Determing the Force in Each Member of the Loaded Truss

[Northbysouth]

Homework Statement

Determine the force in each member of the loaded truss. The force is positive if in tension, negative if in compression.

I have attached an image of the problem

Homework Equations

The Attempt at a Solution

I defined the positive y-axis to be from B to A and hence the positive x-axis is from B to C.

To find AB I took the sum of the force in the y-direction on point B, my calculations are:

0 = AB - (224kg)(9.8)cos(37)

AB = 1753.2 N

This answer is correct.

Then to find BC I found the forces in the x-direction at point B

0 = -BC + (224)(9.8)sin(37)
BC = 1321.1 N

However it says my answer is wrong. I suspect that it should be -1321.1 N but I have not tried this.

I am stuck on finding AC.

Some of the my classmates tried:

(BC)cos(37) which gives me 1055 N but it says this is wrong.

Any help would be appraciated.

 

[Northbysouth]

I have gotten the answer now.

BC = -1321.1 N

AC = BCcos(53) = 795.05 N but I don't understand why these are correct.

 

[PhanthomJay]

Your method of solving for AB and BC is very good. Note that at joint B, the comp. of the weight along your chosen x-axis points in toward the joint, to the left; thus, the force in BC must point in toward the joint to the right. Forces in members that point in toward the joint are compressive (designated as minus), while forces that point away from the joint are tensile (designated as plus).
For the force in AC, look at joint C and use conventional horiz and vert x and y axes, and apply the equilibrium equations. Note that the roller support at C cannot support vertical forces.