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| موضوع: كتاب Advanced Strength and Applied Stress Analysis الجمعة 23 أبريل 2021, 11:10 pm | |
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أخوانى فى الله أحضرت لكم كتاب Advanced Strength and Applied Stress Analysis Second Edition Richard G. Budynas
و المحتوى كما يلي :
LIST OF SYMBOLS area, area of cross section, tight-wave vector amplitude, analyzer filter axis area bounded by perimeter centerline of a thin-wallcd tube dimension, crack width, varying amplitude of a light-wave vector dimension, beam width equivalent width of a composite beam section material calibration constant for transmission photoelasticity correction factor for photoelastic coatings distance from the neutral axis to an outer beam fiber, speed of light, strain pulse speed flexural rigidity of a thin plate, diameter diameter directional numbers of a plane modulus of elasticity, voltage modulus of elasticity scale factor eccentricity, distance &om the centtoidal axis to the neutral axis of a curved beam concentrated force force scale factor equivalent concentrated force body forces per unit volume material calibration constant for photoelastic coatings, finite element nodal force, coefficient of friction strength uncertainty factor stress uncertainty factor shear modulus, Griffith energy release rate gravitational constant dimension, depth of beam depth of plastic region second-area moments (area moments of inertia) of a cross section principal second-area moments (area moments of inertia) of a cross section stress invariants unit vectors in the x, y, z directions respectively polar second-area moment (polar moment of inertia) of a cross section equivalent polar second-area moment (polar moment of inertia) of a cross section column support factor fatigue stress concentration factor stress intensity factor critical stress intensity factor static stress concentration factor, strain gage transverse sensitivity factor spring constant, form correction factor for shear, stress optic coefficient AAab CC , Dd df , dy, dt EEe FF F 1 F F JV * y* * z f UuG8h Iyr /j, ly* /1.4/3 l,J, k Jh K ,K,Kc,Kk xvfixvlit LIST OF SYMBOLS length length scale factor directional cosines strain gage length strain pulse length applied or reaction concentrated bending moment (couple) moment scale factor limit (plastic) moment plate bending moments per unit length in polar coordinates plate bending and twisting moments per unit length in rectangular coordinates yield moment net internal bending moments about axes parallel to the y and z axes respectively mass, margin of safety axes of the principal second-area moments normal force, number of cycles, photoelastic isochromatic fringe order, shape functions photoelastic isochromatic fringe order at an angle of incidence 8 design factor, index of refraction, angular speed (rpm) directional cosines concentrated force, polarizer filter axis pressure scale factor critical buckling load limit force pressure, press-fit interference pressure first-area moment of a partial area of a beam section shear force per unit length, distributed load intensity, notch sensitivity factor reaction force, radius, crack resistance force, electrical resistance strain gage nominal resistance radius cylindrical coordinates the distance from the center of curvature to the centroidal axis of a curved beam radiusof gyration the distance from the center of curvature to the neutral axis of a curved beam plastic zone radius elastic section modulus perimeter length of the centerline of a closed thin-walled tube strain gage axial sensitivity endurance strength fatigue strength strain gage factor strain gage transverse sensitivity yield strength ultimate strength position, curvilinear coordinate LL,/ m, n lI P'MM MP Mr, Me Mx, My, Myy M y My, ML mm , n N n„n rty, n. PP Per Pi PQ f) RRr,r 8, z rc r* ri, r; 5SS0 SE S F s * S y So sLIST OF SYMBOLS xlx beam shape factor torsional moment (couple), temperature thickness, time pulse time directional cosines of the net shear stress on an isolated surface strain energy strain energy per unit volume displacements in the JC, y, t directions respectively displacements in \htr, 8, z directions respectively net internal shear force, input voltage plate shear force per unit length in polar coordinates plate shear forces per unit length in rectangular coordinates beam shear forces in rectangular coordinates displacement of beam centroida! axis weight, work complementary work work potential force per unit length, work per unit volume, width, weighting factor rectangular coordinates inelastic section modulus SF Tx uu,u v, w M,. «0. V V V ’ x> r y V V 'y* ri Vc W w,x y, z Z Greek angle, coefficient of thermal expansion, angular location of the neutral plane for unsyrnmetrical bending relative to the m axis angle, angular location of the neutral plane for unsyrnmetrical bending relative to the y axis change, shift in phase of light waves deflection, press-fit radial interference deflection scale factor Kronecker delta normal strain strain scale factor axial strain transverse strain shear strain, weight density, temperature coefficient of resistivity angular deflection angle, angular deflection angular deflection per unit length wavelength, Lam£ constant Lamfc constant Poisson’s ratio natural coordinates potential energy radius of curvature, mass density, resistivity Neuber constant normal stress alternating and mean stresses in fatigue applications stress scale factor principal stresses a 0 A88 ee ,ey0e'9A v b y np'p T< 'O ’G li ^2» ^3LIST OF SYMBOLS critical buckling stress equivalent von Mises stress shear stress equivalent Tresca shear stress Airy stress function, complementary strain energy Prandtrs stress function angle, helix angle of twist angular speed (rad/s) O’ er T 4 > 4> (t) Mathematical V2 Laplacian operator Jacobian matrix Transformation matrix [J ] [T]CONTENTS Principal Strains 81 2.3 Generalized Stress-Strain Relations 82 2.4 The Equilibrium Equations 86 2.5 Compatibility 89 2.6 Summary of Important Equations 97 2.7 Problems 101 List of Symbols xvii 2.2.2 O N I BASIC CONCEPTS OF FORCE, STRESS, STRAIN, AND DISPLACEMENT 1 1.0 Introduction 1 1.1 Force Diagrams 2 1.2 Force Distributions 2 1.3 Stress 10 1.4 Strain, Stress-Strain Relations 20 1.4.1 Normal Strains 20 1.4.2 Shear Strains 23 1.4.3 Thermal Strains 24 1.5 Displacements, Strain-Displacement Relations 24 1.5.1 Rectangular Coordinates 24 1.5.2 Cylindrical Coordinates 29 1.6 Summary of Important Relationships 33 1.7 Problems 37 C H A REVIEW OF THE FUNDAMENTAL FORMULATIONS OF STRESS, STRAIN, AND DEFLECTION 113 Introduction 113 Assumptions and Limitations 114 Axial Loading 114 3.2.1 Axial Stresses 114 3.2.2 Axial Strains and Deflections 117 Torsion of Circular Shafts 129 3.3.1 Torsional Stresses 129 3.3.2 Torsional Strains and Deflections 130 Beams in Bending 132 3.4.1 Shear Force and Bending Moment Equations and Diagrams 132 3.4.2 Bending Stresses 138 3.4.3 Transverse Shear Stresses 143 3.4.4 Bending Strains and Deflections 152 Bending of Symmetric Beams in Two Planes 158 Thin-Walled Pressure Vessels 162 3.6.1 Stresses 162 3.6.2 Strains and Deflections in a Circular Cylinder 166 Superposition 166 Statically Indeterminate Problems 175 Stress and Strain Transformations 185 3.9.1 Plane Stress 185 3.9.2 Principal Stress 186 3.9.3 Maximum In-Plane Shear Stress - 189 3.9.4 Strain Transformations 191 3.0 3.1 3.2 3.3 ( H A P T I R T W O STRESS AND STRAIN. TRANSFORMATIONS, EQUILIBRIUM, AND COMPATIBILITY 46 3.4 2.0 Introduction 46 2.1 Stress Transformations 47 General Three-Dimensional Stress Transformations 47 Plane Stress Transformations 56 Mohr’s Circle for Plane Stress 57 Three-Dimensional Stress Transformation Simplified 62 Principal Stresses 66 Mohr’s Circles in Three Dimensions 72 Maximum Shear Stress 75 2.2 Strain Transformations 78 Strain Transformations, General 78 3.5 2.1.1 3.6 2.1.2 11.3 11.4 3.7 11.5 3.8 11.6 3.9 11.7 12.1 xlxll CONTENTS 5.4.1 Shear Flow in Open Thin'Walled Beams 280 5.4.2 Shear Center for Open Thin-Walled Beams with One Axis of Symmetry 283 5.4.3 Shear Center for Open Unsymmetric Thin-Walled Beams 291 54.4 Shear in Closed Thin-Walled Sections 296 5.5 Composite Beams in Bending 302 5.6 Curved Beams 309 5.6.1 Tangential Stresses 309 5.6.2 Approximate and Numerical Calculations of e 317 5.6.3 Radial Stresses 322 5.7 Bending of Thin Flat Plates 324 5.7.1 Governing Equations in Rectangular Coordinates 324 5.7.2 Tabulated Solutions of Uniformly Loaded Rectangular Plates 329 5.7.3 Governing Equations for Axisymmetric Circular Plates in Bending 330 5.7.4 Tabulated Solutions of Circular Plates 336 5.7.5 Superposition 341 5.8 Thick-Walled Cylinders and Rotating Disks 348 5.9 Contact Stresses 357 5.9.1 Distributed Contact Loading 357 5.9.2 Contact Between Curved Surfaces 361 5.10 Stress Concentrations 364 5.11 Problems 371 5.12 References 403 3.10 Budding Instability of Columns in Compression 192 3.11 Problems 199 3.12 References 219 C H A P T I R F O U R CONCEPTS FROM THE THEORY OF ELASTICITY 220 4,0 Introduction 220 4.1 Plane Elastic Problems 221 Definition 221 Governing Equations 222 Conversion between Plane Stress and Plane Strain Problems 224 4.2 The Airy Stress Function 225 Rectangular Coordinates 225 Polar Coordinates 230 Curved Beam in Bending 233 Circular Hole in a Plate Loaded in Tension 235 Concentrated Force on a Flat Boundary (Flamant Solution ) 238 Disk with Opposing Concentrated Forces 240 4.3 Prandtl’s Stress Function for Torsion 244 General Formulation 244 Torsion on a Rectangular Cross Section 251 4.4 Discussion 255 4.5 Problems 255 4.6 References 260 4.1.1 4.1.2 4,1.3 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.3.1 4.3.2 C H A P T I R F I V I TOPICS FROM ADVANCED MECHANICS OF MATERIALS 261 C H A P T I R S I X ENERGY TECHNIQUES IN STRESS ANALYSIS 404 5.0 Introduction 261 5.1 Shear Flow 261 , 5.2 Torsion of Closed Thin Walled Tubes 262 Single Cell Sections in Torsion 263 Multiple Cell Sections in Torsion 267 5.3 Bending of Unsymmetrical Beams 272 Stresses 272 Deflections 279 5.4 Further Discussion of Transverse Shear Stresses 280 6.0 Introduction 404 6.1 Work 409 5.2.1 6.2 Strain Energy 410 5.2.2 6.2.1 Uniaxial Case 410 Additional Normal Stresses 411 Shear Stress 411 General State of Stress 412 Plane Stress 413 6.2.2 6.2.3 5.3.1 6.2.4 5.3.2 6.2.5 6.3 Total Strain Energy in Bars with Simple Loading Conditions 414CONTENTS Kill 7.3.5 Coulomb-Mohr Theory for Brittle Materials 513 7.3.6 Design Equations 515 7.4 Fracture Mechanics 518 7.4.1 Introduction 518 7.4.2 Crack Modes and the Stress Intensity Factor 520 7.4.3 The Plastic Zone Collection 526 7.5 Fatigue Analysis 532 7.5.1 Fatigue Strength and Endurance Limit 532 7.5.2 Cyclic Stress with a Static Component 534 7.5.3 Fatigue Strength Reduction Factors 538 7.5.4 Equivalent Stresses (Plane Stress) 541 7.5.5 Estimating Ufe for Nonreveising or Nonrepetitive Stress Cycles 543 7.6 Structural Stability 546 7.6.1 Column Buckling 547 7.6.2 Buckling of Plates 556 7.7 Inelastic Behavior 561 7.7.1 EPP Materials 561 7.7.2 Plastic Behavior of Straight Beams in Bending 564 7.7.3 Depth of the Plastic Zone (Rectangular Beam) 568 7.7.4 Residual Stresses (Rectangular Beam) 569 7.7.5 Residual Stresses and Fatigue (Rectangular Beam) 571 7.8 Engineering Approximations Used in Statically Indeterminate Problems 573 7.8.1 Considering Deflections of Flexible Elements Only 573 7.8.2 Limit Analysis 579 7.9 Problems 584 7.10 References 596 Axial Loading 414 Torsional Loading of a Solid Circular Bar 414 Transverse Loading 415 6.4 Castigliano’s First Theorem 419 6.5 The Complementary-Energy Theorem 424 6.6 Castigliano’s Second Theorem 428 Deflections of Statically Determinate Problems 428 Deflections Due to Temperature Changes 445 6.7 Deflections of Thick-Walled Curved Beams 446 6.8 Castigliano’s Second Theorem Applied to Statically Indeterminate Problems 450 6.9 The Virtual Load Method 456 Axial Loading 458 Torsional Loading 459 Bending 460 6.10 The Virtual Load Method Applied to Statically Indeterminate Problems 462 6.11 Rayleigh’s Method Applied to Beams in Bending 464 6.12 The Rayleigh-Ritz Technique Applied to Beams in Bending 469 6.13 Straight Beams Undergoing the Combined Effects of Axial and Transverse Loading 471 6.13.1 Unconstrained Beams 471 6.13.2 Constrained Beams 479 6.14 Problems 483 6.3.1 6.3,2 6.3,3 6.6.1 6,6.2 6.9.1 6.9.2 6.9.3 C H A P T I R S I V I N STRENGTH, FAILURE MODES, AND DESIGN CONSIDERATIONS 498 7.0 Introduction 498 7.1 “Strength” 498 7.2 The Design Factor 500 7.3 Strength Theories 505 Basis of Theories 505 Tresca (Maximum-Shear-Stress) Theory for Ductile Materials 509 von Mises (Maximum-Energy-ofDistortion) Theory for Ductile Materials 509 Comparison between the Tresca and von MisesTheories (Plane Stress) 512 C H A P T I R I I G H T EXPERIMENTAL STRESS ANALYSIS 597 7.3.1 8.0 Introduction 597 8.1 Dimensional Analysis 598 8.2 Analysis Techniques 601 8.2.1 Symmetry 601 When a Surface Perpendicular to a Free Surface Exists Without Shear Stress 602 7.3.2 7.3.3 8.2.2 7.3.4xhr CONTENTS The One-Dimensional Truss Element —The Rayleigh-Ritz Method 681 The Assembly Process 683 Distributed Loads 692 Thermal Stress 694 The Two-Dimensional Truss Element 698 Skew Supports 708 The Three-Dimensional Truss Element 711 9.3 Beam and Frame Elements 718 The Planar Beam Element 718 Distributed Loading 727 Pin Releases (Hinges) in Beam Elements 736 Beams in Two-Plane Bending 741 The Frame Element 742 Three-Dimensional Transformation of the Frame Element 743 Load-Stiffening and Buckling of Beams 747 9.4 Two-Dimensional Elastic Elements 757 The Two-Dimensional Constant Strain Triangle (CST) Element 758 The Two-Dimensional Isoparametric Quadrilateral Element 767 9.5 Higher-Order and Three-Dimensional Elastic Elements 777 9.6 Problems 778 9.7 References 788 8.3 Strain Gages, General 604 9.2.2 8.4 Strain Gage Configurations 607 8.5 Strain Gage Instrumentation 610 The Wheatstone Bridge 610 Commercial Strain Gage Indicator Systems 613 8.6 Characteristics of Strain Gage Measurements 616 Linearity of the Grid Material 617 Transverse Sensitivity of the Gage 617 Temperature Effects 620 Lead-Wire Connection 623 Strain Gradient 624 Zero Shift and Hysteresis Effects 624 Dynamic Response 624 Gage-Current Heating Effects 625 Noise from Electric and/or Magnetic Fields 626 8.7 The Theory of Photoelasticity 626 Electromagnetic Wave Representation of Light 626 Polarization 628 Refraction 630 9.2.3 8.5.1 8.5.2 9.2.4 9.2.5 9.2.6 9.2.7 8.6.1 9.2.8 8.6.2 8.6.3 9.3.1 8.6.4 9,3.2 8.6.5 9.3.3 8.6.6 8.6.7 9.3.4 8.6.8 9.3.5 8.6.9 9.3.6 9.3.7 8.7,1 8.7.2 8.7.3 9.4.1 8.7.4 Birefringence 631 8.7.5 Stress and Birefringence 634 Isoclinic Fringe Analysis 637 8.7,7 Isochromatic Fringe Analysis 642 8.8 Techniques Used in Photoelastic Applications 645 8.8.1 Photoelastic Material Calibration 645 8.8.2 Fractional Fringe Orders 647 8.8.3 Separation of the Principal Stresses, cT\ and 8.8.4 Reflection Photoelasticity 654 Stress Freezing in Three-Dimensional Photoeiasticity 660 9.4.2 8.7.6 C H A P T E R T I N FINITE ELEMENT MODELING 8.8.5 TECHNIQUES 789 10.0 Introduction 789 10.1 Planning and Creating the Finite Element Model (Preprocessing) 791 10.2 Element Selection and Mesh Strategy 792 10.2.1 Introductory Remarks 792 10.2.2 Element Selection 796 10.2.3 Element Input Information 802 10.2.4 Mesh Generation 803 10.2.5 Two-Dimensional Meshing Strategies 808 10.2.6 Submodeling 811 10.2.7 Symmetry 812 8.9 Problems 662 8.10 References 672 C H A P T I R M I N I INTRODUCTION TO THE FINITE ELEMENT METHOD 673 9.0 Introduction 673 9.1 Node and Element Subscript Notation 677 9.2 The Truss Element 677 The One-Dimensional Truss ElementDirect Stiffness Method 678 9.2.1I N D E X A Abrupt change in cross section, 115-116, 235, 365-371, 873-878 Adjoint matrix, 894 Airy stress function: polar coordinates, 230-244 rectangular coordinates, 225-229 Alternating stress component, 535 Analysis techniques, experimental, 601-604 Analyzer filter, 629 Angle of twist: circular shafts, 130-131 closed thin-walled tubes, 264-265, 268 noncircular shafts, 245-249 Area moment of inertia (see Second-area moment) Area properties, tables, 845-847 Assumptions and limitations of theory, 114 Axial and transverse loading of beams, 471-482 Axial deflection of beam due to lateral loading, 473-474 Axial loading of bars: combined with bending, 471-482 composite materials, (example 3,2-1) 118 deflections, 118 effects of loading conditions, 115-116 restrictions to basic formulation, 115 strain energy, 414 strains, 117 stresses, 114-117 with sudden change in section, 115-116, 235, 365-371, 873-877 using finite elements, 678-717 913•14 INDEX B Babinet-Soldi compensator, 645, 647, 648-650 Bathe, K. J„ 788, 842 Bazant, Z. P., 596 Beams in bending (see Bending) Belegundu, A. D., 788 Belyayev, N. M., 403 Bending: composite beams, 302-309 carved beams Airy’s stress function, 233-235 deflections: thick-walled, 446-449 thin-walled, 441-145 eccentricity, e, 311 approximate, 317-318 numerical determination, 318-321 neutral axis, 310 radial stresses, 322-324 strain energy, 446-448 tangential stresses, 309-317 straight beams: axially constrained, 479-482 circular, in wo planes, 158-162 combined with axial loading, 471 482 composite, 302-309 deflections: Castigliano’s method, 432-439 compatibility, (example 2.5-1 ) 90 correction for wide beams, (problem 4.4) 256 direct integration, 152-157 Rayleigh-Ritz method, 469-471 Rayleigh’s method: combined with axial loading, 473-482 simple bending, 464-469 singularity functions, (example 3.4-7) 154, (example D.2-3) 865 superposition, 166-172 tables, 849-857 virtual load method, 460 integral relations, 859-860 neutral axis, 140, 276, 278 singularity functions, 858-867 strain energy, 417 strains, 152 stress functions, 226, (example 4.2-2) 226 stresses: from equilibrium equations, 87-89 flexural, 138-143 lateral, (example 2.4-1) 87INDEX 915 Bending: (continued ) transverse shear, solid beams, 143-151 compound, 151-152 thin-walled, 280-302 unsymmetric, 272-279 thin flat plates: axisymmetric circular, 330-348 rectangular, 324-330 Bending moment equations and diagrams: by sections, 133-138 sign convention: single-plane, 133 two-plane, 158 singularity functions, 137-138, 860-867 superposition, 166-168 tables, 849-857 Bending moment relation to: deflection, 153 strain energy, 417 transverse shear force, 136, 859-860 Bending test specimen, fatigue test, 532 Biharmonic equation: Cartesian coordinates, 225 polar coordinates, 231 Birefringence, 631-637 BLH Electronics, Inc., 607,621 Body forces, 18, 87 Brittle materials, strength theories, 507, 513-515, 516 Broek, D„ 596 Buckling ( see Columns in compression; Stability) C Calibration of photoelastic materials, 645-647, (example R.R-1) 657 Canale, R. P„ 219 Castigliano’s theorems ( see Energy methods) Cedolin, L., 596 Centroid of rivet areas, 574 Centroids of plane areas, 845-847 Chandmpatla, T. R., 788 Chapra, S. C„ 219 Circular plates in bending, 330-348 Circular shafts in: torsion, 129-132 two-plane bending, 158-162 Coefficient of thermal expansion: definition, 24 effect on strain gages, 620 Cofactor, 893916 INDEX Cofactor matrix, 893-894 Collapse modes, 580-584 Columns in compression, 192-19B, 547-555 critical force, 115, 193, 548 critical stress, 195, 549 design equations, 554-555 eccentric loading, 552-554 Euler buckling theory, 192-198 Euler load, 193-194 Euler’s curve, 195, 551-554 inelastic, 549 modes, 548-549 parabolic equation, 551 secant formula, 554 tangent-modulus method, 549-551 Compatibility: correction of an incompatible stress field, (example 2.5-3) 95 discussion, 89-97 equations, 96-97, 100 Compensating gage, 612-613 Complementary energy, 424 Complementary energy theorem: Castigliano's second theorem, 428 discussion, 424 —428 virtual load method, 456-457 Complementary virtual energy, 457 axial loading, 458 bending, 460-462 temperature changes, 461 torsional loading, 459 Complementary virtual work, 457 Complementary work, 424 Composite beams: axially loaded, (example 3.2-1) 118 bending, 302-309 Compound beams, 151-152 Compressive stress, 10-11 Concentrated force acting on a flat boundary, 238-240 Considfcre, A. G., 549 Constantan, 605 Contact between curved surfaces, 361-364 Contact stresses, 357-364 Conversion of isoclinic fringes to stress trajectories, 637-641 Conversion factors, USCU to SI units, 843-844 Cook, R. D., 260, 788, 842 Correction factors for photoelastic coatings, 656-657 Coulomb-Mohi theory of failure, 507, 513-515, 516 Crack growth, 518-520 Crack modes, 520 Crack resistance force, 520INDEX 917 Critical buckling force, 115, 548 Critical stress intensity factor, 524-526 Cubic structure, 83 Cumulative damage, fatigue, 545 Curved beams in bending: Airy’s stress function, 233-235 deflections: thick-walled, 446-449 thin-walled, 441-445 eccentricity, e, 311 approximation, 317-318 numerical determination, 318-321 neutral axis, 310 radial stresses, 322-324 strain energy, 446-448 tangential stresses, 309-317 Cyclic loading ( see Fatigue) Cylinders, pressurized: thick-walled, 348-357 thin-walled, 162-166 Cylindrical coordinates: displacements: definition, 30-32 relation to strain, 30-32 stress components, 29-30 stress-strain relations, 29-30 Cylindrical surfaces in contact, 364 D Dally, J. W., 672 Deflections: axial loading, 118, 120—128 large deflections, 125-128 bending, 152-157 axially constraint Castigliano’s first th< Castigliano’s second combined bending and axial loading, 471-482 composite beams, 304 complementary energy theorem, 408, 424-428 curved beams: thick-walled, 446-449 thin-walled, 441-445 Rayleigh-Ritz method, 408, 469-471 Rayleigh’s method, 408, 464-469, 473-482 relation to strain: cylindrical coordinates, 30-32, 35-36 rectangular coordinates, 24-27, 34-35 singularity functions, (example 3.4-7) 154, (example D.2-3) 86591» INDEX Deflections: (continued) superposition, 166-162 thick.-walled curved beams, 446-449 thin-walled pressurized circular cylinder, 166 torsion: circular shafts, 130-132 closed thin-walled tubes, 264—266, 268 unsymmetric bending, 279 virtual load method, 408, 456-464 Delta rosette, 607, 881-882, 887-888 Depth of plastic zone in beams loaded inelastically, 564, 568-569 Design factor, 500 rationalization, 500-504 used in design equations, 515-516 Determinant of a matrix, 892-893 Dimensional analysis, 598-601 Diphase behavior of polymers, stress freezing, 660-662 Directional cosines: net shear stress on an oblique surface, 64 normal to an oblique surface, 48-50 principal stresses, 67, 99 Directional numbers, 48 Disk: rotating, 348-350, 355-357 subjected to two opposing concentrated forces, 240-244 photoelastic fringe patterns, 638-639, 643, 644, 648 stress trajectories, 637-641 Distortion, energy of, 507, 510 Ductile materials: limit analysis, 579-584 plastic behavior, 561-573 strength theories, 509-513 Dynamic response of strain gages, 624-625 iimaataH Elastic constants for an isotropic material -ta, 21 .5,-23 896 , (example 2.2-1) 80, 84 Elastic limit, 505 Elastic -plastic hehavior, 561-573 Elasticity: mathematical theory, 220-255 modulus, 21 E-LP material, 562 Endurance limit, 533 Energy methods, 404-482 Castigliano’s first theorem, 408, 419-424 Castigliano’s second theorem, 408 deflections due to temperature changes, 445 statically determinate problems, 428-449INDEX #1# Energy methods: {continued ) statically indeterminate problems, 450-456 complementary energy theorem, 408, 424-428 Rayleigh-Ritz method, 408, 469-471 Rayleigh’s method, 408, 464-469, 473-482 virtual load method, 408, 456-464 Engesser, E, 549 E-PP material, 561-564 Equilibrium equations, 86-89, 100 Equivalent force, 5 Equivalent section of a composite beam, 302 area properties, 304 Euler buckling theory, 192-198 Euler load, 193-194 Experimental methods, 597-662 P Factor of safety (see Design factor) Failure of materials {see Fatigue; Fracture mechanics; Strength theories) Fatigue: alternating stress component, 535 bending test, 532 combined with static failure theories, 541-542 cyclic stress with a static component, 534-535 cumulative damage, 545 discussion, 532-534 endurance limit, 533 equivalent alternating stress, 543 equivalent von Mises stress, 541-542 Gerber line, 535 Goodman line, 535 mean stress component, 535 Miner’s method, 545 Neuber’s constant, 539-540 notch radius, 539 number of cycles to failure, 533-534 residual stresses, improvements by, 571-573 S~N diagram, 534 Sodeiberg line, 535 strength, 532 reduction factors, 538 Stress concentrations, effects of, 539-540 surface effects, 538 Finite element method: assembly process, 683, axisymmetric element, 795, 816-817 beam element: offsets, 800-801 planar, 718,»20 INDEX Finite element method: (continued) load stiffening and buckling, 747-757 pin (hinge) releases for beams, 736 two-plane, 741 boundary elements, 708, 818, 820-822 consistent load vector, 729 degrees of freedom, 673, 793, 796-801 direct stiffness method, 678 discussion, 673 distributed loading, 692, 727 element library, 674 errors, 674-676 force-stress matrix, 679 the frame element, 742, 743 Gaiiss-Legendre quadrature, 772 Gauss points, 772 global coordinate system, 698 global transformation matrix, 700, 713, 746 higher-order elements, 777 inverse of reduced stiffne^matrix, 685 interpolation functions (see Shape functions) isoparametric element, 768 isoparametric quadrilateral element, 767 local coordinate system, 698 modeling techniques, 789-835 multipoint constraints, 826-829 nodal loads, 679, 718 node, 673 numerical integration of [k], 772 parasitic shear, 777 partitioning, 685 the penalty method, 818 the Rayleigh-Ritz method, 681 reduced stiffness matrix, 685 rigid elements, 826-829 shape functions, 679, 720, 760, 768, 769 skew supports, 708 static and work equivalent (consistent) load vector, 729 static equivalent (lumped) load vector, 727 stiffness matrix, 680, 682, 722, 746, 749, 762, 772, 774 strain-deflection matrix, 679 stress-strain matrix: plane strain, 766 plane stress, 761 subparametric element, 768 subscript notation, 677 superpardmetric element, 7 system stiffness matrix, 684INDEX »21 Finite element method: (continued) thermal stress, 694 transformed stiffness matrix, 698, 711, 743 truss element: one dimensional, 677-698 three-dimensional, 711 two dimensional, 698 two-dimensional triangular element, 758 Finite element modeling techniques, 789-835 aspect ratio, 795 boundary conditions (see constraints below ) connecting different element types, 796-801 constraints, 823-829 contour plots, 831-832 smoothing, 832 degrees of freedom, 793, 796-801 discussion, 789-791 echo of the input, 791 , 830 dement input information: geometric properties, 802 material properties, 802 element loads, 820 element selection, 792-801 elements suited to structural characteristics, 797-798 load application, 818-823 load scale factors, 823 mesh density, 803 mesh generation, 803 automated, 807-808 manual, 803 semiautomatic, 803-807, 808-810 mesh refinement, 803 mesh strategy, 792-796, 808-811 multiple load cases, 818, 822-823 nodal loads. 679, 718, 819-820 offset beams to model plate ribs, 800-801 planning, 791 preprocessing, 790, 791-830 postprocessing, 790, 830-834 processing, 790, 830 skew, 795 submodeling, 811-812 symmetry, SI2-818 axisymmetry, 816 cyclic symmetry, 815-816 load antisymmetry,814-815 reflective symmetry, 812-815 superposition, 816922 INDEX Finite element modeling techniques:{continued ) text output, 834 transition region, 796 units, 792 warp, 798 First-area moment, Q, 145 Flamant solution, 238-240 Flexural rigidity of a thin flat plate, 327, 332 Flexure formula, bending: in one plane, 138 in two planes, 158, 272, 278 Flow analogy, 367-369 Force diagrams, 2 Force distributions, 2-9 Forces, body, 18, 87 Form correction factor for transverse shear,418 Fracture mechanics, 518-532 Fracture toughness, 524-526 Free-body diagrams, 2 Free surface conditions, 280, 602 Fringe order, 636.643-645 Fully plastic conditions, 564 Gage: compensating, 612-613 strain, 604-626 Gage factor, 617, 883 Gauss-Legendre quadrature, 772 Gauss points, 772 Generalized Hooke’s law, 82-85 Gerber line, 535 Gere, J. M„ 596 Goodier, J. N„ 219, 260, 403 Goodman line, 535 Griffith, 518 Griffith criterion. 519-520 Griffith energy release rate, 520, 522 H Hardrath, H. F., 596 Hertz, H„ 361, 403 Hertzian stresses, 361 Hoersch, V. A., 403 Hooke’s law: generalized, 82-85 isotropic material, 21—24, 29-30, 33-34, 84INDEX 923 Hoop stress in a pressurized cylinder, 164 Hydrostatic state of stress, 66, 509-510 Hysteresis in strain gages, 624 I Indicial notation, 84 Inelastic behavior: beam of rectangular cross section in bending: depth of plastic zone, 564, 568-569 elastic limit moment, 564 maximum strain, 569 plastic limit moment, 564 plastic section modulus, 566 residual strains and stresses (rectangular beam), 569-573 plate with hole, loaded in tension, 563 relation to fatigue, 571-573 shape factor, 565-566 shifting of neutral axis, 566-568 Inglis, 518 Integral relations for beanos in bending, 859-860 Internal forces, 10 Interpolation functions ( see Shape functions) Invariants, stress, 69 Inverse of matrix, 894-895 Irwin, C. R., 528, 596 Isochromatic fringes, 636 Isoclinic fringes, 636 Isoelastic, 605 Isoparametric element, 774 Isotropic material, 84 Isotropic point (in plane of analysis), 71, 187, 637 J Jacobian matrix, 770 Johnson, B. G., 596 Johnson, J. E., 596 Johnson, R. C., 596 Juvinall, R. C., 5% K Karma, 605 Kela, A., 842 Kirsch, G„ 235 Kirsch’s problem, 235 Kobayashi, A. S., 672 Kronecker delta, 85 Kuhn, P., 596934 INDEX L Lamp’s constants, 84 Laplacian operator,— 2, 223 Lateral contraction, 118 Light, behavior, 626-628 Light field, 648 Limit analysis, 579-584 Limit load, 579 Limit moment, 564 Limitations of theory, 114 Localized yielding, 366, 526 Logan, D. L„ 788 Lohner, R., 842 Longitudinal stress in a pressurized cylinder, 164 Love, A. E. H., 260 M Macaulay’s functions, 860 Malleus, D. S„ 788, 842 Margin of safety, 500 Mathematical theory of elasticity, 220-255 Matrix: stiffness (see Stiffness matrix) strain, 46-47 stress, 19, 46 stress*strain, 761, 767 system stiffness, 684 transformation, 55-56, 98, 896-899 Matrix algebra, 889-896 Matrix transformation, 55-56, 98, 896-899 Maximum shear stress, 75-78, 99 Maxwell’s reciprocity theorem, 83 Maxwell’s wave theory, 626-628 Mean stress component, 535 Measurements Group, Inc., 614, 615, 616, 646, 650, 654, 658, 660, 662 Membrane equation, 162-163 Membrane stresses, 163 Micro-Measurements Division of Measurements Group, Inc., 606, 607 Miner, M. A., 596 Miner’s method, 545 Minor (of a matrix), 893 Mixed second-area moment, 272, 868 Modeting load conditions, 818-823 Modulus: elasticity, 21 section: elastic, 143 plastic, 566INDEX 915 Modulus: (continued) shear, 23 Young’s, 21 Mohr’s circle: strain gage rosette, 608 stress: three-dimensional, 72—75 two-dimensional, 57-62 Moment of inertia ( see Second-area moment) Monochromatic light, 626 Murakami, Y., 596 N Neuber, H„ 539, 596 Neuber's constant, 539-540 Neutral axis in bending: curved beams, 310 straight beams; symmetric, 140 unsymmetric, 276, 278 Neutral axis shift due to plastic behavior, 566-568 Newton-Raphson method, 125, (example 3.2-5) 126 Nichrome V, 605 Nodal loads, 679, 718, 819-820 Node, 673 Normal stress, 11, 14 Norton, R. L., 596 Notch radius, 539 Null-balance, 613 O Oblique incidence method,651-652, 658-660 Octahedral shear stress, (prob. 2.8) 103, 507, (prob. 7.32) 586 Orthotropic material, 83 Osgood. C. C., 596 Parallel-axis theorem, 868 Parikh, R, 842 Paris, P, C., 596 Peterson, R. E-, 219, 403 Perucchio, R., 842 Phase shift, 632 Photoelastic coating, 654 Photoelasticity, 626-662 analyzer filter, 629926 INDEX Photoelasticity: (continued ) Babinet-Soleil compensator, 645, 647, 648-650 birefringence, 631-634 due to stress, 634-637 coating used in reflection method, 654 correction factors for photoelastic coatings, 656-657 fast axis, 631 fractional fringe orders, 647-650 fringe order.636, 643-645 isochromatic fringe, 636 isochromatic fringe analysis, 642-645 isoclinic fringe, 636 isoclinic fringe analysis, 637-642 light field, 648 material calibration: reflection, (example 8.8-1) 657 transmission, 645-647 material properties, 646 Maxwell’s wave theory, 626-628 oblique incidence method, 651-652, 658-660 phase shift, 632 polariscope: circular, 642 plane, 635 reflection, 655 polarization: circular, 633-634 linear, 628-629 polarizer filter, 628 principal axes of stress, location, 636 principal strain difference equation, 656 principal stress difference equation, 635, 646 principal stresses, separation, 650-654 quarter-wave plate, 632-634 reflection, 654-660 refraction: index, 630 principle, 630 shear difference method, 652-654 slow axis, 631 stress concentration, example, 365-366 stress freezing, 660-662 stress-optic coefficient, 635 stress separation techniques, 650-654, 658-660 stress trajectories, construction, 637-642 Tardy method, 647-648 three-dimensional methods, 660-662 tint of passage, 645INDEX 917 Photoelasticity: (continued ) transmission methods, 626-654 wavelength, light, 626 Pilkey, W. D., 403, 596 Plane elastic problems: conversions between plane stress and plane strain problems, 224 definition, 221-222 governing equations, 222-224 Plane strain, 222, 223, 766 Plane stress, 19, 22, 33, 56-62, 70-72, 87, 98-100, 185, 221, 222, 224, 761 Plastic hinges in beams, 579 Plastic limit moment, 564, 568 Plastic section modulus, 566 Plastic zone correction, 526-530 Plate in tension with central circular hole, 235-238, 365-369 Plates (thin, flat): buckling, 556-561 coefficient, 560-561 circular, 330-348 flexural rigidity, 327, 332 rectangular, 324-330 superposition of axisymmetric circular plates, 341-348 tables: axisymmetric circular, 336-340 rectangular, 329-330 Plesha, M. E„ 788, 842 Poisson’s ratio, 21 Polar coordinates: Airy stress function, 230-244 axisymmetric problems, 232 Polar moment of inertia ( see Polar second-area moment) Polar second-area moment: circular section, 130 effective, noncircular sections, 253-254, 265 Polariseope: circular, 642 plane, 634 reflection, 655 Polarization of light: circular, 633-634 plane, 628-629 Polarizer filter, 628 Prandtl's stress function, 244-247 Press fits, 352-355 Pressure vessels, thin-walled, 162-166 Pressurized cylinders: thick-walled, 348-357 thin-walled, 162-166 *92* INDEX Principal axes for second-area moments: directions, 868-872 restrictions, beams in bending. 140 Principal strains, 81-82 Principal stresses: determination: three-dimensional, 66-69, 99 two-dimensional, 70-72, 99, 186-189 difference, by photoelastic method, 635, 646 directions, by photoelastic method, 636 separation, by photoelastic method, 650-654 Product of inertia ( see Mixed second-area moment) Properties of areas, 845-848 Q Quarter-wave plate: behavior, 632-634 in a circular polariscope, 642 R Radius of: curvature, 153 gyration, 195 Rayleigh-Ritz method, 408, 469-471 Rayleigh’s method, 408, 464-469, 473-482 Rectangular plates in bending, 324-330 Rectangular rosette, 607-610, 879-881, 885-887 Reddy, J. N„ 788 Redundant supports (see Statically indeterminate problems) Reflection photoelasticity, 654-660 Reflection polariscope, 655 Refraction: basic principles, 630 relative index, 630 Residual strains, 569 Residual stresses: fatigue, related to, 571-573 rectangular beam in bending, 569-573 Rigid elements, 826-829 Riley, W. F„ 672 Rosettes, strain gage, 607-610, 619, 879-888 Rotating disks, 348-350, 355-357 Rotation of an elastic element, 26-27, 31-32 9 Saint-Venant’s principle, 4, 114 Salmon, C. G, 596INDEX 929 Saxena, M., 842 Scaling factors, 599-600 Second-area moment: mixed, 272, 868 parallel-axis theorem for, 868 plane areas, 138, 868 polar, 253-254, 265 principal axes, 871 tables, 845-847 Section modulus: elastic, 143 plastic, 566 Shanley, F. R., 549 Shape factor, 565-566 Shape functions, 679, 720, 760, 768, 769 Shear center: closed thin-walled sections, 296-302 open thin-walled beams with one axis of symmetry, 283-291 open unsymmetric thin-walled beams, 291-295 Shear difference method, 652-654 Shear flow, 129, 261-262, 263, 280-283 Shear force equations and diagrams {see entries for bending moment equations and diagrams ) Shear modulus: definition, 23 relationship with E and v, 23, (example 2.2-1) 80 Shear strain: elasticity definition, 47 engineering definition, 23-24, 46 Hooke’s law: cartesian coordinates, 23-24, 33-34 cylindrical coordinates, 29-30, 35 generalized, 82-85 relation to deflection: cylindrical coordinates, 30-32, 35-36 rectangular coordinates, 26-27, 34 Shear stress: absence, on lines of symmetry, 601-602 components, 15-17 definition, 12, 15 direction, 64 maximum, 75-78, 99 in-plane, 189-191 net: definition, 16 determination, 62-65 octahedral, (prob. 2.8) 103 relation between cross shear stresses, 19 torsional: circular shafts in torsion, 129-130930 INDEX Shear stress; {continued ) closed thin-walled tubes in torsion, 262-271 noncircular shafts in torsion, 244-255 open thin-walled beams in torsion, 253-255 transverse, in bending of beams, 280-302 Shear yield strength, 506 SI units, 843-844 Sih, G. C., 596 Singular matrix. 895 Singularity functions, 858-867 Skew supports, 708 Slenderness ratio, 195 S' N diagram, 534 Soderberg line, 535 Sokolnikoff, I, S„ 260 Spherical pressure vessel, 164 Spherical surfaces in contact, 363-364 Stability (structural), 546-561 Statically indeterminate problems: approximations used in design, 573-584 energy methods, 450-456, 462-464 geometry of deformation, 175-185 Stiffness matrix; bending element: combined with axial loading, 749 single-plane bending, 722 two-plane bending, 741 frame element, 743, 745-746 isoparametric quadrilateral element, 774 system, 684 two-dimensional, 701 three-dimensional, 713 triangular element, 762 Strain: compatibility, equations, 96-97, 100 displacement relations: cartesian coordinates, 24-29, 34-35 cylindrical coordinates, 30-32, 35-36 inelastic distribution in rectangular beam, 569 normal , 20-22 relations with displacements: cylindrical coordinates, 30-32, 35-36 rectangular coordinates, 24-27, 34-35 shear: engineering definition, 23-24, 46 theory of elasticity definition, 47 thermal, 25INDEX 9*1 Strain energy: axial loading. 414 definition, 410-411 form correction factor for transverse shear, 418 per unit volume, 411 general state of stress, 412-413 shear stress, 411-412 state of plane stress, 413 triaxial stress, 411 thick-walled curved beams, 446-448 torsional loading of circular shafts, 414-415 transverse loading of beams, bending and direct shear, 415-419 Strain gage instrumentation, 610-616 commercial strain indicators, 613-616 switching and balancing units, 615 Wheatstone bridge circuit, 610-612 Strain gages, 604-626 adhesive, 606 compensating (temperature), 612, 620-623 configurations, 605, 607 corrections for transverse sensitivity, 619, 883-888 data sheet, 621 delta rosette, 607, 881-882, 887-888 dynamic response, 624-625 gage current heating effects, 625-626 gage factor, 617, 883 variation due to temperature change, 621-622 hysteresis, 624 installations, 606 lead-wire connections, 623-624 linearity of grid material, 617 materials, 605-606 measurement characteristics, 616-626 noise from electric and/or magnetic fields, 626 resistance change due to: strain, 604 temperature change, 612, 620-623 resistivity, 604 < rectangular rosette: three-element, 607-610, 879-881, 885-887 two-element, 607, 619, 884-885 self-temperature-compensating gages, 620-621 sensitivity, 604 stain gradient, effects, 624 temperature effects, methods of correction, 612, 620-623 transverse sensitivity, 617-619, 883-888 corrections, 619, 883-888 transverse sensitivity coefficient, 618, 883 zero shift, 624922 INDEX Strain indicators, 613-616 Strain matrix, 46-47 Strain-stress relations (see Stress-strain relations) Strain transformations, 78-82, 100, 191-192 Strength; definition, 498-500 fatigue, 532 offset yield, 505 ultimate, 499 yield, 505 Strength theories; basis, 505-508 Coulomb-Mohr theory for brittle materials, 507, 513-515, 516 maximum distortion energy ( see von Mises theory) maximum octahedral shear stress, 507, (prob. 7.32) 586 maximum principal strain, 506 maximum principal stress, 506 maximum shear stress (see Tresca theory) maximum strain energy, 506 Tresca theory, 506, 509, 512, 515 von Mises, 507, 509-511, 512, 515 Strength uncertainty factor, 500-501 Stress: alternating component, 535 axial, 114 bearing, 115 bending; curved beams, 309-317, 322-324 straight beams, 138-143 thin flat plates, 324-348 compressive, 10-11 concentrations, 364-371 factor: charts, 873-878 defined, 117, 365 plate in tension with central circular hole, 116-117, 235-238, 365-369 contact, 357-364 definition, 10-20 equilibrium equations for, 86-89, 100 flexure formula: bending: single-plane, 138 two-plane, 158, 272, 278 freezing, 660-662 function: Airy’s, 225-244 PrandU’s, 244-247 hoop, 164 hydrostatic, 66, 509-510INDEX 933 Stress: (continued ) inelastic, 568 intensity factor. 520, 522-525 invariants, 69 longitudinal, 164 matrix, 19, 46 mean component, 538 normal, 10-12, 14-15 plane, 19, 221 principal: three-dimensional analysis, 66-70, 99 two-dimensional analysis, 70-72, 99, 186-189 radial, (fig. 1.5-3a) 30 residual, 569-571 shear: definition, 12, 15-16 net, 16 octahedral, (problem 2.8) 103 superposition, 172-175 tangential, (fig. 1.5-3a) 30 tensile, 11 torsional shear, 129-130 trajectories, 637 transformation simplified, 62-65, 98-99 transformations: three dimensional analysis, 47-51, 62-70, 72-78, 97-99 two-dimensional analysis, 56-57, 70-72, 98-99 transverse (straight beams), 143-151 Tresca (equivalent), 509 uncertainty factor, 501-502 von Mises (equivalent), 511, 512 Stress-optic coefficient, 635 Stress-optic equation, 635 Stress-strain relations, 21-24, 29-30, 33-34, 35, 82-85 * Stress-strain matrix: plane strain, 766 plane stress, 761 Superposition, principle, 166-175 Switching and balancing units, 615 T Tada, H., 596 Tangential stress, (fig. 1.5-3a) 30 Tardy method, 647-648 Taylor, R. L„ 788, 842 Temperature compensation of strain gages, 612-613, 620-623 Tensile stress, 11 Tensor, 896-899934 INDEX Theories of failure (.see Strength theories) Thermal coefficient of resistivity, 604 Thermal expansion, coefficient of, 24 Thermal strains, 24 Thick-walled cylinders, 348-357 Thin-walled cylinders, 162-166 Thin-walled tubes in torsion: closed sections, 262-271 open sections, 253-255 Thomas, H. R., 403 Three-dimensional pfiotoelasticity, 660-662 Three-element rosettes: delta, 607, 881-882, 887-888 rectangular, 607-610, 879-881, 885-887 Timoshenko, S. P., 219, 260, 403, 596 Tint of passage, 645 Toroidal shell, (example 3.6-1) 164 Torsion: angle of twist, 130-131 circular shaft, 129-130 closed thin-walled tubes, 262-271 multiple cell, 267-271, 296-302 single cell, 263-267 elliptical cross section, (problem 4.15) 258 helix angle, 130 open thin-walled sections, 253-255 PrandtTs stress function, 244-247 rectangular cross section, 251-253 strain energy, 414-415 triangular cross section, (example 4.3-2) 249 Trajectories, stress, 637 Transformation: coordinate, 46 directional cosines, 48-50 • second-area moments, 871 strain, 78-82, 100, 191-192 stress, 47-78, 97-99, 185-191 stress tensor, 896-899 Transpose matrix, 892 Transverse sensitivity of strain gages, 617-619, 883-888 Transmission photoelasticity, 626-654 Transverse shear stresses in straight beams, 143-151 Tresca stress, 509 Tresca theory, 506, 509, 512, 515 Triangular finite element, 758-767 U Ugural, A. C., 403 Ultimate strength, 499
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