Advances in theory of plastic mechanism control: closed form solution for MR-Frames

In this paper new advances in the application of “Theory of Plastic Mechanism Control” (TPMC) are presented. TPMC is aimed at the design of structures assuring a collapse mechanism of global type. The theory has been developed in the nineties with reference to moment-resisting frames (MRFs) and progressively extended to all the main structural typologies commonly adopted as seismic-resistant structural systems. In particular, the outcome of the theory is the sum of the plastic moments of the columns required, at each storey, to prevent undesired failure modes, i.e. partial mechanisms and soft-storey mechanisms. The theory is used to provide the design conditions to be satisfied, in the form of a set of inequalities where the unknowns are constituted by the column plastic moments. This set of inequalities was originally solved by means of an algorithm requiring an iterative procedure. The advances presented in this paper are constituted by the identification of a “closed form solution”. This result is very important, because the practical application of TPMC can now be carried out even with very simple hand calculations. The practical application of TPMC is herein presented with reference to the design of a multi-storey frame whose pattern of yielding is validated by means of both push-over analysis and incremental dynamic analyses.