考虑P-△效应的桥梁结构震后概率残余位移分析

Probabilistic residual displacement analysis of bridge structures considering P-△ effect

残余位移是评价桥梁结构震后可修复性和可用性的重要指标,而P-△效应对桥梁结构的残余位移影响显著。综合考虑P-△效应和地震动随机特性的影响,通过大量的非弹性动力时程分析,定量地分析桥梁结构震后残余位移的概率统计特征和经验预测方程。首先根据动力平衡原理,建立考虑P-△效应的桥梁结构非弹性地震动力响应分析的运动控制微分方程,然后结合所筛选的69条强震记录,利用概率统计方法定量地分析P-△效应、屈服后刚度比、规一化屈服强度和自振周期等因素对震后残余位移的概率统计特征的影响,进而对残余位移与峰值位移之间的相关性进行讨论,并建立残余位移与峰值位移之间的经验预测方程。分析结果表明:P-△效应、屈服后刚度比和规一化屈服强度对残余位移的均值影响较大,而对残余位移的变异性影响相对较小;桥梁结构的震后残余位移可以描述为对数正态分布或威布尔分布随机变量;残余位移与峰值位移之间具有较强的相关性,且二者比值的均值(变异系数)随着自振周期和稳定系数的增大而增大(减小)。

Residual displacement is one of the most important parameters to assess the repairability and usability of bridge structures after an earthquake,while the P-Δeffect has significant influences on the residual displacement of bridge structures.Probabilstic characteristics and empirical prediction equations of residual displacements for bridge structures were quantitatively investigated based on the large number of nonlinear time history analyses by taking the P-Δeffect and randomness of strong ground motion into account.The governing differential equation of motion for bridge structures including the P-Δeffect was developed based on the dynamic balance theory.The influences of the P-Δeffect,post-yield stiffness ratio, normalized yield strength and natural period of vibration on statistical characteristics of residual displacement were quantitatively investigated based on the inelastic dynamic responses of bridge structures under the excitation of 69 selected records of strong ground motions.The correlation between the peak and residual displacements was discussed and the prediction equation for the residual-to-peak displacement ratio was also proposed.The results show that the P-Δeffect,the post-yield stiffness ratio and the normalized yield strength have significant impact on the mean of residual displacements;the residual displacement can be described as a lognormal or Weibull distribution variable;the correlation between the residual and peak displacements is remarkable and the mean （dispersion）of the residual-to-peak displacement ratios increases （decreases）with the increase of the natural period of vibration and the stability factor.