基于条件Newmark-Hall三联谱的时程分析选波方法

条件均值谱（CMS）已成为目前国内外广受关注及认可的结构抗震时程分析选波的目标谱，但其无法同时兼顾多个周期点谱加速度具有相同的地震危险水平，对于须考虑多阶振型影响的长周期结构尚存局限。Newmark-Hall三联谱是基于加速度峰值（PGA）、速度峰值（PGV）和位移峰值（PGD）并联合短、中、长周期相关放大系数建立的反应谱，与短、中、长周期结构均具有天然良好的相关性，其与概率地震危险性分析（PSHA）结合较弱及具有经验化特征。将两种反应谱的优势相结合，即将CMS的“条件分布”理念引入Newmark-Hall三联谱，建立了条件Newmark-Hall三联谱（即CN-H），并提出了以CN-H为目标谱的选波方法（即CN-H方法）。以美国SAC计划设计的3层和9层抗弯钢框架结构为例，将CN-H方法与以CMS为目标谱的选波方法所得结果进行了对比。CN-H方法对于结构反应均值的估计与CMS方法具有一致的准确性，且所得结构反应的离散性也较低，可见CN-H方法对于结构弹塑性时程分析选波具有良好的适用性。

Selection and scaling of ground motions using Conditional Newmark-Hall spectrum as target spectrum

The Conditional mean spectrum (CMS) has attracted widespread attention and has been used in many applications for selection and scaling the ground motions for time history analysis. However, it cannot be realized that the spectral accelerations at several mode periods have equal probability of exceedance by using the CMS. Therefore, the CMS has not the best correlation with the dynamic responses of long-period structures for which the high mode effects must be considered in the analysis. The Newmark-Hall spectrum, which was built based on spectrum amplification factors of the PGA, PGV, and PGD in different sensitive period regions, has a natural and perfect correlation with the short, medium, and long-period structural responses. However, the Newmark-Hall spectrum has very little connection to attenuation relationships for Probabilistic Seismic Hazard Analysis (PSHA) and has empirical features. The advantages of both the two types of response spectra were combined in this study. The theory "conditional distribution" of the CMS was embedded into the Newmark-Hall spectrum, and the Conditional Newmark-Hall spectrum (CN-H) was proposed. The CN-H was used as a target spectrum in nonlinear structural time-history analyses (CN-H method) and the CMS was also used as a target spectrum (CMS method) for comparison. The 3-story and 9-story steel moment resisting frame structures, which are two designed buildings in the U.S. SAC Steel Project, were used as examples. The two methods had similar accuracies for the estimation of the structural mean response. The CN-H method has an excellent capacity to reduce the variability of the structural response results. Therefore, the CN-H method has a better feasibility in nonlinear structural time-history analysis.