Partially restrained seismically isolated continuous (PRSI) bridges are a particular class of isolated bridges in which isolation bearings are placed only between the superstructure and the piers, while steel-plate stoppers or other devices restrain the transverse motion of the deck at the abutments.

This study illustrates a simplified model for the assessment and preliminary design of these systems. The dynamic problem of PRSI bridges is described in a variational form, in order to obtain a simplified solution based on a pre-fixed sinusoidal transverse deformed shape of the deck. Simple formula are derived for estimating the relevant response quantities of interest. Additional formula are also proposed to account for the contribution of higher modes of vibration, which are of extreme importance in this problem.

Based on the proposed simplified model, a procedure for the preliminary design of the isolation bearing properties is proposed. The objective of the design procedure is to control the internal actions on the piers by means of an appropriate configuration of the isolation bearings. Possible applications are the design of new bridges and the retrofit of existing bridges.

Validation studies are undertaken in order to assess the ability of the proposed method to control the force demand at the piers.