Torsional Analysis of Box Culvert Using Vlasov's Theory

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ABSTRACT

The traditional method, De Saint-Venant theory which was used in the previous analysis of thin-walled structures assumed free warping of all thin-walled structures, which is very rare in engineering. In this research work, Vlasov’s torsion theory which incorporates restraint warping was employed in the analysis of box culvert. The incorporation of restraint warping by Vlasov made the equation for computing angle of twist extremely rigorous as compared to Saint Venant’s equation. For appropriate use of Vlasov’s theory by engineers, Vlasov’s differential equation was derived and solved in this work for three cases viz: cantilevered, simply supported and fixed-ended box culverts. Computer program was also developed to facilitate the use of Vlasov’s theory in the torsional analysis of box culverts. The three cases of thin-walled box culvert were analysed using both De Saint-Venant’s theory and Vlasov’s theory. The results obtained from Vlasov’s theory showed that the deformation of the box culvert due to angle of twist is smaller than that found with De Saint-Venant’s theory. Hence, restrained warping substantially reduces the structural deformation of box culvert due to angle of twist, but, however introduces large axial stresses at the restrained sections. In conclusion, this work has proven the adequacy of the use of Vlasov’s theory for torsional analysis and design of thin- walled box culvert for both economy and safety.

CHAPTER ONE:

1.1 Background of Study .. ..
1.2 Statement of the Problem..
1.3 Objectives of the Study.. ..
1.4 Justification of the Study..
1.5 Scope of the Work.. ..

CHAPTER TWO: LITERATURE REVIEW

TABLE OF CONTENTS

2.1 Thin-Walled Structures.. .. ..
2.2 Theories of Thin-Walled Structures..
2.3 Theories of Torsion.. .. ..

2.3.1 De Saint-Venant Torsion Theory..
2.3.2 Vlasov Torsion Theory.. .. ..
2.3.3 Limitations of Vlasov’s Torsion Theory..
2.3.4 Generalized Warping Torsion Formulation..

2.4 Review of Past Works on Thin-Walled Structure..
2.5 Historical Background of Culvert.. .. .. ..

CHAPTER THREE: TORSIONAL ANALYSIS OF STEEL MEMBERS

3.1 Preamble.. .. .. ..
3.2 Torsion.. .. .. ..

3.2.1 Torsional Stresses.. ..

3.3 Significance of Warping Constant..
3.4 Vlasov’s Torsion Theory.. ..
3.5 Vlasov’s Differential Equation....

3.5.1 Derivation of Warping Torsion Moment.. ..
3.5.2 Vlasov’s Torsional Resistance.. .. .. ..
3.5.3 Solutions of Vlasov’s Differential Equation....

3.5.3.1 Case 1: Solution of Vlasov’s Differential Equation for A Cantilever Girder/Box Culvert.. .. .. .. ..

3.5.3.2 Case 2: Solution of Vlasov’s Differential Equation for

A Fixed-Ended Girder/Box Culvert.... .. ..

3.5.3.3 Case 3: Solutions of Vlasov’s Differential Equation ASimplySupportedGirder/BoxCulvert.. .. ..

3.6 General Vlasov Stresses.... .. .. .. ..

CHAPTER FOUR: DESIGN EXAMPLE

4.1 Procedure For Torsional Analysis of Box Culvert ..

4.2 Manual Analysis.. .. .. ..

4.2.1 Numerical Examples.. .. ..
4.2.2 Comparative Analysis of Results..

4.2.3 Comparison of Vlasov And Venant Results.. 4.3 Computer Analysis.. .. .. ..

4.3.1 Algorithm of the Computer Program. ..
4.3.2 Flow Chart.. .. .. .. .. ..
4.3.3 Computer Program.. .. .. ..

4.3.4 Executed Computer Program .. ..
4.3.5 Numerical Comparison of Vlasov And De Saint-Venant Results.. 134
4.3.6 NumericalComparisonofComputerandManualResultofVlasov and De Saint-Venant.. .. .. .. .. .. .. .. 135

CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS

5.1 Conclusion .. .. .. .. .. .. .. .. .. 136
5.2 Recommendations .. .. .. .. .. .. .. .. 137

REFERENCES

APPENDIX

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Torsional Analysis of Box Culvert Using Vlasov's Theory

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