INELASTIC DISPLACEMENT RATIOS FOR ... - CiteSeerX

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Oct 10, 2000 - San Francisco, Telegraph Hill 58133. AB. 88.0. 96.9. 90 .... rigation District. 117. D. 45.0. 29.5 .... Richmond, City Hall Parking lot. 58505. D. 92.7.
INELASTIC DISPLACEMENT RATIOS

FOR

STRUCTURES

ON

FIRM SITES

By Eduardo Miranda,1 Member, ASCE ABSTRACT: The results of a comprehensive statistical study of inelastic displacement ratios that permit the estimation of maximum lateral inelastic displacement demands on a structure from maximum lateral elastic displacement demands are presented. These ratios were computed for single-degree-of-freedom systems undergoing different levels of inelastic deformation when subjected to a relatively large number of recorded earthquake ground motions. The study is based on 264 acceleration time histories recorded on firm sites during various earthquakes in California. Three types of soil conditions with shear-wave velocities higher than 180 m/s are considered. The influences of period of vibration, level of ductility demand, site conditions, earthquake magnitude, and epicentral distance are carefully evaluated and discussed. Inelastic displacement ratios associated with mean values are presented. Special emphasis is given to the disperson of the results. It is concluded that for sites with average shear-wave velocities higher than 180 m/s the influence of soil conditions is relatively small and can be neglected for design purposes. Finally, results from nonlinear regression analyses are presented that provide a simplified expression to be used in the design to approximate mean inelastic displacements ratios for structures on firm sites.

INTRODUCTION In general, nonlinear time history analyses of structures may produce a good estimation of global and local deformation demands for a given acceleration time history. However, at the present time these analyses are still considered unpractical for everyday design situations. Furthermore, the results of such analyses tend to be sensitive to the specific characteristics of the ground motion and in some cases to the assumptions regarding the behavior of individual structural components. Thus, simple, yet reliable methods for estimating lateral inelastic displacements demands on structures are needed for the design of new structures or during the seismic evaluation and rehabilitation of existing structures. A particularly appealing simplified approach is to try to estimate the maximum inelastic response, and, in particular, the maximum lateral inelastic displacement demand, using the results from a linear elastic analysis. Efforts in this direction began many years ago. One of the first studies was done by Veletsos and Newmark (1960) and Veletsos et al. (1965), who pointed out that ‘‘it is instructive to relate the maximum deformation of the elastoplastic system to that of an elastic system having the same stiffness as the initial stiffness of the inelastic system.’’ Using single-degree-of-freedom (SDOF) systems subjected to simple pulses and to three earthquake ground motions, they noticed that in the low frequency range (frequencies smaller than 0.38 Hz) the maximum deformation of the inelastic and the associated elastic systems may be considered the same. This observation gave rise to the so-called equal displacement rule, which is the basis for estimating maximum deformations in certain spectral regions in most building codes. This study also concluded that, in the high frequency and moderately high frequency regions, the inelastic displacements are significantly higher than their elastic counterparts. While searching for an energy criterion to rationalize the use of reduced forces in design, Shimazaki and Sozen (1984) noticed that, in the spectral region of nearly constant energy response, the maximum nonlinear drift of reinforced concrete structures could be determined as a function of the linear drift. Additionally, they noticed that this observation held for a wide 1 Asst. Prof., Dept. of Civ. and Envir. Engrg., Stanford Univ., Stanford, CA 94305-4020. Note. Associate Editor: Brad Cross. Discussion open until March 1, 2001. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on September 20, 1999. This paper is part of the Journal of Structural Engineering, Vol. 126, No. 10, October, 2000. 䉷ASCE, ISSN 0733-9445/00/0010-1150– 1159/$8.00 ⫹ $.50 per page. Paper No. 21903.

range of hysteretic-response types, oscillator-spring strengths, and ground motion characteristics. Based on this information, they developed an equation based on the ratio of the characteristic period of the structure to the characteristic period of the ground motion and on the ratio of the base shear strength to the base shear for linear response to evaluate cases where the ratio of maximum inelastic displacement to maximum elastic displacement was