Statics in 3d question

1. Apr 12, 2016

goonking

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Free body diagram

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?

2. Apr 12, 2016

SteamKing

Staff Emeritus
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.

3. Apr 13, 2016

goonking

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: Apr 13, 2016
4. Apr 13, 2016

goonking

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 = Cy

12 Ay = -8 Cx = -8(12/10 Az) = 8(12/10) Bz = . . . and so on