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Optimal design of reinforced concrete beams: A review

  • Rahmanian, Ima (School of Engineering, The University of British Columbia) ;
  • Lucet, Yves (Computer Science, The University of British Columbia) ;
  • Tesfamariam, Solomon (School of Engineering, The University of British Columbia)
  • Received : 2013.05.31
  • Accepted : 2014.02.01
  • Published : 2014.05.30

Abstract

This paper summarizes available literature on the optimization of reinforced concrete (RC) beams. The objective of optimization (e.g. minimum cost or weight), the design variables and the constraints considered by different studies vary widely and therefore, different optimization methods have been employed to provide the optimal design of RC beams, whether as isolated structural components or as part of a structural frame. The review of literature suggests that nonlinear deterministic approaches can be efficiently employed to provide optimal design of RC beams, given the small number of variables. This paper also presents spreadsheet implementation of cost optimization of RC beams in the familiar MS Excel environment to illustrate the efficiency of the exhaustive enumeration method for such small discrete search spaces and to promote its use by engineers and researchers. Furthermore, a sensitivity analysis is performed on the contribution of various design parameters to the variability of the overall cost of RC beams.

Keywords

References

  1. Adamu, A. and Karihaloo, B.L. (1994a), "Minimum cost design of RC beams using DCOC, Part I : beams with freely-varying cross-sections", Struct. Optim., 7(4), 237-251. https://doi.org/10.1007/BF01743718
  2. Adamu, A. and Karihaloo, B.L. (1994b), "Minimum cost design of RC beams using DCOC, Part II : beams with uniform cross-sections", Struct. Optim., 7(4), 252-259. https://doi.org/10.1007/BF01743720
  3. Adamu, A. and Karihaloo, B.L. (1994c), "Minimum cost design of reinforced concrete beams using continuum-type optimality criteria", Struct. Optim., 7(1-2), 91-102. https://doi.org/10.1007/BF01742512
  4. Al-salloum, Y.A. and Siddiqi, G.H. (1995), "Cost-optimum design of reinforced concrete beams", ACI Struct. J., 91(6), 647-655.
  5. American Concrete Institute (2005), "Building code requirements for structural concrete and commentary", ACI 318-05.
  6. Balaguru, P.N. (1980a), "Cost optimum design of doubly reinforced concrete beams", Build. Environ., 15(4), 219-222. https://doi.org/10.1016/0360-1323(80)90002-5
  7. Balaguru, P.N. (1980b), "Optimum design of T-beam sections", Build. Environ., 15(2), 91-94. https://doi.org/10.1016/0360-1323(80)90013-X
  8. British Standards Institution (2007), "Eurocode 2: Design of concrete structures", BS EN 1992.
  9. Burer, S., Letchford, A.N. (2012), "Non-convex mixed-integer nonlinear programming: A survey", Surv. Oper. Res. Manage. Sci., 17(2), 97-106.
  10. Camp, C. V, Pezeshk, S. and Hansson, H. (2003), "Flexural design of reinforced concrete frames using a genetic algorithm", Struct. Eng., 129(1), 105-115. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:1(105)
  11. Canadian Standards Association (2004), "Design of Concrete Structures", CSA A23.3-04.
  12. Ceranic, B. and Fryer, C. (2000), "Sensitivity analysis and optimum design curves for the minimum cost design of singly and doubly reinforced concrete beams", Struct. Multidiscip. Optim., 20(4), 260-268. https://doi.org/10.1007/s001580050156
  13. Chakrabarty, B.K. (1992a), "A model for optimal design of reinforced concrete beam", Struct. Eng., 118(11), 3238-3242. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:11(3238)
  14. Chakrabarty, B.K. (1992b), "Models for optimal design of reinforced concrete beams", Comput. Struct., 42(3), 447-451. https://doi.org/10.1016/0045-7949(92)90040-7
  15. Chen, D.-S., Batson, R.G. and Dang, Y. (2010), Applied Integer Programming: Modeling and Solution, John Wiley and Sons Inc., New York.
  16. Chou, T. (1977), "Optimum reinforced concrete T-beam sections", J. Struct. Div., 103(8), 1605-1617.
  17. Chung, T.T. and Sun, T.C. (1994), "Weight optimization for flexural reinforced concrete beams with static nonlinear response", Struct. Optim., 8(2), 174-180. https://doi.org/10.1007/BF01743315
  18. Coello, C.C. and Hernandez, F.S. (1997), "Optimal design of reinforced concrete beams using genetic algorithms", Expert Syst. Appl., 12(1), 101-108. https://doi.org/10.1016/S0957-4174(96)00084-X
  19. Colin, B.M.Z. and Macrae, A.J. (1984), "Optimization of structural concrete beams", J. Struct. Eng., 110(7), 1573-1588. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:7(1573)
  20. Dole, M.R., Ronghe, G.N. and Gupta, L.M. (2000), "Optimum design of reinforced concrete beams using polynomial optimization technique", Adv. Struct. Eng., 3(1), 67-79. https://doi.org/10.1260/1369433001502021
  21. Ferreira, C.C., Barros, M.H.F.M. and Barros, A.F.M. (2003), "Optimal design of reinforced concrete Tsections in bending", Eng. Struct., 25(7), 951-964. https://doi.org/10.1016/S0141-0296(03)00039-7
  22. Friel, L.L. (1974), "Optimum singly reinforced concrete sections", J. Am. Concrete Inst., 71(11), 556-558.
  23. Garcia, J.S.D., Avila, S.L. and Carpes, W.P. (2006), "Introduction to optimization methods: a brief survey of methods", IEEE Multidisciplinary Engineering Education Magazine, 1(2), 1-5.
  24. Goble, G.G. and Moses, F. (1975), "Practical applications of structural optimization", J. Struct. Div., 101(4), 635-648.
  25. Goldberg, D.E. (1989), Genetic ALorithms in Search, Optimization, and Machine Learning, Addison Wesley Longman, New York, USA.
  26. Gonzalez-Vidosa, F., Yepes, V., Alcala, J., Carrera, M., Perea, C. and Paya-Zaforteza, I. (2008), Optimization of Reinforced Concrete Structures by Simulated Annealing, In Simulated Annealing, I-Tech Education and Publishing, Vienna, pp. 307-320.
  27. Guerra, A. and Kiousis, P.D. (2006), "Design optimization of reinforced concrete structures", Comput. Concrete, 3(5), 313-334. https://doi.org/10.12989/cac.2006.3.5.313
  28. Hare, W., Nutini, J. and Tesfamariam, S. (2013), "A survey of non-gradient optimization methods in structural engineering", Adv. Eng. Software, 59, 19-28. https://doi.org/10.1016/j.advengsoft.2013.03.001
  29. Hock, W. and Schittkowski, K. (1983), "A comparative performance evaluation of 27 nonlinear programming codes", Computing, 30, 335-358. https://doi.org/10.1007/BF02242139
  30. Juenger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G. and Wolsey, L.A. (Eds. 2010), 50 Years of Integer Programming 1958-2008, Springer-Verlag, Berlin Heidelberg, Germany.
  31. Lasdon, L.S. and Waren, A.D. (1978), "Generalized Reduced Gradient Software for Linearly and Nonlinearly Constrained Problems", (In H.J. Greenberg, ed.), Design and Implementation of Optimization Software, Sitjhoff and Noordhoff.
  32. Lee, C. and Ahn, J. (2003), "Flexural design of reinforced concrete frames by genetic algorithm", J. Struct. Eng., 129(6), 762-774. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:6(762)
  33. Leps, M. and Sejnoha, M. (2003), "New approach to optimization of reinforced concrete beams", Comput. Struct., 81(18-19), 1957-1966. https://doi.org/10.1016/S0045-7949(03)00215-3
  34. Linderoth, J.T. and Savelesbergh, M.W.P. (1999), "A computational study of search strategies for mixed integer programming", INFORMS J. Computing, 11(2), 173-187. https://doi.org/10.1287/ijoc.11.2.173
  35. McCluskey, S. and McCarthy, T.J. (2009), "A particle swarm optimisation approach to reinforced concrete beam design according to AS3600", First International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering, Civil-Comp Press, Madeira, Portugal, pp. 1-14.
  36. Medeiros, G.F. and Kripka, M. (2013), "Structural optimization and proposition of pre-sizing parameters for beams in reinforced concrete buildings", Comput. Concrete, 11(3), 253-270. https://doi.org/10.12989/cac.2013.11.3.253
  37. Michell, A.G.M. (1904), "The Limits of Economy of Materials in Frame Structures", Philosophical Magazine Series 6, 8(47), 589-597. https://doi.org/10.1080/14786440409463229
  38. Narayan, K.S.B. and Venkataramana, K. (2007), "Shape optimization of steel reinforced concrete beams", Comput. Concrete, 4(4), 317-330. https://doi.org/10.12989/cac.2007.4.4.317
  39. Nemhauser, G.L. and Wolsey, L.A. (1999), Integer and Combinatorial Optimization, John Wiley and Sons Inc., New York, USA.
  40. Nocedal, J. and Wright, S. (2006), Numerical Optimization, Springer, New York, USA.
  41. Norman, D.G. (1964), "Economic aspects in the design of some reinforced concrete structural members", J. Am. Concrete Inst., 61(4), 419-440.
  42. Olsson, A.E. (2011), Particle Swarm Optimization: Theory, Techniques and Applications, Nova Science Pub. Inc.
  43. Ozturk, H.T., Durmus, Ay. and Durmus, Ah. (2013), "Optimum design of a reinforced concrete beam using artificial bee colony algorithm", Comput. Concrete, 10(3), 295-306. https://doi.org/10.12989/cac.2012.10.3.295
  44. Powell, M.J.D. (1964), "An efficient method of minimizing a function of several variables without calculating derivatives", Comput. J., 7(2), 155-162. https://doi.org/10.1093/comjnl/7.2.155
  45. Prakash, A., Agarwala, S.K. and Singh, K.K. (1988), "Optimum design of reinforced sections", Comput. Struct., 30(4), 1009-1011. https://doi.org/10.1016/0045-7949(88)90142-3
  46. Rajeev, S. and Krishnamoorthy, C.S. (1998), "Genetic algorithm-based methodology for design optimization of reinforced concrete frames", Comput. Aided Civil Infrastruct. Eng., 13(1), 63-74. https://doi.org/10.1111/0885-9507.00086
  47. Revelle, C.S., Whitlatch, E.E. and Wright, J.R. (2004), Civil and Environmental Systems Engineering, (2nd ed., W.J. Hall, ed.), Pearson Education Inc., New Jersey, USA.
  48. Robinson, S.M. (1972), "A quadratically-convergent algorithm for general nonlinear programming problems", Math. Program., 3(1), 145-156.
  49. Salamon, P., Sibani, P. and Frost, R. (2002), Facts, Conjectures, and Improvements for Simulated Annealing, Society for Industrial and Applied Mathematics (SIAM).
  50. Sandhu, B.S. (1971), "Economical design of reinforced concrete slabs and walls", Civil Eng. ASCE, 41(7), 68-69.
  51. Sivanandam, S.N. and Deepa, S.N. (2008), Introduction to Genetic Algorithms, Springer, Berlin Heidelberg, Germany.
  52. Structural Engineering Institute Technical Committee on Optimal Structural Design (2002), Recent Advances in Optimal Structural Design, (S.A. Burns, ed.), American Society of Civil Engineers.
  53. Veaux, R.D.De, Velleman, P.F., Bock, D.E., Vukov, A.M. and Wong, A.C.M. (2012), Stats: Data and Models, Pearson Canada Inc., Toronto, Ontario, Canada.

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