GATE ME 2014 Set 3 — Question 17
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Strength of Materials → Beams & Columns → Torsion of Shafts
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Question
Two solid circular shafts of radii and are subjected to same torque. The maximum shear stresses developed in the two shafts are and . If , then is _______
Correct answer
7.9 to 8.1
Solution
The maximum shear stress () in a solid circular shaft of radius subjected to a torque is given by the torsion formula:where is the polar moment of inertia of the cross-section. For a solid circular shaft:Substituting into the shear stress equation:From this, we can see that for a constant torque , the maximum shear stress is inversely proportional to the cube of the radius:Given two shafts with radii and and maximum shear stresses and respectively:Given the ratio of radii :Thus, the ratio is 8.
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