Final answer:
The bending moment at a fixed support in static equilibrium is zero because the fixed support must provide a moment that counters the applied forces and maintains the system in a state of balance.
Step-by-step explanation:
The bending moment at a fixed support is typically equal to zero. When a structure, such as a beam, is supported at a point and is subjected to various forces and moments, the fixed support must supply enough moment to keep the beam from rotating. In problems dealing with static equilibrium, like the ones described in your exercises, the sum of all torques around the point of support must be zero for the system to remain stationary. For example, if a beam is subject to a force at one end, the fixed support at the other end must provide an equal and opposite moment to maintain equilibrium.
In the scenario where a structure is supported at a point P, the magnitude of force F and the force applied at P can be found by setting the sum of the torques around point P equal to zero, using the lever arm distances and the applied forces. A key point in solving these types of problems is that the lever arm distance to the point of the support force (Fp) is zero, thus the torque is zero at that point.