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أخواني في الله أحضرت لكم كتاب Strength of Materials (2nd Edition) BY R. Subramanian
![كتاب Strength of Materials S_o_m_15](https://i.servimg.com/u/f61/15/36/74/14/s_o_m_15.jpg) و المحتوى كما يلي :
Brief Contents Preface to the Second Edition Preface to the First Edition List of Symbols 1. Review of Basic Concepts 2. Properties of Sections 3. Simple Stresses and Strains 4. Bending Moments and Shear Forces 5. Stresses in Beams 6. Combined Direct and Bending Stresses 7.Deformations in Beams 8. Torsion 9. Analysis of Principal Planes, Stresses, and Strains 10. Strain Energy 11.Columns 12. Special Topics 13. Pin-jointed Plane Frames 14. Introduction to Indeterminate Structural Analysis 15. Fixed and Continuous Beams Appendices Index 1028Detailed Contents Preface to the Second Edition Preface to the First Edition List of Symbols 1. Review of Basic Concepts Introduction Structural Engineering Basic Principles of Mechanics Statics 1.4.1 Force Equilibrium 1.5.1 Conditionsof Equilibrium Body Constraints and Free Body Diagrams 1.6.1 Body Constraints 1.6.2 FreeBody Diagram Loads on Structures Centroid Structural Elements and Structural Behaviour Structural Design: Strength, Stiffness, and Stability Symbols & Units 2. Properties of Sections Introduction Centre of Gravity and Centroid Moment of Inertia Computation of Second Moment of Area 2.4.1 Parallel Axis Theorem 2.4.2 PerpendicularAxes Theorem 2.4.3 Polar Moment of Inertia 2.4.4 Moment of Inertia of a CompositeArea 2.4.5 Radius of Gyration Section Modulus Product of Inertia Principal Axes for MI Mohr’s Circle for MI Graphical Construction to Find Moments of inertia 3. Simple Stresses and Strains Introduction Stress and Strain 3.2.1 Stress 3.2.2 Types of Stresses 3.2.3 Strain 3.2.4 Hooke’s Law a5xii I Detailed Contents 3.3 Tapering Sections 3.4 Deformation under Self-weight 3.5 Composite Sections 3.6 Stresses Due to Temperature Change 3.6.1 Effectof Temperature 3.6.2 Thermal Stressin Bars of SingleMaterial 3.6.3 Thermal Stressin CompositeBars 3.7.1 Complementary Shear Stress 3.7.2 Shear Strain and Stateof Pure Shear 3.7.3 Stresses and Strains Along the Diagonals 3.8 Lateral Strain and Poisson’s Ratio 3.8.1 Lateral Strains 3.8.2 Poisson’s Ratio 3.8.3 Uniaxial, Biaxial,andMulti-axialstresses 3.8.4 Multi-axial Stressesand Generalized Hooke’sLaw 3.8.5 VolumetricStrain 3.8.6 Bulk Modulus 3.7 Shear Stress and Strain 3.9 Relationship between Elastic Constants 3.10 Some Indeterminate Problems 3.11 Stresses due to Shrink Fit 3.12 Mechanical Properties of Materials 3.13 Stress-Strain Diagram 3.13.1 Mild Steel 3.13.2 Other Materials 3.14 Obtaining Yield Stress by the Offset Method 3.15 Proof Stress 3.16 Working Stress and Factor of Safety 3.17 Tangent Modulus and Secant Modulus 3.18 Stress Concentration 3.19 Residual Stresses 3.20 Fatigue 4. Bending Moments and Shear Forces 4.1 Introduction 4.1.1 Beams 4.1.2 Structural Action of a Beam 4.2 Bending Moment and Shear Force 4.3 Sign Convention 4.4 Bending Moment and Shear Force Diagrams 4.5 Differential Relationship between Load Intensity, SF, and BM 4.6 Standard Cases 4.5.1 Interpretationof Differential Relationships 4.6.1 Cantilever Beams 4.6.2 SimplySupportedBeams 4.6.3 OverhangingBeams 4.7 Inclined Beams 209Detailed Contents 4.8 Hinged Beams 4.9 Statically Determinate Rigid Frames 4.10 Graphical Method for Drawing SF and BM Diagrams 4.11 Singularity Function Approach for SF and BM 4.1 1.1 Load Intensity Function 5. Stresses in Beams 5.1 Introduction 5.2 Behaviour of Beams 5.3 Bending Stresses 5.3.1 Pure Bending 5.3.2 Theoryof Pure Bending: Bernoulli’s Equation 5.3.3 StressVariationAlong the Length and in the Beam Section 5.3.4 Effect of Shape of Beam Sectionon StressInduced 5.4 Design of Beams for Strength 5.4.1 Section Modulus 5.4.2 Modulus of Rupture 5.4.3 Load Carrying Capacity 5.4.4 Proportioningof Sections 5.5.1 Behaviourof a CompositeBeam 5.5 Composite Sections 5.6 Shear Stress in Beams 5.7 Shear Stress Distribution 5.8 Economical Sections 5.9 Beams of Uniform Strength 5.10 Design of Beams for BM and SF 5.11 Shear Flow in Thin-walled Sections 5.12 The Concept of Shear Centre 5.13 Unsymmetrical Bending 5.13.1 General Equations for Unsymmetrical Bending 5.13.2 Resolving Moments Along PrincipalAxes 5.13.3 Centroidal Principal Axes of Section 5.13.4 Location of Neutral Axis 5.13.5 Sectionswith No Axis of Symmetry: UnsymmetricalSections 6. Combined Direct and Bending Stresses 6.1 Introduction 6.2 Eccentricity Along One Principal Axis 6.2.1 Changing EccentricLoad intoAxial Load and Couple 6.2.2 Resultant Stresses in Rectangular Section 6.2.3 Middle-third Rule:No Tension in the Section 6.3 Biaxial Bending: Load Eccentric to Both Axes 6.3.1 Rectangular Section 6.3.2 Resultant Stress 6.3.3 Location of Neutral Axis 6.4 Rules for No Tension in Sections: Core/Kernel of Sections 6.4.1 RectangularSection:Middle-thirdRule 6.4.2 Circular Section: One-fourth Diameter Rule 350xiv I Detailed Contents 6.4.3 Hollow Circular Section 6.4.4 Box Section 6.5 Unsymmetrical Sections 6.6 Structures Subjected to Lateral Pressure 6.6.1 Behaviour of Structures Subjected to Lateral Pressure 6.6.2 Conditions for Stability 6.6.3 Analysis of Dams,Walls, and Chimneys 7.Deformations in Beams 7.1 Introduction 7.1.1 Slopeand Deflection 7.1.2 Strength and Stiffness 7.2 Equation of the Elastic Curve 7.2.1 Elastic Curve 7.2.2 DifferentialEquation of Elastic Curve 7.3 Sign Convention 7.4 Methods for Calculating Deflection 7.5 The Double Integration Method 7.5.1 Bending Moment Equation 7.6 Macaulay’s Method 7.6.1 Uniformly Distributed Load not Extendingto the RightEnd 7.6.2 TriangularLoad 7.6.3 Couple Load Acting in Between the Supports 7.7 Standard Cases of Loading 7.7.1 Cantilevers 7.7.2 SimplySupportedBeams 7.7.3 OverhangingBeams 7.7.4 More Examples 7.8.1 The Basic Principle 7.8.2 The First Area-moment Theorem 7.8.3 The Second Area-moment Theorem 7.8.4 Drawing Moment Diagramsby Parts 7.9.1 Basic Proposition 4.9.2 Real Beam andConjugateBeam 7.8 The Area-moment Method 7.9 The Conjugate-beam Method 7.10 Standard Cases 7.11 Deflections in Unsymmetrical Bending 8. Torsion 8.1 Introduction 8.2 Torque and Torsional Element 8.3 Behaviour of a Member under Torsion 8.4 Torsion Theory for Axisymmetric Sections 8.4.1 Torsional Rigidity 8.4.2 Polar Section Modulus 8.4.3 Torsional Moment of Resistance 8.5 Stepped Shafts and Shafts of Varying Sections 4658.6 Shafts in Series and Parallel 8.7 Power and Torque 8.8 Design of Shafts 8.8.1 Strength and Stiffness 8.9 Statically Indeterminate Shafts 8.10 Thin-walled Tube 8.11 Torsion of Sections Other than Circular 8.12 Flanged Couplings for Shafts 8.13 Bending Moment and Axial Thrust in Shafts Detailed Contents zl 9. Analysis of Principal Planes, Stresses, and Strains 9.1 Introduction 9.2 Complex Stresses 9.3 Uniaxial Stress: Stresses on an Oblique Section 9.4 Two Normal Stesses on Orthogonal Planes 9.4.1 Ellipseof Stress 9.5 Plane Stress Analysis 9.6 Stress Transformation: Stresses on an Oblique Plane 9.7 The Graphical Method: Mohr’s Circle 9.7.1 Deriving the Equation for Mohr’s Circle 9.7.2 Drawing MOWsCircle 9.8 Interpreting Mohr’s Circle 9.8.1 Principal Planes and Stresses 9.8.2 More Observations from Mohr’s Circle 9.8.3 Originof Planes 9.8.4 Mohr’s Circle forUniaxial and Biaxial StressSystems 9.9.1 MaximumShear Stress 9.9.2 MaximumShear StressValues 9.9.3 Two Principal Stresses,oland o2 9.10 Stress Trajectories 9.11 Combined Stresses Due to Bending and Torsion 9.11.1 EquivalentTorque, Te,and EquivalentBM,M e 9.11.2 Torque, BM, and Axial Thrust 9.12 Principal Strains 9.13 Measurement of Strain, and Strain Rosettes 9.13.1 Strain Rosettes 9.13.2 Graphical Construction (Murphy’sConstruction) 9.13.3 Calculationof Stresses from Strains 9.14 Three-dimensional Stress Analysis 9.14.1 General Stress System 9.14.2 Transformation of Stresses 9.14.3 Sphericaland Deviatric Components 9.14.4 Maximum ShearingStress 9.9 Principal Planes and Stresses: Analytical Solution 10. Strain Energy 10.1 Introduction 10.2 Strain Energy 574xvi I Detailed Contents 10.3 Strain Energy due to Normal Stresses 10.3.1 Gradually Applied Load 10.3.2 Suddenly Applied Load 10.3.3 Load Applied with Impact 10.4 Unit Strain Energy: Modulus of Resilience or Proof Resilience 10.5 Strain Energy due to Bending 10.5.1 Impact Loading on Beams 10.5.2 Finding Deformationsin Beams 10.6 Elastic Strain Energy due to Shearing Stresses 10.7 Elastic Strain Energy due to Torsion 10.8 Strain Energy under Compound Stress 10.9 Applications 10.9.1 GeneralEnergy Principles 10.9.2 Castigliano’s Theorems 10.9.3 Unit Load Method 10.9.4 Maxwell’sReciprocal Theorem 10.9.5 Betty’sLaw 11. Columns 11.1 Introduction 11.2 Behaviour and Classification of Columns 11.2.1 Axially Loaded Compression Members 11.2.2 Buckling 11.2.3 Stability 11.2.4 Criticalor Buckling Load 11.2.5 End Conditions 11.3 Euler’s Theory on Columns 11.3.1 Assumptions in Euler’s Theory 11.3.2 Critical Load for Columnswith Hinged Ends 11.3.3 Column with One End Fixed and the Other End Hinged 11.3.4 Column with One End Fixed and the Other End Free 11.3.5 Columnwith Both Ends Fixed 11.4 Effective Length and Slenderness Ratio 11.5 Limitations andApplicability of Euler’s Formula 11.6 Empirical Formulae 11.6.1 TheRankine-Gordon Formula 11.6.2 Limitationsof Rankine-Gordon Formula 11.6.3 Straight Line Formula 11.6.4 Johnson’sParabolic Formula 11.6.5 IS Code Formula 11.7 Secant Formula for Eccentrically Loaded Columns 11.8 Columns with Initial Curvature 11.9 Beam Columns 11.9.1 Beam Columnwith TransverseUniformly DistributedLoad 11.9.2 Beam Column with Transverse CentralPoint Load 11.10 Structural Sections as Struts 686Detailed Contents xvii I 12. SpecialTopics 692 12.1 Introduction 692 12.2 Carriage or Leaf Springs 692 12.2.1 Maximum Deflectionin the Leaf Spring 694 12.2.2 Strain Energy of Leaf Spring 695 12.2.3 Quarter Elliptic Springs 698 12.3 Helical Springs 699 12.3.1 Close-Coiled Springs 700 12.3.2 Wahl Correction 707 12.3.3 Open-coiled Springs 708 12.3.4 Springin Seriesand Parallel Configurations 721 12.3.5 Flat Spiral Springs 723 12.4 Thin-walled Pressure Vessels 725 12.4.2 Thin-WalledSphericalVessels 732 12.4.1 Thin-WalledCylindrical PressureVessels 726 12.5 Thick Cylindrical Vessels 735 12.5.1 Lame’stheory 736 12.5.2 GraphicalMethod for Determiningo,~ and O, 739 12.5.3 Thick Spherical Shells 747 12.6 Compound Cylinders 750 754 12.7.1 Bars with Large Curvature 755 12.7.2 Sign Convention 759 12.7.5 Stressesin a Closed Ring 765 12.7 Bending of Curved Bars 12.7.3 Location of the Neutral Surface 759 12.7.4 Stress Distribution 761 12.7.6 Stressesin Chain Links 766 12.8 Theories of Elastic Failure 771 12.8.1 The Maximum Principal StressTheory 771 12.8.2 TheMaximumPrincipal StrainTheory 772 12.8.3 TheMaximum Shear StressTheory 773 12.8.4 TheMaximumTotal EnergyTheory 774 12.8.5 The Maximum Shear Strain EnergyTheory 774 12.8.6 Limitationsof the Theoriesof Failure 776 13. Pin-jointed Plane Frames 786 13.1 Introduction 786 13.2 Pin-jointed Plane Frames 786 13.2.1 Stabilityof Frames 787 13.2.2 Classificationof Frames: Perfect,Deficient, and RedundantFrames 788 13.2.3 Types of Trusses 788 13.3 Structural Action 790 13.3.1 Sign Convention 791 13.4 Methods of Analysis 792 13.4.1 Section Around a Joint or Method of Joints 792 13.4.2 Ritter’sMethod of Sections 793 13.4.3 Member Force and Its Components 793xviiiI Detailed Contents 13.5 The Method of Joints 13.6 Special Technique for Parallel Chord Frames 13.6.1 ShearForceDiagram 13.6.2 Nature of Forcesin a Diagonal Member 13.6.3 Magnitude of Diagonal Member Forces 13.7 Method of Tension Coefficients 13.7.1 Joint Coordinates 13.7.2 Tension Coefficient 13.7.3 Joint Equilibrium Equations 13.8 Ritter’s Method of Sections 13.9 Graphical Methods 13.9.1 Culmann’sMethod 13.9.2 Graphical Method of Joints 13.10.1 Internal Stability 13.10.2 External Stability 13.10.3 StaticDeterminacy 13.10.4 CompoundFrames:Fink Roof Truss 13.11.1 Unit Load Method 13.11.2 Castigliano’sTheorem 13.1 1.3 Graphical Method:Williot-Mohr Diagram 13.10 Stability and Determinacy of Frames 13.11 Deflections in Trusses 14. Introduction to Indeterminate Structural Analysis 14.1 Introduction 14.2 Indeterminacy 14.3 Static Indeterminacy 14.3.1 Beams 14.3.2 Rigid Frames 14.4 Method of Analysis 14.4.1 Method of ConsistentDeformations 14.4.2 Force (Flexibility)Method of Analysis 14.5.1 Stiffnessof a Member 14.5.2 Methods of Analysis 14.6 Slope-deflection Equations 14.6.1 Developmentof Slope-deflection Equations 14.6.2 Application of Slope-deflection Equations 14.6.3 Iterative Techniques 14.6.4 Matrix Methods of Analysis 14.7 Analysis of Indeterminate Trusses 14.7.1 Methods of Analysis 14.7.2 Castigliano’sTheorem 14.7.3 Unit Load Method 14.7.4 Forces due to Lack of Fit and Temperature Change 14.5 Kinematic Indeterminacy 15. Fixed and Continuous Beams 15.1 Introduction 92015.2 Fixed Beams 15.2.1 StructuralAction of a Fixed Beam 15.3 Methods of Analysis of Fixed Beams 15.3.1 Method of ConsistentDeformation 15.3.2 Area-momentMethod 15.3.3 Double Integration Method 15.4 Advantages and Disadvantages of Fixed Beams 15.5 Settlement of Supports 15.6 Continuous Beams 15.6.1 Structural Action of a ContinuousBeam 15.6.2 Clapeyron’s Theoremof Three Moments 15.6.3 Three-moment Equationwith Support Settlements 15.6.4 Dealingwith aFixed End 15.6.5 Table of Moments of Area 15.7 Flexibility Matrix Method 15.8 Stiffness Methods of Analysis 15.8.1 Slope-deflection Equations 15.8.2 Moment Distribution Method 15.9 Generalization of Stiffness Method 15.9.1 StiffnessMatrix Method 15.10 Advantages and Disadvantages of Continuous Beams Appendices Appendix 1: Centroids and Moments of Inertia Appendix 2: Material Properties Appendix 3: Beam Formulae Appendix 4:Answers to Problems Index Detailed Contents xix I INDEX Index Terms Links A analysis of dams, walls, and chimneys 363 area-moment method 410 area-moment theorem 411 first 411 second 412 axial force 178 axial force thrust sign convention 179 axially loaded compression members 649 axial thrust 552 B beams 174 211 246 261 274 292 682 behaviour and classification 648 behaviour of 246 design of 261 flitched 274 hinged 211 of uniform strength 292 structural action 175 types of 175 beam columns 682 Index Terms Links bending moment 176 178 183 diagrams 183 sign convention 179 bending moment equation 380 bending stresses 247 Betty’s law 636 biaxial bending 345 biaxial stress system 500 body constraints 21 Bow’s notation 8 box section 351 breaking stress 153 buckling 650 load 669 bulk modulus 128 C cantilever beams 187 carriage spring 692 deflection of 694 strain energy of 695 carry-over moment 892 Castigliano’s theorem 610 898 centroid 28 centroidal principal axes of section 316 circular section 350 Clapeyron’s theorem of three moments 946 947 close-coiled springs 700 702 under axial load 700 deflection 701 strain energy 701Index Terms Links close-coiled springs (Cont.) under axial twist 702 deflection 702 strain energy 703 columns 647 648 671 675 680 behaviour and classification 648 eccentrically loaded 675 with initial curvature 680 complementary energy, theorem of 610 complex stresses 493 nomenclature 494 sign convention 494 composite bars 111 composite sections 99 274 behaviour of 274 equivalent section 276 compound cylinders 750 concentrated load or point load 227 conditions for stability 361 conjugate-beam method 429 proposition 429 conservation of energy, law of 3 605 continuous beams 946 advantages and disadvantages of 997 structural action of 946 support settlements 949 core/kernel of sections 349 couple 7 load 228Index Terms Links critical or buckling load 651 for columns with hinged ends 652 Culmann’s graphical method 823 curved bars 754 bending of 754 neutral surface, location of 759 with large curvature 755 cylindrical vessels 725 thin-walled 728 wire-wound 728 D deflection 374 375 deformable body 2 609 deformation under self-weight 94 differential relationships 184 interpretation of 185 dilatation 128 129 distortion energy theory 774 distribution factor 895 double integration method 379 E eccentricity 336 along one principal axis 336 economical sections 291 efficiency of joints 727 effective length 656 elastic constants 129 relationship between 129Index Terms Links elastic curve 374 375 equation for 376 elastic failure 771 theories of 771 776 limitations of 776 principal strain 772 principal stress theory 771 shear strain energy 774 shear stress 773 total energy 774 elastic limit 152 153 ellipse of stress 504 506 construction of 506 Engesser’s energy theorem 610 equilibrium 13 conditions of 13–17 Euler’s formula 658 limitations of 658 Euler’s theory on columns 652 assumptions in 652 F fatigue 159 160 testing 160 fixed beams 920 922 943 advantages and disadvantages of 943 area-moment method 925 double integration method 937 method of consistent deformation 922 methods of analysis 922 settlement of supports in 944Index Terms Links fixed beams (Cont.) structural action of 921 flexibility method 865 flexural rigidity 255 375 force(s) 4 composition 4 parallelogram law of 4 polygon 5 resultant 4 systems 4 triangle law of 4 force method 865 funicular polygon 8 G general stress system 563 graphical method 217 for drawing SF and BM diagrams 217 of joints 825 H hollow circular section 350 Hooke’s law 85 127 generalized 127 I impact loading on beams 591 inclined beams 209Index Terms Links indeterminacy 860 861 880 degree of 862 kinematic 880 static 861 inertia 2 IS code formula 673 J Johnson’s parabolic formula 673 joints in thin cylindrical vessels 727 L Lame’s lines 739 Lame’s theorem 19 Lame’s theory 736 lateral pressures 359 lateral strains 125 limit of proportionality 153 load carrying capacity 270 load intensity function 226 loads 28 applied with impact 578 suddenly applied 577 location of neutral axis 317 347 long columns 647 M Macaulay’s method 384 Mohr’s circle 528Index Terms Links Maximum shear stress 528 534 absolute 545 analytical solution 534 from Mohr’s circle 528 planes of 528 Maxwell’s reciprocal theorem 634 Maxwell stress diagram 825 mechanical properties 150 of materials 150 member force and its components 793 method of joints 795 method of substitution 835 middle-third rule 338 minimum potential energy, theorem of 609 modular ratio 100 modulus of rigidity 86 modulus of elasticity, Young’s 85 modulus of resilience 579 modulus of rupture 263 Mohr’s circle 516 518 521 533 drawing 518 for MI 70 for uniaxial and biaxial stress systems 533 interpreting 521 equation for 517 moment 6 centre 6 principle 7 of a force 6 moment diagrams by parts 424Index Terms Links moment distribution 894 basic concepts of 894 moment of inertia 44 50 of a composite area 50 moment of resistance 270 moments 7 Murphy’s construction 559 N neutral axis 54 Newton’s law of gravitation 3 Newton’s laws of motion 3 non-uniformly varying load 227 O open-coiled spring 708 714 under axial load 708 deformation 711 rotation 712 strain energy 716 under axial twist 714 axial deflection 715 rotation 716 strain energy 717 origin 532 of normal 532 of planes 532 overhanging beams 199Index Terms Links P parallel axis theorem 46 parallel chord frames 803 forces in a diagonal member 804 shear force diagram 804 special technique for 803 parallelogram law 3 perpendicular axes theorem 47 pin-jointed plane frames 786 assumptions 790 stability and determinacy of 831 stability of 787 structural action 790 visual inspection 794 plane stress analysis 510 point of contraflexure 200 Poisson’s ratio 124 125 polar moment of inertia 47 power 469 pressure vessels 725 726 Lamè’s lines 739 Lamé’s theory 736 thin-walled 725 732 cylindrical 726 joints in 727 spherical 732 volumetric change 727 wire-wound 728 thick-walled 736 cylindrical 736Index Terms Links principal axes for MI 64 principal planes and stresses 525 534 analytical solution 534 Mohr’s circle 525 principal strains 554 principle of superposition 3 principle of transmissibility 3 product integrals, table of 630 product of inertia 59 62 transfer of axes for 62 proof resilience 579 proof stress 155 proportional limit 152 proportioning of sections 270 pure bending 248 249 equation of 251 theory of 249 R radius of gyration 53 Rankine 669 buckling load 669 constants 669 Rankine–Gordon formula 668 limitations of 672 rectangular section 346 349 residual stresses 159 resultant stress 346 rigid body 2 607 rigid frames 213 statically determinate 213Index Terms Links Ritter’s method of sections 817 rules for no tension in sections 349 S secant formula 675 second moment of area 45 graphical construction 72 section modulus 54 262 461 polar 461 shafts 465 471 476 485 design of 471 fixed at both ends 476 flanged couplings for 485 indeterminate 476 in series and parallel 468 of varying sections 465 stepped 465 shear centre 305 shear flow 302 in thin-walled sections 302 shear force 176 183 definition of 178 diagrams for 183 sign convention for 179 shear resilience 596 shear stress 120 279 assumptions and limitations of the formula 282 distribution 279 283 formula 282 horizontal 279Index Terms Links simple bending see pure bending simply supported beams 193 singularity function approach 225 slenderness ratio 657 slope 375 slope-deflection equations 883 spring 721 springs 692 698 699 708 723 carriage or leaf 692 flat spiral 723 helical 699 in series and parallel 721 open-coiled 708 quarter elliptic 698 St Venant’s principle 157 stability 38 650 standard cases of loading 386 cantilevers 387 overhanging beams 397 simply supported beams 391 stiffness 38 882 criterion 471 method 882 of a member 882 relative 895 straight line formula 672 strain 84 120 556 557 along diagonals 123 124 129Index Terms Links compressive 84 electrical 556 gauge 556 measurement of 556 rosettes 557 shear 84 tensile 84 strain energy 574 576 589 595 596 applications 604 due to bending 589 due to normal stresses 576 due to shearing stresses 595 due to torsion 596 gradually applied load 576 under compound stress 602 unit 579 strength 38 strength design 471 sress(es) 549 combined, due to bending and torsion 549 complementary shear 122 compressive 82 due to self-weight 94 due to shrink fit 147 due to temperature 109 hoop 83 in composite sections 99 in tapering sections 91 longitudinal 82 strain (Cont.)Index Terms Links sress(es) (Cont.) nomenclature 494 on an oblique plane 511 plane 510 pure shear 123 shear 83 sign convention 494 495 tangential 83 tensile 82 transformation of 564 ultimate 153 uniaxial 495 yield 153 stress concentration 157 stress distribution 758 759 stress-strain diagram for mild steel 151 for other materials 154 stress trajectories for beams 548 for shafts 549 structural design 38 support fixed 23 hinged or pinned 23 roller 23 T tangent modulus and secant modulus 156 tapering sections 91 tapering shafts 468Index Terms Links tension coefficients 810 method of 810 thermal stress 109 111 in bars of single material 109 in composite bars 111 thick spherical shells 747 thin-walled tube 482 three-dimensional stress analysis 563 torque 453 469 diagram 454 torsion 453 455 457 484 behaviour under 455 formulae 465 of sections other than circular 484 theory for axisymmetric sections 457 torsional moment of resistance 462 torsional resilience 597 torsional rigidity 461 torsional stiffness 460 trusses 786 indeterminate, analysis of 897 U uniformly distributed load 226 uniformly varying load 227 unit load method 622 unsymmetrical bending 312 315 439 deflections in 439 general equations for 315 unsymmetrical sections 321 357Index Terms Links V Varignon’s theorem 7 virtual displacement and virtual work, theorem of 606 volumetric strain 128 W Wahl correction 707 Winkler–Bach formula 755 758 Y yield point 153
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