Impact Coefficient Analysis of Curved Box Girder Bridge Based on Vehicle-Bridge Coupling

Abstract

In the current vehicle-bridge dynamics research studies, displacement impact coefficients are often used to replace the moment and shear force impact coefficients, and the vehicle model is also simplified as a moving-load model without considering the contribution of vehicle stiffness and damping to the system in some concerned research studies, which cannot really reflect the mechanical behavior of the structures under vehicle dynamic loads. This paper presents a vehicle-bridge coupling model for the prediction of dynamic responses and impact coefficient of the long-span curved bending beam bridge. The element stiffness matrix and mass matrix of a curved box girder bridge with 9 freedom degrees are directly deduced based on the principle of virtual work and dynamic finite element theory. The vibration equations of vehicle-bridge coupling are established by introducing vehicle mode with 7 freedom degrees. The Newmark-β method is adopted to solve vibration response of the system under vehicle dynamic loads, and the influences of flatness of bridge surface, vehicle speed, load weight, and primary beam stiffness on the impact coefficient are comprehensively discussed. The results indicate that the impact coefficient presents a nonlinear increment as the flatness of bridge surface changes from good to terrible. The vehicle-bridge coupling system resonates when the vehicle speeds reach 60 km/h and 100 km/h. The moment design value will maximally increase by 2.89%, and the shear force design value will maximally decrease by 34.9% when replacing moment and shear force impact coefficients with the displacement impact coefficient for the section internal force design. The load weight has a little influence on the impact coefficient; the displacement and moment impact coefficients are decreased with an increase in primary beam stiffness, while the shear force impact coefficient is increased with an increase in primary beam stiffness. The theoretical results presented in this paper agree well with the ANSYS results.

Analysis of Vehicle-Bridge Coupling Vibration Characteristics of Curved Girder Bridges

“…In the finite element analysis (FEA) of curved girder bridges, the curved beam element, the straight beam element, the mass point element, and the spring element can be selected to discretize the bridge structure [16][17][18]. By calculating the kinetic and potential energies of each unit and structure, the vibration equation of the bridge structure is derived through Hamilton's principle.…”

“…Similarly, by substituting Equations ( 14)-( 16) into Equation (17), respectively, a submatrix form similar to Equation ( 19) is achieved. The damping matrix of a single two-axle vehicle is obtained via superimposing and combining all submatrices.…”