Elastic buckling of columns with a discrete elastic torsional restraint

Cold-formed steel haunched portal frames are popular structures in industrial and housing applications. They are mostly used as sheds, garages, and shelters, and are common in rural areas. Cold-formed steel portal frames with spans of up to 30 m are now being constructed in Australia. As they are relatively new to the market, current design recommendations are fairly limited. In the specific frame system analyzed herein, the column is partially restrained against twist rotation at an intermediate point where the knee brace joining the column and rafter is connected. An experimental program was carried out on a series of portal frame systems composed of back-to-back channels for the columns and rafters. It was found that changing the knee brace and knee brace-to-column connection bracket significantly affected the buckling capacity of the column, however this was not captured in design calculations. In order to correctly predict frame behavior and ultimate loads for design purposes, the column buckling capacity must be accurately calculated. This paper presents an energy method approach to calculate the buckling load of a column with an intermediate elastic torsional restraint. Various end conditions of the column are considered including column base semi-rigidity, as well as multiple loading conditions. Displacement functions are determined based on measured experimental data. The Southwell and Meck plot methods to determine column buckling loads are discussed. The column buckling loads determined from the plot methods and calculated by the energy analysis are compared to the experimental column buckling loads. It is shown that the energy method outlined herein predicts the buckling load within 6% for columns with an intermediate elastic torsional restraint.