Explanation:

The shape of BMD (Bending Moment Diagram) is the graphical representation of the variation of bending moment along the length of the beam. The shape of the BMD depends on the type of loading and support conditions. In this case, a simply supported beam of length ‘l’ is subjected to a point load at mid-span.

The BMD can be determined by the method of superposition. The bending moment at any point on the beam is the sum of the bending moments due to the point load and the bending moments due to the reactions at the supports.

The BMD can be divided into three regions- the left-hand side of the mid-span, the mid-span, and the right-hand side of the mid-span.

- BMD on the left-hand side of the mid-span:

The bending moment at any point on the left-hand side of the mid-span is due to the reaction at the left-hand support. Since the beam is simply supported, the left-hand support provides an upward reaction. The BMD on the left-hand side of the mid-span is a downward triangle.

- BMD at the mid-span:

The bending moment at the mid-span is the maximum bending moment due to the point load. The BMD at the mid-span is a positive triangle.

- BMD on the right-hand side of the mid-span:

The bending moment at any point on the right-hand side of the mid-span is due to the reaction at the right-hand support. Since the beam is simply supported, the right-hand support provides an upward reaction. The BMD on the right-hand side of the mid-span is an upward triangle.

Therefore, the shape of the BMD for a simply supported beam of length ‘l’ subjected to a point load at mid-span is a positive triangle. Hence, option 'B' (Triangle) is the correct answer.

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