PSI - Issue 84

Tommaso Pivetta et al. / Procedia Structural Integrity 84 (2026) 1286–1293 T. Pivetta et al. / Structural Integrity Procedia 00 (2026) 000–000

1290

5

Table 2. Young’s Modulus of the linear elastic materials. Material

E c (N/mm 33155.02 27329.97 28238.59

2 )

Girders concrete

Cross-beams concrete

Slab concrete

3.2. Iterative Calibration Scheme For the calibration of the model, the first two vibration modes were considered. From the system identification results, the first mode exhibited a predominantly flexural behavior of the deck, while the second mode was characterized by a torsional response. Based on these outcomes, the calibration phase was performed by iteratively updating the Young’s modulus of girders, cross-beams and slab, imposing a target error threshold of 1%. Since the elastic modulus values of the cross-beams and the slab resulted to be very similar and both primarily affect the torsional behavior of the deck, the same elastic modulus was assumed for these two components in order to simplify the calibration procedure.

Fig. 6. Flowchart of the iterative calibration process.

The iterative calibration scheme is illustrated in Fig. 6. As previously discussed, a unified elastic modulus was adopted for the slab and the cross-beams, thus making the number of calibration parameters equal to the number of target parameters (i.e., the natural frequencies of the first two vibration modes). The procedure consists in performing a modal analysis and extracting the first two natural frequencies. For each frequency, an error is computed as the ratio between the numerical and the target value. Then, the Root Mean Square Error (RMSE) of the two frequency errors is calculated and compared with the predefined tolerance threshold. If the RMSE is lower than the tolerance, the model is considered calibrated; otherwise, the elastic modulus of the girders ( E 1 ) and the unified elastic modulus of the slab and cross-beams ( E 2 ) are updated according to Eq. (1):