The bending equation is written as:
Try it first: pick an option, then read the explanation.
Correct answer: A. M/I = σb/y = E/R
Asked in SSC JE 2009
Detailed Explanation
The three ratios in the bending equation each have units of N/mm³ — that is a quick way to check which form is right.
\[ \frac{M}{I} = \frac{\sigma_b}{y} = \frac{E}{R} \]
Why “M/I = σb/y = E/R” Is Correct
Only M/I = σb/y = E/R has all three ratios with matching units and the correct physical meaning.
| Term | Meaning | Unit |
|---|---|---|
| M | Bending moment at the section | N·mm |
| I | Moment of inertia of the section about the neutral axis | mm⁴ |
| σ (f) | Bending stress at distance y from the neutral axis | N/mm² |
| y | Distance of the fibre from the neutral axis | mm |
| E | Young's modulus of the material | N/mm² |
| R | Radius of curvature of the neutral surface | mm |
Bending equation: M/I = σ/y = E/R. So σ = My/I, curvature 1/R = M/EI, and σmax = M/Z with Z = I/ymax.
Why the Other Options Are Wrong
- B. I/M = σb/y = E/R: I/M is inverted (units mm³/N).
- C. M/I = σb/y = R/E: R/E is inverted.
- D. M/I = y/σb = E/R: y/σb is inverted.
Key Point
M/I = σ/y = E/R.
Key Concepts for Students
- Each ratio has units N/mm³.
- From it: σ = My/I and 1/R = M/EI.
- Derived from linear strain ε = y/R and σ = Eε.
Practice more: this is question 41 in Bending and Shear Stress MCQs – Part 3. Try the whole set and check every answer instantly.