UNIFORM RISK SPECTRA FOR NEGATIVE STIFFNESS SYSTEMS

This paper presents uniform risk spectra for negative stiffness systems that do not exhibit hysteretic damping, named Negative Stiffness Bilinear Elastic (NSBE) systems.The NSBE oscillator can be used to describe the dynamics of deformable rocking systems with or without restraining systems flexible enough to lead to an overall negative stiffness.It can also be used to describe rocking systems equipped with curved extensions at their base.It has been shown that the response of an NSBE system can be well predicted using the response of a Zero Stiffness Bilinear Elastic (ZSBE) system, which is a bilinear system of constant restoring force.The ZSBE system is a single parameter system; therefore it is simple to construct design spectra for it.For a wide range of ZSBE system strength values, this paper employs Incremental Dynamic Analysis using 105 ordinary (non-pulse-like, non-long-duration) ground motions to obtain the fragility functions for predefined limit-states of the ZSBE seismic response.Fragility functions per limit-state are convolved with the seismic hazard to compute the Mean Annual Frequency of exceedance (MAF).For this study, the seismic hazard curve for a site at Athens Greece is used as it is obtained via probabilistic seismic hazard analysis.Finally, uniform risk spectra per limit-state are obtained by computing the MAF for all the ZSBE oscillators.These spectra can be used for the design of NSBE systems, including rocking oscillators.