Shear Force and Bending Moment MCQ with answer and solution

Concept

Relationship between shear force and load intensity

Formula

dV/dx = -w

Step-by-step solution

1. From equilibrium of a beam element, the differential equation relating shear force V and distributed load intensity w is dV/dx = -w. 2. Mathematically, the first derivative dV/dx represents the slope of the shear force diagram. 3. Hence, the slope of the shear force diagram at any point along the beam equals the load intensity at that point. Answer: D

Explanation

The governing differential relation between shear force and distributed loading states that dV/dx = -w. Therefore, the rate of change or slope of the shear force diagram at any cross section directly represents the intensity of the applied distributed load.

Why the other options are wrong

A) Curvature equals M/(EI), which is proportional to bending moment. B) Deflection is obtained by integrating slope twice. C) Bending moment is obtained from the area under the shear force diagram, not its slope.

Shortcut

Slope of BMD = Shear Force; Slope of SFD = Load Intensity.

Common mistake

Confusing the slope of the shear force diagram (load intensity) with the slope of the bending moment diagram (shear force).