Predicting torsional strength of RC beams by using Evolutionary Polynomial Regression Alessandra Fiore b,⇑ , Luigi Berardi b , Giuseppe Carlo Marano a a Department of Environmental Engineering and Sustainable Development, Technical University of Bari, viale del Turismo 10, 74100 Taranto, Italy b Department of Civil and Environmental Engineering, Technical University of Bari, via Orabona 4, 70125 Bari, Italy article info Article history: Received 19 April 2011 Received in revised form 19 July 2011 Accepted 2 November 2011 Available online 10 December 2011 Keywords: Reinforced concrete beam Evolutionary Polynomial Regression Torsional strength Building code Theoretical model Soft computing abstract A new view for the analytical formulation of torsional ultimate strength for reinforced concrete (RC) beams by experimental data is explored by using a new hybrid regression method termed Evolutionary Polynomial Regression (EPR). In the case of torsion in RC elements, the poor assumptions in physical models often result into poor agreement with experimental results. Nonetheless, existing models have simple and compact mathematical expressions since they are used by practitioners as building codes pro- visions. EPR combines the best features of conventional numerical regression techniques with the effectiveness of genetic programming for constructing symbolic expressions of regression models. The EPR modeling paradigm allows to figure out existing patterns in recorded data in terms of compact mathematical expressions, according to the available physical knowledge on the phenomenon (if any). The procedure output is represented by different formulae to predict torsional strength of RC beam. The multi-objective search paradigm used by EPR allows developing a set of formulae showing different complexity of math- ematical expressions as resulting into different agreement with experimental data. The efficiency of such approach is tested using experimental data of 64 rectangular RC beams reported in technical literature. The input parameters affecting the torsional strength were selected as cross- sectional area of beams, cross-sectional area of one-leg of closed stirrup, spacing of stirrups, area of longitudinal reinforcement, yield strength of stirrup and longitudinal reinforcement, concrete compressive strength. Those results are finally compared with previous studies and existing building codes for a complete comparison considering formulation complexity and experimental data fitting. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In last decades a number of advancements has been observed in the field of reinforced concrete elements analysis; among them a number of remarkable research studies were aimed at overcoming problems in predicting final strength under different actions by using simple and effective formulations. Moreover differently from other situations, the torsional design of structural concrete ele- ments is a complex problem which still remains an open question. In particular a more rational design formulation for RC structures under these specific actions still needs to be defined. The aim is to develop direct formulations which can be used without incur- ring the computational burden of numerical approaches like FEM. Such formulas, eventually, could be used for upgrading both exist- ing best practices and current building codes. Moreover, such explicit formulations should be easily included into existing design codes, without significantly increasing the computational burden while improving prediction accuracy. In this field (i.e. final torsional strength evaluation) there is an evident lack of efficient models to describe real physical behavior. In fact, for a given beam section, different current design codes might return quite different predictions which can vary by factors of more than two. This is deeply different from other situations, such as the flex- ural strengths, whose predictions by the same codes may differ from each other by less than 10%. Actually, for flexure ultimate states some detailed models are used which take into account equilibrium, capability and non-linear stress–strain relationship of material. On the contrary, most of design equations for torsional strength derive directly from the equilibrium condition of the sim- ple truss model theory proposed by Ritter and Morsch at the turn of the 20th century. This strong discrepancy is due to the difficulty in modeling the complex phenomena underlying the mechanical behavior of torsion by standard synthetic models. 0965-9978/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2011.11.001 ⇑ Corresponding author. Address: Politecnico di Bari, via Orabona 4, 70125 Bari, Italy. Tel.: +39 0805963525; fax: +39 0805963719. E-mail address: a.fiore@poliba.it (A. Fiore). Advances in Engineering Software 47 (2012) 178–187 Contents lists available at SciVerse ScienceDirect Advances in Engineering Software journal homepage: www.elsevier.com/locate/advengsoft