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Stochastic seismic response analysis of hysteretic multi‐degree‐of‐freedom structures
Author(s) -
Wen YiKwei
Publication year - 1979
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290070206
Subject(s) - structural engineering , structural system , random vibration , stiffness , vibration , computation , frame (networking) , monte carlo method , restoring force , finite element method , degrees of freedom (physics and chemistry) , engineering , computer science , mathematics , algorithm , statistics , physics , mechanical engineering , quantum mechanics
Analytical 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.