AbstractThe governing equations of motion for bridges with rocking piers of unequal height and unequal span lengths are derived accounting for the effect of the end joint gaps and the abutment-backfill system. The attenuation of the rocking motion stems from the impacts at the rocking interfaces, described through the coefficient of restitution, and also from the impacts (pounding) of the superstructure on the abutment backwalls. This is the first study to the author’s knowledge that combines both energy-dissipation sources in the analytical derivation of the equations of motion. The results of response-history analysis of bridges with different levels of asymmetry in their pier height show that the performance of both the symmetric and asymmetric configurations is very similar with regard to longitudinal displacements. Although the studied bridges safely resisted ground motions with an intensity about twice that of the design earthquake, regardless of the degree of asymmetry, it was found that the higher the difference in the pier height, the larger the rotation of the superstructure due to the differential uplift of the piers, a point that must be addressed in seismic design for rocking response.