A rectangular beam of uniform strength, subjected to a bending moment M, has a constant width. The depth varies in proportion to:
Try it first: pick an option, then read the explanation.
Correct answer: C. √M
Asked in SSC JE 03/03/2017 (Evening)
Detailed Explanation
Same principle as before — constant extreme-fibre stress — but now the width is fixed and the depth varies.
\[ d^2 = \frac{6M}{b\,\sigma} \Rightarrow d \propto \sqrt{M} \]
Why “√M” Is Correct
The depth varies as √M. For a cantilever with UDL (M ∝ x²) this makes the depth vary linearly with x.
Why the Other Options Are Wrong
- A. 1/M: Depth must grow, not shrink, as M grows.
- B. M: d ∝ M applies to the width when the depth is constant.
- D. M²: d ∝ M² is far too fast; Z ∝ d² gives d ∝ √M.
Key Point
Constant width ⇒ d ∝ √M.
Key Concepts for Students
- Cantilever + UDL, constant width: d ∝ x (linear taper).
- Cantilever + end point load, constant width: d ∝ √x (parabolic profile).
- Haunched beams follow this idea near supports.
Practice more: this is question 59 in Bending and Shear Stress MCQs – Part 4. Try the whole set and check every answer instantly.