MODELING OF CABLE-STAYED BRIDGES FOR ANALYSIS OF TRAFFIC INDUCED VIBRATIONS

This paper presents a method for modeling and analysis of cable-stayed bridges under the action of moving vehicles. Accurate and efficient finite elements are used for modeling the bridge structure. A beam element is adopted for modeling the girder and the pylons. Whereas, a two-node catenary cable element derived using exact analytical expressions for the elastic catenary, is adopted for modeling the cables. The vehicle model used in this study is a so-called suspension model that includes both primary and secondary vehicle suspension systems. Bridge damping, bridge-vehicle interaction and all sources of geometric nonlinearity are considered. An iterative scheme is utilized to include the dynamic interaction between the bridge and the moving vehicles. The dynamic response is evaluated using the mode superposition technique and utilizing the deformed dead load tangent stiffness matrix. To illustrate the efficiency of the solution methodology and to highlight the dynamic effects, a numerical example of a simple cable-stayed bridge model is presented. NOMENCLATURE uyx, , LLL projected and unstressed lengths of the cable element 41,, uu horizontal and vertical nodal displacements 41,, PP horizontal and vertical end forces of the cable element ji TT, tension forces at the two nodes of the cable element E modulus of elasticity A cross section area I moment of inertia w weight per unit length m mass ρ density sp cc, damping coefficient of vehicle viscous dampers sp kk, stiffness of vehicle springs t time v vehicle speed ξ bridge damping ratio ω circular frequency µ mass ratio p internal force vector f external force vector qqq , , nodal displacement, velocity, and acceleration vectors M mass matrix C damping matrix F flexibility matrix K stiffness matrix tK tangent stiffness matrix TMD tuned mass damper 1