Problem $2(30$ Points$)$

Design one corner, one side, and one interior structural steel column of grade $50$ steel for a $4-$story building shown below. The height of each floor is $12ft.$ The loads on the columns are as follows:

$\backslash$table$[[$Column$,$Roof Load,$4^($th $)$ Floor Load,$3^($rd $)$ Floor Load,$\backslash$table$[[2\_($nd $)$ Floor$],[$Load$]]],[$Corner$,$ C$1,14$kips,$30$kips,$30$kips,$30$Kips$],[$Side$,$ C$2,28$kips,$60$kips,$60$kips,$60$kips$],[$Interior$,$ C$3,40$kips,$125$kips,$125$kips,$125$kips$]]$

Assume same section will be used throughout the length of the column. Ends of the columns are bolted with the beams at each floor level and with the roof. E for steel is $30{10}^6.$ Make suitable assumptions if needed.