$2-$ A building column carries a factored ultimate vertical downward load of $320$ k $.$ It is to be supported on a $3-ft$ deep, square footing. The soil beneath this footing has the following properties: $=115l\frac{b}{f}{t}^3,c^{\text{'}}=100l\frac{b}{f}{t}^2,{}^{\text{'}}=36.$ The groundwater table is at a depth of $5$ ft below the ground surface. Using LRFD$,$ with a resistance factor of $0\mathrm{.}5$ and a dead load factor of $1\mathrm{.}2,$ compute the required footing width.