The maximum shear stress produced in a solid circular shaft under torque T is:
Try it first: pick an option, then read the explanation.
Correct answer: B. 16T/(πD³)
Asked in SSC JE 2011
Detailed Explanation
From T/J = τ/R with J = πD⁴/32 and R = D/2.
\[ \tau_{max} = \frac{T R}{J} = \frac{T\,(D/2)}{\pi D^4/32} = \frac{16T}{\pi D^3} \]
Why “16T/(πD³)” Is Correct
The maximum shear stress is 16T/(πD³).
Why the Other Options Are Wrong
- A. 16T/(πD⁴): D⁴ gives wrong units (stress needs force/length²).
- C. 32T/(πD⁴): 32T/πD⁴ is T/J, not τ.
- D. 32T/(πD³): 32/πD³ is the bending-stress constant (32M/πD³).
Key Point
Solid shaft: τmax = 16T/πD³.
Key Concepts for Students
- Hollow shaft: 16TD/π(D⁴ − d⁴).
- Stress ∝ 1/D³.
- Max at the outer surface.
Practice more: this is question 32 in Torsion MCQs – Part 3. Try the whole set and check every answer instantly.