QUESTION $2[20$ Marks$]$

A rolled$-$steel column $AB$ with a $W25052$ cross$-$section is subjected to axial loads of

magnitude $P=820kN$ applied parallel to the geometric axis. The loads intersect the $x-$axis at

a distance eccentricity $($e$)$ from the geometric axis. The steel has an allowable stress $({}_{\text{a}\text{l}\text{l}})$ of

$130$ MPa plus the last digit of your student ID and a modulus of elasticity $(E)$ of $200$GPa.

Determine the largest permissible length $L$ of the column for two cases: $($a$)$ when the

eccentricity $e$ is $5\mathrm{.}5mm,$ and $($b$)$ when the eccentricity $e$ is $15mm.$

Figure $1$