Mechanics of Materials SI Version

Chapter 1 Stress

1.1 Introduction

1.2 Normal Stress Under Axial Loading

1.3 Direct Shear Stress

1.4 Bearing Stress

1.5 Stresses on Inclined Sections

1.6 Equality of Shear Stresses on Perpendicular Planes



Chapter 2 Strain

2.1 Displacement, Deformation and the Concept of Strain

2.2 Normal Strain

2.3 Shear Strain

2.4 Thermal Strain



Chapter 3 Mechanical Properties of Materials

3.1 The Tension Test

3.2 The Stress--Strain Diagram

3.3 Hooke's Law

3.4 Poisson's Ratio



Chapter 4 Design Concepts

4.1 Introduction

4.2 Types of Loads

4.3 Safety

4.4 Allowable Stress Design

4.5 Load and Resistance Factor Design



Chapter 5 Axial Deformation

5.1 Introduction

5.2 Saint-Venant's Principle

5.3 Deformations in Axially Loaded Bars

5.4 Deformations in a System of Axially Loaded Bars

5.5 Statically Indeterminate Axially Loaded Members

5.6 Thermal Effects on Axial Deformation

5.7 Stress Concentrations



Chapter 6 Torsion

6.1 Introduction

6.2 Torsional Shear Strain

6.3 Torsional Shear Stress

6.4 Stresses on Oblique Planes

6.5 Torsional Deformations

6.6 Torsion Sign Conventions

6.7 Gears in Torsion Assemblies

6.8 Power Transmission

6.9 Statically Indeterminate Torsion Members

6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings

6.11 Torsion of Noncircular Sections

6.12 Torsion of Thin-Walled Tubes: Shear Flow



Chapter 7 Equilibrium of Beams

7.1 Introduction

7.2 Shear and Moment in Beams

7.3 Graphical Method for Constructing Shear and Moment Diagrams

7.4 Discontinuity Functions to Represent Load, Shear and Moment



Chapter 8 Bending

8.1 Introduction

8.2 Flexural Strains

8.3 Normal Stresses in Beams

8.4 Analysis of Bending Stresses in Beams

8.5 Introductory Beam Design for Strength

8.6 Flexural Stresses in Beams of Two Materials

8.7 Bending Due to Eccentric Axial Load

8.8 Unsymmetric Bending

8.9 Stress Concentrations Under Flexural Loadings



Chapter 9 Shear Stress in Beams

9.1 Introduction

9.2 Resultant Forces Produced by Bending Stresses

9.3 The Shear Stress Formula

9.4 The First Moment of Area Q

9.5 Shear Stresses in Beams of Rectangular Cross Section

9.6 Shear Stresses in Beams of Circular Cross Section

9.7 Shear Stresses in Webs of Flanged Beams

9.8 Shear Flow in Built-Up Members

9.9 Shear Stress and Shear Flow in Thin-Walled Members

9.10 Shear Centers of Thin-Walled Open Sections



Chapter 10 Beam Deflections

10.1 Introduction

10.2 Moment-Curvature Relationship

10.3 The Differential Equation of the Elastic Curve

10.4 Deflections by Integration of a Moment Equation

10.5 Deflections by Integration of Shear-Force or Load Equations

10.6 Deflections Using Discontinuity Functions

10.7 Method of Superposition



Chapter 11 Statically Indeterminate Beams

11.1 Introduction

11.2 Types of Statically Indeterminate Beams

11.3 The Integration Method

11.4 Use of Discontinuity Functions for Statically Indeterminate Beams

11.5 The Superposition Method



Chapter 12 Stress Transformations

12.1 Introduction

12.2 Stress at a General Point in an Arbitrarily Loaded Body

12.3 Equilibrium of the Stress Element

12.4 Plane Stress

12.5 Generating the Stress Element

12.6 Equilibrium Method for Plane Stress Transformations

12.7 General Equations of Plane Stress Transformation

12.8 Principal Stresses and Maximum Shear Stress

12.9 Presentation of Stress Transformation Results

12.10 Mohr's Circle for Plane Stress

12.11 General State of Stress at a Point



Chapter 13 Strain Transformations

13.1 Introduction

13.2 Plane Strain

13.3 Transformation Equations for Plane Strain

13.4 Principal Strains and Maximum Shearing Strain

13.5 Presentation of Strain Transformation Results

13.6 Mohr's Circle for Plane Strain

13.7 Strain Measurement and Strain Rosettes

13.8 Generalized Hooke's Law for Isotropic Materials



Chapter 14 Thin-Walled Pressure Vessels

14.1 Introduction

14.2 Spherical Pressure Vessels

14.3 Cylindrical Pressure Vessels

14.4 Strains in Pressure Vessels



Chapter 15 Combined Loads

15.1 Introduction

15.2 Combined Axial and Torsional Loads

15.3 Principal Stresses in a Flexural Member

15.4 General Combined Loadings

15.5 Theories of Failure



Chapter 16 Columns

16.1 Introduction

16.2 Buckling of Pin-Ended Columns

16.3 The Effect of End Conditions on Column Buckling

16.4 The Secant Formula

16.5 Empirical Column Formulas--Centric Loading

16.6 Eccentrically Loaded Columns



Chapter 17 Energy Methods

17.1 Introduction

17.2 Work and Strain Energy

17.3 Elastic Strain Energy for Axial Deformation

17.4 Elastic Strain Energy for Torsional Deformation

17.5 Elastic Strain Energy for Flexural Deformation

17.6 Impact Loading

17.7 Work-Energy Method for Single Loads

17.8 Method of Virtual Work

17.9 Deflections of Trusses by the Virtual-Work Method

17.10 Deflections of Beams by the Virtual-Work Method

17.11 Castigliano's Second Theorem

17.12 Calculating Deflections of Trusses by Castigliano's Theorem

17.13 Calculating Deflections of Beams by Castigliano's Theorem



Appendix A Geometric Properties of an Area

A.1 Centroid of an Area

A.2 Moment of Inertia for an Area

A.3 Product of Inertia for an Area

A.4 Principal Moments of Inertia

A.5 Mohr's Circle for Principal Moments of Inertia

Appendix B Geometric Properties of Structural Steel Shapes

Appendix C Table of Beam Slopes and Deflections

Appendix D Average Properties of Selected Materials

Answers to Odd Numbered Problems

Index