Can Castigliano's Second Theorem Solve a Statically Determined Beam?

[Dell]

i recently learned castiglianos second theorem, and going over the lecture i tried to solve the following beam,

i know that this beam is statically determined and i can use statics to find Ay=ql MA=ql²/2

but i wanted to use castiglianos second theorem, using 2 equations (angle and deflection at A is 0) with my unknowns being Ay and MA and got the wrong answers

the answers i got fit the statically indetermined beam with supports (like at point A) at both ends.


is it impossible to solve this beam (for A and MA) using castiglianos second theorem? or am i making a mistake somewhere?

 

[Valkarie]

It is not impossible to solve this beam using Castigliano's second theorem, however it is not the most efficient way to do so. The best way to solve this beam would be to use statics, which you have already done. Castigliano's second theorem is more useful for beams that are statically indeterminate and require another condition to allow for a solution.