Skip to main content

Advertisement

SpringerLink
Log in

Performance-based multi-objective collaborative optimization of steel frames with fuse-oriented buckling-restrained braces

  • Industrial Application
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A multi-objective collaborative optimal design procedure for steel frames equipped with buckling-restrained braces (BRBs) is proposed under the framework of performance-based seismic design (PBSD) in order to minimize the damage of the primary structure as well as the material cost. For this purpose, a so-called BRB energy dissipation ratio is defined and introduced in the optimization to characterize the involvement of fuse-type BRBs in hysteretic energy dissipation in building stories. Three groups of constraints obtained from the rules on geometrical and conceptual design, the requirements regarding strength and stability, and the PBSD-based story drift limits are considered. To address the discrete-continuous hybrid design variables, a hybrid coding scheme is proposed to modify the non-dominated sorting genetic algorithm II (NSGA-II). The rationality of the proposed procedure is demonstrated by a case study on a seven-story planar steel frame with BRBs. The demonstration indicates that the proposed optimization procedure can make BRBs play the role of a structural fuse successfully in steel frames. The BRB energy dissipation ratios of case C are distributed nearly uniformly along the structural height. The weak-beam-strong-column design principle can be satisfactorily achieved through the maximization of the story BRB energy dissipation ratios. Additionally, the modified hybrid coding NSGA-II algorithm is computationally efficient and stable.

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

Similar content being viewed by others

References

  • Akiyama H (1985) Earthquake-resistant limit-state design for buildings. University of Tokyo Press, Tokyo

    Google Scholar 

  • American Institute of Steel Construction (2016) Seismic provisions for structural steel buildings. ANSI/AISC 341-16, Chicago

  • Atamturktur S, Liu Z, Cogan S, Juang H (2015) Calibration of imprecise and inaccurate numerical models considering fidelity and robustness: a multi-objective optimization-based approach. Struct Multidisc Optim 51(3):659–671

    Google Scholar 

  • Bojórquez E, Reyes-Salazar A, Terán-Gilmore A, Ruiz SE (2010) Energy-based damage index for steel structures. Steel Compos Struct 10(4):331–348

    Google Scholar 

  • Bojórquez E, Terán-Gilmore A, Ruiz SE, Reyes-Salazar A (2011) Evaluation of structural reliability of steel frames: interstory drift versus plastic hysteretic energy. Earthquake Spectra 27(3):661–682

    Google Scholar 

  • Cardoso MF, Salcedo RL, de Azevedo SF, Barbosa D (1997) A simulated annealing approach to the solution of MINLP problems. Comput Chem Eng 21(12):1349–1364

    Google Scholar 

  • Castaldo P, De Iuliis M (2014) Optimal integrated seismic design of structural and viscoelastic bracing-damper systems. Earthq Eng Struct Dyn 43(12):1809–1827

    Google Scholar 

  • Cheung BKS, Langevin A, Delmaire H (1997) Coupling genetic algorithm with a grid search method to solve mixed integer nonlinear programming problems. Comput Math Appl 34(12):13–23

    MathSciNet  MATH  Google Scholar 

  • Choi H, Kim J (2006) Energy-based seismic design of buckling-restrained braced frames using hysteretic energy spectrum. Eng Struct 28(2):304–311

    Google Scholar 

  • Curadelli O, Amani M (2014) Integrated structure-passive control design of linear structures under seismic excitations. Eng Struct 81:256–264

    Google Scholar 

  • Deb K, Sundar J (2006) Reference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of the 8th annual Conference on Genetic and Evolutionary Computation, pp. 635–642

  • Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Google Scholar 

  • Deep K, Thakur M (2007a) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188(1):895–911

    MathSciNet  MATH  Google Scholar 

  • Deep K, Thakur M (2007b) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193(1):211–230

    MathSciNet  MATH  Google Scholar 

  • Deep K, Singh KP, Kansal ML, Mohan C (2009) A real coded genetic algorithm for solving integer and hybrid integer optimization problems. Appl Math Comput 212(2):505–518

    MathSciNet  MATH  Google Scholar 

  • Fajfar P (1999) Capacity spectrum method based on inelastic demand spectrum. Earthq Eng Struct Dyn 28(8):979–993

    Google Scholar 

  • Federal Emergence Management Agency (1997) NEHRP guidelines for the seismic rehabilitation of buildings. FEMA 273, Washington, DC

  • Federal Emergence Management Agency (2000) Prestandard and commentary for the seismic rehabilitation of buildings. FEMA 356, Washington, DC

    Google Scholar 

  • Fragiadakis M, Lagaros ND, Papadrakakis M (2006) Performance-based multiobjective optimum design of steel structures considering life-cycle cost. Struct Multidisc Optim 32.1:1

    Google Scholar 

  • Ganzerli S, Pantelides CP, Reaveley LD (2000) Performance-based design using structural optimization. Earthq Eng Struct Dyn 29(11):1677–1690

    Google Scholar 

  • Geoffrion AM (1972) Generalized benders decomposition. J Optim Theory Appl 10(4):237–260

    MathSciNet  MATH  Google Scholar 

  • Gilbert MG, Schmidt DK (1991) Integrated structure/control law design by multilevel optimization. J Guid Control Dyn 14(5):1001–1007

    MATH  Google Scholar 

  • Gupta OK, Ravindran A (1985) Branch and bound experiments in convex nonlinear integer programming. Manag Sci 31(12):1533–1546

    MathSciNet  MATH  Google Scholar 

  • Habibi A, Chan RW, Albermani F (2013) Energy-based design method for seismic retrofitting with passive energy dissipation systems. Eng Struct 46:77–86

    Google Scholar 

  • Haftka RT (1990) Integrated structure-control optimization of space structures. In: Proceedings of the AIAA Dynamics Specialists Conference, pp. 1–9

  • Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12(4):265–319

    MATH  Google Scholar 

  • Housner GW (1956) Limit design of structures to resist earthquakes. In: Proceedings of the First World Conference on Earthquake Engineering: 5:1–512

  • Khampanit A, Leelataviwat S, Kochanin J, Warnitchai P (2014) Energy-based seismic strengthening design of non-ductile reinforced concrete frames using buckling-restrained braces. Eng Struct 81:110–122

    Google Scholar 

  • Kim J, Seo Y (2004) Seismic design of low-rise steel frames with buckling-restrained braces. Eng Struct 26(5):543–551

    Google Scholar 

  • Krawinkler H (1995) New trends in seismic design methodology. Proceedings of the 10th European Conference on Earthquake Engineering: 821–830

  • Kunnath SK, Reinhorn AM, Lobo RF (1992) IDARC version 3.0: a program for the inelastic damage analysis of reinforced concrete structures. Technical report NCEER-92-0022. National Center for Earthquake Engineering Research, Buffalo

    Google Scholar 

  • Liu Z, Atamturktur S, Juang CH (2013) Performance based robust design optimization of steel moment resisting frames. J Constr Steel Res 89:165–174

    Google Scholar 

  • Liu Z, Atamturktur S, Juang CH (2014) Reliability based multi-objective robust design optimization of steel moment resisting frame considering spatial variability of connection parameters. Eng Struct 76(1):393–403

    Google Scholar 

  • Mauldin M (1984) Maintaining genetic diversity in genetic search. In: Proceedings of the National Conference on Artificial Intelligence: 247–250

  • Ministry of Housing and Urban-Rural Development of the People’s Republic of China (2010) Code for seismic design of buildings (GB50011–2010). China Architecture & Building Press, Beijing

    Google Scholar 

  • Ministry of Housing and Urban-Rural Development of the People’s Republic of China (2017) Standard for design of steel structures (GB 50017-2017). China Architecture & Building Press, Beijing

    Google Scholar 

  • OpenSees version 2.5.0 (2016) Computer software. Pacific Earthquake Engineering Research Center, Berkeley, CA http://opensees.berkeley.edu/

    Google Scholar 

  • Sahoo DR, Chao SH (2010) Performance-based plastic design method for buckling-restrained braced frames. Eng Struct 32(9):2950–2958

    Google Scholar 

  • Schluter M, Egea JA, Banga JR (2009) Extended ant colony optimization for non-convex mixed integer nonlinear programming. Comput Oper Res 36(7):2217–2229

    MathSciNet  MATH  Google Scholar 

  • Soong TT, Cimellaro GP (2009) Future directions in structural control. Struct Control Health Monit 16(1):7–16

    Google Scholar 

  • Surahman A (2007) Earthquake-resistant structural design through energy demand and capacity. Earthq Eng Struct Dyn 36(14):2099–2117

    Google Scholar 

  • Teran-Gilmore A, Virto-Cambray N (2009) Preliminary design of low-rise buildings stiffened with buckling-restrained braces by a displacement-based approach. Earthquake Spectra 25(1):185–211

    Google Scholar 

  • Tsai KC, Hsiao PC (2008) Pseudo-dynamic test of a full-scale CFT/BRB frame—Part II: Seismic performance of buckling-restrained braces and connections. Earthq Eng Struct Dyn 37(7):1099–1115

    Google Scholar 

  • Uang CM, Bertero VV (1990) Evaluation of seismic energy in structures. Earthq Eng Struct Dyn 19:77–90

    Google Scholar 

  • Uang CM, Nakashima M (2004) Steel buckling-restrained braced frames. In: Bozorgnia Y, Bertero VV (editors). Earthquake engineering from engineering seismology to performance-based engineering. CRC Press, Boca Raton (FL), [chapter 16]

    Google Scholar 

  • Usami T, Kasai A, Kato M (2003) Behavior of buckling-restrained brace members. Behavior of steel structures in seismic areas, In: Proceedings of the 4th international conference: 211–216

  • Vargas R, Bruneau M (2009) Analytical response and design of buildings with metallic structural fuses. I. J Struct Eng 135(4):386–393

    Google Scholar 

  • Watanabe A, Hitomi Y, Seaki E, Wada A, Fujimoto M (1988) Properties of brace encased in buckling-restraining concrete and steel tube. In: Proceedings of the 9th World Conference on Earthquake Engineering: 719–724

  • Westerlund T, Pettersson F (1995) An extended cutting plane method for solving convex MINLP problems. Comput Chem Eng 19:131–136

    Google Scholar 

  • Wong KK, Yang R (2001) Effectiveness of structural control based on control energy perspectives. Earthq Eng Struct Dyn 30(12):1747–1768

    Google Scholar 

  • Zhou K, Chen X, Shao Z, Wan W, Biegler LT (2014) Heterogeneous parallel method for mixed integer nonlinear programming. Comput Chem Eng 66:290–300

    Google Scholar 

Download references

Funding

This research is financially supported by the National Natural Science Foundation of China (Grant No. 51878123).

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Dalian University of Technology, Dalian, 116024, China

    Xiang Tu & Zheng He

  2. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Zheng He

  3. China Machinery International Engineering Design & Research Institute Co., Ltd, Changsha, 410007, China

    Guohui Huang

Authors
  1. Xiang Tu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guohui Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zheng He.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Responsible Editor: Pingfeng Wang

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tu, X., He, Z. & Huang, G. Performance-based multi-objective collaborative optimization of steel frames with fuse-oriented buckling-restrained braces. Struct Multidisc Optim 61, 365–379 (2020). https://doi.org/10.1007/s00158-019-02366-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-019-02366-9

Keywords

Search

Navigation