Apago PDF Enhancer This page intentionally left blank Apago PDF Enhancer Mechanics of Materials Apago PDF Enhancer Vice President and Editorial Director, ECS: Marcia J. Horton Acquisitions Editor: Norrin Dias Vice-President, Production: Vince O’Brien VP/Director of Marketing: Patrice Jones Executive Marketing Manager: Tim Galligan Marketing Assistant: Jon Bryant Senior Managing Editor: Scott Disanno Production Project Manager: Clare Romeo Operations Specialist: Lisa McDowell Associate Director of Design: Blair Brown Cover Designer: Blair Brown Interior Design: Blair Brown, Paul S. Steif Manager, Rights and Permissions: Beth Brenzel Image Permission Coordinator: Karen Sanatar Composition: MPS Limited, a Macmillan Company Project Management Liaison: Anoop Chaturvedi Printer/Binder: Courier Kendalville Typeface: 9/11 Times Roman Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Copyright © 2012 by Pearson Higher Education, Inc., Upper Saddle River, NJ 07458.
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Pearson Education—Japan Pearson Education Australia PTY, Limited Pearson Education North Asia, Ltd., Hong Kong Pearson Educación de Mexico, S. Pearson Education Malaysia, Pte. Pearson Education, Inc., Upper Saddle River, New Jersey Library of Congress Cataloging-in-Publication Data on File 10 9 8 7 6 5 4 3 2 1 ISBN-13: 978-0-13-220334-0 ISBN-10: 0-13-220334-0 Mechanics of Materials Apago PDF Enhancer Paul S. Steif Carnegie Mellon University This page intentionally left blank Apago PDF Enhancer Visual Contents INTRODUCTION Chapter 1.
Design of products, systems, and structures demands the engineer to consider a broad range of issues. The issues addressed by Mechanics of Materials are excessive deformation and material failure. A few general principles enable us to design against excessive deformation and failure for a wide range of part geometries, materials, and loadings. We consider the body to be composed of elements, we study common deformation modes, and we combine contributions of each deformation mode, as needed, to assess deformation and failure.
Body Composed Common Design Against of Elements Deformation Modes Chapter 2. Axial Force and Excessive Deformation in Deformations an Element Apago PDFChapterEnhancer 4. Material Failure Chapter 5. Buckling Unit 1 Unit 2 Unit 3 VISUAL CONTENTS | v Contents Unit 2 Common Deformation Modes Preface viii 3 To the Student (pg.
viii) To the Instructor (pg. viii) Axial Loading 84 Resources for Instructors (pg.1 Internal Force–Deformation–Displacement (pg. 86) Resources for Students (pg.2 Varying Internal Force (pg.3 Systems of Axially Loaded Members (pg. 100) About the Author (pg.4 Statically Indeterminate Structures (pg.5 Thermal Effects (pg.6 Wrapped Cables, Rings, and Bands (pg.1 Why Study Mechanics of Materials? Torsion 136 (pg.2 How Mechanics of Materials Predicts 4.
138) Deformation and Failure (pg.2 Shear Strain in Circular Shafts (pg.3 Review of Statics—Forces, Subsystems, 4.3 Application and Transmission and Free Body Diagrams (pg. 8) of Torque (pg.4 Review of Statics—Representing Force 4.4 Shear Stress in Circular Shafts (pg. 150) Interactions Simply (pg.5 Strength and Stiffness (pg.5 Review of Statics—Conditions of Equilibrium 4.6 Dependence of Stiffness and Strength on Shaft (pg.6 Road Map of Book (pg.7 General Guidelines for Torsional Stiffness Apago PDF Enhancer of Non-Circular Cross-Sections (pg.8 Torsion of Shafts with Rectangular Cross-Sections (pg.10 Torsion of Shafts with Thin-Walled Cross-Sections (pg. 178) Shafts with Non-Uniform Twisting Along Their Body Composed of Elements Lengths (pg.11 Internal Torque and the Relation to Twist and Stress (pg.12 Relation Between Senses and Signs of Internal Torque,Twist, and Stress (pg.13 Shafts with Varying Cross-Sections (pg.
192) Internal Force, Stress, 4.14 Statically Indeterminate Structures Subjected and Strain 18 4.15 to Torsion (pg. 202) Power-Torque-Speed Relations for Rotating Shafts (pg.2 Internal Force (pg.3 Normal Stress (pg.5 Normal Strain (pg. 40) Measuring Stress and Strain (pg.6 Elastic Behavior of Materials (pg.7 Failure and Allowable Limit on Stress Bending 218 (pg.8 Variety of Stress–Strain Response (A) Shear Forces and Bending Moments (pg.1 Deformation in Bending (pg.9 Shear Strain and Shear Stress (pg.2 Beams, Loads, and Supports (pg.10 Shear and Bearing Stress in Pin Joints 5.3 Internal Loads in Beams (pg.4 Internal Loads by Isolating Segments (pg.5 Variation of Internal Loads with Applied Loads (pg. 232) vi | C O N T E N T S (B) Stresses Due to Bending Moments 7.7 Failure for Stresses in 3-D (pg.6 Strain Distribution in Bending (pg.8 2-D Strain Transformations and Strain 5.7 Stresses in Bending (pg.8 Bending Equations (pg.9 Bending of Composite Cross-Sections (pg.10 Stress Concentrations (pg.10 Bending Stresses Under a Non-Uniform Bending Moment (pg.12 Dependence of Stiffness and Strength on Cross-Section (pg.
290) Bending of a Beam Composed of Multiple 8 Layers (pg.13 Bending of General (Non-Symmetric) Cross-Sections (pg.1 Buckling of Axially Loaded, Simply Supported (C) Stresses Due to Shear Forces Members (pg.14 Transverse Shear Stress (pg.2 Buckling of Axially Loaded Members—Alternative 5.15 Shear Flow—Thin-Walled and Built-Up Support Conditions (pg. 484) Cross-Sections (pg.3 Design Equations for Axial Compression (pg. 486) (D) Deflections Due to Bending Moments 5.16 Deflections Related to Internal Loads (pg.17 Deflections Using Tabulated Solutions (pg.18 Simple Generalizations of Tabulated Solutions (pg. Focused Applications for Problems (pg.19 Complex Generalizations of Tabulated A-1 Bicycles (pg.
344) A-2 Cable-Stayed Bridges (pg.20 Statically Indeterminate Structures Subjected A-3 Drilling (pg. 506) to Bending (pg. 354) A-4 Exercise Equipment (pg. 508) A-5 Fracture Fixation (pg.
510) A-6 Wind Turbines (pg. Theory of Properties of Areas (pg. 514) B-1 Centroid and Second Moment of Inertia (pg. 514) B-2 Products of Inertia and Principal Axes of Inertia Design Against (pg.
516) Apago PDF Enhancer C. Tabulated Properties of Areas (pg. Material Properties (pg. Geometric Properties of Structural Shapes (pg.
Wood Structural Member Properties (pg. Tabulated Beam Deflections (pg. 536) G-1 Deflections and Slopes of Cantilever Beams 6.1 Determining Internal Loads (pg.2 Drawing Stresses on 3-D Elements (pg. 372) G-2 Deflections and Slopes of Simply Supported Beams 6.3 Pressure Vessels (pg.4 Elastic Stress–Strain Relations (pg.
Stress Concentration Factors (pg.5 Deflections Under Combined Internal Loads I. Advanced Methods and Derivations (pg. 392) I-1 Shear Stress and Twist in Thin-Walled Shaft 6.6 Strain Energy (pg. 398) Subjected to Torsion (pg.7 Solving Problems Using Conservation I-2 Method of Singularity Functions (pg.
544) of Energy (pg. 400) I-3 Derivation of Stress Transformation Formulas (pg. 548) I-4 Derivation of Equations for Maximum Normal 7 and Shear Stress (pg. 549) Stress Transformations Answers to Selected and Failure 412 Problems 552 7.1 Goal of Chapter, and Strain is in the Eye of the Beholder (pg.2 Defining Stresses on General Surfaces (pg.3 Stress Transformation Formulas (pg.4 Maximum and Minimum Stresses (pg.5 Mohr’s Circle (pg.6 Failure Criteria (pg.
446) CONTENTS | vii Preface To the Student This book introduces you to an exciting subject of immense application: how the forces acting on a material relate to its deformation and failure. The range of technologies that rely on insights from Mechanics of Materials is vast. They span applications that have seen continual innovation and refinement over many years, such as aerospace structures and propulsion, bridge design, automotive technologies, and prosthetic devices. And, Mechan- ics of Materials underlies applications that were scarcely imaginable a few years ago: atomic force microscopes, micro-scale robotics, wireless sensors for structural monitoring, and engineered biological tissues.
Mechanics of Materials can be satisfying in another more personal way. It helps us make sense of countless interactions that we have with everyday artifacts: why some are too flimsy, too rigid, or prone to break at certain points. It is likely you are studying this subject because it is required for your major. But you may have multiple goals: to pass the course or get a good grade, to be intellectually engaged and exercise your mind and curiosity, and to learn something that you can use in later courses or in life outside your courses.
Every one of those goals points you in the same direction— to genuinely learn the subject. That means gaining a physical and intuitive feel for its ideas, seeing the big picture, and fitting the ideas together. By just thumbing through this book, you will know it is different from most books you have seen. Let me tell you how the arrangement of this book might help you learn.
We can only communicate the ideas of Mechanics of Materials with a combination of words, diagrams, and equations. The equation might be necessary to get a quantitative answer or to judge a trend; for example, should a part be thicker or thinner, longer or shorter. But, in real life you are rarely handed the right equations. Someone explains a situation to you with words and diagrams, and you need to make sense of it.
Only after you have thought Apago PDF Enhancer about the words and the diagrams, might you see an equation as useful. For this reason, I have tried to write a book in which words, diagrams, and equations are in balance. In addition, I have laid out this book so the words, diagrams, and equations are near each other on the page to better help you solidify the ideas. You might also notice a high degree of organization.
Each chapter is a series of two-page spreads or sections, with each section dedicated to developing one idea or concept. Further, each two-page spread consists of subsections that break the idea into bite-size pieces. Not only do we break this subject apart for you, we help you put it back together. The Chapter Opener presents the major ideas of the chapter in diagrams and words.
At the end of each chapter, we summarize its sections, including the major equations, concepts, and key terms. Finally, Chapters 2 through 8 are grouped into 3 units that capture the overall structure of the subject. You might also notice many everyday objects depicted on the pages. Familiar, everyday objects can often illustrate the ideas of Mechanics of Materials.
To genuinely learn this subject, the ideas must ultimately make sense to you. But you are more likely to make sense of new ideas if you see them first in a familiar context. This book tries to take situations that you can already picture, and reframe them in more general, powerful ways. I hope you come to rely on those general ideas and wield them effectively as you explore new applications unimagined today.
To the Instructor I wrote this book because I love to help other people understand mechanics. I have taught this subject for many years, and I still get excited when I come upon a new way of explain- ing or illustrating some concept. Often, I bring an object into class—a bungee cord, a pool noodle, a ruler—and I deform it, sometimes with students’ help. I point to the deformation, which they can see, and I ask the student helpers what they feel.
With this book, I hope to capture some of that classroom experience. viii | P R E F A C E Let me share some of the pedagogic philosophy that informs this book.
