Effects of column imperfections on capacity of steel frames in variable loading

Abstract

The presence of column initial imperfections in a steel frame can increase deflections and decrease its load carrying capacity. A method is proposed for evaluating the lateral stiffness, inter-storey displacement and deflected column shapes in a semi-braced, semi-rigidly connected planar storey frame subjected to gravity loading and column initial imperfections. An equation is proposed for calculating the inter-storey displacement, which contains the notional load associated with out-of-plumbness imperfections, in addition to a new notional load term associated with out-of-straightness imperfections. Additionally, when the lateral stiffness calculated by the proposed method diminishes, the frame is considered unstable. Different gravity loading scenarios can exist that equally result in the various criteria of capacity being reached defined as either instability, the maximum permissible deflection associated with structural integrity, or the onset of yielding in columns. The proposed method extends the variable loading approach to identify the worst- and best-case scenarios of gravity loading for this to occur. Unlike traditional proportional loading analyses, loads are varied independently of each other in the variable loading approach. Numerical models for the frame subjected to variable loading with accounting for the presence of column initial imperfections are established. It is demonstrated that although the presence of column initial imperfections does not affect the buckling loads of frames, it increases deflections and can significantly reduce the capacity even if the frames are constructed within the allowable tolerances for initial imperfections.