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D1019 Pages:

Derive the expression for various stresses developed in thick cylinder subjected
to internal pressure only?

Derive the expression for stress developed in curved beam subjected to bending
moment 9

PART C
Answer any four full questions, each carries 10marks.
State and prove Castiglione’s First and Second theorems

A cantilever beam supports a uniformly distributed load of ‘w’ per unit length
and a concentrated load ‘P’ at the free end in downward direction .Take the
length as “1”. Determine the downward deflection at free end?

A hollow aluminium section having rectangular cross section. The thickness of
the section is 6 mm. Outer sides of the section having width 100 mm and height
56 mm. Find the twisting moment taken by the section and angle of twist?
Modulus of rigidity is given by 28 GPa .The maximum shear stress induced is 35
N/mm’.

Derive the equilibrium equation based on the membrane stress analogy?

Find the maximum shear stress induced in an elliptical shaft having semi major
axis 15 cm and semi minor axis 7.5 cm? Applied torque is 1500 Nm.

State and explain virtual work principle?

State and explain minimum potential energy theorem?

Derive expressions for (i) Angle of twist per unit length, (ii) Torsional rigidity

and (iii) Stresses, for elliptical cross section under torsion, by Prandtl’s method?

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