PSI - Issue 84

Donatella de Silva et al. / Procedia Structural Integrity 84 (2026) 1353–1360

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(SC2). In this study, PL III and PL IV are considered as representing the most relevant states for post-fire functionality and resilience assessment. The analysis is limited to the SC1 criterion, which governs the structural response under fire exposure and provides a conservative measure of instantaneous vulnerability. 2.1. Fire scenarios selection and advanced thermo-mechanical analyses and modelling of passive fire protection In structural fire engineering, defining representative fire scenarios is essential to evaluate the thermal and mechanical response of bridges under realistic conditions. Scenarios are characterized by intensity, duration, and spatial distribution, with the Heat Release Rate (HRR) curve playing a central role (de Silva, 2022). Realistic scenarios may include single or multi-vehicle fires, depending on traffic and risk conditions. Thermal analyses consider different vehicle types, each with a specific HRR curve, to investigate structural response under varying fire intensities. Numerical modelling then computes the transient temperature field, heat transfer within sections, and resulting thermo-mechanical response, including stresses and deformations.For open-air fires, such as on bridges, flashover is unlikely (de Silva, 2023), so simplified models like the Hasemi correlation (EN 1991-1-2, Annex C) are generally sufficient, while CFD simulations are used for enclosed or highly non-uniform fires. Temperature-dependent material properties are defined according to EN 1992-1-2 and EN 1993-1-2, accounting for strength and stiffness degradation at elevated temperatures. Passive fire protection is essential for maintaining the structural performance of steel elements exposed to high temperatures, as steel’s high thermal conductivity causes rapid heating under fire conditions. Without adequate protection, structural components can reach critical temperatures quickly, threatening overall stability. Common passive protection systems include intumescent coatings (de Silva et al. 2017, Lucherini et al. 2018, Weisheim and Schaumann 2019, Yasir 2020), which expand to increase thermal insulation; insulating panels (Hopkin et al. 2012, Dodangoda et al. 2019, Steau and Mahendran, 2021, Zehfuss, J., and Sander, 2021), applied to surfaces to slow heating; and cementitious or spray-applied plasters (Braxtan and Pessiki, 2011, Kodur and Shakya, 2013, Zhang et al. 2021), which provide a uniform protective layer directly on steel. In this study, spray-applied plaster was used on steel elements for thermo-mechanical simulations. Both bare and protected structures were analyzed to evaluate the effectiveness of the passive layer in reducing heating and delaying structural failure. The plaster was modelled using thermo-physical properties from experimental studies (Venezia et al 2025, Cibelli et al. 2025), which provide temperature-dependent correlations for thermal conductivity, specific heat, and density, enabling realistic implementation within the SAFIR numerical model. 2.1. Fragility assessment and life cycle cost assessment and cost-benefit analysis Fragility curves represent the probability that a structure exceeds a given performance level under a specific fire intensity. In this study, a log-linear regression is used to link the structural demand, expressed as the maximum demand-capacity ratio (DCR PL ), to fire intensity parameters, following an approach analogous to Cloud Analysis (Jalayer et al, 2020, Jalayer et al., 2021, Miano et al. 1024) in seismic engineering, largely used in literature (Miano et al., 2024). DCR PL is defined as the ratio between the maximum vertical displacement of the deck and the displacement limit for the selected performance level, as in de Silva et al., 2025.Two fire-related intensity measures (IMs) are considered due to their strong correlation with structural response: the peak heat release rate, especially relevant for steel elements, and the fire load, which better reflects duration effects for materials with high thermal inertia, such as reinforced concrete (de Silva, 2022). These curves provide a probabilistic measure of vulnerability and are fundamental for linking fire intensity to expected structural performance. The Life-Cycle Cost Analysis (LCCA) is used to assess the long-term economic performance of different bridge configurations, comparing the unprotected structure with those equipped with passive fire protection layers of varying thicknesses (10, 14, 20 and 30 cm). The approach follows the model proposed by Ma et al. 20240, in which the total present value of life-cycle costs (PVLCC) is expressed as: PVLCC=C 1 +C M +D D +D ID (1) where C 1 is the initial construction cost, including installation of fire protection; C M is the discounted life maintenance cost of both structural and protective elements; D D is the direct damage cost, corresponding to repair or replacement following a fire; and D ID accounts for indirect losses such as business interruption and service downtime.