Question

The structure shown in Figure 2.1 supports a weight of 2000 lb. A free body diagram of the entire structure is given in Figure 2.2. A free body diagram of just the top pin is given in Figure 2.3. In Figure 2.2, there are three unknown forces: T the tension in the wire, and RH and RV, the reaction forces at the pinned connection to the wall. In Figure 2.3, there are two unknown forces, T and F, the compressive force in the bar.

Answer 1

To find T, we will take moments about the hinge.

For the clockwise (CW) moment, it is 2000*50cos(30).

To calculate the counter-clockwise (CCW) moment, we multiply T by the moment arm d, which is the distance of the hinge from the force T.

Summing CW and CCW moments, we get
2000*50cos(30)+T*d = 0
from which T can be solved once the moment arm d is found.

To find the moment arm, we need to solve the triangle with sides 10 and 50, with included angle 90-30=60 degrees.
Would you be able to find d?

Answer 2

thanks man, perfect.

Answer 3

so then F=T+2000

Answer 4

Yes, but the addition is done vectorially.