Elastica of an axially loaded column/ footing system resting on elastic base

The exact non-linear differential equation of large deformations of an axially loaded column fixed into a rigid eccentric footing, resting on elastic base, is formulated, along with the accompanying exact non-linear boundary conditions. The above differential equation is solved using the theory of elliptic integrals and elliptic functions. Employing a quadratic polynomial approximation in the expression for the curvature of the central line of the deformed column, an extended parametric study is carried out, in which as basic geometric parameters the height as well as the eccentricity of the footing have been adopted. The content of the parametric study consists in determining the relations among the basic variables: axial load, rotation angle of the footing and footing rotational stiffness. These relations are presented in the form of families of curves.