Critical load for column with torsional spring constraint

[taureau20]

Knowing that the torsional spring is of constant K and that the rigid bar is of length L, determine the critical load $$P_{cr}$$ beyond which the column would buckle. See pic for the problem.
[As the spring uncurls, it applies moment $$K \theta$$ to the bar.]

The answer is $$P_{cr}=K/L$$

 

[taureau20]

I solved this problem.