For the truss shown, the vertical support reaction

at node $3$ is elastic with a stiffness $k_s=270$kip$\frac{s}{i}n.$

Both members have $E=14,000$ksi, and $A=7i{n}^2.$

Determine the member global stiffness matrices,

$[K{]}^{(i)}$ and the complee structure stiffness matrix,

$[$S$].$ Node $($circles$),$ member $($rectangles$),$ and DOF

$($purple diamonds$)$ numbers are shown, as well as

DOF directions $($purple arrows$),$ member local $x-$

axis directions $($blue arrowheads$),$ and global

coordinate system $($green$).$