A $20320386$ UC Grade $43$ steel supported on a concrete foundation of characteristic strength $30\frac{N}{m}{m}^2$ has been selected for the ground floor and first floor of a structure with loading arrangement as shown in Figure $2.$

$($a$)$ Assuming loads as presented are design loads and include the self weight of the beams supporting the loads and are factored, check the adequacy of the $5\mathrm{.}0m$ long ground floor column. Include the factored self weight of the column in your calculations

$($b$)$ Design a suitable base plate for the column.

Figure $2$