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This paper investigates the seismic response characteristics of long-span domes. The natural periods of the prominent modes are longer than medium-span domes, which leads to a greater contribution from the higher modes to the response of the long-span dome. The acceleration distributions, particularly the vertical acceleration distributions are sensitive to the dominant mode shapes of these higher modes. This leads to inaccuracies when applying the previously proposed response evaluation methods. The vibration modes of multi-storey supporting substructures also affect the excited vibration modes of the roof. In this paper, the dynamic characteristics and seismic response of 150m-span domes supported by multi-storey substructures are studied. The effects of the post- yield stiffness of multi-storey substructures are also analysed by considering two structural systems, buckling- restrained braced frames (BRBF) and damped spine frames. A simple design procedure to evaluate the equivalent static loads using amplification factors and incorporating the effects of higher modes is proposed based on response spectrum analysis and equivalent linearisation procedures. The accuracy of the proposed method is evaluated by comparing the responses with those obtained from non-linear response history analysis.

In this study, a computational seismic design routine is proposed based on a generalized response spectrum analysis for highly indeterminate structures with energy-dissipation members, such as viscous or elasto-plastic dampers. Complex stiffness terms are introduced to account for displacement-dependent damping, and a three-dimensional (3-D) element stiffness matrix with complex axial stiffness is proposed for elasto-plastic dampers. A modified complete quadratic combination method previously developed for real symmetric damped systems is extended to complex asymmetric damped systems, based on a theoretical analysis of eigenvalue equations. The response is evaluated by iteratively conducting complex eigenvalue analysis and modal combination. The accuracy is confirmed through comparison to nonlinear response history analysis of 2-D frame models. Finally, an example application is presented of a 3-D truss tower seismically retrofitted by replacing the braces with viscoelastic and then elasto-plastic dampers. The proposed design routine is used to rapidly identify novel and efficient damper arrangements and sizing distributions, avoiding computationally intensive nonlinear response history analysis.

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This paper presents a design method for highly indeterminate seismically isolated structures utilizing generalized response spectrum analysis, which has been extended to simulate both of an elasto-plastic damper with isolator and a nonlinear oil damper. This enables a more efficient design process than trial-and-error approaches with non-linear response history analysis. The design example using the proposed method are demonstrated in a series of studies using a base isolation system with a tall building and mid-story isolation or roof isolation systems having substructures with dampers.