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

This study aims at proposing seismic reliability‐based relationships betweenthe behavior factors and the displacement demand for nonlinear hardeningand softening structures isolated by friction pendulum system devices consider-ing several structural properties. An equivalent 2dof model having both a hard-ening and softening postyield slope is used to describe the superstructurebehavior, whereas a velocity‐dependent model is adopted for the friction pen-dulum system response. The yielding characteristics of the superstructures,related to life safety limit state, are designed according to the seismic hazardof L'Aquila site (Italy) for increasing behavior factors, as provided fromNTC08. Considering natural seismic records and several elastic and inelasticbuilding properties, different postyield hardening and softening stiffnessvalues, different seismic intensity levels, and modeling the friction coefficientas a random variable, incremental dynamic analyses are performed to evaluatethe seismic fragility of these structural systems. By means of the convolutionintegral between the fragility curves and the seismic hazard curves correspond-ing to L'Aquila site (Italy), the reliability curves of the equivalent hardeningand softening base‐isolated structural systems, with a lifetime of 50 years, aredefined. Specifically, seismic reliability‐based linear and multilinear regressionexpressions between the displacement ductility demand and the behavior fac-tors for the superstructure as well as seismic reliability‐based design abacusesfor the friction pendulum devices are proposed.