Problem $08\mathrm{.}013.$a $-$ Determine an appropriate wide flange section.

Determine the section modulus and select the most economical S$-$shape beam to support the loading shown using the table given below. $($Round the final answer to the nearest whole number. You must provide an answer before moving to the next part.$)$

The section modulus is $\backslash (\backslash$boldsymbol$\{\backslash$alpha$\}\backslash$times $10^\{3\}\backslash$mathrm$\{$~mm$\}^\{3\}\backslash ).$

The most economical S$-$shape beam is