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AschheimYdPtSpectra

AschheimYdPtSpectra - Seismic Design Based on the Yield...

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Seismic Design Based on the Yield Displacement Mark Aschheim, a) M.EERI Although seismic design traditionally has focused on period as a primary design parameter, relatively simple arguments, examples, and observations discussed herein suggest that the yield displacement is a more stable and more useful parameter for seismic design. The stability of the yield displace- ment is illustrated with four detailed examples, consisting of moment- resistant frame buildings. Each frame is designed to limit roof drift for a spe- cific ground motion using an ‘‘equivalent’’ SDOF model in conjunction with Yield Point Spectra. The effectiveness of the simple design method is estab- lished by nonlinear dynamic analysis. Yield displacements were stable and consistent while the fundamental periods of vibration (and lateral stiffness) required to meet the performance objective differed substantially. [DOI: 10.1193/1.1516754] INTRODUCTION Since the introduction of the response spectrum by Benioff (1934) and Biot (1941) it has become second nature to think of the seismic design task in terms of the fundamen- tal period of vibration of a structure. Contemporary and traditional design approaches rely upon the fundamental period of vibration of the structure to determine the required strength (or stiffness) for the design level seismic actions. This use of the fundamental period of vibration is based on the premise that it may be estimated given the initial structural concept and dimensions of the structure. This paper develops the idea that the yield displacement is a more natural and more useful parameter to use in the seismic design of structures responding nonlinearly. The use of period as a fundamental design parameter draws directly from the equa- tion of motion for linear elastic response, for which the peak displacement, S d , is a func- tion of the period of vibration, T . Because T 5 2 p ( m / k ) 0.5 , structures of varied heights (Figure 1) having the same ratio of mass, m , and stiffness, k , all have the same peak displacement. The period of vibration is useful for characterizing the peak response of an infinite variety of systems (such as those in Figure 1) whose response is linear elastic. Although many formulas and design procedures are based on the idea that the period of vibration of the structure can be estimated early in the design process, the reality is that the period of vibration may vary significantly as the initial design concept is refined into the final product, particularly if the lateral strength and stiffness must be adjusted to a) Mid-America Earthquake Center, University of Illinois, 2118 Newmark Laboratory, 205 N. Mathews, Urbana, IL 61801 581 Earthquake Spectra , Volume 18, No. 4, pages 581–600, November 2002; © 2002, Earthquake Engineering Research Institute
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satisfy precisely defined performance objectives. The difficulty of accurately estimating the period of vibration of the final design is apparent in the work of Chopra and Goel (2000), who examined a large number of buildings in California.
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