The Non-linear Dynamic Buckling Analysis Of High Pier Under The Foundation Shakes By The Earthquake

As the high pier mainly suppoting the axial load and its great flexibility, the stability problem is the important problem of the high pier under the impact of the vehicles on the bridge or the foundation motion by the earthquake and the research of dynamic characteristics and the dynamic stability of the high pier caused great attention. In the paper, including the large deformation, the basic nonlinear dynamic equations are established. By assumping the shape functions of displacement and using the Galerkin method, the time-dependent equations of the high pier under the impact of the foundation motion by earthquake are founded. By processing numerical calculation, the displacement response curves of the high pier are gained. By using B-R criterion, the critical seismic accelerations and the instability times of the high pier are given. The theory is offered for the engineering application. The following contents are mainly discussed in this paper.(1) The research status and theory of the buckling of the high pier is introduced firstly. According to the characteristic supporting pressure and dynamic buckling property of the high pier, the basic equations of the dynamic buckling of the high pier are established by including the geometric nonlinearity. The Runge-Kutta method is utilized in the computational process. The program design and the basic theory of the Galerkin method are introduced in details in this paper.(2) Under the impact of the foundation perpendicular motion by earthquake, the dynamic buckling of the high pier is investigated. The deflection curves of the high pier are presented. The influence of the different seismic peaks, the geometric parameters on the instability of the high pier is analyzed. By the numerical example, the influence of the different seismic peak, the slenderness ratio and the weight of the bridge on the displacement response, the critical seismic acceleration and the instability time are described.(3) The instability of the high pier under the foundation horizontal motion and the foundation ellipse motion caused by Rayleigh wave by earthquake are discussed. The different critical seismic accelerations are got with the different earthquake magnitude, the slenderness ratio and the weight of the bridge. Compared the results, the variation of the critical seismic acceleration and the instability time versus the weight of the bridge, the softness ratio the seismic magnitude is analyzed.