WIT Press


Moment Formulation For Random Eigenvalue Problems In Beams

Price

Free (open access)

Paper DOI

10.2495/ERES110161

Volume

120

Pages

9

Page Range

185 - 193

Published

2011

Size

387 kb

Author(s)

B. W. Yeigh & J. A. Hoffman

Abstract

This paper proposes a moment formulation model to handle eccentric load imperfections in beams on elastic foundation taking into consideration the randomness of imperfections. An alternative approach to the secant formula to capture the effects of load imperfections is described. The study demonstrates eccentricity is the most detrimental form of structural imperfections and that it aggressively and adversely interacts with other imperfections. Keywords: stability, load imperfections, beam on elastic foundation, regular perturbation, eigenvalue, energy method, stochastic, spectral representation. 1 Introduction One fundamental problem still remains to be explored in structural engineering are the stability of imperfection sensitive structures. Unlike tension and flexural members that fail when the applied loads cause stresses that exceed material limitations, slender columns most often fail by buckling. Furthermore, column buckling does not depend on the proportional limit of the member. Buckling is a complex failure mechanism that is often catastrophic with little or no warning. It depends not only on the material and section properties of the column, but also on the contributions and interactions of its length, end support conditions, lateral supports, and location of the applied load. The classical stability analysis [5, 7], is actually developed largely from the work of Leonhard Euler who first analytically investigated the column buckling phenomenon in 1744. Over the years, much has been done to extend and refine Euler’s work. Buckling formulations based on the Euler equation had some rational consideration for the behavior of the material in question. They all

Keywords

stability, load imperfections, beam on elastic foundation, regular perturbation, eigenvalue, energy method, stochastic, spectral representation