188 E. Mola et al. though, natural frequencies and modal damping coefficients can still be obtained, but mode shapes can not be mass- scaled since the excitation force is unknown. A very important advantage of OMA is the fact that it does not require disruption of use, which is very important for a bridge, so it can be easily repeated over time under operational conditions to monitor the evolution of the dynamic properties, for both monitoring and early damage detection purposes. This, together with its reduced costs, was the main reason why the Owner chose to perform OMA tests only, in view of a future monitoring protocol to be implemented for the bridge, including periodic repetitions of OMA tests in operating conditions. The modal parameter identification methods based on Operational Modal Analysis can be classified into frequency domain methods and time domain methods. In this paper, the Poly-reference Least Squares Complex Frequency Domain method is adopted to modal parameter identification for operational data, which is a polyreference version of the LSCF method, using a so-called right matrix-fraction model [4]. In the following, the numerical analysis and the experimental activity carried out on the bridge will be presented and the results compared and discussed. 23.2 Description of the Bridge The Ticino Bridge is part of A4 highway which connects the two main cities in Italy (Milan and Turin respectively) and it is one of the oldest and most important European motorways. Therefore, it is of great significance and importance. The bridge is designed so that the two ways (MI-TO and TO-MI), consisting of three lanes each, are separated. Each way consists of 16 reinforced concrete piers supporting a continuous steel beam deck of 17 spans without joints. The steel girder sections of the deck, composed by four main beams and horizontal braces, which support a reinforced concrete slab (Fig. 23.1a), were assembled and launched by pushing them independently at both the river banks for optimizing and reducing construction time (Fig. 23.1b). The TO-MI way is 16.9 m wide while the MI–TO way is 18.4 m due to an additional pedestrian lane. In order to guarantee the necessary seismic performance of the bridge, as well as the compensation of the thermal deformations, the deck rests on friction pendula allowing a relative displacement in the horizontal direction. 23.3 Structural Analysis and Modelling Assumptions The dynamic properties of the Ticino Bridge were numerically predicted by means of a finite element (FE) model that was developed using the commercial software for structural analysis Midas Gen v.2014 (Fig. 23.2). The friction pendulum damping devices between the piers and the deck elements were modeled considering their force displacement curve provided by producers and reported in Fig. 23.3a. The horizontal stiffness of these devices, k, is function of vertical load, V, and is higher for small displacements (<d1 D2 mm) and lower for large displacements, as reported in Fig. 23.3a). For the analysis of the dynamic properties of the flyover to be compared with the experimental results from operational modal analysis, the horizontal stiffness of each friction pendulum was taken equal to ki D V/d1, where D0.025 is the friction coefficient, V is the vertical load on the device (actually in place during the dynamic tests), d1 D2 mm is the limit value of the displacement for which the slope of the bi-linear curve representing the stiffness of the bearing changes, as can be observed in Fig. 23.3a). In order to correctly represent the boundary conditions and distribute the stiffness of the bearing on the beams, nine nodal isolators were modeled by means of nine springs acting on the beam (Fig. 23.3b). The value of the horizontal stiffness of these springs was taken equal toki* Dki/9 as a function of the vertical load. The bridge substructure, consisting of reinforced concrete piers, was not included in the numerical model since its contribution to the dynamic vibration characteristics of the deck was judged negligible, mainly because the stiffness of the piers is much higher than those of the friction pendulum bearings. Moreover, because most of the mass of a bridge is in the deck, the first modes usually involve mainly the deck and not the piers. As a matter of fact, the deck can thus be considered restrained to the ground by means of systems of two springs in series, one corresponding to the isolator with low stiffness and the other to the pier with much higher stiffness. Therefore, for very different stiffness values, the global stiffness of the series springs is dominated by the lower value and the higher one could be neglected. The model has been accordingly limited to the deck and the supporting isolating system. The developed finite element model is three-dimensional and was implemented using a refined mesh of shell elements. This choice allows a realistic description of the deck geometry (Fig. 23.2) and of the mass and loads distribution together with a more reliable definition of the mode shapes, especially those involving the torsional behavior of the bridge deck. All shell elements have four node rectangular shapes, adopting meshing
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