Seventh Edition Mechanics of Materials Ferdinand P. Beer Late of Lehigh University E. Russell Johnston, Jr. Late of University of Connecticut John T.
DeWolf University of Connecticut David F. Mazurek United States Coast Guard Academy MECHANICS OF MATERIALS, SEVENTH EDITION Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2015 by McGraw-Hill Education. All rights reserved.
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The photo on the cover shows the steel sculpture “Venture” by Alex Liberman (1912-1999) in front of the Bank of America Building in Dallas, Texas. The building is supported by a combination of structural steel and reinforced concrete. Library of Congress Cataloging-in-Publication Data on File The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.com About the Authors John T.
DeWolf, Professor of Civil Engineering at the University of Con- necticut, joined the Beer and Johnston team as an author on the second edition of Mechanics of Materials. degree in civil engi- neering from the University of Hawaii and M. degrees in structural engineering from Cornell University. He is a Fellow of the Amer- ican Society of Civil Engineers and a member of the Connecticut Academy of Science and Engineering.
He is a registered Professional Engineer and a member of the Connecticut Board of Professional Engineers. He was selected as a University of Connecticut Teaching Fellow in 2006. Profes- sional interests include elastic stability, bridge monitoring, and structural analysis and design. Mazurek, Professor of Civil Engineering at the United States Coast Guard Academy, joined the Beer and Johnston team as an author on the fifth edition.
degree in ocean engineering and an M. degree in civil engineering from the Florida Institute of Technol- ogy, and a Ph. degree in civil engineering from the University of Con- necticut. He is a registered Professional Engineer.
He has served on the American Railway Engineering & Maintenance of Way Association’s Com- mittee 15—Steel Structures since 1991. He is a Fellow of the American Society of Civil Engineers, and was elected into the Connecticut Academy of Science and Engineering in 2013. Professional interests include bridge engineering, structural forensics, and blast-resistant design. iii Contents Preface ix Guided Tour xiii List of Symbols xv 1 Introduction—Concept of Stress 3 1.1 Review of The Methods of Statics 4 1.2 Stresses in the Members of a Structure 7 1.3 Stress on an Oblique Plane Under Axial Loading 27 1.4 Stress Under General Loading Conditions; Components of Stress 28 1.5 Design Considerations 31 Review and Summary 44 2 Stress and Strain—Axial Loading 55 2.1 An Introduction to Stress and Strain 57 2.2 Statically Indeterminate Problems 78 2.3 Problems Involving Temperature Changes 82 2.5 Multiaxial Loading: Generalized Hooke’s Law 95 *2.6 Dilatation and Bulk Modulus 97 2.8 Deformations Under Axial Loading—Relation Between E, n, and G 102 *2.9 Stress-Strain Relationships For Fiber-Reinforced Composite Materials 104 2.10 Stress and Strain Distribution Under Axial Loading: Saint- Venant’s Principle 115 2.13 Residual Stresses 123 Review and Summary 133 *Advanced or specialty topics iv Contents v 3 Torsion 147 3.1 Circular Shafts in Torsion 150 3.2 Angle of Twist in the Elastic Range 167 3.3 Statically Indeterminate Shafts 170 3.4 Design of Transmission Shafts 185 3.5 Stress Concentrations in Circular Shafts 187 *3.6 Plastic Deformations in Circular Shafts 195 *3.7 Circular Shafts Made of an Elastoplastic Material 196 *3.8 Residual Stresses in Circular Shafts 199 *3.9 Torsion of Noncircular Members 209 *3.10 Thin-Walled Hollow Shafts 211 Review and Summary 223 4 Pure Bending 237 4.1 Symmetric Members in Pure Bending 240 4.2 Stresses and Deformations in the Elastic Range 244 4.3 Deformations in a Transverse Cross Section 248 4.4 Members Made of Composite Materials 259 4.7 Eccentric Axial Loading in a Plane of Symmetry 291 4.8 Unsymmetric Bending Analysis 302 4.9 General Case of Eccentric Axial Loading Analysis 307 *4.10 Curved Members 319 Review and Summary 334 5 Analysis and Design of Beams for Bending 345 5.1 Shear and Bending-Moment Diagrams 348 5.2 Relationships Between Load, Shear, and Bending Moment 360 5.3 Design of Prismatic Beams for Bending 371 *5.4 Singularity Functions Used to Determine Shear and Bending Moment 383 *5.5 Nonprismatic Beams 396 Review and Summary 407 vi Contents 6 Shearing Stresses in Beams and Thin-Walled Members 417 6.1 Horizontal Shearing Stress in Beams 420 *6.2 Distribution of Stresses in a Narrow Rectangular Beam 426 6.3 Longitudinal Shear on a Beam Element of Arbitrary Shape 437 6.4 Shearing Stresses in Thin-Walled Members 439 *6.6 Unsymmetric Loading of Thin-Walled Members and Shear Center 454 Review and Summary 467 7 Transformations Strain 477 of Stress and 7.1 Transformation of Plane Stress 480 7.2 Mohr’s Circle for Plane Stress 492 7.3 General State of Stress 503 7.4 Three-Dimensional Analysis of Stress 504 *7.5 Theories of Failure 507 7.6 Stresses in Thin-Walled Pressure Vessels 520 *7.7 Transformation of Plane Strain 529 *7.8 Three-Dimensional Analysis of Strain 534 *7.9 Measurements of Strain; Strain Rosette 538 Review and Summary 546 8 Principal Stresses Under a Given Loading 557 8.1 Principal Stresses in a Beam 559 8.2 Design of Transmission Shafts 562 8.3 Stresses Under Combined Loads 575 Review and Summary 591 Contents vii 9 Deflection of Beams 599 9.1 Deformation Under Transverse Loading 602 9.2 Statically Indeterminate Beams 611 *9.3 Singularity Functions to Determine Slope and Deflection 623 9.4 Method of Superposition 635 *9.5 Moment-Area Theorems 649 *9.6 Moment-Area Theorems Applied to Beams with Unsymmetric Loadings 664 Review and Summary 679 10 Columns 691 10.1 Stability of Structures 692 *10.2 Eccentric Loading and the Secant Formula 709 10.3 Centric Load Design 722 10.4 Eccentric Load Design 739 Review and Summary 750 11 Energy Methods 759 11.2 Elastic Strain Energy 763 11.3 Strain Energy for a General State of Stress 770 11.8 Deflections by Castigliano’s Theorem 806 *11.9 Statically Indeterminate Structures 810 Review and Summary 823 viii Contents Appendices A1 A Moments of Areas A2 B Typical Properties of Selected Materials Used in Engineering A13 C Properties of Rolled-Steel Shapes A17 D Beam Deflections and Slopes A29 E Fundamentals of Engineering Examination A30 Answers to Problems AN1 Photo Credits C1 Index I1 Preface Objectives The main objective of a basic mechanics course should be to develop in the engineering stu- dent 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 mechanics of materials—or strength of materials—offered to engineering students in the sophomore or junior year. The authors hope that it will help instructors achieve this goal in that particular course in the same way that their other texts may have helped them in statics and dynamics. To assist in this goal, the seventh edition has undergone a complete edit of the language to make the book easier to read. 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.
This approach makes it possible to develop all the necessary formulas in a rational and logical manner, and to indicate clearly the conditions under which they can be safely applied to the analysis and design of actual engineering struc- tures and machine components. Free-body Diagrams Are Used Extensively. Throughout the text free-body diagrams are used to determine external or internal forces. The use of “picture equations” will also help the students understand the superposition of loadings and the resulting stresses and deformations.
The SMART Problem-Solving Methodology is Employed. New to this edition of the text, students are introduced to the SMART approach for solving engineering problems, whose acronym reflects the solution steps of Strategy, Modeling, Analysis, and Reflect & T hink. This methodology is used in all Sample Problems, and it is intended that students will apply this approach in the solution of all assigned problems. Design Concepts Are Discussed Throughout the Text Whenever Appropriate.
A dis- cussion of the application of the factor of safety to design can be found in Chap. 1, where the concepts of both allowable stress design and load and resistance factor design are presented. A Careful Balance Between SI and U. Customary Units Is Consistently Main- tained.
Because it is essential that students be able to handle effectively both SI metric units and U. customary units, half the concept applications, sample problems, and problems to be assigned have been stated in SI units and half in U. Since a large number of problems are available, instructors can assign problems using each system of units in what- ever proportion they find desirable for their class. Optional Sections Offer Advanced or Specialty Topics.
Topics such as residual stresses, torsion of noncircular and thin-walled members, bending of curved beams, shearing stresses in non-symmetrical members, and failure criteria have been included in optional sections for use in courses of varying emphases. To preserve the integrity of the subject, these topics are presented in the proper sequence, wherever they logically belong. Thus, even when not ix x Preface covered in the course, these sections are highly visible and can be easily referred to by the students if needed in a later course or in engineering practice. For convenience all optional sections have been indicated by asterisks.
Chapter Organization It is expected that students using this text will have completed a course in statics. 1 is designed to provide them with an opportunity to review the concepts learned in that course, while shear and bending-moment diagrams are covered in detail in Secs. The properties of moments and centroids of areas are described in Appendix A; this material can be used to reinforce the discussion of the determination of normal and shearing stresses in beams (Chaps. The first four chapters of the text are devoted to the analysis of the stresses and of the corresponding deformations in various structural members, considering successively axial load- ing, torsion, and pure bending.
Each analysis is based on a few basic concepts: namely, the conditions of equilibrium of the forces exerted on the member, the relations existing between stress and strain in the material, and the conditions imposed by the supports and loading of the member. The study of each type of loading is complemented by a large number of concept applications, sample problems, and problems to be assigned, all designed to strengthen the students’ understanding of the subject. The concept of stress at a point is introduced in Chap.