Elementary Mechanics of Solids

The Commonwealth and International Library: Structure and Solid Body Mechanics

1st Edition - January 1, 1965

Author: P. P. Benham

Editor: B. G. Neal

eBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 8 5 5 6 - 9

Elementary Mechanics of Solids presents the three fundamental principles, namely, equilibrium of forces, stress-strain relationship, and geometry and compatibility of… Read more

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Elementary Mechanics of Solids presents the three fundamental principles, namely, equilibrium of forces, stress-strain relationship, and geometry and compatibility of deformations. This book discusses the concept of simplifying assumptions about behavior to obtain the simpler engineering solutions. Organized into seven chapters, this book begins with an overview of the theory of elasticity. This text then presents a detailed discussion of biaxial stress and strain systems as well as the generalized stress-strain relationships. Other chapters consider the determination of deflections of straight and curved beams due to shearing and bending action. This book discusses as well the elastic torsion of various thin-walled closed and open sections as well as the shaft of solid circular cross section. The final chapter discusses some cases in which the combined effects of torsion and bending occur. This book is a valuable resource for students who wish to obtain a university degree in engineering, diploma of technology, or higher national certificate.

Preface

1. Concepts of Force and Stress

1.1 Introduction

1.2 Statically Determinate Problems

1.3 Force and Moment

1.4 Equilibrium

1.5 Stress

1.6 Statically Determinate Stress Systems

1.7 Principle of Superposition: Forces and Stresses in a Statically Determinate System

Examples

2. Concepts of Deformation and Strain

2.1 Introduction

2.2 Deformation

2.3 Strain

2.4 Elastic Load-Deformation Behaviour of Materials

2.5 Elastic Stress-Strain Behaviour of Materials

2.6 Plastic Stress-Strain Behaviour of Materials

2.7 Solution of Some Statically Indeterminate Problems

2.8 General Stress-Strain Relationships

2.9 Material Under Constraint

2.10 Strains in a Statically Determinate Problem

2.11 Volume Changes

Examples

3. Analysis of Stress and Strain

3.1 Introduction

3.2 Plane Stress

3.3 Stress Components on Any Plane in Terms of Coordinate Stresses

3.4 Mohr's Circle for Stress

3.5 Strain Components in Any Direction

3.6 Mohr's Circle for Strain

3.7 Strain Rosettes

3.8 Relationships Between the Elastic Constants

3.9 Further Stress-Strain Relationships

3.10 Strain Energy

3.11 Maximum Stress Due to Suddenly Applied Load

3.12 Maximum Stress Due to Impact

3.13 Strain Energy in Three-Dimensional Stress System

3.14 Shear Strain Energy Owing to Distortion or Shear

3.15 Criteria for Yielding Under Complex Stress

3.16 Failure of Brittle Materials

Examples

4. Theory of Bending

4.1 Introduction

4.2 Forms of Loading and Support

4.3 Shear Force and Bending Moment

4.4 Load, Shear and Moment Equilibrium Relationships

4.5 Stresses and Deformation in Pure Bending

4.6 Transverse Deformation of a Beam Cross Section

4.7 Stresses in Symmetrical Beams Under General Loading Conditions

4.8 Bending and Shear Stresses in I-Section Beams

4.9 Unsymmetrical Pure Bending

4.10 Shear Stress in Thin-Walled Open Sections; Shear Centre

4.11 Principal Stresses and Yield Criteria in Bending

4.12 Combined Bending and Direct Stress

4.13 Composite Beams

4.14 Curved Bars

Examples

5. Deflections Due to Bending

5.1 Introduction

5.2 Curvature, Slope and Deflection Relationships

5.3 Discontinuous Loading: Macaulay's Method

5.4 Deflections by Geometry of Deformation

5.5 Deflection of Beams Due to Shear Force

5.6 Strain Energy Solution for Beam Deflection

5.7 Application of Castigliano's Theorem (Part II) to Beams

5.8 Deflection of Slender Curved Bars

5.9 Deflection in a Statically Indeterminate Problem: A Slender Ring

Examples

6. Elementary Theory of Torsion

6.1 Introduction

6.2 Pure Torsion of a Thin-Walled Circular Tube

6.3 Pure Torsion of a Solid Circular Shaft

6.4 Hollow Circular Shafts

6.5 Combined Torsion and Axial Loading of a Shaft

6.6 Strain Energy in Simple Shear and in Torsion

6.7 Thin-Walled Closed Tubes of Non-Circular Cross Section

6.8 Torsion of a Thin Rectangular Strip

6.9 The Effect of Warping on Torsion of Open Sections

6.10 Torsion of an I-Beam with Warping Restrained

Examples

7. Problems in Bending and Torsion

7.1 Introduction

7.2 Combined Bending and Torsion of a Circular Shaft

7.3 Bending and Torsion of a Member Curved in Plan

7.4 Helical Springs

7.5 Close Coiled Springs Subjected to Axial Force

7.6 Close Coiled Spring Subjected to Axial Couple

7.7 Open Coiled Helical Spring

7.8 Approximate Theory for Leaf Springs

Examples

Appendix: Sign Conventions in Bending Theory

Answers to Examples

Index