For a beam, the term M/EI is:
Try it first: pick an option, then read the explanation.
Correct answer: C. curvature
Asked in SSC JE 2010
Detailed Explanation
The bending equation links the moment, the stiffness of the section and the shape the beam takes.
\[ \frac{M}{I} = \frac{E}{R} \Rightarrow \frac{1}{R} = \frac{M}{EI} \approx \frac{d^2y}{dx^2} \]
Why “curvature” Is Correct
1/R is the curvature of the bent beam. This is why the M/EI diagram is used in the moment-area and conjugate-beam methods for slope and deflection.
| 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. stress: Stress is My/I, not M/EI.
- B. rigidity: Rigidity is EI itself (flexural rigidity).
- D. shear force: Shear force is dM/dx.
Key Point
Curvature 1/R = M/EI; EI = flexural rigidity.
Key Concepts for Students
- EI d²y/dx² = M is the differential equation of the elastic curve.
- Area of the M/EI diagram between two points = change in slope.
- Larger EI means less curvature.
Practice more: this is question 22 in Bending and Shear Stress MCQs – Part 2. Try the whole set and check every answer instantly.