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Advanced Strength and Applied Elasticity, 4th Edition

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Advanced Strength and Applied Elasticity, 4th Edition


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A systematic and practical exploration of stress analysis for real-world aeronautical, civil, and mechanical engineering environments.

° Updated to reflect the latest stress analysis techniques and methods.

° Extensive set of illustrative examples and real-life problems and tables covering a wide range of important topics.

° Distinguished by its exceptional visual interpretations.


  • Copyright 2003
  • Edition: 4th
  • Book
  • ISBN-10: 0-13-047392-8
  • ISBN-13: 978-0-13-047392-9

This systematic exploration of real-world stress analysis has been completely revised and updated to reflect state-of-the-art methods and applications now in use throughout the fields of aeronautical, civil, and mechanical engineering and engineering mechanics. Distinguished by its exceptional visual interpretations of the solutions, it offers an in-depth coverage of the subjects for students and practicing engineers. The authors carefully balance comprehensive treatments of solid mechanics, elasticity, and computer-oriented numerical methods. In addition, a wide range of fully worked illustrative examples and an extensive problem sets–many taken directly from engineering practice–have been incorporated.

Key additions to the Fourth Edition of this highly acclaimed textbook are materials dealing with failure theories, fracture mechanics, compound cylinders, numerical approaches, energy and variational methods, buckling of stepped columns, common shell types, and more. Contents include stress, strain and stress-strain relations, problems in elasticity, static and dynamic failure criteria, bending of beams and torsion of bars, finite difference and finite element methods, axisymmetrically loaded members, beams on elastic foundations, energy methods, elastic stability, plastic behavior of materials, stresses in plates and shells, and selected references to expose readers to the latest information in the field.

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Analysis of Stress

Two-Dimensional Problems in Elasticity

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Table of Contents

(NOTE: Each chapter ends with Problems.)

Preface to the Fourth Edition.

List of Symbols.

1. Analysis of Stress.

Introduction. Scope of Treatment. Definition of Stress. Components of Stress: Stress Tensor. Some Special Cases of Stress. Internal Force-Resultant and Stress Relations. Stresses on Inclined Planes in an Axially Loaded Member. Variation of Stress within a Body. Two-Dimensional Stress at a Point. Principal Stresses and Maximum Shear Stress in Two Dimensions. Mohr's Circle for Two-Dimensional Stress. Three-Dimensional Stress at a Point. Principal Stresses in Three Dimensions. Normal and Shear Stresses on an Oblique Plane. Mohr's Circle for Three-Dimensional Stress. Boundary Conditions in Terms of Surface Forces.

2. Strain and Stress-Strain Relations.

Introduction. Deformation. Strain Defined. Equations of Compatibility. State of Strain at a Point. Engineering Materials. Stress-Strain Diagrams. Hooke's Law and Poisson's Ratio. Generalized Hooke's Law. Measurement of Strain: Bonded Strain Gages. Strain Energy. Strain Energy in Common Structural Member. Components of Strain Energy. Saint-Venant's Principle.

3. Two-Dimensional Problems in Elasticity.

Introduction. Fundamental Principles of Analysis. Part A-Formulation and Methods of Solution. Plane Strain Problems. Plane Stress Problems. Airy's Stress Function. Solution of Elasticity Problems. Thermal Stresses. Basic Relations in Polar Coordinates. Part B-Stress Concentrations. Stresses Due to Concentrated Loads. Stress Distribution near Concentrated Load Acting on a Beam. Stress Concentration Factors. NEUBER'S DIAGRAM. Contact Stresses.

4. Failure Criteria.

Introduction. Failure. Failure by Yielding. Failure by Fracture. Yield and Fracture Criteria. Maximum Shearing Stress Theory. Maximum Distortion Energy Theory. Octahedral Shearing Stress Theory. Comparison of the Yielding Theories. Maximum Principal Stress Theory. Mohr's Theory. Coulomb-Mohr Theory. Introductory Fracture Mechanics. Failure Criteria for Metal Fatigue. Fatigue Life under Combined Loading. Impact or Dynamic Loads. Dynamic and Thermal Effects.

5. Bending of Beams.

Introduction. Part A-Exact Solutions. Pure Bending of Beams of Symmetrical Cross Section. Pure Bending of Beams of Asymmetrical Cross Section. Bending of a Cantilever of Narrow Section. Bending of a Simply Supported, Narrow Beam. Part B-Approximate Solutions. Elementary Theory of Bending. Bending and Shearing Stresses. Effect of Transverse Normal Stress. Composite Beams. Shear Center. Statically Indeterminate Systems. Energy Method for Deflections. Part C-Curved Beams. Exact Solution. Tangential Stress. Winkler's Theory. Combined Tangential and Normal Stresses.

6. Torsion of Prismatic Bars.

Introduction. Elementary Theory of Torsion of Circular Bars. General Solution of the Torsion Problem. Prandtl's Stress Function. Prandtl's Membrane Analogy. Torsion of Thin-Walled Members of Open Cross Section. Torsion of Multiply Connected Thin-Walled Sections. Fluid Flow Analogy and Stress Concentration. Torsion of Restrained Thin-Walled Members of Open Cross Section. Curved Circular Bars: Helical Springs.

7. Numerical Methods.

Introduction. Finite Differences. Finite Difference Equations. Curved Boundaries. Boundary Conditions. Finite Element Method. Properties of a Finite Element. Formulation of the Finite Element Method. Triangular Finite Element. Use of Digital Computers.

8. Axisymmetrically Loaded Members.

Introduction. Thick-Walled Cylinders. Maximum Tangential Stress. Application of Failure Theories. Compound Cylinders. Rotating Disks of Constant Thickness. Rotating Disks of Variable Thickness. Rotating Disks of Uniform Stress. Thermal Stresses in Thin Disks. Thermal Stress in Long Circular Cylinders. Finite Element Solution. Formulation of Axisymmetric Element.

9. Beams on Elastic Foundations.

Introduction. General Theory. Infinite Beams. Semi-Infinite Beams. Finite Beams: Classification of Beams. Beams Supported by Equally Spaced Elastic Elements. Simplified Solutions for Relatively Stiff Beams. Solution by Finite Differences. Applications.

10. Energy Methods.

Introduction. Work Done in Deformation. Reciprocity Theorem. Castigliano's Theorem. Unit or Dummy Load Method. Crotti-Engesser Theorem. Statically Indeterminate Systems. Principle of Virtual Work. Principle of Minimum Potential Energy. Application of Trigonometric Series. Rayleigh-Ritz Method.

11. Elastic Stability.

Introduction. Critical Load. Buckling of a Column. End Conditions. Critical Stress in a Column. Allowable Stress. Initially Curved Members Eccentrically Loaded Columns: Secant Formula. Energy Methods Applied to Buckling. Solution by Finite Differences. Finite Difference Solution for Unevenly Spaced Nodes.

12. Plastic Behavior of Materials.

Introduction. Plastic Deformation. True Stress-True Strain Curve in Simple Tension. Instability in Simple Tension. Plastic Deflection of Beams. Analysis of Perfectly Plastic Beams. Collapse Load of Structures. Elastic-Plastic Torsion. Elastic-Plastic Stresses in Rotating Disks. Plastic Stress-Strain Relations. Plastic Stress-Strain Increment Relations. Stresses in Perfectly Plastic Thick-Walled Cylinders.

13. Plates and Shells.

Part A-Bending of Thin Plates.

Basic Assumptions. Strain-Curvature Relations. Stress, Curvature, and Moment Relations. Governing Equations of Plate Deflection. Boundary Conditions. Simply Supported Rectangular Plates. Axisymmetrically Loaded Circular Plates. Deflections of Rectangular Plates by the Strain Energy Method. Finite Element Solution.

Part B-Membrane Stresses in Thin Shells.

Basic Assumptions. Simple Membrane Action. Symmetrically Loaded Shells of Revolution. Some Common Cases of Shells of Revolution. Cylindrical Shells of General Shape.

Appendix A. Indicial Notation.Appendix B. Solution of the Stress Cubic Equation.

Principal Stresses. Direction Cosines.

Appendix C. Moments of Composite Areas.

Centroid. Moments of Inertia. Parallel-Axis Theorem. Principal Moments of Inertia.

Appendix D. Tables.

Average Properties of Common Engineering Materials. Conversion Factors: SI Units to U.S. Customary Units. SI Unit Prefixes. Deflections and Slopes of Beams.

References.Answers to Selected Problems.Index.


Preface to the Fourth Edition


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 authors have endeavored to make the text 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, 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. The authors have thus attempted to emphasize those aspects of theory and application that prepare a 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 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 of materials. The physical significance of the solutions and practical applications are given emphasis. The authors have made a special effort 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 elasticity texts, as well as to that most often employed in the numerical analysis of complex structures.

Text Arrangement

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 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.

This fourth edition of Advanced Strength 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: failure criteria; fracture mechanics; compound cylinders; numerical methods; 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 pursue further certain aspects of a subject, have been updated and identified at the end of the text. I have resisted the temptation to increase the material covered except where absolutely necessary. However, it was considered desirable to add a number of illustrative examples and a large number of problems important in engineering practice and design. Most changes in subject-matter coverage were prompted by the suggestions of faculty familiar with earlier editions.

As before, it is hoped that I 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.


The book is accompanied by a 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.


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