WARPING BEHAVIOUR OF CANTILEVER STEEL BEAM WITH OPENINGS TAN YU CHAI A thesis submitted in fulfillment of the requirements for the award of the degree of Master of Engineering (Civil-Structure) Faculty of Civil Engineering Universiti Teknologi Malaysia OCTOBER, 2005
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WARPING BEHAVIOUR OF
CANTILEVER STEEL BEAM WITH OPENINGS
TAN YU CHAI
A thesis submitted in fulfillment
of the requirements for the award of the degree
of Master of Engineering (Civil-Structure)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
OCTOBER, 2005
2
“I declare that this thesis entitled WARPING BEHAVIOUR OF CANTILEVER
STEEL BEAM WITH OPENINGS is the results of my own research except as
cited in references. This thesis has not been accepted for any degree and is not
concurrently submitted in candidature of any degree.”
Signature : …………………
Name of Candidate : Tan Yu Chai
Date : 30 October 2005
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“The journey of a thousand miles begins with a single step.
A Man without dream is nothing at all.
Dare to dream!! ”
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ACKNOWLEDGEMENTS
First of all, the author wishes to express the deepest gratitude to his
supervisors Professor Ir. Dr. Abdul Karim Mirasa and Associate Professor Ir. Dr.
Mohd. Hanim Osman, for their insight and greatest guidance during this project.
Without their noble approach, this study will never finish so smoothly.
Acknowledgement is extended to Mr. Koh Heng Boon for his great advice
which helped author to complete his study especially in understanding LUSAS
software. The author is thankful to Puan Fatimah Denan for her encouragement and
help. Acknowledgements are also due to Mr. Moumouni Moussa Idrissou, Mr.
Felix Ling Ngee Leh, Mr. Tan Che Siang and Mr. Sia Chee keong for their advice
and helpful cooperation during this research. Besides, appreciation is
acknowledged for those who ever direct or indirectly involved in the completion of
this project.
The author will never forget the internal supports from his family members
especially the countless blessing from his parents which have always been the source
of motivation in achieving success to a higher level. Last but no least, the author
wishes to acknowledge the most important people in his life, Ms. Loke Chai Yee for
her endless support and motivation.
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ABSTRACT
This project presents a short study on warping behaviour of cantilever steel
beam with openings subjected to coupled torsional force at the free end. Thus far
there has not been any research regarding the relationship between warping and
web’s openings. Finite element software, LUSAS 13.6, was used to perform
analysis on seven groups of modelling. The analysis of the results showed that
opening has a close relationship with warping since opening can reduce web stiffness.
When warping resistance decrease, warping displacements and warping normal
stress will increase. Opening with bigger size, installed at the free end and central
of the web will induce greater warping and vice versa. Simple approximation of
installing stiffeners is proposed in this study to provide section’s warping resistance
effectively.
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ABSTRAK
Projek sarjana ini mengkaji kelakuan ledingan (warping) pada rasuk julur
keluli berlubang yang mana hujung bebasnya dipiuhkan terhadap paksi membujurnya.
Hingga kini, tiada sebarang kajian mengenai hubungan antara kelakuan ledingan
dengan lubang pada web rasuk. Perisian LUSAS 13.6 digunakan untuk mengkaji 7
kumpulan model di dalamprojek ini. Keputusan yang diperolehi menunjukkan
lubang boleh mempengaruhi kelakuan ledingan rasuk dengan mengurangkan
kekukuhan web rasuk. Anjakan dan tegasan paksi akan meningkat berikutan
dengan pengurangan kekukuhan ledingan. Lubang berbentuk lebih besar yang
dipasang pada hujung bebas dan tengah web akan membentuk piuhan yang lebih
ketara dan sebaliknya. Fahaman ringkas terhadap pemasangan pengukuh turut
dikaji bagi meningkatkan keupayaan ledingan rasuk dengan berkesan.
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TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENT vii
LIST OF TABLE x
LIST OF FIGURES xi
NOTATION xiii
LIST OF APPENDIX xv
I INTRODUCTION 1
1.1 Introduction 1
1.2 Background of Study 3
1.3 Problem Statement 5
1.4 Objectives of Study 5
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1.5 Scope of Study 6
1.6 Research Significance 6
II REVIEW OF LITERATURE STUDIES 8
2.1 Introduction 8
2.2 Review of Published Work 10
2.3 Basic Theory 11
2.3.1 Torsion 11
2.3.2 Significance of Warping Constant 16
2.4 Conclusion 19
III LINEAR FINITE ELEMENT ANALYSIS 22
3.1 Introduction 22
3.2 Modeling 23
3.2.1 Model Geometry 25
3.2.2 Types of Elements 26
3.2.3 Meshing 26
3.2.4 Material Properties 27
3.2.5 Support Conditions 28
3.2.6 Loads Arrangement 28
3.3 Convergence 28
3.4 Model Validation 29
3.5 Conclusion 31
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IV RESULTS AND DISCUSSIONS 37
4.1 Introduction 37
4.2 Stress Concentration Zone 38
4.3 Stress Distribution 38
4.4 Stress Across Flange Width 39
4.5 Discussion for every group of models 39
4.5.1 Various Horizontal Location of Opening 40
4.5.2 Various Vertical Location of Opening 40
4.5.3 Various Sizes of Opening 41
4.5.4 Various Numbers of Openings 41
4.5.5 Comparison between Circular and Square
Openings 41
4.5.6 Various Spacing between Two Openings 42
4.5.7 Comparison between Two Types of Stiffener 42
4.6 Summary 43
V CONCLUSION AND SUGGESTION 54
5.1 Conclusion 54
5.2 Suggestion 55
REFERENCES 56
BIBLIOGRAPHY 58
APPENDIX A 59
APPENDIX B 64
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LIST OF TABLES
NO. OF TABLE TITLE PAGE
3.1 Results obtained from various numbers of elements 29
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LIST OF FIGURES
FIGURE NO. TITLE PAGE
1.1 Torsional shear flow in a solid bar by Englekirk 7