Effective-Length Reference
Reference for effective length factors, rotational and translational restraint, and the relationship between end fixity and buckling load.
Definition
The effective length L_e = K * L is the length of an equivalent pinned-pinned column that has the same buckling load as the actual column with its actual end conditions. The effective length factor K accounts for the rotational and translational restraint at the column ends.
Theoretical K values
| End condition | K (theoretical) |
|---|---|
| Pinned-pinned | 1.0 |
| Fixed-pinned | 0.707 |
| Fixed-fixed | 0.5 |
| Fixed-free (cantilever) | 2.0 |
| Pinned-pinned with lateral translation | 1.0 |
| Fixed-fixed with lateral translation | 1.0 |
| Fixed-free with lateral translation | 2.0 |
Practical K values
In practice, idealised fixed conditions are rarely achieved. Partial rotational restraint gives K values between the theoretical fixed and pinned values. Recommended design values are typically more conservative than theoretical values. When end restraint is uncertain, use K = 1.0 as a conservative default.
Effect on buckling load
P_cr proportional to 1 / K^2 Halving K (from 1.0 to 0.5) quadruples the buckling load. Doubling K (from 1.0 to 2.0) quarters the buckling load.
Different end conditions about each axis
For sections with different end restraints about the two principal axes (e.g. braced about one axis but not the other), compute L_e/r for each axis separately. The larger slenderness ratio governs.