A square footing is to be designed to support a column. The design loads on the column are all downward and concentric. Calculations of the design loads using the required load combinations specified by ASCE $7-11$ show that the controlling load combination gives a design column load of $450$ k $($assume this includes the footing$).$ The embedment depth of the square footing is to be $3$ ft$.$ The underlying soil has an undrained shear strength of $2,000$ lb$/$ft$2$ and a unit weight of $109$ lb$/$ft$3.$ The groundwater table is at a depth of $4$ ft$.$ Using Terzaghis method$/$formula$,$ determine the minimum required footing width to maintain a factor of safety of $3$ against a bearing capacity failure.