Determining the forces in a framework

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SUMMARY

The discussion focuses on solving for forces in a statically indeterminate framework. The user encounters difficulties at joint B due to three unknown members and expresses confusion regarding joint J. It is established that the standard equations of statics are insufficient for solving the member forces, necessitating the introduction of additional equations related to member properties, specifically AE. The recommended approach includes utilizing Castigliano's theorems to resolve the unknowns effectively.

PREREQUISITES
  • Understanding of statics and equilibrium in structures
  • Familiarity with joint analysis in frameworks
  • Knowledge of Castigliano's theorems
  • Basic concepts of member properties, specifically axial rigidity (AE)
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  • Research Castigliano's theorems and their applications in structural analysis
  • Study methods for analyzing statically indeterminate structures
  • Explore axial rigidity and its impact on member forces
  • Learn about alternative methods for solving for unknown forces in frameworks
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Civil engineers, structural analysts, and students studying mechanics of materials who are dealing with statically indeterminate frameworks.

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The framework is attached below. I've tried going to each joint and resolving the forces vertically and horizontally. I've got to joint B and I'm stuck, because I have three unknown members there. And its the same if I go to joint J.

what do I do?
 

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I don't see a joint J.

Can you set up 2 equations at 4 joints and solve for 8 unknowns?
 
You are stuck because the frame is statically indeterminate. This means that the equations of statics alone are insufficent to solve for the member forces. If you want to proceed you have to introduce another equation related to the member properties AE. There are a number of different approaches to this, including use of Castigliano's theorems. That is what I suggest you look up.
 

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