Problem $2(10$ points$)$

A column of length $\backslash ($ L $\backslash )$ and the bending rigidity $\backslash ($ E I $\backslash )$ is pin$-$pin connected at both ends and at the same time is connected at the lower end to a torsional spring $($resisting rotation$)$ having a spring constant of $\backslash ($ K$\_\{$T$\}\backslash )$ as shown below. The column is subjected to an axial load $\backslash ($ P $\backslash ).$ Solve the critical load $\backslash ($ P$\_\{$c r$\}\backslash )$ for buckling. Hint: You don't have to finish complex algebra calculations. Show the major steps will be fine.