PSI - Issue 84

Ivan Beltracchi et al. / Procedia Structural Integrity 84 (2026) 1015–1022

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To this end, Guyon–Massonnet theory (Bares & Massonnet), which models the deck as an orthotropic plate governed by partial differential equations, was employed. The analytical results were subsequently benchmarked against elastic finite-element models of the bridge deck. As shown in Fig. 4, beam T2, located directly beneath the heavy-vehicle lane, may carry up to 40% of the total load. The figure also compares the analytical predictions with FEM results obtained using Midas Gen. Beam T2 was selected for detailed investigation and instrumented with a laser displacement sensor to measure midspan deflection. To estimate the instantaneous net bridge deflection, each measurement was baseline-corrected by subtracting the median value computed over a reduced time interval immediately before and after each load passage, assumed to represent the unloaded reference state. Deflection records from the monitoring period 3–8 February 2025 (shown in Fig. 5) were used to calibrate the algorithm, revealing higher average deflections around midday, consistent with increased heavy-vehicle traffic.

Fig. 5 Purified readings of the laser, representing the net deflection of the bridge over time. From the complete dataset, only vehicles accurately recorded by the weighing platform were retained, yielding approximately 3,300 heavy vehicles classified into five weight ranges. For each vehicle, the gross weight and the corresponding deflection measured on beam T2 were extracted (Fig. 6). A regression analysis indicated an approximately linear relationship (R²=0.75). By the calculation of the maximum bending moment associated with the actual load distribution, reconstructed from the WIM data (vehicle speed, number of axles, axle loads, and axle spacing/footprint geometry), an equivalent uniformly distributed load producing the same bending moment was computed and used as a representative load metric. Fig. 6 reports this equivalent load together with the corresponding deflection of beam T2. Expressing the traffic actions in terms of equivalent and uniform distributed load reduces the scatter of the measurements (R²=0.80) thus strengthening the linear relationship.

(a) (b) Fig. 6 (a) Total load of vehicle vs. mid-span deflection and (b) Equivalent distributed load of vehicle vs. mid-span deflection. Each point corresponds to one vehicle. 4. Prediction moments The development of advanced structural behaviour predictions based on non-linear finite-element (FE) models makes it possible to compare the deformations induced by heavy-vehicle passages with reliable numerical estimates of the bridge response and to evaluate safety-related performance indicators. In this study, the SHM measurements were