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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 bee