contribution of longitudinal gfrp bars in concrete · draft page 4 of 41 69 calculated at ultimate...

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Contribution of Longitudinal GFRP Bars in Concrete

Cylinders under Axial Compression

Journal: Canadian Journal of Civil Engineering

Manuscript ID cjce-2017-0481.R1

Manuscript Type: Article

Date Submitted by the Author: 06-Nov-2017

Complete List of Authors: Fillmore, Brandon; Dalhousie University, Civil and Resource Engineering Sadeghian, Pedram; Dalhousie University, Civil and Resource Engineering

Is the invited manuscript for consideration in a Special

Issue? : N/A

Keyword: Reinforcing Bar, GFRP, Crushing, Compression, Contribution

https://mc06.manuscriptcentral.com/cjce-pubs

Canadian Journal of Civil Engineering

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Contribution of Longitudinal GFRP Bars in Concrete Cylinders 1

under Axial Compression 2

Brandon Fillmore and Pedram Sadeghian1 3

Department of Civil and Resource Engineering, Dalhousie University, 1360 Barrington Street, 4

Halifax, NS, B3H 4R2, Canada. 5

Abstract: Contribution of longitudinal glass fiber-reinforced polymer (GFRP) bars in concrete 6

columns under compression has been ignored by current design guidelines. This paper 7

challenges this convention by testing 21 concrete cylinders (150 mm × 300 mm) reinforced with 8

longitudinal GFRP and steel bars in compression. It was observed that GFRP bars could sustain 9

high level of compressive strains long after the peak load of the specimens without any 10

premature crushing. The results of a new coupon test method showed that the elastic modulus of 11

GFRP bars in compression is slightly higher than that of in tension, however the compressive 12

strength was obtained 67% of tensile strength. An analytical model was successfully 13

implemented to predict the axial capacity of the tests specimens and it was found that the 14

contribution of the bars in the load capacity of the specimens was within 4.5-18.4% proportional 15

to the bars reinforcement ratio normalized to the elastic modulus of steel bars. 16

Keywords: GFRP, Reinforcing Bar, Compression, Crushing, Contribution. 17

18

1. INTRODUCTION 19

Using fiber-reinforced polymer (FRP) bars and especially glass FRP (GFRP) to reinforce 20

concrete structures has become increasingly common in the past three decades. The corrosion 21

resistant nature of GFRP bars against de-icing salt, ocean water, and other harsh environments 22

1 Corresponding Author. Email: [email protected]

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has been the main advantage over steel bars and therefore the use of GFRP bars would be of 23

great benefit in many structural applications. Moreover, GFRP bars’ high strength and light 24

weight within reasonable cost are other advantages. The application of longitudinal GFRP bars in 25

concrete beams and slabs as tensile reinforcement has been relatively established (Nanni 1993; 26

Benmokrane et al. 1995; El-Sayed et al. 2005; and Bischoff 2005). However, the use of 27

longitudinal GFRP bars in concrete columns has been very limited. The topic of whether to 28

include the compressive contribution of longitudinal GFRP bars in the calculation of column 29

capacity has been a subject of discussion. 30

In a study by De Luca et al. (2010), longitudinal GFRP bars were found to contribute 31

from 2.9% to 4.4% to the capacity of large-scale axially loaded columns which compared to an 32

11.6% contribution by longitudinal steel bars with the same reinforcement ratio of 1%. This 33

study concluded that the axial capacity can be computed neglecting the contribution of the 34

internal GFRP reinforcement and considering the only force carried by the concrete. Pantelides 35

et al. (2013) tested medium-scale concrete columns and found that the axial capacity of columns 36

reinforced with 1.6% longitudinal GFRP bars achieved 84% of the axial capacity of control 37

column reinforced with 1.0% steel bars. It was concluded that columns must be reinforced with a 38

larger reinforcement ratio GFRP bars to achieve a similar performance of control columns. 39

On the other hand, several other experimental studies have demonstrated a significant 40

contribution of longitudinal GFRP bars in concrete columns. Tobbi et al. (2012) tested large-41

scale columns and reported that GFRP bars contributed 10% of column capacity, which is close 42

enough to steel’s contribution (12%). It was concluded that GFRP bars could be used in 43

compression members if adequate transverse bars provide to eliminate bar buckling. Tobbi et al. 44

(2014) expanded the previous study and investigated concrete columns reinforced longitudinally 45

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with GFRP, carbon FRP (CFRP), and steel bars plus GFRP and CFRP transverse reinforcement. 46

It was concluded that the contribution of longitudinal FRPs in concrete columns subjected to 47

axial concentric loading should not be neglected. Also, Afifi et al. (2013) tested 12 full-scale 48

circular concrete columns reinforced with longitudinal GFRP bars under concentric axial loads 49

and concluded that ignoring the contribution of GFRP bars in design equation underestimated the 50

maximum capacity of the tested specimens. 51

Recently, Karim et al. (2016) and Hadhood et al. (2017) tested GFRP-reinforced concrete 52

columns under combined axial load and bending moment. Karim et al. (2016) found that 53

longitudinal GFRP bars improved the peak load and the ductility of the columns. Hadhood et al. 54

(2017) reviewed and discussed the compressive contribution of GFRP bars and found that 55

ignoring the contribution of the compression GFRP bars underestimated the nominal axial load 56

and moment capacity of the tested columns (27% on average). Integrating the contribution of the 57

compression GFRP bars, however, returned a more reasonable estimation (17% on average). 58

Moreover, Hadi et al. (2016) and Maranan et al. (2016) studied the effect of hoops and spirals 59

reinforcements with different spacing on the behavior of GFRP-reinforced concrete columns. 60

Design guidelines including ACI 440.1R (2015) and CAN/CSA S806 (2012) currently 61

neglect the compressive contribution of GFRP bars. The approach has been rooted in concerns 62

surrounding the compressive strength and elastic modulus of GFRP bars and the possibility of 63

premature failure of the bars in compression. For example, per ACI 440.1R (2015), the 64

contribution of FRP bars should be neglected when used as reinforcement in columns, in 65

compression members, or as compression reinforcement in flexural members. However, it is 66

acceptable for FRP tension reinforcement to experience compression due to moment reversals or 67

changes in load pattern. It is believed that the maximum contribution of compression FRP bars 68

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calculated at ultimate concrete strain (typically at εcu = 0.003) is small due to: (i) the relatively 69

lower elastic modulus of FRPs compared with steel; and (ii) the lower elastic modulus of FRP 70

bars in compression as compared to tension. The authors of this paper believe the first reasoning 71

is logical for GFRP bars as majority of GFRP bars in the market have an elastic modulus ranging 72

from 40 to 60 GPa (20 to 30% steel’s elastic modulus). However, the effect of low modulus can 73

be calculated based on elastic theory as proposed by Tobbi et al. (2014). The axial capacity of a 74

concrete column reinforced with longitudinal FRP bars can be calculated as follows: 75

( ) ffccfgcn AEAAfP ε ′+−′= 85.0 (1)

where Pn is the nominal axial capacity, f’c is the concrete compressive strength, ε’c is the strain of 76

concrete at peak load (typically taken as 0.002 mm/mm), Ag is the gross cross-sectional area, Af 77

is the area of longitudinal FRP bars, and Efc is the elastic modulus of FRP bars in compression. It 78

should be highlighted that the concrete compressive strength f’c is based on 150 mm × 300 mm 79

standard cylinders. Per Hognestad (1951), it is not applicable for concrete columns and the 80

maximum stress of 0.85 f’c was proposed. This value was found as an average in numerous tests 81

of vertically-cast concentrically loaded columns. Effects of size and shape of the columns as well 82

as of the casting position was included in the factor 0.85. In this paper, concrete cylinders were 83

tests and as s results the factor 0.85 is not considered. The second term in Equation (1) 84

corresponds to the contribution of longitudinal FRP bars at the peak load. If the elastic modulus 85

of FRPs in compression was less than tension one, it would be considered automatically. 86

As there is no standard test method for FRP bars in compression, there are multiple and 87

even controversial opinions in the literature regarding the strength and elastic modulus of FRP 88

bars in compression. De Luca et al. (2010) specified that testing of FRP bars in compression is 89

typically complicated by the occurrence of fiber micro-buckling due to the anisotropic and non-90

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homogeneous nature of the FRP material, and can lead to inaccurate measurements. Therefore, 91

standard test methods are not established yet. For the case of GFRP bars, reductions in the 92

compressive strength and elastic modulus by up to 45 and 20% with respect to the values in 93

tension, respectively, have been reported (De Luca et al. 2010). Deitz et al. (2003) tested GFRP 94

bars (15 mm diameter) in compression with unbraced length of 50 to 110 mm (length/diameter 95

of 3.3 to 6.7). The test results indicated that the compressive strength of the bars was varied from 96

about 50 to 120% (average = 85%) of the tensile strength. Moreover, the elastic modulus showed 97

to be the same in compression and tension. On the other hand, Tobbi et al. (2014) concluded that 98

the ultimate axial compressive strain for columns reinforced longitudinally and transversally 99

with FRP bars can reach a value on the same order of magnitude as the FRP ultimate tensile 100

strain of the longitudinal bars under good confinement conditions. 101

The lack of consensus and clear understanding surrounding the compressive behavior of 102

GFRP reinforcement means that more research is required to understand their behavior, 103

especially in concrete. This paper is a part of a comprehensive project on behavior of 104

longitudinal FRPs as internal and external reinforcements of short and long concrete specimens 105

under concentric and eccentric loading. Fillmore and Sadeghian (2017) applied additional 106

fiberglass threads spirally around GFRP bars and studied its effect on the compressive behavior 107

of the bars in concrete cylinders comparing with GFRP bars without the spiral threads, briefly. 108

Moreover, Khorramian and Sadeghian (2017a, 2017b, and 2017c) studied the compressive 109

behavior longitudinal FRPs in small-scale concrete specimens with square cross-section under 110

combined axial and bending moment. 111

This paper aims to examine how GFRP bars behave in short reinforced concrete cylinders 112

under concentric loading. Analyzing the compressive behavior GFRP bars at this level is 113

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fundamental to understanding the failure mechanism of the bars surrounded with concrete. The 114

test data is implemented to quantify the contribution of GFRP bars when concrete reached to its 115

peak stress. For this reason, several concrete cylinders were reinforced with steel and GFRP bars 116

and testes under axial compressive loading up to failure. The number of bars was varied to 117

establish a meaningful comparison for different reinforcement ratios. The load capacity and 118

toughness of the specimens and strain of the bars were compared and the contribution of bars at 119

peak load was obtained. An analytical study was also performed on the load capacity and 120

verified with the experimental data. Also, a new test method is proposed to determine the 121

compressive properties of GFRP bars. 122

123

2. RESEARCH SIGNIFICANCE 124

The use of GFRP bars as tensile internal reinforcement of concrete structures has become 125

popular, especially for beams and slabs. However, there is a concern in the literature regarding 126

application of GFRP bars in compression. North American design guidelines including ACI 127

440.1R (2015) and CAN/CSA S806 (2012) currently neglect the compressive contribution of 128

GFRP bars in beams and columns. It is commonly believed that GFRP bars are not as effective 129

as steel bars in load bearing capacity of concrete columns. The approach has been rooted in 130

concerns surrounding the compressive strength and elastic modulus of GFRP bars and the 131

possibility of premature failure of the bars in compression. In addition, the lower elastic modulus 132

of GFRP bars with respect to steel bars has magnified the concern. This study was designed to 133

investigate compressive behavior of GFRP bars in concrete. Moreover, it proposes a new test 134

method of testing GFRP bar coupons in compression. 135

136

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3. EXPERIMENTAL PROGRAM 137

Several concrete cylinders were reinforced with steel and GFRP bars and testes under axial 138

compression. This section presents the details of the experimental program including specimen 139

layout, material properties, specimen preparation, test set-up and instrumentation. 140

3.1. Specimen Layout 141

A total of 21 concrete cylinders with a diameter of 150 mm and a height of 300 mm were 142

prepared and tested under uniaxial compressive loading. As shown in Table 1, the testing matrix 143

included 7 groups of specimens, namely, plain (unreinforced/control), steel-reinforced concrete 144

specimens (3 groups), and GFRP-reinforced concrete specimens (3 groups). Reinforced 145

specimens were built in 4, 6, and 8 bar arrangements with axisymmetric distribution. Three 146

identical specimens were prepared for each group. The specimen identification (ID) numbers 147

consist of a two-part naming system “X-N”: the first part “X” being the type of reinforcing bar, 148

namely “P” (Plain, no reinforcement), “S” (Steel-reinforced concrete), and “G” (GFRP-149

reinforced concrete); and the second part “N” being the number of bars arranged in the specimen, 150

namely 4, 6, and 8. 151

3.2. Material Properties 152

Concrete was delivered in a ready-mix batch with maximum aggregate size of 12.7 mm and 153

slump of 100 mm. The average compressive strength of concrete at the time of test was 36.2 154

MPa. The manufacturer’s specifications for the GFRP bars (#4) are for a nominal cross-sectional 155

area of 126.7 mm2 with the tensile properties of peak load, ultimate strength, and elastic modulus 156

being specified as 95.90 kN, 758 MPa and 46 GPa, respectively (manufacturer: Hughes Brothers, 157

Seward, NE, USA). The steel bars used were 10M (nominal cross-sectional area of 100 mm2) 158

with a specified tensile strength of 400 MPa and an elastic modulus of 200 GPa. 159

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3.2.1. Tension Coupon Tests 160

Three GFRP bar specimens were prepared and tested in tension per ASTM D7205/D7205M-06. 161

(2006). Steel tubes were used as end anchors and connected to the GFRP bars using a mixture of 162

epoxy resin and silica sand. Two strain gauges were attached on the surface of the bars at the 163

mid-length of the specimen. Tensile load was applied in a displacement control rate of 2 164

mm/min. The specimens ruptured in a brittle mode. The average of two strain gauges was used to 165

plots stress-strain curves as shown in Figure 2(a). The average ± standard deviation of the tensile 166

strength, tensile elastic modulus, and tensile rupture strain of GFRP bars were obtained as 167

839±49 MPa, 44.2±1.7 GPa, and 0.0209±0.0021 mm/mm, respectively. The compressive elastic 168

modulus was calculated based on a chord modulus ranging from a strain of 0.001 to 0.003 169

mm/mm. It should be noted that the GFRP bars used in this study were available at Dalhousie 170

University from an old batch at the time of the research and were not the latest product of the 171

manufacturer. Also, three steel bar specimens were prepared and tested in tension. The average ± 172

standard deviation of the yield strength of steel bars were obtained as 464±19 MPa. 173

3.2.2. Compression Coupon Tests 174

As there is no standard method for testing FRP bars in compression, a new test method proposed 175

by Khorramian and Sadeghian (2017a) was implemented through applying pure compression 176

load on five short GFRP bar specimens with a free length twice the diameter of the bars. To 177

eliminate the stress concentration and premature failure at the ends of bar specimens, two steel 178

caps including a steel hollow cylindrical section with inner diameter of 32 mm and depth of 12.7 179

mm were used. The caps were filled with a high strength epoxy-based adhesive to fix the rebar 180

specimens. Two strain gauges were attached on the surface of the bars at mid-length. 181

Compression load was applied with a rate of 2mm/min. For the compression test, a spherical 182

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platen was used at the bottom of the specimens to align them with the axis of loading minimizing 183

accidental eccentricities. Mode of failure of rebars in compression test was crushing and no 184

global buckling was observed during the test. It should be highlighted that the test was designed 185

to prevent global buckling of the bars using the length/diameter ration of 2. However, the local 186

buckling of individual fibers at the failure section was observed. Figure 2(b) shows the stress-187

strain curves of the specimens. The average ± standard deviation of compressive strength, elastic 188

modulus, and ultimate strain of GFRP were obtained as 559 ±36 MPa, 45.5±1.5 GPa, and 189

0.0122±0.0012 mm/mm, respectively. Figure 2(b) shows the stress-strain diagram obtained from 190

the compression tests. The compressive elastic modulus was calculated based on a chord 191

modulus ranging from a strain of 0.001 to 0.003 mm/mm. The tests set-up and tested specimens 192

are shown in Figure 3. 193

It was observed that the compressive strength of GFRP bars in compression was 67% of 194

tensile strength. Also, the elastic modulus of GFRP rebar tested in compression was slightly 195

higher than that of in tension, which justify the assumption of having the same elastic modulus in 196

tension and compression. It means ignoring compressive strength of GFRP bars and considering 197

their strength and modulus like concrete in compression is not realistic. It should be noted that 198

the performance of GFRP bars in concrete could be different than coupon test. That is another 199

reason for designing the experimental program 200

3.3. Specimen Preparation 201

The dimensions and compressive testing procedure followed ASTM C39M-16 (2016) but with 202

specimen-construction modifications to accommodate and isolate the effects of the GFRP and 203

steel reinforcement. As shown in Figure 1, The reinforcing bars were radially located at equal 204

angles about the centre of the specimen, such that concrete cover was consistently 25 mm and 205

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the clear space between bars was at least 20 mm. Since alignment of the reinforcing was crucial 206

to achieving consistent and meaningful data, a method of specimen preparation was developed to 207

maintain the integrity of the reinforcement geometry throughout the building process. 208

After applying strain gauges to selected bars as shown in Figure 4(a), the bars were 209

installed in cylindrical plastic molds. Limited space within the 150×300 mm specimen size lead 210

to the development of a method whereby the bars would be end-bearing and keep precise 211

longitudinal orientation without the use of internal ties: this was done by creating a temporary 212

base beneath the mold to support the extruded ends of the bars during consolidation as shown in 213

Figure 4(b). The base functioned as cantilever, holding the bars in place using a rigid polymer-214

fine aggregate mixture. While the bonding mixture cured in the cantilever base, the bars were 215

braced for proper alignment. This method allowed the faces of the consolidated concrete 216

specimens to be ground smooth such that specimens were able to be axially loaded through a 217

uniform cross section. The cantilever base also proved to be sufficiently strong to maintain the 218

reinforcement alignment during placement and consolidation of the concrete. As shown in Figure 219

4(c), The fresh concrete was placed and consolidated in two layers using scoops, a vibration 220

table, and then the surface was carefully troweled smooth as shown in Figure 4(d). The 221

consolidated concrete was left in the molds and covered to moist cure for 4 days before the 222

molds were removed and the specimens were relocated to the laboratory to be tested 4 weeks 223

later. 224

3.4. Test Setup and Instrumentation 225

As shown in Figure 4(e), deformation of the specimens was measured using three linear variable 226

differential transformer (LVDT) units fixed to the cylinder using a point-bearing yolk: two 227

longitudinal LVDT units with 200 mm gauge lengths were placed on opposite sides to measure 228

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axial deformation while the third measured lateral (i.e. radial) deformation across the full 150 229

mm diameter until spalling occurred. The reinforced specimens also implemented two 12 mm 230

longitudinal strain gauges each with 6 mm gauge length, which were bonded to flat surfaces 231

machined in-house into the outward facing sides of the bars before pouring concrete. The strain 232

gauges were also protected by a protective coating and covered with aluminum tape. In each 233

reinforced specimen, the two bars with strain gauges were placed in a similar polar opposite 234

arrangement to the longitudinal LVDT units, with the strain gauges facing the outside of the 235

specimens. As shown in Figure 4(f), the compressive testing was done on a 2 MN universal 236

testing frame and was programmed to deform the specimens at a rate of 0.6 mm per minute. The 237

specimens were compressed until either the internal reinforcement began to crush (long after 238

peak load) or until it did not seem safe to deform the specimen any further. 239

240

4. EXPERIMENTAL RESULTS AND DISCUSSIONS 241

Main test results are load capacity and load-strain responses of the specimens. Table 2 presents 242

the summary of test results based on average of three identical specimens of each group. The 243

following sections present the detail of the test results with in-depth discussions on failure 244

modes, the effect of bars on peak load, strain at peak load, toughness, and load-strain diagrams. 245

4.1. Failure Mode 246

Figure 5 shows all GFRP- and steel-reinforced specimens after the test. Every specimen 247

exhibited an observable initiation of micro-cracks, causing an audible fracturing in the concrete 248

and development of the longitudinal surface cracks, which had originally appeared approaching 249

peak load. The peak load of steel-reinforced concrete specimens was typically associated with 250

crushing of concrete and yielding of steel bars. When concrete cover was spalled, the steel bar 251

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started to buckle too. For GFRP-reinforced concrete specimens, no GFRP crushing or buckling 252

was observed up to peak load. After the peak load, concrete cover started to spall and gradually 253

bars started to buckle as they lost the lateral support of concrete cover. Few GFRP bars crushed 254

in the process, long after the peak load. 255

Overall, as shown in Figure 6, after crushing of concrete, three modes of failure were 256

observed, namely, (a) inelastic buckling of steel bars; (b) elastic buckling of GFRP bars; and (c) 257

crushing of GFRP bars. As the buckling of steel bars was inelastic, the steel bars kept a 258

permanent deformed shape after unloading, however buckled GFRP bar were returned to almost 259

original shape after unloading. After the specimens were removed from the testing frame, it 260

became clear that the steel reinforcing separated a concrete core from the exterior concrete which 261

ultimately spalled. The concrete fracturing in most of the steel-reinforced specimens resembled 262

the conical failure of the plain concrete specimens but with the core being protected, except for 263

the 4-bar steel reinforced specimens, where the shear cone permeated the perimeter of the core as 264

defined by the reinforcement bars. 265

The GFRP-reinforced specimens had similar intragroup trends for 4-, 6-, and 8-bar 266

arrangements to that of the steel group. Since the GFRP bars had greater diameter than that of 267

steel, the difference in the behavior of the 8-bar GFRP reinforced specimens to the 4- and 6-bar 268

arrangements is more profound than in the steel group. The 6-bar GFRP reinforced concrete 269

composite effectively cancelled the independent brittle failure modes of its individual 270

components and resulted in a pseudo-ductile failure mode, albeit with much less of an increase in 271

the peak load compared to a similar steel specimen. The loading of the specimens showed high 272

deformability of GFRP bars for safe post-peak behaviour and considerable resiliency after 273

unloading. 274

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4.2. Effect of Bars on Peak Load 275

The average peak load of all the specimen groups are shown in Figure 7. In the figure, the error 276

bars illustrate the standard deviation of peak load of 3 identical specimens in each group. The 277

steel bars proved to have larger effect than GFRP bars in increasing the peak load of the 278

cylinders. The 4-bar steel arrangement increased the peak load over plain concrete from 639 kN 279

to 792 kN (24% increase), and further increases to 585 and 911 kN (34 and 43% increase over 280

plain) were made with the 6- and 8-bar steel arrangement, respectively, as shown in Table 2. The 281

4-bar GFRP arrangement increased the peak load over plain concrete from 639 kN to 709 kN 282

(11% increase), and further increases to 725 kN (13% increase over plain) were made with the 6-283

bar GFRP arrangement. The 8-bar GFRP arrangement showed an average peak load of 723 kN 284

showing only 2 kN lower than that of 6-bar GFRP arrangement, which is within the standard 285

deviation of the peak load of 8-bar GFRP arrangement (i.e. 25 kN, see Table 2). As shown in 286

Figure 7, GFRP bars are not as effective as steel bars. However, as it is discussed in following 287

sections, the low effectiveness of GFRP bars with respect to steel bars is due to lower elastic 288

modulus not crushing nor buckling. 289

4.3. Effect of Bars on Strain at Peak Load 290

As shown in Figure 8, both steel and GFRP bars increased the axial strain at peak load of the 291

specimens, except 8 GFRP bars. The 6-bar specimens increased the strain at peak the most. The 292

strain at peak load of plain specimens were 0.0021 mm/mm and both steel and GFRP bars 293

increased it to an average of 0.0026 (24% increase). According to Equation (1), contribution of 294

GFRP bars is proportional to its elastic modulus in compression and the axial strain at peak load 295

of reinforced concrete. The mechanism is different for concrete reinforced with steel bars, as 296

yielding of steel at typical strain of 0.002 mm/mm marks the maximum resisting force of steel 297

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bars. As GFRP bars have linear behavior, more axial strain means more contribution for GFRP 298

bars. This affects the contribution of GFRP bars in the load capacity. Thus, Equation (2) was 299

adopted from Hognestad (1951) to be used for the strain at peak of the test specimens rather than 300

the conventional value of 0.002 mm/mm. 301

c

cc

E

f ′=′ 2ε

(2)

In Equation (2), ε’c is the strain of concrete at peak load, f’c is the concrete compressive 302

strength, and Ec is the elastic modulus of concrete. The equation predicts 0.0026 and 0.0027 303

mm/mm for the strain at peak load of the specimens using the elastic modulus of concrete per 304

ACI 318 (2014) and CAN/CSA A23.3 (2014), respectively, which are compatible with the 305

average experimental value of both steel and GFRP reinforced concrete specimens. It should be 306

highlighted that the validity of Equation (2) for large-scale concrete columns reinforced with 307

GFRP bars should be verified based on large-scale test specimens. 308

4.4. Effect of Bars on Load-Strain Behavior 309

The effect of both steel and GFRP bars is demonstrated in the representative load-strain curves 310

comprising Figure 9. Each specimen had two 6 mm axial strain gauges located on the externally-311

facing shallow-milled surfaces of two reinforcement bars, as well as the two axial LVDTs of 150 312

mm gauge length. The axial deformation as measured by the LVDTs and the strain gauges were 313

close up to peak load. However, the strain gauge data for steel specimens began to measure 314

higher strains than the LVDTs with further deformation beyond the peak load resistance. Thus, 315

the load-strain curves of the steel-reinforced specimens are based on LVDT data. With the GFRP 316

reinforcement, the difference between the LVDT and strain gauge measurements were minor, 317

and there was almost no difference between the data from each measurement source in the 318

modified GFRP groups. Thus, for the GFRP-reinforced specimens, all 4 measurements (2 strain 319

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gauges and 2 LVDTs) were averaged to determine accurate load-strain data for each specimen, 320

then used to compute the average curve for each group of three identical specimens. This 321

computation process means that each individual curve of GFRP bars in Figure 9 represents the 322

data from 12 axial strain measurements. 323

Overall, GFRP bars enhanced the peak load and area under the curve of the concrete 324

specimens over plain concrete specimens. However, GFRP bars were not as effective as steel 325

bars. The specimens with 6 GFRP bars resulted in a much broader peak in the load-strain curves, 326

whereas the specimens with 8 GFRP and steel bars showed a sudden drop after the peak load. As 327

shown in Figure 9, the GFRP bars sustained large strains long after the peak load and beyond the 328

crushing strain of 0.0122 mm/mm from coupon compression tests as described in Sec. 2.2. 329

during the tests, few GFRP bars crushed and due to a sudden drop the test was terminated. For 330

example, one of specimens with 8 GFRP bars experienced GFRP crushing as presented in Figure 331

6(c). The axial strain corresponding to GFRP crushing was larger than the crushing strain of 332

0.0122 mm/mm from coupon compression tests. It shows that the proposed test method in Sec. 333

2.2 can capture the crushing strain of GFRP bars close to real condition in concrete. 334

4.5. Effect of Bars on Toughness 335

The toughness was computed by numerical integration of the area under the axial load vs. axial 336

strain curve of each specimen. The value was divided by the volume of the cross-section of 337

concrete cylinder to obtain a toughness value with a unit of N-mm/mm3. In order to make a 338

comparison between toughness of specimens, the procedure numerical integration was 339

terminated when a specimen’s load resistance decreased to 85% of its peak load. Figure 10 340

shows the variation of toughness for the test specimens. Overall, the toughness of GFRP-341

reinforced specimens was slightly less than that of steel-reinforced specimens. As shown in 342

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Table 2 and Figure 10, the only anomaly was the 6-bar GFRP-reinforced specimens, where 343

gradual post-peak behavior of the specimens resulted in higher axial strain at 85% of peak load. 344

An important distinction between the 8-bar specimens and those with fewer bars is that they 345

showed the least toughness. The 8-bar specimens achieved the highest peak loads within their 346

group, but it came at a price as the high reinforcement ratio led to brittle failure after the peak 347

load was reached. Since the radial distance of the bars is constant throughout all reinforced 348

specimens, the 8-bar reinforcement geometry decreases the concrete-to-concrete bonding area 349

between the core and the cover; which meant that the cover was prone to spalling with transverse 350

expansion through the Poisson’s effect. As a result, the 8-bar specimens proved to have a lower 351

toughness than even the 4-bar specimens. These results suggest that there is an optimization of 352

the reinforcement ratio to achieve the maximum toughness. As there was no transverse 353

reinforcements, the unbraced length of bars was slightly less than 300 mm. It means real-size 354

concrete columns with high GFRP reinforcement ratio need to have less spacing of transverse 355

reinforcement preventing buckling of bars and increasing the toughness and energy absorption of 356

the system. Since GFRP bars are linear elastic until crushing at a high strain, their contribution 357

consistently increases until the specimen relies almost entirely on the GFRP bars buried within 358

fractured concrete. The post peak behavior of GFRP-reinforced concrete specimens with high 359

reinforcement ratio can be enhanced with more transverse reinforcements. 360

4.6. Effect of GFRP Reinforcement Ratio 361

The reinforcement ratio of specimens reinforced with 4-, 6-, and 8-bar steel arrangements were 362

2.26, 3.40, and 4.53%; respectively. Also, the reinforcement ratio of specimens reinforced with 363

4-, 6-, and 8-bar GFRP arrangements were 2.87, 4.30, and 5.74%; respectively. As shown in 364

Figure 7, increasing reinforcement ratio of both steel and GFRP increased the load capacity of 365

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the specimens. However, the rate of the increase for GFRP bars was much lower than that of 366

steel bars. This can be explained with lower modulus of GFRP bars. It should be highlighted that 367

there is a fundamental difference between GFRP-reinforced concrete specimens and steel-368

reinforced ones. In conventional concrete specimens reinforced with steel bars, peak load of 369

specimens is reached at a strain level close to yielding strain of steel bars. As a result, after the 370

peak load, the stress of steel bars does not increase. However, the story for GFRP bars is 371

different. As GFRP bars are linear elastic, if concrete sustains high strains, the stress of GFRP 372

bars increases until concrete cover spalls and GFRP bars are buckled and/or crushed. This study 373

showed that GFRP bar crushing occurs long after peak load, so the lateral support and spacing of 374

transverse bars are critical. In addition, using high-strength concrete with high strain at peak load 375

will be beneficial, especially with high reinforcement ratio of GFRP bars to increase the 376

contribution of the bars. 377

378

5. ANALYTICAL STUDIES 379

In this section, the axial load capacity of the concrete specimens reinforced with longitudinal 380

GFRP bars and the contribution of the bars in load bearing capacity of the specimens are 381

formulized and the results are compared to the experimental data. 382

5.1. Load Capacity 383

The nominal axial capacity of a concrete specimen reinforced with longitudinal FRP bars in 384

compression can be calculated as follows: 385

fcn PPP += (3)

where Pn is the nominal axial capacity, Pc is the concrete contribution, Pf is the FRP contribution. 386

It should be highlighted that the second term corresponds to the contribution of FRP bars at the 387

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peak load, not their ultimate capacity in compression. As FRP bars have linear elastic behavior 388

up to the crushing, the contribution of FRP bars can be obtained as follows: 389

ffccf AEP ε ′= (4)

where Af is the area of longitudinal FRP bars, Efc is the elastic modulus of FRP bars in 390

compression, and ε’c is the strain of concrete at peak load. The axial capacity of the concrete 391

specimens reinforced with GFRP bars presented in this study were calculated using the analytical 392

procedure. The results in the form of the ratio of the analytical capacity (Pn) over the 393

experimental value are presented in Figure 11. It shows that the analytical procedure can predict 394

the axial capacity of the specimens very well. The prediction is a little at the safe side, which is 395

acceptable for design applications. The figure also shows the contribution of GFRP bars (Pf) and 396

concrete (Pc) to the ratio. It should be noted that the factor 0.85 in Equation (1) was not applied 397

to the concrete strength as the reinforced specimens were fabricated with the same size and 398

method of the plain specimens. Also, the proposed Equation (2) was used for the strain of 399

reinforced concrete at the peak load. Using lower values such as conventional value of 0.002 400

mm/mm for the strain at peak will be more conservative. 401

5.2. Normalized Reinforcement Ratio 402

For each type of reinforcing bar used in this study, it was observed that there were similar trends 403

within each group as the number of bars was increased. The load strain behavior up to the peak 404

of the curve depends on the elastic modulus and reinforcement ratio. Thus, a normalized 405

reinforcement ratio (ρn) for FRP-reinforced specimens was defined by multiplying the FRP 406

reinforcement ratio (ρf) by the ratio of the elastic modulus of FRP reinforcement (Ef) to the 407

elastic modulus of steel reinforcements (Es) as follows: 408

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s

f

fnE

Eρρ =

(5)

Figure 12 presents the experimental load capacity of the specimens versus the normalized 409

reinforcement ratio. The figure clearly indicates a linear trend from plain to GFRP-and steel-410

reinforced specimens, which justify the normalized reinforcement ratio. It also indicates that 411

providing higher amount of GFRP bars can compensate the lack of the elastic modulus as long as 412

a maximum reinforcement ratio criteria regarding enough space for placement of concrete is 413

satisfied. 414

5.3. GFRP Bars Contribution 415

The contribution of GFRP bars in concrete columns have been interest of researchers and 416

engineers. In this study, two methods were used to determine the GFRP bars contribution at peak 417

of the test specimens and these values were averaged. The first was the force method which uses 418

the difference between the observed load resistance (Pu) of a specimen and that which is 419

predicted by the crushing strength of concrete (Pc) and the area of concrete in the cross-section 420

of the specimen as follows: 421

u

cu

P

PP −=β

(6)

where β is the bar contribution in percent. The second method employs the elastic modulus of the 422

bars and the strain at peak load as follows: 423

u

ffcc

P

AEεβ

′=

(6)

The bar contribution at peak load of the specimens tested in this study (based on the 424

average of the two methods) are shown in Figure 13. It observed that the bar contribution at peak 425

is directly proportional to the normalized reinforcement ratio. For comparison, as shown in 426

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Figure 13, data from this current study was plotted alongside Fillmore and Sadeghian (2017) on 427

smaller GFRP bars, which analyzed compressive behavior of GFRP reinforcement alongside 428

conventional steel reinforced concrete. This external data also fit the linear relationship that was 429

found in the current study. 430

In this study, the coefficient of variation (COV) of the peak load of plain, steel-431

reinforced, and GFRP-reinforced concrete cylinders was obtained 4.7, 1.1, and 2.5%; 432

respectively. The average COV of bar contribution for steel and GFRP bars was calculated 0.7 433

and 11.2%; respectively. This shows that GFRP-reinforced specimens experienced more 434

variability than steel-reinforced specimens. It should be noted that average strength of plain 435

concrete was used to calculate the bar contribution of both steel- and GFRP-reinforced 436

specimens. 437

Figure 13 indicates that GFRP bars contribution in the concrete cylinders is within 4.5-438

18.4% contribution, which is a function of its normalized reinforcement ratio ranging 0.37-439

1.32%. Overall, the contribution of both GFRP and steel bars shows a linear relationship with a 440

slope of 8.5 with respect to the normalized reinforcement ration. For example, a steel 441

reinforcement ratio of 2% will result in a bar contribution of 17%. However, the same 442

reinforcement ratio of a GFRP bar with elastic modulus of 50 GPa (i.e. 25% of steel’s elastic 443

modulus) will result in a bar contribution of 4.2%. In conclusion, lower contribution of GFRP 444

bars in concrete cylinders is only due to lower elastic modulus of GFRP bars with respect to steel 445

bars. 446

It should be noted that the results are based on small-scale concrete cylinders and the 447

effect of size of test specimens should be further evaluated for possible application of the results 448

in design of large-scale concrete columns reinforced with GFRP bars. It is expected to have less 449

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contribution of GFRP bars in large-scale concrete columns. In addition, the authors are planning 450

to test large-scale concrete columns reinforced with GFRP bars adding required data to existing 451

data in the literature to calibrate resistance reduction factors (Phi factors) of GFRP-reinforced 452

concrete columns for design applications. 453

454

455

6. CONCLUSION 456

In this study the effect of longitudinal GFRP bars on the behavior of axially loaded concrete 457

cylinders was examined and benchmarked to steel reinforced and unreinforced control groups. 458

The following conclusions can be drawn: 459

• In the experimental program on concrete cylinders reinforced with GFRP bars, no premature 460

crushing of GFRPs was observed. It was shown that GFRP bars were able to sustain large 461

strains long after the peak load of test specimens. 462

• Smaller modulus of GFRP bars resulted in a smaller gain in the peak load of concrete 463

cylinders than those reinforced with steel bars. However, GFRP reinforcement results in 464

comparable toughness and deformability for safe post-peak behaviour and resiliency. 465

• An analytical procedure was implemented to compute the axial capacity of GFRP-reinforced 466

concrete cylinders. It was shown the analytical procedure can predict the axial capacity of the 467

small-scale test specimens very well. 468

• GFRP bars made a meaningful contribution to the strength of concrete specimens, which was 469

proportional to reinforcement ratio and elastic modulus. When the reinforcement ratio was 470

normalized by multiplying it by the ratio of the elastic modulus of the reinforcement to that 471

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of conventional steel reinforcement, the axial load capacity of the test specimens was found 472

to be a linear function. 473

• GFRP bar contribution in concrete cylinders under axial compression was formularized and 474

found to be a function of its normalized reinforcement ratio within 4.5-18.4% contribution 475

within the small-scale cylinders tested in this study. 476

• The results of this study showed that GFRP bars have similar elastic modulus in tension and 477

compression, compressive strength close to two-third of tensile strength, and an appreciable 478

effect on the peak load resistance of concrete cylinders in uniaxial compression. Thus, 479

neglecting the contribution of GFRP bars in compression is too conservative. However, the 480

effect of size of test specimens should be further evaluated for possible application of the 481

results in design of large-scale concrete columns reinforced with GFRP bars. 482

483

7. ACKNOWLEDGEMENTS 484

The authors are grateful for the financial support of the Natural Sciences and Engineering 485

Research Council of Canada (NSERC) and Dalhousie University in conducting this study. 486

487

8. REFERENCES 488

ACI 440.1R. 2015. Guide for the Design and Construction of Structural Concrete Reinforced 489

with Fiber-Reinforced Polymer (FRP) Bars, American Concrete Institute, Farmington Hills, 490

MI, USA. 491

ACI 318. (2014). Building Code Requirements for Structural Concrete American Concrete 492

Institute. Farmington Hills, MI, USA. 493

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Afifi, M.Z., Mohamed, H.M. and Benmokrane, B., 2013. Axial capacity of circular concrete 494

columns reinforced with GFRP bars and spirals. Journal of Composites for Construction, 495

18(1), p.04013017. 496

ASTM C39M-16. 2016. Standard Test Method for Compressive Strength of Cylindrical 497

Concrete Specimens, American Society of Testing and Materials, West Conshohocken, PA, 498

USA. 499

ASTM D7205/D7205M-06. 2006. Standard Test Method for Tensile Properties of Fiber 500

Reinforced Polymer Matrix Composite Bars, American Society of Testing and Materials, 501

West Conshohocken, PA, USA. 502

Bazhenov, S.L., Kuperman, A.M., Zelenskii, E.S. and Berlin, A.A., 1992. Compression failure of 503

unidirectional glass-fibre-reinforced plastics. Composites science and technology, 45(3), 504

pp.201-208. 505

Benmokrane, B., Chaallal, O. and Masmoudi, R., 1995. Glass fibre reinforced plastic (GFRP) 506

rebars for concrete structures. Construction and Building Materials, 9(6), 353-364. 507

Bischoff, P.H., 2005. Reevaluation of deflection prediction for concrete beams reinforced with 508

steel and fiber reinforced polymer bars. Journal of Structural Engineering, 131(5), pp.752-509

767. 510

CAN/CSA A23.3. 2014. Design of Concrete Structures, Canadian Standard Association. 511

Mississauga, ON, Canada. 512

CAN/CSA S806-12. 2012. Design and Construction of Building Structures with Fibre-513

Reinforced Polymers. Canadian Standards Association, Mississauga, ON, Canada. 514

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De Luca, A., Matta, F. and Nanni, A. 2010. Behavior of Full-Scale Glass Fiber-Reinforced 515

Polymer Reinforced Concrete Columns under Axial Load. ACI Structural Journal, 107(5): 516

589-596. 517

Deitz, D.H., Harik, I.E. and Gesund, H., 2003. Physical properties of glass fiber reinforced 518

polymer rebars in compression. Journal of Composites for Construction, 7(4), pp.363-366. 519

El-Sayed, A., El-Salakawy, E. and Benmokrane, B., 2005. Shear strength of one-way concrete 520

slabs reinforced with fiber-reinforced polymer composite bars. Journal of Composites for 521

Construction, 9(2), pp.147-157. 522

Fillmore, B. and Sadeghian, P., 2017. Compressive Behaviour of Concrete Cylinders Reinforced 523

with Glass Fiber Reinforced Polymer Bars. Canadian Society for Civil Engineering (CSCE) 524

Annual Conference, Vancouver, BC, Canada. 525

Hadhood, A., Mohamed, H.M., Ghrib, F. and Benmokrane, B., 2017. Efficiency of glass-fiber 526

reinforced-polymer (GFRP) discrete hoops and bars in concrete columns under combined 527

axial and flexural loads. Composites Part B: Engineering, 114, pp.223-236. 528

Hadi, M.N., Karim, H. and Sheikh, M.N., 2016. Experimental investigations on circular concrete 529

columns reinforced with GFRP bars and helices under different loading conditions. Journal 530

of Composites for Construction, 20(4), p.04016009. 531

Hognestad, E., 1951. Study of combined bending and axial load in reinforced concrete members. 532

Bulletin Series No. 399, University of Illinois at Urbana Champaign, Champaign, IL, USA. 533

Karim, H., Sheikh, M.N. and Hadi, M.N., 2016. Axial load-axial deformation behavior of 534

circular concrete columns reinforced with GFRP bars and helices. Construction and 535

Building Materials, 112, pp.1147-1157. 536

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Khorramian, K. and Sadeghian, P., 2017a. Experimental and analytical behavior of short 537

concrete columns reinforced with GFRP bars under eccentric loading. Engineering 538

Structures, 151, pp.761-773. 539

Khorramian, K. and Sadeghian, P., 2017b. Strengthening Concrete Columns using NSM CFRP 540

Laminates. The 6th Asia-Pacific Conference on FRP in Structures (APFIS 2017), Singapore. 541

Khorramian, K. and Sadeghian, P., 2017c. Strengthening Short Concrete Columns Using 542

Longitudinally Bonded CFRP Laminates. The 13th International Symposium on Fiber-543

Reinforced Polymer Reinforcement for Concrete Structures (FRPRCS-13), Anaheim, CA, 544

USA. 545

Maranan, G.B., Manalo, A.C., Benmokrane, B., Karunasena, W. and Mendis, P., 2016. Behavior 546

of concentrically loaded geopolymer-concrete circular columns reinforced longitudinally 547

and transversely with GFRP bars. Engineering Structures, 117, pp.422-436. 548

Nanni, A., 1993. Flexural behavior and design of RC members using FRP reinforcement. Journal 549

of structural engineering, 119(11), pp.3344-3359. 550

Pantelides, C.P., Gibbons, M.E. and Reaveley, L.D., 2013. Axial load behavior of concrete 551

columns confined with GFRP spirals. Journal of Composites for Construction, 17(3), 552

pp.305-313. 553

Tobbi, H., Farghaly, A.S. and Benmokrane, B. 2012. Concrete Columns Reinforced 554

Longitudinally and Transversally with Glass Fiber-Reinforced Polymer Bars. ACI Structural 555

Journal, 109(4): 551-558. 556

Tobbi, H., Farghaly, A.S. and Benmokrane, B., 2014. Behavior of concentrically loaded fiber-557

reinforced polymer reinforced concrete columns with varying reinforcement types and 558

ratios. ACI Structural Journal, 111(2), p.375. 559

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560

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Table 1. Test matrix 561

Group

#

ID # Reinforcement

type

Bar

count

Bar

size

Bar nominal

diameter

(mm)

Bars

area

(mm2)

Reinforcement

ratio (%)

1 P None - - - 0 0

2 S-4 Steel 4 10M 11.3 400 2.26

3 S-6 Steel 6 10M 11.3 600 3.40

4 S-8 Steel 8 10M 11.3 800 4.53

5 G-4 GFRP 4 #4 13 507 2.87

6 G-6 GFRP 6 #4 13 760 4.30

7 G-8 GFRP 8 #4 13 1014 5.74

Note: Three identical specimens per group were prepared and tested.

562

563

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Table 2. Summary of test results 564

Groupe

#

ID

#

Normalized

reinforcement

ratio (%)

Peak load (kN) Strain at peak load

(mm/mm)

Toughness

(N-mm/mm3)

Average SD Average SD Average SD

1 P 0.00 639.0 29.9 0.00210 0.00035 0.101 0.028

2 S-4 2.26 792.1 4.0 0.00255 0.00011 0.173 0.006

3 S-6 3.40 858.0 16.1 0.00292 0.00046 0.216 0.051

4 S-8 4.53 911.1 7.6 0.00240 0.00022 0.160 0.085

5 G-4 0.66 709.3 15.0 0.00255 0.00008 0.173 0.066

6 G-6 0.99 724.7 14.4 0.00325 0.00057 0.244 0.064

7 G-8 1.32 722.7 25.3 0.00202 0.00065 0.102 0.067

565

566

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567

Figure 1. Specimens’ geometry and reinforcing details: (a) elevation view; (b) cross-section 568

of plain and 4-, 6-, and 8-bar specimens. 569

570

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Draft

Page 30 of 41

571

572

Figure 2. GFRP bar coupon test results: (a) tension; (b) compression. 573

574

0

200

400

600

800

1000

0 0.01 0.02 0.03 0.04

Str

ess

(M

Pa

)

Strain (mm/mm)

GFRP bar #4

Tension test

Avg. elastic modulus= 44.2 GPa

Avg. tensile strength = 839 MPa

Avg. rupture strain = 0.0209 mm/mm

Average

(a)

0

200

400

600

800

1000

0 0.01 0.02 0.03 0.04

Str

ess

(M

Pa

)

Strain (mm/mm)

GFRP bar #4

Compression test

Avg. elastic modulus= 45.5 GPa

Avg. comp. strength = 559 MPa

Avg. crushing strain = 0.0122 mm/mm

Average

(b)

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575

Figure 3. GFRP bar compression tests: (a) test set-up; (b) geometry of specimens; (c) 576

diagonal crushing; (d) longitudinal splitting; and (e) all tested specimens. 577

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Page 32 of 41

578

Figure 4. Specimen preparation and test set-up: (a) strain gauged bars; (b) bars installed in 579

forms; (c) pouring concrete; (d) surface preparation; (e) external instrumentation; and (f) 580

test set-up. 581

582

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583

Figure 5. Tested specimens: (a) 4-bar steel S-4; (b) 6-bar steel S-6; (c) 8-bar steel S-8; (d) 4-584

bar GFRP G-4; (e) 6-bar GFRP G-6; and (f) 8-bar GFRP G-8. 585

586

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587

Figure 6. Failure modes: (a) inelastic buckling of steel bars; (b) elastic buckling of GFRP 588

bars; and (c) crushing of GFRP bars. 589

590

Page 34 of 41



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591

Figure 7. Effect of steel and GFRP bars on peak load (Note: each bar shows the average of 592

three identical specimens, and error bars show the standard deviation). 593

594

300

400

500

600

700

800

900

1000

1100

1200

P S-4 S-6 S-8 G-4 G-6 G-8

Pe

ak

Lo

ad

(k

N)

Specimen ID

Page 35 of 41



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Page 36 of 41

595

Figure 8. Effect of steel and GFRP bars on axial strain at peak load. 596

597

598

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

P S-4 S-6 S-8 G-4 G-6 G-8

Str

ain

at

pe

ak

lo

ad

(m

m/m

m)

Specimen ID

Page 36 of 41



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Page 37 of 41

599

600

601

Figure 9. Axial load-axial strain curves of test specimens: (a) 4-bar groups; (b) 6-bar 602

groups; and (c) 8-bar groups (Note: each curve is average of three identical specimens. Two 603

strain gauges were used to obtain strain values of each specimens). 604

605

0

200

400

600

800

1000

0 0.005 0.01 0.015 0.02

Ax

ial

loa

d (

kN

)

Axial strain (mm/mm)

Steel, S-4 (Avg)

GFRP, G-4 (Avg)

Plain, P (Avg)

(a)

Crushing strain of

GFRP coupons

0.0122 mm/mm

0

200

400

600

800

1000

0 0.005 0.01 0.015 0.02

Ax

ial

loa

d (

kN

)


Steel, S-6 (Avg)

GFRP, G-6 (Avg)

Plain, P (Avg)

(b)

Crushing strain of

GFRP coupons

0.0122 mm/mm

0

200

400

600

800

1000

0 0.005 0.01 0.015 0.02

Ax

ial

loa

d (

kN

)


Steel, S-8 (Avg)

GFRP, G-8 (Avg)

Plain, P (Avg)

(c)

Crushing strain of

GFRP coupons

0.0122 mm/mm

Page 37 of 41



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Page 38 of 41

606

Figure 10. Effect of steel and GFRP bars on toughness. 607

608

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

P S-4 S-6 S-8 G-4 G-6 G-8

To

ug

hn

ess

(N

-mm

/mm

3)

Specimen ID

Page 38 of 41



Draft

Page 39 of 41

609

Figure 11. Analytical/experimental axial capacity ratio of concrete cylinders reinforced 610

with GFRP bars (Note: contribution of concrete and GFRP bars in analytical model are 611

shown). 612

613

0

0.2

0.4

0.6

0.8

1

1.2

1.4

G-4

-1

G-4

-2

G-4

-3

G-6

-1

G-6

-2

G-6

-3

G-8

-1

G-8

-2

G-8

-3

An

aly

tica

l/e

xpe

rim

en

tal

cap

aci

ty r

ati

o

Specimen ID

GFRP Concrete

Page 39 of 41



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Page 40 of 41

614

Figure 12. Peak load vs. normalized reinforcement ratio 615

616

y = 57.89x + 656.27

R² = 0.96

0

200

400

600

800

1000

1200

0 1 2 3 4 5

Pe

ak

lo

ad

(k

N)

Normalized reinforcement ratio (%)

Steel bars

GFRP bars

Plain

Page 40 of 41



Draft

Page 41 of 41

617

Figure 13. Comparison of steel and GFRP bar contribution to axial capacity of concrete 618

cylinders at peak load. 619

0

10

20

30

40

50

0 1 2 3 4 5

Ba

rs c

on

trib

uti

on

at

pe

ak

(%

)

Normalized reinforcement ratio (%)

Fillmore and Sadeghian (2017)

Current Study

4.5%-18.4%

Average = 10.8%

GFRP barsSteel bars

Page 41 of 41



contribution of longitudinal gfrp bars in concrete · draft page 4 of 41 69 calculated at ultimate...

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