Strength of Materials – Mechanics of Solids

Strength of Materials – Mechanics of Solids
R. K. Rajput
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1. Simple Stresses and Strains 1-90
   U_ Classification of loads
   L2 Stress
   L3 Simple stress
   1.4 Strain
   L4J Tensile strain
   1 .4.2 Compressive strain
   L43 Shear strain
   L4A Volumetric strain
   L5 Stress and Elongation Produced in a bar
   Due to itsself*weight
   1.6 He Bar of Uniform Strength
   L7 Stress in a Bar due to Rotation
   1.8 Elongation in Case of a Taper Rod
   1.9 Elongation of a Conical Bar due to its Self-weight
   IIP Poisson’s Ratio
   1^11 Rotation Between the Elastic Modulii
   LI1.1 Relation between E and C
   LLL2Relationbe^ K
   1.12 Stresses Induced in Compound Tics or Struts
   L13 Thermal Stress andStrain
   1.14 Hoop Stress
   Typical Examples (For Competitive Examinations)
   Highlights
   Objective Type Questions
   Unsolved Examples
   12234444
   20
   20
   22
   22
   22
   27
   27
   28
   29
   35
   5.1
   69
   70
   82
   83
   86
2. Principal Stresses and Strains 91-145
   2.1 Stresses in a Tensile Member
   2.2 Stresses due to Pure Shearing
   2.3 Two Mutually Perpendicular Direct Str
   2.4 Principal Planes and Principal Stresses
   2.5 Ttoo-dimensional Stress System (Generali
   2.6 Graphical Methods
   2,63.Mohrs.circle
   2AL1 Mohr’s circle construction for like stresses
   2.6.1.3 Mohr’s circle construction for two perpendicular
   direct stresses as the state of simple shear
   2.6J .4 Mohr’s circle construction for principal stresses
   91
   92
   93
   24
   94
   97
   97
   97
   98
   99
   101
   1262.7 Combined Bending and Torsion
   2.8 Analysis of Strain
   2.8.1 Direct strain on oblique plane due to a direct pull on a plane
   2.8.2 Direct strain on a oblique plane due to shear stress.
   2.8.3 Direct strain on an oblique plane due to two normal pulls
   and a shear force
   2.8.4 Strain on an inclined section due to two perpendicular
   normal strains
   2.8.5 Ellipse of strains
   2.8+6 Mohr’s circle of strains
   2.8.7 Principal strains and strain energy due to principal stresses
   2.8JJ Principal strains due to principal stresses
   2.8.7.2 Strain energy due to principal stresses
   Highlights
   Unsolved Examples
   128
   131
   131 .
   13J
   L32
   135
   _ 136
   137
   137
   _ 137
   138 .
   ~ 142 .
   .. 143
3. Centroid and Moment of Inertia 146-205
   3.1 Centre of Gravity of a Body
   3.2 Determination Centre of Gravity
   3J Centroid
   14 Position of Centroids,of Plane Geumdritrui
   Figures
   3.5 Positions of Centre of Gravity of Regular
   Solids
   3.6 Centroids of Composite Areas
   3:7 Centre of Gravity of Simple Solids
   3.8 Area and Volumes Centroid Method
   3.9 Centre of Gravity in a Few Simple Cases
   Ufl Moment of Inertia (M.O.L) – Introduction
   3.11 Moment of Inertia (Second moment of an area)
   3.12 Theorem of Parallel Axes (or Transfer Formula)
   3.13 Theorem of Perpendicular Axes
   3.14 Radius of Gyration
   3J5 Moment of Inertia of Laminae of Different Shapes
   3.16.1 Parallel axes theorem for product of inertia
   3467 Principal axes and principle moments of inertia
   3.16.2.1 Determination of principal moments of inertia and
   directions of principal axes
   346.27 Mohr s circle for principal moments of inertia
   Typical Examples (For Competitive Examinations}
   Highlights
   Objective Type Questions
   Theoretical Questions
   Unsolved Examples
   146
   147
   147
   147
   148
   149
   150
   150
   151
   160
   161
   163
   163
   164
   164
   181
   182
   183
   183
   185
   19J
   195
   197
   198
   1981
4. Bending Moments and Shearing Forces 206-260
   4J_ Introduction
   4.2 Some Basic Definitions
   43 Classification of Reams
   4.4 Shear Force (S.F.) and Bending Moment (B.M.)
   43 Sign conventions
   4.6 Cantilever with an End Load
   4,7 Cantilever with Uniformly Distributed Load
   4.8 Cantilever with Uniformly Distributed load and
   Concentrated Load at the Free End
   206
   206
   207
   208
   208
   209
   209
   210
   4.9 Cantilever Carrying Uniformly Distributed Ixrad for a Pail uf iLs
   Length from the Free End
   4.10 Cantilever Carrying Load Whose Intensity Varies Uniformly from
   Zero al the Free End to the Per unit Run at the Fixed End
   4J 1 CantileyerCanying load Whose Intensity varies Uniformly from
   Zero al the Fixed Point End to iv Pei Unit-Rua al the Free End
   4.12 Simply Supported Beam Carrying Concentrated Load at the Mid Span
   4.13 Simply Supported Beam Carrying Concentrated Load not at Mid Span
   4J 4 Simply Supported Beam Carrying a UniformlyJ3fctnbuiedLaad
   of tv Per unit Run over the Whole Span
   4d5 General Relation between the Loadt the Shearing Force and the
   Bending Moment
   4J6 Simply Supported Beam Carrying a Load whose Intensity varies
   Uniformly from Zero at each End to n per Unit Run at the Mid Span
   4.17 Simply Supported Beam cartying a Load whose Intensity varies
   Uniformly from Zero at one end to tv per unit Run at the other End
   4.18 Simply Supported Beam with Equal Overhangs and carrying a
   Uniformly Distributed Load of per w Unit Run over the Whole Length
   435 .Thc.Points.Qf.Contiaflcxure
   4.20 Loading and B.M. diagrams from SE Diagrams
   Typical Examples (For Competitive Examinations)
   Highlights
   Objective Type Questions
   Unsolved Examples
   210
   212
   214
   218
   218
   219
   220
   224
   225
   23.4
   235
   245
   248
   255
   255
   25.7
5. Bending Stresses in Beams 261-329
   54 Theory of Simple Bending (Bending equation)
   53 Position of .Neutral Axis
   53 Section Modulus
   5.4 Practical Application of Bending Equation
   5.5 Beam of Heterogeneous Materials
   (Flitched beam)
   5.6 Beams of Uniform Strength
   5.7 Bimetallic Strip
   5,8 Reinforced CemenLConcrete1R.CCJ
   Typical Examples (For Competitive Examinations)
   261
   263
   263
   266
   289
   296
   301
   304
   309Highlights
   Objective Type Questions
   Unsolved Examples
   … 324
   … 325
   … 326
   6^Combined Direct and Bending Stresses 330-365
   6J Introduction
   6J Load acd ng EcccntricalIy to One Axis
   6J Condilionfor.No Tension in the.Section
   6.4 Wind Pressure on Chimneys
   6.5 Earth Pressure on retaining Walls
   6,5.1 Angle of repose
   6,5.2 Earth pressure
   Typical Examples (For Competitive Examinations)
   Highlights
   Objective Type questions
   Theoretical Questions
   Unsolved Examples
   330
   330
   332
   342
   348
   348
   349
   355
   362
   362
   363
   363
6. Shearing Stresses 366-398
   7J Introduction
   7.2 Shearing Stress Variation
   Closs section
   7.4 Shear Stress Distribulion for Typical Sections
   Typical Examples (For Competitive
   Examinations)
   Highlights
   Objective Type Questions
   Theoretical Questions
   Unsolved Examples
   366
   367
   368
   371
   382
   396
   396
   397
   397
7. Deflection of Beams 399-528
   8J
   822
   8J
   8.4
   8.5
   8.6
   8J
   8.8
   Introduction
   Beam Deflection
   Relation between Slope. Deflection and
   Radius of Curvature
   Sign Conventions
   Slope and Deflection al a Section
   Double Integration Method
   Macaulay’s Method
   Moment Area Method
   8,8.1 Determination of maximum slope
   and deflection in important cases
   8.9 Conjugate Beam Method
   8.10 Propped Cantilevers and Beams
   Typical Examples (For Competitive Examinations)
   399
   399
   400
   40J
   401
   40J
   420
   jj1
   448
   469
   492
   507Highlights
   Objective Type Questions
   Unsolved Examples
   523
   523
   524
8. Fixed and Continuous Beams 529-588
   9.1. Introduction
   42 Fixed Beams
   9.2.1 Analysis of a fixed beam
   9.2.2 Fixed beam with ends at
   different levels (Effect of
   sinking of supports)
   9-3 Continuous Beam
   9.3.1 Introduction
   9.3.2 Clapeyron’s theorem of three
   moments
   9.3.3 Beams with overhangs
   9.3.4 Sinking of supports
   Typical Examples
   Highlights
   Objective Type Questions
   Unsolved Examples
   HX Thin Shells 589-623
   10.1 Introduction
   10.2 Thin Cylindrical Shells
   10.2.1 Circumferential or hoop stresses
   10.2.2 Longitudinal stresses
   10.23 Maximum shear stress
   10,2.4 Design of thin cylindrical shells
   10.2.5 Cy1indrical shell with
   hemispherical ends
   10.2.6 Built-up cylindrical shells
   10.2.7 Change in dimensions of a thin cylindrical shell due to an
   internal pressure
   10.2,8 Wire wound cylinders
   103 Sphericalsheils
   Typical Examples {Fp^ompetijiv^Exan^
   Highlights
   Objective Type Questions
   Unsolved Examples
   IL Thick Shells 624-683
   HJ Thick Cylinders
   LLLL Introduction
   [LI.2 Lame*s theory
   …. 624
   624
   62411.1.2.1 Special cases
   1 LL2.2 Longitudinal and shear stresses
   niLSJJesjgncf thick cylindrical shell
   1LL24 Compound or shrunk cylinders
   1 1.1.23 Necessary difference of radii for
   shrinkage
   1 1 2 Thick Spherical Shells
   Typical Examples
   Highlights
   Objective Type Questions
   Unsolved Examples 680
9. Riveted and Welded Joints 684-723
   12.1 Introduction
   12.2 Riveted joints
   12.2J Types of riveted joints
   1 2.22 ImportantJenns used in riveting
   12.2.3 Fai1ure of riveted joints
   1 2 3 4 Efficiency of a riveted joint
   1 2.2.5 Thickness of cover plates
   12.2.6 Diamond riveting
   1232 Relation between d and r
   1223 Determination ofj)hch (p) 690
   12.3 Welded Joints 707
   12.3.1 Advantages and disadvantages of welded joints 707
   123.2 Types of welds 708
   1233 Strength of butt welds 709
   Typical Examples 714
   Highlights 720
   Objective Type Questions 720
   Unsolved Examples … 721
10. Torsion of Circular and Non-circular
    Shafts
    Shulls
    Torsion of Shafts
    Torsion Equation
    Hollow Circular Shafts
    Torsional Rigidity
    Power Transmitted by the Shaft
    Importance of Angle of Twist and Various
    Stresses in Shaft
    Modulus of Rupture
    13.9 Comparison of Solid and Hollow Shafts _ 737
    13JO Shafts in Series 744
    L3.ll Shafts in Parallel 745L3.12 Torsional Resilience … 756
    13.13 Shaft Couplings … 758
    13J 4 Combined Bending and Torsion … 76J
    13.15 Torsion of a Tapering Shaft … 767
    13J6 ThinCir^ Sub[ected jo Torsion .„ 721
    13.17 Torsion of Non-circular Solid Section … 773
    13.18 Torsion of Non-circular Thin Tubular Sections 779
    13,19 Torsion of Thin Rectangular Sections … 781
    13.20 Torsion of Thin-walled Multi-cell Sections … 791
    Typical Examples … 794
    Highlights … 804
    Objective Type Questions 807
    Unsolved Examples … 808
11. Springs 812-860
    14J Introduction
    14.2 Helical Springs
    14.3 The Close-coiled Helical Springs
    14.3.1 Close-coiled helical spring with Axial load’
    1432 Subjected to ‘Axial twist1
    144 Open-coiled Helical Springs
    14.4.1 With ‘Axial load’
    14.4.2 With Axial thrust1
    1443 Stresses in circular wire of
    open coil spring
    14.5 Springs in Series
    14.6 Springs in Parallel
    14.7 Flat Spiral Springs
    14.8 Laminated Springs
    14.8.1 Semi’elliptical spring
    14.82 Quarter-elliptical spring
    Typical Examples
    Highlights
    ObjeenyeJTyp^Questions
    Unsolved Examples
12. Strain Energy and Deflection Due to
    Shear and Bending
    15.1 Strain Energy or Resilience
    152 Strain Energy in Simple Tension and Compression
    15.3 Stresses Due to Different Types of Loads
    15.4 Strain Energy in Pure Shearing
    15.5 Strain Energy in Torsion
    1 5,6 Strain Energy Due to Bending
    15.6.1 Bending under gradually
    applied loads
    _ 88115.6.2 Bending under impact
    loads 889
    15.7 Strain Energy Due co Principal
    Stresses -Strain Energy in a
    General Case 892
    15.8 Energy of Distortion (Shear Strain Energy > ” $95
    15.9 Strain Energy and Deflection Due to Shear – 896
    15.10 Castiglianos Theorem f … 900 15.11 Maxwell’s Theorem 916 TypicaiExampies ” 918
    Highlights 924
    Objective Type Questions 926
    Unsolved Examples 927
13. Columns and Struts
    16.1 Introduction
    16.2 Definitions
    16,3 Classification of Columns
    16.4 Strength of Columns
    16.5 End Conditions
    1 6.6 Equivalent Length
    16 7 Euler s Theory (For long columns) < UL 931 16.8 Sign Conventions for … 931 L6JI Euler’s Formula 931 16.IQ Limitations for the use of Euler’s Formula … 932 16.11 Applicability of Euler Theory 933 1642 Deviations of Eul.er’s Formula (For Different End Conditions) … 933 16.13 Rankine’s Hypothesis for Struts/Columns … 943 16.14 John’s Parabolic Formula … 945 16.15 Straight Line Formula 945 1^U> Columns Subjected to Eccenttic Loading 962
    16.17 Prof. Perry’s formula 967
    16.18 Columns with Initial Curvature (Axial loading) … 970
    16J9 Beam Columns … 972
    Typical Examples 978
    Highlights 986
    Objective Type Questions … 987
    Unsolved Examples … 989
    17, Analysis of Framed Structures
    introduction
    Determination of Reactions-Graphical
    Method
    Determination of Stresses
    17.3.1 Graphical Method
    17.3.2 Analytical Methods17.3.2.1 Method of joints
    173.2.2 Method of sections (or
    Method of moments)
    Highlights
    ObjectiyeT^pe Questions
    Theoretical Questions
    Unsolved Examples
14. Theories of Failure
    18.1 Introduction
    18.2 Maximum Principal Stress Theory
    18.3 Maximum Shear Stress or Stress Difference Theory
    18.4 Strain Energy Theory
    18.5 Shear Strain Energy Theory
    18,6 Maximum Principal Strain Theory
    18.7 Graphical Representation of Theories for Two
    Dimensional Stress System
    Typical..Examples
    Highlights
    Objective Type Questions
    Unsolved Examples
15. Stresses Due to Rotation 1129-1162
    19.1 Introduction
    19.2 Rotating Ring
    19,3 Rotating Thin Disc
    19.4 Disc of Uniform Strength
    19.5 Rotating Long Cylinders
    1953 Solid Cylinder
    19,53 Hollow Cylinder
    Highlights
    Objective Type Questions
    Unsolved Examples
16. Bending of Curved Bors
    20,1 Introduction 1163
    20.2— Stresses in Curved Bars (Winkler’Bach Theory )
    203 Values of h2 for Various Sections
    203.1 Rectangular section
    203,2 Circular section
    2033 Triangular section
    203.4 Trapezoidal section
    2033 T-section
    203,6 T-section
    20,4 Stresses in a Ring
    20.5 Stresses in a Chain Link 120120.6 Deflection of Curved Bars 1207
    20,6.1 Deflection of a Closed Ring
    2062 Deflection af a Chain Link
    Typical Examples
    Highlights
    Objective Type Questions
    Unsolved Examples
17. Unsymmetrical Bending and Shear
    21J Introduction
    2L2 Product of Inertia
    product of inertia
    2L2.2 Principal aaes and principal
    momcuts of inertia
    21,3 Stresses Due to Unsymmetrical
    Bending
    2L4 DeflectioiLof Beams Due to
    Unsymmetrical bending
    2L5 Shear Ccntr
    2t .5.1 Shear centre for channeI-section
    .**1222
    _ 1223
    1223
    21.5.2 Shear centre for unequal-section … 1237
    Highlight _ 1245
    Objective Type Questions … 1245
    Unsolved Examples 1246
18. Competitive Examinations (UPSC, GATE etc.)
    Questions with Solutions 1247-1341
    Additional Objective Type Questions
    (Including Questions for ESE, CSE, GATE etc., exams.) 1343-1385
    Material Testing-Experiments 1387-1419
    Index 1420-1424

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