A solid square rod is cantilevered at one end. The rod is $0\mathrm{.}700$ m long and supports a completely reversing transverse load at the other end of$1\mathrm{.}20$kN$.$ The material is AISI $1080$ hot$-$rolled steel. If the rod must support this load for$2\mathrm{.}500105$ 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.

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

B$)$ What will the strength$$of the metal be at$2\mathrm{.}5105$cycles$2\mathrm{.}5105$cycles in MPa?