Find Reaction forces using energy methods (curved beam portion)

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SUMMARY

The discussion focuses on determining the reaction forces and moments at the pin joints of a curved beam using energy methods, specifically the strain energy approach. The problem involves distributing an applied force F across two sections: a straight bar and a curved beam, with given parameters for Young's modulus (E), moment of inertia (I), and cross-sectional area (A). Participants emphasize the need to equate the strain energy of both sections to find the distribution of the applied force, highlighting the importance of Castigliano's theorem in this context.

PREREQUISITES
  • Understanding of strain energy methods in structural analysis
  • Familiarity with Castigliano's theorem for calculating deflections
  • Knowledge of beam theory, including properties like E, I, and A
  • Basic principles of statics, particularly regarding pin joints and reaction forces
NEXT STEPS
  • Study the application of Castigliano's theorem in curved beam problems
  • Learn about the distribution of forces in composite beams
  • Explore advanced strain energy methods for complex structures
  • Review examples of reaction force calculations in structural engineering
USEFUL FOR

Structural engineers, civil engineering students, and anyone involved in analyzing curved beams and applying energy methods in mechanics.

chucknorris10
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Homework Statement


I think I am just overthinking this...

So, the problem is as the picture details. It asks for the reaction forces and moments at each of the two ends (pin joints) using (strain) ENERGY METHODS in terms of the applied force F. the labeled lengths are the lengths of the segments and the radius of curvature. E,I,A 'given'

I suppose right off the bat is there a way to divide up F to both sections (right now i have the L bar and the curved beam as the two main sections) simply just be inference or will i have to solve something to find how F is distributed? perhaps i need to set the two halves' strain energy equal to each other there? but even then id need the force value...

please let me know if there's any detail i may have omitted. thanks!

2vlpagn.png



Homework Equations


I have the equations for all possible castigliano/energy method calculations. just ned how to distribute the applied force...


The Attempt at a Solution


http://tinypic.com/r/ie47yx/7
doesnt appear as if the pic loads http://tinypic.com/r/ie47yx/7
 
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If the ends are pinned, then how many reaction components are there that are greater than zero?
 

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