PART Each question carries 9 marks )

q | (3 3 1 3. 2
‏گے‎ [2
4) . Show 0414 = 80] ˆ -30 5००
and hence find the stress field it represents.

-2c2)}is an acceptable stress ftnction

5) . Given the following strain field. Find the condition under which it is a possible strain
field.

(*بر+ ‎=a, + 4, (४२ + y?) +(x‘‏ رع
‎€५= bo + bl(x2+ + +)‏

Ya= % + qxy(x 2 + 4௦2)

2, 57, 72७70
6) Derive Beltrami-Michell's Equations

PART C( Each question carries 12 marks )
7)
a) Derive the Poisson's equation for torsion of prismatic bars of non circular cross
sections.
b) Explain the torsion in thin walled closed tubes.
8) ൧ thick cylinder of inner radius 10 cm and outer radius 15 cm is subjected to an internal

pressure of 12 N/mm7?. Determine the radial and hoop stress in the cylinder at the inner
and outer surfaces.

9) Derive the expression for shear stress for an equilateral triangular cross section