Question

Which of the following statements is correct?

• A. Shear force is the first derivative of bending moment
• B. Shear force is the first derivative of intensity of load on the beam
• C. Bending moment is the first derivative of shear force
• D. Intensity of load on the beam is the first derivative of bending moment

Hint:

Key chain rule: $w = -dV/dx$, $V = dM/dx$. Always remember load–shear–moment relationship.

Answer 1

The Correct Option is A

Step 1: Fundamental differential relationships.
For a beam: \[ \frac{dM}{dx} = V, \frac{dV}{dx} = -w \] where $M =$ bending moment, $V =$ shear force, $w =$ load intensity.

Step 2: Analyze options.
- (1) True: $V = dM/dx$, shear is first derivative of bending moment.
- (2) False: Shear is not derivative of load; rather $dV/dx = -w$.
- (3) False: Bending moment is not derivative of shear, but its integral.
- (4) False: Load intensity is derivative of shear, not bending moment.

Step 3: Conclusion.
Correct statement is (1).