$(25)1.$ Consider the $2$D truss structure shown below which is the same as in HW #$4$ Problem $1-$A$.$ Assume

that there are foundation settlements, $u_{y_2}=-0\mathrm{.}5mm$ and $u_{y_4}=-0\mathrm{.}1mm.$ Start your solution from the

global unconstrained stiffness matrix and the global load vector computed in HW #$4$ Problem $1-$A

and answer the following questions. Use the same parameters as in HW #$4$: $A=0\mathrm{.}01m^2$ and $E=$

$200$ GPa for each element.

$($i$)$ Determine the vertical deflection at node $1.$

$($ii$)$ Determine the axial forces in every member.

$($iii$)$ Determine the reaction forces at supports.

$($iv$)$ Check the overall equilibrium of the structure: Check the resultant external forces and

moment about a point.

$($v$)$ Check equilibrium of joint $1.$