Advanced Mechanics of Materials

Cover......Page 1
Title......Page 2
Copyright......Page 3
PREFACE......Page 4
CONTENTS......Page 6
1.1 REVIEW OF ELEMENTARY MECHANICS OF MATERIALS......Page 12
1.2 METHODS OF ANALYSIS......Page 16
1.3 STRESS-STRAIN RELATIONS......Page 19
1.4 FAILURE AND LIMITS ON DESIGN......Page 27
PROBLEMS......Page 33
2.1 DEFINITION OF STRESS AT A POINT......Page 36
2.2 STRESS NOTATION......Page 37
2.3 SYMMETRY OF THE STRESS ARRAY AND STRESS ON AN ARBITRARILY ORIENTED PLANE......Page 39
2.4 TRANSFORMATION OF STRESS, PRINCIPAL STRESSES, AND OTHER PROPERTIES......Page 42
2.5 DIFFERENTIAL EQUATIONS OF MOTION
OF A DEFORMABLE BODY......Page 61
3.1 FIRST LAW OF THERMODYNAMICS, INTERNAL-ENERGY DENSITY, AND COMPLEMENTARY INTERNAL-ENERGY DENSITY......Page 64
3.2 HOOKE’S LAW: ANISOTROPIC ELASTICITY......Page 69
3.3 HOOKE'S LAW: ISOTROPIC ELASTICITY......Page 70
3.4 EQUATIONS OF THERMOELASTICITY FOR ISOTROPIC MATERIALS......Page 76
3.5 HOOKE’S LAW: ORTHOTROPIC MATERIALS......Page 78
PROBLEMS......Page 86
4.1 LIMITATIONS ON THE USE OF UNIAXIAL
STRESS-STRAIN DATA......Page 89
4.2 NONLINEAR MATERIAL RESPONSE......Page 92
4.3 YIELD CRITERIA: GENERAL CONCEPTS......Page 98
4.4 YIELDING OF DUCTILE METALS......Page 102
4.5 ALTERNATIVE YIELD CRITERIA......Page 111
5.1 PRINCIPLE OF STATIONARY POTENTIAL ENERGY......Page 113
5.2 CASTIGLIANO’S THEOREM ON DEFLECTIONS......Page 118
5.3 CASTIGLIANO'S THEOREM ON DEFLECTIONS
FOR LINEAR LOAD-DEFLECTION RELATIONS......Page 121
5.4 DEFLECTIONS OF STATICALLY DETERMINATE
STRUCTURES......Page 129
5.5 STATICALLY INDETERMINATE STRUCTURES......Page 143
6.1
TORSION OF A PRISMATIC BAR OF CIRCULAR CROSS SECTION......Page 145
6.2 SAINT-VENANT'S SEMI
INVERSE METHOD......Page 154
6.3 LINEAR ELASTIC SOLUTION......Page 158
6.4 THE PRANDTL ELASTIC-MEMBRANE (SOAP-FILM)
ANALOGY......Page 161
6.5 NARROW RECTANGULAR CROSS SECTION......Page 164
6.6 TORSION OF RECTANGULAR CROSS SECTION
MEMBERS......Page 167
6.7 HOLLOW THIN-WALL TORSION MEMBERS AND MULTIPLY CONNECTED CROSS SECTIONS......Page 173
6.8 THIN-WALL TORSION MEMBERS
WITH RESTRAINED ENDS......Page 179
7.1 FUNDAMENTALS OF BEAM BENDING......Page 180
7.2
BENDING STRESSES IN BEAMS SUBJECTED TO NONSYMMETRICAL BENDING......Page 189
7.3 DEFLECTIONS OF STRAIGHT BEAMS SUBJECTED
TO NONSYMMETRICAL BENDING......Page 197
7.4 EFFECT OF INCLINED LOADS......Page 201
7.5
FULLY PLASTIC LOAD FOR NONSYMMETRICAL BENDING......Page 202
PROBLEMS......Page 204
8.1 APPROXIMATIONS FOR SHEAR IN THIN-WALL BEAM CROSS SECTIONS......Page 212
8.2 SHEAR FLOW IN THIN-WALL BEAM CROSS SECTIONS......Page 213
8.3 SHEAR CENTER FOR A CHANNEL SECTION......Page 215
8.4 SHEAR CENTER OF COMPOSITE BEAMS FORMED FROM STRINGERS AND THIN WEBS......Page 220
8.5 SHEAR CENTER OF BOX BEAMS......Page 223
PROBLEMS......Page 229
9.1 INTRODUCTION......Page 236
9.2 CIRCUMFERENTIAL STRESSES IN A CURVED BEAM......Page 237
9.3 RADIAL STRESSES IN CURVED BEAMS......Page 250
9.4 CORRECTION OF CIRCUMFERENTIAL STRESSES IN CURVED BEAMS HAVING I, T, OR SIMILAR CROSS SECTIONS......Page 255
9.5 DEFLECTIONS OF CURVED BEAMS......Page 260
9.6 STATICALLY INDETERMINATE CURVED BEAMS:
CLOSED RING SUBJECTED TO A CONCENTRATED LOAD......Page 265
9.7 FULLY PLASTIC LOADS FOR CURVED BEAMS......Page 267
PROBLEMS......Page 269
10.1 GENERAL THEORY......Page 274
10.2
INFINITE BEAM SUBJECTED TO A CONCENTRATED LOAD: BOUNDARY CONDITIONS......Page 277
10.3 INFINITE BEAM SUBJECTED TO A DISTRIBUTED LOAD SEGMENT......Page 286
10.4 SEMIINFINITE BEAM SUBJECTED TO LOADS
AT ITS END......Page 291
10.5 SEMIINFINITE BEAM WITH CONCENTRATED
LOAD NEAR ITS END......Page 293
10.6 SHORT BEAMS......Page 294
10.7 THIN-WALL CIRCULAR CYLINDERS......Page 295
PROBLEMS......Page 301
11.1
BASIC RELATIONS......Page 306
11.2 STRESS COMPONENTS AT SECTIONS FAR FROM ENDS FOR A CYLINDER WITH CLOSED ENDS......Page 309
1 1.3 STRESS COMPONENTS AND RADlAL DISPLACEMENT FOR CONSTANT TEMPERATURE......Page 312
1 1.4 CRITERIA OF FAILURE......Page 316
11.5 FULLY PLASTIC PRESSURE AND AUTOFRETTAGE......Page 322
11.6 CYLINDER SOLUTION FOR TEMPERATURE
CHANGE ONLY......Page 326
11.7 ROTATING DISKS OF CONSTANT THICKNESS......Page 328
PROBLEMS......Page 336
CHAPTER 12. ELASTIC AND INELASTIC
STABILITY OF COLUMNS......Page 340
12.1 INTRODUCTION TO THE CONCEPT OF COLUMN
BUCKLING......Page 341
12.2 DEFLECTION RESPONSE OF COLUMNS TO COMPRESSIVE LOADS......Page 342
12.3 THE EULER FORMULA FOR COLUMNS WITH PINNED ENDS......Page 345
12.4 EULER BUCKLING OF COLUMNS WITH LINEARLY ELASTIC END CONSTRAINTS......Page 353
12.5 LOCAL BUCKLING OF COLUMNS......Page 357
12.6 INELASTIC BUCKLING OF COLUMNS......Page 359
PROBLEMS......Page 367
13.1 INTRODUCTION......Page 374
13.2 STRESS RESULTANTS IN A FLAT PLATE......Page 375
13.3 KINEMATICS: STRAIN-DISPLACEMENT RELATIONS FOR PLATES......Page 378
13.4 EQUILIBRIUM EQUATIONS FOR SMALL-DISPLACEMENT THEORY OF FLAT PLATES......Page 383
13.5 STRESS-STRAIN-TEMPERATURE RELATIONS
FOR ISOTROPIC ELASTIC PLATES......Page 386
13.6 STRAIN ENERGY OF A PLATE......Page 389
13.7 BOUNDARY CONDITIONS FOR PLATES......Page 390
13.8 SOLUTION OF RECTANGULAR PLATE
PROBLEMS......Page 393
13.9 SOLUTION OF CIRCULAR PLATE PROBLEMS......Page 403
PROBLEMS......Page 417
CHAPTER 14. STRESS CONCENTRATIONS......Page 419
14.1 NATURE OF A STRESS CONCENTRATION PROBLEM AND THE STRESS CONCENTRATION FACTOR......Page 421
14.2 STRESS CONCENTRATION FACTORS: THEORY OF ELASTICITY......Page 424
14.3 STRESS CONCENTRATION FACTORS: COMBINED LOADS......Page 432
14.4 STRESS CONCENTRATION FACTORS: EXPERIMENTAL TECHNIQUES......Page 439
14.5 EFFECTIVE STRESS CONCENTRATION FACTORS......Page 447
14.6 EFFECTIVE STRESS CONCENTRATION FACTORS: INELASTIC STRAINS......Page 453
PROBLEMS......Page 456
CHAPTER 15. FRACTURE MECHANICS......Page 460
15.1 FAILURE CRITERIA AND FRACTURE......Page 461
15.2 THE STATIONARY CRACK......Page 468
15.3 CRACK PROPAGATION AND THE STRESS INTENSITY FACTOR......Page 472
15.4 FRACTURE: OTHER FACTORS......Page 478
PROBLEMS......Page 481
CHAPTER 16. FATIGUE: PROGRESSIVE FRACTURE......Page 484
16.1 FRACTURE RESULTING FROM CYCLIC LOADING......Page 485
16.3 EFFECTIVE STRESS CONCENTRATION FACTORS: OTHER INFLUENCES......Page 492
16.4 LOW CYCLE FATIGUE AND THE ε-N RELATION......Page 497
PROBLEMS......Page 502
17.1 INTRODUCTION......Page 506
17.2 THE PROBLEM OF DETERMINING CONTACT STRESSES......Page 507
17.3 GEOMETRY OF THE CONTACT SURFACE......Page 508
17.4 NOTATION AND MEANING OF TERMS......Page 513
17.5 EXPRESSIONS FOR PRINCIPAL STRESSES......Page 514
17.6 METHOD OF COMPUTING CONTACT STRESSES......Page 515
17.7 DEFLECTION OF BODIES IN POINT CONTACT......Page 524
17.8 STRESS FOR TWO BODIES IN LINE CONTACT: LOADS NORMAL TO CONTACT AREA......Page 528
17.9 STRESSES FOR TWO BODIES IN LINE CONTACT: LOADS NORMAL AND TANGENT TO CONTACT AREA......Page 530
PROBLEMS......Page 539
18.1 DEFINITION OF CREEP AND THE CREEP CURVE......Page 541
18.3 ONE-DIMENSIONAL CREEP FORMULAS FOR METALS SUBJECTED TO CONSTANT STRESS AND ELEVATED TEMPERATURE......Page 543
18.4 ONE-DIMENSIONAL CREEP OF METALS SUBJECTED TO VARIABLE STRESS AND TEMPERATURE......Page 548
18.5 CREEP UNDER MULTIAXIAL STATES OF STRESS......Page 557
18.6 FLOW RULE FOR CREEP OF METALS SUBJECTED TO MULTIAXIAL STATES OF STRESS......Page 560
18.7 AN APPLICATION OF CREEP OF METALS......Page 566
18.8 CREEP OF NONMETALS......Page 567
APPENDIX A. AVERAGE MECHANICAL PROPERTIES OF SELECTED MATERIALS......Page 573
AUTHOR INDEX......Page 576
SUBJECT INDEX......Page 588