Rigid/plastic, rigid/elastic, elastic/plastic material behaviour. Tensile testing. Relationships between nominal/true stress/strain. Power law plasticity behaviour. Experimental determination of work hardening and strength coefficients. Considere’s method. Elastic/plastic work done. Strain energy stored.

Introduction to the theory of elasticity: equations of equilibrium in 3D. The stress tensor. Variation of stress within a body. Two and three dimensional stress at a point. Principal stresses in three dimensions. Matrix rotation method. Matrices solution techniques for magnitudes and direction cosines of principal stresses. Cofactors of determinant method. Stresses on an oblique plane in terms of principal Stresses. Octahedral shearing stress. Mohr’s Circle of 3D stress. Stress-strain relations. Equation of compatibility in 3D. State of strain at a point.

Function of theories. Maximum principal stress/maximum shear stress/maximum principal strain/total and shear strain energy theories of elastic failure. Comparison of the yielding theories. Graphical representations. 3D envelopes of failure. Load-line solutions. Theories of fracture.

Failure criteria for fatigue. Soderberg, Gerber, modified Goodman, SAE criteria. Combined states of stress. Maximum and minimum stress tensor fatigue life evaluation. Composite strength. Impact performance and fatigue strengths of metals and composites.

Simple bending theory for bars of small initial curvature. Non-linear stress evaluation in bars of large initial curvature of rectangular, trapezoidal and circular cross-sections. Comparison with photoelastic determination of curved bar stresses. Application of Castigliano’s Theorem to the solution of elastic deflections and statically indeterminate members and structures. Concepts of strain energy due to thrust, shear force and bending moment. Evaluation of shear force correction factors. Use of dummy loads. Calculation of deflections/redundant forced in curved bars / comparison with experimentally determined deflections.

Development of Lamé theory. Variation of circumferential, radial and longitudinal stresses in thick-walled cylinders. Principal/maximum shear stress in 3D. Change of dimensions and volume. Comparison of thin/thick vessel theory. Limitations of applicability. Lamé line graphical treatment. Application of boundary condition approach to solution of Lamé constants. Compound cylinders. Shrinkage/interference allowances. Force fit. Hub on solid shaft. Uniform heating of compound cylinders of different materials. Application of failure/fatigue theories to pressurised vessels.

Development of theory for variation of stresses in rotating solid and hollow discs. Determination of location and magnitude of maximum design stresses for thin-walled plane stress rotating structures. Application of plane stress/plane strain transformations to develop theory for variation of stresses in rotating thick cylinders and solid shafts. Rotating disc of uniform strength. Combined rotational and thermal stresses in uniform discs and thick cylinders including linear thermal variation and steady heat flow applications.

Assumptions in plastic theory, plastic bending of beams, elastic design moment, partially plastic moment, fully plastic moment, plastic hinge, shape factor. Symmetrical and unsymmetrical sections. Deflection of partially plastic beams. Residual stresses. Collapse mechanisms, collapse load and load factors. Plastic torsion, elastic design torque, partially plastic torque, fully plastic torque in solid and hollow shafts. Angle of twist of shapes in plastic torsion. Case-hardened shafts. Residual stresses in plastic torsion. Autofrettage of thick cylinders. Tresca criterion. Plastic penetration of pressurised cylinders. Development of theory analysing variation of circumferential, radial and longitudinal stresses in plastic and elastic regions under autofrettage pressure. Residual and working stress distributions. Plastic theory for frames. Theorem of independent mechanisms. Determination of load factor through combination of mechanisms.

Introduction to finite element analysis. Hands on computer laboratory finite element stress/strain/displacement analysis application. Interpretation of results.