The Journal of The Textile Institute
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Flexural design of textile-reinforced concrete (TRC) using warp-knitted fabric with improving fiber performance index (FPI) Roohollah Kamani, Mehdi Kamali Dolatabadi & Ali. A. A. Jeddi To cite this article: Roohollah Kamani, Mehdi Kamali Dolatabadi & Ali. A. A. Jeddi (2017): Flexural design of textile-reinforced concrete (TRC) using warp-knitted fabric with improving fiber performance index (FPI), The Journal of The Textile Institute, DOI: 10.1080/00405000.2017.1356000 To link to this article: http://dx.doi.org/10.1080/00405000.2017.1356000
Published online: 07 Aug 2017.
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Date: 07 August 2017, At: 22:41
The Journal of The Textile Institute, 2017 https://doi.org/10.1080/00405000.2017.1356000
Flexural design of textile-reinforced concrete (TRC) using warp-knitted fabric with improving fiber performance index (FPI) Roohollah Kamania, Mehdi Kamali Dolatabadia
and Ali. A. A. Jeddib
a Department of Textile Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran; bTextile Engineering Department, Amirkabir University of Technology, Tehran, Iran
ARTICLE HISTORY
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ABSTRACT
Bending capacity of textile-reinforced concrete (TRC) is often limited by low penetration of the concrete into inner filaments of fabric rovings. To improve this limitation, we used warp-knitted fabric with different rovings as weft inserted then introduce a fibers performance index (FPI) as sign of the textile reinforcing efficiency. On the base of equilibrium condition models and comparing with experimental data, the FPI is simulated. The influence of different number of rovings and also different layers, on the maximum load, displacement, toughness, and failure modes is discussed. Furthermore, the FPI was improved by partially impregnated fabrics with spotted epoxy. This technique considerably increased FPI from 0.21 for the fabric without epoxy to 0.5 and improved bending properties of TRC.
1. Introduction Concrete is brittle in nature by low tensile strength and strain capacity. Fibrous materials are developed for reinforcing concrete due to favorable mechanical properties. The advantages of using this structure as compared to the conventional materials are light weight with high load-bearing capacity, quick application, corrosion resistance, and flexibility design shape (Brameshuber, 2006; Hegger, Zell, & Horstmann, 2008; Mobasher, 2011). Fibers with high modulus of elasticity such as Glass, Carbon, and Kevlar with the aim of improving toughness and strain hardening behavior of the composite are used in wide range of textile architectures. Fibers with low modulus of elasticity such as polypropylene (PP) and polyethylene (PE) with the aim of improving the ductility of the composite are applicable (Peled & Mobasher, 2007). The carbon fibers in comparison with other fibers of reinforced concrete have higher mechanical properties, long-term durability, alkaline resistance, and also low-cost maintenance of these structures during its service life (Brameshuber, 2006; Hegger & Voss, 2005; Hegger, Voss, & Bruckermann, 2005). Fibers can be utilized in different forms including: mono filament, multi filaments (roving), and two- or three-directional fabrics with numerous geometry. These fabrics are more advantageous to rovings that improved ease of rovings assembly and cost effectiveness of manufacturing and controlling of fabric geometry, and roving orientations as desired in the fabric structure (Brückner, Ortlepp, & Curbach, 2006; Peled, 2005). There are various methods to produce fabrics like weaving, warp and weft knitting, bonding, and nonwoven. Warp-knitted fabrics are well suited to use as textile-reinforced concrete (TRC). The
CONTACT Mehdi Kamali Dolatabadi © 2017 The Textile Institute
[email protected]; Ali. A. A. Jeddi 
Received 30 May 2017 Accepted 12 July 2017 KEYWORDS
Textile-reinforced concrete (TRC); bending behavior; fibers performance index (FPI), warp-knitted fabric, weft-inserted
advantages of this technique as compared to others are high automation, cost-effectiveness, minimum damage and wide diversity of configurations and geometries. The load-bearing behaviors of TRCs are influenced by the types of fibers, fiber surfaces, fiber and fabric geometry, number of fabric layers, fabric producing technique, etc. Overall, fabrics with high dimensional stability, no crimp and larger mesh size are more efficient for TRC (Colombo, Magri, Zani, Colombo, & Di Prisco, 2013; Dolatabadi, Janetzko, & Gries, 2014; Leong, Ramakrishna, Huang, & Bibo, 2000; Peled & Bentur, 2003; Varsei, Shaikhzadeh Najar, Hosseini, & Seyed Razzaghi, 2013). Beside fiber and fabric issue, there are some factors which can influence load-bearing capacity of TRCs. Some of these factors reveal the level and modality of fiber contribution to bear load. For instance, fine-grained concrete penetrated within the bundle of fibers (rovings) partially. Consequently, the external filaments (‘sleeve’) are bonded directly with the concrete and the internal dry filaments (‘core’) are relatively free. The sleeve filaments are fractured during loading, thereby increasing the composite strength. The core filaments slide against sleeve filaments and each other, thereby increasing the composite ductility partly. As a result, the fabric reinforcement efficiency is limited by low penetration concrete within rovings and the bonded sleeve filaments are the key aspect in manufacturing TRCs (Cohen & Peled, 2010; Dolatabadi, Janetzko, Gries, Kang, & Sander, 2011). For improving fabric efficiency, Peled and Mobasher (Peled & Mobasher, 2007) used Pultrusion process for producing composite. Dvorkin and Peled (Dvorkin & Peled, 2016) and Nadiv et al. (Nadiv, Peled, Mechtcherine, Hempel, & Schroefl, 2017) applied Nano and Micro mineral fillers and
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R. KAMANI ET AL.
epoxy fillers to increased sleeve/core ratio, and finally increased fabric efficiency. Balanced reinforcement ratio is another effective factor to assessing the flexural capacity and the failure mode of the member. There are three possible flexural failure modes of TRC: balanced failure (simultaneous rupture of fabrics and crushing of concrete), compression failure (concrete crushing before rupture of fabrics), and tension failure (rupture of fabrics before crushing of concrete). The balanced reinforcement ratio for reinforced concrete is calculated by force equilibrium in the beam section and strain compatibility equations (Bank, 2006; ISIS Canada, 2007; Kara, Ashour, & Köroğlu, 2016). This ratio for conventional reinforced concrete beams has been reported by various standards like ACI (ACI 440.IR-06, 2006; ACI 318-08, 2008) In this work, the influence of weft insertion warp-knitted fabrics by different number of carbon rovings on the flexural strength, ductility, toughness, and failure mode are evaluated experimentally. In addition, on the base of balance equations as compared to the test result, the fiber performance index (FPI) is introduced as representative of fabric efficiency. Moreover, for increasing FPI the impregnated fabric partially by epoxy resin was addressed.
2. Material and test method 2.1. Matrix The fine-grained concrete with the maximum aggregate size of 0.6 mm is used as matrix. The matrix in this study consisted of; Portland cement (I), silica fume, Superplasticizer with a basis of polycarboxylate, and sands (Table 1) (Brameshuber, 2006). By following ASTM 30109 standards, the compressive strength of cured concrete for 28 days was 65.32MP (standard deviation 2.27). 2.2. Textile reinforcement fabrics Three different fabrics with chain stitches (2–0/0–2) produced on the weft-insertion warp-knitting Raschel machine with gage of 14(npi) were produced from polyester 16.5 tex for chain stitches with arrangement of threading 1 full 6 out and carbon roving 1200 tex (12,000 mono filament) for weft. The chain stitch density for all samples was 12(cpc) but, the interval of weft insertion for different samples was a roving per 12, 9, and 6 chain stitches, respectively. Therefore, the mesh sizes of these fabrics were 10 × 10, 7.5 × 10 mm and 5 × 10 mm, respectively (Figure 1). The carbon weft specifications are summarized in the Table 2. 2.3. Sample preparation To produce composite samples, we used rectangular molds with dimensions of 360 × 50 × 20 mm. At first, pouring concrete into the molds was up to 5 mm, after that, fabrics were fixed
manually by use of slight tension to keep the fabrics in place. The carbon rovings weft orientated longitudinally such that they carried the tensile load resulting from the bending. Thereafter, concrete was poured into the mold. The mixture is vibrated for a five minutes. The samples were demolded after 24 h and laid up on 100% relative humidity at room temperature for 28 days. Two groups of composite samples were produced with three trials for each categories. In the first group (group A), fabrics which have different numbers of carbon weft without epoxy. These fabrics were molding in one, two, and three different layers. In group B, fabrics which have different numbers of carbon weft with partially impregnated epoxy in the one or two layers. We used 0.2 cc epoxy for each point on the corner of mesh size, exactly on the interlace of carbon weft and chain stitch. Table 3 represents the category specifications. The sample categories were similar to T 1 b − Ec − d where T: Textile, a: the number of chain stitches a between a roving inserted that shows the mesh size, b: the number of roving in the composite samples, E: Epoxy, c: Distance between the epoxy segment (mm), d: the number of layers. 2.4. Bending test The flexural properties have been investigated by four-point bending test according to ASTM c947 standards (ASTM C94703, 2009). Zwick’s testing machine type 1494 was used. The 10 kN load cell capacity was handled, and the jaw speed was set as 5 mm/min. The number of samples for each categories was three. The four-point bending test setup is illustrated in Figure 2.
3. Results and discussion Flexural properties of all composite samples in the group A and B have been studied and compared with each other and reference samples. The area under load–displacement curve contemplated as toughness. Flexural characteristics were obtained from load– displacement curve including; the bearing load at first crack (fcr), displacement at first crack (δcr), toughness up to first crack (Acr), maximum bearing load (fmax), flexural strength (σmax), maximum displacement at maximum bearing load (δfmax), toughness up to maximum displacement (Afmax), and ultimate toughness (Ault) (Figures 3 and 5). 3.1. Bending behavior of composite samples (group A) The average flexural properties of three composite samples for each category in the group A are represented in Table 4. The ANOVA test results of these data for samples reinforced with different rovings numbers show that there is significant difference for fmax, σmax, δfmax, Afmax, and Ault at level of 95%. But, for fcr, δcr, and Acr insignificant difference is obtained at level of 95% (Table 5). This table also does not show any significant effective on the flexural properties of reinforced samples with different layers by equal number of carbon rovings. As a result,
Table 1. The composition of fine-grained concrete. Portland cement(I) (kg/m3) 650
Silica fume (kg/m3) 65
Superplasticizer (kg/m3) 16
Water (kg/m3) 255
Siliceous fine sand (0–0.125 mm) (kg/m3) 500
Siliceous sand (0.125– 0.6 mm) (kg/m3) 714
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Figure 1. Three different weft-insertion -knitted fabrics by three mesh size (a) 10 × 10 mm, (b) 7.5 × 10 mm and (c) 5 × 10 mm.
Table 2. The carbon-fiber specifications. Number of fibers (No.) 12 K
Tensile Strength (ffu ) (MPa) 4900
Tensile Modulus (Ef ) (GPa) 230
Strain (𝜀fu ) 0.021
Table 3. The sample specifications.
Number of roving
Distance between epoxy segment
Layer
T1 5−1
0 5
0 Without epoxy
0 1
T1 6 − 1
6
Without epoxy
1
T1 8 − 1
8
Without epoxy
1
T 1 10 − 1
10
Without epoxy
1
T 1 10 − 2
10
Without epoxy
2
Category code REF Group A
12
9
6
6
12
Group B
T 1 3 − E10 − 1
3
10 mm
1
T 1 5 − E10 − 1
5
10 mm
1
T 1 8 − E5 − 1
8
5 mm
1
T 1 10 − E5 − 1
10
5 mm
1
T 1 10 − E5 − 2
10
5 mm
2
12
12
6
6
6
by increasing the carbon weft in the reinforcing fabrics (until 10 weft in this study), the flexural properties improved. Therefore, we can say that for improving flexural properties in the concrete beams reinforced with weft-insertion warp-knitted fabrics the number of carbon is more important than layers. Figure 3 shows average of Load–displacement relations all of composite samples of group A under four-point bending tests. The influence of different numbers of carbon rovings-reinforced samples (Figure 3(a)) and different layers (Figure 3(b)) on the bending properties of TRCs were investigated. According to the experimental tests’ observations, the failure mechanism of
Density (g/cm3) 1.80
Fibers cross section area (mm2) 0.462
Filament diameter (μm) 7
reference samples was catastrophic, and separated suddenly after the first crack. While, in the composite samples group A, the ductile failure mechanism occurs. It means that the composite samples exhibited flexural resistance and hardening post-cracking ductility after the first crack. The load–displacement relationship in the Figure 3 can be divided in three sections on the basis of our observation. I is the elastic section, the composite samples are un-cracked and it implies that the concrete is bearing the loads. II is the cracked section consisting of multi cracking (IIa) and strain hardening (IIb) regions. When the cementitious matrix is reached to ultimate tensile strength, the composite samples cracked and the force is transferred through the crack to the fabric. By increasing the load, the multi-crack pattern occurs along the specimen duo to bonding of concrete and fabrics (section IIa). Atypical crack pattern of TRC is shown in Figure 4. In section IIb, the crack width is only increased without creating any new crack due to continuing the increase in loading (Brameshuber, 2006; Colombo et al., 2013). III is the failure of TRCs section that consists of failure of sleeve fibers and sliding of core fibers in the fabrics. The sharp reduction in load-bearing in section IIIa can be attributed to the failure of sleeve fibers when they reach their ultimate strain at the maximum load. Thereafter, the core fiber in the fabrics slide in telescopic forms. This failure mode happens slowly by high deformations (IIIb). 3.2. Bending behavior of composite samples (group B) The average flexural properties of three composite samples for each category in the group B are represented in Table 6.
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R. KAMANI ET AL.
layers by equal number of carbon rovings, shows that there is significant difference for fmax, σmax, Afmax, Ault, fcr, and Acr at level of 95%. But, for δcr and δfmax insignificant difference is obtained at a level of 95%. Figure 5 showed the average of load–displacement of composite samples in the group B under four-point bending tests. The effect of different numbers of carbon rovings-reinforced samples (Figure 5(a)) and different layers (Figure 5(b)) on the bending properties of TRCs were discussed. The failure mechanism and crack pattern of composite reinforced with the 3-, 5-, and 8-carbon weft ) ( T 1 3 − E10 − 1, T 1 5 − E10 − 1 and T 1 8 − E5 − 1, in this 12
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Figure 2. Four-point bending test setup (ASTM C947-03, 2009).
The ANOVA test results of these data indicate significant effect on the flexural properties at the level of 95% for samples reinforced with different rovings numbers in the group B as shown in Table 7. This table, also for samples with different
12
6
group are similar to group A. The flexural strength and displacement of these categories in comparison with group A are increased. The TRCs’ category code T 1 8 − E5 − 1 has the largest 6 displacement. In the case of composite reinforced with 10-carbon ) ( weft T 1 10 − E5 − 1 and T 1 10 − E5 − 2, , the flexural strength 6 6 increased but the displacement is decreased. The failure mechanism of these TRCs is catastrophic. It may be attributed to closing and connecting of the epoxy points because of the lower mesh size of these samples. In this condition, the fabrics are like brittle FRP and the de-bonding failure mode after concrete crashing occurs as shown in Figure 6.
Figure 3. Load–displacement curves of composite samples (group A) (a) different carbon roving weft and (b) different layers. Table 4. Flexural properties of composite samples (group A). Category code Unit T1 5−1 12
T1 6 − 1 9
T1 8 − 1 6
T 1 10 − 1 6
T 1 10 − 2 12
REF *
fcr
δcr
Acr
fmax
δfmax
Afmax
σmax
Ault
(N) 395.32 (87.94)* 366.56 (110.70) 509.08 (138.75) 399.50 (47.18) 405.02 (187.58) 435.63 (87.36)
(mm) 0.47 (0.03) 0.58 (0.19) 0.63 (0.11) 0.50 (0.15) 0.51 (0.08) 0.50 (0.09)
(N.mm) 61.46 (12.14) 58.71 (28.64) 122.97 (47.07) 89.18 (23.31) 66.00 (39.03) 113.74 (16.71)
(N) 624.90 (40.27) 648.65 (44.37) 1007.95 (71.80) 1061.41 (149.35) 1149.65 (168.16)
(mm) 5.44 (0.55) 5.29 (0.46) 5.87 (0.16) 6.47 (0.44) 6.49 (0.43)
(N.mm) 2731.43 (350.89) 2494.92 (627.50) 4125.30 (12.49) 4877.07 (321.69) 5696.13 (482.61) –
(MPa) 11.42 (0.74) 11.86 (0.81) 18.43 (1.31) 19.41 (2.73) 21.02 (3.07) 7.96 (1.60)
(N.mm) 8447.55 (1492.71) 9342.09 (1457.87) 5696.44 (424.45) 14,529.02 (1150.42) 17,168.98 (1781.75)
Parenthesis values are standard deviation.
–
–
–
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Table 5. ANOVA statistical analysis for flexural properties of composite samples in group A. Parameters different rovings numbers different layers
fcr .103 Insignificant .963 Insignificant
δcr .462 Insignificant .899 Insignificant
Acr .391 Insignificant .427 Insignificant
fmax .000 Significant .534 Insignificant
δfmax .038 Significant .957 Insignificant
Afmax .000 Significant .071 Insignificant
σmax .000 Significant .535 Insignificant
Ault .000 Significant .097 Insignificant
4. Evaluating maximum force in bending test
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The strength design method of FRP reinforcement ratio follows the ACI 440.1R-06 are balanced, under- and over-reinforced section (Bank, 2006; GangaRao, Taly, & Vijay, 2006). The strains, stresses, and section forces in the balance situation FRP-reinforced concrete section can be shown in Figure 8. The balanced FRP reinforcement ratio of an FRP-reinforced concrete section is:
𝜌fb = 0.85𝛽1 Figure 4. Crack pattern of TRCs code T 1 8 − 1on tension face.
fc� Ef 𝜀cu ffu Ef 𝜀cu + ffu
(1)
6
The ANOVA test was performed to compare the effect of using partially impregnated epoxy on the fabrics (to increase bending properties of composite samples) with the fabrics without epoxy (group A). The results show that there is significant difference for fmax, σmax, Afmax, and δfmax at level of 95%. But, for fcr, δcr, Acr, and Ault insignificant difference is obtained at level of 95% (Table 8). The method of using partially epoxy is effective for improving bending properties of TRCs. The unique bonding mechanism of TRCs in the group B is created. When TRCs are cracked due to load increasing, the crack(s) propagation occurs through the samples and reaches to the impregnated fabrics. Thus, two modes may happen: (1) the cracks reach the fibers between two impregnated points of epoxy, thus the load transfers to fibers and causes rupture of fibers individually. (2) When the cracks reached the epoxy impregnated points, the crack redirected and propagated horizontally looks like shear cracks (Figure 7).
where 𝜌fb Balanced reinforcement ratio, 𝛽1 Whitney’s assumptions, fc′ ultimate compression strength of concrete, ffu ultimate tensile strength of FRP, Ef the modulus of FRP, 𝜀cu ultimate strain of the concrete, 𝜀fu ultimate strain of FRP. The nominal moment capacity of the over-reinforced section (𝜌f > 𝜌fb , C > Cb ) is given as: (2)
Mn = Af ff (d − a∕2) Where
a=
Af ff
(3)
0.85fc� b
and Mn the nominal moment capacity, Af cross-sectional area of FRP, d effective depth, b beam width, 𝛼 is the depth of the Whitney stress block in the concrete. The nominal moment capacity of an under-reinforced section (𝜌f < 𝜌fb , C < Cb ) is given as:
Table 6. Flexural properties of composite samples (group B). δcr
Acr
fmax
δfmax
Afmax
σmax
Ault
T 1 10 − E5 − 1
(N) 400.10 (23.43)* 392.81 (2.27) 472.24 (44.42) _
(mm) 0.47 (0.10) 0.52 (0.20) 0.40 (0.03) _
(N.mm) 101.29 (22.97) 47.02 (8.99) 104.16 (15.98) _
T 1 10 − E5 − 2
_
_
(N) 789.24 (46.84) 1077.09 (89.70) 1501.63 (146.83) 1831.32 (29.74) 2159.80 (76.98)
(mm) 5.12 (0.17) 7.99 (0.81) 9.05 (0.69) 7.67 (0.41) 8.32 (0.19)
(N.mm) 2664.13 (157.71) 5872.56 (627.66) 8551.35 (1415.49) 8791.03 (771.11) 11,026.39 (127.76)
(MPa) 14.43 (0.86) 19.69 (1.15) 27.45 (2.68) 33.48 (0.54) 39.49( 1.41)
(N.mm) 5444.84 (1069.81) 7739.99 (994.42) 10485.9 9(897.78) 9563.95 (1058.45) 11656.78 (687.03)
Category code Unit T 1 10 − E10 − 1 12
T 1 5 − E10 − 1 12
T 1 8 − E5 − 1 6
fcr
6
6
_
*
Parenthesis values are standard deviation.
Table 7. ANOVA statistical analysis for flexural properties of reinforced concrete samples in the group B. Parameters different rovings numbers different layers
fcr .000 Significant .002 Significant
δcr .000 Significant .069 Insignificant
Acr .000 Significant .008 Significant
fmax .000 Significant .002 Significant
δfmax .000 Significant .069 Insignificant
Afmax .000 Significant .008 Significant
σmax .000 Significant .002 Significant
Ault .001 Significant .045 Significant
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R. KAMANI ET AL.
Figure 5. Load–displacement curves of composite samples (group B), (a) different carbon roving weft and (b) different layers.
(a)
(b)
Figure 6. Failure mechanism of composite with 10-carbon roving weft : concrete destroying (T 1 10 − E5 − 2) (b): de-bonding failure (T 1 10 − E5 − 1). 6
6
Table 8. ANOVA statistical analysis for flexural properties of TRCs in the group A and B. Parameters Epoxy
fcr .067 Insignificant
δcr .071 Insignificant
Acr .065 Insignificant
fmax .001 Significant
δfmax .000 Significant
Afmax .000 Significant
σmax .001 Significant
Ault .840 Insignificant
Table 9. Relative error of prediction FIP. FPI 0.1 0.2 0.21 0.3 0.4 0.5 Relative errors 0.48 0.084 0.07 0.245 0.41 0.54 group A Relative errors 0.72 0.47 0.45 0.27 0.13 0.075 group B Note: The bold values show the minimum error among other values.
0.6 0.66 0.11
Figure 8. Strains, stresses, and section forces in the balanced condition of an FRPreinforced beam (Bank, 2006).
Mn = Af ffu (d − 𝛽1 Cb ∕2)
Figure 7. Failure mechanism and cracks pattern of TRCs’ beam code T 1 8 − E5 − 1 6 (lateral view).
(4)
where Cb is the depth of the neutral axis at the balanced reinforcement ratio. In the case of TRC, it cannot be utilized, the nominal capacity of all fibers. Because, the penetration of cement matrix within inner filaments of rovings is imperfect. Consequently,
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Figure 9. Maximum bearing load as a function of reinforced carbon roving: influence of FPI (α).
Table 10. Model prediction of maximum load bearing vs. some experimental values of TRCs. Number of roving 1 2 3 4 5 6 7 8 9 10 11 12
Over-Reinforcement c 0.73 1.02 1.24 1.42 1.58 1.72 1.85 1.97 2.08 2.18 2.28 2.37
𝜀f 0.0588 0.0412 0.0334 0.0287 0.0255 0.0232 0.0213 0.0199 0.0187 0.0176 0.0167 0.0160
Mn(over) 19200.24 26648.84 32174.18 36707.77 40609.90 44065.06 47182.73 50034.12 52668.63 55122.17 57421.84 59588.62
Under-Reinforcement c 0.73 1.03 1.25 1.43 1.59 1.73 1.86 1.98 2.09 2.20 2.29 2.39
𝜀c 0.0011 0.0015 0.0019 0.0022 0.0025 0.0027 0.0030 0.0032 0.0034 0.0036 0.0038 0.0040
Mn(under) 6984.45 13876.47 20710.28 27498.07 34246.88 40961.45 47645.24 54300.95 60930.73 67536.37 74119.37 80681.02
we introduce a new index (𝛼) for fibers’ performance to limit of volume fraction of fibers in the TRC sections. This index should be less than one and can be estimated experimentally in comparison with calculating of nominal bending capacity. The balance equation of TRCs’ beam with considering FPI and numbers of carbon rovings is:
Nb 𝛼Af × ffu = 0.85 × fc� × b × 𝛽1 × cb
(5)
where Nb number of balanced carbon rovings in the fabrics, 𝛼 = fibers performance index (FPI). On the base of uniform deformation assumption during bend test, a linear strain in both compression and tension area can be contemplated. Therefore, Equation 6 can be derived from Figure 8 as following. 𝜀fu 𝜀cu = (6) cb d − cb
Mn(over) − Mn(under) 12215.79 12772.38 11463.90 9209.70 6363.02 3103.62 −462.51 −4266.83 −8262.10 −12414.20 −16697.53 −21092.39
Mn (Theory) min 6984.45 13876.47 20710.28 27498.07 34246.88 40961.45 47182.73 50034.12 52668.63 55122.17 57421.84 59588.62
fmax (Theory) 126.99 252.30 376.55 499.96 622.67 744.75 857.87 909.71 957.61 1002.22 1044.03 1083.43
Average of fmax Exp. groupA – – – – 624.89 648.65 – 1007.95 – 1061.40 – –
Average of fmax Exp. groupB – – 789.24 – 1077.09 – – 1501.63 – 1831.32 – –
According to FPI, the strength design method of textile reinforcement ratio in the balanced, under-and over-reinforced section are as following: The balanced FRP reinforcement ratio of a TRC section is derived as:
Nb =
0.85 × b × fc� × 𝛽1 × cb 𝛼Af × ffu
(1′)
The nominal moment capacity of the over-reinforced TRC section (𝜌f > 𝜌fb , C > Cb ) can be obtained as:
Mn(over) = N𝛼Af × 𝜀f Ef (d −
𝛽1 × C ) 2
(2′)
The nominal moment capacity of an under-reinforced TRC section (𝜌f < 𝜌fb , C < Cb ) can be derived as:
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R. KAMANI ET AL.
c Mn(under) = N𝛼Af × ffu (d − ) 3
(4′)
The minimum bending moment is considered as possible bending moment of TRC beam.
Mn = Min(Mn(over) , Mn(under) )
(7)
The maximum force which leads to maximum moment bend test of each conditions could be computed as Equation (8):
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fmax
6Mn = lspan
(8)
where lspan is span length of four-point bend test (330 mm in this study). For estimating FPI, we assumed that FPI is a constant value. On the base of balance condition, the section equilibrium forces and strain compatibility have been calculated by given the mechanical properties of concrete and carbon rovings. After that, the moment capacity of under- and over-reinforcement section is computed (Equation 2′ and 4′). The failure moment of section is the minimum of under-and over-reinforcement moments (Equation 7). So, the maximum load bearing of section is obtained (Equation 8). Table 9 tabulated the results of theoretical and experimental data. To estimate FPI for the samples of group A and B, we simulate a range of FPI value to obtain minimum relative error as follows in Equation 9 (Figure 9).
Relative error =
f(max)theory − f(max)experimental f(max)experimental
(9)
The final results of this simulation are calculated in Table 10. Predicted values of maximum bearing load are summarized in Figure 9 by using different values of FPI (α). These models are sensitive to balanced ratio of fabrics in such a way that the rate of change of bearing bending load is a function of reinforcement ratio. According to Table 9, the best value of FPI for the samples in the group A would be 0.21. While this value for group b is 0.5. Therefore, we conclude that the method of fabric partially impregnated epoxy shows significant effect on the load bearing. It means that this method can improve FPI considerably (from 0.21 to 0.5).
5. Conclusion In the case of TRC, the nominal capacity of all fibers cannot be utilized . For this reason, a special index FPI was introduced to represent fibers’ efficiency for TRC. This index was developed based on an analytical method from section balance conditions to evaluate the maximum force capacity of TRC. It was simulated by calculation of the nominal bending capacity and empirical results. The experimental results show that the bending behavior of TRCs increased on increasing the number of carbon roving while the layers have no significant effect. With increase in the number of rovings in the fabrics’ maximum bearing load (fmax), flexural strength (σmax), maximum displacement at maximum bearing load (δfmax), toughness up to maximum displacement (Afmax), and ultimate toughness (Ault) are increased.
To increase fibers’ efficiency in TRCs, we used partially impregnated reinforced roving with spotted epoxy on the fabrics. It was found that this method increases FPI considerably from 0.21 for the fabric without epoxy to 0.5 and improves bending properties of TRCs. This method also improves the failure mechanism of the composite samples.
Disclosure statement The authors declare that they have no conflict of interest.
ORCID Mehdi Kamali Dolatabadi
http://orcid.org/0000-0002-4841-5315
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