Vertical ductility demand and residual displacement of roof-type steel structures subjected to vertical earthquake ground motions

The vertical component of seismic ground motions (VGM) may induce severe responses in roof-type structures such as mega canopies, large floors, etc. This paper proposes a ductility-based approach for estimating the inelastic responses of roof-type steel structures under VGMs. Due to the pre-loaded gravity, a roof-type steel structure exhibits obvious asymmetric hysteresis properties in the vertical direction. Accordingly, this kind of structure could be idealized as “one-side yielding” systems which only yield in the lower side of vibration, wherein the gravity effect and the VGM effect positively super-positions with each other. Based on the idealized model, the vertical ductility demand spectra and the vertical residual displacement spectra for roof-type steel structures are computed using 53 recorded strong near-fault VGMs. Taking into account the vertical strength reduction factor and the vertical post-yielding stiffness ratio, a vertical ductility demand model in the μ-T format is proposed for roof-type steel structures under VGMs. Meanwhile, the vertical residual displacement model is derived from the vertical ductility demand model, since the vertical residual displacement could be computed as the peak vertical displacement subtracted by the recoverable elastic displacement. An application of these proposed models is given in the paper. The vertical seismic responses of a large-span steel floor under VGMs are predicted based on the proposed models, and the obtained results (including both the peak and the residual responses in the vertical direction) show good accuracy as compared with the results given by nonlinear response history analysis.