Question

The bending moment diagram for a cantilever beam subjected to a couple at the free end would be a

• A. Triangle
• B. Parabola
• C. Cubic parabola
• D. Rectangle

Hint:

For a cantilever beam: \[ \boxed{ \begin{array}{c|c} \text{Loading} & \text{BMD Shape}\\ \hline \text{End Couple} & \text{Rectangle}\\ \text{Point Load} & \text{Triangle}\\ \text{UDL} & \text{Parabola} \end{array} } \]

Answer 1

The Correct Option is D

Step 1: Recall the effect of an end couple. A pure couple produces a constant bending moment throughout the entire length of the cantilever beam.

Step 2: Draw the bending moment diagram. Since the bending moment remains constant, \[ M=\text{constant}, \] the bending moment diagram is a rectangle. Hence, \[ \boxed{\text{Rectangle}} \] is the correct answer. Therefore, \[ \boxed{(D)} \] is the correct answer.