On the seismic collapse capacity of optimally designed steel braced frames


The main purpose of this study is to respond to an important question in the field of structural engineering: is the seismic collapse capacity of optimally designed concentrically steel braced frames acceptable or not? The present work includes two phases: performance-based design optimization and seismic collapse safety assessment. In the first phase, three nature-inspired metaheuristic algorithms, namely improved fireworks algorithm, center of mass optimization, and enhanced colliding-bodies optimization are employed to carry out the optimization task. In the second phase, seismic collapse capacity of the optimally designed concentrically steel braced frames is evaluated by performing incremental dynamic analysis and generating fragility curves. Two design examples of 5- and 10-story concentrically steel braced frames with two different topologies of braces are presented. The numerical results indicate that the center of mass optimization algorithm outperforms the other algorithms. However, all of the optimal designs found by all algorithms are of acceptable seismic collapse safety.

This is a preview of subscription content, log in to check access.

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


  1. 1.

    ASCE-41-13 (2014) Seismic evaluation and retrofit of existing buildings. American Society of Civil Engineers, Reston

    Google Scholar 

  2. 2.

    Fragiadakis M, Vamvatsikos D, Karlaftis MG, Lagaros ND, Papadrakakis M (2015) Seismic assessment of structures and lifelines. J Sound Vib 334:29–56

    Article  Google Scholar 

  3. 3.

    Gholizadeh S, Fattahi F (2019) Multi-objective design optimization of steel moment frames considering seismic collapse safety. Eng Comput (In press). https://doi.org/10.1007/s00366-019-00886-y

    Article  Google Scholar 

  4. 4.

    Hassanzadeh A, Gholizadeh S (2019) Collapse-performance-aided design optimization of steel concentrically braced frames. Eng Struct 197:109411

    Article  Google Scholar 

  5. 5.

    Degertekin SO, Tutar H, Lamberti L (2020) School-based optimization for performance-based optimum seismic design of steel frames. Eng Comput (In press). https://doi.org/10.1007/s00366-020-00993-1

    Article  Google Scholar 

  6. 6.

    Bertero VV (1977) Strength and deformation capacities of buildings under extreme environments. Struct Eng Struct Mech 53:29–79

    Google Scholar 

  7. 7.

    Bazzurro P, Cornell CA (1994) Seismic hazard analysis of nonlinear structures. I: methodology. J Struct Eng 120:3320–3344

    Article  Google Scholar 

  8. 8.

    Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Struct Dyn 31(3):491–514. https://doi.org/10.1002/eqe.141

    Article  Google Scholar 

  9. 9.

    Vamvatsikos D, Cornell CA (2004) Applied incremental dynamic analysis. Earthq Spectra 20:523–553

    Article  Google Scholar 

  10. 10.

    Brunesi E, Nascimbene R, Parisi F, Augenti N (2015) Progressive collapse fragility of reinforced concrete framed structures through incremental dynamic analysis. Eng Struct 104:65–79

    Article  Google Scholar 

  11. 11.

    Wijesundara KK, Bolognini D, Nascimbene R, Calvi GM (2009) Review of design parameters of concentrically braced frames with rhs shape braces. J Earthq Eng 13:109–131

    Article  Google Scholar 

  12. 12.

    Wijesundara KK, Nascimbene R, Rassati GA (2018) Evaluation of the seismic performance of suspended zipper column concentrically braced steel frames. J Constr Steel Res 150:452–461

    Article  Google Scholar 

  13. 13.

    Gholizadeh S, Milany A (2018) An improved fireworks algorithm for discrete sizing optimization of steel skeletal structures. Eng Optim 50:1829–1849

    MathSciNet  Article  Google Scholar 

  14. 14.

    Gholizadeh S, Ebadijalal M (2018) Performance based discrete topology optimization of steel braced frames by a new metaheuristic. Adv Eng Softw 123:77–92

    Article  Google Scholar 

  15. 15.

    Kaveh A, Ilchi Ghazaan M (2014) Enhanced colliding bodies optimization for design problems with continuous and discrete variables. Adv Eng Softw 77:66–75

    Article  Google Scholar 

  16. 16.

    FEMA P-695 (2009) Quantification of building seismic performance factors. Federal Emergency Management Agency, Washington (DC)

    Google Scholar 

  17. 17.

    OpenSees (2012) Version 2.4.0. PEER, Berkeley

  18. 18.

    MATLAB (2016) The Language of Technical Computing. The MathWorks Inc.

  19. 19.

    AISC-LRFD (2001) Manual of steel construction: load & resistance factor design, 2nd edn. American Institute of Steel Construction, Chicago

    Google Scholar 

  20. 20.

    Vanderplaats G (1984) Numerical optimization techniques for engineering design: with application. McGraw-Hill, New York

    Google Scholar 

  21. 21.

    Tan Y, Zhu Y (2010) Fireworks Algorithm for Optimization. Springer, Berlin

    Google Scholar 

  22. 22.

    Tan Y (2015) Fireworks Algorithm, A Novel Swarm Intelligence Optimization Method. Peking University, Beijing

    Google Scholar 

  23. 23.

    FEMA-274 (1997) NEHRP commentary on the guidelines for the seismic rehabilitation of buildings. Federal Emergency Management Agency, Washington, DC

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Saeed Gholizadeh.

Additional information

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

Verify currency and authenticity via CrossMark

Cite this article

Gholizadeh, S., Hassanzadeh, A., Milany, A. et al. On the seismic collapse capacity of optimally designed steel braced frames. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-01096-7

Download citation


  • Performance-based design
  • Optimization
  • Incremental dynamic analysis
  • Seismic safety
  • Fragility assessment
  • Concentrically braced frame