$4$: The $8-$ft high two column $+$ slab storage system shown below supports a collection of rigid crates hun slied as : $10ft10ft10ft$ cube and weighing $50$kips total. Each column has a lateral stiffness of $5$ hi$.$js$/$in$.$ An explosion near the str cture loads one side of the structure area over $0\mathrm{.}01sec$ with an ave age presisure of $10.$ Initially the crate arrangement is intact. However once the structure reaches its first maximum displacement $($i$.$e the

fi$.$st raximum displacement away from the blast side$),$ the strups holdirig the crate assembly hrmak, wio i$/4$ of the crates fall from the supporting slab.

Find the amplitude of the nex: maximum displac ment $($i$.$e$.,$ the first maximum displacement in the direction of th:e ulast location$).$ Also state how $k$ it it ${?}^{+}$'kes for the siructure to arrive at that dist acemint state after the blast?

Ccinpared to the crates, columns and the slab have negligible weight. Ignore the blast load on the frame of the tructure and damping in the structure. Assume the slab to be rigid and neglect the axial a$$ shear deformation in the columns, and assume the structure behaves linear elastically.