空间结构多维地震反应两阶段推覆分析方法

Two-stage pushover analysis procedure for seismic evaluation of spatial structures under multidimensional earthquake

现有的推覆分析方法在计算空间结构多维地震响应组合值时,采用的“平方根式”组合准则丢弃了响应的正负符号,造成结构响应模式“正向膨胀”的失真现象,且针对响应进行组合的计算方式也丧失了推覆分析能够观察结构弹塑性发展全过程的特有优势。针对此问题,提出空间结构多维地震反应两阶段推覆分析方法,该方法在基于振型刚度的第一阶段非线性推覆分析基础上,引入能够考虑多维地震响应相关性的组合准则,通过振型组合得到多维推覆荷载模式,并对结构进行第二阶段非线性推覆分析得到最终结果,从而在保留地震响应正负符号的前提下,获得符合实际的空间结构灾变破坏模式。将此方法运用于单层球面网壳、双层柱面网壳算例以及上海国际会议中心钢网壳工程实例的多维地震反应分析,并与多维时程分析方法和传统多维推覆分析方法进行对比。计算结果表明:基于推导的多维推覆荷载模式进行两阶段非线性推覆分析,能够准确预测空间结构在多维地震作用下的结构变形形态和响应分布规律,节点位移、单元应力以及屈服杆件数量等结构响应的平均误差基本控制在30%以内,计算精度满足工程要求,大位移区域和高应力区域的结构响应预测效果良好;相比传统多维推覆分析方法,计算精度显著提高,相比多维时程分析方法,计算耗时大大缩减。

The quadratic combination rules applied in the existing pushover analysis methods usually ignore the sign reversals of multidimensional response of spatial structures,and unreasonably cause the positive expansion of failure pattern.In this way,the basic advantage of pushover method on revealing the plastic developing process of structures disappears.To bridge the gaps,the two-stage pushover analysis procedure for multidimensional seismic evaluation of spatial structures was proposed.Based on the first-stage nonlinear pushover analysis with the modal stiffness and the multicomponent correlated combination rule,the multidimensional pushover load profile was derived according to modal superposition principle.Based on the load profile,the second-stage nonlinear pushover analysis was conducted.In this way,the sign reversals of response were retained and a more rational failure pattern of the spatial structure was obtained.To validate the applicability of the proposed procedure,a single-layer spherical latticed shell,a double-layer cylindrical latticed shell,and the latticed shell of Shanghai International Convention Center were taken as examples of comparative evaluation using the two-stage pushover procedure,the conventional multidimensional pushover method,and the time history analysis method.The results show that,the two-stage pushover procedure,which is based on the derived multidimensional load profile,is able to effectively predict the deformation pattern and response distribution of spatial structures under multidimensional earthquake.The nodal displacement,element stress,and quantity of yielded members can be calculated with errors less than 30%,satisfying the demand of practical engineering.In the more important regions of large displacement and high stress,the two-stage pushover procedure also provides valid response assessment,resulting in a more favorable results on the safe side.Besides,the two-stage push-over procedure exhibits a remarkable improvement in the accuracy of calculation when compared with the conventional multidimensional pushover method,and a significant reduction in computation cost when compared with the time history analysis method.