The current work presents a simplified multi-mode nonlinear static procedure based on normalizing the deformation demands (called NMP) for estimating the seismic demands of structures with significant higher mode effects. The proposed procedure is conceptually based on the extended N2 (where N stands for nonlinear analysis and 2 for two mathematical models) method (Kreslin and Fajfar in Earthquake Engineering & Structural Dynamics 40:1571–89, 2011). However, the modal combination procedure used in the proposed method to take the higher mode effects into account is different. The NMP procedure generally encompasses two major steps. First, the structure is pushed using a conventional pushover procedure, namely the basic N2 method, the first-mode pushover analysis, or a pushover analysis with a triangular or a uniform load pattern, which mostly controls the responses at the lower part of the structures. Second, the modal story displacements and drifts computed based on the modal response analysis concept for all the modes of interest are algebraically added. These combined responses are normalized based on the predetermined target displacement. The final responses are the envelope of the results obtained from the two aforementioned steps. The approach used in the second step can preserve the signs of modal responses. Therefore, the effects of sign reversal due to the contribution of higher modes are included in the proposed method. Moreover, the NMP procedure mitigates the computational burden compared to nonlinear response history analysis or adaptive pushover procedures. In order to evaluate the accuracy of the proposed procedure in estimating the seismic demands of structures, it is applied to two sets of steel structures including three special moment frames (SMFs) with 6-, 12-, and 18-story heights, and a 12-story SMF with soft stories as the first set and the 9-, and 20-story SAC steel moment frames as the second set. Comparing the results of the NMP procedure with those obtained by the nonlinear response history analysis (NL-RHA) as the benchmark solution and two other pushover approaches, including a conventional first-mode-based pushover analysis and the extended N2 method, demonstrate the sufficiency of the NMP procedure in accurately estimating the global and local response quantities.

当前的工作提出了一种基于标准化变形需求（称为 NMP）的简化多模非线性静态程序，用于估计具有显着更高模态效应的结构的抗震需求。建议的程序在概念上基于扩展的 N2（其中 N 代表非线性分析，2 代表两个数学模型）方法（Kreslin 和 Fajfar in Earthquake Engineering & Structural Dynamics 40:1571–89, 2011）。然而，在所提出的方法中使用的模态组合程序来考虑更高的模态效应是不同的。NMP 程序通常包括两个主要步骤。首先，使用传统的 Pushover 程序推动结构，即基本 N2 方法、第一模态 Pushover 分析或具有三角形或均布荷载模式的 Pushover 分析，它主要控制结构下部的响应。其次，基于所有感兴趣模式的模态响应分析概念计算的模态楼层位移和漂移是代数相加的。这些组合响应基于预定目标位移被归一化。最终的响应是从上述两个步骤获得的结果的包络。第二步中使用的方法可以保留模态响应的符号。因此，由于更高模式的贡献而产生的符号反转的影响包含在所提出的方法中。此外，与非线性响应历史分析或自适应 pushover 程序相比，NMP 程序减轻了计算负担。为了评估所提出的程序在估计结构抗震要求方面的准确性，将其应用于两组钢结构，包括三个具有 6、12 和 18 层高度的特殊力矩框架 (SMF)，以及一个12层SMF，软层为第一组，9层和20层SAC钢框架为第二组。将 NMP 程序的结果与作为基准解决方案的非线性响应历史分析 (NL-RHA) 以及其他两种 pushover 方法（包括传统的基于第一模态的 pushover 分析和扩展的 N2 方法）获得的结果进行比较，证明了充分性NMP 程序在准确估计全局和局部响应量方面的作用。18层高，12层SMF，软层为第一组，9、20层SAC钢框架作为第二组。将 NMP 程序的结果与作为基准解决方案的非线性响应历史分析 (NL-RHA) 以及其他两种 pushover 方法（包括传统的基于第一模态的 pushover 分析和扩展的 N2 方法）获得的结果进行比较，证明了充分性NMP 程序在准确估计全局和局部响应量方面的作用。18层高，12层SMF，软层为第一组，9、20层SAC钢框架作为第二组。将 NMP 程序的结果与作为基准解决方案的非线性响应历史分析 (NL-RHA) 以及其他两种 pushover 方法（包括传统的基于第一模态的 pushover 分析和扩展的 N2 方法）获得的结果进行比较，证明了充分性NMP 程序在准确估计全局和局部响应量方面的作用。