LAUSR

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.