GNGTS 2015 - Atti del 34° Convegno Nazionale

226 GNGTS 2015 S essione 2.3 (Fig. 2b, box) resulted in 48,000 solid elements with average length 0.2 m. Possible soil-to-pier interaction was fully neglected, and the pier was rigidly restrained at its base. The mechanical interaction between the bridge deck and the RC pier (Fig. 2b, detail E), e.g. the unidirectional supporting devices, were described by means of slot connectors able to provide null relative displacements along the transverse and vertical bridge directions, between the connected nodes. At the same time, longitudinal displacements and relative rotations between the interested nodes were kept unrestrained. Globally, the so implemented FE model resulted in 700,000 DOFs and 160,000 elements. Concerning the characterization of materials, both concrete and steel were assumed to behave linear elastically, with isotropic mechanical properties derived from technical drawings and small samples. For the concrete fo the deck slab,specifically, experimental test on cylindrical cores provided an average Young’s modulus equal to E c = 42 GPa. A weight per unit volume ρ c = 25 kN/m 3 was assumed for the RC structural members with ν c = 0.3 the Poisson’s ratio. The Young’s modulus, weight for unit volume and Poisson’s ratio of steel were assumed equal to E s = 206 GPa, ρ s = 78.5 kN/m 3 and ν s = 0.3, respectively. Solving method. A static incremental, nonlinear analysis under the effects of the bridge self- weight and dead loads (e.g., footways and asphalt layer) was preliminary carried out on the FE model (Step I), in order to determine the equilibrium reference configuration. In the subsequent step (Step II), the first 20 analytical vibration modes were predicted by means of linear modal analysis around the reference configuration derived in Step I. Interpretation of dynamic test results and EMA-FE correlation. The high modeling and computational cost of the FE model, geometry refinement of the bridge components, as well as their reciprocal interaction, generally resulted in dynamic estimations in rather close agreement with test measurements. Vibration frequencies and mode shapes. Tab.1 proposes a comparison of EMA and FE natural frequencies, with the corresponding MAC values. The FE mode shapes associated to the identified vibration frequencies are collected in Fig. 2c. The primary effect of the accurate FE model, based on the interpretation of dynamic results, was represented by the prediction of a fundamental vibration mode of the bridge not detected in a preliminary experimental interpretation of ambient vibration test data (‘EMA 0’). The corresponding mode shape is characterized by torsional motion of the deck and large deformation of the steel tower (Fig. 2c). While the singular value curves of the spectral density matrix did not show the presence of this first torsional mode, probably since the corresponding natural frequency is very close to the fundamental flexural one (EMA 1), in a subsequent phase the modal parameters were separately estimated in the frequency domain, for the half-sum and half-difference of the recorded time histories. The advantage of this approach, based on the vertical oscillations of two control points located on the opposite sides of the same transverse deck cross-section, is that if a vibration mode is mainly flexural, the measured amplitude oscillation at the selected pair of control points are similar, and their difference is small. The half-sum of time histories, consequently, magnifies the presence of vertical bending modes and hides the peaks corresponding to torsional ones. Conversely, if a mode is mainly torsional, the vertical modal components at the same control points are similar in amplitude, but have opposite sign, so their sum is small. The half-difference of the corresponding time histories, as a result, automatically excludes the peaks associated to bending modes. Apart from the EMA 0 mode, a general close agreement was found for the identified EMA and FE modes. The numerical simulations carried out on the FE-OPT model, in particular, highlighted the importance of refined geometrical description of few, but crucial, bridge components, and specifically the proper geometrical and mechanical characterization of the bridge supports (details C and D of Fig. 2b), as well as the stays-to-deck and stays-to-pylon connections (details A and B of Fig. 2b). On the other hand, the progressive increase of the modelling complexity