THEORY OF ELASTICITY AND PLASTICITY

MODEL QUESTIONS

Part A (5 x 2=10)

1) Differentiate between inverse method and semi inverse method (L)2) Compute the radial and circumferential stress components for the Airy’s stress function

(Ap)3) Mention examples for Plane stress and plane strain conditions (R)4) State and explain Axisymmetric problems with example. (R)5) Explain what type of problem is solved by the following polynomial:

(Ap)Part B (8 +16 +16 =40)

6 a) i) State the biharmonic equation for plane strain. (R)ii) Determine the radial stress component at a point (2,30 in polar coordinates from Airy’s stress function where c is constant. (L)iii) Write the polynomial equation for first and second degree functions if (L)iv)What is meant by Airy’s stress equations? (L)

(Or)6 b) Prove that for the Airy’s stress function which is independent of r (L)7 a) Derive the stress distribution for an infinite plate with a central hole subjected to tension. (L)

(Or)7 b) Derive the deflection for a cantilever beam subjected to load P at its free end. Take . (L)

8a) Determine the constants A and C in Lame’s equations given that a cylinder is subjected to internal pressure only and the axial strain is zero. Plot the distribution and derive the general expression for radial displacement. (L)

(Or)

8b) Apply the stress function on a beam of rectangular section of breadth ‘2h’ and depth ‘d’. Determine what kind of problem is solved by this stress function (L)

Part A (5 x 2=10)

1. Prove that the following is an Airy’s stress function and examine the stress distribution.. (L)

2. State the expression for finding stress in polar coordinates (R)3. Write down any two examples for plane stress problems (R)4. A thick cylinder of inner radius 10cmand outer radius 15cm is subjected to internal

pressure of 12MN/Sq.m. Find the radial and hoop stresses at the inner and outer surfaces (L)

5. Show that the following strains and displacements are all compatible in plane stress:. (L)

Part B (8 + 16 + 16 =40)

6. a) i)State the relation between Cartesian coordinates and polar coordinates. (R) ii) State the kirch problem? (R) iii) Mention the equilibrium equations in polar coordinates for plane stress case. (L) iv)What do you understand by Axisymmetric problems? (U)

(Or)

6. b)Show that Airy’s stress function represents stress distribution in a cantilever beam loaded at free end with load P. Find the value of A if where b and h are width and depth respectively of the cantilever. (AP)

7. a) Derive Bi harmonic equation in Polar coordinates (L)

(Or)

7 b) Derive the stress distribution for an infinite plate with central hole subjected to shear field. (L)

8a). Find the stresses in polar coordinates for a hollow cylinder subjected to inner and external pressure (L)

(Or)

8b) Find the stress distribution for an infinite plate with central hole subjected to tensile field. (L)