A solid square rod is cantilevered at one end. The rod is $0\mathrm{.}5m$ long and supports a completely reversing transverse load at the other end of $+-1kN.$ The material is AISI $1080$ hot$-$rolled steel. If the rod must support this load for $1\mathrm{.}5{10}^5$ 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.

Determine the endurance limit for this application. Assume that the size modification factor $k_b$ is $0\mathrm{.}85$ until a size for the section is known.

The endurance limit is MPa.