The 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.[3][4][5]

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.[6] Similar concept has also been extended to applications in the analysis of offshore platforms under water waves.[7]

Development history

The basic concepts of the endurance time method were published in 2004.[8] 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.[9] Procedures for multi-component seismic analysis were subsequently developed.[10][11][12][13]

ET excitation functions

ET excitation functions are generated by using numerical optimization methods.[14][15] ET excitation functions are publicly available through internet websites.[1][16] ET excitation functions can be categorized into five 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.[8]
  2. Second-generation ETEFs incorporate response spectrum matching. These ETEFs produce numerically significant analysis results.[17]
  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.[18]
  5. Fifth-generation ETEFs are optimized to include damage consistency.[19]
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:

Structural type applications

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

Advantages of ET method

Major advantages of the endurance time method are as follows:

Limitations of ET method

Major limitations of the endurance time method are as follows:

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., Mashayekhi, M., Vafai, H., Ahmadi, G., Mirfarhadi, S. A., & Harati, M. (2020, October). A state-of-knowledge review on the Endurance Time Method. In Structures (Vol. 27, pp. 2288-2299). Elsevier. https://doi.org/10.1016/j.istruc.2020.07.062
  4. ^ Estekanchi, H., & Vafai, H. (2018). Seismic analysis and design using the endurance time method, Volume I: Concepts and development. Momentum Press.
  5. ^ Estekanchi, H., & Vafai, H. (2018). Seismic analysis and design using the endurance time method, Volume II: Advanced topics and application. Momentum Press.
  6. ^ 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
  7. ^ 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
  8. ^ a b 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
  9. ^ 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
  10. ^ 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
  11. ^ 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
  12. ^ 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
  13. ^ 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
  14. ^ Valamanesh, V; Estekanchi, H. E. and Vafai, A. (2010), Characteristics of Second Generation Endurance Time Accelerograms, Scientia Iranica, v17, n1, p53-61, Link
  15. ^ 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
  16. ^ Estekanchi HE. 2012. Website of the Endurance Time method. [Online]. http://sharif.edu/~stkanchi/ET
  17. ^ 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
  18. ^ Mashayekhi, M., Estekanchi, H. E., Vafai, A., & Mirfarhadi, S. A. (2018). Simulation of cumulative absolute velocity consistent endurance time excitations. Journal of Earthquake Engineering, 1-26. https://doi.org/10.1080/13632469.2018.1540371
  19. ^ Mashayekhi, M., Estekanchi, H. E., Vafai, H., & Mirfarhadi, S. A. (2018). Development of hysteretic energy compatible endurance time excitations and its application. Engineering Structures, 177, 753-769. https://doi.org/10.1016/j.engstruct.2018.09.089
  20. ^ 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
  21. ^ 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
  22. ^ 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
  23. ^ 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
  24. ^ Shirkhani A., Farahmand Azar, B., Charkhtab Basim, M., & Mashayekhi M. (2021). Performance-based optimal distribution of viscous dampers in structure using hysteretic energy compatible endurance time excitations. International Journal of Numerical Methods in Civil Engineering, 5 (3), 46-55. http://dx.doi.org/10.52547/nmce.5.3.46
  25. ^ Shirkhani, A., Mualla, I. H., Shabakhty, N., & Mousavi, S. R. (2015). Behavior of steel frames with rotational friction dampers by endurance time method. Journal of Constructional Steel Research, 107, 211-222. https://doi.org/10.1016/j.jcsr.2015.01.016
  26. ^ Shirkhani, A., Farahmand Azar, B., & Basim, M. C. (2020). Optimum slip load of T-shaped friction dampers in steel frames by endurance time method. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 173(10), 746-760. https://doi.org/10.1680/jstbu.18.00169
  27. ^ Shirkhani, A., Farahmand Azar, B., & Charkhtab Basim, M. (2021). Seismic loss assessment of steel structures equipped with rotational friction dampers subjected to intensifying dynamic excitations. Engineering Structures, 238. https://doi.org/10.1016/j.engstruct.2021.112233
  28. ^ Application of Endurance Time (ET) method in optimal design of energy dissipation systems [Online]. https://sites.google.com/view/ascivil/endurance-time/
  29. ^ 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
  30. ^ 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
  31. ^ Mirzaee, A., & Estekanchi, H. E. (2015). Performance-based seismic retrofitting of steel frames by the endurance time method. Earthquake Spectra, 31(1), 383-402. https://doi.org/10.1193/081312EQS262M
  32. ^ Basim, M. C., & Estekanchi, H. E. (2015). Application of endurance time method in performance-based optimum design of structures. Structural safety, 56, 52-67. https://doi.org/10.1016/j.strusafe.2015.05.005
  33. ^ Charkhtab Basim, M., E Estekanchi, H., & Vafai, A. (2016). A methodology for value based seismic design of structures by the endurance time method. Scientia Iranica, 23(6), 2514-2527. https://dx.doi.org/10.24200/sci.2016.2310
  34. ^ Mirfarhadi, S. A., & Estekanchi, H. E. (2020). Value based seismic design of structures using performance assessment by the endurance time method. Structure and Infrastructure Engineering, 1-19. https://doi.org/10.1080/15732479.2020.1712436
  35. ^ 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
  36. ^ Sarcheshmehpour, M., Estekanchi, H. E., & Ghannad, M. A. (2020). Optimum placement of supplementary viscous dampers for seismic rehabilitation of steel frames considering soil–structure interaction. The Structural Design of Tall and Special Buildings, 29(1), e1682. https://doi.org/10.1002/tal.1682
  37. ^ Bai, J., Jin, S., Zhao, J., & Sun, B. (2019). Seismic performance evaluation of soil-foundation-reinforced concrete frame systems by endurance time method. Soil Dynamics and Earthquake Engineering, 118, 47-51. https://doi.org/10.1016/j.soildyn.2018.12.011
  38. ^ 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
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  40. ^ Ghaffari, E., E Estekanchi, H., & Vafai, A. (2020). Application of endurance time method in seismic analysis of bridges. Scientia Iranica, 27(4), 1751-1761. https://dx.doi.org/10.24200/sci.2018.5041.1382
  41. ^ Guo, A., Shen, Y., Bai, J., & Li, H. (2017). Application of the endurance time method to the seismic analysis and evaluation of highway bridges considering pounding effects. Engineering Structures, 131, 220-230. https://doi.org/10.1016/j.engstruct.2016.11.009
  42. ^ He, H., Wei, K., Zhang, J., & Qin, S. (2020). Application of endurance time method to seismic fragility evaluation of highway bridges considering scour effect. Soil Dynamics and Earthquake Engineering, 136, 106243. https://doi.org/10.1016/j.soildyn.2020.106243
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