F.Y. M.Tech. (Civil Structures) (Semester (CBCS)
Examination, 2018
advanced solid mechanics
Day and Date Thursday, 6-12-2018 Total Marks 70
Time 10.00 a.m. to 2.00 p.m.
Instructions In Section Q. No. 1 is compulsory. Solve any two
from remaining questions.
In Section II, Q. No. 5 is compulsory. Solve any two
from remaining questions.
Use of non-programmable calculator is allowed.
Numbers to right hand indicate full marks.
Use suitable data if necessary and mention it clearly.
SECTION I
1. Obtain Strain compatibility equations for 3D problems in elasticity. 6
Derive differential equations of equilibrium for 2D problems of elasticity in
Rectangular Coordinate System. 5
2. Explain Airy's stress function. 4
Investigate what problem is solved by Airy's stress function,
A x2 B xy C y2
defined on x y d 8
3. Explain state of stress at a point in 2D problems of elasticity. 3
At a point in a body, the strain tensor is given by array,
Determine the principal strains and principal directions. 9
Seat
4. Explain Polar coordinate and Cylindrical coordinate systems. 3
Obtain differential equations of equilibrium for 3-D problems in cylindrical
coordinate system. 9
SECTION II
5. Write notes on 11
Saint Venant's Method.
Prandtl's Membrane Analogy.
6. Explain following terms 12
Strain Hardening.
Von Mises Yield criteria.
Principle of Normality and Plastic Potential.
7. Draw bending stress distribution diagrams for a T section beam in
Elastic, Elasto-plastic and Plastic condition. Show the stresses. 6
State and explain Isotropic hardening. 6
8. Describe Torsion of rectangular tubes and thin tubes. 6
Write a note on stress strain relations in Plastic states of materials. 6