Euler Critical Load for a Compressed Column

For a straight, slender elastic column, Euler's critical load is:

$$N_{cr}=\frac{\pi^2 E I_{min}}{l_{eff}^2}=\frac{\pi^2 E I_{min}}{(\mu L)^2}.$$

• $N_{cr}$ — critical compressive load;
• $E$ — Young's modulus;
• $I_{min}$ — minimum centroidal second moment of area;
• $L$ — actual column length;
• $\mu$ — effective-length factor;
• $l_{eff}=\mu L$ — effective length.

The minimum $I$ identifies the weakest buckling plane. The formula applies to elastic buckling under conditions close to Euler's idealized column model.

The calculator does not treat $\mu$ as an independent unknown; use the already determined effective length $l_{eff}$.