Static Equilibrium question...?

Question

The question reads:

A roof truss is made of two rafters, and a tie beam. Each end of the tie beam is supported by a wooden post. If a 100kg mass is suspended from the rafters, as shown, determine:

a.) The compression in each post
b.) The compression in each rafter
c.) The tension in each tie beam

So the diagram is an isoceles triangle sitting on two posts. The length of the base of the triangle is 12.0m, and the 100kg mass is hung from the top of the triangle.

I got the force of gravity on the mass (981N [Down]), and the length of each rafter (6.5m) and their angle to the 12.0m base (25* each).

But I don't know what to do from there.

Answer 1

Good start
Next write force equilibrium equations
The sum of x forces=0
The sum of y forces=0

(Note: place the weight on the y-axis where x=0.)

Also, just in case, don't forget that the sum of moments about any point is also 0.


The sum of x forces=0
Force components along the rafters
F1 cos(25) + F2cos(25) + F3=0

F3=tension on the beam
F1=F2= compression on each rafter.


The sum of y forces=0

W - F1 sin(25) - F2sin(25) =0
F1=F2 and F1 sin(25)=Fp (post compression)