Solving Truss Structures: Troubleshooting and Equilibrium Equations

[Karstedt]

Homework Statement

I'm having trouble with this structure, but I think I finally figured it out. I'm hoping to get a confirmation or a push in the right direction if I'm wrong. I'm trying to solve the truss in terms of the weight at the end.

Homework Equations

Standard equilibrium

The Attempt at a Solution

I sectioned the upper left portion cutting through the pivot members and 3 sections of cable (in blue) to try and solve for tension T in terms of W using the moment about the pivot point where the trusses are joined, but my solution went bad when I tried to apply that to the full structure in order to determine reactions at the supports.

I think what happened was that I don't know how to apply the tension force to the full FBD. I applied the tension only to the point of contact with the ground, which resulted in the roller having a downward force (impossible). I now suspect that I need to apply the tension at every point and basically treat it like a bunch of external forces to the full truss (resulting in 4 total applications of T). Am I correct?

I was also wondering if the tension force can be applied at the joints since a FBD of the pulleys gives a resultant at the joint equal to T in whatever directions the the cable runs. Or do I have to aplpy the forces at the radius of the pulleys?

 

[PhanthomJay]

If I read your figure correctly, this is not a pure trussed structure because there is no bracing in the lower main frame. And if all joints are pinned, this is an unstable structure as it will collapse under any amount of horizontal load. Beyond that, the structure is statically indeterminate because there are 4 unknown forces and only 3 equilibrium equations , and you'd have to resort to deflection analysis to solve.
And if taking a FBD of the entire frame, then only the tension force in the vertical cable, plus the external reaction loads at the pin or roller supports, and the load W, are considered, even though the internal tension forces in all parts of the cable will be the same if the pulleys are massless and frictionless at their bearings. Did you make this problem up?

 

[Karstedt]

I didn't include the braces in the lower portion, they didn't seem relevant, but they go from the top left to right mid and right mid to lower left corner.

I was thinking it's indeterminate as well, but the course doesn't cover indeterminate structures or how to solve them. Everything is equilibrium. Though I don't need to solve W, I just need to get the 3 unknowns in terms of W... but since they are all parallel I only have 2 equations, M and Fy.

I didn't make it up.

 

[PhanthomJay]

Still looks indeterminate to me, are you sure that T is not given also, such that is is a known applied force and not an anchored cable unknown force?