Euler Buckling Limit, Euler Critical Load
X = critical bucking load, E = Young's Modulus, I = ∫ A y 2 d ⁢ A = second moment of area of cross section, L = length of bar
A slender bar under an axial load (a load applied down the length of the bar) will buckle at the Euler critical load, given as above.
Introductory Solid Mechanics, J McD Baxter Brown, John Wiley & Sons, 1973