Continuum Model for Static and Dynamic Analysis of Suspension Bridges with a Floating Girder

In this paper, a continuum model for a three-span suspension bridge with a floating girder is newly proposed to investigate its static and dynamic behaviors. This model can consider the extensibility of hangers and thus vertical differential motions between a main cable and a girder. Coupled differential equations for the vertical displacements of the main cable and the girder subjected to external loads are derived. The equations of motion are obtained in matrix form by utilizing the Galerkin method with the shape functions for the main cable and the floating girder. A numerical example is used to verify the continuum model against a finite element model. Verification results prove that the continuum model can accurately determine the static and dynamic responses of a suspension bridge with a floating girder subjected to static distributed loads on the girder, temperature changes in the main cable and hangers, and moving loads on the girder. The continuum model can determine nonzero displacements of the girder at its intersection with the towers. The displacements of the girder at this intersection are much smaller than those at its center because the motion of the girder at this intersection is largely restrained by the tower top. The results also show that the main cable and the girder have clearly different accelerations around the towers because the main cable is vertically restrained by the tower tops, whereas the girder is not restrained at the intersection.