基于模态能量分析的结构滞回能量估算方法

建立能量谱和结构能量反应的关系,是基于能量抗震设计需解决的关键问题之一。根据多层结构体系在地震动作用下的能量平衡方程,运用弹性体系的振型分解思路,将多层结构的能量反应平衡关系拆解为多模态的能量反应平衡关系,推导出多层结构与其模态等效单自由度体系的能量反应平衡关系。运用考虑塑性反应阶段振型的“等效振型”替代弹性振型。建立通过模态滞回能量反应估算多层结构总滞回能量的方法。针对硬、中、软三类场地设计3栋6层模型,选取各类场地下的地震记录作为结构模型的水平激励进行非线性动力时程分析。结果表明,在一些情况下,通过模态能量分析能较准确地估算地震作用下多层结构总滞回能量。

A Method for Estimating Structural Hysteretic Energy based on Modal Energy Analysis

The relationship between energy spectra and energy responses of structures is one of the key problems of Energy-based seismic design. The energy balance equation of multi-sto-rey structures is expanded as the multi-modal energy equations, based on the assumption of e-lastic-plastic modal analysis, and the relation equation of seismic energy responses between multi-storey structures and modal equivalent SDOF systems is derived. The elastic modes are replaced by“equivalent modes” for considering the inelastic modes of inelastic response phase. According to the derivation, a method is established in which the modal hysteretic energy is uti-lized to estimate total hysteretic energy of multi-storey structures. The examples are provided, in which hard, medium and soft soil site are considered and three six-storey structural models are designed based on the three kinds of soil sites. The corresponding earthquake records are se-lected as horizontal excitations of the structural models and nonlinear dynamic time history analy-sis are implemented. The analytical results show that：in some case, the method of modal energy analysis can be used to estimate total hysteretic energy of multi-storey structures subjected to earthquake motions accurately.