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.
Highlights
Shear force at left side Shear force at right side e effect of vehicle speed on the dynamic impact force design value. e shear force is maximally underestimated by 34.9% as the vehicle speed reaches 120 km/h, which is insecure for bridge structures
A vehicle-bridge coupling model was proposed to predict the dynamic responses of the system in the present work, and the effect of flatness of bridge deck, vehicle speed, vehicle weight, and the primary beam stiffness on the impact coefficients are considered
When the curvature radius is greater than 1000 m, the dynamic responses of the curved bridge can be computed according to the straight bridge
Summary
Bridge structures will bear dynamic loads except for constant loads during their service period, and vehicle load is the most common dynamic load. e research on the vehicle-bridge coupling mainly focuses on the dynamic responses of the system [1,2,3,4,5]. e bridge will vibrate when the vehicles pass over it, leading to an increase in the internal force and displacement. e impact coefficient, a dynamic amplification coefficient, reflects the magnitude of the impact action. e impact coefficient value is of great importance to the safety of bridge structures, and the impact effect is prominent especially when the bridge vibration frequency and the vehicle frequency are equal (resonance occurs). A great deal of research studies on vehicle-bridge coupling vibration responses and dynamic impact coefficients have been carried out so far, in which the dynamic interactions of the bridge-vehicle system and wheel-rail contact are critical issues. E wheel and rail are always in contact, and there is no separation of the two components To deal with this problem, Fan et al [11] investigated the vehicle jumping phenomenon caused by irregularity based on the penalty stiffness algorithm. E result indicated that for rail irregularity, the interfacial contact algorithm is more suitable for the simulation of interaction condition of vehicle-bridge dynamics than the Hertzian spring method. E displacement, moment, and shear force impact coefficients are respectively calculated, and the influences of the flatness of bridge surface, vehicle speed, load weight, and stiffness on the impact coefficient are considered Replacing moment and shear force impact coefficients with the displacement impact coefficient cannot really reflect the mechanical behavior of the structures under vehicle dynamic loads. is paper presents a vehicle-bridge coupling model by directly deducing the element stiffness matrix and mass matrix and introducing the vehicle model. e Newmark-β method is used in the present work to solve the dynamic response of the system. e displacement, moment, and shear force impact coefficients are respectively calculated, and the influences of the flatness of bridge surface, vehicle speed, load weight, and stiffness on the impact coefficient are considered
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
