Strength of Materials

Simple Stresses and Strain:

Introduction,

Definition and concept of stress and strain.

Hooke’s law,

Stress-Strain diagrams for ferrous and non-ferrous materials,

factor of safety,

Elongation of tapering bars of circular and rectangular cross sections,

Elongation due to selfweight.

Saint Venant’s principle,

Compound bars,

Temperature stresses,

Compound section subjected to temperature stresses,

state of simple shear,

Elastic constants and their relationship.
Problems on volumetric stress and elastic constants.

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.

Shear Force and Bending Moment in Beams:

Introduction to types of beams,

Supports and loading.

Definition of bending moment , shear force and Sign conventions

Relationship between load intensity

Numerical on SFD and BMD on Cantilever Beams
Numerical on SFD and BMD on Simply Supported Beams
Numerical on SFD and BMD on Over hanging Beams

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.

Shear centre(only concept)

Columns and Struts:

Introduction 

Euler’s theory 

Euler’s theory Assumptions
Limitations of Euler's theory 

Derivation for Euler’s Buckling load for different end conditions,

Limitations of Euler’s theory.

Rankine-Gordon’s formula for columns.

Difference between Columns and Struts

Difference between Long Columns and Short Columns

Questions and Numerical problems on Columns and Struts

Numerical Problems on Rankine’s formula.

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,

Combined bending and torsion.

Theories of Failure: 

Introduction

Maximum principal stress theory (Rankine’s theory),

Maximum shearing stress theory (Tresca’s theory),

Strain energy theory (Beltrami and Haigh),

Maximum strain theory (St. Venant’s theory).