77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:33 AM Page ii 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:33 AM Page i Mechanics of Materials Eighth Edition Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:33 AM Page ii Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:33 AM Page iii Mechanics of Materials Eighth Edition James M. Gere Professor Emeritus, Stanford University Barry J. Goodno Georgia Institute of Technology Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:33 AM Page ii This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:33 AM Page iv Mechanics of Materials, Eighth Edition © 2013, 2009Cengage Learning James M. Gere and Barry J. Goodno ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by Publisher, Global Engineering: any means graphic, electronic, or mechanical, including but not limited to Christopher M. 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Copyeditor: Shelly Gerger-Knechtl Library of Congress Control Number: 2011940308 Proofreader: Pamela Ehn ISBN-13: 978-1-111-57773-5 Indexer: Shelly Gerger-Knechtl ISBN-10: 1-111-57773-0 Compositor: Integra Senior Art Director: Michelle Kunkler Cengage Learning Internal Designer: Juli Cook/Plan-It-Publishing 200First Stamford Place, Suite 400 Stamford, CT 06902 Cover Designer: Andrew Adams/4065042 USA Canada Inc. Cover Image: © Bruno Ehrs/Corbis Cengage Learning is a leading provider of customized learning solutions Rights Acquisitions Specialist: Deanna Ettinger with office locations around the globe, including Singapore, the Text and Image Permissions Researcher: UnitedKingdom, Australia, Mexico, Brazil, and Japan. Locate your local Kristiina Paul office at: international.cengage.com/region. Manufacturing Planner: Doug Wilke Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions, visit www.cengage.com/engineering. Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com. Printed in Canada 1 2 3 4 5 6 7 15 14 13 12 11 Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:34 AM Page v C O N T E N T S James Monroe Gere ix 3. TORSION 254 Preface xi 3.1 Introduction 256 Symbols xviii 3.2 Torsional Deformations of a Circular Greek Alphabet xx Bar 257 1. TENSION, COMPRESSION, AND SHEAR 2 3.3 Circular Bars of Linearly Elastic Materials 260 1.1 Introduction to Mechanics of Materials 4 3.4 Nonuniform Torsion 272 1.2 Statics Review 6 3.5 Stresses and Strains in Pure Shear 283 1.3 Normal Stress and Strain 27 3.6 Relationship Between Moduli of Elasticity E 1.4 Mechanical Properties of Materials 37 and G 290 1.5 Elasticity, Plasticity, and Creep 45 3.7 Transmission of Power by Circular 1.6 Linear Elasticity, Hooke’s Law, and Shafts 291 Poisson’s Ratio 52 3.8 Statically Indeterminate Torsional 1.7 Shear Stress and Strain 57 Members 296 1.8 Allowable Stresses and Allowable 3.9 Strain Energy in Torsion and Pure Shear 300 Loads 68 3.10 Torsion of Non-Circular Prismatic 1.9 Design for Axial Loads and Direct Shafts 307 Shear 74 3.11 Thin-Walled Tubes 316 Chapter Summary & Review 80 *3.12 Stress Concentrations in Torsion 324 Problems 83 Chapter Summary & Review 328 2. AXIALLY LOADED MEMBERS 118 Problems 330 2.1 Introduction 120 4. SHEAR FORCES AND BENDING 2.2 Changes in Lengths of Axially Loaded MOMENTS 352 Members 120 2.3 Changes in Lengths Under Nonuniform 4.1 Introduction 354 Conditions 130 4.2 Types of Beams, Loads, and Reactions 354 2.4 Statically Indeterminate Structures 138 4.3 Shear Forces and Bending Moments 361 2.5 Thermal Effects, Misfits, and 4.4 Relationships Between Loads, Shear Forces, Prestrains 149 and Bending Moments 371 2.6 Stresses on Inclined Sections 164 4.5 Shear-Force and Bending-Moment 2.7 Strain Energy 176 Diagrams 375 *2.8 Impact Loading 187 Chapter Summary & Review 388 *2.9 Repeated Loading and Fatigue 195 Problems 390 *2.10 Stress Concentrations 197 5. STRESSES IN BEAMS (BASIC TOPICS) 402 *2.11 Nonlinear Behavior 205 5.1 Introduction 404 *2.12 Elastoplastic Analysis 210 5.2 Pure Bending and Nonuniform Chapter Summary & Review 216 Bending 404 Problems 218 5.3 Curvature of a Beam 405 *Specialized and/or advanced topics v Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:34 AM Page vi vi Contents 5.4 Longitudinal Strains in Beams 407 7.7 Plane Strain 633 5.5 Normal Stresses in Beams (Linearly Elastic Chapter Summary & Review 648 Materials) 412 Problems 652 5.6 Design of Beams for Bending 8. APPLICATIONS OF PLANE STRESS Stresses 426 (PRESSURE VESSELS, BEAMS, 5.7 Nonprismatic Beams 435 AND COMBINED LOADINGS) 670 5.8 Shear Stresses in Beams of Rectangular 8.1 Introduction 672 Cross Section 439 8.2 Spherical Pressure Vessels 672 5.9 Shear Stresses in Beams of Circular Cross 8.3 Cylindrical Pressure Vessels 678 Section 448 5.10 Shear Stresses in the Webs of Beams with 8.4 Maximum Stresses in Beams 685 Flanges 451 8.5 Combined Loadings 694 *5.11 Built-Up Beams and Shear Flow 458 Chapter Summary & Review 712 *5.12 Beams with Axial Loads 462 Problems 714 *5.13 Stress Concentrations in Bending 468 9. DEFLECTIONS OF BEAMS 728 Chapter Summary & Review 472 9.1 Introduction 730 Problems 476 9.2 Differential Equations of the Deflection Curve 730 6. STRESSES IN BEAMS (ADVANCED 9.3 Deflections by Integration of the TOPICS) 506 Bending-Moment Equation 735 6.1 Introduction 508 9.4 Deflections by Integration of the 6.2 Composite Beams 508 Shear-Force and Load Equations 746 6.3 Transformed-Section Method 517 9.5 Method of Superposition 752 6.4 Doubly Symmetric Beams with Inclined 9.6 Moment-Area Method 760 Loads 526 9.7 Nonprismatic Beams 769 6.5 Bending of Unsymmetric Beams 533 9.8 Strain Energy of Bending 774 6.6 The Shear-Center Concept 541 *9.9 Castigliano’s Theorem 779 6.7 Shear Stresses in Beams of Thin-Walled *9.10 Deflections Produced by Impact 791 Open Cross Sections 543 *9.11 Temperature Effects 793 6.8 Shear Stresses in Wide-Flange Beams 546 Chapter Summary & Review 798 6.9 Shear Centers of Thin-Walled Open Problems 800 Sections 550 *6.10 Elastoplastic Bending 558 10. STATICALLY INDETERMINATE BEAMS 820 Chapter Summary & Review 566 10.1 Introduction 822 Problems 569 10.2 Types of Statically Indeterminate Beams 822 7. ANALYSIS OF STRESS AND STRAIN 588 10.3 Analysis by the Differential Equations of 7.1 Introduction 590 the Deflection Curve 825 7.2 Plane Stress 590 10.4 Method of Superposition 832 7.3 Principal Stresses and Maximum Shear *10.5 Temperature Effects 845 Stresses 598 *10.6 Longitudinal Displacements at the Ends of 7.4 Mohr’s Circle for Plane Stress 607 a Beam 853 7.5 Hooke’s Law for Plane Stress 623 Chapter Summary & Review 856 7.6 Triaxial Stress 629 Problems 858 Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:34 AM Page vii Contents vii 11. COLUMNS 868 REFERENCES AND HISTORICAL NOTES 987 11.1 Introduction 870 APPENDIX A: FE EXAM REVIEW 11.2 Buckling and Stability 870 PROBLEMS 995 11.3 Columns with Pinned Ends 878 APPENDIX B: SYSTEMS OF UNITS 11.4 Columns with Other Support AND CONVERSION FACTORS 1037 Conditions 889 APPENDIX C: PROBLEM SOLVING 1051 11.5 Columns with Eccentric Axial Loads 899 APPENDIX D: MATHEMATICAL 11.6 The Secant Formula for Columns 904 FORMULAS 1057 11.7 Elastic and Inelastic Column Behavior 909 APPENDIX E: PROPERTIES OF PLANE 11.8 Inelastic Buckling 911 AREAS 1063 11.9 Design Formulas for Columns 916 APPENDIX F: PROPERTIES OF Chapter Summary & Review 934 STRUCTURAL-STEEL SHAPES 1069 Problems 936 APPENDIX G: PROPERTIES OF STRUCTURAL 12. REVIEW OF CENTROIDS AND MOMENTS LUMBER 1081 OF INERTIA 954 APPENDIX H: DEFLECTIONS AND SLOPES 12.1 Introduction 956 OF BEAMS 1083 12.2 Centroids of Plane Areas 956 APPENDIX I: PROPERTIES OF 12.3 Centroids of Composite Areas 959 MATERIALS 1089 12.4 Moments of Inertia of Plane Areas 962 ANSWERS TO PROBLEMS 1095 12.5 Parallel-Axis Theorem for Moments NAME INDEX 1123 of Inertia 965 12.6 Polar Moments of Inertia 969 SUBJECT INDEX 1124 12.7 Products of Inertia 971 12.8 Rotation of Axes 974 12.9 Principal Axes and Principal Moments of Inertia 976 Problems 980 Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 77735_00_fm_p00i-001.qxd:77735_00_fm_p00i-001.qxd 10/25/11 11:34 AM Page viii Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.