Problem $4(20$ Marks$)$

A solid square bar is cantilevered at one end. The bar is $0\mathrm{.}6m$ long and supports a completely reversing transverse load of $+-2kN$ at the free end. The material is AISI $1080$ hot$-$rolled steel. If the bar must support this load for ${10}^4$ cycles with a design factor of $1\mathrm{.}5,$ what dimension should the square cross section have?

$\{$Neglect any stress concentrations at the support end$\}$