The shape of the bending moment diagram for a uniformly distributed load is parabolic. This can be explained by considering the nature of the load and its effect on the beam.

1. Uniformly distributed load:
- A uniformly distributed load refers to a load that is evenly distributed along the length of the beam. This means that the load per unit length remains constant throughout the beam.
- Examples of uniformly distributed loads include the weight of a beam itself, a continuous line of people standing on a beam, or a distributed load applied by a crane.

2. Bending moment:
- Bending moment is the internal moment that causes a beam to bend. It is a measure of the distribution of loads along the length of the beam.
- The bending moment varies along the length of the beam and is represented by a bending moment diagram.

3. Bending moment diagram:
- The bending moment diagram represents the variation of bending moment along the length of the beam.
- The shape of the bending moment diagram depends on the type of load applied to the beam.
- For a uniformly distributed load, the bending moment diagram takes the shape of a parabola.

4. Explanation:
- When a uniformly distributed load is applied to a beam, the load is evenly distributed along the length of the beam.
- As a result, the bending moment is maximum at the center of the beam and decreases towards the supports.
- This variation in bending moment can be represented by a parabolic curve, where the maximum bending moment occurs at the center and the bending moment decreases symmetrically towards the ends of the beam.
- The shape of the parabolic bending moment diagram is a result of the load distribution and the beam's resistance to bending.

In conclusion, the shape of the bending moment diagram for a uniformly distributed load is parabolic. This shape represents the variation of bending moment along the length of the beam, with the maximum bending moment at the center and decreasing symmetrically towards the ends.