**AE1001 THEORY OF ELASTICITY 3 0 0 100**

**OBJECTIVE**

To understand the theoretical concepts of material behaviour with particular emphasis on their elastic property

**1. ASSUMPTIONS IN ELASTICITY 4**

Definitions- notations and sign conventions for stress and strain, Equations of equilibrium.

**2. BASIC EQUATIONS OF ELASTICITY 15**

Strain – displacement relations, Stress – strain relations, Lame’s constant –

cubical dilation, Compressibility of material, bulk modulus, Shear modulus, Compatibility equations for stresses and strains, Principal stresses and principal strains, Mohr’s circle, Saint Venant’s principle.

**3. PLANE STRESS AND PLANE STRAIN PROBLEMS 8**

Airy’s stress function, Bi-harmonic equations, Polynomial solutions, Simple two-dimensional problems in Cartesian coordinates like bending of cantilever and simply supported beams, etc.

**4. POLAR COORDINATES 10**

Equations of equilibrium, Strain displacement relations, Stress – strain relations, Axi – symmetric problems, Kirsch, Michell’s and Boussinesque problems.

**5. TORSION 8**

Navier’s theory, St. Venant’s theory, Prandtl’s theory on torsion, The semi- inverse method and applications to shafts of circular, elliptical, equilateral triangular and rectangular sections.

**TOTAL : 45**

**TEXT BOOK**

1. Timoshenko, S., and Goodier, T.N., “Theory of Elasticity”, McGraw–Hill Ltd., Tokyo, 1990.

**REFERENCES**

Enrico Volterra & J.H. Caines, “Advanced Strength of Materials”, Prentice Hall New Jersey, 1991.

Wng, C.T., “Applied Elasticity”, McGraw–Hill Co., New York, 1993.

Sokolnikoff, I.S., “Mathematical Theory of Elasticity”, McGraw–Hill New York, 1978.

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