The effective length factor of columns in unsymmetrical frames asymmetrically loaded

Abstract

The concept of the effective length factor represents an important parameter with regard to the elastic buckling analysis. This concept makes possible computational of the elastic critical load using a single formula for any situation of boundary conditions. We noted that substantial research has been done by many researchers in this field. The work developed in this paper, is focused on the resoluteness of the exact value of the effective length factor of columns belonging to unsymmetrical frames, with asymmetrical loading. For this purpose we chose to study an unsymmetrical frames asymmetrically loaded where the geometry and loading are set by means of a great number of a dimensionless parameters. At first, a theoretical approach is adopted to investigate the global elastic buckling of an irregular frame. This is done by considering the classical stability functions which introduce the coupling between axial loading and the bending stiffness of the columns. Thus, the governing equilibrium equations were established for the structure being studied, leading to the global nonlinear stiffness matrix of the structure. Therefore, the global elastic buckling occurs when the determinant of the nonlinear stiffness matrix vanishes. Thereafter, a wide parametrical analysis was done from the theoretical results previously obtained. In determining the effective length factor K, a marked difference was noted between the results obtained using the Eurocode 3 approach and those obtained by the current study.