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
2.6 DEFORMATION OF A DEFORMABLE BODY......Page 65
2.7 STRAIN THEORY, TRANSFORMATION OF STRAIN,
AND PRINCIPAL STRAINS......Page 66
2.8 SMALL DISPLACEMENT THEORY......Page 72
2.9 STRAIN MEASUREMENT AND STRAIN ROSElTES......Page 81
PROBLEMS......Page 83
3.1 FIRST LAW OF THERMODYNAMICS, INTERNAL-ENERGY DENSITY, AND COMPLEMENTARY INTERNAL-ENERGY DENSITY......Page 90
3.2 HOOKE’S LAW: ANISOTROPIC ELASTICITY......Page 95
3.3 HOOKE'S LAW: ISOTROPIC ELASTICITY......Page 96
3.4 EQUATIONS OF THERMOELASTICITY FOR ISOTROPIC MATERIALS......Page 102
3.5 HOOKE’S LAW: ORTHOTROPIC MATERIALS......Page 104
PROBLEMS......Page 112
4.1 LIMITATIONS ON THE USE OF UNIAXIAL
STRESS-STRAIN DATA......Page 115
4.2 NONLINEAR MATERIAL RESPONSE......Page 118
4.3 YIELD CRITERIA: GENERAL CONCEPTS......Page 124
4.4 YIELDING OF DUCTILE METALS......Page 128
4.5 ALTERNATIVE YIELD CRITERIA......Page 137
4.6 GENERAL YIELDING......Page 140
PROBLEMS......Page 152
5.1 PRINCIPLE OF STATIONARY POTENTIAL ENERGY......Page 158
5.2 CASTIGLIANO’S THEOREM ON DEFLECTIONS......Page 163
5.3 CASTIGLIANO'S THEOREM ON DEFLECTIONS
FOR LINEAR LOAD-DEFLECTION RELATIONS......Page 166
5.4 DEFLECTIONS OF STATICALLY DETERMINATE
STRUCTURES......Page 174
5.5 STATICALLY INDETERMINATE STRUCTURES......Page 188
PROBLEMS......Page 198
6.1
TORSION OF A PRISMATIC BAR OF CIRCULAR CROSS SECTION......Page 211
6.2 SAINT-VENANT'S SEMI
INVERSE METHOD......Page 220
6.3 LINEAR ELASTIC SOLUTION......Page 224
6.4 THE PRANDTL ELASTIC-MEMBRANE (SOAP-FILM)
ANALOGY......Page 227
6.5 NARROW RECTANGULAR CROSS SECTION......Page 230
6.6 TORSION OF RECTANGULAR CROSS SECTION
MEMBERS......Page 233
6.7 HOLLOW THIN-WALL TORSION MEMBERS AND MULTIPLY CONNECTED CROSS SECTIONS......Page 239
6.8 THIN-WALL TORSION MEMBERS
WITH RESTRAINED ENDS......Page 245
6.9 NUMERICAL SOLUTION OF THE TORSION PROBLEM......Page 250
6.10 INELASTIC TORSION: CIRCULAR CROSS SECTIONS......Page 253
6.11 FULLY PLASTIC TORSION: GENERAL CROSS SECTIONS......Page 261
PROBLEMS......Page 265
7.1 FUNDAMENTALS OF BEAM BENDING......Page 274
7.2
BENDING STRESSES IN BEAMS SUBJECTED TO NONSYMMETRICAL BENDING......Page 283
7.3 DEFLECTIONS OF STRAIGHT BEAMS SUBJECTED
TO NONSYMMETRICAL BENDING......Page 291
7.4 EFFECT OF INCLINED LOADS......Page 295
7.5
FULLY PLASTIC LOAD FOR NONSYMMETRICAL BENDING......Page 296
PROBLEMS......Page 298
8.1 APPROXIMATIONS FOR SHEAR IN THIN-WALL BEAM CROSS SECTIONS......Page 306
8.2 SHEAR FLOW IN THIN-WALL BEAM CROSS SECTIONS......Page 307
8.3 SHEAR CENTER FOR A CHANNEL SECTION......Page 309
8.4 SHEAR CENTER OF COMPOSITE BEAMS FORMED FROM STRINGERS AND THIN WEBS......Page 314
8.5 SHEAR CENTER OF BOX BEAMS......Page 317
PROBLEMS......Page 323
9.1 INTRODUCTION......Page 330
9.2 CIRCUMFERENTIAL STRESSES IN A CURVED BEAM......Page 331
9.3 RADIAL STRESSES IN CURVED BEAMS......Page 344
9.4 CORRECTION OF CIRCUMFERENTIAL STRESSES IN CURVED BEAMS HAVING I, T, OR SIMILAR CROSS SECTIONS......Page 349
9.5 DEFLECTIONS OF CURVED BEAMS......Page 354
9.6 STATICALLY INDETERMINATE CURVED BEAMS:
CLOSED RING SUBJECTED TO A CONCENTRATED LOAD......Page 359
9.7 FULLY PLASTIC LOADS FOR CURVED BEAMS......Page 361
PROBLEMS......Page 363
10.1 GENERAL THEORY......Page 368
10.2
INFINITE BEAM SUBJECTED TO A CONCENTRATED LOAD: BOUNDARY CONDITIONS......Page 371
10.3 INFINITE BEAM SUBJECTED TO A DISTRIBUTED LOAD SEGMENT......Page 380
10.4 SEMIINFINITE BEAM SUBJECTED TO LOADS
AT ITS END......Page 385
10.5 SEMIINFINITE BEAM WITH CONCENTRATED
LOAD NEAR ITS END......Page 387
10.6 SHORT BEAMS......Page 388
10.7 THIN-WALL CIRCULAR CYLINDERS......Page 389
PROBLEMS......Page 395
11.1
BASIC RELATIONS......Page 400
11.2 STRESS COMPONENTS AT SECTIONS FAR FROM ENDS FOR A CYLINDER WITH CLOSED ENDS......Page 403
1 1.3 STRESS COMPONENTS AND RADlAL DISPLACEMENT FOR CONSTANT TEMPERATURE......Page 406
1 1.4 CRITERIA OF FAILURE......Page 410
11.5 FULLY PLASTIC PRESSURE AND AUTOFRETTAGE......Page 416
11.6 CYLINDER SOLUTION FOR TEMPERATURE
CHANGE ONLY......Page 420
11.7 ROTATING DISKS OF CONSTANT THICKNESS......Page 422
PROBLEMS......Page 430
CHAPTER 12. ELASTIC AND INELASTIC
STABILITY OF COLUMNS......Page 434
12.1 INTRODUCTION TO THE CONCEPT OF COLUMN
BUCKLING......Page 435
12.2 DEFLECTION RESPONSE OF COLUMNS TO COMPRESSIVE LOADS......Page 436
12.3 THE EULER FORMULA FOR COLUMNS WITH PINNED ENDS......Page 439
12.4 EULER BUCKLING OF COLUMNS WITH LINEARLY ELASTIC END CONSTRAINTS......Page 447
12.5 LOCAL BUCKLING OF COLUMNS......Page 451
12.6 INELASTIC BUCKLING OF COLUMNS......Page 453
PROBLEMS......Page 461
13.1 INTRODUCTION......Page 468
13.2 STRESS RESULTANTS IN A FLAT PLATE......Page 469
13.3 KINEMATICS: STRAIN-DISPLACEMENT RELATIONS FOR PLATES......Page 472
13.4 EQUILIBRIUM EQUATIONS FOR SMALL-DISPLACEMENT THEORY OF FLAT PLATES......Page 477
13.5 STRESS-STRAIN-TEMPERATURE RELATIONS
FOR ISOTROPIC ELASTIC PLATES......Page 480
13.6 STRAIN ENERGY OF A PLATE......Page 483
13.7 BOUNDARY CONDITIONS FOR PLATES......Page 484
13.8 SOLUTION OF RECTANGULAR PLATE
PROBLEMS......Page 487
13.9 SOLUTION OF CIRCULAR PLATE PROBLEMS......Page 497
PROBLEMS......Page 511
CHAPTER 14. STRESS CONCENTRATIONS......Page 513
14.1 NATURE OF A STRESS CONCENTRATION PROBLEM AND THE STRESS CONCENTRATION FACTOR......Page 515
14.2 STRESS CONCENTRATION FACTORS: THEORY OF ELASTICITY......Page 518
14.3 STRESS CONCENTRATION FACTORS: COMBINED LOADS......Page 526
14.4 STRESS CONCENTRATION FACTORS: EXPERIMENTAL TECHNIQUES......Page 533
14.5 EFFECTIVE STRESS CONCENTRATION FACTORS......Page 541
14.6 EFFECTIVE STRESS CONCENTRATION FACTORS: INELASTIC STRAINS......Page 547
PROBLEMS......Page 550
CHAPTER 15. FRACTURE MECHANICS......Page 554
15.1 FAILURE CRITERIA AND FRACTURE......Page 555
15.2 THE STATIONARY CRACK......Page 562
15.3 CRACK PROPAGATION AND THE STRESS INTENSITY FACTOR......Page 566
15.4 FRACTURE: OTHER FACTORS......Page 572
PROBLEMS......Page 575
CHAPTER 16. FATIGUE: PROGRESSIVE FRACTURE......Page 578
16.1 FRACTURE RESULTING FROM CYCLIC LOADING......Page 579
16.3 EFFECTIVE STRESS CONCENTRATION FACTORS: OTHER INFLUENCES......Page 586
16.4 LOW CYCLE FATIGUE AND THE ε-N RELATION......Page 591
PROBLEMS......Page 596
17.1 INTRODUCTION......Page 600
17.2 THE PROBLEM OF DETERMINING CONTACT STRESSES......Page 601
17.3 GEOMETRY OF THE CONTACT SURFACE......Page 602
17.4 NOTATION AND MEANING OF TERMS......Page 607
17.5 EXPRESSIONS FOR PRINCIPAL STRESSES......Page 608
17.6 METHOD OF COMPUTING CONTACT STRESSES......Page 609
17.7 DEFLECTION OF BODIES IN POINT CONTACT......Page 618
17.8 STRESS FOR TWO BODIES IN LINE CONTACT: LOADS NORMAL TO CONTACT AREA......Page 622
17.9 STRESSES FOR TWO BODIES IN LINE CONTACT: LOADS NORMAL AND TANGENT TO CONTACT AREA......Page 624
PROBLEMS......Page 633
18.1 DEFINITION OF CREEP AND THE CREEP CURVE......Page 635
18.3 ONE-DIMENSIONAL CREEP FORMULAS FOR METALS SUBJECTED TO CONSTANT STRESS AND ELEVATED TEMPERATURE......Page 637
18.4 ONE-DIMENSIONAL CREEP OF METALS SUBJECTED TO VARIABLE STRESS AND TEMPERATURE......Page 642
18.5 CREEP UNDER MULTIAXIAL STATES OF STRESS......Page 651
18.6 FLOW RULE FOR CREEP OF METALS SUBJECTED TO MULTIAXIAL STATES OF STRESS......Page 654
18.7 AN APPLICATION OF CREEP OF METALS......Page 660
18.8 CREEP OF NONMETALS......Page 661
APPENDIX A. AVERAGE MECHANICAL PROPERTIES OF SELECTED MATERIALS......Page 667
AUTHOR INDEX......Page 670
SUBJECT INDEX......Page 682