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

Elide Nastri,Alessandra Longo,Vincenzo Piluso

doi:10.2174/1874836801408010262

Elide Nastri, Alessandra Longo

Open Access

https://doi.org/10.2174/1874836801408010262

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Abstract

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.

Highlights

A fundamental principle of capacity design of seismicresistant structures is that plastic hinge formation in columns during an earthquake should be avoided, in order to make sure that the seismic energy is dissipated by the preselected dissipative zones only
The advances presented in this paper provide, on one hand, an unitary presentation dealing with Moment Resisting Frames (MRFs), MRF-Eccentrically Braced Frames (EBFs) dual systems and MRF-Concentrically Braced Frames (CBFs) dual systems and, on the other hand, provide a closed form solution starting from the observation that type-1 mechanism and type-3 mechanism for are coincident, while type-2 mechanism for is just the desired mechanism, i.e. the global one
It is interesting to point out that, if reference is made to the peak ground acceleration leading to ultimate conditions, the best seismic performance is gained by means of the MR-Frame, because, due to its high lateral deformability compared to dual systems, the increase of the period of vibration leads to a significant increase of the PGA value corresponding to the attainment of the spectral acceleration value leading to collapse

Summary

INTRODUCTION

A fundamental principle of capacity design of seismicresistant structures is that plastic hinge formation in columns during an earthquake should be avoided, in order to make sure that the seismic energy is dissipated by the preselected dissipative zones only. Moment Resisting Frames (MRFs) are the most common seismic-resistant structures They are characterized by high dissipation capacity, because of the large number of dissipative zones under cyclic bending represented by the beam end sections. Such structural system could be not able to provide sufficient lateral stiffness, as required to fulfil serviceability limit states. The exploitation of the dissipative capacity of the beam ends, of the lateral stiffness provided by the diagonals of the braced part and of the dissipation capacity of link elements allow to obtain high global ductility and limited inter-storey drifts, so that both the ultimate and serviceability limit state requirements can be satisfied. A comparison in terms of structural weight of the designed structures and the corresponding seismic performances are discussed

Basic Principles

Mechanism Equilibrium Curves

Column Design Requirements to Prevent Undesired Collapse Mechanisms

WORKED EXAMPLE

VALIDATION OF THE DESIGN PROCEDURE

STRUCTURAL WEIGHT AND ECONOMIC ISSUES

Findings

CONCLUSION