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?

 

[rezeew]

As a scientist, it is important to carefully analyze the problem and the attempted solution in order to provide an accurate response. Based on the information provided, it seems like the individual has a good understanding of the concept of equilibrium and is on the right track with their attempt at solving the truss structure. However, there are a few things that need to be clarified in order to accurately determine the solution.

Firstly, it is important to make sure that all the forces acting on the truss structure have been accounted for. This includes the weight at the end, as well as any external forces or reactions at the supports. It is also important to consider the direction of these forces and how they may affect the equilibrium of the structure.

Secondly, when applying the tension force, it is necessary to consider the entire truss structure as a whole, rather than just individual sections. This means that the tension force should be applied at every point where the cable is in contact with the truss, as this is where the force is being transmitted. Additionally, the direction of the tension force should be consistent throughout the entire truss structure.

Lastly, when considering the pulleys, it is important to remember that the tension force is being transmitted through the cable, not the pulley itself. Therefore, the tension force should be applied at the point where the cable is in contact with the truss, rather than at the pulley itself. This will ensure that the equilibrium equations are accurately represented.

In summary, it seems like the individual is on the right track with their attempt at solving the truss structure. However, it is important to carefully consider all forces and their directions, as well as the correct application of the tension force, in order to accurately solve the problem.