# Mechanics of Materials

## 2nd Edition

### An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Components

**Authors:**E. J. Hearn

**eBook ISBN:**9781483105543

**Imprint:**Butterworth-Heinemann

**Published Date:**1st January 1985

**Page Count:**542

## Description

Mechanics of Materials, Second Edition, Volume 2 presents discussions and worked examples of the behavior of solid bodies under load. The book covers the components and their respective mechanical behavior. The coverage of the text includes components such cylinders, struts, and diaphragms. The book covers the methods for analyzing experimental stress; torsion of non-circular and thin-walled sections; and strains beyond the elastic limit. Fatigue, creep, and fracture are also discussed. The text will be of great use to undergraduate and practitioners of various engineering braches, such as materials engineering and structural engineering.

## Table of Contents

Contents of Volume 1

Introduction

Notation

16 Unsymmetrical Bending

Summary

Introduction

16.1 Product Second Moment of Area

16.2 Principal Second Moments of Area

16.3 Mohr's Circle of Second Moments of Area

16.4 Land's Circle of Second Moments of Area

16.5 Rotation of Axes: Determination of Moments of Area in Terms of the Principal Values

16.6 The Ellipse of Second Moments of Area

16.7 Momental Ellipse

16.8 Stress Determination

16.9 Alternative Procedure for Stress Determination

16.10 Alternative Procedure Using the Momental Ellipse

16.11 Deflections

Examples

Problems

17 Struts

Summary

Introduction

17.1 Euler's Theory

17.2 Equivalent Strut Length

17.3 Comparison of Euler Theory with Experimental Results

17.4 Euler "Validity Limit"

17.5 Rankine or Rankine—Gordon Formula

17.6 Perry—Robertson Formula

17.7 British Standard Procedure (BS 449)

17.8 Struts with Initial Curvature

17.9 Struts with Eccentric Load

17.10 Laterally Loaded Struts

17.11 Alternative Procedure for Any Strut-Loading Condition

17.12 Struts with Unsymmetrical Cross-Sections

Examples

Problems

18 Strains Beyond the Elastic Limit

Summary

Introduction

18.1 Plastic Bending of Rectangular-Sectioned Beams

18.2 Shape Factor — Symmetrical Section

18.3 Application to I-Section Beams

18.4 Partially Plastic Bending of Unsymmetrical Sections

18.5 Shape Factor — Unsymmetrical Section

18.6 Deflection of Partially Plastic Beams

18.7 Length of Yielded Area in Beams

18.8 Collapse Loads — Plastic Limit Design

18.9 Residual Stresses after Yielding: Elastic Perfectly Plastic Material

18.10 Torsion of Shafts beyond the Elastic Limit — Plastic Torsion

18.11 Angles of Twist of Shafts Strained beyond the Elastic Limit

18.12 Plastic Torsion of Hollow Tubes

18.13 Plastic Torsion of Case-Hardened Shafts

18.14 Residual Stresses after Yield in Torsion

18.15 Plastic Bending and Torsion of Strain-Hardening Materials

(a) Inelastic Bending

(b) Inelastic Torsion

18.16 Residual Stresses — Strain-Hardening Materials

18.17 Influence of Residual Stresses on Bending and Torsional Strengths

18.18 Plastic Yielding in the Eccentric Loading of Rectangular Section

18.19 Plastic Yielding and Residual Stresses under Axial Loading with Stress Concentrations

18.20 Plastic Yielding of Axially Symmetric Components

(a) Thick Cylinders — Collapse Pressure

(b) Thick Cylinders— "Auto Frettage"

(c) Rotating Discs

Examples

Problems

19 Rings, Discs and Cylinders Subjected to Rotation and Thermal Gradients

Summary

19.1 Thin Rotating Ring or Cylinder

19.2 Rotating Solid Disc

19.3 Rotating Disc with a Central Hole

19.4 Rotating Thick Cylinders or Solid Shafts

19.5 Rotating Disc of Uniform Strength

19.6 Combined Rotational and Thermal Stresses in Uniform Discs and Thick Cylinders

Examples

Problems

20 Torsion of Non-Circular and Thin-Walled Sections

Summary

20.1 Rectangular Sections

20.2 Narrow Rectangular Sections

20.3 Thin-Walled Open Sections

20.4 Thin-Walled Split Tube

20.5 Other Solid (non-Tubular) Shafts

20.6 Thin-Walled Closed Tubes of non-Circular Section (Bredt—Batho Theory)

20.7 Use of "Equivalent J" for Torsion of non-Circular Sections

20.8 Thin-Walled Cellular Sections

20.9 Torsion of Thin-Walled Stiffened Sections

20.10 Membrane Analogy

20.11 Effect of Warping of Open Sections

Examples

Problems

21 Experimental Stress Analysis

Introduction

21.1 Brittle Lacquers

21.2 Strain Gauges

21.3 Unbalanced Bridge Circuit

21.4 Null Balance or Balanced Bridge Circuit

21.5 Gauge Construction

21.6 Gauge Selection

21.7 Temperature Compensation

21.8 Installation Procedure

21.9 Basic Measurement Systems

21.10 D.C. and A.C. Systems

21.11 Other Types of Strain Gauge

21.12 Photo-elasticity

21.13 Plane Polarized Light — Basic Polariscope Arrangements

21.14 Temporary Birefringence

21.15 Production of Fringe Patterns

21.16 Interpretation of Fringe Patterns

21.17 Calibration

21.18 Fractional Fringe Order Determination — Compensation Techniques

21.19 Isoclinics — Circular Polarization

21.20 Stress Separation Procedures

21.21 Three-Dimensional Photo-elasticity

21.22 Reflective Coating Technique

21.23 Other Methods of Strain Measurement

Bibliography

22 Circular Plates and Diaphragms

Summary

A. Circular Plates

22.1 Stresses

22.2 Bending Moments

22.3 General Equation for Slope and Deflection

22.4 General Case of a Circular Plate or Diaphragm Subjected to Combined Uniformly Distributed Load q (Pressure) and Central Concentrated Load F

22.5 Uniformly Loaded Circular Plate with Edges Clamped

22.6 Uniformly Loaded Circular Plate with Edges Freely Supported

22.7 Circular Plate with Central Concentrated Load F and Edges Clamped

22.8 Circular Plate with Central Concentrated Load F and Edges Freely Supported

22.9 Circular Plate Subjected to a Load F Distributed Round a Circle

22.10 Application to the Loading of Annular Rings

22.11 Summary of End Conditions

22.12 Stress Distributions in Circular Plates and Diaphragms Subjected to Lateral Pressures

22.13 Discussion of Results — Limitations of Theory

22.14 Other Loading Cases of Practical Importance

B. Bending of Rectangular Plates

22.15 Rectangular Plates with Simply Supported Edges Carrying Uniformly Distributed Loads

22.16 Rectangular Plates with Clamped Edges Carrying Uniformly Distributed Loads

Examples

Problems

23 Introduction to Advanced Elasticity Theory

23.1 Types of Stress

23.2 The Cartesian Stress Components: Notation and Sign Convention

23.2.1 Sign Conventions

23.3 The State of Stress at a Point

23.4 Direct, Shear and Resultant Stresses on an Oblique Plane

23.4.1 Line of Action of Resultant Stress

23.4.2 Line of Action of Normal Stress

23.4.3 Line of Action of Shear Stress

23.4.4 Shear Stress in Any other Direction on the Plane

23.5 Principal Stresses and Strains in Three-Dimensions — Mohr's Circle Representation

23.6 Graphical Determination of Direction of Shear Stress Tn on an Inclined Plane

23.7 The Combined Mohr Diagram for Three-Dimensional Stress and Strain Systems

23.8 Application of the Combined Circle to Two-Dimensional Stress Systems

23.9 Graphical Construction for the State of Stress at a Point

23.10 Construction for the State of Strain on a General Strain Plane

23.11 State of Stress — Tensor Notation

23.12 The Stress Equations of Equilibrium

23.13 Principal Stresses in a Three-Dimensional Cartesian Stress System

23.13.1 Solution of Cubic Equations

23.14 Stress Invariants — Eigen Values and Eigen Vectors

23.15 Stress Invariants

23.16 Reduced Stresses

23.17 Strain Invariants

23.18 Alternative Procedure for Determination of Principal Stresses

23.18.1 Evaluation of Direction Cosines for Principal Stresses

23.19 Octahedral Planes and Stresses

23.20 Deviatoric Stresses

23.21 Deviatoric Strains

23.22 Plane Stress and Plane Strain

23.22.1 Plane Stress

23.22.2 Plane Strain

23.23 The Stress Strain Relations

23.24 The Strain—Displacement Relationships

23.25 The Strain Equations of Transformation

23.26 Compatibility

23.27 The Stress Function Concept

23.27.1 Forms of Airy Stress Function in Cartesian Coordinates

23.27.2 Case 1 - Bending of a Simply Supported Beam by a Uniformly Distributed Loading

23.27.3 The Use of Polar Coordinates in Two Dimensions

23.27.4 Forms of Stress Function in Polar Coordinates

23.27.5 Case 2 - Axi-Symmetric Case: Solid Shaft and Thick Cylinder Radially Loaded with Uniform Pressure

23.27.6 Case 3 - The Pure Bending of a Rectangular Section Curved Beam

23.27.7 Case 4 - Asymmetric Case n = 1. Shear Loading of a Circular Arc Cantilever Beam

23.27.8 Case 5 - The Asymmetric Cases n ≥ 2 — Stress Concentration at a Circular Hole in a Tension Field

23.27.9 Other Useful Solutions of the Biharmonic Equation

Examples

Problems

24 Miscellaneous Topics

24.1 Bending of Beams with Initial Curvature

24.2 Bending of Wide Beams

24.3 General Expression for Stresses in Thin-Walled Shells Subjected to Pressure or Self-Weight

24.4 Bending Stresses at Discontinuities in Thin Shells

24.5 Viscoelasticity

24.6 Introduction to the Finite Element Method

24.6.1 Applicability of the Finite Element Method (F.E.M.)

24.6.2 Boundary Value Problems

24.6.3 Formulation of the F.E.M.

24.6.4 The Displacement Method

24.6.5 The F.E.M. Applied to a Continuum

24.6.6 General Procedure of the F.E.M.

References

Examples

Problems

25 Contact Stress; Residual Stress and Stress Concentrations

Summary

25.1 Contact Stresses

Introduction

25.1.1 General Case of Contact between Two Curved Surfaces

25.1.2 Special Case 1 - Contact of Parallel Cylinders

25.1.3 Combined Normal and Tangential Loading

25.1.4 Special Case 2 - Contacting Spheres

25.1.5 Design Considerations

25.1.6 Contact Loading of Gear Teeth

25.1.7 Contact Stresses in Spur and Helical Gearing

25.1.8 Bearing Failures

25.2 Residual Stresses

Introduction

25.2.1 Reasons for Residual Stresses

25.2.2 The Influence of Residual Stress on Failure

25.2.3 Measurement of Residual Stresses

25.2.4 Summary of the Principal Effects of Residual Stress

25.3 Stress Concentrations

Introduction

25.3.1 Evaluation of Stress Concentration Factors

25.3.2 St. Versant's Principle

25.3.3 Theoretical Considerations of Stress Concentrations due to Concentrated Loads

25.3.4 Fatigue Stress Concentration Factor

25.3.5 Notch Sensitivity

25.3.6 Strain Concentration — Neuber's Rule

25.3.7 Designing to Reduce Stress Concentration

25.3.8 Use of Stress Concentration Factors with Yield Criteria

25.3.9 Design Procedure

References

Examples

Problems

26 Fatigue, Creep and Fracture

Summary

26.1 Fatigue

Introduction

26.1.1 The S/N Curve

26.1.2 P/S/N Curves

26.1.3 Effect of Mean Stress

26.1.4 Effect of Stress Concentration

26.1.5 Cumulative Damage

26.1.6 Cyclic Stress-Strain

26.1.7 Combating Fatigue

26.1.8 Slip Bands and Fatigue

26.2 Creep

Introduction

26.2.1 The Creep Test

26.2.2 Presentation of Creep Data

26.2.3 The Stress—Rupture Test

26.2.4 Parameter Methods

26.2.5 Stress Relaxation

26.2.6 Creep-Resistant Alloys

26.3 Fracture Mechanics

Introduction

26.3.1 Energy Variation in Cracked Bodies

26.3.2 Linear Elastic Fracture Mechanics (L.E.F.M.)

26.3.3 Elastic Plastic Fracture Mechanics (E.P.F.M.)

26.3.4 Fracture Toughness

26.3.5 Plane Strain and Plane Stress Fracture Modes

26.3.6 General Yielding Fracture Mechanics

26.3.7 Fatigue Crack Growth

26.3.8 Crack Tip Plasticity under Fatigue Loading

26.3.9 Measurement of Fatigue Crack Growth

References

Examples

Problems

Appendix 1. Typical Mechanical and Physical Properties for Engineering Materials

Appendix 2. Typical Mechanical Properties of Non-Metals

Appendix 3. Other Properties of Non-Metals

Index

Other Titles in the Series

## Details

- No. of pages:
- 542

- Language:
- English

- Copyright:
- © Butterworth-Heinemann 1985

- Published:
- 1st January 1985

- Imprint:
- Butterworth-Heinemann

- eBook ISBN:
- 9781483105543