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

TLDR

The theory of Plastic Mechanism Control was developed in the 1990s for moment‑resisting frames and later extended to all major seismic‑resistant structural typologies. This paper presents new advances in applying Theory of Plastic Mechanism Control (TPMC) to design structures with a global collapse mechanism, introducing a closed‑form solution and a more systematic design approach. TPMC derives design conditions as inequalities on column plastic moments to prevent partial and soft‑storey mechanisms, originally solved iteratively, but this work provides a closed‑form solution and demonstrates its application to a multi‑storey frame validated by push‑over and incremental dynamic analyses. The closed‑form solution enables practical application of TPMC using simple hand calculations, as confirmed by the validated push‑over and incremental dynamic analyses. © 2014 John Wiley & Sons, Ltd.

Abstract

Summary 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’ and by the use of TPMC in a more systematic design approach. 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. Copyright © 2014 John Wiley & Sons, Ltd.