Advanced Mechanics of Materials and Elasticity

1 Advanced Mechanics of Materials andApplied ElasticityFifth EditionThis page intentionally left blank Advanced Mechanics of Materials andApplied ElasticityFifth EditionANSELC. UGURALSAULK. FENSTERU pper Saddle River, NJ Boston Indianapolis San FranciscoNew York Toronto Montreal London Munich Paris MadridCapetown Sydney Tokyo Singapore Mexico CityMany of the designations used by manufacturers and sellers to distinguish their products are claimed astrademarks. Where those designations appear in this book, and the publisher was aware of a trademarkclaim, the designations have been printed with initial capital letters or in all authors and publisher have taken care in the preparation of this book, but make no expressed orimplied warranty of any kind and assume no responsibility for errors or omissions.

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3 Ugural, Saul 5th ed. of: Advanced strength and applied Elasticity . 4th ed. bibliographical references and 0-13-707920-6 (hardcover : alk. paper)1. Strength of Materials . 2. Elasticity . 3. Materials Mechanicalproperties. I. Fenster, Saul K., 1933- II. Ugural, A. C. Advanced strengthand applied Elasticity . III. '12 dc232011012705 Copyright 2012 Pearson Education, rights reserved. Printed in the United States of America. This publication is protected by copyright,and permission must be obtained from the publisher prior to any prohibited reproduction, storage in aretrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,recording, or likewise.

4 To obtain permission to use material from this work, please submit a written re-quest to Pearson Education, Inc., Permissions Department, One Lake Street Upper Saddle River, NewJersey 07458, or you may fax your request to (201) : 978-0-13-707920-9 ISBN-10:0-13-707920-6 Text printed in the United States on recycled paper at Courier in Westford, printing, August 2012 ContentsPrefacexiiAcknowledgmentsxivAbou t the AuthorsxvList of SymbolsxviChapter 1 Analysis of of and of and Components of Force-Resultant and Stress Relations on Inclined Sections of Stress within a Stresses and Maximum In-Plane Shear s Circle for Two-Dimensional Stress Stresses in Three and Shear Stresses on an Oblique Plane s Circles in Three Conditions in Terms of Surface Forces Notation 48 References49 Problems49 chapter 2 Strain and material of of Strain at a Strain versus Plastic s Law and Poisson s Hooke s s Law for Orthotropic of Strain.

5 Strain Rosette Energy Energy in Common Structural of Strain s Principle108 References 110 Problems111 chapter 3 Problems in Principles of Analysis125 Part A Formulation and methods of Solution Strain Stress of Two-Dimensional Isotropic s Stress of Elasticity Relations in Polar Coordinates142 Part B Stress Due to Concentrated Distribution Near Concentrated Load Acting on a Concentration and Cylindrical Stress Distribution Contact167 References 170 Problems171 chapter 4 Failure by by and Fracture Criteria Shearing Stress Distortion Energy Shearing Stress of the Yielding Principal Stress s Mohr Criteria for Metal or Dynamic and Thermal Effects215 References217 Problems218 chapter 5 Bending of A Exact Bending of Beams of Symmetrical Cross Bending of Beams of Asymmetrical Cross of a Cantilever of Narrow of a Simply Supported Narrow Beam238 Part B Approximate Theory of and Shear of Transverse Normal Indeterminate Method for Deflections264 Part C Curved Beam

6 Of the Results of Various Theories Tangential and Normal Stresses276 References 280 Problems280 chapter 6 Torsion of Prismatic Theory of Torsion of Circular on Inclined Solution of the Torsion s Stress s Membrane of Narrow Rectangular Cross of Multiply Connected Thin-Walled Flow Analogy and Stress of Restrained Thin-Walled Members of Open Cross Circular Bars: Helical Springs 327 References 330 Problems330 chapter 7 Numerical methods A Finite Difference Difference Conditions346 Part B Finite Element Bar Element Oriented Bar Element Force Relations for a Element of Two-Dimensional Formulation of the Finite Element Finite Studies in Plane Tools394 References 395 Problems 396 chapter 8 Axisymmetrically Loaded Cylinders Tangential of Failure Cylinders.

7 Press or Shrink Disks of Constant of Disk Disks of Variable Disks of Uniform Stresses in Thin Stresses in Long Circular Element Element 437 References441 Problems442viiiContentsChapter 9 Beams on Elastic of Supported by Equally Spaced Elastic Solutions for Relatively Stiff by Finite 10 Applications of Energy Done in s or Dummy-Load Engesser Indeterminate of Virtual of Minimum Potential by Trigonometric Ritz Method493 References 496 Problems496 chapter 11 Stability of Columns of Pinned-End Response of Columns with Different End Stress: Classification of in Loaded Columns: Secant methods Applied to by Finite Difference Solution for Unevenly Spaced Nodes534 References 536 Problems536 ContentsixChapter 12 Plastic Behavior of Deformation Stress Strain Diagrams in Simple Axial Deformation and Residual Defection of of Perfectly Plastic Load of Structures: Limit Plastic Torsion of Circular Torsion.

8 Membrane Plastic Stresses in Rotating Stress Strain Stress Strain Increment in Perfectly Plastic Thick-Walled Cylinders586 References 590 Problems590 chapter 13 Plates and A Bending of Thin Curvature , Curvature, and Moment Equations of Plate Supported Rectangular Loaded Circular of Rectangular Plates by the Strain-Energy Element Solution615 Part B Membrane Stresses in Thin and Behavior of Membrane Loaded Shells of Common Cases of Shells of Stresses in Compound Shells of General Shape628 References631 Problems631 Appendix AProblem Formulation and Solution637xContentsAppendix BSolution of the Stress Cubic Cosines641 Appendix CMoments of Composite of Moments of Inertia652 Appendix DTables and Properties of Common Engineering Factors.

9 SI Units to Customary Unit and Slopes of Deflections of Statically Indeterminate Concentration Factors for Bars and Shafts with Fillets,Grooves, and Holes665 Answers to Selected Problems669 Index677 ContentsxiPrefaceINTRODUCTIONThis text is a development of classroom notes prepared in connection withadvanced undergraduate and first-year graduate courses in Elasticity and themechanics of solids. It is designed to satisfy the requirements of courses subsequentto an elementary treatment of the strength of Materials . In addition to its applica-bility to aeronautical, civil, and mechanical engineering and to engineering mechan-ics curricula, the text is useful to practicing engineers.

10 Emphasis is given tonumerical techniques(which lend themselves to computerization) in the solution ofproblems resisting analytical treatment. The stress placed on numerical solutions isnot intended to deny the value of classical analysis, which is given a rather fulltreatment. It instead attempts to fill what the authors believe to be a void in theworld of effort has been made to present a balance between the theory necessary togain insight into the Mechanics , but which can often offer no more than crudeapproximations to real problems because of simplifications related to geometryand conditions of loading, and numerical solutions, which are so useful in present-ing stress analysis in a more realistic setting.