Index

Airy, G. B., 102

Airy’s stress function, 102

Almroth, B. O., 531

Angle of twist, 242, 245

Anisotropy, 64

Anticlastic surface, 187

Area coordinates, 295

Areas, properties of, table, 511

Avallone, E. A., 528

Axial rigidity, 68

Bathe, K. I., 531

Baumeister III, T., 528

Beams

asymmetrical section of, 188

basic equations for, 199

cantilever, 106, 192, 200, 213

classification of, 358

composite, 206

curvature of, 186

curved, 221

deflections of, table, 527

on elastic foundations, 349–368

infinite, 350

kinematic relations of, 186

plastic bending of, 438

pure bending of, 184, 188, 440

semi-infinite, 355

simply supported, 195

slopes of, table, 527

strain energy in, 80, 220

stress in, 201

symmetrical section of, 185

Beam-column, 430

Becker, S. J., 531

Bending, theory of, 197, 473

Bernoulli-Euler law, 187

Betti, E., 371

Body forces, 2

Boley, B. A., 529

Boresi, A. P., 528, 529

Boundary conditions

geometric, 284, 391

in plates, 479

static, 391

in three-dimensional problems, 38

in torsion problems, 246–247

in two-dimensional problems, 98

Bredt’s formulas, 259

Brittle material, 65, 146

Brush, D. O., 531

Buckling load

allowable, 413

by energy method, 413

by equilibrium method, 403

Euler’s, 404

by finite differences, 420

inelastic, 406

Budynas, R. G., 530

Bulk modulus, 71

Castigliano’s theorem, 372, 385

Center of twist, 244

Centroid, 510

Chong, K. P., 528

Chou, P. C., 528

Cold working, 147

Collapse load, 447

Column

allowable stress in, 408

classification of, 406, 408

critical stress in, 406

eccentrically loaded, 411

effective length of, 405

end conditions, 405

with initial curvature, 410

Compatibility equations

in polar coordinates, 116

in thermoelasticity, 109

in three-dimensional problems, 57

in torsion problems, 246

in two-dimensional problems 57, 99, 101

Complementary energy, 76

Constant strain triangle, 295

Contact stresses, 129

Conversion factors, table, 526

Cook, R. D., 530

Coulomb, C. A., 152

Cozzarelli, F. A., 528

Crack, 163

Creep, 147

Critical load, 401

Crotti-Engesser theorem, 380

Curved beam factor, 225

Cylinder

compound, 322

plastic stress in, 457, 462, 464

thermal stress in, 336

thick-walled, 315, 464

thin-walled, 11, 496

Deformation, 51

Deformational theory, 455

Design, 3

Deutschman, A. D., 530

Dilatation, 67

Direction cosines, 26, 506

Disk, rotating

of constant thickness, 325, 453

of variable thickness, 330

of uniform stress, 333

Disk, thermal stress in, 334

Dislocation, 434

Dynamic loading, 172, 175

Dynamics, 1

Ductile material, 64, 146

Dummy (unit) load method, 378

Effective strain increment, 461

Einstein, A., 504

Elastic material, 63

Elastic range, 63

Elastic-plastic material, 435

Elasticity, conditions imposed in, 96

Elasticity, two-dimensional problems in, 95

Elastic stability, 401

Endurance limit, 150

Energy methods, 369, 413

Engesser stress, 407

Equilibrium, 402–403

Equilibrium equations

in polar coordinates, 113

for plates, 477–478

in three-dimensional problems, 16

in two-dimensional problems, 15, 98

Euler’s buckling load, 404

External forces, 2

Factor of safety, 4, 409

Failure, definition of, 145

Failure, by fracture, 148

Failure, by yielding, 146

Failure theories

comparison of yielding, 157

Coulomb-Mohr, 160

maximum energy of distortion, 153

maximum principal stress, 158

maximum shear stress, 152

Mohr’s, 159

octahedral shear stress, 154

Fatigue, 149

Fatigue criterion, table, 168

Fatigue life, 150

Fatigue strength, 150

Fauppel, J. H., 529

Fisher, F. E., 529

Flexural center, 210

Flexural rigidity, 186, 476

Flexure formula, 186, 189

Flügge, W., 529

Fluid flow analogy, 262

Ford, H., 528

Form factor, 220

Fourier series, 387

Fracture, 149

Fracture criteria, 151

Fracture mechanics, 163

Frame, collapse load of, 450

Fracture toughness, 164

Fundamental principles, 2, 96

Galilei, Galileo, 2

Gallagher, R. H., 530

Gerber relation, 168

Gere, J., 528, 531

Goodier, J., 529

Goodman relation, modified, 168

Griffith, A. A., 148

Griffith theory, 148

Harris, C. M., 530

Hencky, H., 153

Hencky equations, 455

Hencky yield condition, 153

Hertz problem, 130

Hetényi, M., 528, 531

Hodge, P. G., 532

Hoffman, D., 532

Homogeneous material, 63

Hooke’s Law

generalized, 69

for plane strain, 98

for plane stress, 100

in polar coordinates, 115

in thermoelasticity, 109

for uniaxial stress, 66

Hooke, R., 2

Huber, T. M., 153

Impact factor, 173

Impact loading, 172

Incremental theory, 461

Indicial (tensor) notation, 7, 54, 503

Instability phenomenon, 436

Interaction curves, 445

Internal force resultants, 9

Inverse method, 103

Irwin, G. R., 529

Isotropy, 64

Iyengar, K. T., 531

Johnston, P. R., 530

Juvinall, R. C., 530

Kinematic relations, 54

Kirchoff’s force, 479

Knight, E., 530

Koiter, W. T., 529

Lagrange, J. L., 531

Lamé’s constants, 71

Langhaar, H. L., 531

Lévy-Mises equations, 461

Limit design, 447

Limit load, 411

Linear strain triangle, 295

Linearly elastic material, 63

Logan, D. L., 530

Love, A. E. H., 528

Marin, J., 529

Material properties, table, 424, 425

Matrix

displacement, 289

elasticity, 291

nodal force, 292

stiffness, 292

strain, 290

stress, 291

Membrane analogy, 252

Membrane-roof analogy, 451

Mendelson, A., 531

Messal, E. E., 532

Method of sections, 5

Michaels, J. W., 530

Michell, J. H., 529

Midsurface, 492

Mischke, C. R., 530

Mises, R. von, 153

Mises-Hencky yield criterion, 154

Modulus

bulk, 71

of elasticity, 61

of elasticity in shear, 61

of foundation, 349

of plasticity, 456

of resilience, 76

of rupture, 186

secant, 456

section, 186, 442

tangent, 407

toughness, 77

Mohr, Otto, 21n

Mohr’s circle

for curvature of plates, 474

for moment of inertia, 518

for strain, 61

for stress, 20, 34

Mohr’s theory, 159

Mollick, L., 531

Moment

bending, 9, 475

of inertia, 513

sign convention for, 9, 184, 476

twisting, 9, 475

ultimate, 442

yield, 441

Nadai, A., 529

Navier, L., 481n

Neou, C. Y., 529

Neuber, H. P., 529

Neuber’s diagram, 127

Neutral axis, 185

Neutral surface, 185

Nonlinearly elastic material, 76

Nowacki, W., 529

Numerical methods

finite differences, 276–288

finite element, 288–308

Oden, W. R., 531

Offset method, 64

Orthogonal functions, 388, 389

Osgood, W. R., 531

Pagano, N. J., 528

Parallel-axis theorem, 514

Park, F. R., 531

Pawlik, P. S., 532

Pearson, K., 528

Perfectly plastic material, 434

Peterson, R. E., 529

Pívot, 117

Plane strain problems, 97

Plane stress problems, 99

Plastic

deformation, 63, 434

hinge, 442

hinge moment, 442

material, 63, 435

range, 65

Plasticity, 433

Plates

bending of, 472

boundary conditions for, 478

circular, 483

with circular hole, 124

equilibrium equations for, 477–478

of irregular geometry, 488

rectangular, 481

strain energy in, 486

stresses in, 475–476, 478

Poisson, S. D., 67

Poisson’s ratio, 67

Polar coordinates, 112

Polar moment of inertia, 514

Polynomial solutions, 104

Potential energy, 385

Potential energy, principle of, 385

Prandtl and Reuss equations, 462

Prandtl’s membrane analogy, 252

Prandtl’s stress function, 246

Principal curvature, 133, 493

Principal moment of inertia, 517

Proportional limit, 63

Pure shear, 8

Quinney, H., 530

Radius of curvature, 187, 474

Radius of gyration, 514

Ramberg, W., 531

Ramu, S. A., 531

Rankine, W. J. M., 158

Ranov, T., 531

Rayleigh, Lord, 371

Rayleigh-Ritz method, 391

Reciprocal theorem, 370

Redheffer, R. M., 530

Reismann, H., 532

Residual stress, 64, 464

Rigid-plastic material, 435

Rippinger, E. A., 531

Ritz, W., 591

SAE relation, 168

Saint-Venant,

Barré de, 83

principle, 83

semi-inverse method, 245

Sand-hill analogy, 452

Schmidt, R. J., 529

Secant formula, 411

Segerlind, L. J., 530

Semi-inverse method, 103

Shaffer, B. W., 531

Shames, I. H., 528

Shanley, R. F., 531

Shear, center, 212

Shear, flow, 202, 259

Shear, pure, 8

Shear diagonal, 20

Shear stress formula, 202

Shells

conical, 496

cylindrical, 496–497

membrane action of, 491

of revolution, 493

spherical, 495

theories of, 491

Shigley, J. E., 530

Shock loads, 172

Slenderness ratio, 406

Slip, 146, 434

Slope, 198

Sochs, G., 532

Soderberg relation, 168

Sokolnikoff, I. S., 528, 530

Spring constant, 173

Statically indeterminate systems, 217, 382

Static load, 2, 146

Statics, 1

Sternberg, E., 529

Strain

definition of, 52

effective, 456

engineering, 64

initial, 291

invariants of, 60

logarithmic, 65

mean, 81

normal, 53

plane, 17, 53, 97

principal, 59

shear, 54

sign convention for, 54

state of, 57

tensor, 55

thermal, 109

transformation of, 58–59

true, 65

Strain-displacement relations

in plate bending, 473

in polar coordinates, 113

in three-dimensional problems, 54

in two-dimensional problems, 54, 97

Strain energy

density, 76–78

dilatational, 81

distortional, 82

in structural members, 78

total, 78

Strain gages, 72

Strain hardening, 147

index, 435

Strain rosette, 72

Strength coefficient, 435

Stress

allowable (working), 4, 408

average, 149

combined, 12

complete plastic, 466

completely reversed, 150

components of, 5

critical, 420

definition of, 4

deviator, 82

dilatational, 81

effective, 153, 456

elementary formulas for, 10–11

ellipsoid, 34

engineering, 64

hydrostatic, 34

invariants of, 30

mean, 167

normal, 5

octahedral, 34

plane, 8, 17, 99

principal, 8, 19, 29, 505

pure shear, 8

range, 167

residual, 64, 468

resultant, 18

rupture, 65

shear, 5

sign convention for, 6

state of, 17, 26

tensor, 6

thermal, 108

transformation of, 12, 18, 26, 33

transverse normal, 204

triaxial, 8

true, 64, 65

ultimate tensile, 65

uniaxial, 8

variation of, 14

von Mises, 153, 456

Stress concentration, 117

Stress concentration factor, 123

Stress cubic equation, 30, 505

Stress function, 102; 249

Stress intensity factors, 164

Stress relaxation, 147

Stress resultants, 9

Stress-strain diagrams, 64, 435

Stress trajectories, 18

Sullivan, J. L., 530

Sundara, R., 531

Superposition, method of, 52, 217

Surface forces, 2

Surface tractions, 38

Systems of units, 2

Tangent modulus theory, 406

Taylor, G. J., 530

Taylor, R. I., 530

Terry, E. S., 532

Thermal effects, 175

Thermoelasticity, 109

Timoshenko, S. P., 528–532

Ting, B. Y., 531

Todhunter, I., 528

Torsion

of circular bars, 241

of curved bars, 267

elastic-plastic, 251

of elliptical bar, 248

with one section restrained, 264

of prismatic bars, 240

of thin-walled sections, 258

stress and deformation in, table, 255

Torsional rigidity, 242

Torsion formula, 242

Transfer formula, 514

Transformed section method, 206

Transition, ductile-brittle, 175

Tresca yield criterion, 152

Triangular element, 295

Twist center, 244

Ugural, A. C., 528, 529, 531

Ultimate load, 186, 448

Ultimate moment, 442

Ultimate pressure, 465

Ultimate torque, 452

Unit-load method, 378

Van Vlack, L. H., 529

Variational methods, 369

Virtual displacement, 384

Virtual work, principle of, 384, 413, 420

Viscoelastic material, 63

Volume change, 67, 71

von Mises stress, 153, 456

von Mises theory, 153, 154

Wahl, A. M., 530

Warping deformation, 240

Weaver, W., Jr., 530

Wedge

bending of, 119

compression of, 118

Weiner, J. H., 529

Woinowsky-Krieger, S., 532

Wilson, C. E., 530

Winkler, E., 224

Winkler foundation, 350

Winkler’s formula, 226

Winkler’s theory, 224

Work-strain energy, 370

Yang, T. Y., 530

Yield criteria, 151

Yielding, 146

Yield moment, 441

Yield point, 65

Young, T., 66

Young, W. C., 529

Young’s modulus, 66

Zienkiewicz, O. C., 530