Problem $2$

Consider a clamped$-$clamped column subjected to a compressive load, as shown:

$($a$)$ Using the rinite tlement Metnod $($and modeling the column using IWO elements$),$ obtain the critical buckling load, $\backslash (\backslash$mathrm$\{$P$\}\_\{\backslash$mathrm$\{$cr$\}\}\backslash ).$

$($b$)$ Now obtain the critical buckling load when a spring of stiffness K is introduced at the midpoint, as shown:

$($c$)$ Explain what happens as the spring stiffness K increases.