Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods

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 stiffnessdegradation, 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 sitespecific 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 λk and the strength ratio λF of the top to bottom story are both considered. It is found that the SFRFs for λF ≤λk are smaller than those for λF > λk. 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 λF(= λk0.75), 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.