Euler Elastica — Column Buckling Mode Shapes

Load P/P_cr1: 0.80 Mode n: 1 EI (stiffness): 1.00 Animate load sweep

Euler buckling: P_cr(n) = n²π²EI/L². Below P_cr(n), the column is straight. At P = P_cr(n), the n-th mode shape sin(nπx/L) becomes unstable. Higher modes require higher loads to excite. Pinned-pinned boundary conditions.