Finding Equilibrium in a 3D System of Forces

[Gauss M.D.]

Homework Statement

See attachment

Homework Equations

Let u be the angle between AC and AO and v the angle between BE and BD.
Ta is the tension at point A and Tb is the tension at point B.

The Attempt at a Solution

Tried starting with the OAB body and got:

-mg + Ta sin(u) + Tb sin(v) = 0
-Oz + Ta cos(u) + Tb cos(v) = 0

for the force equilibrium. For the moment equilibrium, I chose point A as reference. The moment due to mg is -mg*0.75, and the moment due to the vertical component of Tb should be Tb sin(v)*1.5.

But doesn't the horizontal component of Tb cause a moment about point A here too? If so, what's preventing the beam OAB from rotating about point O?

 

[haruspex]

You've left out cable BE. Because u > v this will be under tension. Take moments about O.