Md. Arman Chowdhury^{*} and Md. Mashfiqul Islam  
Ahsanullah University of Science and Technology Dhaka, Bangladesh  
Corresponding Author :  Md. Arman Chowdhury Ahsanullah University of Science and Technology Dhaka, Bangladesh Tel: (8802)8870422 Email: [email protected] 
Received: June 20, 2015 Accepted: August 12, 2015 Published: August 22, 2015  
Citation: Chowdhury A, Islam M (2015) Shear Strength Prediction of FRPreinforced Concrete Beams: A StateoftheArt Review of Available Models. J Civil Environ Eng 5:186. doi:10.4172/2165784X.1000186  
Copyright: © 2015 Chowdhury A, et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.  
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The use of Fiber Reinforced Polymer (FRP) bars to reinforce concrete structures has received a great deal of interest in recent days due to their high tensile strength, corrosion resistance and good nonmagnetization properties. Whether to pick FRP bars due to their low modulus of elasticity over conventional steel, to be used in beams, is the major concern of a designer. FRP bars show low strength in shear as they are more elastic than steel. Recently, researchers have developed a number of models to predict the shear strength of FRPreinforced concrete, but none of them have yet been capable of determining the results satisfactorily. Here a comparative study among different codes and models as suggested by the researchers has been conducted to predict the shear strength of FRP reinforced concrete beams. To facilitate the comparison a database of 104 beams have been presented, which are composed of shear spantodepth ratio, a/d ranged from 2.5 to 6.5, shear span, (a) ranges from, 600 to 1219, concrete compressive strength, (fc’) 24.1Mpa to 81.4MPa, Modulus of elasticity of FRP bars, (Ef) varies between 32GPa to 145GPa, longitudinal reinforcement ratio, (Pf) varies between 0.25 to 3.02. The database contains beams and slabs without transverse reinforcement. The guidelines, codes and models that have been implemented and compared in this study consist of ACI 440.1R03, CSA S80606, CSA S80608, CSA S80611, JSCE1997, ISISM0301 2001, BISE guideline 1999. It was observed from the statistical analysis that model proposed by Kara 2011 exhibited the overall best performance to predict the shear strength of FRPreinforced beams.
Keywords 
Concrete beams; Elasticity; Nonmagnetization; Reinforced 
Introduction 
Over the last couple of decades, fiber reinforced polymers (FRPs) have become alternatives to conventional steel reinforcement for concrete structures owing to their noncorrosive and nonmagnetic properties [13]. Concrete members reinforced longitudinally with FRP bars develop wider and deeper cracks than those reinforced with steel due mainly to the relatively low elastic modulus of FRPs [413]. Wider cracks decrease the shear resistance contributions from aggregate interlock and residual tensile stresses, whereas deeper cracks reduce the shear resistance contribution from the uncracked concrete in compression [4,6]. Additionally, owing to the relatively wider cracks and small transverse strength of FRP bars, dowel action contribution to shear resistance can be very small compared with that of steel reinforcement [6]. Hence, the overall shear resistance of concrete members reinforced with longitudinal FRP bars is lower than that of concrete members reinforced with steel reinforcement. 
Due to the difference in mechanical properties in between FRP bar and steel bars, the failure mode of FRPreinforced concrete beams are different from that of RC beams [4]. This indicates the importance and the requirement of a design approach that can sufficiently predict the capacity of a FRP reinforced beam more specifically, the shear strength of that beam. Although a sufficient amount of research has been done on flexural capacities of FRP reinforced beams, due to their complex behavior in shear, they are in need of further evaluation. Over the last few decades a number of researches have been conducted to accurately predict the shear strength of FRP RC beams [4,14]. This paper will compare the available shear design and code equations with the experimental database collected from published literature. The compared code equations are: ACI 440.1R03, CSA S80606, CSA S80608 and CSA S80611 various models [57,11,13,1522]. All the formulae required by the models for the calculation of the shear strength are included in the Appendix. The codes and models are evaluated and compared with the following performance check: Experimental shear strength over predicted shear strength by the model (V_{exp}/V_{pred}), Standard deviation (SD), Coefficient of Variation (COV) and Average Absolute Error (AAE). Since FRP is a relatively new material, standard guidelines are needed to overcome the additional cost that may be included due to the over conservativeness of the existing models. As most of the models and codes are based on the models that are available for concrete (ACI 31802) [23], comparative study should be done using a large experimental database. This study considers all state of the art models and codes for predicting the shear strength of FRP RC beams and presents all the models/code equations in a systematic manner. The performance of these existing code equations and models are evaluated against the current and larger database. 
Shear failure mechanism of FRP reinforced concrete beams 
For FRP RC beams and oneway slabs (subsequently referred to as beams) without stirrups, shear failure generally occurs in association with the formation of one or more diagonal cracks, which for simplicity are assumed to form linearly as suggested by Hoang and Jensen [24], Hong and Nielsen [25], Jensen and Hoang [26], Jensen et al. [27]. Most of the shear predictions models and design procedures and standards assume that the shear resistance mechanisms for FRP RC beam will contribute in a similar manner to the nominal shear capacity of concrete member reinforced with steel [4]. These provisions use the wellknown V_{c}+ V_{s} method of shear design, which is based on truss analogy [15]. 
Concrete flexural members that are longitudinally reinforced with steel bars for flexure without stirrups resist the applied shear stresses via a number of mechanisms [3,4,6,15,22,2830] including: (1) Shear resistance of uncracked concrete, (2)Interlocking action of aggregate, (3) dowel action of the longitudinal reinforcement, (4) arch action, and (5) residual tensile stresses across cracks. Shear contribution of concrete partly comes from friction forces, which are transferred over cracked surfaces and aggregate interlocking. Shear friction is affected by three properties, the aggregate size, the concrete strength and the crack width [29,30]. The dowel action refers to the shear force resisting transverse displacement between two parts of a structural element split by a crack that is bridged by the reinforcement [22]. As FRP is an anisotropic material with very low transverse stiffness, the dowel action of FRP reinforcement is negligible [22,30]. Arching action occurs in deep members or in the members in which the shear spanto depth ratio (a/d) is less than 2.5 [22]. Compared to the amount of research on arc actions for flexural members that are longitudinally reinforced with steel bars, a limited number of studies have been done for the FRP reinforced beams [6]. The shear resistance also depends on concrete strength and the depth of an uncracked concrete section. Shear resistance increases as the concrete strength decreases and if the cracked section remains shallow. The basic explanation of residual tensile stresses is that when concrete first cracks, a clean break doesn’t occur. Residual tension exists in cracked concrete for cracks less than 0.15 mm wide [4,15,22,28,31]. 
Experimental database 
In order to study the shear behavior of FRP RC beams and check the performance of the available design codes and models, a database of 104 beams reinforced with FRP bars and those that failed in shear was compiled [3,15,18,29,3238]. Only slender beams (a/d>2.5) were considered in this study. In the CAN/CSAS806 recommendation, a coefficient λ_{d} is used to consider the concrete density effect; a value of λ_{d} =1.0 was used in this research (see also Liu and Pantelides [39], Machial et al. [4]. The specimens included 91 beams and 13 one way slabs; all were simply supported and were tested either in three point or four point bending. These specimens included 2 specimens reinforced with aramid FRP bars, 42 specimens reinforced with carbon FRP bars and 60 specimens reinforced with glass FRP bars. All specimens had zero transverse reinforcement (Table 1). 
Parameter that Influence Shear Strength 
While considerable research activities have been conducted to quantify the flexural behavior of FRPreinforced members, considerably less is known about the shear behavior of FRPreinforced concrete beams [10,15,20,21,40,41]. Based on the provided database from literature this section will analyze and compare the existing models and codes. The effect of different controlling parameters on those models and codes will also be analyzed in detail. 
Shear spantodepth ratio (a/d) 
The shear span to the effective depth ratio, (a/d) is an important parameter that influences the shear strength. Considering 100 data points, Figure 1b shows the scatter of experimental shear strength with varying the span to depth ratio (a/d) of the beams. Experimental data showing a decreasing trend with increasing ratio which is supported by the theoretical prediction in Figure 1a. 
Effective depth, d 
The shear strength contribution of FRPRC beams was found to be directly related to the effective depth of the beams. The entire model assumes that shear strength increases linearly with increasing effective depth as shown in Figure 2a and Experimental shear strength also shows an increase in compressive strength with effective depth in Figure 2b. The mechanical explanation for this is that, due to the increase concrete compressive zone, resistance against shear force increases. ACI 440 shows conservative response comparative to the other models. 
Shear Span, a 
Most of the design guidelines and models assume that there is no significant effect of the shear span on shear strength of FRP RC beams. Design codes and models: CSA S80611, Machial et al. [4], Machida A [42], ISISM0301 [43], BISE guideline [44], Razaqpur et al. [20], CSA S80606 [45], Hoult et al. [21] shows no response with the varying shear span while Wegian et al. [7], Zhao et al.[19], Kara [22] shows nonlinear response with a decreasing rate with the increasing shear strength. Experimental result showing a decreasing trend in Figure 3a and 3b so all other codes and models has the scope to improve in this part. 
Axial stiffness of reinforcing bars, p_{f}E_{f} 
Axial stiffness of reinforcement is determined by multiplying the reinforcement ratio and the modulus of elasticity (E) of the reinforcement, i.e. p_{f}E_{f}. The lower the axial stiffness the greater the tensile strain in the longitudinal reinforcing bars. This in turn will cause a reduction in the compression zone leading to wider shear cracks and overall reduction in V_{c}. In another study, Elsayed et al. [15], found that the concrete shear strength is a function of the longitudinal stiffness. Longitudinal stiffness of FRP RC beam increases as the concrete shear strength increases and it is evident from experimental results in Figure 4a and 4b. 
Compressive strength of concrete 
To investigate the effect of concrete compressive strength on shear a strength prediction a number of compressive strength is selected and evaluated with the design of guidelines and codes. The shear design method provided by ACI 440.1R03 assumes that the shear strength of FRPreinforced concrete beams decrease with the increase in concrete compressive strength, but all other model assume that the shear strength of FRP RC beams increase with the increasing concrete compressive strength as shown in Figure 5a. Experimental result shows an increasing trend in shear strength with the increasing concrete compressive strength in Figure 5b. 
Longitudinal reinforcement ratio, p_{f} 
The longitudinal reinforcement ratio, p_{f} is the area of the longitudinal reinforcement divided by the beam width and the effective depth of the beam. Several researcher observed that p_{f} is related to the concrete shear strength Vc in a nonlinear manner [4,13,15,16,29,32] as also showed in the Figure 6a and 6b. Crack depth and crack width decrease with the increase in longitudinal reinforcement ratio [15] and this reduction in the crack depth increases the shear resistance of the uncracked concrete block. Razaqpur et al. [29] and Gross et al. found a relationship between longitudinal reinforcement ratio and the concrete shear strength which is later on implemented by CSAS80602 [46], Kara [22], JSCE97 [47], Alam and Hussein [48], Elsayed et al. [15], Wegian et al. [7] applied the same factor which is cubic root of reinforcement ratio in modelling shear strength. Nedhi et al. [13] determined the relationship between reinforcement ratio and concrete strength by a power of 0.3 which is replaced by 0.23 in further study. CNR DT suggests a linear relationship between p_{f} and V_{c}. From Figure 6b it is not clear whether this relationship is linear or nonlinear but the increasing trend in the experimental results agree with the theoretical predictions by different models and codes. 
Beam width (b_{w}) 
All available models and codes assume a linear relationship between Concrete shear strength and beam width (ACI 440.1R03 [1], CSA S80606, CSA S80608, CSA S80611, JSCE1997 [47], ISISM0301 [43], BISE guideline [44], Elsayed et al.[15], Tureyen and Frosch [16], Wegian et al. [7], Michaluk et al. [17], Deitz et al. [18], Nedhi et al. [13], Zhao et al. [19], Razaqpur et al. [29], CNRDT 203 [49], Hoult et al. [21], Kara [22], Nasrollahzadeh et al. [5], Kim et al. [11], and Lee and Lee [6]. It was observed from the statistical analysis that model proposed by Kara [22]) and this relationship is visible from Figure 7a and 7b. 
Modulus of elasticity of FRP bar, E_{f} (GPa) 
Modulus of Elasticity of FRP bar is an important parameter to predict the shear strength of FRPRC beams. The difference between the modulus of elasticity of steel and FRP bar has become the point of interest for the researchers. ACI 440 guidelines assumed a linear relationship between concrete shear strength and the FRP bar but most of the research shows a cubic root relationship between them (CSA S80602 [46], Kara [22], JSCE97 [42], Alam and Hussein [48], Elsayed et al. [15], Wegian et al. [7], CNR DT 203 [49], BISE design guideline [44], Razaqpur et al. [29]) and some other assumed a square root relationship (CSA S80606, CNR DT 203 [49], ISISM0301 [43] design manual). Figure 8a and 8b shows the increasing tendency of the FRP RC beams shear strength with the increasing modulus of elasticity of FRP bars. 
Model and Codes Comparison: Results and Discussion 
In order to compare the performance of existing codes and models in predicting the shear strength of FRP RC beams, a total of five performance checks were utilized: Standard Deviation (SD), Coefficient of Variation (COV), Mean and Average Absolute Error (AAE). The AAE gives an indication of total error that, the design algorithm produced with the database. 
The performance of design equations in predicting the concrete contribution to shear strength is presented in Figure 9a9v and Table 2. The design equation provided by Kara 2011 had the most accurate prediction with a mean of 1.03 and AAE of 13.78%. CSA S806 [46] and Tureyen and Frosch 2001 has the least scattered results compared to others models and equations, and had a mean of 2.08 and 1.88, AAE 45.37% and 15.76% respectively. Tureyen and Frosch 2001 also show a best balance of results with a lowest COV (Coefficient of Variation). Kara [22], Elsayed et al. [15] and Wegian et al. [7] have the second best COV as 17.77%, 18.59% and 18.62%. Although Nasrollahzadeh 2014 have a lower AAE and lesser scatter of results it shows an over estimation in predicting the result by a mean value of 0.97. All other values obtained from the statistical analysis are given in Table 2 and bolded values indicating the minimum value in that column. 
Conclusion 
The paper has presented an overview of analytical models developed to predict the shear capacity of FRP reinforced concrete beams. A through literature review was conducted on the shear strength of concrete beams reinforced with FRPRC beams. A database of 104 beams was composed and used in statistical analysis for comparing the performance of existing models and codes. Moving from the first theoretical studies, all of which were based on empirical model only considering the difference between modulus of elasticity of steel and FRP bars, the paper highlights the work done by successive researchers to improve the accuracy of predictions for analysis and design purposes. 
Many published provisions and methods for shear resistance of FRP reinforced concrete members (ACI 440.1R03, CSA S80606, CSA S80608, CSA S80611, JSCE1997 [47], ISISM0301 [43], BISE guideline [44], Elsayed et al. [15], Tureyen and Frosch [34], Wegian et al. [7], Michaluk et al. [17], Deitz et al. [18], Nehdi et al. [41], Nedhi et al. [13], Zhao et al. [19], Razaqpur et al. [29], CNRDT 203 [49], Hoult et al. [21], Kara [22], Nasrollahzadeh [5], Kim et al. [11], and Lee and Lee [6] have been considered in this study. 
Kara [22] shows the allround best performance to predict the shear strength of FRP RC beams although improvement may be made to minimize the Average Absolute Error (AAE) and also the COV (Coefficient of Variation). Genetic programming used by Kara [22,50] shows significant improvement over conventional models based on truss analogy and other empirical methods. So, Research should be done on implementing this approach in much more accurate way. 
However, more experimental testing of both slender and deep beams reinforced with FRP for longitudinal reinforcement would assist in developing models that can accurately predict the shear strength. 
References 

Table 1  Table 2 
Figure 1  Figure 2  Figure 3  Figure 4  Figure 5 
Figure 6  Figure 7  Figure 8  Figure 9 
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