Castiglianos second theorem for indeterminate structures

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SUMMARY

The discussion focuses on applying Castigliano's second theorem to solve for reactions and internal forces in a statically indeterminate structure. The specific problem involves a rod BD with axial internal forces, where the relationship AL2=10*I is given. The correct answers derived from the calculations are Cy=0.346P and Q=0.042P. The user emphasizes the need for two equations to resolve the two unknowns due to the structure's indeterminate nature.

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  • Knowledge of statically indeterminate structures
  • Familiarity with axial internal forces in structural analysis
  • Basic principles of moment and energy in mechanics
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Structural engineers, civil engineering students, and professionals involved in analyzing and designing statically indeterminate structures will benefit from this discussion.

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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

002.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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