The structures of cable-stayed bridges are quite different from that of continuous beam bridge,so their vibration characteristics and seismic response are also different.A(64+115+115 +64)m three tower and double cable plane cable-stayed bridge was chosen as the analysis example. At pier 2# of this bridge,the tower,beam,and pier are rigidly connected together.At the other movable pier,the tower and beam are rigidly connected together,and separated with the pier.The bridge has a seismic intensity protection rating of seven.To analyze the seismic response and evaluate the seismic performance of a cable-stayed bridge,a whole bridge space dynamic calculation model was established using the MIDAS program.The spatial beam finite-element model was used to simulate the tower,pier,and beam.The cable was simulated by the tension-only spatial truss element which also took the geometrical non-linearity into account.The bearings were considered as the ideal constraint according to the actual constraint conditions.The SSI effect was also taken into account by the application of a soil spring both in the translation and rotation directions.Natural vibration characteristics were analyzed;therefore,the dynamic characteristics and vibration mode of cable-stayed bridges with multi-span and low towers were well understood.The first five vibration modes including the vibration shape and the self vibration period were extracted.The first vibration shape is an anti-symmetric vertical bending of the beam,which is similar to the continuous beam bridge.However, they differ in the vibration shape that includes the vibration of the tower and cable compared with continuous beam bridge.For low-level earthquakes,the response spectrum method was adopted to analyze the elastic response in horizontal and transverse directions.The first 300 vibration modes were used in the spectrum method,and the CQC method was used in combination with seismic response in each vibration mode.The bending-moment and shear-force diagrams of the bridge structure were drawn in horizontal and transverse directions,whereby,the results show that the longitudinal earthquake response of fixed pier 2# was the biggest and dominates the seismic design.Under low-level earthquake ground motion,the bridge is in an elastic condition,that is,the pier and tower are in an elastic state and can return to their original shape after the low-level earthquake.Under low-level earthquake ground motion,the allowable stress method was adopted in the design.The stress was calculated in accordance with the eccentric compression member and results show that the bridge can meet the required specifications to achieve performance level I.For high-level earthquake ground motion,the non-linear time-history analysis method was adopted to analyze the elastic-plastic response.The maximum plastic rotation angle should be limited within a safe range.To acquire the maximum plastic rotation angle,the artificial seismic waves under high-level earthquake conditions were input into the model,and results showed that the plastic deformation capacity can meet the required specifications and also have a degree of safety reserves.Under high level earthquake ground motion,the bridge may suffer great damage without overall collapse,which can play a role under limited traffic and after repairs;it can achieve performance level III.
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李建明.铁路多跨矮塔斜拉桥抗震性能评估[J].地震工程学报,2014,36(1):34-38. LI Jian-ming. Evaluation of Seismic Performance of a Railway Cable stayed Bridge with Multi span and Low Towers[J]. China Earthquake Engineering Journal,2014,36(1):34-38.