An approximate method for non-linear seismic analysis of three-dimensional two-way asymmetric buildings resting on flexible foundations under bi-directional ground motions is presented. To take into account the soil–structure interface effect, the sub-structuring method with frequency-independent soil springs and dashpots was employed. To consider the non-linear behaviour of the structure, a modal stick with five degrees of freedom was used to simulate the multi-degree-of-freedom modal equations for the soil–structure system. Using the bifurcation characteristic of modal pushover curves, the modal stick was modified, by which the coupled modal non-linear translation and rotation deformations were simulated. The seismic responses of two flexibly supported asymmetric buildings (three and eight storeys) were evaluated by the uncoupled modal response history analysis (UMRHA) method employing the proposed modal stick. The seismic responses of the structures were also obtained by employing the rigorous non-linear response history analysis and the results were compared with the corresponding outcomes from UMRHA method. The comparison showed good agreement between the outcomes of the two analysis methods, thus demonstrating that the proposed three-dimensional non-linear analysis technique developed in this study is an effective and applicable tool for dealing with the non-linear analysis of flexibly supported two-way asymmetric-plan structures.

中文翻译：

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弹性土上非对称结构的三维非线性地震分析

提出了一种基于柔性地基的三维二维非对称建筑物在双向地震动作用下的非线性地震分析的近似方法。考虑到土壤-结构界面效应，采用了与频率无关的土壤弹簧和阻尼器的子结构方法。为考虑结构的非线性行为，采用五自由度模态棒模拟土-结构体系的多自由度模态方程。利用模态pushover曲线的分岔特性，对模态棒进行了修正，模拟了耦合的模态非线性平移和旋转变形。通过采用所提出的模态棒的非耦合模态响应历史分析 (UMRHA) 方法评估了两座柔性支撑的不对称建筑物（三层和八层）的地震响应。通过采用严格的非线性响应历史分析，还获得了结构的地震响应，并将结果与​​ UMRHA 方法的相应结果进行了比较。比较表明两种分析方法的结果之间具有良好的一致性，从而表明本研究中提出的三维非线性分析技术是一种有效且适用的工具，用于处理柔性支撑的二元非线性分析。方式不对称计划结构。通过采用严格的非线性响应历史分析，还获得了结构的地震响应，并将结果与​​ UMRHA 方法的相应结果进行了比较。比较表明两种分析方法的结果之间具有良好的一致性，从而表明本研究中提出的三维非线性分析技术是一种有效且适用的工具，用于处理柔性支撑的二元非线性分析。方式不对称计划结构。通过采用严格的非线性响应历史分析，还获得了结构的地震响应，并将结果与​​ UMRHA 方法的相应结果进行了比较。比较表明两种分析方法的结果之间具有良好的一致性，从而表明本研究中提出的三维非线性分析技术是一种有效且适用的工具，用于处理柔性支撑的二元非线性分析。方式不对称计划结构。