$($a$)$ A square spread shallow foundation is shown in figure below, subjected to the loads as listed $($DL$=$dead, $LL=$ live, $SW=$ self weight$).$

The footing is about to be cast on a fully compacted sandy soil, with a maximum allowable soil bearing capacity, qa $=5000psf.$ Assume the footing weight is $60$ kips.

Determine the required cross sectional area, and size of the suggested foundation to support the load above imposed from the column.

Use ASD load combination.

$($b$)$ If the foundation $($designed in part $($a$)$ is about to be cast on a different site with bed rock with a high allowable bearing capacity of qa $=12,000$ psf$,$ determine how much extra dead load $($DL$)$ can be applied to the footing size that was calculated in part $($a$)$ of this problem. Use qa$=12,000$ for your calculation in part $($b$).(10$ points$)$