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