Lin J.L.Tsaur C.C.KEH-CHYUAN TSAI2026-03-122026-03-122021https://www.scopus.com/record/display.uri?eid=2-s2.0-105027898900&origin=resultslisthttps://scholars.lib.ntu.edu.tw/handle/123456789/736246Vertically irregular buildings with strong or stiff-and-strong lower stories such as setback buildings are common in engineering practice. This study proposes a seismic evaluation method for setback buildings. The conventional single-degree-of-freedom (SDOF) modal equations of motion for vertically irregular buildings with strong or stiff-and-strong lower stories are decomposed into two-degree-of-freedom (2DOF) modal equations of motion. In addition to the 2DOF modal equations of motion, the two pushover curves simultaneously obtained from the n-th modal pushover analysis were used together to construct the n-th 2DOF modal system for the target buildings. One of the two pushover curves represents the relationship between the top displacement of the upper-structure and the base shear. The other represents the relationship between the top displacement of the base-structure and the base shear. The two pushover curves presented in the acceleration–displacement–response spectra format fully overlap each other as the building remains elastic, whereas the two curves bifurcate after the building yields. This study showed that the 2DOF modal system is identical to the SDOF modal system for elastic buildings with the specific vertical irregularities. In addition, it was found that the more inelastic excursions a building with the specific vertical irregularities experiences, the less effective using the SDOF modal system to simulate the distinct modal responses for the upper-structure and base-structure will be. The proposed 2DOF modal system precisely overcame the stated deficiency of the SDOF modal system for buildings with the specific vertical irregularities. Through incorporating the 2DOF modal systems into the uncoupled modal response history analysis, the peak inter-story drift ratios (IDR) of four 9-story and four 20-story vertically irregular buildings, which have the lower stories stronger or stiffer-and-stronger than the upper stories, were satisfactorily estimated, compared with those estimated by adopting the SDOF modal systems. The investigation results highlight that the drastic change in the peak IDRs, over the two stories where the abrupt change in strength occurs, was poorly reflected by using the SDOF modal systems. In contrast, the 2DOF modal systems adequately captured this characteristic.falsemodal response history analysismodal systemsetback buildingsvertically irregular buildingsconference paper2-s2.0-105027898900