Optimization and Engineering

, Volume 11, Issue 3, pp 471–496 | Cite as

Fuzzy genetic optimization on performance-based seismic design of reinforced concrete bridge piers with single-column type

  • Yu-Chi Sung
  • Chin-Kuo Su


This paper presents a fuzzy genetic optimization for performance-based seismic design (PBSD) of reinforced concrete (RC) bridge piers with single-column type. The design is modeled as a constrained optimization problem with the objective of minimizing construction cost subject to the constraints of qualified structural capacity and suitable reinforcement arrangements for the designed RC pier. A violation of the constraints is combined with construction cost to serve as the objective function. The fuzzy logic control (FLC), which adapts the penalty coefficients in the genetic algorithm (GA) optimization solver, was employed to avoid a penalty that is too strong or too weak through the entire calculation so that a feasible solution can be obtained efficiently.

The reported results of cyclic loading tests for three piers with square section, rectangular section and circular section, respectively, were employed as the data-base of investigation. Furthermore, a case study on the PBSD of a square RC bridge pier with four required performance objectives (fully operational, operational, life safety and near collapse) corresponding to different peak ground accelerations (PGAs) of earthquakes was analyzed. Six feasible designs of the pier were determined successfully and the optimal one with minimum construction cost was obtained accordingly. The result obtained shows that the proposed algorithm gives an acceptable design for the PBSD of the RC bridge piers.

The superiorities of GA and FLC were incorporated and the availability of the proposed procedure was investigated. Moreover, through the proposed systematic design procedure, the discrepancy in the PBSD from different design engineers will be lessened effectively and the design efficiency as well as the design precision will also be enhanced significantly.


Minimum construction cost Penalty coefficient Pushover analysis Structural performance 


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  1. ACI Committee 318x (2005) Building code requirements for reinforced concrete and commentary (ACI 318-05), American Concrete Institute, Farmington Hill, USA Google Scholar
  2. ATC-40 (1996) Seismic Evaluation and Retrofit of Concrete Building, Applied Technology Council, Redwood City, California Google Scholar
  3. Bazaraa MS, Shetty CM (1979) Nonlinear programming: theory and algorithms. Wiley, New York MATHGoogle Scholar
  4. Chang KC (1999) Seismic investigation of bridge damage in Chi–Chi Earthquake. Report no NCREE-90-055, National Center for Research on Earthquake Engineering, Taipei, Taiwan Google Scholar
  5. Chang KC, Chang HF (1999) Seismic retrofit study of rectangular bridge column with CFRP jackets. Report no NCREE-00-030, National Center for Research on Earthquake Engineering, Taipei, Taiwan Google Scholar
  6. Chung LL (2000) Seismic retrofit study of RC bridge columns. Report no NCREE-00-035, National Center for Research on Earthquake Engineering Taipei, Taiwan Google Scholar
  7. Harp DR, Taha MR, Ross TJ (2009) Genetic-fuzzy approach for modeling complex systems with an example application in masonry bond strength prediction. J Comput Civil Eng 23:193–199 CrossRefGoogle Scholar
  8. Haupt RL, Haupt SE (2004) Practical genetic algorithms, 2nd edn. Wiley, New Jersey MATHGoogle Scholar
  9. Kelesoglu O (2007) Fuzzy multiobjective optimization of truss-structures using genetic algorithm. Adv Eng Softw 38:717–721 CrossRefGoogle Scholar
  10. Nagaya K, Kawashima K (2001) Effect of aspect ratio and longitudinal reinforcement diameter on seismic performance of reinforced concrete bridge columns. Report no TIT/EERG 01, Institute of Technology, Tokyo, Japan Google Scholar
  11. Nanakorn P, Messomklin K (2001) An adaptive penalty function in genetic algorithms for structural design optimization. J Comput Struct 79:2527–2539 CrossRefGoogle Scholar
  12. Pourzeynali S, Lavasani HH, Modarayi AH (2007) Active control of high rise building structures using fuzzy logic and genetic algorithms. Eng Struct 29:346–357 CrossRefGoogle Scholar
  13. Sarma KC, Adeli H (2000) Fuzzy genetic algorithm for optimization of steel structures. J Struct Eng ASCE 126(5):596–604 CrossRefGoogle Scholar
  14. SEAOC (1995) Performance-Based Seismic Engineering of Buildings, Structural Association of California, Sacramento, CA, USA Google Scholar
  15. Soh CK, Yang J (1996) Fuzzy controlled genetic algorithm search for shape optimization. J Comput Civil Eng ASCE 10(2):143–150 CrossRefGoogle Scholar
  16. Sung YC, Liu KY, Su CK, Tsai IC, Chang KC (2005) A study on pushover analyses of reinforced concrete columns. J Struct Eng Mech 21(1):35–52 Google Scholar
  17. Sung YC, Lin TW, Tsai IC, Chang SY, Lai MC (2007) Application of normalized spectral acceleration-displacement (NSAD) format on performance-based seismic design of bridge structures. J Mech 23(2):86–93 Google Scholar
  18. Xue Q, Wu CW (2006) Preliminary detailing for displacement-based seismic design of buildings. J Eng Struct 28(3):431–440 CrossRefMathSciNetGoogle Scholar
  19. Zadeh LA (1965) Fuzzy sets. J Inf Control 8:338–353 MATHCrossRefMathSciNetGoogle Scholar
  20. Zou XK, Chan CM (2005) Optimal seismic performance-based design of reinforced concrete buildings using nonlinear pushover analysis. J Eng Struct 27:1289–1302 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Taipei University of TechnologyTaipeiTaiwan

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