Euler's critical load
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: P c r = π 2 E I ( K L ) 2 {\displaystyle P_{cr}={\frac {\pi ^{2}EI}{(KL)^{2}}}} where P c r {\displaystyle P_{cr}} , Euler's critical load (longitudinal compression load on column), E {\displaystyle E} , Young's modulus of the column material, I {\displaystyle I} , minimum second moment of area of the cross section of the column (area moment of inertia), L {\displaystyle L} , unsupported length of column, K {\displaystyle K} , column effective length factor This formula was derived in 1744 by the Swiss mathematician Leonhard Euler.