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Higher modes contribution for estimating the inelastic deformation ratios and seismic demands of structures

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Abstract

In order to estimate the seismic demand by using the nonlinear static procedure, different approximate methods have been developed. One of the most useful methods is called displacement coefficient method (DCM), which is based on some modification factors. One of these coefficients denoted C1, concerns the inelastic deformation ratio and usually depends on either the yield-strength reduction factor or the ductility factor. In general the evaluation of the inelastic deformation ratio is based on the response of single degree of freedom (SDOF) systems, where the response of the structure is mainly controlled by the fundamental mode, knowing that the inelastic deformation ratio will not capture the contribution of higher modes in the overall structural response. A developed theoretical approach with the aim of estimating the inelastic deformation ratio for structures, considering contribution of higher modes of vibration, is introduced. In this assessment, the normalized yield strength coefficient (η) and the post-to-preyield stiffness ratio (α) are key factors. The results are compared to the uncoupled modal response history analysis (UMRHA) procedure and some existing formulations for a nine story building subjected to the El Centro 1940 ground motion. It appears that the new theoretical approach leads to enough accurate estimation of the inelastic deformation ratio compared to the UMRHA one.

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References

  1. FEMA, Building Seismic Safety Council, NEHRP guidelines for the seismic rehabilitation of buildings, FEMA–273, Federal Emergency Management Agency, Washington (DC) (1997).

  2. FEMA, Prestandard, Commentary for the seismic rehabilitation of buildings, FEMA–356, Federal Emergency Management Agency, Washington, DC (2000).

  3. A. S. Veletsos and N. M. Newmark, Effect of Inelastic Behavior on the Response of Simple Systems to Earthquake Motions, Department of Civil Engineering, University of Illinois (1960).

    Google Scholar 

  4. N. M. Newmark and W. J. Hall, Earthquake Spectra and Design, Earthquake Eng, Research Institute, Berkeley, CA (1982).

    Google Scholar 

  5. K. Shimazaki and M. A. Sozen, Seismic Drift of Reinforced Concrete Structures, Hazama–gumi (1984).

    Google Scholar 

  6. X. Qi and J. P. Moehle, Displacement Design Approach for Reinforced Concrete Structures Subjected to Earthquakes, Earthquake Engineering Research Center, College of Engineering/University of California, 91 (2) (1991).

    Google Scholar 

  7. E. Miranda, Seismic Evaluation and Upgrading of Existing Structures, CA, USA: University of California at Berkeley (1991).

    Google Scholar 

  8. E. Miranda, Evaluation of site–dependent inelastic seismic design spectra, Journal of Structural Engineering, 119 (5) (1993) 1319–1338.

    Article  MathSciNet  Google Scholar 

  9. W. D. Iwan, Estimating inelastic response spectra from elastic spectra, Earthquake Engineering & Structural Dynamics, 8 (4) (1980) 375–388.

    Article  Google Scholar 

  10. A. Whittaker, M. Constantinou and P. Tsopelas, Displacement estimates for performance–based seismic design, Journal of Structural Engineering, 124 (8) (1998) 905–912.

    Article  Google Scholar 

  11. E. Miranda, Inelastic displacement ratios for structures on firm sites, Journal of Structural Engineering, 126 (10) (2000) 1150–1159.

    Article  Google Scholar 

  12. A. K. Chopra and C. Chiatanapakdee, Inelastic deformation ratios for design and evaluation of structures, Rep. No. EERC–2003–09, EERC, Univ. of California, Berkeley, California (2003).

    Google Scholar 

  13. T. Vidic, P. Fajfar and M. Fischinger, Consistent inelastic design spectra: strength and displacement, Earthquake Engineering & Structural Dynamics, 23 (5) (1994) 507–521.

    Article  Google Scholar 

  14. E. Miranda, Estimation of inelastic deformation demands of SDOF systems, Journal of Structural Engineering, 127 (9) (2001) 1005–1012.

    Google Scholar 

  15. E. Miranda, Evaluation of iterative schemes in equivalent linear methods, Earthquake Spectra (2002).

    Google Scholar 

  16. R.–G. Jorge and E. Miranda, Inelastic displacement ratios for evaluation of existing structures, Earthquake Engineering & Structural Dynamics, 32 (8) (2003) 1237–1258.

    Article  Google Scholar 

  17. A. K. Chopra and C. Chintanapakdee, Inelastic deformation ratios for design and evaluation of structures: Singledegree–of–freedom bilinear systems, Journal of structural engineering, 130 (9) (2004) 1309–1319.

    Article  Google Scholar 

  18. R.–G. Jorge and E. Miranda, Inelastic displacement ratios for design of structures on soft soils sites, Journal of Structural Engineering, 130 (12) (2004) 2051–2061.

    Article  Google Scholar 

  19. R.–G. Jorge and E. Miranda, Inelastic displacement ratios for evaluation of structures built on soft soil sites, Earthquake Engineering & Structural Dynamics, 35 (6) (2006) 679–694.

    Article  Google Scholar 

  20. E. Miranda and R.–G. Jorge, Evaluation of approximate methods to estimate maximum inelastic displacement demands, Earthquake Engineering & Structural Dynamics, 31 (3) (2002) 539–560.

    Article  Google Scholar 

  21. S. S. F. Mehanny and A. S. Ayoub, Variability in inelastic displacement demands: Uncertainty in system parameters versus randomness in ground records, Engineering Structures, 30 (4) (2008) 1002–1013.

    Article  Google Scholar 

  22. G. D. Hatzigeorgiou and D. E. Beskos, Inelastic displacement ratios for SDOF structures subjected to repeated earthquakes, Engineering Structures, 31 (11) (2009) 2744–2755.

    Article  Google Scholar 

  23. C. Málaga–Chuquitaype and A. Y. Elghazouli, Inelastic displacement demands in steel structures and their relationship with earthquake frequency content parameters, Earthquake Engineering & Structural Dynamics, 41 (5) (2012) 831–852.

    Article  Google Scholar 

  24. R.–G. Jorge and E. J. González, Implementation of displacement coefficient method for seismic assessment of buildings built on soft soil sites, Engineering Structures, 59 (2014) 1–12.

    Article  Google Scholar 

  25. M. Dicleli and C. Durucan, Evaluation of displacement coefficient method for seismically retrofitted buildings with various ductility capacities, Earthquake Engineering & Structural Dynamics, 43 (9) (2014) 1285–1306.

    Article  Google Scholar 

  26. C.–H. Zhai et al., Inelastic displacement ratios for design of structures with constant damage performance, Engineering Structures, 52 (2013) 53–63.

    Article  Google Scholar 

  27. S. Akkar and E. Miranda, Improved displacement modification factor to estimate maximum deformations of short period structures, 13th World Conference on Earthquake Engineering (2004).

    Google Scholar 

  28. S. D. Akkar and E. Miranda, Statistical evaluation of approximate methods for estimating maximum deformation demands on existing structures, Journal of Structural Engineering, 131 (1) (2005) 160–172.

    Article  Google Scholar 

  29. S. Akkar and A. Metin, Assessment of improved nonlinear static procedures in FEMA–440, Journal of Structural Engineering, 133 (9) (2007) 1237–1246.

    Article  Google Scholar 

  30. A. K. Chopra and K. G. Rakesh, Direct displacementbased design: use of inelastic vs. elastic design spectra, Earthquake Spectra, 17 (1) (2001) 47–64.

    Article  Google Scholar 

  31. E. Miranda and S. D. Akkar, Dynamic instability of simple structural systems, Journal of Structural Engineering, 129 (12) (2003) 1722–1726.

    Article  Google Scholar 

  32. A. Nassar and H. Krawinkler, Seismic Demands for SDOF and MDOF Systems, John Blume Earthquake Engineering, Ctr. Dept. of Civil Engineering, Rep. 95 (1991).

    Google Scholar 

  33. R. Riddell and N. M. Newmark, Statistical Analysis of The Response of Nonlinear Systems Subjected to Earthquakes, University of Illinois Engineering Experiment Station, College of Engineering, University of Illinois at Urbana–Champaign (1979).

    Google Scholar 

  34. R. Riddell, J. E. Garcia and E. Garces, Ine lastic deformation response of SDOF systems subjected to earthquakes, Earthquake Engineering & Structural Dynamics, 31 (3) (2002) 515–538.

    Article  Google Scholar 

  35. C. Zhai et al., Study on inelastic displacement ratio spectra for near–fault pulse–type ground motions, Earthquake Engineering and Engineering Vibration, 6 (4) (2007) 351–355.

    Article  Google Scholar 

  36. H. Krawinkler and A. A. Nassar, Seismic design based on ductility and cumulative damage demands and capacities, Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings (1992) 23–39.

    Google Scholar 

  37. FEMA, A. 440, Improvement of Nonlinear Static Seismic Analysis Procedures, FEMA–440, Redwood City (2005).

  38. B. Chikh et al., Seismic structural demands and inelastic deformation ratios: A theoretical approach, Earthquakes and Structures, International Journal, 12 (4) (2017) 397–407.

    Google Scholar 

  39. B. Chikh et al., Seismic structural demands and inelastic deformation ratios: A theoretical approach, Earthquakes and Structures, International Journal, 12 (4) (2017) 397–407.

    Google Scholar 

  40. A. K. Chopra and R. K. Goel, A Modal Pushover Analysis Procedure to Estimate Seismic Demands for Buildings: Theory and Preliminary Evaluation, PEER, Berkely, California, March (2001).

    Google Scholar 

  41. A. K. Chopra and K. G. Rakesh, A modal pushover analysis procedure for estimating seismic demands for buildings, Earthquake Engineering & Structural Dynamics, 31 (3) (2002) 561–582.

    Google Scholar 

  42. T. S. Jan, M. W. Liu and Y. C. Kao, An upper–bound pushover analysis procedure for estimating the seismic demands of high–rise buildings, Engineering Structures, 26 (1) (2004) 117–128.

    Article  Google Scholar 

  43. B. Chikh, Y. Mehani and M. Leblouba, Simplified procedure for seismic demands assessment of structures, Structural Engineering and Mechanics, 59 (3) (2016) 455–473.

    Article  Google Scholar 

  44. C. Benazouz, L. Moussa and Z. Ali, Ductility and inelastic deformation demands of structures, Structural Engineering and Mechanics, 42 (5) (2012) 631–644.

    Article  Google Scholar 

  45. Y.–K. Wen, Method for random vibration of hysteretic systems, Journal of the Engineering Mechanics Division, 102 (2) (1976) 249–263.

    Google Scholar 

  46. A. K. Chopra, Dynamics of Structures: Theory and Applications to Earthquake Engineering, Upper Saddle River, NJ: Pearson/Prentice Hall, 3 (2007).

    Google Scholar 

  47. S. A. Mahin and J. Lin, Construction of inelastic response spectra for single–degree–of–freedom systems, Rep. No. UCB/EERC–83 17 (1983).

    Google Scholar 

  48. Uniform Building Code (UBC), International Conference of Building Materials, 2, Whittier, California (1997) 492.

  49. MathWorks, Inc., MATLAB: The language of technical computing. Desktop tools and development environment, Version 7, MathWorks, 9 (2005).

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Author information

Authors and Affiliations

  1. Civil Engineering Department, University of Abbés Laghrour, BP 1252 Route de Batna, Khenchela, 40004, Algeria

    Abdelmounaim Mechaala

  2. National Earthquake Engineering Research Center, CGS, Rue Kaddour Rahim, BP 252 Hussein-Dey, Algiers, Algeria

    Chikh Benazouz, Hamma Zedira & Youcef Mehani

  3. TPITE Laboratory, High National School of Built and Ground Works Engineering (ENSTP), Algiers, Algeria

    Chikh Benazouz, Hamma Zedira & Youcef Mehani

  4. National Institute of Applied Sciences (INSA), N° 20 Voie Avenue Des Buttes de Coesme, Rennes, France

    Samy Guezouli

Authors
  1. Abdelmounaim Mechaala
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  2. Chikh Benazouz
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  3. Hamma Zedira
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  4. Youcef Mehani
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  5. Samy Guezouli
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Correspondence to Abdelmounaim Mechaala.

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Recommended by Associate Editor Junhong Park

Abdelmounaim Mechaala received his master degree from the Department of Civil Engineering, Civil Engineering, Hydraulics and Architecture Institute of Hadj Lakhde University, Batna, Algeria in 2013. Now he is preparing for a Ph.D. degree in Science and Technology Faculty of Abbes Laghrour University, Khenchela, Algeria. His research interests include earthquake engineering and structural dynamics.

Chikh Benazouz, Ph.D., is an Associate Professor of earthquake engineering at ENSTP (High National School of Built and Ground Works Engineering, Algiers, Algeria) and Senior Researcher at CGS (National Earthquake Engineering Research Center, Algiers, Algeria).

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Mechaala, A., Benazouz, C., Zedira, H. et al. Higher modes contribution for estimating the inelastic deformation ratios and seismic demands of structures. J Mech Sci Technol 33, 591–601 (2019). https://doi.org/10.1007/s12206-019-0113-8

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  • DOI: https://doi.org/10.1007/s12206-019-0113-8

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