PSI - Issue 78

Eleonora Bruschi et al. / Procedia Structural Integrity 78 (2026) 49–56

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The retrofit intervention is designed to upgrade the buildings for a seismic demand corresponding to high-seismicity conditions, simulating an update in seismic hazard maps or code regulations. The target seismic demand corresponds to the Life-Safety Limit State (LLS) as per D.M. 2018 for two reference sites in southern Italy: Benevento (Latitude 41.1305°, Longitude 14.787°) and Tramutola (Latitude 40.3176°, Longitude 15.7919°). Both are classified as seismic zone 1 in the former national seismic classification (OPCM 3274). For both sites, a nominal life =50 years and a use class coefficient =1.0 (typical for residential buildings) are assumed, resulting in a reference life = ⋅ =50 years. Topographic conditions are set as T 1 , while soil classes are type B for Benevento and type C for Tramutola. The corresponding design PGAs are 2.94 m/s² for Benevento and 3.41 m/s² for Tramutola. It should be noted that this study is developed as a pilot investigation, focusing on two specific sites. However, future developments will extend the methodology to additional locations with varying seismic and geotechnical conditions to broaden the applicability of the results. The retrofit solution consists of the installation of diagonal steel braces equipped with hysteretic dampers (referred to as damped braces ), placed on the facades — four units per floor in both principal directions (X and Z) — according to the layout in Fig. 1. The hysteretic devices are modeled with an elastic-perfectly plastic behavior, characterized by a bilinear force – displacement relationship, as shown in Fig. 2. The key design parameters include the yield force ( V dbd ), the design displacement ( d bd ), the ultimate displacement ( d u ), the elastic stiffness ( K D ), and the damper ductility factor ( µ D ), defined as the ratio between the design displacement and the yield displacement ( d bd / d y ). The devices are sized to ensure that their ultimate displacement capacity ( d u ) is sufficient to accommodate the displacement demands across the considered hazard levels.

Fig. 2. Elastic-perfectly plastic behavior assumed for the dampers and typical values of µ DB and ξ DB of hysteretic damped braces, resulting from the combination of µ D and K B /K D

The damping system is designed to achieve the Immediate Occupancy performance level, which ensures that the structure remains fully operational and accessible after the design earthquake (return period T R of 475 years, equivalent to a 10% probability of exceedance in 50 years), with no compromise in the strength or stiffness of the primary structural elements. To meet this objective, the Direct Displacement-Based Design (DDBD) procedure, developed by the authors in previous studies (Bruschi et al., 2022a; Bruschi et al., 2023), is applied, which allocates damper stiffness and strength to match the first-mode response of the original structure. This methodology is particularly suited for low- to mid-rise buildings with regular configurations, similar to the case-study buildings. The design considers ranges of ductility ( µ DB ) and equivalent damping ratio ( ξ DB ) for the damped braces, as reported in the Table of Fig. 2, where K B /K D is the ratio between the stiffnesses associated to the steel brace K B and the damper K D , respectively, and is taken ≥ 2 in order to guarantee that the largest part of the deformation of the story is concentrated in the damper. These values are selected to reflect typical parameters commonly found in the literature (Bruschi et al., 2022a,b; Bruschi et al., 2024a,b; Nuzzo et al., 2019; Gandelli et al., 2019) and are representative of currently available commercial devices.