GATE ME 2016 Set 3 — Question 44
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Strength of Materials → Beams & Columns → Torsion of Shafts
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Question
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, is the twist and is the maximum shear stress in the solid shaft, whereas is the twist and is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?
Correct answer
(D) θ_S = θ_H and τ_S < τ_H
Solution
For a shaft under torsion, the relationship is given by .
For a hollow shaft: .
Given , we have , which implies .
Since the maximum shear stress occurs at the outer radius, and . Because , it follows that .
1.Twist (): . Since the torque (), length (), shear modulus (), and polar moment of inertia () are the same for both shafts, their twists are equal: .
2.Maximum Shear Stress (): . Since and are the same, .
For a solid shaft: .For a hollow shaft: .
Given , we have , which implies .
Since the maximum shear stress occurs at the outer radius, and . Because , it follows that .
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