Strength of Materials

Preface to the Fourth Edition
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Strength of Materials
Contents
About the Author
1
Simple Stresses and Strains
1.1 Introduction
1.2 Stress-strain curves in tension
1.3 True stress-strain curve
1.4 Poisson’s Ratio
1.6 Elongation produced in a test specimen
1.7 Shear Stress and Shear Strain
1.8 Volumetric strain
1.9 Bulk modulus of elasticity
1.10 Elastic constants and their relationships
1.10.1 Relationship between E and G
1.10.2 Relationship between E and K
1.10.3 Relationship between G and K
1.11 Factor of safety
1.12 Thermal stress and strain
1.12.1 Thermal Stress and Strain in a Simple Bar
1.12.2 Thermal Stress and Strain in a Compound Bar
2
Principal Stresses
2.1 Introduction
2.2 Stresses on an inclined plane (Principal planes and principal stresses)
2.3 Mohr’s circle of plane stress
3
Centroid and Moment of Inertia
3.1 Centre of gravity
3.2 First moment of area and centroid
3.3 Moment of inertia
3.3.1 Mass Moment of Inertia
3.3.2 Radius of Gyration w.r.t. Mass Moment of Inertia
3.3.3 Second Moment of Area
3.3.4 Radius of Gyration w.r.t. Second Moment of Area
3.4 Product of inertia
3.5 Principal axes and principal moments of inertia
3.6 Mohr’s circle for second moments of area
3.7 Parallel-axes theorem
3.8 Moment of inertia of a rectangular section
3.9 Moment of inertia of a solid circular section
3.10 Moment of inertia of a hollow circular section
3.11 Moment of inertia of a semi-circle
3.12 Moment of inertia of a quarter-circle
4
Shear Forces and Bending Moments in Beams
4.1 What is a beam?
4.2 Classification of beams
4.3 Types of loadings
4.4 Calculation of beam reactions
4.5 Shear forces in a beam
4.6 Bending moments in a beam
4.7 Sign conventions for shear force and bending moment
4.8 Shear force and bending moment diagrams (SFD and BMD)
4.9 Point of Contraflexure
4.10 SFD and BMD for cantilever beams
4.10.1 Cantilever Beam carrying a Point Load at its Free End
4.10.2 Cantilever Beam carrying Uniformly Distributed Load (udl) throughout the Span
4.10.3 Cantilever Beam carrying Uniformly Distributed Load over a certain Length from the Free End
4.10.4 Cantilever Beam carrying Uniformly Distributed Load over a certain Length from the Fixed End
4.10.5 Cantilever Beam carrying Uniformly Distributed Load over its Entire Span and a Point Load at its Free End
4.10.6 Cantilever Beam carrying several Point Loads
4.10.7 Cantilever Beam carrying Uniformly Varying Load
4.11 SFD and BMD for simply supported beams
4.11.1 Simply Supported Beam carrying a Central Point Load
4.11.2 Simply Supported Beam carrying an Eccentric Point Load
4.11.3 Simply Supported Beam carrying Uniformly Distributed Load (udl) over its Entire Span
4.11.4 Simply Supported Beam carrying Uniformly Varying Load which varies from Zero at Each End to w per unit length at the Midpoint
4.11.5 Simply Supported Beam carrying Uniformly Varying Load which varies from Zero at One End to w per unit length at Other End
4.11.6 Simply Supported Beam subjected to a Couple
4.12 Relations among load, shear force and bending moment
4.13 SFD and BMD for overhanging beams
4.13.1 Overhanging Beam with equal Overhangs on Each Side and loaded with Point Loads at the Ends
4.13.2 Overhanging Beam with equal Overhangs on Each Side and loaded with a Uniformly Distributed Load over its Entire Span
5
Stresses in Beams
5.1 Pure bending in beams
5.2 Simple bending theory
5.3 Position of the neutral axis
5.4 Section modulus
5.5 Composite beam
5.6 Beams of uniform strength
5.7 Shear stresses in beams
5.8 Shear stress distribution (general case)
5.9 Shear stress distribution in a rectangular cross-section
5.10 Shear stress distribution in a circular cross-section
5.11 Shear stress distribution in an I-section
6
Deflections of Beams
6.1 Introduction
6.2 Differential equation of flexure
6.3 Sign conventions
6.4 Double integration method
6.4.1 Cantilever Beam carrying a Point Load at its Free End
6.4.2 Cantilever Beam carrying udl over its Entire Span
6.4.3 Cantilever Beam subjected to a Pure Couple at its Free End
6.4.4 Cantilever Beam carrying a Point Load anywhere on its Span
6.4.5 Cantilever Beam carrying Gradually Varying Load
6.4.6 Simple Beam carrying a Central Point Load
6.4.7 Simple Beam carrying udl over its Entire Span
6.5 Macaulay’s method
6.6 Moment-area method
6.6.1 Cantilever Beam carrying a Point Load at its Free End
6.6.2 Cantilever Beam carrying a udl over its Entire Span
6.6.3 Simple Beam carrying a Central Point Load
6.6.4 Simple Beam carrying a udl over its Entire Span
6.7 Conjugate beam method
6.7.1 Simple Beam carrying a Point Load at its Centre
6.7. 2 Simple Beam carrying a Point Load not at the Centre
6.8 Method of superposition
7
Torsion of Circular Members
7.1 Introduction
7.2 Torsion equation
7.3 Torsional rigidity
7.4 Polar modulus
7.5 Power transmitted by a shaft
7.6 Effect of stress concentration
7.7 Torsion of a tapered shaft
7.8 Torsion of a thin circular tube
7.9 Strain energy due to torsion
8
Springs
8.1 Introduction
8.2 Spring terminology
8.3 Classification of springs
8.4 Load-deflection curve
8.5 Leaf spring
8.6 Quarter-elliptic leaf spring
8.7 Spiral spring
8.8 Helical spring
8.8.1 Close Coiled Helical Spring subjected to an Axial Load
8.8.2 Close Coiled Helical Spring subjected to an Axial Twist
8.8.3 Open Coiled Helical Spring subjected to an Axial Load
8.8.4 Open Coiled Helical Spring subjected to an Axial Twist
8.9 Combination of springs
8.9.1 Series Combination
8.9.2 Parallel Combination
9
Strain Energy
9.1 Introduction
9.2 Strain energy due to direct loads
9.2.1 Strain Energy due to Gradually Applied Load
9.2.2 Strain Energy due to Suddenly Applied Load
9.2.3 Strain Energy due to Impact or Shock Load
9.3 Strain energy due to shear
9.4 Strain energy due to pure bending
9.5 Strain energy due to principal stresses
9.6 Strain energy due to volumetric strain
9.7 Shear strain energy due to principal stresses
9.8 Castigliano’s theorem
10
Theory of Elastic Failure
10.1 Introduction
10.2 Maximum Normal stress theory
10.3 Maximum Normal strain theory
10.4 Maximum Total strain energy theory
10.5 Maximum shear stress theory
10.6 Maximum Distortion energy theory
11
Buckling of Columns
11.1 Introduction
11.2 Important terminology
11.3 Classification of columns
11.4 Euler’s theory
11.4.1 Euler’s Formula (when Both Ends of the Column are Hinged or Pinned)
11.4.2 Euler’s Formula (when Both Ends of the Column are Fixed)
11.4.3 Euler’s Formula (when One End of the Column is Fixed and Other End Hinged)
11.4.4 Euler’s Formula (when One End of the Column is Fixed and Other End Free)
11.4.5 Crippling Stress
11.5 Empirical formulae
11.5.1 Rankine-Gordon Formula
11.5.2 Johnston’s Parabolic Formula
11.5.3 Straight Line Formula
11.6 IS Code formula (IS: 800-1962)
11.7 Secant formula (for eccentric loading)
12
Pressure Vessels
12.1 Introduction
12.2 Stresses in A thin cylindrical shell
12.3 Volumetric strain for A thin cylindrical shell
12.4 Wire wound thin cylinders
12.5 Stresses in a thin spherical shell
12.6 Volumetric strain for A thin spherical shell
12.7 Cylindrical shell with hemispherical ends
12.8 Stresses in thick cylinders (Lame’s theory)
12.8.1 General Case (when Internal and External Pressures both are acting)
12.8.2 When only Internal Pressure is acting
12.8.3 When only External Pressure is acting
12.8.4 When a Solid Circular Shaft is subjected to External Pressure
12.9 Longitudinal stress
12.10 Strains in thick cylinders
12.11 Compound cylinders
12.11.1 Stress due to Shrinkage
12.11.2 Stresses due to Fluid Pressure
12.11.3 Resultant Stresses
12.11.4 Shrinkage Allowance
12.12 Stresses in A thick spherical shell
13
Plane Trusses
13.1 Introduction
13.2 Types of trusses
13.3 Forces in the truss
13.4 Analysis of Trusses
13.4.1 Analysis of Trusses by Method of Joints
13.4.2 Analysis of Trusses by Method of Sections
13.5 Zero-force members
14
Combined Loadings
14.1 Introduction
14.2 Combined Bending And Axial Loads
14.3 Combined bending and torsion of circular shafts
14.4 Combined Torsion and axial loads
14.5 Combined Bending, Torsion and Direct Thrust
14.6 Other Cases of combined loadings
14.6.1 Eccentric Loading on One Axis (Single Eccentricity)
14.6.2 Eccentric Loading on Two Axes (Double Eccentricity)
14.6.3 Biaxial Bending
14.6.4 Loading on a Chimney
14.6.5 Loading on a Dam
14.6.6 Loading on Retaining Walls
15
Unsymmetrical Bendingand Shear Centre
15.1 Symmetrical bending and simple bending theory
15.2 Unsymmetrical Bending
15.3 Doubly symmetric beaMs with skew or inclined loads
15.4 Pure Bending of Unsymmetrical Beams
15.5 Deflection in Unsymmetrical Bending
15.6 Shear Centre
15.6.1 Shear Centre for a Channel Section
15.6.2 Shear Centre for an Equal-leg Angle Section
16
Fixed Beams
16.1 Introduction
16.2 Shear Force and Bending Moment diagrams
16.3 Fixed Beam carrying a central point load
16.4 Fixed Beam carrying an eccentric point Load
16.5 Fixed Beam carrying Uniformly Distributed Load (UDL) over the Entire span
16.6 Fixed Beam carrying Uniformly Varying Load
16.7 Fixed Beam subjected to a couple
16.8 Sinking of a support
17
Rotating Rings, Discs and Cylinders
17.1 Introduction
17.2 Rotating Ring
17.3 Rotating Thin Disc
17.3.1 Hoop and Radial Stresses in a Rotating Solid Disc
17.3.2 Hoop and Radial Stresses in a Rotating Disc with a Central Hole
17.3.3 Hoop and Radial Stresses in a Rotating Disc with a Pin Hole at the Centre
17.4 Rotating Disc of uniform strength
17.5 Rotating long cylinder
17.5.1 Hoop and Radial Stresses in a Rotating Solid Cylinder or a Solid Shaft
17.5.2 Hoop and Radial Stresses in a Rotating Hollow Cylinder
18
Mechanical Testing of Materials
18.1 Introduction
18.2 Hardness test
18.2.1 Brinell Test
18.2.2 Rockwell Test
18.2.3 Vickers Test
18.3 Fatigue
18.4 Creep
18.5 Tension test
18.6 Compression test
18.7 Stiffness test
18.8 Torsion test
18.9 Bend test
18.10 Impact test
Model Multiple Choice Questions for Competitive Examinations
Appendix A
Appendix B
References
Subject Index