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.
- With no distributed load ($w=0$), shear force $V$ is constant across spans, except at the point of the applied couple.
- A couple implies no net vertical force, therefore the shear force is zero everywhere.

Step 3: Shape of SFD.
Consequently, the shear force diagram (SFD) is a horizontal line along the zero axis.

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