Skip to main content
SpringerLink
Log in

Equivalent viscous damping for displacement-based seismic design of hysteretic damped braces for retrofitting framed buildings

  • Original Research Paper
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

A displacement-based design (DBD) procedure aiming to proportion hysteretic damped braces (HYDBs) in order to attain, for a specific level of seismic intensity, a designated performance level of a structure is proposed for the retrofitting of framed buildings. A key step for the reliability of the DBD procedure is the selection of the equivalent viscous damping in order to account for the energy dissipated by the damped braced frame. In this paper, expressions of the equivalent damping are obtained considering the energy dissipated by the HYDBs and the framed structure. To this end, dynamic analyses of an equivalent single degree of freedom system, whose response is idealized by a trilinear model, are carried out considering real accelerograms matching, on the average, Eurocode 8 (EC8) response spectrum for a medium subsoil class. Then, a three-storey reinforced concrete (r.c.) framed structure of a school building, designed in a medium-risk seismic region according to the Italian code in force in 1975, is supposed as retrofitted as if in a high-risk seismic region of the current seismic code (NTC08) by the insertion of HYDBs. Nonlinear static analyses are carried out to evaluate the vulnerability of the primary structure, characterized by the lack of interior girders along the floor slab direction, and to select optimal properties of the HYDBs. The effectiveness of the retrofitting solutions is checked referring to nonlinear dynamic analyses, considering artificially generated accelerograms whose response spectra match those adopted by NTC08 for the earthquake design levels corresponding to the serviceability and ultimate limit states.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Bertero VV (2002) G Oliveto (ed) Innovative approaches to earthquake engineering. University of Catania (Italy), WIT Press, pp 1–84

  • Christopoulos C, Filiatrault A (2007) Principles of passive supplemental damping and seismic isolation. IUSS Press, Istituto Universitario di Studi Superiori di Pavia, Italy

  • CSI, Computers and Structures Inc (2004) SAP2000 v10 integrated finite element analysis and design of structures. Berkeley

  • Dipartimento di Protezione Civile (2004) Fornitura ed installazione di venti sistemi di monitoraggio permanente della risposta sismica di strutture civili—Sito SSN n. 10, Bisignano, Scuola elementare Collina Castello. Rel. 031/10a

  • Dolce M (2004) Seismic safety of schools in Italy. In: Proceedings of the Ad Hoc expert group meeting on earthquake safety in schools, vol 3. Paris, France, pp 52–63

  • Dolsek M, Fajfar P (2008) The effect of masonry infills on the seismic response of a four-storey reinforced concrete frame: a deterministic assessment. Eng Struct 30:3186–3192

    Article  Google Scholar 

  • Dwairi HM, Kowalsky MJ, Nau JM (2007) Equivalent damping in support of direct displacement-based design. J Earthq Eng 11:512–530

    Article  Google Scholar 

  • Eurocode 8 (2003) Design of structures for earthquake resistance—part 1: general rules, seismic actions and rules for buildings. C.E.N, European Committee for Standardization

  • Eurocode 8 (2004) Design of structures for earthquake resistance—part 3: assessment and retrofitting of buildings. C.E.N, European Committee for Standardization

  • European Commission for Community Research. European Strong Motion Database. http://www.isesd.cv.ic.ac.uk/ESD

  • Fajfar P (1999) Capacity spectrum method based on inelastic spectra. Earthq Eng Struct Dyn 28:979–993

    Article  Google Scholar 

  • Federal Emergency Management Agency, FEMA 356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings. American Society of Civil Engineers, Reston, Virginia

  • Foti D, Bozzo LM, Lopez-Almansa F (1998) Numerical efficiency assessment of energy dissipators for seismic protection of buildings. Earthq Eng Struct Dyn 27:543–556

    Article  Google Scholar 

  • Foti D, Diaferio M, Nobile R (2010) Optimal design of a new seismic passive protection device made in aluminium and steel. Int J Struct Eng Mech 35(1):119–122

    Article  Google Scholar 

  • Foti D, Diaferio M, Nobile R (2013) Dynamic behavior of new aluminum-steel energy dissipating devices. Struct Control Health Monit 20(7):1106–1119

    Article  Google Scholar 

  • Gasparini D, Vanmarcke E (1976). Simulated earthquake motions compatible with prescribed response spectra. Massachusetts Institute of Technology, Department of Civil Engineering, USA

  • Italian Ministry of Public Works (Ministero dei Lavori Pubblici) (1975) Norme tecniche per le costruzioni in zone sismiche

  • Italian code NTC08 (2008) Technical Regulations for the Constructions. Italian Ministry of the Infrastructures (in italian)

  • Jacobsen LS (1930) Steady forced vibrations as influenced by damping. ASME Trans 52(1):169–181

    Google Scholar 

  • Kim JK, Choi HH, Min KW (2003) Performance-based design of added viscous dampers using capacity spectrum method. J Earthq Eng 7(1):1–24

    Google Scholar 

  • Kim JK, Choi HH (2006) Displacement-based design of supplemental dampers for seismic retrofit of a framed structure. J Struct Eng 132(6):873–883

    Article  Google Scholar 

  • Mazza F, Mazza M (2010) Nonlinear analysis of spatial framed structures by a lumped plasticity model based on the Haar-Kàrmàn principle. Comput Mech 45:647–664

    Article  Google Scholar 

  • Mazza F, Mazza M (2011) Nonlinear modeling and analysis of r.c. spatial frames to study the effects of the vertical component of near-fault ground motions. In: Proceeding of III ECCOMAS thematic conference on computational methods in structural dynamics and earthquake (COMPDYN 2011), Corfù, Greece, paper no 322

  • Mazza F, Mazza M (2012) Nonlinear modeling and analysis of r.c. framed buildings located in a near-fault area. Open Constr Build Technol J 6:364–372

    Google Scholar 

  • Mazza F, Vulcano A (2007) Control of the along-wind response of steel framed buildings by using viscoelastic or friction dampers. Wind Struct 10(3):233–247

    Article  Google Scholar 

  • Mazza F, Vulcano A (2008a) Displacement-based seismic design procedure for framed buildings with dissipative braces. Part I: theoretical formulation. 2008 Seismic engineering international conference commemorating the 1908 Messina and Reggio Calabria earthquake (MERCEA08), Reggio Calabria, Italy, American Institute of Physics conference proceedings, vol 1020, USA (part two)

  • Mazza F, Vulcano A (2008b). Displacement-based seismic design procedure for framed buildings with dissipative braces. Part II: numerical results. 2008 Seismic engineering international conference commemorating the 1908 Messina and Reggio Calabria earthquake (MERCEA08), Reggio Calabria, Italy, American Institute of Physics conference proceedings, USA, vol 1020 (part two)

  • Mazza F, Vulcano A (2009) Nonlinear response of rc framed buildings with isolation and supplemental damping at the base subjected to near-fault earthquakes. J Earthq Eng 13(5):690–715

    Article  Google Scholar 

  • Mazza F, Vulcano A (2010) Nonlinear dynamic response of r.c. framed structures subjected to near-fault ground motions. Bull Earthq Eng 8:1331–1350

    Article  Google Scholar 

  • Mazza F, Vulcano A (2011) Control of the earthquake and wind dynamic response of steel-framed buildings by using additional braces and/or viscoelastic dampers. Earthq Eng Struct Dyn 2:155–174

    Article  Google Scholar 

  • Mazza F, Vulcano A, Mazza M (2012) Nonlinear dynamic response of rc buildings with different base-isolation systems subjected to horizontal and vertical components of near-fault ground motions. Open Constr Build Technol J 6:373–383

    Article  Google Scholar 

  • Mazza F, Vulcano A (2013) Nonlinear seismic analysis to evaluate the effectiveness of damped braces. Int J Mech 7(3):251–261

    Google Scholar 

  • Paulay TN, Priestley MJ (1992) Seismic design of RC and masonry structures. Wiley, New York

    Google Scholar 

  • Ponzo FC, Di Cesare A, Nigro D, Vulcano A, Mazza F, Dolce M, Moroni C (2012) JET-PACS project: dynamic experimental tests and numerical results obtained for a steel frame equipped with hysteretic damped chevron braces. J Earthq Eng 16:662–685

    Article  Google Scholar 

  • Priestley MJN, Calvi GM, Kowalsky MJ (2007) Displacement-based seismic design of structures. IUSS Press, Istituto Universitario di Studi Superiori di Pavia, Italy

  • Ragni L, Zona A, Dall’Asta A (2011) Analytical expressions for preliminary design of dissipative bracing systems in steel frames

  • Soong TT, Dargush GF (1997) Passive energy dissipation systems in structural engineering. Wiley, Chichester Italian code, NTC08 (2008) Technical Regulations for the Constructions. Italian Ministry of the Infrastructures (in italian)

  • Tirca LD, Foti D, Diaferio M (2003) Response of middle-rise steel frames with and without passive dampers to near-field ground motions. Eng Struct 25(2):169–179

    Article  Google Scholar 

  • Vincenzi L, Savoia M (2009) Miglioramento sismico mediante sistemi dissipativi: il caso studio della scuola di Bisignano (in italian). Atti del XIII Convegno Nazionale “L’Ingegneria Sismica in Italia”, ANIDIS, Bologna, paper S12_39

Download references

Acknowledgments

The present work was financed by Re.L.U.I.S. (Italian network of university laboratories of earthquake engineering), according to “convenzione D.P.C.—Re.L.U.I.S. 2010-2013, task 2.3.2”.

Author information

Authors and Affiliations

  1. Università della Calabria, Rende, Cosenza, Italy

    Fabio Mazza & Alfonso Vulcano

Authors
  1. Fabio Mazza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfonso Vulcano
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabio Mazza.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mazza, F., Vulcano, A. Equivalent viscous damping for displacement-based seismic design of hysteretic damped braces for retrofitting framed buildings. Bull Earthquake Eng 12, 2797–2819 (2014). https://doi.org/10.1007/s10518-014-9601-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-014-9601-5

Keywords

Search

Navigation