Stress and Strain: Definition of Stress, Strain and Stress-strain relations, Mechanical behaviour of materials, Linear elasticity, Young’s modulus of elasticity and Poisson's ratio, Stress-Strain curves in tension for Mild steel, Cast iron and non-ferrous metals. Bars of uniform cross section, varying cross section and discontinuous/stepped cross section, Extension / Shortening under point (axial) load, body force (selfweight), temperature change, Compound bars, Composite Sections, Numerical examples
Compound Stress: Uniaxial, Biaxial, General 2D stress state, Definition of Plane stress and Plane strain states, Stresses on inclined sections, Principal stresses, Principal planes, Principal axes, Maximum shear stress, Mohr's circle, Numerical examples. Expression for Volumetric strain, Elastic constants, Numerical examples Cylinders: Determination of deformations, strains and stresses in thin cylinders subjected to internal pressure, Numerical examples
Bending Moment and Shear Force diagrams: Types of beams, loads and reactions, Definition of shear force and bending moment, sign conventions, Relationship between shear force, bending moment and rate of loading, Shear force and bending moment diagrams for different beams, Numerical examples involving beams subjected to concentrated loads, uniformly distributed load (UDL), uniformly varying load (UVL) and couple.
Stresses in Beams: Euler-Bernoulli beam theory, Relationship between bending moment, bending stress, and radius of curvature. Transverse Shear stresses, shear stress across rectangular, circular, symmetrical I and T- sections only, Numerical examples. Deflection of Beams : Governing differential equation and its solution, Double integration method for cantilever and simply supported beams for point load, UDL, UVL and Couple, Macaulay's method, Numerical examples
Torsion of shafts with circular cross section: Derivation of governing equation, Torsional rigidity, Torsional strength, Power transmitted by solid and hollow shafts, Numerical examples Elastic stability of Columns: Euler's theory for axially loaded elastic long columns, Derivation of Euler's load for various end conditions, limitations of Euler's theory, Rankine's formula, Numerical examples