Question $5$: Buckling Analysis $(30$ marks$)$

Re$-$consider the original beam configuration that you have analysed in Question $1$ and complete the following tasks, supposing that the beam is not carrying any bending loads but is instead only carrying a compressive load acting through the centroid of the section. Under these conditions, the beam can be treated as a column, and some form of buckling analysis should be performed. For the analysis in this question, adopt the same material properties you have already identified for the beam in Question $1$ Which is the same as question $3$ below $.$

$($a$)$ Based on the configuration considered in Question $1,$ define the effective length of the column that you are going to adopt for the analysis.

$[5$ marks$]$

$($b$)$ Calculate the Euler critical buckling load for this configuration and identify the direction in which the column would bow$-$out if buckling occurs.

$[20$ marks$]$

$($c$)$ If buckling is prevented from occurring, what compressive load would be required to generate yield in the column, and therefore would you say this column is "long" or "short"?

$[5$ marks$]$

Question $3$: Stress Visualisation and failure theories

A cantilever beam with a symmetrical $\text{'}T\text{'}$ shaped cross$-$section is loaded with a distributed load as shown below. The parameters of the problem are shown in the table below. The intensity of the distributed load is $100\frac{N}{m}m.$

$\backslash$table$[[$Parameter$,$Description,Value,Units$],[L,$Beam length,$1\mathrm{.}0,m$