Contents
Preface ............................................................................................................................................................ 4
Acknowledgments .......................................................................................................................................... 5
About the Authors .......................................................................................................................................... 5
List of Symbols............................................................................................................................................... 6
Chapter 1. Analysis of Stress ......................................................................................................................... 7
Chapter 2. Strain and Material Properties .................................................................................................... 68
Chapter 3. Problems in Elasticity ............................................................................................................... 127
Chapter 4. Failure Criteria .......................................................................................................................... 184
N
Chapter 5. Bending of Beams ..................................................................................................................... 226
Chapter 6. Torsion of Prismatic Bars ......................................................................................................... 292
U
Chapter 7. Numerical Methods................................................................................................................... 336
Chapter 8. Axisymmetrically Loaded Members ........................................................................................ 408
Chapter 9. Beams on Elastic Foundations .................................................................................................. 450
R
Chapter 10. Applications of Energy Methods ............................................................................................ 469
Chapter 11. Stability of Columns ............................................................................................................... 508
SE
Chapter 12. Plastic Behavior of Materials.................................................................................................. 548
Chapter 13. Plates and Shells ..................................................................................................................... 605
Appendix A. Problem Formulation and Solution ....................................................................................... 645
Appendix B. Solution of the Stress Cubic Equation .................................................................................. 646
Appendix C. Moments of Composite Areas............................................................................................... 650
D
Appendix D. Tables and Charts.................................................................................................................. 663
Answers to Selected Problems ................................................................................................................... 673
O
Index ........................................................................................................................................................... 682
Footnotes .................................................................................................................................................... 700
C
S
-3-
,Preface
Introduction
This text is a development of classroom notes prepared in connection with advanced undergraduate and first-
year graduate courses in elasticity and the mechanics of solids. It is designed to satisfy the requirements of
courses subsequent to an elementary treatment of the strength of materials. In addition to its applicability to
aeronautical, civil, and mechanical engineering and to engineering mechanics curricula, the text is useful to
practicing engineers. Emphasis is given to numerical techniques (which lend themselves to computerization) in
the solution of problems resisting analytical treatment. The stress placed on numerical solutions is not intended
to deny the value of classical analysis, which is given a rather full treatment. It instead attempts to fill what the
authors believe to be a void in the world of textbooks.
An effort has been made to present a balance between the theory necessary to gain insight into the mechanics,
N
but which can often offer no more than crude approximations to real problems because of simplifications
related to geometry and conditions of loading, and numerical solutions, which are so useful in presenting stress
analysis in a more realistic setting. This text emphasizes those aspects of theory and application that prepare a
U
student for more advanced study or for professional practice in design and analysis.
The theory of elasticity plays three important roles in the text: it provides exact solutions where the
configurations of loading and boundary are relatively simple; it provides a check on the limitations of the
R
mechanics of materials approach; and it serves as the basis of approximate solutions employing numerical
analysis.
To make the text as clear as possible, attention is given to the presentation of the fundamentals of the mechanics
SE
of materials. The physical significance of the solutions and practical applications are given emphasis. A special
effort was made to illustrate important principles and applications with numerical examples. Consistent with
announced national policy, problems are included in the text in which the physical quantities are expressed in
the International System of Units (SI). All important quantities are defined in both SI and U.S. Customary
System of units. A sign convention, consistent with vector mechanics, is employed throughout for loads,
internal forces, and stresses. This convention conforms to that used in most classical strength of materials and
D
elasticity texts, as well as to that most often employed in the numerical analysis of complex structures.
Text Arrangement
O
Because of the extensive subdivision into a variety of topics and the employment of alternative methods of
analysis, the text should provide flexibility in the choice of assignments to cover courses of varying length and
content. Most chapters are substantially self-contained. Hence, the order of presentation can be smoothly
altered to meet an instructor’s preference. It is suggested, however, that Chapters 1 and 2, which address the
C
analysis of basic concepts, should be studied first. The emphasis placed on the treatment of two-dimensional
problems in elasticity (Chapter 3) may differ according to the scope of the course.
S
This fifth edition of Advanced Mechanics of Materials and Applied Elasticity seeks to preserve the objectives
and emphases of the previous editions. Every effort has been made to provide a more complete and current text
through the inclusion of new material dealing with the fundamental principles of stress analysis and design:
stress concentrations, contact stresses, failure criteria, fracture mechanics, compound cylinders, finite element
analysis (FEA), energy and variational methods, buckling of stepped columns, and common shell types. The
entire text has been reexamined and many improvements have been made throughout by a process of
elimination and rearrangement. Some sections have been expanded to improve on previous expositions.
The references, provided as an aid to the student who wishes to further pursue certain aspects of a subject, have
been updated and identified at the end of each chapter. We have resisted the temptation to increase the material
covered except where absolutely necessary. However, it was considered desirable to add a number of
-4-
,illustrative examples and a large number of problems important in engineering practice and design. Extra care
has been taken in the presentation and solution of the sample problems. All the problem sets have been
reviewed and checked to ensure both their clarity and numerical accuracy. Most changes in subject-matter
coverage were prompted by the suggestions of faculty familiar with earlier editions.
It is hoped that we have maintained clarity of presentation, simplicity as the subject permits, unpretentious
depth, an effort to encourage intuitive understanding, and a shunning of the irrelevant. In this context, as
throughout, emphasis is placed on the use of fundamentals in order to build student understanding and an ability
to solve the more complex problems.
Supplements
The book is accompanied by a comprehensive Solutions Manual available to instructors. It features complete
solutions to all problems in the text. Answers to selected problems are given at the end of the book. PowerPoint
N
slides of figures and tables and a password-protected Solutions Manual are available for instructors at the
Pearson Instructor Resource Center, pearsonhighered.com/irc.
Acknowledgments
U
It is a particular pleasure to acknowledge the contributions of those who assisted in the evolution of the text.
Thanks, of course, are due to the many readers who have contributed general ideas and to reviewers who have
R
made detailed comments on previous editions. These notably include the following: F. Freudenstein, Columbia
University; R. A. Scott, University of Michigan; M. W. Wilcox and Y. Chan Jian, Southern Methodist
University; C. T. Sun, University of Florida; B. Koplik, H. Kountouras, K. A. Narh, R. Sodhi, and C. E. Wilson,
New Jersey Institute of Technology; H. Smith, Jr., South Dakota School of Mines and Technology; B. P. Gupta,
SE
Gannon University; S. Bang, University of Notre Dame; B. Koo, University of Toledo; J. T. Easley, University
of Kansas; J. A. Bailey, North Carolina State University; W. F. Wright, Vanderbilt University; R. Burks, SUNY
Maritime College; G. E. O. Widera, University of Illinois; R. H. Koebke, University of South Carolina; B. M.
Kwak, University of Iowa; G. Nadig, Widener University; R. L. Brown, Montana State University; S. H.
Advani, West Virginia University; E. Nassat, Illinois Institute of Technology; R. I. Sann, Stevens Institute of
Technology; C. O. Smith, University of Nebraska; J. Kempner, Polytechnic University of New York; and P. C.
D
Prister, North Dakota State University; R. Wetherhold, University of Buffalo, SUNY; and Shaofan Li,
University of California at Berkeley.
Accuracy checking of the problems and typing of Solutions Manual were done expertly by my former student,
O
Dr. Youngjin Chung. Also contributing considerably to this volume with typing new inserts, assiting with some
figures, limited proofreading, and cover design was Errol A. Ugural. Their hard work is much appreciated. I am
deeply indebted to my colleagues who have found the text useful through the years and to Bernard Goodwin,
publisher at Prentice Hall PTR, who encouraged development of this edition. Copy editing and production were
C
handled skillfully by Carol Lallier and Elizabeth Ryan. Their professional help is greatly appreciated. Lastly, I
am very thankful for the support and understanding of my wife Nora, daughter Aileen, and son Errol during
preparation of this book.
S
Ansel C. Ugural
About the Authors
Ansel C. Ugural, Ph.D., is visiting professor at New Jersey Institute of Technology. He has held various
faculty and administrative positions at Fairleigh Dickinson University, and he taught at the University of
Wisconsin. Ugural has considerable industrial experience in both full-time and consulting capacities. A member
of several professional societies, he is the author of the books Mechanics of Materials; Stresses in Beams,
Plates and Shells; and Mechanical Design: An Integrated Approach.
-5-
, Saul K. Fenster, Ph.D., served as president and tenured professor at New Jersey Institute of Technology for
more than two decades. In addition, he has held varied positions at Fairleigh Dickinson University and taught at
the City University of New York. His experience includes membership on a number of corporate boards and
economic development commissions. Fenster is a fellow of the American Society of Mechanical Engineers, the
American Society for Engineering Education, and the American Society for Manufacturing Engineers. He is
coauthor of a text on mechanics.
List of Symbols
N
U
R
SE
D
O
C
S
-6-
Preface ............................................................................................................................................................ 4
Acknowledgments .......................................................................................................................................... 5
About the Authors .......................................................................................................................................... 5
List of Symbols............................................................................................................................................... 6
Chapter 1. Analysis of Stress ......................................................................................................................... 7
Chapter 2. Strain and Material Properties .................................................................................................... 68
Chapter 3. Problems in Elasticity ............................................................................................................... 127
Chapter 4. Failure Criteria .......................................................................................................................... 184
N
Chapter 5. Bending of Beams ..................................................................................................................... 226
Chapter 6. Torsion of Prismatic Bars ......................................................................................................... 292
U
Chapter 7. Numerical Methods................................................................................................................... 336
Chapter 8. Axisymmetrically Loaded Members ........................................................................................ 408
Chapter 9. Beams on Elastic Foundations .................................................................................................. 450
R
Chapter 10. Applications of Energy Methods ............................................................................................ 469
Chapter 11. Stability of Columns ............................................................................................................... 508
SE
Chapter 12. Plastic Behavior of Materials.................................................................................................. 548
Chapter 13. Plates and Shells ..................................................................................................................... 605
Appendix A. Problem Formulation and Solution ....................................................................................... 645
Appendix B. Solution of the Stress Cubic Equation .................................................................................. 646
Appendix C. Moments of Composite Areas............................................................................................... 650
D
Appendix D. Tables and Charts.................................................................................................................. 663
Answers to Selected Problems ................................................................................................................... 673
O
Index ........................................................................................................................................................... 682
Footnotes .................................................................................................................................................... 700
C
S
-3-
,Preface
Introduction
This text is a development of classroom notes prepared in connection with advanced undergraduate and first-
year graduate courses in elasticity and the mechanics of solids. It is designed to satisfy the requirements of
courses subsequent to an elementary treatment of the strength of materials. In addition to its applicability to
aeronautical, civil, and mechanical engineering and to engineering mechanics curricula, the text is useful to
practicing engineers. Emphasis is given to numerical techniques (which lend themselves to computerization) in
the solution of problems resisting analytical treatment. The stress placed on numerical solutions is not intended
to deny the value of classical analysis, which is given a rather full treatment. It instead attempts to fill what the
authors believe to be a void in the world of textbooks.
An effort has been made to present a balance between the theory necessary to gain insight into the mechanics,
N
but which can often offer no more than crude approximations to real problems because of simplifications
related to geometry and conditions of loading, and numerical solutions, which are so useful in presenting stress
analysis in a more realistic setting. This text emphasizes those aspects of theory and application that prepare a
U
student for more advanced study or for professional practice in design and analysis.
The theory of elasticity plays three important roles in the text: it provides exact solutions where the
configurations of loading and boundary are relatively simple; it provides a check on the limitations of the
R
mechanics of materials approach; and it serves as the basis of approximate solutions employing numerical
analysis.
To make the text as clear as possible, attention is given to the presentation of the fundamentals of the mechanics
SE
of materials. The physical significance of the solutions and practical applications are given emphasis. A special
effort was made to illustrate important principles and applications with numerical examples. Consistent with
announced national policy, problems are included in the text in which the physical quantities are expressed in
the International System of Units (SI). All important quantities are defined in both SI and U.S. Customary
System of units. A sign convention, consistent with vector mechanics, is employed throughout for loads,
internal forces, and stresses. This convention conforms to that used in most classical strength of materials and
D
elasticity texts, as well as to that most often employed in the numerical analysis of complex structures.
Text Arrangement
O
Because of the extensive subdivision into a variety of topics and the employment of alternative methods of
analysis, the text should provide flexibility in the choice of assignments to cover courses of varying length and
content. Most chapters are substantially self-contained. Hence, the order of presentation can be smoothly
altered to meet an instructor’s preference. It is suggested, however, that Chapters 1 and 2, which address the
C
analysis of basic concepts, should be studied first. The emphasis placed on the treatment of two-dimensional
problems in elasticity (Chapter 3) may differ according to the scope of the course.
S
This fifth edition of Advanced Mechanics of Materials and Applied Elasticity seeks to preserve the objectives
and emphases of the previous editions. Every effort has been made to provide a more complete and current text
through the inclusion of new material dealing with the fundamental principles of stress analysis and design:
stress concentrations, contact stresses, failure criteria, fracture mechanics, compound cylinders, finite element
analysis (FEA), energy and variational methods, buckling of stepped columns, and common shell types. The
entire text has been reexamined and many improvements have been made throughout by a process of
elimination and rearrangement. Some sections have been expanded to improve on previous expositions.
The references, provided as an aid to the student who wishes to further pursue certain aspects of a subject, have
been updated and identified at the end of each chapter. We have resisted the temptation to increase the material
covered except where absolutely necessary. However, it was considered desirable to add a number of
-4-
,illustrative examples and a large number of problems important in engineering practice and design. Extra care
has been taken in the presentation and solution of the sample problems. All the problem sets have been
reviewed and checked to ensure both their clarity and numerical accuracy. Most changes in subject-matter
coverage were prompted by the suggestions of faculty familiar with earlier editions.
It is hoped that we have maintained clarity of presentation, simplicity as the subject permits, unpretentious
depth, an effort to encourage intuitive understanding, and a shunning of the irrelevant. In this context, as
throughout, emphasis is placed on the use of fundamentals in order to build student understanding and an ability
to solve the more complex problems.
Supplements
The book is accompanied by a comprehensive Solutions Manual available to instructors. It features complete
solutions to all problems in the text. Answers to selected problems are given at the end of the book. PowerPoint
N
slides of figures and tables and a password-protected Solutions Manual are available for instructors at the
Pearson Instructor Resource Center, pearsonhighered.com/irc.
Acknowledgments
U
It is a particular pleasure to acknowledge the contributions of those who assisted in the evolution of the text.
Thanks, of course, are due to the many readers who have contributed general ideas and to reviewers who have
R
made detailed comments on previous editions. These notably include the following: F. Freudenstein, Columbia
University; R. A. Scott, University of Michigan; M. W. Wilcox and Y. Chan Jian, Southern Methodist
University; C. T. Sun, University of Florida; B. Koplik, H. Kountouras, K. A. Narh, R. Sodhi, and C. E. Wilson,
New Jersey Institute of Technology; H. Smith, Jr., South Dakota School of Mines and Technology; B. P. Gupta,
SE
Gannon University; S. Bang, University of Notre Dame; B. Koo, University of Toledo; J. T. Easley, University
of Kansas; J. A. Bailey, North Carolina State University; W. F. Wright, Vanderbilt University; R. Burks, SUNY
Maritime College; G. E. O. Widera, University of Illinois; R. H. Koebke, University of South Carolina; B. M.
Kwak, University of Iowa; G. Nadig, Widener University; R. L. Brown, Montana State University; S. H.
Advani, West Virginia University; E. Nassat, Illinois Institute of Technology; R. I. Sann, Stevens Institute of
Technology; C. O. Smith, University of Nebraska; J. Kempner, Polytechnic University of New York; and P. C.
D
Prister, North Dakota State University; R. Wetherhold, University of Buffalo, SUNY; and Shaofan Li,
University of California at Berkeley.
Accuracy checking of the problems and typing of Solutions Manual were done expertly by my former student,
O
Dr. Youngjin Chung. Also contributing considerably to this volume with typing new inserts, assiting with some
figures, limited proofreading, and cover design was Errol A. Ugural. Their hard work is much appreciated. I am
deeply indebted to my colleagues who have found the text useful through the years and to Bernard Goodwin,
publisher at Prentice Hall PTR, who encouraged development of this edition. Copy editing and production were
C
handled skillfully by Carol Lallier and Elizabeth Ryan. Their professional help is greatly appreciated. Lastly, I
am very thankful for the support and understanding of my wife Nora, daughter Aileen, and son Errol during
preparation of this book.
S
Ansel C. Ugural
About the Authors
Ansel C. Ugural, Ph.D., is visiting professor at New Jersey Institute of Technology. He has held various
faculty and administrative positions at Fairleigh Dickinson University, and he taught at the University of
Wisconsin. Ugural has considerable industrial experience in both full-time and consulting capacities. A member
of several professional societies, he is the author of the books Mechanics of Materials; Stresses in Beams,
Plates and Shells; and Mechanical Design: An Integrated Approach.
-5-
, Saul K. Fenster, Ph.D., served as president and tenured professor at New Jersey Institute of Technology for
more than two decades. In addition, he has held varied positions at Fairleigh Dickinson University and taught at
the City University of New York. His experience includes membership on a number of corporate boards and
economic development commissions. Fenster is a fellow of the American Society of Mechanical Engineers, the
American Society for Engineering Education, and the American Society for Manufacturing Engineers. He is
coauthor of a text on mechanics.
List of Symbols
N
U
R
SE
D
O
C
S
-6-
