QUESTION $2(50\%)$

The truss shown in the figure is under a horizontal load at node $3.$ The cross$-$section area of the elements and the Young's modulus $($please use $E_1)$ are given in Table $1$:

$($v$)$ Write the stiffness matrix for each element.

$($vi$)$ Assemble the total stiffness matrix.

$($vii$)$ What are the horizontal and vertical displacements at nodes $2$ and $3?$

$($viii$)$ What are the support reactions?

a$=5$m$,$ F$=20$kN$,$ A$=0\mathrm{.}001$m$^2,$ E$=210$x$10^9$ N$/$m$^2$