Support reactions, castigliano's second.

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SUMMARY

The discussion focuses on determining support reactions for a statically indeterminate structure using Castigliano's Second Theorem. The key equation utilized is delta = dU / dP, where delta represents displacement and U is the strain energy. Participants emphasize the importance of differentiating with respect to displacement rather than force and caution against assuming the right-hand reaction is P/2 due to the encastre support at point A. Proper verification of external equilibrium and initial reactions is crucial before proceeding with integrals.

PREREQUISITES
  • Understanding of Castigliano's Second Theorem
  • Familiarity with strain energy concepts
  • Knowledge of statically indeterminate structures
  • Basic principles of equilibrium in structural analysis
NEXT STEPS
  • Study the application of Castigliano's Theorem in structural mechanics
  • Learn about methods for analyzing statically indeterminate structures
  • Explore strain energy calculations in structural analysis
  • Review external equilibrium conditions in engineering mechanics
USEFUL FOR

Structural engineers, civil engineering students, and anyone involved in analyzing support reactions in complex structures.

kantti
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Homework Statement



Determine the support reactions for the given structure(see attachment) due to flexural deformations using castigliano's second theorem. Axial deformations are considered negilible.

Homework Equations



delta = dU / dP

The Attempt at a Solution



See attachment. I could use some advice on how to continue. Thanks.
 

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in such questions u don't have to differentiate with respect to force...do it with respect to displacement...n then by using relations replace it with the support reactions..
 
It would help if you didn't assume that the Right hand reaction was P/2. It is less than that because the encastre support at A attracts load to it, this being a statically indeterminate structure. Have you obtained all the reactions and checked external equilibrium before starting all those integrals?
 

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