Higher mode effects of multistorey substructures on the seismic response of double-layered steel gridshell domes

Abstract

The seismic response of gridshell roofs with substructures is strongly influenced by the relative mass and stiffness of the roof and substructure, and particularly by how close the periods of the dominant roof and substructure modes are. Multistorey substructures may exhibit a significant higher-mode acceleration response, primarily due to the contribution of the shorter second translational substructure mode to the roof response. This paper presents parametric studies conducted on steel gridshell domes with 60, 100 and 150 m spans and six-storey substructures to investigate the interaction between the higher substructure modes and dominant roof modes. The contribution of each substructure mode to the overall response was characterised by a newly proposed dominance response ratio. In contrast to previous studies of long-period single-storey substructures, which only minimally excited the roof modes, the higher modes of the long-period multistorey substructures investigated in this study significantly contributed to the roof response. The roof vertical accelerations were amplified by up to three times the substructure roofline acceleration, as the curved roof geometry couples the horizontal substructure and vertical roof response. The substructure higher-mode contribution was quantified using amplification factors and developed into equivalent static loads that were found to be in good agreement with response spectrum analysis results. The proposed equivalent static loads provide insight into the complex dynamic characteristics of gridshell roofs with multistorey substructures and offer an efficient method for preliminary seismic design.