Research On Multiple Poundings Of Bridges Under Vertical Earthquakes

With the observations of bridge damages which can't be explained by the tradition views, it's found the effect of vertical earthquake is underestimated. So there are more attentions for possible structural failure due to vertical earthquake. Vertical earthquake may causes the multiple poundings between girders and piers, which lead to contact surface damage, girders moment overloaded, the concrete broken and the reinforcement buckling in the bottom of piers. However, since these are related to variable contact topology, wave effect and nonlinear effect, the theoretical and numerical studies on multiple-pounding are difficult. In this paper, the multiple elastic poundings responses under vertical earthquakes are solved using the expansion of transient wave functions in a series of eigenfunctions. The main researches are shown as followings:(1) A basic theory of using the expansion of transient wave functions in a series of eigenfunctions is developed to account for multiple poundings dynamics of bridge structures based on a single-pier and two-span bridge model under vertical earthquake. The determination method for the start time of pounding phase and separation phase which appear alternately is presented. The multiple poundings force is obtained based on the transient internal force of contact surface of combined impact body.(2) By the use of the artificial vertical earthquake in the form of a sinusoidal excitation, the theoretical solution of transient wave responses of continuous rigid frame bridge are derived from the expansion of transient wave functions in a series of eigenfunctions. The propagations of stress wave including reflection, reaction and wave impacts throughout the pier and the girders are studied. The effects of the vertical earthquake intensity and the length of girder are analyzed for the structures responses of bridges.(3) By the use of the artificial sinusoidal earthquake, the multiple poundings problem of continuous bridge is studied. The transient responses of alternative phases of pounding and separation are derived from the present method. The pounding force is proved convergent for the time step length and the truncation of wave modes. The propagations of earthquake wave and the pounding-induced transient waves can be depicted. The effects of the vertical earthquake period and the bridge parameters are analyzed for the structures responses of bridges.(4) By comparison of transient responses of continuous rigid frame bridge and continuous bridge with same structure parameters based on the artificial sinusoidal earthquake, it's shown the connection forms of girders and pier have obvious effects for bridge dynamics. Influences of the vertical earthquake period and the bridge parameters on pounding (contact) force, girders moment and pier axial force are studied.(5) The method of studying multiple poundings problem of continuous bridge under real vertical earthquake is proposed. Real vertical earthquake can be equal to sinusoidal wave superposition throughout FFT analysis. The multiple poundings response is derived from using the expansion of transient wave functions in a series of eigenfunctions. Influences of the frequency spectrum characteristics of vertical earthquake and the bridge parameters are analyzed for the multiple poundings responses of bridges.