Consider the truss system shown below $,$ the cross$-$sectional area of each bar is $75m{m}^2)$ with a load $P=250kN$ applied $40$ degrees off of the vertical. The dimensions $A,B,$ and C are $5m,7m,$ and $6$ m $,$ respectively. $($a$)$ Form the element stiffness matrices for the truss system, defined in the global coordinate system $($GCS$).$ Be sure to clearly identify the GCS$,$ the element connectivity, and the angle used in forming each element stiffness matrix. $($b$)$ Use the stiffness method to compute the displacements at node $a.$ Do not form a global stiffness matrix, but rather clearly illustrate balance of forces $($Free$-$Body Diagrams$)$ at nodes $a,b,c,$ and $d$ where elemental forces are expressed as functions of displacements. $($c$)$ Compute the element forces expressed in the GCS$,$ element forces defined in the local coordinate systems $($LCS$),$ and axial force and stress for each element. $($d$)$ Compute reactions by clearly illustrating balance of forces $($Free$-$Body Diagrams$)$ at nodes as required. $($e$)$ Sketch the deflected shape.