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: Basic Differential Relationships.
For a beam: \[\frac{dM}{dx} = V, \frac{dV}{dx} = -w\] Here, $M$ is the bending moment, $V$ is the shear force, and $w$ is the load intensity.

Step 2: Evaluate Statements.
- (1) True: The shear force ($V$) is the first derivative of the bending moment ($M$) with respect to the position ($x$), as $V = dM/dx$.
- (2) False: The shear force is not the derivative of the load intensity. The relationship is $dV/dx = -w$.
- (3) False: The bending moment is the integral of the shear force, not its derivative.
- (4) False: The load intensity is the negative derivative of the shear force ($dV/dx = -w$), not the derivative of the bending moment.

Step 3: Final Determination.
Statement (1) is the only correct assertion.