The section modulus of a rectangular section is:
Try it first: pick an option, then read the explanation.
Correct answer: C. bd²/6
Asked in SSC JE 2010
Detailed Explanation
For a rectangle of width b and depth d, I = bd³/12 about the centroidal axis parallel to b, and the extreme fibre is d/2 away.
\[ Z = \frac{I}{y_{max}} = \frac{bd^3/12}{d/2} = \frac{bd^2}{6} \]
Why “bd²/6” Is Correct
The section modulus is bd²/6.
| 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. bd²/36: bd²/36 is not a rectangle property (36 belongs to the triangle's I).
- B. bd³/6: bd³/6 has the wrong power of d (units mm⁴).
- D. bd³/12: bd³/12 is the moment of inertia I, not Z.
Key Point
Rectangle: I = bd³/12, Z = bd²/6.
Key Concepts for Students
- Z depends on d², so depth is more effective than width.
- Square: Z = a³/6.
- Plastic modulus of a rectangle = bd²/4 (shape factor 1.5).
Practice more: this is question 38 in Bending and Shear Stress MCQs – Part 3. Try the whole set and check every answer instantly.