The first theorem of Castigliano’s state that in a beam or truss subjected to any load system, the deflection at any point y is given by the partial differential coefficient of X w.r.t. force P, acting at the point y in the direction in which the deflection is desired, where X is:
1
angular deflection
2
moment of inertia
3
load with respect to position
4
total strain energy
5
Moment of area