Question

A shaft was initially subjected to bending moment and then subjected to torsion. If the magnitude of bending moment is same as that of torque, the ratio of maximum bending stress to shear stress would be:

• A. 0.50
• B. 0.25
• C. 2.0
• D. 4.0

Hint:

Memorize: \(\sigma_b : \tau = 2:1\) when \(M = T\) for circular shafts.

Answer 1

The Correct Option is C

Concept: For a circular shaft subjected to bending and torsion, the stress relations are: \[ \sigma_b = \frac{32M}{\pi d^3}, \quad \tau = \frac{16T}{\pi d^3} \] These formulas are derived from fundamental bending and torsion theory.

Step 1: Understand given condition.
We are given: \[ M = T \]

Step 2: Write ratio of stresses.
\[ \frac{\sigma_b}{\tau} = \frac{\frac{32M}{\pi d^3}}{\frac{16T}{\pi d^3}} \]

Step 3: Simplify expression carefully.
Cancel \(\pi d^3\): \[ \frac{\sigma_b}{\tau} = \frac{32M}{16T} \] Substitute \(M = T\): \[ \frac{\sigma_b}{\tau} = \frac{32}{16} = 2 \]

Step 4: Interpretation.
This shows that for equal bending moment and torque, bending stress is twice the shear stress. Final Answer: \[ \boxed{2.0} \]