The slope of a bending moment diagram gives:
Try it first: pick an option, then read the explanation.
Correct answer: B. shear force
Asked in SSC JE 23/09/2019 (Evening)
Detailed Explanation
Moment equilibrium of a short beam element of length dx gives dM = V dx.
\[ \frac{dM}{dx} = V \qquad\text{and}\qquad \frac{dV}{dx} = w \]
Why “shear force” Is Correct
The slope of the BMD is the shear force — option (b). Where the BMD is flat (maximum or minimum), the shear is zero.
| 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. compressive force: Axial (compressive) forces are not given by the BMD.
- C. couple: A couple shows up as a jump in the BMD, not its slope.
- D. tensile force: Axial tension is not related to the BMD slope.
Key Point
dM/dx = V; dV/dx = w.
Key Concepts for Students
- BM max where V = 0.
- Area of SFD = change in BM.
- Constant shear ⇒ straight-line BMD.
Practice more: this is question 58 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.