Buckling loads of linearly tapered columns laterally restrained by multiple elastic springs

Abstract

This paper discusses the numerical methods that were developed for calculating the buckling loads with the corresponding buckled shapes of linearly tapered columns laterally restrained by multiple elastic springs. In formulating the governing equation of the column, each elastic spring was modeled as a discrete Winkler foundation of the finite longitudinal length. By using this model, the differential equation governing the free vibration of the column was first derived, which was subjected to an axial compressive load, after which the differential equation governing the buckled shapes of the column was formulated using the relationship between the natural frequencies and the loads. The Runge-Kutta method was used to integrate the differential equation, and the determinant search method combined with the Regula-Falsi method was used to determine the eingenvalues, namely, the buckling loads. In the numerical examples, clamped-clamped, clamped-hinged, hinged-clamped and highed-hinged end constraints were considered. The numerical results including the buckling load parameters and the buckled shapes of the columns were presented in non-dimensional forms.