The bending stress in a prismatic beam is given by:
Try it first: pick an option, then read the explanation.
Correct answer: B. My/I
Asked in SSC JE 2011
Detailed Explanation
Rearrange the bending equation M/I = σ/y for the stress at a fibre at distance y from the neutral axis.
\[ \sigma = \frac{M\,y}{I} \qquad (\text{and } \sigma_{max} = M/Z) \]
Why “My/I” Is Correct
The bending stress is My/I: proportional to the moment and to the distance from the neutral axis, inversely proportional to I.
| 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
- A. My/Z: My/Z has the wrong units (N/mm instead of N/mm²); the extreme-fibre stress is M/Z.
- C. MZ/y: MZ/y has units of N·mm³ — not a stress.
- D. MI/y: MI/y has the wrong units entirely.
Key Point
σ = My/I; σmax = M/Z.
Key Concepts for Students
- Check units: M (N·mm) × y (mm) / I (mm⁴) = N/mm².
- σ is zero at the N.A. (y = 0).
- Sign: compression on the concave side.
Practice more: this is question 36 in Bending and Shear Stress MCQs – Part 3. Try the whole set and check every answer instantly.