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Computing input energy response of MDOF systems to actual ground motions based on modal contributions

  • Ucar, Taner (Department of Architecture, Dokuz Eylul University)
  • Received : 2019.08.03
  • Accepted : 2020.01.18
  • Published : 2020.02.25

Abstract

The use of energy concepts in seismic analysis and design of structures requires the understanding of the input energy response of multi-degree-of-freedom (MDOF) systems subjected to strong ground motions. For design purposes and non-time consuming analysis, however, it would be beneficial to associate the input energy response of MDOF systems with those of single-degree-of-freedom (SDOF) systems. In this paper, the theoretical formulation of energy input to MDOF systems is developed on the basis that only a particular portion of the total mass distributed among floor levels is effective in the nth-mode response. The input energy response histories of several reinforced concrete frames subjected to a set of eleven horizontal acceleration histories selected from actual recorded events and scaled in time domain are obtained. The contribution of the fundamental mode to the total input energy response of MDOF frames is demonstrated both graphically and numerically. The input energy of the fundamental mode is found to be a good indicator of the total energy input to two-dimensional regular MDOF structures. The numerical results computed by the proposed formulation are verified with relative input energy time histories directly computed from linear time history analysis. Finally, the elastic input energies are compared with those computed from time history analysis of nonlinear MDOF systems.

References

  1. Alici, F.S. and Sucuoglu, H. (2016), "Prediction of input energy spectrum: attenuation models and velocity spectrum scaling", Earthq. Eng. Struct. Dyn., 45(13), 2137-2161. https://doi.org/10.1002/eqe.2749. https://doi.org/10.1002/eqe.2749
  2. Alici, F.S. and Sucuoglu, H. (2018), "Elastic and inelastic near-fault input energy spectra", Earthq. Spectra, 34(2), 611-637. https://doi.org/10.1193/090817EQS175M. https://doi.org/10.1193/090817EQS175M
  3. Amiri, G.G., Darzi, G.A. and Amiri, J.V. (2008), "Design elastic input energy spectra based on Iranian earthquakes", Can. J. Civ. Eng., 35(6), 635-646. https://doi.org/10.1139/L08-013. https://doi.org/10.1139/L08-013
  4. ASCE (2014). Seismic evaluation and retrofit of existing buildings (ASCE 41-13), American Society of Civil Engineers; Reston, Virginia, U.S.A.
  5. Beiraghi, H. (2018), "Energy dissipation of reinforced concrete wall combined with buckling-restrained braces subjected to near- and far-fault earthquakes", Iran. J. Sci. Technol., Trans. Civ. Eng., 42(4), 345-359. https://doi.org/10.1007/s40996-018-0109-0. https://doi.org/10.1007/s40996-018-0109-0
  6. Benavent-Climent, A., Pujades, L.G. and Lopez-Almansa, F. (2002), "Design energy input spectra for moderate-seismicity regions", Earth. Eng. Struct. Dyn., 31(5), 1151-1172. https://doi.org/10.1002/eqe.153. https://doi.org/10.1002/eqe.153
  7. Benavent-Climent, A., Lopez-Almansa, F. and Bravo-Gonzalez, D.A. (2010), "Design energy input spectra for moderate-to-high seismicity regions based on Colombian earthquakes", Soil Dyn. Earthq. Eng., 30(11), 1129-1148. https://doi.org/10.1016/j.soildyn.2010.04.022. https://doi.org/10.1016/j.soildyn.2010.04.022
  8. Bommer, J.J. and Martinez-Pereira, A. (1999), "The effective duration of earthquake strong motion", J. Earthq. Eng., 3(2), 127-172. https://doi.org/10.1080/13632469909350343. https://doi.org/10.1080/13632469909350343
  9. Cheng, Y., Lucchini, A. and Mollaioli, F. (2014), "Proposal of new ground motion prediction equations for elastic input energy spectra", Earthq. Struct., 7(4), 485-510. https://doi.org/10.12989/eas.2014.7.4.485. https://doi.org/10.12989/eas.2014.7.4.485
  10. Chopra, A.K. (2012), Dynamics of Structures, Theory and Applications to Earthquake Engineering, Prentice Hall, One Lake Street, Upper Saddle River, N.J. U.S.A.
  11. Chou, C.C. and Uang, C.M. (2003), "A procedure for evaluating seismic energy demand of framed structures", Earthq. Eng. Struct. Dyn., 32(2), 229-244. https://doi.org/10.1002/eqe.221. https://doi.org/10.1002/eqe.221
  12. Chou, C.C. and Uang, C.M. (2004), "Evaluating distribution of seismic energy in multistory frames", 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August.
  13. Decanini, L.D. and Mollaioli, F. (1998), "Formulation of elastic earthquake input energy spectra", Earthq. Eng. Struct. Dyn., 27(12), 1503-1522, https://doi.org/10.1002/(SICI)1096-9845(199812)27:12<1503::AID-EQE797>3.0.CO;2-A. https://doi.org/10.1002/(SICI)1096-9845(199812)27:12<1503::AID-EQE797>3.0.CO;2-A
  14. Decanini, L., Mollaioli, F. and Mura, A. (2001), "Equivalent SDOF systems for the estimation of seismic response of multistory frame structures", WIT Trans. Built Environ., 57, 101-110. https://doi.org/ 10.2495/ERES010101.
  15. Decanini, L.D. and Mollaioli, F. (2001), "An energy-based methodology for the assessment of seismic demand", Soil Dyn. Earthq. Eng., 21(2), 113-137. https://doi.org/10.1016/S0267-7261(00)00102-0. https://doi.org/10.1016/S0267-7261(00)00102-0
  16. Dindar, A.A., Yalcin, C., Yuksel, E., Ozkaynak H. and Buyukozturk, O. (2015), "Development of earthquake energy demand spectra", Earthq. Spectra, 31(3), 1667-1689. https://doi.org/10.1193/011212EQS010M. https://doi.org/10.1193/011212EQS010M
  17. EC8 (2004), Eurocode 8: Design of structures for earthquake resistance-part 1: General rules, seismic actions and rules for buildings, European Committee for Standardization; Brussels, Belgium.
  18. Ganjavi, B. and Rezagholilou, A.R. (2018), "An intensity measure for seismic input energy demand of multi-degree-of-freedom systems", Civ. Eng. Infrastruct. J., 51(2), 373-388. https://doi.org/10.7508/ceij.2018.02.008.
  19. Gharehbaghi, S., Gandomi, A.H., Achakpour, S. and Omidvar, M.N. (2018), "A hybrid computational approach for seismic energy demand prediction", Expert Syst. Appl., 110, 335-351. https://doi.org/10.1016/j.eswa.2018.06.009. https://doi.org/10.1016/j.eswa.2018.06.009
  20. Gullu, A., Yuksel, E., Yalcin, C., Anil Dindar, A. and Ozkaynak, H. (2017), "Experimental verification of the elastic input energy spectrum and a suggestion", Proceedings of the Interdisciplinary Perspectives for Future Building Envelopes, Istanbul, Turkey, May.
  21. Gullu, A., Yuksel, E., Yalcin, C., Anil Dindar, A., Ozkaynak, H. and Buyukozturk, O. (2019), "An improved input energy spectrum verified by the shake table tests", Earthq. Eng. Struct. Dyn., 48(1), 27-45. https://doi.org/10.1002/eqe.3121. https://doi.org/10.1002/eqe.3121
  22. Habibi, A., Chan, R.W.K. and Albermani, F. (2013), "Energy-based design method for seismic retrofitting with passive energy dissipation systems", Eng. Struct., 46, 77-86. https://doi.org/10.1016/j.engstruct.2012.07.011. https://doi.org/10.1016/j.engstruct.2012.07.011
  23. Hori, N. and Inoue, N. (2002), "Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response", Earthq. Eng. Struct. Dyn., 31(9), 1657-1679. https://doi.org/10.1002/eqe.183. https://doi.org/10.1002/eqe.183
  24. Kalkan, E. and Kunnath, S.K. (2007), "Effective cyclic energy as a measure of seismic demand", J. Earthq. Eng., 11(5), 725-751. http://dx.doi.org/10.1080/13632460601033827. https://doi.org/10.1080/13632460601033827
  25. Kalkan, E. and Kunnath, S.K. (2008), "Relevance of absolute and relative energy content in seismic evaluation of structures", Adv. Struct. Eng., 11(1), 17-34. https://doi.org/10.1260/136943308784069469. https://doi.org/10.1260/136943308784069469
  26. Kanno, H., Nishida, T. and Kobayashi, J. (2012), "Estimation method of seismic response based on momentary input energy considering hysteresis shapes of a building structure", 15th World Conference on Earthquake Engineering, Lisboa, Portugal, September.
  27. Karimzadeh, S., Ozsarac, V., Askan, A., and Erberik, M.A. (2019). "Use of simulated ground motions for the evaluation of energy response of simple structural systems", Soil Dyn. Earthq. Eng., 123,525-542. https://doi.org/10.1016/j.soildyn.2019.05.024. https://doi.org/10.1016/j.soildyn.2019.05.024
  28. Khashaee, P., Mohraz, B., Sadek, F., Lew, H.S. and Gross, J.L. (2003), "Distribution of earthquake input energy in structures", Report No. NISTIR 6903, National Institute of Standards and Technology, Gaithersburg.
  29. Lei, C., Xianguo, Y. and Kangning, L. (2008), "Analysis of seismic energy response and distribution of RC frame structures", The 14th World Conference on Earthquake Engineering, Beijing, China, October.
  30. Lopez-Almansa, F., Yazgan, A.U. and Benavent-Climent, A. (2013), "Design energy input spectra for high seismicity regions based on Turkish registers", Bull. Earthq. Eng., 11(4): 885-912. https://doi.org/10.1007/s10518-012-9415-2. https://doi.org/10.1007/s10518-012-9415-2
  31. Manfredi, G. (2001), "Evaluation of seismic energy demand", Earthq. Eng. Struct. Dyn., 30(4), 485-499. https://doi.org /10.1002/eqe.17. https://doi.org/10.1002/eqe.17
  32. Merter, O. (2019), "An investigation on the maximum earthquake input energy for elastic SDOF systems", Earthq. Struct., 16(4), 487-499. https://doi.org/10.12989/eas.2019.16.4.487. https://doi.org/10.12989/EAS.2019.16.4.487
  33. Mezgebo, M.G. (2015), "Estimation of earthquake input energy, hysteretic energy and its distribution in MDOF structures", Ph.D. Dissertation, Syracuse University, New York.
  34. Mezgebo, M. and Lui, E.M. (2016), "Hysteresis and soil site dependent input and hysteretic energy spectra for far-source ground motions", Adv. Civ. Eng., 2016, https://doi.org/10.1155/2016/1548319.
  35. Mezgebo, M.G. and Lui, E.M. (2017), "A new methodology for energy-based seismic design of steel moment frames", Earthq. Eng. Eng. Vib., 16(1), 131-162. https://doi.org/10.1007/s11803-017-0373-1. https://doi.org/10.1007/s11803-017-0373-1
  36. Mollaioli, F., Bruno, S., Decanini,L. and Saragoni, R. (2011), "Correlations between energy and displacement demands for performance-based seismic engineering", Pure Appl. Geophys., 168(1-2), 237-259. https://doi.org/10.1007/s00024-010-0118-9. https://doi.org/10.1007/s00024-010-0118-9
  37. Morales-Beltran, M., Turan, G., Yildirim, U., and Paul, J. (2018), "Distribution of strong earthquake input energy in tall buildings equipped with damped outriggers", Struct. Des. Tall Spec. Build., 27(8), e1463. https://doi.org/10.1002/tal.1463. https://doi.org/10.1002/tal.1463
  38. Okur, A. and Erberik, M.A. (2012), "Adaptation of energy principles in seismic design of Turkish RC frame structures. Part I: Input energy spectrum", 15th World Conference on Earthquake Engineering, Lisboa, Portugal, September.
  39. Ordaz, M., Huerta, B. and Reinoso, E. (2003), "Exact computation of input-energy spectra from Fourier amplitude spectra", Earthq. Eng. Struct. Dyn., 32(4), 597-605. https://doi.org/10.1002/eqe.240. https://doi.org/10.1002/eqe.240
  40. Ozsarac, V., Karimzadeh, S., Erberik, M.A., Askan, A. (2017), "Energy-based response of simple structural systems by using simulated ground motions", Procedia Eng., 199, 236-241. https://doi.org/10.1016/j.proeng.2017.09.009. https://doi.org/10.1016/j.proeng.2017.09.009
  41. PEER (2019), PEER Ground Motion Database, NGA-West2. Pacific Earthquake Engineering Research Center. http://ngawest2.berkeley.edu/
  42. PRISM for Earthquake Engineering. (2010), A Software for Seismic Response Analysis of Single-Degree-of-Freedom-Systems, Version 2.0.1, Department of Architectural Engineering, INHA University.
  43. Quinde, P., Reinoso, E. and Teran-Gilmore, A. (2016), "Inelastic seismic energy spectra for soft soils: Application to Mexico City", Soil Dyn. Earthq. Eng., 89, 198-207. https://doi.org/10.1016/j.soildyn.2016.08.004. https://doi.org/10.1016/j.soildyn.2016.08.004
  44. SAP2000 Ultimate. (2018), Integrated Solution for Structural Analysis and Design, Version 20.2.0, Computers and Structures Inc. (CSI), Berkeley, California, U.S.A.
  45. Sari, A. (2003), "Energy considerations in ground motion attenuation and probabilistic seismic hazard studies", Ph.D. Dissertation, The University of Texas at Austin, Austin. U.S.A.
  46. Shargh, F.H. and Hosseini, M. (2011), "An optimal distribution of stiffness over the height of shear buildings to minimize the seismic input energy", J. Seismol. Earthq. Eng., 13(1), 25-32.
  47. Shargh, F.H., Hosseini, M. and Daneshvar, H. (2012), "An optimal distribution of stiffness over the height of buildings and its influence on the degree and distribution of earthquake induced damages and distribution of earthquake induced damages", 15th World Conference on Earthquake Engineering, Lisboa, Portugal, September.
  48. Shiwua, A.J., Rutman, Y. (2016), "Assessment of seismic input energy by means of new definition and the application to earthquake resistant design", Archit. Eng., 1(4), 26-35. https://doi.org/10.23968/2500-0055-2016-1-4-26-35.
  49. Surahman, A. (2007), "Earthquake-resistant structural design through energy demand and capacity", Earthq. Eng. Struct. Dyn., 36(14), 2099-2117. https://doi.org/10.1002/eqe.718. https://doi.org/10.1002/eqe.718
  50. Taflampas, I.M., Maniatakis, Ch.A. and Spyrakos, C.C. (2008), "Estimation of input seismic energy by means of a new definition of strong motion duration duration", The 14th World Conference on Earthquake Engineering, Beijing, China, October.
  51. Takewaki, I. (2004), "Frequency domain modal analysis of earthquake input energy to highly damped passive control structures", Earthq. Eng. Struct. Dyn., 33(5), 575-590. https://doi.org/10.1002/eqe.361. https://doi.org/10.1002/eqe.361
  52. Takewaki, I. and Fujita, K. (2009), "Earthquake input energy to tall and base-isolated buildings in time and frequency dual domains", Struct. Des. Tall Spec. Build., 18(6), 589-606. https://doi.org/10.1002/tal.497. https://doi.org/10.1002/tal.497
  53. Takewaki, I. and Tsujimoto, H. (2011), "Scaling of design earthquake ground motions for tall buildings based on drift and input energy demands", Earthq. Struct., 2(2), 171-187. https://doi.org/10.12989/eas.2011.2.2.171. https://doi.org/10.12989/eas.2011.2.2.171
  54. Tselentis, G-A., Danciu, L. and Sokos, E. (2010), "Probabilistic seismic hazard assessment in Greece - Part 2: Acceleration response spectra and elastic input energy spectra", Nat. Hazards Earth Syst. Sci., 10(1), 41-49. https://doi.org/10.5194/nhess-10-41-2010. https://doi.org/10.5194/nhess-10-41-2010
  55. TSDC (2018). Turkish seismic design code, Ministry of Public Works and Settlement; Ankara, Turkey.
  56. Wong, K.K.F. and Yang, R. (2002), "Earthquake response and energy evaluation of inelastic structures", J. Eng. Mech., 128(3), 308-317. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:3(308). https://doi.org/10.1061/(ASCE)0733-9399(2002)128:3(308)
  57. Yang, T.Y., Tung, D.P., and Li, Y. (2018), "Equivalent energy design procedure for earthquake resilient fused structures", Earthq. Spectra, 34(2), 795-815. https://doi.org/10.1193/122716EQS254M. https://doi.org/10.1193/122716EQS254M
  58. Ye, L., Cheng, G. and Qu, Z. (2009), "Study on energy-based seismic design method and the application for steel braced frame structures", Sixth International Conference on Urban Earthquake Engineering, Tokyo Institute of Technology, Tokyo, Japan, March.
  59. Zhou, Y., Song, G., Huang, S. and Wu, H. (2019), "Input energy spectra for self-centering SDOF systems", Soil Dyn. Earthq. Eng., 121, 293-305. https://doi.org/10.1016/j.soildyn.2019.03.017. https://doi.org/10.1016/j.soildyn.2019.03.017