Seismic reliability-based ductility demand for hardening and softening structures isolated by friction pendulum bearings

This study aims at proposing seismic reliability-based relationships between the behavior factors and the displacement demand for nonlinear hardening and softening structures isolated by friction pendulum system devices considering several structural properties. An equivalent 2dof model having both a hardening and softening postyield slope is used to describe the superstructure behavior, whereas a velocity-dependent model is adopted for the friction pendulum system response. The yielding characteristics of the superstructures, related to life safety limit state, are designed according to the seismic hazard of L'Aquila site (Italy) for increasing behavior factors, as provided from NTC08. Considering natural seismic records and several elastic and inelastic building properties, different postyield hardening and softening stiffness values, different seismic intensity levels, and modeling the friction coefficient as a random variable, incremental dynamic analyses are performed to evaluate the seismic fragility of these structural systems. By means of the convolution integral between the fragility curves and the seismic hazard curves corresponding to L'Aquila site (Italy), the reliability curves of the equivalent hardening and softening base-isolated structural systems, with a lifetime of 50 years, are defined. Specifically, seismic reliability-based linear and multilinear regression expressions between the displacement ductility demand and the behavior factors for the superstructure as well as seismic reliability-based design abacuses for the friction pendulum devices are proposed.