Explanation:
In this scenario, a static load is mounted at the center of a shaft that is rotating at a uniform angular velocity. The question asks for the design consideration of the shaft based on different factors.

a) Maximum Compressive Stress (Static):
When a static load is applied to the center of the shaft, the maximum compressive stress occurs at the surface of the shaft directly under the load. This is because the load is trying to compress the material at that point. However, since the shaft is rotating at a uniform angular velocity, the load is continuously changing its position. As a result, the compressive stress will vary throughout the shaft, and it is not a critical factor for its design.

b) Maximum Tensile Stress (Static):
Similar to the maximum compressive stress, the maximum tensile stress occurs at the surface of the shaft opposite to the load. This is because the load is trying to pull the material apart at that point. However, since the shaft is rotating, the load is continuously changing its position. Therefore, the tensile stress will also vary throughout the shaft and is not a critical factor for its design.

c) Maximum Bending Moment (Static):
The maximum bending moment occurs at the point where the load is applied. In this case, since the load is mounted at the center of the shaft, the maximum bending moment will occur at the center. However, since the shaft is rotating at a uniform angular velocity, the bending moment will also vary throughout the shaft. Therefore, the maximum bending moment is not a critical factor for the design of the shaft.

d) Fatigue Loading:
Fatigue loading refers to the repeated application of loads over time. When a shaft is subjected to fatigue loading, it experiences cyclic stress that can lead to fatigue failure. Since the load is static and mounted at the center of the shaft, there is no cyclic stress or fatigue loading. Therefore, the design of the shaft does not need to consider fatigue loading in this scenario.

Therefore, the correct answer is option 'D' - Fatigue Loading. The design of the shaft needs to consider other factors such as static strength, torsional stiffness, and material selection to ensure its safe and reliable operation.