A classical bridge girder is considered, with three spans and four piers. The piers are supposed to be elastically flexible, so that the structure can be reduced to a beam on four elastic supports. If the elastic cedibility of the two side supports is conveniently varied, it is possible to recover some classical cases, such clamped-clamped beams and simply supported beams. The cross section of the beam is assumed to vary with a general law, as well as its moment of inertia. The masses on the beam are also distributed according to a general law, while the axis of the beam is rectilinear. The structure is subjected to an earthquake, which is simulated through alternate vertical displacements of the four supports. It is also possible to study the effect of an earthquake with different phases and amplitudes on two different supports; this can be especially interesting if the spans of the bridge are very large, or if the geological situation of the two extremes is different. First of all, eigenfrequencies and eigenfunctions of free vibrations are calculated, and then the effect of the earthquake is detected by means of modal superposition analysis. Various response spectra are adopted, in which the structural damping is taken into account by imposing an upper bound to the response coefficients. Comparisons among different amplitudes were also performed, which allowed us to obtain the most dangerous earthquake. The analysis is mainly numerical, the structure is reduced to a rigid-elastic model, following the cell procedure. According to this method, the strain energy and the masses are concentrated at discrete sections on the beam, and these sections are linked together by means of rigid bars. Finally, a recently realized bridge is examined, in which the two main piers are shown to have a not negligible cedibility.

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