Website of the Endurance Time method
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Endurance Time (ET) method is a dynamic analysis procedure where seismic performance of structures at various excitation intensities are estimated by subjecting them to predesigned intensifying dynamic excitations. The concept of ET method is somewhat similar to the exercise test conducted in medicine in order to assess the cardiovascular condition of athletes or heart patients. In exercise test, the subject is asked to walk on a treadmill while its slope and speed is gradually increased. The test is continued until the subject is exhausted or abnormal biological conditions are observed. Based on the maximum speed and slope that the subject has been capable of enduring, his or her cardiovascular condition is assessed. ET method follows the similar concept applied to structures. In this method, numerical or experimental models of structures are subjected to intensifying dynamic excitation. Relevant structural responses, such as displacements, drifts, stresses, plastic rotations or any other appropriate Damage Measures (DMs) are monitored as the excitation intensity increases. The response is compared to allowable values at target time(s) corresponding to the relevant excitation level(s) matching desired design hazard level(s). By providing an estimate of the structural response at the full range of intensity levels of interest in a single response history analysis, ET can hugely reduce the computational demand required in customary nonlinear dynamic procedures. Being able to assess relative performance of different designs in this way, one can conduct a trial and error design optimization using performance measures in a direct manner.

>Published Material on ET method                                                                                         

For understanding the basic principles of ET method the following articles are recommended:

General concepts: Estekanchi, H. E; Vafai, A.; Valamanesh, V.; Mirzaee, A.; Nozari, A. and Bazmuneh A. (2011) "Recent Advances in Seismic Assessment of Structures by Endurance Time Method", Proceedings of a U.S.-Iran-Turkey Seismic Workshop - Seismic Risk Management in Urban Areas; PEER report 2011/07, December 14-16, 2010, Istanbul, Turkey; pp 289-301 [Link

Basic application: Estekanchi, H.E., Valamanesh, V. and Vafai, A. (2007), ''Application of Endurance Time Method in Linear Seismic Analysis'', Engineering Structures, v29, n10, p2551-2562, doi:10.1016/j.engstruct.2007.01.009


Nonlinear SDOF analysis: Riahi, H. T. ; Estekanchi, H. E. and Vafai, A. (2009), ''Application of Endurance Time Method in Nonlinear Seismic Analysis of SDOF Systems'', Journal of Applied Sciences, v9, n10, p1817-1832,  [Link], doi:10.3923/jas.2009.1817.1832

Nonlinear MDOF analysis: Riahi, H. T. and Estekanchi, H. E, (2010), "Seismic Assessment of Steel Frames with Endurance Time Method", Journal of Constructional Steel Research, v66, n6, p780-792, doi:10.1016/j.jcsr.2009.12.001

After familiarization with the basic concepts and methods, one may follow with other relevant publications based on the topic of interest.

Visit the following web site for our latest publications regarding the ET method by H. E. Estekanchi:


>ET excitation functions                                                                                                           

Currently available ET excitation functions (ETEFs) are in the form of ground accelerations. These are applied to the considered structure like ordinary ground motions.

ETA20a01-03_These ET records are generated to be compatible with soil type II of Iranian National Building Code (standard 2800). Find bellow the files for these set of records. Note that these records are not appropriate for nonlinear analysis.

Also available from:

ETA20b01-3_These ET records are similar to ETA20a01-3 series with different optimization initial starting points.


Also available from:

ETA20e01-3_This is series of 3 accelerograms optimized to match response spectrum of  selected ground motions. These record have been made to match ground motions average response spectrum in the long period range and therefore produce reasonable estimates of response in nonlinear analysis.


Also available from:

ETA20f01-3_This is series of 3 accelerograms optimized to match RS of selected ground motions. The starting point of optimization for these series has been ETA20b series respectively. These records are similar to ETA20e series and can be used as verification set along with that series or to make larger set of records.


Also available from:

Other ETEFs are also available in:

ET Design Methodology

A simplified general design methodology using the ET method is presented in opposite figure. The first step in this procedure is as usual the preparation of an appropriate dynamic model of the intended structure or dynamic system. As a starting point, any conventional method such as equivalent static method can be used to produce a design. The next step is to select a set of ET excitation functions (ETEFs) compatible with specified design spectrum. If compatible ETEFs are not available, a standard scaling procedure should be adopted to match acceleration response from 0.2T to 1.5T (or other appropriate IM) of ETAFs at a target time to required design spectrum. In the next step, the structure is subjected to the ET acceleration function and a response history analysis is carried out. Then ET curves based on the considering EDP are sketched and compared with the allowable limit curve at target time(s). If the performance of the structure is acceptable, and the optimality criterion is satisfied, the design can be considered as final. If not, the design can be modified and the analysis cycle is repeated.