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Cracking control comparison in the specifications of serviceability in cracking for FRP reinforced concrete beams
Accepted Manuscript Cracking Control Comparison In The Specifications Of Serviceability In Cracking For Frp Reinforced Concrete Beams Minkwan JU, Youngwhan Park, Cheolwoo Park PII: DOI: Reference:
S0263-8223(17)30923-6 http://dx.doi.org/10.1016/j.compstruct.2017.09.016 COST 8879
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
21 March 2017 28 July 2017 14 September 2017
Please cite this article as: JU, M., Park, Y., Park, C., Cracking Control Comparison In The Specifications Of Serviceability In Cracking For Frp Reinforced Concrete Beams, Composite Structures (2017), doi: http://dx.doi.org/ 10.1016/j.compstruct.2017.09.016
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CRACKING CONTROL COMPARISON IN THE SPECIFICATIONS OF SERVICEABILITY IN CRACKING FOR FRP REINFORCED CONCRETE BEAMS Minkwan JU1, Youngwhan PARK2, and Cheolwoo PARK3 1
Department of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-
gu, Seoul, 03722, Republic of Korea. 2
Korea Institute of Civil Engineering and Building Technology, 315 Goyang-dae-ro, Ilsan-seo-gu,
Goyang-si, Gyenggi-Do, 10223, Republic of Korea. 3
Department of Civil Engineering, Kangwon National University, 346 Joongang-ro, Samcheok-si,
Kangwon, 25913, Republic of Korea.
ABSTRACT : The purpose of this study is to examine the level of applicability of the four specifications of the serviceability in cracking for concrete beams reinforced with ribbed glass fiber-reinforced polymer (GFRP) bar. The four-point bending test was conducted with measuring the crack width at the bottom of the beams. For investigating the level of applicability of the four specifications of the serviceability in cracking, applied moment-maximum bar spacing was obtained by ACI 440 1R-15 for varying the bond coefficient, crack width, concrete cover depth, and the equivalent reinforcement ratio. Then, it compared with the relationships with the serviceability region specified by the four specifications. It was found that the evaluation of serviceability in cracking by the four specifications have provided quite different results according to the bond coefficient, allowable crack width as well as the equivalent reinforcement ratio. As a result, the four serviceability specifications should be seriously discussed for the cracking control of FRP reinforced concrete beams in case of considering some of influencing factor, especially for the equivalent reinforcement ratio. Keywords: Ribbed GFRP bar, Serviceability in cracking, four-point bending test, equivalent reinforcement ratio.
1
1. INTRODUCTION Steel bar corrosion rapidly accelerates the structural durability of reinforced concrete (RC) members in a marine environment. The corrosion is caused by chloride attack, which can be found in de-icing salt as well as in a wreathing and chemical environment. Fiber-reinforced polymers (FRP) are the most durable materials used as a substitute reinforcement to the conventional steel-reinforced concrete structures. Accordingly, studies on the FRP-reinforced concrete structures showed that their load-carrying capacity was higher and the maximum deflection was larger than those of steel reinforcements [1–5]. FRP bars have a lower modulus of elasticity and no ductility like the steel bars. Hence, the specification recommends the structural design to show the concrete crushing for the FRP-reinforced concrete members [6–7]. The low modulus of elasticity of the FRP bars causes serviceability problems like crack widths and deflection. The structural requirement is typically governed in the serviceability limit state rather than the ultimate state [8]. For mechanically enhancing the structural stiffness, the hybrid reinforcing approach with steel and FRP bars effectively enhanced the load-carrying capacity with a higher flexural stiffness [9]. Another research developed a GFRP and a deformed steel hybrid bar. The hybridization showed an excellently improved modulus of elasticity [10]. The abovementioned research efforts show that the serviceability evaluation of the FRP-reinforced concrete structures is essential for the structural design. The evaluation of the serviceability in cracking has been an important issue for FRP reinforced concrete members due to the low flexural stiffness of FRP bar so that it brings somewhat large deflection under flexure. Accordingly, the prediction of crack width is a part of significant problem to be as accurate as possible so far. However, the crack occurs from various reasons, hence, it was reported that the prediction or calculation is hard to be well done and quite impractical according to ACI 224R-01 [11]. Accordingly, the ACI 440 1R-15
2
recently amended the methodology of cracking control from the directly calculation of the crack width to indirect approach suggesting the maximum bar spacing in design of cracking. Thus, the crack width was controlled by specifying the spacing of the FRP reinforcements according to the design crack width. The serviceability state should be reasonably determined because the GFRP bar behaves linearly, and no apparent yielding point is observed like the steel bar. Some empirical criteria of the serviceability recommendations have been published. ISIS Canada [12] recommends a limit of 2,000 microstrains of the GFRP bars in tension. The CSA-S6-10 [13] and CSA-S6-14 [14] specifies the serviceability limit with 1,000 microstrains of compressive concrete and 0.25ffrpu, respectively. AASHTO [15] specifies the serviceability deflection limit for the flexural deflection up to span length L/800 for the simply supported condition. Abovementioned criteria is employed by the judgement of structural engineer and it usually depends on the use of specification in the society. There are some of related research with above the serviceability recommendations for the experimental tests in compliance with the strain-based serviceability state [1, 9]. For the design equation of cracking control, a research on the crack width of the GFRP-reinforced concrete member developed a new modified equation of estimating the crack width based on the ACI 440 1R-06 [16]. One of the latest research reported that the bond coefficient kb is influenced by FRP bar type, bar diameter, and concrete strength. It concluded that the same kb could not be used for the different types of FRP bars [17]. This study investigates the feasibility of the serviceability specifications based on the strain or deflection criteria. As the basis for the comparison, the latest design equation of cracking control by ACI 440 1R-15 was selected, which was suggested for easy and simple cracking design for the flexural members. Initially, applied moment-maximum bar spacing relationship is analyzed by ACI 440 1R-15 according to the designated bond coefficient and allowable
3
crack width, concrete cover depth, and the equivalent reinforcement ratio. Four-point bending tests were conducted for the concrete beams reinforced with FRP bars and crack width was measured on the bottom of the test beams where the cracks occur. The used GFRP bar had a ribbed outer shape to enhance the bond strength and the modulus of elasticity was promoted as compared with the commercial FRP bars [18]. Lastly, individual criteria for the cracking control specified by the serviceability specifications is obtained and compared with the relationship of the moment and the bar spacing by ACI 440 1R-15. Accordingly, the level of applicability of the serviceability specifications is discussed whether the recommendations can be employed for any case on cracking control of flexural members reinforced with FRP bars.
2. SPECIFICATIONS OF SERVICEABILITY Some of the specified recommendations for the serviceability in cracking are discussed in the statements that follow. The four specifications defined the serviceability in cracking with respect to the strain or deflection approach and they suggested different recommendation to the serviceability in cracking of cracking.
- ISIS Canada 2007 [12] The parameters that influence crack width are the crack spacing, the quality of bond between the concrete and reinforcing bars and, above all, the strain in the bars. To control the width of cracks, ACI 318-14 (2014) limits the stress in steel reinforcement at service to 67 percent of fy. When fy = 400 MPa, the allowable strain in steel bars in service, εs, is calculated as follows.
(1) 4
The deterring of corrosion of steel is one motive for controlling the width of cracks. When steel reinforcing bars are used, allowable crack widths of 0.4 mm and 0.3 mm for interior and exterior exposure, respectively, are normally used. When FRP bars are employed, there is no risk of corrosion. It is recommended that limiting the crack width to 0.7 mm and 0.5 mm for interior and exterior exposure, respectively, is acceptable for FRP-reinforced components. From this, it is seen that the width of cracks allowed for FRP-reinforced members is 1.7 or 1.5 times the value allowed for steel-reinforced members. It is assumed that the ratio between crack widths of FRP and steel reinforced beams is 5/3. Thus, the allowable strain in the FRP reinforcement at service may be assumed as follows.
(2)
- CSA-S6-10 [13] In this specification, it recommends the serviceability in cracking with respective to ductility. Because FRP reinforced beam shows the linear response up to failure, CSA-S6-10 recommends that the service moment, Ms, and the curvature of the beam corresponding to a maximum compressive concrete strain of 0.001.
- CSA-S6-14 [14] CSA-S6-14 limits the stress in FRP reinforcing bars to 0.25ffrpu and 0.60ffrpu for GFRP and CFRP bars, respectively, where ffrpu is the characteristic tensile strength of the FRP reinforcing bars (average – 3×standard deviation). In this study, the tensile stress limit of 0.25ffrpu was used for the GFRP bar which had the different ultimate strength for the bar diameter. 5
- AASHTO LRFD Bridge design specification [15] In contrast with above two specifications using strain approach, a typical approach for evaluating serviceability in cracking is to apply the allowable deflection. AASHTO LRFD recommends the allowable limit of deflection for simply supported beam structure not to exceed span length / 800 when structural designer check the serviceability in cracking in structural design.
3. EXPERIMENTAL PROGRAM
3.1 GFRP bar in this study The GFRP bar used in this study was fabricated through a braided pultrusion process. The bar consisted of an E-glass fiber and a vinyl–ester resin. The volume fraction was designed equal to 78.0% in weight. Fig. 1 shows the GFRP bars and Table 1 summarizes the material properties obtained from previous study [19]. Another research [20] reported that the bond strength of the ribbed GFRP bar was approximately 42% higher than that of commercial GFRP bars (e.g., Aslan and V-Rod). The GFRP bar could uniformly behave with concrete as a perfect bond as much as the steel bar does. The diameter must be known with a nominal or measured one to calculate the tensile strength of the GFRP bar. The ASTM D 3916 [21] specified that the diameter should be measured at several points along the length of the bar to obtain the smooth bar diameter. However, this method was impractical for the ribbed GFRP bar because of the presence of variation in the cross-sectional dimensions along the bar. A better approach was reported to calculate the average diameter from the mass, length, and density of the bar [22]. The bar diameter herein was measured through an immersing test. The weight and density per unit length of the GFRP bars were measured in a laboratory
6
condition. The measured lengths ranged from 194 mm to 202 mm. The total number of 13 specimens per diameter was tested and averaged. Table 1 summarizes the results.
(a) Braided pultrusion process
(b) GFRP bar of D13, D16, and D19
Fig. 1 Ribbed GFRP bars developed in this study
Table 1 Results of measured diameter of ribbed GFRP bar by immersing test Average GFRP
Unit weight
Volume
Density
Length (mm) bar ID
diameter (kgf/m)
(mL)
3
(kg/m ) (mm)
D13
197.0±1.8
0.270±0.001
27.8±0.4
1913.8±30.8
13.4
D16
197.8±1.5
0.426±0.002
43.0±0.5
1958.8±16.9
16.6
D19
198.0±1.8
0.590±0.004
58.8±2.0
1985.9±66.8
19.4
The uniaxial tensile test of the GFRP bar was performed in compliance with the ASTM D 3916. Table 2 shows the resulting mechanical property. The cross-sectional area was obtained by using the average diameter as a result of the immersing test. This area was used to determine the tensile strength of the ribbed GFRP bar as a reinforcement to the test beams. The average tensile strength and modulus of elasticity were determined by averaging the tensile test results of the test specimens, excluding the maximum and minimum values. The 7
modulus of elasticity was determined in compliance with the CSA S806-12. The equation consisted of the applied loads P1 and P2 corresponding to 50% and 25%, respectively, of the ultimate load to ε1 and ε2 of the corresponding strains. The strain gauges were installed at L/2 for ε1 and L/4 for ε2 of the GFRP bar section. The average value was used for the tensile strength and the modulus of elasticity. The modulus of elasticity showed a relatively high value compared to the other identically used GFRP bars (35–45 GPa) reported in a previous research [20]. Table 2 Mechanical properties of the ribbed GFRP bar in this study Ultimate Ultimate GFRP bar tensile strength, ID (mm)
tensile strain, εfu
ffub (N/mm2)
Guaranteed tensile strength,
Guaranteed tensile strain,
Modulus of elasticity,
ffu*c (N/mm2)
εfu*c (%)
Ef (N/mm2)
(%) D13 (13.4)a
1,010
1.79
930
1.40
56,600
D16 (16.6)
1,210
2.12
1,130
1.31
57,000
D19 (19.4)
880
1.48
770
1.25
61,200
a
values of diameter in parentheses are obtained from the immersing test
b
average ultimate value obtained by tensile test
c
average ultimate value - 3×standard deviation (ACI 440 1R-15)
3.2 Concrete All the beam specimens had a target compressive strength of 30.0 MPa using ordinary Portland cement (OPC). The concrete compressive test was conducted using the cylindrical concrete specimens. The number of concrete cylindrical specimens considered was three. Consequently, the average concrete strength was concluded at 34.0 MPa.
8
3.3 Test specimens Fig. 2 show the schematics of the test specimens and the designed cross-section. All beams were 3,400 mm long with rectangular cross-sections of 300 mm × 400 mm. The beams were reinforced with the ribbed GFRP bars arranged with a single layer in the tensile section. For shear reinforcing, steel stirrups that were 9.53 mm in diameter were applied with two different spacing, including the 50 mm spacing along the shear span, to guarantee sufficient shear reinforcing against the maximum shear forces. Two longitudinal steel bars with 9.53 mm diameter were placed in the compression zone and served as hanger for the stirrup and confinement effect along the longitudinal direction. A clear concrete cover for the test variables was set equal to 30 mm or 50 mm and it must be the effect of the effective depth, d, because the height of the beam is constant. The minimum concrete cover for an unprotected main reinforcing steel for durability was recommended according to the AASHTO LRFD bridge specification (2012) [23]. The concrete cover for the bottom of the cast in place slabs up to No. 11 bar shall be 25.4 mm. The cover for the coastal environment should be over 75 mm. However, the GFRP bar was a non-corrosive reinforcement. Hence, some redundancies may be applied to the minimum concrete cover. P/2
9@100
12@50
500
P/2
12@50
9@100
3,000
200
D10 (steel)
D10 (steel) GFRP (D13, D16, D19)
400
300
D10 (steel)
D10 (steel) GFRP (D13, D16, D19)
400
50
30
200
400
50
30 300
300
400
300
Fig. 2 Reinforcements and geometry details of the test beams (unit in mm) [17]
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Table 3 Details of test specimens Reinforced Beam ID
2
Af (mm )
fc’ (MPa)
ρf (%)
ρfb (%)
ρf / ρfb* type
2D13G-C30
282.0
34.0
0.266
0.744
0.36
Rupturea
2D19G-C30
590.9
34.0
0.410
1.095
0.51
Rupture
3D16G-C30
649.0
34.0
0.614
0.528
1.16
Crushingb
3D19G-C30
886.3
34.0
0.842
1.095
0.77
Rupture
2D13G-C50
282.0
34.0
0.282
0.545
0.52
Rupture
2D19G-C50
590.9
34.0
0.595
1.095
0.54
Rupture
3D16G-C50
649.0
34.0
0.651
0.528
1.23
Crushing
3D19G-C50
886.3
34.0
0.893
1.095
0.82
Rupture
a
GFRP rupture in case of ρf < ρfb
b
concrete crushing failure in case of ρf > ρfb
c
ρfb = 0.85β1fc’/ffu(Efεcu/Efεcu+ffu) [6]
All the test beams were designed to show the mode of failure, such as GFRP rupture, balanced, and concrete crushing failure, according to the ACI 440 1R-15. Table 3 summarizes the details of the test specimens. The reinforcement ratio is differently calculated according to the bar diameter and the effective depth varying by the concrete cover. The reinforcement ratio was obtained by using different amounts of longitudinal reinforcements with a measured diameter of the GFRP bars from 13.4 mm to 19.4 mm. For the effective depth, two depth values were obtained as a result of the concrete cover depth variation. The sectional (ρf) to balanced (ρfb) ratio was investigated for the intended mode of failure.
10
3.4 Loading test and measurement The loading was applied in a four-point loading by using a universal test machine (UTM) with 500 kN capacity (Fig. 3). A constant moment region with a length of 500 mm and a loading rate was as 12.5 kN/min to failure. The boundary was considered a simply supported condition. The clear span was 3,000 mm. The span-to-depth ratio was designed equal to 3.5– 3.7, in which the beam was fully subjected to the flexural behavior. Identical two beams was tested for each test variable. The cracking patterns were checked at the increment of 25.0 kN until failure. Three numbers of the linear variable displacement transducer (LVDT) were installed at the top and bottom of the test beam in the mid-section to measure the deflection. The two LVDTs on the center-top edges of the concrete beam could check the eccentricity at the lateral direction of the test beam. The elastic resistance strain gauges for the compression and tensile zones were installed at the surface of the tensile GFRP bar and extreme top fiber of the concrete. The deflection and strain data were automatically collected by a data acquisition system. In order to measure the crack width by the measurement limit of the PI displacement transducer (PI gauge), it is important to find the initial cracking. For the initial cracking, the loading rate of 5.0 kN/min was slowly applied. Once the first crack is detected at the midbottom section of the constant moment region, the load is immediately eliminated. After the first crack is fully closed, one pi-typed gauge (see Table 4) is installed (see Fig. 3) right across the cracking formation with the parallel direction to the span length. And the loading is started again until failure. The 5.0 kN/min is only applied for the first cracking and it may not affect to the consistence of the structural behavior. The measurement limit is set as 4 mm for the safe use of the PI gauge. Once the crack width approaches to 4 mm, the PI gauge is detached. This measurement limit must be enough as compared with 0.7 mm, which is considered the allowable crack width in this study. 11
Table 4 Specification of PI gauge use in this study Type
PI-5-50
Gauge length
50
Capacity
±5 mm
Sensitivity (με/mm)
1,000
Allowable temperature range
0~40 ℃
Input/output resistance
350 Ω
Allowable exciting voltage
10V
Note : provided by http://www.tml.jp/e/product/transducers/catalog_pdf/PI.pdf [24]
(a) Four point bending test
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(b) Measurement details Fig. 3 Loading and measurement details (unit in mm)
4. EXPERIMENTAL RESULTS AND DISCUSSION
4.1 Cracking patterns Fig. 4 shows the cracking patterns of the test beams at failure. All specimens showed typical flexural crack patterns. The cracks were initiated in the maximum moment region between the two load points or right below one of the load points. More cracks appeared along the beam length as the load increased. They then propagated toward to the loading points with an inclined irregular shape. The failure for 2D13 and 3D16 specimens occurred by a GFRP rupture and concrete crushing for the other specimen cases, respectively, which it was predicted. Moreover, the sound caused by pulling out the GFRP bar was detected. Crack width was measured by PI gauge at the different location of the bottom surface of the beams within the loading points. It can represent the maximum crack width during the test.
13
(a) Concrete cover of 30 mm
(b) Concrete cover of 50 mm Fig. 4 Cracking patterns of test beams
14
Fig. 5 shows the flexural response based on the relationship of the applied load and deflection. The initial cracking load was observed at around 30.0 kN. All tested specimens exhibited the intended structural behavior in design of GFRP rupture or concrete crushing failure. 3D16 series expected in the concrete crushing failure had no sudden drop after the peak load, where the sudden drop of the applied load was detected for the 2D13 and 2D19 series. For 3D19 series, they showed tensile and compressive failure without the sudden drop of the applied load. Actually, Fig. 5 shows the load-deflection relationship until the peak load because the measurement of deflection was limited right before the sudden fracture of the beams for measuring safety. For the load-carrying capacity, it was significantly different between the low and high reinforcement ratios. The deeper effective depth affected to increase the nominal moment resistance as it was predicted. This phenomenon was more apparently observed for the mid-level reinforcement ratio of 0.595–0.651%, where it rarely affected the increase of the structural capacity for 3D19 series with the highest reinforcement ratio. This may be because the structural capacity is mainly governed by the higher reinforcement ratio rather than the variation of the effective depth within the same concrete compressive strength.
15
Fig. 5 Load-deflection relationship
5. MOMENT-CRACK WIDTH RELATIONSHIP
5.1 Crack control by ACI 440 1R-15 The ACI 318-99 [25] replaced the traditional approach with an indirect procedure for crack control through a maximum reinforcing bar spacing because of concerns on the adequacy of the empirically tuned models. The ACI 440 1R-15 recommended the design equation of effective moment of inertia based on the Branson’s equation. An additional factor was used to consider the reduced tension stiffening of the FRP-reinforced concrete member. This equation was identically used to calculate the moment of inertia of the GFRP-reinforced concrete member, such that the deflection of the cracked section could be calculated. The maximum FRP bar spacing would indirectly comply with a target maximum allowable crack width through the proposed flexural crack control equation. The equation was introduced in Eq. (3). 16
(3)
where smax = maximum permissible center to center bar spacing for flexural crack control (mm); Ef = design or guaranteed modulus of elasticity of FRP defined as mean modulus of sample of test specimens (MPa); = maximum allowable crack width (mm); = stress level induced in FRP at service loads (=efsEf) (MPa); = strain level induced in FRP at service loads cc = clear cover (mm); and b
= bond dependent coefficient.
For bond dependent coefficient kb was considered an important variable. Based on the design equation of ACI 440 1R-15, the upper and lower bound of kb was usually set as kb = 1.0 for having bond behavior similar to uncoated steel bars and kb = 1.4 for the case where kb = is not known from experimental data, is that a conservative value of 1.4 should be assumed, respectively. Weak bond case for kb =1.4 expects that the bar spacing results in the smaller value than that of the case of kb =1.0. From the relationship between the bar spacing and the applied moment, the cracking control comparison between the ACI 440 1R-15 and serviceability specifications is going to be examined and discussed for an appropriate boundary for evaluating the cracking control of FRP bar reinforced concrete beam. For the maximum allowable crack width, the designated two value, 0.5 mm for exposed and 0.7 mm unexposed, was used for cracking control analysis as introduced in ACI 440 1R-06. ACI 440 1R-15 denotes that the crack widths are limited by aesthetic reasons and the range of 0.4 to 17
0.7 mm is generally acceptable. The selection of the allowable crack width depends on the intended use of the structure. For aggressive environmental condition, very narrow crack width should be appropriate where wider cracks may acceptable due to the superior corrosion resistant of FRP reinforcement.
5.2 Moment-crack width comparison Fig. 6 exhibits the moment–crack width relationship of the test specimens. The crack width was plotted with the values from the Eq. (3) by ACI 440 1R-15. In order to investigate the effect of the reinforcing type such as the GFRP rupture and concrete crushing failure, the relative ratio of the sectional to balanced reinforcement ratio was considered. There could be two groups to be discussed. Fig. 6 shows that the relative ratio under 0.54 tended to estimate the calculated crack width to be large. Whereas, the specimens with a ratio over 0.77, including the concrete crushing failure, evaluated the calculated crack width to be small. For the diameter of reinforcement, the calculated crack width was lager that that of experimental results for the larger diameter specimens. It might be concluded that a larger reinforcement diameter generally had relatively lower bond capacity than that of the smaller diameter of reinforcement. Thus, it can explain that the tensile stress of the specimens reinforced with smaller diameter reinforcements is well distributed so that the experimental crack width may be lesser than the calculated crack width. As regards the effect of the concrete cover to the calculated crack width, the calculated crack width and concrete cover behaved proportionally, except for the 2D19 specimens. The effect was more understandable at around 20.0 kN·m. This result was in good agreement with the increased structural capacity caused by the deeper effective depth in flexure. The cracking control of a flexural member reinforced with the FRP bar should be dealt with in a more conservative aspect. kb was one of the most influential factors in determining the
18
cracking control of the FRP bar-reinforced flexural members. For FRP bar, however, there is insufficient data to determine or generalize the bond coefficient and it is varied by the bar types, diameter, concrete compressive strength. And crack width comparison is quite hard because cracking is unstructured manner and the measurement of crack is sensitive too. Accordingly, the calculation and prediction of the crack width may be inappropriate and impractical approach for cracking control in structural design of FRP bar reinforced concrete structures.
(a) 2D13G-C30
(b) 2D19G-C30
(c) 3D16G-C30
(d) 3D19G-C30
19
(e) 2D13G-C50
(f) 2D19G-C50
(g) 3D16G-C50
(h) 3D19G-C50
Fig. 6 Moment-crack width relationship according to the upper and lower bound of kb
6. CRACKING CONTROL COMPARISON OF SERVICEABILITY SPECIFICATIONS AND DESIGN EQUATION OF ACI 440 1R-15
6.1 Cracking control of experimental test by ACI 440 1R-15 The relationship between calculated bar spacing and applied moment is illustrated in Figure 7. The considered value of bond coefficient is 1.0 for good bond and 1.4 for poor bond, where 20
the crack width is 0.5 and 0.7 mm respectively. Above values were employed from ACI 440 1R-15, which provided upper or lower bound value if there are not appropriate recommendations. These four considered value were combined in the analysis of relationship between calculated bar spacing and applied moment as shown in Figure 7. There were quite different curves and it varied according to the combination of bond coefficient and crack width for each test specimen. The general aspect from the curves was the descending as applied moment was increased. This is true that the more amount of flexural reinforcements is needed to resist larger applied moment so that the bar spacing have to be narrower. Another significant result was that the bar spacing went to be narrow too if the bond property was poor (i.e. kb=1.4) or the allowable crack width was the more conservative (i.e. w=0.5). The relationship between calculated bar spacing and applied moment was also affected by the equivalent reinforcement ratio of ρf Ef/Es, which was employed to normalize the reinforcement ratio of the FRP bars to the steel bar [26]. As the reinforcement ratio is higher, the calculated bar spacing goes to the wider at the designated applied moment. This is the reason that the flexural capacity enhanced by the increased reinforcement ratio can effectively resist the crack opening to the longitudinal direction of the test beams for the same of bond coefficient and the allowable crack width.
6.2 Level of applicability of the serviceability in cracking Figure 7 additionally exhibits the bar spacing of two experimental cases (XX mm and XX mm) at the serviceable moment corresponding to the four serviceability specifications, which is based on the tensile strain of reinforcement for ISIS Canada 2007, allowable deflection for AASHTO 2009, compressive concrete strain for CSA-S6-10, and stress limit of GFRP bar for CSA-S6-14. The four dots stand for the results obtained above four specifications. The comparison can be explained that the cracking control is satisfied in case the dot is placed 21
within the relationship curve between the calculated bar spacing and applied moment. The dots which is out of the relationship curve can not explain the cracking control in present state so that the degree of serviceability may have to be varied to the lower state to meet the relationship curve. Thus, the existing serviceability specifications can provide different serviceability evaluation for the concrete beam reinforced with FRP bar. For the 2D13 specimens, with a low equivalent reinforcement ratio, only the serviceability in cracking of the ISIS Canada 2007 satisfied the bar spacing corresponding to the serviceable moment. Any no three of AASHTO LRFD 2009, CSA-S6-10 and CSA-S6-14 could meet the bar spacing for the serviceability in cracking. The 3D19G-C50 specimen with the highest equivalent reinforcement ratio of 0.273 could be valid for explaining the four serviceability specifications. This specimen also showed a sufficient spacing margin for the ISIS Canada 2007 and the AASHTO LRFD 2009. For the specimens with a mid-level equivalent reinforcement ratio from 0.125 to 0.258, only CSA S6-10 could not explain the serviceability in cracking of all specimens. Accordingly, serviceability recommendation of 0.001 strain of concrete compressive strength may provide overestimated serviceable capacity of FRP bar reinforced concrete structures under flexure. The finding is that the four serviceability specifications could differently evaluate the serviceability in cracking by the bond coefficient, allowable crack width, and the equivalent reinforcement ratio, respectively.
22
(a) 2D13G-C30
(b) 2D19G-C30
(c) 3D16G-C30
(d) 3D19G-C30
23
(e) 2D13G-C50
(f) 2D19G-C50
(g) 3D16G-C50
(h) 3D19G-C50
Fig. 7 Maximum bar spacing and applied moment relationship by ACI 440 1R-15 and comparison with the serviceability specifications
Table 5 summarizes the possible criteria of the serviceability specifications to examine the level of applicability of serviceability in cracking. It explained that the ISIS Canada 2007 could be employed in most of the relationship between calculated bar spacing and applied moment, whereas the CSA S6-10 was rarely satisfied. For the case of kb = 1.4 and w = 0.5 mm, shown as the lowest curve in Figure 7, it was quite hard to be explained with the serviceability specifications because this was a relatively tough level for serviceability in cracking. Only the test beam with the equivalent reinforcement ratio of 0.273 which has the highest value satisfied the serviceability recommendation of the CSA S6-10 for the case of kb = 1.0 and w = 0.7 mm. This case is the good bond property as well as the most wide crack width, which may be acceptable for the superior corrosion resistance of FRP reinforcement. Table 4 denotes that the equivalent reinforcement ratio is correlated with the level of applicability of serviceability in racking. It provides a significant finding that the four serviceability specifications should be seriously discussed for the cracking control of FRP 24
reinforced concrete beams in case of considering some of influencing factor, especially for the equivalent reinforcement ratio.
Table 5 Possible criteria of serviceability recommendations for the cracking control for the test specimens Beam ID
ρf E f / E s
kb=1.0
kb =1.4
w=0.5 mm
w =0.7 mm
w=0.5 mm
w =0.7 mm
2D13G-C30
0.075
ISIS Canada
ISIS Canada
N/A
ISIS Canada
N/A
ISIS Canada
ISIS Canada 2D19G-C30
0.125
ISIS Canada
AASHTO CSA S6-14
3D16G-C30
0.175
ISIS Canada AASHTO ISIS Canada
3D19G-C30
0.258
AASHTO CSA S6-14
2D13G-C50
0.08
ISIS Canada
2D19G-C50
0.182
ISIS Canada
3D16G-C50
0.186
0.273
AASHTO
AASHTO ISIS Canada
ISIS Canada
AASHTO
AASHTO
ISIS Canada
N/A
ISIS Canada
N/A
ISIS Canada
ISIS Canada AASHTO
AASHTO
AASHTO
CSA S6-14
ISIS Canada
ISIS Canada
ISIS Canada
AASHTO
ISIS Canada
CSA S6-14
ISIS Canada
ISIS Canada 3D19G-C50
ISIS Canada
ISIS Canada AASHTO
ISIS Canada
AASHTO CSA S6-14
ISIS Canada AASHTO
ISIS Canada
ISIS Canada
AASHTO
AASHTO
CSA-S6
CSA S6-14
7. CONCLUSIONS This study investigated the relationship between the FRP bar spacing and the applied moment based on the ACI 440 1R-15 for the experimental tests. And also, the level of applicability of
25
the four serviceability specifications for serviceability in cracking was examined. The following conclusions are drawn from this study:
1. The GFRP-reinforced concrete beam showed an intended mode of failure and structural capacity, such as linear behavior up to failure. Even though the bond strength was reported higher than those of the commercial FRP bars, the ribbed GFRP bar used in this study still had 28–31% lower modulus of elasticity than that the steel bar. Accordingly, the serviceability in cracking should be further examined to apply the GFRP bar as a substitute of the steel bars.
2. The crack width could not be predictably obtained when or where the crack occurs as well as it is sensitive during the loading. From the result of the relationship between the applied moment and the crack width, hence, the comparison of crack width obtained from the calculation and the real state may be impractical to be verified in structural design.
3. For good bond property of kb=1.0, it was found that the calculated bar spacing corresponding to the applied moment was more released than that of poor bond property of kb=1.4, which was shown in all of test specimens. For the allowable crack width in narrower case (w=0.5 mm), the calculated bar spacing corresponding to the applied moment was more tightened than that of the allowable crack width in wider case (w=0.7 mm). These trends are globally same for all of the test specimens, however, the relationship between the calculated bar spacing and the applied moment is quite different according to varying the equivalent reinforcement ratio.
26
4. For investigating the level of applicability of the serviceability specifications, the bar spacing corresponding to the serviceable moment base on the four specifications was compared with the relationship between the calculated bar spacing and the applied moment. The ISIS Canada 2007 could be employed in most of the relationship between the calculated bar spacing and the applied moment, whereas the CSA S6-10 rarely satisfied the relationship. As a result, the four serviceability specifications can provide quite different serviceability in cracking of FRP bar reinforced concrete structures. Therefore, the four serviceability specifications should be seriously discussed for the cracking control of FRP reinforced concrete beams in case of considering some of influencing factor, especially for the equivalent reinforcement ratio. The conclusions of this study was from somewhat limited experimental test results so that it can be incorporated further experimental studies into this study.
REFERENCES 1. Adam MA, Said M, Mahmoud AA, Shanour, AS, Analytical and experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars. Construction and Building Materials, 2015;84:354-66. 2. Abdul Rahman MS, Narayan SR. Flexural behavior of concrete beams reinforced with glass fibre reinforced polymer bars. Journal of Engineering, 2005;17(1):49-57. 3. Maranan GB, Manalo AC, Benmokrane B, Karunasena W, Mendis P. Evaluation of the flexural strength and serviceability of geopolymer concrete beams reinforced with glassfibre-reinforced polymer (GFRP) bars. Engineering Structures, 2015;101:529-41. 4. Barris C, Torres LI, Turon A, Baena M, Catalan A. An experimental study of the flexural behavior of GFRP RC beams and comparison with prediction models. Composite Structures, 2009;91:286-95. 27
5. Wang H, Belarbi A. Flexural durability of FRP bars embedded in fiber-reinforced concrete. Construction and Building Materials, 2013;44:541-50. 6. ACI Committee 440. Guide for the design and construction of concrete reinforced with FRP bars (ACI 440.1R-15). American Concrete Institute, Farmington Hills, MI, USA, 2015. 7. ISIS Canada Design Manuals. Reinforcing concrete structures with fibre reinforced polymers. ISIS Canada Corp., Winnipeg, Canada, 2007. 8. Mousavi SR, Esfahani MR. Effective moment of inertia prediction of FRP-reinforced concrete beams based on experimental results. Journal of Composite for Construction, 2012; 16(5):490-98. 9. El Refai A, Abed F, Al-Rahmani A. Structural performance and serviceability of concrete beams reinforced with hybrid (GFRP and steel) bars. Construction and Building Materials, 2015;86:518-29. 10. Park C, Park Y, Kim S, Ju M. New emerging surface treatment of hybrid GFRP bar for stronger durability of concrete structures. Smart Structures and Systems, 2016;17(4):593610. 11. ACI Committee 224. Control of cracking of concrete structures (ACI 224R-01). American Concrete Institute, Farmington Hills, MI, USA, 2001. 12. ISIS Canada. Reinforced concrete structures with fibre reinforced polymers design manual No. 3. Manitoba, Canada, 2007. 13. Canadian Standards Association (CSA). Canadian highway bridge design code CSA-S610. Mississauga, ON, Canada, 2010. 14. Canadian Standard Association (CSA). Canadian highway bridge design code. CAN/CSA S6-14, Rexdale, ON, Canada, 2014.
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15. AASHTO. LRFD bridge design guide specifications for GFRP-reinforced concrete bridge decks and traffic railings. American Association of State Highway and Transportation Officials, Washington, DC, USA, 2009. 16. ACI Committee 440. Guide for the design and construction of concrete reinforced with FRP bars (ACI 440.1R-06). American Concrete Institute, Farmington Hills, MI, USA, 2006. 17. Noel M, Soudki K. Estimation of the crack width and deformation of FRP-reinforced concrete flexural members with and without transverse shear reinforcement. Engineering Structures, 2014;59:393-98. 18. El-Nemr EA, Barris C, Benmokrane B. Bond-dependent coefficient of glass and carbon FRP bars in normal- and high-strength concretes. Construction and Building Material 2016;01(01):21–38. 19. Ju M, Park C, Kim Y. Flexural capacity and deflection of concrete beam reinforced with a ribbed GFRP bars. Computer and Concrete, 2017;6(6) (In press). 20. You YJ, Kim JHJ, Kim SJ, Park YH. Methods to enhance the guaranteed tensile strength of GFRP rebarto 900 MPa with general fiber volume fraction. Construction and Building Materials, 2015;75:54-62. 21. ASTM D 3916. Standard test method for tensile properties of pultruded glass fiber reinforced plastic rods. American Standard Test Method, 2002. 22. Castro PF,Carino NJ. Tensile and nondestructive testing of FRP bars, Journal of Composites for Construction, 1998;2(1):17-27. 23. AASHTO. LRFD bridge design specifications. American Association of State Highway and Transportation Officials, Washington, DC, USA, 2012. 24. http://www.tml.jp/e/product/transducers/catalog_pdf/PI.pdf
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25. ACI Committee 318. Building Code Requirements for Structural Concrete & Commentary. American Concrete Institute, Farmington Hills, MI, USA, 1999. 26. Toutanji HA, Saafi M. Flexural behavior of concrete beams reinforced with glass fiberreinforced polymer (GFRP) bars. ACI Structural Journal, 2000;97(5):712–19.
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S0263-8223(17)30923-6 http://dx.doi.org/10.1016/j.compstruct.2017.09.016 COST 8879
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
21 March 2017 28 July 2017 14 September 2017
Please cite this article as: JU, M., Park, Y., Park, C., Cracking Control Comparison In The Specifications Of Serviceability In Cracking For Frp Reinforced Concrete Beams, Composite Structures (2017), doi: http://dx.doi.org/ 10.1016/j.compstruct.2017.09.016
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CRACKING CONTROL COMPARISON IN THE SPECIFICATIONS OF SERVICEABILITY IN CRACKING FOR FRP REINFORCED CONCRETE BEAMS Minkwan JU1, Youngwhan PARK2, and Cheolwoo PARK3 1
Department of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-
gu, Seoul, 03722, Republic of Korea. 2
Korea Institute of Civil Engineering and Building Technology, 315 Goyang-dae-ro, Ilsan-seo-gu,
Goyang-si, Gyenggi-Do, 10223, Republic of Korea. 3
Department of Civil Engineering, Kangwon National University, 346 Joongang-ro, Samcheok-si,
Kangwon, 25913, Republic of Korea.
ABSTRACT : The purpose of this study is to examine the level of applicability of the four specifications of the serviceability in cracking for concrete beams reinforced with ribbed glass fiber-reinforced polymer (GFRP) bar. The four-point bending test was conducted with measuring the crack width at the bottom of the beams. For investigating the level of applicability of the four specifications of the serviceability in cracking, applied moment-maximum bar spacing was obtained by ACI 440 1R-15 for varying the bond coefficient, crack width, concrete cover depth, and the equivalent reinforcement ratio. Then, it compared with the relationships with the serviceability region specified by the four specifications. It was found that the evaluation of serviceability in cracking by the four specifications have provided quite different results according to the bond coefficient, allowable crack width as well as the equivalent reinforcement ratio. As a result, the four serviceability specifications should be seriously discussed for the cracking control of FRP reinforced concrete beams in case of considering some of influencing factor, especially for the equivalent reinforcement ratio. Keywords: Ribbed GFRP bar, Serviceability in cracking, four-point bending test, equivalent reinforcement ratio.
1
1. INTRODUCTION Steel bar corrosion rapidly accelerates the structural durability of reinforced concrete (RC) members in a marine environment. The corrosion is caused by chloride attack, which can be found in de-icing salt as well as in a wreathing and chemical environment. Fiber-reinforced polymers (FRP) are the most durable materials used as a substitute reinforcement to the conventional steel-reinforced concrete structures. Accordingly, studies on the FRP-reinforced concrete structures showed that their load-carrying capacity was higher and the maximum deflection was larger than those of steel reinforcements [1–5]. FRP bars have a lower modulus of elasticity and no ductility like the steel bars. Hence, the specification recommends the structural design to show the concrete crushing for the FRP-reinforced concrete members [6–7]. The low modulus of elasticity of the FRP bars causes serviceability problems like crack widths and deflection. The structural requirement is typically governed in the serviceability limit state rather than the ultimate state [8]. For mechanically enhancing the structural stiffness, the hybrid reinforcing approach with steel and FRP bars effectively enhanced the load-carrying capacity with a higher flexural stiffness [9]. Another research developed a GFRP and a deformed steel hybrid bar. The hybridization showed an excellently improved modulus of elasticity [10]. The abovementioned research efforts show that the serviceability evaluation of the FRP-reinforced concrete structures is essential for the structural design. The evaluation of the serviceability in cracking has been an important issue for FRP reinforced concrete members due to the low flexural stiffness of FRP bar so that it brings somewhat large deflection under flexure. Accordingly, the prediction of crack width is a part of significant problem to be as accurate as possible so far. However, the crack occurs from various reasons, hence, it was reported that the prediction or calculation is hard to be well done and quite impractical according to ACI 224R-01 [11]. Accordingly, the ACI 440 1R-15
2
recently amended the methodology of cracking control from the directly calculation of the crack width to indirect approach suggesting the maximum bar spacing in design of cracking. Thus, the crack width was controlled by specifying the spacing of the FRP reinforcements according to the design crack width. The serviceability state should be reasonably determined because the GFRP bar behaves linearly, and no apparent yielding point is observed like the steel bar. Some empirical criteria of the serviceability recommendations have been published. ISIS Canada [12] recommends a limit of 2,000 microstrains of the GFRP bars in tension. The CSA-S6-10 [13] and CSA-S6-14 [14] specifies the serviceability limit with 1,000 microstrains of compressive concrete and 0.25ffrpu, respectively. AASHTO [15] specifies the serviceability deflection limit for the flexural deflection up to span length L/800 for the simply supported condition. Abovementioned criteria is employed by the judgement of structural engineer and it usually depends on the use of specification in the society. There are some of related research with above the serviceability recommendations for the experimental tests in compliance with the strain-based serviceability state [1, 9]. For the design equation of cracking control, a research on the crack width of the GFRP-reinforced concrete member developed a new modified equation of estimating the crack width based on the ACI 440 1R-06 [16]. One of the latest research reported that the bond coefficient kb is influenced by FRP bar type, bar diameter, and concrete strength. It concluded that the same kb could not be used for the different types of FRP bars [17]. This study investigates the feasibility of the serviceability specifications based on the strain or deflection criteria. As the basis for the comparison, the latest design equation of cracking control by ACI 440 1R-15 was selected, which was suggested for easy and simple cracking design for the flexural members. Initially, applied moment-maximum bar spacing relationship is analyzed by ACI 440 1R-15 according to the designated bond coefficient and allowable
3
crack width, concrete cover depth, and the equivalent reinforcement ratio. Four-point bending tests were conducted for the concrete beams reinforced with FRP bars and crack width was measured on the bottom of the test beams where the cracks occur. The used GFRP bar had a ribbed outer shape to enhance the bond strength and the modulus of elasticity was promoted as compared with the commercial FRP bars [18]. Lastly, individual criteria for the cracking control specified by the serviceability specifications is obtained and compared with the relationship of the moment and the bar spacing by ACI 440 1R-15. Accordingly, the level of applicability of the serviceability specifications is discussed whether the recommendations can be employed for any case on cracking control of flexural members reinforced with FRP bars.
2. SPECIFICATIONS OF SERVICEABILITY Some of the specified recommendations for the serviceability in cracking are discussed in the statements that follow. The four specifications defined the serviceability in cracking with respect to the strain or deflection approach and they suggested different recommendation to the serviceability in cracking of cracking.
- ISIS Canada 2007 [12] The parameters that influence crack width are the crack spacing, the quality of bond between the concrete and reinforcing bars and, above all, the strain in the bars. To control the width of cracks, ACI 318-14 (2014) limits the stress in steel reinforcement at service to 67 percent of fy. When fy = 400 MPa, the allowable strain in steel bars in service, εs, is calculated as follows.
(1) 4
The deterring of corrosion of steel is one motive for controlling the width of cracks. When steel reinforcing bars are used, allowable crack widths of 0.4 mm and 0.3 mm for interior and exterior exposure, respectively, are normally used. When FRP bars are employed, there is no risk of corrosion. It is recommended that limiting the crack width to 0.7 mm and 0.5 mm for interior and exterior exposure, respectively, is acceptable for FRP-reinforced components. From this, it is seen that the width of cracks allowed for FRP-reinforced members is 1.7 or 1.5 times the value allowed for steel-reinforced members. It is assumed that the ratio between crack widths of FRP and steel reinforced beams is 5/3. Thus, the allowable strain in the FRP reinforcement at service may be assumed as follows.
(2)
- CSA-S6-10 [13] In this specification, it recommends the serviceability in cracking with respective to ductility. Because FRP reinforced beam shows the linear response up to failure, CSA-S6-10 recommends that the service moment, Ms, and the curvature of the beam corresponding to a maximum compressive concrete strain of 0.001.
- CSA-S6-14 [14] CSA-S6-14 limits the stress in FRP reinforcing bars to 0.25ffrpu and 0.60ffrpu for GFRP and CFRP bars, respectively, where ffrpu is the characteristic tensile strength of the FRP reinforcing bars (average – 3×standard deviation). In this study, the tensile stress limit of 0.25ffrpu was used for the GFRP bar which had the different ultimate strength for the bar diameter. 5
- AASHTO LRFD Bridge design specification [15] In contrast with above two specifications using strain approach, a typical approach for evaluating serviceability in cracking is to apply the allowable deflection. AASHTO LRFD recommends the allowable limit of deflection for simply supported beam structure not to exceed span length / 800 when structural designer check the serviceability in cracking in structural design.
3. EXPERIMENTAL PROGRAM
3.1 GFRP bar in this study The GFRP bar used in this study was fabricated through a braided pultrusion process. The bar consisted of an E-glass fiber and a vinyl–ester resin. The volume fraction was designed equal to 78.0% in weight. Fig. 1 shows the GFRP bars and Table 1 summarizes the material properties obtained from previous study [19]. Another research [20] reported that the bond strength of the ribbed GFRP bar was approximately 42% higher than that of commercial GFRP bars (e.g., Aslan and V-Rod). The GFRP bar could uniformly behave with concrete as a perfect bond as much as the steel bar does. The diameter must be known with a nominal or measured one to calculate the tensile strength of the GFRP bar. The ASTM D 3916 [21] specified that the diameter should be measured at several points along the length of the bar to obtain the smooth bar diameter. However, this method was impractical for the ribbed GFRP bar because of the presence of variation in the cross-sectional dimensions along the bar. A better approach was reported to calculate the average diameter from the mass, length, and density of the bar [22]. The bar diameter herein was measured through an immersing test. The weight and density per unit length of the GFRP bars were measured in a laboratory
6
condition. The measured lengths ranged from 194 mm to 202 mm. The total number of 13 specimens per diameter was tested and averaged. Table 1 summarizes the results.
(a) Braided pultrusion process
(b) GFRP bar of D13, D16, and D19
Fig. 1 Ribbed GFRP bars developed in this study
Table 1 Results of measured diameter of ribbed GFRP bar by immersing test Average GFRP
Unit weight
Volume
Density
Length (mm) bar ID
diameter (kgf/m)
(mL)
3
(kg/m ) (mm)
D13
197.0±1.8
0.270±0.001
27.8±0.4
1913.8±30.8
13.4
D16
197.8±1.5
0.426±0.002
43.0±0.5
1958.8±16.9
16.6
D19
198.0±1.8
0.590±0.004
58.8±2.0
1985.9±66.8
19.4
The uniaxial tensile test of the GFRP bar was performed in compliance with the ASTM D 3916. Table 2 shows the resulting mechanical property. The cross-sectional area was obtained by using the average diameter as a result of the immersing test. This area was used to determine the tensile strength of the ribbed GFRP bar as a reinforcement to the test beams. The average tensile strength and modulus of elasticity were determined by averaging the tensile test results of the test specimens, excluding the maximum and minimum values. The 7
modulus of elasticity was determined in compliance with the CSA S806-12. The equation consisted of the applied loads P1 and P2 corresponding to 50% and 25%, respectively, of the ultimate load to ε1 and ε2 of the corresponding strains. The strain gauges were installed at L/2 for ε1 and L/4 for ε2 of the GFRP bar section. The average value was used for the tensile strength and the modulus of elasticity. The modulus of elasticity showed a relatively high value compared to the other identically used GFRP bars (35–45 GPa) reported in a previous research [20]. Table 2 Mechanical properties of the ribbed GFRP bar in this study Ultimate Ultimate GFRP bar tensile strength, ID (mm)
tensile strain, εfu
ffub (N/mm2)
Guaranteed tensile strength,
Guaranteed tensile strain,
Modulus of elasticity,
ffu*c (N/mm2)
εfu*c (%)
Ef (N/mm2)
(%) D13 (13.4)a
1,010
1.79
930
1.40
56,600
D16 (16.6)
1,210
2.12
1,130
1.31
57,000
D19 (19.4)
880
1.48
770
1.25
61,200
a
values of diameter in parentheses are obtained from the immersing test
b
average ultimate value obtained by tensile test
c
average ultimate value - 3×standard deviation (ACI 440 1R-15)
3.2 Concrete All the beam specimens had a target compressive strength of 30.0 MPa using ordinary Portland cement (OPC). The concrete compressive test was conducted using the cylindrical concrete specimens. The number of concrete cylindrical specimens considered was three. Consequently, the average concrete strength was concluded at 34.0 MPa.
8
3.3 Test specimens Fig. 2 show the schematics of the test specimens and the designed cross-section. All beams were 3,400 mm long with rectangular cross-sections of 300 mm × 400 mm. The beams were reinforced with the ribbed GFRP bars arranged with a single layer in the tensile section. For shear reinforcing, steel stirrups that were 9.53 mm in diameter were applied with two different spacing, including the 50 mm spacing along the shear span, to guarantee sufficient shear reinforcing against the maximum shear forces. Two longitudinal steel bars with 9.53 mm diameter were placed in the compression zone and served as hanger for the stirrup and confinement effect along the longitudinal direction. A clear concrete cover for the test variables was set equal to 30 mm or 50 mm and it must be the effect of the effective depth, d, because the height of the beam is constant. The minimum concrete cover for an unprotected main reinforcing steel for durability was recommended according to the AASHTO LRFD bridge specification (2012) [23]. The concrete cover for the bottom of the cast in place slabs up to No. 11 bar shall be 25.4 mm. The cover for the coastal environment should be over 75 mm. However, the GFRP bar was a non-corrosive reinforcement. Hence, some redundancies may be applied to the minimum concrete cover. P/2
9@100
12@50
500
P/2
12@50
9@100
3,000
200
D10 (steel)
D10 (steel) GFRP (D13, D16, D19)
400
300
D10 (steel)
D10 (steel) GFRP (D13, D16, D19)
400
50
30
200
400
50
30 300
300
400
300
Fig. 2 Reinforcements and geometry details of the test beams (unit in mm) [17]
9
Table 3 Details of test specimens Reinforced Beam ID
2
Af (mm )
fc’ (MPa)
ρf (%)
ρfb (%)
ρf / ρfb* type
2D13G-C30
282.0
34.0
0.266
0.744
0.36
Rupturea
2D19G-C30
590.9
34.0
0.410
1.095
0.51
Rupture
3D16G-C30
649.0
34.0
0.614
0.528
1.16
Crushingb
3D19G-C30
886.3
34.0
0.842
1.095
0.77
Rupture
2D13G-C50
282.0
34.0
0.282
0.545
0.52
Rupture
2D19G-C50
590.9
34.0
0.595
1.095
0.54
Rupture
3D16G-C50
649.0
34.0
0.651
0.528
1.23
Crushing
3D19G-C50
886.3
34.0
0.893
1.095
0.82
Rupture
a
GFRP rupture in case of ρf < ρfb
b
concrete crushing failure in case of ρf > ρfb
c
ρfb = 0.85β1fc’/ffu(Efεcu/Efεcu+ffu) [6]
All the test beams were designed to show the mode of failure, such as GFRP rupture, balanced, and concrete crushing failure, according to the ACI 440 1R-15. Table 3 summarizes the details of the test specimens. The reinforcement ratio is differently calculated according to the bar diameter and the effective depth varying by the concrete cover. The reinforcement ratio was obtained by using different amounts of longitudinal reinforcements with a measured diameter of the GFRP bars from 13.4 mm to 19.4 mm. For the effective depth, two depth values were obtained as a result of the concrete cover depth variation. The sectional (ρf) to balanced (ρfb) ratio was investigated for the intended mode of failure.
10
3.4 Loading test and measurement The loading was applied in a four-point loading by using a universal test machine (UTM) with 500 kN capacity (Fig. 3). A constant moment region with a length of 500 mm and a loading rate was as 12.5 kN/min to failure. The boundary was considered a simply supported condition. The clear span was 3,000 mm. The span-to-depth ratio was designed equal to 3.5– 3.7, in which the beam was fully subjected to the flexural behavior. Identical two beams was tested for each test variable. The cracking patterns were checked at the increment of 25.0 kN until failure. Three numbers of the linear variable displacement transducer (LVDT) were installed at the top and bottom of the test beam in the mid-section to measure the deflection. The two LVDTs on the center-top edges of the concrete beam could check the eccentricity at the lateral direction of the test beam. The elastic resistance strain gauges for the compression and tensile zones were installed at the surface of the tensile GFRP bar and extreme top fiber of the concrete. The deflection and strain data were automatically collected by a data acquisition system. In order to measure the crack width by the measurement limit of the PI displacement transducer (PI gauge), it is important to find the initial cracking. For the initial cracking, the loading rate of 5.0 kN/min was slowly applied. Once the first crack is detected at the midbottom section of the constant moment region, the load is immediately eliminated. After the first crack is fully closed, one pi-typed gauge (see Table 4) is installed (see Fig. 3) right across the cracking formation with the parallel direction to the span length. And the loading is started again until failure. The 5.0 kN/min is only applied for the first cracking and it may not affect to the consistence of the structural behavior. The measurement limit is set as 4 mm for the safe use of the PI gauge. Once the crack width approaches to 4 mm, the PI gauge is detached. This measurement limit must be enough as compared with 0.7 mm, which is considered the allowable crack width in this study. 11
Table 4 Specification of PI gauge use in this study Type
PI-5-50
Gauge length
50
Capacity
±5 mm
Sensitivity (με/mm)
1,000
Allowable temperature range
0~40 ℃
Input/output resistance
350 Ω
Allowable exciting voltage
10V
Note : provided by http://www.tml.jp/e/product/transducers/catalog_pdf/PI.pdf [24]
(a) Four point bending test
12
(b) Measurement details Fig. 3 Loading and measurement details (unit in mm)
4. EXPERIMENTAL RESULTS AND DISCUSSION
4.1 Cracking patterns Fig. 4 shows the cracking patterns of the test beams at failure. All specimens showed typical flexural crack patterns. The cracks were initiated in the maximum moment region between the two load points or right below one of the load points. More cracks appeared along the beam length as the load increased. They then propagated toward to the loading points with an inclined irregular shape. The failure for 2D13 and 3D16 specimens occurred by a GFRP rupture and concrete crushing for the other specimen cases, respectively, which it was predicted. Moreover, the sound caused by pulling out the GFRP bar was detected. Crack width was measured by PI gauge at the different location of the bottom surface of the beams within the loading points. It can represent the maximum crack width during the test.
13
(a) Concrete cover of 30 mm
(b) Concrete cover of 50 mm Fig. 4 Cracking patterns of test beams
14
Fig. 5 shows the flexural response based on the relationship of the applied load and deflection. The initial cracking load was observed at around 30.0 kN. All tested specimens exhibited the intended structural behavior in design of GFRP rupture or concrete crushing failure. 3D16 series expected in the concrete crushing failure had no sudden drop after the peak load, where the sudden drop of the applied load was detected for the 2D13 and 2D19 series. For 3D19 series, they showed tensile and compressive failure without the sudden drop of the applied load. Actually, Fig. 5 shows the load-deflection relationship until the peak load because the measurement of deflection was limited right before the sudden fracture of the beams for measuring safety. For the load-carrying capacity, it was significantly different between the low and high reinforcement ratios. The deeper effective depth affected to increase the nominal moment resistance as it was predicted. This phenomenon was more apparently observed for the mid-level reinforcement ratio of 0.595–0.651%, where it rarely affected the increase of the structural capacity for 3D19 series with the highest reinforcement ratio. This may be because the structural capacity is mainly governed by the higher reinforcement ratio rather than the variation of the effective depth within the same concrete compressive strength.
15
Fig. 5 Load-deflection relationship
5. MOMENT-CRACK WIDTH RELATIONSHIP
5.1 Crack control by ACI 440 1R-15 The ACI 318-99 [25] replaced the traditional approach with an indirect procedure for crack control through a maximum reinforcing bar spacing because of concerns on the adequacy of the empirically tuned models. The ACI 440 1R-15 recommended the design equation of effective moment of inertia based on the Branson’s equation. An additional factor was used to consider the reduced tension stiffening of the FRP-reinforced concrete member. This equation was identically used to calculate the moment of inertia of the GFRP-reinforced concrete member, such that the deflection of the cracked section could be calculated. The maximum FRP bar spacing would indirectly comply with a target maximum allowable crack width through the proposed flexural crack control equation. The equation was introduced in Eq. (3). 16
(3)
where smax = maximum permissible center to center bar spacing for flexural crack control (mm); Ef = design or guaranteed modulus of elasticity of FRP defined as mean modulus of sample of test specimens (MPa); = maximum allowable crack width (mm); = stress level induced in FRP at service loads (=efsEf) (MPa); = strain level induced in FRP at service loads cc = clear cover (mm); and b
= bond dependent coefficient.
For bond dependent coefficient kb was considered an important variable. Based on the design equation of ACI 440 1R-15, the upper and lower bound of kb was usually set as kb = 1.0 for having bond behavior similar to uncoated steel bars and kb = 1.4 for the case where kb = is not known from experimental data, is that a conservative value of 1.4 should be assumed, respectively. Weak bond case for kb =1.4 expects that the bar spacing results in the smaller value than that of the case of kb =1.0. From the relationship between the bar spacing and the applied moment, the cracking control comparison between the ACI 440 1R-15 and serviceability specifications is going to be examined and discussed for an appropriate boundary for evaluating the cracking control of FRP bar reinforced concrete beam. For the maximum allowable crack width, the designated two value, 0.5 mm for exposed and 0.7 mm unexposed, was used for cracking control analysis as introduced in ACI 440 1R-06. ACI 440 1R-15 denotes that the crack widths are limited by aesthetic reasons and the range of 0.4 to 17
0.7 mm is generally acceptable. The selection of the allowable crack width depends on the intended use of the structure. For aggressive environmental condition, very narrow crack width should be appropriate where wider cracks may acceptable due to the superior corrosion resistant of FRP reinforcement.
5.2 Moment-crack width comparison Fig. 6 exhibits the moment–crack width relationship of the test specimens. The crack width was plotted with the values from the Eq. (3) by ACI 440 1R-15. In order to investigate the effect of the reinforcing type such as the GFRP rupture and concrete crushing failure, the relative ratio of the sectional to balanced reinforcement ratio was considered. There could be two groups to be discussed. Fig. 6 shows that the relative ratio under 0.54 tended to estimate the calculated crack width to be large. Whereas, the specimens with a ratio over 0.77, including the concrete crushing failure, evaluated the calculated crack width to be small. For the diameter of reinforcement, the calculated crack width was lager that that of experimental results for the larger diameter specimens. It might be concluded that a larger reinforcement diameter generally had relatively lower bond capacity than that of the smaller diameter of reinforcement. Thus, it can explain that the tensile stress of the specimens reinforced with smaller diameter reinforcements is well distributed so that the experimental crack width may be lesser than the calculated crack width. As regards the effect of the concrete cover to the calculated crack width, the calculated crack width and concrete cover behaved proportionally, except for the 2D19 specimens. The effect was more understandable at around 20.0 kN·m. This result was in good agreement with the increased structural capacity caused by the deeper effective depth in flexure. The cracking control of a flexural member reinforced with the FRP bar should be dealt with in a more conservative aspect. kb was one of the most influential factors in determining the
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cracking control of the FRP bar-reinforced flexural members. For FRP bar, however, there is insufficient data to determine or generalize the bond coefficient and it is varied by the bar types, diameter, concrete compressive strength. And crack width comparison is quite hard because cracking is unstructured manner and the measurement of crack is sensitive too. Accordingly, the calculation and prediction of the crack width may be inappropriate and impractical approach for cracking control in structural design of FRP bar reinforced concrete structures.
(a) 2D13G-C30
(b) 2D19G-C30
(c) 3D16G-C30
(d) 3D19G-C30
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(e) 2D13G-C50
(f) 2D19G-C50
(g) 3D16G-C50
(h) 3D19G-C50
Fig. 6 Moment-crack width relationship according to the upper and lower bound of kb
6. CRACKING CONTROL COMPARISON OF SERVICEABILITY SPECIFICATIONS AND DESIGN EQUATION OF ACI 440 1R-15
6.1 Cracking control of experimental test by ACI 440 1R-15 The relationship between calculated bar spacing and applied moment is illustrated in Figure 7. The considered value of bond coefficient is 1.0 for good bond and 1.4 for poor bond, where 20
the crack width is 0.5 and 0.7 mm respectively. Above values were employed from ACI 440 1R-15, which provided upper or lower bound value if there are not appropriate recommendations. These four considered value were combined in the analysis of relationship between calculated bar spacing and applied moment as shown in Figure 7. There were quite different curves and it varied according to the combination of bond coefficient and crack width for each test specimen. The general aspect from the curves was the descending as applied moment was increased. This is true that the more amount of flexural reinforcements is needed to resist larger applied moment so that the bar spacing have to be narrower. Another significant result was that the bar spacing went to be narrow too if the bond property was poor (i.e. kb=1.4) or the allowable crack width was the more conservative (i.e. w=0.5). The relationship between calculated bar spacing and applied moment was also affected by the equivalent reinforcement ratio of ρf Ef/Es, which was employed to normalize the reinforcement ratio of the FRP bars to the steel bar [26]. As the reinforcement ratio is higher, the calculated bar spacing goes to the wider at the designated applied moment. This is the reason that the flexural capacity enhanced by the increased reinforcement ratio can effectively resist the crack opening to the longitudinal direction of the test beams for the same of bond coefficient and the allowable crack width.
6.2 Level of applicability of the serviceability in cracking Figure 7 additionally exhibits the bar spacing of two experimental cases (XX mm and XX mm) at the serviceable moment corresponding to the four serviceability specifications, which is based on the tensile strain of reinforcement for ISIS Canada 2007, allowable deflection for AASHTO 2009, compressive concrete strain for CSA-S6-10, and stress limit of GFRP bar for CSA-S6-14. The four dots stand for the results obtained above four specifications. The comparison can be explained that the cracking control is satisfied in case the dot is placed 21
within the relationship curve between the calculated bar spacing and applied moment. The dots which is out of the relationship curve can not explain the cracking control in present state so that the degree of serviceability may have to be varied to the lower state to meet the relationship curve. Thus, the existing serviceability specifications can provide different serviceability evaluation for the concrete beam reinforced with FRP bar. For the 2D13 specimens, with a low equivalent reinforcement ratio, only the serviceability in cracking of the ISIS Canada 2007 satisfied the bar spacing corresponding to the serviceable moment. Any no three of AASHTO LRFD 2009, CSA-S6-10 and CSA-S6-14 could meet the bar spacing for the serviceability in cracking. The 3D19G-C50 specimen with the highest equivalent reinforcement ratio of 0.273 could be valid for explaining the four serviceability specifications. This specimen also showed a sufficient spacing margin for the ISIS Canada 2007 and the AASHTO LRFD 2009. For the specimens with a mid-level equivalent reinforcement ratio from 0.125 to 0.258, only CSA S6-10 could not explain the serviceability in cracking of all specimens. Accordingly, serviceability recommendation of 0.001 strain of concrete compressive strength may provide overestimated serviceable capacity of FRP bar reinforced concrete structures under flexure. The finding is that the four serviceability specifications could differently evaluate the serviceability in cracking by the bond coefficient, allowable crack width, and the equivalent reinforcement ratio, respectively.
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(a) 2D13G-C30
(b) 2D19G-C30
(c) 3D16G-C30
(d) 3D19G-C30
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(e) 2D13G-C50
(f) 2D19G-C50
(g) 3D16G-C50
(h) 3D19G-C50
Fig. 7 Maximum bar spacing and applied moment relationship by ACI 440 1R-15 and comparison with the serviceability specifications
Table 5 summarizes the possible criteria of the serviceability specifications to examine the level of applicability of serviceability in cracking. It explained that the ISIS Canada 2007 could be employed in most of the relationship between calculated bar spacing and applied moment, whereas the CSA S6-10 was rarely satisfied. For the case of kb = 1.4 and w = 0.5 mm, shown as the lowest curve in Figure 7, it was quite hard to be explained with the serviceability specifications because this was a relatively tough level for serviceability in cracking. Only the test beam with the equivalent reinforcement ratio of 0.273 which has the highest value satisfied the serviceability recommendation of the CSA S6-10 for the case of kb = 1.0 and w = 0.7 mm. This case is the good bond property as well as the most wide crack width, which may be acceptable for the superior corrosion resistance of FRP reinforcement. Table 4 denotes that the equivalent reinforcement ratio is correlated with the level of applicability of serviceability in racking. It provides a significant finding that the four serviceability specifications should be seriously discussed for the cracking control of FRP 24
reinforced concrete beams in case of considering some of influencing factor, especially for the equivalent reinforcement ratio.
Table 5 Possible criteria of serviceability recommendations for the cracking control for the test specimens Beam ID
ρf E f / E s
kb=1.0
kb =1.4
w=0.5 mm
w =0.7 mm
w=0.5 mm
w =0.7 mm
2D13G-C30
0.075
ISIS Canada
ISIS Canada
N/A
ISIS Canada
N/A
ISIS Canada
ISIS Canada 2D19G-C30
0.125
ISIS Canada
AASHTO CSA S6-14
3D16G-C30
0.175
ISIS Canada AASHTO ISIS Canada
3D19G-C30
0.258
AASHTO CSA S6-14
2D13G-C50
0.08
ISIS Canada
2D19G-C50
0.182
ISIS Canada
3D16G-C50
0.186
0.273
AASHTO
AASHTO ISIS Canada
ISIS Canada
AASHTO
AASHTO
ISIS Canada
N/A
ISIS Canada
N/A
ISIS Canada
ISIS Canada AASHTO
AASHTO
AASHTO
CSA S6-14
ISIS Canada
ISIS Canada
ISIS Canada
AASHTO
ISIS Canada
CSA S6-14
ISIS Canada
ISIS Canada 3D19G-C50
ISIS Canada
ISIS Canada AASHTO
ISIS Canada
AASHTO CSA S6-14
ISIS Canada AASHTO
ISIS Canada
ISIS Canada
AASHTO
AASHTO
CSA-S6
CSA S6-14
7. CONCLUSIONS This study investigated the relationship between the FRP bar spacing and the applied moment based on the ACI 440 1R-15 for the experimental tests. And also, the level of applicability of
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the four serviceability specifications for serviceability in cracking was examined. The following conclusions are drawn from this study:
1. The GFRP-reinforced concrete beam showed an intended mode of failure and structural capacity, such as linear behavior up to failure. Even though the bond strength was reported higher than those of the commercial FRP bars, the ribbed GFRP bar used in this study still had 28–31% lower modulus of elasticity than that the steel bar. Accordingly, the serviceability in cracking should be further examined to apply the GFRP bar as a substitute of the steel bars.
2. The crack width could not be predictably obtained when or where the crack occurs as well as it is sensitive during the loading. From the result of the relationship between the applied moment and the crack width, hence, the comparison of crack width obtained from the calculation and the real state may be impractical to be verified in structural design.
3. For good bond property of kb=1.0, it was found that the calculated bar spacing corresponding to the applied moment was more released than that of poor bond property of kb=1.4, which was shown in all of test specimens. For the allowable crack width in narrower case (w=0.5 mm), the calculated bar spacing corresponding to the applied moment was more tightened than that of the allowable crack width in wider case (w=0.7 mm). These trends are globally same for all of the test specimens, however, the relationship between the calculated bar spacing and the applied moment is quite different according to varying the equivalent reinforcement ratio.
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4. For investigating the level of applicability of the serviceability specifications, the bar spacing corresponding to the serviceable moment base on the four specifications was compared with the relationship between the calculated bar spacing and the applied moment. The ISIS Canada 2007 could be employed in most of the relationship between the calculated bar spacing and the applied moment, whereas the CSA S6-10 rarely satisfied the relationship. As a result, the four serviceability specifications can provide quite different serviceability in cracking of FRP bar reinforced concrete structures. Therefore, the four serviceability specifications should be seriously discussed for the cracking control of FRP reinforced concrete beams in case of considering some of influencing factor, especially for the equivalent reinforcement ratio. The conclusions of this study was from somewhat limited experimental test results so that it can be incorporated further experimental studies into this study.
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