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Cantilever beam analogy for modal analysis of rocking core-moment frames

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Abstract

Unlike conventional seismic resisting systems, rocking core-moment frame (RCMF) combinations as low-damage assemblies are being developed to mitigate, or even eliminate structural damage and residual deformations following a severe earthquake. Despite extensive studies on the performance of specific rocking cores, dynamic characteristics and strength demands of a generic RCMF have not been addressed. By utilizing cantilever beam analogy, the current article proposes a modal analysis method to formulate RCMF demands. The proposed model and obtained analytical charts provide a manual method for rapid study and preliminary design of low- to mid-rise RCMFs with relatively uniform properties over the height. An extensive parametric study investigates the effects of rocking core base-fixity and frame-to-core stiffness on demand values. An independent computer analysis verifies the validity and accuracy of the proposed formulas. Findings show significant higher-mode effects in several RCMF combinations.

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References

  • ASCE (American Society of Civil Engineers) (2010) Minimum design loads for buildings and other structures. ASCE Standard ASCE/SEI 7-10. Reston, VA: American Society of Civil Engineers

  • Bozdogan KB (2009) An approximated method for static and dynamic analyses of symmetric wall-frame buildings. Struct Des Tall Build. https://doi.org/10.1002/tal.409

    Google Scholar 

  • Chancellor NB, Akbas G, Sause R, Joo A (2012) Evaluation of performance-based design methodology for steel self-centering braced frame. In: Proceedings of 7th international conference on behavior of steel structures in seismic areas STESSA 2012, CRC Press, London

  • Chopra AK (2012) Dynamics of structures: theory and applications to earthquake engineering, 4th edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Eatherton M, Hajjar J (2010) Large-scale cyclic and hybrid simulation testing and development of a controlled-rocking steel building system with replaceable fuses. NSEL Rep. NSEL-025, University of Illinois at Urbana, Champaign, IL

  • Gray MG, Christopoulos C, Packer JA (2014) Cast steel yielding brace system for concentrically braced frames: Concept development and experimental validations. J Struct Eng 140(4):04013095

    Article  Google Scholar 

  • Grigorian M, Grigorian C (2015a) An introduction to the structural design of rocking wall-frames with a view to collapse prevention, self-alignment and repairability. Struct Des Tall Spec Build 25(2):93–111

    Article  Google Scholar 

  • Grigorian C, Grigorian M (2015b) Performance control and efficient design of rocking wall moment frames. J Struct Eng. https://doi.org/10.1061/(ASCE)ST.1943-541X.000141104015139

    Google Scholar 

  • Grigorian M, Moghadam, AS, Mohammadi H (2017) On rocking core-moment frame design. In: Proceedings of 16th world conference on earthquake engineering, Santiago, Chile

  • Latham DA, Reay AM, Pampanin S (2013) Kilmore street medical centre: application of a post-tensioned steel rocking system. In: Proceedings of steel innovations conference 2013, Steel Construction New Zealand, Manuakau City, New Zealand

  • Ma X (2010) Seismic design and behavior of self-centering braced frame with controlled rocking and energy-dissipating fuses. Dissertation. Stanford Univ

  • Ma X, Krawinkler H, Deierlein GG (2011) Seismic design, simulation and shake table testing of self-centering braced frame with controlled rocking and energy dissipating fuses. Rep. No. 174, John A. Blume Earthquake Engineering Center, Stanford Univ

  • NRCC (National Research Council of Canada) (2010) National building code of Canada, Ottawa

  • OpenSees version 2.3.2 [Computer software]. Pacific Earthquake Engineering Research Center, Berkeley, CA

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

    Google Scholar 

  • Qu Z, Wada A, Motoyui S, Sakata H, Kishiki S (2012) Pin-supported walls for enhancing the seismic performance of building structures. Earthq Eng Struct Dyn 41(14):2075–2091

    Article  Google Scholar 

  • Rafezy B, Zare A, Howson PW (2007) Coupled lateral-torsional frequencies of asymmetric, three dimensional frame structures. Int J Solids Struct 44:128–144

    Article  Google Scholar 

  • Rahgozar N, Moghadam SA, Aziminejad A (2016) Quantification of seismic performance factors for self centering controlled rocking special concentrically braced frame. Struct Des Tall Spec Build 25(14):700–723

    Article  Google Scholar 

  • Rahgozar N, Moghadam SA, Aziminejad A (2018) Continuum analysis approach for rocking core-moment frames. J Struct Eng. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001986144(3):04018006

    Google Scholar 

  • Roke D, Sause R, Ricles JM, Gonner N (2008) Design concepts for damage-free seismic resistant self-centering steel concentrically-braced frames. In: Proceedings of 14th world conference on earthquake engineering, International Association for Earthquake Engineering, Tokyo

  • Rutenberg A (2013) Seismic shear forces on RC walls: review and bibliography. Bull Earthq Eng 11:1726–1751

    Article  Google Scholar 

  • Stanford SB (1991) Tall building structures. Wiley, Chichester

    Google Scholar 

  • Tremblay R, et al. (2008) Innovative viscously damped rocking braced frames. In: Proceedings of 14th world conference on earthquake engineering, International Association for Earthquake Engineering, Tokyo

  • Tse KT, Song J (2015) Modal analysis of a linked cantilever flexible building system. J Struct Eng 141:04015008

    Article  Google Scholar 

  • Wiebe L, Christopoulos C (2015) A cantilever beam analogy for quantifying higher mode effects in multistorey buildings. Earthq Eng Struct Dyn 44:1697–1716

    Article  Google Scholar 

  • Wiebe L, Christopoulos C, Tremblay R, Leclerc MA (2008) Mechanisms to limit higher mode effects in a controlled rocking steel frame 1: concept, modelling, and low-amplitude shake table testing. Earthq Eng Struct Dyn 42(7):1053–1068

    Article  Google Scholar 

  • Young D, Felgar RP (1949) Tables of characteristic functions representing normal modes of vibration of a beam, Publication 4913 Univ of Texas

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Authors and Affiliations

  1. Department of Structural Engineering, Science and Research Branch, Islamic Azad University, Tehran, 1477893855, Iran

    Nima Rahgozar & Armin Aziminejad

  2. Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran, 1953714453, Iran

    Abdolreza S. Moghadam

Authors
  1. Nima Rahgozar
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  2. Abdolreza S. Moghadam
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  3. Armin Aziminejad
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Correspondence to Abdolreza S. Moghadam.

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Rahgozar, N., Moghadam, A.S. & Aziminejad, A. Cantilever beam analogy for modal analysis of rocking core-moment frames. Bull Earthquake Eng 16, 4081–4106 (2018). https://doi.org/10.1007/s10518-018-0401-1

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  • DOI: https://doi.org/10.1007/s10518-018-0401-1

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