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CONVERSIONS BETWEEN U.S.CUSTOMARY UNITS AND SI UNITS Times conversion factor U.S.Customary unit Equals SI unit Accurate Practical Acceleration (linear) foot per second squared ft/s2 0.3048* 0.305 meter per second squared m/s2 inch per second squared in./s2 0.0254* 0.0254 meter per second squared m62 Area square foot f 0.09290304* 0.0929 square meter 03 square inch in.2 645.16* 645 square millimeter mm2 Density (mass) slug per cubic foot slug/f3 515.379 515 kilogram per cubic meter kg/m3 Density (weight) pound per cubic foot Ib/ft3 157.087 157 newton per cubic meter N/m3 pound per cubic inch Ib/in.3 271.447 271 kilonewton per cubic meter kN/m3 Energy:work foot-pound ft-lb 1.35582 1.36 joule (N-m) inch-pound in.-Ib 0.112985 0.113 joule J kilowatt-hour kWh 3.6* 3.6 megajoule MJ British thermal unit Btu 1055.06 1055 joule J Force pound Ib 4.44822 4.45 newton(kg.m/s2) N kip (1000 pounds) k 4.44822 4.45 kilonewton kN Force per unit length pound per foot 1b/ 14.5939 14.6 newton per meter N/m pound per inch Ib/in. 175.127 175 newton per meter N/m kip per foot k/ft 14.5939 14.6 kilonewton per meter kN/m kip per inch k/in. 175.127 175 kilonewton per meter kN/m Length foot ft 0.3048* 0.305 meter m inch in. 25.4* 25.4 millimeter mm mile mi 1.609344* 1.61 kilometer km Mass slug lb-s2/ft 14.5939 14.6 kilogram kg Moment of a force;torque pound-foot lb-ft 1.35582 1.36 newton meter N.m pound-inch Ib-in. 0.112985 0.113 newton meter N.m kip-foot k-ft 1.35582 1.36 kilonewton meter kN-m kip-inch k-in. 0.112985 0.113 kilonewton meter kN.m
CONVERSIONS BETWEEN U.S. CUSTOMARY UNITS AND SI UNITS Times conversion factor U.S. Customary unit Accurate Practical Equals SI unit Acceleration (linear) foot per second squared ft/s2 0.3048* 0.305 meter per second squared m/s2 inch per second squared in./s2 0.0254* 0.0254 meter per second squared m/s2 Area square foot ft2 0.09290304* 0.0929 square meter m2 square inch in.2 645.16* 645 square millimeter mm2 Density (mass) slug per cubic foot slug/ft3 515.379 515 kilogram per cubic meter kg/m3 Density (weight) pound per cubic foot lb/ft3 157.087 157 newton per cubic meter N/m3 pound per cubic inch lb/in.3 271.447 271 kilonewton per cubic meter kN/m3 Energy; work foot-pound ft-lb 1.35582 1.36 joule (Nm) J inch-pound in.-lb 0.112985 0.113 joule J kilowatt-hour kWh 3.6* 3.6 megajoule MJ British thermal unit Btu 1055.06 1055 joule J Force pound lb 4.44822 4.45 newton (kgm/s2 ) N kip (1000 pounds) k 4.44822 4.45 kilonewton kN Force per unit length pound per foot lb/ft 14.5939 14.6 newton per meter N/m pound per inch lb/in. 175.127 175 newton per meter N/m kip per foot k/ft 14.5939 14.6 kilonewton per meter kN/m kip per inch k/in. 175.127 175 kilonewton per meter kN/m Length foot ft 0.3048* 0.305 meter m inch in. 25.4* 25.4 millimeter mm mile mi 1.609344* 1.61 kilometer km Mass slug lb-s2 /ft 14.5939 14.6 kilogram kg Moment of a force; torque pound-foot lb-ft 1.35582 1.36 newton meter N·m pound-inch lb-in. 0.112985 0.113 newton meter N·m kip-foot k-ft 1.35582 1.36 kilonewton meter kN·m kip-inch k-in. 0.112985 0.113 kilonewton meter kN·m
CONVERSIONS BETWEEN U.S.CUSTOMARY UNITS AND SI UNITS(Continued) Times conversion factor U.S.Customary unit Equals SI unit Accurate Practical Moment of inertia(area) inch to fourth power in.4 416,231 416.000 millimeter to fourth power mm inch to fourth power in.4 0.416231×10-6 0.416×10-6 meter to fourth power Moment of inertia(mass) slug foot squared slug-f2 1.35582 1.36 kilogram meter squared kg.m2 Power foot-pound per second ft-Ib/s 1.35582 1.36 watt (J/s or N.m/s) W foot-pound per minute ft-lb/min 0.0225970 0.0226 watt W horsepower(550 ft-lb/s) hp 745.701 746 watt w Pressure;stress pound per square foot psf 47.8803 47.9 pascal (N/m2) Pa pound per square inch psi 6894.76 6890 pascal Pa kip per square foot ksf 47.8803 47.9 kilopascal kPa kip per square inch ksi 6.89476 6.89 megapascal MPa Section modulus inch to third power i血.3 16,387.1 16,400 millimeter to third power mm3 inch to third power in.3 16.3871×10-6 16.4×10-6 meter to third power 0m3 Velocity (linear) foot per second ft/s 0.3048* 0.305 meter per second m/s inch per second in./s 0.0254* 0.0254 meter per second m/s mile per hour mph 0.44704* 0.447 meter per second m/s mile per hour mph 1.609344* 1.61 kilometer per hour km/h Volume cubic foot fe 0.0283168 0.0283 cubic meter m3 cubic inch in.3 16.3871×10-6 16.4×10-6 cubic meter m cubic inch 血3 16.3871 16.4 cubic centimeter (cc) cm3 gallon (231 in.3) gal. 3.78541 3.79 liter L gallon (231 in.3) gal. 0.00378541 0.00379 cubic meter *An asterisk denotes an exact conversion factor Note:To convert from SI units to USCS units,divide by the conversion factor Temperature Conversion Formulas T0=高n9-30=TK-273.15 7K=高n间-3+27315=Tg+273.15 Tp=2C+32= 9 TK)-459.67 51 5
Temperature Conversion Formulas T(°C) 5 9 [T(°F) 32] T(K) 273.15 T(K) 5 9 [T(°F) 32] 273.15 T(°C) 273.15 T(°F) 9 5 T(°C) 32 9 5 T(K) 459.67 CONVERSIONS BETWEEN U.S. CUSTOMARY UNITS AND SI UNITS (Continued) Times conversion factor U.S. Customary unit Accurate Practical Equals SI unit Moment of inertia (area) inch to fourth power in.4 416,231 416,000 millimeter to fourth power mm4 inch to fourth power in.4 0.416231 106 0.416 106 meter to fourth power m4 Moment of inertia (mass) slug foot squared slug-ft2 1.35582 1.36 kilogram meter squared kg·m2 Power foot-pound per second ft-lb/s 1.35582 1.36 watt (J/s or N·m/s) W foot-pound per minute ft-lb/min 0.0225970 0.0226 watt W horsepower (550 ft-lb/s) hp 745.701 746 watt W Pressure; stress pound per square foot psf 47.8803 47.9 pascal (N/m2 ) Pa pound per square inch psi 6894.76 6890 pascal Pa kip per square foot ksf 47.8803 47.9 kilopascal kPa kip per square inch ksi 6.89476 6.89 megapascal MPa Section modulus inch to third power in.3 16,387.1 16,400 millimeter to third power mm3 inch to third power in.3 16.3871 106 16.4 106 meter to third power m3 Velocity (linear) foot per second ft/s 0.3048* 0.305 meter per second m/s inch per second in./s 0.0254* 0.0254 meter per second m/s mile per hour mph 0.44704* 0.447 meter per second m/s mile per hour mph 1.609344* 1.61 kilometer per hour km/h Volume cubic foot ft3 0.0283168 0.0283 cubic meter m3 cubic inch in.3 16.3871 106 16.4 106 cubic meter m3 cubic inch in.3 16.3871 16.4 cubic centimeter (cc) cm3 gallon (231 in.3 ) gal. 3.78541 3.79 liter L gallon (231 in.3 ) gal. 0.00378541 0.00379 cubic meter m3 *An asterisk denotes an exact conversion factor Note: To convert from SI units to USCS units, divide by the conversion factor
CENGAGE Learning Mechanics of Materials.Seventh Edition 2009 Cengage Learning James M.Gere and Barry J.Goodno ALL RIGHTS RESERVED.No part of this work covered by the copyright herein may be Director,Global Engineering Program:Chris Carson reproduced,transmitted,stored or used in any form or by any means graphic,electronic, Senior Developmental Editor:Hilda Gowans or mechanical,including but not limited to photocopying,recording,scanning,digitizing. taping,Web distribution,information networks,or information storage and retrieval Permissions:Nicola Winstanley systems,except as permitted under Section 107 or 108 of the 1976 United States Production Service:RPK Editorial Services,Inc Copyright Act,without the prior written permission of the publisher. Copy Editor:Rose Kernan Proofreader:Martha McMaster For product information and technology assistance,contact us at Cengage Learning Customer Sales Support,1-800-354-9706 Indexer:Shelly Gerger-Knechtl For permission to use material from this text or product,submit all requests online at Creative Director:Angela Cluer cengage.com/permissions Text Designer:Peter Papayanakis Further permissions questions can be emailed to permissionrequest@cengage.com Cover Designer:Andrew Adams Cover Image:Guggenheim Bilbao Photo graficart.net/Alamy, Library of Congress Control Number:2008923451 Lee Chin Crystal Building Photo Courtesy of Alan I5BN-13:978-0-534-55397-5 Marsh/First Light 15BN-10:0-534-55397-4 Compositor:Integra Printer:Quebecor World Cengage Learning 1120 Birchmount Road Toronto ON MIK 5G4 Canada Cengage Learning is a leading provider of customized learning solutions with office locations around the globe,including Singapore,the United Kingdom,Australia,Mexico, Brazil,and Japan.Locate your local office at:international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions,visit academic.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 123456711100908
Mechanics of Materials, Seventh Edition James M. Gere and Barry J. Goodno Director, Global Engineering Program: Chris Carson Senior Developmental Editor: Hilda Gowans Permissions: Nicola Winstanley Production Service: RPK Editorial Services, Inc Copy Editor: Rose Kernan Proofreader: Martha McMaster Indexer: Shelly Gerger-Knechtl Creative Director: Angela Cluer Text Designer: Peter Papayanakis Cover Designer: Andrew Adams Cover Image: Guggenheim Bilbao Photo © graficart.net/Alamy; Lee Chin Crystal Building Photo Courtesy of Alan Marsh/First Light Compositor: Integra Printer: Quebecor World © 2009 Cengage Learning 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 any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Library of Congress Control Number: 2008923451 ISBN-13: 978-0-534-55397-5 ISBN-10: 0-534-55397-4 Cengage Learning 1120 Birchmount Road Toronto ON M1K 5G4 Canada Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions, visit academic.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 1 2 3 4 5 6 7 11 10 09 08
Contents James Monroe Gere ix Photo Credits x Preface xi Symbols xv Greek Alphabet xviii 1 Tension,Compression,and Shear 2 1.1 Introduction to Mechanics of Materials 5 1.2 Normal Stress and Strain 7 13 Mechanical Properties of Materials 15 1.4 Elasticity,Plasticity,and Creep 24 1.5 Linear Elasticity,Hooke's Law,and Poisson's Ratio 27 1.6 Shear Stress and Strain 32 1.7 Allowable Stresses and Allowable Loads 43 1.8 Design for Axial Loads and Direct Shear 49 Chapter Summary Review 55 Problems 57 2 Axially Loaded Members 88 2.1 Introduction 91 2.2 Changes in Lengths of Axially Loaded Members 91 23 Changes in Lengths Under Nonuniform Conditions 100 2.4 Statically Indeterminate Structures 107 2.5 Thermal Effects,Misfits,and Prestrains 116 2.6 Stresses on Inclined Sections 128 2.7 Strain Energy 140 *2.8 Impact Loading 153 *2.9 Repeated Loading and Fatigue 162 *2.10 Stress Concentrations 164 *2.11 Nonlinear Behavior 170 Specialized and/or advanced topics 体
Contents James Monroe Gere ix Photo Credits x Preface xi Symbols xv Greek Alphabet xviii 1 Tension, Compression, and Shear 2 1.1 Introduction to Mechanics of Materials 5 1.2 Normal Stress and Strain 7 1.3 Mechanical Properties of Materials 15 1.4 Elasticity, Plasticity, and Creep 24 1.5 Linear Elasticity, Hooke’s Law, and Poisson’s Ratio 27 1.6 Shear Stress and Strain 32 1.7 Allowable Stresses and Allowable Loads 43 1.8 Design for Axial Loads and Direct Shear 49 Chapter Summary & Review 55 Problems 57 2 Axially Loaded Members 88 2.1 Introduction 91 2.2 Changes in Lengths of Axially Loaded Members 91 2.3 Changes in Lengths Under Nonuniform Conditions 100 2.4 Statically Indeterminate Structures 107 2.5 Thermal Effects, Misfits, and Prestrains 116 2.6 Stresses on Inclined Sections 128 2.7 Strain Energy 140 ★2.8 Impact Loading 153 ★2.9 Repeated Loading and Fatigue 162 ★2.10 Stress Concentrations 164 ★2.11 Nonlinear Behavior 170 iii ★ Specialized and/or advanced topics
iv CONTENTS ★2.12 Elastoplastic Analysis 175 Chapter Summary Review 181 Problems 182 3 Torsion 220 3.1 Introduction 222 3.2 Torsional Deformations of a Circular Bar 223 33 Circular Bars of Linearly Elastic Materials 226 3.4 Nonuniform Torsion 238 3.5 Stresses and Strains in Pure Shear 245 3.6 Relationship Between Moduli of Elasticity E and G 252 3.7 Transmission of Power by Circular Shafts 254 3.8 Statically Indeterminate Torsional Members 259 3.9 Strain Energy in Torsion and Pure Shear 263 3.10 Thin-Walled Tubes 270 *3.11 Stress Concentrations in Torsion 279 Chapter Summary Review 282 Problems 283 4 Shear Forces and Bending Moments 304 4.1 Introduction 306 4.2 Types of Beams,Loads,and Reactions 306 43 Shear Forces and Bending Moments 313 4.4 Relationships Between Loads,Shear Forces, and Bending Moments 320 4.5 Shear-Force and Bending-Moment Diagrams 325 Chapter Summary Review 337 Problems 338 5 Stresses in Beams(Basic Topics) 350 5.1 Introduction 353 5.2 Pure Bending and Nonuniform Bending 353 53 Curvature of a Beam 354 5.4 Longitudinal Strains in Beams 356 55 Normal Stresses in Beams(Linearly Elastic Materials)361 5.6 Design of Beams for Bending Stresses 374 5.7 Nonprismatic Beams 383 5.8 Shear Stresses in Beams of Rectangular Cross Section 387 5.9 Shear Stresses in Beams of Circular Cross Section 397 5.10 Shear Stresses in the Webs of Beams with Flanges 400
★2.12 Elastoplastic Analysis 175 Chapter Summary & Review 181 Problems 182 3 Torsion 220 3.1 Introduction 222 3.2 Torsional Deformations of a Circular Bar 223 3.3 Circular Bars of Linearly Elastic Materials 226 3.4 Nonuniform Torsion 238 3.5 Stresses and Strains in Pure Shear 245 3.6 Relationship Between Moduli of Elasticity E and G 252 3.7 Transmission of Power by Circular Shafts 254 3.8 Statically Indeterminate Torsional Members 259 3.9 Strain Energy in Torsion and Pure Shear 263 3.10 Thin-Walled Tubes 270 ★3.11 Stress Concentrations in Torsion 279 Chapter Summary & Review 282 Problems 283 4 Shear Forces and Bending Moments 304 4.1 Introduction 306 4.2 Types of Beams, Loads, and Reactions 306 4.3 Shear Forces and Bending Moments 313 4.4 Relationships Between Loads, Shear Forces, and Bending Moments 320 4.5 Shear-Force and Bending-Moment Diagrams 325 Chapter Summary & Review 337 Problems 338 5 Stresses in Beams (Basic Topics) 350 5.1 Introduction 353 5.2 Pure Bending and Nonuniform Bending 353 5.3 Curvature of a Beam 354 5.4 Longitudinal Strains in Beams 356 5.5 Normal Stresses in Beams (Linearly Elastic Materials) 361 5.6 Design of Beams for Bending Stresses 374 5.7 Nonprismatic Beams 383 5.8 Shear Stresses in Beams of Rectangular Cross Section 387 5.9 Shear Stresses in Beams of Circular Cross Section 397 5.10 Shear Stresses in the Webs of Beams with Flanges 400 iv CONTENTS
CONTENTS ★*5.11 Built-Up Beams and Shear Flow 408 ★★5.12 Beams with Axial Loads 412 ★*5.13 Stress Concentrations in Bending 418 Chapter Summary Review 421 Problems 424 6 Stresses in Beams (Advanced Topics) 454 6.1 Introduction 457 6.2 Composite Beams 457 6.3 Transformed-Section Method 466 6.4 Doubly Symmetric Beams with Inclined Loads 472 6.5 Bending of Unsymmetric Beams 479 6.6 The Shear-Center Concept 487 6.7 Shear Stresses in Beams of Thin-Walled Open Cross Sections 489 6.8 Shear Stresses in Wide-Flange Beams 492 6.9 Shear Centers of Thin-Walled Open Sections 496 ★*6.10 Elastoplastic Bending 504 Chapter Summary Review 514 Problems 516 7 Analysis of Stress and Strain 536 7.1 Introduction 539 7.2 Plane Stress 540 73 Principal Stresses and Maximum Shear Stresses 548 7.4 Mohr's Circle for Plane Stress 558 7.5 Hooke's Law for Plane Stress 575 7.6 Triaxial Stress 580 7.7 Plane Strain 584 Chapter Summary Review 600 Problems 602 8 Applications of Plane Stress(Pressure Vessels,Beams,and Combined Loadings) 618 8.1 Introduction 621 8.2 Spherical Pressure Vessels 621 8.3 Cylindrical Pressure Vessels 627 B.4 Maximum Stresses in Beams 635 8.5 Combined Loadings 645 Chapter Summary Review 661 Problems 663 *Advanced topics
★★5.11 Built-Up Beams and Shear Flow 408 ★★5.12 Beams with Axial Loads 412 ★★5.13 Stress Concentrations in Bending 418 Chapter Summary & Review 421 Problems 424 6 Stresses in Beams (Advanced Topics) 454 6.1 Introduction 457 6.2 Composite Beams 457 6.3 Transformed-Section Method 466 6.4 Doubly Symmetric Beams with Inclined Loads 472 6.5 Bending of Unsymmetric Beams 479 6.6 The Shear-Center Concept 487 6.7 Shear Stresses in Beams of Thin-Walled Open Cross Sections 489 6.8 Shear Stresses in Wide-Flange Beams 492 6.9 Shear Centers of Thin-Walled Open Sections 496 ★★6.10 Elastoplastic Bending 504 Chapter Summary & Review 514 Problems 516 7 Analysis of Stress and Strain 536 7.1 Introduction 539 7.2 Plane Stress 540 7.3 Principal Stresses and Maximum Shear Stresses 548 7.4 Mohr’s Circle for Plane Stress 558 7.5 Hooke’s Law for Plane Stress 575 7.6 Triaxial Stress 580 7.7 Plane Strain 584 Chapter Summary & Review 600 Problems 602 8 Applications of Plane Stress (Pressure Vessels, Beams, and Combined Loadings) 618 8.1 Introduction 621 8.2 Spherical Pressure Vessels 621 8.3 Cylindrical Pressure Vessels 627 8.4 Maximum Stresses in Beams 635 8.5 Combined Loadings 645 Chapter Summary & Review 661 Problems 663 CONTENTS v ★★ Advanced topics
i CONTENTS 9 Deflections of Beams 676 9.1 Introduction 679 9.2 Differential Equations of the Deflection Curve 679 93 Deflections by Integration of the Bending-Moment Equation 685 9.4 Deflections by Integration of the Shear-Force and Load Equations 696 9.5 Method of Superposition 702 9.6 Moment-Area Method 711 9.7 Nonprismatic Beams 720 9.8 Strain Energy of Bending 725 ★*9.9 Castigliano's Theorem 731 ★★9.10 Deflections Produced by Impact 744 *9.11 Temperature Effects 746 Chapter Summary Review 749 Problems 751 10 Statically Indeterminate Beams 770 10.1 Introduction 773 10.2 Types of Statically Indeterminate Beams 773 10.3 Analysis by the Differential Equations of the Deflection Curve 777 10.4 Method of Superposition 784 **10.5 Temperature Effects 797 ★*10.6 Longitudinal Displacements at the Ends of a Beam 801 Chapter Summary Review 805 Problems 806 11 Columns 816 11.1 Introduction 819 11.2 Buckling and Stability 819 113 Columns with Pinned Ends 823 11.4 Columns with Other Support Conditions 834 11.5 Columns with Eccentric Axial Loads 845 11.6 The Secant Formula for Columns 850 11.7 Elastic and Inelastic Column Behavior 856 ★★Advanced topics
9 Deflections of Beams 676 9.1 Introduction 679 9.2 Differential Equations of the Deflection Curve 679 9.3 Deflections by Integration of the Bending-Moment Equation 685 9.4 Deflections by Integration of the Shear-Force and Load Equations 696 9.5 Method of Superposition 702 9.6 Moment-Area Method 711 9.7 Nonprismatic Beams 720 9.8 Strain Energy of Bending 725 ★★9.9 Castigliano’s Theorem 731 ★★9.10 Deflections Produced by Impact 744 ★★9.11 Temperature Effects 746 Chapter Summary & Review 749 Problems 751 10 Statically Indeterminate Beams 770 10.1 Introduction 773 10.2 Types of Statically Indeterminate Beams 773 10.3 Analysis by the Differential Equations of the Deflection Curve 777 10.4 Method of Superposition 784 ★★10.5 Temperature Effects 797 ★★10.6 Longitudinal Displacements at the Ends of a Beam 801 Chapter Summary & Review 805 Problems 806 11 Columns 816 11.1 Introduction 819 11.2 Buckling and Stability 819 11.3 Columns with Pinned Ends 823 11.4 Columns with Other Support Conditions 834 11.5 Columns with Eccentric Axial Loads 845 11.6 The Secant Formula for Columns 850 11.7 Elastic and Inelastic Column Behavior 856 vi CONTENTS ★★ Advanced topics
CONTENTS vii 11.8 Inelastic Buckling 858 11.9 Design Formulas for Columns 863 Chapter Summary Review 882 Problems 883 12 Review of Centroids and Moments of Inertia 900 12.1 Introduction 902 12.2 Centroids of Plane Areas 902 12.3 Centroids of Composite Areas 905 12.4 Moments of Inertia of Plane Areas 909 12.5 Parallel-Axis Theorem for Moments of Inertia 912 12.6 Polar Moments of Inertia 916 12.7 Products of Inertia 918 12.8 Rotation of Axes 921 12.9 Principal Axes and Principal Moments of Inertia 923 Problems 927 References and Historical Notes 935 Appendix A Systems of Units and Conversion Factors 943 A.1 Systems of Units 943 A.2 SI Units 944 A.3 U.S.Customary Units 951 A.4 Temperature Units 952 A.5 Conversions Between Units 953 Appendix B Problem Solving 956 B.1 Types of Problems 956 B.2 Steps in Solving Problems 957 B.3 Dimensional Homogeneity 958 B.4 Significant Digits 959 B.5 Rounding of Numbers 961 Appendix C Mathematical Formulas 962 Appendix D Properties of Plane Areas 966 Appendix E Properties of Structural-Steel Shapes 972
11.8 Inelastic Buckling 858 11.9 Design Formulas for Columns 863 Chapter Summary & Review 882 Problems 883 12 Review of Centroids and Moments of Inertia 900 12.1 Introduction 902 12.2 Centroids of Plane Areas 902 12.3 Centroids of Composite Areas 905 12.4 Moments of Inertia of Plane Areas 909 12.5 Parallel-Axis Theorem for Moments of Inertia 912 12.6 Polar Moments of Inertia 916 12.7 Products of Inertia 918 12.8 Rotation of Axes 921 12.9 Principal Axes and Principal Moments of Inertia 923 Problems 927 References and Historical Notes 935 Appendix A Systems of Units and Conversion Factors 943 A.1 Systems of Units 943 A.2 SI Units 944 A.3 U.S. Customary Units 951 A.4 Temperature Units 952 A.5 Conversions Between Units 953 Appendix B Problem Solving 956 B.1 Types of Problems 956 B.2 Steps in Solving Problems 957 B.3 Dimensional Homogeneity 958 B.4 Significant Digits 959 B.5 Rounding of Numbers 961 Appendix C Mathematical Formulas 962 Appendix D Properties of Plane Areas 966 Appendix E Properties of Structural-Steel Shapes 972 CONTENTS vii
viii CONTENTS Appendix F Properties of Structural Lumber 983 Appendix G Deflections and Slopes of Beams 984 Appendix H Properties of Materials 990 Answers to Problems 995 Name Index 1016 Subject Index 1017
Appendix F Properties of Structural Lumber 983 Appendix G Deflections and Slopes of Beams 984 Appendix H Properties of Materials 990 Answers to Problems 995 Name Index 1016 Subject Index 1017 viii CONTENTS
