$6-(10$ pts$)$ Consider a simply supported beam shown below. The beam is subjected to the load $F$ that varies between $850$ N to $-425$ N $.$ Assumd the weight of the beam is negligible. Also, assume machined surface finish and $90\%$ reliability. The beam has a rectangular cross section. Specify the ultimate strength of the material $($steel$)$ required for a safety factor of $2\mathrm{.}5.$ Also, from the tables of steel properties, select the type of steel that provides the approximately the same ultimate strength $($i$.$e$.,1020,1040,.....)$

$l=\mathrm{.}7m,b=$