MODULE 1:
Deformation behaviour of elastic solids in equilibrium under the action of a system of forces, method of sections. Stress vectors on Cartesian coordinate planes passing through a point, stress at a point in the form of a matrix. Equality of cross shear, Cauchy’s equation. Displacement, gradient of displacement, Cartesian strain matrix, strain- displacement relations (small-strain only), Simple problems to find strain matrix.Stress tensor and strain tensor for plane stress and plane strain conditions. Principal planes and principal stress,meaning of stress invariants, maximum shear stress. Mohr’s circle for 2D case.
MODULE 2:
Stress-strain diagram, Stress–Strain curves of Ductile and Brittle Materials, Poisson’s ratio. Constitutive equations-generalized Hooke’s law, equations for linear elastic isotropic solids in terms of Young’s Modulus and Poisson’s ratio, Hooke’s law for Plane stress and plane strain conditions Relations between elastic constants E, G, ν and K(derivation not required). Calculation of stress, strain and change in length in axially loaded members with single and composite materials, Effects of thermal loading – thermal stress and thermal strain. Thermal stress on a prismatic bar held between fixed supports.
MODULE 3:
Torsional deformation of circular shafts, assumptions for shafts subjected to torsion within elastic deformation range, derivation of torsion formula Torsional rigidity, Polar moment of inertia, basic design of transmission shafts. Simple problems to estimate the stress in solid and hollow shafts.
Shear force and bending moment diagrams for cantilever and simply supported beams. Differential
equations between load, shear force and bending moment.
Normal and shear stress in beams: Derivation of flexural formula, section modulus, flexural rigidity, numerical problems to evaluate bending stress, economic sections.
Shear stress formula for beams: (Derivation not required), shear stress distribution for a rectangular section.
MODULE 4:
Deflection of beams using Macauley’s method
Elastic strain energy and Complementary strain energy. Elastic strain energy for axial loading,
transverse shear, bending and torsional loads. Expressions for strain energy in terms of load,
geometry and material properties of the body for axial, shearing, bending and torsional loads.
Castigliano’s second theorem, reciprocal relation(Proof not required for Castigliano’s second
theorem, reciprocal relation). Simple problems to find the deflections using Castigliano’s theorem.
MODULE 5:
Fundamentals of bucking and stability, critical load, equilibrium diagram for buckling of an idealized structure. Buckling of columns with pinned ends, Euler’s buckling theory for long columns. Critical stress, slenderness ratio, Rankine’s formula for short columns.
Introduction to Theories of Failure, Rankine’s theory for maximum normal stress, Guest’s theory for maximum shear stress, Saint-Venant’s theory for maximum normal strain, Hencky-von Mises theory for maximum distortion energy, Haigh’s theory for maximum strain energy