Problem $2$ A plane truss structure consists of two bars subjected to a load $F$ as shown in the figure. Assume $E=10{10}^6$ psi, $h=50in.,=60,=36\mathrm{.}87.$ Both bar $1$ bar $2$ have the square cross section shape and their side dimensions are $0\mathrm{.}5$ in $.$ and $0\mathrm{.}6$ in $.$ respectively. The applied load $F=100lb.$ Use finite element method to solve the problem.

a$)$ Express the reduced FE system equation $\{F\}=[K]\{d\}$ in numerical form $(\{d\}$ is unknown$).$

b$)$ Solved for the displacements $\{d\}$ at node $3.$c$)$ Find the internal forces $\{f\}$ of the two elements. Note: the direction for the two bars is: $13,23.$