PSI - Issue 78

Antonio Cibelli et al. / Procedia Structural Integrity 78 (2026) 1221–1228

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temperatures, passive fire protection systems (e.g. boards, intumescent coatings, sprayed plaster) are generally adopted. The design of the protective layer must consider not only technical effectiveness, but also economic sustain ability. In this study a comprehensive methodology, based on advanced thermo-mechanical analyses and the derivation of fragility curves, is presented and validated through the application to a representative steel building, intended for vehicle storage. The analysis is carried out on both the unprotected structure and on configurations protected with sprayed plaster of different thickness. Finally, a cost-benefit analysis is developed, aimed at comparing protective strategies in terms of performance and associated installation and maintenance costs. The goal is to provide quantita tive criteria to support optimized design choices in terms of both safety and cost-effectiveness. 2. Methodology for building fire fragility assessment The proposed methodology is structured in five phases and is aimed at (i) assessing the fire fragility of industrial steel buildings and (ii) developing a cost-benefit evaluation, based on feasible fire scenarios. In the first phase, repre sentative structural typologies and relevant fire scenarios are identified, along with the definition of reference Key Performance Indicators (KPI), such as deformations, displacements, and internal forces. The second phase involves performing thermo-mechanical analyses for the selected scenarios to evaluate the structural behaviour under natural fire exposures. These analyses account for material degradation at high temperatures. In the third phase, target perfor mance parameters, such as the maximum mid-span deflection of the beam and the horizontal displacement at the top of the column, are collected. The first three phases are repeated for all fire scenarios deemed relevant for the structural typology under investigation. The fourth phase focuses on the evaluation of demand-to-capacity ratios (DCRs) and the derivation of fragility curves using the Cloud Method (Jalayer et al, 2020). Finally, in the fifth phase, a life-cycle cost-benefit analysis is conducted for each scenario. This analysis, based on the previously derived fragility curves, allows to estimate the expected costs and benefits associated with different fire protection strategies, thereby support ing a more aware and optimized decision-making process within the design of passive protection. 2.1. Performance levels International standards (EN 1991‑1‑2 , 2002) and national regulations (Italian Fire Prevention Code, 2015) define five performance levels for structural fire response. The first refers to the absence of external consequences in the event of collapse, while the second ensures sufficient fire resistance time to allow for safe occupant evacuation. The third, identified with conventional structural failure, requires that the structure maintains its resistance for the full duration of the fire. The fourth applies to cases where the structure sustains limited damage and acceptable defor mations but retains essential integrity, whereas the fifth level implies full operational functionality is preserved after fire exposure. In this study, Performance Level III is considered as conventional structural collapse, while Levels IV and V represent, respectively, limited damage and full functionality after fire exposure. To quantify structural capacity, these performance levels are translated into threshold KPI values, selected by the authors based on the structural typology. In this work, the adopted KPIs are: (i) the maximum mid-span deflection of the beam and (ii) the maximum horizontal displacement at the top of the column. For Performance Level V, the allowable deformations are limited to L/200 for beams and h/150 for columns, in compliance with standards which ensure full structural operability under characteristic loads. For Performance Level IV, the limit is set to L/100 for both parameters (Italian Fire Prevention Code, 2015). The loss of load-bearing capacity R, associated with Performance Level III, is assumed to occur once the critical deflection is reached, defined as L²/400d. 2.2. Derivation of fragility curves Fragility curves are derived for both unprotected and protected steel structures with respect to Performance Levels III, IV, and V using the Cloud Method, which integrates the results of advanced thermo-mechanical analyses into a probabilistic model based on linear logarithmic regressions (Jalayer et al, 2020). Each fire scenario is characterized by two intensity measures (IMs): (i) fire load q fd and (ii) peak heat release rate HRR peak . In case of complex scenarios