Implementation of inelastic displacement patterns in direct displacement-based design of continuous bridge structures

Through the use of nonlinear time-history analysis, the displacement patterns of bridges subjected to transverse seismic attack are investigated. The variables considered in the study consist of bridge geometry, superstructure stiffness, substructure strength and stiffness, abutment support conditions, and earthquake ground motion. A series of three inelastic displacement pattern scenarios were identified: (1) rigid body translation (2) rigid body translation with rotation, and (3) flexible pattern. A relative stiffness index that is a function of the superstructure and substructure stiffness was shown to be a key variable in determining the type of displacement pattern a bridge is likely to follow. The results described in this paper have significant implications for performance-based seismic design procedures such as direct displacement-based design (DDBD). If the displacement pattern for a bridge can be identified with significant confidence at the start of the design process, application of approaches such as DDBD can be simplified. However, if the characteristics of the bridge are such that prescribing a pattern at the start of the process is not feasible, then an alternative approach must be employed for DDBD to proceed. Of the three displacement pattern scenarios defined in this paper, the first two require minimal effort in the design. For the third scenario, an iterative algorithm is proposed. Lastly, as a means for verification and demonstration, a series of bridges with various configurations was designed using DDBD for rigid body translation and flexible pattern scenarios. The designs for the flexible scenario showed good agreement with selected target profiles for bridges with up to five spans.