Column Bending Induced by Applied Loads in Excess of the Euler Critical Load

This paper presents the underlying theory and a closed form analytical solution to the problem of progressive column buckling. The locus of the tip of the free end of the column is established and various deformed shapes are presented for loads applied in excess of the Euler load. The analytical results are compared and agree with a numerical solution obtained with a computer by direct numerical integration of the basic differential equation.