Curved gridshells are excited not only in the horizontal direction but also experience large anti-symmetric vertical accelerations when subjected to horizontal earthquake ground motions. In addition to the coupled response, gridshells exhibit closely spaced modes and substructure-roof interaction. Nevertheless, previous studies have proposed elastic horizontal and vertical equivalent static seismic forces considering these complex dynamic response characteristics. These are determined from the input horizontal acceleration at the substructure’s roof level, an assumed acceleration distribution, nodal roof masses and amplification factors derived from the dynamic characteristics of the dome and substructure. To extend this methodology to nonlinear substructures with displacement-dependent damping devices, this paper investigates the applicability of ductility reduction factors (or R_μ factors) to estimate the inelastic response spectra and an alternative equivalent linearisation approach to compute the peak horizontal acceleration of multistorey substructures with buckling-restrained braces. This is achieved by modelling the curved roof as a rigid mass for the substructure model, and using its idealised base shear-roof displacement relationship obtained from modal pushover analyses. The peak horizontal acceleration of the substructure is then used to obtain the equivalent static loads of the curved roof using amplification factors, and the accuracies are verified against the results from nonlinear response history analyses. It was confirmed that the R_μ R μ factors combined with the roof amplification factors provide a simple way to estimate the peak roof response with sufficient accuracy for preliminary design of domes with multistorey substructures having low post-yield stiffness.

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Equivalent static loads for double-layered domes supported by multistorey buckling-restrained braced frames