Solving 3D Statics Homework with Free Body Diagram

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Discussion Overview

The discussion revolves around solving a 3D statics homework problem using free body diagrams and moment equations. Participants explore methods to reduce the number of unknowns and apply the equations of statics to find the forces acting on a system.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a free body diagram and sets up moment equations, noting that they have too many unknowns to solve the problem directly.
  • Another participant suggests using one of the three rings as a reference point for the moment equation instead of the origin, arguing that this approach could eliminate one of the forces and simplify the problem.
  • A later reply proposes a specific moment equation using the forces and dimensions provided, indicating a method to relate the forces to the applied load.
  • One participant later claims to have resolved their issue by substituting values, concluding that Ay equals Cy and providing specific numerical results for these forces.

Areas of Agreement / Disagreement

The discussion shows a progression from initial confusion about the number of unknowns to a resolution by one participant. However, there is no consensus on the best method to approach the problem initially, as different strategies are proposed.

Contextual Notes

Participants express uncertainty regarding the sufficiency of their equations and the number of unknowns, indicating potential limitations in their approaches. The discussion also reflects the complexity of applying statics principles in three dimensions.

Who May Find This Useful

This discussion may be useful for students studying statics, particularly those working on similar 3D problems involving free body diagrams and moment equations.

goonking
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Homework Statement


upload_2016-4-12_19-53-5.png


Homework Equations

The Attempt at a Solution

Free body diagram
upload_2016-4-12_20-3-27.png
Setting moment at the origin = 0

(Rb X B) + (Ra X A) + (Rc X C) = 0

solving the 3 determinants and setting the coefficients of i, j, and k to 0, I get:

8Bz - 10 Cy = 0

-12 Az + 10 Cx = 0

12 Ay - 8Bx = 0

I have too many unknowns.

summing forces :

∑Fx = Bx + Cx = 0

∑Fy = Ay + Cy - P = 0 => Ay + Cy = 380

∑Fz = Az + Bz = 0

I still have too many unknowns.Any suggestions?
 
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goonking said:

Homework Statement


View attachment 99005

Homework Equations

The Attempt at a Solution

Free body diagram
View attachment 99006

Setting moment at the origin = 0

(Rb X B) + (Ra X A) + (Rc X C) = 0

solving the 3 determinants and setting the coefficients of i, j, and k to 0, I get:

8Bz - 10 Cy = 0

-12 Az + 10 Cx = 0

12 Ay - 8Bx = 0

I have too many unknowns.

summing forces :

∑Fx = Bx + Cx = 0

∑Fy = Ay + Cy - P = 0 => Ay + Cy = 380

∑Fz = Az + Bz = 0

I still have too many unknowns.Any suggestions?
Just like you would do when solving a 2-D problem, it is better to write a moment equation using one of the three rings as the reference, rather than picking another arbitrary point like the origin. Using one of the rings as the reference for the moment equation eliminates one of the forces, and you should be able to solve for the remaining forces using the two equations of statics which you are allowed to write.
 
SteamKing said:
Just like you would do when solving a 2-D problem, it is better to write a moment equation using one of the three rings as the reference, rather than picking another arbitrary point like the origin. Using one of the rings as the reference for the moment equation eliminates one of the forces, and you should be able to solve for the remaining forces using the two equations of statics which you are allowed to write.
you mean for example, taking ∑Mc = 0 along the x-axis : (Bz)(8) + (Ay)(15.62) - (P)(10in) = 0

(Bz)(8) + (Ay)(15.62) = (380)(10) = 3800
 
Last edited:
actually, I was wrong, I had all I needed already, it was just A LOT of substituting but in the end, I got Ay = Cy
plugging into Ay + Cy = 380

Ay = Cy = 190

A lot of subbing to find Ay = Cy12 Ay = -8 Cx = -8(12/10 Az) = 8(12/10) Bz = . . . and so on
 

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