Question

Shape of the "shear force diagram" for a simply supported beam subjected to pure moment $M$ at the center of span, will be:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Remember: A pure moment does not produce shear—SFD is zero everywhere; only bending moment diagram shows a jump.

Answer 1

The Correct Option is C

Step 1: Recall relation between load, shear, and moment.
\[ \frac{dV}{dx} = -w, \frac{dM}{dx} = V \] where $w =$ load intensity, $V =$ shear force, $M =$ bending moment.

Step 2: Apply to given condition.
- A pure couple $M$ is applied at the center.
- Since no distributed load $w=0$, shear force $V$ must be constant across spans except at the location of applied couple.
- For a couple, there is no net vertical force $\Rightarrow$ shear force is zero everywhere.

Step 3: Shape of SFD.
Thus, the shear force diagram is a straight line along zero axis.

Step 4: Conclusion.
The correct SFD shape is option (3).