A solid square rod is cantilevered at one end. The rod is $0\mathrm{.}6$ m long and supports a completely reversing transverse load at the other end of $+-2kN.$ The material is AISI $1080$ hot$-$rolled steel. If the rod 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 concentration at the support end.

$[$Hints: Solution: Square cross$-$sectional side length $b=30mm.$ For initial calculation the size factor $k_b$ can be assumed as $0\mathrm{.}85$ as the cross$-$sectional dimensions are unknown. Once the cross$-$sectional dimensions are determined, validate the size factor $k_b-$a process of trial and error $(k_b=0\mathrm{.}85$ is a very good trial value without further iteration$).$