Given:

A rectangular cross$-$section column supports compressive axial load P$.$

The base of the column is fixed.

The support at the top allows rotation of the column in the $x-y$ plane $($i$.$e$.,$ bending about the strong axis$)$ but prevents

rotation in the $x-z$ plane $($i$.$e$.,$ bending about the weak axis$).$

$L=1960mm,b=31mm,$ and $h=42mm.$

Using a Factor of Safety of $1\mathrm{.}95$ with respect to buckling, determine the allowable axial load $P_{\text{a}\text{l}\text{l}\text{o}\text{w}}$ that may

be applied to the column if:

a$)$ The column is made from $6061-$T$6$ Aluminum alloy.

b$)$ The column is made from ASTM$-$A$36$ structural steel.

Sketch the expected buckling shape for both planes $(x-y)$ and $(x-z)$ in the figure above.

Report the following: