# Strength of Materials and Structures

## 2nd Edition

### An Introduction to the Mechanics of Solids and Structures

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

**eBook ISBN:**9781483183275

**Imprint:**Arnold

**Published Date:**1st January 1971

**Page Count:**416

## Description

Strength of Materials and Structures: An Introduction to the Mechanics of Solids and Structures provides an introduction to the application of basic ideas in solid and structural mechanics to engineering problems.

This book begins with a simple discussion of stresses and strains in materials, structural components, and forms they take in tension, compression, and shear. The general properties of stress and strain and its application to a wide range of problems are also described, including shells, beams, and shafts. This text likewise considers an introduction to the important principle of virtual work and its two special forms—leading to strain energy and complementary energy. The last chapters are devoted to buckling, vibrations, and impact stresses.

This publication is a good reference for engineering undergraduates who are in their first or second years.

## Table of Contents

Preface

Principal Notation

Note on SI Units

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 and Stiffness 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

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

3 Shearing Stresses

3.1 Introduction

3.2 Measurement of Shearing Stress

3.3 Complementary Shearing Stresses

3.4 Shearing Strain

3.5 Strain Energy Due to Shearing Actions

4 Joints and Connections

4.1 Importance of Connections

4.2 Modes of Failure of Simple and Riveted Joints

4.3 Efficiency of a Connection

4.4 Group-Bolted and -Riveted Joints

4.5 Eccentric Loading of Bolted and Riveted Connections

4.6 Welded Connections

4.7 Welded Connections Under Bending Actions

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

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

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

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

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 while 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

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 Centre

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

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

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

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

15 Plastic Bending of Mild-Steel Beams

15.1 Introduction

15.2 Beam of Rectangular Cross-Section

15.3 Elastic-Plastic Bending of a Rectangular 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

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

17 The Principle of Virtual Work and Its Applications

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

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

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

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

21 Vibrations of Beams

21.1 Introduction

21.2 Free Vibrations of a Mass on a Beam

21.3 Free Vibrations of a Beam with Distributed Mass

21.4 Forced Vibrations of a Beam Carrying a Single Mass

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

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:
- 416

- Language:
- English

- Copyright:
- © Arnold 1971

- Published:
- 1st January 1971

- Imprint:
- Arnold

- eBook ISBN:
- 9781483183275