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, Mohr’s diagram for 3dimensional state of stress.
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. Principle of super position, Saint Venant principle.
Two-Dimensional classical elasticity:
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, stress concentration, stress distribution in an infinite plate with a circular hole subjected to uniaxial and biaxial loads. General equations in polar coordinates, stress distribution symmetrical about an axis, Thick wall cylinder subjected to internal and external pressures.
Stress analysis in Axisymmetric body:
Stresses in rotating discs of uniform thickness and cylinders. Numerical Problems.
Torsion:
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.
Thermal stress:
Thermo elastic stress strain relations, equations of equilibrium, thermal stresses in thin circular discs and in long circular cylinders.
Course Outcomes:
At the end of the course, the student will be able to:
CO1: Understand the Basic field equations of linear elastic solids, force, stress, strain and equilibrium in solids.
CO2: Analyse the 2D structural elements, beams, cylinders.
CO3: Use analytical techniques to predict deformation, internal force and failure of simple solids and structural components.
CO4: Analyse the axisymmetric structural elements.
CO5: Analyse the structural members subjected to torsion
CO6: Determine the thermal stresses in plain stress and plane stain conditions.
Question paper pattern:
Textbook/s
1 Theory of Elasticity S. P. Timoshenko and J. N Gordier Mc-Graw Hill International 3rd edition, 2010
2 Advanced Mechanics of solids L. S. Srinath Tata Mc. Graw Hill 2009
Reference Books
1 Theory of Elasticity Sadhu Singh Khanna Publications 2004
2 Applied Elasticity T.G. Seetharamuand Govindaraju Interline Publishing 2008.