Castiglianos second theorem for indeterminate structures

AI Thread Summary
The discussion focuses on applying Castigliano's second theorem to determine the reaction at point C and the internal force Q in a statically indeterminate structure. The rod BD is specified to have only axial internal forces, and the relationship between AL2 and I is given as AL2=10*I. The user has attempted to solve the problem multiple times but has not arrived at the correct answers, which are Cy=0.346P and Q=0.042P. It is emphasized that two equations are necessary to find the two unknowns due to the structure's double statically indeterminate nature. The challenge lies in accurately applying the theorem while considering the negligible energy of normal forces compared to moments.
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in the following question it is known that the rod BD has only axial internal forces, (which i called Q) if AL2=10*I, find the reaction at C and the internal force Q.
Assume that the energy of normal forces is negligible compared to moment where there are both.

question.PNG

instead of using L/4 i defined L/4=a

the correct answers are supposed to be Cy=0.346P and Q=0.042P

these are my calculations

i have tried solving it 4 times now and can't get the correct answer.
001.jpg

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the structure is twice statically indeterminate therefore i need to use 2 equations to find the 2 unknowns
 
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