Castigaliano's Theorem for cantilever beam

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SUMMARY

This discussion focuses on deriving the deflection of a cantilever beam using Castigliano's Theorem. The user seeks clarification on the origin of the term b^3 in the final expression of the solution provided. The conversation emphasizes the importance of understanding the symbols and relevant equations involved in the derivation process, suggesting that a detailed breakdown of the integral is necessary for full comprehension.

PREREQUISITES
  • Understanding of Castigliano's Theorem
  • Familiarity with cantilever beam mechanics
  • Knowledge of integral calculus
  • Ability to interpret engineering symbols and equations
NEXT STEPS
  • Study the derivation of deflection formulas for cantilever beams
  • Learn about the application of Castigliano's Theorem in structural analysis
  • Review integral calculus techniques relevant to beam deflection
  • Examine examples of deflection calculations in engineering literature
USEFUL FOR

Engineering students, structural engineers, and anyone involved in mechanical design or analysis of cantilever beams will benefit from this discussion.

hatchelhoff
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Hi I am trying to derive an expression for the deflection in a cantilever beam using castigliano's theorem.
I have found and attached an example of the solution. I understand the most of what is going on in the attached solution but I don't understand where the b^3 came from in the last line.
castigliano for beam deflection.PNG
 

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  • castigliano for beam deflection.PNG
    castigliano for beam deflection.PNG
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Hi. Post in homework, use the full template to explain the symbols and relevant equations and show us what you get from the integral !
 
I will do that cheers
 

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