# STRENGTH OF MATERIALS (BCV301)

## STRENGTH OF MATERIALS

### Module-1

Simple Stresses and Strains: Introduction, Properties of Materials, Stress, Strain, Hooke’s law, Poisson’s Ratio, Stress – Strain Diagram for structural steel, Principles of superposition, Total elongation of tapering bars of circular and rectangular cross sections. Composite section, Volumetric strain, expression for volumetric strain, Elastic constants, relationship among elastic constants. Thermal stresses and strains, Compound bars subjected to thermal stresses, state of simple shear. (L1, L2, L3)

### Module-2

Bending moment and shear force diagrams in beams: Introduction to types of beams, supports and loadings. Definition of shear force and bending moment, sign convention, Relationship between loading, shear force and bending moment, Shear force and bending moment equations, development of Shear Force Diagram(SFD) and Bending Moment Diagram (BMD) with salient values for cantilever, simply supported and overhanging beams for point loads, UDL (Uniformly Distributed Load), UVL (Uniformly Varying Load), Couple and their combinations (L1,L2,L3)

### Module-3

Bending and Shear Stresses in Beams: Introduction, pure bending theory, Assumptions, derivation of bending equation, modulus of rupture, section modulus, flexural rigidity. Expression for transverse shear stress in beams, Bending and shear stress distribution diagrams for circular, rectangular, ‘I’, and ‘T’ sections. Torsion in Circular Shaft: Introduction, pure torsion, Assumptions, derivation of torsion equation for circular shafts, torsional rigidity and polar modulus Power transmitted by a shaft. (L1, L2, L3)

### Module-4

Deflection of Beams: Definition of slope, Deflection and curvature, Sign conventions, Derivation of moment- curvature equation. Double integration method and Macaulay’s method: Slope and deflection for standard loading cases and for determinate prismatic beams subjected to point loads, UDL, UVL and couple. Columns and Struts: Introduction, short and long columns. Euler’s theory; Assumptions, Derivation for Euler’s Buckling load for different end conditions, Limitations of Euler’s theory. Rankine-Gordon’s formula for columns. (L1,L2,L3)

### Module-5

Compound Stresses: Introduction, state of stress at a point, General two dimensional stress system, Principal stresses and principal planes. Mohr’s circle of stresses Thin and Thick Cylinders: Introduction, Thin cylinders subjected to internal pressure; Hoop stresses, Longitudinal stress and change in volume. Thick cylinders subjected to both internal and external pressure; Lame’s equation, radial and hoop stress distribution. (L1,L2,L3)

#### Suggested Learning Resources: Text Books

 B.C Punmia Ashok Jain, Arun Jain, “Strength of Materials”, Laxmi - 2018-22 Publications, 10th Edition-2018
 R K Bansal, “A Textbook of Strength of Materials”, 4th Edition, Laxmi Publications, 2010
 S.S. Rattan “Strength of Materials” McGraw Hill Education (India) Pvt. Ltd., 2nd Edition (Sixth reprint 2013).
 Vazirani, V N, Ratwani M M. and S K Duggal "Analysis of Structures Vol. I", 17th Edition, Khanna Publishers, New Delhi.
 R.K. Rajput, “Strength of materials” S. Chand Publishing (6th Edition)
 S S Bhavikatti, “Strength of Materials” Vikas Publishing (5th Edition)
 B.S. Basavarajaiah, P. Mahadevappa “Strength of Materials” in SI Units, University Press (India) Pvt. Ltd., 3rd Edition,2010