Seismic force reduction factor (SFRF) spectra of shear-type multi-degree-of-freedom (MDOF) structures are investigated. The modified Clough model, capable of considering the strength-degradation/hardening and stiffness-degradation, is adopted. The SFRF mean spectra using 102 earthquake records on a typical site soil type (type C) are constructed with the period abscissa being divided into three period ranges to maintain the peak features at the two site-specific characteristic periods. Based on a large number of results, it is found that the peak value of SFRF spectra may also exist for MDOF, induced by large high-mode contributions to elastic base shear, besides the mentioned two peak values. The variations of the stiffness ratio λ_k and the strength ratio λ_F of the top to bottom story are both considered. It is found that the SFRFs for λ_F ≤ λ_k are smaller than those for λ_F > λ_k. A SFRF modification factor for MDOF systems is proposed with respect to SDOF. It is found that this factor is significantly affected by the story number and ductility. With a specific λ_F (= λ_k^0.75), SFRF mean spectra are constructed and simple solutions are presented for MDOF systems. For frames satisfying the strong column/weak beam requirement, an approximate treatment in the MDOF shear-beam model is to assign a post-limit stiffness 15%-35% of the initial stiffness to the hysteretic curve. SFRF spectra for MDOF systems with 0.2 and 0.3 times the post-limit stiffness are remarkably larger than those without post-limit stiffness. Thus, the findings that frames with beam hinges have smaller ductility demand are explained through the large post-limit stiffness.

中文翻译：

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通过两个特征周期归一化的MDOF系统的地震力折减系数谱

研究了剪切型多自由度（MDOF）结构的地震力折减系数（SFRF）谱。采用改进的Clough模型，该模型能够考虑强度退化/硬化和刚度退化。利用102个地震记录在典型场地土壤类型（C型）上建立的SFRF平均谱图，将横坐标周期划分为三个周期范围，以保持两个特定地点特征周期的峰值特征。根据大量结果，发现除了上述两个峰值外，MDOF的SFRF谱图峰值也可能存在，这是由高模量对弹性基础剪力的较大贡献引起的。刚度比的变化λ _ķ和强度比λ _˚F从上到下的故事都被考虑了。据发现，对于SFRFs λ _˚F ≤ λ _ķ比对于较小的λ _˚F > λ _ķ。针对SDOF提出了MDOF系统的SFRF修改因子。发现该因素受故事数量和延展性的显着影响。与特定的λ _˚F（= λ _ķ ^0.75），构造了SFRF平均光谱，并为MDOF系统提供了简单的解决方案。对于满足强柱/弱梁要求的框架，MDOF剪力梁模型中的一种近似处理方法是将极限刚度的15％-35％作为初始刚度分配给滞后曲线。具有极限后刚度的0.2倍和0.3倍的MDOF系统的SFRF光谱要比没有极限后刚度的SFRF光谱大得多。因此，通过大的极限后刚度解释了具有梁铰链的框架具有较小延性要求的发现。