PSI - Issue 44

Devis Sonda et al. / Procedia Structural Integrity 44 (2023) 115–122 Devis Sonda et al. / Structural Integrity Procedia 00 (2022) 000–000

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1. The energy-based approach Industrial precast RC buildings usually have a very simple structural scheme consisting in single-storey isostatic frame structures with columns fixed at the base supporting beams and roof elements. There are not many specific methodologies currently documented to quickly evaluate seismic behavior for this type of structure (Calvi G.M. et al. 2006; Bovo M. et al. 2022). The currently available rapid assessment methodologies quantify the seismic vulnerability through the attribution of a capacity to the structure compared with the seismic input of the site, defined by the building code (Mazzotti C. et al. 2013, De Matteis G. et al. 2019). The procedure proposed in this paper considers the balance energy between seismic input and structural response. An earthquake causes effects on structural masses by creating a motion that can be described through dynamic equations, which give an instant description of the behaviour of the structure. To consider the global effects of the seismic action on a structure, the earthquake should be described as the application of energy to the structure. The seismic event is a stochastic input to the structure and is governed by different parameters: intensity, duration, frequency content, etc. The energy represents the integral of different parameters that describe the seismic motion and therefore it is a synthetic description of seismic action. In structural engineering, seismic vulnerability assessment is intended as an approximated procedure, aimed at quantifying the seismic adequacy of the structure respect to a target earthquake defined for the site with a probabilistic approach. Each earthquake is characterized by specific energy content and the site target earthquake has a defined energy content. The building code defines the characteristics of a specific earthquake, through a response spectrum which represents a synthesis of the parameters that describe the seismic motion for a given site. The code provisions, aimed at guaranteeing the formation of stable dissipative mechanisms, implicitly also consider the duration of the seismic action and, therefore, the energy absorbed by the structure. Designing an anti-seismic structure means following the criteria of the seismic code to create a building capable of dissipating part of the energy and deforming without collapsing. Evaluating the seismic vulnerability of an existing structure, in terms of energy, means quantifying how far the structure is from the ideal situation of the new anti-seismic building. An energetic approach in quantifying the seismic action has the advantage of considering all its different parameters together, starting with intensity and duration. In addition, energy is a measure of the effects of seismic action on structures including resistance, displacements, and hysteretic dissipation of the structure (Dindar A.A. et al. 2015). In general terms, the energy equation can be derived from the motion equation, and, for a single degree of freedom (SDOF) system, it is possible to write: 3 . 2 . ) 4 2 5 0 / 3 + (1) where, in addition to the obvious meaning of the symbols used, it is assumed: 3 + = ground acceleration; ) 4 2 5 = return force as a function of displacement and velocity. The integration considering the relative displacement, as proposed by Chopra A.K. (1995), leads to the equation of relative energy. 3 - . 2 - . ) 4 2 5 - 0 / 3 - + (2) The relative energy does not significantly differ from the absolute energy if we do not consider rigid motions and it is more significant in structural engineering (Choi H. et al. 2009). Setting 0 2 , the equation can be written, again with reference to a SDOF system: 3 2 , . 4 2 5 , . ) 4 2 5 2 , 0 / 3 , + 2 (3) Then, we can define: Kinetic Energy E K = 3 2 , Damped Energy E D = 4 2 5 , Absorbed Energy E A = ) 4 2 5 2 , Seismic Input Energy E I = / 3 , + 2 .