Stability and second-order non-linear analysis of 2D multi-column systems with semirigid connections: Effects of initial imperfections

An analytical method and closed-form equations that evaluate the elastic stability and second-order response of 2D multi-column systems with initial geometric imperfections (i.e., columns with initial curvature or out-of-straightness and out-of-plumbness in the plane of bending) and semirigid connections subjected to eccentric axial loads and to a lateral load at the top floor level are derived 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 subjected to gravity loads. The combined effects of initial imperfections and semirigid connections in the plane of bending are condensed into the proposed equations, which can also be used to evaluate the induced elastic bending moments and second-order deflections along each column member of a multi-column system as the lateral and axial loads are applied. The effects of torsion, shear and axial deformations along each column and out-of-plane deformations are not included. Three examples are presented in detail that demonstrate the effectiveness of the proposed method and the corresponding closed form equations showing the importance of initial imperfections, semirigid connections and lateral bracing on the stability and second-order behavior of multi-column systems.

► Stability and second-order analysis of multi-column systems are presented in a classical manner.
► The concept of end-fixity factor is used to characterize the rotational end restraints of each column.
► Closed form expressions based on the classical Euler–Bernoulli theory are proposed.
► The effects of initial imperfections and semirigid connections are condensed into these expressions.
► These effects are critical and must be included in structural analysis.