Euler Column Buckling

Pcr = π²EI/L²  |  Post-buckling bifurcation & mode shapes

Column shape (mode n)
Bifurcation diagram: P/Pcr vs deflection δ
Boundary Conditions
Mode shape
Pcr,n = n²π²EI / (KL)²
K: 1.0 (pin-pin)
K: 2.0 (fixed-free)
K: 0.5 (fixed-fixed)
Critical slenderness:
(L/r)cr = π√(E/σy)