Lower Bound Approximation for Elastic Buckling Loads

An approximate method for the elastic buckling analysis of two-dimensional frames is introduced. The method can conveniently be explained with reference to a physical interpretation: In the frame every member is replaced by two new members: - a flexural member without extensional rigidity to transmit the shear force and the bending moments; - a pin-ended rigid rocker member to transmit the normal force. The buckling load of such a model can be calculated in a relatively simple manner. It is shown that, if no tensile forces occur in the frame, the buckling load of the model is an upper bound for the buckling load of the actual structure. By means of a simple formula a lower bound for the buckling load can then be determined. The method is more particularly of educational value. By means of this convenient and systematic method engineering students can fairly quickly gain an insight into the buckling behaviour of framed structures