18 (a)

(b)

19 (a)

(b)

20 (a)
(b)

0800MET201122001

A structure as shown is loaded by a Force P
vertically downward force ‘P at the free
end’. Find deflection at the free end, in
the direction of the load using
Castigliano’s method. Consider strain
energy due to Bending Moment Alone
(Neglect other effects). Use a=2m, b=4m,
P=30 X 10°N, EI (applicable for both

legs) is 30 X 10°Nm’,

Derive strain energy expressions in terms of the geometry, material property and
load during (i) Bending and (ii) Torsion.

Module 5
Using the expression for Euler’s critical buckling load, formulate an expression
for Rankine’s Crippling load in terms of Rankine’s constant(q)
A column has a square cross-section of 40 mm side. If it has to carry a load of
89,600 N, what should be its limiting length if both ends are assumed to be
pinned. Rankine constant @ = 1/1600, and compressive strength is 560 N/mm’.

OR

Formulate an expression for the yield criterion according 10 von-Mises’ theory
If the principal stresses at a point are: (61, ‏,وہ‎ 63} = {10,0,-4} MPa and if the

yield strength of the material under consideration is 40 MPa, find the factor of
safety in design as per (a) Max. Normal Stress Theory (b) Max. Shear Stress
Theory and (c) Max. Distortion Energy Theory.

मे मर ‏ماد‎

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