Analysis and design of laterally unsupported portal frames for out-of-plane stability

A methodology for the analysis and design of laterally unsupported portal frames is proposed. A finite element model is developed to predict the elastic critical load and associated buckling mode. Regression analysis is then conducted to find lateral displacement and rotation field expressions that closely approximate the buckled configurations predicted by the finite element analysis. The obtained functions are then substituted into the total potential energy expression, and the stationarity conditions are evoked. The resulting eigen-value problem is solved for the out-of-plane buckling loads that are then compared with those based on the finite element model. The agreement between the two solutions provides an indication of the accuracy of the simplified energy solution. The member destabilizing effects induced by axial forces are separated from those induced by strong axis bending. The separation of these two effects is subsequently exploited in a two-step eigen-value procedure, aimed at determining the key member resistances defined in the interaction check of the standard CSA-S16-01, while accurately modeling the boundary conditions of the member. These are (i) compressive resistance of the member in the absence of bending effects and (ii) flexural resistance of the member in the absence of axial force effects.