PSI - Issue 84

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

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The initial cost considers both structural and labor expenses, as well as the cost of the fire protection system. Maintenance costs are evaluated according to Miano et al., 2019, as: C M =∫ C m e −λ d t dt = C m λ d (1−e −λ d t life ) t life 0 (2) - where l is the annual discount rate (3%). Direct fire damage costs are estimated using empirical fragility curves, which relate damage state to proportional repair costs relative to the bridge replacement value, based on HAZUS datasets: D D =EL STR =FV STR RV B ∑ (PSTR PLi ∙ STRD PLi ) n i=1 (3) Here is the expected repair cost, the fraction of replacement value for structural components FV STR , the total replacement value RV B , the probability of reaching a performance level PSTR PLi , the repair cost ratio for that level STRD PLi . Indirect damage captures broader socio-economic impacts, estimated using the empirical formulation of Hicks and Liebermann (Hicks, 1979): = ( ) (4) where and b depend on the event scale and severity. Overall, this cost-benefit model allows the comparison of scenarios with and without passive fire protection, providing a practical tool for evaluating sustainable and economically efficient fire safety strategies over the bridge life cycle. 3. Application The proposed methodology is applied to a typological steel–concrete composite (SCC) bridge previously investigated in the literature (de Silva et. At 2025). Fire fragility analyses are carried out for five structural configurations: an unprotected bridge and bridges protected with sprayed fire-resistant plaster layers of increasing thickness (10, 14, 20, and 30 mm). The aim is to evaluate the effectiveness of passive fire protection in mitigating the fire-induced vulnerability of a typical SCC bridge and to support the design of such protection by considering structural performance and life-cycle costs. The bridge consists of four simply supported spans, three with a length of about 30 m and one of approximately 20 m. The analyses focus on the longest span, which also exhibits the minimum vertical clearance between the ground and the deck intrados (about 7.95 m), and is therefore identified as the most fire-critical configuration. The structural scheme is modelled as simply supported, with one fixed bearing and the remaining ones allowing longitudinal sliding. The main geometric and mechanical parameters of the typological SCC bridge are summarized in de Silva et al. 2025. The applied loading scheme follows the exceptional load combination prescribed by the Eurocodes and the Italian Technical Standards, Traffic loads are neglected, since their combination factor is equal to zero under fire conditions according to the relevant standards. Temperature-dependent material properties for steel and concrete are defined in accordance with EN 1992-1-2 and EN 1993-1-2. The thermo mechanical analyses of the typological SCC bridge were performed using the validated SAFIR software, extensively applied to structural and infrastructural systems, including bridges and tunnels. The bridge model included main and cross beams as well as the concrete deck, focusing on a single span identified as critical under fire conditions. An isostatic scheme was adopted to maximize displacements and allow longitudinal thermal expansion, minimizing restraint-induced stresses, consistent with previous observations (de Silva, 2025). Boundary conditions were applied at the beam supports: one end fully restrained in both directions, the other fixed transversely while allowing rotations around the beam axis. Structural components were modelled using beam elements for the girders and cross beams, and shell elements for the deck, discretized into a quadrilateral mesh of approximately 0.3 m × 0.3 m. The analyses accounted for both geometric and material nonlinearities, and simulations were run until either the end of the thermal transient or structural collapse, depending on the scenario. 3.1. Fire scenarios and fire modelling and passive protective modelling The fire scenarios were defined by considering fires generated by vehicles located beneath the bridge deck. Each vehicle category was associated with a representative HRR curve derived from experimental results or literature sources, as in a previous work by de Silva et al., 2025. Previous studies have shown that fire events involving more than one vehicle are plausible and should be included in probabilistic vulnerability analyses. In such cases, the overall fire scenario can be modelled by superimposing the HRR curves of individual vehicles. The same combined fire