GNGTS 2015 - Atti del 34° Convegno Nazionale

228 GNGTS 2015 S essione 2.3 between T group,EXP and the axial force measured on a single cable. It can be seen that the calculated deviation is negligible, e.g., 2–3% the average group value, for the four cables of group 1, both on the upstream (1U) and downstream side (1D). On the contrary, the axial forces in groups 2 and 3 show larger deviations from the corresponding average values, e.g., up to 16% and 11%, for groups 2D and 3U respectively. In this context, the marked difference of estimated axial forces in cables belonging to the same groups (e.g., 2D and 3U) should be considered as a symptom of potential anomaly of the suspension system of the bridge, thus requiring further extended investigations. Sensitivity of the bridge to damage in the cables. During the year 2010, two cables belonging to the group 2U were separately interested by the collapse of the stays-to-deck connection detail (e.g. Fig. 1b). According to Tab. 2, the marked difference in identified axial forces on the cables belonging to groups 2 and 3 could be considered a symptom of a potential anomaly of the suspension system. Consequently, with the aim of investigating the sensitivity of the natural frequencies, vibration modes and axial forces on the stays with respect to a possible damage on the suspending system, an extensive numerical analysis was carried out by using the refined FE-OPT model as reference configuration for the undamaged bridge. Among several parametric numerical simulations, six main damage scenarios were considered, as obtained by separately removing one or two cables from the groups 1U, 2U and 3U of cables. For all these scenarios, the corresponding FE-DAM models were derived by imposing a null cross-sectional area to the cable of interest for the simulation of damage. The same solving method taken into account for the reference undamaged model FE-OPT (e.g. Step I for the application of dead loads and Step II for the modal analysis of the bridge) was considered for each one of them. The main results of these additional numerical simulations are collected in Fig. 3, where the labels ‘1U-1’ and ‘1U-2’ in them denote the damage in one or in two cables belonging to the group 1U, respectively, and so on. A generally appreciable sensitivity of the bridge dynamic response to the induced damage was found, hence highlighting the usefulness of diagnostic investigations based on modal data. In terms of natural frequencies, all the damaged models showed small reduction, compared to the reference undamaged values (see Fig. 3a). Negligible frequency sensitivity to damage was also generally noticed for the higher order modes, e.g., the EMA modes 5 and 6. Although in few cases only, large variations (up to 5%) were found in some cases. Worth of interest is the effect of damage on the lower vibration modes of the bridge. Especially the introduction of damage in the 2U group manifested in fact a very high sensitivity of the FE mode shapes 1 and 2 (e.g., EMA modes 0 and 1 in the notation of Tab. 1 and Fig. 3). As expected, the progressive removal of a single or two cables in the groups 1 and 3 generally Tab. 2 - Experimental and FE axial forces on the cables. U = upstream; D = downstream. Axial force discrepancy: Δ Cn = 100×( T cable,EXP – T group,EXP )/ T group,EXP ( n =1,..4). TEST FE-OPT Group T group,EXP Δ C1 Δ C2 Δ C3 Δ C4 T group,FE [-] [kN] [%] [%] [%] [%] [kN] 1D 380.1 1.9 3.2 -2.2 -2.9 262.4 1U 386.5 -1.9 1.6 2.8 -2.5 263.9 2D 545.2 -10.3 -13.4 15.9 7.8 604.3 2U 529.6 0.0 2.7 4.4 -7.1 605.3 3D 452.5 -5.7 1.6 -4.4 8.5 524.8 3U 460.6 5.8 -2.3 6.8 -10.3 525.1 T total [kN] 11142.6 11080.0