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A seismic design method for reinforced concrete moment resisting frames using modal strength reduction factors

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Abstract

A performance-based seismic design method for plane reinforced concrete (R/C) moment-resisting frames (MRF) is proposed. The method is a force-based seismic design one, utilizing not a single strength reduction factor as all modern codes do, but different such factors for each of the first significant modes of the frame. These modal strength reduction factors incorporate dynamic characteristics of the structure, different performance targets, and different soil types. Thus, the proposed method can automatically satisfy deformation demands at all performance levels without requiring deformation checks at the end of the design process, as it is the case with code-based design methods. Empirical expressions for those modal strength reduction factors as functions of the period, deformation/damage and soil types, which can be used directly in conjunction with the conventional elastic pseudo-acceleration design spectra with 5% damping for seismic design of R/C MRFs, are provided. These expressions have been obtained through extensive parametric studies involving non-linear dynamic analyses of 38 frames under 100 seismic motions. The method is illustrated by numerical examples which demonstrate its advantages over code-based seismic design methods.

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References

  • ATC72-1 (2010) Modeling and acceptance criteria for seismic design and analysis of tall buildings. Applied Technology Council, Redwood City, CA

  • Biskinis DE, Fardis MN (2008) Cycling deformation capacity, resistance and effective stiffness of R/C members with or without retrofitting. In: Proceedings of 14th world conference on earthquake engineering, Beijing, China

  • Bozorgnia Y, Bertero VV (eds) (2004) Earthquake engineering: from engineering seismology to performance–based engineering, 1st edn. CRC Press, Boca Raton

    Google Scholar 

  • Carr AJ (2006) Theory and user guide to associated programs. Ruaumoko Manual. Department of Engineering, University of Canterbury, Christchurch

  • Chopra AK (2011) Dynamics of structures, 4th edn. Pearson, Upper Saddle River

    Google Scholar 

  • Chryssanthopoulos MK, Dymiotis C, Kappos AJ (2000) Probabilistic evaluation of behaviour factors in EC8-designed R/C frames. Eng Struct 22:1028–1041

    Article  Google Scholar 

  • EC2 (2004) Eurocode 2: design of concrete structures. In: Brussels: Part 1.1: general rules for buildings, European standard EN 1992-1-1, European Committee for Standardization (CEN)

  • EC8 (2004) Eurocode 8: design of structures for earthquake resistance, Part 3: assessment and retrofitting of buildings. In: European Standard EN 1998-3, European Committee for Standardization (CEN), Brussels

  • EC8 (2005) Eurocode 8: design of structures for earthquake resistance, Part 1: general rules, seismic actions and rules for buildings. European Standard EN 1998-1, Stage 51 Draft, European Committee for Standardization (CEN), Brussels

  • Elwood KJ, Matamoros AB, Wallace JW, Lehman DE, Heintz JA, Mitchell AD, Moore MA, Valley MT, Lowes LN, Comartin CD, Moehle JP (2007) Update to ASCE/SEI 41 concrete provisions. Earthq Spectra 23(3):493–523

    Article  Google Scholar 

  • Fajfar P (2000) A nonlinear analysis method for performance–based seismic design. Earthq Spectra 16(3):573–592

    Article  Google Scholar 

  • Fardis MN (2009) Seismic design, assessment and retrofitting of concrete buildings. Springer, Dordrecht

    Book  Google Scholar 

  • Fardis MN, Carvalho E, Elnashai A, Faccioli E, Pinto P (2005) Designers’ guide to EN 1998–1 and EN 1998–5 Eurocode 8: Design of structures for earthquake resistance. Thomas Telford, London

    Google Scholar 

  • FEMA-356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings, prepared for the SAC Joint Venture, published by the Federal Emergency Management Agency. American Society of Civil Engineers (ASCE), Washington, D.C

  • Ghobarah A (2004) On drift limits associated with different damage levels. In: Fajfar P, Krawinkler H (eds) Proceeding of the international workshop on performance-based seismic design : concepts and implementation, Bled, Slovenia, PEER Report 2004/05, University of California, Berkley, pp 321–332

  • Ghobarah A, Safar M (2010) A damage spectrum for performance-based design. In: Fardis MN (ed) Advances in performance-based earthquake engineering. Springer, Berlin, pp 193–201 no. 13

    Chapter  Google Scholar 

  • Ghobarah A, Abou-Elfath H, Biddah A (1999) Response-based damage assessment of structures. Earthq Eng Struct Dyn 28(1):79–104

    Article  Google Scholar 

  • Haselton CB, Liel AB, Taylor Lange S, Deierlein GG (2008) Beam-column element model calibrated for predicting flexural response loading to global collapse of R/C frame buildings. PEER Report2007/03, Pacific Earthquake Engineering Research Center, University of California, Berkley, California

  • Hatzigeorgiou GD, Beskos DE (2007) Direct damage-controlled design of concrete structures. J Struct Eng ASCE 133(2):205–215

    Article  Google Scholar 

  • Kamaris GS, Hatzigeorgiou GD, Beskos DE (2014) Direct damage controlled seismic design of plane steel degrading frames. Bull Earthq Eng 13(2):587–612

    Article  Google Scholar 

  • Kappos AJ, Manafpour A (2001) Seismic design of R/C buildings with the aid of advanced analytical techniques. Eng Struct 23:319–332

    Article  Google Scholar 

  • Kappos AJ, Panagopoulos G (2004) Performance-based seismic design of 3-D R/C buildings using inelastic static and dynamic analysis procedures. ISET J Earthq Technol 41:141–158

    Google Scholar 

  • Kappos AJ, Stefanidou S (2009) A deformation-based seismic design method for 3-D R/C irregular buildings using inelastic dynamic analysis. Bull Earthq Eng 8(4):875–895

    Article  Google Scholar 

  • Karavasilis TL, Bazeos N, Beskos DE (2007) Behavior factor for performance-based seismic design of plane steel moment resisting frames. J Earthq Eng 11(4):531–559

    Article  Google Scholar 

  • Lin YY, Chang KC (2003) Study on damping reduction factor for buildings under earthquake ground motions. J Struct Eng ASCE 129:206–214

    Article  Google Scholar 

  • Loeding S, Kowalsky MJ, Priestley M (1998) Direct displacement-based design of reinforced concrete building frames. University of California, San Diego

    Google Scholar 

  • MATLAB (2009) The language of technical computing, version 2009a, The MathWorks, Inc., Natick, MA, USA

  • Mazzolani F, Piluso V (1996) Theory and design of seismic resistant steel frames. CRC Press, Boca Raton

    Book  Google Scholar 

  • Miranda E, Bertero VV (1994) Evaluation of strength reduction factors for earthquake resistant design. Earthq Spectra 10:357–379

    Article  Google Scholar 

  • Mondal A, Ghosh S, Reddy GR (2013) Performance-based evaluation of the response reduction factor for ductile R/C frames. Eng Struct 56:1808–1819

    Article  Google Scholar 

  • Muho EV (2017) Seismic design of planar concrete frames using modal strength reduction factors. University of Patras, Patras, Greece, Ph.D. Thesis, Department of Civil Engineering (in Greek)

  • Mwafy AM, Elnashai AS (2002) Calibration of force reduction factors of R/C buildings. J Earthq Eng 6:239–273

    Google Scholar 

  • New Zealand Standard NZS 3101: Part 1. Code of practice for the design of concrete structures, Wellington, NZ (1995)

  • Panagiotakos TB, Fardis MN (1999) Deformation-controlled earthquake-resistant design of R/C buildings. J Earthq Eng 3(4):495–518

    Google Scholar 

  • Panagiotakos TB, Fardis MN (2001) A displacement-based seismic design procedure for R/C buildings and comparison with EC8. Earthq Eng Struct Dyn 30(10):1439–1462

    Article  Google Scholar 

  • Papagiannopoulos GA, Beskos DE (2010) Towards a seismic design method for plane steel frames using equivalent modal damping ratios. Soil Dyn Earthq Eng 30:1106–1118

    Article  Google Scholar 

  • Papagiannopoulos GA, Beskos DE (2011) Modal strength reduction factors for seismic design of plane steel frames. Earthq Struct 2:65–88

    Article  Google Scholar 

  • Papagiannopoulos GA, Hatzigeorgiou GD, Beskos DE (2013) Recovery of spectral absolute acceleration and spectral relative velocity from their pseudo-spectral counterparts. Earthq Struct 4:489–508

    Article  Google Scholar 

  • PEER (2013) Pacific earthquake engineering research centre, strong ground motion database

  • Priestley MJN (2003) Myths and fallacies in earthquake engineering, revised. The 9th Mallet Milne Lecture

  • Priestley MJN (1997) Displacement-based seismic assessment of reinforced concrete buildings. J Earthq Eng 1(1):157–192

    Google Scholar 

  • Priestley MJN, Calvi GM, Kowalsky MJ (2007) Displacement based seismic design of structures, 1st edn. IUSS Press, Pavia

    Google Scholar 

  • Rivera JA, Petrini L (2011) On the design and seismic response of R/C frame buildings designed with Eurocode 8. Bull Earthq Eng 9:1593–1616

    Article  Google Scholar 

  • SAP2000 (2016) Structural Analysis Program, Computers and Structures, Inc., California, USA. https://www.csiamerica.com/products/sap2000

  • SEAOC (1999) Recommended lateral force requirements and commentary. Structural Engineers Association of California, Sacramento, CA

  • Seismosoft (2016) SeismoMatch–a computer program for spectrum matching of earthquake records

  • Skalomenos KA, Hatzigeorgiou GD, Beskos DE (2015) Seismic behavior of composite steel/concrete MRFs: deformation assessment and behavior factors. Bull Earthq Eng 13:3871–3896

    Article  Google Scholar 

  • Vasilopoulos AA, Beskos DE (2006) Seismic design of plane steel frames using advanced methods of analysis. Soil Dyn Earthq Eng 26:1077–1100

    Article  Google Scholar 

  • Vasilopoulos AA, Beskos DE (2009) Seismic design of space steel frames using advanced methods of analysis. Soil Dyn Earthq Eng 29:194–218

    Article  Google Scholar 

  • Xue Q, Chen C-C (2003) Performance-based seismic design of structures: a direct displacement-based approach. Eng Struct 25:1803–1813

    Article  Google Scholar 

Download references

Acknowledgements

The first author (E. V. Muho) acknowledges with thanks the support provided for him by the National Key Research and Development of China (Grand No. 2017YFC1500701) and the State Key Laboratory of Disaster Reduction in Civil Engineering (Grand No. SLDRCE15-B-06)

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Correspondence to Dimitri E. Beskos.

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Muho, E.V., Papagiannopoulos, G.A. & Beskos, D.E. A seismic design method for reinforced concrete moment resisting frames using modal strength reduction factors. Bull Earthquake Eng 17, 337–390 (2019). https://doi.org/10.1007/s10518-018-0436-3

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  • DOI: https://doi.org/10.1007/s10518-018-0436-3

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