In seismic codes, the force strength reduction factor is proposed to transform elastic to inelastic strength. The ductility reduction factor, Rμ, plays a key role on R factor if no overstrength is present. The Rμ is determined by SDOF systems. But the higher mode (HM) and Multi-Degree-of-Freedom (MDOF) effects need to be considered to extract the R factor. These effects are studied by proposing αv-MDOF via at least 1764 Nonlinear dynamic Analysis of 2D-frames. Also a sensitivity study has been performed on Rμ and αv-MDOF. Results obtained from studies conducted on the frames, indicate that HM and MDOF effects have a considerable influence on the base shear. Also the αv-MDOF is typically higher than unity both for ordinary and for near-field earthquakes and it is affected by period, span number and ductility level. These effects are remarkable for near-field motions. Finally, a simplified practical expression is proposed to estimate the αv-MDOF.
Gerami, M., Siahpolo, N., & Vahdani, R. (2017). Effects of higher modes and MDOF on strength reduction factor of elastoplastic structures under far and near-fault ground motions. Ain Shams Engineering Journal, 8(2), 127–143. https://doi.org/10.1016/j.asej.2015.08.015