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A cantilever of rectangular cross section of breadth 4cm and depth 6cm is (10) subjected
to an inclined load W at free end as shown in figure. The length of cantilever is 2.5m
and the angle of inclination of the load with vertical is 25°. What is the maximum value
of W if the maximum stress due to bending is not to exceed 20014 സ്വന്‌.

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a) A thick walled tube with an internal radius of 12cm is subjected to an internal (6)
pressure of 200MPa. (E=2.1x10°MPa) and 0 0.3). Determine the optimum value of
the external radius if the maximum shear stress developed is limited to 350MPa.
Determine the change in internal radius due to the applied pressure. (4)
PARTC
Answer any four questions. Each question carries 10 marks.

a) Obtain the general expression for strain energy in terms of components of stress. (5)
b) Explain the Maxwell reciprocal theorem. (5)

The cantilever beam supports a uniformly distributed load w and a concentrated (10)
load P as shown in figure. Also it is given that L=2m, w=4kN/m, P=6kN and
EI=5MN.m’. Determine the deflection at the free end using Castigliano’s theorem.

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A rod with rectangular cross section is used to transmit torque to a machine (10) frame
(see figure). It has a width of 40mm. The first 3.0m length of rod has a depth of 60mm
and the remaining 1.5 m length has a depth of 30mm. The rod is made of steel having
G=77.5 GPa. Given Ti=750Nm and T2=400Nm, determine the maximum shear stress in
the rod. Also determine the angle of twist of the free end.

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