$5\mathrm{.}12-18$ A short column with a wide$-$flange shape is subjected to a compressive load that produces a resultant force $P=55kN$ acting at the midpoint of one flange $($see figure$).$

$($a$)$ Determine the maximum tensile and compressive stresses ${}_t$ and ${}_c,$ respectively, in the column.

$($b$)$ Locate the neutral axis under this loading condition.

$($c$)$ Recompute maximum tensile and compressive stresses if a $120mm10mm$ cover plate is added to one flange as shown.

PROBLEM $5\mathrm{.}12-18$

$5\mathrm{.}12-18$

$($a$){}_t=3\mathrm{.}27$MPa,${}_c=-24\mathrm{.}2$MPa;

$($b$)y_0=-76\mathrm{.}2mm$; $($c$){}_t=1\mathrm{.}587$MPa,

${}_c=-20\mathrm{.}3$MPa,$y_0=-100\mathrm{.}8mm$