The moment curve for a simple beam with a concentrated load at the middle span takes the shape of a ______:

The moment curve for a simple beam with a concentrated load at the middle span indeed takes the shape of a triangle. This triangular shape arises because, under such loading conditions, the bending moment is greatest at the center of the beam, where the load is applied. As one moves away from the center towards the supports, the bending moment decreases linearly to zero at the supports.

This linear variation in moment results in a triangular distribution on a moment versus position graph. The peak of the triangle corresponds to the maximum moment at the center, while the endpoints at the supports signify that there is no moment acting there, characteristic of simple supports.

Understanding this behavior is crucial for analyzing and designing beams in practical applications, as the shape of the moment curve influences the selection of materials and sizes for strength and stability in structural design.