كتاب Strength of Materials
منتدى هندسة الإنتاج والتصميم الميكانيكى
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منتدى هندسة الإنتاج والتصميم الميكانيكى
بسم الله الرحمن الرحيم

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 كتاب Strength of Materials

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عدد المساهمات : 17473
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تاريخ التسجيل : 01/07/2009
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العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى

كتاب Strength of Materials  Empty
مُساهمةموضوع: كتاب Strength of Materials    كتاب Strength of Materials  Emptyالأحد 24 أبريل 2022, 7:47 am

أخواني في الله
أحضرت لكم كتاب
Strength of Materials (2nd Edition)
BY R. Subramanian

كتاب Strength of Materials  S_o_m_15
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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