كتاب Intermediate Mechanics of Materials
منتدى هندسة الإنتاج والتصميم الميكانيكى
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Intermediate Mechanics of Materials

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تاريخ التسجيل : 01/07/2009
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كتاب Intermediate Mechanics of Materials  Empty
مُساهمةموضوع: كتاب Intermediate Mechanics of Materials    كتاب Intermediate Mechanics of Materials  Emptyالخميس 14 يناير 2021, 9:13 pm

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Intermediate Mechanics of Materials
J.R. Barber  

كتاب Intermediate Mechanics of Materials  I_m_o_11
و المحتوى كما يلي :


Contents
1 Introduction . 1
1.1 The Engineering design process 1
1.2 Design optimization 2
1.2.1 Predicting the behaviour of the component . 3
1.2.2 Approximate solutions 5
1.3 Relative magnitude of different effects . 5
1.4 Formulating and solving problems 8
1.4.1 Use of procedures 8
1.4.2 Inverse problems . 10
1.4.3 Physical uniqueness and existence arguments . 11
1.5 Review of elementary mechanics of materials . 11
1.5.1 Definition of stress components 11
1.5.2 Transformation of stress components 13
1.5.3 Displacement and strain . 13
1.5.4 Hooke’s law 15
1.5.5 Bending of beams 17
1.5.6 Torsion of circular bars . 18
1.6 Summary . 18
Problems . 19
2 Material Behaviour and Failure 25
2.1 Transformation of stresses . 26
2.1.1 Review of two-dimensional results 27
2.1.2 Principal stresses in three dimensions . 30
2.2 Failure theories for isotropic materials . 36
2.2.1 The failure surface . 37
2.2.2 The shape of the failure envelope . 39
2.2.3 Ductile failure (yielding) 39
2.2.4 Brittle failure 51
2.3 Cyclic loading and fatigue . 63
2.3.1 Experimental data 64vi Contents
2.3.2 Statistics and the size effect 68
2.3.3 Factors influencing the design stress 74
2.3.4 Effect of combined stresses 78
2.3.5 Effect of a superposed mean stress 78
2.3.6 Summary of the design process 83
2.4 Summary . 87
Problems . 88
3 Energy Methods . 99
3.1 Work done on loading and unloading 100
3.2 Strain energy 101
3.3 Load-displacement relations . 103
3.3.1 Beams with continuously varying bending moments . 106
3.3.2 Axial loading and torsion . 107
3.3.3 Combined loading . 108
3.3.4 More general expressions for strain energy . 109
3.3.5 Strain energy associated with shear forces in beams . 109
3.4 Potential energy 110
3.5 The principle of stationary potential energy . 113
3.5.1 Potential energy due to an external force . 115
3.5.2 Problems with several degrees of freedom . 115
3.5.3 Non-linear problems . 118
3.6 The Rayleigh-Ritz method . 120
3.6.1 Improving the accuracy . 124
3.6.2 Improving the back of the envelope approximation 126
3.7 Castigliano’s first theorem . 131
3.8 Linear elastic systems . 135
3.8.1 Strain energy 136
3.8.2 Bounds on the coefficients . 138
3.8.3 Use of the reciprocal theorem 140
3.9 The stiffness matrix . 141
3.9.1 Structures consisting of beams . 142
3.9.2 Assembly of the stiffness matrix 146
3.10 Castigliano’s second theorem . 146
3.10.1 Use of the theorem . 148
3.10.2 Dummy loads . 151
3.10.3 Unit load method 154
3.10.4 Formal procedure for using Castigliano’s second theorem 155
3.10.5 Statically indeterminate problems 155
3.10.6 Three-dimensional problems . 159
3.11 Summary . 161
Problems . 162Contents vii
4 Unsymmetrical Bending 185
4.1 Stress distribution in bending . 185
4.1.1 Bending about the x-axis only 186
4.1.2 Bending about the y-axis only 187
4.1.3 Generalized bending . 188
4.1.4 Force resultants 189
4.1.5 Uncoupled problems . 190
4.1.6 Coupled problems . 192
4.2 Displacements of the beam . 195
4.3 Second moments of area . 199
4.3.1 Finding the centroid 199
4.3.2 The parallel axis theorem . 200
4.3.3 Thin-walled sections . 204
4.4 Further properties of second moments . 207
4.4.1 Coordinate transformation . 207
4.4.2 Mohr’s circle of second moments . 208
4.4.3 Solution of unsymmetrical bending problems in principal
coordinates . 213
4.4.4 Design estimates for the behaviour of unsymmetrical sections 215
4.4.5 Errors due to misalignment 219
4.5 Summary . 220
Problems . 221
5 Non-linear and Elastic-Plastic Bending . 235
5.1 Kinematics of bending 235
5.2 Elastic-plastic constitutive behaviour 237
5.2.1 Unloading and reloading 238
5.2.2 Yield during reversed loading 239
5.2.3 Elastic-perfectly plastic material 240
5.3 Stress fields in non-linear and inelastic bending . 241
5.3.1 Force and moment resultants . 242
5.4 Pure bending about an axis of symmetry . 243
5.4.1 Symmetric problems for elastic-perfectly plastic materials 244
5.4.2 Fully plastic moment and shape factor . 249
5.5 Bending of a symmetric section about an orthogonal axis . 250
5.5.1 The fully plastic case . 251
5.5.2 Non-zero axial force 254
5.5.3 The partially plastic solution . 255
5.6 Unsymmetrical plastic bending . 258
5.7 Unloading, springback and residual stress 263
5.7.1 Springback and residual curvature 264
5.7.2 Reloading and shakedown . 268
5.8 Limit analysis in the design of beams 269
5.8.1 Plastic hinges . 269
5.8.2 Indeterminate problems . 270viii Contents
5.9 Summary . 272
Problems . 274
6 Shear and Torsion of Thin-walled Beams . 287
6.1 Derivation of the shear stress formula 288
6.1.1 Choice of cut and direction of the shear stress 292
6.1.2 Location and magnitude of the maximum shear stress 297
6.1.3 Welds, rivets and bolts 299
6.1.4 Curved sections . 301
6.2 Shear centre . 303
6.2.1 Finding the shear centre . 304
6.3 Unsymmetrical sections . 311
6.3.1 Shear stress for an unsymmetrical section 311
6.3.2 Determining the shear centre . 311
6.4 Closed sections 313
6.4.1 Determination of the shear stress distribution . 313
6.5 Pure torsion of closed thin-walled sections . 318
6.5.1 Torsional stiffness 319
6.5.2 Design considerations in torsion 322
6.6 Finding the shear centre for a closed section 323
6.6.1 Twist due to a shear force . 324
6.6.2 Multicell sections 327
6.7 Torsion of thin-walled open sections . 328
6.7.1 Loading of an open section away from its shear centre . 331
6.8 Summary . 334
Problems . 336
7 Beams on Elastic Foundations . 353
7.1 The governing equation . 354
7.1.1 Solution of the governing equation 355
7.2 The homogeneous solution . 356
7.2.1 The semi-infinite beam . 357
7.3 Localized nature of the solution . 361
7.4 Concentrated force on an infinite beam . 362
7.4.1 More general loading of the infinite beam 364
7.5 The particular solution 365
7.5.1 Uniform loading . 366
7.5.2 Discontinuous loads 367
7.6 Finite beams . 370
7.7 Short beams . 373
7.8 Summary . 375
Problems . 376Contents ix
8 Membrane Stresses in Axisymmetric Shells . 385
8.1 The meridional stress . 386
8.1.1 Choice of cut 389
8.2 The circumferential stress 391
8.2.1 The radii of curvature . 393
8.2.2 Sign conventions . 395
8.3 Self-weight 398
8.4 Relative magnitudes of different loads . 401
8.5 Strains and Displacements . 402
8.5.1 Discontinuities 404
8.6 Summary . 406
Problems . 407
9 Axisymmetric Bending of Cylindrical Shells . 419
9.1 Bending stresses and moments . 419
9.2 Deformation of the shell . 421
9.3 Equilibrium of the shell element 423
9.4 The governing equation . 424
9.4.1 Solution strategy . 426
9.5 Localized loading of the shell 429
9.6 Shell transition regions 430
9.6.1 The cylinder/cone transition . 433
9.6.2 Reinforcing rings 436
9.7 Thermal stresses . 437
9.8 The ASME pressure vessel code 439
9.9 Summary . 440
Problems . 441
10 Thick-walled Cylinders and Disks 449
10.1 Solution method . 449
10.1.1 Stress components and the equilibrium condition 450
10.1.2 Strain, displacement and compatibility 451
10.1.3 The elastic constitutive law 452
10.2 The thin circular disk . 454
10.3 Cylindrical pressure vessels 460
10.4 Composite cylinders, limits and fits . 464
10.4.1 Solution procedure . 464
10.4.2 Limits and fits . 468
10.5 Plastic deformation of disks and cylinders 468
10.5.1 First yield 470
10.5.2 The fully-plastic solution 470
10.5.3 Elastic-plastic problems . 472
10.5.4 Other failure modes 476
10.5.5 Unloading and residual stresses 476x Contents
Problems . 479
11 Curved Beams . 487
11.1 The governing equation . 487
11.1.1 Rectangular and circular cross sections 489
11.1.2 The bending moment . 491
11.1.3 Composite cross sections 494
11.1.4 Axial loading . 494
11.2 Radial stresses . 499
11.3 Distortion of the cross section 502
11.4 Range of application of the theory . 504
11.5 Summary . 504
Problems . 505
12 Elastic Stability 511
12.1 Uniform beam in compression 512
12.2 Effect of initial perturbations . 517
12.2.1 Eigenfunction expansions . 520
12.3 Effect of lateral load (beam-columns) 521
12.4 Indeterminate problems . 525
12.5 Suppressing low-order modes 526
12.6 Beams on elastic foundations . 530
12.6.1 Axisymmetric buckling of cylindrical shells 532
12.6.2 Whirling of shafts 533
12.7 Energy methods 538
12.7.1 Energy methods in beam problems 540
12.7.2 The uniform beam in compression 541
12.7.3 Inhomogeneous problems . 543
12.8 Quick estimates for the buckling force . 545
12.9 Summary . 546
Problems . 547
A The Finite Element Method . 559
A.1 Approximation . 560
A.1.1 The ‘best’ approximation 560
A.1.2 Choice of weight functions 561
A.1.3 Piecewise approximations . 563
A.2 Axial loading 567
A.2.1 The structural mechanics approach . 567
A.2.2 Assembly of the global stiffness matrix 569
A.2.3 The nodal forces . 570
A.2.4 The Rayleigh-Ritz approach . 571
A.2.5 Direct evaluation of the matrix equation . 576
A.3 Solution of differential equations . 577
10.6 Summary . 478Contents xi
A.4.1 Nodal forces and moments 584
A.5 Two and three-dimensional problems 587
A.6 Computational considerations 588
A.6.1 Data storage considerations 590
A.7 Use of the finite element method in design 590
A.8 Summary . 591
Problems . 592
B Properties of Areas . 599
C Stress Concentration Factors 603
D Answers to Even Numbered Problems 607
Index .
Index
Alternating stress, 79
Anisotropy, 36
Anticlastic curvature, 396
Antiplane shear, 52
Approximation, 560
piecewise approximation, 563
ASME pressure vessel code, 439
Axial loading, 254, 567
in the plastic range, 254
of curved beams, 494
Auxiliary problem, 140
Banded matrix, 142, 570, 588
Barber’s exception, 6
Beam-columns, 521
Bending of beams, 17, 185 et seq.
in the plastic range, 241 et seq.
curved beams, 488
on elastic foundations, 353
Bending of shells, 419 et seq.
Boiler, 401, 437
Bolts, 299
Brake disc, 6, 458
Brittle fracture, 25, 51
Buckling, 322, 511 et seq.
force, 516, 526, 530, 545
initial perturbations, 517
lateral loads, 521
mode suppression, 526
of shells, 532
Bulk modulus, 485
Castigliano’s first theorem, 131
Castigliano’s second theorem, 146 et seq.
Centroid, 190, 199 et seq., 599–602
Circumferential stress, 391, 472, 489
Circumferential strain, 403, 421, 422
Closed section, 305, 313
torsion of, 318
Coefficient of thermal expansion, 7, 16,
439, 458
Column, 512
Collocation, 560
Collocation points, 561
Compatibility, 450, 451
Compatibility equation, 452
Complementary energy, 148
Complementary shear stress, 12, 291
Compliance matrix, 136
Composite cylinders, 464 et seq.
Constitutive law, 450, 452
Constraints, 123
Contact pressure, 465
Coordinate transformation, 26–36, 146,
207, 393
Crack opening displacement, 53
Critical force, 515
Critical speed, 534
Cubic spline, 581
Cyclic loading, 63 et seq., 268
Curved beams, 487 et seq.
Decay length, 361, 425
Degrees of freedom, 111, 113, 116, 120,
143, 560, 562, 582, 587
Design, 1, 74, 83, 123, 215, 269, 298, 401,
459, 535
against torsion, 322
use of finite element method, 590616 Index
optimization, 3
Deviatoric strain energy, 45
Deviatoric stress, 44
Diametral interference, 466
Dilatation, 41, 45
Dirac delta function, 363
Direction cosines, 31
Discontinuities, 368, 404
Dislocations, 40
Distortion, 45
Displacement, 13, 451
Double integrals, 599
Ductile, 25, 39
Dummy loads, 151
Economics, 2
Eigenfunction, 517
series, 520
Eigenvalues, 32, 517
Elastic behaviour, 100
Elastic foundation, 353
modulus of, 354
Elastic instability, 511 et seq.
Elastic-plastic behaviour, 237
Elastic-perfectly plastic, 240, 472
in a cylinder, 472
Embedded elastic beam, 246, 247
Endurance limit, 66
Energy methods, 99 et seq., 538
Engineering shear strain, 14
Equation of motion, 451
Equilibrium, 112, 288, 355, 363, 387, 390,
392, 423, 450, 451, 462, 578
Equivalent tensile stress, 47
Equivalent determinate problem, 18, 155,
159
Failure envelope, 38, 39, 48, 49, 60–62
Failure theories, 36 et seq.
Failure surface, 37
Fatigue, 25, 63 et seq.
low cycle, 67
Fatigue limit, 66
Flexible axis, 209
Fillet radius, 74
Finite element method, 125, 559 et seq.
for beam problems, 579
First yield moment, 242
Flexural rigidity, 102, 106, 211, 354, 358,
518, 581
Floating beams, 374
Foundation modulus, 354
Fourier series, 124
Fourier transform, 366
Fracture, brittle, 25
Fracture mechanics, 52
Fracture toughness, 52, 54
Fully-plastic moment, 242, 249, 251
Generalized coordinates, 148
Goodman diagram, 80
Gradient factor, 71
Griffith criterion, 52, 53
Heat exchanger, 437, 439
Homogeneous equation, 514
Homogeneous solution, 356, 514, 518
Hooke’s law, 15, 403, 421, 422, 437, 450,
452
Hoop stress, 391
Hydrostatic stress, 42
Hysteresis, 100
Indeterminacy, 155, 270, 525
Influence coefficients, 136
Initial imperfections, 517, 545
Initial perturbations, 517
Instability, 111, 113, 511 et seq.
Interference, 465, 466
Invariants, 32, 34
Inverse problems, 10
Isotropic hardening, 239
Isotropy, 15, 36
Laplace transform, 366
Least squares fit, 120, 215, 561, 577
Limit analysis, 269
Limits and fits, 468
Linear elastic systems, 135 et seq.
Longitudinal stress, 387
Manufacturing errors, 221, 468, 517, 520,
536, 545
Material failure, 25 et seq.
Mathematical shear strain, 14
Maxwell’s reciprocal theorem, 138 et seq.,
323
Melan’s theorem, 268
Metal forming, 235, 273, 283
Membrane displacement, 425
Median line, 252
Meridional stress, 386
Misalignment, 219, 517
Mode suppression, 526
Modified Mohr criterion, 61Index 617
Modulus, bulk, 485
of a foundation, 354
of rigidity, 16
shear, 16
Young’s, 15
Mohr’s circle, 28, 35
of second moments, 208
Mohr’s failure theory, 61
Multiply-connected section, 305
Neutral axis, 193, 216, 241, 489
Neutral plane, 188
Neutrally stable, 514, 515
Newton’s second law, 449, 451
Nodes, 141, 142, 563
Nodal displacements, 568, 579
Nodal forces, 570, 584
Nodal values, 563
Nominal stress, 74
Non-linearity, 118
Non-local displacement, 353, 362
Notch sensitivity, 76
Octahedral normal stress, 46
Octahedral plane, 45
Octahedral shear stress, 45, 46
Open section, 305
Orthogonality, 32, 125, 521
Parallel axis theorem, 200, 201
Particular solution, 365, 518
Periodic loading, 63 et seq., 268
Perturbations, 517
Plane sections remain plane, 186, 235, 236
Plane stress, 37, 453
Plane strain, 453, 461
Plastic hinge, 242, 269
Plastic moment, 242, 249, 251
Plates, 385
Poisson’s ratio, 15
strains, 422, 427, 453, 462
Potential energy, 110, 115
Pressure vessels, 460
plastic deformation, 468
Pressure vessel code, 439
Procedures, 8–10
Principal axes, 13, 29, 31, 209
Principal coordinates, 213
Principal second moments, 209
Principal stress, 29, 30
Process zone, 54
Product second moment (product inertia),
190, 199
Radial clearance, 466
Radial interference, 465
Radial stress, 472, 499
Rayleigh-Ritz method, 120 et seq., 540,
560, 571
Reciprocal theorem, 138 et seq., 323
Redundant reactions, 17, 155, 525
Reinforcing ringes, 436
Reliability, 68, 70
Residual stress, 263, 476
Residual curvature, 264
Rotation, 451, 456, 473, 534
S–N curve, 65
Safety factor, 47, 57, 63, 64, 78, 80, 84, 87
Saint Venant’s principle, 236
Second moments of area, 199, 599–602
Series, 124, 520, 560
eigenfunction, 520
Fourier, 124
Shakedown, 268
Shape factor, 249
Shape functions, 560, 564, 580
Shear centre, 303 et seq.
for angle sections, 312
for closed sections, 323 et seq.
Shear flow, 291, 294
Shear force, 287 et seq.
twist due to, 324, 331
Shear modulus, 16
Shells, 385 et seq.
displacements, 403
bending stresses in, 419 et seq.
membrane stresses in, 386 et seq.
radii, 393
self weight, 398
transitions, 430
Shrink fit, 482
Simply connected section, 305
Size effect, 68, 71
Springback, 264, 273, 283
Stability, 111, 113, 511 et seq.
Statically indeterminate, 155, 270, 525
Stationary potential energy, 113
Stiff axis, 209
Stiffness, 101
of a shell, 422618 Index
Stiffness matrix, 141 et seq., 559, 566
assembly, 146, 559, 569, 582
element stiffness matrix, 569
global stiffness matrix, 569
Strain, 11
circumferential, 403, 421, 422
normal, 13
shear, 14, 42
Strain energy, 43, 101 et seq., 492
in axial loading, 108
in bending, 102, 106
in a spring, 101
in torsion, 108, 319
Strain energy density, 44, 109
Strain energy release rate, 58
Stress, 11
alternating, 79
circumferential, 391, 472, 489
complementary shear, 12, 291
coordinate transformation, 26–36
deviatoric, 44
equivalent tensile, 47
hydrostatic, 42
invariants, 32, 34
longitudinal, 386
meridional, 386
nominal, 74
normal, 12
octahedral shear, 45
principal, 29, 30
radial, 472, 499
residual, 263, 476
shear, 12, 291
Stress concentration factor, 74, 603
Stress intensity factor, 51 et seq.
Surface energy, 52
Surface factor, 72
Surface finish, 71
coefficient of, 16
Taylor, series, 386, 419
Thermal conductivity, 437
Thermal expansion, 16
Thermal stress, 437, 458
Thin-walled sections, 204, 287 et seq., 511
Tolerances, 468
Toroidal transition, 431 et seq.
Torque wrench, 133
Torsion, 18, 108
of closed thin-walled sections, 318
design considerations, 322
multicell sections, 327
of open thin-walled sections, 328
Torsional stiffness, 319
Transformation of coordinates, 26–36, 146,
207, 393
Twist, 319, 324
Tresca’s theory, 43, 48, 469
Ultimate strength, 67, 80, 81
Unilateral support, 360
Uniqueness, 11
Unit load method, 154
Unloading, 238, 263, 476
Unsymmetrical bending, 185 et seq.
plastic, 258
shear stresses, 311
Variational methods, 99 et seq.
Volume change, 41, 45
von Mises theory, 43, 48
Weibull distribution, 68
Weight functions, 561
Welds, 299
Whirling of shafts, 533
Whirling speed, 534
Winkler foundation, 354
Work done, 100, 319
Work hardening, 167, 238
Yielding, 25, 39
Young’s modulus, 15


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