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The spatial variability of the earthquake strong ground motion (SVEGM) leads to significant aspects in the structural response of long-plan structures, such as long-span and medium-span bridges. The main purpose of this study is to investigate the effects of the asynchronism of the ground motion on the structural response of a medium-span cable-stayed bridge, and in doing so the SVEGM takes only into account the time delay between the arrival of the shear waves, without taking into account their incoherency. The studied structure is the bridge over the Cuiabà River; it is a prestressed composite cablestayed bridge, built up from 2000 to 2001 in Mato Grosso, Brazil, with three spans of 71.75 m, 157 m, 71.75 m, for a total length of about 300 m. The piers have an height of 51.8 m over the foundation plinths. The seismic input has been assigned by the application of different spostograms, obtained by the double integration of 10 accelerograms, spectra-compatible with the ones proposed by the Eurocode 8 for an "A-type" soil; the accelerograms have been generated with the Simqke software (Gasparini, Vanmarcke, Liu, 1976) and are opportunely filtered by the use of the Butterworth filter, applied with the Seismosignal software (Seismosoft, 2004). It has been considered different velocities of the seismic waves Vs in the soil. The applied spostograms have been translated in function of the time delay; the asynchronism is taken into account only in the longitudinal direction. The analysis, conducted with the finite element program ANSYS, is a nonlinear time stepping analysis, done with the Newmark's method, with a Newton-Rhapson approach. After having compared the results obtained, under a same seismic event, in the cases of different time steps, one has chosen to use a time step of 0.05 s. Although the studies are principally conducted by a 3-D model of the structure, which one will call "frame model", developed using the finite element software Ansys, the structure has been studied using another model, which one will call "shell model", in order to evaluate how the differences in the modeling lead to different results. The substantial difference between these two models is how the bridge's slab is modeled: a gridwork in the frame model and a 2-D continuous in the shell model. The geometric characteristics (area and inertia) of the gridwork have been evaluated by the application of the kinematics criterion: applying forces equipollent to the ones applied on the continuous, the corresponding deformations should be equal (Toniolo, Malerba, 1981). The comparison of the results obtained in both the models shows the similar behaviour of the two models, confirmed by the small differences in percentage of the values reached by monitored static and kinematical. Figure 1 shows an image of the main 3-D used model and a list of the monitored parameters.

The spatial variability of the earthquake strong ground motion (SVEGM) leads to significant aspects in the structural response of long-plan structures, such as long-span and medium-span bridges. The main purpose of this article is to investigate the effects of the asynchronism of the ground motion on the structural response of a medium-span cable-stayed bridge, and in doing so the SVEGM takes only into account the time delay between the arrival of the shear waves, without taking into account their incoherency. Referring to the article named "Effective framework for seismic analysis of cable-stayed bridges, pt.1: modeling of the structure and of the seismic action" (Bontempi, Sgambi, Santoboni, 2006), in which the studied structure and its modeling are discussed, once having established a list of the monitored parameters of the bridge, it has been done the evaluation of their values in a statistic way, in order to evaluate if the number of the considered seismic events may be enough to obtain reliable results. One has considered the estimation of the average, variance and standard deviation of the results of both the synchronous and asynchronous motion. Histograms have been evaluated, showing, for established intervals, the number of the registered events; the gaussian distribution has been drawn, considering the obtained values as continuous variables. The statistic reliability of the obtained results has been evaluated by the comparison of the shape of the gaussian distribution with the histograms, by the use of the parametrical χ2 Pearson's test, and doing some physical evaluations. An evaluation has been made of the differences in percentage of the averages of the maximum values reached by each monitored parameter, during the time histories, in both the cases of synchronous and asynchronous motion. Figure 1 shows these differences. Since the time delay depends on the shear wave velocity, the response of the structure under different values of the velocity has been studied with the purpose to establish the dependence between the wave velocity and the structural response and to evaluate the possible existence of a critical value, which may show a particular behavior of the structural response. With those purposes, the response of the structure has been evaluated under a range of velocity which goes from 200 m/s to 1000 m/s, even if the lower values are not compatible with a "Eurocode type A" soil, used for the evaluation of the response spectra. The main results of these studies are: 1. Neglecting the effects of asynchronous ground motion can lead to serious mistakes also into the evaluation of the structural response of medium-span bridges. Considerable differences in the observed parameters are registered only in the axial force in the middle of the longitudinal beam, with an underestimation of 60%; 2. Considering the structural response under different values of the shear wave velocity, from 200 m/s up to 1000 m/s, shows that the differences at the lower velocities are really high; the trend of the values reached by the monitored parameters shows a nonlinear behavior of the structural response; 3. The statistical evaluation of the results shows that the reliability of the results can be improved by the use of a higher number of considered events.