Abstract
This paper describes a method of analysing the shakedown load of elastic perfectly-plastic frames considering combined stresses. The authors have achieved the technique of fictitious yield convex polyhedron in order to develop the dual static and kinematic LP statements of the incremental collapse load analysis. This technique states that the fictitious yield convex polyhedron shrinks according to the expantion of envelope of varying elastic stresses in equilibrium with magnified external loads. This paper also reports that the nonlinear conditions of yield surface can be linearized by means of the yield convex polyhedron, which is modified in repetition to obtain as much value of the collapse load under the actual yielding conditions as possible. The process introduced herein features mainly as follows. 1) The stress resultants of the yielding cross sections at different instances in the loading cycle can be given as a solution of some mere simultaneous linear equations by aid of degeneracy. 2) Since the safety factors at both the upper and 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.
