An improved version of the direct displacement-based design (DDBD) method for the seismic design of plane moment resisting frames in the framework of performance-based design approach is presented. The method employs a multi-degree-of-freedom equivalent system instead of the single-degree-of-freedom equivalent system used by the conventional DDBD method. Thus, the proposed method can take more rationally and with higher accuracy into account the higher mode and P-Δ effects than the conventional one. This is accomplished with the aid of the concept of deformation dependent equivalent modal damping ratios previously developed by the present authors for other purposes and the concept of the design modal displacements developed herein. These design modal displacements are determined on the basis of target inter-storey drift ratios for every performance level and the first few modes significantly contributing to the structural response. Thus, one can determine from the displacement spectrum with high amounts of viscous damping the required modal periods for known values of the design modal displacements. From those modal periods, the corresponding required modal stiffness and hence the modal base shear forces can be obtained. The final required design base shear can be obtained by a combination rule, like the SRSS rule. Numerical examples involving the seismic design of two moment resisting reinforced concrete plane frames are presented in detail for illustrating the proposed approach and demonstrating its merits over the conventional DDBD method and the force-based design method of Eurocode 8.

中文翻译：

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基于MDOF等效系统的基于位移的直接抗震设计方法：在R / C框架结构中的应用

在基于性能的设计方法框架内，提出了一种基于直接位移的设计（DDBD）方法的改进版本，用于平面抗弯框架的抗震设计。该方法采用了多自由度等效系统，而不是传统的DDBD方法所使用的单自由度等效系统。因此，与传统方法相比，所提出的方法可以更合理，更准确地考虑更高的模式和P-Δ效应。这是借助于本发明人先前为其他目的而提出的依赖于变形的等效模态阻尼比的概念以及本文提出的设计模态位移的概念来实现的。这些设计模态位移是根据每个性能水平的目标层间漂移比和对结构响应有重大贡献的前几个模态确定的。因此，可以从具有高粘性阻尼的位移谱中确定设计模态位移的已知值所需的模态周期。从这些模态周期中，可以获得相应的所需模态刚度，从而获得模态基础剪切力。最终所需的设计基础剪力可以通过组合规则（如SRSS规则）获得。