This comprehensive textbook focuses on the torsion in thin walled structures, highlights the nuances of the problems faced and succinctly discusses warping, bimoment, etc. Since in several thin walled structures, torsion is the only or dominant loading, this book addresses such unique structures as well. It provides a concise explanation of the warping properties and how they are evaluated. Thin walled structures with torsion as the preponderant loading are then treated using classical and finite element methods. No prior knowledge of the finite element method is required as the method is introduced from the basics. The same problem is worked out by both approaches so that the concepts are clearly understood by the readers. The book includes pedagogical features such as end-of-chapter questions and worked out examples to augment learning and self-testing. The book will be useful for graduate courses as well as for professional development coursework for structural engineers in the aerospace, mechanical, and civil engineering domains.
Author(s): Krishnaiyengar Rajagopalan
Publisher: Springer
Year: 2022
Language: English
Pages: 235
City: Singapore
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
