Castigliano's Theorem: Problem Solving

The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a p...

Consider a simply supported beam PQ of length L, carrying a point load F at the center. What will be the deflection at the center of the beam?

Here, the reactions at both ends of the beam are equal, and each is half of the central load.

Consider the segment PC and choose any point at a distance x from the end P. At this point, the ...