PE Exam Cable Practice Problem

[swooneyWOODSTRUCT]

Please help me figure out what I am doing wrong in the attached problem. My calc is in the red rectangle. I got the same answer as the solution up until they solved the equilibrium equations at C (the last step). I summed the forces in the y direction instead of the x and got a different answer.

When I sum the forces in the x direction like they did, I get the correct solution. Why the difference? Don't the x and y forces BOTH have to sum to zero?

I assumed I was just making an algebraic mistake so I plugged it into a calculator and I still got the same, wrong answer.

 

[Goatenstein]

I think your answer of 27.5K for Fbc is correct. If you sum the vertical components of Fab and Fbc, they must sum to 50K. They only sum to 50K if Fbc is 27.5K, not if it's 51.9K.
I still cannot figure out why there is a difference when the different methodologies are used.

 

[Once20036]

I couldn't figure it out. I started by calculating all of the forces at the restraints, but then my summation of forces at node B didn't sum to zero.

 

[dylansdad]

Is not cable BC at a 2/4 slope rather than 1/4? I have not gone through the problem to try and solve it yet, just a quick observation.

 

[Goatenstein]

I solved for the forces at each joint independently, and found the force in Fbc is different depending on which joint it's solved at.
I think that, for the given forces and cable lengths, the cable angles are wrong. Alternatively, either the load at joint B needs to increase, or the load at joint C needs to decrease.

 

[dylansdad]

Goatenstein,
See my post 15:58 directly preceding yours.

 

[Goatenstein]

dlansdad,
Cable BC is at a 2/8 slope which simplifies to a 1/4 slope.

 

[azcats]

Maybe the system is not in equilibrium in it's current state?

 

[dylansdad]

Goatenstein,
I stand corrected.