Problem $2$

Consider a three$-$member truss shown. Suppose that all members of the truss have identical areas of cross section $A=5{10}^{3}m{m}^2$ and Young modulus $E=200$GPa. The hinged supports at joints $A,B$ and C allow free rotation of the members about the $z-$axis $($taken positive into the plane of the nage$)$

$1/$ For each bar member, find its length, its stiffness, and the inclination angle

$\frac{2}{?}$ Give the stiffness matrix for each bar member in the global coordinates

$3/$ Assemble the above matrices to obtain the global stiffness matrix of the system.

$4/$ Give the boundary conditions at nodes $(1)$ and $(3)$ and the components of the applied force.

$5/$ solve the system's equation and give the nodal displacements $\frac{6}{?}$ what are the reactions at nodes $(1)$ and $(3)?$