Question $3(25$ points$)$

$-$ A $24$ft high one$-$story building consists of four columns at hinged base with rigid diaphragm $(4$ strong beams with composite deck$).$ Each column is W$8$x$40.$ Neglecting damping, determine the maximum response of the frame due to a rectangular pulse force of amplitude $8$ kips and duration td $\backslash (=0\mathrm{.}5\backslash$mathrm$\{$sec$\}\backslash ).$ Determine displacement at the top of the frame and maximum bending stress in the columns. Decide the adequacy of the columns. Assume the natural period of the building is $0\mathrm{.}2$ sec $.$