Study On The Second-order Effect Of Sdof System Of High Bridge Pier Under Horizontal Earthquake

The main study object of this thesis is single-degree-of-freedom system which is the simplification of the high piers of bridges, the main study objective of this thesis is evaluate the influence two kinds of second order effect(P—Δeffect and P—δeffect) of single-degree-of freedom, and the relation between two kinds of second order effect.From the view of domestic and foreign study result about second order effect, the understanding about P—Δeffect is explicit, but the understanding about P—δeffect is little. The main reason about this is most of program's pole element is stiffness method element, Stiffness method element can only consider contribution of the ends deformation to the force, can't consider the contribution of element's inner deformation to the force. However, The stiffness method element can consider P—δeffect through the way of dividing the object into many element, but this decrease the compute efficiency. Flexibility method element use force interpolation function and can consider the contribution of element's inner deformation and the ends deformation to the force simultaneity. This provide the feasibility of research seismic P—δeffect and the affect of P—δeffect to P—Δeffect.The main research work finished in this thesis is as follows:①Based on the theory about flexibility method element which instituted by SouZa, build new element. The new element can consider first order, P—Δand P—δeffect respectively. This provide feasibility of research seismic second order effect and the affect of the effect of P—δeffect to P—Δeffect with one element model.②Build the formulation of static and seismic P—Δeffect and P—δeffect of single-degree-freedom systems, ascertain the main effect factor of seismic second effect, ascertain the affect of P—δeffect to P—Δeffect.③Analysis the seismic second order effect of single-degree-freedom systems as material is elastic with program.④Analysis the seismic second order effect of single-degree-freedom systems as material is plastic.From the finished research work above, the main conclusions can be drawn preliminarily as follows: ①The new element built in OpenSees can consider P—Δand P—δeffect simultaneity and respectively.②The main effect factor of static second effect is stability factor; the main effect factors of seismic second effect are stability factor, period of system and frequency of ground records. Seismic second order effect can increase or decrease structure's response.③As the period of structure is small, seismic second order effect is bigger than static second order effect. Base on the criterion, build the formulation which can consider seismic second order effect.④For structure's period which is in the seismic effect coefficient descending range, as the stability coefficient and yield strength reduction factor greater, the second order effect decrease the cantilever column's base force more. For the middle moment, the change of yield strength reduction factor is not obvious to the effect of the second order effect to middle moment. For the displacement, at beginning ,as yield strength reduction factor greater, the second order effect increase displacement, but then, as yield strength reduction factor greater, the second order effect is decreasing.