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 |  موضوع: كتاب Mechanics of Materials الجمعة 21 أغسطس 2020, 2:31 am | |
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أخوانى فى الله
أحضرت لكم كتاب
Mechanics of Materials
R. C. Hibbeler
Tenth Edition in Si Units
Si Conversion by
Kai Beng Yap
و المحتوى كما يلي :
Contents
Axial Load 141
Chapter Objectives 141
4.1 Saint-venant’s Principle 141
4.2 Elastic Deformation of an Axially Loaded
Member 143
4.3 Principle of Superposition 158
4.4 Statically Indeterminate Axially Loaded
Members 158
4.5 the Force Method of Analysis for Axially
Loaded Members 165
4.6 Thermal Stress 173
4.7 Stress Concentrations 180
*4.8 Inelastic Axial Deformation 183
*4.9 Residual Stress 185
Stress 21 4
Chapter Objectives 21
1.1 Introduction 21
1.2 Equilibrium of a Deformable Body 22
1.3 Stress 40
1.4 Average Normal Stress in an Axially
Loaded Bar 42
1.5 Average Shear Stress 50
1.6 Allowable Stress Design 64
1.7 Limit State Design 66
1
Strain 87
Chapter Objectives 87
2.1 Deformation 87
2.2 Strain 88
2
Mechanical Properties
Of Materials 103
Chapter Objectives 103
3.1 the Tension and Compression Test 103
3.2 the Stress–strain Diagram 105
3.3 Stress–strain Behavior of Ductile and
Brittle Materials 109
3.4 Strain Energy 113
3.5 Poisson’s Ratio 124
3.6 the Shear Stress–strain Diagram 126
*3.7 Failure of Materials Due to Creep
And Fatigue 129
3
Torsion 201
Chapter Objectives 201
5.1 Torsional Deformation of a Circular
Shaft 201
5.2 the Torsion Formula 204
5.3 Power Transmission 212
5.4 Angle of Twist 224
5.5 Statically Indeterminate Torque-loaded
Members 240
*5.6 Solid Noncircular Shafts 247
*5.7 Thin-walled Tubes Having Closed Cross
Sections 250
5.8 Stress Concentration 260
*5.9 Inelastic Torsion 263
*5.10 Residual Stress 265
518 Contents
Stress Transformation 463
Chapter Objectives 463
9.1 Plane-stress Transformation 463
9.2 General Equations of Plane-stress
Transformation 468
9.3 Principal Stresses and Maximum in-plane
Shear Stress 471
9.4 Mohr’s Circle—plane Stress 487
9.5 Absolute Maximum Shear Stress 499
9
Strain Transformation 511
Chapter Objectives 511
10.1 Plane Strain 511
10.2 General Equations of Plane-strain
Transformation 512
*10.3 Mohr’s Circle—plane Strain 520
*10.4 Absolute Maximum Shear Strain 528
10.5 Strain Rosettes 530
10.6 Material Property Relationships 534
*10.7 Theories of Failure 546
10
Design of Beams and
Shafts 563
Chapter Objectives 563
11.1 Basis for Beam Design 563
11.2 Prismatic Beam Design 566
*11.3 Fully Stressed Beams 580
*11.4 Shaft Design 584
11
Bending 281
Chapter Objectives 281
6.1 Shear and Moment Diagrams 281
6.2 Graphical Method for Constructing Shear
And Moment Diagrams 288
6.3 Bending Deformation of a Straight
Member 307
6.4 the Flexure Formula 311
6.5 Unsymmetric Bending 328
*6.6 Composite Beams 338
*6.7 Reinforced Concrete Beams 341
*6.8 Curved Beams 345
6.9 Stress Concentrations 352
*6.10 Inelastic Bending 362
6
Combined Loadings 431
Chapter Objectives 431
8.1 Thin-walled Pressure Vessels 431
8.2 State of Stress Caused by Combined
Loadings 438
8
Chapter Objectives 385
7.1 Shear in Straight Members 385
7.2 the Shear Formula 386
7.3 Shear Flow in Built-up Members 404
7.4 Shear Flow in Thin-walled Members 413
*7.5 Shear Center for Open Thin-walled
Members 418
7 Transverse Shear 385contents 19
Deflection of Beams
And Shafts 595
Chapter Objectives 595
12.1 the Elastic Curve 595
12.2 Slope and Displacement by
Integration 599
*12.3 Discontinuity Functions 617
*12.4 Slope and Displacement by the
Moment-area Method 629
12.5 Method of Superposition 644
12.6 Statically Indeterminate Beams
And Shafts 652
12.7 Statically Indeterminate Beams and
Shafts—method of Integration 653
*12.8 Statically Indeterminate Beams and
Shafts—moment-area Method 658
12.9 Statically Indeterminate Beams and
Shafts—method of Superposition 664
12 14
Buckling of Columns 683
Chapter Objectives 683
13.1 Critical Load 683
13.2 Ideal Column With Pin Supports 686
13.3 Columns Having Various Types of
Supports 692
*13.4 the Secant Formula 704
*13.5 Inelastic Buckling 710
*13.6 Design of Columns for Concentric
Loading 718
*13.7 Design of Columns for Eccentric
Loading 728
13
Energy Methods 741
Chapter Objectives 741
14.1 External Work and Strain Energy 741
14.2 Elastic Strain Energy for Various Types
Of Loading 746
14.3 Conservation of Energy 759
14.4 Impact Loading 766
*14.5 Principle of Virtual Work 777
*14.6 Method of Virtual Forces Applied
To Trusses 780
*14.7 Method of Virtual Forces Applied
To Beams 788
*14.8 Castigliano’s Theorem 797
*14.9 Castigliano’s Theorem Applied
To Trusses 799
*14.10 Castigliano’s Theorem Applied
To Beams 802
Appendix
A Geometric Properties of an Area 810
B Geometric Properties of Structural
Shapes 824
C Slopes and Deflections of Beams 829
Solutions and Answers for
Preliminary Problems 831
Fundamental Problems Partial
Solutions and Answers 841
Selected Answers 863
Index 883
Index
A
Absolute Maximum Shear Strain,
528–529, 558
Absolute Maximum Shear Stress (?max),
204–205, 207, 260–262, 277, 499–502, 507
In-plane Determination of, 499–502, 507
Mohr’s Circle for, 499–502
Stress Concentration and, 260–262, 277
Torsional Loads and, 204–205, 207,
260–262, 277
Allowable Stress Design (Asd), 64–65, 67, 82
Aluminum Column Specifications, 720
Angle of Twist F(X), 201–203, 224–232, 248,
252, 276
Circular Shafts, 201–203, 224–232, 276
Constant Torque and, 225–226
Material Deformation and, 202–203
Multiple Torques and, 226
Noncircular Shafts, 247
Procedure for Analysis of, 228
Right-hand Rule for, 204, 227
Rotation and, 202–203, 212, 224–232
Sign Convention for, 227
Thin-walled Tubes, 252
Torsional Deformation and, 201–203,
224–232, 248, 252, 276
Anisotropic Materials, 42
Annulus (Differential Ring), 206, 264
Area (a), 810–822
Centroid, 810–812
Composite, 811, 814
Inclined Axes, 820–822
Moment of Inertia for, 813–816, 820–822
Parallel-axis Theorem, 813–814, 818
Principle Moments of Inertia, 821
Product of Inertia for, 817–819
Transformation Equations, 820
Axial Loads, 42–49, 82, 141–199, 746–747
Average Normal Stress Distribution,
42–49, 82
Compatibility (Kinematic) Conditions,
159–166, 195
Constant, Stress Distribution From, 42–43,
144–145, 195
Deformation and, 141–150, 195
Displacement (D), 143–150, 158–166,
173–176, 195–196
Elastic Deformation From, 143–150,
173–176, 180–183, 195–196
Elastic Strain Energy (Ui), 746–747
Equilibrium and, 43–44, 145, 158–166, 195
Force (Flexibility) Method of Analysis,
165–166
Inelastic Deformation From, 183–184, 196
Internal Axial Force, 43, 45, 746
Load-displacement Relationship, 159,
166, 195
Material Properties of, 42
Normal Stress (S) in, 42–49
Plastic Material Behavior, 183–184, 196
Prismatic Bars, 42–49
Procedures for Analysis of, 45, 146, 160,
165–166
Relative Displacement (D) of, 143–150, 195
Residual Stresses (?r) From, 185–189, 196
Saint Venant’s Principle, 141–143, 195
Sign Convention for, 145, 195
Statically Indeterminate Members, 158–166,
173–174, 185, 195
Stress Concentrations From, 180–183, 196
Superposition, Principle of, 158–159, 195
Thermal Stress (Dt) and, 173–176, 196
Uniaxial Stress, 43–44
Uniform Deformation, 42–43
Axis of Symmetry, 307, 329, 418–420
B
Beams, 165–166, 281–383, 385–428, 563–583,
591, 595–681, 760, 788–792, 802–807
Basis of Strength, 563–565, 569
Bearing Plates for, 564
Bending, 281–383
Bending Moments (M) in, 307–309,
328–334, 347–348
Built-up Members, 404–408, 427, 568, 591
Cantilevered, 281
Castigliano’s Theorem Applied to, 802–807
Circumferential Stress in, 348
Composite, 338–340, 379
Concentrated Force and Moment
Regions, 290
Conservation of Energy for, 760
Curved, 345–351, 380
Deflection of, 564, 595–681
Deformation of by Bending, 307–310
Design of, 563–583, 591
Discontinuity Functions, 617–625, 678
Displacement, 595–598, 599–609, 629–637,
644–648, 653–655, 658–662, 678–679
Distributed Load Regions, 282, 288–290, 378
Elastic Curve for, 595–598, 602, 617–625,
629–637, 678
Energy Methods for, 760, 788–792, 802–807
Fabricated, 580
Fastener Spacing for, 405, 427
Flexure Formula for, 311–318, 379
Force (Flexibility) Method of Analysis,
165–166, 664–672
Fully Stressed, 580–583, 591
Hyperbolic Stress Variations, 346–347
Inelastic Bending of, 362–372, 380
Integration Method for, 599–609, 653–655,
678–679
Linear Stress Variations, 312–313
Longitudinal Shear Stress in, 385–386
Moment-area Method for, 629–637,
658–662, 679
Neutral Axis of, 307, 312, 331, 346
Nonprismatic, 580–583, 591
Overhanging, 281
Principal Axis of, 328–331
Prismatic, 566–573, 591
Procedures for Analysis of, 283, 291, 314,
349, 392, 420, 569, 602, 622, 631, 667,
790, 804
Radial Stresses in, 348
Reinforced Concrete, 341–344
Residual Stress of, 365–366, 380
Section Modulus (S), 566, 580
Shear and Moment Diagrams for,
281–297, 378
Shear Center (O), 418–423, 428
Shear Flow (Q), 404–408, 413–417, 427–428
Shear Force (V) in, 385–386
Shear Formula for, 386–397, 427
Shear Stresses (?) in, 385–428
Sign Conventions for, 282
Simply Supported, 281
Slope for, 595–609, 629–637, 678
Strain and, 309–310
Statically Indeterminate, 652–672, 679
Steel, 567
Straight Members, 307–344, 378–379,
385–386
Stress Concentrations in, 352–354, 380
Stress Distribution in, 311–318, 345–351,
380
Stress Trajectories, 564–565
Structural Shapes and Properties of,
823–831
Superposition Method for, 644–648,
658–662, 664–672, 679
Thin-walled Members, 413–423, 428
Transformation Factor (N) for, 339–340, 379
Transverse Shear in, 385–428
Twisting, 418–420
Unsymmetric Bending of, 328–334, 379
Virtual Forces, Method of for, 788–792
Warping, 386–387
Wood, 567
Bearing Plates, 564
Bearing Stress, 65
Bending, 281–383
Composite Beams, 338–340, 379
Curved Beams, 345–351, 380
Deformation, 307–310
Elastic Behavior, 311–314, 338, 345–346,
353, 379–380
883bending (Continued)
Flexure Formula for, 311–318, 379
Inelastic, 362–372, 380
Linear Strain Distribution, 362
Neutral Axis Location and, 307, 312, 331, 346
Plastic Moment, 363–364
Procedures for Analysis of, 283, 291, 314, 349
Reinforced Concrete Beams, 341–344
Residual Stress by, 365–366, 380
Resultant Forces (Fr), 362, 380
Resultant Moment (Mr), 362
Shear and Moment Diagrams for,
281–297, 378
Sign Conventions for, 282–283, 311, 378
Straight Members, 307–344, 378–379
Stress Concentrations and, 352–354, 380
Transformation Factor (N), 339–340, 379
Ultimate, 366–367, 380
Unsymmetric, 328–334, 379
Bending Moment (M), 26–27, 282, 290,
307–309, 312–314, 328–334, 347–348,
379–380, 439, 748–750
Change in, 290
Combined Load Analysis for, 439
Concentrated Force and, 290
Curved Beams, 347–348, 380
Deformation of Beams, 281, 307–309, 379
Elastic Strain Energy (Ui) and, 748–750
Equilibrium and Internal Loadings as, 26–27
Flexure Formula and, 312–314
Shear and Moment Diagrams and, 282, 290
Sign Convention for, 282
Unsymmetric Bending, 328–334, 379
Biaxial Stress, 433
Bifurcation Point, 685
Blocks, Impact Loading From, 766–771
Body Force, 23
Boundary Conditions, 600
Brittle Failure, 130–131, 137, 261
Brittle Materials, 111, 114, 136, 261, 353,
550–551, 559
Bending and, 353
Fracture, 550–551
Fracture Stress (Sf), 111
Material Failure of, 111, 136, 261,
550–551, 559
Maximum Normal Stress Theory, 550
Mohr’s Failure Criterion, 550–551
Multiaxial Stress and, 550–551, 559
Strain Transformation and, 550–551, 559
Stress Concentrations and, 261, 353
Torsional Loadings and, 261
Buckling, 683–739. See Also Columns
Bifurcation Point for, 685
Concentric Loading, 718–724
Critical Load (Pcr), 683–695, 737
Eccentric Loading, 704–708, 728–732
Engesser’s Equation for, 711, 737
Euler Load, 688, 737
Ideal Columns, 686–691, 737
Inelastic, 710–712, 737
Lateral Deflection as, 683–685
Least Moment of Inertia and, 689
Maximum Deflection (Ymax), 706–707, 737
Secant Formula for, 704–708, 737
Tangent Modulus (Et), 710–711
Built-up Members, 404–408, 427, 568, 591
Bulging, 247
Bulk Modulus (K), 537, 559
C
Cantilevered Beams, 281
Cartesian Components of Strain, 89
Castigliano’s Theorem, 797–807
Centroid, 810–812
Circular Shafts, 201–246, 276. See Also
Shafts; Tubes
Circumferential (Hoop) Stress, 348, 432–433
Cohesive Material, 40
Columns, 683–739
Aluminum Specifications, 720
Buckling, 683–739
Classification of, 710
Concentric Loading, 718–724
Critical Load (Pcr), 683–695, 737
Deflection, Maximum (Ymax), 706–707, 737
Design of, 708, 718–724, 728–732
Eccentric Loading, 704–708, 728–732
Eccentricity Ratio (Ec/r²), 708
Effective Length (Le), 693
Engesser’s Equation for, 711, 737
Equilibrium of, 684–685
Euler Load, 688, 737
Fixed Supports for, 692–695, 737
Ideal, 686–691, 737
Inelastic Buckling, 710–712, 737
Interaction Formula for, 728–729
Least Moment of Inertia in, 689
Pin-supported, 686–691, 737
Radius of Gyration (R), 689
Secant Formula for, 704–708, 737
Slenderness Ratio (L/r), 689–690, 693,
719–720
Steel Specifications, 719
Tangent Modulus (Et), 710–711
Wood (Timber) Specifications, 720
Combined Loadings, 431–461
Biaxial Stress, 433
Circumferential (Hoop) Stress Direction,
432–433
Cylindrical Vessels, 432–433, 458
Longitudinal Stress, 432–433
Procedure for Analysis of, 438–439
Radial Stress, 433
Spherical Vessels, 433, 458
State of Stress Caused by, 438–446, 458
Superposition of Stress Components for,
439, 458
Thin-walled Pressure Vessels, 431–434,
439, 458
Compatibility (Kinematic) Conditions,
159–166, 195, 664–667, 798
Composite Areas, 811, 814
Composite Beams, 338–340, 379
Compression (Tension) Test, 103–104, 135
Compressive Stress, 41, 728
Concentrated Force, 22, 290
Concentric Loading, 718–724
Conservation of Energy, 759–762, 807
Constant Load, 42–43, 144–145, 195, 225–226
Continuity Conditions, 600
Continuous Material, 40
Coplanar Forces (Loadings), 22–24, 27
Couple Moment, Work of, 743
Couplings, 260
Creep, 129–131, 137
Critical Load (Pcr), 683–695, 737
Column Buckling, 683–695, 737
Fixed-supports, 686–695, 737
Lateral Deflection and, 683–685
Pin-supports, 686–691, 737
Curved Beams, 345–351, 380
Cylindrical Thin-walled Vessels, 432–433, 458
D
Dead Loads, 66
Deflection, 165–166, 564, 595–681, 683–739.
See Also Buckling
Beams, 564, 595–681
Columns, 683–739
Coordinates, 601
Critical Load (Pcr), 683–695, 737
Discontinuity Functions, 617–625, 678
Displacement, 596–597, 599–609, 629–637,
644–648
Elastic Curve and, 595–598, 602, 617–625,
629–637, 678
Flexibility (Force) Method of Analysis,
165–166, 664–672
Flexural Rigidity (Ei) for, 599–600
Integration Method for, 599–609, 653–655,
678–679
Lateral (Buckling), 683–685
M/ei Diagrams for, 629–637
Maximum (Ymax), 706–707, 737
Moment-area Method for, 629–637,
658–662, 679
Moment-curvature Relationship, 598
Moment Diagrams for, 658–662
Procedures for Analysis of, 602, 622,
631, 667
Radius of Curvature, 598, 678
Shafts, 595–681
Sign Conventions for, 601
Slope and, 595–609, 629–637, 678
Statically Determinate Members, 595–651
Statically Indeterminate Shafts and Beams,
652–672, 679
Superposition, Method of, 644–648,
664–672, 679
Deformable Bodies, 22–32
Equations of Equilibrium, 24, 28
Equilibrium of, 22–32
External Loads, 22–23
Internal Resultant Loads, 25–27
Procedure for Analysis of, 28
Right-hand Rule for, 26
Support Reactions, 23
884 Indexindex 885
Deformation, 42–43, 87–93, 106, 109–118,
124–125, 129–131, 135–137, 141–199,
201–279, 307–310, 379, 463–509, 511–561.
See Also Displacement (D); Strain (?)
Angle of Twist F(X), 201–203, 224–232, 248,
250–255, 276
Axially Loaded Members, 42–43, 141–199
Beams (Bending), 307–310, 379
Bending, 282, 307–310, 379
Bulging, 247, 277
Changes in a Body, 87
Circular Shafts, 201–213, 276
Creep, 129–130, 137
Displacement (D), 143–150, 158–166,
173–176, 195–196
Elastic, 106, 110, 129–136, 143–150, 173–176,
180–183, 195–196
Fatigue Failure and, 130–131, 137
Inelastic, 183–184, 196
Localized, 141–143
Mechanical Material Properties and, 106,
109–118, 124–125, 135–136
Noncircular Shafts, 247–249, 277
Plastic Behavior, 106, 112, 135–136,
183–184
Poisson’s Ratio (V), 124–125, 137
Principal Stresses, 471–477, 489, 506
Principal Strains, 516, 558
Procedure for Analysis of, 146, 160, 165–166
Relative Displacement (D), 143–145, 195
Saint Venant’s Principle, 141–143, 195
Shear Strain (G) and, 89–90, 202–203
Shear Stress (?) and, 204–211, 247–255
Strain and, 87–93
Strain Energy, 113–118, 136
Strain Transformation and, 511–561
Stress Concentration Distortion, 180–183,
196
Stress Distribution and, 42–43
Stress—strain Behavior, 109–118, 135–136
Stress Transformation and, 463–509
Superposition, Principle of, 158–159, 195
Thermal Stress (Dt) and, 173–176, 196
Thin-walled Tubes, 250–255
Torsional, 201–279
Twisting, 201, 247, 250, 418–420
Uniform, 42–43
Warping, 247, 277
Yielding, 106, 109–110, 135
Degree of Indeterminacy, 652
Design, 64–72, 82, 212–213, 276, 563–593,
708, 718–724, 728–732
Allowable Stress Design (Asd), 64–65, 67,
82
Aluminum Column Specifications, 720
Basis of Strength, 563–565
Beams, 563–583, 591
Columns, 708, 718–724, 728–732
Concentric Loading, 718–724
Criteria, 67
Eccentric Loading, 728–732
Effective Slenderness Ratio (Kl/r) for, 693,
719–720
Factor of Safety (F.s.), 64–65, 82, 719
Fully Stressed (Nonprismatic) Beams,
580–583, 591
Interaction Formula for, 728–729
Limit State Design (Lsd), 66–72
Load and Resistance Factor Design (Lrfd),
66–72, 82
Load Factor (G), 66
Power (P) Transmission and, 212–213, 276
Prismatic Beams, 566–573, 591
Procedures of Analysis for, 67, 569
Resistance Factors (F), 66
Secant Formula for, 708
Section Modulus (S) for, 566, 580
Shafts, 212–213, 276, 584–587, 591
Simple Connections, 64–65, 82
Steel Column Specifications, 719
Torque Diagrams for, 584
Wood (Timber) Column Specifications, 720
Dilatation (E), 536–537, 559
Discontinuity Functions, 617–625, 678
Application of, 621
Macaulay Functions, 618–619
Procedure for Analysis Using, 622
Singularity Functions, 619–620
Displacement (D), 143–150, 158–166,
173–176, 195–196, 595–598, 599–609,
629–637, 644–648, 653–655, 658–662,
678–679, 797–807
Axially Loaded Members, 143–150, 158–166,
173–176, 195–196
Castigliano’s Theorem for, 797–807
Compatibility (Kinematic) Conditions,
159–166, 195
Constant Loads and, 144–145
Deflection, 596–597, 599–609, 629–637,
644–648, 653–655, 658–662, 678–679
Elastic Curve for, 595–598, 602, 617–625,
629–637, 678
Elastic Deformation, 143–150, 195
Force (Flexibility) Method of Analysis,
165–166
Integration Method for, 599–609, 653–655,
678–679
Internal Forces and, 144–146
Load-displacement Relationship, 159–166,
195
Moment-area Method, 629–637, 658–662,
679
Procedures for Analysis of, 146, 160,
165–166
Relative, 143–150, 195
Sign Convention for, 145
Slope and, 596–597, 599–609, 629–637
Statically Indeterminate Members, 158–166,
173–174, 195, 653–655, 658–662, 679
Superposition, Principle of, 158–159, 195
Thermal Stress (Dt) and, 173–176, 196
Distortion, Stress Concentration Causing,
180–183, 196
Distributed Loads, 22–24, 27, 82, 282, 288–290,
378, 618
Bending and, 282, 288–290, 378
Coplanar Forces and, 22–24, 27
Discontinuous Functions for, 282
Equilibrium Equations for, 24, 82
Macaulay Functions for, 618
Shear and Moment Diagram Regions, 282,
288–290, 378
Support Reactions, 23
Ductile Materials, 109–110, 114, 135, 261,
353, 546–549, 559
Bending (Beams), 353
Failure of, 261, 353, 546–549, 559
Lüder Lines, 546–547
Maximum Distortion Energy Theory,
548–549
Maximum Shear Stress Theory, 546–547
Multiaxial Stress in, 546–549, 559
Offset Method for, 109–110
Percent Elongation, 109, 135
Percent Reduction in Area, 109, 135
Slipping, 546–547, 551
Strain-energy Density, 548
Strain Transformation and, 546–549, 559
Stress Concentrations, 261, 353
Stress—strain Diagrams for, 109–110,
114, 135
Torsional Loadings, 261
Tresca Yield Criterion, 547
Yield Strength, 108–109
Yielding, 546–547
E
Eccentric Loading, 704–708, 728–732
Eccentricity Ratio (Ec/r²), 708
Effective Length (Le), 693
Effective Slenderness Ratio (Kl/r), 693,
719–720
Elastic Behavior, 105–114, 126–127, 135,
137, 143–150, 173–176, 180–183, 195–196,
260–262, 264, 277, 352–353, 380. See Also
Inelastic Behavior
Axially Loaded Members, 143–150, 173–176,
180–183, 195–196
Bending (Beams), 352–353, 380
Deformation, 106, 135, 143–150, 173–176,
180–183, 195–196
Displacement (D) and, 143–150, 173–176,
195–196
Elastic Limit, 105–106, 135
Internal Forces and, 144–146
Modulus of Elasticity (E), 105–106, 108,
126, 135
Necking, 107, 114, 135
Nonlinear, 110
Perfectly Plastic (Elastoplastic) Materials,
106, 183–184, 196, 264
Procedure for Analysis of, 146
Proportional Limit (?pl), 105–106, 114, 126
Relative Displacement (D) of, 143–150, 195
Shear Modulus (G), 126–127, 137
Sign Convention for, 145
Strain Hardening, 107, 112, 114, 135
Stress Concentrations, 180–183, 196,
260–262, 277, 352–353, 380elastic Behavior (Continued)
Stress—strain (S—e) Diagrams for,
105–114, 126, 135, 137
Thermal Stress (Dt) and, 173–176, 196
Torsion Formula and, 204–205
Torsional Loads, 260–262, 277
Yielding, 106, 109–110, 135
Young’s Modulus (E), 105–106, 135
Elastic Curve, 595–598, 602, 617–625,
629–637, 678
Construction of, 595–598, 678
Discontinuity Functions for, 617–625, 678
M/ei Diagrams for, 629–637
Moment-area Method for, 629–637
Moment-curvature Relationship, 598
Procedures for Analysis of, 602, 622
Radius of Curvature, 598, 678
Elastic Strain Energy (Ui), 113, 746–754, 807
Axial Loads, 746–747
Bending Moments, 748–750
Density, 113
Development of, 113
Internal Work and, 743–754, 807
Transverse Shear, 751–752
Torsional Moments, 753–754
Elastic Torque (Ty), 264
Elastoplastic Materials, 183–184, 185
Electrical-resistance Strain Gauge, 104, 530
Endurance (Fatigue) Limit (Sel), 130–131
Energy Methods, 741–809
Castigliano’s Theorem, 797–807
Conservation of Energy, 759–762, 807
Couple Moment, Work of, 743
Displacement (D), 780–784, 807
Elastic Strain Energy (Ui), 113, 746–754, 807
External Work, 741–745, 759, 807
Force, Work of, 742
Impact Loading, 766–768
Internal Work, 746–754, 759, 779
Method of Virtual Forces, 778, 780–784,
788–792
Procedures for Analysis of, 782, 790, 800, 804
Strain Energy, 741–754, 807
Stress and, 743–745
Virtual Work, 777–796, 807
Engesser’s Equation, 711, 737
Engineering (Nominal) Stress or Strain, 105
Equilibrium, 22–33, 43–44, 51, 82, 145,
158–166, 195, 684–685
Axial Loads, 43–44, 145, 158–166, 195
Balance of Forces and Moments, 24–27, 82
Bifurcation Point for, 685
Column Buckling and, 684–685
Coplanar Loads, 27
Deformable Bodies, 22–33
Displacement and, 145, 195
Equations of, 24, 28, 82
External Loads, 22–24
Free-body Diagrams, 25–28
Internal Resultant Loads, 25–27
Load Distribution and, 22–33
Neutral, 685
Normal Stress (S), 43–44
Procedure for Analysis of, 28
Shear Stress (?), 51
Spring Force and, 684–685
Stable, 684–685
Statically Indeterminate Members,
158–166, 195
Stress and, 22–32, 43–44, 51, 82
Support Reactions, 23
Unstable, 684–685
Equivalent Spring, 768
Euler Load, 688, 737
Extensometer, 104
F
Fabricated Beams, 580
Fabrication Error, 781
Factor of Safety (F.s.), 64–65, 82, 719
Failure, 129–131, 137, 207, 247, 260–262, 277,
352–354, 385–397, 546–553, 559, 683–739
Brittle Behavior, 130, 137
Brittle Materials, 261, 353, 550–551, 559
Buckling, 683–739
Creep, 129–130, 137
Ductile Materials, 261, 378, 546–549, 559
Endurance (Fatigue) Limit (Sel), 130–131
Fatigue, 130–131, 137, 261
Fracture, 550–551
Maximum Distortion Energy Theory,
548–549
Maximum Normal Stress Theory, 550
Maximum Shear Stress Theory, 546–547
Mohr’s Circle for, 546–547
Mohr’s Failure Criterion, 550–551
Multiaxial Stress and, 546–549, 559
Shear Formula for, 386–397
Slipping, 546–547, 551
Strain Transformation and, 546–553, 559
Stress Concentrations and, 130–131, 137,
180–183, 196, 207, 260–262, 352–354
Stress—cycle (S—n) Diagrams for, 130–131
Theories of, 546–553, 559
Torsional Loadings, 207, 247, 261, 277
Transverse Shear and, 385–397
Tresca Yield Criterion, 547
Warping, 247, 277, 386–387
Yielding, 546–547
Fastener Spacing (Beams), 405, 427
Fatigue, 130–131, 137
Flexibility (Force) Method of Analysis,
165–166, 664–672
Flexural Rigidity (Ei), 599–600
Flexure Formula, 311–318, 379
Force (F), 22–28, 40–50, 82, 113, 144–146,
282, 290, 312, 362, 367, 380, 385–386,
684–685, 742, 746, 766–767, 778, 780–784,
788–792
Axially Loaded Bars, 42–44
Balance of, 24
Bending (Beams) and, 312, 362, 367, 380
Body, 23
Buckling From, 684–685
Compression (Internal), 282
Concentrated, 22, 290
Coplanar, 22–24, 27
Disturbing, 684
Equilibrium and, 24–27, 385–386, 684–685
External Loads, 22–24
Internal Axial, 144–146, 746
Internal Resultant Loads, 25–28, 42–44
Loading and Distribution of, 22–28, 82
Normal (N), 26, 42–45
Restoring, 684
Resultant (Fr), 22, 25–26, 312, 362, 367, 380
Shear (V), 26, 50, 282, 385–386
Shear and Moment Diagrams for, 282, 290
Stress and Distribution of, 40–49, 82
Spring, 684–685, 766–767
Support Reactions, 23
Virtual, Method of, 778, 780–784, 788–792
Weight (W) as, 23
Work of, 113, 742
Force (Flexibility) Method of Analysis,
165–166, 664–672
Fracture Stress (Sf), 107, 111
Free-body Diagrams, 25–28
Frequency of Rotation (F), 212
Fully Stressed (Nonprismatic) Beams,
580–583, 591
G
Gage-length Distance, 104
Gage Pressure, 431
Glulam Beams, 568
H
Homogeneous Material, 42
Hooke’s Law, 106, 113, 126, 135, 534–536, 559
Elasticity and, 106, 113, 126, 135
Relationships Between E, V, and G, 532, 559
Shear, 126, 535
Strain Energy, 113
Strain Transformation and, 534–536, 559
Triaxial Stress and, 534–535, 559
Hoop (Circumferential) Stress, 348, 432–433
Hyperbolic Variation, 346–347
I
Impact Factor (N), 768
Impact Loading, 766–768
Inclined Axes, 820–822
Inelastic Behavior, 183–189, 196, 261,
263–270, 277, 362–372, 380
Axial Loads, 183–189, 196
Bending (Beams), 362–372, 380
Deformation From, 183–184, 196
Elastic-plastic Torque, 264
Linear Normal-strain Distribution, 362
Perfectly Plastic (Elastoplastic) Materials,
183–184, 196
Plastic Load (Np), 183–184
Plastic Moment (My), 364–365, 380
Plastic Torque (Tp), 265, 277
Residual Stress (?r), 185–189, 196, 265–270,
277, 365–366, 380
Resultant Force (Fr), 362
Resultant Moment (Mr), 362
886 Indexindex 887
Stress Concentration and, 261
Torsional Loads, 261, 263–265, 277
Ultimate Moment, 366–367, 380
Inelastic Buckling, 710–712, 737
Inertia (I), 206–207, 312–313, 328–334, 689,
813–822
Area (a) Moments of, 813–822
Bending (Beams), 312–313, 328–334
Column Buckling, 689
Composite Areas, 814
Inclined Axes, 820–822
Least Moment of, 689
Moments of, 312–313, 328–334, 813–816,
820–822
Parallel-axis Theorem for, 813–814, 818
Polar Moment of (J), 206–207, 813
Principal Axes of, 329–331, 821
Product of, 329, 817–819
Torsional Loading, 205–206
Unsymmetric Bending, 328–334
Inflection Point, 596
In-plane Principal Stress, 471–477, 506
Integration Method, 599–609, 653–655,
678–679
Boundary Conditions, 600
Continuity Conditions, 600
Deflection and, 599–609, 653–655,
678–679
Displacement by, 599–609
Flexural Rigidity (Ei) for, 599–600
Procedure for Analysis Using, 602
Sign Conventions for, 601
Slope by, 599–609
Statically Determinate Shafts and Beams,
599–609
Statically Indeterminate Shafts and Beams,
653–655, 679
Interaction Formula, 728–729
Internal Loadings, 25–28, 40, 42–44, 50, 82,
144–146
Axial Loaded Members, 144–146
Bending Moment (M) and, 26–27
Coplanar Forces and, 24, 27
Force (F) Distribution and, 25–28, 82
Method of Sections for, 25–28
Normal Force (N) and, 26
Procedure for Analysis of, 28, 45, 146
Relative Displacement (D) of, 144–146
Resultant Force (P), 42–44
Shear Force (V) and, 26, 50
Stress and, 40, 42–43, 45, 82
Three-dimensional Resultant, 26
Torque (T) and, 26
Isotropic Material, 42
K
Keyways, 260
L
Least Moment of Inertia, 689
Limit State Design (Lsd), 66–72, 82
Linear Coefficient of Thermal
Expansion, 173
Linear Variations in Stress/strain, 204,
311–312, 329, 379, 564–565
Live Loads, 66
Load (P), 22–33, 40–49, 66, 82, 141–199,
224–232, 240–243, 276, 282, 288–290, 378,
431–461, 617–625, 683–685, 688, 704–708,
718–724, 728–732, 737, 746–747, 766–771.
See Also Force; Torsion
Axial, 42–49, 141–199, 746–747
Bifurcation Point, 685
Column Bucking, 683–685, 688, 704–708,
718–724, 728–732, 737
Combined, 431–461
Concentric, 718–724
Constant, 144–145, 195, 225–226
Coplanar, 27
Critical (Pcr), 683–685, 737
Dead, 66
Deflection and, 617–625
Deformable Bodies, 22–33
Direct (Simple) Shear, 50
Discontinuity Functions for, 617–625
Distributed, 22, 282, 288–290, 378, 618
Eccentric, 704–708, 728–732
Elastic Strain Energy for, 746–747
Equations of Equilibrium for, 24, 28, 82
Equilibrium and, 22–33, 684–685
Euler Formula for, 688, 737
External, 22–24
Force (F) Distribution and, 22–33, 40–49
Free-body Diagrams for, 25–28
Impact, 766–471
Inelastic Behavior and, 183–184
Internal, 25–28, 40, 42–44
Live, 66
Method of Sections for, 25–28
Moments (M) and, 24–27
Plastic (Np), 183–184
Procedure for Analysis of, 28, 438–439
Shear and Moment Diagram Regions, 282,
288–290, 378
Statically Indeterminate Members, 158–166,
195, 240–243, 276
Stress (S) and, 40, 42–43, 82
Support Reactions, 23
Surface, 22
Three-dimensional Resultant, 26
Torque (T), 26, 224–232, 240–243, 276
Load and Resistance Factor (Lrfd),
66–72, 82
Load-displacement Relationship, 159–166,
195, 664
Load Factor (G), 66
Localized Deformation, 141–143
Longitudinal Shear Stress (Beams), 385–386
Longitudinal Stress (Thin-walled Vessels),
432–433
Lüder Lines, 546–547
Mm/
Ei Diagrams, 629–637
Macaulay Functions, 618–619
Magnitude, 32, 404
Material Properties, 40, 42–43, 103–139,
534–541, 558
Anisotropic Materials, 42
Brittleness, 111, 114, 130–131, 136
Bulk Modulus (K), 537, 559
Cohesive Material, 40
Continuous Material, 40
Creep, 129–131, 137
Dilatation (E), 536–537, 559
Ductility, 109–110, 114, 135
Elastic Behavior, 105–114, 126, 135, 137
Failure, 129–131, 137
Fatigue, 130–131, 137
Homogeneous Material, 42
Hooke’s Law, 106, 113, 126, 135,
534–536, 559
Isotropic Material, 42
Mechanical, 103–139
Modulus of Elasticity (E), 105–106, 108,
126, 135
Modulus of Resilience (Ur), 113, 136
Modulus of Rigidity (G), 126–127, 137
Modulus of Toughness (Ut), 114, 136
Multiaxial Stress and, 534–541
Necking, 107, 114, 135
Permanent Set, 112, 136
Plastic Behavior, 106, 112, 135–136
Poisson’s Ratio (Y), 124–125, 131, 137
Relationships Between E, V, and G, 537, 559
Shear Modulus (G), 126, 131, 137, 537, 559
Stiffness, 112
Strain Energy, 113–118, 136
Strain Hardening, 107, 112, 114, 135–136
Strain Transformation Relationships and,
534–541, 558
Stress (S) and, 40, 42–43, 105, 107
Stress—cycle (S—n) Diagrams for, 130–131
Stress—strain (S—e) Diagrams for, 105–
114, 126–128, 131, 135–137
Tension (Compression) Test for,
103–104, 135
Uniform Deformation, 42–43
Yielding, 106, 109–110, 135
Maximum Deflection (Ymax), 706–707, 737
Maximum Distortion Energy Theory, 548–549
Maximum in-plane Shear Strain, 516, 558
Maximum in-plane Shear Stress, 473–477,
489, 506
Maximum Normal Stress Theory, 550
Maximum Shear Stress Theory, 546–547
Mechanics of Materials, 21–22
Method of Sections, 25–28
Modulus of Elasticity (E), 105–106, 108, 126,
135, 536
Modulus of Resilience (Ur), 113, 136
Modulus of Rigidity (G), 126–127, 131,
137, 536
Modulus of Rupture (?r or Sr), 266, 365–366
Modulus of Toughness (Ut), 114, 136
Mohr’s Circle, 487–493, 499–502, 507,
520–524, 528–529, 546–547, 558
Absolute Maximum Shear Strain,
528–529, 558mohr’s Circle (Continued)
Absolute Maximum Shear Stress (?max),
499–502
Failure Probability Using, 546–547
Plane-strain Transformation, 520–524, 558
Plane-stress Transformation, 487–493, 507
Procedures for Analysis of, 489–490,
520–521
Mohr’s Failure Criterion, 550–551
Moment-area Method, 629–637, 658–662, 679
Moment-curvature Relationship, 598
Moment Diagrams, 658–662
Moments (M), 24–27, 32, 82, 201, 205–206,
282, 290, 307–309, 312–314, 328–334,
345–348, 362–372, 378–380, 387–389,
427, 439, 619–620, 743, 748–750, 753–754,
810–822
Area (a), 810–822
Area About Neutral Axis (Q), 387–389, 427
Arbitrarily Applied, 330
Balance of, 24
Bending (Beams), 26–27, 282, 290, 307–309,
312–314, 328–334, 347–348, 362–372,
378–380, 439, 748–750
Combined Load Analysis for, 439
Concentrated Force and, 290
Coplanar Loads, 27
Couple, Work of, 743
Curved Axis, 255–348
Direction of, 32
Elastic Strain Energy (Ui), 748–750,
753–754
Energy and, 743, 748–750, 753–754
Equilibrium and, 24–27, 82
Inelastic Bending, 362–372, 376
Flexure Formula and, 312–314
Inertia (I), 312–313, 328–334, 813–816,
820–822
Internal, 25–27, 282
Magnitude of, 32
Neutral Axis Orientation and, 331
Plastic (My), 364–365, 380
Polar Moment of Inertia (J), 206–207
Principal Axis, 328–329, 821
Resultant (Mr), 25–26, 328, 362, 585
Shear and Moment Diagram Regions, 282,
290
Singularity Functions and, 619–620
Torsional (T), 26, 82, 201, 439, 753–754
Ultimate, 366–367, 380
Unsymmetric Bending, 328–334, 379
Multiaxial Stress, 534–541, 546–549, 745
N
Necking, 107, 114, 135
Neutral Axis (Beams), 307, 312, 331, 346, 362,
387–389, 427
Bending, Orientation of in, 307, 312, 331,
346, 362
Transverse Shear, Area About (Q),
387–389, 427
Neutral Surface, 307
Nominal Dimensions, 567
Noncircular Shafts, 247–259, 277. See Also
Shafts
Nonlinear Elastic Behavior, 110
Nonprismatic Beams, 580–583, 591
Normal Force (N), 26, 42–45
Normal Strain (E), 88–90, 311, 346, 379,
511–515, 558
Bending (Beams) and, 311, 379
Hyperbolic Variation of, 346
Linear Variation of, 311, 379
Plane-strain Transformation Orientation,
511–515, 558
Principal Strains, 516, 558
Small Strain Analysis, 90
Normal Stress (S), 41–49, 64–65, 82, 203–204,
311, 329, 346–347, 460–461, 463–469,
471–472, 506, 743–744
Allowable (Sallow), 64–65, 82
Average, 42–49, 82
Axially Loaded Bars, 42–49
Bending (Beams), 202–203, 311, 329
Compressive, 41
Constant, 42–43
Distribution of Average, 42–43
Equilibrium and, 43–44
Hyperbolic Variation of, 346–347
In-plane Principal Stresses, 471–472, 506
Internal Force Loading (P), 42–44
Linear Variation of, 203–204, 311, 329
Maximum Average, 44
Plane-stress Transformation Orientation,
468–469, 506
Prismatic Bars and, 42–49, 82
Procedure for Analysis of, 45
Strain Energy and, 743–744
Stress Transformation, 463–469, 506
Tensile, 41
O
Offset Method, 109–110
Overhanging Beams, 281
P
Parabolic Shear Stress Distribution, 394,
564–565
Parallel-axis Theorem, 813–814, 818
Percent Elongation, 109, 135
Percent Reduction in Area, 109, 135
Perfectly Plastic (Elastoplastic) Materials,
106, 183–184, 196
Permanent Set, 112, 136
Plane Strain, 511–524, 558
Maximum in-plane Shear, 516, 558
Mohr’s Circle for, 520–524, 558
Normal and Shear Component Orientation,
511–515, 558
Principal Strains, 516, 558
Procedure for Analysis of, 520–521
Sign Convention for, 512
Transformation Equations for, 512–519, 558
Plane Stress, 463–477, 487–493, 506–507
Component Orientation, 461–467, 506
In-plane Principal Stresses, 471–477, 506
Maximum in-plane Shear, 473–477, 506
Mohr’s Circle for, 487–493, 507
Normal Stress (N), 468–469, 471–472, 506
Shear Stress (?), 463–469, 506
Procedures for Analysis of, 465, 469,
489–490
Sign Convention for, 468
State of, 463–467
Transformation Equations for, 468–470, 506
Plastic Behavior, 106, 112, 135–136, 183–184,
196, 265–270, 277. See Also Inelastic
Behavior
Axial Loads, 183–184, 196
Deformation, 106, 183–184, 196,
265–270, 277
Elastic-plastic Torque, 264
Elastoplastic Materials, 183–184, 185
Perfectly, 106, 183–184, 196
Permanent Set, 112, 136
Strain Hardening, 112, 136
Torsional Loading, 265–270, 277
Yielding, 106, 135
Plastic Load (Np), 183–184
Plastic Moment (My), 364–365, 380
Plastic Torque (Tp), 265–270, 277
Plate Girder, 568
Poisson’s Ratio (V), 124–125, 131, 137
Polar Moment of Inertia (J), 206–207, 813
Posts (Short Columns), 710
Power (P) Transmission, 212–213, 276
Principal Axes, 328–331, 821
Principal Strains, 516, 558
Principal Stresses, 471–477, 489, 506
Prismatic Bars, 42–49
Prismatic Beam Design, 566–573, 591
Product of Inertia, 329, 817–819
Proportional Limit (Spl), 105–106, 114, 126
Pure Shear, 51, 126
R
Radial Distance (R), 203, 208
Radial Stress, 348, 433
Radius of Curvature, 598, 678
Radius of Gyration (R), 689
Redundants, 652
Reinforced Concrete Beams, 341–344
Relative Displacement (D), 143–150, 195
Residual Stresses (?r), 185–189, 196, 265–270,
277, 365–366, 380
Axial Loadings, 185–189, 196
Bending (Beams), 365–366, 380
Modulus of Rupture (?r or Sr), 266,
365–,366
Statically Indeterminate Members, 185,
187–189
Superposition for, 185
Torsional Loadings, 265–270, 277
Resistance Factors (F), 66
Resultant, 25–26, 312, 328, 362, 367, 380, 585
Bending (Beams), 328, 362, 367, 380
Force (Fr), 22, 25–26, 312, 362, 367, 380
Internal Loadings and, 25–26
Moments (Mr), 25–26, 328, 362, 585
888 Indexindex 889
Neutral Axis and, 312, 362
Shaft Design and, 585
Right-hand Rule, 26, 204, 227
Rolled Shapes, 567
Rotation of Shafts, 202–203, 212, 224–232
S
Saint Venant’s Principle, 141–143, 195
Secant Formula, 704–708, 737
Section Modulus (S), 566, 580
Shafts, 201–279, 584–587, 591, 595–681
Angle of Twist (F), 201–203, 224–232, 248,
252, 276
Average Shear Stress (?avg), 251–252, 277
Bulging, 247, 277
Circular, 201–246, 276
Constant Torque and, 225–226
Deflection of, 595–681
Design of, 212–213, 584–587, 591
Discontinuities in Cross Sections, 260–262
Discontinuity Functions for, 617–625, 678
Elastic Curve for, 595–598, 602, 617–625,
629–637, 678
Force (Flexibility) Method of Analysis,
664–672
Frequency of Rotation (F), 212
Inelastic Torsion, 261, 263–265, 277
Integration Method for, 599–609, 653–655,
678–679
Moment-area Method for, 629–637,
658–662, 679
Multiple Torques Along, 226
Noncircular, 247–259, 277
Polar Moment of Inertia (J), 206–207
Power (P) Transmission by, 212–213, 276
Procedures for Analysis of, 208, 228, 241,
602, 622, 631, 667
Residual Stress (?r) in, 265–270, 277
Resultant Moment for, 585
Rotation of, 202–203, 212, 224–232
Shape Variations, 248
Shear Strain (G) Along, 202–203, 264–267
Shear-stress (?) Distribution, 204–211,
247–255, 260–261, 277
Slope for, 595–609, 629–637, 678
Statically Indeterminate, 240–243, 276,
652–672, 679
Stress Concentration Factor (K),
260–262, 277
Superposition Method for, 644–648,
658–662, 664–672, 679
Torque Diagrams for, 229, 584
Torque Loads on, 224–232, 240–243, 276
Torsion Formula for, 204–211, 276
Torsional Deformation and, 201–279
Tubular, 206–208, 212, 250–255, 276–277
Warping, 247, 277
Shear and Moment Diagrams, 281–297, 378
Bending (Beams), 281–297, 378
Concentrated Force and Moment Regions, 290
Discontinuous Functions of, 282
Distributed Load Regions, 282, 288–290, 378
Functions of, 282–283
Graphical Method for Construction of,
288–297, 378
Internal Moments (Compression), 282
Procedures for Analysis of, 283, 291,
314, 349
Slope of, 289–290, 378
Sign Convention for, 282
Support Reactions and, 281–283, 291
Shear Center (O), 418–423, 428
Shear Flow (Q), 250–251, 404–408, 413–417,
427–428
Built-up Members, 404–408, 427
Directional Sense of, 413, 416
Fastener Spacing and, 405
Flanges, 414
Magnitude of, 404
Thin-walled Members, 413–417, 428
Thin-walled Tubes, 250–251
Torsional Loading and, 250–251
Transverse Shear and, 404–408, 413–417,
427–428
Web, 415–416
Shear Force (V), 26, 50, 282, 290,
385–386, 439
Average Shear Stress From, 50
Bending Moments (M) and, 282, 290
Combined Load Analysis for, 439
Development of, 26
Transverse Shear Distribution and, 385–386
Sign Convention for, 282
Shear Formula, 386–397, 427
Shear Modulus (G), 126, 131, 137, 537, 559
Shear Strain (G), 89, 202–203, 264–267,
511–515, 528–529, 558
Absolute Maximum, 528–529, 558
Component Orientation, 511–515, 558
Determination of, 89
Inelastic Torsion and, 264–265
Linear Variation in, 203
Maximum in-plane, 516, 528–529, 558
Maximum Torsional (Gmax), 204, 264–267
Plane-strain Transformation, 511–516,
528–529, 558
Torsional Deformation and, 202–203,
264–267
Shear Stress (?), 41, 50–55, 64–65, 82,
126–128, 137, 204–211, 247–255, 260–261,
266–267, 277, 385–428, 463–469, 473–477,
489, 499–502, 506, 744
Absolute Maximum (?max), 204–205, 207,
499–502, 507
Allowable (?allow), 64–65, 82
Average (?avg), 50–55, 82, 251–252, 277
Beams, 385–428
Complementary Property of, 51
Component Orientation, 461–467, 506
Determination of, 41, 82
Direct (Simple) Loads, 50
Equilibrium and, 51
In-plane Transformations, 471–477, 506
Linear Variation in, 204
Longitudinal, 385–386
Maximum in-plane, 473–477, 489, 506
Maximum Torsional (?max), 205, 208, 248,
260–261, 266–267, 277
Modulus of Elasticity/rigidity (G),
126–128, 137
Parabolic Distribution, 394
Plane-stress Transformation, 468–470,
499–502, 506
Procedure for Analysis of, 52, 465, 469
Proportional Limit (?pl), 126
Pure, 51, 126
Residual, 265–270, 277
Right-hand Rule for, 204
Shafts, Distribution in, 204–205, 207, 247–
255, 260–261, 277
Simple (Direct) Loads, 50
Strain Energy and, 744
Thin-walled Tubes, 250–255, 277
Torsional Loads and, 204–211, 247–255,
260–261, 277
Transverse, 385–428
Ultimate (?u), 126
Shear Stress—strain (S—e) Diagrams,
126–128, 137
Simple Connections, Asd for, 65, 82
Simple (Direct) Shear, 50
Simply Supported Beams, 281
Singularity Functions, 619–620
Slenderness Ratio (L/r), 689–690, 693,
719–720
Slipping, 546–547, 551
Slope, 289–290, 378, 595–609, 629–637, 678
Bending (Shear), 289–290, 378
Deflection and, 595–609, 629–637, 678
Displacement and, 596–597, 599–609,
629–637
Elastic Curve, 595–598, 602, 629–637, 678
Integration Method for, 599–609, 678
Moment-area Method for, 629–637, 678
Procedures for Analysis of, 602, 631
Radius of Curvature, 598, 678
Shear and Moment Diagrams, 289–290, 378
Sign Conventions, 601
Small Strain Analysis, 90
Spherical Thin-walled Vessels, 433, 458
Spring Force, 684–685, 766–767
Stable Equilibrium, 684–685
State of Stress, 41, 438–446, 458, 463–467
Combined Loadings and, 438–446, 458
Determination of, 41
Plane Stress Transformation, 463–467
Procedures for Analysis of, 438–439, 465
Statically Indeterminate Members, 158–166,
173–174, 185, 187–190, 195, 240–243, 276,
652–672, 679
Axially-loaded, 158–166, 173–174,
185, 195
Beams, 652–672, 679
Compatibility (Kinematic) Conditions,
159–166, 195, 664–667
Deflection of, 652–672, 679
Degree of Indeterminacy, 652
Displacement (D), 159–166, 173–174, 195
Equilibrium of, 158–166, 195statically Indeterminate Members
(Continued)
Force (Flexibility) Method of Analysis,
165–166, 664–672
Integration Method for, 653–655, 679
Load-displacement Relationship, 159–166,
195, 664
Moment-area Method for, 658–662, 679
Procedures for Analysis of, 160, 165–166,
241, 667
Redundants, 652
Residual Stresses (?r), 185, 189
Shafts, 240–243, 276, 652–672, 679
Superposition Method for, 185, 658–660,
664–672, 679
Thermal Stress (Dt), 173–174
Torque-loaded, 240–243, 276
Steel Beam Design, 567
Steel Column Specifications, 719
Step Shafts, 260
Stiffness, 112
Stiffness Factor (K), 684–685, 766–767
Straight Members, See Beams
Strain, 87–101, 105, 107, 124–125, 129–130,
137, 202–203, 309–310, 362, 511–561. See
Also Normal Strain (E); Shear Strain (G)
Bending of Beams and, 309–310
Cartesian Components of, 89
Component Orientation, 511–515, 558
Creep, 129–131, 137
Deformation and, 87–93, 309–310
Engineering (Nominal), 105
Inelastic Bending and, 362
Linear Distribution, 362
Maximum in-plane Shear, 516, 558
Multiaxial Stress and, 534–541
Normal (E), 88–90, 511–515, 558
Plane, 511–519, 558
Poisson’s Ratio (V), 124–125, 131, 137
Principals, 516, 558
Procedure for Analysis of, 520–521
Shear (G), 89, 202–203, 511–516, 558
Small Strain Analysis, 90
State of, 90
Transformation, 511–561
True, 107
Units of, 88
Strain Energy (U), 113–118, 136, 548,
741–754, 807
Deformation and, 113–118, 136
Density, 113, 548
Elastic, 113, 746–754, 807
External Work and, 741–745, 807
Material Properties and, 113–118, 136
Modulus of Resilience (Ur), 113, 136
Modulus of Toughness (Ut), 114, 136
Multiaxial Stress and, 548, 745
Normal Stress (S) and, 743–744
Shear Stress (?), 744
Work and, 113, 741–745, 807
Strain Gauge, 516, 530
Strain Hardening, 107, 112, 114, 135–136
Strain Rosettes, 530–531
Strain Transformation, 511–561
Absolute Maximum Shear Strain,
528–529, 558
Bulk Modulus (K), 537, 559
Dilatation (E), 536–537, 559
Equations for, 512–519, 558
Failure and, Theories of, 546–553, 559
Hooke’s Law and, 534–536, 559
In-plane Shear Strain, 516, 558
Material Property Relationships,
534–541, 558
Mohr’s Circle, 520–524, 528–529,
546–547, 558
Multiaxial Stress and, 534–541
Normal and Shear Component Orientation,
511–515, 558
Plane Strain, 511–524, 558
Principal Strains, 516, 558
Procedure for Analysis of, 520–521
Relationships Between E, V, and G, 537, 559
Sign Convention for, 512
Strain Rosettes, 530–531
Strength, Basis of for Beam Design,
563–565, 569
Stress, 21–85, 105–108, 130–131, 135–137,
173–176, 180–183, 185–189, 196, 203–211,
260–262, 265–270, 276–277, 311–318,
345–348, 365–366, 380, 431–460, 463–509,
546–549, 560–561, 563–565, 728–729,
743–745. See Also Normal Stress (S);
Shear Stress (?); Torque (T); Transverse
Shear
Allowable Stress Design (Asd), 64–65, 82
Axially Loaded Members, 42–49, 82, 173–
176, 180–183, 185–189, 196
Bearing, 65
Bending (Beams) and, 311–318, 345–354,
365–366, 380, 385–428
Biaxial, 433
Circumferential (Hoop), 348, 432–433
Columns, Distribution in, 728–729
Combined Loadings, 431–461
Component Orientation, 462–467, 506
Compressive, 41, 728
Concentration, 180–183, 196, 260–262, 277,
352–354, 380
Constant, 42–43
Curved Beams, 345–351
Deformable Bodies, 22–32
Elastic Behavior, 180–183, 196
Endurance (Fatigue) Limit, 130–131, 137
Engineering (Nominal), 105
Equilibrium and, 22–32, 43–44, 51, 82
Factor of Safety (F.s.), 64–65, 82
Fatigue Failure and, 130–131, 137
Force Distribution and, 40–41, 82
Fracture (Sf), 107, 111
Hoop (Circumferential), 348, 432–433
Hyperbolic Variation, 346–347
In-plane Shear, 471–477, 506
Inelastic Bending and, 365–366, 380
Internal Force (F) and, 40, 42–44, 82
Limit State Design (Lsd), 66–72, 82
Linear Variations, 204, 311–312
Load and Resistance Factor (Lrfd),
66–72, 82
Longitudinal, 385–386, 432–433
Material Properties and, 40, 42–43
Mechanics of Materials and, 21–22
Multiaxial, 534–541, 546–549, 745
Necking, 107, 135
Normal (S), 41–49, 64–65, 82, 460–461,
463–469, 471–472, 506, 743–744
Plane, 463–477, 487–493, 506–507
Principal, 471–477, 506
Prismatic Bars, 42–49
Prismatic Beam Design and, 563–565
Procedures for Analysis of, 45, 52, 67,
438–439
Proportional Limit (Spl), 105–106, 114, 126
Radial, 348, 433
Residual (?r), 185–189, 196, 265–270, 277,
365–366, 380
Shear (?), 41, 50–55, 64–65, 82, 126–128, 137,
385–428, 463–469, 473–477, 489, 499–502,
506, 744
Simple Connections, 65, 82
State of, 41, 438–446, 458, 463–467
Strain Energy and, 743–745
Superposition of Combined Components,
439, 458
Tensile, 41
Theories of Failure and, 546–549
Thermal (Dt), 173–176, 196
Torsional, 203–211, 260–262, 265–270,
276–277
Trajectories, 564–565
Transformation, 468–470, 506
Triaxial, 534–535
True, 107
Ultimate (Su), 107, 126
Uniaxial, 43–44
Units of, 41
Yield Point (Sy), 106, 108, 135
Stress Concentration, 180–183, 196, 260–262,
277, 352–354, 380
Absolute Maximum Shear Stress (?max),
260–262, 277
Axial Loads, 180–183, 196
Bending (Beams), 352–354, 380
Distortion From, 180–183, 196
Elastic Behavior and, 180–183, 196
Factor (K), 181–183, 196, 260–262, 277,
352–354, 380
Failure and, 260–262, 352–354
Torsional Loads, 260–262, 277
Stress—cycle (S—n) Diagrams, 130–131
Stress—strain (S—e) Diagrams for, 105–114,
126–128, 131, 135–137
Brittle Materials, 111, 114, 136
Conventional, 105–107
Ductile Materials, 109–110, 114, 135
Elastic Behavior, 105–114, 126, 135, 137
Endurance (Fatigue) Limit (Sel), 130–131
Fracture Stress (Sf), 107, 111
Hooke’s Law, 106, 113, 126, 135
890 Indexindex 891
Modulus of Elasticity (E), 105–106, 108,
126, 135
Modulus of Resilience (Ur), 113, 136
Modulus of Rigidity (G), 126–127, 131, 137
Modulus of Toughness (Ut), 114, 136
Necking, 107, 114, 135
Nominal (Engineering) Stress or Strain, 105
Offset Method, 109–110
Plastic Behavior, 106, 112, 135–136
Poisson’s Ratio (Y), 124–125, 131, 137
Proportional Limit (?pl), 105–106, 114, 126
Shear, 126–128, 137
Strain Energy, 113–118, 136
Strain Hardening, 107, 112, 114, 135–136
True, 107–108
Ultimate Stress (Su), 107, 126
Yield Point (Sy), 106, 108, 135
Yielding, 106, 109–110, 135
Stress Trajectories, 564–565
Stress Transformation, 463–509
Absolute Maximum Shear (?max),
499–502, 507
Equations for, 468–470, 506
In-plane Principal Stress, 471–477, 506
Mohr’s Circle for, 487–493, 499–502, 507
Normal and Shear Component Orientation,
468–469, 506
Plane Stress, 463–477, 487–493, 506–507
Principal Stresses, 471–477, 489, 506
Procedures for Analysis of, 465, 469,
489–490
Sign Convention for, 468
State of Stress and, 463–467
Structural Shapes, Geometric Properties of,
824–831
Superposition, 158–159, 195, 439, 458,
644–648, 658–662, 664–672, 679
Axially Loaded Members, 158–159, 195
Combined Stress Components, 439, 458
Compatibility Equations, 664–667
Deflection Solutions by, 644–648,
664–672, 679
Moment Diagrams Constructed by, 658–662
Principle of, 158–159, 195
Procedure for Analysis Using, 667
Statically Indeterminate Shafts and Beams,
664–672, 679
Support Reactions, 23
Supports for Columns, 686–695, 737
Surface Loadings, 22
T
Tangent Modulus (Et), 710–711
Temperature Change, 781
Tensile Stress, 41
Tension (Compression) Test, 103–104, 135
Thermal Stress (Dt), 173–176, 196
Thin-walled Elements, 250–251, 404–408,
413–423, 427–428, 431–434, 458
Angle of Twist F(X), 252
Average Shear Stress (?avg), 251–252, 277
Axis of Symmetry, 418–420
Beams, 404–408, 413–417, 427–428
Biaxial Stress, 433
Circumferential (Hoop) Stress, 432–433
Closed Cross Sections, 250–255
Combined Loadings, 431–434, 458
Cylindrical Vessels, 432–433, 458
Flanges, 414
Gage Pressure, 431
Longitudinal Stress, 432–433
Pressure Vessels, 431–434, 458
Procedure for Analysis of, 420
Radial Stress, 433
Shear Center (O), 418–423, 428
Shear Flow (Q), 250–251, 404–408, 413–417,
427–428
Spherical Vessels, 433, 458
Transverse Shear in, 404–408, 413–423,
427–428
Tubes, 250–255, 277
Twisting, 250, 418–420
Web, 415–416
Three-dimensional Load Resultant, 26
Torque (T), 26, 201–211, 224–232, 263–270,
276–277
Angle of Twist F(X) and, 201–203,
224–232, 276
Constant, 225–226
Deformation From, 201–203
Elastic (Ty), 264
External, 201–203
Inelastic Torsion and, 263–265, 277
Internal, 204–211, 224–232, 276
Loads and, 26
Maximum Elastic (Ty), 264
Multiple, 226
Plastic (Tp), 265–270, 277
Residual Stress (?r) and, 265–270, 277
Right-hand Rule for, 26, 204, 227
Sign Convention for, 227
Torsion Formula for, 204–211, 276
Torsional Moment, as, 26, 201
Ultimate (Tu), 267
Torque Diagram, 229, 584
Torsion, 201–279, 439, 753–754. See Also
Torque (T)
Angle of Twist F(X), 201–203, 224–232, 248,
250–255, 276
Combined Load Analysis for, 439
Deformation and, 201–279
Elastic Strain Energy (Ui) and, 753–754
Formula for, 204–211, 276
Inelastic, 261, 263–265, 277
Linear Elastic Behavior and, 204–205
Linear Shear Stress/strain Variations,
203–204
Modulus of Rupture (?r) for, 266
Power Transmission and, 212–213, 276
Procedures for Analysis of, 208, 228, 241
Residual Stress (?r), 265–270, 277
Right Hand Rules for, 204, 227
Shafts, 201–279
Shear Strain (G) and, 202–203
Shear Stress (?) Distribution, 204–211,
247–255, 260–261, 277
Static Loadings, 261
Statically Indeterminate Members,
240–243, 276
Stress Concentration Factor (K), 260–262,
277
Stress Distribution, 203–211, 260–262,
265–270, 276–277
Torque Application and Deformation,
201–203
Tubes, 206–207, 212, 228, 250–255, 277
Warping and Bulging From, 247, 277
Torsional Moments (T), 26, 82, 201, 439,
753–754
Transformation Equations, 820
Transformation Factor (N), 339–340, 379
Transverse Shear, 385–428, 751–752
Beams and, 385–428
Built-up Members, 404–408, 427
Elastic Strain Energy (Ui) and, 751–752
Procedures for Analysis of, 392, 420
Shear Center (O), 418–423, 428
Shear Flow (Q), 404–417, 427–428
Shear Formula for, 386–397, 427
Straight Members, 385–386
Thin-walled Members, 413–423, 428
Tresca Yield Criterion, 547
Triaxial Stress, 534–535
True Stress—strain (S—e) Diagrams, 107–108
Trusses, 759, 780–784, 799–801
Castigliano’s Theorem, 799–801
Conservation of Energy for, 759
Fabrication Errors, 781
Procedures for Analysis of, 782, 800
Temperature Changes and, 781
Virtual Forces, Method of for, 780–784
Tubes, 206–207, 212, 228, 250–255, 277
Angle of Twist (F), 252
Average Shear Stress (?avg), 251–252, 277
Closed Cross Sections, 250–255
Polar Moment of Inertia (J), 205, 208
Procedure for Analysis of, 208, 228
Power Transmission by, 212
Shear Stress Distribution, 207
Shear Flow (Q) in, 250–251
Thin-walled, 250–255, 277
Torsion Formula for, 206–208
Twisting, 201, 247, 250, 418–420
U
Ultimate Moment, 366–367, 380
Ultimate Shear Stress (?u), 126
Ultimate Stress (Su), 107, 126
Ultimate Torque (Tu), 267
Uniaxial Stress, 43–44
Uniform Deformation, 42–43
Unstable Equilibrium, 684–685
Unsymmetric Bending, 328–334, 379
V
Virtual Work, 777–796, 807
Beams, 788–792
Energy and, 777–796, 807
Fabrication Error and, 781virtual Work (Continued)
Internal, 779
Method of Virtual Forces, 778, 780–784,
788–792
Principle of, 777–779
Procedures for Analysis of, 782, 790
Temperature Change and, 781
Trusses, 780–784
W
Warping, 247, 277, 386–387
Weight (W), Force as, 23
Wood (Timber) Column Specifications, 720
Wood Beam Design, 567
Work, 113, 212, 741–754, 759–762,
777–796, 807
Conservation of Energy for,
759–762, 807
Couple Moment, 743
Elastic Strain Energy (Ui) and, 113,
746–754, 807
External, 741–745, 759, 807
Force (F) as, 113, 742
Internal, 746–754, 759, 779
Power (P) as, 212
Procedures for Analysis of, 782, 790
Strain Energy, 741–745
Virtual, 777–796, 807
Y
Yield Point (Sy), 106, 108, 135
Yield Strength, 108–109
Yielding, 106, 109–110, 135, 546–547. See Also
Ductile Materials
Deformation From, 106, 109–110, 135
Failure From, 546–547
Maximum Shear Stress Theory for,
546–547
Stress—strain (S—e) Diagrams and, 106,
109–110, 135
Tresca Yield Criterion, 547
Young’s Modulus (E), 105–106, 135
892 Index
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