Column effective lengths considering inter-story and inter-column interactions in sway-permitted frames

The physical meaning of the traditional effective length coefficients (ELCs) in a sway permitted frame is first explained. It is found through an example that the critical loads of columns in a story have the same percentage increase or decrease after considering the inter-story interaction. It is also pointed out that the ELCs obtained by an overall buckling analysis are applicable only in the weakest story, for the other stories their ELCs simply implied the proportional loading assumption.With three assumptions of the conventional effective length approach discarded, this paper presents a mergence approach for buckling analysis of frames in which the column linear rigidities and axial loads are summed up, and the rotational restraints provided to columns by beams are summed at the merged beam-to-column joints. Effective lengths considering both inter-story and inter-column interactions are determined in unbraced two-story and three-story frames by simple algebraic operations. For frames with more than three stories, a three-story sub-assemblage, which includes beams at far ends of the columns above and below the story under consideration, is used to find the effective lengths of columns in the middle story.For frames with different bases, a equivalence procedure transforms the frames into those with the same type of bases before the mergence. For multi-span frames, the mergence approach overestimate the story lateral stiffness, a modification is proposed to eliminate this overestimation.Although overall buckling analysis of frames is easily carried out today, the findings and the proposed method of this paper will help to understand the inter-column and the inter-story interactions in frames.