Index
Abraham, L. H., 631
Airy, G. B., 132
Airy’s stress function, 132
Almroth, B. O., 536
Anisotropy, 81
Anticlastic surface, 230
Area coordinates, 379
Areas, properties of, table, 646
Axial rigidity, 90
Azar, J. J., 536
Beams
asymmetrical section of, 230
basic equations for, 242
cantilever, 135, 235, 243, 258
composite, 250
curvature of, 229
curved, 266
deflections of, table, 663, 664
on elastic foundations, 448–468
infinite, 449
kinematic relations of, 228
plastic bending of, 553
pure bending of, 227, 230, 267, 554
semi-infinite, 454
simply supported, 238
slopes of, table, 663
stress in, 244
symmetrical section of, 227
Beam column, 543
Becker, S. J., 441
Bernadou, M., 396
Bernoulli-Euler theory, 230
Betti, E., 472
Body forces, 2
Boley, B. A., 170
Boresi, A. P., 49, 110, 171, 280, 395, 536
Boundary conditions
in plates, 605
static, 494
in three-dimensional problems, 47
in torsion problems, 302–303
in two-dimensional problems, 127
Bredt’s formulas, 318
Brock, D., 217
Brush, D. O., 536
Buckling load
allowable, 522
by equilibrium method, 506
Euler’s, 508
by finite differences, 529
inelastic, 515
Bulk modulus, 93
Burr, A. H., 496
Carey, G. F., 395
Castigliano’s theorem, 472, 488
Center of twist, 300
Centroid, 645
Cheatham, J. B., 496
Chong, K.P., 49
Cold working, 183
Collapse load, 565
Column
allowable stress in, 517
critical stress in, 513
eccentrically loaded, 520
effective length of, 511
end conditions, 511
with initial curvature, 519
Compatibility equations
in polar coordinates, 146
in thermoelasticity, 140
in three-dimensional problems, 72
in torsion problems, 302
in two-dimensional problems, 72, 128, 132
Complementary energy, 102
Constant strain triangle, 379
Contact stresses, 159
Conversion factors, table, 662
Coulomb, C. A., 188
Crack, 200
Creep, 183
Critical load, 505
Crotti-Engesser theorem, 481
Cylinder
compound, 416
plastic stress in, 579, 584, 586
thermal stress in, 432
Deformation, 66
Deformational theory, 578
Design, 5
Deutschman, A. D., 217
Dieter, G. E., 217
Dilatation, 89
Disk, rotating
of constant thickness, 419, 575
of variable thickness, 426
of uniform stress, 429
Disk, thermal stress in, 431
Dislocation, 546
Dynamics, 2
Dummy (unit) load method, 479
Effective strain increment, 584
Elastic material, 80
Elastic range, 80
Elastic-plastic material, 547
Elasticity, conditions imposed in, 125
Elasticity, two- and three-dimensional problems in, 125
Elastic instability, 505
Endurance limit, 186
Engesser stress, 515
Equilibrium equations, 8
in polar coordinates, 143
for plates, 603–605
in three-dimensional problems, 21
in two-dimensional problems, 21, 127
Euler’s buckling load, 508
External forces, 2
Failure, definition of, 181
Failure, by fracture, 184
Failure, by yielding, 182
Failure theories
comparison of yielding, 193
Coulomb-Mohr, 196
maximum energy of distortion, 189
maximum principal stress, 195
maximum shear stress, 188
Mohr’s, 195
octahedral shear stress, 190
Fatigue, 186
Fatigue criterion, table, 207
Fatigue strength, 186
Faupel, J. H., 171, 496, 590, 631
Fisher, F. E., 171, 496, 590, 631
Flexural center, 257
Flügge, W., 110, 171, 466, 496
Fluid flow analogy, 321
Form factor, 265
Fourier series, 489
Fracture, 186
Fracture criteria, 187
Fracture mechanics, 200
Frame, collapse load of, 568
Fracture toughness, 203
Fundamental principles, 4, 5, 125
Galilei, Galileo, 2
Gallagher, R.H., 395
Gerber relation, 207
Goodier, J., 110, 170, 171, 280, 330
Goodman relation, modified, 207
Griffith, A. A., 184
Griffith theory, 184
Harris, C. M., 217
Hencky, H., 189
Hencky equations, 583
Hencky yield condition, 189
Hertz problem, 160
Homogeneous material, 81
Hooke’s Law
generalized, 91
for plane strain, 127
for plane stress, 129
in polar coordinates, 145
in thermoelasticity, 139
for uniaxial stress, 89
Hooke, R., 2
Huber, T. M., 189
Impact factor, 213
Impact loading, 212
Incremental theory, 583
Indicial (tensor) notation, 48, 69
Inglis, C. E., 170
Instability phenomenon, 549
Interaction curves, 562
Internal force resultants, 13
Inverse method, 133
Irwin, G. R., 217
Isotropy, 81
Iyengar, K. T., 466
Johnston, P. R., 395
Juvinall, R. C., 217
Kinematic relations, 69
Kirchhoff’s force, 605
Knight, E., 395
Knott, J. F., 217
Koiter, W. T., 529
Kotter, T., 110
Lamé’s constants, 93
Langhaar, H. L., 496
Lévy-Mises equations, 583
Limit design, 565
Limit load, 520
Linear strain triangle, 379
Linearly elastic material, 80
Logan, D. L., 395
Love, A. E. H., 49
Malkus, D. S., 395
Marin, J., 217
Martin, H. C., 395
Messal, E. E., 644
Material properties, table, 660, 661
Matrix
displacement, 372
elasticity, 374
nodal force, 375
stiffness, 352
strain, 373
stress, 374
Meguid, S. A., 217
Membrane-roof analogy, 574
Mendelson, A., 590
Method of sections, 9
Messal, E. E., 644
Michell, J. H., 170
Michels, W. J., 217
Midsurface, 618
Mises, R. von, 189
Mises-Hencky yield criterion, 190
Modulus
bulk, 93
of elasticity, 88
of elasticity in shear, 88
of foundation, 448
of plasticity, 578
of resilience, 102
of rupture, 228
secant, 578
tangent, 515
toughness, 102
Mohr, Otto, 28n
Mohr’s circle
for curvature of plates, 601
for moment of inertia, 653
for strain, 77
for stress, 28
Mohr’s theory, 195
Mollick, L., 441
Moment
of inertia, 648
sign convention for, 14, 227, 602
ultimate, 558
yield, 556
Neou, C. Y., 170
Neuber, H. P., 170
Neutral axis, 227
Neutral surface, 227
Nonlinearly elastic material, 101
Nowacki, W., 170
Numerical methods
finite differences, 338–350
finite element, 350–394
Oden, J. T., 496
Offset method, 83
Orthogonal functions, 490
Parallel-axis theorem, 649
Park, F. R., 441
Pawlik, P. S., 49
Peery, D. J., 536
Perfectly plastic material, 546, 597
Peterson, R. E., 158, 170, 668
Pívot, 147
Plane strain problems, 126
Plane stress problems, 128
Plastic
hinge, 558
hinge moment, 559
range, 84
Plasticity, 545
Plates
bending of, 598
boundary conditions for, 605
circular, 610
with circular hole, 154
equilibrium equations for, 603–605
of irregular geometry, 615
rectangular, 607
strain energy in, 613
stresses in, 601–604
Poisson, S. D., 89
Poisson’s ratio, 89
Polar coordinates, 142
Polar moment of inertia, 649
Polynomial solutions, 134
Potential energy, 487
Potential energy, principle of, 487
Prandtl and Reuss equations, 585
Prandtl’s membrane analogy, 310
Prandtl’s stress function, 302
Principal moment of inertia, 652
Proportional limit, 80
Pure shear, 13
Radius of gyration, 649
Ramberg, W., 590
Ramu, S. A., 466
Rankine, W. J. M., 195
Ranov, T., 441
Rayleigh, Lord, 472
Rayleigh-Ritz method, 493, 494
Reciprocal theorem, 471
Reismann, H., 49
Residual stress, 81, 551, 558, 586
Rigid-plastic material, 547
Ripperger, E. A., 496
Ritz, W., 493
SAE relation, 207
Saint-Venant,
Barré de, 108
principle, 108
semi-inverse method, 300
Sand-hill analogy, 575
Schmidt, R. J., 49, 171, 280, 395, 536
Secant formula, 520
Semi-inverse method, 133
Shaffer, B. W., 466
Shanley, R. F., 536
Shear, pure, 13
Shear diagonal, 27
Shear stress formula, 245
Shells
conical, 623
cylindrical, 623–624
membrane action of, 618
of revolution, 620
spherical, 622
theories of, 618
Shock loads, 212
Slenderness ratio, effective, 512
Slope, 242
Soderberg relation, 207
Sokolnikoff, I. S., 49, 110, 170, 280, 395, 496
Spring constant, 213
Statically indeterminate systems, 262, 483
Statics, 2
Sternberg, E., 110
Strain
definition of, 67
effective, 578
engineering, 82
initial, 374
invariants of, 76
logarithmic, 84
mean, 107
normal, 67
principal, 75
shear, 68
sign convention for, 68
state of, 73
tensor, 69
thermal, 139
transformation of, 73–76
true, 84
Strain-displacement relations
in plate bending, 599
in polar coordinates, 143
in three-dimensional problems, 69
in two-dimensional problems, 67, 68
Strain energy
density, 101–104
dilatational, 107
distortional, 107
in structural members, 104
total, 102
Strain gages, 97
Strain hardening, 183
index, 548
Strain rosette, 97
Strength coefficient, 548
Stress
average, 185
combined, 15
complete plastic, 588
completely reversed, 186
components of, 9
critical, 513
deviator, 107
dilatational, 107
elementary formulas for, 16
ellipsoid, 42
engineering, 82
hydrostatic, 42
invariants of, 38
normal, 10
octahedral, 42
pure shear, 13
range, 206
rupture, 83
shear, 10
sign convention for, 11
thermal, 138
transformation of, 17, 24, 33, 42
transverse normal, 249
true, 82–85
uniaxial, 13
variation of, 19
Stress concentration, 147
Stress concentration factor, 154
Stress cubic equation, 38, 640
Stress intensity factors, 201
Stress relaxation, 184
Stress resultants, 13
Stress-strain diagrams, 82, 547
Stress trajectories, 25
Sullivan, J. L., 217
Sundara, R., 466
Superposition, method of, 66, 262
Surface forces, 2
Surface tractions, 47
Systems of units, 2
Tangent modulus theory, 515
Taylor, G. I., 194, 217, 441, 631
Taylor, R. I., 395
Terry, E. S., 644
Thermal effects, 215
Thermoelasticity, 139
Timoshenko, S. P., 49, 110, 170, 171, 217, 280, 330, 496, 536, 631
Timoshenko’s theory, 230
Ting, B. Y., 466
Torsion
of circular bars, 293
of curved bars, 327
elastic-plastic, 569
of elliptical bar, 304
with one section restrained, 323
of prismatic bars, 292
of thin-walled sections, 317
stress and deformation in, table, 313
Torsional rigidity, 295
Torsion formula, 294
Transfer formula, 649
Transformed section method, 251
Transition, ductile-brittle, 215
Tresca yield criterion, 188
Triangular element, 379
Twist center, 300
Ugural, A. C., 49, 110, 171, 217, 280, 330, 395, 441, 466, 496, 536, 590, 631, 639, 668
Ultimate load, 566
Ultimate pressure, 588
Ultimate torque, 575
Unit-load method, 479
Van Vlack, L. H., 217
Variational methods, 469
Virtual displacement, 486
Virtual work, principle of, 486, 522, 529
Viscoelastic material, 80
Wahl, A. M., 330
Warping deformation, 292
Weaver, W., Jr., 395
Wedge
bending of, 149
compression of, 148
Weiner, J. H., 170
Woinowsky-Krieger, S., 631
Wilson, C. E., 217
Winkler, E., 269
Winkler foundation, 449
Winkler’s formula, 273
Winkler’s theory, 269
Work-strain energy, 470
Yield criteria, 187
Yielding, 182
Yield moment, 558
Yield point, 83
Young, T., 88
Young, W. C., 170, 280, 330, 658, 668
Young’s modulus, 88