Torsion of Shafts MCQ with answer and solution

Concept

Relation between bending moment and torque in shafts

Formula

σ = 32M / (π × d³), τ = 16T / (π × d³)

Step-by-step solution

1. Maximum bending stress for a solid circular shaft of diameter d is σ = 32M / (πd³). 2. Maximum shear stress due to torque T is τ = 16T / (πd³). 3. Setting σ = τ gives 32M / (πd³) = 16T / (πd³), which simplifies to 32M = 16T, hence M = T / 2. Answer: B

Explanation

The maximum bending stress in a solid circular shaft is given as 32 M divided by π times d to the power of 3, while the maximum torsional shear stress is 16 T divided by π times d to the power of 3. Equating these two expressions simplifies to 32 M equals 16 T, which gives M equal to T divided by 2. Thus, the applied bending moment must be equal to half of the torque.

Why the other options are wrong

A) If M = T, maximum bending stress would be twice the maximum shear stress. C) If M = 4T, maximum bending stress would be eight times the maximum shear stress. D) If M = 2T, maximum bending stress would be four times the maximum shear stress.

Shortcut

Maximum bending stress (32M/πd³) equals maximum shear stress (16T/πd³) when M = T/2.

Common mistake

Inverting the relationship in the stress formulas and concluding M = 2T instead of M = T/2.