GNGTS 2014 - Atti del 33° Convegno Nazionale

326 GNGTS 2014 S essione 2.3 belonging to different planes were then established by means of internal rigid-body constraints. The average dimensions of shell elements was comprised between 0.25 m - 0.50 m in the mid part of central span, whereas a refined mesh pattern was used in the regions close to the pier and to the lateral supports. The thickness of these shell elements was defined based on the actual longitudinal profile of the deck (Fig. 1a). The same shell element type was adopted also for the pier. The mass contribution offered by footways was then taken into account in the form of lumped masses. Concrete was mechanically characterized as for the 3D models. Each isolator, finally, was described in the form of three linear elastic springs applied at the intersection point between the vertical axis of the real isolator and the extrados of the deck. These springs, reacting separately along vertical, transverse and longitudinal directions with stiffnesses K Z , K X and K Y respectively, were calibrated in accordance with the 3D-OPT model. In addition, two elastic rotational springs reacting in the longitudinal plane y - z and in the transverse plane x - z were placed at the constrained points, to take into account the elastic contrast offered by isolators. The stiffness K φ of these rotational springs was evaluated as K φ = π R 4 /4 K Z , with R = 0.60 m signifying the nominal radius of the isolator basis (Fig. 1b). Dynamic simulations highlighted that the calibrated 2D FE-model (2D-OPT) of the bridge reproduces well the vibration modes of the 3D-OPT Model. Discrepancies on natural frequencies generally resulted negligible for quasi-rigid body motions and for bending vibrational modes, with errors lower than 2%. Larger deviations (≈4-6% ) were found for torsional modes. In any case, the 2D-OPT model was considered sufficiently refined to perform further investigations on the bridge. Accuracy of the 2D-OPT model was suggested not only by agreement with experimental frequencies, but also by additional validation performed against static truck-load tests (e.g. Fig. 3d). Seismic analysis of the bridge. In order to appreciate the benefits of the isolated systemunder earthquake motions, the seismic response of the isolated bridge was finally analyzed (2D-OPT) and compared to the dynamic behavior of the same structural system not equipped by seismic isolators (2D-FIX). In doing so, a bilinear constitutive shear force-shear displacement along the X and Y directions was used for the mechanical characterization of seismic devices (Fig. 1b), by Tab. 2 - Correspondence between experimental (EMA) and numerical mode shapes of the preliminary (3D-NOM), refined (3D-REF) and optimal (3D-OPT) FE-models. Natural frequencies f and errors. ∆� ����� = 100×( f r (3D) – f r (EMA) )/ f r (EMA) . r = mode order; w.c. = without correspondence. EMA 3D-NOM 3D-REF 3D-OPT r f r f Δ MAC r f Δ MAC r f Δ MAC [-] [Hz] [-] [Hz] [%] [%] [-] [Hz] [%] [%] [-] [Hz] [%] [%] 1 2.022 1 2.045 1.12 99.4 1 1.985 -1.84 99.4 1 1.993 -1.46 99.4 2 3.053 2 2.442 -20.01 93.6 2 2.857 -6.41 87.3 2 2.989 -2.10 85.3 3 3.180 4 3.292 3.53 89.6 3 3.165 -0.48 89.5 3 3.171 -0.29 89.6 4 3.605 3 2.682 -25.59 100.0 4 3.369 -6.56 100.0 4 3.609 0.10 100.0 5 4.831 5 3.696 -23.49 95.9 5 4.611 -4.56 94.3 5 4.918 1.81 93.4 6 6.887 7 7.656 11.17 85.1 6 6.605 -4.09 83.6 6 6.684 -2.95 83.8 7 6.924 8 7.105 2.46 98.0 7 6.809 -1.80 97.5 7 6.824 -1.59 97.5 8 7.995 10 10.254 28.26 89.7 9 8.829 10.43 89.0 9 8.833 10.48 89.0 9 9.107 9 9.361 2.79 83.5 10 8.903 -2.24 73.7 10 8.906 -2.20 73.8 10 12.910 w.c. - - - w.c. - - - - - - - 11 14.228 16 19.581 37.62 53.3 15 16.488 15.88 56.5 15 16.507 16.02 56.5 12 14.433 w.c. - - - w.c. - - - - - - -