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Prediction of ultimate load of CFRP concrete interface in pure shear mode

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https://www.eduzhai.net International Journal of Composite Materials 2016, 6(6): 183-195 DOI: 10.5923/j.cmaterials.20160606.03 Prediction of Ultimate Load at the CFRP-Concrete Interface under Pure Shear Mode Mohsen A. Issa1,*, Momenur Rahman2, Rajai Alrousan3 1Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, USA 2University of Illinois at Chicago, Chicago, USA 3Department of Civil Engineering, Jordan University of Science and Technology, Irbid, Jordan Abstract The bond strength characteristics between Carbon Fiber Reinforced Polymer (CFRP) and concrete were investigated by conducting double face shear type pullout test. A simplified experimental setup was designed for the test to eliminate the eccentricity of active load across the bond interface. The objective of the study is to determine the ultimate bond strength and corresponding slip of CFRP-concrete interface using maximum bond stress (τmax). The effect of the concrete compressive strength (f 'c) and CFRP bond width (bf) were considered as key parameters. The results indicated that the ultimate load (Pu) increased with the increase in f 'c and bf. On the other hand, the slip (so) at τmax increased as a result of increasing concrete f 'c and decreased with increasing bf. Moreover, the failure mode was more brittle with higher concrete f 'c and/or smaller CFRP bf. An analytical model is proposed to predict the ultimate pullout load (Pu) and slip (so) at ultimate load. The proposed model provided a good prediction for Pu, τmax, and so for the bond between the CFRP and concrete. Keywords CFRP, Concrete, Bond stress, Ultimate bond capacity, CFRP-concrete interface 1. Introduction Externally bonded Fiber Reinforced Polymer (FRP) plates or sheets have been widely used to retrofit and rehabilitate deteriorated concrete structures. These materials provide several advantages attributed to their light weight, high strength characteristics, and ease of installation. The design of FRP plates or sheets is controlled by the bond characteristics between the FRP and concrete substrate [1, 2]. Plenty of research was carried out in the past decade to evaluate the bond stress-slip behavior at the FRP-concrete interface both experimentally and analytically. Several prediction models were developed; however, a unified simple formula is desired to estimate the pullout load or the anchorage area for strengthening or retrofitting of RC structures with CFRP. The paper presents an experimental investigation to evaluate the ultimate bond strength between CFRP laminates and concrete. The CFRP laminates were adhered on both faces of the concrete prism using epoxy. Previous studies measured the bond stress and slip at different levels using strain gauges and/or Linear Variable Displacement Transducers (LVDTs) in order to determine the effective bond length (Le) and the maximum bond strength (τmax) at the * Corresponding author: missa@uic.edu (Mohsen A. Issa) Published online at https://www.eduzhai.net Copyright © 2016 Scientific & Academic Publishing. All Rights Reserved FRP concrete interface. The test was simplified by using a single LVDT on each side of the CFRP-concrete interface. The study took into account of different bond configurations and concrete strength. In addition, an analytical model was developed to predict the test results. The analytical model can be used to determine the bond area required to resist a given load for strengthening RC structural members with externally bonded CFRP sheet. 2. Background Chen and Teng [3] investigated the anchorage strength properties of both FRP-to-concrete and steel plate-to-concrete bonded joints. They reviewed and assessed existing anchorage strength models using experimental data collected from literature and proposed a new design model based on existing experimental observations. Lu et al. [4] proposed three different models to predict the strength characteristics and bond slip between FRP and concrete. They collected experimental data from the literature and observed that most of the studies did not consider enough parameters to capture the bond-slip behavior. Moreover, they observed some scattering in the experimental results for several studies [5-8] in their database [4]. The scattering was detected in the trend of the ultimate load (Pu) between specimens with different configurations as well as between identical specimens. This scattering and inconsistency in the test results can affect the accuracy of the prediction model [4]. Therefore, it is essential to investigate all the factors 184 Mohsen A. Issa et al.: Prediction of Ultimate Load at the CFRP-Concrete Interface under Pure Shear Mode influencing the bond properties including the testing setup and equipment when testing the bond slip behavior between FRP and concrete. Dai et al. [9] conducted a single lap pullout test using 26 specimens to capture the bond stress-slip behavior at the FRP-concrete interface using different FRP types (CFRP, Aramid FRP, Glass FRP) and three different types of adhesives. They developed a nonlinear model based on interfacial fracture energy (Gf) and interfacial ductility index. McSweeney and Lopez [10] investigated the bond-slip behavior at the CFRP-concrete interface using different CFRP bond width (bf), thickness (tf), bond lengths (L), and varying concrete f 'c. They observed that the CFRP bf and tf and the concrete f 'c significantly affected the Pu while the FRP L didn’t show any notable effect. Fawzia et al. [11] concluded that the FRP tf has significant effect on Pu, while L exceeding the effective bond length (Le) didn’t show any notable effect. Ko et al. [12] reported that concrete f 'c, FRP stiffness, and Gf are the main contributing factors for the bond stress-slip behavior. They observed that the adhesive’s strength and stiffness have no significant effect on the bond-slip behavior. Studies reported in literature considered the FRP L effect on Pu as insignificant when it exceeds Le. Maeda et al. [13] reported that the Pu for CFRP strips did not increase for any L above 100 mm. Nakaba et al. [14] reported that the bond failure by FRP delamination occurs when L is less than 100 mm, while failure by FRP rupture takes place when the anchorage length is relatively large (greater than 300 mm). Several studies [3, 4, 13-18] proposed empirical formulas to estimate the Le. Table 1 summarizes the proposed Le models obtained from the literature. Another notable factor reported by previous studies on the bond-slip behavior at the FRP-concrete interface is the effect of acting load’s eccentricity. This eccentricity can occur due to misalignment in the tested specimens and/or applied load. The eccentricity of acting force when testing the bond between FRP and concrete under a single shear/lap joint test can induce undesirable flexural stresses that can influence the failure mode of the bonded assembly [19]. Nakaba et al. [14] performed experiments using laminates in both faces of the concrete prism and observed that it was not possible to avoid load eccentricity when specimens were set on the loading machine. In order to eliminate the effect of acting force’s eccentricity they modified Pu by multiplying it with a correction factor. A special experimental setup was designed for this study to eliminate the eccentricity across the concrete-bond interface. The bond slip behavior was investigated by conducting a double face shear type pullout test. The double shear type pullout test was conducted by holding the concrete blocks to the testing bed with a steel plate covering the top surface and anchored to the testing bed using threaded bolts. The steel plate was designed to cover the entire concrete surface in order to prevent failure of the concrete block at its leading edge with the CFRP. 3. Research Objective and Significance Two parameters were considered for investigation: (1) effect of CFRP bond width (bf), and (2) effect of concrete ultimate compressive strength (f 'c) on the bond strength behavior at the CFRP-concrete interface. This study has the following research significances: 1. The study developed a simple experimental setup that eliminates the acting load’s eccentricity across the CFRP-concrete bond interface. 2. Performed a parametric study with ample number (thirty) of test specimens considering the major aforementioned key parameters, so that the characteristics of CFRP-concrete bond interface can be captured. 3. A prediction model to calculate ultimate bond strength and corresponding slip model was developed based on regression analysis of experimental test results. The proposed model is simple and capable of predicting the ultimate bond strength, and the slip in terms of maximum bond stress. Table 1. Existing Models for Ultimate Load (Pu) and Effective Bond Length (Le) Source Maeda et al. (1997) Khalifa et al. (1998) Chen and Teng (2001) Yang et al. (2001)* Iso (2003)* Lu et al. (2005) Wu et al. (2009) Ultimate Bond Load Model, Pu 110.2x10-6 Ef tf Le bf 110.2x10-6 (f 'c /42)2/3Ef tf Le bf 0.427 βw (f 'c)0.5 Le bf (0.5+0.08 (Ef tf /100 ft)0.5) Le bf τu 0.93 f΄c0.44 bf Le Where Le=L if Le > L bf βl (2Ef tf Gf)0.5 if L > Le , βl =1 if L < Le , βl =sin(π.L/2Le) 0.595bp f 'c 0.1 (Ef tf )0.54 0.595bp f 'c 0.1 (Ef tf )0.54 (L/Le)1.2 if L > Le if L < Le Effective Bond Length, Le ???????????????? = ????????6.13−0.58???????????????? ???????????????? ???????????????? ???????????????? = ????????6.13−0.58???????????????? ???????????????? ???????????????? Le = (Ef tf /( f 'c)0.5)0.5 Le = 100 mm, τu = 0.5 ft Le = 0.125 (Ef tf )0.57 ???????????????? = ???????? + 1 2????????1 ???????????????? ????????1 ????????1 + − ????????2????????????????????????(????????2????????) ????????2????????????????????????(????????2????????) Le = 0.395 (Ef tf )0.54/ f 'c0.09 Note: All units are in SI. *Referred to Ahmed, E.Y. S et al. [18] International Journal of Composite Materials 2016, 6(6): 183-195 185 4. Experimental Program Test Specimens The mechanical properties of CFRP sheets and the epoxy bonding agent (epoxy resin) are summarized in Table 2. Rectangular concrete prism of 150 × 150 × 525 mm (6 × 6 × 21 in.) were cast and cured in the lab and then were cut into small prisms using a diamond blade saw-cut according to the desired length required for testing. Fig. 1 shows the bond-slip test configuration for CFRP sheets and concrete for all the specimens. The CFRP sheets were adhered to the concrete specimens after being moisture cured for 28 days. The details of the tested specimens are shown in Table 3. Specimen Details Fifteen different CFRP-concrete bond configurations were used. Each configuration consisted of two specimens, thus total of thirty (30) specimens were tested. The test configurations were divided into three groups (see Table 3). Each group represents different concrete f 'c. Each group consisted of ten specimens with five different CFRP bf ranging from 25 to 75 mm (1 to 3 in.). For the specimen designation shown in Table 3, the first letter “C” indicates the concrete f 'c and is followed by the numbers 6.2, 7.7, and 8.8 that stand for the f 'c of 6200 psi, 7700 psi, and 8800 psi, respectively. This is followed by the letter "L" which stands for the CFRP L and is followed by a numbers 4.5 indicating the L in inches. Finally, the letter "B" stands for the CFRP bf and is followed by the numbers 1, 1.5, 2, 2.5 and 3 indicating the bf in inches. Table 2. Materials Properties of CFRP and Epoxy CFRP(1) Epoxy(2) Ultimate strength Design strength Modulus of elasticity Ultimate strain Thickness Maximum stress Stress at rupture Maximum strain Yield strain Modulus of elasticity 620 ksi (4275 MPa) 570 ksi (3930 MPa) 33,500 ksi (231 GPa) 0.017 mm/mm 0.0065 inch (0.165 mm) 8 ksi (55 MPa) 7.9 ksi (54.5 MPa) 0.03 mm/mm 0.025 mm/mm 440 ksi (3 GPa) (1) Mechanical Properties were tested at UIC laboratory (2) Mechanical properties were provided by the manufacturer Table 3. Details of the Bond Slip Specimens Group Number Specimen Designation C8.8L4.5B1 f 'c, MPa (psi) L, mm (in.) bf , mm (in.) 25 (1) τmax, MPa (psi) 4.05(587) s0, mm (in.) 0.122 (0.0048) Pu, kN (Kips) 7.3 (1.64) C8.8L4.5B1.5 38 (1.5) 4.06 (588) 0.109 (0.00428) 11 (2.46) I C8.8L4.5B2 60.7 (8800) 113 (4.5) 50 (2) 4.39 (637) 0.096 (0.00377) 15.8 (3.55) C8.8L4.5B2.5 63 (2.5) 4.55 (661) 0.086 (0.00338) 19.9 (4.47) C8.8L4.5B3 75 (3) 4.54 (658) 0.08 (0.00316) 23.7 (5.33) C7.7L4.5B1 25 (1) 3.01 (436) 0.00417 (0.106) 5.9 (1.33) C7.7L4.5B1.5 38 (1.5) 3.24 (469) 0.0036 (0.0912) 9.5 (2.15) II C7.7L4.5B2 53.1 (7700) 113 (4.5) 50 (2) 3.30 (479) 0.0032 (0.0822) 13 (2.92) C7.7L4.5B2.5 63 (2.5) 3.49 (505) 0.0029 (0.0739) 16.6 (3.73) C7.7L4.5B3 75 (3) 3.61 (523) 0.0026 (0.0655) 20.6 (4.64) C6.2L4.5B1 25 (1) 3.44 (499) 0.00478 (0.1214) 6.4 (1.44) C6.2L4.5B1.5 38 (1.5) 3.81 (552) 0.004 (0.1016) 10.6 (2.39) III C6.2L4.5B2 42.7 (6200) 113 (4.5) 50 (2) 3.89 (564) 0.00361 (0.0916) 14.5 (3.26) C6.2L4.5B2.5 63 (2.5) 4.09 (593) 0.00325 (0.0826) 18.5 (4.15) C6.2L4.5B3 75 (3) 4.15 (601) 0.0029 (0.0748) 22.4 (5.04) Note: Two specimens were tested for each case 186 Mohsen A. Issa et al.: Prediction of Ultimate Load at the CFRP-Concrete Interface under Pure Shear Mode Figure 1. Typical layout of bond slip test setup and specimen Test setup A double face shear type pullout test was designed specifically to eliminate the acting load’s eccentricity on the CFRP-concrete interface (see Fig. 1). The test setup consists of a 25.4 mm (1 in.) thick steel plate with four 19.1 mm (0.75 in.) size anchor bolts, and a 152.4mm (6 in.) diameter steel smooth cylindrical roller. The diameter of the cylindrical roller was designed to match the width of the concrete prisms and assure a pure shear/sliding state mode along the CFRP-concrete interface. The plate and anchor bolts system were used to fix the concrete prism to the machine’s steel bed during testing. The CFRP strip was wrapped around the cylindrical roller, and the two ends were bonded to both sides of the concrete prism using epoxy resin. The steel roller was directly attached to the load cell using mechanical fasteners. Instron 8800 hydraulic machine (capacity 225 KN) was used to apply load on the specimens. The fixture was adjusted manually so that the face of cylindrical roller is in perfect alignment with concrete block’s face. Two LVDTs were mounted at each side of the CFRP-concrete interface to measure the slip/displacement while pulling out the CFRP sheet. The load and displacement readings were collected through a portable data acquisition system (model TDS-303). Eccentricity was eliminated by averaging the readings obtained from the two LVDTs readings attached on each side of the specimen. 5. Experimental Results and Discussion Load and displacement data were collected for each specimen. The slip (s), which is the relative displacement between concrete and the CFRP strip, was measured directly from the LVDTs. The bond stress (τ) was calculated by dividing the respective pullout load (P) by the area of the bonded CFRP strip to concrete (Ab = L × bf). The P on each strip was taken as half of the overall load applied on the specimen. Max bond strength (τmax) is taken as the ultimate load (Pu) divided by Ab i.e., (Pu/Ab). The τmax represents the maximum value of bond stress along the bond length and the corresponding slip (so) is measured from the LVDTs. Mode of Failure The failure of the specimens was brittle and followed by interfacial debonding of the CFRP strips from the concrete surface by removing a thin layer of concrete. For a given boundary conditions, all the tested specimens exhibited similar failure mode (i.e., interface debonding) irrespective of the concrete f 'c, and bf. Typical failure was initiated by making a peeling off sound during the early to middle stage of loading signifying the starting point of the interfacial bond delamination. When the ultimate load was approached, the CFRP strip debonded from the concrete surface following a loud noise due to the sudden release of energy. After debonding, the specimens experienced a significant loss in resistance and the load dropped gradually. Fig. 2 shows the modes of failures of specimens with different f 'c and CFRP bf, respectively. The interface debonding of CFRP strip from the concrete surface was expected, since the bond interface of CFRP to concrete was subjected to pure shear mode during the load application. It is noteworthy to mention that the test setup for this study was designed to prevent any failure initiating by either splitting or cracking at the leading edge of the concrete prism. The bond stress vs. slip behaviors for all specimens are shown in Fig. 3. Investigation of Fig. 3 reveals that the bond slip behavior is formed of an ascending branch and a descending or softening branch with the bond stress (τ) approaching zero at maximum slip. The test results revealed that the initial stiffness of the CFRP concrete bonding increased with the increase in bf. It was observed during testing that the specimens with lower concrete f 'c or larger CFRP bf experienced more brittle failure. Effective bond length (Le) Maeda et al. [13] reported the concept of effective bond length (Le). The ultimate pullout load between CFRP and concrete interface under single/double shear type specimens does not increase after a certain bond length (L); which is known as effective bond length (Le). They proposed an empirical formula to estimate the effective bond length (Le) International Journal of Composite Materials 2016, 6(6): 183-195 187 which is a function of axial stiffness (Ef tf) of FRP strips. Chen and Teng [3] proposed a new formula to calculate the Le incorporating the effect of the ultimate compressive strength of concrete (f 'c). According to Chen and Teng [3], the effective bond length increases with increasing the FRP axial stiffness (Ef tf) and decreases with increasing concrete f 'c. Nakaba et al. [14] reported that the interface debonding takes place when the bond length is short (less than 100 mm). However, debonding takes place by rupturing of FRP strips or splitting of concrete when the bond length is relatively large (greater than 300 mm). Yang et al. [16], Iso [18], Lu et al. [4], and Wu et al. [17] proposed different empirical formulas to estimate the Le. The calculated Le using Table 1 varies from 55 mm (2.2 in.) to 82 mm (3.2 in.) for a single layer of CFRP strips (tf = 0.165 mm) and concrete f 'c of 60.7 MPa. The study adopted the Cheng and Teng model [3] to calculate the Le because the formula incorporated both axial stiffness and f 'c. It was found to be more consistent with the test data. In this study, the L was chosen such that L > Le for all of the specimens to make sure bond failure of CFRP-concrete interface is controlled by the delamination of CFRP strips from the concrete substrata. Effect of Bond Width (bf) The effect of CFRP bf on the maximum bond stress (τmax), ultimate load (Pu), and the corresponding slip (so) is shown in Fig. 4. The test results of τmax, so, and Pu for all specimens with variable bf (Groups I, II, and III) are reported in Table 3. Inspection of Fig. 4 reveals that the τmax increased and the so decreased as a result of increasing the CFRP bf /bc ratio. The change in both τmax and so over CFRP bf /bc ratio demonstrates a linear trend with a good correlation coefficient (R2 value exceeding 0.9). The Pu also increased with increasing bf /bc ratio (see Fig. 4(b)) demonstrating a linear trend between Pu and bf /bc. It was revealed that a 14 mm (0.55 in.) increase in bf increased the Pu by 4.4 KN (1.0 Kips). The experimental results of Ueda et al. [20], Tan [7], Ren [8], and McSweeney and Lopez [10] exhibited a significant increase in the Pu as a result of increasing FRP bf. Chen and Teng [3] stated that the FRP bf has significant effect on the load transfer from the FRP strips to the concrete blocks. If FRP bf is comparatively narrower than the width of the concrete block, it can result in non-uniform load transfer from the FRP strip to the concrete. This behavior leads to high stress concentration at the bond interface that is close to the point of load application, thereby reducing the Pu at bond failure. This signifies that concrete blocks with smaller CFRP bf may have experienced higher stress concentration at locations close to the leading edge of CFRP-concrete interface. Effect of Concrete Compressive Strength (f 'c) The effect of concrete f 'c on the τmax, so, for different bf /bc is shown in Fig. 5 & 6 respectively. Inspection of Fig. 5 and Fig. 6 indicates that the increase in concrete f 'c cause an increase in the τmax and so significantly. However, it does not have any significant effect on the ultimate load Pu (See Fig 4 (b)); because Le is a function of f 'c and it decreases with increasing f 'c. The maximum bond strength τmax increased as a result of increasing the concrete f 'c for any particular bf /bc. The effect of the concrete f 'c, varying from 42.7 to 60.7 MPa, on the Pu is presented in Fig. 4(b). The Fig. 4(b) demonstrates that the effect of concrete f 'c was very low for specimens with CFRP bf /bc ratio less than 0.30 but showed significant effect on the Pu for specimens with CFRP bf /bc above 0.40. However, the increase in concrete f 'c increases both τmax, and so significantly and demonstrates a linear increasing trend over �????????????????′ . The Pu increase due to concrete f 'c was observed less significant compared to other studies (Lu et al. [4] database). These studies observed that the Pu will increase as a result of increasing f 'c. Their specimens failed by either splitting of the concrete block or by stripping out a concrete chunk at the leading edge of the FRP concrete interface however, the present study observed interface deboning between CFRP and concrete surface. Varying Bond Width (bf) Figure 2. Mode of failure in specimens 188 Mohsen A. Issa et al.: Prediction of Ultimate Load at the CFRP-Concrete Interface under Pure Shear Mode Bond stress (τ), ksi Bond stress (τ), MPa Bond stress (τ), ksi Bond stress (τ), MPa 0 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 Slip (s), in. 0.02 0.04 0.06 Group I f'c = 60.7 MPa (8800 psi) L = 112.5 mm (4.5 in.) bf= 75 mm (3 in.) bf = 62.5 mm (2.5 in.) bf = 50mm (2 in.) bf = 37.5 mm (1.5 in.) bf = 25 mm (1 in.) 0.5 1 1.5 Slip (s), mm 0.08 0.6 0.5 0.4 0.3 0.2 0.1 0 2 (a) Bond stress vs. slip for Group I (f 'c = 60.7 MPa; L = 112.5 mm) 0 4.5 Slip (s), in. 0.02 0.04 0.06 0.08 0.6 4 Group II 3.5 f'c = 53.1 MPa (7700 psi) L = 112.5 mm (4.5 in.) 0.5 3 0.4 2.5 bf= 75 mm (3 in.) 0.3 2 bf = 62.5 mm (2.5 in.) 1.5 bf = 50mm (2 in.) 0.2 1 bf = 37.5 mm (1.5 in.) 0.1 0.5 bf = 25 mm (1 in.) 0 0 0 0.5 1 1.5 2 Slip (s), mm (b) Bond stress vs. slip for Group II (f 'c = 53.1 MPa; L = 112.5 mm) Slip (s), in. 0 0.02 0.04 0.06 0.08 4 0.6 3.5 Group III f'c = 42.7 MPa (6200 psi) 0.5 3 L = 112.5 mm (4.5 in.) 2.5 0.4 bf= 75 mm (3 in.) 2 0.3 bf = 62.5 mm (2.5 in.) 1.5 bf = 50mm (2 in.) 0.2 1 bf = 37.5 mm (1.5 in.) 0.5 0.1 bf = 25 mm (1 in.) 0 0 0 0.5 1 1.5 2 Slip (s), mm (c) Bond stress vs. slip for Group III (f 'c = 42.7 MPa; L = 112.5 mm) Figure 3. Bond vs. Slip behavior of all the tested specimens Bond stress (τ), ksi Bond stress (τ), MPa International Journal of Composite Materials 2016, 6(6): 183-195 189 τmax (MPa) Pu (KN) 5 4 R² = 0.86 R² = 0.92 3 R² = 0.98 2 f'c = 60.7 MPa 1 f'c= 53.1 MPa f'c= 42.7 MPa 0 0 0.2 0.4 0.6 bf /bc (a) τmax vs. bf /bc and concrete f 'c 0.15 R² = 0.97 R² = 0.96 0.1 R² = 0.98 30 f'c = 42.7 MPa 25 f'c = 53.1 MPa 20 f'c = 60.7 MPa 15 10 R² = 0.998 R² = 0.999 5 R² = 0.998 0 0 0.2 bf /bc 0.4 0.6 (b) Pu vs. bf /bc and concrete f 'c so (mm) 0.05 f'c = 60.7 MPa f'c= 53.1 MPa f'c= 42.7 MPa 0 0 0.2 0.4 0.6 bf /bc (c) so vs. bf /bc and concrete f 'c Figure 4. Effect of bf/bc and concrete f 'c on the maximum bond stress (τmax) 6. Development and Validation of Prediction Model Development of Prediction Model for CFRP-Concrete Bond A prediction model for Pu and so was proposed based on the regression analysis of the results obtained from the 30 pullout test specimens. The proposed prediction model is an enhancement of ultimate load prediction model originally proposed by Chen and Teng [3]. The model is based on prediction of effective CFRP bond area. The effective bond area is defined as Ab = Le x bf; where Le is the effective bond length. According to studies in literatures it was observed that τmax is proportional to tensile strength of concrete which is a function of �????????????????′ . The data for τmax for every specimen and corresponding �????????????????′ of that specimen were shown in Fig 7(a). Inspection of Fig. 7(a) revealed that there is a strong linear correlation (R2 = 0.99) between τmax and �????????????????′ . Similarly, so and the corresponding �????????????????′ for all specimen were shown in Fig. 7 (b). Fig. 7 revealed that the both τmax and so are affected by the change of �????????????????′ . The proposed equations for τmax and so are shown in Eqs. (1) and (2): ???????????????????????????????? = ????????1????????????????,???????? ????????????????�????????′???????? (1) ???????????????? = ????????2????????????????,????????????????????????�????????′???????? (2) Where α1 and α2 are the regression constants; and βw and βL are the correction factors for CFRP bf and L, respectively. The Equations for βw and βL for CFRP-concrete bond interface are given in Eq. (3) ???????????????? ,???????? = ��21..2255−−???????????????? ???????? ???????? /???????????????? /???????????????? � (3a) ???????????????? ,???????? = ��21−+???????????????????????????????? /???????????????? /???????????????? � (3b) ???????????????? = ��21..2255−+????????????????//????????????????????????????????� (3c) The α1 values was obtained by performing regression analysis between the maximum bond stress (τmax) and ????????????????,???????? ????????????????�????????′???????? (see Fig. 7(a)). Similarly, α2 was found from the relation between the normalized slip at τmax (so) and 190 Mohsen A. Issa et al.: Prediction of Ultimate Load at the CFRP-Concrete Interface under Pure Shear Mode ????????????????,????????????????????????�????????′???????? (see Fig. 7(b)). Based on the regression analysis of experimental results, the values of α1 and α2 are 0.385, and 0.0132, respectively. Once the τmax and so are calculated, the ultimate load Pu can be estimated by using Eq. (4) ???????????????? = ???????????????????????????????? ???????????????? ???????? When, L>Le; L=Le (4) The final equations for τmax and so are listed in Eqs. 5 & 6. ???????????????????????????????? = 0.385????????????????,???????? ????????????????�????????′???????? (5) ???????????????? = 0.0132????????????????,????????????????????????�????????′???????? (6) Prediction of Ultimate Load (Existing vs. Proposed Model) According to the proposed model The experimental ultimate load can be found from Eq. (7): ???????????????? = ???????????????????????????????? ???????????????? ???????? When, L>Le; L=Le (7) ???????????????? = ???????????????? ???????????????? � �????????????????′ (8) τmax (MPa) τmax (MPa) τmax (MPa) τmax (MPa) 5 4 R² = 0.96 3 2 1 bf /bc = 0.16 0 0 2 4 6 8 10 �????????′???????? 5 4 R² = 0.86 3 2 1 0 0 2 4 bf /bc = 0.25 6 8 10 �????????′???????? 5 4 R² = 0.99 3 2 1 0 0 2 4 τmax (MPa) bf /bc = 0.33 6 8 10 �????????′???????? 5 4 R² = 1.00 3 2 1 0 0 2 4 5 4 R² = 1.00 3 2 1 0 0 2 4 bf /bc = 0.42 6 8 10 �????????′???????? bf /bc = 0.5 6 8 10 �????????′???????? Figure 5. Effect of concrete f 'c on the maximum bond stress (τmax) International Journal of Composite Materials 2016, 6(6): 183-195 191 so (mm) so (mm) so (mm) so (mm) 0.15 0.1 R² = 0.86 0.15 0.1 R² = 0.98 0.05 bf/bc = 0.16 0.05 bf/bc = 0.25 0 0 2 4 6 8 10 0 0 2 4 6 8 10 �????????′???????? 0.15 �????????′???????? 0.15 0.1 R² = 0.99 0.05 bf/bc = 0.33 0 0 2 4 6 8 10 �????????′???????? 0.15 0.1 R² = 1.00 0.05 bf/bc = 0.42 0 0 2 4 6 8 10 �????????′???????? so (mm) 0.1 R² = 1.00 0.05 bf/bc = 0.50 0 0 2 4 6 8 10 �????????′???????? Figure 6. Effect of concrete f 'c on the slip at maximum bond stress (so) 0.15 5 4 R2=0.99 3 R2 = 0.92 0.1 2 1 0.05 τmax=????????.???????????????????????? ????????????????????????????????�????????′???????? S0=????????.???????????????????????????????? ????????????????????????????????�????????′???????? 0 0 0 5????????????????????????????????�????????′???????? 10 15 0 5????????????????????????????????�????????′???????? 10 15 Figure 7. Relationship between maximum bond strength (τmax) and slip at τmax (so) with f 'c ratio τmax (MPa) so (mm) 192 Mohsen A. Issa et al.: Prediction of Ultimate Load at the CFRP-Concrete Interface under Pure Shear Mode Predicted (KN) Predicted (KN) 0 30 25 20 15 10 5 0 0 5 10 15 20 25 Maeda et al. (1997) R2 = 0.99 CV = 0.08 5 10 15 20 25 Test (KN) 30 0 30 30 25 25 20 20 15 15 10 10 5 5 0 0 30 0 5 10 15 20 25 Khalifa et al. (1998) R2 = 0.95 CV =0.05 5 10 15 20 25 30 30 25 20 15 10 5 0 30 0 30 25 20 15 10 5 0 0 5 10 15 20 25 30 0 30 30 Chen and Teng (2001) 25 25 20 20 15 15 R2 = 0.99 CV=0.14 10 10 5 5 0 0 5 10 15 20 25 30 0 5 10 15 Yang et al. (2001) 5 10 15 20 25 R2 = 0.99 CV= 0.06 20 25 30 30 25 20 15 10 5 0 30 0 30 25 20 15 10 5 0 0 5 10 15 Lu et al. (2005) 5 10 15 20 25 30 0 30 30 25 25 20 20 15 15 R2 = 0.98 CV= 0.15 10 10 5 5 0 0 20 25 30 0 5 10 15 Iso et al. (2003) 5 10 15 20 25 30 30 25 20 15 10 R2 = 0.99 CV=0.05 5 0 20 25 30 0 30 25 20 15 10 5 0 0 5 10 15 Wu et al. (2009) 5 10 15 20 25 30 0 30 30 25 25 20 20 15 15 R2 = 0.98 CV=0.07 10 10 5 5 0 0 20 25 30 0 Test (KN) 5 10 15 proposed model 5 10 15 20 25 30 30 25 20 15 R2 = 1.00 10 CV=0.03 5 0 20 25 30 Figure 8. Proposed model and other research models for Pu vs. Experimental Pu

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