Stochastic seismic response analysis of hysteretic multi‐degree‐of‐freedom structures

Abstract

AbstractAnalytical study of random vibration of non‐linear mutli‐degree‐of‐freedom (MDF) systems is generally difficult. This is particularly true for MDF inelastic systems due to the highly non‐linear and hereditary behaviour of the restoring force. On the other hand, to obtain the response statistics using a step‐by‐step Monte Carlo simulation requires a large sample, and it could be very costly. The purpose of this paper is to present a practical analytical‐empirical method for an MDF yielding system. The method is based on a substitute structure (SS) concept in which the SS parameters are determined from empirical results of single‐degree‐of‐freedom systems, i.e. each element in the system is replaced by a linear counterpart with ductility‐dependent stiffness and damping. Based on a linear random vibration response analysis, the statistics of the maximum response (ductility) of each element are obtained by iteration. Numerical examples are given for multi‐storey buildings with deteriorating (reinforced concrete frame) or non‐deteriorating (steel frame) restoring forces. Comparisons with empirical results are satisfactory qualitatively. The main advantage of this method is that it requires relatively insignificant computation time, e.g. 1 s of execution time on the IBM 360–75 system for an eight‐storey steel frame.