Barber J.R. Intermediate Mechanics of Materials
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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, 590
616 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, 61
Index 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, 422
618 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