# Shear Strengthening Performance of Hybrid FRP-FRCM

Authors: Kyusan Jung; Kinam Hong; Sanghoon Han; Jaekyu Park; Jaehyun Kim
Journal: Advances in Materials Science and Engineering
 (2015)

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## Abstract

The effectiveness of a hybrid fiber reinforced polymer- (FRP-) fabric reinforced cementitious matrix (FRCM) for shear strengthening was investigated though an experimental study. FRP materials of FRCM are usually fabricated in the form of a fabric to enhance the bond strength between the FRP material and the cementitious matrix. The hybrid FRP fabric used in this study consisted of carbon FRP (CFRP) and glass FRP (GFRP) in warp and weft directions, respectively. A total of 11 beams were fabricated and 8 beams among them were strengthened in shear with externally bonded hybrid FRP-FRCM. The number of plies, the bond types, and the spacing of the hybrid FRP fabric were considered as experimental variables. Additionally, a shear capacity model for a FRCM shear strengthened beam was proposed. The values predicted by the proposed model were compared with those by the ACI 549 code and test results. It was confirmed from the comparison that the proposed model predicted the shear strengthening performance of the hybrid FRP-FRCM more reliably than the ACI 549 code did.


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## Body

## 1. Introduction

FRP has been widely used as a strengthening material to strengthen deteriorated reinforced concrete (RC) structures all over the world [1]. As a strengthening material, FRP possesses excellent material properties including being lightweight and noncorrosive and providing high tensile strength [2]. On this basis, FRP has been applied for strengthening RC structures in various forms such as sheets, plates, and strips since the early 1990s [3]. Many studies on FRP have validated the effectiveness of its use as a strengthening material [4]. However, FRP is accompanied by several distinct disadvantages. The performance of FRP strengthening for RC structures, which may be exposed to sunlight or high temperature conditions, is degraded due to the low glass transition temperature of epoxy resin, a bonding agent. FRP strengthening using epoxy resin is also vulnerable to fire. Additionally, epoxy resin cannot be used under a wet condition due to its low hardening property.In order to solve these problems, a strengthening method using a fabric-reinforced cementitious matrix (FRCM) was developed [5]. FRCM consists of FRP fabric and a cementitious matrix. The mineral cementitious matrix can solve various problems caused by using epoxy resin as a bonding agent. FRCM was first introduced as textile reinforced concrete (TRC) in a report published by RILEM Technical Committee 201 [6]. It has since then been widely reported on in the literature with various names including textile reinforced mortar (TRM) [7], fiber reinforced concrete (FRC) [8], and mineral based composites (MBC) [9].Research using FRCM as a shear strengthening material has been performed by researchers worldwide. Baggio et al. performed experimental research on RC beams strengthened in shear with CFRP, GFRP, FRCM, and FRP anchors [10]. The effectiveness of each material in terms of shear strengthening was evaluated and test results were compared with predicted values by the Canadian design code. Beams strengthened by using FRCM with and without anchors showed a 31% and 34% increase in shear capacity relative to the Control specimen, respectively. The Canadian design code appropriately predicted the shear capacity of beams strengthened with FRP sheets but overestimated those of FRCM strengthened beams. Triantafillou and Papanicolaou carried out an experimental study to investigate the effectiveness of CFRP-FRCM shear strengthening [7]. Although the effectiveness of FRCM shear strengthening was relatively lower than FRP shear strengthening, the applicability of FRCM as a shear strengthening material was validated. Ombres experimentally examined the effectiveness of polyparaphenylene benzobisoxazole (PBO) FRCM for shear strengthening [11]. Its shear strengthening performance was predicted by a model based on Ritter-Morsch criteria failure. He reported that the PBO-FRCM strengthening system significantly improved the shear capacity of reinforced concrete beams and prediction by the model based on the Ritter-Morsch criteria failure is effective to predict the PBO-FRCM performance. Brückner et al. experimentally explored the effectiveness of GFRP-FRCM for shear strengthening [12, 13]. The number of GFRP plies, the use of mechanical anchors, and anchorage methods were considered as experimental variables in their study. Their test results showed that FRCM is effective for shear strengthening and the mechanical anchor improves the FRCM shear strengthening performance by 200%. Al-Salloum et al. also reported that FRCM is effective in increasing the shear capacity of beams subjected to a four-point load [14]. Recently, a design code for strengthening RC structures and masonry walls with externally bonded FRCM was issued by ACI Committee 549 [15].Nevertheless, the applicability of existing design codes should be established by experimentally exploring the influence of various experimental parameters such as concrete strength, cementitious matrix type, and FRP material type on shear strengthening. Experimental research on RC beams strengthened in shear with externally bonded FRCM, which was made from a hybrid fabric and a cementitious matrix, was performed in this study. The number of plies, the bond type, and the spacing of a hybrid FRP fabric were considered as experimental variables. The effect of test variables on the shear strengthening capacity was evaluated through test results and a shear strength prediction model for a hybrid FRP-FRCM strengthened beam was proposed. The values predicted by the proposed model were compared with those by ACI 549 [15] and test results.


## 2. Test Program

### 2.1. Used Materials

Type I ordinary Portland cement (OPC) was used in the mixture. Crushed gravel was used as the coarse aggregate and the maximum aggregate size was 25 mm. In addition, AE water-reducing admixture and a vibrator were used to improve the workability and consolidation of the concrete. Table1 shows the mixture properties of the used concrete.Table 1
Mixture properties of the concrete.
W/C (%)
S/a (%)
Unit weight (kg/m3)
W
C
S
G
Ad(a)
48.4
48.1
168
345
860
949
2.07
(a)AE water-reducing admixture.Concrete compressive strength was determined from a compression test for six cylinders with dimensions of ø100 mm × 200 mm according to ASTM C39/C39M [18]. The average concrete compressive strength was 28.0 MPa at the age of 28 days. The mechanical properties of each used rebar were determined from tension tests for three coupons according to ASTM A370 [19] and the results are given in Table 2.Table 2
Mechanical properties of rebar.
Nominal diameter(mm)
Modulus of elasticity(MPa)
Yield strength(MPa)
Tensile strength(MPa)
Elongation(%)
9.53
2.0 × 105
480
590
17.1
15.9
515
610
16.6The cementitious matrix and the hybrid FRP fabric used for shear strengthening of RC specimens in this study are shown in Figures1(a) and 1(b), respectively. Cementitious matrix consisted of microcement, fine aggregate, polypropylene staple fiber, and admixtures. The compressive strength of the cementitious matrix was determined from a compression test for five cubes of 50 mm size according to ASTM C109/C109M [20] and taken as 45 MPa at the age of 28 days. As shown in Figure 1(b), the hybrid FRP fabric consisted of CFRP and GFRP strips. Black CFRP and white GFRP strips were laid in the warp direction and weft direction, respectively, at spacing of 17 mm and 33 mm. Mechanical properties of the FRCM composite made from the hybrid FRP fabric and the cementitious matrix were determined by a direct tensile test in accordance with AC 434 [16], as shown in Figure 2. Table 3 presents the mechanical properties of the hybrid FRP fabric and the cementitious matrix offered by manufacturers and those of the FRCM composite obtained from the direct tensile test.Table 3
Hybrid FRP-FRCM mechanical properties.
Nominal thickness
Elastic modulus
Ultimate tensile strength
Ultimate tensile strain
Compression strength
(mm)
(GPa)
(MPa)
(%)
(MPa)
Hybrid fabric
0.107
240
4,300
1.75
—
Cementitious matrix
—
40
—
—
45
FRCM composite
—
160(cracked specimen)
800
0.5
—Figure 1
Components of hybrid FRP-FRCM system.
(a)
Cementitious matrix
(b)
Hybrid FRP fabricFigure 2
Direct tensile testing by AC 434 [16].
(a)
Test setup for direct tensile testing of a flat hybrid FRP-FRCM coupon
(b)
Idealized tensile stress-strain curve for FRCM


### 2.2. Test Variables

As shown in Table4, specimens were classified into four groups. Specimens in Group I consisted of nonstrengthened specimen and steel stirrup-strengthened specimens to evaluate the relative shear-strengthening performance of the hybrid FRP-FRCM.Table 4
Test variables.
Group
Specimen ID
Strengthening type
Layer
Width × number
Installation
I
Control
None
None
None
None
S300
Steel stirrup
None
None
None
S200
II
W600-L1
Side-bonding
1
600 mm × 1
W600-L2
2
W50-N4
U-jacketing
1
50 mm × 4
III
W50-N5
50 mm × 5
W50-N6
50 mm × 6
W100-N3
100 mm × 3
IV
W100-N4
100 mm × 4
W600-N1
600 mm × 1The nonstrengthened specimen was designated as Control, and the specimens reinforced with steel stirrups at spacing of 200 mm and 300 mm were denoted by S200 and S300, respectively. Specimens in Group II consisted of specimens strengthened in shear by side-bonding. The specimens were named according to the width and the number of plies of the used hybrid FRP fabric. The specimens strengthened with 1-ply and 2-ply 600 mm hybrid FRP fabric were designated as W600-L1 and W600-L2, respectively. Specimens in Groups III and IV consisted of specimens strengthened by U-jacketing. The specimens strengthened by U-jacketing were named according to the width and number of plies of hybrid FRP fabric. For example, W50-N5 was strengthened with 5 pieces of 50 mm wide hybrid FRP fabric. The sixth column of Table4 shows hybrid FRP fabric attached on the shear span according to experimental variables.


### 2.3. Specimen Fabrication and Strengthening

As shown in Figure3, a total of 11 specimens having a length of 2,000 mm with a rectangular cross-section 150 mm wide and 300 mm high and a net span of 1,800 mm were fabricated for the tests. All specimens were reinforced with two rebars with a nominal diameter of 15.9 mm as tension reinforcement and two rebars with a nominal diameter of 9.53 mm as compression reinforcement.Figure 3
Test specimen layout.Specimens S200 and S300 were reinforced by rebars with a nominal diameter of 9.53 mm with spacing of 200 mm and 300 mm as shear reinforcement, respectively. After curing of 28 days, the shear strengthening specimens were strengthened with the hybrid FRP-FRCM as follows. First, the specimen surface was cleaned with tap water to remove impurities before strengthening. In order to keep the humid condition, the specimen surface was then covered with damp cloth until strengthening work. Specimens strengthened by U-jacketing were reversed and then chamfered to a radius of 10 mm to avoid damage to the hybrid FRP fabric due to stress concentration during the tests. Specimens were strengthened with hybrid FRP-FRCM according to the test variables. The strengthening procedure of the FRCM composite was as follows: (1) the first layer of cementitious matrix with a nominal thickness of 2 mm was applied on the side surface of the specimen; (2) the precut hybrid FRP fabric was laid on the cementitious matrix; and (3) the second layer of cementitious matrix with a nominal thickness of 2 mm was applied on the hybrid FRP fabric. In the case of strengthening with 2-ply hybrid FRP fabric, the above procedure was repeated two times. The nominal thickness of hybrid FRP-FRCM with 1-ply hybrid FRP fabric was taken as approximately 5 mm. Tests were performed after 28 days of strengthening for the cementitious matrix to develop sufficient strength.


### 2.4. Test Setup

The shear tests for 11 specimens were performed by four-point loading, as shown in Figure4. The specimens were simply supported and the load was applied at two points 300 mm apart at both the left and right sides of the midspan. The load was applied by stroke control loading at a rate of 0.4 mm/min with a hydraulic actuator with a maximum capacity of 2,000 kN. The load was measured by a load cell. The vertical displacement at the midspan was measured by two linear variable differential transformers (LVDTs).Figure 4
Test setup.As shown in Figure3, the strain of the hybrid FRP fabric was measured by eight strain gauges attached on the CFRP fabric strips at both the left and right sides of the shear span. The CFRP strip of the hybrid FRP fabric was grinded and cleaned with acetone before attachment of strain gauges. Load and strains were recorded by using a data logger. Crack propagation and FRCM composite damage were visually monitored and recorded during all tests.


## 2.1. Used Materials

Type I ordinary Portland cement (OPC) was used in the mixture. Crushed gravel was used as the coarse aggregate and the maximum aggregate size was 25 mm. In addition, AE water-reducing admixture and a vibrator were used to improve the workability and consolidation of the concrete. Table1 shows the mixture properties of the used concrete.Table 1
Mixture properties of the concrete.
W/C (%)
S/a (%)
Unit weight (kg/m3)
W
C
S
G
Ad(a)
48.4
48.1
168
345
860
949
2.07
(a)AE water-reducing admixture.Concrete compressive strength was determined from a compression test for six cylinders with dimensions of ø100 mm × 200 mm according to ASTM C39/C39M [18]. The average concrete compressive strength was 28.0 MPa at the age of 28 days. The mechanical properties of each used rebar were determined from tension tests for three coupons according to ASTM A370 [19] and the results are given in Table 2.Table 2
Mechanical properties of rebar.
Nominal diameter(mm)
Modulus of elasticity(MPa)
Yield strength(MPa)
Tensile strength(MPa)
Elongation(%)
9.53
2.0 × 105
480
590
17.1
15.9
515
610
16.6The cementitious matrix and the hybrid FRP fabric used for shear strengthening of RC specimens in this study are shown in Figures1(a) and 1(b), respectively. Cementitious matrix consisted of microcement, fine aggregate, polypropylene staple fiber, and admixtures. The compressive strength of the cementitious matrix was determined from a compression test for five cubes of 50 mm size according to ASTM C109/C109M [20] and taken as 45 MPa at the age of 28 days. As shown in Figure 1(b), the hybrid FRP fabric consisted of CFRP and GFRP strips. Black CFRP and white GFRP strips were laid in the warp direction and weft direction, respectively, at spacing of 17 mm and 33 mm. Mechanical properties of the FRCM composite made from the hybrid FRP fabric and the cementitious matrix were determined by a direct tensile test in accordance with AC 434 [16], as shown in Figure 2. Table 3 presents the mechanical properties of the hybrid FRP fabric and the cementitious matrix offered by manufacturers and those of the FRCM composite obtained from the direct tensile test.Table 3
Hybrid FRP-FRCM mechanical properties.
Nominal thickness
Elastic modulus
Ultimate tensile strength
Ultimate tensile strain
Compression strength
(mm)
(GPa)
(MPa)
(%)
(MPa)
Hybrid fabric
0.107
240
4,300
1.75
—
Cementitious matrix
—
40
—
—
45
FRCM composite
—
160(cracked specimen)
800
0.5
—Figure 1
Components of hybrid FRP-FRCM system.
(a)
Cementitious matrix
(b)
Hybrid FRP fabricFigure 2
Direct tensile testing by AC 434 [16].
(a)
Test setup for direct tensile testing of a flat hybrid FRP-FRCM coupon
(b)
Idealized tensile stress-strain curve for FRCM


## 2.2. Test Variables

As shown in Table4, specimens were classified into four groups. Specimens in Group I consisted of nonstrengthened specimen and steel stirrup-strengthened specimens to evaluate the relative shear-strengthening performance of the hybrid FRP-FRCM.Table 4
Test variables.
Group
Specimen ID
Strengthening type
Layer
Width × number
Installation
I
Control
None
None
None
None
S300
Steel stirrup
None
None
None
S200
II
W600-L1
Side-bonding
1
600 mm × 1
W600-L2
2
W50-N4
U-jacketing
1
50 mm × 4
III
W50-N5
50 mm × 5
W50-N6
50 mm × 6
W100-N3
100 mm × 3
IV
W100-N4
100 mm × 4
W600-N1
600 mm × 1The nonstrengthened specimen was designated as Control, and the specimens reinforced with steel stirrups at spacing of 200 mm and 300 mm were denoted by S200 and S300, respectively. Specimens in Group II consisted of specimens strengthened in shear by side-bonding. The specimens were named according to the width and the number of plies of the used hybrid FRP fabric. The specimens strengthened with 1-ply and 2-ply 600 mm hybrid FRP fabric were designated as W600-L1 and W600-L2, respectively. Specimens in Groups III and IV consisted of specimens strengthened by U-jacketing. The specimens strengthened by U-jacketing were named according to the width and number of plies of hybrid FRP fabric. For example, W50-N5 was strengthened with 5 pieces of 50 mm wide hybrid FRP fabric. The sixth column of Table4 shows hybrid FRP fabric attached on the shear span according to experimental variables.


## 2.3. Specimen Fabrication and Strengthening

As shown in Figure3, a total of 11 specimens having a length of 2,000 mm with a rectangular cross-section 150 mm wide and 300 mm high and a net span of 1,800 mm were fabricated for the tests. All specimens were reinforced with two rebars with a nominal diameter of 15.9 mm as tension reinforcement and two rebars with a nominal diameter of 9.53 mm as compression reinforcement.Figure 3
Test specimen layout.Specimens S200 and S300 were reinforced by rebars with a nominal diameter of 9.53 mm with spacing of 200 mm and 300 mm as shear reinforcement, respectively. After curing of 28 days, the shear strengthening specimens were strengthened with the hybrid FRP-FRCM as follows. First, the specimen surface was cleaned with tap water to remove impurities before strengthening. In order to keep the humid condition, the specimen surface was then covered with damp cloth until strengthening work. Specimens strengthened by U-jacketing were reversed and then chamfered to a radius of 10 mm to avoid damage to the hybrid FRP fabric due to stress concentration during the tests. Specimens were strengthened with hybrid FRP-FRCM according to the test variables. The strengthening procedure of the FRCM composite was as follows: (1) the first layer of cementitious matrix with a nominal thickness of 2 mm was applied on the side surface of the specimen; (2) the precut hybrid FRP fabric was laid on the cementitious matrix; and (3) the second layer of cementitious matrix with a nominal thickness of 2 mm was applied on the hybrid FRP fabric. In the case of strengthening with 2-ply hybrid FRP fabric, the above procedure was repeated two times. The nominal thickness of hybrid FRP-FRCM with 1-ply hybrid FRP fabric was taken as approximately 5 mm. Tests were performed after 28 days of strengthening for the cementitious matrix to develop sufficient strength.


## 2.4. Test Setup

The shear tests for 11 specimens were performed by four-point loading, as shown in Figure4. The specimens were simply supported and the load was applied at two points 300 mm apart at both the left and right sides of the midspan. The load was applied by stroke control loading at a rate of 0.4 mm/min with a hydraulic actuator with a maximum capacity of 2,000 kN. The load was measured by a load cell. The vertical displacement at the midspan was measured by two linear variable differential transformers (LVDTs).Figure 4
Test setup.As shown in Figure3, the strain of the hybrid FRP fabric was measured by eight strain gauges attached on the CFRP fabric strips at both the left and right sides of the shear span. The CFRP strip of the hybrid FRP fabric was grinded and cleaned with acetone before attachment of strain gauges. Load and strains were recorded by using a data logger. Crack propagation and FRCM composite damage were visually monitored and recorded during all tests.


## 3. Test Results and Discussion

### 3.1. Shear Resisting Capacity

The test results, the maximum load, the displacement corresponding to the maximum load, the gain of the maximum load, and the failure mode are presented in Table5.Table 5
Summary of test results.
Specimen ID
Maximum load(kN)
Displacement corresponding to maximum load(mm)
Gain of maximum load(%)
Failure mode
Control
105
7.2
—
Shear
S300
172
20.2
63.8
Flexure
S200
168
19.2
60.0
W600-L1
143
8.3
36.2
Debonding
W600-L2
152
10.2
44.8
W50-N4
117
6.7
11.4
W50-N5
123
5.3
17.1
W50-N6
127
7.4
21.0
W100-N3
121
6.2
15.2
W100-N4
144
8.6
37.1
W600-N1
162
9.2
54.3The specimen Control failed due to a diagonal shear crack at the maximum load of 105 kN (see Figure5(a)), while specimens S200 and S300 strengthened with steel stirrup failed due to the yielding of the tensile steel followed by the crushing of concrete at maximum load of 168 kN and 172 kN, respectively (see Figure 5(b)). Specimens W600-L1 and W600-L2 strengthened by side-bonding failed due to debonding of the FRCM composite at maximum load of 132 kN and 152 kN, respectively (see Figure 5(c)). The maximum loads of specimens W600-L1 and W600-L2 increased by 36.2% and 44.8%, respectively, when compared with the Control specimen. Although the maximum load increased with an increasing number of plies of hybrid fabric, it did not increase in proportion to the amount of the hybrid fabric.Figure 5
Specimens after test.
(a)
Control
(b)
S300
(c)
W600-L2
(d)
W600-N1Specimens in Group III failed due to debonding of the FRCM composite at the maximum load from 117 kN to 127 kN according to the amount of hybrid FRP fabric. The maximum loads of specimens W50-N4, W50-N5, and W50-N6 increased by 11.4%, 17.1%, and 21.0% relative to the unstrengthened specimen, respectively. The maximum loads of specimens W100-N3 and W100-N4 in Group IV were 121 kN and 144 kN, respectively, and their strength increased by 15.2% and 37.1% relative to the unstrengthened specimen, respectively. All specimens in Group IV failed due to debonding of the FRCM composite, similar to specimens in Group III. The maximum load of specimen W600-N1 was 162 kN and increased by 54.3% relative to the Control specimen (see Figure5(d)). The difference in the maximum load of specimens W50-N6 and W100-N3 with the same amount of hybrid FRP fabric was about 6 kN. This resulted from the difference in the spacing of the hybrid FRP with specimens W50-N6 and W100-N3. The difference in the maximum loads of W600-L1 and W600-N1 with the same amount of hybrid FRP fabric was 30 kN. It can be confirmed from this result that U-jacketing is more effective than side-bonding.


### 3.2. Load-Displacement Relationship

The load-displacement curves of specimens in Group I are presented in Figure6.Figure 6
Load-displacement curves of specimens in Group I.For the specimen Control, the load started to decrease with the occurrence of diagonal shear cracks at displacement of 4.4 mm and it failed due to a shear crack at displacement of 7.2 mm. For specimens S200 and S300 reinforced with steel stirrups, the maximum load increased over that of specimen Control and they failed due to the yielding of tensile reinforcement followed by the crushing of concrete. The load-displacement curves of specimens in Group II are shown in Figure7. This figure shows that specimen W600-L2 has higher shear capacity and ductility than specimen W600-L1. The load-displacement curves of specimens in Group III are presented in Figure 8.Figure 7
Load-displacement curves of specimens in Group II.Figure 8
Load-displacement curves of specimens in Group III.Figure8 shows that although the load-displacement curve of specimen W50-N5 is different from those of W50-N4 and W50-N6, the shear capacity increases with a higher amount of hybrid FRP fabric. The load-displacement curves of specimens in Group IV are presented in Figure 9. The load of specimen W100-N3 started to decrease at a displacement of 6.2 mm and it failed due to debonding of the FRCM composite at a displacement of 8.4 mm. For specimens W100-N4 and W600-N1, although their stiffness decreased at a displacement of 5 mm, at which a shear crack of specimen Control occurred, the load continued to increase. In particular, the maximum load of specimen W600-N1 was similar to that of specimen S300. Therefore, it can be confirmed that U-jacketing is more effective for FRCM shear strengthening, and hybrid FRP-FRCM is applicable for shear strengthening of RC beams.Figure 9
Load-displacement curves of specimens in Group IV.


### 3.3. Strain of Hybrid FRP Fabric

Strains of hybrid FRP fabric obtained from specimens W600-L1 and W600-L2 are, respectively, presented in Figure10. The strains were measured from strain gauges on the hybrid FRP fabric installed at the center of the shear span. The hybrid FRP fabric strain of specimens W600-L1 and W600-L2 did not increase before the initial shear crack occurred. The strain of W600-L1 started to move after the initial diagonal shear crack and increased sharply after a load of 80 kN, at which the shear crack was completely formed. The strain of specimen W600-L2 with 2 plies of hybrid FRP fabric started to increase at a higher load than specimen W600-L1 with 1 ply of hybrid FRP fabric. The maximum strains of the hybrid FRP fabric of these specimens were much smaller than 0.0175, the strain corresponding to rupture of the CFRP fabric strip. This result indicates that the failure of the specimen strengthened in shear with the hybrid FRP-FRCM composite is not due to rupture of the hybrid FRP fabric but rather due to debonding between concrete and the FRCM composite.Figure 10
Load-strain curves of hybrid FRP-FRCM system.


### 3.4. Prediction of Shear Capacity

#### 3.4.1. ACI Code

In order to predict the shear capacity of beams strengthened with FRCM, ACI Committee 549 [15] has proposed the following equation:(1)Vn=Vc+Vs+Vf,where Vn is the nominal shear strength and Vc, Vs, and Vf are the contribution of concrete, existing steel reinforcement, and FRCM composite material to the nominal shear strength, respectively.The contribution of concrete and steel reinforcement to the nominal shear strength is calculated according to the following equation proposed by ACI 318 [21]:(2)Vc=0.17fc′bwd,Vs=Avfytds,where fc′ is the specified compressive strength of concrete; bw is the web width and d is the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement; Av is the area of shear reinforcement; fyt is the specified yield strength of transverse reinforcement; and s is the center-to-center spacing of transverse reinforcement.The contribution of FRCM to the nominal shear strength is calculated according to the following equation proposed by ACI 549 [15]:(3)Vf=nAfffvdf,where n is the number of layers of mesh reinforcement; Af is the area of mesh reinforcement by unit width; and df is the effective depth of the FRCM shear reinforcement.The design tensile strength of the FRCM composite,ffv, is calculated from the following:(4)ffv=Efεfv,(5)εfv=εfu≤0.004,where Ef, εfv, and εfu are the tensile modulus of elasticity of FRCM, the design tensile strain of FRCM shear reinforcement, and the ultimate tensile strain of FRCM, respectively.The design tensile strain of the FRCM composite,εfv, is limited to 0.004 according to ACI 549 [15].


#### 3.4.2. Proposed Equation

All beams strengthened with the hybrid FRP-FRCM in this study failed due to debonding of the FRCM composite. The debonding failure mode is governed by the bond strength between the concrete surface and the FRCM composite. Therefore, a prediction model of the contribution of the FRCM composite to the shear strength was proposed based on the bond strength between the concrete surface and the hybrid FRP-FRCM in this study. When the bond stress at the free end of FRCM reaches the ultimate bond stress, the distribution of the bond stress at the interface can be described as in Figure11 [17].Figure 11
Distribution of shear stress in each strengthening method [17].
(a)
Side-bonding type
(b)
U-jacketing typeThe average bond stress of side-bonding and U-jacketing can be calculated from the following equations, respectively [22]:(6)τp.Side-bonding=∫-hf/2hf/24τult/hf2x2dxh,(7)τp.U-jacketing=∫0hfτult/hf2x2dxh,where h is the height of the beam, hf is the height of the FRCM composite, τult is the ultimate bond stress, and τp.Side-bonding and τp.U-jacketing are the average bond stress for side-bonding and U-jacketing, respectively.Meanwhile, the average bond stress can be expressed as follows regardless of the FRCM bond type as the ultimate bond stress is the same:(8)τp=τp.Side-bonding=τp.U-jacketing.Therefore, the contribution of the hybrid FRP-FRCM to the nominal shear strength can be defined as follows:(9)Vf=2Tf=2τphfwfwdcotθ,where Tf is the bond strength of FRCM, d is the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement, θ is the inclination of the shear crack, w is the length of the shear span, and wf is the width of the hybrid FRP fabric bonded on the shear span.In (9), the average bond stress, τp, was determined from direct shear tests according to variation of the bond length, as shown in Figure 12. Bricks with dimensions of 100 mm × 100 mm × 200 mm were produced with concrete used in the beam manufacture process, and hybrid FRP-FRCM was bonded on both sides of the brick in the same manner as the beams were strengthened. The average bond stress according to the bond length was measured, and the test results are presented in Figure 13. The average bond stress tends to decrease with an increase of bond length until 140 mm and thereafter converges to 0.28 MPa. Therefore, the average shear stress, τp, was defined as 0.28 MPa in the proposed model. In addition, the inclination of the shear crack, θ, was defined as 45°. Vc and Vs were calculated by the ACI 318 code [21].Figure 12
Setup of direct shear test.Figure 13
Average bond stress according to bond length.


#### 3.4.3. Comparison between Experimental and Analytical Results

The shear strengths of FRCM shear strengthened beams predicted by ACI 549 [15] and the proposed model are tabulated in Table 6. Also, the ratios of the test results to the shear strengths predicted by ACI 549 [15] and the proposed model are presented in Table 6.Table 6
Comparisons between predicted values and experimental results.
Specimen ID
P
EXP  (kN)
ACI 549 [15]
Proposed model
V
c
V
s
V
FRCM
P
ACI
P
EXP
/
P
ACI
V
c
V
s
V
FRCM
P
Prop
.
P
EXP
/
P
Prop
.
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
Control
105
36
—
—
72
1.46
—
—
72
1.46
S300
172
51
—
174
0.99
51
—
174
0.99
S200
168
77
—
226
0.74
77
—
226
0.74
W600-L1
143
—
37
146
0.98
—
45
162
0.88
W600-L2
152
—
74
220
0.69
—
45
162
0.94
W50-N4
117
—
12
96
1.22
36
—
15
102
1.15
W50-N5
123
—
15
102
1.21
—
19
110
1.12
W50-N6
127
—
19
110
1.15
—
23
118
1.08
W100-N3
121
—
19
110
1.10
—
23
118
1.03
W100-N4
144
—
25
122
1.18
—
30
132
1.09
W600-N1
162
—
37
146
1.11
—
45
162
1.00
Mean
1.08
1.04The ratios by ACI 549 [15] for specimens W600-L1 and W600-L2 strengthened by side-bonding were 0.98 and 0.69, respectively. It can be confirmed from these results that ACI 549 [15] overestimates the shear strength of FRCM shear strengthened beams by side-bonding and the prediction error increases with an increase of the amount of hybrid FRP. In contrast, the ratios by ACI 549 [15] for shear strengthened beams by U-jacketing ranged from 1.10 to 1.22. Namely, ACI 549 [15] underestimates the shear strength of shear strengthened beams by U-jacketing.The ratios by the predicted model for specimens W600-L1 and W600-L2 strengthened by side-bonding were 0.88 and 0.94, respectively. Although the proposed model also overestimates the shear strength of the beams strengthened by side-bonding, the prediction error was smaller than that of the ACI 549 code [15]. Moreover, the ratios by the proposed model for the shear strengthened beams by U-jacketing ranged from 1.00 to 1.15, which are smaller than those given by the ACI 549 code [15]. This validates that the proposed model predicted the shear strength of beams strengthened by U-jacketing more reliably than ACI 549 [15] did.


#### 3.4.4. Comparison between the Proposed Model and Existing Experimental Results

The performance of the proposed model was evaluated through a comparison between the numerically predicted values and existing experimental results [4, 10, 11, 14]. The geometry and material properties of RC beam specimens of the existing tests are presented in Table 7. Table 8 shows comparisons between the proposed model and existing experimental results. ACI 549 [15] requires the tensile modulus of elasticity for the FRCM, which is obtained from direct tensile test for the FRCM, to calculate the shear capacity of FRCM strengthened beams. However, the references in Table 7 did not present the tensile modulus of elasticity for the FRCM. Thus, the comparison between ACI 549 [15] and the existing experimental results has been excluded in the present study.Table 7
Geometry and material properties of RC beam specimens of experimental test database.
Reference
Specimen ID
b
d
h
f
f
′
c
A
v
f
y
t
s
w
w
f
a
/
d
(mm)
(mm)
(mm)
(MPa)
(mm2)
(MPa)
(mm)
(mm)
(mm)
[4]
SB-GT
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-GT
150
307.5
350
37.5
—
—
—
1000
1000
3.25
SB-CT1
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-CT1
150
307.5
350
37.5
—
—
—
1000
1000
3.25
SB-CT2
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-CT2
150
307.5
350
37.5
—
—
—
1000
1000
3.25
[10]
Beam 4
150
295
350
50.1
56.55
384
180
900
675
3.05
[11]
TRA1
150
225
250
30.76
100.53
446.06
292
675
675
3.00
TRA2
150
225
250
30.76
100.53
446.06
260
675
345
3.00
TRB1
150
225
250
45.02
100.53
442.25
210
625
625
2.78
TRB2
150
225
250
29.16
100.53
442.25
210
625
625
2.78
TRB3
150
225
250
29.16
100.53
442.25
210
625
295
2.78
TRB4
150
225
250
38.26
100.53
442.25
210
625
295
2.78
TRB5
150
225
250
38.26
100.53
442.25
210
625
295
2.78
[14]
BS2
150
175
200
20
—
—
—
400
400
2.29
BS3
150
175
200
20
—
—
—
400
400
2.29
BS4
150
175
200
20
—
—
—
400
400
2.29
BS5
150
175
200
20
—
—
—
400
400
2.29Table 8
Comparisons between the existing experimental results and proposed model.
Reference
Specimen ID
Type of bond
Type of fiber
ρ
f
P
Exp
V
c
V
s
V
FRCM
P
Prop
.
P
Exp
/
P
Prop
.
(%)
(kN)
(kN)
(kN)
(kN)
(kN)
[4]
SB-GT
S
G
0.297
146.3
48.02
—
60.27
216.6
0.68
UW-GT
U
G
0.297
180.2
48.02
—
60.27
216.6
0.83
SB-CT1
S
C
0.229
155.5
48.02
—
60.27
216.6
0.72
UW-CT1
U
C
0.229
151.8
48.02
—
60.27
216.6
0.70
SB-CT2
S
C
0.516
245.4
48.02
—
60.27
216.6
1.13
UW-CT2
U
C
0.516
253.4
48.02
—
60.27
216.6
1.17
[10]
Beam 4
U
G
0.096
294.0
53.25
35.59
43.37
264.4
1.11
[11]
TRA1
S
P
0.135
188.7
31.82
34.55
31.47
195.7
0.96
TRA2
U
P
0.034
170.4
31.82
38.81
16.10
173.5
0.98
TRB1
S
P
0.202
279.1
31.82
38.81
47.02
235.3
1.19
TRB2
S
P
0.202
191.7
31.82
38.81
39.47
220.2
0.87
TRB3
U
P
0.095
191.9
31.82
38.81
22.87
187.0
1.03
TRB4
U
P
0.095
200.0
31.82
38.81
27.37
196.0
1.02
TRB5
U
P
0.095
199.8
31.82
38.81
27.37
196.0
1.02
[14]
BS2
S
B
0.195
82.7
19.96
—
19.6
79.1
1.05
BS3
S
B
0.195
83.5
19.96
—
19.6
79.1
1.06
BS4
S
B
0.390
88.7
19.96
—
19.6
79.1
1.12
BS5
S
B
0.390
92.5
19.96
—
19.6
79.1
1.17
Mean
0.99
Coefficient of variation
0.16
Note. S = side-bonding; U = U-jacketing; G = glass; C = carbon; P = PBO; B = basalt.From Table8, it can be confirmed that the proposed model predicts the existing experimental results well: the mean of the ratio between the proposed model and corresponding experimental results is 0.99 and its coefficient variable (COV) is 0.16. Accordingly, it can be concluded that the shear prediction model from this study could be widely used for shear capacity estimation of FRCM strengthened beams.


## 3.1. Shear Resisting Capacity

The test results, the maximum load, the displacement corresponding to the maximum load, the gain of the maximum load, and the failure mode are presented in Table5.Table 5
Summary of test results.
Specimen ID
Maximum load(kN)
Displacement corresponding to maximum load(mm)
Gain of maximum load(%)
Failure mode
Control
105
7.2
—
Shear
S300
172
20.2
63.8
Flexure
S200
168
19.2
60.0
W600-L1
143
8.3
36.2
Debonding
W600-L2
152
10.2
44.8
W50-N4
117
6.7
11.4
W50-N5
123
5.3
17.1
W50-N6
127
7.4
21.0
W100-N3
121
6.2
15.2
W100-N4
144
8.6
37.1
W600-N1
162
9.2
54.3The specimen Control failed due to a diagonal shear crack at the maximum load of 105 kN (see Figure5(a)), while specimens S200 and S300 strengthened with steel stirrup failed due to the yielding of the tensile steel followed by the crushing of concrete at maximum load of 168 kN and 172 kN, respectively (see Figure 5(b)). Specimens W600-L1 and W600-L2 strengthened by side-bonding failed due to debonding of the FRCM composite at maximum load of 132 kN and 152 kN, respectively (see Figure 5(c)). The maximum loads of specimens W600-L1 and W600-L2 increased by 36.2% and 44.8%, respectively, when compared with the Control specimen. Although the maximum load increased with an increasing number of plies of hybrid fabric, it did not increase in proportion to the amount of the hybrid fabric.Figure 5
Specimens after test.
(a)
Control
(b)
S300
(c)
W600-L2
(d)
W600-N1Specimens in Group III failed due to debonding of the FRCM composite at the maximum load from 117 kN to 127 kN according to the amount of hybrid FRP fabric. The maximum loads of specimens W50-N4, W50-N5, and W50-N6 increased by 11.4%, 17.1%, and 21.0% relative to the unstrengthened specimen, respectively. The maximum loads of specimens W100-N3 and W100-N4 in Group IV were 121 kN and 144 kN, respectively, and their strength increased by 15.2% and 37.1% relative to the unstrengthened specimen, respectively. All specimens in Group IV failed due to debonding of the FRCM composite, similar to specimens in Group III. The maximum load of specimen W600-N1 was 162 kN and increased by 54.3% relative to the Control specimen (see Figure5(d)). The difference in the maximum load of specimens W50-N6 and W100-N3 with the same amount of hybrid FRP fabric was about 6 kN. This resulted from the difference in the spacing of the hybrid FRP with specimens W50-N6 and W100-N3. The difference in the maximum loads of W600-L1 and W600-N1 with the same amount of hybrid FRP fabric was 30 kN. It can be confirmed from this result that U-jacketing is more effective than side-bonding.


## 3.2. Load-Displacement Relationship

The load-displacement curves of specimens in Group I are presented in Figure6.Figure 6
Load-displacement curves of specimens in Group I.For the specimen Control, the load started to decrease with the occurrence of diagonal shear cracks at displacement of 4.4 mm and it failed due to a shear crack at displacement of 7.2 mm. For specimens S200 and S300 reinforced with steel stirrups, the maximum load increased over that of specimen Control and they failed due to the yielding of tensile reinforcement followed by the crushing of concrete. The load-displacement curves of specimens in Group II are shown in Figure7. This figure shows that specimen W600-L2 has higher shear capacity and ductility than specimen W600-L1. The load-displacement curves of specimens in Group III are presented in Figure 8.Figure 7
Load-displacement curves of specimens in Group II.Figure 8
Load-displacement curves of specimens in Group III.Figure8 shows that although the load-displacement curve of specimen W50-N5 is different from those of W50-N4 and W50-N6, the shear capacity increases with a higher amount of hybrid FRP fabric. The load-displacement curves of specimens in Group IV are presented in Figure 9. The load of specimen W100-N3 started to decrease at a displacement of 6.2 mm and it failed due to debonding of the FRCM composite at a displacement of 8.4 mm. For specimens W100-N4 and W600-N1, although their stiffness decreased at a displacement of 5 mm, at which a shear crack of specimen Control occurred, the load continued to increase. In particular, the maximum load of specimen W600-N1 was similar to that of specimen S300. Therefore, it can be confirmed that U-jacketing is more effective for FRCM shear strengthening, and hybrid FRP-FRCM is applicable for shear strengthening of RC beams.Figure 9
Load-displacement curves of specimens in Group IV.


## 3.3. Strain of Hybrid FRP Fabric

Strains of hybrid FRP fabric obtained from specimens W600-L1 and W600-L2 are, respectively, presented in Figure10. The strains were measured from strain gauges on the hybrid FRP fabric installed at the center of the shear span. The hybrid FRP fabric strain of specimens W600-L1 and W600-L2 did not increase before the initial shear crack occurred. The strain of W600-L1 started to move after the initial diagonal shear crack and increased sharply after a load of 80 kN, at which the shear crack was completely formed. The strain of specimen W600-L2 with 2 plies of hybrid FRP fabric started to increase at a higher load than specimen W600-L1 with 1 ply of hybrid FRP fabric. The maximum strains of the hybrid FRP fabric of these specimens were much smaller than 0.0175, the strain corresponding to rupture of the CFRP fabric strip. This result indicates that the failure of the specimen strengthened in shear with the hybrid FRP-FRCM composite is not due to rupture of the hybrid FRP fabric but rather due to debonding between concrete and the FRCM composite.Figure 10
Load-strain curves of hybrid FRP-FRCM system.


## 3.4. Prediction of Shear Capacity

### 3.4.1. ACI Code

In order to predict the shear capacity of beams strengthened with FRCM, ACI Committee 549 [15] has proposed the following equation:(1)Vn=Vc+Vs+Vf,where Vn is the nominal shear strength and Vc, Vs, and Vf are the contribution of concrete, existing steel reinforcement, and FRCM composite material to the nominal shear strength, respectively.The contribution of concrete and steel reinforcement to the nominal shear strength is calculated according to the following equation proposed by ACI 318 [21]:(2)Vc=0.17fc′bwd,Vs=Avfytds,where fc′ is the specified compressive strength of concrete; bw is the web width and d is the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement; Av is the area of shear reinforcement; fyt is the specified yield strength of transverse reinforcement; and s is the center-to-center spacing of transverse reinforcement.The contribution of FRCM to the nominal shear strength is calculated according to the following equation proposed by ACI 549 [15]:(3)Vf=nAfffvdf,where n is the number of layers of mesh reinforcement; Af is the area of mesh reinforcement by unit width; and df is the effective depth of the FRCM shear reinforcement.The design tensile strength of the FRCM composite,ffv, is calculated from the following:(4)ffv=Efεfv,(5)εfv=εfu≤0.004,where Ef, εfv, and εfu are the tensile modulus of elasticity of FRCM, the design tensile strain of FRCM shear reinforcement, and the ultimate tensile strain of FRCM, respectively.The design tensile strain of the FRCM composite,εfv, is limited to 0.004 according to ACI 549 [15].


### 3.4.2. Proposed Equation

All beams strengthened with the hybrid FRP-FRCM in this study failed due to debonding of the FRCM composite. The debonding failure mode is governed by the bond strength between the concrete surface and the FRCM composite. Therefore, a prediction model of the contribution of the FRCM composite to the shear strength was proposed based on the bond strength between the concrete surface and the hybrid FRP-FRCM in this study. When the bond stress at the free end of FRCM reaches the ultimate bond stress, the distribution of the bond stress at the interface can be described as in Figure11 [17].Figure 11
Distribution of shear stress in each strengthening method [17].
(a)
Side-bonding type
(b)
U-jacketing typeThe average bond stress of side-bonding and U-jacketing can be calculated from the following equations, respectively [22]:(6)τp.Side-bonding=∫-hf/2hf/24τult/hf2x2dxh,(7)τp.U-jacketing=∫0hfτult/hf2x2dxh,where h is the height of the beam, hf is the height of the FRCM composite, τult is the ultimate bond stress, and τp.Side-bonding and τp.U-jacketing are the average bond stress for side-bonding and U-jacketing, respectively.Meanwhile, the average bond stress can be expressed as follows regardless of the FRCM bond type as the ultimate bond stress is the same:(8)τp=τp.Side-bonding=τp.U-jacketing.Therefore, the contribution of the hybrid FRP-FRCM to the nominal shear strength can be defined as follows:(9)Vf=2Tf=2τphfwfwdcotθ,where Tf is the bond strength of FRCM, d is the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement, θ is the inclination of the shear crack, w is the length of the shear span, and wf is the width of the hybrid FRP fabric bonded on the shear span.In (9), the average bond stress, τp, was determined from direct shear tests according to variation of the bond length, as shown in Figure 12. Bricks with dimensions of 100 mm × 100 mm × 200 mm were produced with concrete used in the beam manufacture process, and hybrid FRP-FRCM was bonded on both sides of the brick in the same manner as the beams were strengthened. The average bond stress according to the bond length was measured, and the test results are presented in Figure 13. The average bond stress tends to decrease with an increase of bond length until 140 mm and thereafter converges to 0.28 MPa. Therefore, the average shear stress, τp, was defined as 0.28 MPa in the proposed model. In addition, the inclination of the shear crack, θ, was defined as 45°. Vc and Vs were calculated by the ACI 318 code [21].Figure 12
Setup of direct shear test.Figure 13
Average bond stress according to bond length.


### 3.4.3. Comparison between Experimental and Analytical Results

The shear strengths of FRCM shear strengthened beams predicted by ACI 549 [15] and the proposed model are tabulated in Table 6. Also, the ratios of the test results to the shear strengths predicted by ACI 549 [15] and the proposed model are presented in Table 6.Table 6
Comparisons between predicted values and experimental results.
Specimen ID
P
EXP  (kN)
ACI 549 [15]
Proposed model
V
c
V
s
V
FRCM
P
ACI
P
EXP
/
P
ACI
V
c
V
s
V
FRCM
P
Prop
.
P
EXP
/
P
Prop
.
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
Control
105
36
—
—
72
1.46
—
—
72
1.46
S300
172
51
—
174
0.99
51
—
174
0.99
S200
168
77
—
226
0.74
77
—
226
0.74
W600-L1
143
—
37
146
0.98
—
45
162
0.88
W600-L2
152
—
74
220
0.69
—
45
162
0.94
W50-N4
117
—
12
96
1.22
36
—
15
102
1.15
W50-N5
123
—
15
102
1.21
—
19
110
1.12
W50-N6
127
—
19
110
1.15
—
23
118
1.08
W100-N3
121
—
19
110
1.10
—
23
118
1.03
W100-N4
144
—
25
122
1.18
—
30
132
1.09
W600-N1
162
—
37
146
1.11
—
45
162
1.00
Mean
1.08
1.04The ratios by ACI 549 [15] for specimens W600-L1 and W600-L2 strengthened by side-bonding were 0.98 and 0.69, respectively. It can be confirmed from these results that ACI 549 [15] overestimates the shear strength of FRCM shear strengthened beams by side-bonding and the prediction error increases with an increase of the amount of hybrid FRP. In contrast, the ratios by ACI 549 [15] for shear strengthened beams by U-jacketing ranged from 1.10 to 1.22. Namely, ACI 549 [15] underestimates the shear strength of shear strengthened beams by U-jacketing.The ratios by the predicted model for specimens W600-L1 and W600-L2 strengthened by side-bonding were 0.88 and 0.94, respectively. Although the proposed model also overestimates the shear strength of the beams strengthened by side-bonding, the prediction error was smaller than that of the ACI 549 code [15]. Moreover, the ratios by the proposed model for the shear strengthened beams by U-jacketing ranged from 1.00 to 1.15, which are smaller than those given by the ACI 549 code [15]. This validates that the proposed model predicted the shear strength of beams strengthened by U-jacketing more reliably than ACI 549 [15] did.


### 3.4.4. Comparison between the Proposed Model and Existing Experimental Results

The performance of the proposed model was evaluated through a comparison between the numerically predicted values and existing experimental results [4, 10, 11, 14]. The geometry and material properties of RC beam specimens of the existing tests are presented in Table 7. Table 8 shows comparisons between the proposed model and existing experimental results. ACI 549 [15] requires the tensile modulus of elasticity for the FRCM, which is obtained from direct tensile test for the FRCM, to calculate the shear capacity of FRCM strengthened beams. However, the references in Table 7 did not present the tensile modulus of elasticity for the FRCM. Thus, the comparison between ACI 549 [15] and the existing experimental results has been excluded in the present study.Table 7
Geometry and material properties of RC beam specimens of experimental test database.
Reference
Specimen ID
b
d
h
f
f
′
c
A
v
f
y
t
s
w
w
f
a
/
d
(mm)
(mm)
(mm)
(MPa)
(mm2)
(MPa)
(mm)
(mm)
(mm)
[4]
SB-GT
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-GT
150
307.5
350
37.5
—
—
—
1000
1000
3.25
SB-CT1
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-CT1
150
307.5
350
37.5
—
—
—
1000
1000
3.25
SB-CT2
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-CT2
150
307.5
350
37.5
—
—
—
1000
1000
3.25
[10]
Beam 4
150
295
350
50.1
56.55
384
180
900
675
3.05
[11]
TRA1
150
225
250
30.76
100.53
446.06
292
675
675
3.00
TRA2
150
225
250
30.76
100.53
446.06
260
675
345
3.00
TRB1
150
225
250
45.02
100.53
442.25
210
625
625
2.78
TRB2
150
225
250
29.16
100.53
442.25
210
625
625
2.78
TRB3
150
225
250
29.16
100.53
442.25
210
625
295
2.78
TRB4
150
225
250
38.26
100.53
442.25
210
625
295
2.78
TRB5
150
225
250
38.26
100.53
442.25
210
625
295
2.78
[14]
BS2
150
175
200
20
—
—
—
400
400
2.29
BS3
150
175
200
20
—
—
—
400
400
2.29
BS4
150
175
200
20
—
—
—
400
400
2.29
BS5
150
175
200
20
—
—
—
400
400
2.29Table 8
Comparisons between the existing experimental results and proposed model.
Reference
Specimen ID
Type of bond
Type of fiber
ρ
f
P
Exp
V
c
V
s
V
FRCM
P
Prop
.
P
Exp
/
P
Prop
.
(%)
(kN)
(kN)
(kN)
(kN)
(kN)
[4]
SB-GT
S
G
0.297
146.3
48.02
—
60.27
216.6
0.68
UW-GT
U
G
0.297
180.2
48.02
—
60.27
216.6
0.83
SB-CT1
S
C
0.229
155.5
48.02
—
60.27
216.6
0.72
UW-CT1
U
C
0.229
151.8
48.02
—
60.27
216.6
0.70
SB-CT2
S
C
0.516
245.4
48.02
—
60.27
216.6
1.13
UW-CT2
U
C
0.516
253.4
48.02
—
60.27
216.6
1.17
[10]
Beam 4
U
G
0.096
294.0
53.25
35.59
43.37
264.4
1.11
[11]
TRA1
S
P
0.135
188.7
31.82
34.55
31.47
195.7
0.96
TRA2
U
P
0.034
170.4
31.82
38.81
16.10
173.5
0.98
TRB1
S
P
0.202
279.1
31.82
38.81
47.02
235.3
1.19
TRB2
S
P
0.202
191.7
31.82
38.81
39.47
220.2
0.87
TRB3
U
P
0.095
191.9
31.82
38.81
22.87
187.0
1.03
TRB4
U
P
0.095
200.0
31.82
38.81
27.37
196.0
1.02
TRB5
U
P
0.095
199.8
31.82
38.81
27.37
196.0
1.02
[14]
BS2
S
B
0.195
82.7
19.96
—
19.6
79.1
1.05
BS3
S
B
0.195
83.5
19.96
—
19.6
79.1
1.06
BS4
S
B
0.390
88.7
19.96
—
19.6
79.1
1.12
BS5
S
B
0.390
92.5
19.96
—
19.6
79.1
1.17
Mean
0.99
Coefficient of variation
0.16
Note. S = side-bonding; U = U-jacketing; G = glass; C = carbon; P = PBO; B = basalt.From Table8, it can be confirmed that the proposed model predicts the existing experimental results well: the mean of the ratio between the proposed model and corresponding experimental results is 0.99 and its coefficient variable (COV) is 0.16. Accordingly, it can be concluded that the shear prediction model from this study could be widely used for shear capacity estimation of FRCM strengthened beams.


## 3.4.1. ACI Code

In order to predict the shear capacity of beams strengthened with FRCM, ACI Committee 549 [15] has proposed the following equation:(1)Vn=Vc+Vs+Vf,where Vn is the nominal shear strength and Vc, Vs, and Vf are the contribution of concrete, existing steel reinforcement, and FRCM composite material to the nominal shear strength, respectively.The contribution of concrete and steel reinforcement to the nominal shear strength is calculated according to the following equation proposed by ACI 318 [21]:(2)Vc=0.17fc′bwd,Vs=Avfytds,where fc′ is the specified compressive strength of concrete; bw is the web width and d is the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement; Av is the area of shear reinforcement; fyt is the specified yield strength of transverse reinforcement; and s is the center-to-center spacing of transverse reinforcement.The contribution of FRCM to the nominal shear strength is calculated according to the following equation proposed by ACI 549 [15]:(3)Vf=nAfffvdf,where n is the number of layers of mesh reinforcement; Af is the area of mesh reinforcement by unit width; and df is the effective depth of the FRCM shear reinforcement.The design tensile strength of the FRCM composite,ffv, is calculated from the following:(4)ffv=Efεfv,(5)εfv=εfu≤0.004,where Ef, εfv, and εfu are the tensile modulus of elasticity of FRCM, the design tensile strain of FRCM shear reinforcement, and the ultimate tensile strain of FRCM, respectively.The design tensile strain of the FRCM composite,εfv, is limited to 0.004 according to ACI 549 [15].


## 3.4.2. Proposed Equation

All beams strengthened with the hybrid FRP-FRCM in this study failed due to debonding of the FRCM composite. The debonding failure mode is governed by the bond strength between the concrete surface and the FRCM composite. Therefore, a prediction model of the contribution of the FRCM composite to the shear strength was proposed based on the bond strength between the concrete surface and the hybrid FRP-FRCM in this study. When the bond stress at the free end of FRCM reaches the ultimate bond stress, the distribution of the bond stress at the interface can be described as in Figure11 [17].Figure 11
Distribution of shear stress in each strengthening method [17].
(a)
Side-bonding type
(b)
U-jacketing typeThe average bond stress of side-bonding and U-jacketing can be calculated from the following equations, respectively [22]:(6)τp.Side-bonding=∫-hf/2hf/24τult/hf2x2dxh,(7)τp.U-jacketing=∫0hfτult/hf2x2dxh,where h is the height of the beam, hf is the height of the FRCM composite, τult is the ultimate bond stress, and τp.Side-bonding and τp.U-jacketing are the average bond stress for side-bonding and U-jacketing, respectively.Meanwhile, the average bond stress can be expressed as follows regardless of the FRCM bond type as the ultimate bond stress is the same:(8)τp=τp.Side-bonding=τp.U-jacketing.Therefore, the contribution of the hybrid FRP-FRCM to the nominal shear strength can be defined as follows:(9)Vf=2Tf=2τphfwfwdcotθ,where Tf is the bond strength of FRCM, d is the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement, θ is the inclination of the shear crack, w is the length of the shear span, and wf is the width of the hybrid FRP fabric bonded on the shear span.In (9), the average bond stress, τp, was determined from direct shear tests according to variation of the bond length, as shown in Figure 12. Bricks with dimensions of 100 mm × 100 mm × 200 mm were produced with concrete used in the beam manufacture process, and hybrid FRP-FRCM was bonded on both sides of the brick in the same manner as the beams were strengthened. The average bond stress according to the bond length was measured, and the test results are presented in Figure 13. The average bond stress tends to decrease with an increase of bond length until 140 mm and thereafter converges to 0.28 MPa. Therefore, the average shear stress, τp, was defined as 0.28 MPa in the proposed model. In addition, the inclination of the shear crack, θ, was defined as 45°. Vc and Vs were calculated by the ACI 318 code [21].Figure 12
Setup of direct shear test.Figure 13
Average bond stress according to bond length.


## 3.4.3. Comparison between Experimental and Analytical Results

The shear strengths of FRCM shear strengthened beams predicted by ACI 549 [15] and the proposed model are tabulated in Table 6. Also, the ratios of the test results to the shear strengths predicted by ACI 549 [15] and the proposed model are presented in Table 6.Table 6
Comparisons between predicted values and experimental results.
Specimen ID
P
EXP  (kN)
ACI 549 [15]
Proposed model
V
c
V
s
V
FRCM
P
ACI
P
EXP
/
P
ACI
V
c
V
s
V
FRCM
P
Prop
.
P
EXP
/
P
Prop
.
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
(kN)
Control
105
36
—
—
72
1.46
—
—
72
1.46
S300
172
51
—
174
0.99
51
—
174
0.99
S200
168
77
—
226
0.74
77
—
226
0.74
W600-L1
143
—
37
146
0.98
—
45
162
0.88
W600-L2
152
—
74
220
0.69
—
45
162
0.94
W50-N4
117
—
12
96
1.22
36
—
15
102
1.15
W50-N5
123
—
15
102
1.21
—
19
110
1.12
W50-N6
127
—
19
110
1.15
—
23
118
1.08
W100-N3
121
—
19
110
1.10
—
23
118
1.03
W100-N4
144
—
25
122
1.18
—
30
132
1.09
W600-N1
162
—
37
146
1.11
—
45
162
1.00
Mean
1.08
1.04The ratios by ACI 549 [15] for specimens W600-L1 and W600-L2 strengthened by side-bonding were 0.98 and 0.69, respectively. It can be confirmed from these results that ACI 549 [15] overestimates the shear strength of FRCM shear strengthened beams by side-bonding and the prediction error increases with an increase of the amount of hybrid FRP. In contrast, the ratios by ACI 549 [15] for shear strengthened beams by U-jacketing ranged from 1.10 to 1.22. Namely, ACI 549 [15] underestimates the shear strength of shear strengthened beams by U-jacketing.The ratios by the predicted model for specimens W600-L1 and W600-L2 strengthened by side-bonding were 0.88 and 0.94, respectively. Although the proposed model also overestimates the shear strength of the beams strengthened by side-bonding, the prediction error was smaller than that of the ACI 549 code [15]. Moreover, the ratios by the proposed model for the shear strengthened beams by U-jacketing ranged from 1.00 to 1.15, which are smaller than those given by the ACI 549 code [15]. This validates that the proposed model predicted the shear strength of beams strengthened by U-jacketing more reliably than ACI 549 [15] did.


## 3.4.4. Comparison between the Proposed Model and Existing Experimental Results

The performance of the proposed model was evaluated through a comparison between the numerically predicted values and existing experimental results [4, 10, 11, 14]. The geometry and material properties of RC beam specimens of the existing tests are presented in Table 7. Table 8 shows comparisons between the proposed model and existing experimental results. ACI 549 [15] requires the tensile modulus of elasticity for the FRCM, which is obtained from direct tensile test for the FRCM, to calculate the shear capacity of FRCM strengthened beams. However, the references in Table 7 did not present the tensile modulus of elasticity for the FRCM. Thus, the comparison between ACI 549 [15] and the existing experimental results has been excluded in the present study.Table 7
Geometry and material properties of RC beam specimens of experimental test database.
Reference
Specimen ID
b
d
h
f
f
′
c
A
v
f
y
t
s
w
w
f
a
/
d
(mm)
(mm)
(mm)
(MPa)
(mm2)
(MPa)
(mm)
(mm)
(mm)
[4]
SB-GT
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-GT
150
307.5
350
37.5
—
—
—
1000
1000
3.25
SB-CT1
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-CT1
150
307.5
350
37.5
—
—
—
1000
1000
3.25
SB-CT2
150
307.5
350
37.5
—
—
—
1000
1000
3.25
UW-CT2
150
307.5
350
37.5
—
—
—
1000
1000
3.25
[10]
Beam 4
150
295
350
50.1
56.55
384
180
900
675
3.05
[11]
TRA1
150
225
250
30.76
100.53
446.06
292
675
675
3.00
TRA2
150
225
250
30.76
100.53
446.06
260
675
345
3.00
TRB1
150
225
250
45.02
100.53
442.25
210
625
625
2.78
TRB2
150
225
250
29.16
100.53
442.25
210
625
625
2.78
TRB3
150
225
250
29.16
100.53
442.25
210
625
295
2.78
TRB4
150
225
250
38.26
100.53
442.25
210
625
295
2.78
TRB5
150
225
250
38.26
100.53
442.25
210
625
295
2.78
[14]
BS2
150
175
200
20
—
—
—
400
400
2.29
BS3
150
175
200
20
—
—
—
400
400
2.29
BS4
150
175
200
20
—
—
—
400
400
2.29
BS5
150
175
200
20
—
—
—
400
400
2.29Table 8
Comparisons between the existing experimental results and proposed model.
Reference
Specimen ID
Type of bond
Type of fiber
ρ
f
P
Exp
V
c
V
s
V
FRCM
P
Prop
.
P
Exp
/
P
Prop
.
(%)
(kN)
(kN)
(kN)
(kN)
(kN)
[4]
SB-GT
S
G
0.297
146.3
48.02
—
60.27
216.6
0.68
UW-GT
U
G
0.297
180.2
48.02
—
60.27
216.6
0.83
SB-CT1
S
C
0.229
155.5
48.02
—
60.27
216.6
0.72
UW-CT1
U
C
0.229
151.8
48.02
—
60.27
216.6
0.70
SB-CT2
S
C
0.516
245.4
48.02
—
60.27
216.6
1.13
UW-CT2
U
C
0.516
253.4
48.02
—
60.27
216.6
1.17
[10]
Beam 4
U
G
0.096
294.0
53.25
35.59
43.37
264.4
1.11
[11]
TRA1
S
P
0.135
188.7
31.82
34.55
31.47
195.7
0.96
TRA2
U
P
0.034
170.4
31.82
38.81
16.10
173.5
0.98
TRB1
S
P
0.202
279.1
31.82
38.81
47.02
235.3
1.19
TRB2
S
P
0.202
191.7
31.82
38.81
39.47
220.2
0.87
TRB3
U
P
0.095
191.9
31.82
38.81
22.87
187.0
1.03
TRB4
U
P
0.095
200.0
31.82
38.81
27.37
196.0
1.02
TRB5
U
P
0.095
199.8
31.82
38.81
27.37
196.0
1.02
[14]
BS2
S
B
0.195
82.7
19.96
—
19.6
79.1
1.05
BS3
S
B
0.195
83.5
19.96
—
19.6
79.1
1.06
BS4
S
B
0.390
88.7
19.96
—
19.6
79.1
1.12
BS5
S
B
0.390
92.5
19.96
—
19.6
79.1
1.17
Mean
0.99
Coefficient of variation
0.16
Note. S = side-bonding; U = U-jacketing; G = glass; C = carbon; P = PBO; B = basalt.From Table8, it can be confirmed that the proposed model predicts the existing experimental results well: the mean of the ratio between the proposed model and corresponding experimental results is 0.99 and its coefficient variable (COV) is 0.16. Accordingly, it can be concluded that the shear prediction model from this study could be widely used for shear capacity estimation of FRCM strengthened beams.


## 4. Conclusion

Conclusions obtained from this study are as follows.(1)
It was validated that the maximum load of shear strengthened beams with hybrid FRP-FRCM increased from 11.4% to 54.3% according to the amount of hybrid FRP, and the effectiveness of hybrid FRP for shear capacity is not proportional to the amount used.(2)
It was confirmed from test results that U-jacketing was more effective than side-bonding for FRCM shear strengthening.(3)
ACI 549 [15] overestimated the shear strength of beams strengthened by side-bonding with hybrid FRP-FRCM and the prediction error increases with an increase of the amount of hybrid FRP. In addition, ACI 549 [15] underestimated the shear strength of shear strengthened beams by U-jacketing.(4)
Although the proposed model also overestimated the shear strength of beams strengthened by side-bonding with hybrid FRP-FRCM, the prediction error was smaller than that of ACI 549 [15]. Moreover, for shear-strengthened beams by U-jacketing, the proposed model predicted the shear strength more reliably than ACI 549 [15] did.(5)
The agreement between the proposed model and the existing experimental results was very good. Accordingly, it can be concluded that the shear prediction model from this study could be widely used for shear capacity estimation of FRCM strengthened beams.



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*Source: 564876-2015-10-04.xml*