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

[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.

 

[SteamKing]

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.

 

[pongo38]

Best to take moments about an axis rather than a point.

 

[member 392791]

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??

 

[member 392791]

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

 

[member 392791]

Solved it. I just made one sign error in the matrix on one of my determinants!