Structural optimization

, Volume 8, Issue 2–3, pp 174–180 | Cite as

Weight optimization for flexural reinforced concrete beams with static nonlinear response

  • T. T. Chung
  • T. C. Sun
Technical Papers


The weight optimization of reinforced concrete (RC) beams with material nonlinear response is formulated as a general nonlinear optimization problem. Incremental finite element procedures are used to integrate the structural response analysis and design sensitivity analysis in a consistent manner. In the finite element discretization, the concrete is modelled by plane stress elements and steel reinforcement is modelled by discrete truss elements. The cross-sectional areas of the steel and the thickness of the concrete are chosen as design variables, and design constraints can include the displacement, stress and sizing constraints. The objective function is the weight of the RC beams. The optimal design is performed by using the sequential linear programming algorithm for the changing process of design variables, and the gradient projection method for the calculations of the search direction. Three example problems are considered. The first two are demonstrated to show the stability and accuracy of the approaches by comparing previous results for truss and plane stress elements, separately. The last one is an example of an RC beam. Comparative cost objective functions are presented to prove the validity of the approach.


Design Variable Reinforced Concrete Concrete Beam Reinforced Concrete Beam Gradient Projection Method 
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  1. Arora, J.S.; Cardoso, J.B. 1989: A design sensitivity analysis principle and its implementation into ADINA.Comput. & Struct. 32 691–705Google Scholar
  2. Arora, J.S.; Haug, E.J. 1979: Methods of design sensitivity analysis in structural optimization.AIAA J. 17, 970–974Google Scholar
  3. ASCE Report 1986:Finite element analysis of reinforced concrete structures. New York: ASCEGoogle Scholar
  4. Bathe, K.J. 1975a: ADINA - a finite element program for automatic dynamic incremental nonlinear analysis.Acoustics and Vibration Laboratory Report 82448-1, Dept. of Mech. Engng., MITGoogle Scholar
  5. Bathe, K.J. 1975b: Static and dynamic geometric and material nonlinear analysis using ADINA.Acoustics and Vibration Laboratory Report 82448-2, Dept. of Mech. Engng., MITGoogle Scholar
  6. Bathe, K.J. 1982:Finite element procedures in engineering analysis. New York: Prentice HallGoogle Scholar
  7. Bathe, K.J.; Cimento, A.P. 1980: Some practical procedures for the solution of nonlinear finite element equations.Comp. Meth. Appl. Mech. Engng. 22, 59–85Google Scholar
  8. Bathe, K.J.; Ramaswamy, S. 1979: On three-dimensional nonlinear analysis of concrete structures.Nucl. Eng. Des. 52, 385–409Google Scholar
  9. Bosco, C.; Carpinteri, A.; Debernardi, P.G. 1990: Minimum reinforcement in high-strength concrete.ASCE J. Struct. Engng. 116, 427–437Google Scholar
  10. Ezeldin, A.S. 1991: Optimum design of reinforced fiber concrete subjected to bending and geometrical constraints.Comp. Struct. 41, 1095–1100Google Scholar
  11. Grierson, D.E.; Moharrami, H. 1993: Design optimization of reinforced concrete building frameworks. In: Rozvany, G.I.N. (ed.)Optimization of large structural systems, pp. 833–842 (Proc. NATO/DFG ASI, held in Berchtesgaden, Germany 1991). Dordrecht: KluwerGoogle Scholar
  12. Haftka, R.T.; Mróz, Z. 1986: First- and second-order sensitivity analysis of linear and nonlinear structures.AIAA J. 24, 1187–1192Google Scholar
  13. Harrian, M.; Arora, J.S. 1986: Optimization of nonlinear structural response with the computer program ADINA.Technical Report No. ODL86.7 Google Scholar
  14. Harrian, M.; Cardoso, J.B.; Arora, J.S. 1987: Use of ADINA for design optimization of nonlinear structures.Comp. & Struct. 26, 123–133Google Scholar
  15. Kirsch, U. 1981:Optimum structural design. New York: McGraw-HillGoogle Scholar
  16. Kumar, V.; Lee, S.J.; German, M.D. 1989: Finite element design sensitivity analysis and its integration with numerical optimization techniques for structure design.Comp. & Struct. 32, 883–897Google Scholar
  17. Kupfer, H.; Hilsdorf, H.K.; Rusch, H. 1969: Behavior of concrete under biaxial stresses.ACI 66, 656–666Google Scholar
  18. Liu, T.C.Y.; Nilson, A.H.; Slate, F.O. 1972: Biaxial stress-strain relations for concrete.J. Struct. Div. 98, 1025–1034Google Scholar
  19. Matthies, H.; Strang, G. 1979: The solution of nonlinear finite element equations.Int. J. Numer. Meth. Engng. 14, 1613–1626Google Scholar
  20. Ryu, Y.S.; Harrian, M.; Wu, C.C.; Arora, J.S. 1985: Structure design sensitivity analysis of nonlinear response.Comp. & Struct. 21, 245–255Google Scholar
  21. Schmit, L.A.; Farshi, B. 1974: Some approximation concepts for structural synthesis.AIAA J. 12, 692–699Google Scholar
  22. Spires, D.; Arora, J.S. 1990: Optimal design of tall RC-framed tube buildings.ASCE J. Struct. Engng. 116, 877–897Google Scholar
  23. Wu, C.C.; Arora, J.S. 1987: Design sensitivity analysis of nonlinear response using incremental procedure.AIAA J. 25, 1118–1125Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • T. T. Chung
    • 1
  • T. C. Sun
    • 1
  1. 1.Department of Mechanical EngineeringNational Taiwan UniversityTaipeiRepublic of China

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