Mechanics of Materials

Contents of Volume 1IntroductionNotation16 Unsymmetrical Bending Summary Introduction 16.1 Product Second Moment of Area 16.2 Principal Second Moments of Area 16.3 Mohr's Circle of Second Moments of Area 16.4 Land's Circle of Second Moments of Area 16.5 Rotation of Axes: Determination of Moments of Area in Terms of the Principal Values 16.6 The Ellipse of Second Moments of Area 16.7 Momental Ellipse 16.8 Stress Determination 16.9 Alternative Procedure for Stress Determination 16.10 Alternative Procedure Using the Momental Ellipse 16.11 Deflections Examples Problems17 Struts Summary Introduction 17.1 Euler's Theory 17.2 Equivalent Strut Length 17.3 Comparison of Euler Theory with Experimental Results 17.4 Euler "Validity Limit" 17.5 Rankine or Rankine—Gordon Formula 17.6 Perry—Robertson Formula 17.7 British Standard Procedure (BS 449) 17.8 Struts with Initial Curvature 17.9 Struts with Eccentric Load 17.10 Laterally Loaded Struts 17.11 Alternative Procedure for Any Strut-Loading Condition 17.12 Struts with Unsymmetrical Cross-Sections Examples Problems18 Strains Beyond the Elastic Limit Summary Introduction 18.1 Plastic Bending of Rectangular-Sectioned Beams 18.2 Shape Factor — Symmetrical Section 18.3 Application to I-Section Beams 18.4 Partially Plastic Bending of Unsymmetrical Sections 18.5 Shape Factor — Unsymmetrical Section 18.6 Deflection of Partially Plastic Beams 18.7 Length of Yielded Area in Beams 18.8 Collapse Loads — Plastic Limit Design 18.9 Residual Stresses after Yielding: Elastic Perfectly Plastic Material 18.10 Torsion of Shafts beyond the Elastic Limit — Plastic Torsion 18.11 Angles of Twist of Shafts Strained beyond the Elastic Limit 18.12 Plastic Torsion of Hollow Tubes 18.13 Plastic Torsion of Case-Hardened Shafts 18.14 Residual Stresses after Yield in Torsion 18.15 Plastic Bending and Torsion of Strain-Hardening Materials (a) Inelastic Bending (b) Inelastic Torsion 18.16 Residual Stresses — Strain-Hardening Materials 18.17 Influence of Residual Stresses on Bending and Torsional Strengths 18.18 Plastic Yielding in the Eccentric Loading of Rectangular Section 18.19 Plastic Yielding and Residual Stresses under Axial Loading with Stress Concentrations 18.20 Plastic Yielding of Axially Symmetric Components (a) Thick Cylinders — Collapse Pressure (b) Thick Cylinders— "Auto Frettage" (c) Rotating Discs Examples Problems19 Rings, Discs and Cylinders Subjected to Rotation and Thermal Gradients Summary 19.1 Thin Rotating Ring or Cylinder 19.2 Rotating Solid Disc 19.3 Rotating Disc with a Central Hole 19.4 Rotating Thick Cylinders or Solid Shafts 19.5 Rotating Disc of Uniform Strength 19.6 Combined Rotational and Thermal Stresses in Uniform Discs and Thick Cylinders Examples Problems20 Torsion of Non-Circular and Thin-Walled Sections Summary 20.1 Rectangular Sections 20.2 Narrow Rectangular Sections 20.3 Thin-Walled Open Sections 20.4 Thin-Walled Split Tube 20.5 Other Solid (non-Tubular) Shafts 20.6 Thin-Walled Closed Tubes of non-Circular Section (Bredt—Batho Theory) 20.7 Use of "Equivalent J" for Torsion of non-Circular Sections 20.8 Thin-Walled Cellular Sections 20.9 Torsion of Thin-Walled Stiffened Sections 20.10 Membrane Analogy 20.11 Effect of Warping of Open Sections Examples Problems21 Experimental Stress Analysis Introduction 21.1 Brittle Lacquers 21.2 Strain Gauges 21.3 Unbalanced Bridge Circuit 21.4 Null Balance or Balanced Bridge Circuit 21.5 Gauge Construction 21.6 Gauge Selection 21.7 Temperature Compensation 21.8 Installation Procedure 21.9 Basic Measurement Systems 21.10 D.C. and A.C. Systems 21.11 Other Types of Strain Gauge 21.12 Photo-elasticity 21.13 Plane Polarized Light — Basic Polariscope Arrangements 21.14 Temporary Birefringence 21.15 Production of Fringe Patterns 21.16 Interpretation of Fringe Patterns 21.17 Calibration 21.18 Fractional Fringe Order Determination — Compensation Techniques 21.19 Isoclinics — Circular Polarization 21.20 Stress Separation Procedures 21.21 Three-Dimensional Photo-elasticity 21.22 Reflective Coating Technique 21.23 Other Methods of Strain Measurement Bibliography22 Circular Plates and Diaphragms Summary A. Circular Plates 22.1 Stresses 22.2 Bending Moments 22.3 General Equation for Slope and Deflection 22.4 General Case of a Circular Plate or Diaphragm Subjected to Combined Uniformly Distributed Load q (Pressure) and Central Concentrated Load F 22.5 Uniformly Loaded Circular Plate with Edges Clamped 22.6 Uniformly Loaded Circular Plate with Edges Freely Supported 22.7 Circular Plate with Central Concentrated Load F and Edges Clamped 22.8 Circular Plate with Central Concentrated Load F and Edges Freely Supported 22.9 Circular Plate Subjected to a Load F Distributed Round a Circle 22.10 Application to the Loading of Annular Rings 22.11 Summary of End Conditions 22.12 Stress Distributions in Circular Plates and Diaphragms Subjected to Lateral Pressures 22.13 Discussion of Results — Limitations of Theory 22.14 Other Loading Cases of Practical Importance B. Bending of Rectangular Plates 22.15 Rectangular Plates with Simply Supported Edges Carrying Uniformly Distributed Loads 22.16 Rectangular Plates with Clamped Edges Carrying Uniformly Distributed Loads Examples Problems23 Introduction to Advanced Elasticity Theory 23.1 Types of Stress 23.2 The Cartesian Stress Components: Notation and Sign Convention 23.2.1 Sign Conventions 23.3 The State of Stress at a Point 23.4 Direct, Shear and Resultant Stresses on an Oblique Plane 23.4.1 Line of Action of Resultant Stress 23.4.2 Line of Action of Normal Stress 23.4.3 Line of Action of Shear Stress 23.4.4 Shear Stress in Any other Direction on the Plane 23.5 Principal Stresses and Strains in Three-Dimensions — Mohr's Circle Representation 23.6 Graphical Determination of Direction of Shear Stress Tn on an Inclined Plane 23.7 The Combined Mohr Diagram for Three-Dimensional Stress and Strain Systems 23.8 Application of the Combined Circle to Two-Dimensional Stress Systems 23.9 Graphical Construction for the State of Stress at a Point 23.10 Construction for the State of Strain on a General Strain Plane 23.11 State of Stress — Tensor Notation 23.12 The Stress Equations of Equilibrium 23.13 Principal Stresses in a Three-Dimensional Cartesian Stress System 23.13.1 Solution of Cubic Equations 23.14 Stress Invariants — Eigen Values and Eigen Vectors 23.15 Stress Invariants 23.16 Reduced Stresses 23.17 Strain Invariants 23.18 Alternative Procedure for Determination of Principal Stresses 23.18.1 Evaluation of Direction Cosines for Principal Stresses 23.19 Octahedral Planes and Stresses 23.20 Deviatoric Stresses 23.21 Deviatoric Strains 23.22 Plane Stress and Plane Strain 23.22.1 Plane Stress 23.22.2 Plane Strain 23.23 The Stress Strain Relations 23.24 The Strain—Displacement Relationships 23.25 The Strain Equations of Transformation 23.26 Compatibility 23.27 The Stress Function Concept 23.27.1 Forms of Airy Stress Function in Cartesian Coordinates 23.27.2 Case 1 - Bending of a Simply Supported Beam by a Uniformly Distributed Loading 23.27.3 The Use of Polar Coordinates in Two Dimensions 23.27.4 Forms of Stress Function in Polar Coordinates 23.27.5 Case 2 - Axi-Symmetric Case: Solid Shaft and Thick Cylinder Radially Loaded with Uniform Pressure 23.27.6 Case 3 - The Pure Bending of a Rectangular Section Curved Beam 23.27.7 Case 4 - Asymmetric Case n = 1. Shear Loading of a Circular Arc Cantilever Beam 23.27.8 Case 5 - The Asymmetric Cases n ≥ 2 — Stress Concentration at a Circular Hole in a Tension Field 23.27.9 Other Useful Solutions of the Biharmonic Equation Examples Problems24 Miscellaneous Topics 24.1 Bending of Beams with Initial Curvature 24.2 Bending of Wide Beams 24.3 General Expression for Stresses in Thin-Walled Shells Subjected to Pressure or Self-Weight 24.4 Bending Stresses at Discontinuities in Thin Shells 24.5 Viscoelasticity 24.6 Introduction to the Finite Element Method 24.6.1 Applicability of the Finite Element Method (F.E.M.) 24.6.2 Boundary Value Problems 24.6.3 Formulation of the F.E.M. 24.6.4 The Displacement Method 24.6.5 The F.E.M. Applied to a Continuum 24.6.6 General Procedure of the F.E.M. References Examples Problems25 Contact Stress; Residual Stress and Stress Concentrations Summary 25.1 Contact Stresses Introduction 25.1.1 General Case of Contact between Two Curved Surfaces 25.1.2 Special Case 1 - Contact of Parallel Cylinders 25.1.3 Combined Normal and Tangential Loading 25.1.4 Special Case 2 - Contacting Spheres 25.1.5 Design Considerations 25.1.6 Contact Loading of Gear Teeth 25.1.7 Contact Stresses in Spur and Helical Gearing 25.1.8 Bearing Failures 25.2 Residual Stresses Introduction 25.2.1 Reasons for Residual Stresses 25.2.2 The Influence of Residual Stress on Failure 25.2.3 Measurement of Residual Stresses 25.2.4 Summary of the Principal Effects of Residual Stress 25.3 Stress Concentrations Introduction 25.3.1 Evaluation of Stress Concentration Factors 25.3.2 St. Versant's Principle 25.3.3 Theoretical Considerations of Stress Concentrations due to Concentrated Loads 25.3.4 Fatigue Stress Concentration Factor 25.3.5 Notch Sensitivity 25.3.6 Strain Concentration — Neuber's Rule 25.3.7 Designing to Reduce Stress Concentration 25.3.8 Use of Stress Concentration Factors with Yield Criteria 25.3.9 Design Procedure References Examples Problems26 Fatigue, Creep and Fracture Summary 26.1 Fatigue Introduction 26.1.1 The S/N Curve 26.1.2 P/S/N Curves 26.1.3 Effect of Mean Stress 26.1.4 Effect of Stress Concentration 26.1.5 Cumulative Damage 26.1.6 Cyclic Stress-Strain 26.1.7 Combating Fatigue 26.1.8 Slip Bands and Fatigue 26.2 Creep Introduction 26.2.1 The Creep Test 26.2.2 Presentation of Creep Data 26.2.3 The Stress—Rupture Test 26.2.4 Parameter Methods 26.2.5 Stress Relaxation 26.2.6 Creep-Resistant Alloys 26.3 Fracture Mechanics Introduction 26.3.1 Energy Variation in Cracked Bodies 26.3.2 Linear Elastic Fracture Mechanics (L.E.F.M.) 26.3.3 Elastic Plastic Fracture Mechanics (E.P.F.M.) 26.3.4 Fracture Toughness 26.3.5 Plane Strain and Plane Stress Fracture Modes 26.3.6 General Yielding Fracture Mechanics 26.3.7 Fatigue Crack Growth 26.3.8 Crack Tip Plasticity under Fatigue Loading 26.3.9 Measurement of Fatigue Crack Growth References Examples Problems Appendix 1. Typical Mechanical and Physical Properties for Engineering MaterialsAppendix 2. Typical Mechanical Properties of Non-MetalsAppendix 3. Other Properties of Non-MetalsIndexOther Titles in the Series