ON THE COMMENT OF THE NEW ZEALAND SEISMIC CODE OF PRACTICE REGARDING INTEGRATION STEP SIZES WHEN IMPLEMENTED IN NONLINEAR ANALYSIS OF SOME MODERN EARTHQUAKE RESISTANT SYSTEMS

Abstract eng:
The true behavior of structural systems is nonlinear and dynamic. Specifically in analyses of structural systems against earthquakes, time integration of the semi-discretized equations of motion is the most versatile analysis tool of the behaviors. The parameter of time integration, i.e. integration step size, affects the accuracy and the computational cost in different ways and hence assigning an appropriate value to the step size is of high significance. Considering the major comment existing on the integration step size selection when the structures are subjected to earthquakes (proposed by the seismic code of New Zealand), and the theoretical ambiguities addressed in the literature regarding its adequacy, the objective in this paper is to present a brief overview on the adequacy of the comment, by comparing the accuracies of some nonlinear analyses with the accuracies in the corresponding linear problems. Three three-floor three-span two dimensional steel frames each equipped with a special modern earthquake resistant system are taken under consideration. The three modern systems are flexural frames with buckling restrained braces (BRBs), flexural frames with nonlinear viscous dampers, and flexural frames on base isolators. After finite element discretization, the time integration analyses are carried out by the average acceleration method of Newmark, while, at nonlinearity detections, the conventional value of 10E-5 is considered as the tolerance of the nonlinearity iterations. In all analyses, the values assigned to integration step sizes were according to the current seismic code of New Zealand, and after the analyses, they were repeated after elimination of the sources of nonlinearities. The exact responses were also determined by considering sufficiently small integration steps and the convergence providable also for nonlinear analyses. The relative errors of top displacement and base shear at each nonlinear analysis is compared with the corresponding errors of the linear analyses. As the conclusion, in agreement with theoretical expectations, the comment in the seismic code of New Zealand is not necessarily providing a specific accuracy, and the accuracy can be more or less than the accuracy in the linear analyses, and hence may entail large errors not acceptable in practice. For the strength of the study, the numerical study will be repeated in the frame of the existing time interval, considering other cases of the structural systems and time integration methods.

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