PSI - Issue 78

Raffaele Laguardia et al. / Procedia Structural Integrity 78 (2026) 678–685

679

cycle (LC) approach. Within the literature, LC approaches have been widely adopted for economic assessment (i.e., Life Cycle Cost Assessment) and applied to structure and infrastructure systems (Padgett et al., 2010; Gencturk, 2013; Wei et al., 2016), only recently some contributions that accounts also for social and environmental aspects have been delivered (Mortagi and Ghosh, 2022; Welsh-Huggins et al., 2020; Dong and Frangopol, 2016). To perform a LC anal ysis, the beginning and the end of the product’s life must be adequately considered, as well as any possible event that may occur during its life, such as natural hazard events (e.g. earthquakes, floods etc.), therefore, considering the uncertain nature of those events, a probabilistic procedure is needed. Limiting the interest to the case of earthquakes, the reference methodology for this purpose is the one proposed by FEMA P-58 ATC (2012) that nowadays provides fragilities and consequences database for numerous structural and non-structural components and accounts for both environmental and economic aspects. Nonetheless, the economic and environmental loss assessment is often obtained by the means of Monte-Carlo approaches whose computational burden is not compatible with engineering practice. There is thus the need to provide new methods capable to pursue the goal of an integrated assessment of sustainable metrics by accounting for uncertainties and, possibly, reducing the computational e ff ort. Within the literature there are several contributions that tried to pursue this goal by the means of Multi-Criteria Decision Making (MCDM) pro cedures (Caruso et al., 2023, 2024; Clemett et al., 2023), multi-objective optimization algorithms (Park et al., 2018), economic equivalent assessment of environmental impacts (Lamperti Tornaghi et al., 2018; Calvi et al., 2016). A very broad state of the art review on the topic is provided in Passoni et al. (2021) and Menna et al. (2022). Among the various types of interventions suitable for sustainability-based design, dissipative bracing systems emerge as one of the most promising, due to their high flexibility, low material consumption, and reversibility. Moreover, they are highly compatible with integrated energy retrofit interventions, which are crucial to ensuring adequate building performance from an energy-e ffi ciency perspective, as highlighted in several works (Zanni et al., 2021; Menna et al., 2021; Di Bari et al., 2020; Passoni et al., 2020; Caruso et al., 2021; Labo` et al., 2020). These characteristics make them particularly appropriate within a life cycle thinking (LCT) approach, as they o ff er advantages throughout the en tire building lifespan, including ease of installation and removal, damage reduction through energy dissipation, lower maintenance requirements, and potential reusability at end-of-life. Given their potential, it becomes even more im portant to develop design methodologies that explicitly incorporate sustainability-oriented parameters, enabling more informed and e ff ective use of these technologies in both current and future renovation strategies. This work deals with an application of an optimal design method for a Buckling Restrained Braces (BRBs) system by minimizing an objective function that considers both economic and environmental aspects. At the same time, the safety requirements are guaranteed by the means of a constraint function that controls the Mean Annual Frequency (MAF) of exceedance of collapse limit state. The key features of the procedures stems from previous works on opti mization of bracing systems developed by the authors (Laguardia and Franchin, 2022; Laguardia et al., 2023, 2024) and rely on the use of SAC-FEMA approach (Cornell et al., 2002) for performance assessment, thus accounting for uncertainties, and on the use of Modal Spectral Analyses (MSAs) on linearized models for the structural response assessment. This paper provides a procedure for design of retrofit intervention through bracing that considers economic, en vironmental and social aspects. There are several ways to obtain this goal, multi-objective algorithms, MCDM ap proaches or economic equivalent ones. In this paper we propose a constrained single-objective optimization that accounts for economic and environmental aspects by the means of an economic-equivalency of environmental impact in the objective function formulation. At the same time, the social requirements are fulfilled by constraining the value of the MAF of collapse limit state, thus in terms of safety. The objective function considers the economic costs of intervention ( C I ) and seismic repair ( C S ), along with the environmental impacts of intervention ( I I ) and repair ( I S ), all expressed as functions of the brace areas, i.e., the in dependent variables (IVs) of the problem, as briefly described in this section. Since the economic cost is expressed through a monetary metric (i.e., e ) while the environmental impact is expressed in terms of Green House Gas emis sions (i.e., CO 2 , eq ), a conversion of the environmental impact in terms of monetary metric is performed by the means 2. METHODOLOGY