PSI - Issue 78

Pasquale Bencivenga et al. / Procedia Structural Integrity 78 (2026) 1545–1552

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As can be observed, the evolution of design codes over time corresponds to a gradual decrease in bending moment capacity ratios, with average values decreasing from 3.19 for the 1939 code, to 2.72 for the 1972 code, and down to 2.30 for the 1980 code. Despite the apparent linear trend, a significant dispersion in the capacity ratios should be noted. This scatter is particularly pronounced for the 1939 code, where a coefficient of variation (C.o.V.) exceeding 30% was observed. For the more recent codes, the C.o.V. remains substantial, around 20%. To identify the parameters that most significantly influence the results, correlations between each input variable and the bending moment ratios were investigated for every design code. In particular, the Spearman correlation coefficient was used, as it captures the presence of monotonic relationships (where 0 indicates no correlation, +1 indicates perfect positive correlation, and –1 indicates perfect negative correlation). The results are summarized in Table 4.

Table 4 – Spearman correlation of the analyzed parameters

H B f yk 1939 -0.03 0.03 0.46 -0.07 -0.81 - 1972 -0.03 0.01 0.63 -0.03 -0.60 0.28 1980 -0.08 -0.03 0.41 -0.04 -0.74 0.30 ρ ρ'/ ρ R ck

As expected, in all cases, the most influential parameters were the material properties and the tensile reinforcement ratio ρ. A seemingly contradictory result is the negative Spearman coefficient obtained for the concrete cube strength. In fact, negative values of this coefficient indicate an inverse relationship between strength and the resulting capacity ratios. This behaviour can be primarily attributed to the fact that, within the ultimate limit state approach, concrete strength has a limited influence on the bending capacity of the section. 4. Conclusions The simplified checks provided by Level 3 of the recent multilevel approach in the Italian Guidelines represent a valuable tool for defining a preliminary safety index for a sample of structures. The results of this study suggest that, in addition to considering the seismic demand, it is also important to account for structural capacity when performing a Level 3 check. In fact, relying solely on demand-based assessments may lead to misleading conclusions, especially for structures designed according to different methodologies, such as the Allowable Stress Method. Given the heterogeneity of the results, future analyses should incorporate more detailed input data derived from real case studies. The study will also be extended to include shear verification. Furthermore, to reduce uncertainty in the assessment, assumptions regarding reinforcement ratios and typical section geometries will be introduced. Ultimately, the results can be combined with demand-related indicators to produce more reliable preliminary safety indices than those currently provided by the Italian Guidelines. Acknowledgements This study was supported by FABRE – “Research consortium for the evaluation and monitoring of bridges, viaducts and other structures” (www.consorziofabre.it/en). Any opinion expressed in the paper does not necessarily reflect the view of the funder. References Bencivenga, P., Buratti, G., Cosentino, A., De Matteis, G., Morelli, F., Salvatore, W., et al, 2022. Evolution of Design Traffic Loads for Italian Road Bridges. Proceedings of the 1st Conference of the European Association on Quality Control of Bridges and Structures. EUROSTRUCT 2021. Lecture Notes in Civil Engineering, vol 200. https://doi.org/10.1007/978-3-030-91877-4_154. Bozza, S., Fasan, M., Noè, S., 2023. Vulnerability to traffic loads of typical Italian bridges in relation to the evolution of the code framework. Proceedings of the 2nd Conference of the European Association on Quality Control of Bridges and Structures. pp.760-767. https://doi.org/10.1002/cepa.2038.