Buckling load of planar frames with semi-rigid joints using weighted symmetric graphs

The main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. This is achieved by decomposing a symmetric weighted graph model into two submodels and using canonical forms in such a manner that the union of the eigenvalues of the submodels result in the eigenvalues of the entire model. Thus the critical load of the frame is obtained as the smallest eigenvalue obtained for the submodels.