Two beams of equal cross-sectional area are subjected to equal bending moments. If one beam has a square cross-section and the other a circular section:
Try it first: pick an option, then read the explanation.
Correct answer: C. the square section beam will be stronger
Asked in SSC JE 01/03/2017 (Evening)
Detailed Explanation
For the same moment, the beam with the larger section modulus has the lower bending stress and is therefore stronger.
\[ a = 0.886\,d,\qquad \frac{Z_s}{Z_c} = \frac{a^3/6}{\pi d^3/32} = 1.18 \]
Why “the square section beam will be stronger” Is Correct
The square has about 18 % more section modulus for the same area, so the square section beam will be stronger.
| Section | I about centroidal axis | y max | Section modulus Z |
|---|---|---|---|
| Rectangle b × d (axis ∥ b) | bd³/12 | d/2 | bd²/6 |
| Square side a (sides horizontal) | a⁴/12 | a/2 | a³/6 |
| Square side a (diagonal horizontal) | a⁴/12 | a/√2 | a³/(6√2) |
| Solid circle, diameter d | πd⁴/64 | d/2 | πd³/32 |
| Triangle b × h (axis ∥ base) | bh³/36 | 2h/3 | bh²/24 |
| Hollow circle D, d | π(D⁴ − d⁴)/64 | D/2 | π(D⁴ − d⁴)/(32D) |
Why the Other Options Are Wrong
- A. both beams will be equally strong: Their Z values differ, so they are not equally strong.
- B. the circular section beam will be stronger: The circle has the smaller Z for the same area.
- D. the strength will depend on the nature of loading: The moments are equal, so only Z decides — not the type of loading.
Key Point
Same area: square stronger than circle in bending (Z ratio ≈ 1.18).
Key Concepts for Students
- Same as Q97 in a different form.
- Square with diagonal vertical is weaker than square with sides horizontal.
- I-section beats both.
Practice more: this is question 43 in Bending and Shear Stress MCQs – Part 3. Try the whole set and check every answer instantly.