Free Vibration Analysis of Curved Thin‐Walled Girder Bridges

Abstract

The purpose of this paper is to present a theory that incorporates a special treatment of warping in the free vibration analysis of continuous curved thin‐walled girder bridges. The theory uses an additional degree of freedom for curved beam elements with thin‐walled sections to capture the effects of warping. The ability to use flexible piers or hinge supports with the curved‐girder warping theory is included. Formulation of both element stiffness and mass matrices is discussed. The element stiffness matrix is determined by inverting the flexibility matrix. Two example calculations using the theory are presented. The examples include a three‐span, continuously curved bridge with two flexible piers and a three‐span, continuously curved bridge with four flexible piers. The results obtained are compared to results based on other theories. Effects of warping, noncoincidence of shear center and centroid of section, flexibility of piers, and radius of curvature are shown.