Quantification of floor seismic response: Formulated PFA for non-classically damped structure and empirical PFV for elasto-plastic structure

The earthquake-induced acceleration & velocity responses at the structural floor level are the key issues to be considered in the aseismic design of non-structural components (NSC). To date, the floor seismic acceleration and velocity of the classically-damped structure have been well quantified in the linear-elastic range. Some additional proposals also appropriately addressed the peak floor acceleration (PFA) at the inelastic stage. For the nonclassically damped structure, a well-recognized method for the linear PFA is yet to come. Meanwhile, the peak floor velocity (PFV) of the inelastic structure is not well quantified. These problems certainly bring troubles to the aseismic design of the NSCs. In this paper, the PFA for the non-classically damped structure and the PFV for the inelastic structure are quantified theoretically or semi-theoretically. Firstly, the complex complete quadratic combination (CCQC) method is derived for the PFA of the non-classically damped structure. In the CCQC approach, the peak acceleration of each complex mode is combined by the CQC rule. To better consider the correlation between the different complex modes, the seismic input is assumed to be a stationary process. Secondly, the PFV for the inelastic structure is analyzed via a nonlinear modal combination method. In the method, the contribution of each mode to the linear PFV is modified so as to account for the nonlinearity-induced reduction, and the modified modal contributions are combined via the CQC method to form an inelastic CQC (ICQC) approach for the inelastic PFV. Thirdly, several structural models are selected to validate the proposed methods for the PFA and the PFV. Numerical results show that the accuracies of the proposed formulas are satisfying. This study is an extension and supplement to the current analytical approaches for the floor seismic response, which is useful for the aseismic design of NSCs in the referred scenarios.