Bounding of Frame Buckling Loads

Frame stability calculations are recast into the form of a low order, nonlinear eigenvlaue problem. It is shown that at each stage of the iterative solution of the problem, upper and lower bounds on the sway buckling load are established. The conditions needed for convergence and bounding are examined and verified by several numerical problems. It is shown that under usual conditions bounding and convergence are obtained for any reasonable starting assumption of load factor. For unusual cases, the use of submembers is interpreted to be a means of avoiding numerical difficulties.