PSI - Issue 78

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

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involving multiple vehicles, the IM is defined by combining the HRR curves of each vehicle (Italian Fire Prevention Code, 2015), weighted based on the distance from the nearest structural member, with a full contribution (100%) for the closest vehicle, zero for those beyond 20 meters, and proportional for intermediate ones. This approach allows for a realistic representation of heat propagation within the structure. To develop the fragility curves, a linear logarithmic regression is applied to describe the relationship between the demand-to-capacity ratio Y and intensity measure, IM: (1)

(2)

where η Y|IM and σ logY|IM are the median and logarithmic standard deviation for Y , given IM . The fragility function, defined as the probability that Y exceeds the critical threshold, is expressed as:

(3)

Therefore, to define the fragility function, the analysis results are first mapped in terms of demand-to-capacity ratio. Subsequently, the parameters in Eq. 3 are estimated for each intensity measure and performance level consid ered, thereby completing the probabilistic characterization of structural fragility. 2.3. Fire scenarios selection and advanced thermo-mechanical analyses The thermo-mechanical analyses, carried out using the software SAFIR ® (Frannsen and Gernay, 2017), assess the structural response under various fire scenarios. The selection of these scenarios is crucial to realistically represent structural behaviour under emergency conditions. Scenarios are primarily described by heat release rate (HRR) curves, whic h quantify the thermal power over time and are characterized by means of peak value (HRRₚₑₐₖ) and fire load, i.e., the integral of HRR over time. These scenarios are selected based on building type and functional use, covering a wide range of intensities to ensure a comprehensive assessment of fragility. The analyses include both protected and unprotected structures, accounting for the evolution of the chemical and physical properties of passive fire protections, modelled through experimentally calibrated simplified correlations. 2.4. Life cycle cost-benefit analysis framework The Life Cycle Cost-Benefit Analysis (LCCA) is developed with the aim of comparing the unprotected configura tion and the one equipped with fire protection measures in terms of economic sustainability. The methodology follows the model proposed by Chenzhi Ma et al. (2024), defining the total life-cycle cost as: (4) The term C 1 represents the initial cost of the structure, including any additional cost for the protection system. The contribution C M accounts for maintenance costs related to both the structure and the protective system, while D D and D ID quantify, respectively, the direct and indirect damages, both linked to the probability of exceeding the considered performance level. The estimation of maintenance costs is based on the approach formulated by Miano et al. (2019) , according to which the discounted expenditure is calculated as: = 1 + + + = � − = (1 − − ) 0 (5)