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Endurance time method
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<h2 id="the-concept-of-endurance-time-method">The concept of endurance time method</h2> <p>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 <a href="/facts/Cardiac_stress_test/kL4ovnza">exercise test</a> applied in medicine.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> Similar concept has also been extended to applications in the analysis of offshore platforms under water waves.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p> <h2 id="development-history">Development history</h2> <p>The basic concepts of the endurance time method were published in 2004.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> Application in linear seismic analysis appeared in 2007.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> ET was subsequently extended to nonlinear analysis of single degree of freedom (SDOF) and multi degree of freedom systems.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> Procedures for multi-component seismic analysis were subsequently developed.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a><a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a><a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> </p> <h2 id="et-excitation-functions">ET excitation functions</h2> <p>ET excitation functions are generated by using <a href="/facts/Numerical_optimization/oRn8Iv5I">numerical optimization</a> methods.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a><a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> ET excitation functions are publicly available through internet websites.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a><a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> ET excitation functions can be categorized into five generations as follows: </p> <ol><li>First generation of ET excitation functions (ETEFs) are essentially a filtered and profiled <a href="/facts/White_noise/wJ0SR21n">white noise</a>. These were used for demonstrating the concept of ET and have limited practical significance.<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></li> <li>Second-generation ETEFs incorporate <a href="/facts/Response_spectrum/00leyG7f">response spectrum</a> matching. These ETEFs produce numerically significant analysis results.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a></li> <li>Third-generation ETEFs are optimized in nonlinear range. These ETEFs deliver improved analysis performance.</li> <li>Fourth-generation ETEFs are optimized to include duration consistency.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a></li> <li>Fifth-generation ETEFs are optimized to include damage consistency.<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></li></ol> <h2 id="application-areas-in-earthquake-engineering">Application areas in earthquake engineering</h2> <p>Endurance time method has been applied in the following areas of <a href="/facts/Earthquake_engineering/rF0Yv7co">earthquake engineering</a>: </p> <ul><li><a href="/facts/Seismic_analysis/dQJKCP7n">Nonlinear dynamic analysis</a> of structures<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></li> <li>Seismic evaluation of jacket-type offshore platforms <a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></li> <li>Optimal damper placement in framed buildings<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a><a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a></li> <li>Optimal design of energy dissipation systems <a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a><a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a><a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a><a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a></li> <li>Seismic assessment of structures<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a></li> <li>Performance-based seismic design method <a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a><a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a><a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a><a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a><a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a></li> <li>Collapse-based seismic design method <a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a></li> <li>Value-based seismic design <a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a><a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a></li> <li>Structural optimization<a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a></li> <li>Multi-component seismic analysis<a class="footnote-ref" id="fnref:42" href="#fn:42"><sup>42</sup></a></li> <li>Soil–structure interaction<a class="footnote-ref" id="fnref:43" href="#fn:43"><sup>43</sup></a><a class="footnote-ref" id="fnref:44" href="#fn:44"><sup>44</sup></a></li> <li>soil-pile-superstructure interaction <a class="footnote-ref" id="fnref:45" href="#fn:45"><sup>45</sup></a></li> <li>Liquid–structure interaction<a class="footnote-ref" id="fnref:46" href="#fn:46"><sup>46</sup></a></li> <li>Dam engineering<a class="footnote-ref" id="fnref:47" href="#fn:47"><sup>47</sup></a></li> <li>Bridge engineering<a class="footnote-ref" id="fnref:48" href="#fn:48"><sup>48</sup></a><a class="footnote-ref" id="fnref:49" href="#fn:49"><sup>49</sup></a><a class="footnote-ref" id="fnref:50" href="#fn:50"><sup>50</sup></a></li> <li>Seismic rehabilitation<a class="footnote-ref" id="fnref:51" href="#fn:51"><sup>51</sup></a></li> <li>Collapse analysis<a class="footnote-ref" id="fnref:52" href="#fn:52"><sup>52</sup></a></li></ul> <h2 id="structural-type-applications">Structural type applications</h2> <p>ET method has been applied in seismic assessment of the following structural types: </p> <ul><li>Single degree of freedom systems</li> <li>Moment and braced <a href="/facts/Steel_frame/jNHlGJtx">steel frames</a><a class="footnote-ref" id="fnref:53" href="#fn:53"><sup>53</sup></a><a class="footnote-ref" id="fnref:54" href="#fn:54"><sup>54</sup></a><a class="footnote-ref" id="fnref:55" href="#fn:55"><sup>55</sup></a></li> <li>Concrete frames</li> <li>Bridges<a class="footnote-ref" id="fnref:56" href="#fn:56"><sup>56</sup></a><a class="footnote-ref" id="fnref:57" href="#fn:57"><sup>57</sup></a></li> <li><a href="/facts/Dam/BroJFhEI">Gravity dams</a><a class="footnote-ref" id="fnref:58" href="#fn:58"><sup>58</sup></a></li> <li><a href="/facts/Arch_dam/A42zfPY9">Arch dams</a><a class="footnote-ref" id="fnref:59" href="#fn:59"><sup>59</sup></a></li> <li><a href="/facts/Concrete_shell/GdSbA8A8">Shell structures</a><a class="footnote-ref" id="fnref:60" href="#fn:60"><sup>60</sup></a></li> <li><a href="/facts/Oil_tank/8xqIeRjU">Steel tanks</a><a class="footnote-ref" id="fnref:61" href="#fn:61"><sup>61</sup></a><a class="footnote-ref" id="fnref:62" href="#fn:62"><sup>62</sup></a></li> <li><a href="/facts/Offshore_platform/n1eKvqpy">Offshore structures</a><a class="footnote-ref" id="fnref:63" href="#fn:63"><sup>63</sup></a></li></ul> <h2 id="advantages-of-et-method">Advantages of ET method</h2> <p>Major advantages of the endurance time method are as follows: </p> <ul><li>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.<a class="footnote-ref" id="fnref:64" href="#fn:64"><sup>64</sup></a></li> <li>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.</li> <li>ET method is reasonably simple and sensible when a realistic dynamic analysis of a complex structure is required</li></ul> <h2 id="limitations-of-et-method">Limitations of ET method</h2> <p>Major limitations of the endurance time method are as follows: </p> <ul><li>ET is an approximate method for predicting the structural response.</li> <li>The production of usable ETEFs that are applicable in a particular situation can be complicated.</li> <li>The procedure is still under development and sufficient background information may not be available for specific applications.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Endurance Time Method website[Online]. https://sites.google.com/site/etmethod/ <a href="https://sites.google.com/site/etmethod/" target="_blank">https://sites.google.com/site/etmethod/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>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 <a href="https://dx.doi.org/10.1016/j.engstruct.2007.01.009" target="_blank">https://dx.doi.org/10.1016/j.engstruct.2007.01.009</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>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 <a href="https://doi.org/10.1016/j.istruc.2020.07.062" target="_blank">https://doi.org/10.1016/j.istruc.2020.07.062</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Estekanchi, H., & Vafai, H. (2018). Seismic analysis and design using the endurance time method, Volume I: Concepts and development. Momentum Press. <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Estekanchi, H., & Vafai, H. (2018). Seismic analysis and design using the endurance time method, Volume II: Advanced topics and application. Momentum Press. <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>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 <a href="http://www.bhrc.ac.ir/Portal/LinkClick.aspx?fileticket=6MYAQ2Vrz%2bY%3d&tabid=562" target="_blank">http://www.bhrc.ac.ir/Portal/LinkClick.aspx?fileticket=6MYAQ2Vrz%2bY%3d&tabid=562</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>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 <a href="https://dx.doi.org/10.1016/j.apor.2012.04.003" target="_blank">https://dx.doi.org/10.1016/j.apor.2012.04.003</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>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 <a href="http://scientiairanica.sharif.ir/PDF/Articles/00000163/Estekanchi.pdf" target="_blank">http://scientiairanica.sharif.ir/PDF/Articles/00000163/Estekanchi.pdf</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>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 <a href="https://dx.doi.org/10.1016/j.engstruct.2007.01.009" target="_blank">https://dx.doi.org/10.1016/j.engstruct.2007.01.009</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>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 <a href="https://dx.doi.org/10.1016/j.jcsr.2009.12.001" target="_blank">https://dx.doi.org/10.1016/j.jcsr.2009.12.001</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>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 <a href="http://www.bhrc.ac.ir/portal/LinkClick.aspx?fileticket=xP8PAPaJPa8%3d&tabid=749" target="_blank">http://www.bhrc.ac.ir/portal/LinkClick.aspx?fileticket=xP8PAPaJPa8%3d&tabid=749</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>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 <a href="https://dx.doi.org/10.1002/tal.666" target="_blank">https://dx.doi.org/10.1002/tal.666</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>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 <a href="https://dx.doi.org/10.1016/j.scient.2011.03.024" target="_blank">https://dx.doi.org/10.1016/j.scient.2011.03.024</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>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 <a href="https://dx.doi.org/10.1002/tal.1054" target="_blank">https://dx.doi.org/10.1002/tal.1054</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Valamanesh, V; Estekanchi, H. E. and Vafai, A. (2010), Characteristics of Second Generation Endurance Time Accelerograms, Scientia Iranica, v17, n1, p53-61, Link <a href="http://scientiairanica.sharif.ir/PDF/Articles/00001298/estekanchi.pdf" target="_blank">http://scientiairanica.sharif.ir/PDF/Articles/00001298/estekanchi.pdf</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>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 <a href="http://ijoce.iust.ac.ir/browse.php?a_id=87&sid=1&slc_lang=en" target="_blank">http://ijoce.iust.ac.ir/browse.php?a_id=87&sid=1&slc_lang=en</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Endurance Time Method website[Online]. https://sites.google.com/site/etmethod/ <a href="https://sites.google.com/site/etmethod/" target="_blank">https://sites.google.com/site/etmethod/</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Estekanchi HE. 2012. Website of the Endurance Time method. [Online]. http://sharif.edu/~stkanchi/ET <a href="http://sharif.edu/~stkanchi/ET" target="_blank">http://sharif.edu/~stkanchi/ET</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>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 <a href="http://scientiairanica.sharif.ir/PDF/Articles/00000163/Estekanchi.pdf" target="_blank">http://scientiairanica.sharif.ir/PDF/Articles/00000163/Estekanchi.pdf</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>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 <a href="http://www.bhrc.ac.ir/portal/LinkClick.aspx?fileticket=VZNVowDsp_Q%3d&tabid=1121" target="_blank">http://www.bhrc.ac.ir/portal/LinkClick.aspx?fileticket=VZNVowDsp_Q%3d&tabid=1121</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>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 <a href="https://doi.org/10.1080/13632469.2018.1540371" target="_blank">https://doi.org/10.1080/13632469.2018.1540371</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>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 <a href="https://doi.org/10.1016/j.engstruct.2018.09.089" target="_blank">https://doi.org/10.1016/j.engstruct.2018.09.089</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>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 <a href="https://dx.doi.org/10.1016/j.jcsr.2007.05.010" target="_blank">https://dx.doi.org/10.1016/j.jcsr.2007.05.010</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>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 <a href="http://scientiairanica.sharif.ir/PDF/Articles/00001120/estekanchi.pdf" target="_blank">http://scientiairanica.sharif.ir/PDF/Articles/00001120/estekanchi.pdf</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> <li id="fn:25"><p>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 <a href="http://scientiairanica.sharif.edu/article_4275_f79d8b4fdd0cc8d159b91b1a3b968585.pdf" target="_blank">http://scientiairanica.sharif.edu/article_4275_f79d8b4fdd0cc8d159b91b1a3b968585.pdf</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li> <li id="fn:26"><p>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 <a href="https://dx.doi.org/10.1002/tal.689" target="_blank">https://dx.doi.org/10.1002/tal.689</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li> <li id="fn:27"><p>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 <a href="https://dx.doi.org/10.52547/nmce.5.3.46" target="_blank">https://dx.doi.org/10.52547/nmce.5.3.46</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></p></li> <li id="fn:28"><p>Shirkhani, A., Mualla, I. H., Shabakhty, N., & Mousavi, S. R. (2015). 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