Resolving forces using Compatibility of Displacements?

mm391

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

F_A→B = F_A→D = F_A→C* cos(30)^2

F_A→C +2*F_A→B cos(30) = 50kN

3. 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 [b] for F_A→C I actually get= 25.6kN. can anyone help me find my error?

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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?