GATE ME 2016 Set 2 — Question 42
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Strength of Materials → Beams & Columns → Torsion of Shafts
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Question
A rigid horizontal rod of length is fixed to a circular cylinder of radius as shown in the figure. Vertical forces of magnitude are applied at the two ends as shown in the figure. The shear modulus for the cylinder is and the Young’s modulus is .
The vertical deflection at point A is
Correct answer
(D) 4PL³/(π R⁴ G)
Solution
The two vertical forces at the ends of the rod of length create a pure twisting moment (torque) on the cylinder. The torque is . The cylinder has length and radius . The angle of twist at the end of the cylinder is given by , where is the polar moment of inertia. So, . The vertical deflection at point , which is at a distance from the axis of the cylinder, is .
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