Structural Forces and Unknowns: Solving for Reaction Forces in a Complex System

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Discussion Overview

The discussion revolves around solving for unknown reaction forces in a complex structural system using equations of force and moment analysis. Participants explore the application of these equations in the context of a free body diagram (FBD) and the implications of choosing different points or axes for moment calculations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about whether splitting a moment equation into components provides additional independent equations for solving unknowns.
  • Another participant suggests focusing on a reaction point when writing moment equations to simplify calculations, comparing it to solving for reactions in a loaded beam.
  • A different participant recommends taking moments about an axis instead of a point for clarity in calculations.
  • One participant questions the implications of taking moments about the X-axis, seeking clarification on which forces contribute to zero moments.
  • A participant reports an inconsistency in their calculations after taking moments around point B, indicating a potential error in their approach.
  • A later reply indicates that the issue was resolved due to a sign error in the matrix used for determinants.

Areas of Agreement / Disagreement

Participants generally agree on the importance of choosing appropriate points or axes for moment calculations, but there are differing opinions on the best approach to take. The discussion includes unresolved questions about the implications of specific choices in moment analysis.

Contextual Notes

Some assumptions regarding the independence of equations and the effects of forces on moments remain unaddressed, and the discussion does not resolve the implications of taking moments about different points or axes.

member 392791

My problem here seems that I can't figure out how to solve for my unknowns. I have 3 equations for force, and I'm not sure if that equation I have for the moment around the origin counts as 3 new independent equations if I split them up into i, j, and k components. If that is allowed, then I have 6 equations and 6 unknowns, which should be solvable. Otherwise, I only have 4 equations and can't solve this thing.

Is my analysis of the moments ok as well as the forces present on my FBD? I figured the rings cannot oppose motion in the directions where the hole of the ring is perpendicular to the force, thus has no reaction force.
 

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When writing moment equations, it's usually a good idea to pick one of the locations where an unknown reaction occurs. Look at it like solving a loaded beam on two supports: the sum of the forces involves both R1 and R2, but by writing a moment equation about one of the reaction points, say point 1, there is no moment produced by R1 but the resulting equation contains only R2, which can then be calculated. R1 is found by plugging R2 into the force equation.

You have your force equations involving the reactions. Instead of writing a moment equation about the origin, pick one of the reaction points and write a moment equation for it.
 
Best to take moments about an axis rather than a point.
 
If I take the moment about the X-axis, does that mean the moments caused by all forces that originate at points on the axis (A_y and A_z) go to zero, or is it that the moment caused by forces that act along the x-axis (B_x) go to zero, or is it something else??
 
I did the moment around point B, I get Cy = -Ay, which if I put into the summation of F_x equation, I get 1200 = 0, so something is wrong here
 

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Last edited by a moderator:
Solved it. I just made one sign error in the matrix on one of my determinants!
 
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