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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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