$3.($adapted from Hibbeler $\backslash (10^\{\backslash$text $\{$th $\}\}\backslash )$ ed$.$ probs. $13-119$ and $13-120)$

The $2014-$T$6$ aluminum hollow column shown is fixed at its base and free at its top. The thickness of the wall for the section is $\backslash (\backslash$mathrm$\{$t$\}=0\mathrm{.}5\backslash$mathrm$\{$in$\}\backslash ).$ The allowable bending stress is $30$ ksi $.$ Determine the maximum eccentric force $\backslash ($ P $\backslash )$ that can be safely supported by the column using the Aluminum Association's equations, and...

a$.$ the allowable stress method.

b$.$ the interaction formula.

Answers: $($a$.)2\mathrm{.}788$ kip; $($b$.)11\mathrm{.}73$ kip