Investigation on the Effect of Windowing Functions and Time Steps in Stochastic Finite Fault Method on the Dynamic Nonlinear Response of SDOF

In the event of an earthquake that is an unusual and reciprocal loading, it’s permitted in many structures, according to their importance and ductility, to go to their inelastic range of behavior and dissipate some of the input energy in this zone through nonlinear hysteresis loops. Ductility demand should be determined on the members that yielded, so nonlinear analysis is needed. For nonlinear dynamic analysis of structures and determining the ductility demand on the members, and for analyzing the structures in which seismic isolator or damping elements are used, it is needed to provide sufficient number of suitable accelerogram, moreover. With increasing of the knowledge and the interest for using performance design and assessment of structures, using time history analysis is on the rise. In many areas, there is no suitable recorded accelerogram, but there are historical evidences for large earthquakes. Therefore, we need to use scaled or simulated accelerogram for engineering purposes. In the building regulations, it is allowed that simulation of ground motion can be used as a tool for producing accelerogram. A favorite method in earthquake engineering to produce accelerograms is the finite-fault stochastic method. In finite-fault modeling of earthquake ground motion, a large fault is divided into N sub-faults, where each sub-fault is considered as a small point source. In the point-source method for simulating a record, first, a white noise is generated for duration given by duration of the motion. This noise is then windowed. The windowed noise is transformed into the frequency domain. The spectrum of noise is normalized by the square-root of the mean square amplitude spectrum. The normalized spectrum is multiplied by the ground motion spectrum. The resulting spectrum is transformed back to the time domain. Two types of window function that generally use in the stochastic methods are Saragoni-Hart and Boxcar window. Therefore, it may affect [or may be affected by] the response of structures. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms. This provides a means by which the results of the rigorous studies reported in other papers can be incorporated into practical predictions of ground motion. Since the dynamic time history analysis results, depending on the type and content of input information, it's required to consider good accuracy in selection of data. In this study, it has investigated the effect of window functions used to shape white noise on the ductility demand of single degree of freedom systems, showing that the types of window functions do not have any effect on the response of single degree of freedom systems. Besides, it has investigated the effects of time step, used to produce white noise, on the ductility demand and pseudo acceleration response of single degree of freedom systems, showing that the time step equal to 0.02 produces higher ductility demand and lower pseudo acceleration response in the frequencies higher than 2 Hz compared with 0.005 and 0.01.