A simplified analytical model and formulation are defined to describe the nonlinear seismic behavior of multi-span bridges with dissipative piers and a continuous deck transversally restrained at the abutments. These structural systems have a "dual load path" behaviour and their failure may occur in the piers or in the deck, depending mainly on geometry and stiffness distribution.  

By using a variational approach, the properties of an elasto-plastic single-degree-of-freedom system equivalent to the bridges are derived, and analytical expressions are proposed for describing the post-elastic system behaviour, the global dissipative capacity, and the failure modalities. These expressions are based on non-dimensional characteristic parameters and permit to make explicit the relationship between the seismic capacity and the bridge properties.

The proposed analytical formulation is applied to the analysis of a set of continuous multi-span steel-concrete composite bridges with different static schemes and stiffness distributions. The accuracy of the simplified model is tested and validated by comparison with the results of incremental dynamic analysis performed on three-dimensional nonlinear finite element models.