Design Seismic Demands from Seismic Response Analyses: A Probability-Based Approach

Abstract

Earthquake-resistant design guidelines commonly prescribe that when conducting seismic response analyses: (i) a minimum of three ground motions can be used; (ii) if less than seven ground motions are considered, the maximum of the responses should be used in design; and (iii) if seven or more ground motions are considered the average of the responses should be used in design. Such guidelines attempt to predict the mean seismic response from a limited number of analyses, but are based on judgment without a sound, yet pragmatic, theoretical basis. This paper presents a rational approach for determining design seismic demands based on the results of seismic response analyses. The proposed method uses the 84thpercentile of the distribution of the sample mean seismic demand as the design seismic demand. This approach takes into account: (i) the number of ground motions considered; (ii) how the ground motions are selected and scaled; and (iii) the differing variability in estimating different types of seismic response parameters. A simple analytic function gives a ratio which, when multiplied by the mean response obtained from the seismic response analyses, gives the value to be used in design, thus making the proposed approach suitable for routine design implementation.