Discussion
A simply supported beam of span L is subjected to a couple Mo at a distance a from support A. Among the four options (Option-I to Option-IV) shown, the correct shear force diagram of the beam is
Answer: A
The shear force diagram is Option-I, a constant \(M_{o}/L\) of positive sign.
A couple has no net vertical force, so the support reactions form an equal and opposite pair. Taking moments about B for the counter-clockwise couple gives \(R_{A} = M_{o}/L\) upward and \(R_{B} = M_{o}/L\) downward. These are the only vertical forces, and a concentrated couple changes the bending moment, not the shear force, so the shear is \(M_{o}/L\) along the whole span. With the sign convention shown (upward force on the left face positive) it is positive.
Option II shows a jump in shear at the couple, which only a concentrated force can cause. Options III and IV show sloping shear, which needs a distributed load, and none acts on the beam. The jump at the couple belongs in the bending moment diagram instead.
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