Abstract
This paper describes a method of analysing the collapse load of frame structures considering combined stresses. The nonlinear conditions of a frame structure, reports the paper, can be linearized by means of the yield condition convex polyhedron, which is modified in repetition to obtain as much value of the collapse load under the actual yielding conditions as possible. The mathematical way of the said process is S. L. P.. The process introduced herein features mainly as follows. 1) This can provide with more correct results than the refference (11) or (12) does. 2) An example of the stress distribution under the ultimate load can be given as a solution of some mere simultaneous linear equations by the aid of degeneracy. 3) Since the safety factors at both the upper and the lower bounds are always obtainable, wherever of the stage of repetition should the modification be ceased, the range within the true solution exists is apparent. This paper introduces an analysing process based upon the upper and the lower bound theorem, stating that the linearization by S. L. P. of nonlinear equations, representing the theme of the limit analysis is quite equivalent to establishing the linearized yield convex polyhedron. The paper also especially clarifies the course of analysis based on the upper bound theorem while most of the essays presented so far treats the upper bound theorem simply as a dual problem to the lower bound theorem which the theme of limit analysis is based on to formulate.
