GNGTS 2022 - Atti del 40° Convegno Nazionale

306 GNGTS 2022 Sessione 2.2 empirical, hybrid or expert judgment elicitation approaches. In particular, in order to assess the vulnerability of a glass façade, the empirically based approach has been the most used so far. In general, glass cracking or fall-out and gasket seal degradation are indicated as collapse references as a consequence of the observed experimental failures. The research work of O’Brien et al. (2012) embodies several experimental campaigns addressed by different authors (Behr, 1998; Behr A.R. and Belarbi A., 1996; Memari et al. , 2003; Memari et al. , 2011) with the aim of deriving fragility curves for 15 glazing system configurations, in which variable features include materials, panel sections and geometrical properties. Firstly, the seismic evaluation of glass systems response in terms of probability of damage, for each damage state considered, need to identify the inter-story drift ratios as EDP (engineering demand parameter) which was obtained from test results. Therefore, the Method A and Methods B were used to derive the dynamic fragility curves depending on the occurrence of the failure. As can be easily deduced, the disadvantages of using the empirical approach relate to the availability of specific testing machines, significant time and high costs. Consequently, an analytical procedure was proposed by Nuzzo et al., 2020 based on the same configurations in order to investigate the accuracy of the method by a comparison of results. Further support is given by the application of numerical Cloud Method (Jalayer et al., 2014) in Mattei S. and Bedon C. (2021) by considering structural and non-structural glass systems, with different geometries and boundaries. In this case, the extended and expertly developed numerical modelling in a Finite Element software is a required contribution. Discussions of results. In order to determine the dynamic response of a structure it is necessary to carry out an analysis of the vibrations induced on it by external actions or by assigned initial boundary conditions. Vibration means a mechanical oscillation around an equilibrium point, and can be harmonic, periodic or random. Recalling also the D’Alembert’s principle of dynamic equilibrium, a system is in equilibrium at each time instant if all the forces acting on the mass are considered (the elastic or inelastic resisting force f S , the damping resisting force f D and the arbitrary external force p(t)) including the fictitious inertia force f I : (2) Moreover, the system is assumed to have linear viscous damping, instead for the contribution of static force, both hypotheses of elastic and inelastic behaviour of the system are considered. Thus, the two equations of motion governing the response of a single degree of freedom system are reported as function of displacement u, velocity u. and acceleration ü : (3) Where m, b and k represent respectively the mass, the critical damping factor and the stiffness of the SDOF system. Finally, ü g ( t ) denotes the seismic input applied to the overall system, i.e. the ground acceleration. On the other hand, for inelastic systems the Eq. 3 should be replaced by Eq. 4: (4) Where f s (u) is the inelastic resisting force. The closed-form solution of these equations does not exist because of the variability of the action and the non-linearity of the system. This type of problem can be solved numerically for each time step i , having each accelerogram as discretized with a constant Δt equals to 0.005 s.