Behavior and analytical modeling of natural flax frp tube confined plain concrete and coir fibre reinforced concrete
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Behavior and analytical modeling of natural flax frp tube confined plain concrete and coir fibre reinforced concrete

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As reinforcement flax fibre has the potential to replace glass fibre in fibre-reinforced polymer, composite and coir fibre ...

As reinforcement flax fibre has the potential to replace glass fibre in fibre-reinforced polymer, composite and coir fibre
can be used in concrete. To achieve sustainable construction, this study presents an experimental investigation of a flax
fibre-reinforced polymer tube as concrete confinement. Results of 24 flax fibre-reinforced polymer tube-confined plain
concrete and coir fibre-reinforced concrete cylinders under axial compression are presented. Test results show
that both flax fibre-reinforced polymer tube-confined plain concrete and fibre-reinforced concrete offer high axial
compressive strength and ductility. A total of 23 existing design- and analysis-oriented models were considered to
predict the ultimate axial compressive strength and strain of flax fibre-reinforced polymer tube-confined plain concrete
and fibre-reinforced concrete. It was found that a few existing design- and analysis-oriented models predicted the
ultimate strengths of all the flax fibre-reinforced polymer tube-confined plain concrete and fibre-reinforced concrete
cylinders accurately. However, no strain models considered match the ultimate strains of these specimens. Two new
equations are proposed to evaluate the ultimate axial strain of flax fibre-reinforced polymer tube-confined plain concrete
and fibre-reinforced concrete.

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    Behavior and analytical modeling of natural flax frp tube confined plain concrete and coir fibre reinforced concrete Behavior and analytical modeling of natural flax frp tube confined plain concrete and coir fibre reinforced concrete Document Transcript

    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] JOURNAL OF COMPOSITE Article M AT E R I A L S Journal of Composite Materials 0(0) 1–16 ! The Author(s) 2012 Behavior and analytical modeling of Reprints and permissions: sagepub.co.uk/journalsPermissions.nav natural flax fibre-reinforced polymer DOI: 10.1177/0021998312454691 jcm.sagepub.com tube confined plain concrete and coir fibre-reinforced concrete L Yan and N Chouw Libo Yan and Nawawi Chouw Abstract As reinforcement flax fibre has the potential to replace glass fibre in fibre-reinforced polymer, composite and coir fibre can be used in concrete. To achieve sustainable construction, this study presents an experimental investigation of a flax fibre-reinforced polymer tube as concrete confinement. Results of 24 flax fibre-reinforced polymer tube-confined plain concrete and coir fibre-reinforced concrete cylinders under axial compression are presented. Test results show that both flax fibre-reinforced polymer tube-confined plain concrete and fibre-reinforced concrete offer high axial compressive strength and ductility. A total of 23 existing design- and analysis-oriented models were considered to predict the ultimate axial compressive strength and strain of flax fibre-reinforced polymer tube-confined plain concrete and fibre-reinforced concrete. It was found that a few existing design- and analysis-oriented models predicted the ultimate strengths of all the flax fibre-reinforced polymer tube-confined plain concrete and fibre-reinforced concrete cylinders accurately. However, no strain models considered match the ultimate strains of these specimens. Two new equations are proposed to evaluate the ultimate axial strain of flax fibre-reinforced polymer tube-confined plain concrete and fibre-reinforced concrete. Keywords Flax FRP, coir fibre reinforced concrete, ductility, stress–strain behaviour, confinement model, analytical modeling Introduction potential for increasing service life and environmental The corrosion of steel reinforcement is one of the major benefits for a variety of structural engineering challenges that current civil engineers are facing. In the applications, such as bridge piers, marine fender piles United States, the upgrading of civil engineering infra- and poles.4 structure has been estimated as $20 trillion.1 In the Currently, a wider application of G/CFRP materials European Union, nearly 84,000 reinforced and in civil infrastructure is limited by the high initial cost, prestressed concrete bridges require maintenance, the insufficiency of long-term performance data, the repair and strengthening with an annual budget of lack of standard manufacturing techniques and design ƒ215 M, excluding traffic management cost.2 Recently, standards, risk of fire, environmental impact (FRP con- there has been a growing interest in utilizing glass/ tains chlorine which is associated to the toxins of diox- carbon fibre-reinforced polymer (G/CFRP) composite ins and furans) and the concern that the non-yielding materials in construction industry due to their relatively characteristic of FRP materials could result in sudden low density, high strength and resistance to corrosion. The use of FRP is an innovative solution to the corro- Department of Civil and Environmental Engineering, The University of sion problem. One attractive application of G/CFRP Auckland, Auckland, New Zealand composites is in the form of wrapped-jacket and tube to confine concrete columns and thus may enhance Corresponding author: L Yan, Department of Civil and Environmental Engineering, the University compressive strength and structural ductility remark- of Auckland, Auckland Mail Centre, Private Bag 92019, Auckland 1142, ably.3 The use of G/CFRP composites as an alternative New Zealand. of steel reinforcement for concrete structures provides a Email: lyan118@aucklanduni.ac.nz
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 2 Journal of Composite Materials 0(0) failure of the structure without prior warning.2,5–10 Assarar et al. confirmed that the tensile stress Among these limitations, cost and concern of brittle and strain at failure of flax fabric-reinforced epoxy poly- failure of FRP materials are probably the most influ- mer composites are 300 MPa and 2.0%, respectively – ential factors when assessing the merits of FRP as a putting them close to GFRP composites.21 A study by construction material. Gu showed that the tensile strength of coir fibre rein- In most cases, failure of G/CFRP-confined concrete forced polypropylene composite reaches up to 600 MPa was dominated by the rupture of the FRP jacket or tube and the elongation at break is 14.5%.22 These investiga- in the hoop direction. After removing the jacket or the tions have shown encouraging mechanical properties of tube, the concrete cores had large wide cracks, or bio-composites. Additionally, natural fibres, such as crushed or spalled into blocks, or even crushed into flax, hemp, coir and jute, are also cost-effective, have powder, as observed in the studies.11–13 In flexure, the low density with high specific strength and stiffness failure starts by the tensile rupture of the FRP jacket or and are readily available. tube at the lowest point in the bottom section of the Most recently, the authors proposed a new natural column; the tensile cracks begin on the bottom section flax FRP (FFRP) tube–confined CFRC structure. In and progress towards the upper section resulting in the this system, a relatively inexpensive flax fibre is used as development of a major crack. The concrete core devel- reinforcement of FFRP tube confining the concrete. ops excessive larger flexural cracks at the mid-span of the Coir fibre in the cementitious matrix further increases columns and the cracks propagate up to the mid-depth compressive strength. In this study, the experimental of the columns, as observed in previous research.3,14,15 results of 24 FFRP tube–confined PC and confined Therefore, G/CFRP-confined concrete structures may CFRC cylinders under axial compression are presented. lose load bearing capacity suddenly after the rupture The experimental variables include four different tube of the FRP since they are elastic up to failure. thicknesses and two different coir fibre weight contents. Research on fibre-reinforced concrete has shown For the safety and economic design of FFRP tube– that short discrete fibres, used in cementitious matrices, confined concrete, an accurate axial stress–strain can modify tensile and flexural strength, and fracture confinement model is required. To date, several energy.16 Pacheco-Torgal and Jalali reviewed the mech- confinement models have been developed to predict anical properties of cementitious building materials the ultimate axial compressive strength and ultimate reinforced with several vegetable fibres, i.e. sisal, axial strain of G/CFRP-confined concrete.23–40 hemp, coir, banana and sugar cane bagasse.17 Coir Therefore, another purpose of this study is to evaluate fibre, as one of the reinforcement fibres in concrete, the effectiveness of the existing confinement models on was investigated due to its highest toughness among FFRP tube–confined PC and CFRC. To achieve a com- natural fibres, and the extremely low cost and availabil- prehensive assessment, a total of 23 design-oriented and ity.18 Baruah and Talukdar reported that the compres- analysis-oriented models are considered. The evaluation sive, tensile and shear strengths of coir fibre reinforced is focused on the prediction of the ultimate axial com- concrete (CFRC) with 2% fibre (by volume of concrete pressive strength and axial strain of the FFRP-confined and fibre length of 40 mm) increased by 13.7%, 22.9% concrete because they are the two most significant par- and 32.7%, respectively, compared with the plain con- ameters for FRP-confined concrete design. crete (PC) specimens. Tensile splitting test indicated that PC was broken into two halves without contact. In contrast, CFRC specimen was crushed into two Experiments halves but still kept as a whole due to coir fibre bridging effect.19 However, natural fibres immersed in Portland Materials and specimen preparation cement will degrade due to the alkaline environment, FFRP tubes were fabricated using the hand lay-up thus weakening the durability of the structure. process. Commercial bidirectional woven flax fabric To improve the durability of natural fibre reinforced (550 g/m2) was used for this study. The structure of concrete, two methods could be considered: (1) matrix the flax fabric was given in previous study by the modification using low alkaline concrete by adding poz- author.41 The epoxy used was the SP High Modulus zolanic by-products to Portland cement and (2) coating Ampreg 22 resin and slow hardener. Fabrication of of natural fibres to avoid water absorption and free FFRP tubes were similar as that described in another alkalis with application of water-repellent agents or study.42 Details for fabrication of FFRP tubes are fibre impregnation using sodium silicate, sodium sul- given in Figure 1. Fabric fibre orientation was at 90 phite or magnesium sulphate.17 from the axial direction of the tube. Tensile and flexural Research on bio-composites concluded that natural properties of FFRP composites were determined by a fibres, i.e. flax fibres, have the potential to replace glass flat coupon test on Instron 5567 machine according fibres as reinforcement in polymer composites.20 to ASTM D303943 and ASTM D790,44 respectively.
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] Yan and Chouw 3 Figure 1. Flax fibre-reinforced polymer (FFRP) tubes (a) flax fabrics and epoxy, (b) FFRP tubes with aluminium mould, (c) demoulded FFRP tubes, and (d) FFRP tubes for concrete pouring. Table 1. Physical/mechanical properties of flax FRP composites Composite Tensile Tensile Tensile Flexural Flexural Fibre volume Density of thickness (mm) strength (MPa) modulus (GPa) strain (%) strength (MPa) modulus (GPa) fraction (%) FFRP (g/cm3) 2.65 102 8.0 3.6 103 5.9 53.8 1.268 5.30 125 9.2 4.4 128 8.5 55.7 1.275 3.25 106 8.7 3.7 109 6.0 54.2 1.270 6.50 134 9.5 4.3 144 8.7 55.1 1.273 FFRP: flax fibre-reinforced polymer. The physical/mechanical properties of FFRP compos- and 4 layers) were considered, as the same as that ites are listed in Table 1. given in test matrix A. However, in matrix B, the coir All the concrete specimens are divided into two parts: fibre length was 50 mm and weight content was test matrix A and B. For specimens in test matrix A, the increased to 1% of cement, and the fabric overlap fabric layer arrangement of FFRP tube was two and length was 157 mm, which was half of the inner perim- four layers, respectively. When fabricating FFRP eter of the tube. tubes, the considered overlap length was 100 mm, Table 2 lists the test matrix of all the specimens. which was the inner diameter of the tube. Two batches Three PC and three CFRC specimens were considered of concrete were prepared. Both batches were designed as control groups. The other cylinders were FFRP as PC with a 28-day compressive strength of 25 MPa. tube–confined PC and CFRC specimens with 100 mm The first batch was PC. For the second batch, coir fibre core diameter and 200 mm height. For each FFRP was added during mixing. The fibre length was 40 mm tube, one end was capped with a wooden plate before and fibre weight content was 1 % of PC. Concrete mix concrete pouring. Then concrete was cast, poured, com- design followed the ACI Standard 211. 1.45 The mix pacted and cured in a standard curing water tank for 28 ratio by weight was 1 : 0.58 : 3.72 : 2.37 for days. Both end sides of the specimens were treated with cement : water : gravel : sand, respectively. For speci- high-quality mortar to have a uniform bearing surface mens in test matrix B, two batches of concrete were and a blade was used to cut the upper and lower edges also designed with compressive strength of 25 MPa of tube–confined specimen to avoid it directly from and two different fabric layer arrangements (2 layers bearing the axial compression (Figure 2(a)).
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 4 Journal of Composite Materials 0(0) Table 2. Test matrix of cylinders with core diameter of 100 mm and height of 200 mm No. of Coir fibre Coir fibre Fabric overlap Tube Specimen cases* specimens Length (mm) mass content length (mm) thickness (mm) PC-A 3 — — — — CFRC-A 3 40 1% of concrete — — 2L-FFRP-PC-A 3 — — 100 2.65 4L-FFRP-PC-A 3 — — 100 5.30 2L-FFRP-CFRC-A 3 40 1% of concrete 100 2.65 4L-FFRP-CFRC-A 3 40 1% of concrete 100 5.30 PC-B 3 — — — — CFRC-B 3 50 1% of cement — — 2L-FFRP-PC-B 3 — — 157 3.25 4L-FFRP-PC-B 3 — — 157 6.50 2L-FFRP-CFRC-B 3 50 1% of cement 157 3.25 4L-FFRP-CFRC-B 3 50 1% of cement 157 6.50 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete. Note: In * column, ‘‘2L’’ and ‘‘4L’’ indicate 2-layer fabric and 4-layer fabric, respectively. ‘‘FFRP-PC’’ and ‘‘FFRP-CFRC’’ indicate flax FRP tube-confined plain concrete and confined coir fibre-reinforced concrete, respectively. ‘‘A’’ and ‘‘B’’ indicate specimens for test matrix A and test matrix B, respectively. Figure 2. Axial compression test setup: (a) flax fibre-reinforced polymer (FFRP)-confined coir fibre-reinforced concrete (CFRC) and (b) unconfined plain concrete (PC). axially compressed up to failure. Readings of the strain Axial compression test gauges and LVDTs were taken using a data logging For each cylinder, two strain gauges were mounted at system. mid-height of a cylinder aligned along the hoop direc- tion to measure hoop strain. Two linear variable dis- placement transducers (LVDTs) were placed 180 apart Experimental results and covered and spaced 130 mm centred at the mid- Stress–strain relationship height to measure axial strain, as shown in Figure 2. Compression test was conducted on an Avery-Denison The stress–strain curves of FFRP tube–confined PC machine under stress control with a constant rate of and CFRC are displayed in Figures 3–6. These curves 0.20 MPa/s based on ASTM C39.46 Each sample was can be divided into three regions. In the first purely
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] Yan and Chouw 5 Figure 3. Stress–strain behaviour of flax fibre-reinforced polymer (FFRP)-confined plain concrete (PC) (Test matrix A). Figure 4. Stress–strain behaviour of flax fibre-reinforced polymer (FFRP)-confined coir fibre-reinforced concrete (CFRC) (Test matrix A). linear region, the stress–strain behaviour of both FFRP mainly dominated by the structural behaviour of tube–confined PC and CFRC specimens are similar to FFRP composites where the tube is fully activated to the corresponding unconfined PC or CFRC. In this confine the core, leading to a considerable enhancement region, the applied axial stress is low, lateral expansion of concrete compressive strength and ductility. When of the confined PC or CFRC is inconsiderable and con- axial stress increases, the hoop tensile stress in the finement of FFRP tube is not activated. When the FFRP tube also increases. Once this hoop stress applied stress approaches the ultimate strength of exceeds the ultimate tensile strength of FFRP tube unconfined PC or CFRC, the curve enters the second obtained from the flat coupon tensile test, failure of nonlinear transition region where considerable micro- the FFRP tube starts. cracks are propagated in concrete and the lateral expansion significantly increased. With the growth of Compressive results of the specimens micro-cracks, the tube starts to confine the concrete core and counteracts the stiffness degradation of the Table 3 lists the average values for each considered 0 concrete. The third approximately linear region is concrete type. fco is peak compressive strength of the
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 6 Journal of Composite Materials 0(0) Figure 5. Stress–strain behaviour of flax fibre-reinforced polymer (FFRP)-confined plain concrete (PC) (Test matrix B). Figure 6. Stress–strain behaviour of flax fibre-reinforced polymer (FFRP)-confined coir fibre-reinforced concrete (CFRC) (Test matrix B). 0 unconfined concrete, fcc is ultimate compressive where fFRP and t are the hoop tensile strength and the strength of the confined concrete, "co is the axial thickness of the FFRP tube, respectively. D is the inner strain at peak strength of unconfined PC or CFRC, diameter of the tube, EFRP is the tensile modulus of "cc is the ultimate axial strain of FFRP-confined PC FFRP tube and "h is the corresponding tensile hoop or CFRC, fl is the lateral confining pressure between strain. 0 0 the FRP tube and concrete core, fcc =fco is confinement In general, Table 3 indicates that FFRP tube as 0 effectiveness and fl =fco is the confinement ratio of FRP- concrete confinement increased the ultimate compres- confined concrete. The value of fl is calculated using the sive strength and ultimate axial and hoop strains of all following equations:23 confined PC and CFRC specimens significantly, with the increase in strength and ductility being proportional 2fFRP t to the increase in tube thickness. fl ¼ ð1Þ D Table 3 shows that coir fibre inclusion in test matrix B (fibre length of 50 mm and fibre content of 1% of fFRP ¼ EFRP Á "h ð2Þ cement) increased the peak compressive strength while
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] Yan and Chouw 7 Table 3. Average test results of the specimens 0 Tube fcc fl "cc 0 fco fco0 Concrete type thickness (mm) 0 fco (MPa) "co (%) 0 fcc (MPa) "cc (%) "hrup (%) fl (MPa) "co PC-A — 25.7 0.18 — — — — — — — CFRC-A — 23.4 0.41 — — — — — — — 2L-FFRP-PC-A 2.65 25.7 0.18 37.8 1.50 2.80 5.81 1.47 0.23 8.53 4L-FFRP-PC-A 5.30 25.7 0.18 50.2 1.90 4.50 14.25 1.95 0.54 10.92 2L-FFRP-CFRC-A 2.65 23.4 0.41 33.0 1.50 3.50 5.81 1.42 0.25 3.75 4L-FFRP-CFRC-A 5.30 23.4 0.41 48.3 2.20 4.20 14.25 2.06 0.61 6.11 PC-B — 25.8 0.20 — — — — — — — CFRC-B — 28.2 0.54 — — — — — — — 2L-FFRP-PC-B 3.25 25.8 0.20 37.0 1.72 2.91 7.08 1.43 0.27 8.60 4L-FFRP-PC-B 6.50 25.8 0.20 53.7 2.25 4.54 18.72 2.08 0.73 11.25 2L-FFRP-CFRC-B 3.25 28.2 0.54 38.8 1.89 3.62 7.08 1.38 0.25 3.50 4L-FFRP-CFRC-B 6.50 28.2 0.54 56.2 2.70 4.29 18.72 2.00 0.66 5.00 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete. coir fibre in test matrix A (length of 40 mm and fibre content of 1% of PC) reduced the peak strength, com- Table 4. Parameters of the typical design-oriented confinement pared with the corresponding unconfined PC in test models matrix A and B. However, coir fibre increased the Models m k axial strain at peak strength significantly for both test matrices. Xiao and Wu12 and 1.0 4.1 It is also observed that the ultimate compressive Richart and Brandtzaeg48 strength and ultimate axial and hoop strains of FFRP Lam and Teng23 1.0 3.3 tube–confined CFRC in test matrix B are larger than Wu et al.24 and Lam and Teng25 1.0 2.0 the corresponding results of confined CFRC specimens Saaman et al.26 0.70 3.38 in matrix A when the fabric layers are the same, i.e. at 2 Saafi27 0.84 2.2 layers and 4 layers, respectively. In comparison with Toutanji28 0.85 3.5 specimens in matrix A, the increase in the ultimate Karbhari and Gao29 0.87 2.1 strength and strains of specimens in matrix B is believed Miyauhi et al.30 1.0 2.98 attributable to a combination factors due to the Cheng et al.31 1.0 2.4 increase in overlap length, coir fibre length and fibre weight content. account of the interaction between FRP and the con- fined concrete core via radial displacement compatibility Effectiveness of existing confinement models and equilibrium conditions. They are modes versatile To date, several stress–strain models have been devel- and accurate in general.23 Compared to the complexity oped to predict the ultimate compressive strength and resulting from incremental process of analysis-oriented strain for FRP tube–confined concrete and FRP- model, a simple and accurate design-oriented model is wrapped concrete.3,12,23–40 These models are divided particularly suitable for direct application in design into two categories: design-oriented and analysis- calculations. oriented. Design-oriented models are closed-form equa- tions and are directly based on the interpretation of Performance of design-oriented models on ultimate experimental results. These models consider FRP- confined concrete as a single ‘‘composite’’ material and compressive strength are thus simple and convenient to apply in design.23 The The most common form of design-oriented models can analysis-oriented models, on the other hand, are gener- be represented by the following expression: ated using an incremental numerical procedure, such as   m  the one by Mander et al.47 Analysis-oriented models 0 fcc fl ¼ 1þk 0 ð3Þ treat the FRP and concrete core separately and predict 0 fco fco the behaviour of FRP-confined concrete by an explicit
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 8 Journal of Composite Materials 0(0) 5 [12] [28] [26] [23] 4 [30] [31] [27] [29] 3 [24]&[25] cc co f ′ /f ′ 2 1 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 ′ fl /f co Figure 7. Comparison of results with other confinement models for flax fibre-reinforced polymer (FFRP)-confined concrete. Table 5. Comparison of experimental ultimate compressive strength with predicted ultimate compressive strength by design- oriented models FFRP tube-confined PC FFRP tube-confined CFRC 2L-FFRP-PC Absolute 4L-FFRP-PC Absolute 2L-FFRP-CFRC Absolute 4L-FFRP-CFRC Absolute (MPa) error (%) (MPa) error (%) (MPa) error (%) (MPa) error (%) Models A B A B A B A B A B A B A B A B Test result 37.8 37.0 — — 50.2 53.7 — — 33.0 38.8 — — 48.3 56.2 — — Xiao and Wu12 49.9 54.4 32.0 47.0 83.8 103 67.2 91.8 47.5 57.1 43.9 47.2 81.9 104 69.6 85.9 Lam and Teng23 45.2 48.8 19.6 31.9 72.4 88.0 44.0 63.9 42.6 51.5 29.1 32.7 70.4 89.6 45.8 59.4 Wu et al.24 and 37.5 39.7 0.7 7.3 52.9 62.3 5.4 16.0 35.1 42.3 6.3 9.0 51.8 65.4 7.2 16.3 Lam and Teng25 Samaan et al.26 56.5 60.7 49.7 34.3 82.7 95.7 64.7 78.2 53.4 64.3 61.8 59.3 79.3 99.5 64.2 77.0 Saafi27 42.1 44.7 13.6 20.8 59.9 69.4 19.3 29.2 39.3 47.6 19.1 22.7 57.3 72.0 18.9 28.1 Toutanji28 51.4 55.4 36.0 49.7 80.0 94.9 59.4 76.7 48.7 58.6 47.5 51.0 76.9 97.5 59.7 73.5 Karbhari and Gao29 40.6 43.1 7.4 16.5 57.8 67.3 15.1 25.3 38.1 45.9 15.4 18.3 55.5 69.5 14.9 23.7 Miyauchi30 41.1 46.6 8.7 25.9 67.8 81.9 35.1 52.5 39.5 49.2 19.7 26.8 66.0 83.7 36.6 48.9 Cheng et al.31 39.8 42.5 5.3 14.9 59.6 71.0 18.7 32.2 37.4 45.1 13.3 16.2 57.6 72.9 19.3 29.7 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete.
    • Note: ‘‘A’’ and ‘‘B’’ indicate specimens from test matrix A and B, respectively. Absolute error ¼
    • predictionÀtest
    • Â 100 . test where, k is effectiveness coefficient and m is the power Comparison of the experimental ultimate strengths coefficient of the confinement ratio. The axial behav- of FFRP tube–confined PC and CFRC with their pre- iour of confined concrete was primarily proposed by dictions based on design-oriented models is displayed in Richart et al. in 1928.48 The majority of the design- Figure 7, where black square marks indicate FFRP oriented models have the similar expression as tube–confined PC (2 layer and 4 layers) and triangular Richart et al. in equation (3). The different relations points represent the FFRP-confined CFRC specimens for k and m of some design-oriented modes are listed (2 layer and 4 layers) from test matrix A. The (Â) marks in Table 4. indicate the FFRP tube–confined PC (2 layers and 4
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] Yan and Chouw 9 100 2L-FFRP-PC-A 90 2L-FFRP-PC-B 4L-FFRP-PC-A 80 4L-FFRP-PC-B 2L-FFRP-CFRC-A Absolute error (%) 70 2L-FFRP-CFRC-B 4L-FFRP-CFRC-A 60 4L-FFRP-CFRC-B III 50 40 30 II 20 10 I 0 [12] [23] [24] & [25] [26] [27] [28] [29] [30] [31] Figure 8. Absolute error of design-oriented models in predictions of ultimate compressive strength. 100 2L-FFRP-PC-A 90 2L-FFRP-PC-B 4L-FFRP-PC-A 80 4L-FFRP-PC-B Absolute error (%) 70 2L-FFRP-CFRC-A 2L-FFRP-CFRC-B 60 4L-FFRP-CFRC-A III 4L-FFRP-CFRC-B 50 40 30 20 II 10 I 0 [3]&[32-35] [36] [37] [38] [39] Figure 9. Absolute error of analysis-oriented models in predictions of ultimate compressive strength. layers) and (þ) marks denote FFRP tube–confined in Figures 8 and 9. Figure 8 shows that the models by CFRC (2 layers and 4 layers) from test matrix B, Wu et al.24 and Lam and Teng25 predict the ultimate respectively. Figure 7 depicts that the existing design- strengths of all the FFRP tube–confined PC and CFRC oriented models vary considerably because the models specimens accurately. The absolute error is 7.3% and are directly generated based on the interpretation of 0.7% for 2-layer FFRP–confined PC and it is 5.4% and experimental data. Figure 7 also shows that the ultim- 16.0% for 4-layer FFRP–confined PC, respectively. ate strength of FFRP tube–confined PC and CFRC is For confined CFRC, the absolute error is 6.3% and highly dependent on the lateral confinement pressure fl. 9.0% for specimens confined by 2-layer FFRP tube The increase in confinement effectiveness is directly and it is 7.2% and 16.3% for specimens confined by proportional to the increase in confinement ratio. 4-layer FFRP tube, respectively (Table 5). The strength Table 5 makes a comparison of experimental models by Saafi27 and Karbhari and Gao29 fit the ultimate strengths with the predictions based on the ultimate strength of the majority of the experimental design-oriented strength models. Figure 8 illustrates results relative accuracy, with most of the absolute the absolute error curves of the design-oriented errors ranging from 15% to 30%. The model by models on ultimate compressive strength prediction. Cheng et al.31 may also be defined as category II, The accuracy of a model is classified into three except for the prediction of 4-layer FFRP tube– categories: Category I of good accuracy (absolute confined PC (test matrix B). All the other models error 15%), Category II of relative accuracy overestimate the ultimate strengths of the FFRP (15% < absolute error 30%) and Category III tube–confined PC or confined CFRC. It should be of inaccuracy (absolute error > 30%), as marked noted here that the design-oriented confinement
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 10 Journal of Composite Materials 0(0) models are directly developed according to the inter- Performance of analysis-oriented models on ultimate pretation of their experimental database based on G/ CFRP-confined concrete. It is true that the tensile compressive strength strength and modulus of G/CFRP composites obtained Analysis-oriented models have the analytical expres- from flat coupon tensile tests are significantly larger sions for predicting the ultimate compressive strength than the FFRP composites given in Table 1. This which follow the well-known model of Mander et al.47 may lead to the overestimation in the strength predic- The model of Mander et al. was derived from the tions of FFRP tube–confined concrete. William-Warnke failure surface49 for tri-axial compres- sion state with equal effective lateral confining pressure:48 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 fcc fl fl 0 ¼ 2:254 1 þ 7:94 0 À 2 0 À 1:254 ð4Þ fco fco fco Table 6. Equations of typical analysis-oriented confinement models Fam and Rizkalla,3 Saadatmanesh et al.,32 Restrepol Authors Models and De Vino,33 Spoelstra and Monti,34 Samaan et al.,26 Fam and Rizkalla,3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and Chun and Park35 are adopting the similar expres- Saaman et al.,26 0 fcc fl fl sions as equation (4) for their study. Table 6 gives the Saadatmanesh et al.,32 0 ¼ 2:254 1 þ 7:94 0 À 2 0 À 1:254 fco fco fco expressions of some existing analysis-oriented models. Restrepol and De Vino,33 Spoelstra and Monti,34 In general, most analysis-oriented strength models and Chun and Park35 do not match the ultimate compressive strengths of Harries and Kharel36 all the FFRP tube–confined PC and CFRC, as dis- fcc ¼ fco þ 4:629fl 0:587 0 0 played in Figure 9 and Table 7. Only the model by Binici37 Harries and Kharel36 predicts the strengths of all the sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 0 0 fl fl experimental results accurately, although the con- fcc ¼ fco 1 þ 9:9 0 þ 0 fco fco sidered coir fibre weight content and tube thickness vary from test matrix A to matrix B. The absolute Marques et al.38 error of 2-layer FFRP–confined PC for test matrix A fcc ¼ fco þ 6:7fl 0:83 0 0 and test matrix B is 0.3% and 9.2%, respectively. For Teng et al.39 the other three sets of FFRP tube–confined PC and 0 0 fcc ¼ fco þ 3:5fl CFRC with different tube thickness and coir fibre Table 7. Comparison of experimental ultimate compressive strength with predicted ultimate compressive strength by analysis- oriented models FFRP-confined PC FFRP-confined CFRC 2L-FFRP-PC Absolute 4L-FFRP-PC Absolute 2L-FFRP-CFRC Absolute 4L-FFRP-CFRC Absolute (MPa) error (%) (MPa) error (%) (MPa) error (%) (MPa) error (%) Models A B A B A B A B A B A B A B A B Test result 37.8 37.0 — — 50.2 53.7 — — 33.0 38.8 — — 48.3 56.2 — — Fam and Rizkalla,3 53.3 53.5 41.0 44.6 46.1 81.6 8.2 52.0 50.0 55.2 51.5 42.3 67.7 78.9 40.2 40.4 Saadatmanesh et al.,32 Restrepol and De Vino,33 Spoelstra and Monti,34 Chun and Park,35 and Harries and Kharel36 Harries and Kharel36 37.7 40.4 0.3 9.2 47.7 51.6 5.0 3.9 35.4 42.8 7.3 10.3 43.7 54.1 10.5 3.7 Binici37 54.7 56.4 44.7 52.4 86.5 92.8 56.6 72.8 49.5 59.6 50.0 53.6 79.0 96.0 63.6 70.9 Marques et al.38 54.6 58.8 44.4 58.9 75.6 102.0 72.3 89.9 52.3 62.2 58.5 60.3 84.1 104.4 74.1 85.8 Teng et al.39 46.0 50.6 21.7 36.8 73.2 91.3 50.6 70.0 43.7 53.0 32.4 36.6 73.3 93.7 51.8 66.7 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete. Note: ‘‘A’’ and ‘‘B’’ indicate specimens from test matrix A and B, respectively. Calculation of absolute error refers to Table 5.
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] Yan and Chouw 11 weight content, the absolute errors range from 3.7% to seen that the ultimate axial strain is relevant to the 10.5%. All the other models overestimate the ultimate axial strain "co at peak strength of unconfined PC and 0 0 strengths significantly. This may also be attributed to the the confinement effectiveness fcc =fco . fact that the tensile properties of FFRP materials Comparison of the experimental ultimate axial obtained from flat coupon tensile test were significantly strains with the predictions is given in Table 9. lower than that of glass or carbon FRP, as displayed in Absolute error of strain models in predictions of Table 1. In addition, most analysis-oriented models fol- ultimate axial strains is given in Figure 10. It shows lowed the model by Mander et al.47 based on steel-based that the strain model by Miyauchi et al.30 fits the confinement. The formulation is based on ultimate experimental ultimate strains of all the FFRP tube– strength surfaces modeled on triaxial test data, and confined PC specimens, and it also accurately predicts therefore Mander et al. predict the improvement in com- the strains of 2-layer and 4-layer FFRP tube-confined pressive strength of the confined concrete as a function CFRC specimens in test matrix A. However, it slightly of one value of lateral confining pressure, assumed to be underestimates the ultimate strains of 4-layer FFRP constant throughout the loading history. However, this tube-confined CFRC specimens in test matrix A (with is not the case for FRP-confined concrete. absolute error of 23.3%) and B (with absolute error of 25.9%). This may be attributable to the addition of coir Performance of confinement models on ultimate fibre, since coir fibre in test matrix A reduced the aver- age peak compressive strength while it increased the axial strain average peak compressive strength in test matrix B, Table 8 lists the expressions of several confinement compared with the corresponding unconfined PC. models for ultimate axial strain prediction. It can be The prediction results based on the model by Wu et al.24 relatively matches the ultimate axial strains of Table 8. Prediction equations for ultimate axial strain by FFRP tube-confined PC, with the absolute errors ran- various confinement models ging from 20% to 30%. However, it considerably over- estimates the strains for FFRP tube–confined CFRC. It Authors Models is easily understandable because the average axial strain Wu et al.24   "co at peak stress of unconfined CFRC specimens used f0 for derivation of ultimate strain is 0.0041 and 0.0054, "cc ¼ "co 1:3 þ 6:3 cc 0 fco respectively, rather other 0.0018 and 0.002 for uncon- Fam and Rizkalla,3   0  fined PC specimens given in Table 3. If "co of 0.0018 is Samaan et al.,26 f "cc ¼ "co 1 þ 5 cc À 1 used for FFRP tube–confined CFRC calculation, the 0 Saadatmanesh et al.,32 fco predicted ultimate axial strains for 2-layer and 4-layer Restrepol and De Vino,33 FFRP tube–confined CFRC in test matrix B will be Spoelstra and Monti,34 1.83% and 2.53%, the corresponding absolute errors Chun and Park,35 Harries and Kharel,36 will be 22% and 15% for specimens in test matrix A. Binici,37 For specimens in test matrix B, "co of 0.002 leads to the Marques et al.,38 predicted ultimate axial strains for 2-layer and 4-layer Teng et al.,39 FFRP tube–confined CFRC which will be 2.00% and and Mander et al.47 2.78%, respectively, the corresponding absolute errors Richart et al.48 EFRP t will be 5.8% and 3.0%. This data indicates that the "cc ¼ 0:002 þ 0:001 Dfco0 strain model by Wu et al.24 could predict the ultimate axial strains of FFRP tube–confined CFRC structures Saafi27   0  f when the axial strain at peak stress of PC is considered "cc ¼ "co 1 þ ð537"FRP þ 2:6Þ cc À 1 0 fco for calculation, rather other that of CFRC. For all the other models in the Table 9, no matter for Miyauchi et al.30 " #   FFRP–confined PC or CFRC; they either overestimate 2tfFRP 0:373 "cc ¼ 0:002 1 þ 10:6 0 Dfco the values or underestimate the values significantly. Based on the discussions above, it is observed that Lam and Teng40 for GFRP tube  0 0:7 the existing analysis-oriented strength model by Harries "cc f ¼ 2 þ 27 cc and Kharel36 (with prediction absolute error from 0.3% "co 0 fco to 10.5%) and design-oriented strength models by Wu Lam and Teng40 for CFRP sheet  0 et al.24 and Lam and Teng25 (with prediction absolute "cc f error from 0.7% to 16.3%) can predict for ultimate ¼ 2 þ 15 cc0 "co fco compressive strengths of all the FFRP tube–confined PC and CFRC specimens accurately. The prediction
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 12 Journal of Composite Materials 0(0) Table 9. Comparison of ultimate axial strains of experimental results with the predictions by the existing models FFRP-confined PC FFRP-confined CFRC 2L-FFRP-PC Absolute 4L-FFRP-PC Absolute 2L-FFRP-CFRC Absolute 4L-FFRP-CFRC Absolute (%) error (%) (%) error (%) (%) error (%) (%) error (%) Models A B A B A B A B A B A B A B A B Test result 1.5 1.72 — — 1.9 2.25 — — 1.5 1.89 — — 2.2 2.70 — — Wu et al.24 1.9 2.06 26.7 17.4 2.4 2.88 26.3 28.0 4.2 5.40 180 185.7 5.9 7.51 168.2 178.1 Fam and Rizkalla,3 0.6 0.63 60.0 63.4 1.0 1.28 47.4 43.1 1.3 1.57 13.3 16.9 5.6 3.24 154.5 20.0 Saadatmanesh et al.,32 Restrepol and De Vino,33 Spoelstra and Monti,34 Chun and Park,35 Harries and Kharel,36 Binici,37 Marques et al.,38 Teng et al.,39 and Mander et al.47 Richart and Brandtzaeg48 0.7 0.92 52.0 6.5 2.1 2.59 10.5 14.7 0.8 0.86 46.7 54.5 2.3 2.39 4.5 11.5 Saafi27 1.7 1.77 13.3 4.1 4.7 6.03 147.3 168.0 4.0 5.04 166.7 166.7 11.3 14.38 413.6 432.6 Miyauchi et al.30 1.4 1.50 6.7 12.8 1.8 2.05 5.3 8.9 1.4 1.45 6.7 23.3 2.0 2.00 9.1 25.9 Lam and Teng40C 6.7 7.30 346.7 324.4 8.1 9.41 326.3 318.2 14.9 19.3 893.3 921.2 19.2 24.77 772.8 817.4 Lam and Teng40D 4.3 4.69 186.7 172.7 5.6 6.64 194.7 195.1 9.5 12.26 533.3 548.7 13.4 17.28 509.1 540.0 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete. Note: ‘‘A’’ and ‘‘B’’ indicate specimens from test matrix A and B, respectively. C indicates GFRP tube strain model. D indicates CFRP sheet strain model given by Lam and Teng.40 Calculation of absolute error refers to Table 5. 1000 2L-FFRP-PC-A 900 2L-FFRP-PC-B 800 4L-FFRP-PC-A Absolute error (%) 700 4L-FFRP-PC-B 2L-FFRP-CFRC-A 600 2L-FFRP-CFRC-B 500 4L-FFRP-CFRC-A 4L-FFRP-CFRC-B 400 300 200 100 0 [24] [3]&[48] [47] [27] [30] [40]C [40]D Figure 10. Absolute error of strain models in predictions of ultimate axial strains. based on strain models by Miyauchi et al.30 relatively fit the experimental ultimate axial strains of all the FFRP tube–confined PC and CFRC, with absolute errors ran- Proposed strain models ging from 1.4% to 25.9%. The strain model by Wu It is easily understandable that the GFRP tube strain et al.24 may predict the experimental ultimate strains model and CFRP sheet strain model proposed by Lam relative accurately when the axial strain of unconfined and Teng40 significantly overestimate the experimental PC is considered for ultimate strain calculation of ultimate axial strains of FFRP tube–confined PC and FFRP tube–confined CFRC. Therefore, an accurate CFRC, as listed in Table 9. This is because their equa- strain mode is required for both FFRP tube–confined tions are directly developed from the experimental PC and CFRC. results of G/CFRP-confined concrete specimens, and
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] Yan and Chouw 13 Table 10. Experimental/prediction ultimate axial strain ratios of the considered specimens based on strain model by Lam and Teng.40 FFRP-confined PC FFRP-confined CFRC 2L-FFRP-PC Strain 4L-FFRP-PC Strain 2L-FFRP-CFRC Strain 4L-FFRP-CFRC Strain (%) ratio (%) ratio (%) ratio (%) ratio Models A B A B A B A B A B A B A B A B Test result 1.5 1.72 — — 1.9 2.25 — — 1.5 1.89 — — 2.2 2.70 — — Lam and Teng40C 6.7 7.30 0.224 0.236 8.1 9.41 0.235 0.239 14.9 19.3 0.100 0.098 19.2 24.77 0.115 0.109 Lam and Teng40D 4.3 4.69 0.349 0.368 5.6 6.64 0.339 0.339 9.5 12.26 0.158 0.154 13.4 17.28 0.177 0.156 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete. Note: ‘‘A’’ and ‘‘B’’ indicates specimens from test matrix A and B, respectively. C indicates GFRP tube strain model. D indicates CFRP sheet strain model given by Lam and Teng.40 Calculation of absolute error refers to Table 5. Table 11. Comparison of proposed strain models and experimental results FFRP-confined PC FFRP-confined CFRC 2L-FFRP-PC Absolute 4L-FFRP-PC Absolute 2L-FFRP-CFRC Absolute 4L-FFRP-CFRC Absolute (%) error (%) (%) error (%) (%) error (%) (%) error (%) Models A B A B A B A B A B A B A B A B Test result 1.5 1.72 — — 1.9 2.25 — — 1.5 1.89 — — 2.2 2.70 — — Model 1 1.55 1.69 3.33 1.74 1.87 2.17 1.58 3.56 1.54 1.65 2.67 12.7 1.94 2.11 11.8 21.9 Model 2 1.55 1.68 3.33 2.33 2.01 2.37 5.79 5.33 1.51 1.63 0.67 13.7 2.13 2.30 3.2 14.8 FFRP: flax fibre-reinforced polymer; CFRC: coir fibre-reinforced concrete; PC: plain concrete. Note: ‘‘A’’ and ‘‘B’’ indicates specimens from test matrix A and B, respectively. Calculation of absolute error refers to Table 5. the tensile modulus of the G/CFRP composite is taken factor 2 is 0.359 based on CFRP sheet model. into account when developing the strain model.40 Therefore, the proposed two models can be simplified as Actually, it is true that the tensile modulus of FFRP " composite is significantly lower than the G/CFRP.  0 0:7 # "cc f Based on the predicted ultimate axial strains obtained Strain model I : ¼ 1 2 þ 27 cc 0 "co fco from the GFRP and CFRP models, the strain ratios,  0 0:7 defined as the experimental ultimate strains of FFRP f ¼ 0:46 þ 6:21 cc ð5Þ tube-confined PC and CFRC divided by the correspond- fco0 ing predicted ultimate strains, are given in Table 10.   0  Considering the difference in tensile modulus of "cc f FFRP and G/CFRP, a material stiffness reduction Strain model II : ¼ 2 2 þ 15 cc 0 "co fco factor () is introduced to develop an accurate design-  0 f oriented strain model for FFRP tube–confined PC and ¼ 0:718 þ 5:385 cc 0 ð6Þ fco CFRC based on the GFRP tube and CFRP sheet models proposed by Lam and Teng.40 This stiffness reduction factor is derived directly from the where "co is the compressive strength of unconfined PC, experimental/prediction ultimate strain ratios given in which is used for calculation for both FFRP tube– Table 10. The average value of strain ratio for 2-layer confined PC and CFRC specimens. It is 0.0018 and FFRP-confined PC from test matrix A and matrix B is 0.0020 for test matrix A and test matrix B, respectively considered as the stiffness reduction factor based on the (Table 3). GFRP and CFRC models of Lam and Teng. For FFRP- Comparison of experimental ultimate axial strains of confined PC and CFRC of the composite with a lower FFRP-confined PC and CFRC with the predictions tensile modulus, the material stiffness factor 1 is 0.230 obtained from the proposed models is given in based on the GFRP model and the material stiffness Table 11. In general, the proposed two equations
    • XML Template (2012) [27.7.2012–10:26am] [1–16]K:/JCM/JCM 454691.3d (JCM) [PREPRINTER stage] 14 Journal of Composite Materials 0(0) predict the ultimate axial strains of FFRP tube– and coir fibre mass contents are limited to 1% of PC confined PC and CFRC with low tensile modulus in test matrix A and 1% of cement of the PC in test effectively. Compared to the Model I, Model II also matrix B. To verify the effectiveness of the existing can predict the results of 4-layer FFRP tube–confined strength models (Wu et al.,24 Lam and Teng,25 and PC much accurately. Comparing the proposed strain Harries and Kharel36) and the proposed strain model II with the one by Miyauhi et al.30 (Table 9), it models, more FFRP tube–confined PC and CFRC spe- is observed that the proposed model II is superior to cimens with different fabric layers, different unconfined that by Miyauhi et al. in prediction of the ultimate axial concrete compressive strength and different coir fibre strains for all the FFRP tube–confined PC and CFRC content are necessary. in this study. Funding Conclusions This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. This study concerned the axial compressive behaviour of a new FFRP tube–confined PC and CFRC. The experimental results of 24 FFRP-confined PC and Conflict of interest CFRC cylinders were presented. A total of 23 existing No conflict of interest. design-oriented and analysis-oriented models were con- sidered to predict the ultimate axial compressive strength and axial strains of the experimental results. Nomenclature The study reveals: . The compressive strength of CFRC can increase or t Thickness of FRP tube or jacket decrease by the addition of coir fibre with different D Inner diameter of FRP tube or jacket fibre weight content, compared with unconfined PC. EFRP Modulus of elasticity of FRP . Coir fibre inclusion with length of 50 mm and fibre 0 fco Peak compressive strength of uncon- weight content of 1% of cement increased the ultim- fined concrete ate compressive strength and ultimate strains of 0 fcc Ultimate compressive strength of con- FFRP tube–confined CFRC specimens, compared fined concrete with the FFRP tube–confined PC specimens. fl Lateral confining pressure between . FFRP tube confinement enhances the compressive FRP and concrete strength and ductility of both PC and CFRC. The fFRP Hoop tensile strength of FRP increase in tube thickness leads to an increase in 0 0 fcc =fco Confinement effectiveness of FRP-con- compressive strength and ductility. fined concrete . The axial stress–strain behaviour of FFRP tube– 0 fl =fco Confinement ratio of FRP-confined confined PC and CFRC is approximately bilinear. concrete . For the test conditions considered in this study, the "co Axial strain at peak compressive design-oriented models by Wu et al.24 and Lam and strength of unconfined concrete Teng25 and an analysis-oriented model by Harries "cc Axial strain at peak compressive and Kharel36 can predict the ultimate axial compres- strength of confined concrete sive strength of FFRP tube–confined PC and CFRC "h Tensile hoop strain of FRP tube or accurately. jacket . No considered strain models predict the ultimate m Power coefficient of confinement ratio, axial strains of FFRP-confined PC and FFRP-con- defined in Eq. [3] fined CFRC accurately. Two proposed strain k Effectiveness coefficient of confinement models, with an introduction of a stiffness reduction ratio, defined in Eq. [3] factor of the composite material, match the experi- 1 Flax FRP material stiffness factor, mental strains of both FFRP tube–confined PC and defined in Eq. [5] CFRC effectively. 2 Flax FRP material stiffness factor, defined in Eq. [6] However, it should be noted that the amount of the database is limited. The newly proposed equations are applicable for flax FRP tube–confined concrete with a References lower strength of the FRP material. The considered 1. NSF. NSF 93-4 engineering brochure on infrastructure. unconfined concrete compressive strength is 25 MPa Arlington, VA: US National Science Foundation, 1993.
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