Bifurcation Analysis of Multistory Building Frames

By assuming incompressible beams and columns in a multistory building frame, the frame may assume either a primary state equal to its underformed shape or a buckling mode when it is subjected to a set of primary axial forces that constitute the bifurcation loading. This article describes the theory and algorithm for a computer program by which the buckling load factor for a set of proportionate primary axial forces and the shape of the buckling mode may be obtained. It is shown that the buckling load factor thus obtained can be used to produce and effective length ratio for every column so that the Euler load of a pin-ended column with this effective length is identical to the actual buckling load of that column in the multistory building frame.