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# THEORY OF ELASTICITY

Semester : VI

Course Code : 18ME643

CIE Marks : 40                       SEE Marks : 60

Module – 1

Printed Notes

Module – 2

Printed Notes

Module – 3

Printed Notes

Module – 4

Printed Notes

Module – 5

Printed Notes

## THEORY OF ELASTICITY 18ME643

### Module-1

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.

### Module-2

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.

### Module-3

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.

### Module-4

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.

### Module-5

Thermal stress: Thermo elastic stress strain relations, equations of equilibrium, thermal stresses in thin circular discs and in long circular cylinders