Date of Completion


Embargo Period



Multi-Frame Bridge, Seismic Transverse Response, In-Span Hinge Shear Key, Modal Displacement Ductility, Modified Elastic Dynamic Analysis

Major Advisor

Arash E. Zaghi

Associate Advisor

Richard Christenson

Associate Advisor

Lanbo Liu

Field of Study

Civil Engineering


Doctor of Philosophy

Open Access

Open Access


Long concrete bridges are often constructed in multiple frames separated by in-span hinges. Shear key elements at in-span hinges preserve the transverse integrity of adjacent frames. This method of construction facilitates post-tensioning and lowers adverse effects of creep and thermal deformations. The transverse response of multi-frame system has not been comprehensively studied. In Addition, no rational method is available for estimating seismic design forces of shear keys. In the course of this study, approximately 9,400 nonlinear response history analyses were performed on the high-fidelity models of realistic prototype bridges. The seismic demands on columns, abutments, and in-span hinge shear keys were studied. Statistical methods such as the analysis of variance (ANOVA) and factorial analysis were implemented to understand the effect of independent factors including the number of frames, substructure system, valley shape, soil type, intensity of ground motions, etc.

It was found that in multi-frame system seismic demands on columns are smaller than those in equivalent continuous system where the heights of columns vary along the length of a bridge. The interaction of transverse and longitudinal displacement increases the probability of seismic unseating in in-span hinges. In multi-frame bridges, considerable damage to the abutment is expected. Contribution of the higher modes of vibrations to shear key forces is significant. In multi-frame bridges, higher modes may generate large plastic deformations in the columns. An easy-to-implement formulation was developed for seismic design of shear keys using the concept of spectral analysis. In this method, modal shear key forces are modified separately by their corresponding modal displacement ductility before the modal combination. This concept was developed and proposed as a new analysis methodology. The proposed method accounts for the effect of impact on shear keys due to transverse gaps, and the effect of non-uniform base excitation.