Local compliance with Castigliano's theorem

[swahlgren]

According to Castigliano's theorem, the local compliance of an elastic structure, e.g. a cantilever, can be determined by integrating the products of stress intensity factor weight functions over the length of said structure. However, if I do that for a double cantilever beam using simple beam theory it yields an incorrect answer but I get the right one if I change the limits of the integration. Anyone have an explanation to that?

I've attached a hand written note demonstrating the details.

 

[swahlgren]

I just wrote a better looking mathcad sheet!