**Strength of Materials – Mechanics of Solids
A Textbook for the students of B.E./B.Tech., A.M.I.E., U.P.S.C. (Engg. Services) and other Engineering Examinations]
R.s. Khurmi
1. Introduction 1 – 11
1. Definition.
2. Fundamental Units.
3. Derived Units.
4. Systems of Units.
5. S.I. Units (International Systems of Units).
6. Metre.
7. Kilogram.
8. Second.
9. Presentation of Units and Their Values.
10. Rules for S.I. Units.
11. Useful Data.
12. Algebra.
13. Trigonometry.
14. Differential Calculus.
15. Integral Calculus.
16. Scalar Quantities.
17. Vector Quantities.
18. Force.
19. Resultant Force.
20. Composition of Forces.
21. Parallelogram Law of Forces.
22. Triangle Law of Forces.
23. Polygon Law of Forces.
24. Moment of a Force.
2. Simple Stresses and Strains 12 – 24
1. Introduction.
2. Elasticity.
3. Stress.
4. Strain.
5. Types of Stresses.
6. Tensile Stress.
7. Compressive Stress.
8. Elastic Limit.
9. Hooke′s Law.
10. Modulus of Elasticity (or Young′s Modulus).
11. Deformation of a Body Due to Force Acting on it.
12. Deformation of a Body Due to Self Weight.
13. Principle of Superposition.
3. Stresses and Strains in Bars of Varying Sections 25 – 46
1. Introduction.
2. Types of Bars of Varying Sections.
3. Stresses in the Bars of Different Sections.
4. Stresses in the Bars of Uniformly Tapering Sections.
5. Stresses in the Bars of Uniformly Tapering Circular Sections.
6. Stresses in the Bars of Uniformly Tapering Rectangular Sections.
7. Stresses in the Bars of Composite Sections.
4. Stresses and Strains in Statically Indeterminate Structures 47 – 71
1. Introduction.
2. Types of Statically Indeterminate Structures.
3. Stresses in Simple Statically Indeterminate Structures.
4. Stresses in Indeterminate Structures Supporting a Load.
5. Stresses in Composite Structures of Equal Lengths.
6. Stresses in Composite Structures of Unequal Lengths.
7. Stresses in Nuts and Bolts.
Contents
5. Thermal Stresses and Strains 72 – 90
1. Introduction.
2. Thermal Stresses in Simple Bars.
3. Thermal Stresses in Bars of Circular Tapering Section.
4. Thermal Stresses in Bars of Varying Section.
5. Thermal Stresses in Composite Bars.
6. Superposition of Thermal Stresses.
6. Elastic Constants 91 – 107
1. Introduction.
2. Primary or Linear Strain.
3. Secondary or Lateral Strain.
4. Poisson′s Ratio.
5. Volumetric Strain.
6. Volumetric Strain of a Rectangular Body Subjected to an Axial Force.
7. Volumetric Strain of a Rectangular Body Subjected to Three
Mutually Perpendicular Forces.
8. Bulk Modulus.
9. Relation Between Bulk Modulus and Young′s Modulus.
10. Shear Stress.
11. Principle of Shear Stress.
12. Shear Modulus or Modulus of Rigidity.
13. Relation Between Modulus of Elasticity and Modulus of Rigidity.
7. Principal Stresses and Strains 108 – 147
1. Introduction.
2. Principal Planes.
3. Principal Stress.
4. Methods for the stresses on an Oblique Section of a Body.
5. Analytical Method for the Stresses on an oblique Section of a
Body.
6. Sign conventions for Analytical Method.
7. Stresses on an Oblique Section of a Body subjected to a Direct
Stress in One Plane.
8. Stresses on an oblique Section of a Body subjected to Direct
Stresses in Two Mutually Perpendicular Directions.
9. Stresses on an Oblique Section of a Body subjected to a Simple
Shear Stress.
10. Stresses on an Oblique Section of a Body Subjected to a Direct
Stress in One Plane and Accompanied by a simple shear Stress.
11. Stresses on an oblique Section of a Body Subjected to Direct
Stresses in Two Mutually Perpendicular Directions and Accompanied
by a Simple Shear Stress.
12. Graphical Method for the Stresses on an Oblique Section of a
Body
13. Sign Conventions for Graphical Method
14. Mohr′s Circle for Stresses on an Oblique Section of a Body
Subjected to a Direct Stress in One Plane.
15. Mohr′s circle for Stresses on an Oblique Section of a Body
Subjected to Direct Stresses in Two Mutually Perpendicular Direction.
16. Mohr′s Circle for Stresses on an Oblique Section of a Body
Subjected to Direct Stresses in One Plane Accompanied by a
Simple shear Stress.
17. Mohr′s Circle for Stresses on an Oblique Section of Body Subjected
to Direct Stresses in Two Mutually Perpendicular Directions
Accompanied by Simple Shear Stress.
8. Strain Energy and Impact Loading 148 – 161
1. Introduction.
2. Resilience.
3. Proof Resilience.
4. Modulus of Resilience.
5. Types of Loading.
6. Strain Energy Stored in a Body when the Load is Gradually Applied.
7. Strain Energy Stored in a Body, when the load is Suddenly Applied.
8. Strain Energy Stored in a Body, when the load is Applied with Impact.
9. Strain Energy Stored in a Body of varying section.
10. Strain Energy stored in a Body due to Shear Stress.
9. Centre of Gravity 162 – 183
1. Introduction.
2. Centroid.
3. Methods for Centre of Gravity.
4. Centre of Gravity by Geometrical Considerations.
5. Centre of Gravity by Moments.
6. Axis of Reference.
7. Centre of Gravity of Plane Figures.
8. Centre of Gravity of Symmetrical Sections.
9. Centre of Gravity of Unsymmetrical Sections.
10. Centre of Gravity of Solid Bodies.
11. Centre of Gravity of Sections with Cut out Holes.
10. Moment of Inertia 184 – 207
1. Introduction.
2. Moment of Inertia of a Plane Area.
3. Units of Moment of Inertia.
4. Methods for Moment of Inertia.
5. Moment of Inertia by Routh′s Rule.
6. Moment of Inertia by Integration.
7. Moment of Inertia of a Rectangular Section.
8. Moment of Inertia of a Hollow Rectangular Section.
9. Theorem of Perpendicular Axis.
10. Moment of Inertia of a Circular Section.
11. Moment of Inertia of a Hollow Circular Section.
12. Theorem of Parallel Axis.
13. Moment of Inertia of a Triangular Section.
14. Moment of Inertia of a Semicircular Section.
15. Moment of Inertia of a Composite Section.
16. Moment of Inertia of a Built-up Section.
11. Analysis of Perfect Frames (Analytical Method) 208 – 252
1. Introduction.
2. Types of Frames.
3. Perfect Frame.
4. Imperfect Frame.
5. Deficient Frame.
6. Redundant Frame.
7. Stress.
8. Tensile Stress.
9. Compressive Stress.
10. Assumptions for Forces in the Members of a Perfect Frame.
11. Analytical Methods for the Forces.
12. Method of Joints.
13. Method of Sections (or Method of Moments).
14. Force Table.
15. Cantilever Trusses.
16. Structures with One End Hinged (or Pin-jointed) and the Other
Freely Supported on Rollers and Carrying Horizontal Loads.
17. Structures with One End Hinged (or Pin-jointed) and the Other
Freely Supported on Rollers and Carrying Inclined Loads.
18. Miscellaneous Structures.
12. Analysis of Perfect Frames (Graphical Method) 253 – 285
1. Introduction.
2. Construction of Space Diagram.
3. Construction of Vector Diagram.
4. Force Table.
5. Magnitude of Force.
6. Nature of Force.
7. Cantilever Trusses.
8. Structures with One End Hinged (or Pin-jointed) and the Other
Freely Supported on Rollers and Carrying Horizontal Loads.
9. Structures with One End Hinged (or Pin-jointed) and the Other
Freely Supported on Rollers and Carrying Inclined Loads.
10. Frames with Both Ends Fixed.
11. Method of Substitution.
13. Bending Moment and Shear Force 286 – 343
1. Introduction.
2. Types of Loading.
3. Shear Force.
4. Bending Moment.
5. Sign Conventions.
6. Shear force and Bending Moment Diagrams.
7. Relation between Loading, Shear Force and Bending Moment.
8. Cantilever with a Point Load at its Free End.
9. Cantilever with a Uniformly Distributed Load.
10. Cantilever with a Gradually Varying Load.
11. Simply Supported Beam with a Point Load at its Mid-point.
12. Simply Supported Beam with a Uniformly Distributed Load.
13. Simply Supported Beam with a Triangular Load Varying Gradually
from Zero at Both Ends to w per unit length at the Centre.
14. Simply Supported Beam with a Gradually Varying Load from Zero
at One End to w per unit length at the other End.
15. Overhanging Beam.
16. Point of Contraflexure.
17. Load and Bending Moment Diagrams from a Shear Force Diagram.
18. Beams Subjected to a Moment.
19. Beams Subjected to Inclined Loads.
20. Shear Force and Bending Moment Diagrams for Inclined Beams.
14. Bending Stresses in Simple Beams 344 – 363
1. Introduction.
2. Assumptions in the Theory of Simple Bending.
3. Theory of Simple Bending.
4. Bending Stress.
5. Position of Neutral Axis.
6. Moment of Resistance.
7. Distribution of Bending Stress Across the Section.
8. Modulus of Section.
9. Strength of a Section.
10. Bending Stresses in Symmetrical Sections
11. Bending Stresses in Unsymmetrical Sections.
15. Bending Stresses in Composite Beams 364 – 382
1. Introduction.
2. Types of Composite Beams.
3. Beams of Unsymmetrical Sections.
4. Beams of Uniform Strength.
5. Beams of Composite Sections (Flitched Beams).
16. Shearing Stresses in Beams 383 – 404
1. Introduction.
2. Shearing Stress at a Section in a Loaded Beam.
3. Distribution of Shearing Stress.
4. Distribution of Shearing Stress over a Rectangular Section.
5. Distribution of Shearing Stress over a Triangular Section.
6. Distribution of Shearing Stress over a Circular Section.
7. Distribution of Shearing Stress over an I-section.
8. Distribution of Shear Stress over a T-section.
9. Distribution of Shearing Stress over a Miscellaneous Section.
17. Direct and Bending Stresses 405 – 421
1. Introduction.
2. Eccentric Loading.
3. Columns with Eccentric Loading.
4. Symmetrical Columns with Eccentric Loading about One Axis.
5. Symmetrical Columns with Eccentric Loading about Two Axes.
6. Unsymmetrical Columns with Eccentric Loading.
7. Limit of Eccentricity.
18. Dams and Retaining Walls 422 – 462
1. Introduction.
2. Rectangular Dams.
3. Trapezoidal Dams with Water Face Vertical.
4. Trapezoidal Dams with Water Face Inclined.
5. Conditions for the Stability of a Dam.
6. Condition to Avoid Tension in the Masonry of the Dam at its
Base.
7. Condition to Prevent the Overturning of the Dam.
8. Condition to Prevent the Sliding of Dam.
9. Condition to Prevent the Crushing of Masonry at the Base of the
Dam.
10. Minimum Base Width of a Dam.
11. Maximum Height of a Dam.
12. Retaining Walls.
13. Earth Pressure on a Retaining Wall.
14. Active Earth Pressure.
15. Passive Earth Pressure.
16. Theories of Active Earth Pressure.
17. Rankine′s Theory for Active Earth Pressure.
18. Coulomb′s Wedge Theory for Active Earth Pressure.
19. Conditions for the Stability of Retaining Wall.
19. Deflection of Beams 463 – 489
1. Introduction.
2. Curvature of the Bending Beam.
3. Relation between Slope, Deflection and Radius of Curvature.
4. Methods for Slope and Deflection at a Section.
5. Double Integration Method for Slope and Deflection.
6. Simply Supported Beam with a Central Point Load.
7. Simply Supported Beam with an Eccentric Point Load.
8. Simply Supported Beam with a Uniformly Distributed Load.
9. Simply Supported Beam with a Gradually Varying Load.
10. Macaulay′s Method for Slope and Deflection.
11. Beams of Composite Section.
20. Deflection of Cantilevers 490 – 508
1. Introduction.
2. Methods for Slope and Deflection at a Section.
3. Double Integration Method for Slope and Deflection.
4. Cantilever with a Point Load at the Free End.
5. Cantilever with a Point Load not at the Free End.
6. Cantilever with a Uniformly Distributed Load.
7. Cantilever Partially Loaded with a Uniformly Distributed Load.
8. Cantilever Loaded from the Free End.
9. Cantilever with a gradually Varying Load.
10. Cantilever with Several Loads.
11. Cantilever of Composite Section.
21. Deflection by Moment Area Method 509 – 526
1. Introduction.
2. Mohr′s Theorems.
3. Area and Position of the Centre of Gravity of Parabolas.
4. Simply Supported Beam with a Central Point Load.
5. Simply Supported Beam with an Eccentric Point Load.
6. Simply Supported Beam with a Uniformly Distributed Load.
7. Simply Supported Beam with a Gradually Varying Load.
8. Cantilever with a Point Load at the Free end.
9. Cantilever with a Point Load at any Point.
10. Cantilever with a Uniformly Distributed Load.
11. Cantilever with a Gradually Varying Load.
22. Deflection by Conjugate Beam Method 527 – 547
1. Introduction.
2. Conjugate Beam.
3. Relation between an Actual Beam and the Conjugate Beam.
4. Cantilever with a Point Load at the Free End.
5. Cantilever with a Uniformly Distributed Load.
6. Cantilever with a Gradually Varying Load.
7. Simply Supported Beam with Central Point Load.
8. Simply Supported Beam with an Eccentric Point Load.
9. Simply Supported Beam with a Uniformly Distributed Load.
10. Simply Supported Beam with a Gradually Varying Load.
23. Propped Cantilevers and Beams 548 – 569
1. Introduction.
2. Reaction of a Prop.
3. Cantilever with a Uniformly Distributed Load.
4. Cantilever Propped at an Intermediate Point.
5. Simply Supported Beam with a Uniformly Distributed Load and
Propped at the Centre.
6. Sinking of the Prop.
24. Fixed Beams 570 – 597
1. Introduction.
2. Advantages of Fixed Beams.
3. Bending Moment Diagrams for Fixed Beams.
4. Fixing Moments of a Fixed Beam.
5. Fixing Moments of a Fixed Beam Carrying a Central Point Load.
6. Fixing Moments of a Fixed Beam Carrying an Eccentric Point Load.
7. Fixing Moments of a Fixed Beam Carrying a Uniformly Distributed
Load.
8. Fixing Moments of a Fixed Beam Carrying a Gradually Varying
Load from Zero at One End to w per unit length at the Other.
9. Fixing Moments of a Fixed Beam due to Sinking of a Support.
25. Theorem of Three Moments 598 – 623
1. Introduction.
2. Bending Moment Diagrams for Continuous Beams.
3. Claypeyron′s Theorem of Three Moments.
4. Application of Clapeyron′s Theorem of Three Moments to Various
Types of Continuous Beams.
5. Continuous Beams with Simply Supported Ends.
6. Continuous Beams with Fixed End Supports.
7. Continuous Beams with End Span Overhanging.
8. Continuous Beams with a Sinking Support.
9. Continuous Beams Subjected to a Couple.
26. Moment Distribution Method 624 – 652
1. Introduction.
2. Sign Conventions.
3. Carry Over Factor.
4. Carry Over Factor for a Beam Fixed at One End and Simply
Supported at the Other.
5. Carry Over Factor for a Beam, Simply Supported at Both Ends.
6. Stiffness Factor.
7. Distribution Factors.
8. Application of Moment Distribution Method to Various Types of
Continuous Beams.
9. Beams with Fixed End Supports.
10. Beams with Simply Supported Ends.
11. Beams with End Span Overhanging.
12. Beams With a Sinking Support.
27. Torsion of Circular Shafts 653 – 678
1. Introduction.
2. Assumptions for Shear Stress in a Circular Shaft Subjected to
Torsion.
3. Torsional Stresses and Strains.
4. Strength of a Solid Shaft.
5. Strength of hollow shaft.
6. Power Transmitted by a Shaft.
7. Polar Moment of Inertia.
8. Replacing a Shaft.
9. Shaft of Varying Section.
10. Composite Shaft.
11. Strain Energy due to Torsion.
12. Shaft Couplings.
13. Design of Bolts.
14. Design of Keys.
28. Springs 679 – 694
1. Introduction.
2. Stiffness of a Spring.
3. Types of Springs.
4. Bending Springs.
5. Torsion Springs.
6. Forms of Springs.
7. Carriage Springs or Leaf Springs (Semi-elliptical Type).
8. Quarter-Elliptical Type Leaf Springs.
9. Helical Springs.
10. Closely-coiled Helical Springs.
11. Closely-coiled Helical Springs Subjected to an Axial Load.
12. Closely-coiled Springs Subjected to an Axial Twist.
13. Open-coiled Helical Springs.
14. Springs in Series and Parallel.
29. Riveted Joints 695 – 721
1. Introduction.
2. Types of Riveted Joints.
3. Lap Joint.
4. Butt Joint.
5. Single Cover Butt Joint.
6. Double Cover Butt Joint.
7. Single Riveted Joint.
8. Double Riveted Joint.
9. Multiple Riveted Joint.
10. Chain Riveted Joint.
11. Zig-zag Riveted Joint.
12. Diamond Riveted joint.
13. Pitch of Rivets.
14. Failure of a Joint.
15. Failure of the Rivets.
16. Shearing of the Rivets.
17. Crushing of the Rivets.
18. Failure of the Plates.
19. Tearing off the Plate across a Row of Joints.
20. Tearing off the Plate at an Edge.
21. Strength of a Rivet.
22. Strength of the Plate.
23. Strength of a Riveted Joint.
24. Efficiency of a Riveted Joint.
25. Design of a Riveted Joint.
26. Eccentric Riveted Connections.
27. Transmission of Load Through Rods.
28. Types of Rod Joints.
29. Knuckle Joint.
30. Cotter Joint.
30. Welded Joints 722 – 741
1. Introduction.
2. Advantages and Disadvantages of Welded Joints.
3. Type of Welded Joints.
4. Butt Weld Joint.
5. Fillet Weld Joint.
6. Plug or Slot Weld Joint.
7. Technical Terms.
8. Strength of a Welded Joint.
9. Unsymmetrical Section Subjected to an Axial Load.
10. Eccentric Welded Joints.
11. Eccentric Welded Joint Subjected to Moment.
12. Eccentric Welded Joint Subjected to Torsion.
31. Thin Cylindrical and Spherical Shells 742 – 754
1. Introduction.
2. Failure of a Thin Cylindrical Shell due to an Internal Pressure.
3. Stresses in a Thin Cylindrical Shell.
4. Circumferential Stress.
5. Longitudinal Stress.
6. Design of Thin Cylindrical Shells.
7. Change in Dimensions of a Thin Cylindrical Shell due to an
Internal Pressure.
8. Change in Volume of a Thin Cylindrical Shell due to an Internal
Pressure.
9. Thin Spherical Shells.
10. Change in Diameter and Volume of a Thin Spherical Shell due an
Internal Pressure.
11. Riveted Cylindrical Shells.
12. Wire-bound Thin Cylindrical Shells.
32. Thick Cylindrical and Spherical Shells 755 – 772
1. Introduction.
2. Lame′s Theory.
3. Stresses in a Thick Cylindrical Shell.
4. Stresses in Compound Thick Cylindrical Shells.
5. Difference of Radii for Shrinkage.
6. Thick spherical shells.
33. Bending of Curved Bars 773 – 794
1. Introduction.
2. Assumptions for the Stresses in the Bending of Curved Bars.
3. Types of Curved Bars on the Basis of initial Curvature.
4. Bars with a Small Initial Curvature.
5. Bars with a Large Initial Curvature.
6. Link Radius for Standard Sections.
7. Value of Link Radius for a Rectangular Section.
8. Value of Link Radius for a Triangular Section.
9. Value of Link Radius for a Trapezoidal Section.
10. Value of Link Radius for a Circular Section.
11. Crane Hooks.
12. Rings.
13. Chain Links.
34. Columns and Struts 795 – 820
1. Introduction.
2. Failure of a Column or Strut.
3. Euler′s Column Theory.
4. Assumptions in the Euler′s Column Theory.
5. Sign Conventions.
6. Types of End Conditions of Columns.
7. Columns with Both Ends Hinged.
8. Columns with One End Fixed and the Other Free.
9. Columns with Both Ends Fixed.
10. Columns with One End Fixed and the Other Hinged.
11. Euler′s Formula and Equivalent Length of a Column.
12. Slenderness Ratio.
13. Limitations of Euler′s Formula.
14. Empirical Formulae for Columns.
15. Rankine′s Formula for Columns.
16. Johnson′s Formula for Columns.
17. Johnson′s Straight Line Formula for Columns.
18. Johnson′s Parabolic Formula for Columns.
19. Indian Standard Code for Columns.
20. Long Columns subjected to Eccentric Loading.
35. Introduction to Reinforced Concrete 821 – 834
1. Introduction.
2. Advantage of R.C.C. Structures.
3. Assumptions in the Theory of R.C.C.
4. Neutral Axis.
5. Types of Neutral Axes.
6. Critical Neutral Axis.
7. Actual Neutral Axis.
8. Moment of Resistance.
9. Types of Beam Sections.
10. Under-reinforced Sections.
11. Balanced Sections.
12. Over-reinforced Sections.
13. Design of Beams and Slabs.
36. Mechanical Properties of Materials 835 – 843
1. Introduction.
2. Classification of Materials.
3. Elastic Materials.
4. Plastic Materials.
5. Ductile Materials.
6. Brittle Materials.
7. Classification of Tests.
8. Actual Tests for the Mechanical properties of Materials.
9. Tensile Test of a Mild Steel Specimen.
10. Working Stress.
11. Factor of Safety.
12. Barba′s Law and Unwin′s Formula.
13. Compression Test.
14. Impact Test.
15. Fatigue Test.
Appendix 845 – 852
Index 853 – 862
List of Symbols
A = Area of cross-section
a = Rankine’s constant
B, b = Width
C = Shear modulus of rigidity
(N/mm2)
D, d = Depth
= Diameter
E = Young’s modulus of elasticity
(N/mm2)
e = Linear strain
= Eccentricity
G = Centre of Gravity
= Centroid of area or lamina
g = Acceleration due to gravity
(9.81 m/s2)
H, h = Height (m)
I = Moment of inertia (mm4)
J = Polar moment of inertia (mm4)
K = Bulk modulus of elasticity
(N/mm2)
k = Radius of Gyration
k = Stiffness of Spring (N/mm)
L, l = Length (m)
M, m = Mass (kg)
M = Bending moment (N-m)
N = Speed (r.p.m.)
n = Number
P = Force (N)
p = Pressure (N/mm2)
R, r = Radius
T,
t = Time (s)
T = Torque (N-m)
= Twisting Moment
U = Strain Energy
V = Volume (m3)
W = Load or Weight (N)
w = Load per unit length (N/m)
w = Specific weight (kN/m3)
x, y, z = Cartesian co-ordinates
y = Distance
= Deflection
Z = Section modulus
r, θ = Polar co-ordinates
α = Co-efficient of linear expansion
(/ °C)
α, θ, β = Angle (rad)
μ = Poisson’s ratio or
⎛ ⎞ 1
⎜ ⎟ ⎝ ⎠ m
η = Efficiency
ε = Strain
ρ = Density (kg/m3)
φ = Shear strain
i = Slope
δ = Deflection
Δ = Deflection
δl = Change in length
ω = Angular velocity (rad/s)
µ = Co-efficient of friction
σ = Normal stress (N/mm2)
τ = Shear stress (N/mm2)
σ
c = Circumferential (or hoop) stress
σ
l = Longitudinal stress
σ
r
= Radical stress
σ
t = Tangential stress
= Tearing stress
σ
b = Bending stress
= Bearing stress
σ
1, σ2, σ3 = Principal streses
Le
k = Slenderness ratio
A
Active earth pressure, 449
Actual neutral axis, 823
Actual tests for the mechanical properties
of materials, 836
Advantages of fixed beams, 571
– R.C.C. structures, 822
– welded joints, 723
Algebra (Useful data), 5
Analytical method for the determination
of stresses in oblique section, 109
– finding out the forces, 210
Application of Clapeyron’s theorem of
three moments, 601
– moment distribution method to
various types of continuous
beams, 630
Area amd position of the centre of gravity
of parabolas, 510
Assumption for shear stress in a circular
shaft subjected to torsion, 653
– in Euler’s column theory, 796
– in theory of R.C.C., 822
– in theory of simple bending,
345
– Assumptions for the stresses in
the bending of curved bars, 774
Axis of reference, 165
B
Balanced section, 828
Barba’s law and Unwin’s formula, 839
Bars of uniformly tapering section
Bars with
– a small initial curvature, 774
– a large initial curvature, 776
Beams of composite sections, 486, 375
– of uniform strength, 372
– of unsymmetrical sections, 365
Beams
– with end span overhanging, 637
INDEX**

**
**

854 Strength of Materials

– with fixed end supports, 631

– with simply supported ends, 634

– with sinking support, 645

Beams of unsymmetrical sections, 365

Beams subjected to impact loading, 334

– moment, 329

Bending moment, 287

B.M. diagrams for continuous beams, 598

– for fixed beams, 571

Bending springs, 680

Bending stress, 345

– Distribution of, 349

– in symmetrical section, 356

Brittle materials, 836

Bulk modulus, 101

Butt joint, 696

C

Cantilever beam

– with gradually varying load, 524,

530, 499, 292

– with a point load at any point,

521

– with a point load at free end,

520, 528, 288

– with several loads, 502

– with uniformly distributed load,

523, 529, 494, 290,

Cantilevers of composite section, 505

Cantilever loaded from the free end, 498

Cantilever partially loaded with a u.d.l,

497

Cantilever truss, 223, 266

Carriage springs, 680

Carry over factor, 625

– for a beam fixed at one end and

simply supported at the other,

625

– for a beam simply supported at

both ends, 626

Castigliano’s Theorem

Centre of gravity, 168

– by geometrical considerations,

163

– by method of moments, 165

– of plane figures, 165

– of sections with cut out holes,

175

– of solid bodies, 171

– of symmetrical sections, 166

– of unsymmetrical sections, 168

Centroid, 163

Chain links, 792

Chain riveted joint, 698

Index 855

Change in dimensions of a thin

cylinderical shell subjected to internal

pressure, 746

– of diameter and volume of a thin

spherical shell subjected to an

internal pressure, 750

– of volume of a thin cylindrical

shell subjected to an internal

pressure, 747

Circumferential stress, 743

Clapeyron’s theorem of three moments,

599

Classification of Materials, 835

– Tests, 836

– Application of, 601

Closely coiled helical springs, 686

Column with eccentric loading, 406

– Symmetrical, 406

– Unsymmetrical, 414

Columns with both ends hinged, 797

– one end fixed and the other free,

798

– one fixed and the other hinged,

801

Composite shaft, 670

Composition of forces, 10

Compressive stress, 14, 210

Compression test, 840

Conditions for the stability of a dam, 438,

439, 440

– retaining wall, 449

– conjugate beam, 527

Conjugate beam method, 527

Continuous beam

– subjected to a couple, 621

– with fixed end supports, 605

– with end span over hanging, 611

– with simply supported ends, 601

– with sinking support, 615

Construction of space diagram, 254

– vector diagram, 254

Cotter joint, 717

Coulomb’s wedge theory for active earth

pressure, 456

Crane hooks, 787

Critical neutral axis, 822

Crushing of rivets, 669

Curvature of bending beam, 464

D

Deficient frame, 209

Deformation of a body due to force acting

on it, 15

– self weight, 18

Derived units, 2

Design of beams and slabs, 831

– bolts, 674

856 Strength of Materials

– cylindrical shell, 746

– keys, 675

– riveted joint, 701

Diamond riveted joint, 698

Differential calculus (Useful data), 8

Difference of radii for shrinkage, 763

Disadvantages of welded joints, 723

Distribution factor, 628

Distribution of bending stress, 349

Distribution of shear stress

– over a circular section, 389

– over an I-section, 392

– over miscellaneous section, 397

– over a rectangular section, 385

– over T-section, 396

– over Triangular section, 387

Double integration method for slope and

deflection, 466

Double cover butt joint, 696

– riveted joint, 697

Ductile materials, 836

E

Earth pressure on a retaining wall, 449

Eccentric loading, 406

– riveted connections, 712

– welded joints, 733

Efficiency of riveted joint, 701

Elasticity, 13

– Modulus of, 15

Elastic limit, 14

Elastic materials, 836

Empirical formulae for columns, 808

Equivalent length of a column, 802

Euler’s column theory, 796

F

Factor of safety, 838

Failure of column or strut, 796

– plates, 700

– rivets, 699

– riveted joint, 698

– thin cylindrical shell, 743

Fatigue test, 842

Fillet weld joint, 724

Fixed beams

– Advantages of, 571

– B.M. diagrams for, 571

Fixing moments of a fixed beam, 572

– carrying a central point load,

Index 857

– carrying an eccentric point load,

576

– carrying a gradually varying

load, 589

– carrying a uniformly distributed

load, 582

– due to sinking support, 593

Force, 10

– table, 211, 255

Forms of springs, 680

Frames with both ends fixed, 281

Fundamental units, 2

G

Graphical method of finding out forces

in perfect frames, 253

– for finding out the stresses on

oblique section, 129

H

Helical springs, 686

Hooke’s law, 14

I

Impact test, 841

Imperfect frame, 209

Indian Standard Code of column, 814

Integral calculus (Useful data), 8

J

Johnson’s formula for columns, 813

– parabolic, 814

– straight line, 813

K

Kilogram, 3

Knuckle joint, 715

L

Lame’s theory, 755

Lap joint., 696

Limit of eccentricity, 418

Limitations of Euler’s formula, 803

Link radius for standard sections, 781

Load and B.M. diagrams from S.F.

diagram, 322

Long columns subjected to eccentric

loading, 816

Longitudinal stress, 744

M

Macaulay’s method, 479

Magnitude of forces, 255

Maximum height of a dam, 448

858 Strength of Materials

Maxwell’s Theorem,

Methods for finding out the centre of

gravity, 185

– moment of inertia, 185

– slope and deflection at a section, 466, 490

– stresses on oblique sections,109

Method of joints, 210

– sections, 211

– substitution, 282

Metre, 2

Minimum base width of a dam, 443

Modulus of elasticity, 15

– section, 350

Mohr’s circle for stresses on oblique

sections

– theorems, 130, 131, 139, 134,

509

Moment area method, 509

Moment distribution method, 624

Moment of inertia

– of a built-up section, 202

– of a plain area, 185

– of rectangular section, 186

– of a hollow rectangular section,

187

– of circular section, 188

– of composite sections, 194

– triangular sections, 191

Moment of inertia

– of a built-up section, 202

– of a hollow circular section, 187

– of a semicircular section, 192

Moment of resistance, 349, 750

Multiple riveted joint, 697

N

Nature of forces, 255

Neutral axis, 822

O

Open coiled helical springs, 689

Overhanging beam, 310

Over-reinforced section, 828

P

Parallelogram law of forces,10

Passive earth pressure, 450

Perfect frame, 209

Pitch of rivets, 699

Plastic materials, 836

Plug weld joint, 724

Point of contraflexure, 310

Poisson’s ratio, 92

**Index 859
Polar moment of inertia, 660
Polygon law of forces, 11
Position of neutral axis, 348
Power transmitted by a shaft, 657
Preparation of force table, 255
Presentation of units and their values, 3
Primary strain, 92
Principle of shear stress, 103
– superposition, 20
Proof resilience, 149
Principal plane, 109
– stress, 109
Propped beam, 548
R
Rankine’s formula for columns, 808
– theory for active earth pressure,
450
Reaction of a prop, 549
Rectangular dams, 423
Redundant frame, 209
Relation between actual beam and
conjugate beam, 527
– bulk modulus and Young’s
modulus, 101
– loading, shear force and bending moment, 288
– modulus of elasticity and
modulus of rigidity, 104
Replacing a shaft, 664
Resilience, 149
– Proof, 149
Resultant force, 10
Retaining walls, 449
Rings, 788
Riveted cylindrical shells, 751
S
Scalar quantities, 9
Second, 3
Secondary strain, 92
Shaft couplings, 674
– of varying sections, 667
Shear centre,
Shear force, 287
– and bending moment diagrams,
288
Shearing of the rivet, 669
Shear modulus, 104
Shear stress, 103
– at a section in a loaded beam,
384
– Principle of, 103
S.I. Units, 2
Sign conventions, 287, 796
Simply supported beam
– with a central point load, 510
860 Strength of Materials
– with an eccentric point load,
512, 535, 468
– with a gradually varying load,
524, 540, 477, 306
– with a triangular load, 304
– with uniformly distributed load,
539, 474, 298
Single cover butt joint, 696
– riveted joint, 697
Sinking of the prop, 567
Slenderness ratio, 803
Springs in series and parallel, 692
Stiffness factor, 628
– of spring, 680
Strain, 13
– energy, 156
Strain energy stored in a body when the
load is applied gradually, 149
– when the load is suddenly
applied, 150
– when the load is applied with
impact, 152
– due to shear stress, 160
– due to torsion, 672
Strength of a plate, 701
– rivet, 700
– riveted joint, 701
– shaft, 655
– welded joint, 725
Stress, 13, 209
Stresses in bars of varying sections, 25
– compound thick cylindrical
shells, 759
– composite bars, 41
– uniformly tapering rectangular
sections, 39
– uniformity tapering circular
sections, 35
– section
– nuts and bolts, 67
– thick cylindrical shell, 756
– thin cylindrical shell, 743
Stresses in bars of varying sections
– uniformly tapering rectangular
sections, 39
Stresses-in simple statically indeterminate
structures, 48
– in indeterminate structures
supporting a load, 53
– in composite structures of equal
lengths, 60
Stress on an oblique section of body
subjected to a direct stress
– in one plane, 109
– in two mutually perpendicular
directions, 113
Index 861
Structures with one end hinged or
pinjointed and the other supported
freely on rollers, 273, 277, 232,
237,
Superposition of thermal stresses, 83
Symmetrical columns with eccentric
loading, 406
System of units, 2
T
Tearing of the plate across a row of a
riveted joint, 699
– at an edge, 700
Tensile stress, 14, 209
Tensile test of a mild steel specimen, 835
Theory of active earth pressure, 450
– simple bending, 345
Thermal stresses in simple bars, 73
– bars of tapering section, 74
– bars of varying section, 76
– composite bars, 79
Thick spherical shells, 768
Thin spherical shells, 749
Torsion springs, 680
Transmission of load through rods, 715
Trapezoidal dams with water face
– vertical, 427
– inclined, 435
Triangle law of forces, 11
Trigonometry (Useful data), 5
Types of composite beams, 364
Types of curved bars on the basis of initial
curvature, 774
Types of sections, 827
– end conditions of columns, 797
– frames, 209
– loading, 287, 149
– neutral axis, 822
– riveted joints, 695
– rod joints, 715
– springs, 680
– sections, 828
– statically indeterminate structures, 48
– stresses, 13
– welded joints, 723
U
Under-reinforced sections, 827
Units, System of
Units of moment of inertia, 185
Unsymmetrical columns with eccentric
loading, 414
– section subjected to an axial
load, 730
Unsymmetrical bending
V
Value of
– link radius for a rectangular
section, 781
862 Strength of Materials
– link radius for a triangular
section, 782
– link radius for a trapezium
section, 783
– link radius for a circular section,
784
Vector quantities, 9
Volumetric strain, 94
– of a rectangular body subjected
to an axial force, 94
– of a rectangular body subjected
to three mutually perpendicular
forces, 97
W
Wire bound thin cylindrical shells, 752
Working stress, 838
Y
Young’s modulus, 15
Z
Zig-zag riveted joints, 698
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