PSI - Issue 84

Angela Diana et al. / Procedia Structural Integrity 84 (2026) 623–629

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Figure 2. Relationship between span length and experimental frequencies: (a) first mode flexural frequency f 1 (b) second mode flexural frequency f 2 According to Di Rienzo et al. (2025), a simplified relationship for the first bending natural frequencies can be defined as: = ℎ 2 (1) where in the referenced work the coefficients k 1 and k 2 , related to first and second bending modes of the deck respectively, for simply supported spans were estimated by approximating the ratio E/ρ under the square root as constant, given the limited variability range of those parameters. Here, E denotes the elastic modulus, while ρ represents an equivalent density that also accounts for the contribution of non-structural components as pavements, sidewalks, curbs and railings, based on the analysis of worldwide literature references, with h and L representing the deck depth and the span length, respectively. Fige 3 reports the inclusion of the frequency values determined in this work within the original database presented in Di Rienzo et al. (2025). It can be observed that the range of the geometric parameter h/L 2 associated with the current dataset is more limited than that the referenced dataset; in particular, the analysed values fall within a range between 1.90 and 2.60 [10 -3 m -1 ]. The linear regression, obtained by combining the two datasets, suggests that the current data points are generally distributed close to the resulting regression trend.

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Figure 3. Linear regression of the relationship between frequencies and geometrical parameter h/L 2 : (a) first frequency f

1 (b) second frequency f 2

The final coefficients for Eq.1 evaluated in this work through linear regression of the grouped data from (Di Rienzo et al., 2025) and this work are: