Critical initial geometric imperfection and advanced beam column element for direct analysis method of tapered I-sections

For highly geometrically nonlinear problems, the structural characterizes including the effects of member initial imperfections, the interactions between adjacent members and the buckling can hardly be captured with the linear analysis approach. The prevalent design methods, which are usually developed based on empirical assumptions, cannot correctly reflect the second-order effects of tapered members. Therefore, to accurately simulate the tapered members, this paper proposed an advanced analysis method for tapered I sections based on the direct analysis method. The function representing the critical initial geometric imperfection shape of tapered columns is presented, and the unfavorable effect is incorporated in the advanced tapered beam-column element formulation derived in this paper. The tapered element with an arbitrarily located internal hinge including 12 independent degrees of freedom is introduced for the state-of-the-art design method. Examples verifying the accuracy and efficiency of the proposed formulation are presented. The current research is believed to be a great contribution to the modern design of non-prismatic members.