Advanced Mechanics of Materials

Chapter 1: INTRODUCTION

• • 1.1 Review of Elementary Mechanics of Materials
• • 1.2 Methods of Analysis
• • 1.3 Stress–Strain Relations
• • 1.4 Failure and Limits on Design
• • Problems
• • References

Chapter 2: THEORIES OF STRESS AND STRAIN

• • 2.1 Definition of Stress at a Point
• • 2.2 Stress Notation
• • 2.3 Symmetry of the Stress Array and Stress on an Arbitrarily Oriented Plane
• • 2.4 Transformation of Stress, Principal Stresses, and Other Properties
• • 2.5 Differential Equations of Motion of a Deformable Body
• • 2.6 Deformation of a Deformable Body
• • 2.7 Strain Theory, Transformation of Strain, and Principal Strains
• • 2.8 Small-Displacement Theory
• • 2.9 Strain Measurement and Strain Rosettes
• • Problems
• • References

Chapter 3: LINEAR STRESS–STRAIN–TEMPERATURE RELATIONS

• • 3.1 First Law of Thermodynamics, Internal-Energy Density, and Complementary Internal-Energy Density
• • 3.2 Hooke’s Law: Anisotropic Elasticity
• • 3.3 Hooke’s Law: Isotropic Elasticity
• • 3.4 Equations of Thermoelasticity for Isotropic Materials
• • 3.5 Hooke’s Law: Orthotropic Materials
• • Problems
• • References

Chapter 4: INELASTIC MATERIAL BEHAVIOR

• • 4.1 Limitations on the Use of Uniaxial Stress–Strain Data
• • 4.2 Nonlinear Material Response
• • 4.3 Yield Criteria: General Concepts
• • 4.4 Yielding of Ductile Metals
• • 4.5 Alternative Yield Criteria
• • 4.6 General Yielding
• • Problems
• • References

Chapter 5: APPLICATIONS OF ENERGY METHODS

• • 5.1 Principle of Stationary Potential Energy
• • 5.2 Castigliano’s Theorem on Deflections
• • 5.3 Castigliano’s Theorem on Deflections for Linear Load–Deflection Relations
• • 5.4 Deflections of Statically Determinate Structures
• • 5.5 Statically Indeterminate Structures
• • Problems
• • References

Chapter 6: TORSION

• • 6.1 Torsion of a Prismatic Bar of Circular Cross Section
• • 6.2 Saint-Venant’s Semiinverse Method
• • 6.3 Linear Elastic Solution
• • 6.4 The Prandtl Elastic-Membrane (Soap-Film) Analogy
• • 6.5 Narrow Rectangular Cross Section
• • 6.6 Torsion of Rectangular Cross Section Members
• • 6.7 Hollow Thin-Wall Torsion Members and Multiply Connected Cross Sections
• • 6.8 Thin-Wall Torsion Members with Restrained Ends
• • 6.9 Numerical Solution of the Torsion Problem
• • 6.10 Inelastic Torsion: Circular Cross Sections
• • 6.11 Fully Plastic Torsion: General Cross Sections
• • Problems
• • References

Chapter 7: BENDING OF STRAIGHT BEAMS

• • 7.1 Fundamentals of Beam Bending
• • 7.2 Bending Stresses in Beams Subjected to Nonsymmetrical Bending
• • 7.3 Deflections of Straight Beams Subjected to Nonsymmetrical Bending
• • 7.4 Effect of Inclined Loads
• • 7.5 Fully Plastic Load for Nonsymmetrical Bending
• • Problems
• • References

Chapter 8: SHEAR CENTER FOR THIN-WALL BEAM CROSS SECTIONS

• • 8.1 Approximations for Shear in Thin-Wall Beam Cross Sections
• • 8.2 Shear Flow in Thin-Wall Beam Cross Sections
• • 8.3 Shear Center for a Channel Section
• • 8.4 Shear Center of Composite Beams Formed from Stringers and Thin Webs
• • 8.5 Shear Center of Box Beams
• • Problems
• • References

Chapter 9: CURVED BEAMS

• • 9.1 Introduction
• • 9.2 Circumferential Stresses in a Curved Beam
• • 9.3 Radial Stresses in Curved Beams
• • 9.4 Correction of Circumferential Stresses in Curved Beams Having I, T, or Similar Cross Sections
• • 9.5 Deflections of Curved Beams
• • 9.6 Statically Indeterminate Curved Beams: Closed Ring Subjected to a Concentrated Load
• • 9.7 Fully Plastic Loads for Curved Beams
• • Problems
• • References

Chapter 10: BEAMS ON ELASTIC FOUNDATIONS

• • 10.1 General Theory
• • 10.2 Infinite Beam Subjected to a Concentrated Load: Boundary Conditions
• • 10.3 Infinite Beam Subjected to a Distributed Load Segment
• • 10.4 Semiinfinite Beam Subjected to Loads at Its End
• • 10.5 Semiinfinite Beam with Concentrated Load Near Its End
• • 10.6 Short Beams
• • 10.7 Thin-Wall Circular Cylinders
• • Problems
• • References

Chapter 11: THE THICK-WALL CYLINDER

• • 11.1 Basic Relations
• • 11.2 Stress Components at Sections Far from Ends for a Cylinder with Closed Ends
• • 11.3 Stress Components and Radial Displacement for Constant Temperature
• • 11.4 Criteria of Failure
• • 11.5 Fully Plastic Pressure and Autofrettage
• • 11.6 Cylinder Solution for Temperature Change Only
• • 11.7 Rotating Disks of Constant Thickness
• • Problems
• • References

Chapter 12: ELASTIC AND INELASTIC STABILITY OF COLUMNS

• • 12.1 Introduction to the Concept of Column Buckling
• • 12.2 Deflection Response of Columns to Compressive Loads
• • 12.3 The Euler Formula for Columns with Pinned Ends
• • 12.4 Euler Buckling of Columns with Linearly Elastic End Constraints
• • 12.5 Local Buckling of Columns
• • 12.6 Inelastic Buckling of Columns
• • Problems
• • References

Chapter 13: FLAT PLATES

• • 13.1 Introduction
• • 13.2 Stress Resultants in a Flat Plate
• • 13.3 Kinematics: Strain–Displacement Relations for Plates
• • 13.4 Equilibrium Equations for Small-Displacement Theory of Flat Plates
• • 13.5 Stress–Strain–Temperature Relations for Isotropic Elastic Plates
• • 13.6 Strain Energy of a Plate
• • 13.7 Boundary Conditions for Plates
• • 13.8 Solution of Rectangular Plate Problems
• • 13.9 Solution of Circular Plate Problems
• • Problems
• • References

Chapter 14: STRESS CONCENTRATIONS

• • 14.1 Nature of a Stress Concentration Problem and the Stress Concentration Factor
• • 14.2 Stress Concentration Factors: Theory of Elasticity
• • 14.3 Stress Concentration Factors: Combined Loads
• • 14.4 Stress Concentration Factors: Experimental Techniques
• • 14.5 Effective Stress Concentration Factors
• • 14.6 Effective Stress Concentration Factors: Inelastic Strains
• • Problems
• • References

Chapter 15: FRACTURE MECHANICS

• • 15.1 Failure Criteria and Fracture
• • 15.2 The Stationary Crack
• • 15.3 Crack Propagation and the Stress Intensity Factor
• • 15.4 Fracture: Other Factors
• • Problems
• • References

Chapter 16: FATIGUE: PROGRESSIVE FRACTURE

• • 16.1 Fracture Resulting from Cyclic Loading
• • 16.2 Effective Stress Concentration Factors: Repeated Loads
• • 16.3 Effective Stress Concentration Factors: Other Influences
• • 16.4 Low Cycle Fatigue and the \_–N Relation
• • Problems
• • References

Chapter 17: CONTACT STRESSES

• • 17.1 Introduction
• • 17.2 The Problem of Determining Contact Stresses
• • 17.3 Geometry of the Contact Surface
• • 17.4 Notation and Meaning of Terms
• • 17.5 Expressions for Principal Stresses
• • 17.6 Method of Computing Contact Stresses
• • 17.7 Deflection of Bodies in Point Contact
• • 17.8 Stress for Two Bodies in Line Contact: Loads Normal to Contact Area
• • 17.9 Stresses for Two Bodies in Line Contact: Loads Normal and Tangent to Contact Area
• • Problems
• • References

Chapter 18: CREEP: TIME-DEPENDENT DEFORMATION

• • 18.1 Definition of Creep and the Creep Curve
• • 18.2 The Tension Creep Test for Metals
• • 18.3 One-Dimensional Creep Formulas for Metals Subjected to Constant Stress and Elevated Temperature
• • 18.4 One-Dimensional Creep of Metals Subjected to Variable Stress and Temperature
• • 18.5 Creep Under Multiaxial States of Stress
• • 18.6 Flow Rule for Creep of Metals Subjected to Multiaxial States of Stress
• • 18.7 An Application of Creep of Metals
• • 18.8 Creep of Nonmetals
• • References

Chapter APPENDIX A: AVERAGE MECHANICAL PROPERTIES OF SELECTED MATERIALS

Chapter APPENDIX B: SECOND MOMENT (MOMENT OF INERTIA) OF A PLANE AREA

• • B.1 Moments of Inertia of a Plane Area
• • B.2 Parallel Axis Theorem
• • B.3 Transformation Equations for Moments and Products of Inertia
• • Problems

Chapter APPENDIX C: PROPERTIES OF STEEL CROSS SECTIONS