Euler Buckling Force

      Buckling force, number of buckles, and Young's modulus can be correlated by classical mechanics equation for buckling of a column:
      n = 1, 2, 3, ....      (1)
where M = bending moment, F = force experienced by the column, d = maximum deflection, L = column length, and n = number of buckles.
      The solution to this equation at the maximum deflection can be simplified to:
       or             (2)

where Y = Young's modulus, F = force experienced by the column, and I = (πr4)/4 = stress moment over cross section (r = radius). Euler buckling force when there is only one buckle (n=1) is
      (3)

      (4)