Extended second order approximate analysis of frames with sway-braced column interaction

Present approximate second order methods for the analysis of frames with sway are not capable of reflecting the transition from sway to partially braced, and nearly fully braced behaviour of individual columns in the frames. The main aim of the paper is to extend the approximate storey magnifier approach to account for such a transition. The key to this is in the manner local second order effects are reflected. A high order shear relationship is proposed, and general sway magnifier, critical load and effective length formulations are presented both in terms of first order lateral storey stiffness and critical, free-sway column loads. Their interrelationship, and simplifications leading to existing approaches, and adaptations in present codes and standards, are discussed. Comparisons are made with exact critical loads, sway and moment magnifiers for nearly unbraced, partially braced and nearly fully braced systems. The proposed, extended approach provides predictions that generally are in very good agreement with exact results at all axial load levels. The more simplified approaches provide good agreement for low to moderate load levels for some column end restraint combinations, and up to relatively high load levels for other combinations.