What is Euler's buckling load and what factors affect column buckling?

Euler's critical buckling load Pcr = pi^2 * EI / (KL)^2, where E is modulus, I is moment of inertia, K is effective length factor (depends on end conditions), and L is column length. Factors affecting buckling include slenderness ratio (KL/r), end restraints, initial imperfections, residual stresses, and load eccentricity. Short columns fail by yielding while long columns fail by elastic buckling.