Elastic stability of non-uniform columns

Analysis of Tilt‐buckling of Euler Columns With Varying Flexural Stiffness Using Homotopy Perturbation Method

“…Li [18] gave the exact solution for buckling of non-uniform columns under axial concentrated and distributed loading. Lee and Kuo [17] established an analytical procedure to investigate the elastic stability of a column with elastic supports at the ends under uniformly distributed follower forces. Furthermore, Gere and Carter [10] investigated and established exact analytical solutions for buckling of several special types of tapered columns with simple boundary conditions.…”

Stability of non-uniform columns under the combined action of concentrated follower forces and variably distributed loads

“…With this proposed procedure, the eigenvalue equation for stability of a multi-step non-uniform column with any kind of two end supports including the case of two spring supports at the end of the column and any number of concentrated masses can be conveniently determined from a second order determinant. As a consequence, the decrease in the determinant order as compared with previously developed procedures (e.g., [14]) leads to significant savings in the computational effort. Numerical examples show that the critical buckling forces of non-uniform columns calculated by the proposed method are in good agreement with those determined by FEM, but the present method takes less computational time than the FEM, illustrating the proposed procedure is an exact and efficient method.…”

“…The stability of a non-uniform Timoshenko beam with clamped-free and elastically restrained-free boundary conditions subjected to three types of follower forces was investigated by Irie et al [13]. Lee and Kuo [14] adopted a numerical method to study the non-conservative stability of a non-uniform column by dividing the column into several uniform segments. Massey and Van der Meen [15] investigated the stability of tapered cantilever columns subjected to a tangential tip load for breadth taper only.…”

Stability of Steel Columns with Non-Uniform Cross-Sections

“…There is a relatively large number of theoretical or experimental publications on tapered or stepped columns with or without imperfections [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In the present paper, *Address correspondence to this author at the Civil Engng Dept., National Technical University of Athens, 15780 Greece; Tel: +30-210-7722454; Fax: +30-210-7722482; E-mail: rafto@central.ntua.gr non-uniform steel members with or without imperfections (of any form), loaded by axial forces (concentrically or eccentrically applied) and by concentrated moments applied at its ends or intermediate points are studied.…”