The slope of the shear force diagram at any section equals:
Try it first: pick an option, then read the explanation.
Correct answer: B. the ordinate of the loading diagram at the section
Asked in SSC JE 02/03/2017 (Morning)
Detailed Explanation
Consider a short element dx of a beam carrying load intensity w. Vertical equilibrium of the element gives the relation between the change in shear and the load on it.
\[ dV = w\,dx \;\Rightarrow\; \frac{dV}{dx} = w \]
Why “the ordinate of the loading diagram at the section” Is Correct
The slope of the SFD is the ordinate of the loading diagram (the load intensity) at that section — option (b). The area of the load diagram gives the change in shear, not the slope.
| 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. the slope of the loading at the section: The slope of the load diagram relates to the curvature of the SFD, not its slope.
- C. the area of the loading diagram from the end to that section: The area of the load diagram gives the change in shear between two points.
- D. None of these: Option (b) is correct.
Key Point
dV/dx = w; dM/dx = V.
Key Concepts for Students
- No load ⇒ SFD horizontal.
- UDL ⇒ SFD straight line of slope w.
- Triangular load ⇒ SFD slope changes linearly (parabola).
Practice more: this is question 43 in Bending Moment and Shear Force MCQs – Part 3. Try the whole set and check every answer instantly.