Strength of Materials

Strength of Materials
اسم المؤلف
R. Subramanian
التاريخ
24 أبريل 2022
المشاهدات
71
التقييم
(لا توجد تقييمات)
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Strength of Materials (2nd Edition)
BY R. Subramanian
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
  7. Torsion
  8. Analysis of Principal Planes, Stresses, and Strains
  9. Strain Energy
    11.Columns
  10. Special Topics
  11. Pin-jointed Plane Frames
  12. Introduction to Indeterminate Structural Analysis
  13. Fixed and Continuous Beams
    Appendices
    Index
    1028Detailed Contents
    Preface to the Second Edition
    Preface to the First Edition
    List of Symbols
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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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