PSI - Issue 78

Parvane Rezaei Ranjbar et al. / Procedia Structural Integrity 78 (2026) 615–622

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1. Introduction One of the primary factors contributing to seismic vulnerability is the outdated nature of much of the existing building stock. A significant number of structures were built before the adoption of modern seismic codes, meaning they were not designed to resist lateral seismic forces and often lack adequate detailing for ductile response. This issue is particularly pronounced in areas where buildings were constructed before local authorities had even classified them for seismic risk, resulting in designs based solely on gravity loads. Given this scenario, especially in countries like Italy, assessing and mitigating seismic risk has become a matter of strategic importance. It is essential not only for protecting public safety but also for informing seismic retrofitting strategies and determining how resources should be allocated for strengthening both public and private infrastructure (Rosti et al. , 2021). Among the innovative solutions developed for strengthening vulnerable reinforced concrete (RC) buildings, the use of external dissipative exoskeletons has emerged as a particularly promising approach. These systems consist of steel substructures attached to the exterior of buildings and are designed to provide enhanced seismic performance with minimal disruption to occupants. Unlike conventional retrofitting methods that often involve invasive interventions and require temporary building closures, exoskeletons can be installed while the structure remains in use. Their reversibility and ability to be integrated with energy-efficiency upgrades further add to their appeal. Recent advancements (Ferraioli et al. , 2022, 2023, 2025a-c) have introduced various exoskeleton configurations, such as parallel and orthogonal layouts, and rocking systems equipped with components like shape memory alloy (SMA) devices or prestressed cables that improve re-centering capacity and reduce residual drift following seismic events. The advantages of this retrofit strategy are numerous: modularity and reversibility (allowing for future upgrades or removal without damaging the original structure); efficient installation (making it ideal for critical facilities such as schools and hospitals); cost effectiveness (due to reduced need for occupant relocation and minimal operational disruption); improved seismic performance (offering enhanced strength, ductility, and energy dissipation in line with current performance-based design standards). The flexibility of these systems, whether applied parallel or orthogonal to the building façade, also allows them to be adapted to various architectural and spatial constraints. To quantitatively assess the benefits of such retrofitting measures, fragility curves are often used. These probabilistic tools estimate the likelihood of a structure experiencing specific damage levels under different seismic intensities. By analyzing and comparing the fragility curves before and after retrofit implementation, engineers can measure the reduction in damage probability and gain a better understanding of how the intervention has improved the building’s seismic resilience. Defining the limit states and their associated damage levels is a crucial step in developing fragility curves, as these definitions significantly influence the outcomes. This study conducts a detailed damage assessment of a real case prototype structure retrofitted with a rocking exoskeleton system to establish appropriate limits and damage states for both the existing and retrofitted configurations. 2. Fragility curves 2.1. State-of-the-art overview The fragility curves - probabilistic tools used to estimate the likelihood of structural damage under different levels of seismic intensity - were first developed in the 1970s and 1980s. Their earliest and most significant applications emerged in the nuclear industry, where they were employed to assess the seismic safety of nuclear power plants. In this field, simplified frameworks like the Safety Factor method (Kennedy and Ravindra, 1984) offered practical efficiency by estimating fragility using deterministic safety margins. The seismic vulnerability assessment of buildings at large geographical scales was first carried out in the early 70’s, through the employment of empirical methods initially developed and calibrated as a function of macroseismic intensities. Within this context, fragility curves are fundamental tools in probabilistic risk assessment, which provide the conditional probability that a structure exceeds a given damage threshold under specific hazard intensities. In the 1990s, fragility curves began to be applied to non nuclear civil structures, such as buildings and bridges, often in the context of loss estimation and risk analysis (e.g., FEMA 366, HAZUS, 1999). Nowadays, their application extends to a wide range of hazards, including floods, landslides, and structural systems in both nuclear and civil infrastructures. Different methods for fragility curve construction can be broadly divided into empirical, analytical, and hybrid approaches. Analytical techniques, such as