Probabilistic inelastic seismic demand spectra for large-span planar steel structures subjected to vertical ground motions

Severe vertical ground motions (VGMs) may lead to detrimental seismic damages of large-span planar steel structures (LSPSSs), thus the inelastic seismic demand of LSPSSs under VGMs needs to be quantified so as to ensure the structural seismic reliabilities. In view that the uncertainties of VGMs greatly influence the seismic responses of LSPSSs, the VGMs-induced seismic demands of LSPSSs are investigated in a probabilistic way in this paper. Based on 680 strong VGM records, the vertical ductility demands (μ) of 2,100 equivalent single-degree-of-freedom (ESDF) models representing a series of LSPSSs are computed. It is revealed that the influences of VGM properties, including peak ground acceleration, epicentral distance, hypocenter depth, moment magnitude and local site condition, are tiny and irregular on the values of μ. Accordingly, the probabilistic seismic demand model for LSPSSs under VGMs is established regardless of the VGM properties in this paper. From the 1,428,000 computed values of μ, the VGMs-induced seismic demand of LSPSSs follows a positively skewed probabilistic distribution, and the distribution could be well fitted by the lognormal distribution model. The parameters of the lognormal distribution model for μ are simulated by two elementary functions subsequently, in which the effects of vertical strength reduction factor R, post-yield stiffness ratio α and elastic vibrating period T are accounted for. Using the lognormal model and the proposed functions, a group of probabilistic inelastic seismic demand spectra for LSPSSs under VGMs are generated. The established probabilistic spectra could provide the statistic properties of both the peak and the residual seismic demand of LSPSSs in association with pre-set values of T, R and α. Combining the proposed model with certain seismic hazard models that define the probabilistic characteristics of VGMs, the seismic reliability of LSPSSs could be quantified, and a proper structural seismic performance could be guaranteed.