Design floor spectra for linear and nonlinear SDoF oscillators

The seismic analysis and design of secondary attachments to buildings or industrial facilities is a topic of broad engineering interest, increasingly attracting the attention of researchers and practitioners. Examples of secondary systems include suspended ceilings and non-structural walls, piping systems and antennas, storage tanks, electrical transformers and glass façades. Although not part of the load bearing structure, their significance stems from the survivability requirement in the aftermath of a seismic event and their vast contribution to the overall construction costs. Nevertheless, past earthquakes have demonstrated that current methods for the seismic analysis and design of secondary structures lack the necessary rigor and robustness, resulting in expensive and often unreliable solutions. Secondary systems can be highly sensitive to accelerations and inter-story drifts, and their seismic performance is influenced by the primary-secondary dynamic interaction. In many situations however, the mass of the secondary system may be much lower than the mass of the floor at which it is connected and therefore a cascade approach is admissible. If the secondary system can be realistically modeled as a single-degree-of-freedom (SDoF) system, then the floor response spectra could be a powerful tool for quantifying its seismic response. In this study, the performance of light secondary systems is examined in presence of uncertainties in the seismic input. A set of principal axes of ground shaking is initially identified and an ensemble of bi-directional time series is generated. The response of a set of SDoF secondary oscillators (i.e. linear, Bouc-Wen, sliding and rocking) attached to a representative primary structure is then investigated and their design spectra are established. As demonstrated with Monte Carlo simulations for the selected case study, the angle of seismic incidence causes the highest variations in the engineering demand parameters for the sliding oscillators, while the elasto-plastic oscillator with the Bouc-Wen model experiences the least variations. Furthermore, investigations at different elevations show higher variations in the sliding and linear oscillators, depending on the seismic input. As expected, the viscous damping ratio is found to significantly influence the response of secondary systems vibrating close to the fundamental frequency of the primary structure. Moreover, the peak response of sliding oscillators is shown to be a smooth function of the sliding friction coefficient, while the rocking spectra, due to the strong nonlinear dynamics of the rocking blocks, are characterized by large values of the coefficient of variations.