PSI - Issue 78

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

1228

plaster is economically advantageous, as the expected total costs are lower compared to the unprotected configuration. Furthermore, the analysis highlights the positive impact of increased protective thickness: as the intensity measure rises, a 2 cm thick protection significantly reduces the structure’s vulnerability, resulting in decreased expected losses and, consequently, lower overall costs throughout the entire life cycle.

Fig. 6. Cost-benefit curves. (a) IM: fire load, (b) IM: HRR peak .

5. Conclusions This study proposes a methodology to assess the fire vulnerability of industrial steel buildings through fragility curves, derived using cloud analysis, and perform life cycle cost analysis to identify the optimal fire protection strat egy. The method was applied to a representative typological structure, common in the Italian context, analysing 36 realistic fire scenarios and three performance levels (PL-III, PL-IV, and PL-V), each with thresholds differentiated for trusses and columns. The results show that fragility increases with the performance level, with the curves for PL-V exhibiting lower median values of the intensity measure (IM) and less dispersion. As expected, the unprotected con figuration is significantly more vulnerable to fire, while passive protection with sprayed plaster effectively reduces fragility. The plaster thickness has a notable impact: increasing from 1 cm to 2 cm results in a significant improvement in performance, especially at higher fire intensity levels. From an economic perspective, the cost-benefit analysis conducted over a 50-year life cycle (with a 3% discount rate) shows that, for low to medium values of the intensity measure, passive fire protection is economically convenient, as the expected total costs are lower compared to the unprotected configuration. Furthermore, increasing the thickness of the protective layer leads to additional cost reduc tions due to the decreased probability of exceeding the limit states. References Eurocode 1. EN 1991 –1–2: Actions on structures - Part 1–2: General actions – Actions on structures exposed to fire. Brussels, Belgium; 2002. Eurocode 3. EN 1993: Design of steel structures. Brussels, Belgium; 2005. Eurocode 8. EN 1998: Design of structures for earthquake resistance. Brussels, Belgium; 2004. Frannsen J.-M., Gernay T. (2017). ‘Modeling structures in fire with SAFIR®: Theoretical background and capabilities’, Journal of Structural Fire Engineering, Volume 8(3), 300 -323. Heskestad G. (1984). ‘Engineering relations for fire plumes’. Fire Safety Journal, 7, 25 -32. Italian National Code for fire prevention - D.M. 03/08/2015 (in Italian). Jalayer, F., Ebrahimian, H., & Miano, A. (2020). Intensity-based demand and capacity factor design: A visual format for safety checking. Earth quake Spectra, 36(4), 1952 - 1975. Ma C., Van Coile R., Gernay T. (2024). ‘Fire protection costs in composite buildings for cost-benefit analysis of fire designs’, Journal of Constructional Steel Research, Volume 215, 108517. Miano, A., Sezen, H., Jalayer, F., & Prota, A. (2019). Performance -based assessment methodology for retrofit of buildings. Journal of Structural Engineering, 145(12), 04019144. National Institute of Building Science (NIBS) (2003). HAZUS-MH MR1 Technical Manual, Developed by the Federal Emergency Management Agency, Washington, D.C. Society of Fire Protection Engineers. (SFPE) (2002). Handbook of Fire Protection Engineering* (3rd ed.). National Fire Protection Association. Tondini N., Thauvoye C., Hanus F., Vassart O. (2019). ‘Development of an analytical model to predict the radiative heat flux to a vertical element due to a localised fire’. Fire Safety Journal, 105, 227-243. Venezia V., Portarapillo M., de Silva D., Cibelli A., Luciani G., Bianco N., Nigro E., Di Benedetto A. (2025). ‘Morphological, Physico‐Chemical, and Thermal Characterization of Non‐Reactive Protective Materials for Steel Structures’. Fire and Materials, 0, 1-15.