Probabilistic seismic demand analysis of nonlinear structures

Abstract

This paper presents a probabilistic evaluation of the reduction coefficients used in seismic design of building structures when an elastic analysis is used to estimate the seismic inelastic response. For this purpose, we study the probabilistic seismic response of various single-degree systems with hysteretic models representing different levels of stiffness and strength degradation. Two types of models are given particular attention. The first is an elastoplastic nondegrading model which is used to calibrate reduction coefficients prescribed by general building codes such as UBC and the UCRL 15910. The second is a trilinear degrading model representing masonry structures and other systems with strong degradation. The influence of system properties is studied by systematically varying the period of the structure. The uncertainties in seismic input are accounted for by statistical analysis of the response to a set of 50 synthetic records with frequency content representative of earthquakes of firm to medium stiff sites. The evaluation procedure consists of determining the seismic coefficient required by the nonlinear systems to match a prescribed average target ductility and comparing it to the average coefficient for elastic systems with the same initial (tangent) or secant period. An examination of individual ductility demands shows that the statistical variation of peak seismic response of the nonlinear systems can be represented by a lognormal distribution or with a Gumbel Type I extreme value distribution of largest values.