Mechanics of Materials - Pearsoncatalogue.pearsoned.ca/assets/hip/ca/hip_ca_pearsonhighered/... · Mechanics of Materials ... 4.11 Internal Torque and the Relation to Twist and Stress

Mechanics

of

Materials

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©2012 Pearson Education, Inc., Upper Saddle River, NJ 07458. All Rights Reserved

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Mechanics of

Materials

Paul S. SteifCarnegie Mellon University

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Vice President and Editorial Director, ECS: Marcia J. HortonAcquisitions Editor: Norrin DiasVice-President, Production: Vince O’BrienDirector of Marketing: Margaret WaplesExecutive Marketing Manager: Tim GalliganMarketing Assistant: Jon BryantSenior Managing Editor: Scott DisannoProduction Project Manager: Clare RomeoOperations Specialist: Lisa McDowellAssociate Director of Design: Blair BrownCover Designer: Blair BrownManager, Rights and Permissions: Beth BrenzelImage Permission Coordinator: Karen SanatarComposition: MPS Limited, a Macmillan CompanyProject Management Liaison: Anoop ChaturvediPrinter/Binder: Courier KendalvilleTypeface: 9/11 Times Roman

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V I S U A L C O N T E N T S | v

INTRODUCTION

Chapter 1. Design of products, systems, and structures demands the engineer to considera broad range of issues. The issues addressed by Mechanics of Materials are excessivedeformation and material failure. A few general principles enable us to design againstexcessive deformation and failure for a wide range of part geometries, materials, andloadings. We consider the body to be composed of elements, we study commondeformation modes, and we combine contributions of each deformation mode, as needed,to assess deformation and failure.

Visual Contents

Common Deformation

Modes

Design AgainstBody Composed of Elements

Chapter 2. Force and

Deformation in an Element

Chapter 3. Axial

Chapter 4. Torsion

Chapter 5. Bending

Chapter 6. Excessive

Deformations

Chapter 7. Material Failure

Chapter 8. Buckling

Unit 1 Unit 2 Unit 3

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vi | C O N T E N T S

Contents

Preface viiiTo the Student (pg. viii)To the Instructor (pg. viii)Resources for Instructors (pg. ix)Resources for Students (pg. ix)Acknowledgments (pg. x)About the Author (pg. xi)

1Introduction 3

1.1 Why Study Mechanics of Materials? (pg. 4)

1.2 How Mechanics of Materials PredictsDeformation and Failure (pg. 6)

1.3 Review of Statics—Forces, Subsystems,and Free Body Diagrams (pg. 8)

1.4 Review of Statics—Representing ForceInteractions Simply (pg. 10)

1.5 Review of Statics—Conditions of Equilibrium(pg. 12)

1.6 Road Map of Book (pg. 16)

Unit 1Body Composed of Elements

2Internal Force, Stress,and Strain 18

2.1 Elements (pg. 20)2.2 Internal Force (pg. 22)2.3 Normal Stress (pg. 32)2.4 Normal Strain (pg. 40)2.5 Measuring Stress and Strain (pg. 48)2.6 Elastic Behavior of Materials (pg. 50)2.7 Failure and Allowable Limit on Stress

(pg. 58)2.8 Variety of Stress–Strain Response

(pg. 60)2.9 Shear Strain and Shear Stress (pg. 68)2.10 Shear and Bearing Stress in Pin Joints

(pg.70)

Unit 2Common Deformation Modes

3Axial Loading 84

3.1 Internal Force–Deformation–Displacement (pg.86)3.2 Varying Internal Force (pg. 92)3.3 Systems of Axially Loaded Members (pg. 100)3.4 Statically Indeterminate Structures (pg. 108)3.5 Thermal Effects (pg. 120)3.6 Wrapped Cables, Rings, and Bands (pg. 128)

4Torsion 136

4.1 Rotation (pg. 138)4.2 Shear Strain in Circular Shafts (pg. 140)4.3 Application and Transmission

of Torque (pg. 148)4.4 Shear Stress in Circular Shafts (pg. 150)4.5 Strength and Stiffness (pg. 162)4.6 Dependence of Stiffness and Strength on Shaft

Properties (pg. 164)4.7 General Guidelines for Torsional Stiffness

of Non-Circular Cross-Sections (pg. 166)4.8 Torsion of Shafts with Rectangular Cross-Sections

(pg. 176)4.9 Torsion of Shafts with Thin-Walled Cross-Sections

(pg. 178)4.10 Shafts with Non-Uniform Twisting Along Their

Lengths (pg. 186)4.11 Internal Torque and the Relation to Twist and

Stress (pg. 188)4.12 Relation Between Senses and Signs of Internal

Torque,Twist, and Stress (pg. 190)4.13 Shafts with Varying Cross-Sections (pg. 192)4.14 Statically Indeterminate Structures Subjected to

Torsion (pg. 202)4.15 Power-Torque-Speed Relations for Rotating Shafts

(pg. 210)

5Bending 218

(A) Shear Forces and Bending Moments5.1 Deformation in Bending (pg. 220)5.2 Beams, Loads, and Supports (pg. 222)5.3 Internal Loads in Beams (pg. 224)5.4 Internal Loads by Isolating Segments (pg. 226)5.5 Variation of Internal Loads with Applied Loads

(pg. 232)

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C O N T E N T S | vii

(B) Stresses Due to Bending Moments5.6 Strain Distribution in Bending (pg. 250)5.7 Stresses in Bending (pg. 252)5.8 Bending Equations (pg. 262)5.9 Bending of Composite Cross-Sections (pg. 272)5.10 Bending Stresses Under a Non-Uniform Bending

Moment (pg. 280)5.11 Dependence of Stiffness and Strength

on Cross-Section (pg. 290)5.12 Bending of a Beam Composed of Multiple

Layers (pg. 296)5.13 Bending of General (Non-Symmetric)

Cross-Sections (pg. 298)

(C) Stresses Due to Shear Forces5.14 Transverse Shear Stress (pg. 304)5.15 Shear Flow—Thin-Walled and Built-Up

Cross-Sections (pg. 310)

(D) Deflections Due to Bending Moments5.16 Deflections Related to Internal Loads (pg. 318)5.17 Deflections Using Tabulated Solutions (pg.328)5.18 Simple Generalizations of Tabulated Solutions

(pg. 332)5.19 Complex Generalizations of Tabulated Solutions

(pg. 344)5.20 Statically Indeterminate Structures Subjected to

Bending (pg. 354)

Unit 3Design Against

6Combined Loads 364

6.1 Determining Internal Loads (pg. 366)6.2 Drawing Stresses on 3-D Elements (pg. 372)6.3 Pressure Vessels (pg. 380)6.4 Elastic Stress–Strain Relations (pg. 386)6.5 Deflections Under Combined Internal Loads

(pg. 392)6.6 Strain Energy (pg. 398)6.7 Solving Problems Using Conservation of Energy

(pg. 400)

7Stress Transformations and Failure 412

7.1 Goal of Chapter, and Strain is in the Eye of the Beholder (pg. 414)

7.2 Defining Stresses on General Surfaces (pg. 416)7.3 Stress Transformation Formulas (pg. 424)7.4 Maximum and Minimum Stresses (pg. 432)7.5 Mohr’s Circle (pg. 440)

7.6 Failure Criteria (pg. 446)7.7 Failure for Stresses in 3-D (pg. 454)7.8 2-D Strain Transformations and Strain Rosettes

(pg. 460)7.9 Fatigue (pg. 466)7.10 Stress Concentrations (pg. 468)

8Buckling 480

8.1 Buckling of Axially Loaded, Simply SupportedMembers (pg. 482)

8.2 Buckling of Axially Loaded Members—AlternativeSupport Conditions (pg. 484)

8.3 Design Equations for Axial Compression (pg. 486)

AppendicesA. Focused Applications for Problems (pg. 501)

A-1 Bicycles (pg. 502)A-2 Cable-Stayed Bridges (pg. 504)A-3 Drilling (pg. 506)A-4 Exercise Equipment (pg. 508)A-5 Fracture Fixation (pg. 510)A-6 Wind Turbines (pg. 512)

B. 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

(pg. 516)C. Tabulated Properties of Areas (pg. 522)D. Material Properties (pg. 525)E. Geometric Properties of Structural Shapes (pg. 526)F. Wood Structural Member Properties (pg. 535)G. Tabulated Beam Deflections (pg. 536)

G-1 Deflections and Slopes of Cantilever BeamsG-2 Deflections and Slopes of Simply Supported Beams

H. Stress Concentration Factors (pg. 540)I. Advanced Methods and Derivations (pg. 542)

I-1 Shear Stress and Twist in Thin-Walled ShaftSubjected to Torsion

I-2 Method of Singularity FunctionsI-3 Derivation of Stress Transformation FormulasI-4 Derivation of Equations for Maximum Normal

and Shear Stress

Answers to Selected Problems 553

Key Terms 559

Index 561

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viii | P R E FAC E

Preface

To the StudentThis book introduces you to an exciting subject of immense application: how the forcesacting on a material relate to its deformation and failure. The range of technologies thatrely on insights from Mechanics of Materials is vast. They span applications that have seencontinual innovation and refinement over many years, such as aerospace structures andpropulsion, 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 anothermore personal way. It helps us make sense of countless interactions that we have witheveryday 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 mayhave multiple goals: to pass the course or get a good grade, to be intellectually engaged andexercise your mind and curiosity, and to learn something that you can use in later coursesor 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, youwill know it is different from most books you have seen. Let me tell you how thearrangement of this book might help you learn.

We can only communicate the ideas of Mechanics of Materials with a combination ofwords, diagrams, and equations. The equation might be necessary to get a quantitativeanswer 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 toyou with words and diagrams, and you need to make sense of it. Only after you have thoughtabout 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. Inaddition, I have laid out this book so the words, diagrams, and equations are near each otheron 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-pagespreads 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. Notonly do we break this subject apart for you, we help you put it back together. The ChapterOpener presents the major ideas of the chapter in diagrams and words. At the end of eachchapter, 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 ofthe subject.

You might also notice many everyday objects depicted on the pages. Familiar, everydayobjects can often illustrate the ideas of Mechanics of Materials. To genuinely learn thissubject, the ideas must ultimately make sense to you. But you are more likely to make senseof new ideas if you see them first in a familiar context. This book tries to take situations thatyou can already picture, and reframe them in more general, powerful ways. I hope you cometo rely on those general ideas and wield them effectively as you explore new applicationsunimagined today.

To the InstructorI wrote this book because I love to help other people understand mechanics. I have taughtthis 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 poolnoodle, 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 tocapture some of that classroom experience.

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P R E FAC E | ix

Let me share some of the pedagogic philosophy that informs this book. I think mostinstructors want students:

1. to understand the concepts in some intuitive way;2. to grasp the big picture, that is, to see the forest as well as the individual trees;3. to use the subject to solve problems.

First, to an intuitive understanding of concepts, there are few more important goals thanhelping students attach physical meaning to the variables and symbols we use, and to theirrelations with each other. I rarely start with the general case. Instead, I start with a simplesituation that exemplifies the idea. This helps to anchor the idea in each students’ world.Then, we build a more general mathematical representation, as we need it. Students canpicture deformation far better than they can picture forces. So, for most topics, we beginwith the deformation, to anchor the topic in reality for the students, and next we deal withthe associated forces.

To help students grasp the subject’s larger, coherent structure, we have identified the corequestion that it answers: will a body deform too much or fail (Chapter 1)? And, we havegrouped the remaining chapters into three units that delineate how this question is answered.First, we choose to view a body that deforms and may fail as composed of many small,identical pieces or elements (Chapter 2). This step is necessary to address failure, whichusually occurs locally, and to separate out the respective contributions of the body’s shapeand material to the force-deformation relations. Second, we identify three common modesof deformation: stretching, twisting, and bending, which appear repeatedly in engineeringand nature (Chapters 3–5). Each mode deserves to be studied independently, considering thedeformations and forces overall and within each element. Third, to address deformation andfailure in more general situations, we recognize the presence of these common deformationmodes, and combine their contributions appropriately (Chapters 6–8). To reinforce the bigpicture set forth in Chapter 1, the conceptual overview at the start of each chapter featuresa map that locates the chapter in the overall structure of the subject.

For good reason, the problems in a textbook are very important to most instructors. Thisbook contains problems that illustrate ideas, concepts, and procedures, as well as problemsthat demonstrate applications to real situations. Studying Mechanics of Materials can alsooffer students a chance to learn about interesting applications. To this end, I have devised anumber of problems that highlight selected focused application areas: bicycles, cable-stayedbridges, drilling of wells, exercise equipment, bone fracture fixation, and wind turbines.Focused Application Problems are sprinkled throughout the chapters. The diagram for eachsuch problem references Appendix A, in which that application is described at greaterlength. An interested student can see how the situation depicted in a single problem fits intothe overall application. For different assignments, an instructor can select problems from thesame focused application area or problems from a variety of applications.

I hope this book serves your efforts to motivate and teach your students.

Resources for Instructors• Instructor’s Solutions Manual. An instructor’s solutions manual was preparedby the author. The manual was also checked as part of the Accuracy Checking program.

• Presentation Resources. All art from the text is available in PowerPoint slideand JPEG format. These files are available for download from the Instructor ResourceCenter at www.pearsonhighered.com/steif. If you are in need of a login and password forthis site, please contact your local Pearson Prentice Hall representative.

Resources for Students• Mastering Engineering. Tutorial homework problems emulate the instructor’soffice–hour environment, guiding students through engineering concepts with self-paced individualized coaching. These in-depth tutorial homework problems aredesigned to coach students with feedback specific to their errors and optional hints thatbreak problems down into simpler steps.

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x | P R E FAC E

AcknowledgmentsPrentice Hall has been a pleasure to work with during the development of this book. I amfortunate to have had continuing guidance and encouragement from three AcquisitionsEditors: Eric Svendsen, Tacy Quinn, and Norrin Dias, as well as the insight and enthusiasmthroughout from Editorial Director Marcia Horton. This project has benefited greatly fromthe attention of Marketing Manager Tim Galligan, who helped to shape my appreciationfor the multiple audiences this book should seek to satisfy. I am grateful to SeniorManaging Editor Scott Disanno, who has both overseen the production of the book andprovided the fresh, clear eye that honed the manuscript at its final stages. Designer BlairBrown brought a magical touch and excitement to this unusual project, and I am gratefulfor his efforts and the fun I had working with him. The expertise of J.C. Morgan and leadartist Matt Harshbarger at Precision Graphics has contributed significantly to the finalproduct, and I am grateful for their patience as the book and artwork evolved. Thedistinctive integration of text, equations, and artwork in this book could not have beenrealized without Anoop Chaturvedi and the composition services of MPS Limited. Otherthan perhaps myself, no one spent more time or agonized more in bringing this project tofruition than Sr. Production Project Manager Clare Romeo. She has been a joy to workwith, and I cannot thank her enough for her knowledge, expertise, attention to detail,patience, and humor.

Thank you to the reviewers: Paolo Gardoni, Texas A&M University; Joao Antonio,Colorado State University; Joel J. Schubbe, U.S. Naval Academy; Daniel A. Mendelsohn,Ohio State University; Laurence J. Jacobs, Georgia Tech; Eduard S. Ventsel, PennsylvaniaState University; Dashin Liu, Michigan State University; Candace S. Sulzbach, ColoradoSchool of Mines; Amir G. Rezaei, California State Polytechnic University, Pomona;Marck French, Purdue University; Niki Schulz, Oregon State University; Jim Morgan,Texas A&M University; Shane Brown, Washington State University; Christine B. Masters,Pennsylvania State University; Craig Menzemer, University of Akron; Edwin C. Rossow,Northwestern University; Anna Dollár, Miami University; Mark E. Walter, Ohio StateUniversity; David Baldwin, University of Oklahoma; Kevin Collins, United States CoastGuard Academy; He Liu, University of Alaska Anchorage; and Anthony J. Paris,University of Alaska Anchorage. At several points during its development, extensive andthoughtful input from the reviewers was critically important in helping the book takeshape. Their time and efforts are greatly appreciated.

I am also grateful to faculty members and students who offered ideas for realisticapplications and problems, including Jim Papadopoulos, Yoed Rabin, Dustyn Roberts, andJonathan Wickert. Billy Burkey, Chris D’eramo, Anthony Fazzini, Rob Keelan, MichaelReindl, David Urban, and Derek Wisnieski provided valuable assistance in dimensions andimages for a number of application problems. Advice on graphics from Erick Johnsontowards the end of project was very helpful. I thank my assistant, Bobbi Kostyak, whoprovided help with many details that arose. I have relied often, to my great satisfaction, onthe design and artistic sense of Ariela Steif, for which I am grateful.

This book has benefited from the many years I have fruitfully and joyfully discussed thelearning of mechanics with my long-time friend and collaborator, Anna Dollár. I credit myfriend and collaborator, Marina Pantazidou, for giving a pivotal nudge that convinced me towrite this book, and for supplying ongoing encouragement in education endeavors generally.I want to thank Robbin Steif for the significant role she played at the start of this project.

My own teachers provided the foundation for my fascination with the subject ofmechanics. I have in turn had the pleasure of getting to know many students over the yearsin my classes. They have helped me recognize the challenges in learning mechanics, and thepractical situations in which mechanics comes alive.

During much of the writing of this book, I was fortunate to have the companionship,warmth, and good wishes of many fellow denizens of the Galleria.

My family life provides the perfect counterpoint to my work, and I thank my loved ones,Michelle, Ariela, Talia, and Marigny for making that family life such a desirable distractionto writing this book.

PAUL S. STEIF

Carnegie Mellon University

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P R E FAC E | xi

About the AuthorProfessor Paul S. Steif has been a faculty member in the Department of MechanicalEngineering at Carnegie Mellon University since 1983. He received a Sc.B. degree inengineering mechanics from Brown University; M.S. and Ph.D. degrees in appliedmechanics from Harvard University; and was National Science Foundation NATO Post-doctoral fellow at the University of Cambridge. As a faculty member his research hasaddressed a variety of problems, including the effects of interfacial properties on fiber-reinforced composites, bifurcation and instabilities in highly deformed layered materials,and stress generation and fracture induced by cryopreservation of biological tissues.Dr. Steif has also contributed to engineering practice through consulting and research onindustrial projects, including elastomeric damping devices, blistering of face seals, andfatigue of tube fittings.

Since the mid-1990s, Dr. Steif has focused increasingly on engineering education,performing research on student learning of mechanics concepts, and developing new coursematerials and classroom approaches. Drawing upon methods of cognitive and learningsciences, Dr. Steif has led the development and psychometric validation of the StaticsConcept Inventory—a test of statics conceptual knowledge. He is the co-author of OpenLearning Initiative (OLI) Engineering Statics. Dr. Steif is a Fellow of the American Societyof Mechanical Engineers and recipient of the Archie Higdon Distinguished Educator Awardfrom the Mechanics Division of the American Society for Engineering Education.

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Mechanics

of

Materials

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Mechanics of Materials - Pearsoncatalogue.pearsoned.ca/assets/hip/ca/hip_ca_pearsonhighered/... · Mechanics of Materials ... 4.11 Internal Torque and the Relation to Twist and Stress

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