A rotating step shaft is loaded as shown, where the forces $F_A$ and $F_B$ are constant at $560$ lbf and $280$ lbf $,$ respectively, and the torque $T$ alternates from $0$ to $1800$ lbf in $.$ The shaft is to be considered simply supported at points $O$ and $C$ and is made of AISI $1045$ CD steel with a fully corrected endurance limit of $S_e=40k.$ Let $K_f=2\mathrm{.}1$ and $K_{fs}=1\mathrm{.}7.$ Take the value of design factor to be $2\mathrm{.}5.$

Determine the minimal acceptable diameter of section BC using the DE$-$Goodman criterion. $($Round the final answer to three decimal places.$)$

The minimal acceptable diameter of section $BC$ is in$.$