Theory of Plastic Mechanism Control: State-of-The-Art

In this paper, the state-of-the-art regarding the “Theory of Plastic Mechanism Control” (TPMC) is 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 steel 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. Even though the set of inequalities was originally solved by means of an algorithm requiring an iterative procedure, now, thanks to new advances, a “closed form solution” has been developed. This result is very important, because the practical application of TPMC can now be carried out even with very simple hand calculations. In order to show the simplicity of the new procedure, numerical applications are herein presented in detail with reference to Moment Resisting Frames (MRFs) and dual systems both composed by Moment Resisting Frames and Eccentrically Braces Frames (MRF-EBFs) with inverted Y scheme and composed by Moment Resisting Frames and Concentrically Braced Frames (MRF-CBFs) with X-braced scheme and V-braced scheme. Finally, the pattern of yielding obtained is validated by means of both push-over analyses and incremental dynamic analyses. A comparison in terms of structural weight of the designed structures is also presented and the corresponding seismic performances are discussed.

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