Structural Engineering
Effective Length
A column’s length multiplied by a factor K that accounts for how its ends are restrained.
Euler’s buckling load P_cr = π²EI/(KL)² uses the effective length KL: the length of a pinned-pinned column that would buckle at the same load. Theoretical K is 1.0 for pinned ends, 0.5 for fixed ends, 0.7 for fixed-pinned and 2.0 for a flagpole fixed at the base and free at the top.
Because K is squared, end restraint matters a great deal: freeing the top of a column that was pinned cuts its buckling load to a quarter.