Inelastic Spectra - The generation of in-elastic response...

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Paper Number 076 The generation of in-elastic response spectra for earthquake acceleration records Athol J. Carr University of Canterbury, Christchurch, New Zealand. ABSTRACT: In 1960 Newmark showed that the displacements of inelastic structures subjected to earthquake excitation were similar to those of the same structure when it behaved elastically. Code writers have taken this to develop the equal displacement concept that has been the mainstay of seismic design codes for the past 40 years. Modifications have been made to the approach for structures with short natural periods of free vibration, to use the equal energy and equal acceleration concepts when deriving the inelastic design spectra. It will be shown in this paper that many of these assumptions are not particularly true even for the earthquake accelerograms used by Newmark. With all the advances in the analysis methods and design philosophies, such as capacity design and performance based design, made over the past 40 years that it is appropriate than the basic assumptions used in deriving the inelastic design spectra need to be re-appraised. This paper will outline a method of deriving the inelastic design spectra for any earthquake excitation allowing for almost any stiffness and strength degradation models to be used to represent the structural behaviour. 1 INTRODUCTION The current method of producing the inelastic design spectra used in many building codes including the New Zealand Loadings Code [NZ4203:1992] is to use the equal displacement concept of [Newmark, 1960] which implies that the inelastic structure will have the same displacement as the elastic structure and this implies [Carr, 1994] that if the structure has a design ductility of 4 then the yield force will be a ¼ of the elastic design force. This means that the inelastic acceleration design spectrum will be the elastic acceleration spectrum divided by the ductility factor. For shorter natural period structures the equal energy concept is used. As the natural period tends to zero the inelastic acceleration spectrum will tend to the elastic acceleration spectrum, the equal acceleration concept. In the NZ Loadings Code a linear interpolation of the reduction factor is used between the equal displacement method at natural periods greater than 0.7 seconds and the equal acceleration concept as the natural period tends to zero. In many inelastic analyses carried out over the past 30 years there have been many instances where the equal displacement concept was observed to have been inapplicable. As a result, a combination of the inelastic capabilities of the analysis program Ruaumoko [Carr, 2001] and the response spectra methods to produce a program, INSPECT [Carr, 2002] to produce inelastic response spectra for any earthquake accelerogram using almost any of the 44 hysteretic stiffness degradation rules and for any of the 5 strength degradation rules used in Ruaumoko. 2
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Inelastic Spectra - The generation of in-elastic response...

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