考虑多种耦合效应的多维多点反应谱研究

Research on multi-support and multi-component response spectrum considering multi-coupling effect

准确计算结构在非一致性地震输入下的响应,需要考虑地震动的特性,如多维及空间相关性等;也需考虑结构响应的复杂性,如需要将地震动响应分解为动力响应及拟静力响应等。以上因素非独立,具有耦合性。为此,根据选定的地震动功率谱模型,利用虚拟激励法,推导了基于位移谱的多点多维反应谱公式,该公式可以同时考虑多种耦合效应,包括多维(含方向交叉向)、多点(含行波效应和相干性效应)地震动及动力与拟静力的耦合等多种因素。为了便于在实际工程中应用,公式根据GB 50011-2010《建筑抗震设计规范》中的加速度谱选定了对应位移谱,且公式中的参数也与之相对应。同时,采用反应谱法对一个单层网壳结构在多维多点地震动输入下的反应特性进行了分析,结果表明动静耦合的影响随着视波速的增加而减小,考虑部分相干性效应的柱底面内弯矩最大值比完全相干条件下增加了10%~20%。

In order to get the accurate response under non-uniform seismic wave input, it is necessary to take the characteristics of ground motion into account. Apart from multi-component and spatial correlation, the complexity of structural responses should be considered as well, including the dynamic and static components. In general, these factors are coupled rather than independent. With the chosen seismic input model of power spectrum, a formula based on the displacement response spectrum considering multi-support and multi-component seismic excitations was derived by a pseudo-excitation method. The formula can consider the factors of multi-component(including cross directions) seismic excitations, multi-support(including the influence of wave passage effect and incoherence effect) movements and the response coupling of the dynamic and static components. To facilitate practical use, the displacement response spectrum and the associated the parameters in this paper was modified from the acceleration response spectrum suggested in the current GB 50011-2010 ‘Code for seismic design of buildings’. Finally, the structural response characteristics derived based on the new response spectrum method under multi-support and multi-component seismic excitations were discussed with an example of single-layer reticulated domes. The results indicate that an increase in the apparent wave velocity causes a decrease in the response coupling dynamic and static components. By taking incoherence effect into consideration, the maximum value of the in-plane bending moment at the bottom of the columns is increased by 10% to 20%.