Bulletin of Earthquake Engineering

, Volume 16, Issue 9, pp 4315–4338 | Cite as

Optimal design of isolation devices for mid-rise steel moment frames using performance based methodology

  • Jian Zhang
  • Zhan Shu
Original Research Paper


This paper develops and applies the performance-based analysis and design methodology to assess the seismic vulnerability of mid-rise steel moment frame structures and to optimally design the isolation devices to reduce the direct losses due to earthquake damages. An isolated steel moment frame, originally tested in the 2011 E-Defense blind prediction contest, is selected and modeled in detail. The numerical model and the predicted seismic responses of the structure are validated against the full-scale shaking table test results. Subsequently, the fragility functions are derived for the structure when subject to near-fault ground motions exhibiting distinctive acceleration or velocity pulses and far-field motions with less impulsive characteristics. To quantify the system level damage states of the building, the concept of total loss ratio (TLR) is applied as the performance index to account for the direct loss due to structural, non-structural and isolation components in relation to the total repair cost of the original structure. The TLR considers the failure probability (as defined by fragility functions), the damage percentage and related cost for each damage state. Finally, among various isolation designs, the optimal configuration is derived for cases with the minimum TLR. It is shown that the optimal design can reduce the TLR up to 90% of that of the un-isolated structure and it also outperforms the adopted design in the test program. The study demonstrates a systematic way of achieving the optimal isolation design with considerations of uncertainties in earthquake inputs and the combined structural and non-structural damages.


Steel moment frame Performance based design Base isolation Optimal design Total loss ratio Fragility functions 



This research was partially funded by the following parties: (1) the National Science Foundation under the Grant CMMI-0830391, Joy Pauschke, program manager; (2) the National Natural Science Foundation of China (Grant No. 51708418). The financial support is greatly appreciated.


  1. ASCE (2010) ASCE 7-10 minimum design loads for buildings and other structures. American Society of Civil Engineers, RestonGoogle Scholar
  2. Aslani H, Miranda E (2005) Probabilistic earthquake loss estimation and loss disaggregation in buildings. Technical Report No. 157, The John A. Blume Earthquake Engineering Center, Stanford University, StanfordGoogle Scholar
  3. ATC (1996) ATC-40 seismic evaluation and retrofit of concrete buildings. SSC 96-01, Seismic Safety Commission, Project 40, Applied Technology Council, Redwood CityGoogle Scholar
  4. ATC (2012) ATC-58 seismic performance assessment of buildings. FEMA P-58, Applied Technology Council, Redwood CityGoogle Scholar
  5. Bai JW, Hueste MB, Gardoni P (2009) Probabilistic assessment of structural damage due to earthquakes for buildings in mid-America. J Struct Eng ASCE 135(10):1155–1163CrossRefGoogle Scholar
  6. Blind Analysis Contest (2011) Numerical prediction of shaking table test of 5-story steel frame with and without base isolation.
  7. Bouc R (1971) Modele mathematique d’hysteresis. Acustica 24:16–25Google Scholar
  8. Casciati F (1989) Stochastic dynamics of hysteretic media. Struct Safety 6(2–4):259–269CrossRefGoogle Scholar
  9. Dao ND, Ryan KL (2014) Computational simulation of a full-scale, fixed-base, and isolated-base steel moment frame building tested at E-Defense. J Struct Eng ASCE Spec Issue Comput Simul Struct Eng 140:A4014005CrossRefGoogle Scholar
  10. Dao ND, Ryan KL, Sato E, Sasaki T (2013) Predicting the displacement of triple pendulum bearings in a full scale shaking experiment using a three-dimensional element. Earthquake Eng Struct Dyn 42(11):1677–1695CrossRefGoogle Scholar
  11. Dhakal RP, Mander JB (2006) Financial risk assessment methodology for natural hazards. Bull N Z Soc Earthq Eng 39(2):91–105Google Scholar
  12. Fajfar P, Gašperšič P (1996) The N2 method for the seismic damage analysis of RC buildings. Earthq Eng Struct Dyn 25:31–46CrossRefGoogle Scholar
  13. FEMA (1997a) FEMA 273 NEHRP guidelines for seismic rehabilitation of buildings. Federal Emergency Management Agency, WashingtonGoogle Scholar
  14. FEMA (1997b) FEMA 274 NEHRP commentary on the guidelines for seismic rehabilitation of buildings. Federal Emergency Management Agency, WashingtonGoogle Scholar
  15. FEMA (2003) Multi-hazard loss estimation methodology—earthquake model. HAZUS-MH MR4 Technical Manual, Federal Emergency Management Agency, WashingtonGoogle Scholar
  16. Fenz DM, Constantinou MC (2008) Modeling triple friction pendulum bearings for response-history analysis. Earthq Spectra 24(4):1011–1028CrossRefGoogle Scholar
  17. Graf WP, Lee Y (2009) Code-oriented damage assessment for buildings. Earthq Spectra 25(1):17–37CrossRefGoogle Scholar
  18. Hall JF, Heaton TH, Halling MW, Wald DJ (1995) Near-source ground motion and its effects on flexible buildings. Earthq Spectra 11:569–605CrossRefGoogle Scholar
  19. Haselton CB, Goulet CA, Mitrani-Reiser J, Beck JL, Deierlein GG, Porter KA, Stewart JP, Taciroglu E (2007) An assessment to benchmark the seismic performance of a code-conforming reinforced concrete moment-frame building. PEER Report 07/12, Pacific Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
  20. Ji X, Hikino T, Kasai K, Nakashima M (2013) Damping identification of a full-scale passively controlled five-story steel building structure. Earthq Eng Struct Dyn 42(2):277–295CrossRefGoogle Scholar
  21. Kalpakidis IV, Constantinou M, Whittaker A (2010) Modeling strength degradation in lead-rubber bearing under earthquake shaking. Earthquake Eng Struct Dyn 39(13):1533–1549CrossRefGoogle Scholar
  22. Kasai K, Hikino T, Ito H, Ooki Y, Motoyui S, Kato F, Baba Y (2011) Overall test outline and response of building without dampers. 3D shake table tests on full scale 5-story steel building with dampers, part 1. J Struct Constr Eng AIJ 76(663):997–1006 (in Japanese) CrossRefGoogle Scholar
  23. Kelly JM (1986) Aseismic base isolation: review and bibliography. Soil Dyn Earthq Eng 5(3):202–216CrossRefGoogle Scholar
  24. Kircher CA (2003) It makes dollars and sense to improve nonstructural system performance. In: ATC-29-2 proceedings of seminar on seismic design, performance, and retrofit of nonstructural components in critical facilities, Los Angeles, CAGoogle Scholar
  25. Kumar M, Whittaker A, Constantinou M (2014) An advanced numerical model of elastomeric seismic isolation bearings. Earthq Eng Struct Dyn 43(13):1955–1974CrossRefGoogle Scholar
  26. Lafontaine M, Moroni O, Sarrazin M, Roschke P (2009) Optimal control of accelerations in a base-isolated building using magneto-rheological dampers and genetic algorithms. J Earthq Eng 13:1153–1171CrossRefGoogle Scholar
  27. Lee HJ, Yang GQ, Jung HJ, Spenser BF, Lee IW (2006) Semi-active neurocontrol of a base-isolated benchmark structure. Struct Control Health 13:682–692CrossRefGoogle Scholar
  28. Mackie KR, Stojadinović B (2005) Fragility basis for California highway overpass bridge seismic decision making. PEER Report 05/02, Pacific Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
  29. Mackie KR, Stojadinović B (2007) Performance-based seismic bridge design for damage and loss limits states. Earthq Eng Struct Dyn 36:1953–1971CrossRefGoogle Scholar
  30. Makris N, Vassiliou MF (2011) The existence of “complete similarities” in the response of seismic isolated structures subjected to pulse-like ground motions and their implications in analysis. Earthq Eng Struct Dyn 40:1103–1121CrossRefGoogle Scholar
  31. Makris N, Zhang J (2002) Structural characterization and seismic response analysis of a highway overcrossing equipped with elastomeric bearings and fluid dampers: a case study. PEER Report 02/17, Pacific Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
  32. Moon BY, Kang GJ, Kang BS, Kelly JM (2002) Design and manufacturing of fiber reinforced elastomeric isolator for seismic isolation. J Mater Process Technol 130–131:145–150CrossRefGoogle Scholar
  33. Naeim F, Kelly JM (1999) Design of seismic isolated structures: from theory to practice. Wiley, New YorkCrossRefGoogle Scholar
  34. Nielson BG, DesRoches R (2007) Seismic fragility methodology for highway bridges using a component level approach. Earthq Eng Struct Dyn 36(6):823–839CrossRefGoogle Scholar
  35. OpenSees (2017) Open system for earthquake engineering simulation. Pacific Earthquake Engineering Research (PEER) Center, University of California: Berkeley.
  36. Padgett JE, Nielson BG, DesRoches R (2008) Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios. Earthq Eng Struct Dyn 37(5):711–725CrossRefGoogle Scholar
  37. Plotner SC, Babbitt C, Charest AC, Elsmore C, Gomes J (2016) Building construction costs with RSMeans Data 2017. R.S. Means data from GORDIANGoogle Scholar
  38. Porter KA (2003) An overview of PEER’s performance-based earthquake engineering methodology. In: Proceedings of ninth international conference on applications of statistics and probability in civil engineering, San Francisco, CAGoogle Scholar
  39. Ryan K, Chopra A (2004) Estimation of seismic demands on isolators based on nonlinear analysis. J Struct Eng ASCE 130(3):392–402CrossRefGoogle Scholar
  40. Sabelli R, Mahin S, Chang C (2003) Seismic demands on steel braced frame buildings with buckling restrained braces. Eng Struct 25(5):655–666CrossRefGoogle Scholar
  41. Sayani PJ, Ryan KL (2009) Comparative evaluation of base-isolated and fixed-base buildings using a comprehensive response index. J Struct Eng ASCE 135(6):698–707CrossRefGoogle Scholar
  42. SEAOC (Structural Engineers Association of California) (1995) Vision 2000: performance-based seismic engineering of buildings, vols. I, II. Structural Engineers association of California, SacramentoGoogle Scholar
  43. Shu Z, Li S, Sun X, He M (2017) Performance-based seismic design of a pendulum tuned mass damper system. J Earthq Eng. Google Scholar
  44. Skinner RI, Robinson WH, McVerry GH (1993) An introduction to seismic isolation. Wiley, ChichesterGoogle Scholar
  45. Solberg KM, Dhakal RP, Mander JB, Bradley BA (2008) Computational and rapid expected annual loss estimation methodologies for structures. Earthq Eng Struct Dyn 37(1):81–101CrossRefGoogle Scholar
  46. Tang Y, Zhang J (2011) Response spectrum-oriented pulse identification and magnitude scaling of forward directivity pulses in near-fault ground motions. Soil Dyn Earthq Eng 31:59–76CrossRefGoogle Scholar
  47. Wen YK (1975) Approximate method for nonlinear random vibration. J Eng Mech ASCE 101(EM4):389–401Google Scholar
  48. Wen YK (1976) Method for random vibration of hysteretic systems. J Eng Mech ASCE 102(EM2):249–263Google Scholar
  49. Williams MS, Villemure I, Sexsmith RG (1997) Evaluation of seismic damage indices for concrete elements loaded in combined shear and flexure. ACI Struct J 94(3):315–322Google Scholar
  50. Yu Y, Tsai K, Weng Y, Lin B, Lin J (2010) Analytical studies of a full-scale steel building shaken to collapse. Eng Struct 32(10):3418–3430CrossRefGoogle Scholar
  51. Yu Y, Tsai K, Li C, Weng Y, Tsai C (2013) Earthquake response analyses of a full-scale five-story steel frame equipped with two types of dampers. Earthq Eng Struct Dyn 42(9):1301–1320CrossRefGoogle Scholar
  52. Yun S, Hamburger R, Cornell C, Foutch D (2002) Seismic performance evaluation for steel moment frames. J Struct Eng ASCE Spec Issue Steel Moment Frames After Northridge 128(Part II):534–545Google Scholar
  53. Zhang J, Huo Y (2009) Evaluating effectiveness and optimum design of isolation devices for highway bridges using the fragility function method. Eng Struct 31(8):1648–1660CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of Structural EngineeringTongji UniversityShanghaiChina

Personalised recommendations