Journal of Central South University

, Volume 18, Issue 5, pp 1685–1692 | Cite as

Comparison on construction of strut-and-tie models for reinforced concrete deep beams

  • Yi-ke Qiu (仇一颗)
  • Xia Liu (刘霞)Email author


With consideration of the differences between concrete and steel, three solutions using genetic evolutionary structural optimization algorithm were presented to automatically develop optimal strut-and-tie model for deep beams. In the finite element analysis of the first method, the concrete and steel rebar are modeled by a plane element and a bar element, respectively. In the second method, the concrete and steel are assigned to two different plane elements, whereas in the third method only one kind of plane element is used with no consideration of the differences of the two materials. A simply supported beam under two point loads was presented as an example to verify the validity of the three proposed methods. The results indicate that all the three methods can generate optimal strut-and-tie models and the third algorithm has powerful capability in searching more optimal results with less computational effort. The effectiveness of the proposed algorithm III has also been demonstrated by other two examples.

Key words

reinforced concrete deep beam topology optimization strut-and-tie model genetic evolutionary structural optimization 


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  1. [1]
    DING Da-jun. Deep beam industrial building [J]. Construction Machines of Science, 1995, 25(3): 41–46.Google Scholar
  2. [2]
    ROGOWSKY D, MACGREGOR J. The design of reinforced concrete deep beams [J]. Concrete International, 1986, 8(8): 49–58.Google Scholar
  3. [3]
    COLLINS M, ITCHELL D. A rational approach for shear design— The 1984 canadian code provisions [J]. ACI Structural Journal, 1986, 83(6): 925–933.Google Scholar
  4. [4]
    ANDERHEGGEN E, SCHLAICH M. Computer-aided design of reinforced concrete structures using the truss model approach [C]// Computer Aided Analysis and Design of Concrete Structures. Swansea UK: Pineridge Press, 1990: 539–550.Google Scholar
  5. [5]
    ALSHEGEIR A. Analysis and design of disturbed regions with strut-tie models [D]. West Lafayette: Purdue University, 1992: 11–19.Google Scholar
  6. [6]
    ALI A A, WHITE R N. Automatic generation of truss model for optimal design of reinforced concrete structures [J]. ACI Structural Journal, 2001, 98(4): 431–442.Google Scholar
  7. [7]
    BRUGGI M. Generating strut-and-tie patterns for reinforced concrete structures using topology optimization [J]. Computers and Structures 2009, 87(23/24): 1483–1495.CrossRefGoogle Scholar
  8. [8]
    GUEST J K, MOEN C D. Reinforced concrete design with topology optimization [C]// Proceedings of the 19th Analysis & Computation Specialty Conference. Reston: American Society of Civil Engineers, 2010: 445–454.Google Scholar
  9. [9]
    KWAK H G, NOH S H. Determination of strut-and-tie models using evolutionary structural optimization [J]. Engineering Structures, 2006, 28(10): 1440–1449.CrossRefGoogle Scholar
  10. [10]
    PERERA R, VIQUE J. Strut-and-tie modeling of reinforced concrete beams using genetic algorithms optimization [J]. Construction and Building Materials, 2009, 23(8): 2914–2925.CrossRefGoogle Scholar
  11. [11]
    YUN Y M, KIM B H. Two-dimensional grid strut-tie model approach for structural concrete [J]. Journal of Structural Engineering, 2008, 134(7): 1199–1214.CrossRefGoogle Scholar
  12. [12]
    XIE Y M, STEVEN G P. A simple evolutionary procedure for structural optimization [J]. Computers & Structures, 1993, 49(5): 885–896.CrossRefGoogle Scholar
  13. [13]
    XIE Y M, STEVEN G P. A simple approach to structural frequency optimization [J]. Computers & Structures, 1994, 53(6): 1487–1491.CrossRefGoogle Scholar
  14. [14]
    XIE Y M, STEVEN G P. Evolutionary structural optimization for dynamic problems [J]. Computers & Structures, 1996, 58(6): 1067–1073.CrossRefGoogle Scholar
  15. [15]
    CHU D N. Evolutionary structural optimization method for systems with stiffness and displacement constraints [D]. Melbourne, Australia: Victoria University of Technology, 1997: 25–35.Google Scholar
  16. [16]
    MANICKARAJAH D, XIE Y M, STEVEN G P. An evolutionary method for optimization of plate bucking resistance [J]. Finite Elements in Analysis and Design, 1998, 29(3/4): 205–230.CrossRefGoogle Scholar
  17. [17]
    LIANG Q Q, XIE Y M, STEVEN G P. Generating optimal strut-and-tie models in pre-stressed concrete beams by performance-based optimization [J]. ACI Structural Journal, 2001, 98(2): 226–232.Google Scholar
  18. [18]
    LIANG Q Q, XIE Y M, STEVEN G P. Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure [J]. ACI Structural Journal, 2000, 97(2): 322–332.Google Scholar
  19. [19]
    LIANG Q Q. Performance-based optimization of structures [M]. London and New York: Spon Press, 2005: 134–254.CrossRefGoogle Scholar
  20. [20]
    LIU Xia, YI Wei-jian, SHEN Pu-sheng. Genetic evolutionary structural optimization [J]. Journal of Constructional Steel Research, 2008, 64(3): 305–311.CrossRefGoogle Scholar
  21. [21]
    GB 50010—2002. Ministry of Housing and Urban-Rural Development of China. Code for design of concrete structure [S]. (in Chinese)Google Scholar

Copyright information

© Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Civil EngineeringHunan UniversityChangshaChina

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