THE BEHAVIOUR OF PROFILED STEEL SHEET/CONCRETE COMPOSITE SLABS
The Study on the Behaviour of Plate Girder With Profiled Web
Transcript of 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.
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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.
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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
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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
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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
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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
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Table 5.3 Comparison of Shear Resistances Based on Global Buckling
against Experimental and Finite Element Results 117
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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
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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 4.10 Load Deflection Curves for S450 Series 87
Figure 4.11 Load Deflection Curves for S550 Series 87
Figure 4.12 Load Deflection Curves for D350 Series 88
Figure 4.13 Load Deflection Curves for D450 Series 88
Figure 4.14 Load Deflection Curves for D550 Series 89
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
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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
Figure 4.25 Buckling Modes Obtained at the End of the Analysis for
Model with Different Web Thickness 102
Figure 4.26 Buckling Modes Obtained at the End of the Analysis for
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
Figure B2 Buckling of Conventional Flat Web after Testing (Web Depth
450 mm) 133
Figure B3 Buckling of Conventional Flat Web after Testing (Web Depth
550 mm) 134
Figure B4 Buckling of Singly Webbed Profiled Web after Testing (Web
Depth 350 mm) 135
Figure B5 Buckling of Singly Webbed Profiled Web after Testing (Web
Depth 450 mm) 136
Figure B6 Buckling of Singly Webbed Profiled Web after Testing (Web
Depth 550 mm) 137
Figure B7 Buckling of Doubly Webbed Profiled Webs after Testing (Web
Depth 350 mm) 138
Figure B8 Buckling of Doubly Webbed Profiled Webs after Testing (Web
Depth 450 mm) 139
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Figure B9 Buckling of Doubly Webbed Profiled Webs after Testing (Web
Depth 550 mm) 140
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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
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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
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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
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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.
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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.
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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.
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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.
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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
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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
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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
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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.
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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)
Figure 4.10: Load Deflection Curves for S450 Series
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
Figure 4.11: Load Deflection Curves for S550 Series
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
Figure 4.13: Load Deflection Curves for D450 Series
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 4.14: Load Deflection Curves for D550 Series
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
Standard Deviation 0.09
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
Standard Deviation 0.09
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
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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)
132
Figure B2(c): Buckling of F450-3 after Testing
Figure B2(b): Buckling of F450-2 after Testing
Figure B2(a): Buckling of F450-1 after Testing
Figure B2: Buckling of Conventional Flat Web after Testing (Web Depth 450 mm)
133
Figure B3(b): Buckling of F550-2 after Testing
Figure B3(a): Buckling of F550-1 after Testing
Figure B3(c): Buckling of F550-3 after Testing
Figure B3: Buckling of Conventional Flat Web after Testing (Web Depth 550 mm)
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)
135
Figure B5(b): Buckling of S450-2 after Testing
Figure B5(a): Buckling of S450-1 after Testing
Figure B5(c): Buckling of S450-3 after Testing
Figure B5(b): Buckling of S450-2 after Testing
Figure B5: Buckling of Singly Webbed Profiled Web after Testing (Web Depth 450 mm)
136
Figure B6(b): Buckling of S550-2 after Testing
Figure B6(a): Buckling of S550-1 after Testing
Figure B6(c): Buckling of S550-3 after Testing
Figure B6: Buckling of Singly Webbed Profiled Web after Testing (Web Depth 550 mm)
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
Figure B8(b): Buckling of D450-2 after Testing
Figure B8(a): Buckling of D450-1 after Testing
Figure B8(c): Buckling of D450-3 after Testing
Figure B8(b): Buckling of D450-2 after Testing
Figure B8: Buckling of Doubly Webbed Profiled Webs after Testing (Web Depth 450 mm)
139
Figure B9(b): Buckling of D550-2 after Testing
Figure B9(a): Buckling of D550-1 after Testing
Figure B9(c): Buckling of D550-3 after Testing
Figure B9: Buckling of Doubly Webbed Profiled Webs after Testing (Web Depth 550 mm)
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