New and extended design moment formulations for slender columns in frames with sway

Present first-order based design code formulations for slender columns in frames with sway, employ sway magnification factors (for global second-order effects) also as moment magnifiers for the individual columns of the frame (storey). This approach ignores differences in magnification of individual column moments caused by local second-order effects in the columns. This difference can be significant. Better understanding of this aspect will strengthen approximate first-order based elastic methods, for which the important superposition principle is valid. Towards this end, local second-order effects are considered for shears, end moments and maximum moments, applicable over the full range of axial loads. Specifically, end moment and maximum moment expressions of columns with sway are derived. These represent novel contributions that are suitable in typical design code formats, and in practical design work. They will allow more rational column assessments, and will allow more economical designs than present structural code procedures. Proposals are verified by comparison with results from second-order in-plane elastic analyses of single restrained columns and columns in frame panels. Also, extensions to the general case of load combinations that include both gravity and sideways loading are briefly presented