The Study on the Behaviour of Plate Girder With Profiled Web

UNIVERSITI TEKNOLOGI MARA

THE STUDY ON THE BEHAVIOUR OF PLATE GIRDER WITH PROFILED WEB

MD. HADLI ABU HASSAN

Thesis submitted in fulfillment of the requirements for the degree of

Master of Science

Faculty of Civil Engineering

August 2006

ABSTRACT

Engineers have long realized that corrugated webs enormously increase steel girders’ stability against buckling and can result in very economical design. Recently, the new idea of combining the two profiled webs brought new issues of research. The objective of the research presented in this thesis is to investigate the behavior of steel girders with profiled web subjected to shear. Relative buckling modes are also discovered. The work includes experimental works and nonlinear finite element analyses, which includes the development of material and geometric finite element model, whose results are verified against the test results. All the tested specimens and the model were loaded under three point bending. At the same time, calculations are made to investigate their validity in analyzing this kind of girder. The detailed ultimate shear capacity and buckling modes of the girders subjected to different profiled web arrangement cases were studied. The three buckling modes have occurred in this investigation were local, zonal and global buckling mode. It was found that, within the parametric range studied in this thesis, the typical failure modes of the girder with profiled webs are initially in the local buckling mode which occurred either at the top, middle or bottom of the one corrugation fold. After reaching a peak load the buckling propagated to other folds which transformed to zonal or extended to a global buckling mode in a diagonal direction of tension field action beyond the peak load (post-buckling load) and gradually buckled due to crippling of the web and subsequently buckled till the flanges yielded vertically into the web. In the process of buckling, the load displacement relationship of the girder switched to a sudden and steep descending branch. The buckling can reduce the post-buckling shear capacity in the range of 30% to 50% of the ultimate shear capacity. However, the ultimate or post-buckling capacities of profiled web girder did not depend on their buckling mode. Comparison between experimental results and finite element results were satisfactory. Comparison of the ultimate shear capacities between corrugated web girders with the equivalent conventional girders, the ratios were up to 2.00 and 4.30 for singly and doubly webbed corrugated girders respectively.

ii

CANDIDATE’S DECLARATION

I declare that the work in this thesis was carried out in accordance with the

regulations of Universiti Teknologi MARA. It is original and is the result of my own

work, unless otherwise indicated or acknowledged as referenced work. This topic has

not been submitted to any other academic or non-academic institution for any degree

or qualification.

In the even that my thesis be found to violate the conditions mentioned above, I

voluntarily waive the right of conferment of my degree and agree be subjected to the

disciplinary rules and regulations of Universiti Teknologi MARA.

Name of Candidate Md. Hadli bin Abu Hassan

Candidate’s ID No. 2002200168

Programme Master in Science Civil Engineering

Faculty Civil Engineering

Thesis Title The study on the behaviour of plate girder with profiled

web

Signature of Candidate …………………

Date

10th August 2006

ACKNOWLEDGEMENTS

Thank to Allah, Lord of the Merciful, most Gracious and Nabi Muhammad S.A.W. Being the best creation of Allah, one still to depend for many aspects directly and indirectly. I wish to express my profound gratitude to my supervisor Assoc. Prof. Dr. Azmi bin Ibrahim and co-supervisor Datin Assoc. Prof. Dr Hanizah binti Abdul Hamid for noble guidance and supervision in preparation of this study. They are ever dynamic and also their dedication in encourage of young researchers. A research may bear only the name of the authors, but it required many people to bring it to completion. Deepest gratitude and indebtedness to Institute of Research and Development Centre (IRDC) and Faculty of Civil Engineering, UiTM for giving us support and cooperation throughout this project. I also wish to express appreciation to the all the technical staff in Civil Engineering Faculty and SIRIM Bhd for their contributions in helping the experimental work, especially Mr Razman and Mr Roslan. Special appreciation to my wife, family and friends who inspired and encouraged during this study. They always gave me moral support and rendered towards the completion of the research. To all of them, this thesis is earnestly dedicated.

iii

TABLE OF CONTENTS

TITLE PAGE

ABSTRACT ii

CANDIDATE’S DECLARATION

ACKNOWLEDGEMENT iii

TABLE OF CONTENTS iv

LIST OF TABLES vii

LIST OF FIGURES ix

NOTATION xiv

CHAPTER 1: INTRODUCTION 1

1.1 General Statement 1

1.2 Problem Statement 1

1.3 Advantages 2

1.4 Objectives of Study 3

1.5 Scope of Work 3

1.6 Research Methodology 4

CHAPTER 2: LITERATURE REVIEW

2.1 Summary of Research and Development History on Plate

Girder 7

2.2 Buckling Behaviour of Profiled Web Girder Under Shear Load 11

2.3 Shear Capacity of Plate Girder under Shear Load 14

2.3.1 Shear Capacity of Conventional Flat Web Plate Girder

under Shear Load 14

2.3.2 Shear Capacity of Profiled Web Plate Girder under

Shear Load 16

2.3.2.1 Shear Capacity of Profiled Web Plate Girder

Based on Local Buckling 17

2.3.2.2 Shear Capacity of Profiled Web Plate Girder

Based on Global Buckling 17

iv

2.4 Review on Numerical Simulation 19

2.4.1 Geometric and Material Non-Linearity 19

2.4.2 Initial Geometrical Imperfection 23

2.4.3 Meshing 26

2.5 Effect of Welding on Plate Girder 27

2.6 Precaution of Premature Failure in Unforeseen Mode 29

CHAPTER 3: EXPERIMENTAL STUDY

3.1 Introduction 30

3.2 Test Specimens and Test Set-up 32

3.2.1 Material Properties of Test Specimens 32

3.2.2 Design and Preparation of Specimens 34

3.2.3 Testing of Test Specimens 39

3.3 Experimental Results and Discussions 42

3.3.1 Symmetrical and Unsymmetrical Buckling Behaviour of

Tested Specimens 42

3.3.2 Buckling Behaviour of Conventional Flat Web

Specimens 45

3.3.3 Buckling Behaviour of Profiled Web Specimens 50

3.3.4 Load Deflection Behaviour of Tested Specimens 60

3.4 Discussion Summary 68

CHAPTER 4: FINITE ELEMENT STUDY

4.1 Introduction 69

4.1 Preliminary Investigation for Combine Geometric and Material

Non-Linear Analysis with Initial Imperfection 70

4.3 Non-Linear Finite Element Modelling on Profiled Web Girder 80

4.4 Finite Element Results and Discussions 84

4.4.1 Validation of Non-Linear Finite Element Analysis with

Experimental Results of Profiled Webbed Plate Girder 84

4.4.2 Non-Linear Analysis Buckling Behaviour of Profiled

Web Plate Girder 92

v

4.5 Parametric Study on Singly Webbed Profiled Web Girder 97

4.5.1 Influence of Web Depth 97

4.5.2 Influence of Web Thickness 100

4.5.3 Influence of Flange Thickness 104

4.6 Discussion Summary 108

CHAPTER 5: COMPARISON OF EXPERIMENTAL AND FINITE

ELEMENT RESULTS WITH THEORETICAL FORMULA

5.1 Introduction 110

5.2 Comparison of Conventional Flat Web Girder with Design

Formula 110

5.3 Comparison of Profiled Web Girder with Design Formula 113

CHAPTER 6: CONCLUSION AND RECOMMENDATIONS

6.1 Conclusion 118

6.2 Recommendations 120

BIBLIOGRAPHY 121

APPENDICES

Appendix A: The Results of Welding Procedure Specification 128

Appendix B: Buckling of Girders after Testing 132

LIST OF PUBLICATIONS 141

vi

LIST OF TABLES

Table 2.1 The Summary of Research and Development on Profiled Web

Girder 10

Table 2.2 Buckling Coefficient, k Proposed by other Researchers 18

Table 3.1 Properties of Specimens 31

Table 3.2 Results of Tensile Tests 34

Table 3.3 Principal Strain, ε1 and Orientation of Principal Strain of

Rosette 1 Flat Web Specimen (F450-3) 47

Table 3.4 Buckling Modes of Profiled Webs 51

Table 3.5 Detail Results of Test Specimens 66

Table 3.6 Comparison on Ultimate Shear of Corrugated Profiled

Webbed and Conventional Flat Webbed Specimens,

)(

)(Pr

Flatu

ofiledu

VV

. 67

Table 4.1 Percentage Decreasing of Maximum Load, P Compared to

Smallest Amplitude and Calculated Critical Buckling Load 73

Table 4.2 List of Tested Models using Finite Element Analysis 83

Table 4.3 Comparison of Ultimate Shear Loads of Finite Element

against Experimental Results 91

Table 4.4: Buckling Mode of Finite Element Analysis 93

Table 4.5 Results of Non-Linear Analysis for Different Web Depths 100

Table 4.6 Results of Non-Linear Analysis for Different Web Thickness 103

Table 4.7 Comparison between Models with Single (2.0 mm Thick) to

Double Web Arrangement 103

Table 4.8 Results of Non-Linear Analysis for Different Flange

Thickness 107

Table 5.1 Comparison of Experimental Results with Calculated Design

Formula for Conventional Flat Web 112

Table 5.2 Comparison Shear Resistance Based on Local Buckling

against Experimental and Finite Element Results 116

vii

Table 5.3 Comparison of Shear Resistances Based on Global Buckling

against Experimental and Finite Element Results 117

viii

LIST OF FIGURES

Figure 1.1 Application of Plate Girders for Bridges 5

Figure 1.2 Types of Web Profiled Shapes 6

Figure 2.1 Failure Mechanism of Shear Web Panel 8

Figure 2.2 Buckling Modes of Corrugated Web 12

Figure 2.3 Load-Deflection Curve for Corrugated Web Girder

Investigated by Lou and Edlund [39, 40] under Shear and

Patch Load 13

Figure 2.4 Notation of Corrugation Configurations 18

Figure 2.5 Concept of Yield Surface 20

Figure 2.6 Load Deflection Curve obtain with Different Strain Hardening 22

Figure 2.7 Comparison of Ultimate Strength with Different Initial

Imperfection by Lee et al. [26] 24

Figure 2.8 The Type of Initial Shape Imperfection suggested by C. A.

Graciano and Edlund [57] 25

Figure 2.9 Imperfection Shape Sensitivity of Plate Girder under Patch

Load by C. A. Graciano and Edlund [57] 25

Figure 2.10 Finite Element Model by Elgally et al [35]. 27

Figure 2.11 Stress Distribution at Inclined Fold Weld Toe by Kengo Anami

et al. [41]. 28

Figure 3.1 Dimensions of Profile Steel Sheets 30

Figure 3.2 Dimensions of Tensile Test Pieces 32

Figure 3.3 Tensile Testing 33

Figure 3.4 End Post Design 35

Figure 3.5 Assembling of Webs 37

Figure 3.6 Welding Position (Plan View) 38

Figure 3.7 Welding Work at SIRIM Workshop 38

Figure 3.8 WPS Specimens using MIG and GTAW 39

Figure 3.9 Experimental Instrumentation 41

Figure 3.10 Experimental Set-up of Test Specimens 41

ix

Figure 3.11 Symmetrical and Unsymmetrical Buckling Behaviours of

Typical Girder Specimens 44

Figure 3.12 Principal Strains Distribution in Web Panel of Flat Web

Specimens (Specimen F450-3) 46

Figure 3.14 Typical Failure Mode of Conventional Flat Web Specimen 48

Figure 3.15 Diagonal Tension Field with Different Web aspect Ratio (a/d) 50

Figure 3.16 Typical Zonal Failure Mode of Singly and Doubly Webbed

Specimen 52

Figure 3.17 Typical Global Failure Mode of Singly and Doubly Webbed

Specimen 53

Figure 3.18 Local Buckling Mode at Peak Load 54

Figure 3.19 Principal Strain Distribution in Web Panel of Singly Webbed

Profiled Web Specimen (S450-3) 55

Figure 3.20 Principal Strains Distribution in Web Panel of Doubly Webbed

Profiled Web Specimens (D450-3) 56

Figure 3.21 Flange Buckling Mode with Different Web Buckling Mode

Type 58

Figure 3.22 Deformation and Bending Strain of Compression Flange for

Specimen S450-4 59

Figure 3.23 Bending Strain of Compression Flange for Specimen D450-4 60

Figure 3.24 Load Deflection Curves for all Specimens with Web Depth,

d = 350 62

Figure 3.25 Load Deflection Curves for Specimens with Web Depth,

d = 450 mm 63

Figure 3.26 Load Deflection Curve of all Specimens with Web Depth,

d = 550 mm 64

Figure 4.1 Model Isolated Rectangular Plate Modeling 71

Figure 4.2 Load Shortening Curve of Rectangular Isolated Plate 72

Figure 4.3 Typical Finite Element Modeling of Conventional Flat Web

Specimen 74

Figure 4.4 Finite Element Result of Model F450-Fe with Different

Maximum Imperfection Amplitudes (d = 450 mm) 75

x

Figure 4.5 Finite Element Result of Model F550-Fe with Different

Maximum Amplitude (d = 550 mm) 76

Figure 4.6 Comparison Load-Deflection Curve of Finite Element with

Experimental Tested Results for Conventional Flat Web with

Web Depth 450 mm and 550 mm 78

Figure 4.7 Imperfection Shape Sensitivity of Plate Girder with Different

Shape under Shear Load 79

Figure 4.8 Finite Element Model for Single and Double Web Profiled

Web Girder 82

Figure 4.9 Load Deflection Curves for S350 Series 86



Figure 4.12 Load Deflection Curves for D350 Series 88



Figure 4.15 Load-deflection Curves for Corrugated Web Girder

Investigated by R. Lou and Edlund [39] under Shear with

Different Corrugation Depths 89

Figure 4.16 Final Buckling Shape of Doubly Webbed Models at the End of

Analysis 90

Figure 4.17 Comparison of Principal Strain Distribution of S450-3 and

S450-Fe 92

Figure 4.18 Typical Unsymmetrical Deformation of Profiled Web Girder

(Specimen model S550t2.0-Fe) 94

Figure 4.19 Typical Global and Zonal Buckling Shape of Profiled Web

Girder 94

Figure 4.20 Evolution of Deformation Contours in X-direction of Global

Failure Mode of Profiled Web Girder (S550T12-Fe) 95

Figure 4.21 Evolution of Deformation Contours in X-direction of Zonal

Failure Mode of Profiled Web Girder (S450-Fe) 96

Figure 4.22 Load Deflection Curves for Different Web Depths 98

xi

Figure 4.23 Buckling Modes Obtained at the End of the Analysis for

Models with Different Web Depths 99

Figure 4.24 Load Deflection Curves for Different Web Thickness 101


Model with Different Web Thickness 102


Model with Different Flange Thickness 105

Figure 4.27 Load Deflection Curves for Different Flange Thickness, T with

Web Thickness 1.0 mm 106

Figure 4.28 Load Deflection Curves for Different Flange Thickness, T with

Web Thickness 2.0 mm 106

Figure A1 Welding Procedure Specifications 128

Figure A2 Visual and Dye Penetrate Test Report 129

Figure A3 Bending / Fracture and Nick Break Test Report 130

Figure A4 Microstructure Report 131

Figure B1 Buckling of Conventional Flat Web after Testing (Web Depth

350 mm) 132


450 mm) 133


550 mm) 134

Figure B4 Buckling of Singly Webbed Profiled Web after Testing (Web

Depth 350 mm) 135


Depth 450 mm) 136


Depth 550 mm) 137

Figure B7 Buckling of Doubly Webbed Profiled Webs after Testing (Web

Depth 350 mm) 138


Depth 450 mm) 139

xii


Depth 550 mm) 140

xiii

NOTATION a Panel width

d Web depth

T Flange thickness

t Web thickness

Af Flange cross sectional area

w The biggest of flat sub-panel width

rθ Angle of inclined fold

iθ Angel of inclination tension field

Dx, Dy Orthotropic constants for profiled steel sheet

Iy Moment of inertia of one repeating corrugation (profile) about its neutral axis

Vu Ultimate shear force

Vyw Shear force to produce yielding of web

Exp Experimental

M Applied moment

Mf Plastic moment resistance provide by flanges

VR Ultimate shear resistance

FE Finite element

E Elastic modulus

ν Poisson ratio

σ Stress

trueσ True stress

engσ Engineering stress

yσ Yield stress

tσ Stress in tension

ywσ Yield stress of web material

yfσ Yield stress of flange material ytσ Tension field web membrane stress

f Yield functions of material

xiv

k Shear buckling coefficient

yτ Shear yield stress

ywτ Shear yield stress of web material

crτ Critical shear stress of web

lcre ,τ Elastic local buckling shear stress

gcre,τ Elastic global buckling shear stress

lcri,τ Inelastic local buckling shear stress

gcri ,τ Inelastic global buckling shear stress

lnε Logarithmic strain engε Engineering strain

xv

CHAPTER 1

INTRODUCTION

1.1 General Statement

For many structures, all of the beams may be selected from among the standard range

of rolled sections. Sometimes, none of the available section has sufficient capacity.

Such situation may occur when it is necessary for the beams to bridge a long span

and/or carry heavy static/moving loads. For example, most bridges need to carry

heavy primary live loads such as HA and HB loading. Certain industrial buildings

have girders called gantry girders that carry rails for large-capacity overhead cranes.

Normal (gantry) girders are made up of built-up sections, called plate girders.

Nowadays it is a common practice to fabricate such sections simply by welding

together three plates to form the top and bottom flanges, and the web. Figure 1.1

shows the application of plate girder for bridges.

However, from time to time, a new generation of optimized steel girders is

developed. In general, innovated girder systems would require less material and

result in a lighter structure when compared to a conventional girder system having

webs reinforced with vertical/horizontal stiffeners. According to the author’s

knowledge, the two web profiled shapes which are commonly used for girders, are

trapezoidal (most frequently used), and sinusoidal. Figure 1.2 shows the web profiled

shapes used for girders. Therefore, this study tried to determine the performance of

these newly discovered girders with single or double corrugated webs.

1.2 Problem Statement

The primary function of the top and bottom flange plates is to resist the axial tensile

and compression forces arising from the bending action, whilst the web plate resists

the shear force. Since the efficiency of the cross-section in resisting plane bending

requires that the majority of the material be placed as far as possible from the neutral

1

axis, it follows that minimum material consumption is frequently associated with the

use of very thin web. However, in order to prevent premature failure due to web

buckling in shear, then the web needs to be stiffened using vertical and/or horizontal

stiffeners. In practice, to avoid catastrophic failure associated with shear buckling of

the web, either a thin web with stiffeners spaced close to each other or a thicker web

with stiffeners spaced further apart need to be provided.

Ultimate shear strength of the profiled web girder depend on they are web height,

web thickness, and profiled geometric. However, the maximum thickness of the

available manufactured cold form profiled steel sheet made using rolling technique

or stamping is limited. The use of rolling technique produced and maximum

thickness of 2.0 mm and stamping technique produces up to 10.0 mm thick. Hence,

double web systems are useful in enhancing the ultimate shear strength as compared

to using singly webbed arrangement. To the author’s knowledge, no recent research

done for profiled web girder with double web systems.

1.3 Advantages

This study found that the use of profiled webs is a possible way of achieving

adequate out-of-plane stiffness without using stiffeners. An enhancement to the

existing girder with single profiled web is made through an arrangement of two

identical corrugated profiles to form a cellular web. According to Hanizah et al. [1-

4], by using profiled webbed girders either with a single corrugated web or two

corrugated webs can use thinner webs and no vertical stiffeners are required except at

load application point and reactions. Furthermore, a higher load carrying capacity

also can be achieved. The profiled web can be viewed as uniformly distributed

stiffeners in the transverse direction of the girder. The use of profiled web girder also

leads to a structural system of high strength-to-weight ratio. Wang [5] reported work

of Masami Hamada who had found that a profiled web weighed 9% to 13% less than

the equivalent conventionally stiffened flat web. This finding agreed with Klalid et

al. [6], Khalid [7] and Chan [8] who had reported a 10.6% reduction in weight.

2

According to Huang et al. [9], prestressed concrete (PC) box girders with corrugated

steel webs are one of the promising concrete–steel hybrid structures applied to

highway bridges. Maetani Bridge in Japan, completed in 2001 using cast-in-place

cantilever construction, is one application of this concrete–steel hybrid structure. One

of the advantages of this concrete–steel hybrid box girders with corrugated steel

webs, prestress can be efficiently introduced into the top and bottom concrete flanges

due to the so-called ‘‘accordion effect’’ of the corrugated webs. The external post-

tensioning which is used for PC box girders with corrugated steel webs, has many

advantages over internal bonded tendons.

1.4 Objectives of Study

The primary objective of this research work is to identify the shear load carrying

capacities of profiled web girders with single profile and double profiles. The

research works:

a. studied the nature of buckling and / or yielding of the webs, flanges,

stiffeners and ribs

b. compared the load-carrying capacities of a conventional plate girder with a

profiled girder with a single web and also with a profiled girder with twin

webs

c. compared with the results obtained from the previous theoretical design

method for shear load carrying capacities of corrugated web profiled

girders

d. studied the possibility of exploiting the post buckling strength of web sub-

panels in a profiled web girder

1.5 Scope of Work

The present study focused on the shear load carrying capacities of corrugated

profiled web girder with either single or double webs compared to conventionally

flat web plate girder. The scope of this study covered both the experimental

investigation and numerical analysis using finite element method. In experimental

investigation 29 numbers of specimens were tested using three point bending system

with both ends simply supported with variation of web depth and web configuration.

3

Finite element analysis was used to validate with the experimental results.

Prominence is placed on the investigation of parameters influence the shear capacity

of such girders with profiled web(s). The parameter were included web depth, web

thickness and flange thickness to investigate their influence on ultimate shear

capacity and post-buckling shear capacity of profiled web girder.

1.6 Research Methodology

The aim of this study is to compare shear load capacities between conventional flat

web girder and profiled web girder with either single or double webs. Hence, there

are three types of web configuration with three variations of web depth and three

numbers of each type of specimens and tests under three point bending system. The

load was applied across the width of the flange through the bearing stiffeners.

Conventional flat web specimens are designed according to Cardiff model as control

specimens and the others types of specimens are derived accordingly.

LUSAS finite element software (version 13.6), which is available in the Faculty of

Civil Engineering, Universiti Teknologi MARA was used to simulate the combined

geometric and materials non-linear response of the girder with three different web

systems under shear load. The outcome of it was checked against the experimental

results. The large-deformation elasto-plastic finite element analysis of three-

dimensional assembly of steel plates is complex because of both material and

geometry non-linearity. Material was isotropic and its stress-strain non-linear

behaviour is elastic perfectly plastic with no strain hardening and Total Lagrangian

was used for geometric non-linearity. The entire models were initially imperfect

using global double sine wave which the maximum amplitude was taking 0.1% of

web depth at the centre of the panel.

4

Figure 1.1(a): Application of Conventional Flat Web Plate Girder for Bridges.

Figure 1.1(b): Application of Corrugated Profiled Web Plate Girder for Bridges.

Figure 1.1: Application of Plate Girders for Bridges.

5

Figure 1.2(a): Trapezoidal Shape of Profiled Web

Figure 1.2(b): Sinusoidal Shape of Profiled Web

Figure 1.2: Types of Web Profiled Shapes

6

CHAPTER 2

LITERATURE REVIEW

2.1 Summary of Research and Development History on Plate Girder

Theory on tension field was developed in 1931 by Herbert [10, 11] to access the

post-buckling behaviour of thin panel used in aircraft structures. Wagner established

expressions for magnitude and inclination of the tensile membrane field. Further

study on this diagonal tension fields was carried out by Kuhn [12], Kuhn and

Peterson [13] and Kuhn et al. [14-15] to develop design methods for aircraft

structures utilising the post-buckling reverse of strength. However, these methods for

aircraft structure could not be applied directly to the type of girders normally used in

civil engineering because the girder proportions differ significantly. In civil

engineering application, the flanges usually much less rigid than those of aircraft

girders, such that significant flange distortions can occur under the action of force

imposed upon the flanges by tension field developed in the web.

In the early 1960s, the first attempt to establish a method to predict the ultimate load

of girder of civil engineering proportions was made by Basler [16]. He assumed that

flanges in practical plate girders do not possess sufficient flexural rigidity to resist

the diagonal tension field. The diagonal tension field does not develop near the web-

flange juncture and the web collapses after development of yield zone. In 1970s

Rockey et al. modified these theories to achieve a better correlation between theory

and tested results [17-18]. They assumed that the flanges were able to anchor the

diagonal tension field. They also established that the collapse mode of plate girder

involved the development of plastic hinges in tension and compression flanges from

after development of yield zone and finally web panel fails in sway mechanism.

Extensive study of this failure model was developed by University of Collage Cardiff

since early 1980s to early 2000s by the Evan and Moussef [19], Roberts and

Shahabian [20], Shahabian and Robert [21] and Davies and Roberts [22], hence this

theory is called the Cardiff model. Figure 2.1 has shows the failure mechanism of

7

both theories. The fundamental and theory of plate girder base on Cardiff model also

describe by Narayanan [23] and Allen and Bulson [24].

According to Lee and Yoo [25-26], Yoo and Yoon [27] and Lee et al. [28-29] theory

by Basler has been first adopted in AISC (American Institute of Steel Construction)

Specification in 1963 and ASSTHO (American Association of State Highway and

Transport Official) in 1973. Cardiff model also has been adopted in a few British

Standard code of practice for steel and aluminium structural design like BS 5400:

Part 3, BS 5950: Part 1 and BS 8118: Part 1. However, these introduced codes of

practice are shown to be slightly but not unduly conservative in predicting the

capacities of plate girders. That is the reason why many researchers who are still

trying to investigate the capacity of plate girders.

°45

tσ

tσ

crττ −

crττ −

crττ −crττ −

iθ°135

τττ τ

τ

τ

d

a

Figure 2.1(b): Post-buckled Behaviour of Shear Web Panel

Figure 2.1(a): Unbuckled Behaviour of Shear Web Panel

uVuV

uV

uV

Yield Zone

iθytσ

X

ZY

W

uV

hinge Plastic

φ

uV

Figure 2.1(d): Collapse Behaviour by Rockey et al (Cardiff Model)

Figure 2.1(c): Collapse Behaviour by Basler

Figure 2.1: Failure Mechanism of Shear Web Panel

8

The study on corrugated plate was started in 1952 by Seide [30]. He derived the

corrugated plate using orthotropic plate for flexural and transverses shear stiffness in

both directions. In 1956, Fraser [31] investigated the strength of multi web beams

with corrugated webs. It was concluded that the efficiency of corrugated web beams

was better than channel web beams over a wide range of structural index.

Worldwide, many research and development works on profiled web girders starting

from in 1960 until the present-day have been carried out. The research have not

restricted to only shear capacity of profiled web girder but included variation types of

loading such as patch, bending, combined load and fatigue. Mostly, the researches

were concentrated to trapezoidal and sinusoidal shape profiled configuration.

However, a few researchers such as Hanizah et al. [1-4] and Khalid [7] studied on

rectangular shape profiled. According to the author’s knowledge, there is no recent

research on doubly profiled web girder.

Starting from the year 2000, the research on corrugated web girder was more

energetic including in this country. Three different universities in Malaysia are

conducting research on profiled web girder. In Universiti Teknologi MARA (UiTM)

conducted by Hanizah et al. [1-4] this research started in 2002 and is still ongoing.

Studies at Universiti Teknologi Malaysia (UTM) were performed by Hanim [32],

Fathoni [33], and Nina Imelda [34], started in 2000 until 2003 and at Universiti Putra

Malaysia (UPM) by Khalid et al. [6] and Khallid [7] in 2003. In 1996 to 2003,

Elgaaly et al. [35-36], Elgaaly and Seshadri [37-38] from Drexel University,

Philadelphia conducted a few research on corrugated profiled web girder under

various types of loading also on corrugated web girder with tabular flanges. In 1996,

Lou and Edlund [39, 40] from Sweden investigated the influence of geometric

parameters in the shear capacity of corrugated web girder. The latest date in 2005,

Anami et al. [41] Anami and Sause [42] from Japan investigated the effect of web-

flanges welding due to fatigue load. Nowadays, besides the convenience during

manufacture, this should be the most important reason why the application of such

girders can be widely increased.

9

Table 2.1: The Summary of Research and Development on Profiled Web Girder.

Name of Researcher Year Country

*Peterson and Cord 1960

*Rothwell 1968

*Sherman and Fisher 1971

*Libove 1973

*Wu and Libove 1975

*Easley 1975

United States

*Harrisson 1975 Britain *Hussain and Libove 1977 United States *Korashy and Varga 1979 Hungary

*Bergfeld and Leiva-Aravena 1984 Sweden

*Lindner and Ashinger 1988

*Scheer 1991 Germany

Evan and Mokhtari 1992 Britain Elgally 1996 United States

Lou and B. Edlund 1996 Sweden R.P Johnson and J. Cafolla 1996 Britain

X. Wang and Elgally 2003 United States C. Graciano and B. Edlund 2002 Sweden

Hanim 2002

Fathoni 2002

Nina Imelda 2003

Hanizah, Azmi and Hadli 2003

Khalid 2003

Malaysia

Huang 2004 Japan Anami 2005 Japan

Note: (*) are cited in Elgally et al. [35]

10

2.2 Buckling Behaviour of Profiled Web Girder Under Shear Load

Evan and Mokhtari [43] investigated experimentally the unstiffened conventional

plate girder and profiled web plate girder. Four tests were carried out on the

unstiffened girders and four tests were carried out on the profiled web girders. Evan

and Mokhtari concluded that the four tests on girders with profiled web plates

showed that profiling is extremely effective in increasing the shear buckling load

because it moved material out of the plane of the webs, thereby increasing the

rigidity. It was observed that the local buckling of web was not localised in the web

sub-panel but was extended from flat web elements, through the fold lines, into the

inclined web element. Evan and Mokhtari [43] concluded that, the profiled web

simply tends to flatten out under the action of in-plane tensile stress field developed

in the post buckling range. These, however give little advantage in using such

girders.

Recent research by Hanizah et al [1-4] on intermittent rectangular web profiled

showed that, the ribs are able to act as stiffeners, anchoring the stress tension field

zone. The web buckled in typical shear mode and develops large strain of inclined

tension field in web. It should be noted that if the depth and width of ribs are

increased further, the tension field action would develop in the ribs instead of

causing them to behave as sub-panels.

Lou and Edlund [39] suggested three buckling patterns can occur in a corrugated

web:

a. Local buckling: shear buckling occurs in the plane part of the folds and is

restricted to this region only

b. Global buckling: shear buckling involves several folds and may give rise to

yield lines crossing these folds

c. Zonal buckling: an intermediate type of shear buckling (between local

buckling and global buckling), which involves several folds but only occurs

over a part of the girder depth

11

According to Elgally et al. [35], buckling modes are categorized as either local or

global. Figure 2.2 illustrates the three different buckling modes described by Lou and

Edlund [39].

Figure 2.2(b): Zonal

Buckling Mode Figure 2.2(a): Local

Buckling Mode

Figure 2.2(c): Global

Buckling Mode

Fi b gure 2.2: Buckling Modes of Corrugated We

However, the load-deflection responds from the tested specimens by Hanizah et al

[1-4], Evan and Mokhtari [43], Elgally et al. [35] and also Lou and Edlund [39]

showed sudden drop after reaching peak and the specimens or model exhibited some

residual strength after failure. All authors did not mention the reason for that kind of

the phenomena. However, according to Lou and Edlund [39], there would be a

reduction of post-buckling strength up to 70% of the ultimate shear capacity no

matter what kind of buckling mode it has. Studies by Lou and Edlund [40] on patch

load of corrugated web girder and Khalid et al. [6-8] on sinusoidal profiled web

girder tested on bending, showed that the result of their post-buckling capacity had

better discernible plastic plateau. There was no and/or small reduction in post-

12

buckling capacity of the girder. Figure 2.3 (a) and (b) have shown the different load-

deflection curve behaviour investigated by Lou and Edlund [39, 40] under shear and

patch load respectively.

Figure 2.3(a): Load-Deflection Curve for Girder with Different Depth under Shear Load.

Figure 2.3(b): Load-Deflection Curve for Girder with Different Mesh arrangement under Patch Load.

Figure 2.3: Load-Deflection Curve for Corrugated Web Girder Investigated by Lou and Edlund [39, 40] under Shear and Patch Load.

13

2.3 Shear Capacity of Plate Girder under Shear Load

2.3.1 Shear Capacity of Conventional Flat Web Plate Girder under Shear

Load

According to Cardiff model as shown in Figure 2.1, the ultimate shear resistance, Vu

for conventional flat web girder can be present in three forms as:

21

*2 sin34cotsin3 ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+= p

yw

yt

iyw

yt

iiyw

cr

yw

u Mda

VV

σσ

θσσ

θθττ (2.1)

From equation 2.1

i. The first term represents the shear buckling strength.

ii. The second term represents the part of the post-buckling tension field that

is anchored by transverse stiffener.

iii. The third term which is a function of represents the contribution from

the flange.

*pM

crτ is the critical shear stress of assumed simply supported plate, given by

( )2

2

2

112⎟⎠⎞

⎜⎝⎛

−=

dtEkcr

νπτ (2.2)

Where k is the buckling coefficient as follows,

For 1≥da

2

435.5 ⎟⎠⎞

⎜⎝⎛+=

adk (2.3a)

For 1<da 435.5

2

+⎟⎠⎞

⎜⎝⎛=

adk (2.3b)

The value of iθ cannot be determined directly and iterative procedure has been

adopted in which successive values of iθ are assumed and the corresponding ultimate

shear load is evaluated in each case. This process is repeated until the value of iθ

providing the maximum and therefore the required value of Vu has established. It was

found that an maximum solution of Vu is when iθ is approximately as follows;

⎟⎠⎞

⎜⎝⎛≈ −

ad

i1tan

32θ (2.4)

14

The dimensionless flange parameter is defined as *pM

yw

pfp td

MM

σ2* = (2.5)

where Mpf is the full plastic moment of the flange and is given by

(2.6) yfpf BTM σ225.0=

Basler model [16] is the first one actually used in design to use tension field action in

determining the shear strength without considering flange contribution after the web

has buckled under diagonal compression. The ultimate shear capacity is the

combination of the buckling and post-buckling strength given by:

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎠⎞

⎜⎝⎛+

−+=

2

12

13

da

CCdtV vv

yu σ (2.7)

where y

crvC

ττ

= (2.8)

crτ is defined in equation (2.2)

Simplified equation suggested by Lee and Yoo [25-26] and Lee et al. [28] to

determine the ultimate shear strength for plate girder were:

(2.9) ( 4.06.0 += CVRV ywdu )

Where C was as follows:

C = 1.0 for y

ktd

σ6000

< (2.10a)

y

kCσ

6000= for

yy

ktdk

σσ75006000

≤≤ (2.10b)

( ) ytdkC

σ2

7105.4 ×= for

y

ktd

σ7500

> (2.10c)

15

The strength reduction factor Rd due to initial out-of-flatness D/120 was determined

as

Rd = 0.8 for y

ktd

σ6000

< (2.11a)

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −+=

60006000

2.08.0ktd

R yd

σ for

yy

ktdk

σσ120006000

≤≤ (2.11b)

Rd = 1.0 for y

ktd

σ12000

> (2.11c)

Lee and Yoo [25-26] and Lee et al. [28] modified this shear buckling coefficient, k of

a flat web plate girder. The assumption was that the condition of the web panel was

not simply supported at all edges. The suggested that the coefficient could be

determined as

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−−+=

tTkkkk sssfss 2

321

54 for 2

21

<≤tT (2.12a)

( )sssfss kkkk −+= 8.0 for 0.2≥tT (2.12b)

Where

kss = web panel has simple supported at all four edges.

ksf = two simple and two fix supports.

Shear buckling coefficients kss and ksf can be calculated as

kss = equations (2.3a or 2.3b)

32

99.161.598.8 ⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛+=

ad

adksf for 1≥

da (2.13a)

⎟⎠⎞

⎜⎝⎛+−⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

da

ad

adksf 39.844.331.234.5

2

for 1<da

(2.13b)

2.3.2 Shear Capacity of Profiled Web Plate Girder under Shear Load

Shear capacity of profiled web girder can be calculated based on two types of

buckling either local buckling or global. Shear capacity based on local buckling can

be calculated based on local buckling of the flat part of the corrugation fold being

16

considered. Whenever, global buckling is controlling, the shear capacity can be

calculated for entire corrugated web panel using orthotropic plate buckling theory.

2.3.2.1 Shear Capacity of Profiled Web Plate Girder Based on Local Buckling

Cited in Elgally et al. [35], Galambos suggested that in the local buckling mode, the

corrugated web acted as a series of flat plate sub-panels that mutually support each

other along their vertical (longer) edges and are supported by the flanges at their

horizontal (shorter) edges. These flat plate sub-panels are subjected to shear and

elastic buckling stress:

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−=

2

2

2

, 112 wtEkslcre ν

πτ (2.14)

where:

ks = buckling coefficient which is a function of the panel aspect ratio ⎟⎠⎞

⎜⎝⎛

dw .

Buckling coefficient ks is given by:

For the longer edges are simply supported and the shorter edges are clamped, 32

39.844.331.234.5 ⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛+=

dw

dw

dwks (2.15a)

For all edges are clamped 2

6.598.8 ⎟⎠⎞

⎜⎝⎛+=

dwks (2.15b)

In cases where ylcre ττ 8.0, > inelastic buckling develops and the inelastic buckling

stress lcri,τ can be calculated by

( ) 5.0,, 8.0 ywlcrelcri τττ ××= but ywlcri ττ ≤, (2.16)

2.3.2.2 Shear Capacity of Profiled Web Plate Girder Based on Global Buckling

The global buckling stress has been determined using the orthotropic plate buckling

theory [35, 44-46]. Global elastic buckling stress gcre,τ can be calculated from

2,

43

41

tdDD

k yxgcre =τ (2.17)

17

where Dx and Dy are the bending stiffness of corrugated web, given by

sqEtDx 12

3

= (2.18a)

q

EID y

y = (2.18b)

Iy = moment of inertia of one corrugation about its neutral axis

r

rrry

thhtbIθsin62

232

+⎟⎠⎞

⎜⎝⎛= (2.19)

In equations 2.13, b, hr, q, s and rθ are shown in Figure 2.4.

br

s

dr

q

rθhr

Figure 2.4: Notation of Corrugation Configurations

Buckling coefficient, k in equation 2.17 depends on the boundary conditions of web

panel. Table 2.2 shows the buckling coefficient, k proposed by a few researchers.

According to Elgally et al. [35] when ygcre ττ 8.0, > , inelastic buckling occurs and the

inelastic buckling stress can be calculated by

( ) 5.0,, 8.0 ygcregcri τττ ××= but ygcri ττ ≤, (2.20)

Table 2.2: Buckling Coefficient, k Proposed by other Researchers.

Name of Researcher Year Value of k

Proposed

Boundary

Condition

31.6 Simply supported Galambos, cited in Elgally [35] 1988

59.2 Fixed

Easley, cited in Wang [5] 1975 36 Simply supported

Zeman & Co. [47] - 32.4 Simply supported

18

2.4 Review on Numerical Simulation

Experimental work and numerical simulation are the two approaches to investigate

the structural behaviour of a member like a plate girder. According to Lou and

Edlund [39], it was not until the 1980s that computer-based numerical approaches

have been applied to investigate the load carrying capacity of various plate girders.

Some researchers used both computer-based numerical approach using finite element

method and experimental.

2.4.1 Geometric and Material Non-Linearity

Finite element procedure is one of the methods available for the combined geometric

and material non-linear analysis of geometrically and structurally complex plated

structures. Generally, previous studies from many researchers on numerical analysis

of plate girder or plated structure either unstiffened and stiffened panel in isolation

taking into account both geometrical non-linearities (large deflections) and material

non-linearities (plasticity).

In the problems of plate structural member with large-deflection effect, Lagrangian

approach was adopted whereby the displacement of all points on the plate are refered

to the undeformed state [47-50]. The stress and strain measures utilised in

Lagrangian geometric nonlinearity are the Second Piola-Kirchhoff stress tensor and

the Green-Lagrange strain tensor. These stress and strain measures are referred to a

reference configuration, which is the undeformed configuration in Total Lagrangian

analysis, or the configuration at the last converged solution in Updated Lagrangian

analysis [47-50].

Material non-linearity finite element analysis involves nonlinear stress-strain

relationships and plasticity flow rules. When the stress reaches the yield surface, the

material undergoes plastic deformation. Based on an incremental or flow theory, in

classical plasticity, any stress states that provide a positive value of the yield function

cannot exist. However in numerical models, positive values of the yield function

indicate that yielding should occur and the stress state is modified by accumulating

plastic strains until the yield criterion is reduced to zero. This process is known as the

19

plastic corrector phase or return mapping. Figure 2.5 shows that as long as the stress

can be plotted inside the yield surface, the material is deforming elastically. When

the stress state is exactly on the yield surface, or f = 0, the material has reached yield

and is deforming plastically [47-50]. In addition, strain-hardening rule is required to

define the enlargement of the yield surface with plastic straining as the material

yields.

2σ

f > 0 Stress State not valid

Yield Surface f = 0

1σ

Figure 2.5: Concept of Yield Surface

Most numerical investigations into the shear capacity of plate girders assumed either

a elastic perfectly -plastic model or bilinearly elastic-plastic model. Some researchers

such as Lou and Edlund [39], Azmi [47], assumed perfectly elastic-plastic model so

that hardening parameter is eliminated. Elgally et al [35-38] assumed bilinear elastic

perfectly plastic model, where modulus elasticity for second slope was taken as 1%

of modulus of elasticity when it reached yield stress.

Comparison between used stress-strain relations and perfectly elastic-plastic

hardening model were done by Lou and Edlund [40] and Granath and Lagerqvist

[51] on plate girder under patch loading. Lou and Edlund [40] used Ramberg-Osgood

model and Granath and Lagerqvist [51] used logarithmic strain and true (Cauchy)

stress model. Both stress-strain relations are given as:

Ramberg-Osgood model

n

pp

E ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

σσσε (2.21)

20

Where:

n = factor to describe the sharpness of the knee of stress-strain curve

σp = proof stress

p = plastic strain at proof stress σp

Logarithmic Strain and True (Cauchy) stress model

( )engengtrue εσσ += 1 (2.22a)

( )engεε += 1lnln (2.22b)

Comparison between used stress-strain relations and perfectly elastic-plastic

hardening model showed that the ultimate strength of girder using used stress-strain

relations was higher than perfectly elastic-plastic hardening model. Figure 2.6 shows

load-deflection curve with different hardening model by Lou and Edlund and

Granath and Lagerqvist. According to Lou and Edlund [40], the ultimate strength of

girder was about 8 – 12% higher than that with elastic perfectly plastic model.

However, the limitation in this present study on the investigation of the shear

capacities of plate girders is that the strain hardening models assumed perfectly

elastic-plastic models, which eliminate strain-hardening parameters.

21

Figure 2.6(a): Load Deflection Curve obtain with Different Strain Hardening by Lou and Edlund [40]

Figure 2.6(b): Load Deflection Curve obtained with Different Strain Hardening by Granath and Lagerqvist [51]

Figure 2.5: Load Deflection Curve obtained with Different Strain Hardening

22

2.4.2 Initial Geometrical Imperfection

To rectify the problems related to the overestimation of collapse load of

(geometrically) imperfect plates, a technique was proposed in which progressive

development of plastic zone could be model. Acording to Schafer and Peköz [52],

using nonlinear finite element analysis demonstrate how imperfection magnitude,

imperfection distribution influence the solution results. Generally initial imperfection

could be model using half sine wave given as:

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

dy

axzw oo

ππ sinsin (2.23)

where:

wo = amplitude imperfection

zo = maximum amplitude

x = horizontal distance of web panel

y = vertical distance of web panel

a and d = panel dimension

Initial out-of-plane imperfection performed by Elgally et al. [35] and Elgaaly and

Seshadri [37] assumed different maximum amplitude to get better agreement of

ultimate shear load between analytical and experimental results. According to Baskar

et al. [53] and Shanmugam and Baskar [54] and Xie and Chapman [55, 56]

considered the first mode shape from buckling analysis as an initial imperfection.

Lee et al. [26] allowed initial imperfection for web panels according to AWS D1.5

(American Welding Society – Bridge Welding Code), where the allowable values of

initial imperfection are much greater than d/12000. To investigate the effects of

larger initial imperfection, Lee et al. introduced initial imperfection of d/120 into the

web-panel models as a reasonable upper-bound value of the permissible out-of-

flatness of web panels and then compared with out-of-flatness values between

d/120000 and d/120. Figure 2.7 show the ultimate strengths of web panels with

different initial imperfections. However, according to Lee et al., once a larger initial

imperfection present in the web panel, a considerable out-of-plane bending action is

likely to take place and consequently the induced bending stresses may reduce the

ultimate shear capacity significantly.

23

The study by Graciano and Edlund [57] on longitudinally stiffened plate girder under

patch load considered two types of initial shape imperfections. The types of initial

shape imperfection are called C-shape and S-shape as shown in Figure 2.8. They

found that the shape of initial imperfection of the web affects the load carrying

capacity. For the same imperfection amplitude an S-shape imperfection is more

unfavourable than a C-shape for the patch loading resistance. When comparing the

load carrying capacities having the same initial shapes but with different amplitude

the difference is about 2%. If comparing, but this time with two different shapes,

there is a reduction of about 7% in the patch loading capacity of a longitudinally

stiffened plate girder. Figure 2.9 show the imperfection shape sensitivity of a plate

girder under patch load.

In this present study, the limitation in using the finite element method is that the

initial imperfection was modelled using global double sine wave with maximum

initial imperfection 0.1% of web depth.

Figure 2.7: Comparison of Ultimate Strength with Different Initial Imperfection (d/t = 120) by Lee et al [26]

24

Figure 2.8: The Type of Initial Shape Imperfection suggested by Graciano and Edlund [57]

Figure 2.9(a): Imperfection Shape Sensitivity of Plate Girder with Different Shape under Patch Load

Figure 2.9(b): Imperfection Shape Sensitivity of Plate Girder with Different Amplitude under Patch Load

Figure 2.9: Imperfection Shape Sensitivity of Plate Girder under Patch Load by Graciano and Edlund [57]

25

2.4.3 Meshing

Generally, finite element models of plate girders are using either thick or thin shell

elements. The most popular element is a quadrilateral thin shell element with eight

nodes. Examples on numerical simulation studies described in Lou and Edlund [39,

40], Khalid et al [6] and Chan et al. [8], Baskar et al. [53] and Shanmugam and

Baskar [54], Elgally et al [35-38] used eight-node quadrilateral thin shell elements

for the web only or both flanges and web. In the LUSAS element library [48, 49], a

family of shell elements for the analysis of arbitrarily curved shell geometries,

including multiple branched junctions is allowable. The elements can accommodate

generally curved geometry with varying thickness and anisotropic and composite

material properties. The element formulation takes account of both membrane and

flexural deformations. Numerical study reported by Elgally et al. [35] and Elgaaly

and Seshadri [37] combined eight-node thin shell element for web and three-node

Timoshenko beam element which is available in a computer package called

ABAQUS.

To obtain a sufficiently accurate approximate solution and to minimise the

computational effort without scarifying the accuracy of the results, element density is

the key issue. The study by Elgally et al. [35] and Elgaaly and Seshadri [37] on shear

capacities corrugated web girder for four different models used four different

numbers of elements employed across the width of each fold of corrugation. The

number of elements along the depth of the panel was then determined to keep the

element aspect-ratio less than four. The results from the model with three and four

element across the width of each fold were much closer. They used three elements

across each fold to minimise the computational effort. Figure 2.10 shows finite

element model by Elgally et al. [35] and Elgaaly and Seshadri [37].

26

Figure 2.10: Finite Element Model by Elgally et al [35].

2.5 Effect of Welding on Plate Girder

The effect of welding which induces stresses can reduce the material yield strength

up to 10% [58]. BS 5950: Part 1 [59] and BS 5400: Part 3 [60] recommended that the

value of the yield strength should be reduced by 20 N/mm2. Bulson [61] suggested

the treatment of welded steel section must depend on the section classification.

According to Teh and Hancock [62], tensile strength of the heat-affected-zone

(HAZ) in G450 sheet steel is significantly lower than that of the virgin steel but is

generally higher than the nominal tensile strength. Maquoi [58] investigated on the

flange distortion resulting from welding of the web on to the flanges by means of

one-sided or double sided fillet welds. Greater distortions were found in thinner

flanges, where the ratio of the weld size to flange thickness was 0.5 or higher. Study

conducted by Cooke et al [63], indicated that the initial out-of-plane plate distortion

did not influence the web shear strength but was important in influencing the out-of-

plane distortions and stresses at service load.

According to Samsudin [64], these distortions to be estimated because they can

reduce the strength of the structure. An empirical relationship is known to exist

27

between the weld shrinkage force, Fs and the heat input, Q involving a dimensionless

constant, H and an arc efficiency, η of the welding process. The shrinkage force can

be used to estimate the residual stresses in welded plates. The transverse distortion, β

depends mainly on the plate thickness and heat input

⎟⎠⎞

⎜⎝⎛=υQHFs (2.24)

Anami et al. [41, 42] studied the web-flange weld of corrugated web girder due to

fatigue load. They were found that the corrugation angle rθ is the dominant

parameter and decreasing, rθ decreases the stresses at the weld toe. The influence of

the corrugation depth, hr and longitudinal fold, bc length are not significant. In-plane

bending and plate bending of the flange plate occurred even in the region of constant

bending moment. The highest stress always appeared at the end of the flat part of the

inclined fold, point S. The corrugation angle, rθ and the bend radius, R are the

parameters that most influence the stress conditions near point S as shown in Figure

2.11.

Figure 2.11: Stress Distribution at Inclined Fold Weld Tby Kengo Anami et al [41].

clined Fold Weld Tby Kengo Anami et al [41].

oe oe

28

2.6 Precaution of Premature Failure in Unforeseen Mode

Intermittent fillet welding of the web to the flanges is not advisable as it exerts

geometric imperfections and residual stresses causing a reduction in the capacity of

the compression flange. High stress concentration induces at the end of the

intermittent welds causes rupture of the welded connections. Recent research

conducted by Hanizah et al. [1-4] discovered that one specimen out of five tested

specimens ruptured at the web-to-flange juncture. Similar study done by Elgally et al

[19] showed that the beam failed at load lower than the predicted load.

A comprehensive survey of literature done by Evan and Moussef [19], has yielded

the results of 133 tests on transversely stiffened plate girder and further 64 tests on

longitudinally stiffened girders. These tests carried out world-wide, by many

different investigators, over a period from 1935 to 1988. Evan and Moussef [19]

wrote that out of 133 reports on transversely stiffened girder, 31 have been

discounted on account of premature end post failure that had not been anticipated by

the different investigators. Of the 64 reports on longitudinally stiffened girder, 13

have been discounted because of premature stiffener failure. Premature failure of end

post, stiffeners or both will reduce load lower than predicted load, in order to fully

develop the rotated stress field also can not be achieve.

29

CHAPTER 3

EXPERIMENTAL STUDY

3.1 Introduction

Before any steel girders with corrugated webs can be practically used, their

behaviour under shear load needs to be investigated. Their formulation for shear

capacity has been proposed based on classical elastic shear buckling theory and shear

yielding with inelastic transition regions.

A series of 29 test specimens were prepared to investigate the behaviour of plate

girders with profiled webs of different slenderness under shear load. In order to

achieve the objectives of this study, the configurations of every specimens were kept

constant except on the following parameters:

i) Web depth (350 mm, 450 mm and 550 mm)

ii) Web arrangements (Conventional flat web, Single Profiled Web and

Double Profiled Web)

Figure 3.1 shows the dimensions of a profiled steel sheet. All of the specimens were

labelled according to their depth, web arrangement and number of specimens for

each configuration. Table 3.1 shows the labels and dimensions of the specimens.

30

*Note: All dimensions are in mm

Figure 3.1: Dimensions of Profile Steel Sheets

Table 3.1: Properties of Specimens

Specimen

Name

Welding

Type

Web

Configuration

Depth

(mm)

Web

Thickness

(mm)

Flange

Width x Thickness

(mm x mm)

F350-1

F350-2 MIG

F350-3 GTAW

Flat

S350-1

S350-2 MIG

S350-3 GTAW

Single

Profile

D350-1

D350-2 MIG

D350-3 GTAW

Double

Profiles

350

F450-1

F450-2 MIG

F450-3 GTAW

Flat

S450-1

S450-2 MIG

S450-3 GTAW

S450-4 MIG

Single

Profile

D450-1

D450-2 MIG

D450-3 GTAW

D450-4 MIG

Double

Profiles

450

F550-1

F550-2 MIG

F550-3 GTAW

Flat

S550-1

S550-2 MIG

S550-3 GTAW

Single

Profile

D550-1

D550-2 MIG

D550-3 GTAW

Double

Profiles

550

1.0 125 x 9

Note: 1) MIG – Metal Inert Gas 2) GTAW – Gas Tungsten Arc Welding

31

3.2 Test Specimens and Test Set-up

3.2.1 Material Properties of Test Specimens

For the mechanical properties and tensile strength of the flange and web plates they

were cut according to bone shape. The test pieces were tested in accordance with ISO

6892: Metallic Material - Tensile Testing [65] in order to determine their yield

stresses and Young’s Moduli. Yield stress was taken at 0.2% of the proof stress. The

tensile tests were done using Instron testing machine at Material Research

Laboratory, Faculty of Mechanical Engineering, Universiti Teknologi MARA. The

dimensions of the test pieces are as shown in Figure 3.2. Figure 3.3(a) and 3.3(b)

show the test piece during and after testing. The results are shown in Table 3.2.

Figure 3.2(a): Tensile Test

Piece of 9 mm Thickness

Figure 3.2(b): Tensile Test

Piece of 1 mm Thickness *Note: All units are in mm

Figure 3.2: Dimensions of Tensile Test Pieces

32

Figure 3.3(a): Test Piece during Tensile Testing

Figure 3.3(b): Tensile Test Piece after Failure

Figure 3.3: Tensile Testing

33

Table 3.2: Results of Tensile Tests

Plate Thickness

(mm)

Test Piece

Label yσ

(N/mm2)

E

(kN/ mm2)

Average

yσ

(N/mm2)

Average

E

(N/mm2)

T21 309.30 205.70 T23 305.41 206.36

9.0

(See Figure 3.2) T24 300.10 204.78

304.94 205.61

T01 403.25 198.40 1.0

(See Figure 3.2)

T02 396.80 212.30

400.03 205.35

3.2.2 Design and Preparation of Specimens

Only conventional flat web specimens are designed in accordance with BS 5950:

Part 1 [59] and/or equation (2.1) as control specimens and the others types of

specimens are derived accordingly. The flanges were assumed to be rigid and are

designed thick to be as necessary by letting ( ( TdAMM fyff + )=< σ ). This would

ensure that the stress caused by bending moment would not influence that portion of

the shear force which resisted by the web. Hence, the web is resist shear force only.

End stiffeners and bearing stiffeners are overdesigned to ensure that the plate girder

would not fail prematurely in an unforeseen mode. Tension field forces could only

develop when an adequate anchorage is provided by the members bounding the

panel. To guarantee the test specimens fully develop the rotated stress field, the end

of the specimens are anchored by rigid end posts. End posts are supported by the

flanges, which result in compressive forces at the end of the flanges. In this study,

the size of an end post is 125 mm width and 6.0 mm thick. According to Höglund

[66], a non-rigid end post (only one stiffener at girder end) has only limited ability to

serve as anchors for longitudinal membrane stresses. Hence the ultimate load is less

than for girder with rigid end posts but there is still a substantial post buckling

strength. Figure 3.4 shows the difference between a rigid end post and non-rigid end

post.

34

Figure 3.5(a) shows a piece of the profile steel sheet that has been cut to the required

depth. For the double webs, the profile steel sheets were joint using aluminum rivets

between web-to-web arrangements as shown in Figure 3.5(b). Figure 3.5(c) shows

the positions of the rivets. The size of rivet is 3.97 mm diameter and 6.35 mm length.

The web is welded to the center of the flanges as shown in Figure 3.6. Any

fabricating work is done at the Civil Engineering Laboratory UiTM and welding

work is done by professional welders at Welding and Fabrication Technology

Division SIRIM Berhad (Standard and Industrial Research Institute of Malaysia).

Figure 3.7 shows the welding work done at SIRIM workshop.

Figure 3.4 (a): Rigid End Post

Figure 3.4 (b): Non-Rigid End Post

Figure 3.4: End Post Design

35

To fabricate the specimens, two types of welding gases are used. Static strength

between both types of welding was compared. The comparisons between both gases

are given as below:

i. Metal Inert Gas Welding (MIG)

CO2 shielding gas is used in this study to minimise the cost of welding as

compared to using a mixture of either 75% Argon plus 25% CO2 or Argon

only. Using CO2 shielding gas is good for allowing penetration but too hot

for thin metal and give more spatter.

ii. Gas Tungsten Arc Welding (GTAW)

GTAW produces a common high quality welding and is frequently referred

to as TIG (Tungsten Inert Gas). The benefits of using GTAW are that is

gives precise control of welding, free spatter and low distortion. The

problems of using GTAW include that it is more costly and the welding

process is very slow. Generally, shielding gases used for GTAW is Argon,

Argon plus Helium or Argon plus Helium plus CO2. Helium is generally

added to increase heat input (which can increase welding speed or weld

penetration). In this study, only Argon is used.

To ensure the quality of welding, WPS (Welding Procedure Specification) is made

according to AWS D1.1 [67] and BS EN 287: Part 1 [68]. Figure 3.8 shows the WPS

specimens using both MIG and GTAW. The results of WPS for GTAW are shown

in Appendix A.

36

Figure 3.5(a): Single Web Arrangement

Figure 3.5(b): Joining of Double Profiled Webs

Figure 3.5: Assembling of Webs

Figure 3.5(c): Positions of Rivets for Double Profiled Webs

37

44 mm81 mm

62.5 mm

62.5 mm

62.5 mm62.5 mm

Figure 3.6: Welding Position (Plan View)

Fig er ure 3.6(c): Welding Position of web-to flange for doubly webbed gird

Figure 3.6(b): Welding Position of web-to flange for singly webbed girder

Figure 3.6(a): Welding Position of web-to flange for flat webbed girder

Figure 3.7: Welding Work at SIRIM Workshop

38

Figure 3.8(a): WPS Specimens using MIG

Figure 3.8(b): WPS Specimens using GTAW

Figure 3.8: WPS Specimens using MIG and GTAW

3.2.3 Testing of Test Specimens

Each specimen is assumed as simply supported with a single point load (three point

bending) applied at the centre. LVDT (Linear Voltage Displacement Transducer)

was used at the mid-span of the specimens to measure the deflection. One bracing

was placed on one side panel to restraint the flanges from experiencing lateral

torsional buckling. Two circular solid bars which simulated a line load action were

placed across the width of the flange. This is to ensure that the load is applied

through the bearing stiffeners and also to avoid the top flange from locally buckles

39

into the web due to the concentrated patch load. Nine numbers of LVDTs are placed

on one side of the panel beneath the top flange to measure the deformation of the top

flange due to tension field action. Only three specimens (F450-3, S450-3 and D450-

3) have rosette strain gauges glued along the middle of the web and placed at centre

of the ribs to measure the magnitude and directions of the strain in web. For doubly

webbed specimens rosettes were placed on both sides of the web, three on each side.

Two of the test specimens (S450-4 and D450-4) have linear strain gauges along and

on both sides of the compression flange. These gauges were used to replace LVDTs

and to measure the magnitude of the flange yielding. Figure 3.9 and Figure 3.10

show the experimental instrumentation test setup.

Small initial loading and unloading cycles are used to ensure the specimens are stable

and seated properly on the supports. After the entire instruments are initialized, load

is then applied in small increments of 2.5 kN. The loads, transducer readings and

strains are recorded in a data logger for every load increments.

40

LinearStGau

rain

ge

Applied Load

41

Figure 3.10: Experimental Set-up of Test Specimens

50 50 65 522.5 522.5

LVDTs

8 @ 50 c/c 72.5 8 @ 50 c/c 72.5

LVDT

Rosset Strain Gauges

1R 2R 3R

*Note: All dimensions are in mm

Figure 3.9: Experimental Instrumentation

3.3 Experimental Results and Discussions

In this study, all of the 29 numbers of test specimens were tested to failure. The

findings on the experimental investigation, which include the buckling behaviour,

strain measurements and load-deformation respond, are discussed in this chapter.

3.3.1 Symmetrical and Unsymmetrical Buckling Behaviour of Tested

Specimens

In this experimental investigation, all of the profiled web both singly and doubly

webbed specimens did not buckle in a symmetrical manner. In each case, only one

side panel buckled and pulled the flanges due to tension field action. However, for

each conventional flat webbed specimen, its web and flanges buckled symmetrically.

Both side web panels buckled and pulled the flanges due typical to tension field

actions. This behaviour proved that the experimental set-up was correct. Figure 3.11

shows the different typical buckling behaviours of flat and profiled web girders. The

other specimens are shown in Appendix B. From observations, that phenomena could

be explained due to the unstable part of the corrugation folds. The fold from one of

the panels started to buckle starting from one buckling mode to another buckling

mode. The web panel initially experienced a localised buckling in one part of the

corrugation fold and then developed of large deformation either in one corrugation, a

few corrugations or crossing diagonally into several corrugation folds. However, the

other panel remained stable.

Review from research done by others never mentioned about this unsymmetrical

buckling phenomenon. However, comparison of this unsymmetrical buckling

phenomenon with experimental studies done by a few authors is unsuitable.

Generally, in experimental investigation each specimen was strengthened with cross

bracing on one of the web panels to get a couple set of data for each specimen. In

1996, experimental work conducted by Elgally et al. [35] strengthened one of two the

web panels and tested until these web panel failed. After this panel failed, the girder

was tested again for the other web panel. Before the next test the failed web panel

was first strengthened back. Elgally et al., conducted similar experimental work and

42

he also discovered the same buckling phenomena. Based on these phenomena, it

become very clear on where to place the experimental instrumentation such as strain

gauges and transducers. In 2002, this experimental procedure was followed by

Fathoni [33] and Nina Imelda [34]. In non-linear finite element studies, only half of

the girders were modelled where symmetrical loading arrangement was obtained.

Elgally et al. [35, 37] modelled half of the girder to minimise the computational time.

R. Lou and Edlund [39] modelled the right-half web panel which was 20% longer

than the left-half web panel to ensure that the shear force on the left-half web panel

was larger than on the right-half.

As stated a earlier, the experimental setting-up was correct, since the control

specimens (flat web) showed expected results. All specimens i.e. conventionally flat

web, singly and doubly webbed profiled web girders were loaded at the mid-span

with the same support conditions. Since all of the tested conventional flat web

girders consistently buckled in a symmetrical manner and all profiled webbed girders

consistently buckled in an unsymmetrical manner these phenomena became

insignificant when examining the shear capacities of the girders.

43

Figure 3.11(a): Symmetrical Buckling of Flat Webbed Girder (Specimen F450-1).

Figure 3.11(b): Unsymmetrical Buckling of Single Profiled Webbed Girder (Specimen S550-1)

Figure 3.11 (c): Unsymmetrical Buckling of Double Profiled Webbed Girder (Specimen D350-1)

Figure 3.11: Symmetrical and Unsymmetrical Buckling

Behaviours of Typical Girder Specimens.

44

3.3.2 Buckling Behaviour of Conventional Flat Web Specimens

For the conventional flat web, the web buckled due to typical diagonal tension field

action and developed sway mechanism of the web panel. Throughout the test, it was

observed that the conventional flat web specimens showed the typical buckling

process. The web started to cripple in compression and developed inclined tension

field action and then formed plastic hinges in the flanges at post-buckling stage.

Figure 3.12 shows the distribution of principal strains in the web panel. Principal

strain value was calculated for each rosette at every load increment. R2 (Rosette 2,

placed at the middle of the web) showed that the maximum principal strain, ε1 has

linearly up in tension and developed very large strain after the peak load. The strain

yielded (tensile strain at yield = 3530 µ ) at a load 80.5% of the ultimate load.

However, the minimum principal strain, 2ε of R2 developed a small strain in tension

until the peak load was reached and suddenly it changed to very large in

compression. For R1 and R3 (Rosette 1 and Rosette 3 were placed at ¼ of the width

web panel from the vertical edges) only their minimum principal strains, 2ε were

calculated to show that the web panel was also in compression around R2. However,

the graphs showed that snap-back situations occurred at the starting load and

maximum load because of the inconsistence deformation of web panel at these load

stages. The orientations of maximum principal strain, 1ε of R2 or inclination of

tension field are shown in Table 3.3 and Figure 3.13. The orientation of the principal

strain iθ after reaching the peak load is equal to 27.2°, using equation 2.4. This

situation happened when the web had fully develop the ideal rotated tension field.

According to Evan and Moussef [19], the assumption of this value of iθ would lead

either to the correct prediction or to an underestimation of the shear capacity. It

allowed the second and third terms of equation 2.1 to be considered independently so

that the component of girder capacity that was dependent on the flange strength

was clearly identifiable. The value of

*pM

iθ could not be determined directly and

iterative procedure had to be adopted in which successive values of iθ were assumed

and the corresponding ultimate shear load could be evaluated in each case. However,

the value of iθ in equation 2.4 was adopted in appendix H.2, BS 5950: Part 1 [59].

45

Presented herein are two well-known failure theories of shear web panel called True

Basler and Cardiff Theory. True Basler [16] assumed that nominal flanges in

practical design were not so rigid that diagonal tension field did not develop near the

web-flange juncture and the web collapsed after development of yield zone. Cardiff

Theory [17-24] assumed that the flanges were able to anchor the tension field. Plastic

hinges form after the development of the yield zone and the web failed in sway

mechanism. In this experimental work, the web collapsed after the development of

the yield zone due to crippling of the web and by the formation of plastic hinge in the

flanges. Figure 3.14 shows the typical failure mode of conventional flat web

specimens. That buckling behaviour was similar to the collapsed behaviour by

Cardiff model.

0

10

20

30

40

50

60

70

-6000 -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000

Principal Strain, ε (µ)

Shear Load (kN)

ε1(R2)ε2 (R2)ε2 (R1)ε2(R3)

Figure 3.12: Principal Strains Distribution in Web Panel of Flat Web Specimens (Specimen F450-3)

R3R2R1

46

Table 3.3: Principal Strain, ε1 and Orientation of Principal Strain of Rosette 1 Flat

Web Specimen (F450-3)

Shear Load, V

(kN)

Principal Strain, ε1

( µ )

Orientation of Principal

Strain

( °θ )

0.00 0.0 37.9 0.90 58 34.0 4.85 473 37.6 8.50 106 34.6 10.60 2446 41.9 14.25 2292 38.4 20.30 2422 37.7 26.95 2537 39.4

*34.85 2896 41.1 44.25 3432 42.4 51.50 3595 42.9 57.60 3815 42.2 60.00 4454 40.9 60.90 4707 40.5 62.40 4736 37.9 63.65 4802 41.3 63.95 4526 41.5 63.35 4008 33.7 63.05 3780 17.1

**64.55 4853 22.9 63.65 5994 25.6 64.25 7230 27.2 63.35 8390 28.2 62.40 9642 29.0 63.35 11060 29.5 62.10 12417 29.9 63.35 13933 30.6 62.40 15735 37.9

Note:

1. (*) Represents the post-buckling load

2. (**) Represents the ultimate load

3. Calculated Value of iθ (equation 2.4) = 27.2°

47

°6.37 °1.41

°9.22°2.27

Figure 3.13(b): Inclination of Tension Field at V = 34.85 kN

Figure 3.13(a): Inclination of Tension Field at V = 4.85 kN

Figure 3.13(d): Inclination of Tension Field at V = 64.25 kN (After Peak load)

Figure 3.13(c): Inclination of Tension Field at V = 64.55 kN

Figure 3.13(a): Inclination of Tension Field at Variation of Load for Conventional Flat Web Specimen (F450-3)

Flange Buckling

Figure 3.14: Typical Failure Mode of Conventional Flat Web Specimen

48

In all of the tested conventional flat web specimens, the flanges buckled vertically

into the web associated with tension field action. This happened when the web plate

had lost its capacity to sustain any further increment in compressive stress.

Additional load, beyond the critical shear load was supported by tensile membrane

field which anchored against the top and bottom flange. At this stage of buckling,

four hinges were developed due to large bending action in the flanges to allow the

formation of shear way mechanism in web panel. Research by Lee and Yoo [25],

showed that the flanges buckled in the middle of the panel and near the flange-to-

bearing stiffener junction. This was because the web had large web aspect ratio

where a/d = 3.0. Lee and Yoo [25] also reported that the ultimate shear load was

much lower than the predicted value. Suggested by Höglund [66], most of these

theories started with the elastic buckling load Vcr and then the load was increased

corresponding to the types of diagonal tension fields. These theories gave good

results for girders with small web aspect ratios. However, the results became

conservative when the distance between the transverse stiffeners was large since the

contribution from tension field was small. Figures in Figure 3.15 show the types of

diagonal tension fields with different web aspect ratio. According to Lee and Yoo

[25], both Basler and Cardiff Models yielded reasonable values of ultimate shear

strengths for the web panels having aspect ratio less than 1.5 due to an offset effect

resulting from underestimation of the elastic buckling strength. In this experimental

work, the smallest web aspect ratio was 0.95 and the largest web aspect ratio was

1.49. Hence the results would be of very good accuracy.

49

a

d

Figure 3.15(a): Diagonal Tension Field with Small Web aspect Ratio (a/d)

a

d

Figure 3.15(b): Diagonal Tension Field with Large Web aspect Ratio (a/d)

Figure 3.15: Diagonal Tension Field with Different Web aspect Ratio (a/d)

3.3.3 Buckling Behaviour of Profiled Web Specimens

There are three types of buckling modes for the corrugated webbed specimens. They

are called local, zonal and global buckling mode [39]. According to Elgally et al.

[35], buckling mode could be categorized as local or global buckling mode.

However, this experimental study showed that at failure the buckling modes of the

profiled web specimens were either zonal or global as shown in Table 3.4. Generally

zonal buckling mode mostly occurred in this experimental work program, especially

for specimens with web depth 350 mm. The web buckling was not restricted to only

the plane part of the fold but the buckling crossed over to the other fold. Global

50

buckling mode mostly occurred for higher web depth, where the web buckling

involved several folds and raised yield lines crossing the folds. However, all

buckling modes developed in the post-buckling stage. Figure 3.16 and Figure 3.17

show the typical zonal and global failure mode of singly webbed and doubly webbed

profiled web specimens respectively.

Table 3.4: Buckling Modes of Profiled Webs

Label of Test

Specimens Buckling Mode

S350-1 Zonal

S350-2 Zonal

S350-3 Zonal

D350-1 Zonal

D350-2 Zonal

D350-3 Zonal

S450-1 Zonal

S450-2 Global

S450-3 Global

S450-4 Zonal

D450-1 Zonal

D450-2 Global

D450-3 Zonal

D450-4 Zonal

S550-1 Global

S550-2 Global

S550-3 Global

D550-1 Zonal

D550-2 Zonal

D550-3 Global

51

Figure 3.16(a): Typical Zonal Failure Mode of Singly Webbed Specimen (Specimen S350-1)

Figure 3.16(b): Typical Zonal Failure Mode of Doubly Webbed Specimen (Specimen D450-1)

Figure 3.16: Typical Zonal Failure Mode of Singly and Doubly Webbed Specimen

52

Figure 3.17(a): Typical Global Failure Mode of Singly Webbed Specimen (Specimen S550-1)

Figure 3.17(a): Typical Global Failure Mode of Doubly Webbed Specimen (Specimen D450-2)

Figure 3.17: Typical Global Failure Mode of Singly and Doubly Webbed Specimen

53

From observation, due to applied load, initially the web buckled in the local buckling

mode which occurred either at the top, middle or bottom of the fold. After reaching

the peak load, the buckling propagated to other folds which transformed into zonal or

extended to a global buckling mode in a diagonal direction of tension field action

beyond the peak load (post-buckling load). Lou and Edlund [39] also found the same

buckling phenomena for trapezoidal profiled webbed girders. Figure 3.18 shows the

local buckling mode at peak load before being transformed into zonal or global

buckling mode. At this stage, it was also observed that the profiled web specimens

gradually buckled due to crippling of the web and subsequently buckled till the

flanges yielded vertically into the web. In the other word, initially the specimens

showed crippling of the web followed by buckling of the flanges at ultimate load and

finally buckling is completed at post-buckling stage, before failure. For the doubly

webbed specimens, the rivets were pulled out when the web started to buckle.

Figure 3.18: Local Buckling Mode at Peak Load

Figure 3.19 shows the distributed principal strains in web panel of specimen S450-3.

From the calculated principal strains of single web specimen the maximum ( 1ε ) or

minimum ( 2ε ) principal strain were linear up to peak load with approximately same

magnitude but in different direction. However, the web panel did not buckle at where

the rosette strain gauges were placed and the gauge values did not show that they

were carrying additional strain. At this stage, the principal strain had shown that

there was only a small reduction in strain values which proved that the web panel did

not deform. Double web specimen (Specimen D450-3) also showed that the principal

54

strains were linear up to peak load. Values on both of the webs had approximately

the same magnitude but in different direction as shown in Figure 3.20. However, the

web panel buckled only at the first corrugation fold. The rosette strain gauges placed

at the first corrugation fold (R1 and R4) showed the development of large strain in

tension ( 1ε ) or compression ( 2ε ). In Figure 3.20(b) showed the minimum principal

strain of rosette 4 (R4) changed the direction of strain from compression to tension

due to crippling of the fold and the surface changed the deformation mode from

compression to tension. Corresponding principal strain values for both singly and

doubly webbed specimen did not yielding before reaching the peak load. The web

would yield after peak load at which corrugation fold was buckled.

0

10

20

30

40

50

60

70

80

90

-3000 -2000 -1000 0 1000 2000 3000 4000

Principal Strain,ε (µ)

Shear Load (kN)

ε1 (R1)ε2(R1)ε1(R2)ε2(R2)ε1(R3)ε2(R3)

R3R2R1

Figure 3.19: Principal Strain Distribution in Web Panel of Singly Webbed Profiled Web Specimen (S450-3)

55

0

20

40

60

80

100

120

140

160

180

200

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000

Principal Strain, ε(µ)

Shear Load (kN)

ε1(R1)ε2(R1)ε1(R2)ε2(R2)ε1(R3)ε2(R3)

R1R2R3

Figure 3.20(a): Principal Strain Distribution in Web 1 of Doubly Webbed Profiled Web Specimen (D450-3)

0

20

40

60

80

100

120

140

160

180

200

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000

Principal Strain,ε (µ)

Shear Load (kN)

ε1(R4)ε2(R4)ε1(R5)ε2(R5)ε1(R6)ε2(R6)

R6R5R4

Figure 3.20(b): Principal Strain Distribution in Web 2 of Doubly Webbed Profiled Web Specimen (D450-3)

Figure 3.20: Principal Strains Distribution in Web Panel of Doubly Webbed Profiled Web Specimens (D450-3)

56

For profiled web specimens, the flanges buckled according to the buckling mode of

the web. If the web buckles in zonal buckling mode, the buckling of the flanges

would occur in one of the regions of the corrugation folds. This behaviour could

occur since the contribution of stress field in the web was small and is restricted only

in the corrugation fold. Johnson and Caffolla [45, 70] also found that the local flange

buckling mode occurred in one region of the flat part of the corrugation fold. Johnson

and Caffolla [44, 69] also concluded that local flange buckling depended on the

value of the outstand.

If the web buckles in global buckling mode, the buckling of the flanges would occur

near the yield lines and then crossed the folds. This behaviour was similar to the

conventional flat girder. As mentioned, at this stage, webs buckled in local buckling

and then transformed either in zonal or global buckling mode and then abruptly

pulled the flanges. This implied that the flange started to buckle after peak and

deforms into the web until the specimen could not take anymore load. Figures in

Figure 3.21 show the typical flange buckling with different web buckling modes.

Two numbers of tested specimens namely S450-4 and D450-4 were fixed with linear

strain gauges along their compression flanges. Figure 3.22(a) shows the magnitude of

the deformation and Figure 3.22(b) shows the bending strains of the compression

flange of specimens S450-4. Figure 3.23 shows the bending strain of specimen

D450-4. Specimen D450-4 did not buckle at where the LVDT (Linear Voltage

Displacement Transducer) was placed. Figure 3.22 (b) and Figure 3.23 show that the

flange started to buckle and yield at the post buckling stage. This was clearly seen,

since at the peak load the flange did not yield because the web did not buckle and

pulled the flanges into the web.

57

Flanges Buckling

Figure 3.21(a): Flange Buckling Mode with Zonal Web Buckling Mode Type (Specimen D350-1)

Flange Buckling

Figure 3.21(b): Flange Buckling Mode with Global Web Buckling Mode Type (Specimen S550-1)

Figure 3.21: Flange Buckling Mode with Different Web Buckling Mode Type

58

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300 350 400 450 500

Distance (mm)

Def

orm

atio

n (m

m)

44.95 kN

72.25 kN

90.25 kN

92.2 kN (*at peak)

69.7 kN (*after peak)

Position of End Stiffener

Position of Bearing Stif fener

Shear Load

Figure 3.22(a): Deformation of Compression Flange Specimen S450-4

-4000

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300 350 400 450 500

Distance (mm)

Stra

in ( µ

)

44.95 kN75.25 kN90.25 kN92.2 kN (*at peak)69.7 kN (*after peak)

Sag

ging

oggi

ngH

Position of End Stiffener

Position of Bearing Stiffener

Hinge Position

Shear Load

Figure 3.22(b): Bending Strain of Compression Flange Specimen S450-4

Figure 3.22: Deformation and Bending Strain of Compression Flange for Specimen S450-4

59

-3500

-3000

-2500

-2000

-1500

-1000

-500

00 50 100 150 200 250 300 350 400 450 500

Distance (mm)St

rain

(µ

)

90.9 kN

130.3 kN

162.6 kN

189.3 kN (*at peak)

180.15 kN (*after peak)

Position of End Stif fener

Position of Bearing Stif fener

Hinge Position

Sagg

ing

Shear Load

Figure 3.23: Bending Strain of Compression Flange for Specimen D450-4

3.3.4 Load Deflection Behaviour of Tested Specimens

All conventional flat webbed specimens failed in typical shear failure mechanism.

The failure is characterized as elastoplastic shear buckling, where large strains of

yield zone and inclined tension field are developed and the plastic hinges are formed.

Identical behaviour occurred in the experimental investigation. The load deflection

curves indicate a reasonably stable postpeak behaviour.

As stated earlier there are three types of buckling modes for corrugated webbed

specimens. For all cases the initial buckling mode is local buckling until the peak is

reach. Then, the load deflection behaviour changes to what is referred to as a sudden

and steep descending branch as indicated in the graphs in Figures 3.24, 3.25 and

3.26. The buckling propagates to the other flat part of the fold which is then

transformed to a zonal or extended to a global buckling mode in a diagonal direction

like the tension field action. This occurs when the load is already beyond the peak

load (post-buckling stage), which shows that the ultimate shear capacity does not

depend on the zonal or global buckling mode. Graphs in Figure 3.24(c) show that the

deflection of specimen D350-1 is larger than the other two specimens because

specimen D350-1 was unstable when resting on its supports during the application of

60

the load. However, the ultimate load of these three specimens were almost the same,

hence acceptable. According to Lou and Edlund [39], the ultimate and post-buckling

shear capacities were expressed as reaction forces. The ultimate shear capacities were

taken from the peak load values and the post-buckling capacities were taken from the

corresponding minimum reaction force in the post-buckling stage. In this study the

values of ultimate and post-buckling were similar to what were in the report written

by Lou and Edlund. The unstable part of the post-buckling behaviour of the singly or

doubly corrugated webbed specimens could be identified from the curves. In this

post-buckling stage, the abrupt reduction of the shear capacity was in the range of

30% to 50% of the ultimate shear capacity. These values were different when

compared to results shown in Lou and Edlund [39] and Khalid et al [6-8]. Lou and

Edlund [39] obtained 70% to 80% reduction of post-buckling capacity from the

ultimate capacity and Klalid et al. [6], Khalid [7] and Chan [8] did not get the

percentage reduction in post-buckling capacity. Another recent research by Wang

[5], Elgaaly et al [35] and Evan and Mokhtari [43] presented the reduction on the

ultimate capacity but did not mention the amount of the reduction of the post-

buckling capacity. The experimental works conducted by Fathoni [33], showed that

load deflection curve was terminated at the peak. Table 3.5 shows the reduction in

shear capacity in the post-buckling stage. From the results in this study, it could be

concluded that for any kind of buckling mode that had been developed, there should

be an abrupt reduction in the post-buckling capacity and the ultimate or post-

buckling capacities of profiled web girder do not depend on the buckling mode.

In this experimental work, the flanges were designed to be strong to ensure that the

failure would be only due to shear failure. The failure could switch from web shear

failure to flange bending failure mode when applied bending moment reached the

plastic resistance of the flange, ( ( )TdAM fyff += σ ). From the results tabulated in

Table 3.5, the values of (Mexp/Mf) were less than 1, thereby confirming that failure

occurred due to web shear mode and bending moment did not influence the values.

Occurrence of local flange buckling depended on the web buckling modes. Local

modes did not contribute to such a phenomenon since the contribution of the stress

61

field in the web in this case was small and that it was restricted only in a few isolated

corrugation folds.

020406080

100120140160180200

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Loa

d,V

(kN

)F350-1 (Exp)

F350-2 (Exp)

F350-3 (Exp)

Figure 3.24(a): Load Deflection Curves of Flat Webbed Specimens (d = 350 mm)

020406080

100120140160180200

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Lo

ad, V

(kN)

S350-1 (Exp)

S350-2 (Exp)

S350-3 (Exp)

Figure 3.24(b): Load Deflection Curves of Singly Webbed Specimens (d = 350 mm)

020406080

100120140160180200

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Loa

d, V

(kN

)

D350-1 (Exp)

D350-2 (Exp)

D350-3 (Exp)

i

F gure 3.24(c): Load Deflection Curves of Doubly Webbed Specimens (d = 350 mm)

Figure 3.24: Load Deflection Curves for all Specimens with Web Depth, d = 350

62

020406080

100120140160180200

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Loa

d,V

(kN

)

F450-1 (Exp)

F450-2 (Exp)

F450-3 (Exp)

Figure 3.25(a): Load Deflection Curves of Flat Webbed Specimens (d = 450 mm)

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Loa

d,V

(kN

)

S450-1 (Exp)

S450-2 (Exp)

S450-3 (Exp)

S450-4 (Exp)

63

Fi ) gure 3.25(b): Load Deflection Curves of Singly Webbed Specimens (d = 450 mm

020406080

100120140160180200

0 5 10 15 20 25 30

Def (mm)

V (k

N)

D450-1 (Exp)

D450-2 (Exp)

D450-3 (Exp)

D450-4 (Exp)

Figure 3.25(c): Load Deflection Curves of Doubly Webbed Specimens (d = 450 mm)

Figure 3.25: Load Deflection Curves for Specimens with Web Depth, d = 450 mm

020406080

100120140160180200220240

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Loa

d,V

(kN

)

F550-1 (Exp)

F550-2 (Exp)

F550-3 (Exp)

Figure 3.26(a): Load Deflection Curve of Flat Webbed Specimens (d = 550 mm)

020406080

100120140160180200220240

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Loa

d,V

(kN

)

S550-1 (Exp)

S550-2 (Exp)

S550-3 (Exp)

Figure 3.26(b): Load Deflection Curve of Singly Webbed Specimens (d = 550 mm)

020406080

100120140160180200220240

0 5 10 15 20 25 30

Deflection (mm)

Shea

r Lo

ad,V

(kN)

D550-1(Exp)

D550-2 (Exp)

D550-3 (Exp)

Figure 3.26(c): Load Deflection Curve of Doubly Webbed Specimens (d = 550 mm) Figure 3.26: Load Deflection Curve of all Specimens with Web Depth, d = 550 mm

64

From observation, all of the tested specimens did not rupture at the weld line. In this

experimental program, two different welding processes were used. The results

tabulated in Table 3.5 show that the different welding process i.e. in between MIG

and GTAW was insignificant in influencing the ultimate shear capacities and

buckling modes. According to Davies and Roberts [22], heat affected zone (HAZ)

extent within parent metal approximately 25mm in all direction from the weld.

Comparing with the web depth of these experimental tested specimens, the HAZ was

not significant in influencing the web strength. Experimental works done by Cooke

et al [63] found that the principal residual welding stresses were predominantly

longitudinal tensions and vertical compressions so that their influence on the

diagonal tension field action was small, providing only a small tension component in

the diagonal direction. They also found that the initial out-of-plane plate distortions

did not influence web shear strength but were important in influencing the out-of-

plane distortions and stresses at service load.

Comparison of the ultimate shear capacities between corrugated web girders with

conventional flat web is shown in Table 3.6. Corrugated webbed girders had higher

load carrying capacities when compared to conventional flat web girders. The ratio

of the ultimate shear load for singly webbed corrugated web and conventional flat

web varied from 1.08 to 2.00 and the ratio for singly and doubly webbed corrugated

web varied from 2.51 to 4.30.

65

66

Table 3.5: Detail Results of Test Specimens

Web Depth (mm)

Type of Profiled

Web

Specimens Name

Welding Type

Failure Mode

Vu (kN)

Vb (kN) Vb/Vu Mexp/Mf

F350-1 MIG DTF 50.00 - - 0.23 F350-2 MIG DTF 42.75 - - 0.20 Flat F350-3 TIG DTF 56.05 - - 0.26 S350-1 MIG Zonal 65.75 37.90 0.58 0.30 S350-2 MIG Zonal 85.45 46.05 0.54 0.40 Single S350-3 TIG Zonal 71.20 47.25 0.66 0.33 D350-1 MIG Zonal 161.20 91.80 0.57 0.75 D350-2 MIG Zonal 168.50 104.85 0.62 0.78

350

Double D350-3 TIG Zonal 183.65 117.25 0.64 0.85 F450-1 MIG DTF 67.60 - - 0.24 F450-2 MIG DTF 61.50 - - 0.22 Flat F450-3 TIG DTF 63.95 - - 0.23 S450-1 MIG Zonal 73.05 47.25 0.65 0.26 S450-2 MIG Global 88.80 54.55 0.61 0.32 S450-3 TIG Global 77.90 44.55 0.57 0.28

Single

S450-4 MIG Zonal 92.20 65.8 0.71 0.33 D450-1 MIG Zonal 183.05 92.75 0.51 0.66 D450-2 MIG Global 183.95 107.60 0.58 0.67 D450-3 TIG Zonal 186.95 104.55 0.56 0.68

450

Double

D450-4 MIG Zonal 189.3 106.85 0.56 0.69 F550-1 MIG DTF 81.50 - - 0.24 F550-2 MIG DTF 81.65 - - 0.24 Flat F550-3 TIG DTF 81.85 - - 0.24 S550-1 MIG Global 130.00 75.15 0.58 0.39 S550-2 MIG Global 119.10 80.30 0.67 0.35 Single S550-3 TIG Global 124.50 75.15 0.60 0.37 D550-1 MIG Zonal 215.15 147.25 0.68 0.64 D550-2 MIG Zonal 205.45 133.05 0.65 0.61

550

Double D550-3 TIG Global 210.30 133.20 0.63 0.63

*Note: DTF is Diagonal Tension Field

Specimens Name F350-1 F350-2 F350-3 F450-1 F450-2 F450-3 F550-1 F550-2 F550-3

S350-1 1.32 1.54 1.17 - - - - - -S350-2 1.71 2.00 1.52 - - - - - -S350-3 1.42 1.67 1.27 - - - - - -D350-1 3.22 3.77 2.88 - - - - - -D350-2 3.37 3.94 3.01 - - - - - -D350-3 3.67 4.30 3.28 - - - - - -S450-1 - - - 1.08 1.19 1.14 - - -S450-2 - - - 1.31 1.44 1.39 - - -S450-3 - - - 1.15 1.27 1.22 - - -S450-4 - - - 1.36 1.50 1.44 - - -D450-1 - - - 2.71 2.98 2.86 - - -D450-2 - - - 2.72 2.99 2.88 - - -D450-3 - - - 2.77 3.04 2.92 - - -D450-4 - - - 2.80 3.08 2.96 - - -S550-1 - - - - - - 1.60 1.59 1.59S550-2 - - - - - - 1.46 1.46 1.46S550-3 - - - - - - 1.53 1.52 1.52D550-1 - - - - - - 2.64 2.64 2.63D550-2 - - - - - - 2.52 2.52 2.51D550-3 - - - - - - 2.58 2.58 2.57

Table 3.6: Comparison on Ultimate Shear of Corrugated Profiled Webbed and Conventional Flat Webbed Specimens, )(

)(Pr

Flatu

ofiledu

VV

.

67

3.4 Discussion Summary

From the experimental work it can be concluded that the profiled web girder did not

buckle in a symmetrical manner for singly and doubly webbed specimens, where

only one side web panel were buckled. Comparing with results obtained from control

specimens (conventional flat web girders) with the same setting-up, the above results

was acceptable. The experimental results showed that buckling modes of profiled

web girder were categorised in three different buckling modes, i.e. local, zonal or

global. Local buckling mode occurred at the first stage of buckling generally after the

load reaching the peak. Zonal or global buckling mode occurred at failure load

terminated (final failure). From observation, the buckling phenomena started locally

in flat part of web sub-panel (local buckling) and propagated to another flat part of

web sub-panel which then transformed to zonal or global buckling mode. Since the

geometry of the profile for all specimens was the same, therefore the zonal or global

buckling did not depend on the height of the web.

Load deflection responses for all singly and doubly profiled webbed specimens were

referred to as sudden and steep descending branch after reaching the peak. The

ultimate shear capacity did not depend on the zonal or global buckling mode because

the load started to drop when the web initially experience local buckling within the

flat part of the corrugation fold. Generally, the specimens experienced abrupt

reduction in their shear capacities, which was in the range of 30% to 50% of the

ultimate shear capacity. Comparison of the welding process between MIG and

GTAW was insignificant in influencing the ultimate shear capacity and buckling

mode of the tested specimens. That was because the heat affected zone (HAZ)

extended within parent metal approximately 25mm in all directions from the weld

toe. This was low compared to the web depth of the specimens. Comparison of the

ultimate shear capacities between corrugated web girders with the equivalent

conventional girders, the ratios were up to 2.00 and 4.30 for singly and doubly

webbed corrugated girders respectively.

68

CHAPTER 4

FINITE ELEMENT STUDY

4.1 Introduction

Finite element models were developed for the specimens tested and nonlinear

analysis was performed using the program LUSAS finite element software (version

13.6), which is available in the Faculty of Civil Engineering, Universiti Teknologi

MARA to simulate the combined geometric and materials non-linear response of the

girder with three different web systems under shear load. The main objective of

using finite element method is to validate against the experimental results. This

chapter would also discussed on the parametric that can influence the ultimate shear

capacity.

There are many factors that may influence the ultimate shear capacity and buckling

mode of the girder. Among the factors are:

a. Overall dimensions (Depth and Span)

b. Web and flange thickness

c. Profiled geometry

d. Residual stresses due to cold-forming, welding, temperature and repeated

loading.

e. Initial imperfection

In singly profiled webbed girder model, only the following factors were made to

vary; i.e. the web depth, web thickness and flange thickness. However for the doubly

webbed models, the significance of joint (riveting) was considered which may

influence the ultimate shear capacity. Residual stresses, self weight and strain at

rupture were not included in the analysis.

In this finite element study, effect of large large-deflection was taken into account

where Total Lagrangian approach was adopted. In this Total Lagrangian approach,

69

stress and strain measures were referred to in the undeformed configuration.

However, this study had a limitation which stated that the material strain hardening

model assumed an elastic- perfectly plastic model which eliminated strain hardening

parameters.

4.2 Preliminary Investigation for Combine Geometric and Material Non-

Linear Analysis with Initial Imperfection

Before attempting in employing a suitable user-element for the analysis a complete

plate girder system, a single test case was solved for the purpose of verifying that the

program, written in conjunction with the LUSAS finite element analysis, accurate

and represented the well established mathematical model developed for a particular

class of problem in which yielding and possibly buckling (local distortion)

phenomena could interact. The reason of this preliminary investigation is to get the

idea of nonlinear solution procedure especially for combining geometric and material

non-linear analysis with initial geometric imperfection. Example 6.5.1 in LUSAS

Verification Manual [70] was used as a guide since the behaviour was similar to the

intended model.

In this test model, an isolated steel plate subjected to in-plane compression as shown

in Figure 4.1 was used. The assumed boundary condition was simply-supported in

out-of-plane. In LUSAS Verification Manual, the external edges of the panel were

assumed to be simply-supported and the internal edges were subject to symmetry

enforcing boundary conditions (cut off from the corner of the plate). According to

Azmi [47], earlier analysis of this initially curve simply-supported isolated plate was

subjected to uniaxial in-plane compression by Moxham in 1971 and then developed

by Crisfield in 1973.

For the preliminary investigation an isolated rectangular plate was modelled, where

the material response was assumed to be elastic-perfectly plastic and Total

Lagrangian approach was used for geometry non-linearity. Global distribution load

was applied along the width of the plate as shown in Figure 4.1(a). Single half sine

70

wave shape of geometrical imperfection (equation 2.15) was considered in x as well

y direction. Figure 4.1(b) shows the meshing which used semiloof shell element

(QSL8) with 64 numbers of elements and isotropic stress potential with von Mises

yield condition were adopted for the material attribute. The side length ration was

taken as 0.875. The maximum amplitude was varied to get different peak loads. The

variations of maximum amplitudes were 0.1%b, 0.2%b, 0.5%b and 1.0%b. The

geometrical and material properties were as follow:

a = 875 mm T = 25 mm yσ = 247 N/mm2

b = 1000 mm E =207 kN/mm2

Zo

a

b

Y

X

Y

Zo

XZ

Figure 4.1(a): Isolated Rectangular Plate Subjected to Uniaxial Compression Load

Z XY

Figure 4.1(b): Modeling of an Isolated Plate Subjected to Uniaxial Compression Load with Out-of-Plane Simply Supported Edge Condition.

Figure 4.1: Model Isolated Rectangular Plate Modeling

71

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Shortening (mm)

Load

, P (M

N)

Zo = 0.1%b Zo = 0.2%b Zo = 0.5%b

Zo = 1.0%b Linear Maximum Load

Upper Bound

Po = 6175 kN Pmax = 6099.2 kN

Non-Linear analysis

Linear analysis

Figure 4.2: Load Shortening Curve of Rectangular Isolated Plate

Figure 4.2 shows that when the initial imperfection amplitude increases, the load

decreases. The first part of the slope is linear until it reached the maximum load. The

percentage reduction of maximum compressive load compared to smallest amplitude

(Zo = 0.1%b) and the calculated squash load (upper bound value) were tabulated in

Table 4.1. Squash load could be calculated from yield stress as:

oyo AP ×=σ

31100025247 −×××= ePo

kNPo 6175=

This implies that the non-linear solution strategy with small initial imperfection

(0.1%b) was capable of producing results reasonably close to the calculated squash

load. Comparison initial imperfection between 0.1%b and 0.2%b did not show too

much difference in maximum values but beyond the maximum load, the slopes

crossed each other. However, comparing the slopes beyond the peak loads for 0.2%b

initial imperfection the slope coincided with 0.5%b and for initial imperfection

between 0.1%b and 1.0%b, the slopes were parallel.

72

Table 4.1: Percentage Decreasing of Maximum Load, P Compared to Smallest

Amplitude and Calculated Critical Buckling Load

Maximum

Amplitude, Zo

Maximum Load, P

(kN)

Percentage Reduction

Compared to

Zo = 0.1%b

(%)

Percentage

Reduction

Compared to kNPo 6175=

(%)

0.1%b 6099.2 - 1.2

0.2%b 5954.8 2.4 3.6

0.5%b 5459.6 10.5 11.6

1.0%b 4729.8 22.5% 23.4

For non-linear analysis of a plate girder, the same solution strategy was used but

plate thickness and material properties were changed and cited in Table 3.2. In this

preliminary modelling of a plate girder, only conventional flat web girders were

modelled for specimens with web depth 450 mm and 550 mm which were labelled as

F450-Fe and F550-Fe respectively. The reason was to minimise the computational

time in order to get a suitable non-linear solution strategy for the development of a

profiled web girder modelling. Since the initial imperfection was not measured, this

initial imperfection study assumed half sine wave which was similar as the earlier

analysis which considers isolated plate. Generally initial imperfection could be

modelled using first mode shape in buckling analysis or using half sine wave. In this

LUSAS finite element package which is available in the Faculty of Civil

Engineering, Universiti Teknologi MARA, the extension programme to capture the

first mode shape was not included; therefore, so that the initial imperfection could be

modelled using half sine wave. Initial imperfection was applied to both web panels

with the same magnitude and direction. This is because the buckling of the flanges

was too small compared to the web for the first mode shape in buckling analysis.

The entire plate components such as flanges, web and stiffeners were modelled with

quadrilateral thin shell element (QSL8). Global distributed load was applied to the

line feature along the width of top flange to ensure that the load was applied through

73

the bearing stiffeners and to avoid the top flange from locally buckled into the web

due to concentrated patch load, to simulate the experimental setting-up.

The load was applied using automatic load increment scheme. Arc-length control

using Crisfiled arc-length procedure should be used in advanced non-linear

incremental parameters which are available in LUSAS finite element package. For

these models, arc-length solution was guided with the current stiffness. The models

were simply supported near the two ends. At each end, a hinge support was placed at

the centre between the two end bearing stiffeners. Figure 4.3 shows the model of a

conventional flat web specimen. The results for both models are shown in Figure

4.4(a) and Figure 4.5(a) for web depth 450 mm and 550 mm respectively. Each

model was deformed due to the crippling of the web, subsequent development of

yield zone until plastic hinges were formed at the flanges as shown in Figure 4.4(b)

and Figure 4.5(b).

Figure 4.3: Typical Finite Element Modeling of Conventional Flat Web Specimen

74

55

60

65

3 4 5 6 7 8 9

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Deflection (mm)

She

ar, V

(kN)

F450-0.1% F450-0.2% F450-0.5% F450-1.0%

Figure 4.4(a): Load-Deflection Curve of F450-Fe with Different Maximum Imperfection Amplitudes

Figure 4.4(b): Typical Deform Mesh Shape of F450-Fe Model at Failure

Figure 4.4: Finite Element Result of Model F450-Fe with Different Maximum Imperfection Amplitudes (d = 450 mm)

75

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Deflection (mm)

Shea

r, V

(kN

)

0.1%d 0.2%d 1.0%d

40

50

60

70

1 2 3 4 5

Figure 4.5(a): Load-Deflection Curve of F550-Fe with Different Maximum Imperfection Amplitudes

Figure 4.5(b): Typical Deform Mesh Shape of F550-Fe Model at Failure

Figure 4.5: Finite Element Result of Model F550-Fe with Different Maximum Amplitude (d = 550 mm)

76

Hence, initial imperfection did not greatly affect the ultimate shear load capacity. It

became significant only when the load reached the post-buckling strength. However,

when both models are compared with their experimental results, the values are of

very good accuracy. Both models have load deflection curves within the range of

upper and lower bound values of the experimental data. Figure 4.6 show the load

deflection curves of finite element and experimental results.

In this preliminary investigation of non-linear analysis, different shapes of initial

imperfection were also investigated. Plan views of initial imperfection with S-Shape

and B-shape are shown in Figure 4.7(a). When the direction of the initial

imperfection amplitude on one web panel was changed, the results did not change

from B-shape to S-Shape. The failure modes were seen different but the load

deflection curves coincided each other. The graphs in Figure 4.7(b) shows the load

deflection curves with different initial shape but with the same maximum amplitude

imperfection. According to Graciano and Edlund [57], on longitudinally stiffened

plate girder under patch load, two types of initial shape imperfections called C-shape

and S-shape (side view) were considered, as shown in Figure 2.7. When comparing

the load carrying capacities having two different shapes, there was a reduction of

about 7% in the patch loading capacity of a longitudinally stiffened plate girder.

The above study on the variation of initial imperfection, showed that the ultimate

shear capacities were not greatly affected. Hence, B-shape with maximum initial

imperfection amplitude of 0.1%d was selected for the analysis of profiled web

models.

77

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16 18 20

Deflection (mm)

Sher

a, V

(kN

)

F450-Fe (0.1%)F450-Fe (1.0%)F450-1 (Exp)F450-2 (Exp)

Figure 4.6(a): Comparison Load-Deflection Curve of Specimens F450 Series (Conventional Flat Web, d =450 mm)

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12 14 16 18 20

Deflection (mm)

Sher

a,V

(kN

)

F550-1 (Exp)

F550-3 (Exp)

F550-Fe (0.1%d)

F550-Fe (1.0%d)

Figure 4.6(b): Comparison Load-Deflection Curve of Specimens F550 Series (Conventional Flat Web, d = 550 mm)

Figure 4.6: Comparison Load-Deflection Curve of Finite Element with Experimental Tested Results for Conventional Flat Web with Web Depth 450 mm and 550 mm

78

B-Shape

Zo

Zo

S-Shape

Figure 4.7(a): The Type of Initial Shape Imperfection View on Plan

B-Shape

S-Shape

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12 14 16

Deflection (mm)

Shea

r, V

(kN)

B-Shape S-Shape

Figure 4.7(b): Load-Deflection Imperfection Shape Sensitivity of Plate Girder with Different Shape under Shear Load

Figure 4.7: Imperfection Shape Sensitivity of Plate Girder with Different Shape under Shear Load

79

4.3 Non-Linear Finite Element Modelling on Profiled Web Girder

All models were created in a 3D space. Since the study on isolated plate and

conventional flat web gave good accuracy, all models of profiled web specimens also

used eight-noded quadrilateral thin shell elements (QSL8). The element formulation

was based on an isoparametric approach with constraints to invoke the Kirchhoff

hypothesis for thin shells. The element formulation took account of both membrane

and flexural deformations. All profiled web models use two elements across the

width of each longitudinal and inclined fold of the corrugation as shown in Figure

4.8. The element size ratio for the web was chosen to be close to one. The material

response was assumed to be elastic-perfectly plastic and non-linear geometry of the

girder used Total Lagrangian approach. An isotropic stress potential with von Mises

yield condition was adopted for the material attribute, and material properties were

given in Table 3.2. The initial imperfection was assumed half sine wave which was

similar as the earlier analysis which consider conventional plate girder. Where, B-

shape with maximum initial imperfection amplitude of 0.1%d was selected for the

analysis of all profiled web models.

Global distributed load was applied to the line over the bearing stiffeners along the

flange width, just like the experimental setup. The load was applied using automatic

load increment scheme, where the maximum load increment equal or less than 0.2

times anticipated ultimate load. However, the arc-length control using Crisfiled arc-

length procedure used in advanced non-linear incremental parameters solution did

not refer to the current stiffness. The sign of the current stiffness parameter was good

at coping with bifurcation points, but would always fail when a snap-back situation

was encountered. According to Lou and Edlund [39], the snap-back phenomena

generally occurred on numbers subject to shear loading. Lou and Edlund also used

Crisfield arc-length procedure in ABAQUS, commercial finite element software,

where it was able to efficiently handle snap-through situations. Notably in the

presence of strain-softening, the arc-length method may converge on alternative and

unstable equilibrium paths. To ensure the girder did not buckle prematurely due to

lateral torsional buckling, the flanges were pinned in X-direction as shown in Figure

4.8.

80

For doubly webbed specimens model, slidelines option was brought into the webs

which is available in LUSAS to ensure the nodes in the webs did not penetrate each

other in the analysis. In this finite element study, slidelines type option was used for

general slidelines without friction. Non-rigid surface was used for rigid type option

because rigid surface contact can be used when one contact surface is stiffer than the

other. Referring to LUSAS Manual [48], slidelines may be used to model the contact

behaviour between two or more bodies. Slidelines are the alternatives to joint

elements or constraint equations, and have advantages in the following situations:

• Finite relative surface deformations with arbitrary contact and separation

• No exact prior knowledge of the contact process

• A large number of nodes are defined within the probable contact region

• Highly localised element density in the region of high stress gradients

Joint elements were used as connectors between two webs for a doubly webbed

model. Only one model for doubly webbed specimens (D550C-Fe) was modelled

using joint elements between the two webs, assuming that the rivets did not have

enough potency to take more loads after the webs buckle. It could hardly be clearly

observed in the experimental work, where the webs did not buckle at peak load and

the rivets were pulling out when the web started to buckle. In this study, a

comparison was made between jointed and non-jointed webs for webs depth 550 mm

(the highest depth in experimental work). Joint element called JSL4 was introduced

in the model where a 3D joint element (JSL4) which connected two nodes by three

springs in the local x, y and z-directions and two springs about the local x-direction at

the first and second loof points. Figure 4.8(b) shows the model of a doubly webbed

specimen. Since the elastic stiffness of rivet was not measure, the elastic stiffness of

the aluminium rivet was calculated by:

L

EA=Stiffness Elastic (4.1)

where:

E = 70 kN/mm² L = 6.35 mm

A = 5 mm² yσ = 300 N/mm²

81

Figure 4.8 (a): Finite Element Model for Single Web Profiled Web Girder

Figure 4.8(b): Finite Element Model for Double Web Profiled Web Girder

Figure 4.8: Finite Element Model for Single and Double Web Profiled Web Girder

82

A parametric study was conducted using non-linear finite analysis to study the effect

of the web and flange thickness and web depth of single webbed girders. However,

when the web thickness or depth increases, the bottom flange thickness over the

support area and stiffeners also increased to avoid premature local flange buckling

into the web or buckling of stiffeners due to support reaction. This was possible by

having an extra plate over the support area. This also applied when reducing flanges

thickness. The dimensions of all 17 models created using finite element were

tabulated in Table 4.2.

Table 4.2: List of Tested Models using Finite Element Analysis

Model Name Web

Arrangement

Web Depth

(mm)

Web

Thickness

Flange

Thickness

(mm)

S250-Fe 250 1.0 9.0

*S350-Fe 350 1.0 9.0

*S450-Fe 450 1.0 9.0

*S550-Fe 550 1.0 9.0

S750-Fe 750 1.0 9.0

S1000-Fe 1000 1.0 9.0

S550t0.8-Fe 550 0.8 9.0

S550t1.2-Fe 550 1.2 9.0

S550t2.0-Fe 550 2.0 9.0

S550T3-Fe 550 1.0 3.0

S550T6-Fe 550 1.0 6.0

S550T12-Fe 550 1.0 12.0

S550t2.0T20-Fe

Single

550 2.0 20.0

*D350XC-Fe 350 1.0 9.0

*D450XC-Fe 450 1.0 9.0

*D550XC-Fe 550 1.0 9.0

*D550C-Fe

Double

550 1.0 9.0

Note: 1. (*) with an equivalent specimen

2. XC and C represent the non jointed and jointed webs respectively

83

4.4 Finite Element Results and Discussions

The main objective of analysing and getting results using finite element method is to

validate against the experimental results. This numerical investigation, showing the

load-deformation responds, buckling behaviour and stress and strain plots were

discussed in this chapter. The purpose is to achieve a valid non-linear finite element

modelling.

4.4.1 Validation of Non-Linear Finite Element Analysis with Experimental

Results of Profiled Webbed Plate Girder

To ensure the accuracy of the non-linear finite element modelling, the results needed

to be validated against the experimental results. Figure 4.9 to Figure 4.14 show

comparison of load deflection curves of analytical and experimental results for

different test specimens. The elastic buckling (first slope) part of each curve shows

that the entire finite element results were so stiff compared to the experimental

results. The effect of the first slope of the load deflection curve could be due to the

initial setting of experimental the setup. Loading, the specimens were not fully rested

on the supports especially for specimen D350-1. Another reason effecting the first

slope of the load deflection curve was because initial imperfection of the flanges

(warping) due to welding, was not included in the finite element analysis. Initial

imperfection was modelled only using half sine wave for web panels which was not

exactly like the experimental specimens. However, comparison of their ultimate

shear loads was satisfactory. Table 4.3 shows the comparison of ultimate shear loads

using finite element analysis against experimental results. Specimens S450-1 and

S450-3 show greater differences. However, these results show slightly, although not

unduly, conservative. In fact, the finite element results were acceptable. The mean

ratio of the finite element-to-experimental results is 1.07 with 0.11 a standard

deviation. Beyond the peak load for each load deflection curve there existed a snap

back situation. Non-linear finite element study done by Lou and Edlund [39] also

indicated this snap back situation as shown in Figure 4.15. Guide with current

stiffness in arc-length control was impracticable because it could generally fail when

a snap-back situation was encountered.

84

Every finite element results of doubly webbed models were terminated after reaching

the peak load due to surface interaction of the two webs and slow rate of

convergence. However, only at this stage the models started to buckle. Figure 4.16

shows the buckling shapes of doubly webbed models. The study on steel-concrete

composite plate girder by Baskar et al. [53] and Shanmugam and Baskar [54] also

found that the analysis which was capable of predicting the behaviour up to ultimate

failure load only. The analysis topped after reaching the ultimate load due to slow

rate of convergence, surface interaction between concrete slab and top flange and

cracking effect of the models.

Figure 4.14 shows graph of models with and without rivet connectors. The ultimate

shear load with connectors was 5.6% higher than without connectors. This implies

that the introduction of connectors in the model was slightly significant in

influencing the ultimate shear load. However, the ultimate shear capacity of the

models without connector was closer to all of the experimental results. Therefore,

introducing rivets connectors in the finite element models did not significantly

influence the ultimate shear capacity of a double profiled web girder.

Figure 4.17 shows typical results of principal strain distribution for analytical

analysis in the web sub-panels compared to experimental principal strains up to peak

load. S1, S2 and S3 represent the location of Rosette 1, Rosette 2 and Rosette 3

respectively as in the experimental programme (see Figure 3.9). The results show

that the principal strains were not yielding up to peak load (tensile strain at yield =

3530µ ). As mentioned in Chapter 3, at this stage, the principal strain has shown the

small values of compared to yield strain and proved that the web panel was not

deformed and distributed equally in web panel.

However, comparison of strains or deformations in the compression flange to the

experimental data was not applicable because the positions of plastic hinges were

different. Generally flanges buckled due to zonal or global web sub-panel buckling

behaviour. Unfortunately, the position of plastic hinges of profiled web girder for

singly and doubly webbed could not be determined directly from the flange or web

85

panel geometry. However, the positions were associated with the web-sub panel. As

stated earlier, constricted study by Johnson and Caffolla [69] found that the local

flange buckling mode occurred in one region of the flat part of the corrugation fold.

Johnson and Caffolla [69] concluded that local flange buckling depended on the

value of the outstand.

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 1

Deflection (mm)

Shea

r, V

(kN

)

60

65

70

75

80

2 2.5 3 S350-Fe

S350-1 (Exp)

S350-2 (Exp)

S350-3 (Exp)

4

Figure 4.9: Load Deflection Curves for S350 Series

86

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14

Deflection (mm)

She

ar, V

(kN

)S450-Fe

S450-1 (Exp)

S450-2 (Exp)

S450-3 (Exp)

S450-4 (Exp)


80

85

90

95

100

105

2 2.5 3

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14

Deflection (mm)

Shea

r, V

(kN)

S550-Fe S550-1 (Exp)

S550-2 (Exp) S550-3 (Exp)

100

120

2 2.5


87

0

20

40

60

80

100

120

140

160

180

200

220

240

0 2 4 6 8 10 12 14 16 18 20Deflection (mm)

Shea

r, V

(kN)

D350-Fe

D350-1 (Exp)

D350-2 (Exp)

D350-3 (Exp)

120

140

160

2 3

Figure 4.12: Load Deflection Curves for D350 Series

0

20

40

60

80

100

120

140

160

180

200

220

240

0 2 4 6 8 10 12 14 16 18 20

Deflection (mm)

Shea

r, V

(kN

)

D450-Fe D450-1 (Exp) D450-2 (Exp)

D450-3 (Exp) D450-4 (Exp)

180

200

2.5 3


88

0

20

40

60

80

100

120

140

160

180

200

220

240

0 2 4 6 8 10 12 14 16 18 20

Deflection (mm)

Shea

r, V

(kN

)

D550XC-Fe

D550C-Fe

D550-1 (Exp)

D550-2 (Exp)

D550-3 (Exp)

200

220

240

2 2.5 3


Figure 4.15: Load-deflection Curves for Corrugated Web Girder Investigated by Lou and Edlund [39] under Shear with Different Corrugation Depths

89

Figure 4.16 (a): Final Buckling Shape of D350-Fe at the End of Analysis

Figure 4.16(b): Final Buckling Shape of D450-Fe and D550-Fe at the End of Analysis

Figure 4.16: Final Buckling Shape of Doubly Webbed Models at the End of Analysis

90

Table 4.3: Comparison of Ultimate Shear Loads of Finite Element against

Experimental Results

Specimen

Label Vu (Exp) Vu (FE) (Exp) V

(FE) V

u

u

S350-1 65.75 1.19

S350-2 85.45 0.92

S350-3 71.20

78.21

1.10

S450-1 73.05 1.38

S450-2 88.80 1.13

S450-3 77.90 1.29

S450-4 92.20

100.71

1.09

S550-1 130.00 0.94

S550-2 119.10 1.03

S550-3 124.50

122.29

0.98

D350-1 161.20 0.97

D350-2 168.50 0.93

D350-3 183.65

156.93

0.85

D450-1 183.05 1.10

D450-2 183.95 1.10

D450-3 186.95 1.08

D450-4 189.30

201.59

1.06

D550-1 215.15 1.01

1.07**

D550-2 205.45 1.06

1.12**

D550-3 210.30

217.86

230.96**

1.04

1.10**

Mean 1.07

Standard Deviation 0.11

Note: (**) represent doubly webbed finite element models with connectors

91

Shear, V (kN)

0

20

40

60

80

100

120

-3000 -2000 -1000 0 1000 2000 3000

Principal Strain (µ)

ε1-S1(FE)

ε2-S1(FE)

ε1-S2(FE)

ε2-S2(FE)

ε1-S3(FE)

ε2-S3(FE)

ε1-R1

ε2-R1

ε1-R2

ε2-R2

ε1-R3

ε2-R3

Figure 4.17: Comparison of Principal Strain Distribution of S450-3 and S450-Fe

4.4.2 Non-Linear Analysis Buckling Behaviour of Profiled Web Plate Girder

As mentioned in Chapter 3, all of the singly and doubly webbed specimens did not

buckle in a symmetrical manner. Only one side panel buckled and pulled the flanges

due to tension field action globally in a web panel or zonally in a few web sub-

panels. The finite element study also found the same buckling phenomena. Figure

4.18 shows the unsymmetrical deformed mesh of the profiled web specimens using

finite element analysis. Chapter 3 also discussed about the three types of buckling

modes for the corrugated webbed specimens. They were local, zonal and global

buckling modes. Table 4.4 shows the buckling modes using finite element analysis

and Figure 4.19 shows the typical of failure modes which could be observed in non-

linear finite element analysis.

However, local buckling mode only occurred after the load reached peak and

transformed to zonal or global buckling mode. This kind of deformation behaviour

was clearly observed with finite element analysis, where the web started to buckle in

one flat part of the fold or in a few folds and then developed large deformation

crossing fold lines over a part of panel width. Then, it subsequently buckled till the

flanges yielded vertically into the web. Figure 4.20 and Figure 4.21 show the

92

transformation of global and zonal web failure. In Chapter 3, it was mentioned that

the load deflection behaviour changed to what was referred to as a sudden and steep

descending branch after reaching peak. That confirmed the load sudden and steep

descending branch due to local buckling of flat part of corrugation fold.

Table 4.4: Buckling Mode of Finite Element Analysis

Model Name Buckling Mode

S250-Fe Global

*S350-Fe Global

*S450-Fe Zonal

*S550-Fe Zonal

S750-Fe Zonal

S1000-Fe Zonal

S550t0.8-Fe Zonal

S550t1.2-Fe Zonal

S550t2.0-Fe Zonal

S550T3-Fe Local Flange Buckling

S550T6-Fe Zonal

S550T12-Fe Global

S550t2.0T20-Fe Zonal

93

Figure 4.18: Typical Unsymmetrical Deformation of Profiled Web Girder (Specimen model S550t2.0-Fe)

Figure 4.19(a): Global Buckling Shape of Profiled Web Girder (Specimen Model S550T12-Fe)

Figure 4.19(b): Zonal Buckling Shape of Profiled Web Girder (Specimen Model S450-Fe)

Figure 4.19: Typical Global and Zonal Buckling Shape of Profiled Web Girder

94

95

Step 1

Step 4

Final Failure

Step 3

Step 2

0

20

40

60

80

100

120

140

0 2 4 6 8 10

Deflection (mm)

Shea

r, V

(kN

)

Final Failure

Step 4

Step 3

Step 2

Step 1

Notation of Deformation Step

Figure 4.20: Evolution of Deformation Contours in X-direction of Global Failure Mode of Profiled Web Girder (S550T12-Fe)

Step 2

Step 1

96

Step 3

0

20

40

60

80

100

120

0 2 4 6

Deflection (mm)

Shea

r, V

(kN

)

Final Failure

Step 4

Step 3

Step 2

Step 1

Final Failure

Step 4

Notation of Deformation Step

Figure 4.21: Evolution of Deformation Contours in X-direction of Zonal Failure Mode of Profiled Web Girder (S450-Fe)

4.5 Parametric Study on Singly Webbed Profiled Web Girder

Since the non-linear analysis of doubly webbed girders terminated just after the peak

was reached, therefore this parametric study only considered single web profiled web

girders. In this parametric study, a variation of web thickness, web depth and flange

thickness was used to investigate their influence on the ultimate shear capacities of

the girder. In this study, the profiled geometry and shape were kept constant.

4.5.1 Influence of Web Depth

For this study, six different web depths were chosen:

d = 250 mm d = 550 mm

d = 350 mm d = 750 mm

d = 450 mm d = 1000 mm

Hence, the flange and web thickness for all models were kept constant, where web

thickness and flange thickness was 1.0 mm and 9.0 mm respectively. For model with

web depth 750 mm and 1000 mm the bottom flange and stiffeners over the support

were increased to avoid premature local flange buckling of the web. Figure 4.22

shows the load deflection curves of the model with different web depths and Figure

4.23 shows buckling modes obtained at the end of the analysis. Each graph shows

that the load increased linearly up to peak then it suddenly dropped due to local

buckling. In the post-buckling stage the loads reduce about 20% to 50% of the peak

loads before they remained stable until the end of the analysis. The ultimate shear

and post-buckling capacities were tabulated in Table 4.5. However, the study on

shear capacity of profiled web girders by Lou and Edlund [39], obtained a reduction

of about 70% of the ultimate shear capacity. According to Lou and Edlund [39], the

peak and dale of load deflection response corresponded to the formation of zonal

buckling involving flat sub-panels. The total number of peaks and dales were equal

to the total number of flat parts of the corrugation folds. However in this study, peak

and dale phenomena in load deflection response did not occur. The final mode of

failure of the girder with web depth 250 mm and 350 mm was global buckling.

Nevertheless, for web depth 750 mm and 1000 mm buckling occured at the top of the

girder near the load bearing stiffeners and involved only one rib. For web depth 450

97

mm the web buckled at the top but web depth 550 mm at the bottom of the girder

involved the adjacent ribs. Hence, buckling mode of profiled web girder did not

depend on the size of web panel. However, general initial buckling was always due

to local buckling of the flat part of the corrugation fold and the final buckling could

be classified as zonal or global. It also concluded that the ultimate shear capacity and

post-buckling capacity did not depend on the whether the final buckling modes are

zonal or global.

Shear, V

(kN)

0

20

40

60

80

100

120

140

160

180

200

220

0 1 2 3 4 5 6 7Delection (mm)

d = 250 mm

d = 350 mm

d = 450 mm

d = 550 mm

d = 750 mm

d = 1000 mm

Local buckling

Post-buckling

Final buckling

Figure 4.22: Load Deflection Curves for Different Web Depths

98

(a): Web Depth 250 mm (b): Web Depth 350 mm

(c): Web Depth 450 mm (d): Web Depth 550 mm

(e): Web Depth 750 mm

(f): Web Depth 1000 mm

Figure 4.23: Buckling Modes Obtained at the End of the Analysis for Models with Different Web Depths

99

Table 4.5: Results of Non-Linear Analysis for Different Web Depths

Model

Ultimate Shear

Capacity, Vu

(kN)

Post-Buckling

Capacity, Vb

(kN) u

b

VV

S250-Fe 55.46 40.76 0.73

S350-Fe 78.21 54.11 0.69

S450-Fe 100.71 55.39 0.55

S550-Fe 122.29 75.53 0.62

S750-Fe 164.62 85.00 0.52

S1000-Fe 215.55 110.32 0.51

4.5.2 Influence of Web Thickness

To investigate the influence of the web thickness on the shear capacity, four models

with web thickness 0.8 mm, 1.0 mm, 1.2 mm and 2.0 mm were considered. Profiled

steel sheets 0.8 mm, 1.0 mm and 1.2 mm thick are available in the market. Web

thickness 2.0 mm was considered in order to compare with double web system. The

models followed the geometry of S550-Fe except for t = 2.0 mm, where the bottom

flange thickness over the support area and stiffeners were increased to ensure that the

model would not fail prematurely in an unforeseen mode.

Figure 4.24 show plots of load deflection respond obtained using the non-linear

analysis. Each curve shows that the load reduced suddenly after reaching the peak

which was about 50% of the ultimate capacity. Table 4.6 shows the results for

different web thickness. All of the models buckled in zonal buckling mode as shown

in Figure 4.25. Models with web thickness 1.0 mm and 1.2 mm had the same failure

mode as shown in Figure 4.25(b). No peak and dale occurred in the load deflection

response as could be seen from Figure 4.24. When the models with web thickness

0.8 mm and 1.2 mm were compared to the model with web thickness 1.0 mm the

ultimate shear capacity reduced by 24% or increased by 21% respectively. When the

web thickness was doubled, the ultimate shear was also doubled. However, when the

100

model with web thickness 2.0 mm was compared to doubly web girder, the ultimate

shear capacity increase from 9% to 23% as shown in Table 4.7. This shows that

double web systems were not significant to improve the capacity of the girder. In

terms of welding cost, double web systems cost higher than single web.

However, the maximum thickness of the available manufactured cold form profiled

steel sheet made using rolling technique or stamping is limited. According to

author’s knowledge, the present local manufacture, Asia Roofing Sdn Bhd uses

rolling technique produced and maximum thickness of 2.0 mm only. Another

company, Trapezoid Web Profile Sdn Bhd uses stamping technique and produces up

to 8.0 mm thick. This shows that double web systems are useful in enhancing the

ultimate shear strength as compared to using singly webbed arrangement.

Shear, V (kN)

0

20

40

60

80

100

120

140

160

180

200

220

240

260

0 1 2 3 4 5 6 7 8 9 10

Deflection (mm)

t = 0.8 mm

t = 1.0 mm

t = 1.2 mm

t = 2.0 mm

Figure 4.24: Load Deflection Curves for Different Web Thickness

101

(a): Web Thickness 0.8 mm (b): Web Thickness 1.2 mm

(c): Web Thickness 2.0 mm

Figure 4.25: Buckling Modes Obtained at the End of the Analysis for Model with Different Web Thickness

102

Table 4.6: Results of Non-Linear Analysis for Different Web Thickness

Model

Web

Thickness

(mm)

Ultimate

Shear

Capacity,

Vu

(kN)

Post-

Buckling

Capacity,

Vb

(kN)

u

b

VV

Comparison of

Ultimate Shear

Capacity with

t =1.0 mm

mm) 1.0 (t u

u

VV

=

S550t0.8-Fe 0.8 92.41 50.15 0.54 0.76

S550-Fe 1.0 122.29 58.90 0.48 -

S550t1.2-Fe 1.2 148.13 68.88 0.46 1.21

S550t2.0-Fe 2.0 252.24 140.36 0.56 2.06

Table 4.7: Comparison between Models with Single (2.0 mm Thick) to Double Web

Arrangement

Model

Ultimate Shear Capacity,

Vu

(kN)

Comparison of Ultimate

Shear Capacity with

t =2.0 mm

Web)(Doubleu

mm) 2.0 (t u

VV =

D550-1 215.15 1.17

D550-2 205.45 1.23

D550-3 210.30 1.20

D550XC-Fe 217.86 1.16

D550C-Fe 230.96 1.09

103

4.5.3 Influence of Flange Thickness

For this study, the thickness of both flanges were varied from 3.0 mm to 12.0 mm in

the increment of 3.0 mm, and the web was always 1.0 mm thick. For systems with

2.0 mm thick web, two different flange thickness 9.0 mm and 20.0 mm were

selected. The purpose of this study was to investigate the contribution of the flanges

to the shear capacity of the profiled web girders. Hence, the web depth followed the

depth of the model, S550-Fe and S550t2.0-Fe.

All the models showed the flanges were buckle into the web at the post-peak load as

shown in Figure 4.26. For the flanges thickness 3.0 mm, the top flange was buckled

sharply into the web and it looked like patch loading behaviour. This is because the

flanges were very thin to anchor the tensile force from the web. That also showed

that the tensile force was developing in the small region flat part of corrugation fold.

Figure 4.27 and Figure 4.28 show the load deflection curves with different flange

thickness for constant web thickness 1.0 mm and 2.0 mm respectively. In both

figures the flanges did not have great influence in term of strength. Compared to the

thinnest flanges (T =3.0 mm), the ultimate shear strength increased only about 4%

for web thickness 1.0 mm. For web thickness 2.0 mm, the ultimate shear strength

only increased about 2%. The results in Table 4.8 show that when the slenderness of

the flange element changed from slender to plastic, the influence on ultimate shear

strength was insignificant.

Since the flanges could not contribute in influencing the ultimate shear strength of

the profiled web girder, the use of double web arrangement needed to be considered

in order to improve the ultimate shear strength of the profiled web girder. However,

the use flanges thickness of T = 3.0 mm could lead to a more abrupt reduction in the

post-buckling shear capacity. Figure 4.27 and Table 4.18 show the reduction of post-

buckling shear capacity up to 86% of ultimate shear capacity for model S550T3-Fe

(where the flanges thickness is 3.0 mm).

104

105

Figure 4.26(b): Web Thickness 1.0 mm and Flanges Thickness 6.0 mm

Figure 4.26(a): Web Thickness 1.0 mand Flanges Thickness 3.0 mm

m

m Figure 4.26(c): Web Thickness 1.0 mand Flanges Thickness 9.0 mm

Figure 4.26(d): Web Thickness 1.0 mm and Flanges Thickness 12.0 mm

Figure 4.26(f): Web Thickness 2.0 mm and Flanges Thickness 20.0 mm

Figure 4.26: Buckling Modes Obtained at the End of the Analysis for Model wDifferent Flange Thickness

ith

Figure 4.26(e): Web Thickness 2.0 mm and Flanges Thickness 9.0 mm

106

Shear, V(kN)

020406080

100120140160180200220240260

0 1 2 3 4 5 6 7 8 9 10Deflection (mm)

T = 20 mm

T = 9 mm

Figure 4.28: Load Deflection Curves for Different Flange Thickness, T with Web Thickness 2.0 mm

Shear, V (kN)

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7

De

T = 3 mm T = 6 mm

T = 9 mm T = 12 mm

8 9 10

flection (mm)

Figure 4.27: Load Deflection Curves for Different Flange Thickness, T with Web Thickness 1.0 mm

Model Name

Web

Thickness

(mm)

Flange

Thickness

(mm)

Ultimate

Shear

Capacity,

Vu

(kN)

Post-Buckling

Capacity,

Vb

(kN)

u

b

VV

Comparison of

Ultimate Shear

Capacity for

t =1.0 mm

mm) 3.0 (Tu

u

VV

=

Comparison of

Ultimate Shear

Capacity for

t =2.0 mm

mm) 9.0 (Tu

u

VV

=

S550T3-Fe 1.0 3.0 117.79 17.00 0.14 - -

S550T6-Fe 1.0 6.0 123.07 74.97 0.61 1.04 -

S550-Fe 1.0 9.0 122.29 61.00 0.50 1.04 -

S550T12-Fe 1.0 12.0 122.79 54.25 0.44 1.04 -

S550t2.0-Fe 2.0 9.0 252.24 140.36 0.56 - -

S550t2.0T20-Fe 2.0 20.0 256.04 - - - 1.02

Table 4.8: Results of Non-Linear Analysis for Different Flange Thickness

107

4.6 Discussion Summary

In this finite element study, the effect of large deflection was taken into account

where Total Lagrangian approach has been adopted. The material strain hardening

models assumed elastic- perfectly plastic model that eliminates strain-hardening

parameters. The effects of initial imperfections, i.e. on maximum amplitude or

imperfection shape, on the ultimate shear load capacity are not significant.

The ultimate shear capacities using non-linear finite element analysis had been

validated with experimental results, where the mean ratio of finite element-to-

experimental values was 1.07 and a standard deviation 0.11. Generally all the load

deflection curves showed snap back situation. Using the current stiffness for arc-

length control in LUSAS finite element software was impractical since the curve of

failure had been due to snap-back situation.

Observation from the finite element analysis indicated that the web started to buckle

in one flat part of the fold or in a few folds and then developed large deformation

crossing fold lines and subsequently buckled till the flanges yielded vertically into

the web. The load deflection behaviour changed to what was referred to as a sudden

and steep descending branch after reaching the peak. Subsequent to the initiation of

local ripple(s), irrespective of the buckling modes transformed thereafter, an abrupt

reduction in the post-buckling shear capacity was always observed. Such behaviour

confirmed that the ultimate shear capacity and post-buckling shear capacity did not

depend on the final failure buckling modes. The ultimate shear capacity was depend

on the local buckling of the web. The final failure buckling modes either zonal or

global an abrupt arbitrarily about 30% to 50% of the ultimate shear capacity. Another

finding showed that buckling mode of profiled web girder did not depend on the size

of the web panel.

The analyses of every doubly webbed model were automatically terminated after

reaching peak load due to surface interaction of the two webs and slow rate of

convergence. For doubly webbed models the comparison of the ultimate shear load

with and without connectors did not show great difference, which is only about

108

5.6%. Hence, introducing rivets connectors in the finite element modelling was

insignificant in influencing the ultimate shear capacity of the double web profiled

web girders.

Increasing web depth and thickness influenced the ultimate shear load, where the

ultimate shear capacity was increased. In terms of welding cost, double webs system

had a higher cost than single web, where for double webs both sides needed to be

welded. The available cold form profiled steel sheeting had limited maximum

thickness. This study concluded that double web systems could enhance the ultimate

shear strength as compared to singly webbed arrangement. However, increasing the

flange thickness did not influence the ultimate shear capacity but the use of thinner

flanges would reduce the post-buckling capacity.

109

CHAPTER 5

COMPARISON OF EXPERIMENTAL AND FINITE ELEMENT

RESULTS WITH THEORETICAL FORMULA

5.1 Introduction

In this chapter, the ultimate shear loads from the test results of both experimental and

finite element analysis are compared to establish a design formula. The established

formulas that have been proposed and widely accepted in engineering practice are

applied to estimate the shear capacity of the girders in the previous chapters. These

comparisons are divided into two categories, conventional flat web and profiled web

girder. For profiled web girders, either singly or doubly webbed are compared base

on local and global buckling formula.

5.2 Comparison of Conventional Flat Web Girder with Design Formula

In this section, three designed formulas have been proposed to estimate the shear

capacity of conventional flat web. Theoretical predictions were determined in

accordance with:

a. Cardiff model (Equation 2.1)

This designed formula assumed that all four edges boundary conditions are

simply supported. Cardiff model also that assumed ultimate shear capacity

was contributed by the flanges. This model was adopted in BS 5400: Part 3,

BS 5950: Part 1 and BS 8118: Part 1.

b. Basler model (Equation 2.7)

This model assumed that flanges in practical plate girders did not possess

sufficient flexural rigidity to resist the diagonal tension field and tension field

did not develop near to the web-flange juncture. This model was adopted in

ASSTHO in 1973. Basler assumed that the flanges did not contribute the

ultimate shear capacity.

110

111

c. Modified shear buckling coefficient, k by Lee et al. (Equation 2.9)

These modifications come up from ASSTHO, where Lee et al. assumed that

the conditions of the web panels were not simply supported at all edges. Lee

et al. also assumed that the flanges did not contribute the ultimate shear

capacity.

The comparisons of experimental results of conventional flat web with theoretical

ultimate shear resistance are listed in Table 5.1. In general Cardiff and Basler theory,

the ratio of test results to ultimate shear resistance were closer to the theoretical

values and a standard deviation indicated the spread of results. However, the

modified shear buckling coefficient, k by Lee et al. is more conservative compared to

experimental results, which the ratio varied from 1.21 to 1.58. Basler theory provided

reasonably consistent but conservative for web depth 350 mm, where the mean value

and standard deviation of experimental shear load-to-ultimate shear resistance ratio

were 1.10 and 0.12 respectively. Cardiff theory was the least conservative, where the

ratio were close to 1.00, therefore the contribution of flanges in influencing of

predicted ultimate shear capacity was more accurate. According to Sulyok and

Galambos [71] and Marsh et al. [72], Cardiff model is more suitable for the

reliability level, which has to be achieved with the needed uniformity.

Most of the theory methods that have been proposed for plate girder in shear started

with the elastic buckling load and added a load corresponding to different types of

diagonal tension fields. According to Höglund [66], many of these theories give good

results for girder with small web panel aspect ratio (a/d) but conservative results

when the distance between the transverse stiffeners is large. This is because the

contribution from tension field is small. In BS 5950: Part 1, when web panel aspect

ratio (a/d) was greater than 3.0, the web was designed without using tension filed

action, which meant only based on elastic critical shear stress.

112

Web Flange Yield StressCardiff

Model Basler Model

Modified shear

buckling coefficient, k by Lee et al

Specimen

Name

Ultimate

Shear

Load

VExp

(kN)

t

(mm)

a

(mm)

d

(mm)

T

(mm)

B

(mm)

Web

(N/mm2)

Flange

(N/mm2)VR

U

Exp

VV

VRU

Exp

VV

VRU

Exp

VV

F350-1 50.00 1.03 1.22 1.41

F350-2 42.75 0.88 1.04 1.21

F350-3

56.05

350 48.63

1.15

40.92

1.37

35.47

1.58

F450-1 67.60 1.06 1.12 1.53

F450-2 61.50 0.96 1.02 1.39

F450-3 63.95

450 64.00

1.00

60.23

1.06

44.26

1.44

F550-1 81.50 1.02 1.01 1.53

F550-2 81.65 1.02 1.01 1.54

F550-3

81.85

1.0 522.5

550

9.0 125 304.94 400.03

80.03

1.02

81.00

1.01

53.24

1.46

Mean 1.02 1.10 1.46

Standard Deviation 0.07 0.12 0.12

Table 5.1: Comparison of Experimental Results with Calculated Design Formula for Conventional Flat Web

5.3 Comparison of Profiled Web Girder with Design Formula

As stated earlier, the modes of buckling were local zonal or global buckling of the

web. Local buckling was initial but zonal or global was final failure. There were two

options to calculate shear capacity of profiled web girder, either based on local

buckling or global buckling.

a. Ultimate Shear Resistance of Profiled Web Girder based on Local

Buckling (Equation 2.14).

For calculated shear resistance of profiled web girder based on local

buckling, the corrugated web acted as a series of flat plate sub-panels that

mutually supported each other along their vertical (longer) edges and

were supported by the flanges at their horizontal (shorter) edges. Types of

boundary condition were assumed simply supported for longer edges and

clamped the shorter edges.

b. Ultimate Shear Resistance of Profiled Web Girder base on Global

Buckling (Equation 2.17).

However, calculated shear resistance of profiled web girder based on

global buckling has been determined using the orthotropic plate buckling.

In this comparison the type of boundary condition was considered simply

supported boundaries, where ks equal 31.6.

The comparisons between calculated shear resistances of profiled web girder against

experimental and finite element results are show in Table 5.2 and Table 5.3 based on

local buckling and orthotropic plate buckling respectively. Base on local buckling

stresses were calculated in Table 5.2, the specimens or models was determined base

on yielding of the web except for model S550t0.8-Fe was the local buckling inelastic.

The calculated shear strength base on global buckling in Table 5.3, the strength of

the specimens or models also was determined base on yielding of the web. Only

model S1000-Fe was controlled by inelastic buckling.

113

Shear resistance of profiled web girder singly and doubly webbed were determined

based on yielding of the web because the width of sub-panel of the profiled is too

small that become the stress in the region of flat sub-panel is high. That found the

ultimate shear load-to-ultimate shear resistance of profiled web girder either singly or

doubly webbed in range 0.70 to 1.14 where the mean was 0.93 and standard

deviation was 0.09.

Reported by Elgally et al. [35], local and global buckling stresses were calculated for

the test models with variation corrugation configurations with assuming two

boundaries condition namely clamped and simply supported from the finite element

analysis results. Based on local buckling stresses, for the case of clamped boundaries,

in 12 out of 30, failure resulted from yielding and another 12 model the local

buckling was inelastic. For simply supported boundary condition, only 12 out of 30

models was local buckling inelastic. Comparison with global buckling stresses using

orthotropic plate buckling formula with assuming boundary condition were clamped,

four out of 10 models were determined base on yielding of the web, another four

models were control by inelastic buckling and two by elastic shear buckling.

According to R. Lou and Edlund [39], the ultimate load obtained by the finite

element computation differed very much from those calculated by using Easley

formula (elastic global buckling). A relatively good agreement could only be seen in

four cases of 15 examined girder, of which two cases had a dense corrugation over

the web ((h = 10 mm and b = 35 mm) and the other two cases had a large overall

dimension (D = 1200 mm). The shear capacity given by the elastic buckling theory

(limited by the yield stress) did not differ so much from the ultimate shear capacity

predicted by non-linear finite element analysis, if only the flat sub-panel (simply

supported edges) was consider. R. Lou and Edlund also concluded the ultimate shear

capacity decrease as the flat sub-panel width increase.

However, according to Höglund [66], the reduced strength was more likely due to

local buckling including adjacent flat panels thus initiating the global or zonal

buckling. Höglund [66] also suggested a reduction factor of 0.72 for local buckling

114

strength of corrugated webbed girder. If this reduction factor is used, the results

would be closer to the calculated shear strength value.

It can be concluded that this observation was reasonable with the buckling for all

profiled web girder analyzed in the previous chapter was initiated locally within a

sub-panel which reduced the shear stiffness of the whole web panel, leading to an

abrupt larger reduction of the shear capacity.

115

Table 5.2: Comparison Shear Resistance Based on Local Buckling against

Experimental and Finite Element Results Simply Supported

Specimens / Model Name

Ultimate Load VU

(kN)

Yield Stress in

Shear (N/mm2)

Elastic Shear Stress

(N/mm2)

Inelastic Shear Stress

(N/mm2)

VRR

U

VV

S250-Fe 55.46 230.94 368.80 261.03 57.74 0.96 S350-1 65.75 0.81 S350-2 85.45 1.06 S350-3 71.20 0.88

S350-Fe 78.21

230.94 361.31 258.36 80.83

0.97 D350-1 161.20 1.00 D350-2 168.50 1.04 D350-3 183.65 1.14

D350XC-Fe 156.93

230.94 722.61 516.73 161.66

0.97 S450-1 73.05 0.70 S450-2 88.80 0.85 S450-3 77.90 0.75 S450-4 92.20 0.89

S450-Fe 100.71

230.94 357.28 256.92 103.92

0.97 D450-1 183.05 0.88 D450-2 183.95 0.89 D450-3 186.95 0.90 D450-4 189.3 0.91

D450XC-Fe 201.59

230.94

714.55

513.84

207.85

0.97 S550-1 130.00 1.02 S550-2 119.10 0.94 S550-3 124.50 0.98

S550-Fe 122.29

230.94 354.69 255.99 127.02

0.96 S550t0.8-Fe 92.41 227.00 204.79 95.86 0.96 S550t1.2-Fe 148.13 510.75 307.18 152.42 0.97 S550t2.0-Fe 252.24

230.94 1418.75 511.97 254.03 0.99

S550T3-Fe 117.79 0.93 S550T6-Fe 123.07 0.97 S550T12-Fe 122.79

230.94 354.69 255.99 127.02 0.97

S550t2.0T20-Fe 256.04 230.94 1418.75 511.97 254.03 1.01 D550-1 215.15 0.85 D550-2 205.45 0.81 D550-3 210.30 0.83

D550XC-Fe 217.86 0.86 D550XC-Fe 230.96

230.94 709.38 511.97 254.03

0.91 S750-Fe 164.62 230.94 1406.00 509.67 173.21 0.95

S1000-Fe 215.55 230.94 1396.92 508.02 230.94 0.93 Mean 0.93


116

Table 5.3: Comparison of Shear Resistances Based on Global Buckling against

Experimental and Finite Element Results ks = 31.6

Specimens / Model Name

Ultimate Load VU

(kN)

Yield Stress in

Shear (N/mm2)

Elastic Shear Stress

(N/mm2)

Inelastic Shear Stress

(N/mm2)

VR Vu/VR

S250-Fe 55.46 230.94 4578.68 919.74 57.74 0.96 S350-1 65.75 0.81 S350-2 85.45 1.06 S350-3 71.20 0.88

S350-Fe 78.21

230.94 2336.06 656.96 80.83

0.97 D350-1 161.20 1.00 D350-2 168.50 1.04 D350-3 183.65 1.14

D350XC-Fe 156.93

230.94 4672.12 1313.91 161.66

0.97 S450-1 73.05 0.70 S450-2 88.80 0.85 S450-3 77.90 0.75 S450-4 92.20 0.89

S450-Fe 100.71

230.94 1413.17 510.97 103.92

0.97 D450-1 183.05 0.88 D450-2 183.95 0.89 D450-3 186.95 0.90 D450-4 189.3 0.91

D450XC-Fe 201.59

230.94 2826.34 1021.93 207.85

0.97 S550-1 130.00 1.02 S550-2 119.10 0.94 S550-3 124.50 0.98

S550-Fe 122.29

230.94 946.01 418.06 127.02

0.96 S550t0.8-Fe 92.41 1000.28 429.89 101.61 0.91 S550t1.2-Fe 148.13 903.86 408.64 152.42 0.97 S550t2.0-Fe 252.24

230.94 795.49 383.37 254.03 0.99

S550T3-Fe 117.79 0.93 S550T6-Fe 123.07 0.97 S550T12-Fe 122.79

230.94 946.01 418.06 127.02 0.97

S550t2.0T20-Fe 256.04 230.94 1418.75 511.97 254.03 1.01 D550-1 215.15 0.85 D550-2 205.45 0.81 D550-3 210.30 0.83

D550XC-Fe 217.86 0.86 D550XC-Fe 230.96

230.94 1892.02 836.13 254.03

0.91 S750-Fe 164.62 230.94 508.74 306.58 173.21 0.95

S1000-Fe 215.55 230.94 286.17 229.93 229.93 0.94 Mean 0.93


117

CHAPTER 6

CONCLUSION AND RECOMMENDATIONS

6.1 Conclusion

The shear capacity of girders with corrugated webbed profiled had been studied

using an experimental work program and non-linear numerical simulation. The

report here had indicated the buckling failure of corrugated webbed specimens and

some comparison with non-linear numerical simulation to idealistic behaviour of the

models. From the results found the failure mechanism of corrugated profiled web

were behaving similarity for both experimental and numerical simulation. The

corrugated profiled webbed were buckled initially local buckling after reaching at

peak load and then propagated to other folds. The processed of buckling, the load

was switched to sudden and a steep descending branch.

From the results obtained, the following conclusions could be made of present

investigation:

1. Buckling modes of profiled web girder were categorized in three different

buckling modes i.e. local, zonal or global. Local buckling mode occurs at

the first stage of buckling generally after the load reaching the peak.

Zonal or global buckling mode occurred at failure load terminated (final

failure). From observation, the buckling phenomenon started locally in

flat part of web sub-panel (local buckling) and propagated to another flat

part of web sub-panel which then transformed to zonal or global buckling

mode. Local flange buckling occurred depending on the web buckling

modes. This behaviour occurred because the contribution of stress field in

web was small and restricted only in these corrugation folds.

2. Corrugated webbed girders had higher load carrying capacities when

compared to conventional flat web girders. The ratio of the ultimate shear

load for singly webbed corrugated web and conventional flat web varied

118

from 1.08 to 2.00 and the ratio for singly and doubly webbed corrugated

web varied from 2.51 to 4.30.

3. Three buckling modes had been found in this investigation but after

initially buckled, no matter what kind of buckling modes it had to abrupt

reduction of the post-buckling shear capacity. The buckling could reduce

the post-buckling shear capacity in average about 30% to 50% of the

ultimate shear capacity.

4. Comparison of the shear resistance of profiled web girder based on elastic

local buckling and elastic global buckling was higher than shear yield

stress of either simply supported or fixed boundaries. However, calculated

values based on the elastic local buckling (assuming simply supported

edges) were found more reasonable because buckling was always initiated

locally within a sub-panel which reduced the shear stiffness of the whole

web panel. Therefore, shear resistance of profiled web girder singly and

doubly webbed were determined based on yielding of the web. However,

calculated value based on elastic local buckling stress (assuming simply

supported edges) was more reasonable because the buckling was initiated

locally within a sub-panel which reduced the shear stiffness of the whole

web panel. In this study, the recommended design formula to estimate the

shear capacity of profiled web girder is base on elastic local buckling

stress (Equation 2.14) is more reasonable for routine design of profiled

web girder, but for doubly webbed profiled web girder the shear stress is

twice, 2 lcre ,τ .

119

6.2 Recommendations

Based on the research in this report, it has been found that there are still more studies

need to be carried out in the following areas:

a. The study on the effect of geometric parameters of profiled web. The

geometric parameters are as follows:

• Corrugation depth

• Corrugation angle

• Width of flat part of fold

• Web panel aspect ratio

b. Initial imperfect also affect the influence of profiled web capacity. The

imperfection as due to welding and cold forming of flat sheet.

c. Variable type of loading condition as concentrated patch, fatigue, bending

and lateral torsional buckling.

d. Since the buckling is initially buckled within a sub-panel, the cellular cell

must be filled with core material such as concrete to delay the buckling of

the web to enhance the capacity of the girder.

120

BIBLIOGRAPHY

[1] A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Intermediately stiffened

webbed welded plate girder”, in Proceeding 7th International Conference on

Steel and Space Structures, 2002, pp. 267 – 274.

[2] A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Plate girder under shear load”,

in Proceeding of the 5th Asia-Pacific Structural Engineering Conference, 2003,

pp. 451 – 466.

[3] A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Buckling of singly and doubly-

webbed corrugated web girders under shear loading”, Technical Post

Symposium Universiti Malaya, 2003, pp. 627 – 629.

[4] A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Behaviour of singly and twin-

webbed profiled web girder under shear load”, Proceeding of International

Bridge and Hydraulics Conference, Kuala Lumpur, July, 2004

[5] X. Wang, “Behaviour of steel with trapeziodally corrugated webs and tabular

flanges under static loading”, PhD Thesis, Drexel University, 2003.

[6] Y. A. Khalid, C. L. Chan, B. B. Sahari, and A. M. S. Hamouda, “Bending

behaviour of corrugated web beam”, Journal of Materials Processing

Technology, Vol. 150, pp. 242 – 254, (2004).

[7] Y. A. Khalid, “Bending strength of corrugated web beams”, ASEAN Journal

on Science Technology for Development, Vol. 20, Issue 2, pp 177 – 186,

(2003).

[8] C. L. Chan, Y. A. Khalid, B. B. Sahari, and A. M. S. Hamouda, “Finite element

analysis of corrugated web beams under bending”, Journal of Construction

Steel Research, Vol. 58, pp 1391 – 1406, 2002.

[9] L. Huang, H. Hikosaka, and K. Komine, "Simulation of accordion effect in

corrugated steel web with concrete flanges” Computers and Structures, Vol.

82, pp 2061–2069, 2004

[10] W. Herbert, "Flat sheet metal girder with very thin metal web - Part I - General

theories and assumptions,” National Advisory Committee for Aeronautics,

Technical Memorandum No. 604, 1931

121

[11] W. Herbert, "Flat sheet metal girder with very thin metal web - Part III - Sheet

metal girders with spars resistant to bending - The stress in uprights - diagonal

tension fields”, National Advisory Committee for Aeronautics, Technical

Memorandum. No. 606, 1931

[12] P. Kuhn, “A summary of design formulas for beams having thin webs in

diagonal tension”, National Advisory Committee for Aeronautics, Washington,

Tech. Notes No. 469, August 1933.

[13] P. Kuhn, and J. P. Peterson, "Strength of stiffened beam webs," National

Advisory Committee for Aeronautics, Washington, Tech. Notes No. 1364, July

1947.

[14] P. Kuhn, J. P. Peterson, and L. R Levin, “A summary of diagonal tension, Part

I – Methods of analysis," National Advisory Committee for Aeronautics,

Washington, Tech. Notes, No. 2661, May 1952

[15] P. Kuhn, J. P. Peterson, and L. R Levin, “A summary of diagonal tension, Part

II - Experimental evidence," National Advisory Committee for Aeronautics,

Washington, Tech. Notes, No. 2662, May 1952.

[16] K. Basler, “Strength of Plate Girder in Shear”, Journal of Structural Division,

ASCE, Vol. 87 No. 7, pp 151 – 180, 1961.

[17] K. C. Rockey, H. R. Evan, and D. M. Porter, “A design method for predicting

the collapse behaviour of plate girders”, Proc. Inst. Civil Engrs., Part 2, pp.85 –

112, 1978

[18] K. C. Rockey, G. Valtinat, and K. H. Tang, “The design of transverse stiffeners

on webs loaded in shear – an ultimate load approach”, Proc. Inst. Civil Engrs.,

Part 2, pp.1069 – 1099, 1981

[19] H. R. Evan, and S. Moussef, “Design aid for plate girders’, Proc. Inst. Civil

Engrs.,Part 2, pp. 89 – 104, 1988.

[20] T. M. Roberts, and F. Shahabian, “Ultimate resistance of slender web panel to

combined bending shear and patch loading,” Journal of Construction Steel

Research, Vol. 57, pp 779 – 790, 2001.

[21] F. Shahabian, and T. M. Roberts, “ Combined shear-and-patch loading of plate

girders,” Journal of Structural Engineering, Vol. 126, No. 3, pp. 316-321,

March 2000.

122

[22] A. W. Davies, and T. M. Roberts, “Resistance of welded aluminium alloy plate

girders to shear and patch loading,” Journal of Structural Engineering, Vol.

125, No. 8, pp. 930-938, August 1998.

[23] R. Narayanan, “Plate Structure: Stability and strength”, Applied Science,

University Collage Cardiff, pp. 1 – 37, 1984.

[24] H. G. Allen, and P. S. Bulson, “Background to buckling”, McGraw Hill. 1980

[25] S. C. Lee, and C. H. Yoo, “Experimental study on ultimate shear strength of

web panels”, Journal of Structural Engineering, Vol. 125 No. 8, pp 838 – 846,

August 1999.

[26] S. C. Lee, and C. H. Yoo, “Strength plate girder web Panels under pure shear”,

Journal of Structural Engineering, Vol. 124 No. 2, pp 184 – 194, 1998

[27] C. H. Yoo, and D. Y. Yoon, “Behavior of intermediate transverse stiffeners

attached on web panels”, Journal of Structural Engineering, Vol. 128 No. 3, pp

337 – 345, March 2002.

[28] S. C. Lee, J. S. Davidson, and C. H. Yoo, “Shear buckling coefficients of plate

girder web panels”, Computer and Structure, Vol. 59. No. 5, pp. 789-795,

1996.

[29] S. C. Lee, C. H. Yoo, and D. Y. Yoon, “New design for intermediate transverse

stiffeners attached on web panels,” Journal of Structural Engineering, Vol. 129

No. 12, pp 1607 – 1613, 2003.

[30] P. Seide, "The stability under longitudinal compression of flat symmetric

corrugated-core sandwich plates with simply supported loaded edges and

simply supported or clamped unloaded edges" National Advisory Committee

for Aeronautics, Washington, Tech. Note 2679, April 1952

[31] A. F. Fraser, "Experimental investigation of strength of multiweb beams with

corrugated webs", National Advisory Committee for Aeronautics, Washington,

Tech. Notes No. 3801, October 1956

[32] O. M. Hanim, (Private Communication), Universiti Teknologi Malaysia, 2003

[33] U. Fathoni, “Shear buckling of trapezoidal web plate,” Master Thesis, Faculty

of Civil Engineering, University Technology of Malaysia, 2001.

123

[34] M. S. Nina Imelda, “The effect of opening on the strength of corrugated web

plate girder subjected to shear,” Master Thesis, Faculty of Civil Engineering,

University Technology of Malaysia, 2002.

[35] M. Elgaaly, R. W. Himilton, and A. Seshadri, “Shear strength of beam with

corrugated webs”, Journal of Structural Engineering, Vol. 122 No. 4, pp. 390 –

398, 1996.

[36] M. Elgaaly, A. Seshadri, and R. W. Himilton, “Bending strength of steel beam

with corrugated webs”, Journal of Structural Engineering, Vol. 123 No. 6, pp

772 – 782, 1997

[37] M. Elgaaly, and A. Seshadri, “Depicting the behaviour of girders with

corrugated webs up to failure using non-linear finite element analysis”,

Advances in Engineering Software, Vol. 29. No. 3 -6, pp. 195 – 208, 1998

[38] M. Elgaaly, and A. Seshadri, “Girder with corrugated webs under partial

compressive edge loading”, Journal of Structural Engineering, Vol. 123 No. 6,

pp 783 – 791, 1997.

[39] R. Lou and B. Edlund, “Shear capacity of plate girders with trapezoidal

corrugated webs”, Thin-Walled Structures. Vol. 26, No. 1, pp 19 – 44, 1996.

[40] R. Lou and B. Edlund, “Ultimate strength of girder with trapeziodally

corrugated webs under patch loading”, Thin-Walled Structures. Vol. 24, pp 135

– 156, 1996.

[41] K.Anami, R. Sause, and H. H. Abbas, "Fatigue of web-flange weld of

corrugated web girders: 1. Influence of web corrugation geometry and flange

geometry on web-flange weld toe stresses,” International Journal of Fatigue

Vol. 27, 373–381, 2005

[42] K. Anami, and R. Sause, "Fatigue of web-flange weld of corrugated web

girders: 2. Analytical evaluation of fatigue strength of corrugated web-flange

weld,” International Journal of Fatigue , Vol. 27, pp. 383–393, 2005.

[43] H. R. Evan, and A. R. Mokhtari, “Plate girder with unstiffened or profiled web

plates”, Journal of Singapore Structural Steel Society, Vol. 3 No.1, pp. 15 –22,

1992.

[44] R. P. Johnson, and J. Cafolla, “Corrugated webs in plate girders plate girder for

bridge”, Proc. Inst. Civil Engrs., Struc & Bldgs, Vol. 123, pp. 157– 164, 1997

124

[45] K. M. Anwar Hossain, and H. D. Wright, “Experimental and theoretical

behaviour of composite walling under in-plane shear”, Journal of

Constructional Steel Research, Vol. 60, pp 59 – 83, 2004

[46] Zeman & Co Gesellschaft mbH, "Corrugated Web Beam. Technical

Documentation," http://www.zeman-steel.com/downloads/wellsteg-e.pdf

[47] Azmi Ibrahim, “Behaviour of unstiffened and bolt-stiffened RHS beam under

combined bending moment and concentrated force” PhD Thesis, University of

Sussex, England, 1994

[48] LUSAS, Modeller user manual, Version 13, FEA Ltd, Surrey, United

Kingdom.

[49] LUSAS, Theory manual 1 and 2, Version 13, FEA Ltd, Surrey, United

Kingdom.

[50] J. R. Brauer, “What every engineer should know about finite element”, New

York: Marcel Dekker, 1988

[51] P. Granath, and O. Lagerqvist, “Behaviour of girder webs subjected to patch

loading”, Journal of Constructional Steel Research, Vol. 50, pp. 49–69, 1999.

[52] B.W. Schafer, and T. Peköz, “Computational modelling of cold-formed steel:

Characterizing geometric imperfections and residual stresses”, Journal of

Constructional Steel Research, Vol. 47, pp. 193–210, 1998.

[53] K. Baskar, N. E. Shanmugam, and V. Thevendran, “Finite element analysis of

steel–concrete composite plate girder”, Journal of Structural Engineering, Vol.

128, No. 9, September, 2002

[54] N. E. Shanmugam, and K. Baskar, “Steel-concrete composite plate girders

subjected to shear loading,” Journal of Structural Engineering, Vol. 129, No. 9,

September, 2003.

[55] M. Xie and J.C. Chapman, “Design of web stiffeners: Local panel bending

effects,” Journal of Constructional Steel Research, Vol. 60, pp. 1425–1452,

2004

[56] M. Xie and J.C. Chapman, “Design of web stiffeners: axial forces,” Journal of

Constructional Steel Research, Vol. 59, pp.1035–1056, 2003.

125

[57] C.A. Graciano and B. Edlund, “Nonlinear FE analysis of longitudinally

stiffened girder webs under patch loading”, Journal of Construction Steel

Research, Vol 58, pp 1231 – 1245, 2002

[58] J. H. Maquoi Rene, “Influence of geometric imperfections on the carrying

capacity of compression flanges of plate girders”, Journal of Singapore

Structural Steel Society, Vol. 3 No.1, pp. 61 –70, Dec 1992.

[59] BS 5950: Part 1: Code of practice for design in simple and continuous

construction hot rolled section. British Standard Institution, London, 2000.

[60] BS 5400: Part 3: Code of practice for design of steel bridges, British Standard

Institution, London, 1982.

[61] P.S. Bulson, “The treatment of thin-walled aluminium sections in eurocode 9’.

Thin-Walled Structures. Vol. 29, Nos. 1-4, pp 3 – 12, 1997.

[62] L. H. Teh and G. J. Hancock, "Strength of fillet welded connections in G450

sheet steels," Centre for Advanced Structural Engineering, University of

Sydney, Australia, Research Report No. R802, July 2000.

[63] N. Cooke, P. J. Moss, W. R. Walpole, D. Wayne, and M. H. Harvey, “Strength

and Serviceability of Steel Girder Webs”, Journal of Structural Engineering,

Vol. 109 No. 3, pp 785 – 807, 1983.

[64] B. Samsudin, “ Imperfection in welded steel plates”, PhD Thesis, University of

Birmingham, 1996

[65] International Standard ISO 6892. Metallic materials – Tensile Testing, 1984

[66] T. Höglund, “Shear buckling resistance of steel and aluminium plate girders”,

Thin-Walled Structures. Vol. 29, No. 1-4, pp 13 – 30, 1997

[67] AWS D1.1, Americal Welding Society –Steel. 1996

[68] BS EN 287: Part 1: Approval Testing of Welders for Fusion Welding, British

Standard Institution, 1992.

[69] R. P. Johnson, and J. Cafolla, “Local flange buckling in plate girders with

corrugated webs”, Proc. Inst. Civil Engrs., Struc & Bldgs, Vol. 123, pp. 148 –

156, 1997.

[70] LUSAS, Verification manual, Version 13.4, FEA Ltd, Surrey, United

Kingdom.

126

[71] M. Sulyok, and T. V. Galambos, "Evaluation of web buckling test results on

welded beam and plate girders subjected to shear," Engineering Structure, Vol.

18, No. 6, pp. 459-464, 1996.

[72] C. Marsh, W. Ajam, and H. K. Ha, “Finite Element Analysis of Postbuckled

Shear Webs”, Journal of Structural Engineering, Vol. 114 No. 7, pp 1571 –

1587, 1998

127

APPENDICES

Appendix A

THE RESULTS OF WELDING PROCEDURE SPECIFICATION

Figure A1: Welding Procedure Specifications

128

Figure A2: Visual and Dye Penetrate Test Report

129

Figure A3: Bending / Fracture and Nick Break Test Report

130

Figure A4: Microstructure Report

131

Appendix B

BUCKLING OF GIRDERS AFTER TESTING

Figure B1(a): Buckling of F350-1 after Testing

Figure B1(b): Buckling of F350-2 after Testing

Figure B1(c): Buckling of F350-3 after Testing

Figure B1: Buckling of Conventional Flat Web after Testing (Web Depth 350 mm)

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133





134

Figure B4(b): Buckling of S350-2 after Testing

Figure B4(a): Buckling of S350-1 after Testing

Figure B4(c): Buckling of S350-3 after Testing

Figure B4: Buckling of Singly Webbed Profiled Web after Testing (Web Depth 350 mm)

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136





137

Figure B7(b): Buckling of D350-2 after Testing

Figure B7(a): Buckling of D350-1 after Testing

Figure B7(c): Buckling of D350-3 after Testing

Figure B7: Buckling of Doubly Webbed Profiled Webs after Testing (Web Depth 350 mm)

138






139





140

LIST OF PUBLICATIONS

1. A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Intermediately stiffened webbed

welded plate girder”, in Proceeding 7th International Conference on Steel and

Space Structures, 2002, pp. 267 – 274.

2. A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Plate girder under shear load”, in

Proceeding of the 5th Asia-Pacific Structural Engineering Conference, 2003, pp.

451 – 466.

3. A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Buckling of singly and doubly-

webbed corrugated web girders under shear loading”, Technical Post Symposium

Universiti Malaya, 2003, pp. 627 – 629.

4. A. H. Hanizah, I. Azmi, and A. H. Md. Hadli, “Behaviour of singly and twin-

webbed profiled web girder under shear load”, Proceeding of International

Bridge and Hydraulics Conference, Kuala Lumpur, July, 2004

5. A. H. Md. Hadli, A. H. Hanizah, and I. Azmi, “Comparative Performance of

Welded Girders of Flat and Profiled Web in Shear”, Proceeding of the

International Seminar on Civil and Infrastructure Engineering, Shah Alam, June

2006

6. A. H. Md. Hadli, A. H. Hanizah, and I. Azmi, “Non-linear Shear Behaviour of

Welded Girder with Profiled Web using LUSAS”, Proceeding of the 10th East

Asia-Pacific Conference on Structural Engineering and Construction, Bangkok,

August 2006

141

Documents

The Study on the Behaviour of Plate Girder With Profiled Web