Mechanical model for determining the critical load of plane frames with semi-rigid joints subjected to static loads

The present work deals with the effect of beam-column joint flexibility on the elastic buckling load of plane steel frames. A simple and effective mechanical model is proposed and the corresponding stiffness matrix is presented. The model consists in the development of comprehensive approach taking into account, simultaneously, the effects of the joint rigidity, the elastic buckling load, and this for both sway and non-sway frames. As has been shown by previous research, only one element is required over the length of the element to model stability. This is a marked contribution and advantage of the proposed method, as well as its simplicity, and yet accuracy, to solve practical problem with little computational effort. Also, it includes stability functions in the stiffness matrix, something very often ignored by researchers. Numerical results are obtained for frames with various characteristics and support conditions when three illustrative examples from the literature are presented and discussed. The elastic buckling load is found to be strongly affected by semi-rigid joints and reveals that the proposed model is computationally very efficient with the expressions presented being general. The paper makes reference to the Eurocode 3 approach and those of other researchers in comparing the results. The proposed method is found to be more effective and simple to use, and yielding to very good results.