw b b/tw hw/tw b/hw k cre cri Vcr Vexp Vcr/ Vexp

Mark mm mm mm kN kN

Eq. (1)

CWB 1 355 4.0 351 170 42.5 87.8 0.48 20.4 786.7 158.8 287.8 265.3 1.08

CWB 2 355 4.0 351 170 42.5 87.8 0.48 20.4 786.7 158.8 287.8 247.4 1.16

UCW 1 275 2.4 380 130 55.1 161.0 0.34 27.1 309.6 158.8 142.4 150.0 0.95

UCW 2 275 2.1 380 130 61.9 181.0 0.34 27.1 245.1 158.8 126.7 132.5 0.96

UCW 3 275 1.3 380 130 99.2 290.1 0.34 27.1 95.4 - 47.5 122.5 0.39UCW 5 275 2.1 380 130 63.1 184.5 0.34 27.1 235.9 158.8 124.3 117.5 1.06

UCW 6 275 1.9 380 130 67.4 196.9 0.34 27.1 207.1 158.8 116.4 127.5 0.91

TS 600-3 275 3.0 600 170 56.7 200.0 0.28 33.7 249.5 158.8 285.8 270.0 1.06TS 800-2 275 2.0 800 170 85.0 400.0 0.21 50.6 93.7 - 149.9 169.8 0.88

TS 1300-2 275 2.0 1300 170 85.0 650.0 0.13 115.3 80.9 - 210.3 275.0 0.76

TS 1300-3 275 3.0 1300 170 56.7 433.3 0.13 115.3 182.0 152.1 593.0 650.0 0.91

Note: unit for fy,creandcri is N/mm2

1.4 DISCUSSION

The buckling pattern as shown in Fig. 1.4 indicates that the

inclined parts provide a resistant to shear buckling from crossingfrom one flat sub-panel to the adjacent one. As a comparison tonormal web, the buckling pattern is always in the diagonaldirection of the panel so the trapezoid web will have higherultimate shear strength [6].

Figure 1.4Buckling pattern of the model


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The buckling formula proposed in Eq. (1.3) is given in the functionof the web slenderness parameter; hw/tw, and b/hw. From the

experimental results, the thickness of the web gave significantcontribution to the shear capacity of the model. Fig. 1.5 and Fig.1.6 show that straight line parallel with x-axis is the yield stress ofthe model and the curve was derived from Eq. (1.3). The curve willchange to straight line when inelastic buckling stress is greaterthan the yield stress. Therefore, it can be proposed that thebuckling capacity curve is of straight line and follow the curvefrom Eq. (1.3). The proposed curve is indicated by the dotted line.

Figure 1.5Graph derived form proposed formula compared withexperiment result as on Table 3

UCW3, 246.08

UCW5, 150.10

UCW2, 166.04

UCW1, 167.26UCW6, 173.85

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500 600 700

hw/tw

cr


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Figure 1.6Graph derived form proposed formula compared withexperiment result as on Table 3

1.5 CONCLUSION

Parametrical study with Eigenvalue buckling analysis in the finiteelement method have been successfully employed to built anequation that were to be used to calculate the elastic shear bucklingcapacity of the trapezoid web subjected to shear loading. From theexperimental results and the analytical study, it can be concludedthat:

1. The shape of the buckling pattern shows diagonally occursalong the web panel. The assumption that the corrugated websacts as a series of flat sub-panels that mutually support eachother along their vertical (longer) edges and are supported by

TS1300-2, 105.77

TS1300-3, 166.67

0

50

100

150

200

250

300

350

400

450

500

100 200 300 400 500 600 700 800 900

hw/tw

cr


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the flanges at their horizontal (shorter) edge had been proven.

2. The finite element analysis results show that the proposedformula of shear capacity as in Eq. (1.3) is sufficient

when ycre 8.0 < .

Factor k in the equation is derived with the assumption that theweb is simply supported along the flanges.

NOTATION

b horizontal width of sub panels of a corrugation foldd horizontal width of the inclined foldE Youngs modulusfy yield stresshr thickness of corrugationhw depth of corrugation webk buckling coefficient

tw thickness of webVcr critical shear force

angle of corrugation profiley yield shear stress

cre elastic critical shear stress

cri inelastic critical shear stress

Poissons ratio


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REFERENCES

1. Hamilton R W, Behavior of Welded Girders with CorrugatedWebs, A Ph.D. Thesis, University of Maine, August 1993.2. Turner, S J, Van Erp, G M and Yuen S W, The Influence of

Boundary Conditions on the Shear Buckling Behavior of ThinCorrugated Plates, Faculty of Engineering and Surveying,University of Southern Queensland, Toowoomba, Queensland,Australia.

3. Johnson R P and Cafolla J, Corrugated Webs in Plate Girdersfor Bridges, Proceeding Instn Civil Engineering Structuresand Buildings, May1997.

4. Elgaaly, M, and Seshadri, A., Steel Built-up Girder withTrapezoidally Corrugated Web, Engineering Journal, FisrtQuarter, 1998.

5. Elgaaly, M, and Hamilton, R.W, Shear Strength of Beamswith Corrugated Webs, Journal of Structural Engineering,

April 1996.6. Scheer, J, Beritch Nr. 6203, Institute fur Stahlbau derTechnichen Universitat Braunschweigh, Germany, 1996.

7. Osman, M H, Ibrahim, I S and Tahir, M M, Shear Strength ofTrapezoid Web Plate Girder, Faculty of Civil Engineering,University Teknologi Malaysia, Malaysia, 1999.

8. Osman, M H, Ibrahim, I S and Tahir, M M, StrengthBehaviour of Trapezoid Web Plate Girder, Faculty of Civil

Engineering, University Teknologi Malaysia, Malaysia, 1999.9. LUSAS Modeller User Manual, Version 13, FEA Ltd., United

Kingdom, 1999.10.LUSAS Element Reference Manual, Version 13, FEA Ltd.,

United Kingdom, 1999.11.Narayanan and Rockey, Ultimate Load Capacity of Plate

Girder, Proc. Instn Civ. Engrs, Part 2, 1981.


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2LATERAL TORSIONAL BUCKLING OFBEAM WITH TRAPEZOID WEB

Mohd. Hanim Osman, Sarifuddin Saad, Fatimah Denanand Abdul Karim Mirasa

2.1 INTRODUCTION2.1.1 Trapezoid Web Beam

Economical design of structural steel sections normally requiresthin webs to increase the shear buckling strength. Theconventional method which uses intermediate stiffeners welded to

web to allow the use of thin webs has two disadvantages i.e. highcost of fabrication and reduced service life of the element. The useof corrugated sheets (Fig. 2.1) to replace flat sheets as webs of agirder eliminate both disadvantages [1,2,3]. In addition, it reducesthe total weight of the structure, thus allowing longer spans andsavings in foundation design. Previous researches have beencarried out to study the performance of trapezoid web section inshear in web, secondary bending moment in flange, bending, and

axial buckling [4,5,6].

2.1.2 Lateral Torsional Buckling

When a beam is loaded, it will deflect vertically. If the beam doesnot have sufficient lateral stiffness or lateral support along itslength, the beam will also deflect out of the plane of loading. Theload at which this buckling occurs may be substantially less than

the beams in plane load carrying capacity. For an idealizedperfectly straight elastic beam, there will be no out-of-plane


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Analysis, Design and Performance of Steel Section with Trapezoid Web 13

deformations until the applied moment reaches the critical valueMb, when the beam buckles by deflecting laterally and twisting.

These two deformations are interdependent: when the beamdeflects laterally, the applied moment exerts a component torqueabout the deflected longitudinal axis which causes the beam totwist. This behaviour, which is important for long unrestrained I-beams whose resistances to lateral bending and torsion are low, iscalled elastic lateral torsional buckling.

Experimental and numerical study on lateral torsional buckling of

steel section with trapezoid web is presented in this paper. Theobjectives of the study is to determine the lateral torsional bucklingcapacity of trapezoid web profile in comparison with normal flatweb beams using experimental and finite element method.

Figure 2.1Typical beam sections with trapezoid web and flat web

2.2 EXPERIMENTAL STUDY 2.2.1 Test Procedure

Lateral torsional buckling tests were conducted on three sets ofbeams, each set consists of two specimens i.e. sections withtrapezoid web numbered as TWP3 (TWP3A and TWP3B),

trapezoid web profile TWP4 (TWP4A and TWP4B) and flat webFW3 (FW3A and FW3B). The difference between TWP3 andTWP4 is in their web corrugation thickness, where TWP3 has full


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14 Lateral Torsional Buckling of Beam with Trapezoid Web

corrugation thickness (hr = B) while TWP4 has only halfcorrugation (hr = 0.5B).

The test was designed based on the test method by Dirk [7] andSalina [8]. Fig. 2.2(a) and 2.2(b) show the diagrammatic view ofthe test set-up. The photographs are shown in Fig. 2.3(a) and2.3(b). A point load was loaded at mid span of the specimenthrough a specially designed loading device. The L-shape rollerbearing guide was used to ensure that the jack always seated on ahorizontal surface so that the direction of the loading was kept

vertical under increasing loading. The roller on the top flangeunder the loading was used to ensure that there was no horizontalrestraint that might inhabit lateral buckling during loading.

Two types of lateral restraint at the support were used, i.e. type Aand type B. For type A, the bottom flange of the beam at both endswere fixed, whilst for type B, the bottom flange and web whichwere both restrained from deflect laterally. It is shown in Fig. 2.4.

For each type of beam, two different spans were used i.e. 4000 mmand 5000 mm. Displacement transducers were placed at fivedifferent locations to measure the lateral deflection of the beams.Loads were applied gradually, with the increments of 1.0 kN. Thedisplacement was recorded at each increment. The lateraldisplacements of beam specimens were measured at 400 mm (leftand right) from mid span of the beam (for top and bottom flange)and also at the centre of the web.


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Load actuator

Load cell

Roller

Beamspecimen

fixed at flange

fixed at flange

A

A

Lateral deflection transducer

Figure 2.2(a) The overall view of the test set up

Beam specimen

Test frame

Load actuator

Load cell

bearing guide

Lateral deflectiontransducer

L-Shape roller

Figure 2.2(b) Details of the loading device


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Figure 2.3(a) The overall view of the test set up

Figure 2.3(b) Details of the loading device

Fixed at flange only (Type A) Fixed at flange and web (Type B)Figure 2.4Lateral restraint Type A and B at the beam end support


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2.2.2 Test Results

The test was stopped when buckling occurred, as determined in thegraph of moment versus lateral displacement. In the test, all beamspecimens were found to be still in elastic state after the tests.Relationships between bending moment and lateral deflection wereplotted. In general, the lateral deflection increases linearly with thevertical bending moment. Then, the increase becomes non-linear,followed by a stage when the deflection increases monotonically.

The value of lateral torsional buckling moment resistance wasdetermined from the intersection of tangent of the first and secondcurve. The intersection method was known as knee joint whichhas been used by many researchers [6,7,8,9] to determine themoment resistance of connection. The values of lateral torsionalbuckling resistance, Mb for all specimens were determined when aknee shape was observed. In each graph, two tangent lines weredrawn and the intersection of these two lines gives theMb value.

TWP3A(B)5m

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.00 0.20 0.40 0.60 0.80

Lateral dispalcement (mm)

M

oment,M

(kNm)

Figure 2.5Typical graphs for the determination ofMb

TWP3A(A)5m

0.0

2.0

4.0

6.0

8.0

10.0

0.0 1.0 2.0 3.0Lateral displacement (mm)

Moment, M (kNm)

Mb=8.80 kNm Mb=10.30 kNm


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Table 2.1Test results ofMbfor beams with normal flat web andbeams with trapezoid web profile

Support type A Support type BSpan ofbeam(mm)

Beammark

MbkNm

MbkNm

AverageMb

kNm

AverageMb

kNm

TWP3A 8.80 10.30 10.80

TWP3B 9.20 11.30

9.00

TWP4A 8.00 9.00 9.25TWP4B 8.40 9.50

8.20

FW3A 7.10 8.20 8.55

5000

FW3B 7.00 8.907.05

TWP3A 9.50 11.00 11.20

TWP3B 9.80 11.40

9.65

TWP4A 8.90 9.20 9.60

TWP4B 9.30 10.00

9.10

FW3A 8.10 8.50 8.65

4000

FW3B 8.50 8.808.30

The deflection from the midspan was used for the determination ofMb. TheMb value for each beam was indicated in each graph (Fig.2.5). The result of the experiment is presented in Table 1.

From the table, it is observed that:

(i) Beams with flat webs and 5 m have the average of lateraltorsional buckling moment, Mb lower than that of beam 4m, for each of the Type A and B support. The same findingfor TWP3 and TWP4 was obtained.

(ii) As expected, the beam with Type B support has higher Mbvalue that those with Type A support for both spans.

(iii) TWP section performs better than that of flat web in termsof lateral torsional buckling moment resistance.(iv) The beam with trapezoid web profile section with full


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shape corrugation (hr =B) are better than the beam withtrapezoid web profile section with half shape (hr = 0.5B)

and flat web in their lateral torsional buckling momentresistance.

This is because the Iy value for a TWP beam is higher than Iy offlat web of similar dimensions.

2.3 FINITE ELEMENT STUDY ON LATERAL

TORSIONAL BUCKLING BY FINITE ELEMENT

In this study, all models were assumed to buckle under perfectconditions, where there is no initial imperfectness and eccentricload. The buckling moments were then compared with resultobtained from testing. Eigenvalue analysis of LUSAS Modeller [6]was used to determine the buckling loads.

A linear buckling analysis is a useful technique that can be appliedto relatively stiff structures to estimate the maximum load that canbe supported prior to structural instability or collapse. Theassumptions used in linear buckling analysis are that the linearstiffness matrix does not change prior to buckling and that thestress stiffness matrix is simply a multiple of its initial value.

2.3.1 Modelling

LUSAS models are defined in terms of geometric features thatmust be subdivided into finite elements for solution. This processof sub division is called meshing. Mesh datasets containinformation about element types, element discretisation and meshtype. The I-beam models were assigned ungraded mild steel for its

material property with Youngs modulus, Es = 209 103 N/mm2,

shear modulus, G = 79 103 N/mm2 and Poisson ratio of 0.3. Thebeams are simply supported and unrestrained laterally.


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The convergence of the mesh was established by independentlyincreasing the mesh density in each part of the model beam

section. The model was also analysis with increased mesh densityin all parts of the section simultaneously, and with higher-orderelements (QSL8).

2.3.2 Eigenvalue Buckling Analysis

The main objective in the Eigenvalue buckling analysis is to obtainthe critical buckling load, by solving the associated Eigenvalueproblem. In LUSAS, there are two methods to obtain informationregarding buckling loads and their respective deformation modei.e. The linear Eigenvalue buckling analysis and the fullgeometrically non-linear analysis. Fig. 2.6 shows a typicalbuckling shape in Mode 1.

Modes 1, 2 and 3 represent the buckling shape of the element. In

this study the result of mode one would be considered; because itwas found that all the beam specimen failed in the tests due to thismode. This is also because mode one is the least value. It will beunrealistic to choose the higher modes 2 and 3 to get the criticalbuckling load. The resulted Eigenvalues are actually the loadfactors to be multiplied to the applied loading, to obtain criticalbuckling load. The Eigenvalue buckling analysis in LUSAS

Modeller will provide both local and global buckling modes.Engineering judgment is necessary to determine which bucklingmode is the most critical in order to select the appropriate bucklingload factor. It is, of course possible to visually examine theresultant modes in LUSAS Modeller.


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Figure 2.6The buckling shape mode 1

2.4 RESULT AND DISCUSSION

The results ofMb are summarized in Table 2.2. In addition, theMbvalue derived from the design calculation is given for each beam.The method of calculating the design Mb value is also given in BS5950: Part1: 2000, by neglecting the contribution of web. It can besummarized as follow:

The critical buckling loads and the lateral torsional bucklingmoments results of Eigenvalue analysis theory calculation fortrapezoid web profile and flat web are presented in Table 4, forboth type A and type B support. It is shown that, as expected, asthe lengths of the two beams with trapezoid web profile increase,the lateral torsional buckling moment decreases. It is found that,trapezoid web profile sections need higher load to buckle

compared to flat web.This is because of the higher value ofIy forthe TWP section compared to the flat web section [ ].

In terms of the effect of corrugation shape, the results show that


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web with full corrugation (TWP3; hr =B) have a higher resistanceto lateral torsional buckling compared to that of the half

corrugation shape (TWP4; hr = 0.5B). As a conclusion, trapezoidweb profile section have higher resistance in lateral torsionalbuckling behaviour and hence suitable for structural applications.

Fig. 2.7 shows the comparison between the TWP3, TWP4 and FWin their lateral torsional buckling resistance for Type A support.Both set of results show a similar trend i.e. as the beam lengthincreases, the buckling moment decreases. In all beam cases, the

finite element prediction is more than that of the test.For support Type B, the beam length increases, the bucklingmoment decreases. For all specimens, the buckling moment resultsfrom the finite element predictions are bigger than that of the testresults for all lengths of beams.

Table 2.2Percentage difference ofMb for beams with normal flat web

and beams with trapezoid web profile (finite element analysis)

MbSupport Span(mm)

TWP3 TWP4 (FW)

Mb(design)

6000 5.84 5.54 3.70 3.155000 7.05 6.45 4.09 3.854000 8.30 7.81 4.39 4.73

SupportType A

3500 9.35 8.75 4.40 5.516000 11.62 9.75 7.23 3.325000 14.35 11.28 8.87 8.604000 15.41 13.79 11.50 10.96

SupportType B

3500 15.66 15.05 13.43 13.08


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0

2

4

6

8

10

3000 4000 5000 6000

Mb

(kNm)

Span

Type A

TWP3

TWP4

(FW)

Design

0

5

10

15

20

3000 4000 5000 6000

Mb

(kNm)

Span (m)

Type B

TWP3

TWP4

(FW)

Design

Figure 2.7Buckling moment resistance for different span

Fig. 2.7 shows that as the length increases the value of Mb

decrease. In both figures, comparison between differentcorrugation ratio shows that the value of Mb for TWP3 (half-corrugation) is higher than TWP4 (full-corrugation). The overallobservation shows that the result from the finite element analysis ishigher than the test for support Type B but not for the Type Asupport. In comparison, in all cases, the value of Mb for finiteelement analysis and testing are more than the valueMb from thedesign formula. In finite element analysis, the value ofMb at Type

A support was less than Mb value from design formula. From bothfigures, comparison between different types of restraint shows thatType B gives extra value than Type A support. This is in


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accordance to the theory, i.e. Type B support is supposed to gethigher value ofMb than Type A. This is because of the specimen

was more difficult to move in Type B support. Therefore, the valueofMb will be higher for Type B.

2.5 CONCLUSION

From the experimental and analytical studies on the lateraltorsional buckling on trapezoid web section, it can be concludedthat :

(1) Steel beam with trapezoidally corrugated web section hashigher resistance to lateral torsional buckling compared tothat of section with flat web.

(2) The result shows that corrugation thickness influences theresistance to lateral torsional buckling. Sections with thickercorrugation have higher resistance to lateral torsionalbuckling.

(3) Higher value of moment of inertia about minor axis for thesection with thicker corrugation contributes to the higherresistance to lateral torsional buckling.

(4) Finite element method can be used to determine the elasticlateral torsional buckling moment of the section.

REFERENCES

1. Elgaaly M, Seshadri A, Steel built-up girders withtrapezoidally corrugated webs, 1988, Engineering journal,1st.Quarter, London:AISC.

2. Elgaaly,M, Seshadri,A, Hamilton, R.W, Bending strengthof steel beams with trapezoid corrugated webs, ASCEJournal of Structural Engineering, 1997, Vol.123.

3. Johnson,R.P and Caffola, J, Local flange buckling in plategirders with corrugated webs, Proceeding Instn Civil

Engineering Structures and Buildings, 1997.4. Osman, M.H, Shear buckling of trapezoid web profile

section, International Conference on Numerical Method in


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Structural Engineering, Indonesia, 2001.5. Osman, M.H, Secondary bending moment in trapezoid

web section, Civil Engineering Research Seminar,Universiti Teknologi Malaysia, Johor, Bahru.

6. Osman, M.H, C,H, Tan, Axial buckling of column withtrapezoid web, Asia Pacific Structural EngineeringConference, 2003, Johor Bahru, Malaysia.

7. Dirk, P.P, Lateral torsional buckling of of end notchedsteel beams, International Colloquium on Stability ofStructures under Static & Dynamic Loads, ACSE, 1977.

8. Salina, J , Lateral torsional buckling of beam withtrapezoid web profile, Master thesis, Universiti TeknologiMalaysia, 2003.

9. Anis, Behaviour of connection of composite beam withtrapezoid web profile PhD. Thesis, Universiti TeknologiMalaysia, 2007.


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3ANALYTICAL STUDY ON SECONDARYBENDING MOMENT IN TRAPEZOID

WEB BEAMMohd Hanim Osman, Abd. Latif Saleh, A. Aziz Saim and

Fong Shiaw Ween

3.1 INTRODUCTION

Trapezoid web beam is a type of steel I-section in which the web ismade corrugated in a trapezoidal profile form. The corrugated thinweb is continuously welded to the flanges along the top andbottom edges. Trapezoid web beam is a built up section that able tosupport vertical loads over long spans. The higher bendingcapacity is achieved by increasing the depth of the section.Increasing the depth will increase the slenderness of web andhence reducing the shear buckling capacity. Ordinarily, theeconomic design of steel web I-beam requires thin web. To avoidshear buckling, intermediate stiffener has to be used, oralternatively, the web can be made corrugated in trapezoidal

profile. When beams with corrugated webs are compared withthose with stiffened flat webs, it can be found that trapezoidalcorrugation in the web enables the use of thinner webs andtrapezoidal web beams eliminate costly web stiffeners.

The flange of trapezoid web beam carries the bending moment andthe trapezoidal web carries the shear force. Due to the shear forcesubjected on the trapezoidal web, a lateral bending moment isinduced in the flange, which is known as secondary bendingmoment, Myf. It will cause a minor reduction in the bendingmoment capacity of the web, as given in the second term of the


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interactive equation:

1


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28 Analytical Study on Secondary Bending Moment in Trapezoid Web Beam

value of Co due to the lateral forces were calculated.Subsequently, from the parametric study of various section sizes,

and web depth and thickness, the general formula of Co wasdeveloped.

3.3 SECONDARY BENDING MOMENT IN TRAPEZOIDWEB BEAM

Fig. 3.1 shows a short segment of a web with a trapezoid profile,

subjected to a vertical force at its end. Due to the corrugation ofthe web, it tends to bend laterally, which then exerted lateral forceto the flange which are weld connected to the top and bottomedges of the web. These reactions become imposed lateral force tothe flange, resulted in the bending moment about the minor axis ofthe flanges.

Figure 3.1The lateral reaction created by a shear force

Shearforce Bottom

edgeTop view

Topedge

Lateral force tothe flanges


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The shear force subjected to a corrugated web section is resisted

by its web, through the development of a shear stress flow asshown in Fig. 3.2.

The oblique orientation of alternate web sub panels inducescomponent forces, Q from the shear stress flow, in lateral direction(z direction) of the section in each of the sub panel. Thesecomponent forces act in opposite direction. This will result intocouples and induces secondary bending moment, Myfabout the y-

axis of the section.Myf=Qa (3.2)

The secondary bending moment, Myfin each flange change linearlywith the applied shear force and can be written by:

Myf=VCo (3.3)

where V is the direct shear loading applied to the web, Co is the

geometric constant called secondary bending moment coefficient,in unit mm. From Eq. (3.2) and Eq.(3.3), Co becomes:

V

aQCo

.= (3.4)

The lateral reaction depends on the section properties and increaselinearly with the applied shear force. Thus, secondary bendingmoment coefficient, Co is induced. In a flat web plate, there is no

inclined web, thus no transverse component of shear stress flow.Nina [2] had made some analysis on Co and Co/Mcyf values forvarious web depths. Graphs ofCo and Co/ Mcyfversus web depthfrom the analysis and the existing manufacturers table ofproperties were plotted. She concluded that the values ofMcyfandCo from analysis give reasonable comparison with the existingdesign table.


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Figure 3.2The shear stress flow and secondary bending moment

3.4 FINITE ELEMENT ANALYSIS

A finite element model which was made up of two cycles webpanel was studied. The number of cycles in trapezoidal web wasfound to be of no effect to the result. The model consists of top and

bottom flanges, trapezoidal web and right and left side stiffenersplates as shown in Fig. 3.3.

V

V

V

V V

V

V

V

V

V

V

V

V

V

y

x

z

Shearforce

Shearstressflow

Q

Q

a

Myf=Q.a


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Each surface is formed from 4 nodal lines. Semiloof curved thinshell element (QSL8) which is a family of shell element in 3D

dimension was chosen to represent the element type of model inthis study. Thin shell is selected as the generic element type,Quadrilateral as the element shape with quadratic as theinterpolation order. Regular mesh was assigned by allowedtransition pattern with 1 local xandydivision.

Surface geometric are assigned to the web with the thickness of 2mm. Flange and side plates were of different thicknesses. Isotopic

material properties are assigned to the model with Youngsmodulus of 205 106 kN/m2 and Poissons ratio of 0.3.

The nodes along the supported side were restrained in translationin x, y, z direction. The nodes along the loaded side are restrainedin x and z direction only. Nodes connecting web and flanges arerestrained in z direction. The total concentrated load in verticaldirection, 20 kN is assigned to the points along the loaded side ofthe plate which allowing deformation in vertical direction (ydirection only). Fig. 3.3 shows the loading arrangement assigned tothe model in the analysis.

The finite element analysis was carried out to determine thereactions at lateral direction at the nodes along the top and bottomedges of the web. A parametric study was carried out on more thanforty finite element models with the web depth ranging from 300to 1300 mm, flange width ranging from 120 to 300 mm, flange

thickness from 10 to 30 mm, and web thickness from 2 to 8 mm.


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X

Y

Z

Figure 3.3Support and loading condition assigned to the model

3.5 RESULTS OF THE FINITE ELEMENT ANALYSIS

The lateral reactions of each section size, in each oblique part forthe trapezoidal web are summarized in Table 3.1 for five typicalsizes. Fig. 3.4(a) illustrates the phenomena of the lateral reactionson the nodes along the oblique web of a section with 300 mmdepth web. The sum of the forces, Q on each sub-panel is shownin Fig. 3.4(b), which shows thatQ is equal for all sub-panels.

The sum of lateral forces on one oblique sub-panel at the upperflange and bottom flange is equal in magnitude but is opposite indirection. At the oblique part of the web, the total forces at the topflange are balanced to the total forces at the oblique part of bottomflange. These opposite forces forms a couple, which is known assecondary bending moment, Myf due to the lever arm betweenthem, a= 250 mm for each couple along the section.

Myf=Q 250 (3.5)


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Table 3.1Lateral reaction on nodes of inclined web for some typicalsection sizes

Section sizeLateral reaction each

nodetop flange (kN)

Lateral reaction eachnode

bottom flange (kN)

Web1

Web2

Web3

Web1

Web2

Web3

Q

(Average)

300 120 10 -2.357 1.727 -1.080 2.357 -1.727 1.080

-0.004 0.004 -0.003 0.004 -0.004 0.003

-3.752 3.748 -3.752 3.752 -3.748 3.752

-0.003 0.004 -0.004 0.003 -0.004 0.004

-1.079 1.727 -2.358 1.079 -1.727 2.358

Total, Q -7.195 7.210 -7.197 7.195 -7.210 7.197 7.201

350 120 10 -2.022 1.481 -0.927 2.022 -1.481 0.927

-0.003 0.003 -0.003 0.003 -0.003 0.003

-3.218 3.213 -3.218 3.218 -3.213 3.218

-0.003 0.003 -0.003 0.003 -0.003 0.003

-0.926 1.481 -2.023 0.926 -1.481 2.023

Total, Q -6.172 6.182 -6.173 6.172 -6.182 6.173 6.176

400 120 10 -1.771 1.297 -0.811 1.771 -1.297 0.811

-0.003 0.003 -0.002 0.003 -0.003 0.002

-2.817 2.812 -2.817 2.817 -2.812 2.817

-0.002 0.003 -0.003 0.002 -0.003 0.003

-0.811 1.297 -1.771 0.811 -1.297 1.771


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Table 3.1(continued)Lateral reaction on nodes of inclined web forsome typical section sizes

Section sizeLateral reaction each

nodetop flange (kN)

Lateral reaction eachnode

bottom flange (kN)

Web1

Web2

Web3

Web1

Web2

Web3

Q

(Average)

450 120 10 -1.575 1.153 -0.722 1.575 -1.153 0.722

-0.003 0.003 -0.002 0.003 -0.003 0.002

-2.504 2.499 -2.504 2.504 -2.499 2.504

-0.002 0.002 -0.003 0.002 -0.002 0.003

-0.721 1.153 -1.575 0.721 -1.153 1.575

Total, Q -4.806 4.812 -4.806 4.806 -4.812 4.806 4.808

500 120 10 -1.418 1.039 -0.650 1.418 -1.039 0.650

-0.002 0.002 -0.002 0.002 -0.002 0.002

-2.254 2.250 -2.254 2.254 -2.250 2.254

-0.002 0.002 -0.002 0.002 -0.002 0.002

-0.650 1.038 -1.419 0.650 -1.038 1.419

Total, Q -4.326 4.331 -4.327 4.326 -4.331 4.327 4.328


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(a) Force on each node at the top flange due to the reaction to theoblique web

(b) Total lateral forces at each oblique sub panelFigure 3.4Lateral forces induced in the flanges at oblique sub panel

for the web depth 300 mm

Q varies linearly with V. ThereforeMyfvaries linearly with V andgiving,

Myf=VCo (3.6)

where Co is a coefficient called the coefficient of secondary

2.357

0.004

3.752

0.003

1.079

0.004

3.748

0.004

1.727

1.080

0.003

3.752

0.004

2.358

1.727

7.197kN

7.197kN

7.210kN

7.210kN 7.195kN

7.195kN


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bending moment, which has the unit in mm. Co is obtained bycalibrating between the applied shear loading and the secondary

bending moment resulted from the couples.

Co =Q 250 / V (3.7)

The values ofCo from finite element analysis are calculated basedon the equation above. The values are compared toCo values fromGerman existing table capacities. Table 3.2 shows the ratio ofCo/Mcyf from calculation compared to Co/Msec,o ratio from theexisting capacities table. The relations of Co/Msec,o versus web

depth are illustrated in Fig. 3.5.

Table 3.2The comparison ofCo between the FEM analysis and theexisting manufacturers standard table

D Qavr V Co(mm) Co/Mcyf Co/Msec,o

(mm) (kN) (kN) FEA Existing

McyfkNm

Msec,okNm FEA Existing

300 7.201 20 90.01 98.60 8.52 11.64 10.58 8.47

350 6.176 20 77.20 89.00 8.52 12.38 9.06 7.19

400 5.406 20 67.58 80.30 8.52 12.87 7.93 6.24

450 4.808 20 60.10 73.00 8.52 13.23 7.05 5.52

500 4.328 20 54.10 66.90 8.52 13.53 6.35 4.94

550 3.935 20 49.19 61.10 8.52 13.66 5.77 4.47

600 3.608 20 45.10 56.80 8.52 13.88 5.29 4.09650 3.310 20 41.38 52.60 8.52 13.98 4.86 3.76

700 3.094 20 38.68 49.60 8.52 14.16 4.54 3.50

750 2.888 20 36.10 46.50 8.52 14.32 4.24 3.25

Note: D = overall depth, Flange width = 120 mm, Flange thickness = 10mm, web thickness = 2 mm

The results from the finite element analysis show that the values ofCo and ratio Co/Mcyfdecrease with the increase of the web depth.From the Table 3.2, values ofCo from finite element analysis are


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lower than Co given in the existing manufacturers standard tableof properties. However, values of ratio Co/Mcyf from the analysis

are higher than the existingCo/Msec,o , as shown in Fig. 3.5. This isbecauseMcyf is lower thanMsec,o.

From Fig. 3.5, the pattern of graphs plotted from finite elementanalysis is similar with the existing standard table of capacities.Hence, the derivation of secondary bending moment, Myf andsecondary bending moment, Co from the finite element analysisgive reliable comparison with the existing table capacities.

Figure 3.5Co/Msec,o vs. depth of web, from the finite element analysisand the existing value

3.6 DERIVATION OF THE COEFFICIENT OFSECONDARY BENDING MOMENT

In order to develop a general formulation for the value of Co, a

parametric study was carried out, by using sections with variousdimensions, i.e. depth of section ranging from 300 to 1300 mm,

B =120mmT =10mm

3166.3x-1.000

3252.4x-1.044


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flange width from 120 to 350 mm, flange thickness from 10 to 30mm and web thickness form 2 to 8 mm. It was noted that the web

thickness do not affect much on the secondary bending moment.From the data of the analysis, a best fit equation has beendeveloped for the value of Co/Mcyf, i.e.

)0008.01(2235.3

10102

Tcyf

o

DxB

x

M

C

= (3.8)

whereB is the flange width (mm), D is the web depth (mm),T is

the flange thickness (mm), Co is the coefficient of secondarybending moment (mm) andMcyfis the minor axis moment capacityof each flange (kNm).

By substituting various dimension data, a typical graph relating thesecondary bending, section depth and flange width was plotted, asshown in Fig. 3.6.

The formula developed in Eq. (3.8) is compared with the finite

element results and the values in the existing table, as shown inFig. 3.7. They have a similar pattern of curve. It shows that theformula for the secondary bending moment developed in this studycan be reliably used for design. Another significant note is that thecurve generated from the formula is higher than the curve for theexisting table. This means that the formula will give a moreconservative design because it over estimate the values of thesecondary bending moment.


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Figure 3.6Co/Mcyfvs. web depth from formula result for varioussection


48/140


(a)

(b)Figure 3.7GraphCo/Mcyfvs. section depth and flange width

3.7 CONCLUSION

Secondary bending moment may reduce the bending momentcapacity of a web with trapezoid web. A series of finite elementanalysis on various size and properties of trapezoid web beam


49/140


under shear loading was carried out by using LUSAS finiteelement analysis. The lateral reactions at the top and bottom flange

were obtained for different geometric parameters. The data wereused to calculate the secondary bending moment, Myf induced ineach flange and the coefficient of secondary bending moment, Co.From the parametric studies using a wide range of geometricalsection properties, curves were plotted relating the values of Co,the moment capacity about minor axis of each flange, Mcyf, andvarious section properties, a general formula for Co/Mcyfhas beendeveloped. The formula was verified by comparing with the

existing manufacturers standard table of properties and found tobe more conservative to be used in design. By referring to theformula, it will be become easier for local engineers to performtheir design work, choose and determine a safer and more suitablesize of trapezoid web beam. Various size of trapezoid web beamcan be chosen and manufactured.

It is also suggested that experimental work should be carried out to

obtain the value of lateral reactions in future research. From theexperiment, the results can be compared with the formula of Cothat derived in this study. By comparing the results from both theexperimental and analytical studies, the formula of Co can beimproved and verified. This will result in more reliable value ofCowhich could be considered in the future study and developed intotrapezoid web beam design work.

REFERENCES

1. Hussein, W.Q. (1997), Design Concept of Trapezoid WebProfile, Lecture notes and technical report, Johor: AntaraSteel Mill Sdn. Bhd.

2. Nina Imelda (2003), The Effect of Opening on the Strength ofCorrugated Web Plate Girder Subjected to Shear, Master

Thesis, Universiti Teknologi Malaysia, Skudai.3. R. C. Hibbeler (2003), Mechanics of Materials fifth edition,

Upper Saddle River, New Jersey: Pearson Education, Inc.


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4. Ferdinand P. Beer, E. Russell Johnston, Jr. (1981), Mechanicsof Materials, United States of America: McGraw-Hill, Inc.

5. Hussein, W.Q. (1998), Design Concept for Steel Plate Girderwith Corrugated Webs (TWP), Pasir Gudang, Johor:Trapezoid Web Profile (TWP) Sdn. Bhd.

6. LUSAS Modeller User Manual, Version 13.5 (2002), UnitedKingdom: FEA Ltd.

7. Fong, S,W,Secondary Bending Moment in Trapezoid WebSection subjected to shear force, Master Thesis (2006),Universiti Teknologi Malaysia.


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4BUCKLING ANALYSIS OF COLUMNWITH TRAPEZOID WEB

Mohd Hanim Osman, Tan Cher Siang and Abd. LatifSalleh

4.1 INTRODUCTION

Trapezoidal web section is a type of flanged steel section with theweb part made corrugated in trapezoidal form (Fig. 4.1). Plategirders fabricated from TWP section offer an alternative toconventional hot rolled and welded sections of uniform webprofile. They have been proven to be more economical in terms of

materials used and the time of fabrication [1]. Study on trapezoidweb girder sections has been conducted in the Steel TechnologyCentre, Universiti Teknologi Malaysia to develop a design guidefor beam with trapezoid web profile. For compression member, acomprehensive analytical and experimental study is required tocomplete the design guide. There is no evidence of research effortin this subject.

The objective of this research is to develop the formulation for thebuckling capacity of column with trapezoid web. The scope of thestudy is focused on the comparison of lateral bending behaviourbetween flat web (FW) and TWP section to study the effect ofcorrugated profile on the second moment of area (I) of the section,by experimental, analytical and numerical approaches. It wasfollowed by the study on buckling load using eigenvalue analysisin the LUSAS finite element program. The deflection and buckling

study was for the minor axis only.

For the comparison between theoretical and experimental results,


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Euler buckling load is assumed in the theoretical elastic criticalbuckling load. Based on the results of the finite element analysis,

and in comparison with the experimental results, a design guide forthe design of column with trapezoid web profile is proposed.

Experimental study is the best approach to determine the actualbehaviour of TWP column. K.J .R. Rasmussen [2], Saleh H. Al-Sayed [3,4] and E.M. Basista [5] had done tests on columnsfabricated from slender plates, single angle columns and channel-columns. Their studies show that a direct column testing requires

sophisticate and well-planned set-up. They also involved a largeamount of testing specimens (about 10 ~26 specimens for eachtesting), which may be not practical and fund-effective in thisresearch. Therefore, computer modelling is recommended.

Figure 4.1 Trapezoid web profile

hr

B

x

x

D


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45 Buckling Analysis of Column with Trapezoid Web

4.2 BUCKLING CURVE IN COLUMN DESIGN

4.2.1 Buckling Curve for Columns with Flat Web Section

The basic formula for the buckling of pin ended strut based onEuler is given by:

2

2

L

EIPE

= (4.1)

In BS 5950: Part 1: 2000 [6], the basic buckling formula ismodified empirically according to the types of section, thickness ofsteel and methods of fabrication. For the welded I section, thebuckling curve is given in Table 24(b), which is based on Perry-Robertson formula given in the standard.

4.2.2 Proposed Design Formula for Column with TrapezoidWeb Section

In the design of the compression member with trapezoid web, theproposed design guide is based on the same standard andneglecting web in the calculation of the moment of inertia of thesection. The design buckling strength is reduced by 10% in orderto obtain a conservative but safer design load, after consideringthat the deflection of trapezoid web about its major axis is 10%

higher than flat web [7]. However, no evidence of experimentaland analytical study have proved this proposed method so far, thusit is unclear of the conservativeness level.

4.3 SECOND MOMENT OF INERTIA OF TRAPEZOIDWEB

From the formula, the second moment of area (I) stands as animportant factor in the column strength. The column usually starts


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buckle at weakest axis (minor axis or y-y axis), so Iy will be themain concern in this research. For TWP, Iy cannot be calculated

mathematically because the corrugated web gives a non-uniformprofile. The first approach is to neglect the web, made the Iy valuesmaller but safer in use. There are few alternative proposedformula for the moment of inertia:

(i) Neglect the contribution of web, a simplified formulaproposed by Wail [1] and Osman [8].

(ii) Include the contribution of web by assuming similar to

symmetrical section as is studied herein.

(iii)Similar to (ii) but reducing 10% to consider the finding byIhsan [7] that the deflection of trapezoid web is greater thanthe flat web.

(iv) Include the web as proposed by unquoted reference [1].

In the proposed Eq. (4.1) the formula is given as:

12

x 3BtII

fyfy ==

(4.2)

In the proposed Eq. (4.2) the formula is given as:

+

=+=

12

x

12

x 33wf

ywyfy

tdBtIII

(4.3)

In the proposed Eq. (4.3) the contribution of web is given by:

+

=

sin6

x

2xx2

32

x

hthtdI rwrwyw

(4.4)

Although Eq. (4.4) tries to take into account the contribution ofweb in more detail, it results in an unreliable value of moment of


55/140


inertia, thus is not considered further here.

For the range of standard sections of TWP, it has been found thatthe contribution of web to the moment of inertia about the minoraxis of the section is less than 0.5% which is not significant. Thisis because the web is very thin compared to other element.4.4 STUDY OF LATERAL BENDING

The deflection of simply supported beam, length L under a mid-point load P is given by the simple formula as:

EI

PL

48

3

max = (4.5)

The value of the second moment of area I is the only sectional

parameter influencing the deflection. By knowing the P and value, I can be obtained as :

=

E

LPI

48

3

max(4.6)

For two beams of the same material and length , the ratio of theirmoment of inertia can be written as:

1

2

3

2

3

1

2

1

48

48

=

=

E

LP

E

LP

I

I

(4.7)

i.e. I is inversely proportional to deflection. For the conventionalsection with uniform web profile, I is simply calculated. For non-uniform section such as the trapezoid web, there are a number ofproposed formulas which none of them have been verified.

A load-deflection test was carried out for both beam specimenswith trapezoid web and flat web, 300 120 10 2 (DBTt) sections. The span of beams was 5 m, 4 m and 3 m, with a load


56/140


at mid-span. Load actuator 100 kN capacity was used to applypoint load on the beam and the mid-span deflection was measured

using displacement transducers and recorded in the dataacquisition logger. The result is presented in Fig. 4.2 which showslower deflection of trapezoid web section (range from 2 6%). Itmeans that the moment of inertia of section with trapezoid web ishigher than that of flat web accordingly.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 10.00 20.00 30.00 40.00 50.00

Deflection (mm)

Loading,

P(kN)

TWP Test Result

FW Test Result

Theoretical Value

TWP FEM

FW FEM

Figure 4.2 Load deflection relationship of 5 m length beam section

Numerical study was carried out on the same model using LUSASfinite element method. The finite element model of trapezoid webbeam is shown in Fig. 4.3, which also shows the deflection inminor axis. The deflection of TWP beam was 3% lower than flatweb. The experimental and numerical results, together with theanalytical calculation using Eq. (4.6) were shown in Fig. 4.3 for atypical length of 5 m.

It is shown that the deflection of trapezoid web beam is slightlylower than the flat web beam of about 3%. It is shown that the

result of finite element analysis is equal to the theoretical formulaas in Eq. (5). The experimental results are found to be less than


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the theoretical results. However, this does not affect theconclusion of the study because this is a comparative study which

is based on the flat web section as control.

Figure 4.3The finite element model of beam and the deflection in

minor axis

4.5 CRITICAL BUCKLING LOAD BY FINITEELEMENT METHOD

The Eigenvalue buckling analysis in the finite element method

was used to determine the elastic critical buckling load of column.A total of 23 trapezoid web column models were analysed,ranging from depth 300 to 1500 mm, covering the full range ofstandard sections produced by fabricators.

The lengths of 4, 6 and 8 meter were used for each section, givingthe slenderness of column ranging from 50 to 256, and to the totalof 253. Almost all models ran successfully, few were failed in

local buckling before achieving elastic member buckling. Fig. 4.4shows a typical buckling mode of column.


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Figure 4.4A typical buckling mode of column

The results for the length of 4 meter were presented in Table 4.1.

It is noted that the buckling load increased linearly with theincrease in the second moment of area of the sections, as shown inFig. 4.5. This is as expected by Eq. (4.1) i.e. the buckling load fora certain length of column increase linearly with the secondmoment of inertia of the section. It also verifies the reliability ofthe modelling technique and the use of Eigenvalue bucklinganalysis in the finite element program. The theoretical bucklingload (assuming flat web section) is also shown in the figure. Thebuckling load of trapezoid web column is found to be higher(maximum 2.71%) than the flat web in the range of smaller


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sections, but becomes lower (minimum 1.49%) than the flat webfor larger sections.

The phenomena that the buckling load of trapezoid web decreasesfor larger section is clearly shown in Fig. 4.6. The reason is dueto the ratio between the corrugation thicknesses, hr in relation tothe width of section, B. For the larger sections, the ratio, hr/B islow. This is in agreement with the report by Siang [9], that thedeflection in minor axis direction increases when the corrugationthickness decrease. Since I is inversely proportional to deflection,

it follows that the critical buckling load decrease accordingly.The variation of (Pcr-Pe)/Pe for different hr/B is shown in Fig. 4.7.It seems that there exists a consistent relationship between the twoparameters. Taking the lowest envelop as the conservative values,the point ofhr/B = 0.45 is the reference for which the buckling oftrapezoid web and flat web of the same web and flange thicknessare equal. Therefore, a formula can be derived for the bucklingcapacity of trapezoid web column, Pcr, as follows:

+= 5.4101

B

hPP recr (4.8)

wherePe is the buckling capacity of the section assuming as flatweb, which can be obtained from the buckling curve in BS 5950:2000. In the calculation ofPe, it does not make any difference ofwhether the web is included or not.


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Table 4.1Buckling load finite element method and Euler formula

Web included Web neglected

NoGeometrical dimension

(mm) Iy Pe Iy PE PcrTWP Diff.

D B T t (mm4) (kN) (mm4) (kN) (kN) %

1 300 120 10 2 2880187 364 2880000 364 374 2.71

2 450 140 10 2 4573620 578 4573333 578 587 1.5

3 450 180 12 4 11666272 1475 11664000 1475 1487 0.78

4 550 120 10 2 2880353 364 2880000 364 374 2.71

5 550 180 12 4 11666805 1475 11664000 1475 1487 0.79

6 650 140 10 2 4573753 578 4573333 578 587 1.52

7 650 140 10 2 4573753 578 4573333 578 587 1.52

8 650 160 12 2 8192417 1036 8192000 1036 1040 0.42

9 650 180 12 4 11667339 1475 11664000 1475 1487 0.81

10 750 120 10 2 2880487 364 2880000 364 374 2.72

11 750 180 12 4 11667872 1475 11664000 1475 1487 0.81

12 750 250 20 4 52087120 6587 52083333 6586 6521 -0.99

13 900 140 10 2 4573920 578 4573333 578 587 1.51

14 900 180 12 4 11668672 1476 11664000 1475 1487 0.8215 900 250 20 4 52087920 6587 52083333 6586 6521 -0.98

16 1000 180 12 2 11664651 1475 11664000 1475 1476 0.08

17 1000 200 16 2 21333979 2698 21333333 2698 2687 -0.4

18 1000 240 16 2 36864645 4662 36864000 4662 Fail! 0

19 1000 270 16 4 52493163 6638 52488000 6637 6551 -1.3

20 1200 200 16 2 21334112 2698 21333333 2698 2687 -0.39

21 1500 200 16 3 21336636 2698 21333333 2698 2693 -0.16

22 1500 250 18 3 46878294 5928 46875000 5928 5864 -1.0723 1500 300 20 3 90003285 11381 90000000 11381 11211 -1.49


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(a)

Figure 4.5Buckling load versus the second moment of area

Figure 4.6Variation ofPcr/Pe with the second moment of inertia

0

2000

4000

6000

8000

10000

12000

0 2000 4000 6000 8000 10000

Moment of inertia (cm4)

Bucklingload(kN) Flat web

-2

-1

0

1

2

3

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Moment of inertia (cm4)

(Pcr-

Pe

)/Pe

(%)


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-2

-1

0

1

2

3

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700

hr/B

(Pcr-

Pe

)/P

e

Figure 4.7The influence of corrugation thickness ratio to the bucklingload

4.6 CONCLUSION

From the study on the derivation of buckling capacity of columnsections with trapezoid web profile, it can be concluded that:

(a)The contribution of web to the second moment of area oftrapezoid web of standard sections is negligible.

(b) Experimental results showed that the deflection of trapezoidweb beam is less than the flat web section. The deflection of

beam with trapezoid of lower hr/B is than the flat web, but isgreater for lowhr/b.

(c)The Eigenvalue buckling analysis has been used successfullyto estimate the critical buckling load of compression member.

(d)The buckling of column with trapezoid web has beendetermined. It is higher than flat web for higher hr/B andlower for lower hr/B.

The most important conclusion is that the buckling formula fortrapezoid web column has been proposed.


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REFERENCES

1. Wail Q. Hussein (2001). Design Guide for Steel PlateGirders With Corrugated Webs (TWP). Johor: TrapezoidWeb Profile Sdn. Bhd.

2. Nethercot, D.A. & Lawson, R.M. (1992). Lateral Stability ofSteel Beams and Columns Common Cases of Restraint.Berkshire: The Steel Construction Institute.

3. K.J .R. Rasmussen, al et (1990). Design of ColumnsFabricated from Slender Plates. Journal of Construction Steel

Research Vol. 17. Great Britain: Elsevier Science PublishersLtd.

4. Saleh H. Al-Sayed & Reidar Bjorhovde (1989). ExperimentalStudy of Single Angle Columns. Journal of ConstructionSteel Research Vol.12. Great Britain: Elsevier SciencePublishers Ltd.

5. E.M. Batista & E.C. Rodrigues (1994). Buckling Curve for

Cold-Formed Compressed Members. Journal of ConstructionSteel Research Vol. 28. Great Britain: Elsevier SciencePublishers Ltd.

6. British Standards Institution (2000). BS5950: The StructuralUse of Steelwork in Building, Part 1. London: BSI.

7. Hasni@Ihsan b. Atan (2000). Flexural Behavior of TrapezoidWeb Plate Girder. UTM: Master Thesis.

8. Hanim Osman & Salina Jamali (2001). Report of Design

Guide Using Trapezoid Web Profile (Calculation). UTM Steel Technology Center: Technical Report (Sept).

9. Tan Cher Siang, The second moment of area of trapezoidweb section, Technical Report submitted to Faculty of CivilEngineering, UTM, 2003.


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5PERFORMANCE TEST ON SIMPLYSUPPORTED COMPOSITE BEAM WITH

TWP STEEL SECTIONGoh Kee Keong and Mohd Hanim Osman

5.1 INTRODUCTION

Steel beams with trapezoidal web profile (TWP) have been widelyand increasingly used in recent years mainly due to corrugatedwebs have allowed the use of thin plates without the need forstiffeners. On the other hand, beams with steel-concrete composite

action are one of the most commonly used structural elementsbecause they considerably increase flexural strength and stiffnessof steel beams. However, there are few or no experimental test dataavailable which to check the performance of TWP steel sectionacting compositely with concrete. Consequently, the search for thisexperimental data has been the main concern in this project and theexperiment is briefly described and discussed in this paper.

The objectives of this project are: (a) to compare the ultimateperformance of composite beam with TWP steel section tocomposite beam with I-plate girder; (b) to study the suitability ofadopting composite design method by BS5950: Part 3: Section 3.1[1] for designing composite beam with TWP steel section; (c) toobtain the stress and strain distribution and the position of neutralaxis of the composite beam with TWP steel section. These willalso allow better understanding of the true behaviour of composite

beam with TWP steel section.


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5.2 METHODOLOGY

5.2.1 Test Specimens

A steel-concrete composite beam, with trapezoidal web steelsection, is designed base on BS5950: Part 3: Section 3.1. In which,the design assumed that the ultimate bending strength may betaken as the plastic moment capacity of the steel and concreteacting compositely, given as the function of their plastic section

modulus and their material yield strength. From the design, theproposed test specimen with steel cross section of 300 120 mmand concrete flanges of 1000 mm breadth and 110 mm thickness isshown in Fig. 5.1. As control, a similar set of composite beam withI-plate girder will also be tested.

5.2.2 Test Setup

The apparatus for the testing programme as shown in Fig. 5.2 and5.3 was arranged in such a way that a plastic failure mechanismcould be developed in the specimens without incurring significantfrictional forces [2]. Frictional forces developed at the loading andreaction points were reduced through the use of rollers at thereaction and loading points. Torsion restraint was provided at theloading points by adjustable torsion restraints.

At each section labeled A, B, and C, five strain gauges wereattached; one at concrete and the remaining gauges at the steelsection. Concrete and steel surfaces where gauges will be attachedwere grinded to remove paint and rust as well as to provide asmooth surface for effective bonding.


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58 Performance Test on Simply Supported Composite Beam with TWP Steel Section

(a) Composite beam with TWP section

(b) Composite beam with I-plate girder (Control specimen)

Figure 5.1Test specimens

300

1000

110

120

280

10

1

2

300

1000

110

120

28

10

10

2


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Figure 5.2Elevation of the test arrangement, with strain gaugesattached to provide sections information at A, B, and C. (Torsion

restraints are not shown)

Figure 5.3Plan view of the testing arrangement

AB C

Load Cell

Transfer Beam

Free Rollers

Load Spreader

5m

LOAD

1m2 m

1.0 m

Line Loads

Torsion Restraints

Rollers


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5.3 TEST RESULTS

5.3.1 Composite Beam with I-Plate Girder (ControlSpecimen)

The bottom steel flange of composite beam starts to yield when theload is about 175 kN at mid span, which is at the point ofmaximum bending moment. Following that, at the distance 1.0 m

from mid span at B as shown in Fig. 5.2, the bottom flangestarted to yield at load 180 kN. On the other hand, the yieldingeffects continue to happen and spread towards the neutral axis atthe mid span. However, premature web buckling then occurs atloading 198 kN at section B, which prevents the development ofthe full bending strength.

Elastic neutral axis and plastic axis is different. Neutral axisgradually shifted upwards from elastic condition to plasticcondition. From the experiment, the elastic neutral axis (E.N.A.) is88.50 mm from concrete top surface whereas plastic neutral axis(P.N.A.) is 67.24 mm with reference to the same base line. Theconcrete never reached its maximum compression stressthroughout the experiment. As concrete is known for its weaktension resistance, hairline cracks are observed at mid span of thebeam at the bottom edge of concrete and along the longitudinal

direction at middle of the beam, which is believed to be resultedfrom longitudinal splitting forces. It is concluded that a combinedfailure of bending and shear happens to the beam.

5.3.2 Composite Beam with TWP Steel Section

At the load of 150 kN, the bottom steel flange of the specimenreaches its yield strength at the mid span, it follows that the yieldof bottom flange starts to happen at C after 160 kN. Excessive


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deflection occurs when the load reaches 200 kN, which gave asignificant change of the section from elastic condition to lower

bound of plastic condition. First observed hairline crack appears atthe load of 180 kN, and there is minor vertical buckling of flat webnear mid span at this stage. Starting at 210 kN and onwards, moreminor cracks can be easily observed along both of the concreteedges at the mid span region. These cracks include the longitudinalsplitting cracks on top of the concrete surface. From theexperimental data, both steel flanges and concrete material reachedtheir tensile and compressive strength respectively at 230 kN,

meaning that full plastic section is developed. Trapezoidal webbuckling also initiated at B at this particular loading.

The elastic neutral axis (E.N.A.) is 81.35 mm whereas elastic-plastic neutral axis is 69.71 mm. During the end of experiment,concrete reaches its maximum compression stress at mid span withthe corresponding load of 230 kN.

5.3.3 Data Analysis and Comparison

Considering the deflection of the two specimens in Fig. 5.4, withinthe elastic behaviour of the beams, the composite effect with theconcrete material has brought to the common deflection for bothtypes of steel section. Previous test on the deflection of only the

steel sections has shown that TWP section generally deflect morethan I-plate girder under the same loading. And, some otherresearchers of corrugated web beam have agreed such result.However, within the elastic-plastic region, the composite beam ofTWP section deflects less than the control specimen of I-plategirder.


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Figure 5.4Plot of loading (kN) against mid span deflection (mm)

Figure 5.5The distribution of mid span strain at loadings 50, 100,150, 180, 195, and 198 kN for control specimen. (198 kN is the failure

load)

0

50

100

150

200

250

0 5 10 15 20 25 30 35 40 45

Midspan Deflection (mm)

Loadings(kN)

I-girder

TWP

0

50

100

150

200

250

300

350

400

-1000 -500 0 500 1000 1500 2000 2500

Str ains ()

SectionDepth(mm)

50

100

150

180

195

198

Experimental E.N.A. =88.5mm


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Figure 5.6The distribution of mid span strain at loadings 50, 100,150, 180, and 200 kN for specimen with TWP. (200 kN is the failure

load)

The control specimen gave a set of satisfying plots of straindistribution along the section depth, see Fig. 5.5, in which thevalue of positive strains (showing tensile stresses) increaseproportionally to the distance from neutral axis. Such straindistribution is often been idealized into linear strain distribution.

When composite beam with TWP section is tested, theexperimental results show that the web contributes much lesser tothe tensile strength of the steel section. This effect is particularlyobvious at the diagonal web as shown in Fig. 5.6. For this reason,the flanges of the TWP specimen will have to resist the additionaltension force that is not taken by the trapezoidal web. Thisexplained a slightly higher elastic neutral axis.

0

50

100

150

200

250

300

350

400

-1000 -500 0 500 1000 1500 2000 2500

Str ains ()

S

ectionDepth(mm)

50

100

150

180

200

Experimental E.N.A. =81.35mm


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5.4 DISCUSSION

The objective of stressing the composite beam with I-plate girderto ultimate failure is not reached due earlier occurrence of shearfailure before the whole steel section at mid span yield. Nostiffeners have been provided to stiffen the web at the shear area isthe main reason to this. However, stiffeners are not proposed inthis experiment because that will eliminate the advantage of usingTWP. Thus, the results obtained from this experiment as sgiven in

Table 5.1 correspond to the lower bound condition of the ultimatefailure.

Considering the control specimen of I-girder, the obtained positionof elastic neutral axis is rather accurate with only 0.2% and 2.23%differences to the theoretical and design value respectively.However, the plastic neutral axis is much greater than the expectedvalue. This can be explained through several reasons. Before that,it should be noted that the difference of theoretical and designvalue is due to the introduced partial safety factor of concrete

material, m. The first reason for such difference is that theexperimental value is obtained when the steel section is not fullyyielded. In the rigid plastic theory of composite beam, in order tomaintain equilibrium, the whole steel element must yield and onlypart of the concrete element will be fully yielded [4]. The secondreason is the possible slip strain, which is hardly avoided though

full interaction shear connectors have been provided. Moreover,the strain gauge has not been prepared for the bottom surface ofthe concrete.

When comparing the elastic neutral axis of composite beam withTWP, higher position of neutral axis can be explained through thetension strain that is concentrated at the flanges of TWP steelsection, and not because of a stronger steel section is being used. Aslightly rise in concrete strength might as well be the reasonbecause the concrete ages are different in the two experiment, butits significance is yet to be determined.


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In the elastic-plastic stage, particularly after the yielding of bottomflange, composite beam of TWP steel section is able to enhance

greater force and deflects less before the web buckles whencompared to control specimen of I-girder.

Table 5.1Comparison of the Position of Elastic Neutral Axis andPlastic Neutral Axis

(all values are in mm, calculated from the concrete top surface)

Specimen

NeutralAxis

Theoretical

Design[3]

(BS5950:Part3:

Section3.1)

Experimental

Elastic(E.N.A.)

88.66 86.57 88.50CompositeBeam with

I-plategirder

(Controlspecimen)

Plastic(P.N.A.)

35.10 56.31 67.24 *

Elastic(E.N.A.)

83.16 79.52 81.35Compositebeam with

TWP steelsection

Plastic(P.N.A.)

29.15 46.81 69.71 *

* Position of initial elastic-plastic neutral axis

2.5 CONCLUSION

The performance of composite beam with TWP steel section,before the first yielding occurs, needs to be monitored carefully.TWP section does not show any advantage compared to I-plategirder. However, within the elastic-plastic region, especially afterthe bottom flange reached its yield strength, TWP section shows abetter performance with less deflection and stiffer web from


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buckling. It was also found that elastic neutral axis slightly risewhen I-plate girder is replaced with TWP steel section in

composite beam.The performance of TWP-composite beam, before the first yieldingat bottom flange occurs, does not show any excel advantagecompared to I-girder-composite beam. However, within the elastic-plastic region, especially after the bottom flange reached its yieldstrength, TWP section shows a better performance with lessdeflection as well as stiffer web from buckling.

Finally it is concluded that from the experiment carried out in thisproject, BS5950: Part 3: Section 3.1 is less conservative to be usedin designing TWP-composite beam. However, this remark islimited to the service limit state of the beam. The performance ofTWP-composite beam in ultimate state is yet to be determined.

As an overview to the project, it was found that the flexuralbehaviour of TWP-composite beam is as expected by the BS5950:

Part 3 because the design method neglects the strength of steel webin calculating composite moment capacity. Such behaviour isfound also in the TWP-composite beam from the experiment. Butwhen compared to a conventional I-girder-composite beam, itseems that the TWP-composite is less conservative when BS5950:Part 3 design method is adopted.

Hence, it is concluded that by introducing suitable coefficient intothe design method, particularly for the serviceability limit statedesign, BS5950: Part 3 might still be a practical design method fordesigning TWP-composite beam.

REFERENCES

1. BS5950: Part 3: Section 3.1: 1990.

2. Byfield M.P., Nethercot D.A., An Analysis of the TrueBending Strength of Steel Beams, Institution of CivilEngineers Structures & Buildings, 1998.


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3. Commentary on BS5950: Part 3: Section 3.1-CompositeBeams, The Steel Construction Institute, 1990.

4. Oehlers D.J ., Bradford M.A., Composite Steel And ConcreteStructural Members Fundamental Behaviour, Pergamon,1995.

5. Chapman J.C., Balakrishnan S., Experiments On CompositeBeams, The Structural Engineer, Vol. 42, Nov. 1964.


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6EXPERIMENTAL TEST ON STEELBEAM WITH PARTIAL STRENGTHCONNECTIONS USING TRAPEZOIDWEB PROFILED

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