Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 1005–1019 | Cite as

Optimum energy-based design of BRB frames using nonlinear response history analysis

  • F. Rezazadeh
  • R. Mirghaderi
  • A. Hosseini
  • S. Talatahari


In this paper, an optimum design method for buckling restrained brace frames subjected to seismic loading is presented. The multi-objective charged system search is developed to optimize costs and damages caused by the earthquake for steel frames. Minimum structural weight and minimum seismic energy which including seismic input energy divided by maximum hysteretic energy of fuse members are selected as two objective functions to find a Pareto solutions that copes with considered preferences. Also, main design constraints containing allowable amount of the inter-story drift and plastic rotation of beam, column members and plastic displacement of buckling restrained braces are controlled. The results of optimum design for three different frames are obtained and investigated by the developed method.


Energy based design Buckling restrained brace frame Non-linear response history analysis Optimization Charged system search 


  1. AISC (2010). Specification for structural steel buildings (ANSI/AISC 360-10). Chicago, IL: American Institute of Steel ConstructionGoogle Scholar
  2. Alemdar BN, White DW (2005) Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis. J Struct Eng 131(12):1811–1819CrossRefGoogle Scholar
  3. Chen WF, Toma S (1994) Advanced analysis of steel frames, theory, software, and applications. CRC Press, Boca Raton. isbn:0-8493-8281-5Google Scholar
  4. Chen WF, Goto Y, Liew JYR (1996) Stability Design of Semi-Rigid Frames. Wiley, New York. isbn:0-471-07670-8Google Scholar
  5. Chiorean CG (2009) A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks. Eng Struct 31(12):3016–3033CrossRefGoogle Scholar
  6. Climaco J (1997) Multicriteria analysis. Springer-Verlag, New YorkCrossRefzbMATHGoogle Scholar
  7. Coello CA, Lechuga MS (2002) MOPSO: A proposal for multiple objective particle swarm optimization. Proc Cong Evol Comput 1:1051–1056Google Scholar
  8. Crisfield MA (1991) Non-linear finite element analysis of solids and structures. Wiley, ChichesterzbMATHGoogle Scholar
  9. Daloglu AT, Artar M, Özgan K, Karakas A (2016) Optimum design of steel space frames including soil-structure interaction. Struct Multidiscip Optim 54(1):117–131MathSciNetCrossRefGoogle Scholar
  10. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi objective genetic algorithm:NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  11. Degertekin SO (2008) Optimum design of steel frames using harmony search algorithm. Struct Multidiscip Optim 36(4):393–401CrossRefGoogle Scholar
  12. Degertekin SO, Hayalioglu MS (2010) Harmony search algorithm for minimum cost design of steel frames with semi-rigid connections and column bases. Struct Multidiscip Optim 42(5):755–768CrossRefGoogle Scholar
  13. Fishburn PC (1970) Utility theory for decision making. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  14. Foley CM (2001) Advanced analysis of steel frames using parallel processing and vectorization. Comput Aided Civ Infrastruct Eng 16:305–325CrossRefGoogle Scholar
  15. Foley CM, Vinnakota S (1997) Inelastic analysis of partially restrained un-braced steel frames. Eng Struct 19:891–902CrossRefGoogle Scholar
  16. Foley CM, Vinnakota S (1999a) Inelastic behavior of multistory partially restrained steel frames. Part I J Struct Eng 125:854–861CrossRefGoogle Scholar
  17. Foley CM, Vinnakota S (1999b) Inelastic behavior of multistory partially restrained steel frames. Part II J Struct Eng 125:862–869CrossRefGoogle Scholar
  18. Halliday D, Resnick R, Walker J (2008) Fundamentals of physics, 8th edn. WileyGoogle Scholar
  19. Hjelmstad KD, Taciroglu E (2005) Variational basis of nonlinear flexibility methods for structural analysis of frames. J Eng Mech 131(11):157–1169CrossRefGoogle Scholar
  20. Kaveh A, BolandGerami A (2017) Optimal design of large-scale space steel frames using cascade enhanced colliding body optimization. Struct Multidiscip Optim 55(1):237–256CrossRefGoogle Scholar
  21. Kaveh A, Talatahari S (2009a) Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. Comput Struct 87(5–6):267–283CrossRefGoogle Scholar
  22. Kaveh A, Talatahari S (2009b) A particle swarm ant colony optimization algorithm for truss structures with discrete variables. J Constr Steel Res 65(8–9):1558–1568CrossRefGoogle Scholar
  23. Kaveh A, Talatahari S (2010a) A novel heuristic optimization method: charged system search. Acta Mech 213(3–4):267–289CrossRefzbMATHGoogle Scholar
  24. Kaveh A, Talatahari S (2010b) Optimal design of skeletal structures via the charged system search algorithm. Struct Multidiscip Optim 37(6):893–911CrossRefGoogle Scholar
  25. Kaveh A, Talatahari S (2010c) A charged system search with a fly to boundary method for discrete optimum design of truss structures. Asian J Civ Eng 11(3):277–293Google Scholar
  26. Kaveh A, Talatahari S (2012) Charged system search for optimal design of frame structures. Appl Soft Comput 12(1):82–93CrossRefGoogle Scholar
  27. Kaveh A, Ghafari MH, Gholipour Y (2017) Optimal seismic design of 3D steel moment frames: different ductility types. Struct Multidiscip Optim:1–16Google Scholar
  28. Neuenhofer A, Filippou FC (1997) Evaluation of nonlinear frame finite-element models. J Struct Eng 123(7):958–966CrossRefGoogle Scholar
  29. Nguyen PC, Kim SE (2014) Distributed plasticity approach for time-history analysis of steel frames including nonlinear connections. J Constr Steel Res 100:36–49CrossRefGoogle Scholar
  30. Nguyen PC, Doan NTN, Ngo-Huu C, Kim SE (2014) Nonlinear inelastic response history analysis of steel frame structures using plastic-zone method. Thin-Walled Struct 85:20–233CrossRefGoogle Scholar
  31. Parreiras RO, Maciel JHRD, Vasconcelos JA (2005) Decision making in multi-objective optimization problems. New York: Nova Science. ISE Book Series on Real Word Multi-Objective System Engineering, pp 1–20Google Scholar
  32. Scott M, Fenves G (2006) Plastic hinge integration methods for force-based beam-column elements. J Struct Eng 132(2):244–252CrossRefGoogle Scholar
  33. Scott M, Franchin P, Fenves G, Filippou F (2004) Response sensitivity for nonlinear beam–column elements. J Struct Eng 130(9):1281–1288CrossRefGoogle Scholar
  34. Scott M, Fenves G, McKenna F, Filippou F (2008) Software patterns for nonlinear beam-column models. J Struct Eng 134(4):562–571CrossRefGoogle Scholar
  35. Spacone E, Ciampi V, Filippou FC (1996) Mixed formulation of nonlinear beam finite element. Comput Struct 58(1):71–83CrossRefzbMATHGoogle Scholar
  36. Teh LH, Clarke MJ (1999) Plastic-zone analysis of 3D steel frames using beam elements. J Struct Eng 125:1328–1337CrossRefGoogle Scholar
  37. Thai HT, Kim SE (2011a) Second-order inelastic dynamic analysis of steel frames using fiber hinge method. J Constr Steel Res 67(10):1485–1494CrossRefGoogle Scholar
  38. Thai HT, Kim SE (2011b) Nonlinear inelastic analysis of space frames. J Constr Steel Res 67(4):585–592CrossRefGoogle Scholar
  39. Truong VH, Kim S-E (2017) An efficient method for reliability-based design optimization of nonlinear inelastic steel space frames. Struct Multidiscip Optim 56(2):331–351MathSciNetCrossRefGoogle Scholar
  40. Ziemian RD, McGuire W (2002) Modified tangent modulus approach: a contribution to plastic hinge analysis. J Struct Eng 128(10):1301–1307CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • F. Rezazadeh
    • 1
  • R. Mirghaderi
    • 1
  • A. Hosseini
    • 1
  • S. Talatahari
    • 2
    • 3
  1. 1.Department of Civil Engineering, Faculty of EngineeringUniversity of TehranTehranIran
  2. 2.Department of Civil EngineeringUniversity of TabrizTabrizIran
  3. 3.Engineering FacultyNear East UniversityMersinTurkey

Personalised recommendations