Geotechnical Engineering$-$II HW$-6($Non$-$Uniform Stresses$)$

It is required to provide the dimensions and $B$ of the spread footing giving the following information and subjected to the provided loading conditions:

The $(1^{\text{'}}{3}^{\text{'}})$ column loads at the ground surface are $400$ kips vertical load and a moment of $240k.ft.$ The column has to be placed at the center of the footing.

Four feet of earth overburden of $110$ pcf$,$

No plain concrete footing,

$f_y=60,000$ psi and $f^{\text{'}}{?}^{\text{'}}=4000$ psi., and

The soil allowable bearing capacity is $7000$ psf$.$

Note: The maximum to minimum stress ratio under the footing is limited to