QUESTION $5[20$ Marks$]$

A steel compression member with a length of $6m$ is required to support an eccentric load $P$ of

$350kN.$ Using both the allowable$-$stress method and the interaction method, select the most

suitable wide$-$flange shape with a nominal depth of $250mm$ for this application. The steel has

a modulus of elasticity $(E)$ of $200$GPa, a yield strength $({}_Y)$ of $250$MPa, and an allowable

bending stress $({}_{\text{a}\text{l}\text{l}})$ of $165$MPa.