Earthquake Engineering and Engineering Vibration

, Volume 18, Issue 1, pp 187–201 | Cite as

Sample geometric mean versus sample median in closed form framework of seismic reliability evaluation: a case study comparison

  • M. Abyani
  • B. Asgarian
  • Mohamad ZarrinEmail author


Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytical expressions have been developed to estimate the annual probability of exceeding a limit state. In the process of such seismic assessments, some essential assumptions are adopted to simplify the process. One of these fundamental assumptions declares that drift demand at any seismic intensity level follows a lognormal distribution around its median. To investigate the validity of this assumption, this paper describes a case study of the types of errors that could be produced by using the sample median as the central tendency. Based on the Maximum Likelihood Estimation method as well as other statistical evidence, this paper proposes the use of the sample geometric mean instead of the sample median for the central tendency. Further, the results of seismic reliability evaluations of 4 sample frames are compared based on utilizing both the geometric mean and the sample median. In this process, both first and second order power law fits of the hazard curve are implemented to compare the effects of hazard estimation and the selection of the central tendency on the final results. It is observed in the application example that the sample geometric mean could lead to more accurate results.


seismic reliability closed-form expression SAC/FEMA limit state median geometric mean 


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Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringK.N.Toosi University of TechnologyTehranIran

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