A solid square rod is cantilevered at one end. The rod is $0\mathrm{.}8$ m long and supports a completely reversing transverse load at the other end of $+-1kN.$ The material is AISI $1045$ hot$-$rolled steel. If the rod must support this load for ${10}^{+}$cycles with a factor of safety of $1\mathrm{.}5,$ what dimension should the square cross section have? Neglect any stress concentrations at the support end and assume that $f=0\mathrm{.}9.$

Answer: $758\mathrm{.}8m{m}^2$

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