The Bending Moment Diagram for a Cantilever Subjected to a Couple 'M'

Introduction:
When a cantilever beam is subjected to a couple 'M' at the free end, the bending moment varies along the length of the beam. The bending moment diagram represents the distribution of the bending moment at different points along the beam.

Bending Moment Diagram Types:
There are different types of bending moment diagrams that can be observed for a cantilever beam subjected to a couple 'M'. These include:

1. Triangle
2. Rectangle
3. Parabolic
4. Hyperbolic

Explanation of Correct Answer (Option 'B'): Rectangle
The correct answer for a cantilever beam subjected to a couple 'M' at the free end is a rectangle shaped bending moment diagram. This can be explained as follows:

- When a couple 'M' is applied at the free end of a cantilever beam, the bending moment at the fixed end (near the support) is zero.
- As we move towards the free end, the bending moment increases linearly.
- At the free end of the beam, the bending moment is equal to the applied couple 'M'.

Therefore, the bending moment diagram for a cantilever beam subjected to a couple 'M' at the free end will be a rectangle, where the height of the rectangle represents the magnitude of the bending moment 'M' and the width represents the length of the cantilever beam.

Visualization of the Bending Moment Diagram:
The bending moment diagram can be visualized as follows:

- At the fixed end (near the support), the bending moment is zero. This can be represented as a horizontal line at the bottom of the diagram.
- As we move towards the free end, the bending moment increases linearly. This can be represented as a vertical line starting from zero and reaching the magnitude 'M' at the top of the diagram.
- At the free end, the bending moment is equal to the applied couple 'M'. This can be represented as a horizontal line at the top of the diagram.

Overall, the bending moment diagram for a cantilever beam subjected to a couple 'M' at the free end is a rectangle, where the height represents the magnitude 'M' and the width represents the length of the cantilever beam.