' Fourth Edition in Sl Units MECHANICS OF MATERIAtS · FERDINAND P. BEER Late of Lehigh University E. RUSSELL JOHNSTON, JR. University of Connecticut JOHN T.
DEWOLF University of Connecticut R Higher Education Boston Burr Ridge, IL Dubuque, lA Madison, WI New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Santiagq Seoul Singapore Sydney Taipei Toronto __ /,' I rl:._I I ·'-)_C ,·( '\ The McGraw·Hillcompanles :,?' ;;:., • MECHANICS OF MATERIALS Fourth Edition in SI Units Publication Year: 2006 Exclusive rights by McGraw-Hill Education (Asia), for manufacture and export. This book cannot be re- :::xported from the country to which it is sold by McGraw-HilL Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright© 2006,2001, 1992, 1981 by The McGraw-Hiii Companies, [nc.
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10 09 08 07 06 05 20 09 08 07 IT CTF SLP When ordering this title, use ISBN 007-U4999-0 Printed in Singapore About the Authors As publishers of the books written by Ferd Beer and Russ Johnston, we are often asked how did they happen to write the books together, with one of them at Lehigh and the other at the University of Connecticut. The answer to this question is simple. Russ Johnston's first teach- ing ·appointment was in the Department of Civil Engineering and Mechanics at Lehigh University. There he met Ferd Beer, who had joined that department two years earlier and was in charge of the courses in mechanics.
Born in France and educated in France and Switzerland (he held an M. degree from the Sorbonne and an Sc. degree in the field of theoretical mechanics from the University of Geneva), Ferd had come to the United States after serving in the French army during the early part of World War II and had taught for four years at Williams College in the Williams¥ MIT joint arts and engineering program. Born in Philadelphia, Russ had obtained a B.
degree in civil engineering from the University of Delaware and an Sc. degree in the field of structural engineering from MIT. Ferd was delighted to discover that the young man who had been hired chiefly to teach graduate structural engineering courses was not only willing but eager to help him reorganize the mechanics courses. Both believed that these courses should be taught from a few basic prin- ciples and that the various concepts involved would be best understood and remembered by the students if they were presented to them in a graphic way.
Together they wrote lecture notes in statics and dynam- ics, to which they later added problems they felt would appeal to fu- ture engineers, and soon they produced the manuscript of the first edi- tion of Mechanics for Engineers. The second edition of Mechanics for Engineers and the first edition of Vector Mechanics for Engineers found Russ Johnston at Worcester Polytechnic Institute and the next editions at the University of Connecticut. In the meantime, both Ferd and Russ had assumed administrative responsibilities in their departments, and both were involved in research, consulting, and supervising graduate students-Ferd in the area of stochastic processes and random vibra- tions, and Russ in the area of elastic stability and structural analysis and design. However, their interest in improving the teaching of the basic mechanics courses had not subsided, and they both taught sections of these courses as they kept revising their texts and began v .ut the Authors writing together the manuscript of the first edition of Mechanics of Materials.
Ferd and Russ's contributions to engineering education earned them a number of honors and awards. They were presented with the West~ em Electric Fund Award for excellence in the instruction of engineer~ ing students by their respective regional sections of the American So- ciety for Engineering Education, and they both received the Distinguished Educator Award from the Mechanics Division of the same society. In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engi- neers, and in 1995 Ferd was awarded an honorary Doctor of Engineer~ ing degree by Lehigh University. DeWolf, Professor of Civil Engineering at the University of Connecticut, joined the Beer and Johnston team as an author on the second edition of Mechanics of Materials.
degree in civil engineering from the University of Hawaii and M. degrees in structural engineering from Cornell University. His research interests are in the area of elastic stability, bridge monitoring, and struc- tural analysis and design. He is a member of the Connecticut Board of Examiners for Professional Engineers.
Contents Preface XIII list of Symbols xix 1 INTRODUCTION-CONCEPT OF STRESS 2 1.2 A Short Review of the Methods of Statics 2 1.3 Stresses in the Members of a Structure 5 1.4 Analysis and Design 6 1.5 Axial Loading; Normal Stress 7 1.7 Bearing Stress in Connections 11 1.8 Application to the Analysis and Design of Simple Structures 12 1.9 Method of Problem Solution 14 1.11 Stress on an Oblique Plane under Axial Loading 23 1.12 Stress under General Loading Conditions; Components of Stress 24 1.13 Design Considerations 27 Review and Summary for Chapter 1 38 2 STRESS AND STRAIN-AXIAL LOADING 47 2.2 Normal Strain under Axial Loading 48 2.3 Stress-Strain Diagram 50 '2.4 True Stress and True Strain 55 2.5 Hooke's Law; Modulus of Elasticity 56 2.6 Elastic versus Plastic Behavior of a Material 57 vii mtents 2.7 Repeated Loadings; Fatigue 59 2.8 Deformations of Members under Axial Loading 61 .9 Statically Indeterminate Problems 70 2.10 Problems Involving Temperature Changes 74 2. f2·-Multiaxial Loi!djng_; (3er:>erall~e>LJ:iooke's Law 85 *2;13··· Dilatation; Bulk .15 Further Discussion of Deformations under Axial Loading; Relation among E, v, and G 92 ,_*2~ 16" Stress-Strain Relationships for Fiber-Reinforced Composite Materials 95 2.17 Stress and Strain Distribution under Axial Loading; Saint-Venant's Principle 104 2.20 Residual Stresses 113 Review and Summary for Chapter 2 121 3 TORSION 132 3.2 Preliminary Discussion of the Stresses in a Shaft 134 3.3 Deformations in a Circular Shaft 136 3.4 Stresses in the Elastic Range 139 3.5 Angle of Twist in the Elastic Range 150 ~1:-,r ,"'(~~ Statically Indeterminate Shafts 153 -~-Y.8 Stress Concentrations in Circular Shafts 167 *3.9 Plastic Deformations in Circular Shafts 172 *3.10 Circular Shafts Made of an Elastoplastic Material 174 *3.11 Residual Stresses in Circular Shafts 177 *3.12 Torsion of Noncircular Members 186 ·3.13 Thin-Walled Hollow Shafts 189 Review and Summary for Chapter 3 198 4 PURE BENDING 209 4.2 Symmetric Member in Pure Bending 211 4.3 Deformations in a Symmetric Member in Pure Bending 213 4.4 Stresses and Deformations in the Elastic Range 216 4.5 Deformations in a Transverse Cross Section 220 Contents ix 4.6 Bending of Members Made of Several Materials 230 4.·9 Members Made of an Elastoplastic Material 246 *4.10 Plastic Deformations of Members with a S'1ngle Plane of Symmetry 250 *4.12 Eccentric Axial Loading in a Plane of Symmetry 260 4.14 General Case of Eccentric Axial Loading 276 ·4.15 Bending of Curved Members 285 Review and Summary for Chapter 4 298 5 ANALYSIS AND DESIGN OF BEAMS FOR BENDING 308 5.2 Shear and Bending-Moment Diagrams 311 5.3 Relations among Load, Shear, and Bending Moment 322 5.4 Design of Prismatic Beams for Bending 332 •5.5 Using Singularity Functions to Determine Shear and Bending Moment in a Beam 343 •5.6 Nonprismatic Beams 354 Review and Summary for Chapter 5 363 6 SHEARING STRESSES IN BEAMS AND THIN-WALLED MEMBERS 372 6.2 Shear on the Horizontal Face of a Beam Element 374 6.3 Determination of the Shearing Stresses in a Beam 376 6.4 Shearing Stresses T, in Common Types of Beams 377 *6.5 Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam 380 6.6 Longitudinal Shear on a Beam Element of Arbitrary Shape 388 6.7 Shearing Stresses in Thin-Walled Members 390 *6.9 Unsymmetric Loading of Thin-Walled Members; Shear Center 402 Review and Summary for Chapter 6 414 ents 1 TRANSFORMATIONS OF STRESS AND STRAIN 423 7.2 Transformation of Plane Stress 425 7.3 Principal Stresses: Maximum Shearing Stress 428 7.4 Mohr's Circle for Plane Stress 436 7.5 General State of Stress 446 7.6 Application of Mohr's Circle to the Three-Dimensional Analysis of Stress 448 *7.7 Yield Criteria for Ductile Materials under Plane Stress 451 *7.8 Fracture Criteria for Brittle Materials under Plane Stress 453 7.9 Stresses in Thin-Walled Pressure Vessels 462 ·7.10 Transformation of Plane Strain 470 *7.11 Mohr's Circle for Plane Strain 473 *7.12 Three-Dimensional Analysis of Strain 475 ·7.13 Measurements of Strain; Strain Rosette 478 Review and Summary for Chapter 7 486 8 PRINCIPAL STRESSES UNDER A GIVEN LOADING 496 *8.2 Principal Stresses in a Beam 497 *8.3 Design of Transmission Shafts 500 *8.4 Stresses under Combined Loadings 508 Review and Summary for Chapter 8 521 9 DEFLECTION OF BEAMS 530 9.2 Deformation of a Beam under Transverse Loading 532 9.3 Equation of the Elastic Curve 533 *9.4 Direct Determination of the Elastic Curve from the Load Distribution 538 9.5 Statically Indeterminate Beams 540 *9.6 Using Singularity Functions to Determine the Slope and Deflection of a Beam 549 9.7 Method of Superposition 558 9.8 Application of Superposition to Statically Contents xi Indeterminate Beams 560 *9.9 Moment-Area Theorems 569 *9.10 Application to Cantilever Beams and Beams with Symmetric Loading 571 *9.11 Bending-Moment Diagrams by Parts 573 *9.12 Application of Moment-Area Theorems to Beams with Unsymmetric Loadings 582 *9.14 Use of Moment-Area Theorems with Statically Indeterminate Beams 586 Review and Summary for Chapter 9 594 10 COLUMNS 607 10.2 Stability of Structures 608 10.3 Euler's Formula for Pin-Ended Columns 610 10.4 Extension of Euler's Formula to Columns with Other End Conditions 614 •1o.s Eccentric Loading; the Secant Formula 625 10.6 Design of Columns under a Centric Load 636 10.7 Design of Columns under an Eccentric Load 652 Review and Summary for Chapter 10 662 11 ENERGY METHODS 670 11.3 Strain-Energy Density 672 11.4 Elastic Strain Energy for Normal Stresses 674 11.5 Elastic Strain Energy for Shearing Stresses 677 *11.6 Strain Energy for a General State of Stress 680 11.8 Design for Impact Loads 695 11.9 Work and Energy under a Single Load 696 11.10 Deflection under a Single Load by the Work-Energy Method 698 .11 Work and Energy under Several Loads 709 .13 Deflections by Castigliano's Theorem 712 .14 Statically Indeterminate Structures 716 Review and Summary for Chapter 11 726 mtents APPENDICES 735 A Moments of Areas 736 B Typical Properties of Selected Materials Used in Engineering 746 c Properties of Rolled-Steel Shapes 750 D Beam Deflections and Slopes 762 E Fundamentals of Engineering Examination 763 Photo Credits 757 Index 759 Answers to Problems 768 PREFACE OBJECTIVES The main objective of a basic mechanics course should be to develop in. the engineering student the ability to analyze a given problem in a simple and logical manner and to apply to its solution a few fundamental and well"understood principles. This text is designed for the first course in me- chanics of materials-or strength of materials-offered to enginee1ing stu- dents in the sophomore or junior year.
The authors hope that it will help instmctors achieve this goal in that particular course in the same way that their other texts may have helped them in statics and dynamics. GENERAL APPROACH In this text the study of the mechanics of materials is based on the understanding of a few basic concepts and on the use of simplified models.