PSI - Issue 78

Elisabetta Bonaguro et al. / Procedia Structural Integrity 78 (2026) 1016–1023

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1. Introduction In urbanmasonrycluster buildings(UMCBs) the behavior ofasingle unitis stronglyaffected bythose attached to it,andthisinteraction depends on several factors,hinderingtheprediction ofseismicresponse. Surveys conducted in the last yearshaveconfirmed that structural units (SUs) aremoreor less susceptible to seismicdamage, depending on their position and their degree of interlocking with the attached ones (Borri et al., 2011; Formisano & Massimilla, 2018; Rete dei Laboratori Universitari di Ingegneria Sismica (ReLUIS), 2010). Retrofit interventions, whether on masonry walls or floors, add further complexity to the problem, adding the effect of stiffness variation between original and retrofitted units. Furthermore, the more extensive and fragmented the cluster is, the more combinations of retrofit it has. In fact, it can affect the full cluster or just portions of it. These portions can be either single units or even single flats, according to the subdivision of a building in levels. In this framework, the Italian academic consortium ReLUIS has set a draft of guidelines (2010) for the study of UMCBsandtheirretrofit.Moreover,therecommendations tothereconstruction plansofearthquake-damagedhistoric centres emphasize the importance of carrying out interventions extended over full UMCBs or at least two or more units, when they are structurally or functionally interconnected (Perrone, 2021). However, due to the fragmented ownership of UMCBs and the voluntary nature of retrofit agreements between owners before the emergency phase, seismic retrofit applied only to portions of an aggregate is common and its effects are yet to be assessed. Studies concerning thistopicare still scarce, most of them adopting Equivalent Framemodellingstrategies, useful to quickly obtain global analysis but unable to provide a detailed assessment of stress and strain distributions. This theme can be investigated through the application of retrofit at different extents in a cluster, comparing the transmission of stresses between flexible andrigid slabs, asdid bySorrentino& Fumagalli (2012) and Longobardi & Formisano (2023). Results from non-linear static analyses show that localized floor strengthening lead to worse conditions, concentrating damage where no retrofit has been made; on the other hand, global interventions allow for a significant increase in capacity. Vicente et al. (2011) focused on the dynamic response of a full UMCB, applying increasingly invasive retrofit strategies but always considering the full UMCB: the effect of each technique is evaluated by comparing natural frequencies. This study employs finite element modelling (FEM), allowing to represent also local mechanisms. A similar approach is adopted by Villar et al. (2024), who develop a refined FEM model in OpenSees, in order to evaluate the so- called “cluster effect”, in terms of variations both in the interconnectivitybetween SUs and in the stiffness of floor diaphragms. By combining the approaches adopted in these works, this paper aims to provide an evaluation of the effect of diaphragms strengthening, applied at various scales in a UMCB, both in an individual SU and in a full cluster, considering a unitaryor partial approach. Unitaryretrofit affects all the diaphragms of either a SUor the full cluster, instead a partial one applies only to a subset of them; however, to limit the possible combinations in the case of the full cluster, if individual diaphragms are considered, partial retrofit is applied unitarily to SUs, i.e. to portions of the cluster, coincident with the single SUs. Results are obtained in terms of base shear and displacement capacity of a reference unit, considered both individually and clustered, from non-linear static analyses, developed using FEM modelling with the DIANA FEA software. Preliminarily, a sensitivity analysis is carried out for defining a floor stiffness scale of diaphragms, considering the effect on dynamicanalyses ofsuitable mechanical propertiesfor representing simpletimber, strengthenedtimber and ribbed concrete structures assigned to both floors and roofs. 2. Methodology 2.1. Case study modeling strategies The case study is a UMCB composed of four terraced houses and located in Castelsantangelo sul Nera (Macerata District): being placed on the slope of a mountain, the two main elevations (north and south) have a different number of floors. Considering a subdivision according to the static vertical loads proposed by the Italian seismic code (MIT, 2018), four structural units (SUs) are identified, two end units and twomid ones, resulting from various construction phases.