A pinned base plane frame with four columns spaced at $7\mathrm{.}5$ m centres and a clear height of $4\mathrm{.}5$

m has a lumped weight of $450$ kN at the roof.

The columns are $250$ x $250$ x $80$ UC in grade S$275$ steel with Young$$s Modulus of Elasticity equal

to $200$ kN$/$mm$2$

$.$

It is subject to ground acceleration pulse which has an amplitude of $0\mathrm{.}5$g and a duration of $0\mathrm{.}4$

seconds.

Determine: $($a$)$ the stiffness of the structure and $($b$)$ the maximum deflection.