For a simply supported beam, if the area under the shear force diagram between two points is a constant C, the difference between the bending moments at these points is:
Try it first: pick an option, then read the explanation.
Correct answer: B. C
Asked in SSC JE 11/12/2020 (Evening)
Detailed Explanation
The shear force is the rate of change of bending moment along the beam. Integrating that relation between two sections links the change in moment to the area of the SFD.
\[ \frac{dM}{dx} = V \;\Rightarrow\; M_2 - M_1 = \int_{x_1}^{x_2} V\,dx = \text{area of SFD} = C \]
Why “C” Is Correct
The change in bending moment equals the SFD area, so the difference is C — option (b).
| Relation | Meaning on the diagrams |
|---|---|
| dV/dx = w (load intensity) | Slope of the SFD at a section = ordinate of the load diagram there |
| dM/dx = V (shear force) | Slope of the BMD at a section = ordinate of the SFD there |
| V₂ − V₁ = area of load diagram between 1 and 2 | Change in shear = load between the sections |
| M₂ − M₁ = area of SFD between 1 and 2 | Change in bending moment = area of the SFD |
| V = 0 (or changes sign) | Bending moment is maximum or minimum there |
Why the Other Options Are Wrong
- A. C²: Squaring the area has no physical meaning here.
- C. C²/2: C²/2 confuses the relation with an integral of a linear function.
- D. 2C: There is no factor of 2 in the relation.
Key Point
M₂ − M₁ = area of SFD between the sections.
Key Concepts for Students
- Similarly, V₂ − V₁ = area of the load diagram.
- Where the SFD area from a support adds up to the largest value, the BM is maximum.
- Areas below the axis (negative shear) reduce the moment.
Practice more: this is question 25 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.