Numerical and analytical modeling of concrete beams with steel, FRP and hybrid FRP-steel reinforcements Francesco Bencardino, Antonio Condello, Luciano Ombres ⇑ Department of Civil Engineering, University of Calabria, Via P. Bucci, Cubo 39B, 87036 Rende, Cosenza, Italy article info Article history: Available online 2 January 2016 Keywords: Analytical modeling Aramid fiber Finite element modeling Glass fiber Reinforced concrete abstract The paper presents the results obtained from a numerical and analytical analysis carried out on a set of concrete beams reinforced with steel bars, Fiber Reinforced Polymer (FRP) bars and hybrid combinations of FRP-steel bars. To this purpose a database of experimental results, available in literature, was collected. A simple and reliable two-dimensional Finite Element (FE) model was defined. In the numerical simu- lations, the linear and nonlinear behavior of all materials was adequately modeled by appropriate consti- tutive laws. To simulate the concrete post-cracking tensile behavior a specific tension stiffening model was used. In order to overcome convergence difficulties, to simulate the quasi-static response of RC beams, a dynamic approach was adopted. Furthermore, to assess the effectiveness of the current Italian guideline, on same set of RC beams, an analytical analysis was performed. The comparisons between numerical/analytical results and experimental data highlighted the reliabil- ity of both the proposed FE model and the analytical model. The results show that the tension stiffening model used in the FE analysis provides good results with low and normal reinforcement ratios, whereas the numerical predictions are not acceptable with high reinforcement ratios. The analytical results provided by the Italian guideline are satisfactory, compared to experimental data. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Fiber Reinforced Polymer (FRP) has become an alternative con- struction material to replace steel bars as reinforcement in con- crete structures due to its advantages, such as, corrosion resistance, non-conductivity, high strength-to-weight ratio and lightweight. Some research related to experimental studies of FRP bars in reinforced concrete (RC) structures can be found in [1–6]. A good review of the practical application of FRP bars can be found in [7]. Recently, FRP bars have been used in some countries, such as United Kingdom, Germany, Canada and Switzerland, in bridge decks and roads owing to the seasonal use of deicing salts, which causes traditional steel reinforcement to corrode. Furthermore, some concrete structures require non-metallic material as con- stituent material, such as the Magnetic Resonance Imaging (MRI) rooms in hospital or research laboratories. In these special circum- stances, FRP bars are a good alternative to the conventional steel bars in RC structures. Although FRP bars have many advantages to be adopted as a construction material, they have a brittle behavior and thus lack ductility. Experimental tests have shown that RC structural mem- bers reinforced with FRP bars exhibit less ductility compared to similar members reinforced with the conventional steel reinforce- ment [8–11]. In order to increase the ductility of RC beams, many researchers have experimentally investigated the use of hybrid combinations of steel and FRP reinforcements [8–11]. The high tensile strength of FRP bars enhances the ultimate load carrying capacity of the member, whereas the steel reinforcement provides ductility to the RC member. An optimal solution can be obtained by placing the FRP bars near the outer surface of the tensile zone with small cover thickness values and steel bars at the inner level of the tensile zone. The results emerged from these studies have contributed to the development of analytical models at the basis of design formulas included in standard documents and design guidelines such as ACI 440.1R-15 [12], CNR DT 203/2006 [13], CSA S806-12 [14], Fib Bulletin No. 40 [15], ISIS Design Manual No. 3 [16], JSCE 1997 http://dx.doi.org/10.1016/j.compstruct.2015.12.045 0263-8223/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +39 0984 494024. E-mail address: luciano.ombres@unical.it (L. Ombres). Composite Structures 140 (2016) 53–65 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct