net SIXTH EDITION ADVANCED MECHANICS OF MATERIALS ARTHUR P. BORES1 Professor Emeritus Civil and Architectural Engineering www.net The University of Wyoming at Laramie and Professor Emeritus Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign RICHARD J. SCHMIDT Professor Civil and Architectural Engineering The University of Wyoming at Laramie JOHN WILEY & SONS, INC.net Acquisitions Editor Joseph Hayton Marketing Manager Katherine Hepburn Senior Production Editor Valerie A. Vargas Senior Designer Karin Kincheloe Production Management Services Argosy This book was set in 10/12 Times Roman by Argosy and printed and bound by Hamilton Printing.
The cover was printed by Lehigh Press. This book is printed on acid-free paper.net Copyright 2003 0 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sec- tions 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Pub- lisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470.
Requests to the Publisher for per- mission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6000, fax (201) 748-6088, e-mail: PERMREQ@WILEY. To order books please call 1 (800) 225-5945. Library of Congress Cataloging in Publication Data: Boresi, Arthur P. (Arthur Peter), 1924- Advanced mechanics of materials /Arthur P.
Includes bibliographicalreferences and index. ISBN 0-471-43881-2 (cloth : alk. Strength of materials.1'12--d~21 2002026738 ISBN 978-0-471-43881-6 Printed in the United States of America 10987 www.net PREFACE This book is written as a text for advanced undergraduates and graduate students in aero- space, civil, and mechanical engineering and applied mechanics. It is also intended as a reference for practitioners.
The book contains topics sufficient for two academic semesters or three quarters. Thus, there is enough variety that instructors of a one-semester course or one- or two-quarter courses can choose topics of interest to students. New to this Edition In this sixth edition, we have attempted to thoroughly review the fifth edition with the intention of clarifying and condensing the presentation, updating many of the examples and homework problems, and adding selected new topics. In the face of these additions, we have also attempted to control the growth in size of the book.
Such is a difficult task. Based on a survey of the market, the final chapter, finite element www.net methods, has been removed from the book and is available at no cost from the book Web site: http:llwww. Those topics that we have retained are presented with detail and precision, as in previous editions of the book. Throughout the revision pro- cess, the philosophy of previous editions has been maintained.
That is, we have attempted to develop the topics from basic principles so that the applicability and limitations of the methods are clear. Without an understanding of the underlying principles and assumptions upon which analysis methods are based, users of those methods may be limited to applica- tion of the methods to known problems. Furthermore, they may not have the necessary understanding to extend or adapt the theories and developments to their own applications. Hence, we regard concepts and fundamentals as no less important than application of solu- tion methods in problem solving.
Organization In Chapter 1 basic concepts of one-dimensional load-stress, load-deflec- tion, and stress-strain diagrams are introduced. A discussion of the tension test and associ- ated material properties is presented, followed by a brief introduction to failure theories. Theories of stress and strain follow in Chapter 2. Definitions of the stress tensor and vari- ous stress quantities are developed from detailed examination of equilibrium conditions for a body.
Likewise, definitions of strain are developed from a consideration of deforma- tion of a body. Here, the independence and similarity of the theories of stress and strain become evident. Chapter 3 joins the theories of stress and strain by the theory of linear stress-strain-temperature relations, based upon the requirements of the first law of ther- modynamics. Stress-strain relations and material constants for anisotropic, orthotropic, and isotropic materials are discussed.
Yield theory is developed in Chapter 4. Starting with one-dimensional stress-strain behavior, the concepts of yield criteria, yield functions, and yield surfaces are developed to describe nonlinear material response for multiaxial stress states. The von Mises and Tresca criteria are discussed and compared in detail. The appli- cation of energy methods, Chapter 5, includes a discussion of the dummy load method and its relation to the Castigliano method.net viii PREFACE Chapters 6-12 treat classical topics in mechanics of materials.
That is, these chap- ters use fundamental concepts of equilibrium, compatibility conditions, constitutive rela- tions, and material response to study the behavior of selected mechanical and structural members. Specifically, the following topics are considered: torsion, nonsymmetrical bend- ing, shear center, curved beams, beams on elastic foundations, thick-wall cylinders, and column stability. Key kinematic and material response assumptions are emphasized in order to highlight the applicability and limitations of the analysis methods. Chapters 13-18 contain selected topics that are not generally treated by the mechan- ics of materials method, but are nevertheless areas of interest and advanced study for prac- ticing engineers.
This part of the book contains a mix of topics involving both behavior of structural and mechanical systems (flat plates, stress concentrations, and contact stresses) as well as detailed study of material behavior (fracture mechanics and fatigue). Acknowledgments We thank Joe Hayton, Engineering Editor at Wiley, for his help and advice during the development of this edition. In addition, we also appreciate the help of Valerie Vargas, Production Editor, Adriana Lavergne at Argosy for work on composition, and David Wood at Wellington Studios for work on the illustration program. We acknowl- www.net edge the help of the following reviewers, who offered useful insights into developing this edition: Abhijit Bhattacharyya, University of Alberta Bill Y.
Chao, University of South Carolina Ali Fatemi, University of Toledo Stephen Folkman, Utah State University Stephen M. Heinrich, Marquette University Thomas Lacy, Wichita State University Craig C. Menzemer, University of Akron James A. Nemes, McGill University Steven O’Hara, Oklahoma State University Pizhong Qiao, University of Akron Robert Yuan, University of Texas-Arlington Supplements Instructors who adopt the book for their courses may access solutions to the homework problems from the John Wiley & Sons Web site: http://www.Contact your local sales representative for additional details.
Finally, we welcome comments, suggestions, questions, and corrections that you might wish to offer. Send your remarks to Dr. Boresi, Department of Civil and Archi- tectural Engineering, University of Wyoming, Laramie, WY 8207 1-3295.net CONTENTS CHAPTER 1 INTRODUCTION 1 2.7 Strain Theory, Transformation of Strain, and Principal Strains 55 1.1 Review of Elementary Mechanics of Materials 1 2.1 Strain of a Line Element 55 1.1 Axially Loaded Members 1 2.2 Final Direction of a Line Element 57 1.2 Torsionally Loaded Members 3 2.3 Rotation Between Two Line Elements 1.3 Bending of Beams 3 (Definition of Shear Strain) 58 1.2 Methods of Analysis 5 2.1 Method of Mechanics of Materials 6 2.2 Method of Continuum Mechanics and the 2.1 Strain Compatibility Relations 62 Theory of Elasticity 7 2.2 Strain-Displacement Relations for Orthogonal 1.3 Deflections by Energy Methods 7 Curvilinear Coordinates 63 1.3 Stress-Strain Relations 8 2.9 Strain Measurement and Strain Rosettes 70 www.1 Elastic and Inelastic Response of a Solid 8 Problems 72 1.2 Material Properties 10 References 78 1.4 Failure and Limits on Design 16 1.1 Modes of Failure 19 Problems 22 CHAPTER 3 LINEAR STRESS-STRAIN-TEMPERATURE References 24 RELATIONS 79 3.1 First Law of Thermodynamics, Internal-EnergyDensity, CHAPTER 2 ~~~~~~ THEORIES OF STRESS AND STRAIN 25 and Complementary Internal-Energy Density 79 3.1 Elasticity and Internal-Energy Density 81 2.1 Definition of Stress at a Point 25 3.2 Elasticity and Complementary Internal-Energy 2.2 Stress Notation 26 Density 82 2.3 Symmetry of the S t r e s s h a y and Stress on an Arbitrarily 3.2 Hooke’s Law: Anisotropic Elasticity 84 Oriented Plane 28 3.3 Hooke’s Law: Isotropic Elasticity 85 2.1 Symmetry of Stress Components 28 3.1 Isotropic and Homogeneous Materials 85 2.2 Stresses Acting on Arbitrary Planes 29 3.2 Strain-Energy Density of Isotropic Elastic 2.3 Normal Stress and Shear Stress on an Oblique Materials 85 Plane 30 3.4 Equations of Thennoelasticity for Isotropic 2.4 Transformation of Stress, Principal Stresses, and Other Materials 91 Properties 31 3.5 Hooke’s Law: Orthotropic Materials 93 2.1 Transformation of Stress 31 Problems 101 2.2 Principal Stresses 32 References 103 2.3 Principal Values and Directions 33 2.5 Mean and Deviator Stresses 37 CHAPTER 4 INELASTIC MATERIAL.1 Limitations on the Use of Uniaxial Stress-Strain 2.7 Mohr’s Circle in Two Dimensions 40 Data 104 2.8 Mohr’s Circles in Three Dimensions 43 4.1 Rate of Loading 105 2.5 Differential Equations of Motion of a Deformable 4.2 Temperature Lower Than Room Body 50 Temperature 105 2.1 Specialization of Equations 2.3 Temperature Higher Than Room 2.6 Deformation of a Deformable Body 54 Temperature 105 ix www.4 Unloading and Load Reversal 105 6.2 Stresses at a Point and Equations of 4.5 Multiaxial States of Stress 106 Equilibrium 210 4.2 Nonlinear Material Response 107 6.1 Models of Uniaxial StressStrain Curves 108 6.3 Linear Elastic Solution 213 4.3 Yield Criteria: General Concepts 113 6.1 Elliptical Cross Section 214 4.1 Maximum Principal Stress Criterion 114 6.2 Equilateral Triangle Cross Section 215 4.2 Maximum Principal Strain Criterion 116 6.3 Other Cross Sections 216 4.3 Strain-Energy Density Criterion 116 6.4 The Prandtl Elastic-Membrane (Soap-Film)Analogy 216 4.4 Yielding of Ductile Metals 117 6.1 Remark on Reentrant Corners 219 4.1 Maximum Shear-Stress (Tresca) Criterion 118 6.5 Narrow Rectangular Cross Section 219 4.2 Distortional Energy Density (von Mises) 6.1 Cross Sections Made Up of Long Narrow Criterion 120 Rectangles 221 4.3 Effect of Hydrostatic Stress and the 6.6 Torsion of Rectangular Cross Section Members 222 z-Plane 122 6.7 Hollow Thin-Wall Torsion Members and Multiply 4.5 Alternative Yield Criteria 126 Connected Cross Sections 228 4.1 Mohr-Coulomb Yield Criterion 126 6.1 Hollow Thin-Wall Torsion Member Having 4.2 Drucker-Prager Yield Criterion 128 Several Compartments 230 4.3 Hill’s Criterion for Orthotropic Materials 128 6.8 Thin-Wall Torsion Members with Restrained www.6 General Yielding 129 Ends 234 4.1 Elastic-Plastic Bending 131 6.1 I-Section Torsion Member Having One End 4.2 Fully Plastic Moment 132 Restrained from Warping 235 4.3 Shear Effect on Inelastic Bending 134 6.2 Various Loads and Supports for Beams in 4.4 Modulus of Rupture 134 Torsion 239 4.5 Comparison of Failure Criteria 136 6.9 Numerical Solution of the Torsion Problem 239 4.6 Interpretation of Failure Criteria for General 6.10 Inelastic Torsion: Circular Cross Sections 243 Yielding 137 6.1 Modulus of Rupture in Torsion 244 Problems 142 6.2 Elastic-Plastic and Fully Plastic References 146 Torsion 244 6.3 Residual Shear Stress 246 CHAPTER 5 APPLICATIONS OF ENERGY METHODS 147 6.1 Fully Plastic Torsion: General Cross Sections 250 Problems 254 5.1 Principle of Stationary Potential Energy 147 References 262 5.2 Castigliano’sTheorem on Deflections 152 5.3 Castigliano’sTheorem on Deflections for Linear CHAPTER 7 BENDING OF STRAIGHT BEAMS 263 Load-Deflection Relations 155 5.1 Strain Energy U, for Axial Loading 156 7.1 Fundamentals of Beam Bending 263 5.2 Strain Energies U, and Us for Beams 158 7.1 Centroidal Coordinate Axes 263 5.3 Strain Energy U, for Torsion 160 7.2 Shear Loading of a Beam and Shear Center 5.4 Deflections of Statically Determinate Structures 163 Defined 264 5.1 Curved Beams Treated as Straight Beams 165 7.2 Dummy Load Method and Dummy Unit Load 7.4 Nonsymmetrical Bending 268 Method 170 7.5 Plane of Loads: Symmetrical and 5.5 Statically Indeterminate Structures 177 Nonsymmetrical Loading 268 5.1 Deflections of Statically Indeterminate 7.2 Bending Stresses in Beams Subjectedto Nonsymmetrical Structures 180 Bending 272 Problems 187 7.1 Equations of Equilibrium 272 References 199 7.2 Geometry of Deformation 273 7.3 StressStrain Relations 273 CHAPTER 6 TORSION 200 7.4 Load-Stress Relation for Nonsymmetrical Bending 273 6.1 Torsion of a Prismatic Bar of Circular Cross Section 200 7.1 Design of Transmission Shafts 204 7.
