A sawn lumber column of rectangular cross section has a $2\mathrm{.}2-m$ effective length and supports a $46-$kN load as shown. The sizes available for use have $b$ equal to $90mm,140mm,190mm,$ and $240mm.$ The grade of wood has an adjusted allowable stress for compression parallel to the grain ${}_C=8\mathrm{.}1$MPa and $E=8\mathrm{.}3$GPa. Use the allowable$-$stress method to determine the lightest section that can be used.

The lightest section that can be used should have $b=mm.$