Dynamic Response Analysis Of Beam-like Bridges With Cracks Under Moving Vehicles

As an important part of the modern transportation system,bridge structures have a great effect on the national economic development.The safety of its operating state is connected with the safety of the people's life and property as well as the long-term stability of the society.However,as a functional building,bridges often need to serve for hundreds of years after they are built.As the environmental condition of bridges are very complex,in the process of longterm service,it will be affected by various factors,which inevitably lead to structural damage and the reduction of service performance.Vehicles act as moving loads,resulting in greater deflection and stress in bridge structures than equivalent static loads.When fatigue damage occurs in bridge structures,the reduction of its service performance is mainly reflected in the increase of dynamic response of damaged bridge structures under loads.Therefore,it is of great significance to analyze the displacement response of the existing bridge structures under the action of vehicles for evaluating the operation state of bridge structures.As one of the main damage of bridge structures.The existence of the crack increases the local flexibility,which leads to the decrease of the structural stiffness,and then changes the dynamic response of structures,and endangers the bearing capacity of the bridge structure at the moment.The dynamic response analysis of cracked beam bridges under loads is still a frontier subject in the field of civil engineering.In the structural design of highway bridges in China,medium and small span concrete bridges are widely used.According to the composition of the main girder,the medium and small span girder bridges can be divided into two categories: integral bridges and multi-girder bridges.For the integral bridge,its disease is mainly reflected in the longitudinal cracks caused by the bending of the beam,and for the multi-girder bridge,not only the main beam will occur crack damage,but also the damage of the transverse connection is one of the main diseases.And the typical characteristic is the cracking of the diaphragm junction.The damage of diaphragms will reduce the integrity of the bridge structures,and directly affect the lateral distribution of the load,which leads to the increase of the deflection of the stressed beam and become easily damaged.Therefore,it is of great significance to explore the longitudinal cracks of integral bridges and the transverse cracks of multi-girder bridges to the dynamic response of bridge structures under vehicles.In order to slove the problems above,the main research has been carried out in this paper as follow:(1)The plane and spatial cracked element model with arbitrary cross section were established.Based on the theory of fracture mechanics,the element stiffness matrices of cracked beam elements were derived.According to the shape functions of plate element,plane and spatial intact beam element,their element stiffness matrices and uniform mass matrices were obtained.And the whole stiffness and mass matrices of cracked bridge structures were assembled.Assuming that the damping of the bridge is Rayleigh damping,the motion equations of plane and space cracked beam models were established based on the modal superposition method.(2)The motion equations of the vehicle system were established based on D'Alembert's principle by using the half-vehicle model;The vibration equation of the vehicle-bridge coupling system was established by considering the bridge deck irregularity through the displacement coordination condition and the force balance relation of the vehicle-bridge coupling system;The opening and closing state of breathing crack was determined.The Newmark-b method was used to solve the dynamic response of the beam structure with the breathing crack under moving vehicles;In the numerical example,a concrete cracked continuous integral beam was taken as an example to investigate the effects of the bridge deck irregularity and the moving velocity of the vehicle on the dynamic response of cracked continuous beams.(3)The motion equations of the vehicle system and the vibration equation of the vehiclebridge coupling system were established by using the spatial vehicle model.The corresponding dynamic response of the beam structure with the breathing crack under moving vehicles were solved.In the numerical example,a reinforced concrete simple supported multigirder T-shape beam was taken as an example to investigate the effect of the crack position,the degree of damage and the driving position of the cross bridge on the dynamic response of the simply supported T-shape beam bridge.