Torsion of Thin Walled Structures

Preface
Contents
About the Author
1 Torsion of Thin-Walled Structures
	1.1 Introduction
	1.2 Picture of Sectional Stresses
	1.3 Decoupling of Bending and Warping
	1.4 Historical Overview
	1.5 Review Problems
	1.6 Answers to Review Problems
	Reference
2 St. Venant Torsion
	2.1 Introduction
	2.2 Thin Rectangular Section
	2.3 Single Cell Thin-Walled Section
	2.4 Multicellular Section
	2.5 Stress Concentration
	2.6 Box with Lattice Walls
	2.7 Composite Cross Section
	2.8 Bounds for Torsion Constant
	2.9 Torsion of Multicellular Section Connected by a Base Cell
	2.10 Review Problems
	2.11 Answers to Review Problems
	References
3 Warping Properties of Thin-Walled Sections
	3.1 Introduction
	3.2 Sectorial Area
	3.3 Integrals Involving Sectorial Area
	3.4 Principal Sectorial Area
	3.5 Transformations of Unit Warping
	3.6 Decoupling Equations
	3.7 Contour Warping of Multicell Sections
	3.8 Thickness Warping
	3.9 Sectorial Shear Function
	3.10 Illustrative Examples
	References
4 Theories of Torsion
	4.1 Introduction
	4.2 Basic Assumptions
	4.3 Equilibrium Equations
	4.4 Stress–Strain Relationships
	4.5 Compatibility Equations
		4.5.1 Warping Displacements: Open Profiles
		4.5.2 Warping Displacements: Closed Profiles
	4.6 Stress–Displacement Expressions
	4.7 Differential Equations of Equilibrium
	4.8 Decoupling
	4.9 Benscoter’s Theory
	4.10 The Wagner Effect
	4.11 Review Questions
	4.12 Answers to Review Questions
	Reference
5 Analysis of Thin-Walled Structures
	5.1 Introduction
	5.2 St. Venant Torsion
	5.3 VLASOV (Warping) Torsion
	5.4 Mixed Torsion
	5.5 Warping Restraints
		5.5.1 Other Warping Restraints
	5.6 Review Problems
	5.7 Answers to Review Problems
	Reference
6 Finite Element Analysis of Thin-Walled Structures
	6.1 Introduction
	6.2 Stiffness Matrix
	6.3 Structural Analysis
	6.4 Expression for Stiffness Matrix
	6.5 St. Venant Torsion Element
	6.6 Applications of St. Venant Torsion Element
	6.7 Vlasov Torsion Element
	6.8 Mixed Torsion Finite Element
	6.9 Finite Element Method for Warping Properties of Thin-Walled Sections
	6.10 Review Problems
	6.11 Answers to Review Problems
	Reference
7 Stability Analysis of Thin-Walled Structures in Torsion
	7.1 Introduction
	7.2 Flexural–Torsional Buckling
		7.2.1 Stiffeners for Torsional Buckling
	7.3 Lateral Buckling of Thin-Walled Beams
	7.4 Buckling Under Torsional Loadings
	7.5 Finite Element Analysis of Buckling Problems
	References
8 Plastic Torsion of Thin-Walled Structures
	8.1 Introduction
	8.2 Ultimate Torque of a Thin Rectangle
	8.3 Ultimate St. Venant Torque of Closed Sections
	8.4 Upper-Bound Solution
	8.5 Mixed Torsion
	References
Appendix Analysis for Transverse Shear
Introduction
Review Questions
Answers to Review Questions
Index