An analytical solution to the problem of stability loss of the rod under the combined action of concentrated force and dead weight

Abstract

The exact solution of the differential equation of buckling of the prismatic column under the combined action of a longitudinal concentrated end force and its own weight is constructed. Formulas are written for the state parameters of the rod, expressed in terms of the initial parameters. For six cases of ideal boundary conditions, finite analytical formulas are obtained that establish the dependence of the critical force on the weight of the rod.