Stability of imperfect slender columns with non-linear connections

Abstract

An analytical method that evaluates the stability and induced bending moments and second-order deflections in slender prismatic columns with initial geometric imperfections (i.e., initial curvature, out-of-plumb, and axial load eccentricities) and non-linear semirigid connections subjected to axial load at both ends and lateral load at the top end is presented. The proposed method is based on the classical Euler–Bernoulli theory for slender columns with sidesway uninhibited, partially inhibited, and totally inhibited. The effects of shear and axial deformations along the member are not included. The proposed model is limited to prismatic columns subjected to eccentric axial loads at both ends and a lateral load at the top end, causing bending about one of the principal axes with inelastic behavior taking place at the end rotational connections only. The three-parameter power model developed by Richard and Abbot is adopted to represent the non-linear moment-rotation behavior of the end connections. The effects of initial imperfections and non-linear semirigid connections are condensed into the proposed equations. These effects must be taken into account in the analysis and design of slender columns subjected to high axial loads, particularly when sidesway between their ends is uninhibited or partially inhibited because of possible excessive lateral sway and failure by lateral collapse. The proposed method can be used by researchers and structural engineers to investigate the effects of initial imperfections and non-linear semirigid connections on the inelastic stability and non-linear behavior of columns under heavy eccentric axial loads, including cases with relatively large lateral deflections. Five classical column cases and sensitivity studies are presented and discussed to show the effects of initial imperfections, lateral bracing and semirigid inelastic connections and the effectiveness and accuracy of the proposed iterative method on the non-linear second-order behavior and inelastic stability of prismatic columns.