Stability of multi-column systems with initial imperfections and non-linear connections

The stability and second-order response of multi-column system with initial geometric imperfections (i.e., made of columns with initial curvature, out-of-plumb in the plane of bending under eccentric axial loads at both ends), and non-linear end connections subjected to a lateral load at the top floor level are presented in a classical manner. The proposed method is based on the Euler-Bernoulli theory and limited to 2D multi-column systems with sidesway uninhibited or partially inhibited by lateral bracing at the top level. The combined effects of initial imperfections and non-linear connections in the plane of bending are condensed into the proposed governing equations which also can be used to evaluate the induced moments and second-order deflections along each column as the lateral and axial loads are applied to each column at the top level. The non-linear end connections are modeled using the three-parameter model suggested by Richard and Abbott. The bracing force is defined as a function (linear or non-linear) of the lateral sway. Three comprehensive examples are presented in detail that demonstrate the effectiveness of the proposed method and show the combined effects of initial imperfections and non-linear connections on the stability and second-order response of 2D multi-column systems. The proposed method can be used by structural researchers and engineers to investigate these effects on the stability and second-order response of multi-column systems including cases with relatively large lateral sways.