Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams

Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams

Engineering Structures xxx (2016) xxx–xxx Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate...

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Engineering Structures xxx (2016) xxx–xxx

Contents lists available at ScienceDirect

Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams C. Barris ⇑, L. Torres, I. Vilanova, C. Miàs, M. Llorens Analysis and Advanced Materials for Structural Design (AMADE), Polytechnic School, University of Girona, Campus Montilivi s/n, 17071 Girona, Spain

a r t i c l e

i n f o

Article history: Received 15 April 2016 Revised 16 September 2016 Accepted 3 November 2016 Available online xxxx Keywords: Reinforced concrete Fibre reinforced polymers Crack width Crack spacing DIC

a b s t r a c t Fibre Reinforced Polymers (FRP) have been proven to be adequate substitutes for steel reinforcement under aggressive environments for flexural Reinforced Concrete (RC) elements. Their mechanical properties, basically their lower modulus of elasticity, derive in larger crack widths and deflections, in particular when Glass-FRP (GFRP) bars are used. Moreover, their different bond behaviour, mainly due to their mechanical properties and different surface configurations, make necessary to assess the available equations to determine crack width need to be assessed. This paper presents a study on the cracking behaviour of GFRP RC elements based on the results of an experimental programme involving 15 beams. The paper studies the influence of the reinforcing material, //qeff ratio, concrete cover, stirrup spacing and bond between the concrete and the reinforcement. For this purpose, two different types of GFRP and steel bars were used. The cracking behaviour (crack width and spacing) in the pure bending zone was analysed up to the service load. Crack width was consistently acquired by using a Digital Image Correlation (DIC) technique. The 2D full-field displacements of the pure flexural zone were registered using 4 digital cameras and commercial software that enables the evolution of the specimen cracks to be analysed. Finally, bond coefficients have been adjusted to different formulations in terms of crack spacing and crack width. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction In recent decades, Fibre Reinforced Polymer (FRP) bars have emerged as an alternative to steel in Reinforced Concrete (RC) members due to their non-corrosive properties and magnetic neutrality. However, the mechanical properties of FRP bars, basically their lower modulus of elasticity and different bond behaviour, can yield to large crack widths and deflections. As a result, the design of concrete elements reinforced with FRP bars is often governed by the Serviceability Limit States (SLS) [1–3]. The flexural response of FRP RC elements has been widely investigated and there are many studies concerning deflections in the literature [3–10], but the number of studies dealing with cracking behaviour is still limited [3,8,11–13]. Although crack width of FRP RC members can be relaxed because of the non-corrosive properties of FRP bars, it does need to be controlled to ensure other important serviceability aspects, such as appearance or being watertight. It is well known that due to the low capacity of concrete under tensile stresses, cracking is a phenomenon that cannot be avoided in RC elements under tensile or bending forces. From as early as the ⇑ Corresponding author.

1940s through to present day, there have been many investigations concerning different theories for calculating crack width for steel RC elements [14–22]. Flexural cracks are formed in RC members when the tensile strain in concrete reaches its tensile deformation capacity. At the crack, the tensile force is carried by the reinforcement, and it is considered that at a certain distance, usually referred to as the transfer length, composite action is attained and both the concrete and the reinforcement carry the tensile force with compatibility of strains. Along the transfer length, a slip is assumed which depends on the bond capacity between the concrete and the reinforcement. According to this, crack width in RC flexural members mainly depends on the bond stress between the concrete and the rebar, cover, bar spacing, //qeff ratio, and strain level of the reinforcement [15]. Other theories that do not consider slip in the first stage of cracking [16,17] and that plane sections do not remain plain at the cracked section are also found. In this case, the crack spacing is dependent on the concrete cover c (Eq. (1), [16]) and on the //qeff ratio (Eq. (2), [17]);

wm ¼ sm  em ¼ k  c  em

ð1Þ

wm ¼ sm  em ¼ ½k1  c þ k2  ð/=qeff Þ  em

ð2Þ

E-mail address: [email protected] (C. Barris). http://dx.doi.org/10.1016/j.engstruct.2016.11.007 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Barris C et al. Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.11.007

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where wm is the mean crack width, sm is the mean crack spacing, em is the mean difference of the strain in reinforcement and the strain in concrete, k and k2 are constants that depend on the distribution of bond stresses along the bar, k1 is a multiplication factor of the cover, / is the bar diameter and qeff is the effective reinforcement ratio. The effective reinforcement ratio is usually defined as the reinforcement ratio taking into account the effective area of concrete in tension, Ac,eff, and it is interpreted by [18] as the influence of the stress distribution on the effective tensile area of concrete, where internal cracks are created. Empirical expressions, derived from a large database of steel RC elements, to calculate the maximum crack width are also available in the literature [19,20]. In those equations, the main parameters are the strain of the tensile bar and the effective area of concrete, albeit the concrete cover being a geometrical parameter of minor importance. In some cases, these equations have been adopted by design codes and guidelines for FRP RC elements. For example, ACI 440.1R-01 [23], adopted the approach in [19], with the introduction of a bond coefficient kb to take into account the different bond behaviour of FRPs with respect to steel (Eq. (3)).

wmax ¼

p ffiffiffiffiffiffiffiffiffiffiffi 2:2 3  b  kb  f f  dc  A Ef

ð3Þ

In Eq. (3), Ef is the modulus of elasticity of the rebar, b is (h  x)/ (d  x), h is the height of the beam, x is the neutral axis depth, d is the effective depth, ff is the tensile stress in the reinforcement, dc is the concrete cover and A is the effective area of surrounding concrete divided by the number of bars. ACI 440.1R-06 [24], in turn, adopted the equation in [20] in order to include the effect of bar spacing s (Eq. (4)).

wmax ¼ 2 

ff  b  kb  Ef

rffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 3 2 dc þ 2

ð4Þ

To sum up, the different theories to calculate crack width for steel RC elements state that it is mainly affected by the tensile strain of the rebar, the bond behaviour between the concrete and the rebar, the concrete cover and the distance between bars. Some of these theories have been adapted to FRP RC elements by introducing a bond coefficient, which should be provided, but at present very few studies show particular values according to their experimental data [11,25–27]. On the other hand, crack width has been traditionally measured in experiments with optical magnifiers or microscopes, although such techniques have shown to be subjected to a lack of homogeneity [22]. Other methods, such as the placement of transducers once the crack has appeared, provide greater accuracy in the results, but imply that the test has to be stopped, and only the data at the position where the transducer is placed is registered. Deriving the crack width from the elongation of layer where the reinforcement lies [22] is another means of capturing the mean crack width, but with this technique the test has also to be stopped and few data are recorded. Digital Image Correlation (DIC) is an optical and contactless measurement technique based on the acquisition and treatment of pictures of a previously defined field of interest to obtain fullfield displacements and deformations during the test. In the past decade, DIC has been introduced in the experimental measurement field of structural elements and has been proven to be a powerful tool for measuring full-field absolute and relative displacements [28–30]. The objective of the paper is to analyse the effect of different parameters affecting the cracking patterns of flexural elements reinforced with different types of Glass-FRP (GFRP) and steel bars, in order to assess the influence of these parameters on the cracking behaviour. To this purpose, an experimental programme involving

15 RC beams was performed. Two different GFRP bars and steel bars were used. The measure of crack widths was consistently acquired by using the DIC technique over the entire pure flexural zone. The crack spacing and crack width were registered, and are compared and discussed. An analysis of the main parameters involving cracking behaviour is performed and different bond coefficients are adjusted to the experimental data.

2. Experimental programme 2.1. Experimental test setup The experimental programme aimed at evaluating the influence of the type of reinforcement (implying different modulus of elasticity and surface characteristics), the reinforcement ratio, the concrete cover and the stirrup distance on the crack spacing and crack width of flexural RC elements. For this reason, 15 beam specimens internally reinforced with different types of GFRP or steel bars were tested under a four-point bending configuration. The beams were 180 mm wide, 240 mm high and 2800 mm long, having a clear span of 2600 mm. The flexural span was 1700 mm and was reinforced with different amounts and types of GFRP or steel stirrups (Table 1) to analyse their influence on the cracking patterns. The shear span was 450 mm long and was reinforced with 7/6 mm steel stirrups to avoid shear failure (Fig. 1). The specimens were designated as Mat-Reinf-Cov-Sep, where Mat denotes the material of the reinforcement (G1 or G2, for FRP type G1 or G2, respectively), Reinf the number and diameter of the reinforcement (i.e. 212 for 2 bars of 12 mm of diameter), Cov the concrete clear cover, and Sep the distance between the stirrups. In the case where FRP-G2 stirrups were provided this was indicated by the letter G at the end of the specimen designation. Table 1 summarises the characteristics of the different specimens. The effective reinforcement ratio (qeff) is calculated according to Eurocode 2 [31] taking into account the effective area of concrete in tension surrounding the reinforcement and the experimental dimensions of the reinforcing bars. A hydraulic jack applied the load onto the specimens through a spreader beam. The load was applied in a displacement control mode at a displacement rate of 0.5 mm/min.

2.2. Material properties The target concrete compressive strength for all beam specimens was 30 MPa. The specimens were cast in two different batches in lab conditions with a conventionally vibrating procedure. Batch 1 was used for specimens with FRP-G1 and steel reinforcement and Batch 2 for specimens with FRP-G2 reinforcement. The cement type for both concrete mixtures was I-42,5R with a content of 275 kg/m3. The maximum aggregate size was 15 mm, and the water/cement relationship was 0.36 for Batch 1 and 0.44 for Batch 2. The experimental compressive strength and modulus of elasticity were determined from six cylinder tests, for each batch, according to UNE-EN 12390-3:2003 and ASTM C469-02 standards, respectively, and are summarised in Table 2. The mechanical and geometrical properties of the different bars used as internal reinforcement are summarised in Table 3. The effective bar diameters were obtained from normalised tests to determine the cross-sectional areas of the rebars, according to ACI 440.3R [32] are shown together with the mechanical properties obtained from uniaxial tension tests (three tests for each bar type and diameter).

Please cite this article in press as: Barris C et al. Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.11.007

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C. Barris et al. / Engineering Structures xxx (2016) xxx–xxx Table 1 Test specimens. Reinforcement

a b

Specimen

N.bars

Bar type

G1-216-25-150 G1-216-25-250 G1-216-25-000 G1-212-25-150 G1-212-40-150 G1-212-55-150 G2-213-25-150 G2-213-25-000 G2-310-25-000 G2-213-25-150G G2-213-25-250G G2-216-25-150 G2-313-25-150 S-212-25-150 S-212-25-000

2/16 2/16 2/16 2/12 2/12 2/12 2/13 2/13 3/10 2/13 2/13 2/16 3/13 2/12 2/12

FRP-G1 FRP-G1 FRP-G1 FRP-G1 FRP-G1 FRP-G1 FRP-G2 FRP-G2 FRP-G2 FRP-G2 FRP-G2 FRP-G2 FRP-G2 Steel Steel

Cover

Stirrupsa Type

Sep.

25 25 25 25 40 55 25 25 25 25 25 25 25 25 25

Steel Steel Steel Steel Steel Steel Steel Steel Steel FRP-G2 FRP-G2 Steel Steel Steel Steel

150 250 –b 150 150 150 150 –b –b 150 250 150 150 150 –b

//qeff

Concrete Batch

429 429 429 597 601 605 596 596 525 596 596 468 386 577 577

1 1 1 1 1 1 2 2 2 2 2 2 2 1 1

Stirrups placed in the flexural zone. No stirrups provided in the flexural zone.

Fig. 1. Geometric details of the tested beams (in mm).

Table 2 Mechanical properties of concrete.

Compressive strength, fc (MPa) Modulus of elasticity, Ec (GPa)

Batch 1

Batch 2

33.1 ± 0.3 24.8 ± 1.9

34.3 ± 0.5 27.9 ± 1.2

Fig. 2 shows the different surface characteristics of the bars: an indented surface for FRP-G1 and a helically wrapped surface along with a sand coating for FRP-G2. 2.3. Digital image correlation technique Consistently measuring the crack widths of the beams throughout the tests was one of the objectives of this study. To this purpose, the Digital Image Correlation (DIC) technique was used. The DIC system is a contactless measuring technique that allows displacements and deformations of the surface of an object under any kind of loading to be determined. The system has a number of high-resolution digital cameras and specialised software that processes the data in order to quantify the displacements and deformations. The procedure to calculate displacements is based

on comparing two digital images of the sample surface captured at two different stages during the test. The DIC technique typically uses two different configurations: a 2D configuration, where one digital camera captures the 2D displacements of a defined Field of View (FOV), and a 3D configuration, in which two cameras are needed for a given FOV to capture the 2D displacements and the out-of-plane displacement. For this paper, where only the difference of displacements is computed, the out-of-plane displacement was ignored for calculations and the 2D configuration was used for all specimens. Nevertheless, for comparison purposes, a 3D configuration was placed in the rear face of beams G2-213-25-000 and G2-309-25-000 and the vertical displacement of the midspan section was compared between the two 2D systems and the 3D system. An average relative error between the 2D and 3D systems of 1% was obtained. The test setup comprised 4 high-resolution digital cameras SONY IT CCD ICX655 with a resolution of 2452  2056 pixels, an image sensor format of 8.5  7.1 mm and a maximum temporary resolution of 9 fps. HETLER DX15 and DF15 lamps were used to illuminate the measurement surface. The lenses had an f-number of 1.4 and a focal length of 8.2 mm. The cameras recorded pictures at regular time intervals during each test (2 pictures/s).

Table 3 Properties of GFRP and steel reinforcement. FRP-G1

FRP-G2

Steel

Diameter, /(mm)

12

16

10

13

16

12

Effective diameter, /eff (mm) Modulus of elasticity, Ef (GPa) Ultimate tensile strength, ffu (MPa) Ultimate tensile strain (%)

13.2 64.4 ± 41.7 (60) 1231.5 ± 13.1 (1000) a (0.73)

17.4 69.1 ± 1.4 (60) 1313.3 ± 18.4 (1000) a (0.73)

10.3 45.7 (46) ± 0.6 a (827) a (1.94)

13.5 45.9 ± 0.3 (46) a (827) a (1.79)

16.6 48.8 ± 0.3 (46) a (758) a (1.64)

11.8 201.2 ± 0.1 (200) a (550) a (0.22)

(Values provided by the manufacturer in brackets). a Values not available during the test.

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FRP-G1 FRP-G2 Steel Fig. 2. Bar types and surface characteristics.

The surface preparation of the tested specimens consisted of obtaining a random speckle pattern using a coating of white paint followed by a black airbrush mist of paint. The mean diameter per speckle was 4–6 pixels from the camera [33] and its dimensions were changed according to the distance between the specimen and the camera. In order not to affect uncertainties, special care was taken to regularly paint the surface. The correlation between the deformed images and the undeformed reference image was used to obtain two-dimensional field of displacements for all points of the specimen surface using commercially available software [34]. The correlation criterion was the normalised squared differences, with an interpolation of 8-tap splines and a Gaussian subset weights. For this study, a subset size of 21  21 pixels was used with a step size of 5 pixels. Different FOV were investigated, ranging from 1350  240 mm to 2000  240 mm, except for beam G1-212-25-150, where only crack spacing is studied and this was captured manually. In Table 4, the details related to the 2D configuration are presented for each beam. The DIC technique was previously tested in similar tests in [35]. However, and for comparison purposes, an LVDT was placed in the midspan section (Fig. 3a) to measure the maximum vertical displacement of each specimen, which was compared to the DIC results. For all specimens, the displacement obtained by the LVDT and the DIC were identical. 3. Experimental results on crack spacing In this section crack spacing is evaluated at the stabilised cracking load, which is defined as the experimental load at which no more cracks are created. The stabilised cracking load was 1.2–2.5 times the cracking load, and its measured value is shown in Table 5. The distance between two consecutive cracks was determined center-to center of the crack opening, at the level of the reinforcement. A summary of the test results in terms of minimum, mean, maximum and standard deviation of crack spacing (sr,min, sr,mean, sr,max and sst,dev, respectively) is shown in Table 5. For better interpretation of the results, Fig. 4 shows the location of the cracks

between point loads, as well as the stirrup position using black lines at the bottom face of the beams. The cracks considered for the crack width computation are enumerated numerically and correlatively, and branches of principal cracks follow the numbering of the principal crack with a prime in their number. From Table 5 it is observed that, on average, the maximum crack spacing is 1.32 times the mean crack spacing and 2.14 times the minimum crack spacing. These values are in accordance with those found in the literature [14]. The general theories of cracking indicate that the main parameters affecting crack spacing are the //qeff ratio, the concrete cover and the bond between the concrete and the reinforcement [31], which have also been adopted in this work. The following subsections analyse the influence that these parameters have on the crack spacing in the tested specimens. In addition, the effect of the stirrup spacing, which is not generally taken into consideration for crack spacing calculation, is also studied. 3.1. Influence of //qeff ratio The influence of //qeff ratio on crack spacing is generally attributed to its effect on the transfer length [15] and to internal cracks in the vicinity of the crack [18]. The effect of //qeff ratio on the experimental crack spacing is shown in Table 6, through two comparisons: specimens G2-216-25-150 and G2-313-25-150, and specimens G2-213-25-000 and G2-310-25-000. In both comparisons, specimens have a similar reinforcement ratio, identical clear cover, the same distance between stirrups, but different //qeff ratio. It is observed that the //qeff ratio influences crack spacing: the bigger the //qeff ratio, the larger the crack spacing. This result, which is in accordance with the general formulation for calculating crack spacing, is observed for both maximum and mean values. 3.2. Influence of concrete cover Concrete cover is another main parameter that theoretically affects crack spacing. According to several models of cracking, crack spacing increases with the increase of the cover. The effect of the concrete cover on the crack spacing is evaluated by comparing the results of beams G1-212-25-150, G1-212-40-150 and G1212-55-150 in Table 7. For this comparison, the clear cover changes from 25 to 40 and 55, while the bar diameter and the stirrup spacing are identical, and the //qeff ratio is almost constant. In Fig. 4, it is observed that for specimens with higher covers (G1-212-40-150 and G1-212-55-150), cracks are created independently of the location of the stirrups. However, for the specimen with cover equal to 25 mm (G1-212-25-150), cracks are almost always created at the location of stirrups (separated at 150 mm), and no more cracks appear in between them, thus masking the effect of the concrete cover. Moreover, it is experimentally

Table 4 2D DIC setup for each specimen.

Focal length (mm) Distance from surface (mm) No. of cameras Recording resolution (pixels) Conversion factor (mm/pixel) Subset size (pixels) Step size (pixels) Image displacement accuracya(pixels) Object displacement accuracy (mm) a

G1 and S specimens

G2 specimens with stirrups in the central zone

G2 specimens without stirrups in the central zone

8 mm 660 mm 4 2452  2056 0.289 21  21 5 0.023 0.007

8 mm 475 mm 4 2452  2056 0.211 21  21 5 0.021 0.005

8 mm 905 mm 2 2452  2056 0.305 21  21 5 0.030 0.009

67% confidence for the match.

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Fig. 3. DIC setup (a) general view and (b) speckle pattern.

Table 5 Cracking load, stabilised cracking load, number of cracks analysed and crack spacing (minimum, maximum, mean and standard deviation) at stabilised cracking load. Specimen

G1-216-25-150 G1-216-25-250 G1-216-25-000 G1-212-25-150 G1-212-40-150 G1-212-55-150 G2-213-25-150 G2-213-25-000 G2-310-25-000 G2-213-25-150G G2-213-25-250G G2-216-25-150 G2-313-25-150 S-212-25-150 S-212-25-000 a

Cracking load (kN)

Stabilised cracking load (kN)

18.6 16.6 20.6

22.6 29.5 30.6

a

a

15.4 17.2 14.2 17.8 16.8 14.0 14.1 15.0 14.2 19.8 20.6

34.5 35.8 22.9 41.0 41.2 28.3 32.9 24.8 25.4 29.6 35.6

N. of cracks analysed

9 11 10 10 12 10 9 8 8 9 11 9 9 10 11

Experimental crack spacing, s (mm) smin

smax

smean

sst.dev.

134.3 76.9 125.7 97.0 84.0 53.1 90.5 93.4 100.2 71.3 69.3 96.9 55.1 93.6 75.9

163.6 140.3 173.9 164.6 149.5 191.9 207.5 196.9 187.9 173.0 198.8 181.4 176.1 179.7 178.3

149.2 119.7 145.6 142.6 114.4 154.0 160.8 145.3 135.3 120.9 129.5 152.8 107.5 139.1 121.5

9.5 18.6 16.6 20.6 39.2 40.7 37.3 37.7 29.4 35.0 40.5 43.5 39.3 27.8 31.5

Experimental crack spacing was only analysed at 60 kN.

observed that higher covers provide higher values of crack spacing, although, the standard deviation value increases with the cover, which indicates that high values of cover also imply a higher scatter of results. The effect of concrete cover on crack spacing in steel RC has been widely discussed in the literature [36,22,18,37,17,38]. The experimental crack patterns obtained in this research for FRP RC highlight the influence of cover on crack spacing at the surface of the specimen (higher cover implies higher crack spacing). The effect of cover is further explained in [22] as a need to transmit tension stresses that are generated at the bar-concrete interface to the effective concrete area surrounding the bar. Moreover, the influence of cover is also related to the internal cracks and whether or not these cracks eventually arrive at the surface of the specimen and become visible.

location of the stirrup and then new cracks are created between stirrups when there is enough distance between them (G1-21625-250). The same behaviour is observed for FRP-G2 RC specimens, independently of the material used for the stirrup (either steel or FRP-G2). For the steel RC specimens, in S-212-25-150, where stirrup spacing is 150 mm, in almost all cases cracks first develop at the location of stirrups, and in S-212-25-000, where no stirrups are provided, cracks develop at a shorter distance and branches of cracks appear. Finally, from Fig. 4 and Table 7, and coinciding with the previous subsection, it is observed that the effect of stirrup spacing diminishes as concrete cover increases, as it was previously observed in [22] for steel RC elements.

3.4. Influence of bond between concrete and reinforcement 3.3. Influence of stirrup spacing Stirrup spacing is a variable that is not usually included in crack spacing calculations. Furthermore, most studies dealing with cracking of steel RC avoid the presence of stirrups because of the probable influence of them on the location of the cracks [22]. In this section the influence of stirrup spacing on crack spacing in a GFRP and steel RC flexural member is investigated through several specimens (Fig. 4, Table 8). Observing the surface of the beams in Fig. 4, it is clearly seen that cracks mainly develop at the location of stirrups (NB: all specimens studied in this section had the smallest cover of 25 mm). In the case of the FRP-G1 RC specimens, cracks first appear at the

Bond between concrete and reinforcement influences cracking pattern: bond increase diminishes the transfer length and consequently diminishes crack spacing and crack width. The general formulation for crack spacing proposes a bond coefficient that multiplies the //qeff ratio. Well-established values for the bond coefficient are usually recommended in design codes for steel RC. However, for FRP RC elements complete provisions for the bond coefficient are yet to be proposed, though some studies provide particular values for their experimental data, for either crack spacing or crack width [11,27]. In this section, the bond coefficient is adjusted to the experimental crack spacing for the three types of reinforcing bars,

Please cite this article in press as: Barris C et al. Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.11.007

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Fig. 4. Distribution of flexural cracks between point loads with the location of stirrups marked with a black line.

following the least squares methodology. The sum of the squared residuals (Resi), defined as the difference between the experimental and theoretical crack spacing, is derived and equalled to zero to obtain the optimum value of the bond coefficient kb. The Eurocode 2 [31,39] formulation to calculate the maximum and mean crack spacing is used for this purpose. The resulting adjusted bond coefficients for the studied formulations are shown in Table 9. For the calculation of k1 adjusted to the maximum crack spacing, specimens G1-212-40-150 and G1-212-55-150 have been omitted. This is because the actual relationship between the maximum and mean experimental crack spacing was 1.33 (lower than the value of 1.7 typically assumed in the codes), and consequently, the contribution of the first term (3.4c) of the Eurocode 2 (2004) equation on the total crack spacing was unreasonable for those specimens having large covers. The bond coefficient obtained is generally similar between the different rebar types, indicating no significant differences. However, rebar type FRP-G2 presents a higher bond coefficient compared to steel or FRP-G1 bar, although this is probably due to

Fig. 4 (continued)

surface configuration differences. Moreover, k1 adjusted to the mean crack spacing is higher than that of the adjusted to the maximum value. This is attributed to the actual relationship between the maximum and mean experimental crack spacing (1.32 times instead of 1.7 times). In Fig. 5, the experimental versus theoretical, both maximum and mean crack spacing, are compared by using a typical bond coefficient of 0.80 and the adjusted bond coefficient in Table 9. Whilst maximum crack spacing is generally overestimated by Eurocode 2 (2004) approach, its mean value is somehow underestimated by Eurocode 2 (1992) formulation. As expected, when the adjusted bond coefficient is used, a better fit is obtained between the experimental and theoretical results.

Please cite this article in press as: Barris C et al. Experimental study on crack width and crack spacing for Glass-FRP reinforced concrete beams. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.11.007

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C. Barris et al. / Engineering Structures xxx (2016) xxx–xxx Table 6 Crack spacing comparing //qeff ratios. Specimen

cinf

q (%)

//qeff

Sep.

smax

smean

G2-213-25-000 G2-310-25-000 G2-216-25-150 G2-313-25-150

25 25 25 25

0.8 0.7 1.2 1.2

595 525 468 386

– – 150 150

196.9 187.9 181.4 176.1

145.3 135.3 152.8 107.5

Table 7 Crack spacing comparing concrete covers. Specimen

cinf

q (%)

//qeff

Sep.

smax

smean

G1-212-25-150 G1-212-40-150 G1-212-55-150

25 40 55

0.7 0.8 0.9

597 601 605

150 150 150

164.6 149.5 191.9

142.6 114.4 154.0

Table 8 Crack spacing comparing stirrup spacing. Specimen

cinf

q (%)

//qeff

Sep.

Type

smax

smean

G1-216-25-150 G1-216-25-250 G1-216-25-000 G2-213-25-150 G2-213-25-000 G2-213-25-150G G2-213-25-250G S-212-25-150 S-212-25-000

25 25 25 25 25 25 25 25 25

1.3 1.3 1.3 0.8 0.8 0.8 0.8 0.6 0.6

428 428 428 597 597 597 597 577 577

150 250 – 150 – 150 250 150 –

Steel Steel Steel Steel Steel FRP G2 FRP G2 Steel Steel

163.6 140.3 173.9 207.5 196.9 173.0 198.8 179.7 178.3

149.2 119.7 145.6 160.8 145.3 120.9 129.5 139.1 121.5

Table 9 Bond coefficient k1 for the maximum and average experimental crack spacing.

Eurocode 2 (2004) Eurocode 2 (1992)

Expression

Coef.

FRP-G1

FRP-G2

Steel

smax ¼ 3:4  c þ 0:425  k1  k2  /=qeff

k1

0.47

0.70

0.62

k1

0.79

1.12

0.87

smean ¼ 50 þ 0:25  k1  k2  /=qeff

Notation: k1, kb: bond coefficient (k1: 0.8 for high bond and 1.6 for smooth bars); k2: 0.5 for bending and 1.0 for pure tension;/: bar diameter; qeff: effective reinforcement ratio; c: concrete cover.

Fig. 5. Experimental versus theoretical (a) maximum and (b) mean crack spacing, with a bond coefficient k1 of 0.80 and the adjusted bond coefficient.

4. Experimental results on crack width

4.1. Crack width along the height of the beam

This experimental programme presents the results of crack width monitoring consistently acquired by the DIC technique. The crack width is obtained by the difference between the displacement values of two points, each one at one side of the crack and at the same height. A total of 8–12 cracks per specimen are registered and taken into account in this paper (Fig. 4).

The DIC system allows the full field of displacements for a given FOV to be obtained. Hence, the different values of crack width along the height of the beam can easily be obtained. Fig. 6 represents two different cases of the crack width along the height that have been found for several load values. Both cases belong to G2213-25-150G specimen. For the case of Fig. 6a, the crack progres-

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Fig. 6. Typical case of crack width along the height of the beam.

sively grows from 15 kN until the end of the test in an almost linear manner. Below the position of the reinforcement, crack keeps growing at an almost linear rate, as it is assumed in some design guidelines (CAN/CSA-S806 [40] or ISIS Canada [41]). For the case of Fig. 6b, it is found that the crack opens at about 22.5 kN and crack width grows in an almost linear manner until the height of the reinforcement. Just at the location of the bar, there is a small reduction of the crack width, which could be attributed to the higher stiffness of the bars than that of the concrete around them. Below this position, no linear behaviour is observed, especially at the bottom of the beam. This effect can be attributed to the fact that the deformation field near the bars and near the edges of the elements can be considerably disturbed [36]. Additional factors that may play a role in the crack profile can be related to the effect of curvature in flexural elements (i.e. lower crack width is expected above the reinforcement and larger is expected below) [24] and to the inherent high scatter associated with cracking process due to non-homogeneous nature of concrete that may affect the position and effect of internal cracks. 4.2. Minimum, maximum and mean crack width A summary of test results in terms of maximum, minimum, mean and standard deviation of the crack width at the height of the reinforcement at the stabilised cracking load (45 kN) is given in Table 10. The maximum crack width at the bottom of the beam at 45 kN, which will be later used in the paper to adjust crack width to theoretical models, is also included in this table. Beam

G1-212-25-150 is excluded from this study because only crack spacing was acquired. From Table 10, it is seen that, on average, the maximum crack width at the height of the reinforcement is 1.36 times the mean value, and it is 0.87 times the maximum crack width at the bottom of the beam. These values are similar to those found in previous studies [11]. In Fig. 7, the experimental mean crack width versus the applied load of all the specimens is shown and several comparisons are made. Fig. 7a and b shows the effect of the reinforcement ratio on the crack width. In general, as expected, the higher the reinforcement ratio is, the higher the stiffness of the section and consequently the lower the crack width will be. It is also observed that specimens having similar reinforcement ratios (2/16 and 3/ 13 in Fig. 7a) provide close values of the crack width and with slightly higher values for larger bar diameter and bar spacing. This trend is more difficult to observe when no stirrups are placed (Fig. 7b). Fig. 7c shows a comparison between specimens reinforced with two 16 mm bars, identical cover and stirrup spacing but different types of bar. The specimen reinforced with FRP-G1 bars, which have higher modulus of elasticity and a indented surface, presents narrower crack widths than those of the specimen reinforced with FRP-G2 bars, as expected. Fig. 7d shows specimens with the same reinforcement ratio but different materials (S for steel and G1 for FRP-G1) and different stirrup spacing. The effect of the reinforcement stiffness is clearly shown, with the mean crack width of specimen G1-212-25-150

Table 10 Crack width at the load of stabilised cracking (45 kN). Specimen

G1-216-25-150 G1-216-25-250 G1-216-25-000 G1-212-40-150 G1-212-55-150 G2-213-25-150 G2-213-25-000 G2-310-25-000 G2-213-25-150G G2-213-25-250G G2-216-25-150 G2-313-25-150 S-212-25-150 S-212-25-000

Crack width (w) at the height of the reinforcement, mm

Maximum crack width at the bottom of the beam, mm

wmin

wmax

wmean

wst.dev.

0.24 0.19 0.20 0.17 0.35 0.46 0.22 0.32 0.20 0.18 0.24 0.12 0.06 0.08

0.30 0.33 0.29 0.71 0.68 0.67 0.70 0.62 0.63 0.63 0.48 0.39 0.20 0.21

0.26 0.24 0.23 0.40 0.59 0.58 0.48 0.50 0.50 0.42 0.35 0.27 0.16 0.13

0.02 0.04 0.03 0.16 0.11 0.08 0.19 0.09 0.14 0.15 0.07 0.10 0.04 0.05

0.33 0.37 0.34 0.93 0.90 0.72 0.77 0.63 0.93 0.69 0.54 0.42 0.24 0.21

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Fig. 7. Experimental mean crack width depending on the load.

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bigger than that of S-212-25-XXX. There is a slight effect of the stirrup spacing observed for specimens S-212-25-XXX, in accordance with the crack spacing observed in the previous section: S212-25-150 with stirrups at 150 mm presents moderately higher crack spacing that specimen S-212-25-000 without stirrups. Fig. 7e and f, and also Fig. 7d, show the effect of the distance between stirrups on crack width. Although stirrup spacing is proven to have an effect on the creation of cracks, this parameter does not significantly contribute to the mean crack width. Finally, Fig. 7g shows the influence of the effective depth (by changing the concrete cover) on the crack width. Higher values of the cover imply lower effective depth and lower stiffness of the section, which derive in higher values of the reinforcement strain for the same load. This effect is evident in Fig. 7g: the lower the effective depth is, the higher the crack width. The same behaviour and trends indicated for the mean crack width are also observed for the maximum crack width.

4.3. Bond coefficient adjusted to the experimental maximum crack width As previously stated, the influence of bond between concrete and reinforcement on crack width is one aspect that needs to be studied further for FRP RC members. In this section a bond coefficient kb is adjusted to the experimental maximum crack width for the three types of reinforcing bars by using different formulations from design codes and guidelines. The bond coefficient is calculated at different load levels between 45 kN (an upper bound value of the stabilised cracking load) and 60 kN (3–3.5 times the cracking load, assumed as an upper bound value for the service load). Following the least squares methodology, kb is adjusted to the experimental data. CAN/CSA-S806 [40], ISIS Canada [41] and JSCE [42] formulations are used for this purpose. Their corresponding equations compute the maximum value of crack width. Since these equations calculate

Table 11 Bond coefficient kb for the maximum crack width. Expression CAN/CSA-S806 ISIS Canada JSCE

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi 2 w ¼ 2   b  kb  dc þ 2s pffiffiffiffiffiffiffiffi f w ¼ 2:2  Eff  b  kb  3 dc A ff Ef

w ¼ kb  ð4c þ 0:7  ðs  /ÞÞ 

ff Ef

FRP-G1

FRP-G2

Steel

1.20 ± 0.01

1.35 ± 0.08

1.21 ± 0.04

1.21 ± 0.01

1.31 ± 0.06

1.33 ± 0.05

0.94 ± 0.01

1.00 ± 0.04

0.98 ± 0.03

Notation: ff: stress in the reinforcement; Ef: modulus of elasticity of the reinforcement; b: (h  x)/(d  x); c: concrete cover measured from the bottom of the beam to center of the bar; s: longitudinal FRP bar spacing; Es: modulus of elasticity of steel; A: effective tension area of concrete surrounding the flexural tension reinforcement and having the same centroid as the reinforcement, divided by the number of bars.

Fig. 8. Experimental versus theoretical maximum crack width, with a bond coefficient kb of 1.0 and the adjusted bond coefficient, for (a) CAN/CSA-S806, (b) ISIS Canada, and (c) JSCE design codes.

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the effect of the cover in a different proportion, and the experimental programme only had specimens with different concrete covers with FRP-G1 reinforcement, beams G1-212-40-150 and G1-21255-150 have been excluded from this adjustment, in order to take into account only the effect of the type of reinforcing bar. The results are shown in Table 11. The results obtained in Table 11 shows that FRP-G1 bars provide bond coefficient values slightly lower than those for FRP-G2 and steel. The main reason for this could lie in the type of bar and the surface configuration of the bars. In Fig. 8, a comparison between the experimental and the theoretical maximum crack width is shown for the three empirical equations used in this study, at the load stages of 45 kN (upper bound value for the stabilised cracking load) and 60 kN (estimated service load), for all the beam specimens considered in this part. The theoretical maximum crack width is calculated using a reference bond coefficient kb equal to 1 and the adjusted bond coefficient shown in Table 11. As expected, using the adjusted bond coefficient provides closer values to the experimental ones. However, it should be taken into account that these bond coefficients have been adjusted to the available data in this work, and more experimental and reliable data should be needed to assess their goodness of fit.

5. Conclusions This paper presents an experimental study on the evaluation of the cracking of GFRP RC flexural members. Sixteen RC beams reinforced with different types of GFRP bars and steel have been tested up to their service load, and crack width and spacing has been consistently recorded using the DIC technique. Based on the work presented in this paper, the following conclusions can be drawn.  The adopted 2D full-field displacement measurement technique proved to be a valuable tool in assessing the cracking behaviour of the tested RC beams over the entire loading range. The DIC technique allows not only the crack width at one single position to be acquired, but also the full range of values along the height of the crack.  The tests confirmed that crack spacing increases with //qeff ratio. Stirrup spacing has a direct effect on crack spacing, especially for those specimens with low concrete cover, where the first cracks initiate at the location of stirrups and, in some cases, other cracks appear in between as the load increases. In general terms, crack spacing increases with cover, although high values of cover imply a higher scatter of results.  The crack width along the height of the beam has been examined and different patterns have been obtained. In some cases, crack width grows in an almost linear manner. However, in some cracks, at the height of the reinforcement, the value of crack width diminishes, probably due to the higher stiffness of the bars than that of the concrete around them.  The mean crack width was calculated for every specimen as the mean value of the 8–12 cracks created in the flexural zone. Mean crack width is affected by the modulus of elasticity of the reinforcement, the reinforcement ratio, the effective depth and the bond behaviour between concrete and reinforcement.  Bond coefficients have been adjusted for different existing formulations regarding crack spacing and crack width for steel and FRP RC flexural elements. The coefficients obtained for FRP bars, although they are not meaningfully different to those obtained for steel bars, reveal the influence of the type and surface configuration of the bar on the bond behaviour of the concrete-rebar interface, thus influencing the cracking behaviour.

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Acknowledgements The authors acknowledge the support provided by the Spanish Government (Ministerio de Ciencia e Innovación), Project. BIA2013-46944-C2-2-P. The authors also wish to acknowledge the support of Hughes Brothers, Inc. and Schöck Bauteile GmbH for supplying the GFRP bars. The fourth author acknowledges the support from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/20072013) and from ACCIÓ (Generalitat de Catalunya) under REA grant agreement no. 600388.

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