Explanation:

Strain energy is defined as the energy stored within an elastic material due to deformation. The strain energy stored in a beam is given by the equation U = (1/2)∫Mθ dx, where M is the bending moment and θ is the angle of rotation at a point on the beam. The integral is taken over the entire length of the beam.

The strain energy in a beam depends on various factors such as the type of loading, the support conditions, the material properties, and the geometry of the beam. In this case, we are given that the beam carries a uniformly distributed load throughout its length. Let us examine the four different support conditions and determine which one will result in the maximum strain energy.

A) Cantilever Beam:

- A cantilever beam is a beam that is fixed at one end and free at the other end.
- The maximum bending moment occurs at the fixed end of the beam, where the load is applied.
- The angle of rotation at the fixed end is also maximum.
- Therefore, the strain energy in a cantilever beam will be maximum.

B) Simply Supported Beam:

- A simply supported beam is a beam that is supported at two ends and free to rotate at both ends.
- The bending moment is maximum at the center of the beam.
- The angle of rotation is also maximum at the center of the beam.
- Therefore, the strain energy in a simply supported beam will not be maximum.

C) Propped Cantilever Beam:

- A propped cantilever beam is a beam that is fixed at one end and supported by a prop at some distance from the fixed end.
- The bending moment and the angle of rotation will be maximum at the fixed end of the beam, where the load is applied.
- Therefore, the strain energy in a propped cantilever beam will not be maximum.

D) Fixed Beam:

- A fixed beam is a beam that is fixed at both ends and cannot rotate.
- The bending moment is maximum at the center of the beam.
- The angle of rotation is zero at both ends of the beam.
- Therefore, the strain energy in a fixed beam will not be maximum.

Conclusion:

Based on the above analysis, we can conclude that the strain energy will be maximum in a cantilever beam.