General Mathematical Model for Analysing the Bending Behaviour of Rectangular Concrete Beams with Steel, Fibre-Reinforced Polymers (FRP) and Hybrid FRP–Steel Reinforcements (original) (raw)
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Composite Structures, 2016
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 simulations, the linear and nonlinear behavior of all materials was adequately modeled by appropriate constitutive 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 reliability 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.
Composite Structures, 2020
Fibre-reinforced polymer (FRP) is free from corrosion problem and is a viable alternative reinforcement material for concrete structures in lieu of steel reinforcing bars. Since FRP has lower elastic modulus compared to steel, the serviceability aspect of FRP reinforced concrete (FRP-RC) members should be particularly considered in the structural analysis and design. This study addresses the deformation analysis of FRP-RC flexural members with thorough consideration of the tension-stiffening phenomenon in post-cracking state. The approaches for analyzing the tension-stiffening flexural response of FRP-RC beams are presented. These include the use of empirical or theoretical models to compute effective flexural stiffness, the use of finite element method in conjunction with nonlinear constitutive material models, and the use of tensile stress block in combination with member analysis. Among them, the latter is a relatively simple analysis approach. Aiming for serviceability assessment of FRP-RC beams in structural engineering practice to circumvent sophisticated theoretical approaches and constitutive models, parametrized tensile stress block is derived based on tension stress fields computed from finite element analysis, and is proposed for use in member analysis for prediction of deflections. Four FRP-RC beam specimens tested in the literature are analyzed to verify the proposed tensile stress block. Close agreement between the experimental and analytical results is achieved, thereby endorsing the applicability and reliability of the proposed method.
2013
Present research experimentally and theoretically investigates deformations and tension-stiffening in concrete beams with different types of reinforcement. The paper reports test results of eight beams reinforced with glass fiber reinforced polymer (GFRP) or steel bars, combined with steel fibers. For given uniform reinforcement ratio, different number and distribution of bars was assumed in the section. Experimental curvatures were checked against the predictions by design codes (Eurocode 2, ACI 318 and the new Russian code SP 52-101) and recommendations (Italian CNR-DT 203 and American ACI 440). The study examined capability of different code techniques to predict deformations of beams with varying reinforcement characteristics. It has been shown that distribution of reinforcement had a significant influence on the prediction accuracy. In a more elaborate analysis, the tension-stiffening effect was investigated using an inverse technique earlier developed by the authors. Stress-strain tension-stiffening relationships were obtained for each of the beams using the test moment-curvature diagrams. Unlike the common practice, the analysis took into account the shrinkage effect which was different for steel and GFRP reinforced elements. To verify adequacy of the obtained results of constitutive modeling, the derived tension-stiffening relationships were implemented into finite element simulation as material laws for tensile concrete. It was shown that the above inverse approach offers an alternative and versatile tool for constitutive modeling.
Composite Structures, 2010
The design of concrete beams reinforced with fibre reinforced polymer (FRP) bars is often governed by the serviceability limit state, in which deflections play an important role. One of the most straightforward and easiest methods for calculating time-dependent deflections is based on applying multiplicative coefficients to instantaneous deflections. These methods have been adopted by ACI.440.1R-06 and CSA-S806-02 for FRP reinforced concrete structures (RCS), introducing slight modifications with respect to steel reinforced concrete members. However, the influence of different material mechanical properties and environmental conditions are not accounted for properly. In this paper, a new method based on a simplified coefficient for the prediction of time-dependent deflections is presented. The influence of variations in environmental conditions and the mechanical properties of the materials are taken into account. The numerical predictions obtained are compared to other models available in the literature and experimental results to validate the accuracy and suitability of the methodology presented.
Turkish Journal of Civil Engineering
The effects of hooked end steel and polypropylene (PP) fibers on the behavior of large-scale doubly reinforced concrete beams under flexure were investigated using experimental and numeric methods. For this purpose, a total of eight beam specimens consisting in two groups were produced in the laboratory and three-point bending tests were conducted under monotonically increasing load. The beams in the groups were designed to have 0.86 and 1.30% tensile reinforcement ratios leading to either flexural or shear critical sections. Three out of eight were produced to be control samples and did not have any fiber additive while remaining five had 0, 0.5 and 1.0% steel or PP fibers by volume. Experimental results showed that the existence of 0.5% either type of fiber in densely reinforced specimens contributed to shear strength and allowed flexural capacities to be fully used instead of an improvement in the capacity. However, when the steel fiber ratio increased to 1.0% flexural capacity w...
Moment-Curvature Behaviors of Concrete Beams Singly Reinforced by Steel-FRP Composite Bars
Advances in Civil Engineering
A steel-fiber-reinforced polymer (FRP) composite bar (SFCB) is a kind of rebar with inner steel bar wrapped by FRP, which can achieve a better anticorrosion performance than that of ordinary steel bar. The high ultimate strength of FRP can also provide a significant increase in load bearing capacity. Based on the adequate simulation of the load-displacement behaviors of concrete beams reinforced by SFCBs, a parametric analysis of the moment-curvature behaviors of concrete beams that are singly reinforced by SFCB was conducted. The critical reinforcement ratio for differentiating the beam’s failure mode was presented, and the concept of the maximum possible peak curvature (MPPC) was proposed. After the ultimate curvature reached MPPC, it decreased with an increase in the postyield stiffness ratio (rsf), and the theoretical calculation method about the curvatures before and after the MPPC was derived. The influence of the reinforcement ratio, effective depth, and FRP ultimate strain o...
Experimental and Analytical Study on Reinforced Concrete Beams in Bending Strengthened with FRP
The Open Construction and Building Technology Journal, 2014
The performance of the interface between fiber reinforced polymer (FRP) composites and concrete is one of the key factors affecting the behavior of strengthened reinforced concrete (RC) structures. Existing laboratory research has shown that RC beams strengthened with FRP sheets usually fail because of either debonding of the impregnated fabric from the concrete substrate or fracture of the FRP. This work presents an experimental and analytical investigation of the effectiveness of FRP strengthening sheets on RC beams aiming at increasing their flexural strength and stiffness. Experimental results obtained from beam specimens tested under four-point bending are examined with main parameters being the resin type and the anchoring system. In addition, the procedure suggested by the EC8 - Greek Assessment & Retrofitting Code (EC8-GARC) provisions is applied and compared with the experimental results.
Prediction of load–deflection behavior of multi-span FRP and steel reinforced concrete beams
Composite Structures, 2015
This paper presents a numerical procedure to determine the deflection of concrete members reinforced with fiber reinforced polymer (FRP) or steel bars. This procedure is implemented into the stiffness matrix to allow for general use in the structural analysis. It considers effective flexibilities of members in the cracked state using either the curvature distribution along the member or available effective stiffness models under any loading or support condition. In general, structural concrete members can be considered to have three cracked regions (two at the ends and one at midspan) and two uncracked regions along their length. In this numerical procedure, the contributions of these regions to the member stiffness matrix are computed using a numerical integration technique. Using this procedure, a software program is developed which allows for the load–deflection behavior of a member reinforced with either FRP or steel bars and subjected to any loading or support condition to be rapidly determined. This calculation procedure is evaluated using available experimental data on the load–deflection behavior of simple and two-span beams reinforced with FRP and steel bars. Through comparison of the results, it is observed that the load–deflection behaviors calculated using the proposed approach utilizing the member moment–curvature response are consistent with the experimental data. This approach can provide a useful tool for the general calculation of deflection regardless of reinforcement type and can be used throughout the entire range of member behavior up to flexural failure.
Flexural modelling of steel fibre-reinforced concrete beams with and without steel bars
Engineering Structures, 2013
This paper outlines analytical flexural models for steel fibre reinforced concrete (SFRC) with and without steel bars. The models are developed for strain softening, deflection hardening SFRC. Models for the determination of flexural capacity of SFRC rectangular sections based on equivalent stress blocks for both compression and tension are developed using strain compatibility and force equilibrium principles. The equivalent stress blocks are derived from an elastic perfect-plastic model for compression, and an elasticconstant post-peak response for tension. The models are verified using experimental data. Sensitivity analysis is conducted to assess the predictability of the models with varying model parameters. When compared with existing models, the proposed models fairly predict the flexural capacity of the SFRC beams. The models may allow the user to determine model uncertainties and hence provide for appropriate safety margin for design.