This paper analyzes the dynamic behaviour of bridges with abutment transverse restraint. These are a particular class of multi-span bridges in which seismic stoppers restrain the transverse motion of the deck at the abutments. The dissipation of the seismic energy is promoted either by dissipative piers with plastic hinges forming at their base or by piers with isolation bearings at their top.

The bridges are modelled by two-dimensional simply supported beams with intermediate visco-elastic restraints, whose properties are calibrated to describe substructures' dissipative behaviour. Particular simplified configurations are considered which allow to identify the adimensional parameters controlling the response. The free vibrations problem is analyzed by means of both classic and complex modal analysis, due to the presence of non-classical damping. Parametric studies are undertaken to assess the influence of the restraints on the bridge's components response and global damping, for the most relevant vibration modes.

The results of the study allow to draw some important conclusions which can be useful for the preliminary assessment and design of the particular class of bridges analyzed. Numerical applications to selected case studies are also illustrated in order to validate the findings.