Skip to main content
SpringerLink
Log in

Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods

  • Published:
Earthquake Engineering and Engineering Vibration Aims and scope Submit manuscript

Abstract

Seismic force reduction factor (SFRF) spectra of shear-type multi-degree-of-freedom (MDOF) structures are investigated. The modified Clough model, capable of considering the strength-degradation/hardening and stiffness-degradation, is adopted. The SFRF mean spectra using 102 earthquake records on a typical site soil type (type C) are constructed with the period abscissa being divided into three period ranges to maintain the peak features at the two site-specific characteristic periods. Based on a large number of results, it is found that the peak value of SFRF spectra may also exist for MDOF, induced by large high-mode contributions to elastic base shear, besides the mentioned two peak values. The variations of the stiffness ratio λk and the strength ratio λF of the top to bottom story are both considered. It is found that the SFRFs for λF ≤ λk are smaller than those for λF > λk. A SFRF modification factor for MDOF systems is proposed with respect to SDOF. It is found that this factor is significantly affected by the story number and ductility. With a specific λF (= λk0.75), SFRF mean spectra are constructed and simple solutions are presented for MDOF systems. For frames satisfying the strong column/weak beam requirement, an approximate treatment in the MDOF shear-beam model is to assign a post-limit stiffness 15%-35% of the initial stiffness to the hysteretic curve. SFRF spectra for MDOF systems with 0.2 and 0.3 times the post-limit stiffness are remarkably larger than those without post-limit stiffness. Thus, the findings that frames with beam hinges have smaller ductility demand are explained through the large post-limit stiffness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ayoub A and Chenouda M (2009), “Resp onse Spectra of Degrading Structural Systems,” Engineering Structures, 31(7): 1393–1402.

    Article  Google Scholar 

  • Borzi B and Elnashai AS (2000), “Refined Force Reduction Factors for Seismic Design,” Engineering Structures, 22(10): 1244–1260.

    Article  Google Scholar 

  • Cai J, Zhou J and Fang XD (2006), “Seismic Ductility Reduction Factors for Multi-Degree-of-Freedom Systems,” Advances in Structural Engineering, 9(5): 591–601.

    Article  Google Scholar 

  • Chopra AK (1995), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice Hall.

    Google Scholar 

  • Clough RW and Penzien J (1975), Dynamics of Structures, New York: McGraw-Hill.

    Google Scholar 

  • Daneshjoo F and Gerami M (2003), “Higher Mode Effects on Seismic Behavior of MDOF Steel Moment Resisting Frames,” Journal of Seismology and Earthquake Engineering, 5(3): 41–54.

    Google Scholar 

  • GB 50011-2010 (2016), Code for Seismic Design of Buildings. (in Chinese)

    Google Scholar 

  • Gupta A and Krawinkler H (2000), “Behavior of Ductile SMRFS at Various Seismic Hazard Levels,” Journal of Structural Engineering, 126(1): 98–107.

    Article  Google Scholar 

  • Humar JL and Rahgozar MA (1996), “Application of Inelastic Response Spectral Derived from Seismic Hazard Spectral Ordinates for Canada,” Canadian Journal of Civil Engineering, 23(5): 1051–1063.

    Article  Google Scholar 

  • Ibarra LF and Krawinkler HA (2005), “Global Collapse of Frame Structures Under Seismic Excitations,” The John A. Blume Earthquake Engineering Center, Report No.152.

    Google Scholar 

  • Lee LH, Han SW and Oh YH (1999), “Determination of Ductility Factor Considering Different Hysteretic Models,” Earthquake Engineering and Structural Dynamics, 28(9): 957–977.

    Article  Google Scholar 

  • Miranda E (1993a), “Evaluation of Site-Dependent Inelastic Seismic Design Spectra,” Journal of Structural Engineering, 119(5): 1319–1338.

    Article  Google Scholar 

  • Miranda E (1993b), “Site-Dependent Strength- Reduction Factors,” Journal of Structural Engineering, 119: 3503–3519.

    Article  Google Scholar 

  • Miranda E and Bertero V (1994), “Evaluation of Strength Reduction Factors for Earthquake Resistant Design,” Earthquake Spectra, 10(2): 357–379.

    Article  Google Scholar 

  • Moghaddam H and Mohannadi RK (2001), “Ductility Reduction Factor of MDOF Shear-Building Structures,” Journal of Earthquake Engineering, 5(3): 425–440.

    Google Scholar 

  • Nassar AA and Krawinkler H (1991), “Seismic Demands for SDOF and MDOF Systems,” John A. Blume Earthquake Engineering Center, Department of Civil Engineering, Stanford University.

    Google Scholar 

  • Qu H, Zhang J and Zhao JX (2011), “Strength Reduction Factors for Seismic Analyses of Buildings Exposed to Near-Fault Ground Motions,” Earthquake Engineering and Engineering Vibration, 10(2): 195–209.

    Article  Google Scholar 

  • Santa-Ana FR (2004), “Estimation of Strength Reduction Factors for Elastoplastic Structures: Reduction Factors,” 13th World Conference on Earthquake Engineering, No.126.

    Google Scholar 

  • Santa-Ana FR and Miranda E (2000), “Strength Reduction Factors for Multi-Degree-of-Freedom Systems,” 12th World Conference on Earthquake Engineering, No. 1446.

    Google Scholar 

  • Seneviratna GDPK and Krawinkler H (1997), “Evaluation of Inelastic MDOF Effects for Seismic Design,” The John A. Blume Earthquake Engineering Center, Report No.120.

    Google Scholar 

  • Tong GS, Ye Y and Zhang L (2013), “Seismic Force with Different Ductility Factor in Strength Degrading System,” Journal of Tongji University, 41(8): 1133–1139, 1157.

    Google Scholar 

  • Tong GS and Zhao YF (2007), “Seismic Force Reduction Factors for Modified-Clough Hysteretic Model,” Engineering Structures, 29(11): 3053–3070.

    Article  Google Scholar 

  • Tong GS and Zhao YF (2008), “Inelastic Yielding Strengt h Demand Coefficient Spectra,” Soil Dynamics and Earthquake Engineering, 28: 1004–1013.

    Article  Google Scholar 

  • Veletsos AS and Vann WP (1971), “Response of Ground- Excited Elastoplastic Systems,” Journal of the Structural Division, 97(4): 1257–1281.

    Google Scholar 

  • Vidic T and Fajfar P (1994), “Consistent Inelastic Design Spectra: Strength and Displacement,” Earthquake Engineering and Structural Dynamics, 23: 507–521.

    Article  Google Scholar 

  • Zhai CH, Wen WP, Li S and Xie LL (2015) “The Ductility- Based Strength Reduction Factor for the Mainshock–Aftershock Sequence-Type Ground Mtions,” Bulletin of Earthquake Engineering, 13(10): 2893–2914.

    Article  Google Scholar 

  • Zhao YF and Tong GS (2009), “An Investigation of Characteristic Periods of Seismic Ground Motion,” Journal of Earthquake Engineering, 13: 540–65.

    Article  Google Scholar 

Download references

Acknowledgment

The study is financially supported by the National Key Research and Development Program of China under Grant No. 2016YFC0701201.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, China

    Xiao Li, Genshu Tong & Lei Zhang

Authors
  1. Xiao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Genshu Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Genshu Tong.

Additional information

Supported by: National Key Research and Development Program of China under Grant No. 2016YFC0701201

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X., Tong, G. & Zhang, L. Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods. Earthq. Eng. Eng. Vib. 19, 53–69 (2020). https://doi.org/10.1007/s11803-020-0547-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11803-020-0547-0

Keywords

Search

Navigation