Analysis of Stress:
Definition and notation of stress, equations of equilibrium in differential form, stress components on an arbitrary plane, equality of cross shear, stress invariants, principal stresses,octahedral stress, planes of maximum shear, stress transformation, plane state of stress, Numerical problems
Analysis of Strain:
Displacement field, strains in term of displacement field, infinitesimal strain at a point, engineering shear strains,strain invariants, principal strains, octahedral strains, plane state of strain, compatibility equations, strain transformation, Numerical Problems.
Two-Dimensional classical elasticity Problems:
Cartesian co-ordinates - Relation between plane stress and plane strain, stress functions for plane stress and plane strain state, Airy’s stress functions, Investigation of Airy’s stress function for simple beams, bending of a narrow cantilever beam of rectangular cross section under edge load. Bending of simply supported beam under UDL.General equations in polar coordinates, stress distribution symmetrical about an axis, Thick wall cylinder subjected to internal and external pressures, Numerical Problems.
Axisymmetric and Torsion problems:
Stresses in rotating discs of uniform thickness and cylinders. Torsion of circular, elliptical and triangular bars, Prandtl’s membrane analogy,torsion of thin walled thin tubes, torsion of thin walled multiple cell closed sections. Numerical Problems
Thermal stress and Elastic stability:
Thermo elastic stress strain relations, equations ofequilibrium,thermal stresses in thin circular discs and in long circularcylinders.Euler’s column buckling load: clamped-free, clamped-hinged, clamped-clamped and pin-ended, Numerical Problems
Course outcomes:
1. Describe the state of stress and strain in 2D and 3D elastic members subjected to direct loads and thermal loads.
2. Analyse the structural members: beam, rotating disks, columns. 3. Analyse the torsional rigidity of circular and non-circular sections.
4. Analyse the stability of columns.
TEXT BOOKS:
1. Theory of Elasticity, S. P. Timoshenko and J. N Goodier, Mc. Graw, Hill International, 3rd Ed., 2010.
2. Theory of Elasticity, Dr. Sadhu Singh, Khanna Publications, 2004.
REFERENCE BOOKS
1.Advanced Mechanics of solids, L. S. Srinath, Tata Mc. Graw Hill,2009.
2. Theory of Elastic stability, Stephen P. Timoshenko, Mc Graw Hill, 2nd Ed, 2014.