Resolving forces using Compatibility of Displacements?

[mm391]

Homework Statement

A pin-jointed frame (diagram attached) is formed of steel rods of 10mm diameter with member AC being 2m long. If a load of 50kN is applied at A as shown, determine the deflection of A and the force in the three rods. Take E = 200kN/mm^2.

Homework Equations

F_A→B = F_A→D = F_A→C* cos(30)^2

F_A→C +2*F_A→B cos(30) = 50kN

The Attempt at a Solution

Our tutor has given the answers as:

F_A→C = 21.7kN
F_A→B=F_A→D=16.6kN
And he has said F_A→C = 50kN/1+2cos(30)^3)

But when I solve the equations in for F_A→C I actually get= 25.6kN. can anyone help me find my error?

 

[pongo38]

If you could show your working, you would get more help. Meanwhile, on what principles are the equations "FA→B = FA→D = FA→C* cos(30)^2" based?
At what point in your calculations has the compatibility of the displacements been made?