A uniform cylindrical beam is needed to hold a maximum tension load of $46\mathrm{.}0$ kN $.$ What diameter in millimeters is needed if you were to use the following materials. Assume the stock comes only in even $2$ mm diameter increments $(8mm,10mm,12mm,$dots $).$

a$.1020$ hot$-$rolled steel, allowable stress $230$ MPa $(6$ points$)$

b$.1040$ hot$-$rolled steel, allowable stress $270$ MPa $(6$ points$)$