PSI - Issue 62

Stefano Bozzaa et al. / Procedia Structural Integrity 62 (2024) 323–330 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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[ | ] = [ − 1 − 2 ≤ | ] = ( − 1 − 2 ) (13) The fragility curves were derived by fitting a lognormal distribution to the ratio [(M R − M g1 − M g2 )/M q ] via the maximum likelihood method, minimizing the negative log-likelihood. 5. Results The fragility curves for first class bridges and second class bridges for each construction period were calculated as previously described. Since the span of the deck influences the vulnerability to traffic loads (Bozza et al. (2023)), the fragility curves were evaluate for each span considered in this study. The parameters of the fragility curves are reported in Table 4, whilst fragility curves are graphically reported in Figure 1.

Table 4. Parameters of the fragility curves (mean and standard deviation of the lognormal distribution).

60s

70s

80s

90s

1° class

2° class

1° class

2° class

1° class

2° class

1° class

2° class

Span Moment

μ

σ

μ

σ

μ

σ

μ

σ

μ

σ

μ

σ

μ

σ

μ

σ

10 m

as-built

2.10 1.54 2.20 1.66 2.40 1.89 2.57 2.07 2.98 2.39 3.56 2.78 3.86

0.13 0.37 0.11 0.36 0.19 0.37 0.21 0.36 0.26 0.45 0.36 0.61 0.36

1.46 0.99 1.50 1.08 1.81 1.36 2.04 1.57 2.42 1.89 2.90 2.24 3.07

0.15 0.32 0.14 0.32 0.19 0.59 0.21 0.43 0.27 0.49 0.38 0.70 0.39

1.87 1.40 1.97 1.55 2.14 1.70 2.28 1.86 2.61 2.13 3.06 2.46 3.29

0.13 0.31 0.11 0.29 0.17 0.34 0.19 0.32 0.24 0.38 0.31 0.49 0.31

1.30 0.94 1.33 1.00 1.61 1.26 1.81 1.42 2.12 1.68 2.52 1.99 2.63

0.13 0.26 0.14 0.27 0.17 0.65 0.19 0.44 0.24 0.49 0.32 0.67 0.34

2.03 1.64 2.14 1.77 2.28 1.92 2.43 2.10 2.69 2.30 3.01 2.52

0.11 0.29 0.13 0.28 0.18 0.29 0.18 0.28 0.22 0.33 0.26 0.42 0.26 0.42

1.40 1.11 1.46 1.17 1.63 1.32 1.74 1.42 2.02 1.66 2.36 1.93

0.10 0.23 0.11 0.24 0.16 0.44 0.17 0.39 0.21 0.41 0.29 0.56 0.30

2.23 0.11 2.00 2.08 0.27 1.71 2.29 0.11 1.96 2.04 0.26 1.71 2.36 0.15 2.05 2.10 0.25 1.78 2.45 0.16 2.14 2.23 0.25 1.90 2.63 0.19 2.37 2.43 0.30 2.09 2.87 0.24 2.69 2.72 0.38 2.34 2.92 0.23 2.76

0.13 0.25 0.13 0.23 0.17 0.25 0.19 0.24 0.24 0.29 0.31 0.37 0.31

today

15 m

as-built

today

20 m

as-built

today

25 m

as-built

today

30 m

as-built

today

35 m

as-built

today

40 m

as-built

3.09

2.42

today

3.03 0.64 2.38 0.56 2.66 0.50 2.09 0.49 2.61

2.00 0.40 2.85 0.38 2.43 0.37

As expected, second class bridges are more fragile than first class bridges, and short bridges are more fragile than longer bridges, according to previous study (Bozza et al. (2023)). Considering the “as - built” configuration, first class 60s bridges are the less vulnerable ones, with the exception of bridges shorter than 20 m, which have an higher vulnerability than 90s first class bridges: this indicates that Circular no. 494 of 1960 is very conservative. For first class bridges with span higher than 30 m, 90s bridge are the most vulnerable, while for shorter span 70s bridges are the most vulnerable. For second class bridges, 70s short bridges and 80s long bridges are the most vulnerable (both in the “as - built” configuration and considering the corrosion effects over time).