A shaft was initially subjected to a bending moment and then was subjected to torsion. If the magnitude of a bending moment is found to be the same as that of the torque, then the ratio of maximum bending stress to shear stress would be
- A0.25
- B0.50
- C2.00Correct
- D4.00
Solution
Concept
Ratio of bending stress to shear stress
Formula
σ = 32M/(πd³); τ = 16T/(πd³)
Step-by-step solution
1. With M = T, σ / τ = (32 M) / (16 T) = 2.
Explanation
For a solid circular section, the bending stress is twice the shear stress caused by an equal numerical moment and torque.
Shortcut
σ/τ = 2M/T for solid circular shaft.
Common mistake
Taking the ratio as 1 because M = T.
Correct answer: C) 2.00