# Endurance time method

Endurance time (ET) method is a dynamic structural analysis procedure for seismic assessment of structures. In this procedure, an intensifying dynamic excitation is used as the loading function.[1] Endurance time method is a time-history based dynamic analysis procedure. An estimate of the structural response at different equivalent seismic intensity levels is obtained in a single response history analysis.[2] This method has applications in seismic assessment of various structural types and in different areas of earthquake engineering.

## The concept of endurance time method

Endurance time (ET) method is a dynamic structural analysis procedure in which intensifying dynamic excitation is used as the loading function. An estimate of structural response and/or performance at the entire seismic intensity range of interest is obtained in each response history analysis. The concept of endurance time analysis is similar to the exercise test applied in medicine.[3] Similar concept has also been extended to applications in the analysis of offshore platforms under water waves.[4]

## Development history

The basic concepts of the endurance time method were published in 2004.[5] Application in linear seismic analysis appeared in 2007.[2] ET was subsequently extended to nonlinear analysis of single degree of freedom (SDOF) and multi degree of freedom systems.[6][7] Procedures for multi-component seismic analysis were subsequently developed.[8][9][10][11]

## ET excitation functions

ET excitation functions are generated by using numerical optimization methods.[12][13] ET excitation functions are publicly available through internet websites.[1][14] ET excitation functions are categorized into four generations as follows:

1. First generation of ET excitation functions (ETEFs) are essentially a filtered and profiled white noise. These were used for demonstrating the concept of ET and have limited practical significance.
2. Second-generation ETEFs incorporate response spectrum matching. These ETEFs produce numerically significant analysis results.[15]
3. Third-generation ETEFs are optimized in nonlinear range. These ETEFs deliver improved analysis performance.
4. Fourth-generation ETEFs are optimized to include duration consistency.
Fig. 1. A typical endurance time excitation function (ETA20f03 record)

## Application areas in earthquake engineering

Endurance time method has been applied in the following areas of earthquake engineering:

• Nonlinear dynamic analysis of structures[16][17]
• Seismic evaluation of jacket-type offshore platforms [18]
• Optimal damper placement in framed buildings[19]
• Seismic assessment of structures[7]
• Performance-based design[20][21]
• Structural optimization[22]
• Multi-component seismic analysis[11]
• Soil–structure interaction
• soil-pile-superstructure interaction [18]
• Liquid–structure interaction[23]
• Dam engineering[24]
• Bridge engineering
• Seismic rehabilitation[25]
• Collapse analysis[26]

## Structural type applications

ET method has been applied in seismic assessment of the following structural types:

Major advantages of the endurance time method are as follows:

• ET significantly reduces the computational demand required for performing a standard response history analysis of structures for seismic assessment, especially when response at multiple levels of intensity is to be considered.[32]
• ET is applicable in a wide range of seismic assessment problems and provides a generic approach for the seismic analysis of a wide range of structural types.
• ET method is reasonably simple and sensible when a realistic dynamic analysis of a complex structure is required

## Limitations of ET method

Major limitations of the endurance time method are as follows:

• ET is an approximate method for predicting the structural response.
• The production of usable ETEFs that are applicable in a particular situation can be complicated.
• The procedure is still under development and sufficient background information may not be available for specific applications.

## References

1. ^ a b Endurance Time Method website[Online]. https://sites.google.com/site/etmethod/
2. ^ a b 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
3. ^ Estekanchi, H. E.; Riahi, H. T. and Vafai, A. (2009), Endurance Time Method: Exercise Test as Applied to Structures, Asian Journal of Civil Engineering, v10, n5, p559-577, Link
4. ^ Zeinoddini, M., Nikoo, H. M. and Estekanchi H.E. (2012), "Endurance Wave Analysis (EWA) and its application for assessment of offshore structures under extreme waves", Applied Ocean Research, v37, p98-110, doi: 10.1016/j.apor.2012.04.003
5. ^ Estekanchi, H. E., A. Vafai and M. Sadeghazar (2004), Endurance Time method for seismic analysis and design of structures, Scientia Iranica, v11, n4, p361-370, Link
6. ^ a b 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, doi:10.3923/jas.2009.1817.1832
7. ^ a b 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
8. ^ Valamanesh, V and Estekanchi, H. E. (2010),"A Study of Endurance Time Method in the Analysis of Elastic Moment Frames under Three-Directional Seismic Loading ", Asian Journal of Civil Engineering, v11, n5, p543-562, Link
9. ^ Valamanesh, V and Estekanchi, H. E. (2010), "Compatibility of the endurance time method with codified seismic analysis approaches on three-dimensional analysis of steel frames ", The Structural Design of Tall and Special Buildings, doi:10.1002/tal.666
10. ^ Valamanesh, V and Estekanchi, H. E. (2011), "Endurance time method for multi-component analysis of steel elastic moment frames", Scientia Iranica, v18, n2, p139-142, doi:10.1016/j.scient.2011.03.024
11. ^ a b c Valamanesh V. and Estekanchi H. E. (2012), "Nonlinear Seismic Assessment of Steel Moment Frames under Bi-Directional Loading via Endurance Time Method", The Structural Design of Tall and Special Buildings, doi: 10.1002/tal.1054
12. ^ Valamanesh, V; Estekanchi, H. E. and Vafai, A. (2010), Characteristics of Second Generation Endurance Time Accelerograms, Scientia Iranica, v17, n1, p53-61, Link
13. ^ Kaveh A., Mahdavi V., "Generation of Endurance Time Acceleration Functions Using the Wavelet Transform". Iran University of Science & Technology. 2012; 2 (2) :203–219,Link
14. ^ Estekanchi HE. 2012. Website of the Endurance Time method. [Online]. http://sharif.edu/~stkanchi/ET
15. ^ Mashayekhi, M. and Estekanchi, H.E. (2012), "Significance of effective number of cycles in Endurance Time analysis", Asian Journal of Civil Engineering, v13, n5, p647-657, Link
16. ^ Estekanchi, H. E., Arjomandi, K and Vafai, A. (2008), Estimating Structural Damage of Steel Moment Frames by Endurance Time Method, Journal of Constructional Steel Research, v64, n2, p145-155, doi:10.1016/j.jcsr.2007.05.010
17. ^ Riahi, H. T. ; Estekanchi, H. E. and Vafai, A. (2009), Estimates of Average Inelastic Deformation Demands for Regular Steel Frames by the Endurance Time Method, Scientia Iranica, v16, n5, p388-402, Link
18. ^ a b c Hasani, H., Golafshani, A., Estekanchi, H. Seismic performance evaluation of jacket-type offshore platforms using endurance time method considering soil-pile-superstructure interaction. Scientia Iranica, 2017; 24(4): 1843-1854. doi: 10.24200/sci.2017.4275 http://scientiairanica.sharif.edu/article_4275_f79d8b4fdd0cc8d159b91b1a3b968585.pdf
19. ^ Estekanchi, H. E. and Basim, M. Ch. (2011), "Optimal damper placement in steel frames by the Endurance Time method", The Structural Design of Tall and Special Buildings, v20, n5, p612-630, doi:10.1002/tal.689
20. ^ Mirzai, A, Estekanchi, H. E. and Vafai, A. (2010), "Application of Endurance Time Method in Performance Based Design of Steel Moment Frames", Scientia Iranica, v17, n6, p482-492, Link
21. ^ Mirzai A., Estekanchi, H. E. and Vafai, A. (2012), "Improved methodology for endurance time analysis: From time to seismic hazard return period", Scientia Iranica, doi: 10.1016/j.scient.2012.06.023
22. ^ Nozari, A and Estekanchi, H. E. (2011) "Optimization of Endurance Time acceleration functions for seismic assessment of structures, International Journal of Optimization in Civil Engineering, v1, n2, 257–277, Link
23. ^ a b Estekanchi, H. E. and Alembagheri, , M. (2012), "Seismic analysis of steel liquid storage tanks by Endurance Time method", Thin-Walled Structures, v50, n1, p14-23, doi: 10.1016/j.tws.2011.08.015
24. ^ a b Valamanesh, V; Estekanchi, H. E., Vafai, A and Ghaemian M. (2011), "Application of Endurance time method in seismic analysis of concrete gravity dams", Scientia Iranica A, v18, n3, p326-337, doi:10.1016/j.scient.2011.05.039
25. ^ Bazmooneh, Amirali (2009), Application of Endurance Time method in seismic evaluation of existing steel buildings, Thesis presented to the Department of Civil Engineering as a partial requirement for degree of Master of Science, Sharif University of Technology http://library.sharif.ir/parvan/resource/290141/
26. ^ Avanaki, M. J., Estekanchi H.E. (2012), "Collapse analysis by Endurance Time method", International Journal of Optimization in Civil Engineering, v2, n2, p287-299,Link
27. ^ Estekanchi, H. E., Riahi, H. T. and Vafai, A. (2011), Application of Endurance Time Method in Seismic Assessment of Steel Frames", Engineering Structures, v33, n9, p2535-2546 doi:10.1016/j.engstruct.2011.04.025
28. ^ Ghaffari, Esmail (2010) Application of Endurance Time method in Seismic analysis of bridges, Thesis presented to the Department of Civil Engineering as a partial requirement for degree of Master of Science, Sharif University of Technology http://library.sharif.ir/parvan/resource/291956/
29. ^ Hariri Ardebili M., Mirzabozorg H., Kianoush R., "A Study on Nonlinear Behavior and Seismic Damage Assessment of Concrete Arch Dam-Reservoir-Foundation System Using Endurance Time Analysis". Iran University of Science & Technology. 2012; 2 (4) :573–606 Link
30. ^ Tavazo, M., Estekanchi H.E. and Kaldi P. (2012), "Endurance time method in the linear seismic analysis of shell structures", International Journal of Civil Engineering, v10, n3, p169-178,Link
31. ^ Alembagheri, M and Estekanchi, H. E. (2011), "Seismic Assessment of Unanchored Steel Storage Tanks by Endurance Time Method", Earthquake Engineering and Engineering Vibration, v10, n4, p591-604, doi:10.1007/s11803-011-0092-y
32. ^ Madarshahian, R., Estekanchi, H. E. and Mahvashmohammadi, A. (2011), "Estimating seismic demand parameters with Endurance Time method", Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), v12, n8, p616-626, doi:10.1631/jzus.A1000389