Support reaction on pulley due to cable. Help needed

[kjr]

Hi and greetings from new member.

A problem brought me to these forums and i am hoping someone will be able to explain what is going on here.

I am working on this project, for which i need to design a truss/frame to support a load. So i came up with this design (diagram attached).

Black is the mounting plate that the whole structure has to be mounted on.
Gray is the simplified metal structure (i didn't draw the crossmembers for simplicity).
Red is the cable, one end attached to the intersection of the frame, then the cable is passed through 2 pulleys (gray circles) and the other end is attached to a hook that the load is attached to.

The intersection acts as a support pulley to hold the cable in place (that's where the problem lies).
The idea is to redirect the force to act into the mounting plate, instead of perpendicular to it, so the frame is more stable and less susceptible to bending and buckling.

Problem is, when i try to do calculations for it, i need to know the nature of the support reaction force that the cable exerts by resting on that pulley with load attached.

Does anyone have any ideas?

Thank you

 

[nvn]

kjr: Label all points in your free-body diagram, so it makes it easier to refer to. You might also want to label all dimensions, and draw support reaction forces at each support, if you wish. And you might want to clarify the boundary conditions; i.e., the left-hand end of each gray member is currently shown encased (fixed, welded) to the wall, because no black dot appears at those two attach points. Are the gray members welded to the wall? Or are they pinned at the wall, and therefore free to rotate?

Moving on to your question, the cable exerts three applied loads (they are not called support reaction forces) to the right-hand joint/pulley. Each of the three applied loads is T, each of which is aligned with the three cable lines going to the right-hand joint/pulley. Assuming you have drawn the two left-hand pulleys accurately, and they are really attached to the wall, and not attached to the gray members, then you can replace the cable with three applied forces T, acting on the right-hand joint/pulley. Two of the T forces act at the perimeter of the right-hand pulley, and one of the T forces acts at the black dot.