UPTU B. Tech. (SEM. VIII) EXAMINATION, 2006-07 THEORY OF ELASTICITY & PLASTICITY

Time : 3 Hours

Total Marks : 100

Note : Attempt all questions. All questions carry equal marks. Assume missing data, if any, suitably.

1. Attempt any two parts of the following : 10×2=20

(a) Explain about plane stress and plane strain problems. Give two examples also.

(b) Derive the compatibility equation in terms of stress for a plane stress problem. Is this equation valid for plane strain also ?

(c) The general displacement field in a body in certain coordinates is given as:-

u = 0.015 x^{2}y + 0.03

v = 0.005y^{2} + 0.03 xz

w = 0.003 z^{2} + O.OOlyz + 0.005

Find all the strains for the point (1,0,2)

2. Attempt any two parts of the following : 10×2=20

(a) Derive the expression for circumferential stress in a curved beam with large initial armature and subjected to pure binding. State clearly the assumptions and its limitations.

(b) A circular plate with a circular hole is simply supported around its edge and subjected to linearly varying distributed load. Derive the expressions for maximum stress.

(c) A narrow, simply supported beam of rectangular cross-section is subjected to a uniformly distributed load. Determine the stress distribution in the beam.

**3. **Attempt any one part of the following : 20×1=20

(a) Determine the distribution of stress is a circular cylindrical shell having the ends supported by the diagraphs. The shell has been filled with oil of density P such that

P(Q) = 10′ P^{a cos} Q Where a = radius

(b) Derive the expressions for the stress resultants and displacements for the case of a cylindrical shell with a uniform pressure.

**4. **Attempt any one part of the following: 20×1=20

(a) Derive an expression for strain energy per unit volume for a two-dimentional linearly elastic body for plane stress or plane strain in terms of Airy’s stress function.

(b) How do you determine the stress distribution due to cracks? Explain with a suitable example.

**5. **Attempt any one part of the following: 20×1=20

(a) Derive an expression for strain energy per unit volume for a two dimensional linearly elastic body for plane stress or plane strain in terms of Airy’s stress functions.

(b) How do you determine the stress distribution due to cracks? Explain with a suitable example.