How do different end conditions affect column buckling?

End conditions determine effective length (Le = KL): Fixed-fixed has K=0.5 (strongest), Fixed-pinned has K=0.7, Pinned-pinned has K=1.0, and Fixed-free (cantilever) has K=2.0 (weakest). Since critical load is inversely proportional to Le², a fixed-fixed column can carry 4 times the load of a pinned-pinned column of the same length. End fixity is crucial in structural frame design.