Question $1$: Figure presents a plane truss system. Elasticity modulus and the cross$-$sectional areas of the truss members are $E=200$GPa,$A_1=A_4=0\mathrm{.}01m^2$ and $A_2=A_3=0\mathrm{.}02m^2,$ respectively. The forces acting at the node $3$ and $4$ are $P_y=900kN$ and $P_x=500kN,$ respectively. The nodal coordinates of the points $1,2,3$ and $4$ are $(0,2m),(4m,0),(4m,2m),(0m,0m),$ respectively. Determine,

a$)$ Displacement of the nodes in local and global coordinates,

b$)$ Support reactions,

c$)$ Stresses,

d$)$ Axial forces of the members.