We all would have read about Castigliano’s theorem and its application in analysis of indeterminate structures.For analysis of indeterminate structure suppose say a propped cantilever beam , now considering the prop reaction as a redundant force suppose we apply Castigliano’s theorem for its determination which states that is “the partial derivative of the total strain energy stored in the structure with respect to the force acting at a certain section gives the displacement at that section”. Now since the displacement at the prop section is zero by equating the displacement to zero we very well get the prop reaction, so far so good.
But the reactions in any structure are not independent forces, right??that is we cannot alter the reactions without causing a change in all other forces so how can we have a derivative with respect to the reaction??
I mean any structure if we take external loads as a set of independent forces all the reactions need to be a set of dependent forces.Right??Are we justified in applying Castigliano’s theorem for determination of redundant reactions???If yes how?Please help