# Strength of Materials

## 1st Edition

### An Introduction to the Analysis of Stress and Strain

**Authors:**John Case A. H. Chilver

**eBook ISBN:**9781483221724

**Imprint:**Arnold

**Published Date:**1st January 1959

**Page Count:**402

## Description

Strength of Materials: An Introduction to the Analysis of Stress and Strain is 22-chapter introductory text to the problems of stress and strain analysis. The first chapters explore the fundamental and basic topics on stress and strain, including tension, compression, pin-jointed frames, joints, and connections. The next chapters consider the application of combined simple direct and shearing stresses in practical situations. Other chapters treat topics on plastic, elastic, and strain, as well as problems of thin-walled tubes in bending and torsion. This text also explores the analytical uses of the principle of virtual work, strain energy, and complementary energy. The last chapters review problems of vibrations and dynamic and impact stresses.

This book is directed toward undergraduate engineering students.

## Table of Contents

Chapter 1. Tension and Compression; Direct Stresses

1.1 Introduction

1.2 Stretching of a Steel Wire

1.3 Tensile and Compressive Stresses

1.4 Tensile and Compressive Strains

1.5 Stress-Strain Curves for Brittle Materials

1.6 Ductile Materials

1.7 Proof Stresses

1.8 Working Stresses

1.9 Load Factors

1.10 Lateral Strains Due to Direct Stresses

1.11 Strength Properties of Some Engineering Materials

1.12 Weight-Economy of Materials

1.13 Strain Energy and Work Done in the Tensile Test

1.14 Initial Stresses

1.15 Composite Bars in Tension or Compression

1.16 Temperature Stresses

1.17 Temperature Stresses in Composite Bars

1.18 Circular Ring under Radial Pressure

1.19 Creep of Materials under Sustained Stresses

1.20 Fatigue under Repeated Stresses

Chapter 2. Pin-Jointed Frames

2.1 Introduction

2.2 Statically-Determinate Pin-Jointed Frames

2.3 Displacements of Statically-Determinate Frames

2.4 Frames with Non-Linear Members

2.5 Statically-Indeterminate Problems

Chapter 3. Shearing Stresses

3.1 Introduction

3.2 Measurement of Shearing Stress

3.3 Complementary Shearing Stress

3.4 Shearing Strain

3.5 Strain Energy Due to Shearing Actions

Chapter 4. Joints and Connections

4.1 Riveted Joints

4.2 Modes of Failure of Simple Riveted Joints

4.3 Efficiency of a Connection

4.4 Bolted Joints

4.5 Group-Riveted Joints

4.6 Eccentric Loading of Bolted and Riveted Connections

4.7 Welded Connections

Chapter 5. Analysis of Stress and Strain

5.1 Introduction

5.2 Shearing Stresses in a Tensile Test-Specimen

5.3 Strain Figures in Mild-Steel; Lüder's Lines

5.4 Failure of Materials in Compression

5.5 General Two-Dimensional Stress System

5.6 Stresses on an Inclined Plane

5.7 Values of the Principal Stresses

5.8 Maximum Shearing Stress

5.9 Mohr's Circle of Stress

5.10 Strains in an Inclined Direction

5.11 Mohr's Circle of Strain

5.12 Elastic Stress-Strain Relations

5.13 Principal Stresses and Strains

5.14 Relation between E, G, and v

5.15 Strain 'Rosettes'

5.16 Strain Energy for a Two-Dimensional Stress System

5.17 Three-Dimensional Stress Systems

5.18 Volumetric Strain in a Material under Hydrostatic Pressure

5.19 Strain Energy of Distortion

5.20 Yielding of Ductile Materials under Combined Stresses

5.21 Elastic Breakdown and Failure of Brittle Materials

Chapter 6. Thin Shells under Internal Pressure

6.1 Thin Cylindrical Shell of Circular Cross-Section

6.2 Thin Spherical Shell

6.3 Cylindrical Shell with Hemispherical Ends

Chapter 7. Bending Moments and Shearing Forces

7.1 Introduction

7.2 Concentrated and Distributed Loads

7.3 Relation between the Intensity of Loading, the Shearing Force, and Bending Moment in a Straight Beam

7.4 Sign Conventions for Bending Moments and Shearing Forces

7.5 Cantilevers

7.6 Cantilever with Non-Uniformly Distributed Load

7.7 Simply-Supported Beams

7.8 Simply-Supported Beam Carrying a Uniformly-Distributed Load and End Couples

7.9 Points of Inflection

7.10 Simply-Supported Beam with a Uniformly-Distributed Load over Part of the Span

7.11 Simply-Supported Beam with Non-Uniformly Distributed Load

7.12 a Graphical Method of Drawing Bending Moment Diagrams

7.13 Plane Curved Beams

7.14 More General Case of Bending of a Curved Bar

Chapter 8. Bending Moments and Shearing Forces Due to Slowly Moving Loads

8.1 Introduction

8.2 A Single Concentrated Load Traversing a Beam

8.3 Uniformly-Distributed Load of Sufficient Length to Cover the Whole Span

8.4 Two Concentrated Loads Traversing a Beam

8.5 Several Concentrated Loads

8.6 Influence Lines of Bending Moment and Shearing Force

Chapter 9. Longitudinal Stresses in Beams

9.1 Introduction

9.2 Pure Bending of a Rectangular Beam

9.3 Bending of a Beam about a Principal Axis

9.4 Beams Having Two Axes of Symmetry in the Cross-Section

9.5 Beams Having Only One Axis of Symmetry

9.6 More General Case of Pure Bending

9.7 Elastic Section Modulus

9.8 Longitudinal Stresses Where Shearing Forces are Present

9.9 Calculation of the Principal Second Moments of Area

9.10 Compound Beams

9.11 Elastic Strain Energy of Bending

9.12 Change of Cross-Section in Pure Bending

Chapter 10. Shearing Stresses in Beams

10.1 Introduction

10.2 Shearing Stresses in a Beam of Narrow Rectangular Cross-Section

10.3 Beam of Any Cross-Section Having One Axis of Symmetry

10.4 Shearing Stresses in an I-Beam

10.5 Shearing Stresses in Compound Beams

10.6 Principal Stresses in Beams

10.7 Superimposed Beams

10.8 Shearing Stresses in a Channel Section; Shear Center

Chapter 11. Beams of Two Materials

11.1 Introduction

11.2 Transformed Sections

11.3 Timber Beam with Reinforcing Steel Flange Plates

11.4 Ordinary Reinforced Concrete

Chapter 12. Bending Stresses and Direct Stresses Combined

12.1 Introduction

12.2 Combined Bending and Thrust of a Stocky Strut

12.3 Eccentric Thrust

12.4 Pre-Stressed Concrete Beams

Chapter 13. Deflections of Beams

13.1 Introduction

13.2 Elastic Bending of Straight Beams

13.3 Simply-Supported Beam Carrying a Uniformly-Distributed Load

13.4 Cantilever with a Concentrated Load

13.5 Cantilever with Uniformly-Distributed Load

13.6 Propped Cantilever with Distributed Load

13.7 Simply-Supported Beam Carrying a Concentrated Lateral Load

13.8 Use of Step-Functions

13.9 Simply-Supported Beam with Distributed Load over a Portion of the Span

13.10 Simply-Supported Beam with a Couple Applied at an Intermediate Point

13.11 Beam with End Couples and Distributed Load

13.12 Beams with Non-Uniformly Distributed Load

13.13 Cantilever with Irregular Loading

13.14 Beams of Varying Section

13.15 Non-Uniformly Distributed Load and Terminal Couples; the Method of 'Moment-Areas'

13.16 Use of Fourier Series

13.17 The Funicular Analogue of Beam Deflections

13.18 Deflections of Beams Due to Shear

Chapter 14. Built-in and Continuous Beams

14.1 Introduction

14.2 Built-in Beam with a Single Concentrated Load

14.3 Fixed-End Moments for Other Loading Conditions

14.4 Disadvantages of Built-in Beams

14.5 Effect of Sinking of Supports

14.6 Continuous Beams

14.7 Slope-Deflection Equations for a Single Beam

14.8 The Three-Moment Equation

Chapter 15. Plastic Bending of Mild-Steel Beams

15.1 Introduction

15.2 Beam of Rectangular Cross-Section

15.3 Elastic-Plastic Bending of a Mild-Steel Beam

15.4 Fully-Plastic Moment of an I-Section; Shape Factor

15.5 More General Case of Plastic Bending

15.6 Comparison of Elastic and Plastic Section Moduli

15.7 Regions of Plasticity in a Simply-Supported Beam

15.8 Plastic Collapse of a Built-in Beam

Chapter 16. Torsion of Circular Shafts and Thin-Walled Tubes

16.1 Introduction

16.2 Torsion of a Thin Circular Tube

16.3 Torsion of Solid Circular Shafts

16.4 Torsion of a Hollow Circular Shaft

16.5 Principal Stresses in a Twisted Shaft

16.6 Torsion Combined with Thrust or Tension

16.7 Strain Energy of Elastic Torsion

16.8 Plastic Torsion of a Circular Shaft

16.9 Torsion of Thin Tubes of Non-Circular Cross-Section

16.10 Torsion of a Flat Rectangular Strip

16.11 Torsion of Thin-Walled Open Sections

Chapter 17. The Principle of Virtual Work and Its Applications 289

17.1 Introduction

17.2 The Principle of Virtual Work.

17.3 The Displacements of a Pin-Jointed Frame

17.4 Statically-Indeterminate Pin-Jointed Frames

17.5 Temperature Stresses in Redundant Frames

17.6 Deflections of Beams

17.7 Statically-Indeterminate Beam Problems

17.8 Plastic Bending of Mild-Steel Beams

17.9 Reciprocal Characteristics of Linear-Elastic Systems

Chapter 18. Strain Energy and Complementary Energy

18.1 Properties of the Strain Energy Function

18.2 Complementary Energy

18.3 Statically-Determinate Frame Carrying Two Equal and Opposite External Forces

18.4 Solution of Statically-Indeterminate Frames Using Complementary Energy

18.5 Initial Lack of Fit of Members of the Frame

18.6 Complementary Energy in Problems of Bending

Chapter 19. Springs

19.1 General Properties of Springs

19.2 Coiled Springs

19.3 Geometry of Helical Springs

19.4 Close-Coiled Helical Spring: Axial Pull

19.5 Close-Coiled Helical Spring: Axial Couple

19.6 Open-Coiled Helical Spring: Axial Force

19.7 Open-Coiled Helical Spring: Axial Couple

19.8 Plane Spiral Springs

19.9 Close-Coiled Conical Spiral Spring

19.10 Approximate Theory of Leaf Springs

Chapter 20. Elastic Buckling of Columns and Beams

20.1 Introduction

20.2 Flexural Buckling of a Pin-Ended Strut

20.3 Pin-Ended Strut with Eccentric End Thrusts

20.4 Initially-Curved Pin-Ended Strut

20.5 Design of Pin-Ended Struts

20.6 Strut with Uniformly-Distributed Lateral Loading

20.7 Buckling of a Strut with Built-in Ends

20.8 Buckling of a Strut with One End Fixed, and the Other End Free

20.9 Buckling of a Strut with One End Pinned, and The Other End Fixed

20.10 Flexural Buckling of Struts with Other Cross-Sectional Forms

20.11 Torsional Buckling of a Cruciform Strut

20.12 Modes of Buckling of a Cruciform Strut

20.13 Lateral Buckling of a Narrow Beam

Chapter 21. Vibrations of Beams

21.1 Introduction

21.2 Free Vibrations of a Mass on a Weightless Beam

21.3 Free Vibrations of a Beam with Distributed Weight

21.4 Forced Vibrations of a Beam Carrying a Single Weight

21.5 Damped Free Oscillations of a Beam

21.6 Damped Forced Oscillations of a Beam

21.7 Vibrations of a Beam with End Thrust

Chapter 22. Impact Stresses in Rods

22.1 Introduction

22.2 Velocity of Propagation of Stress in a Straight Rod

22.3 Constant Stress Applied at One End of the Rod

22.4 Reflection of the Stress Wave at the Ends of a Rod

22.5 Longitudinal Impact of Rods

22.6 Rod Struck by a Moving Mass

Answers to Problems

Index

## Details

- No. of pages:
- 402

- Language:
- English

- Copyright:
- © Arnold 1959

- Published:
- 1st January 1959

- Imprint:
- Arnold

- eBook ISBN:
- 9781483221724