Bending moment (M) and torque (T) is applied on a solid circular shaft. If maximum bending stress equals to maximum shear stress developed, then M is equal to
- A0.5 TCorrect
- BT
- C2 T
- D4 T
Solution
Concept
Bending and shear stresses in a solid circular shaft
Formula
σmax = 32M/(πd³); τmax = 16T/(πd³)
Step-by-step solution
1. σmax = 32 M / (π d³). 2. τmax = 16 T / (π d³). 3. Equal stresses: 32 M = 16 T, so M = 0.5 T.
Explanation
For a solid circular shaft the section modulus in bending is πd³/32 while the polar modulus is πd³/16 (twice as large). So the same stress is produced by a bending moment half the torque.
Shortcut
Z = πd³/32 (bending), Zp = πd³/16 (torsion): M = T/2.
Common mistake
Equating M and T directly.
Correct answer: A) 0.5 T