Serviceability Limit State of FRP RC Beams

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1 Serviceability Limit State of FRP RC Beams Cristina Barris 1, Lluís Torres 1,*, Marta Baena 1, Kypros Pilakoutas 2 and Maurizio Guadagnini 2 1 Advanced Materials and Analysis for Structural Design (AMADE), University of Girona, Spain 2 Department of Civil & Structural Engineering, University of Sheffield, United Kingdom Abstract: Owing to the particular mechanical properties of FRPs, the design of Fiber Reinforced Polymer (FRP) Reinforced Concrete (RC) structures is often governed by serviceability requirements, rather than ultimate capacity. The low stiffness of FRPs generally results in large strains being mobilized already at low levels of externally applied load, and in turn can lead to significant crack widths and deflections. This paper reviews and discusses the serviceability limitations inherent in current design codes and guidelines in terms of stress limitation, cracking and deflection control. The predictions obtained in accordance to these code equations, as well as other existing proposals for the design of FRP RC structures, are then compared to the results of an experimental program on 24 GFRP RC beams tested under four-point load. Key words: reinforced concrete, FRP bars, serviceability, deflection, cracking. 1. NTRODUCTON Fibre reinforced polymer (FRP) bars were introduced in the market as an alternative for internal reinforcement in concrete structures exposed to environments likely to cause corrosion in steel reinforcement. Highway infrastructures, bridges, marine environments, or chemical plants are examples of places where applications or demonstration projects have been successfully carried out. Owing to their non corrosive nature, the use of FRP bars can reduce maintenance and rehabilitation costs, leading to economic and environmental benefits (fib 2007; Pilakoutas et al. 2007). Moreover, the magnetic neutrality of FRP bars can be exploited in applications where interferences with magnetic fields have to be avoided. Other specific properties can lead to new uses, as the use for diaphragm walls in temporary applications, for which the high cuttability of FRPs is a major advantage (fib 2007; Pilakoutas et al. 2007). The unique mechanical properties of FRPs, however, have a significant effect on the structural performance of concrete elements reinforced with these unique materials. n particular, the modulus of elasticity is relatively low when compared with steel, especially for Glass Fiber Reinforced Polymer (GFRP). This can yield to large strains being mobilized in the bars at low levels of external loads and lead to large crack widths and deflections. As a result, serviceability requirements often govern the design of FRP RC elements (Matthys and Taerwe 2000). n addition, FRPs may exhibit significant creep rupture (or static fatigue) and fail under sustained loads at stresses lower than their tensile short-term strength (AC Committee ; fib 2007). Finally, the wide range of commercially available products can differ substantially in terms of fibre/matrix make-up, geometry, and surface characteristics, making it difficult for code writers to implement simple design rules that can model adequately the mechanical performance of any type of composite bar *Corresponding author. address: lluis.torres@udg.edu; Fax: ; Tel: Advances in Structural Engineering Vol. 15 No

2 Serviceability Limit State of FRP RC Beams in concrete. Despite several design guidelines, codes and recommendations have already been published (JSCE 1997; StructE 1999; SS Canada 2001; CSA 2000; CSA 2002; AC Committee ; CNR 2007), the lack of agreed standards for design is still perceived as a barrier to the more extensive use of FRPs in construction. This paper introduces and discusses the main factors affecting the behaviour of concrete structures with internal FRP reinforcement under service load. Current provisions on stress limitations, deflections and cracking are examined in detail and existing approaches for the serviceability design of RC elements with FRP reinforcement are presented and commented upon. The results of an experimental program examining the behavior of 24 GFRP RC beams are presented and used to assess the validity of the current provisions examined in this paper. 2. SERVCEABLTY ASPECTS OF FRP RC ELEMENTS Limits on various parameters are imposed for RC structures to ensure their functionality and structural integrity in service conditions. The design approach for conventional RC elements requires that serviceability limit states (SLS) be checked for relevant loading combinations, but rarely does this demand for a considerable redesign. When dealing with FRP RC structures, however, the distinctive mechanical characteristics of FRP rebars are expected to result in a SLS-governed design. t is therefore important to define the serviceability checks and corresponding limits that are required for the design of FRP RC elements. There are no fundamental reasons why the principles underlying the formulation of SLS for FRP RC elements should not be similar to those already established in the codes of practice for steel RC elements, such as Eurocode 2 (2004), CEB-FP Model Code 1990 (CEB 1990), AC318 (AC Committee ), or CSA-S806 (CSA 2002). The current limit values for steel RC, however, do not account for the unique short and longterm properties of FRP reinforcement and their validity needs to be reassessed. The lack of ductility and relatively low stiffness of FRP reinforcement generally demand for the design of over-reinforced sections. The use of a comparatively large amount of reinforcement allows the onset of concrete crushing before bar rupture, resulting into the development of the least brittle of the possible failure modes. n addition, if geometrically similar cross sections were considered, a larger reinforcement ratio would be needed when using FRPs in lieu of steel to satisfy similar serviceability requirements. The SLS considered in available design documents, in terms of stresses in the materials, cracking and deflection behavior, are presented and discussed in turn in the following Durability and Stress Limits in Materials When FRPs are used as internal reinforcement, the strength to stiffness ratio is an order of magnitude greater than that of concrete and, hence, the neutral axis depth for the balanced section is very close to the compressive end (fib 2007). As a result, higher compressive strains than in a steel RC section are expected to develop in the concrete for the same beam depth, reinforcement ratio and applied moment. Consequently, the maximum concrete strain/stress at service load should be considered carefully as to avoid any undesirable effects due to the occurrence of longitudinal cracks, microcracks, inelastic deformations and creep. Eurocode 2 (CEN 2004), for instance, imposes a maximum stress in concrete under a characteristic combination of load of 0.60 f ck to avoid the appearance of longitudinal cracks, which could affect durability. A more restrictive limit of 0.45f ck, is recommended when considering quasi-permanent load conditions to enable the use of a simplified linear model for creep. Although specific limits on concrete compression stresses under service conditions are not prescribed explicitly in all of the existing design provisions, the concrete stresses are generally assumed to be within the linear range. AC440.1R-06 (AC Committee ), for instance, adopted this latter approach. A limiting value of 0.45 f c, however, is explicitly recommended in AC.440.2R.08 (AC Committee ) for concrete elements strengthened with FRPs. The stress in the FRP reinforcement should also be limited to avoid issues arising from its creep rupture or stress corrosion (fib 2007). Stress corrosion related problems are only significant, however, when using glass fiber reinforced composites. Different coefficients are proposed in existing design documents to determine the appropriate limiting stress values for different types of FRP reinforcement (Table 1). The use of these factors takes into account the influence of environmental conditions as well as the effect of sustained permanent loads, which can be considered to act concurrently or separately, and generally leads to severe reductions in the value of the maximum allowable design stress. AC 440.1R-06, for example, takes into account environmental conditions determining the FRP design strength f fu according to Eqn 1, where C E is an environmental reduction factor (Table 1) and f fu * is the guaranteed tensile strength of the FRP bar. Furthermore, to consider the effect of sustained permanent loads on creep rupture, AC440.1R-06 uses an additional coefficient C fs to limit the stress to f f,s (Table 1, Eqn 2). 654 Advances in Structural Engineering Vol. 15 No

3 Cristina Barris, Lluís Torres, Marta Baena, Kypros Pilakoutas and Maurizio Guadagnini Table 1. Reduction factors used in existing guidelines Factor AC R-06 CHBDC-2006 JSCE StructE CNR Reduction for C E Φ FRP 1/γ fm 1/γ m η a environmental GFRP: GFRP: 0.50 GFRP: 0.77 material GFRP: deterioration AFRP: AFRP: 0.60 AFRP: 0.87 factor AFRP: CFRP: CFRP: 0.75 CFRP: 0.87 CFRP: Stress limit for C fs Pre/Post tension: 0.8 creep Stress η 1 permanent load GFRP: 0.20 GFRP: failure strength limits not GFRP: 0.30 AFRP: 0.30 AFRP: specified AFRP: 0.50 CFRP: 0.55 CFRP: GFRP: 0.7 CFRP: 0.90 AFRP: 0.7 CFRP: 0.7 A similar approach has also been adopted by other committees and the various equivalent factors are summarized in Table 1. Other less conservative approaches can be considered if specific data on the durability properties of the reinforcement are available. fib Bulletin 40 (fib 2007) presents a procedure that allows to determine appropriate margins of safety depending on environmental and stress conditions, FRP type, and required design life. According to this procedure, the FRP design strength f fd can be obtained from the characteristic short term strength f fk0, divided by a material factor γ f, and by an environmental strength reduction factor η env, t, f f fu E fu ffs, = Cfsffu = f 0 / ( η, γ ) fd f k env t f The value of η env, t can be obtained from * = C f (1) as internal reinforcement, larger crack widths are expected to develop even at moderate load levels. Nevertheless, as superior durability is expected from (2) FRP reinforcement, crack width limits could be relaxed in those cases where aesthetic appearance is not of primary concern. n the absence of more information, similar limitations to those suggested for steel RC structures could be adopted for FRP RC structures exposed to extreme and aggressive environmental conditions, or for those designed to be water-tight. On the basis of the above considerations, all of the aspects of design that have a direct effect on the overall cracking behaviour of FRP RC elements, such as minimum reinforcement area, maximum bar diameter or bar spacing, should be re-assessed to account for the unique mechanical and physical properties of FRPs. Eqns 5 and 6, for example, illustrate the Eurocode 2 procedure to determine maximum crack spacing, S r,max, and maximum crack width, w k, respectively (CEN 2004). (( ) ) n η env, t = f f k 1000 h / f fk 0 / 100 R10 / 100 (3) (4) in which f fk1000h and R 10 are experimentally determined parameters and correspond to the residual strength at 1000 hours, and the standard reduction in strength per logarithmic decade, respectively. The coefficient n accounts for moisture and temperature conditions, service life (years), and bar diameter. S = 3. 4c k 1 k 2 φ ρ r,max p, eff (5) where c is the concrete cover, k 1 is a coefficient that takes into account the bond properties of the reinforcement, k 2 is a coefficient depending on the form of strain distribution (0.5 for bending and 1 for pure tension), and φ is the diameter of the bar. The parameter ρ p,eff is the effective reinforcement ratio, where the area of the concrete surrounding the reinforcement shall be calculated as the lesser of 2,5b(h-d), b(h-x)/3, or bh/2, being b and h the width and the height of the beam, d the effective depth and x the neutral axis depth Cracking Behaviour Cracking in RC elements at serviceability limit states is controlled for aesthetic reasons and to protect the structure against predefined environmental conditions, thus ensuring adequate durability. When FRPs are used w ( ) k = Sr,max εsm εcm (6) where the mean differential strain, (ε sm ε cm ), can be computed according to Eqn 7 as the difference between the strain in the reinforcement taking into account the Advances in Structural Engineering Vol. 15 No

4 Serviceability Limit State of FRP RC Beams tension stiffening effect, ε sm, and the mean concrete strain in between cracks, ε cm : approach and using a constant effective moment of inertia (Branson 1977): ε sm σ kf s εcm = E s ( 1+ αρ ) E ρ t ct, eff e p, eff s p, eff σ 06. s E s (7) e = g 3 3 Mcr Mcr cr M + 1 M max max g (9) n Eqn 7, σ s is the stress in the tension reinforcement calculated assuming a cracked section, α e is the modular ratio (E s /E c ), and k t is a factor depending on the duration of the load (0.6 for short-term loads and 0.4 for longterm loads). The same underlying principles form the basis of the approach implemented in other design provisions (for example CNR 2007). AC committee 440 adopted the same principles as those included in the AC design code for steel RC and proposed modifications to incorporate the use of FRPs based on the work of Frosch (1999). The modified design equation includes the same fundamental parameters as those considered to affect crack opening in steel RC, but introduces the bond coefficient, k b, to account for the different bond behaviour of FRP bars: f f 2 s w = kb dc + E 2 β 2 f (8) where f f is the bar stress, E f is the modulus of elasticity of the reinforcement, β is the ratio of distance from neutral axis to extreme tension face to distance from neutral axis to centroid of tensile reinforcement, d c is the cover thickness from the tension face to the centre of the closest reinforcing bar, and s is the bar spacing. For FRP reinforcing bars exhibiting better bond characteristics than steel, k b is taken less than unity. For FRP reinforcing bars with inferior bond behaviour, k b is assumed larger than unity. f the k b value is not known, a conservative value of 1.4 is recommended Deflection Behaviour The relatively low stiffness of FRP reinforcement always results in the larger deflections of FRP RC elements in comparison to equivalent concrete elements reinforced with conventional steel reinforcement. As a result, the overall design of FRP RC elements is generally governed by their performance under service conditions rather than at ultimate limit state and the required amount of flexural reinforcement and recommended span to depth ratios should be re-examined in the light of the above considerations. The short-term deflection of a cracked steel RC beam can be obtained by applying the standard linear-elastic 2 where M cr is the cracking moment of the section, M max is the maximum moment in the member due to service loads, g is the moment of inertia of the gross concrete section and cr is the moment of inertia of the transformed cracked section. This equation, however, yields a loaddeflection response that is generally too stiff for FRP RC members, thus underestimating deflections (Yost et al. 2003; Bischoff 2005). A number of approaches to modify this equation or obtain alternative equivalent moments of inertia have been proposed by researchers in the field (Faza and GangaRao 1992; Benmokrane 1996; Toutanji and Saafi 2000). t should be noted that the wide range of material properties and surface finishes of commercially available FRP products add more complexity to the already difficult task of calibrating these equations using experimental data. n the following some of these approaches are presented and discussed. The AC 440.1R-06 provisions adopt a modified version of Branson s equation and introduce a reduction coefficient, β d, to account for the different tension stiffening behaviour of FRP RC elements (Eqns 10 and 11): e Mcr Mcr = dg M + β 1 M max max ρ fb 3 3 β d 1 ρ f = 5 ρ 10. = 0. 85β 1 fb f ε c E f cu f E ε + f fu f cu fu (10) (11) (12) where ρ f is the FRP reinforcement ratio and ρ fb is the FRP reinforcement ratio producing balanced strain conditions, calculated following Eqn 12, where β 1 is the ratio of depth of equivalent rectangular stress block to depth of the neutral axis, f c is the concrete compressive strength, f fu is the rebar tensile strength, E f is the modulus of elasticity of the FRP rebar, and ε cu is the maximum concrete strain (0.003 for AC provisions). Experimental analyses carried out by Pecce et al. (2000) and Toutanji and Deng (2003) pointed out that cr g 656 Advances in Structural Engineering Vol. 15 No

5 Cristina Barris, Lluís Torres, Marta Baena, Kypros Pilakoutas and Maurizio Guadagnini the deflections in GFRP RC beams could be accurately predicted by the approach of AC 440.1R assuming an adequate value for the reduction coefficient. Eqn 11 for β d, however, was derived on the basis of experimental observations and does not build upon the underlying principles of tension stiffening. As such, the equation has been subject of debate by various researchers and alternative expressions have already been proposed (Bischoff 2005). CAN/CSA-S806 (2002) proposes a method to evaluate short-term deflections of FRP RC members through the integration of curvatures along the span. A tri-linear moment-curvature relation ignoring tension-stiffening is assumed, with the flexural stiffness being E c g for the first segment, zero for the second, and E c cr for the third, where E c is the concrete modulus of elasticity. Alternatively, simple deflection equations, clearly derived from the assumed moment-curvature relation, are provided. For a four-point bending configuration, with two loads P acting at a distance a from the supports, the beam deflection shall be calculated as follows: PL max = 24E c cr a a 3 4 L L 3 3 (13) where L g is the distance from the support to the point that M = M cr, in which the beam is uncracked. Eurocode 2 proposes an interpolation between deformations, in lieu of moments of inertia, which is conceptually more meaningful to represent the variation of the stiffness along the length of the beam due to the presence of cracking (Bischoff 2005). nterpolation of sectional curvatures (and subsequent integration), or direct interpolation of deflections between cracked and uncracked states may be carried out. For members subjected to flexure the following expression can be used: α = ξα + ( 1 ξ) α 8 1 ξ = β Mcr 1 M (14) (15) where α is the deformation parameter considered (curvature or deflection), the subscripts and refer to uncracked and cracked conditions respectively, β is the cr 2 g Lg L 3 coefficient for load duration (β is taken as 1 for shortterm loads, and 0.5 for sustained or repeated load), M cr is the cracking moment, and M is the service moment. Al-Sunna (2006) and Barris et al. (2009) reported that the deflections of GFRP RC elements within the service load range can be predicted accurately by implementing the Eurocode 2 approach. Based on a similar approach to that suggested in Eurocode 2, Bischoff (2005) proposed an effective moment of inertia that can be used for both FRP and steel RC structures (Eqn 16 and 17). With the exception of the coefficients for load duration, the use of this effective moment of inertia for the direct calculation of deflections is equivalent to using Eqn 14. (16) (17) SS Canada (2001) adopts a similar equation to estimate the effective moment of inertia of cracked FRP sections which, in fact, only differs in the value of the multiplication factor for the cracking to service moment ratio: e = cr e cr = Mcr 1 η M η = 1 max t cr M M ( t cr ) (18) where t is the moment of inertia of the uncracked section transformed to concrete. 3. EXPERMENTAL PROGRAM 3.1. Beams Specifications The experimental program consisted of two series of six GFRP RC beam types. For each beam type, two specimens were tested (beam a and b), giving a total amount of 24 beams. The beams were 190 mm high and 2050 mm long, whilst their width, B, was varied depending on the concrete cover provided as detailed below. All of the specimens were tested under a four-point bending load. The distance between supports was 1800 mm, the shear span was 600 mm, and the distance between loads 600 mm (Figure 1). cr g cr max 2 2 g Advances in Structural Engineering Vol. 15 No

6 Serviceability Limit State of FRP RC Beams A A P/2 P/2 Steel stirrups 8/ 70 mm For each beam series, three different amounts of longitudinal reinforcement (2φ12, 2φ16 and 3φ16) and two different covers (20 and 40 mm) were used. The width of the beams measured 140 mm or 160 mm to yield a reinforcement ratio of 0.99%, 1.77% and 2.66% for the three different reinforcement layouts. Two types of concrete with a target compressive strength of 30 MPa and 50 MPa were used for the two series of beams. Specimens type a were initially uncracked whilst specimens type b were notched at midspan to ensure the initiation of cracking at a predefined location. The notch was created by placing a 1 mm wide steel rectangular plate into the moulds prior to casting. The height of the steel plate, and thus of the resulting notch, was 5 mm. The beam specimens are identified as Cx-y-Dz, where x stands for the concrete strength (C1 for 30 MPa and C2 for 50 MPa), y stands for the amount of reinforcement (i. e. two diameters of 12 mm is 212) and z stands for the cover to the main rebar (D1 for 20 mm and D2 for 40 mm). The shear spans of each of the beams were reinforced with the required amount of steel stirrups to guarantee the onset of flexural failure before shear failure (φ8 mm). Two steel bars with a nominal diameter of 6mm were used as reinforcement in the compression zone. No shear reinforcement was 125 All dimensions in mm Figure 1. Geometric and reinforcement details c A-A B provided within the constant bending moment zone so as not to affect the crack initiation and development in this region. The geometric details of the tested beams and reinforcement arrangement are given in Figure 1 and Table Materials Concrete All of the C1 specimens were cast together using the same batch of concrete, which was a ready-mix concrete with 12 mm maximum aggregate size, cement type CEM /A-V-42.5R and a water/cement ratio of Specimens designated as C2 were cast in pairs (beams a and b of the same type) using a cement type CEM -52.5, 10 mm maximum aggregate size, and a water/cement ratio of The mechanical properties of the concrete used in this study are summarized in Table 3. The compressive strength of each batch of concrete was evaluated by testing standard cylinders on the same day as the corresponding beam tests (28 35 days after casting). These control specimens were cast at the same time and cured under the same conditions as the beam specimens. The average concrete flexural tensile strength for each pair of beams was calculated through the back analysis of their experimental cracking moments Reinforcement Ribbed GFRP bars with a nominal diameter of 12 mm and 16 mm and a fibre volume fraction of 75% (Schöck Bauteile GmbH 2006) were used as flexural reinforcement. The mean values of rupture tensile strength, f fu, and modulus of elasticity, E f, were obtained from uniaxial tension tests and are shown in Table 4 along with the corresponding nominal values as given by the manufacturer. Table 2. Geometric characteristics of sections Cover, c B (mm) ρ ρ fb Beam Concrete (mm) h (mm) d/h Reinforcement (%) (%) Designation (*) Series 1 (C1) 20 (D1) φ C1-212-D1 30 MPa φ C1-216-D φ C1-316-D1 40 (D2) φ C1-212-D φ C1-216-D φ C1-316-D2 Series 2 (C2) 20 (D1) φ C2-212-D1 50 MPa φ C2-216-D φ C2-316-D1 40 (D2) φ C2-212-D φ C2-216-D φ C2-316-D2 (*) Two specimens were tested for each beam type, -a uncracked, -b notched 658 Advances in Structural Engineering Vol. 15 No

7 Cristina Barris, Lluís Torres, Marta Baena, Kypros Pilakoutas and Maurizio Guadagnini Table 3. Mechanical properties of concrete Compressive Modulus of Tensile Beam strength, elasticity, E c strength designation f c (MPa) (MPa) (*), f ct (MPa) C1-212-D C1-216-D C1-316-D C1-212-D C1-216-D C1-316-D C2-212-D C2-216-D C2-316-D C2-212-D C2-216-D C2-316-D (*) Deduced from the experimental cracking moment Table 4. Mechanical properties of GFRP rebars Diameter (mm) Rupture Tensile Strength, f fu (MPa) 1353 (1000) 995 (1000) Modulus of Elasticity, E f (MPa) (60000) (60000) Ultimate strain, ε fu ( ) (1.8%) (1.8%) Values provided by manufacturer in brackets 3.3. nstrumentation and Test Setup The deflection of the tested beams was measured by three transducers located at midspan and 450 mm away from each of the supports. Displacements at each supports were also measured to enable the evaluation of net deflections. An additional horizontal transducer was located at midspan, at the height of the longitudinal reinforcement, to measure the crack opening. n beams type b, three strain gauges were positioned on the concrete surface within the top portion of the midspan cross-section to examine the development of strain and variation in the neutral axis depth. The GFRP bars of some of the beams type b were instrumented with strain gauges. The gauges were located at midspan to monitor closely the evolution of strain in the area surrounding the first crack as well as along the shear span to examine the variation of strain along the bars. 4. DSCUSSON OF EXPERMENTAL RESULTS The experimental tests discussed in the following are part of a larger program that aims to examine all of the issues considered above, including a fundamental study on bond behaviour Stresses in Materials Stresses in concrete Under service conditions, concrete is generally considered to behave in a linear elastic manner (Eurocode 2; AC 440.1R-06). Figure 2 shows a typical relationship between experimental load and concrete strain measured at midspan for a notched beam. A linear increase in the concrete strain is observed up to a load inducing the initiation of the first crack. Below this load level, all of the three experimental curves indicate a similar behavior, with almost negligible values of strain. After cracking, the difference among the recorded values of strain increases rapidly. As expected, the maximum concrete strain in compression was measured by the strain gauge located on the top side of the beam, whilst the gauge located 48 mm from the top, Gc3, measured either compression or tension strain, depending on the position of the neutral axis. Table 5 shows the estimated load corresponding to the SLS of stress in concrete as indicated in EC2. The reference value of 0.45 f ck refers to a quasi-permanent loading condition, whilst 0.60 f ck corresponds to a characteristic load combination. As it can be observed, if the concrete compressive stress is limited to avoid longitudinal cracking (0.60 f ck ), the service load of the tested GFRP RC beams is about 29% of their ultimate capacity, whilst this decreases to only 22% if creep needs to be controlled (0.45 f ck ). The lower service load equivalent to only 22% of the ultimate load capacity, however, accounts for the sustained nature of the applied loads. f only a portion of the service load is sustained, then the full service load corresponding to limiting the concrete stress to 0.45 f ck would be higher. Load P (kn) Gc3 Gc2 20 mm 48 mm Gc1 Gc1 Gc2 Gc Concrete strain ε c (x10 6 ) Figure 2. Typical concrete strain variation at midspan (Beam C1-212-D1-b) Advances in Structural Engineering Vol. 15 No

8 Serviceability Limit State of FRP RC Beams Table 5. Experimental load corresponding to the SLS of stresses in concrete Service load (compressive stress as Service load (compressive stress as Beam 60% of strength) 45% of strength) designation εc ( 10 6 ) Load P (kn) % of P u ε c ( 10 6 ) Load P (kn) % of P u C1-212-D % % C1-216-D % % C1-316-D % % C1-212-D % % C1-216-D % % C1-316-D % % C2-212-D % % C2-216-D % % C2-316-D % % C2-212-D % % C2-216-D % % C2-316-D % % C3-316-D % % This study provides further evidence that the relatively low stiffness of GFRP reinforcement can result in the development of significant concrete compressive stresses already at early stages of loading, and emphasizes the importance of considering carefully the behavior of FRP RC elements under defined service conditions Stresses in the flexural reinforcement Figure 3 shows a typical distribution of strain along the length of the GFRP reinforcement at different load levels. The vertical dashed lines in the figure indicate the location of the cracks as observed at service load. n general, large increases in the measured strain values were observed in correspondence with the opening of cracks at locations close to the strain gauges. For values of applied load inducing maximum concrete compressive stresses ranging from 45% to 60% of the concrete compressive strength, the corresponding rebar stress varied between 8% and 27% of its tensile strength. These values were lower than that at which creep rupture may become a concern according to fib methodology (fib 2007). AC 440.1R- 06 would limit the rebar tensile strength to 20% its design tensile strength Cracking Behaviour Crack spacing The experimental average and maximum crack spacing for different load steps were determined from the distance between the cracks that developed within the region of constant moment measured at the height of Rebar strain ε f (x10 6 ) Crack location P = 30 kn P = 25 kn P = 20 kn P = 15 kn P = 10 kn P = 8 kn (initiation of midspan crack) Distance from support (mm) P = 5 kn (before cracking) Figure 3. Typical strain distribution along the FRP reinforcement at predefined load values (Beam C1-216-D2-b) 660 Advances in Structural Engineering Vol. 15 No

9 Cristina Barris, Lluís Torres, Marta Baena, Kypros Pilakoutas and Maurizio Guadagnini % P u C1-212-D1 Experimental s r,max (mm) Theoretical s r,max (mm) Figure 4. Maximum experimental vs predicted crack spacing EC2 formulation the reinforcement. The experimental maximum crack spacing for the 24 beams tested in this study is compared to the theoretical models included in Eurocode 2 (Figure 4). The crack spacing for each beam was calculated at the load level at which cracking stabilized. A coefficient k 1 of 0.8, recommended in Eurocode 2 for deformed steel bars, was used when implementing Eqn 5. As shown in the figure, the use of such a value for the bond coefficient generally leads to an overestimation of the crack spacing. The method of least squares was subsequently applied to recalibrate the bond coefficient, k 1, and a value of 0.4 was obtained, indicating the superior bond between the GFRP bars used in this test program and concrete. Similar experimental data on concrete beams reinforced with different types of FRP bars would provide important data and assist in determining the values of the bond coefficient associated to specific FRP products Crack width The width of the cracks that developed within the constant moment zone was measured at every load step using an optical micrometer. The maximum and the average crack widths were recorded. Figure 5 shows a typical variation in the measured maximum crack width in the flexural zone compared with that predicted according to Eurocode 2 (Eqn 5, where k 1 = 0.8) and AC 440.1R-06 (Eqn 8, where k b = 0.8, 1.0 and corresponding to a bond behaviour better than or similar to that of steel bars and poor bond, respectively). t can be seen that the experimental maximum crack width can be predicted fairly well by both approaches if a bond coefficient of 1.0 is adopted. This provides further evidence of the good bond behaviour of the Load P (kn) % P u Beam a Beam b EC 2 AC 440 (k b = 1.4) AC 440 (k b = 1.0) AC 440 (k b = 0.8) Maximum crack width w max (mm) Figure 5. Maximum crack width evolution with load (Beam C1-212-D1) GFRP bars that were used. Moreover, for a service load of around 20 35% of the ultimate load, the measured maximum crack width remained smaller than 0.5 mm, which is considered to be an acceptable limiting service value (AC Committee ; fib 2007) Deflection Behaviour The load-deflection response of the tested beams was compared with the theoretical responses obtained by implementing the methods discussed in AC 440.1R-06, Eurocode 2, and SS Canada Design Manual no. 3, as well as Bischoff s approach (Bischoff 2005) and the CAN/CSA Standard. The experimental cracking load was used when implementing all of the above models. This was preferred to using analytical predictions to eliminate the influence of this parameter on the performance of the deflection models. The use of the experimental cracking load also allowed eliminating the possible influences on it of the inherent variability in the strength of concrete as well as shrinkage or size effects. Following the Eurocode 2 provisions, the curvature corresponding to a given applied moment was found and the corresponding deflections were obtained by double integration of the curvatures. The deflections were evaluated considering a linear constitutive relationship for concrete up to the service load. As shown in Figure 6, all of the experimental approaches compare reasonably well with the experimental data up to the service load (20 35% of the ultimate load). At load levels close to the cracking load, the load-deflection responses predicted by the CAN/CSA and SS Canada formulations are characterized by a large increase in deflections, and rapidly approach the behaviour of a fully cracked Advances in Structural Engineering Vol. 15 No

10 Serviceability Limit State of FRP RC Beams Load P (kn) %P u C1-212-D1 Uncracked state 20%P u Beam -a 10 Beam -b AC 440 Bischoff 5 EC-2 CAN/CSA Cracked state SS Midspan deflection δ (mm) Figure 6. Typical Load-deflection response (Beam C1-212-D1) element. This sudden loss in stiffness, however, was not observed during any of the experimental tests and can be attributed to the good bond characteristics of the GFRP bars used in this study and the resulting tension stiffening effect. Beyond the service range, all of the theoretical approaches examined here underestimate the experimental deflections. This could be attributed to the fact that, at higher load levels, shear induced deflections and other material and geometrical non-linearities become significant. 5. CONCLUSONS The design of concrete structures reinforced with FRP materials is likely to be controlled by the various criteria imposed at serviceability limit states (SLS). The work presented here has provided evidence that the principles underlying the design at SLS of steel RC can be applied to FRP RC elements. Several proposals based on modifications of design rules originally developed for steel RC were presented and discussed. Deflections of FRP RC beams within the service range can be adequately predicted by existing approaches. For higher loads, however, these equations result in lower values than the experimental ones, probably due to the influence of shear induced deflections and other non-linearities that are not taken into account by the current simplified equations. ACKNOWLEDGEMENTS The authors acknowledge support from the Spanish Government, Proj. BA (Ministerio de Educación y Ciencia), and from Schök Bauteile GmbH for the supply of FRP bars. The first author acknowledges the European project En-CORE, for the scholarship MTRN and the Catalan Government for the scholarship BE The second author acknowledges the support from the Spanish Government, contract JC (Mobility of Human Resources). REFERENCES AC Committee 318 (2008). Building Code Requirements for Structural Concrete and Commentary (AC ), American Concrete nstitute, Farmington Hills, Michigan, USA. AC Committee 440 (2006). Guide for the Design and Construction of Concrete Reinforced with FRP Bars (AC 440.1R-06), American Concrete nstitute, Farmington Hills, Michigan, USA. AC Committee 440 (2008). Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (AC 440.2R-08), American Concrete nstitute, Farmington Hills, Michigan, USA. Al-Sunna, R.A.S. (2006). Deflection Behaviour of FRP Reinforced Concrete Flexural Members, PhD Thesis, The University of Sheffield, Sheffield, UK. Barris, C., Torres, Ll., Turon, A., Baena, M. and Catalan, A. (2009). An experimental study of the flexural behaviour of GFRP RC beams and comparison with prediction models, Composite Structures, Vol. 91, No. 3, pp Benmokrane, B., Chaallal, O. and Masmoudi, R. (1996). Flexural response of concrete beams reinforced with FRP reinforcing bars, AC Structural Journal, Vol. 91, No. 2, pp Bischoff, P.H. (2005). Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber reinforced polymer bars, Journal of Structural Engineering, ASCE, Vol. 131, No. 5, pp Branson, D.E. (1997). Deformation of Concrete Structures, McGraw-Hill, New York, USA. CEB (1990). Model Code Design Code, Comité Euro- nternational du Béton, Thomas Telford Services Ltd, London, UK. CEN (2004). Eurocode 2: Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings (EN ), European Committee for Standardization, Brussels, Belgium. CNR (2007). Guide for the Design and Construction of Concrete Structures Reinforced with Fiber-Reinforced Polymer Bars (CNR-DT 203/2006), National Research Council, Rome, taly. CSA (2000). Canadian Highway Bridge Design Code (CHBDC-S6-00), Canadian Standards Association, CSA nternational, Rexdale, Ontario, Canada. CSA (2002). Design and Construction of Building Components with Fibre-Reinforced Polymers (CAN/CSA-S806-02), Canadian Standards Association, Mississauga, Ontario, Canada. Faza, S.S. and Ganga Rao, H.V.S. (1992). Pre- and post-cracking deflection behaviour of concrete beams reinforced with fibrereinforced plastic rebars, Proceedings of the 1 st nternational Conference on the Use of Advanced Composite Materials in Bridges and Structures (ACMBS ), Sherbrooke, Quebec, Canada, October. 662 Advances in Structural Engineering Vol. 15 No

11 Cristina Barris, Lluís Torres, Marta Baena, Kypros Pilakoutas and Maurizio Guadagnini Matthys, S. and Taerwe, L. (2000). Concrete slabs reinforced with FRP grids. : One-way bending, Journal of Composites for Construction, ASCE, Vol. 4, No. 3, pp fib (2000). Bond of Reinforcement in Concrete, State-of-Art Report, Prepared by Task Group Bond Models, nternational Federation for Structural Concrete, fib bulletin 10, Lausanne, Switzerland. fib (2007). FRP Reinforcement in RC Structures, Prepared by Task Group 9.3, nternational Federation for Structural Concrete, fib bulletin 40, Lausanne, Switzerland. Frosch, R.J. (1999). Another look at cracking and crack control in reinforced concrete, AC Structural Journal, Vol. 96, No. 3, pp StructE (1999). nterim Guidance on the Design of Reinforced Concrete Structures Using Fibre Composite Reinforcement, nstitution of Structural Engineers, SETO Ltd., London, UK. SS (2001). Reinforcing Concrete Structures with Fibre Reinforced Polymers, Design Manual No. 3, SS Canada Corporation, University of Manitoba, Manitoba, Canada. JSCE (1997). Recommendation for Design and Construction of Concrete Structures Using Continuous Fiber Reinforcing Materials, Concrete Engineering Series No. 23, Japanese Society of Civil Engineering, Tokyo, Japan. Pecce, M., Manfredi, G. and Cosenza, E. (2000). Experimental response and code models of GFRP RC beams in bending, Journal of Composite Construction, ASCE, Vol. 4 No. 4, pp Pilakoutas, K., Guadagnini, M., Neocleous, K. and Taerwe, L. (2007). Design guidelines for FRP reinforced concrete structures, Proceedings of the Advanced Composites in Construction, University of Bath, Bath, UK. Schöck Bauteile GmbH (2006). Schöck Bauteile GmbH, Germany. ( Toutanji, H.A. and Saafi, M. (2000). Flexural behavior of concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars, AC Structural Journal, Vol. 97, No. 5, pp Toutanji, H.A. and Deng, Y. (2003). Deflection and crack-width prediction of concrete beams reinforced with glass FRP rods, Construction and Building Materials, Vol. 17, No. 1, pp Yost, J.R., Gross, S.P. and Dinehart, D.W. (2003). Effective moment of inertia for glass fiber-reinforced polymer-reinforced concrete beams, AC Structural Journal, Vol. 100, No. 6, pp Advances in Structural Engineering Vol. 15 No

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