PSI - Issue 44

Riccardo Martini et al. / Procedia Structural Integrity 44 (2023) 657–664

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Riccardo Martini et al. / Structural Integrity Procedia 00 (2022) 000–000

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Fig. 1. 2-DoF system circular frequencies as a function of � ratio.

The following comments can be drawn from the observation of Fig. 1: • when the vertical truck (or trucks) stiffness ( 1 ) is much higher than that of the bridge ( 2 ), the frequency ratio � tends to 0; in the graph, the gap between the two circular frequencies of the system increases; in fact, the former tends to infinite and the latter approaches the fundamental frequency of the reduced 1-DoF system, characterized by mass 1 + 2 and stiffness 2 (dashed blue lines). In this case, the BTI phenomena are not predominant, hence, the vertical stiffness of the trucks can be neglected in the evaluation of the fundamental vertical frequency of the loaded bridge. • When the vertical truck stiffness ( 1 ) is much lower than that of the bridge ( 2 ), the ratio � approaches infinite; also in this case, the BTI phenomena do not affect the loaded bridge dynamics; in fact, one circular frequency goes to zero and the other one represents the fundamental frequency of the unloaded bridge. Consequently, the coupled system can be reduced to a 1-DoF system representative of the unloaded bridge, neglecting the additional truck mass. • When the frequencies ratio � is around 1, a typical response of a Tuned Mass Damper (TMD) system is obtained. In this case, the BTI phenomena are not negligible and the dynamic interpretation of the system does not turn into an easy task as reported above. In the professional practice, the graph presented in Fig. 1 represents a valuable tool to preliminary assess the influence of the BTI phenomena on the bridge dynamics during the static proof load tests. Actually, by performing two preliminary AVTs on the unloaded bridge and the truck, just before the proof load test, it is possible to determine the frequency ratio that allows to enter the graph and to estimate the two expected frequencies of the combined bridge truck system, depending on the mass ratio (i.e. depending on the applied loads at each step of the static proof test). 3. Case study In this Section, the graphical tool provided in Fig. 1 is adopted to support the dynamic identification during the proof load test of a real bridge, taking into account the BTI phenomena. The newly built bridge is a steel composite deck characterized by 4 spans, for a total length of 152 m (length of each span equals to 38 m), as shown in Fig. 2(a). The deck is composed by a concrete slab with a thickness of 30 cm, that is connected to the 3 I-shaped girders through Nelson studs; the girders collaboration is assured by truss-beams and I-shaped crossbeams (see Fig. 2(b)).