Mechanics of Materials

Anthony Bedford • Kenneth M. Liechti

Mechanics of Materials

Second Edition

Anthony BedfordUniversity of TexasAustin, TX, USA

Kenneth M. LiechtiUniversity of TexasAustin, TX, USA

ISBN 978-3-030-22081-5 ISBN 978-3-030-22082-2 (eBook)https://doi.org/10.1007/978-3-030-22082-2

1st edition: © Prentice Hall 20002nd edition: © Springer Nature Switzerland AG 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of thematerial is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting, reproduction on microfilms or in any other physical way, and transmission or informationstorage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodologynow known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoes not imply, even in the absence of a specific statement, that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.The publisher, the authors, and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor the authors orthe editors give a warranty, express or implied, with respect to the material contained herein or for anyerrors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Mechanics of materials is the study and the analysis of the internal forces withinmaterials and the deformations that result from those forces. This book appears in atime of transition for education in the mechanics of materials. The traditional coursein “strength of materials” that long formed an important part of the engineeringcurriculum had as one of its primary goals, acquainting the students with the detailsof many analytical and empirical solutions that could be applied to structural design.This reliance on a catalog of results has lessened as the finite element method hasbecome commonly available for stress analysis. Another important development isthat current research in mechanics of materials is beginning to bring to reality thedream of the merger of continuum solid mechanics and material science into aunified field. For these reasons, the emphasis in the first course in mechanics ofmaterials is becoming oriented more toward helping students understand the theo-retical foundations, especially the concepts of stress and strain, the stress-strainrelations including the meaning of isotropy, and the criteria for failure and fracture.

In Chap. 1, we provide an extensive review of statics, with problems, that theinstructor may choose to cover or simply have students read. In reviewing distributedloads, we lay the groundwork for our definitions in Chap. 2 of the normal and shearstresses. Chapter 2 also introduces the longitudinal and shear strains in terms ofchanges in infinitesimal material elements. Chapters 3 and 4 cover bars subjected toaxial and torsional loads and introduce the definitions of the elastic and shear moduli.In Chaps. 5 and 6, we discuss the internal forces and moments and the states of stressin beams. With the examples in Chaps. 2, 3, 4, 5, and 6 as motivation, in Chaps. 7and 8, we discuss the general states of stress and strain and their transformations.Chapters 9 and 10 cover deformations of beams and the buckling of columns.Energy methods are introduced in Chap. 11, and in Chap. 12, we discuss failurecriteria for general states of stress and introduce modern fracture mechanics, which

v

we believe should become an integral part of the first course in mechanics ofmaterials. Most of the topics in Chaps. 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 and selectedtopics from Chapters 11 to 12 can be covered in a typical one-semester course.

The first course in mechanics of materials prepares students for subsequentcourses in structural analysis, structural dynamics, and advanced mechanics ofdeformable media. In comparison with the courses in statics and dynamics, it is aninteresting challenge for instructors and students. Engineering students begin thestudy of statics and dynamics having had some prior experience with the basicconcepts in high school and college physics courses. In contrast, the core concepts inmechanics of materials are new to most students. It is therefore essential that atextbook introduce and explain these concepts with great care and reinforce themwith many examples. This has been our objective in writing this book. Our approachis to present the material as we do in the classroom, emphasizing understanding ofthe basic principles of mechanics of materials and demonstrating them with exam-ples drawn from contemporary engineering applications and design.

Features

• Examples That Teach We continue reinforcing the problem-solving skillsstudents have learned in their introductory mechanics courses. Separate strategysections that precede most examples and selected problems teach students how toapproach and solve problems in engineering: What principles apply? What mustbe determined? And in what order? Many examples conclude with discussionsections that discuss ways of checking and interpreting answers, point outinteresting features of the solution, or suggest alternative methods of solution.

• Free-Body Diagrams Correct and consistent use of free-body diagrams is themost essential skill that students of mechanics must acquire. We review the stepsinvolved in drawing free-body diagrams in Chap. 1 and emphasize their usethroughout the book. Many of our figures are designed to teach how free-bodydiagrams are chosen and drawn.

PAB

A B

F

F

B

C

PBC

• Design The Accreditation Board for Engineering and Technology (ABET) andmany practicing engineers strongly encourage the introduction of design through-out the engineering curriculum. By expressing many of our examples and

vi Preface

problems in terms of design, we demonstrate the use of mechanics of materialswithin the larger context of engineering practice. Chapters 3, 4, 6, and 7 containsections explicitly addressing the design of particular structural elements, and inChap. 12, we discuss failure and fracture criteria used in structural design.

Austin, TX, USA Anthony BedfordKenneth M. Liechti

Preface vii

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Engineering and Mechanics of Materials . . . . . . . . . . . . . . . . . . . 11.2 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 US Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Review of Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.1 Free-Body Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.4 Centroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.3.5 Distributed Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Measures of Stress and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.1 Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.1.1 Traction, Normal Stress, and Shear Stress . . . . . . . . . . . . 382.1.2 Average Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.1.3 Components of Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.2 Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712.2.1 Normal Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712.2.2 Shear Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742.2.3 Components of Strain and the Stress-Strain Relations . . . 78

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3 Axially Loaded Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.1 Stresses in Prismatic Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.1.1 The State of Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.1.2 Stresses on Oblique Planes . . . . . . . . . . . . . . . . . . . . . . 107

3.2 Strains and the Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . 1243.2.1 Axial and Lateral Strains . . . . . . . . . . . . . . . . . . . . . . . . 124

ix

3.2.2 Material Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1253.2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

3.3 Statically Indeterminate Problems . . . . . . . . . . . . . . . . . . . . . . . . 1453.4 Nonprismatic Bars and Distributed Loads . . . . . . . . . . . . . . . . . . 164

3.4.1 Bars with Gradually Varying Cross Sections . . . . . . . . . . 1643.4.2 Distributed Axial Loads . . . . . . . . . . . . . . . . . . . . . . . . . 167

3.5 Thermal Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1813.6 Design Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

3.6.1 Allowable Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1953.6.2 Other Design Considerations . . . . . . . . . . . . . . . . . . . . . 195

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

4 Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2114.1 Pure Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

4.1.1 Components of Stress and Strain . . . . . . . . . . . . . . . . . . 2114.1.2 Stresses on Oblique Planes . . . . . . . . . . . . . . . . . . . . . . 213

4.2 Prismatic Circular Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2184.2.1 Stresses and Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2194.2.2 Polar Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . 2234.2.3 Positive Directions of the Torque and Angle of Twist . . . 225

4.3 Statically Indeterminate Problems . . . . . . . . . . . . . . . . . . . . . . . . 2384.4 Nonprismatic Bars and Distributed Loads . . . . . . . . . . . . . . . . . . 245

4.4.1 Bars with Gradually Varying Cross Sections . . . . . . . . . . 2454.4.2 Distributed Torsional Loads . . . . . . . . . . . . . . . . . . . . . . 248

4.5 Elastic-Perfectly Plastic Circular Bars . . . . . . . . . . . . . . . . . . . . . 2584.6 Thin-Walled Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

4.6.1 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2654.6.2 Angle of Twist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

4.7 Design Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2804.7.1 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2804.7.2 Allowable Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

5 Internal Forces and Moments in Beams . . . . . . . . . . . . . . . . . . . . . . 3015.1 Axial Force, Shear Force, and Bending Moment . . . . . . . . . . . . . 3015.2 Shear Force and Bending Moment Diagrams . . . . . . . . . . . . . . . . 3115.3 Equations Relating Distributed Load, Shear Force,

and Bending Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3225.3.1 Derivation of the Equations . . . . . . . . . . . . . . . . . . . . . . 3225.3.2 Construction of the Shear Force Diagram . . . . . . . . . . . . 3275.3.3 Construction of the Bending Moment Diagram . . . . . . . . 330

x Contents

5.4 Singularity Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3415.4.1 Delta Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3415.4.2 Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3445.4.3 Macaulay Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

6 Stresses in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3616.1 Distribution of the Normal Stress . . . . . . . . . . . . . . . . . . . . . . . . 361

6.1.1 Geometry of Deformation . . . . . . . . . . . . . . . . . . . . . . . 3616.1.2 Relation Between Normal Stress and Bending

Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3676.1.3 Beams Subjected to Arbitrary Loads . . . . . . . . . . . . . . . . 369

6.2 Design Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3836.2.1 Factor of Safety and Section Modulus . . . . . . . . . . . . . . 3836.2.2 Standardized Cross Sections . . . . . . . . . . . . . . . . . . . . . 387

6.3 Composite Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3956.3.1 Distribution of the Normal Stress . . . . . . . . . . . . . . . . . . 3966.3.2 Transformed Area Method . . . . . . . . . . . . . . . . . . . . . . . 401

6.4 Elastic-Perfectly Plastic Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 4106.5 Asymmetric Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

6.5.1 Moment Exerted About a Principal Axis . . . . . . . . . . . . . 4246.5.2 Moment Exerted About an Arbitrary Axis . . . . . . . . . . . 428

6.6 Shear Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4366.6.1 Rectangular Cross Section . . . . . . . . . . . . . . . . . . . . . . . 4426.6.2 Shear Stress on an Oblique Element . . . . . . . . . . . . . . . . 443

6.7 Built-Up Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4566.8 Thin-Walled Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

6.8.1 Distribution of the Shear Stress . . . . . . . . . . . . . . . . . . . 4676.8.2 The Shear Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

7 States of Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5057.1 Components of Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5057.2 Transformations of Plane Stress . . . . . . . . . . . . . . . . . . . . . . . . . 509

7.2.1 Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . 5107.2.2 Maximum and Minimum Stresses . . . . . . . . . . . . . . . . . 517

7.3 Mohr’s Circle for Plane Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 5387.3.1 Constructing the Circle . . . . . . . . . . . . . . . . . . . . . . . . . 5397.3.2 Why Mohr’s Circle Works . . . . . . . . . . . . . . . . . . . . . . 5407.3.3 Determining Maximum and Minimum Stresses . . . . . . . . 542

7.4 Maximum and Minimum Stresses in Three Dimensions . . . . . . . . 5577.4.1 General State of Stress . . . . . . . . . . . . . . . . . . . . . . . . . 5577.4.2 Triaxial Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

Contents xi

7.5 Application: Bars Subjected to Combined Loads . . . . . . . . . . . . . 5667.5.1 The Fundamental Loads . . . . . . . . . . . . . . . . . . . . . . . . 5667.5.2 Combined Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

7.6 Application: Pressure Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . 5797.6.1 Spherical Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5797.6.2 Cylindrical Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5827.6.3 Design Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

7.7 Tetrahedron Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5907.7.1 Determining the Traction . . . . . . . . . . . . . . . . . . . . . . . . 5907.7.2 Determining the Normal and Shear Stresses . . . . . . . . . . 593

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607

8 States of Strain and Stress-Strain Relations . . . . . . . . . . . . . . . . . . . 6118.1 Components of Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6118.2 Transformations of Plane Strain . . . . . . . . . . . . . . . . . . . . . . . . . 614

8.2.1 Strain Gauge Rosette . . . . . . . . . . . . . . . . . . . . . . . . . . . 6188.2.2 Maximum and Minimum Strains . . . . . . . . . . . . . . . . . . 621

8.3 Mohr’s Circle for Plane Strain . . . . . . . . . . . . . . . . . . . . . . . . . . 6398.3.1 Constructing the Circle . . . . . . . . . . . . . . . . . . . . . . . . . 6398.3.2 Determining Maximum and Minimum Strains . . . . . . . . . 639

8.4 Stress-Strain Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6468.4.1 Linear Elastic Materials . . . . . . . . . . . . . . . . . . . . . . . . . 6478.4.2 Isotropic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669

9 Deflections of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6719.1 The Second-Order Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671

9.1.1 Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6719.1.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 674

9.2 Statically Indeterminate Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 6889.3 Singularity Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6979.4 Moment-Area Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706

9.4.1 First Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7069.4.2 Second Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707

9.5 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726

10 Buckling of Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72910.1 Euler Buckling Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72910.2 Other End Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745

10.2.1 Analysis of the Deflection . . . . . . . . . . . . . . . . . . . . . 74510.2.2 Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757

xii Contents

10.3 Eccentric Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76710.3.1 Analysis of the Deflection . . . . . . . . . . . . . . . . . . . . . 76810.3.2 Secant Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 770

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 779

11 Energy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78311.1 Work and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783

11.1.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78311.1.2 Strain Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78711.1.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 790

11.2 Castigliano’s Second Theorem . . . . . . . . . . . . . . . . . . . . . . . . 80411.2.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80511.2.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 820

12 Criteria for Failure and Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . 82312.1 Stress Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823

12.1.1 Axially Loaded Bars . . . . . . . . . . . . . . . . . . . . . . . . . 82312.1.2 Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82712.1.3 Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827

12.2 Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83912.2.1 Overloads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84012.2.2 Repeated Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849

12.3 Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86512.3.1 Overloads and Fast Crack Growth . . . . . . . . . . . . . . . 86512.3.2 Repeated Loads and Slow Crack Growth . . . . . . . . . . 875

Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 890

Appendix A: Results from Mathematics . . . . . . . . . . . . . . . . . . . . . . . . 895

Appendix B: Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901

Appendix C: Centroids and Moments of Inertia . . . . . . . . . . . . . . . . . . 907

Appendix D: Properties of Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953

Appendix E: Structural Steel Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . 959

Appendix F: Deflections and Slopes of Prismatic Beams . . . . . . . . . . . . 969

Appendix G: Answers to Even-Numbered Problems . . . . . . . . . . . . . . . 977

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013

Contents xiii

Unit Conversion Factors

LENGTH

1m ¼ 100 cm ¼ 3:281 ft ¼ 39:37 in

1 in ¼ 0:08333 ft ¼ 0:02540 m

1ft ¼ 12 in ¼ 0:3048 m

ANGLE

1 rad ¼ 180=π deg ¼ 57:30 deg

1 deg ¼ π=180rad ¼ 0:01745 rad

1 revolution ¼ 2π rad ¼ 360 deg

1 rev=min rpmð Þ ¼ 0:1047 rad=s

AREA

1 mm2 ¼ 1:550E‐3 in2 ¼ 1:076E‐5 ft2

1 m2 ¼ 10:76 ft2

1 in2 ¼ 645:2 mm2

1 ft2 ¼ 144 in2 ¼ 0:0929 m2

xv

VOLUME

1 mm3 ¼ 6:102E‐5 in3 ¼ 3:531E‐8 ft3

1 m3 ¼ 6:102E4 in3 ¼ 35:31 ft3

1 in3 ¼ 1:639E4 mm3 ¼ 1:639E‐5 m3

1 ft3 ¼ 0:02832 m3

MASS

1kg ¼ 0:0685 slug

1 slug ¼ 14:59 kg

1 t metric tonneð Þ ¼ 1000 kg ¼ 68:5 slug

FORCE

1 N ¼ 0:2248 lb

1 lb ¼ 4:448 N

1 kip ¼ 1000 lb ¼ 4448 N

1 ton ¼ 2000 lb ¼ 8896 N

WORK AND ENERGY

1 J ¼ 1 N‐m ¼ 0:7376 ft‐lb

1 ft‐lb ¼ 1:356 J

POWER

1 W ¼ 1 N‐m=s ¼ 0:7376 ft‐lb=s ¼ 1:340E‐3 hp

1 ft‐lb=s ¼ 1:356 W

1 hp ¼ 550 ft‐lb=s ¼ 746 W

PRESSURE, STRESS

1 Pa ¼ 1N=m2 ¼ 0:0209 psf ¼ 1:451E‐4 psi

1 bar ¼ 100, 000 Pa

xvi Unit Conversion Factors

1 psi lb=in2� � ¼ 144 psf ¼ 6891 Pa

1 ksi ¼ 1kip=in2 ¼ 1000 psi

1 psf lb=ft2� � ¼ 6:944E‐3 lb=in2 ¼ 47:85 Pa

1 ksf ¼ 1 kip=ft2 ¼ 1000 psf

STRESS INTENSITY FACTOR

1 Pa‐m1=2 ¼ 9:10E‐4 psi‐in1=2 ¼ 0:0379 psf‐ft1=2

1 psi‐in1=2 ¼ 41:57 psf‐ft1=2 ¼ 1100 Pa‐m1=2

1 psf‐ft1=2 ¼ 0:02406 psi‐in1=2 ¼ 26:4 Pa‐m1=2

Unit Conversion Factors xvii

About the Authors

Anthony Bedford is a Professor Emeritus of Aerospace Engineering and Engineer-ing Mechanics at the University of Texas at Austin. He has been on the faculty since1968. He also has industrial experience at Douglas Missiles and Space SystemsDivision, Sandia National Laboratories, and at TRW, where he worked on theApollo program. His main professional activity has been education and research inengineering mechanics. He is the coauthor of Engineering Mechanics: Statics andDynamics (with Wallace T. Fowler) and Introduction to Elastic Wave Propagation(with Douglas S. Drumheller).

xix

Kenneth M. Liechti is a Professor of Aerospace Engineering and EngineeringMechanics at the University of Texas at Austin and holds the Zarrow CentennialProfessorship in Engineering. He received his B.Sc. degree in Aeronautical Engi-neering at Glasgow University and M.S. and Ph.D. degrees in Aeronautics at theCalifornia Institute of Technology. He gained industrial experience at GeneralDynamics Fort Worth Division prior to joining the faculty of the University ofTexas at Austin in 1982.

Dr. Liechti’s main areas of teaching and research are in the mechanics ofmaterials and fracture mechanics. He is the author or coauthor of papers on interfa-cial fracture, mechanics of contact, adhesion and friction at smaller and smallerscales, and the nonlinear behavior of polymers. He has consulted on fracturemechanics problems with several companies.

He is a fellow of the Adhesion Society, the Society of Experimental Mechanics,the American Society of Mechanical Engineers, and the American Academy ofMechanics, and an associate fellow of the American Institute of Aeronautics andAstronautics. He the joint editor of the Journal of the Mechanics of Time-DependentMaterials.

xx About the Authors