A rectangular bar is subjected to torsion. The maximum shear stress will occur:
Try it first: pick an option, then read the explanation.
Correct answer: C. at the middle of the longer side
Asked in SSC JE 01/03/2017 (Evening); UP RVNL AE 2016
Detailed Explanation
Saint-Venant's analysis (or Prandtl's membrane analogy) shows the stress is largest where the boundary is closest to the centre.
\[ \tau_{max} = \frac{T}{\alpha\, b\, t^2} \quad (b = \text{longer side},\ t = \text{shorter side}) \]
Why “at the middle of the longer side” Is Correct
The maximum shear stress occurs at the middle of the longer side.
Why the Other Options Are Wrong
- A. at the centre: Stress at the centre is zero.
- B. at the corner: Corners are stress-free in torsion.
- D. along the diagonal: The diagonal (toward the corners) has low stress.
Key Point
Rectangle in torsion: τmax at the middle of the longer side; zero at corners.
Key Concepts for Students
- Membrane analogy: steepest membrane slope = highest stress.
- α ≈ 0.208 for a square, 0.333 for very thin strips.
- Rectangular sections warp.
Practice more: this is question 23 in Torsion MCQs – Part 2. Try the whole set and check every answer instantly.