Strength of Materials

اسم المؤلف

A.k. Srivastava, P.C. GOPE

التاريخ

5 يناير 2022

التصنيف

هندسة الإنتاج والتصميم الميكانيكى

المشاهدات

352

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Strength of Materials
Second Edition
A.k. Srivastava
Manager (Design)
Aircraft Upgrade Research and Design Centre
Hindustan Aeronautics Limited
Nasik
P.C. GOPE
Professor
College of Technology
G.B. Pant University of Agriculture and Technology
Pantnager
Contents
Foreword xiii
Preface xv
Preface to the First Edition xvii

1. SIMPLE AND COMPOUND STRESS 1–48
   1.1 Introduction 1
   1.2 Stress 1
   1.3 Uniformly Distributed Stress 3
   1.3.1 Tensile and Compressive Stresses 3
   1.3.2 Stress Due to Bending Moment 4
   1.3.3 Stress Due to Twisting Moment 5
   1.4 Complex Stresses 6
   1.4.1 Plane Stress 6
   1.4.2 Stresses on an Inclined Plane 7
   Exercises 46
2. ANALYSIS OF STRESS AND STRAIN 49–94
   2.1 Introduction 49
   2.2 Force Distribution 49
   2.3 The State of Stress at a Point 50
   2.4 Stress Notations 50
   2.5 Stress Tensor at a Point 50
   2.6 Stress Gradient 51
   2.7 Differential Equations of Equilibrium 51
   2.8 Equilibrium Equations for Plane Stress State 53
   2.9 Generalized Hooke’s Law 53
   2.10 Direction Cosines 55
   2.11 Normal and Shear Stresses 56
   Contents
   2.12 Principal Directions 57
   2.13 Stress Components on an Arbitrary Plane 57
   2.14 Principal Stress 59
   2.15 Stress Invariants 60
   2.16 Principal Directions 61
   2.17 Octahedral Stress 68
   2.18 Mean and Deviator Stresses 70
   2.19 Strain Analysis 74
   2.20 Strain-Displacement Relation 75
   2.21 Three-dimensional Strains 79
   2.22 Normal and Shearing Strains 80
   2.23 Principal Strains 80
   2.24 Principal Strain Directions 81
   2.25 Concept of Compatibility 81
   2.26 St-Venant’s Equations of Compatibility 83
   2.27 Solution of Stress Differential Equation 86
   2.28 Types of Airy’s Stress Function 88
   2.29 Application of Airy’s Stress Function 90
   2.30 Mohr’s Circle for the Three-dimensional State of Stress 92
   Exercises 94
3. THEORY OF FAILURE 95–139
   3.1 Introduction 95
   3.2 Failure Theory for Ductile Material 96
   3.2.1 Maximum Shear Stress Theory 96
   3.2.2 Maximum Distortion Energy Theory 102
   3.2.3 Strain Energy Density or Total Strain Energy Criterion 105
   3.3 Theory of Failure or Yield Criterion for Brittle Materials 106
   3.3.1 Maximum Principal Stress Criterion 106
   3.3.2 Maximum Principal Strain Criterion 107
   3.4 Mohr’s Theory 108
   3.5 Experimental Verification of Theory of Failure 111
   3.5.1 Comparison of Failure Criteria 113
   3.6 Theory of Failure for Cyclic Loads 123
   3.6.1 Stress Parameters 123
   3.6.2 Strength Parameter 124
   Exercises 139
4. ENERGY METHODS 140–157
   4.1 Introduction 140
   4.2 Strain Energy 140
   4.2.1 Strain Energy with Simple Loading 143
   4.2.2 Strain Energy due to Moment M 143Contents 
   4.2.3 Strain Energy due to Torsional Loading 143
   4.2.4 Strain Energy due to Transverse Shear 144
   4.3 Castigliano’s First Theorem 147
   Exercises 156
5. DEFLECTION OF BEAMS 158–195
   5.1 Introduction 158
   5.2 Relation between Slope, Deflection and Radius of Curvature 158
   5.3 Method for Slope and Deflection 159
   5.3.1 Double Integration Method for Slope and Deflection 160
   5.3.2 Macaulay’s Method 172
   5.3.3 Moment Area Method 179
   5.3.4 Mohr’s Theorems 181
   5.4 Indeterminate Structure 185
   5.5 Continuous Beam 186
   5.6 Clapeyron’s Theorem of Three Moments 186
   Exercises 194
6. CURVED BEAM 196–224
   6.1 Introduction 196
   6.2 Stresses in Curved Beam (Winkler–Bach Theory) 196
   6.3 Position of Neutral Axis 200
   6.4 Values of h2 200
   6.4.1 Rectangular Cross-section 201
   6.4.2 Circular Cross-section 201
   6.4.3 I-section 202
   6.4.4 T-section 202
   6.4.5 Trapezoidal Cross-section 203
   6.5 Stresses in a Ring 214
   6.6 Stresses in a Chain Link 220
   Exercises 223
7. THIN CYLINDER AND SPHERE 225–240
   7.1 Introduction 225
   7.2 Classification of Pressure Vessels 225
   7.3 Stresses in a Thin Cylindrical Shell due to an Internal Pressure 225
   7.4 Circumferential or Hoop Stress 226
   7.5 Longitudinal Stress 227
   7.6 Effect of Internal Pressure on the Dimensions of a Thin Cylindrical Shell 230
   7.7 The Spherical Shells Subjected to an Internal Pressure 236
   7.8 Change in Dimensions of Thin Spherical Shell due to an Internal Pressure 237
   Exercises 240 Contents
8. THICK AND COMPOUND CYLINDER 241–262
   8.1 Introduction 241
   8.2 Lame’s Theory 241
   8.3 Application of Theories of Failure 250
   8.4 Compound Cylindrical Shell 252
   8.5 Thick Spherical Shells 256
   Exercises 262
9. UNSYMMETRICAL BENDING AND SHEAR CENTRE 263–281
   9.1 Introduction 263
   9.2 Definitions 263
   9.3 Stresses due to Unsymmetrical Bending 264
   9.4 Deflection of Beam due to Unsymmetrical Bending 266
   9.5 Shear Centre 275
   9.5.1 Shear Centre for Channel Section 275
   9.5.2 Shear Centre of Unequal I-section 278
   Exercises 280
10. COLUMNS AND STRUTS 282–307
    10.1 Introduction 282
    10.2 Definitions 282
    10.3 Classification of Column 282
    10.4 Assumptions Made in the Euler’s Column Theory 283
    10.5 Expressions for Crippling Load of Different Cases 283
    10.5.1 Both the Ends are Hinged or Pinned 283
    10.5.2 One End is Fixed and Other is Free 284
    10.5.3 Both Ends are Fixed 286
    10.5.4 One End is Fixed, Other is Hinged 287
    10.6 Effective Length of a Column 288
    10.7 Slenderness Ratio 289
    10.8 Crippling Stress in Terms of Effective Length and Radius of Gyration 289
    10.9 Limitation of Euler’s Formula 290
    10.10 Rankine’s Formula 296
    10.11 Eccentric Loading 302
    10.12 Johnson’s Formula for Columns 304
    10.12.1 Johnson’s Straight Line Formula for Columns 304
    10.12.2 Johnson’s Parabolic Formula for Columns 305
    Exercises 305
11. SPRING 308–333
    11.1 Introduction 308
    11.2 Definitions 308
    11.3 Types of Springs 309Contents 
    11.4 Helical Spring 309
    11.4.1 Closely-coiled Helical Springs 309
    11.4.2 Open-coiled Helical Springs 312
    11.5 Strain Energy in the Spring 314
    11.6 Springs under Impact Load 315
    11.7 Springs in Series 315
    11.8 Springs in Parallel 315
    11.9 Leaf Springs or Carriage Springs 326
    11.9.1 Semi-elliptical Spring 326
    11.9.2 Quarter-elliptical Leaf Spring 330
    Exercises 333
12. ROTATING DISCS AND CYLINDERS 334–349
    12.1 Introduction 334
    12.2 Rotating Disc 334
    12.2.1 Strain Considerations 335
    12.3 Hollow Disc (Disc with a Central Hole) 337
    12.4 Solid Disc 338
    12.5 Disc of Uniform Strength 338
    12.6 Rotating Cylinder 340
    12.7 Solid Cylinder 342
    12.8 Hollow Cylinder 343
    Exercises 348
13. FINITE ELEMENT METHOD AND ITS APPLICATION USING ANSYS
    SOFTWARE 350–391
    13.1 Introduction 350
    13.2 The Steps 350
    13.3 Principle of Minimum Potential Energy 351
    13.3.1 Potential Energy 352
    13.4 Computer Aided Stress Analysis Technique 353
    13.5 Elements Type and Shapes 354
    13.6 One-dimensional Problems 358
    13.6.1 Natural Coordinate (Intrinsic Coordinate) 358
    13.6.2 Isoparametric Element 359
    13.6.3 Element Strain Displacement Matrix 359
    13.6.4 Element Stiffness Matrix 360
    13.6.5 Forces 362
    13.7 Application of Finite Element Analysis Using the Ansys Software 367
    13.7.1 Application of Finite Element Analysis Using 1D Element 367
    13.7.2 Application of Finite Element Analysis Using 2D Element 379
    13.7.3 Application of Finite Element Analysis Using 3D Element 386
    INDEX 393–39
    7
    reduction factor, 127
    Finite element method, 350
    Generalized Hooke’s law, 53
    Gerber equation, 128
    Goodman diagram, 128–129
    Helical spring, 308
    Hooke’s law, 53
    Hoop or circumferential stress, 226, 236
    Indeterminate structure, 185
    Lame’s
    equations, 243
    theory, 241
    Load factor, 126
    Long column, 283
    Longitudinal stress, 225–226
    Macaulay’s method, 159, 172
    Maximum
    distortion energy theory, 102
    normal stress, 10 Index
    principal strain criterion, 107
    principal stress criterion, 106
    shear stress, 10
    shear stress theory, 96
    Mean
    and deviator stresses, 70
    stress, 123
    Medium column, 283
    Mohr’s
    circle, 15
    theory, 108
    Mohr–Coulomb criterion, 111
    Moment area method, 159, 179
    Neutral axis, 196, 200
    Normal stress, 2
    Octahedral
    plane, 68
    stress, 68
    Open-coiled spring, 308
    PI plane, 99
    Plane stress, 6
    Principal stress, 14
    Radial stress, 226
    Radius of gyration, 289
    Rankine’s formula, 296
    Safe load, 282
    Second moment area, 263
    Shear stress, 5, 8
    Short column, 282
    Size factor, 125
    Slenderness ratio, 228–283
    Soderberg criterion, 132, 136
    Solution of stress differential equation, 86
    Spring index, 312
    St. Venant’s equations, 83
    State of pure shear, 71
    State of stress, 71
    Statically indeterminate
    problems, 185
    structures, 185
    Stiffness, 158, 315
    Strain energy density, 105
    Strain-displacement relation, 74–75
    Stress, 1–2
    gradient, 51
    invariants, 60
    on an inclined plane, 7
    tensor, 60
    Strut, 282
    Surface
    finish factor, 125
    forces, 125
    Tensile and compressive stresses, 3
    Theory of failure, 132
    Thick shell, 225
    Thin shell, 225
    Torsional rigidity, 309
    Tresca criterion, 96
    Two-dimensional state of stress, 41
    Unsymmetrical bending, 263
    Variable stress, 124
    von Mises theory, 102
    Wahl’s correction factor, 312
    Winkler-Bach theory, 196
    Yield criterion, 96

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