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Advanced Mechanics of Materials and Applied Elasticity, 6th Edition

Book Description

The Leading Practical Guide to Stress Analysis–Updated with State-of-the-Art Methods, Applications, and Problems

This widely acclaimed exploration of real-world stress analysis reflects advanced methods and applications used in today's mechanical, civil, marine, aeronautical engineering, and engineering mechanics/science environments. Practical and systematic, Advanced Mechanics of Materials and Applied Elasticity, Sixth Edition, has been updated with many new examples, figures, problems, MATLAB solutions, tables, and charts.

The revised edition balances discussions of advanced solid mechanics, elasticity theory, classical analysis, and computer-oriented approaches that facilitate solutions when problems resist conventional analysis. It illustrates applications with case studies, worked examples, and problems drawn from modern applications, preparing readers for both advanced study and practice.
Readers will find updated coverage of analysis and design principles, fatigue criteria, fracture mechanics, compound cylinders, rotating disks, 3-D Mohr's circles, energy and variational methods, buckling of various columns, common shell types, inelastic materials behavior, and more. The text addresses the use of new materials in bridges, buildings, automobiles, submarines, ships, aircraft, and spacecraft. It offers significantly expanded coverage of stress concentration factors and contact stress developments. This book aims to help the reader
  • Review fundamentals of statics, solids mechanics, stress, and modes of load transmission
  • Master analysis and design principles through hands-on practice to illustrate their connections
  • Understand plane stress, stress transformations, deformations, and strains
  • Analyze a body's load-carrying capacity based on strength, stiffness, and stability
  • Learn and apply the theory of elasticity
  • Explore failure criteria and material behavior under diverse conditions, and predict component deformation or buckling
  • Solve problems related to beam bending, torsion of noncircular bars, and axisymmetrically loaded components, plates, or shells
  • Use the numerical finite element method to economically solve complex problems
  • Characterize the plastic behavior of materials

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Table of Contents

  1. Cover Page
  2. About This E-Book
  3. Half Title
  4. Title Page
  5. Copyright Page
  6. Contents
  7. Preface
    1. Introduction
    2. Organization of the Text
    3. Supplements
  8. Acknowledgments
  9. About the Authors
  10. List of Symbols
  11. Chapter 1. Analysis of Stress
    1. 1.1 Introduction
    2. 1.2 Scope of the Book
    3. 1.3 Analysis and Design
    4. 1.4 Conditions of Equilibrium
    5. 1.5 Definition and Components of Stress
    6. 1.6 Internal Force Resultant and Stress Relations
    7. 1.7 Stresses on Inclined Sections
    8. 1.8 Variation of Stress within a Body
    9. 1.9 Plane-Stress Transformation
    10. 1.10 Principal Stresses and Maximum In-Plane Shear Stress
    11. 1.11 Mohr’s Circle for Two-Dimensional Stress
    12. 1.12 Three-Dimensional Stress Transformation
    13. 1.13 Principal Stresses in Three Dimensions
    14. 1.14 Normal and Shear Stresses on an Oblique Plane
    15. 1.15 Mohr’s Circles in Three Dimensions
    16. 1.16 Boundary Conditions in Terms of Surface Forces
    17. 1.17 Indicial Notation
    18. References
    19. Problems
  12. Chapter 2. Strain and Material Properties
    1. 2.1 Introduction
    2. 2.2 Deformation
    3. 2.3 Strain Defined
    4. 2.4 Equations of Compatibility
    5. 2.5 State of Strain at a Point
    6. 2.6 Engineering Materials
    7. 2.7 Stress-Strain Diagrams
    8. 2.8 Elastic versus Plastic Behavior
    9. 2.9 Hooke’s Law and Poisson’s Ratio
    10. 2.10 Generalized Hooke’s Law
    11. 2.11 Orthotropic Materials
    12. 2.12 Measurement of Strain: Strain Gage
    13. 2.13 Strain Energy
    14. 2.14 Strain Energy in Common Structural Members
    15. 2.15 Components of Strain Energy
    16. 2.16 Saint-Venant’s Principle
    17. References
    18. Problems
  13. Chapter 3. Problems in Elasticity
    1. 3.1 Introduction
    2. 3.2 Fundamental Principles of Analysis
    3. Part A: Formulation and Methods of Solution
    4. 3.3 Plane Strain Problems
    5. 3.4 Plane Stress Problems
    6. 3.5 Comparison of Two-Dimensional Isotropic Problems
    7. 3.6 Airy’s Stress Function
    8. 3.7 Solution of Elasticity Problems
    9. 3.8 Thermal Stresses
    10. 3.9 Basic Relations in Polar Coordinates
    11. Part B: Stress Concentrations
    12. 3.10 Stresses Due to Concentrated Loads
    13. 3.11 Stress Distribution Near a Concentrated Load Acting on a Beam
    14. 3.12 Stress Concentration Factors
    15. Part C: Contact Mechanics
    16. 3.13 Contact Stresses and Deflections
    17. 3.14 Spherical and Cylindrical Contacts
    18. 3.15 Contact Stress Distribution
    19. 3.16 General Contact
    20. References
    21. Problems
  14. Chapter 4. Failure Criteria
    1. 4.1 Introduction
    2. Part A: Static Loading
    3. 4.2 Failure by Yielding
    4. 4.3 Failure by Fracture
    5. 4.4 Yield and Fracture Criteria
    6. 4.5 Maximum Shearing Stress Theory
    7. 4.6 Maximum Distortion Energy Theory
    8. 4.7 Octahedral Shearing Stress Theory
    9. 4.8 Comparison of the Yielding Theories
    10. 4.9 Maximum Principal Stress Theory
    11. 4.10 Mohr’s Theory
    12. 4.11 Coulomb–Mohr Theory
    13. 4.12 Introduction to Fracture Mechanics
    14. 4.13 Fracture Toughness
    15. Part B: Repeated and Dynamic Loadings
    16. 4.14 Fatigue: Progressive Fracture
    17. 4.15 Failure Criteria for Metal Fatigue
    18. 4.16 Fatigue Life
    19. 4.17 Impact Loads
    20. 4.18 Longitudinal and Bending Impact
    21. 4.19 Ductile–Brittle Transition
    22. References
    23. Problems
  15. Chapter 5. Bending of Beams
    1. 5.1 Introduction
    2. Part A: Exact Solutions
    3. 5.2 Pure Bending of Beams of Symmetrical Cross Section
    4. 5.3 Pure Bending of Beams of Asymmetrical Cross Section
    5. 5.4 Bending of a Cantilever of Narrow Section
    6. 5.5 Bending of a Simply Supported Narrow Beam
    7. Part B: Approximate Solutions
    8. 5.6 Elementary Theory of Bending
    9. 5.7 Normal and Shear Stresses
    10. 5.8 Effect of Transverse Normal Stress
    11. 5.9 Composite Beams
    12. 5.10 Shear Center
    13. 5.11 Statically Indeterminate Systems
    14. 5.12 Energy Method for Deflections
    15. Part C: Curved Beams
    16. 5.13 Elasticity Theory
    17. 5.14 Curved Beam Formula
    18. 5.15 Comparison of the Results of Various Theories
    19. 5.16 Combined Tangential and Normal Stresses
    20. References
    21. Problems
  16. Chapter 6. Torsion of Prismatic Bars
    1. 6.1 Introduction
    2. 6.2 Elementary Theory of Torsion of Circular Bars
    3. 6.3 Stresses on Inclined Planes
    4. 6.4 General Solution of the Torsion Problem
    5. 6.5 Prandtl’s Stress Function
    6. 6.6 Prandtl’s Membrane Analogy
    7. 6.7 Torsion of Narrow Rectangular Cross Section
    8. 6.8 Torsion of Multiply Connected Thin-Walled Sections
    9. 6.9 Fluid Flow Analogy and Stress Concentration
    10. 6.10 Torsion of Restrained Thin-Walled Members of Open Cross Section
    11. 6.11 Torsion Bar Springs
    12. 6.12 Curved Circular Bars
    13. References
    14. Problems
  17. Chapter 7. Numerical Methods
    1. 7.1 Introduction
    2. Part A: Finite Difference Analysis
    3. 7.2 Finite Differences
    4. 7.3 Finite Difference Equations
    5. 7.4 Curved Boundaries
    6. 7.5 Boundary Conditions
    7. Part B: Finite Element Analysis
    8. 7.6 Fundamentals
    9. 7.7 The Bar Element
    10. 7.8 Arbitrarily Oriented Bar Element
    11. 7.9 Axial Force Equation
    12. 7.10 Force-Displacement Relations for a Truss
    13. 7.11 Beam Element
    14. 7.12 Properties of Two-Dimensional Elements
    15. 7.13 General Formulation of the Finite Element Method
    16. 7.14 Triangular Finite Element
    17. 7.15 Case Studies in Plane Stress
    18. 7.16 Computational Tools
    19. References
    20. Problems
  18. Chapter 8. Thick-Walled Cylinders and Rotating Disks
    1. 8.1 Introduction
    2. 8.2 Thick-Walled Cylinders Under Pressure
    3. 8.3 Maximum Tangential Stress
    4. 8.4 Application of Failure Theories
    5. 8.5 Compound Cylinders: Press or Shrink Fits
    6. 8.6 Rotating Disks of Constant Thickness
    7. 8.7 Disk Flywheels
    8. 8.8 Rotating Disks of Variable Thickness
    9. 8.9 Rotating Disks of Uniform Stress
    10. 8.10 Thermal Stresses in Thin Disks
    11. 8.11 Thermal Stress in Long Circular Cylinders
    12. 8.12 Finite Element Solution
    13. References
    14. Problems
  19. Chapter 9. Beams on Elastic Foundations
    1. 9.1 Introduction
    2. 9.2 General Theory
    3. 9.3 Infinite Beams
    4. 9.4 Semi-Infinite Beams
    5. 9.5 Finite Beams
    6. 9.6 Classification of Beams
    7. 9.7 Beams Supported by Equally Spaced Elastic Elements
    8. 9.8 Simplified Solutions for Relatively Stiff Beams
    9. 9.9 Solution by Finite Differences
    10. 9.10 Applications
    11. References
    12. Problems
  20. Chapter 10. Applications of Energy Methods
    1. 10.1 Introduction
    2. Part A: Energy Principles
    3. 10.2 Work Done in Deformation
    4. 10.3 Reciprocity Theorem
    5. 10.4 Castigliano’s Theorem
    6. 10.5 Unit- or Dummy-Load Method
    7. 10.6 Crotti–Engesser Theorem
    8. 10.7 Statically Indeterminate Systems
    9. Part B: Variational Methods
    10. 10.8 Principle of Virtual Work
    11. 10.9 Principle of Minimum Potential Energy
    12. 10.10 Deflections by Trigonometric Series
    13. 10.11 Rayleigh–Ritz Method
    14. References
    15. Problems
  21. Chapter 11. Stability of Columns
    1. 11.1 Introduction
    2. 11.2 Critical Load
    3. 11.3 Buckling of Pin-Ended Columns
    4. 11.4 Deflection Response of Columns
    5. 11.5 Columns with Different End Conditions
    6. 11.6 Critical Stress: Classification of Columns
    7. 11.7 Design Formulas for Columns
    8. 11.8 Imperfections in Columns
    9. 11.9 Local Buckling of Columns
    10. 11.10 Eccentrically Loaded Columns: Secant Formula
    11. 11.11 Energy Methods Applied to Buckling
    12. 11.12 Solution by Finite Differences
    13. 11.13 Finite Difference Solution for Unevenly Spaced Nodes
    14. References
    15. Problems
  22. Chapter 12. Plastic Behavior of Materials
    1. 12.1 Introduction
    2. 12.2 Plastic Deformation
    3. 12.3 Idealized Stress–Strain Diagrams
    4. 12.4 Instability in Simple Tension
    5. 12.5 Plastic Axial Deformation and Residual Stress
    6. 12.6 Plastic Deflection of Beams
    7. 12.7 Analysis of Perfectly Plastic Beams
    8. 12.8 Collapse Load of Structures: Limit Design
    9. 12.9 Elastic–Plastic Torsion of Circular Shafts
    10. 12.10 Plastic Torsion: Membrane Analogy
    11. 12.11 Elastic–Plastic Stresses in Rotating Disks
    12. 12.12 Plastic Stress–Strain Relations
    13. 12.13 Plastic Stress–Strain Increment Relations
    14. 12.14 Stresses in Perfectly Plastic Thick-Walled Cylinders
    15. References
    16. Problems
  23. Chapter 13. Stresses in Plates and Shells
    1. 13.1 Introduction
    2. Part A: Bending of Thin Plates
    3. 13.2 Basic Assumptions
    4. 13.3 Strain–Curvature Relations
    5. 13.4 Stress, Curvature, and Moment Relations
    6. 13.5 Governing Equations of Plate Deflection
    7. 13.6 Boundary Conditions
    8. 13.7 Simply Supported Rectangular Plates
    9. 13.8 Axisymmetrically Loaded Circular Plates
    10. 13.9 Deflections of Rectangular Plates by the Strain-Energy Method
    11. 13.10 Sandwich Plates
    12. 13.11 Finite Element Solution
    13. Part B: Membrane Stresses in Thin Shells
    14. 13.12 Theories and Behavior of Shells
    15. 13.13 Simple Membrane Action
    16. 13.14 Symmetrically Loaded Shells of Revolution
    17. 13.15 Some Typical Cases of Shells of Revolution
    18. 13.16 Thermal Stresses in Compound Cylinders
    19. 13.17 Cylindrical Shells of General Shape
    20. References
    21. Problems
  24. Appendix A. Problem Formulation and Solution
    1. A.1 Basic Method
    2. Reference
  25. Appendix B. Solution of the Stress Cubic Equation
    1. B.1 Principal Stresses
    2. Reference
  26. Appendix C. Moments of Composite Areas
    1. C.1 Centroid
    2. C.2 Moments of Inertia
    3. Reference
  27. Appendix D. Tables and Charts
    1. D.1 Charts of Stress Concentration Factors
    2. References
  28. Appendix E. Introduction to MATLAB
  29. Answers to Selected Problems
  30. Index
  31. Code Snippets