P R O O F ONL Y. Columns under Axial Compression. Confinement Mechanism

Transcription

1 1 2 1 Optimized FRP Wrapping Schemes for Circular Concrete 3 2 Columns under Axial Compression 4 Thong M. Pham, A.M.ASCE 1 ; Muhammad N. S. Hadi, F.ASCE 2 ; and Jim Youssef 3 5 Abstract: This study investigates the behavior and failure modes of fiber-reinforced polymer (FRP) confined concrete wrapped with differ- 6 ent FRP schemes, including fully wrapped, partially wrapped, and nonuniformly-wrapped concrete cylinders. By using the same amount of 7 FRP, this study proposes a new wrapping scheme that provides a higher compressive strength and strain for FRP-confined concrete, in 8 comparison with conventional fully wrapping schemes. A total of 33 specimens were cast and tested, with three of these specimens acting 9 as reference specimens and the remaining specimens wrapped with different types of FRP (CFRP and GFRP) by different wrapping schemes. 1 For specimens that belong to the descending branch type, the partially-wrapped specimens had a lower compressive strength but a higher 11 axial strain as compared to the corresponding fully-wrapped specimens. In addition, the nonuniformly-wrapped specimens achieved both a 12 higher compressive strength and axial strain in comparison with the fully-wrapped specimens. Furthermore, the partially-wrapping scheme 13 changes the failure modes of the specimens and the angle of the failure surface. A new equation that can be used to predict the axial strain of 14 concrete cylinders wrapped partially with FRP is proposed. DOI: 1.161/(ASCE)CC American Society of 15 Civil Engineers. 16 Introduction 17 Fiber-reinforced polymer (FRP) has been commonly used to 18 3 strengthen existing reinforced concrete (RC) columns in recent 19 years. In such cases, FRP is a confining material for concrete in 2 which the confinement effect leads to increase in the strength 21 and ductility of columns. In early experimental studies that focused 22 on retrofitting RC columns with FRP, the columns were usually 23 wrapped fully with FRP sheets. This wrapping scheme provides 24 continuous confinement to the columns along their longitudinal 25 axes. Most of the studies in the literature focus only on columns 26 fully wrapped with FRP (Chaallal et al. 23; Hadi et al. 213; 27 Pham et al. 213; Pham and Hadi 214a; Smith et al. 21). In 28 addition, columns wrapped partially with FRP have also been 29 proven to show increases in strength and ductility, as compared 3 to equivalent unconfined columns (Colomb et al. 28; Maaddawy 31 29; Turgay et al. 21). However, there is no study that makes a 32 comparison of the confinement efficacy between partially- and 33 fully-wrapping schemes in terms of optimization of the FRP 34 amount. In addition, the progressive failure of those specimens 35 has not been extensively studied. Therefore, it is necessary to in- 36 vestigate the confinement efficacy and failure mechanisms of col- 37 umns partially wrapped versus columns fully wrapped with FRP. 1 Postdoctoral Research Associate, School of Civil and Mechanical Engineering, Curtin Univ., Kent St., Bentley, WA 612, Australia; formerly, Ph.D. Scholar, School of Civil, Mining and Environmental Engineering, Univ. of Wollongong, Wollongong, NSW 2522, Australia. thong.pham@curtin.edu.au 2 Associate Professor, School of Civil, Mining and Environmental Engineering, Univ. of Wollongong, Wollongong, NSW 2522, Australia (corresponding author). mhadi@uow.edu.au 3 Ph.D. Candidate, School of Civil, Mining and Environmental Engineering, Univ. of Wollongong, Wollongong, NSW 2522, Australia. jy21@uowmail.edu.au Note. This manuscript was submitted on December 14, 214; approved on February 17, 215No Epub Date. Discussion period open until, ; separate discussions must be submitted for individual papers. This paper is part of the Journal of Composites for Construction, ASCE, ISSN /()/$25.. In addition, the available design guidelines for columns wrapped with FRP [ACI 44.2 R-8 ACI (28), fib (21), and TR 55 (TR 212)] are utilized to estimate the capacities of partially FRP-wrapped specimens. Among these studies, ACI-44.2 R (ACI 28) and technical report TR 55 (TR 212) do not provide information about the confinement effect of concrete columns partially wrapped with FRP. Meanwhile, fib (21) suggests a reduction factor to take into account the effect of partial wrapping columns. The study by fib (21) adopts an assumption proposed by Mander et al. (1988) for the confinement effect of steel ties in RC columns to analyze the efficacy of FRP-partially-wrapped columns. Therefore, there has been a lack of theoretical and experimental works about partial FRP-confined concrete. For this reason, an experimental program was developed in this study to compare the confinement efficacy of FRP-partially-wrapped columns as compared to FRP-fully-wrapped columns. The same amount of FRP was wrapped onto identical concrete columns by different wrapping schemes to achieve an optimized wrapping design. Confinement Mechanism Fully-Wrapped Columns In the literature, the term FRP-confined concrete is understood automatically as concrete wrapped fully with FRP. Fig. 1(a) shows that when a circular concrete column is horizontally wrapped with FRP around its perimeter, the lateral pressure exerted from the FRP jackets confines the whole column. Many studies have been carried out to investigate the behaviors and estimate the capacities of columns wrapped fully with FRP (De Luca and Nanni 211; Lam and Teng 23; Pham and Hadi 214b, c; Teng et al. 29; Toutanji 1999; Wu and Zhou 21). The confining pressure is assumed to be uniform in the cross section and along the axial axis of the circular columns. Among the existing studies, the model proposed by Lam and Teng (23) is adopted in this study to calculate the compressive strength for columns wrapped fully with FRP as follows: ASCE 1 J. Compos. Constr.

2 fcc fco ¼ 1 þ 3.3 f l fco 72 where fcc and fco are respectively the compressive strength of 73 confined concrete and unconfined concrete; f l is the effective 74 confining pressure as follows: f l ¼ 2E fε fe t ð2þ D 75 where E f = elastic modulus of FRP; t = nominal thickness of FRP 76 jacket; D = diameter of the column section; ε fe = actual rupture 77 strain of FRP in the hoop direction. The model by Lam and Teng 78 (23) is chosen because it provides a reasonable accuracy with a 79 very simple form. The simplicity of the model by Lam and Teng 8 (23) is utilized to establish a new and simple strain model, which 81 is presented in the subsequent sections. The strain model proposed 82 by Pham and Hadi (213) is adopted to calculate the compressive 83 axial strain of confined concrete as follows: 2ktf feε fe ε cc ¼ ε co þ Dfco þ 3.3tf fe 84 where ε cc = ultimate axial strain of confined concrete; ε co = axial 85 strain at the peak stress of unconfined concrete; k ¼ 7.6 is the pro- 86 portion factor; f fe = actual rupture strength of FRP. 87 Partially-Wrapped Columns 88 As mentioned earlier, concrete columns wrapped partially with 89 FRP have been experimentally verified to increase their strength 9 and ductility. Concrete columns partially wrapped with FRP are 91 less efficient in nature than fully-wrapped columns as both con- 92 fined and unconfined zones exist [Fig. 1(b)]. An approach similar 93 to the one proposed by Sheikh and Uzumeri (198) is adopted to 94 determine the effective confining pressure on the concrete core. 95 Fig. 1(b) shows the effective confining pressure is assumed to 96 be exerted effectively on the part of the concrete core where the 97 confining pressure has fully developed due to the arching action. 98 A second-degree parabola with initial slope of 45 is assumed to 99 describe the arching effect. In such a case, a confinement effective 1 coefficient (k e ) is introduced to take the partial wrapping into ac- 11 count as follows: k e ¼ A e ¼ 1 s 2 A c 2D ð4þ 12 where A e and A c are respectively the area of effectively confined 13 concrete core and the cross-sectional area; s = clear spacing be- 14 tween two FRP bands. Consequently, the compressive strength 15 of concrete columns wrapped partially with FRP could be calcu- 16 lated as: fcc fco fl ¼ 1 þ 3.3k e f co ð1þ ð3þ ð5þ 17 where k e is estimated based on Eq. (4) and fl shown in the follow- 18 ing equation is the equivalent confining pressure from the FRP, 19 assumed to be uniformly distributed along the longitudinal axis 11 of the column: l ¼ 2E fε fe t w D w þ s f 111 where w = width of FRP bands; s = clear spacing between FRP 112 bands as shown in Fig. 1(b). ð6þ Experimental Program Design of Experiments (a) (b) Fig. 1. Confinement mechanism: (a) concrete columns wrapped fully with FRP; (b) concrete columns wrapped partially with FRP A total of 33 FRP-confined concrete cylinders were cast and tested at the High Bay Laboratory of the University of Wollongong. The dimensions of the concrete cylinder specimens were 15 mm in diameter and 3 mm in height. All the specimens were cast from the same batch of concrete. The 28-day cylinder compressive strength was 52 MPa. The experimental program was composed of several groups of cylinders in order to evaluate the confinement efficacy between partially- and fully-wrapping schemes in terms of optimization of the wrapping schemes. The notation of the specimens consists of three parts: the first part states the type of confining FRP material, with G and C representing GFRP and CFRP, respectively; the second part is either a letter R, F, and P stating the name of the subgroup, namely, reference group (R), fully-wrapped group (F), and partially-wrapped group (P); the last part of the specimen notation is a number which indicates the number of FRP layers. Table 1 presents details of the specimens. The partially-wrapped specimens contain FRP bands that are 25 mm in width spaced evenly along the height of the specimen. The optimized partially-wrapped specimens include two numbers in the notation, for example GP31. The first number indicates the number of 25-mm evenly spaced partial FRP layers and the second number depicts the number of FRP layers in between these evenly spaced partial layers. These specimens were designed such that they follow a nonuniform wrapping configuration but ensure the F1:1 F1: ASCE 2 J. Compos. Constr.

3 T1:1 Group Table 1. Test Matrix Number of specimens Type of FRP Equivalent FRP layers with full wrapping 14 specimen is fully confined at every location. The thicker band is 141 called a tie band and the thinner band is called a cover band. Taking 142 specimen GP31 as an example, the tie bands have three FRP layers 143 which are 25 mm in width, while the cover bands have one FRP 144 layer as shown in Fig. 2. Three identical specimens were made for 145 each wrapping scheme. 146 In order to analyze the confinement effectiveness between dif- 147 ferent wrapping schemes, the specimens were divided into four 148 groups (as shown in Table 1) such that the specimens in each group 149 incorporate the same amount of FRP but in a different wrapping 15 scheme, either fully, partially, or optimized nonuniformly wrapped. 151 The specimens in the first group are reference specimens which did 152 not include any internal or external reinforcement. The specimens 153 in the second and third groups were confined by GFRP and CFRP, 154 respectively, such that the fully, partially, and optimized nonuni- 155 form wrapping schemes were equivalent to two layers of full wrap- 156 ping. Similarly, the wrapping schemes of the specimens in the 157 fourth group were equivalent to three layers of full wrapping. 158 Table 1 shows, after 28 days, the specimens were wrapped with 159 a number of FRP layers. A mixture of epoxy resin and hardener at Width of each FRP band (w, mm) 5 1 ratio was used as the adhesive. Before the first layer of FRP was attached, the adhesive was spread onto the surface of the specimen and CFRP was attached onto the surface with the main fibers oriented in the hoop direction. After the first layer, the adhesive was spread onto the surface of the first layer of FRP and the second layer was continuously bonded. The third layer of FRP was applied in a similar manner, ensuring that 1-mm overlap was maintained. The ends of each wrapped specimen were strengthened with additional one layer of FRP strips 25 mm in width. Instrumentation Clear spacing (s, mm) Type of wrapping T1:2 R 3 T1:3 GF2 3 GFRP 2 5 Full T1:4 GP Partial T1:5 GP Nonuniform T1:6 CF2 3 CFRP 2 75 Full T1:7 CP Partial T1:8 CP Nonuniform T1:9 CF3 3 CFRP 3 75 Full T1:1 CP Partial T1:11 CP Nonuniform T1:12 CP Nonuniform 4 Note:. F2:1 Fig. 2. Different wrapping schemes In order to measure the hoop strains of the FRP jacket, three strain gauges with a gauge length of 5 mm were attached at the midheight of the specimens and evenly distributed away from the overlap for the fully-wrapped specimens. In the partially-wrapped specimens, three strain gauges were bonded symmetrically on a tie band and other three were bonded on a cover band at midheight of the specimen ASCE 3 J. Compos. Constr.

4 F3:1 5 Fig. 3. Compressometer 178 Furthermore, Fig. 3 shows a longitudinal compressometer was 179 used to measure the axial strain of the specimens. A LVDT was 18 mounted on the upper ring and the tip of the LVDT rested on 181 an anvil. The readability, the accuracy, and the repeatability of 182 the LVDT complies with the Australian standard [Australian 183 Standard-1545 (Australian Standard 1976)]. 184 The compression tests for all the specimens were conducted us- 185 ing the Denison 5,-kN capacity testing machine. The specimens 186 were capped with high-strength plaster to ensure full contact be- 187 tween the loading plate and the specimen. Calibration was carried 188 out to ensure that the specimens were placed at the center of the 189 testing machine. Each specimen was first loaded to around 3% of 19 its unconfined capacity to check the alignment. If required, the 191 specimen was unloaded, realigned, and loaded again. The tests 192 were conducted as deflection controlled with a rate of.5 mm=min. 193 The readings of the load, LVDT, and strain gauges were taken using 194 a data logging system and were subsequently saved in a control 195 computer. 196 Experimental Results 197 Preliminary Tests Compressometer LVDT 198 The actual compressive strength of unconfined concrete calculated 199 from three reference specimens (R1, R2, and R3) was 54 MPa. The 2 axial strain of unconfined concrete at the maximum load was.23%. In this study two types of CFRP were used to confine the concrete, which both had a unidirectional fiber density of 34 g=m 2 and a nominal thickness of.45 mm, but with varying nominal widths of 75 and 25 mm. The GFRP utilized had a unidirectional fiber density of 44 g=m 2, a nominal thickness of.35 mm, and a nominal width of 5 mm. Five coupons for each type of FRP were made according to ASTM D7565 (ASTM 21) and tested to determine the mechanical properties. Table 2 shows the two types of CFRP coupons were made of three layers of FRP with a nominal thickness of 1.35 mm and both types had very similar properties. For simplicity the coupons produced from the 75-mm tape are denoted by CFRP (75) while the coupons from the 25-mm tape are referred to as CFRP (25). For GFRP, two-layered coupons containing two overlapping fiber sheets were prepared and tested. The nominal thickness of the coupons was.7 mm. All coupons had the dimensions mm. The epoxy resin had 54-MPa tensile strength, 2.8-GPa tensile modulus, and 3.4% tensile elongation (West System 215). Failure Modes Table 2. Results of Tensile Tests on FRP Flat Coupons T2:1 Type of coupon specimen Number of FRP layers Width (mm) Nominal thickness (mm) All specimens were tested until failure. The specimens wrapped 221 fully with FRP (CF2, CF3, and GF2) failed by rupture of FRP 222 at the midheight. Fig. 4(a) shows the failure surface of the 6223 fully-wrapped specimens was found to be approximately 45 inclined. 224 Meanwhile, Fig. 4(b) shows the partially-wrapped speci mens (CP4, CP6, and GP4) showed many small cracks on 226 the concrete surface at a stress equal to the unconfined concrete 227 strength. The concrete between the FRP bands, close to the outer 228 surface of the specimen, started crushing while the concrete core 229 was still confined by the FRP. Fig. 4(c) shows cracks on the con- 823 crete surface developed as the applied load increased. At the very 231 high stress level, the concrete between the FRP bands spalled off 232 while the concrete under the FRP bands and the core were still 233 confined. These specimens then failed explosively by FRP rupture 234 at the midheight [Fig. 4(d)] The angle of the failure surface with respect to the horizon for 236 the partially-wrapped specimens was significantly different from 237 the fully-wrapping specimens. Fig. 4(d) shows the failure surface 1238 took place at the spacing between FRP bands. This change of the 239 failure surface depends on the wrapping schemes and the stiffness 24 of the FRP bands. When the axial stress of the confined concrete 241 was higher than the unconfined concrete strength, the 45 -failure 242 surface may have originally transpired in the concrete cores, but 243 cracks were arrested by FRP bands under the high-stress stage. 244 Fig. 4(e) shows if the stiffness of the FRP bands is not strong enough (Specimen GP4) to prevent the development of the cracks, 246 the failure surface takes place at approximately 45. In contrast, 247 Fig. 4(d) depicts the stiffness of the FRP bands in Specimens 1248 CP4 and CP6 is great enough so that it changed the failure 249 surface. It is worth mentioning that the stiffness of the FRP 25 bands affects the tangent modulus of FRP-confined concrete. 251 Average elastic modulus (MN=mm) Average tensile strength (kn=mm) Average ultimate strain (mm=mm) T2:2 CFRP (75) a , T2:3 CFRP (25) b , T2:4 GFRP a CFRP (75) denotes the coupons made of the FRP sheets that have 75 mm width. b CFRP (25) denotes the coupons made of the FRP sheets that have 25 mm width. 22 ASCE 4 J. Compos. Constr.

5 F4:1 Fig. 4. Failure modes of the tested specimens 252 Tamužs et al. (28) suggested that the low value of the tangent 253 modulus causes column stability collapse directly as the uncon- 254 fined concrete strength level is surpassed. 255 Furthermore, specimens with optimized nonuniform-wrapping 256 schemes showed a different failure mode as compared to the others. 257 At a stress level equal to the unconfined concrete strength, the 258 concrete was still confined by the FRP tie bands and cover bands. 259 During the loading process, the lateral strains of the tie bands and 26 the cover bands were almost identical, with the exception of 261 Specimen CP4_3. The failure modes of these specimens are sim ilar to those of the full-wrapping specimens. Fig. 4(f) shows the 263 nonuniform-wrapped specimens failed by FRP rupture simultane- 264 ously at the two bands (tie band and cover band) at the midheight. It 265 is worth mentioning that intermittent confinement resulting from 266 partial confinement (Specimens GP4, CP4, and CP6) makes 267 the concrete to communicate directly with the surroundings, for 268 instance moisture, heat, and evaporation. 269 Stress-Strain Relation 27 Stress-strain relations of the tested specimens were divided into two 271 main types based on the shape of the stress-strain curves. These 272 included specimens in the ascending branch type and descending 273 branch type. An FRP-confined concrete column exhibits the as- 274 cending type curve as a significant improvement of the compressive 275 strength and strain of an FRP-confined concrete column could be 276 expected. Otherwise, FRP-confined concrete with a stress-strain 277 curve of the descending type illustrates a concrete stress at the 278 ultimate strain below the compressive strength of unconfined 279 concrete. Specimens wrapped with glass fiber are designed to be- 28 have as the descending branch type while specimens wrapped with carbon fiber belong to the ascending branch type. Table 3 summarizes details of all tested specimens. Fig. 5 shows the plotting of stress-strain relations of specimens wrapped by equivalent two GFRP layers. The specimens which were wrapped with an equivalent of two layers of FRP had identical stress-strain curves at the early stages of loading and experienced slight differences at the latter stage of testing. Specimens GF2 and GP4 had the descending branch type stress-strain curve while the stress-strain curves of Specimen GP31 kept constant after reaching the unconfined concrete strength and then increased again to failure. Fig. 5(a) shows the axial stress of Specimen GF2 reached the unconfined concrete strength (54 MPa) and then kept constant until the FRP failed by rupture. The average compressive confined concrete strength and strain of Specimen GF2 are 57 MPa and.97%, respectively. Although Specimen GP4 obtained a lower maximum stress (53 MPa) as compared to that of Specimen GF2, they achieved a larger maximum axial strain (1.18%) than the former specimens. The axial strain of Specimen GP4 increased by 21.31% as compared to that of Specimen GF2 [Fig. 5(b)]. Meanwhile, Fig. 5(c) shows specimen GF31 achieved both a higher maximum axial stress (6 MPa) and axial strain (1.2%), as compared to Specimen GF2. Apart from the preceding specimens, Fig. 6 shows the specimens that were wrapped with an equivalent of two layers of FRP had similar stiffness during the whole loading process. The maximum axial stress of Specimen CF2 was 99 MPa and its corresponding axial strain was 2.13%. Specimen CP4 reached the maximum axial stress at 95 MPa and the corresponding axial strain at 2.8%. Specimen CP4_1 failed by premature rupture of FRP (ε l ¼ 1.18%) that resulted in very low maximum axial stress. The ASCE 5 J. Compos. Constr.

6 Table 3. Experimental Results of Tested Specimens Maximum axial stress Maximum axial strain Maximum lateral strain Strain efficiency factor T3:2 fcc Average Increase ε cc Average Increase Average T3:1 Specimen (MPa) (MPa) (%) a (%) (%) (%) a ε l (%) (%) k ε T3:3 GF2_ T3:4 GF2_ T3:5 GF2_ T3:6 GP4_ T3:7 GP4_ T3:8 GP4_ T3:9 GP31_ T3:1 GP31_ T3:11 GP31_ T3:12 CF2_ T3:13 CF2_ T3:14 CF2_ T3:15 CP4_ b T3:16 CP4_ T3:17 CP4_ T3:18 CP31_ T3:19 CP31_ T3:2 CP31_ T3:21 CF3_ T3:22 CF3_ T3:23 CF3_ T3:24 CP6_ T3:25 CP6_ T3:26 CP6_ T3:27 CP51_ T3:28 CP51_ T3:29 CP51_ b T3:3 CP42_ T3:31 CP42_ T3:32 CP42_ Note: =. 15 a Increase of a specimen compared to the fully wrapping specimens in the same group. b Specimens performed premature damage GF2_1 GF2_2 GF2_3 8 (a) GP4_1 GP4_2 GP4_ GP31_ Reference C GP31_2 ε GF2_3 ε c (%) c (%) (c) (d) 7 GP31_3 7 GP4_2 GP31_ ε c (%) ε c (%) (b) F5:1 Fig. 5. Stress-strain relation of Group GF2 ASCE 6 J. Compos. Constr.

7 CF2_1 CF2_2 CF2_ CP31_ CP31_2 c (%) (c) ε c (%) 1 CP31_ average maximum axial stress and axial strain of Specimen CP were 98 MPa and 2.12%, respectively. 313 Fig. 7 shows the specimens that were wrapped with an equiv- 314 alent of three layers of FRP had similar stress-strain curves but ex- 315 perienced a slight difference in the axial stiffness for the whole 316 loading process. Specimen CF3 obtained average maximum axial 317 stress and strain at 122 MPa and 2.84%, respectively [Fig. 7(a)]. 318 The partially-wrapped Specimen CP6 again had a lower compres- 319 sive strength but higher axial strain as compared to those of Speci- 32 men CF3. Fig. 7(b) shows specimen CP6 failed at the average 12 (a) εc (%) CP4_1 CP4_2 CP4_3 F6:1 Fig. 6. Stress-strain relation of Group CF CP6_1 CP6_2 CP6_3 14. CP42_ Reference CP42_2 (d) CP6_2 (e) ε c (%) c (%) c (%) 12 CP42_3 12 CP51_2 CP42_2 CF3_ CF3_1 CF3_2 CF3_3 (a) εc (%) εc (%) F7:1 Fig. 7. Stress-strain relation of Group CF3 14 (b) CP51_1 CP51_2 CP51_3 compressive strength of 116 MPa and axial strain of 3.25%. 321 The axial strain for Specimen CP6 increased by 14.33% in com- 322 parison with Specimen CF3. As compared to Specimen CF3, the 323 nonuniformly wrapped Specimen CP42 had both higher compres- 324 sive strength and axial strain. Fig. 7(d) shows that Specimen CP failed at the average compressive strength of 128 MPa and strain of %. As a result, the compressive strength and axial strain of 327 these specimens respectively increased by 5.29 and 11.16% as 328 compared to Specimen CF3. In order to compare the effectiveness 329 of different wrapping schemes, Fig. 7(e) plots the stress-strain 33 (b) (c) ASCE 7 J. Compos. Constr.

8 curves of five specimens. Fig. 7 shows that the partially-wrapped 332 Specimen CP6 experienced a lower maximum stress and a higher 333 maximum strain, as compared to Specimen CF3. On the hand, the 334 nonuniformly-wrapped Specimen CP42 experienced both a higher 335 maximum strain and stress in comparison with Specimen CF Fig. 5(d) shows specimens in Group GF2 have also confirmed these 337 findings. 338 Analysis and Discussions 339 Lateral Strain Tie band Cover band ε l (%) F8:1 Fig. 8. Lateral strain-axial stress relationship of Specimen CP4_3 34 The lateral strain of all the specimens is obtained by taking the aver- 341 age of readings from three strain gauges evenly placed along the 342 FRP at locations away from the overlap. For each specimen, Table presents the actual rupture strain of FRP. In order to investigate the 344 effectiveness of the fiber, the strain efficiency factor k ε is adopted, 345 which is the ratio of the actual rupture strain of FRP in confined 346 specimens and the rupture strain of the FRP obtained from the ten- 347 sile coupon testing. Table 3 shows the strain efficiency factors of 348 fully-wrapped specimens are approximately.83 and.87 for glass 349 fiber and carbon fiber, respectively. For glass fiber, the strain effi- 35 ciency factor of partially-wrapped specimens was.77 and the cor- 351 responding number for nonuniformly-wrapped specimens was Meanwhile, the strain efficiency factor of specimens partially 353 wrapped with CFRP was.8 and the corresponding number for 354 nonuniformly-wrapped specimens was.91. The experimental 355 results have shown that the effectiveness of the fiber reduces in 356 the partial-wrapping scheme, but increases in the nonuniformly- 357 wrapping scheme. 358 There is a consensus that the presence of the triaxial stress state 359 in FRP affects the actual rupture strain of the fiber (Chen et al ). In this experimental program, it is obvious that the axial 361 stress of the FRP jackets in the fully-wrapped specimens is higher than that of the nonuniformly-wrapped specimens. The discontinuity of the jacket in the nonuniformly wrapped specimens reduces the axial stress of the FRP jacket, which could be a reason for the increase in the strain efficiency factor in these specimens. Thus, the nonuniformly-wrapped specimens had a higher value of k ε, resulting in a higher confined strength and strain. In other words, the discontinuity of the jackets of the partially-wrapped specimens did not increase the strain efficiency factor. The partially-wrapped specimens experienced a different failure mode as compared with the other wrapping schemes. This different failure mode in partially-wrapped specimens may be the reason behind the slight decrease in the strain efficiency factor for these specimens. In addition, the lateral strain of the nonuniformly-wrapped specimens at both the tie bands and cover bands of the FRP is investigated. For example, the lateral strain-axial stress of Specimen CP4_3 (Fig. 8), illustrates that the lateral strain of FRP in a cover band is slightly higher than that of a tie band at any axial stress state. However, there was no difference in the lateral strain in other specimens. Analytical Verification In order to predict the compressive strength of the tested specimens, the procedure in the section Confinement Mechanism is used. It is noted that the actual lateral strain of each specimen was used in these calculations. The maximum axial strain of the tested specimens is predicted based on the study by Pham and Hadi (213), in which the relationship between the energies absorbed by the whole column and the FRP was taken into account. Pham and Hadi (213) assumed that the additional energy in the column core equals the area under the experimental stress-strain curves starting from the value of unconfined concrete strain: Table 4. Verification of the Experimental Results T4:1 Specimen D (mm) t (mm) s (mm) w (mm) k ε f l (MPa) k e a U cc ¼ Z εcc ε co f c dε c ¼ ðε cc ε co Þðfco þ fccþ 2 where U cc = volumetric strain energy of confined concrete; f c = stress of confined concrete; dε c = increment of the axial strain. However, Fig. 1 shows the concrete in the partially-wrapped columns is confined in the effective area. To determine the volumetric strain energy of confined concrete for the whole columns, the value of the confined concrete strength needs to be modified by the confinement effective coefficient (k e ), which leads to the following equation: U cc ¼ Z εcc ε co f c dε c ¼ ðε cc ε co Þðfco þ k e fccþ 2 Similarly, the energy absorbed by FRP could be calculated as follows: Theoretical Experimental f cc (MPa) b ε cc (%) f cc (MPa) ε cc (%) ð7þ ð8þ Δf cc (%) Δε cc (%) T4:2 T4:3 CF T4:4 CP T4:5 CF T4:6 CP Note: Δf cc and Δε cc = difference between the theoretical values and the corresponding experimental values. a The values of k e were calculated based on Eq. (4). b The values of f cc were calculated based on Eq. (5). ASCE 8 J. Compos. Constr.

9 W f ¼ ρ f A c 1 2 f feε fe 42 where W f = strain energy of FRP; ρ f = volumetric ratio of FRP as 43 shown in Eq. (1): ρ f ¼ 4t D ð9þ ð1þ 44 The compressive strain of columns partially wrapped with FRP 45 is calculated as follows: 2ktf feε fe ε cc ¼ ε co þ Dðfco þ k e fccþ ð11þ 46 Table 4 presents the predicted results of the compressive 47 strength and strain of the tested specimens. This table shows that 48 the predicted results are quite close to the experimental results. 49 Conclusions 41 This study presented an experimental study on the optimization of 411 concrete cylinders wrapped with FRP. The same amount of FRP 412 was used in each group of specimens but with different wrapping 413 schemes in order to investigate the confinement efficacy between 414 fully, partially, and a proposed nonuniform wrapping scheme for 415 FRP-confined concrete. The findings presented in this study are summarized as follows: 417 For specimens belonging to the descending branch type, the par- 418 tially-wrapped specimens had a lower compressive strength but 419 a higher strain as compared to the corresponding fully-wrapped 42 specimens. On the other hand, the nonuniform-wrapped speci- 421 mens experienced both a higher compressive strength and axial 422 strain in comparison with the fully-wrapped specimens; 423 For heavily FRP-confined specimens (CF3, CP6, CP51, and 424 CP42), partial- and nonuniform-wrapped specimens provided 425 a higher axial strain as compared to that of fully-wrapped 426 specimens; 427 The partial-wrapping scheme changes the failure modes of the 428 specimens. If the FRP jackets are strong enough, the angle of the 429 failure surface significantly reduces; 43 The actual rupture strain of the FRP jackets is different for 431 each wrapping scheme. The strain efficiency factor in the full- 432 wrapping scheme is greater than that of the partial-wrapping 433 scheme but is less than that of the nonuniform-wrapping 434 scheme; and 435 An equation is proposed to estimate the axial strain of partially 436 FRP-confined concrete circular columns. 437 Finally, this study proposed a new wrapping scheme that uses 438 the same amount of FRP as compared to the conventional fully- 439 wrapping scheme, in order to yield a higher compressive strength 44 and strain. However, further studies are required to theoretically 441 investigate the behavior of nonuniform-wrapped specimens. 442 Acknowledgments 443 The authors would like to acknowledge the technical assistance 444 of Messrs. Alan Grant, Cameron Neilson, Fernando Escribano, 445 Ritchie McLean, and Colin Devenish. The contribution of Mr. 446 Elliot Davison is greatly appreciated. Furthermore, the first author 447 would like to thank the Vietnamese Government and the University 448 of Wollongong for the support of his full Ph.D. scholarship. Notation The following symbols are used in this paper: 45 A c = cross-sectional area; A e = area of effectively confined concrete core; D = diameter of the column section; E f = elastic modulus of FRP; U cc = volumetric strain energy of confined concrete; W f = strain energy of FRP; dε c = increment of the axial strain; f c = stress of concrete; f fe = actual rupture strength of FRP; fcc = confined concrete strength; fco = unconfined concrete strength; f l = effective confining pressure of a column; fl = equivalent confining pressure from the FRP; k = proportion factor; k e = confinement effective coefficient; s = clear spacing between two FRP bands; t = nominal thickness of FRP; w = width of FRP bands; ε fe = actual rupture strain of FRP in hoop direction; ε cc = ultimate axial strain of confined concrete; ε co = axial strain of the unconfined concrete at the maximum stress; and 493 ρ f = volumetric ratio of FRP References ACI. (28). 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