Advanced Strength and Applied Elasticity

Fourth Edition

Ansel C. Ugural
New Jersey Institute of Technology

Saul K. Fenster
New Jersey Institute of Technology

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Prentice Hall
Professional Technical Reference
Upper Saddle River, New Jersey 07458
www.ptr.com

Library of Congress Cataloging-in-Publication Data
Ugural, A.C.
    Advanced strength and applied elasticity/Ansel C. Ugural, Saul K.
Fenster.—4th ed.
          p. cm.
Includes bibliographical references and index.
    ISBN 0-13-047392-8
  1. Strength of materials. 2. Elasticity. I. Fenster, Saul K. II. Title.
    TA405.U42 2003
    620.1′123-dc21

                                                                                          2002153330

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10 9 8 7 6 5 4 3 2
ISBN 0-13-047392-8
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11th Printing             February 2008
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Contents

Preface to the Fourth Edition

List of Symbols

Chapter 1  Analysis of Stress

1.1     Introduction

1.2     Scope of Treatment

1.3     Definition of Stress

1.4     Components of Stress: Stress Tensor

1.5     Some Special Cases of Stress

1.6     Internal Force-Resultant and Stress Relations

1.7     Stresses on Inclined Planes in an Axially Loaded Member

1.8     Variation of Stress within a Body

1.9     Two-Dimensional Stress at a Point

1.10   Principal Stresses and Maximum Shear Stress in Two Dimensions

1.11   Mohr’s Circle for Two-Dimensional Stress

1.12   Three-Dimensional Stress at a Point

1.13   Principal Stresses in Three Dimensions

1.14   Normal and Shear Stresses on an Oblique Plane

1.15   Mohr’s Circle for Three-Dimensional Stress

1.16   Boundary Conditions in Terms of Surface Forces

Problems

Chapter 2  Strain and Stress–Strain Relations

2.1     Introduction

2.2     Deformation

2.3     Strain Defined

2.4     Equations of Compatibility

2.5     State of Strain at a Point

2.6     Engineering Materials

2.7     Stress–Strain Diagrams

2.8     Hooke’s Law and Poisson’s Ratio

2.9     Generalized Hooke’s Law

2.10   Measurement of Strain: Bonded Strain Gages

2.11   Strain Energy

2.12   Strain Energy in Common Structural Members

2.13   Components of Strain Energy

2.14   Saint-Venant’s Principle

Problems

Chapter 3  Two-Dimensional Problems in Elasticity

3.1     Introduction

3.2     Fundamental Principles of Analysis

Part A—Formulation and Methods of Solution

3.3     Plane Strain Problems

3.4     Plane Stress Problems

3.5     Airy’s Stress Function

3.6     Solution of Elasticity Problems

3.7     Thermal Stresses

3.8     Basic Relations in Polar Coordinates

Part B—Stress Concentrations

3.9     Stresses Due to Concentrated Loads

3.10   Stress Distribution near Concentrated Load Acting on a Beam

3.11   Stress Concentration Factors

3.12   Neuber’s Diagram

3.13   Contact Stresses

Problems

Chapter 4  Failure Criteria

4.1     Introduction

4.2     Failure

4.3     Failure by Yielding

4.4     Failure by Fracture

4.5     Yield and Fracture Criteria

4.6     Maximum Shearing Stress Theory

4.7     Maximum Distortion Energy Theory

4.8     Octahedral Shearing Stress Theory

4.9     Comparison of the Yielding Theories

4.10   Maximum Principal Stress Theory

4.11   Mohr’s Theory

4.12   Coulomb–Mohr Theory

4.13   Introductory Fracture Mechanics

4.14   Failure Criteria for Metal Fatigue

4.15   Fatigue Life under Combined Loading

4.16   Impact or Dynamic Loads

4.17   Dynamic and Thermal Effects

Problems

Chapter 5  Bending of Beams

5.1     Introduction

Part A—Exact Solutions

5.2     Pure Bending of Beams of Symmetrical Cross Section

5.3     Pure Bending of Beams of Asymmetrical Cross Section

5.4     Bending of a Cantilever of Narrow Section

5.5     Bending of a Simply Supported, Narrow Beam

Part B—Approximate Solutions

5.6     Elementary Theory of Bending

5.7     Bending and Shearing Stresses

5.8     Effect of Transverse Normal Stress

5.9     Composite Beams

5.10   Shear Center

5.11   Statically Indeterminate Systems

5.12   Energy Method for Deflections

Part C—Curved Beams

5.13   Exact Solution

5.14   Tangential Stress.Winkler’s Theory

5.15   Combined Tangential and Normal Stresses

Problems

Chapter 6  Torsion of Prismatic Bars

6.1     Introduction

6.2     Elementary Theory of Torsion of Circular Bars

6.3     General Solution of the Torsion Problem

6.4     Prandtl’s Stress Function

6.5     Prandtl’s Membrane Analogy

6.6     Torsion of Thin-Walled Members of Open Cross Section

6.7     Torsion of Multiply Connected Thin-Walled Sections

6.8     Fluid Flow Analogy and Stress Concentration

6.9     Torsion of Restrained Thin-Walled Members of Open Cross Section

6.10   Curved Circular Bars: Helical Springs

Problems

Chapter 7  Numerical Methods

7.1     Introduction

7.2     Finite Differences

7.3     Finite Difference Equations

7.4     Curved Boundaries

7.5     Boundary Conditions

7.6     Finite Element Method

7.7     Properties of a Finite Element

7.8     Formulation of the Finite Element Method

7.9     Triangular Finite Element

7.10   Use of Digital Computers

Problems

Chapter 8  Axisymmetrically Loaded Members

8.1     Introduction

8.2     Thick-Walled Cylinders

8.3     Maximum Tangential Stress

8.4     Application of Failure Theories

8.5     Compound Cylinders

8.6     Rotating Disks of Constant Thickness

8.7     Rotating Disks of Variable Thickness

8.8     Rotating Disks of Uniform Stress

8.9     Thermal Stresses in Thin Disks

8.10   Thermal Stress in Long Circular Cylinders

8.11   Finite Element Solution

8.12   Formulation of Axisymmetric Element

Problems

Chapter 9  Beams on Elastic Foundations

9.1     Introduction

9.2     General Theory

9.3     Infinite Beams

9.4     Semi-Infinite Beams

9.5     Finite Beams: Classification of Beams

9.6     Beams Supported by Equally Spaced Elastic Elements

9.7     Simplified Solutions for Relatively Stiff Beams

9.8     Solution by Finite Differences

9.9     Applications

Problems

Chapter 10 Energy Methods

10.1   Introduction

10.2   Work Done in Deformation

10.3   Reciprocity Theorem

10.4   Castigliano’s Theorem

10.5   Unit or Dummy Load Method

10.6   Crotti–Engesser Theorem

10.7   Statically Indeterminate Systems

10.8   Principle of Virtual Work

10.9   Principle of Minimum Potential Energy

10.10 Application of Trigonometric Series

10.11 Rayleigh–Ritz Method

Problems

Chapter 11 Elastic Stability

11.1   Introduction

11.2   Critical Load

11.3   Buckling of a Column

11.4   End Conditions

11.5   Critical Stress in a Column

11.6   Allowable Stress

11.7   Initially Curved Members

11.8   Eccentrically Loaded Columns: Secant Formula

11.9   Energy Methods Applied to Buckling

11.10 Solution by Finite Differences

11.11 Finite Difference Solution for Unevenly Spaced Nodes

Problems

Chapter 12 Plastic Behavior of Materials

12.1   Introduction

12.2   Plastic Deformation

12.3   True Stress–True Strain Curve in Simple Tension

12.4   Instability in Simple Tension

12.5   Plastic Deflection of Beams

12.6   Analysis of Perfectly Plastic Beams

12.7   Collapse Load of Structures

12.8   Elastic–Plastic Torsion

12.9   Elastic–Plastic Stresses in Rotating Disks

12.10 Plastic Stress–Strain Relations

12.11 Plastic Stress–Strain Increment Relations

12.12 Stresses in Perfectly Plastic Thick-Walled Cylinders

Problems

Chapter 13 Plates and Shells

Part A—Bending of Thin Plates

13.1   Basic Assumptions

13.2   Strain–Curvature Relations

13.3   Stress, Curvature, and Moment Relations

13.4   Governing Equations of Plate Deflection

13.5   Boundary Conditions

13.6   Simply Supported Rectangular Plates

13.7   Axisymmetrically Loaded Circular Plates

13.8   Deflections of Rectangular Plates by the Strain Energy Method

13.9   Finite Element Solution

Part B—Membrane Stresses in Thin Shells

13.10 Basic Assumptions

13.11 Simple Membrane Action

13.12 Symmetrically Loaded Shells of Revolution

13.13 Some Common Cases of Shells of Revolution

13.14 Cylindrical Shells of General Shape

Problems

Appendix A Indicial Notation

Appendix B Solution of the Stress Cubic Equation

B.1    Principal Stresses

B.2    Direction Cosines

Appendix C Moments of Composite Areas

C.1    Centroid

C.2    Moments of Inertia

C.3    Parallel-Axis Theorem

C.4    Principal Moments of Inertia

Appendix D Tables

D.1    Average Properties of Common Engineering Materials

D.2    Conversion Factors: SI Units to U.S. Customary Units

D.3    SI Unit Prefixes

D.4    Deflections and Slopes of Beams

References

Answers to Selected Problems

Index

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