Keywords: reinforced concrete beam, evolutionary polynomial regression, torsional strength, experimental data, building codes, physical insight.

Determination of ultimate torsion in reinforced concrete (RC) is still an open question because of the number of parameters involved. These parameters are generally characterised by a significant variability, so that only extremely simplified models are used for the description of the physical phenomena. Moreover this results in simplified physical models frequently exhibiting poor agreement with experimental results. Nonetheless, existing models have simple and compact mathematical expressions since they are used by practitioners as building code provisions.

In this paper a different approach for predicting ultimate torsion in RC beams is proposed by using a recent soft computing method, the evolutionary polynomial regression (EPR) technique [1]. EPR can be defined as a non-linear global stepwise regression, providing symbolic formulæ for models. EPR combines the best features of conventional numerical regression techniques with the effectiveness of genetic programming for constructing symbolic expressions of regression models, and here the input is some experimental results from the technical literature.

The procedure output is represented by different formulae to predict the torsional strength of RC beams. The multi-objective search paradigm used by EPR allows the development of a set of formulae showing different complexities of mathematical expressions resulting from different agreement with experimental data. Thus, it is possible to decide a trade-off between complexity of the mathematical formulae and the accuracy to be used in different design situations.

The efficiency of such an approach is tested using the experimental data from sixty-four rectangular RC beams reported in the technical literature. The input parameters affecting the torsional strength are the cross-sectional area of beams, the dimensions of the closed stirrups, the spacing of the stirrups, the cross-sectional area of one-leg of a closed stirrup, the yield strength of a stirrup and the longitudinal reinforcement, the steel ratio of the stirrups, the steel ratio of the longitudinal reinforcement and the concrete compressive strength.

Final formulations are compared with some building code provisions recently developed for practical structural design [2,3], considering complexity and experimental data fitting. The results show that by using EPR it is possible to obtain models significantly more accurate than the existing building code formulations, although the complexity of their mathematical expressions are comparable.

1

O. Giustolisi, D.A. Savic, "Advances in data-driven analyses and modelling using EPR-MOGA", Journal of Hydroinformatics, 11(3), 225-236, 2009. doi:10.2166/hydro.2009.017

2

ACI Committee 318-2005, "Building code requirements for structural concrete (ACI 318-05) and commentary (318R-05)", American Concrete Institute, Farmington Hills, Mich., 2005.

3

BS8110, "Structural use of concrete. Part 2", British Standards, 1985.

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