Strength of Materials and Structures

Strength of Materials and Structures

An Introduction to the Mechanics of Solids and Structures

2nd Edition - January 1, 1971

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  • Authors: John Case, A. H. Chilver
  • eBook ISBN: 9781483183275

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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


Product details

  • No. of pages: 416
  • Language: English
  • Copyright: © Arnold 2013
  • Published: January 1, 1971
  • Imprint: Arnold
  • eBook ISBN: 9781483183275

About the Authors

John Case

A. H. Chilver

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