Select a W$-$shape that can be used for a $40$ span simply supported girder that

supports a DL of $80$ PSF and a LL of $40$ PSF$.$ The beam has a $10$ tributary width.

$$ Your beam must satisfy l$/360$ deflection limits for live load only

$$ Your beam must also have sufficient moment and shear capacity. You may use ASD or LRFD$,$ but need to clearly state which philosophy you are using.

$$ Your beam must be a compact shape $($i$.$e$.$ does not have a superscript $[$f$]$ in the SCM tables$)$

$$ Your beam must meet the h$/$tw limit for shear $($i$.$e$.$ does not have a superscript $[$v$]$ in the SCM tables$)$