Method for Plastic Design of Frames

An approximate optimizing criterion is introduced in the problem of optimum design of frames. The new criterion, having the form of the elastic energy, drastically reduces the difficulties of the problem by transforming it to one of elastic analysis. In addition, it is more realistic than those previously used in that it does not require the vanishing of the cross section wherever the bending moment becomes zero. This eliminates the mathematical irregularities that complicate the problem and the absurd results to which these irregularities lead. The new criterion is applied to the minimum weight design of a portal frame, of which the continuously varying cross section depends on a single parameter and the strength, derived from resistance to bending alone, is exhausted only at plastic collapse; an upper bound of the approximation error is established. Furthermore, ways are indicated by which the approximation can be improved and the method can be applied to elastic design or the design of structures, the strength of which depends on their resistance to torsion and axial loading as well.