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Computational Science, Engineering & Technology Series
ISSN 1759-3158
CSETS: 29
SOFT COMPUTING METHODS FOR CIVIL AND STRUCTURAL ENGINEERING
Edited by: Y. Tsompanakis and B.H.V. Topping
Chapter 9

Optimization of Reinforced Concrete Frames: A Review

L. Dlouhý1, M. Lepš2 and M. Novák2

1Faculty of Civil Engineering, Brno University of Technology, Czech Republic
2Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic

Full Bibliographic Reference for this chapter
L. Dlouhý, M. Lep, M. Novák, "Optimization of Reinforced Concrete Frames: A Review", in Y. Tsompanakis and B.H.V. Topping, (Editor), "Soft Computing Methods for Civil and Structural Engineering", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 9, pp 205-227, 2011. doi:10.4203/csets.29.9
Keywords: reinforced concrete, design, frame, cost, optimization, evolutionary algorithms, genetic algorithms.

Summary
This chapter presents the history of the computer-based optimization of reinforced concrete (RC) frames. The aim is placed on methodologies that enable current widespread use of practical designs and utilization of contemporary hardware. Several important references have been if not forgotten then at least hidden in printed publications, and therefore, unavailable to the present internet-based community. Through this chapter, we would like to acknowledge the pioneering work of our predecessors.

The first contribution by Choi and Kwak [1] is especially worthwhile for the analysis of the existing RC frames. They pointed out that the majority of existing structures are constructed with a limited number of cross-sectional dimensions. This observation not only limits the infinite search space but also enables transition from a real-valued continuous optimization to the discrete sizing of a given cross-section. Although the discrete space is still huge, references like [2] have shown that the utilization of genetic algorithms can solve the problem of the discrete detailing of a given RC cross-section.

As the first publication that shows a full-scale optimization of a RC frame we consider reference [3] where a combination of a CAD-based system with a logic programming has been implemented. Although limited to rectangular cross-sections only, the paper has shown that RC structures can be optimized up to necessary details, {\em i.e.} at the same level as steel structures. Until now to the best of the authors' knowledge, a more advanced procedure has not been presented in refereed journals. However, we think that such solutions exist in a commercial area, but have not been published yet.

As an addendum, we will introduce the work by Rotter [4] who probably first published integration formulas for the response of an arbitrary reinforced concrete cross-section that enable automatic checking of the load-bearing capacity in the terms of an interaction diagram. Probably, his work has not been available easily for the scientific community because his formulas have been re-developed by several researchers at the end of the last millennium.

Finally, the design of RC frames differs from other designs especially in the number of constraints that are put on a structure by actual standards. The amount of work needed to implement a general optimization of a real RC structure is beyond the scope of a common research team and some cooperation between academia and software developers is required. An example of a combination of an evolutionary algorithm developed at a university and commercially produced statical software will be presented at the end of this chapter.

References
[1]
C.K. Choi, H.G. Kwak, "Optimum RC member design with predetermined discrete sections", Journal of Structural Engineering, 116(10), 2634-2655, 1990.
[2]
M.Y. Rafiq, C. Southcombe, "Genetic algorithms in optimal design and detailing of reinforced concrete biaxial columns supported by a declarative approach for capacity checking", Computers & Structures, 69, 443-457, 1998.
[3]
V.K. Koumousis, S.J. Arsenis, V.B. Vasiloglou, "Detailed design of reinforced concrete buildings using logic programming", Advances in Engineering Software, 25, 161-176, 1996.
[4]
J.M. Rotter, "Rapid exact inelastic biaxial bending analysis", Journal of Structural Engineering, 111(12), 2659-2674, 1985.

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