Which of the following statements is correct?
Show Hint
- Shear force is the first derivative of bending moment
- Shear force is the first derivative of intensity of load on the beam
- Bending moment is the first derivative of shear force
- Intensity of load on the beam is the first derivative of bending moment
The Correct Option is A
Solution and Explanation
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).
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