Simply supported beam—Castigliano's method

[Equations in this post may not look right (or appear at all) in your RSS reader. Go to the original article to see them rendered properly.] Continuing our series on the many ways to get the center deflection of a uniformly loaded beam, we come to another energy-based technique: Castigliano’s method. Castigliano’s second theorem provides a relationship between displacements, forces, and the strain energy in a linearly elastic system. The strain energy, U, is the potential energy of the system due to its deformation. For a generic elastic body, like this, Castigliano’s second theorem can be as: If an elastic system is mounted so that rigid-body displacements of the entire system are impossible and certain external point forces P1, P2, … act on the system, in addition to distributed loads and thermal strains, the displacement component δi of the point of application of force Pi in the direction of force Pi is determined by the equation δi=∂U∂Pi I took this from Henry Langhaar’s Energy…