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An experimental investigation on the shear and flexural behavior of steel reinforced HPSCC beams
Structures 19 (2019) 286–295
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An experimental investigation on the shear and flexural behavior of steel reinforced HPSCC beams
T
⁎
Ehsan Nikbakhta, , Amin Al-Fakiha, Chieng Chew Huia, Lee Yuan Jakea, Mst. Sadia Mahzabinb a b
Department of Civil & Environmental Engineering, Universiti Teknologi Petronas, 32610, Bandar Seri Iskandar, Malaysia Department of Civil Engineering, Universiti Tunku Abdul Rahman (UTAR), 43000 Kajang, Malaysia
A R T I C LE I N FO
A B S T R A C T
Keywords: High performance concrete (HPC) Self-compacting Steel fibre Shear and flexural strength
High-Performance Self-Compacting Concrete (HPSCC) has experienced increasing demand over the past few years due to its enhanced mechanical properties and high bonding strength. These attributes make it preferable for use in structures, such as tall multi-story buildings, where high workability, strength and bending capacity are required. The objective of the present study is to investigate the shear and flexural behavior of HPSCC beams with no coarse aggregate and compressive strength of above 100 MPa. The influence of different types of steel fibre on the mechanical properties and failure modes of reinforced HPSCC beams were studied. In addition, the influence of the beam's span to effective depth ratio (a/d), longitudinal and transverse reinforcement ratios on the behavior of the HPSCC beams was studied. The results showed that the influence of the type of steel fibre is more significant than the influence of longitudinal reinforcement ratio. Moreover, the ultimate load and deformation capacity of HPSCC beams increased considerably for the beam specimens with steel fibre. However, it was shown that the non-fibre beams with d/4 shear link spacing had a higher ductility compared to the counterpart steel fibre beams with d/2 shear link spacing and with the same amount of longitudinal reinforcement ratio.
1. Introduction Conventional concrete performs well under compression and depending on its mixture design, it can have a compressive strength up to 40 MPa. However, it is very brittle and fails under flexural and sudden loading [1–3]. To suppress these flaws presented by the conventional ordinary Portland cement (OPC) concrete, high performance concrete (HPC) that has enhanced mechanical properties and durability was developed [4,5]. The superior mechanical properties of HPC are mainly due to the increasing in the bonding between particles, the use of different types of fibres, such as steel, and a low water-cement ratio in the mixture design. The constituents of HPC contribute most efficiently to different structural requirements, including strength, toughness, energy absorption capacity, durability, corrosion resistance and damage tolerance, when subjected to large deformations in reinforced structural members [6–8]. Recently, a different type of high performance concrete has been developed, namely engineered cementitious concrete (ECC). In particular, the HPC with high compact admixtures and without coarse aggregates has self-compacting capability, which means that it is able to compact itself under the influence of gravity with its own weight and without additional vibration. High-performance self-compacting
⁎
concrete (HPSCC) possesses higher fresh and mechanical properties due to the more compact microstructure. The microstructure is a result of the mixture design that uses a low water-to-binder ratio (W/B) and high-range water reducing agent [9–14]. Because of the enhanced fresh and mechanical properties of HPSCC, there has been increased interest in recent years on the application of it to structural members, particularly for use in congested reinforced concrete structural members. Often two types of steel fibres are used in the mixture design, namely straight and twisted. Moreover, studies have proved that the use of twisted steel fibres enhances the post-cracking tensile strength and strain capacity compared to straight and short steel fibres [15]. On the other hand, Shin and Mitchell [16] stated that despite all the great advantages that the steel fibres bring to the mixture, it can also become a problem because they may create a nonhomogeneous mixture and reduce the workability. Structural performance of reinforced concrete (RC) members cast with conventional self-compacting concrete under shear and flexural monotonic loads have been investigated in the past by other researchers [2,17–19]. It has been shown that due to the lower amount of coarse aggregates in conventional self-compacting concrete, the aggregate interlock is lower than that of vibrated concrete [20,21]. However,
Corresponding author. E-mail addresses: [email protected] (E. Nikbakht), [email protected] (A. Al-Fakih).
https://doi.org/10.1016/j.istruc.2019.01.018 Received 15 November 2018; Received in revised form 22 January 2019; Accepted 22 January 2019 Available online 29 January 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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140
Constituent
Compressive strenght (MPa)
Table 1 HPSCC mix design used in this study. Mix design
3
Portland cement, kg/m Fly ash, kg/m3 Silica fume, kg/m3 Water, kg/m3 River sand, kg/m3 Superplasticizer, kg/m3 Steel fibre, kg/m3 Quartz sand, kg/m3 Water/binder ratio
A
B
C
D
600 450 50 194.45 480 21 117 154.35 0.185
700 450 78.75 194.45 480 21 117 154.35 0.169
700 450 78.75 194.25 480 21 – 154.35 0.169
600 450 78.75 194.45 480 21 117 154.35 0.185
128.27
120.56
120 99.45
100
120
120.5
106.53
97.66
80 60 40 20 0 Mix A SSF
Mix A HSF
Mix B SSF
Mix B HSF
Mix D SSF
Mix D HSF
Mix C
Mix Designs Fig. 1. Comparison of compressive strength with non-fibre (Mix C), SSF and HSF samples.
HPSCC members that have high strength, improved bonding capability and enhanced mechanical properties are more viable for the structural applications where higher strength and workability are required. To date, there are several studies conducted on behavior of high-performance fibre-reinforced cementitious composite (HPFRCC) elements. There has been limited research on shear and flexural behavior of steel reinforced HPSCC members with no coarse aggregate and compressive strength of above 100 MPa. This study investigates the mechanical properties and structural behavior of HPSCC with different mixture designs and steel fibres, including hooked and straight types. Also, the influence of the type of steel fibre is studied in various beams with different shear span-to-effective depth ratio (a/d) and longitudinal reinforcement ratio. Moreover, the influence of longitudinal and transverse shear reinforcement ratios on deformation capacity, ultimate strength and failure modes of HPSCC beams are investigated.
Flexural strength (MPa)
Mix C
Mix B, HSF
Mix B, SSF 19.25
18.03
18.9
15.12 14.26
16.13 9.13
8.55 5.52
7
14
21
28
Days
2. Mechanical properties
Fig. 2. Flexural strength of the samples with Mix B with HSF, Mix B with SSF and Mix C with no fibres.
In this study, four different mixture designs were used, as shown in Table 1. Mix C, without steel fibres, was used as a control mixture to compare with other mixture designs that contained steel fibres. Mix A, B and D were cast with straight and hooked steel fibres to study the impact of the different types on the mechanical properties of HPSCC samples. The characteristics of the straight steel fibre (SSF) and hooked steel fibre (HSF) used in this study are summarized in Table 2. After 28 days of curing, the mixtures containing the SSF presented a greater compressive strength compared to those with HSF, as shown in Fig. 1. The results show that the compressive strength provided by the SSF is greater than that of the HSF by 22.47% in Mix A and by 11.64% in Mix B. The lower compressive strength of the cube samples with hooked steel fibre is due to the formation of higher number of voids at the interfaces of fibres in the concrete matrix due to their hooked ending shape, which makes them less compact compared to the samples with straight steel fibre. In addition, Fig. 2 shows the flexural strength of the samples after 7, 14 and 28 days of curing. As can be seen, Mix C, (without steel fibres) has the lowest flexural strength compared to other samples because of its highly brittle nature. However, Mix B with SSF shows almost similar flexural strength compared to Mix B with HSF, with 19.25 MPa versus 18.9 MPa, respectively.
3. Influence of shear span to effective depth ratio (a/d) Six HPSCC beams with different longitudinal reinforcement ratios and shear span-depth ratios of 1.0 and 2.0 are shown in Fig. 3 for both casted and experimented cases. The beam specimens without transverse reinforcement were designed so that they fail in shear. There are two beam series, namely A1 and A2, with shear span/ effective depth ratios (a/d) of 1.0 and 2.0, respectively, as indicated in Table 3. Series A1 contains one layer of reinforcements with diameter of 16 mm (ρ = 1.34%), and A2 contains two layers of longitudinal reinforcements in the beams (ρ = 2.68%). As shown in the table, there are also 2 beams without steel fibre (NF) as a control beams in order to evaluate the performance of the HPSCC beams with steel fibres. The labelling of the beams is also shown in Table 3. For instance, for the A1–1.0 specimen, A1 represents the beam with 1 layer of reinforcement and 1.0 represents the aspect ratio of the beam (shear span/effective depth ratio). Testing under stress-control has been performed for all test specimens under a constant loading rate of 1.5kN/s until failure. The results of the experimental tests in this section are presented as follows. Fig. 4 compares the load-displacement responses for all six beams with different longitudinal reinforcement and aspect ratios. As can be seen, the specimens with the steel fibres show higher strength and deformation capacity before the failure. Moreover, the control beam without the steel fibres, beam NF-A2-2.0 with two layers of reinforcements (ρ = 2.68%), exhibited a sudden failure with the lowest load among other specimens at only 70 kN applied load. This is due to the fact that too high reinforcement ratio in this specimen causes significant shear demands while adequate shear reinforcement is not provided. Whereas, the same beam but with steel fibre (A2-2.0) shows the highest
Table 2 Properties of steel fibre used in this study. Straight steel fibre
Hooked steel fibre
Specification: WSF0220 Diameter: 0.2 ± 0.05 mm Length: 20 ± 1 mm Aspect ratio (L/D): 100 Tensile strength: > 2300 MPa
Specification: C-GSF0325 Diameter: 0.3 ± 0.05 mm Length: 25 ± 1 mm Aspect Ratio (L/D): 83 Tensile Strength: > 2300 MPa
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Fig. 3. HPSCC beam (a) Elevation view of the specimens, (b) cross-section view of specimen A1 and (c) cross-section view of the specimen A2. (All dimensions in mm).
NF-A1-2.0 NF-A2-2.0
500
strength among all the specimens at 440 kN, which proves that steel fibre in this specimen also provides adequate transverse shear strength and consequently increases the ultimate strength of the beam. However, this difference of the ultimate strength is considerably less for the lower longitudinal reinforcement ratio case (A1). The beam A1-2.0 displayed a 280 kN ultimate load versus 220 kN for beam NF-A1-2.0. As can be seen from Fig. 4, the results also show that raising of reinforcement ratio in the specimens with aspect ratio of 2.0 has an increasing effect on ductility and deformation capacity, i.e. A1-2.0 displays considerably higher ductility and deformation capacity compared to A2-2.0. Whereas, this increasing effect is insignificant for the beams with aspect ratio of 1.0., i.e. A1-1.0 and A2-1.0 show approximately similar ductility and deformation capacity at the failure. Moreover, the results show that increasing the longitudinal reinforcement ratio in the beams with a higher aspect ratio increased the stiffness and strength of the beams more significantly. Specifically, the beam A2–2.0 (ρ = 2.68%) exhibited a higher amount of strength compared to the corresponding beam with one layer of reinforcements, A1-2.0 by about 170 kN. On the other hand, the difference between the load carrying capacity of the beams A1-1.0 and A2-1.0 both with a/ d = 1.0 is insignificant. Fig. 5 compares the failure modes of the specimens, where it can be seen that all specimens failed due to major diagonal shear cracks. A sudden failure accompanied with concrete spalling occurred in both non-fibre beams. The beams with steel fibre mainly failed due to concrete crush at the compression zone under the loading point position and extension of shear cracks across the specimens. It is clear from the results that increasing the reinforcement ratio in the specimens with the same a/d had a little effect on concrete crack patterns and failure modes, as shown in Fig. 5.
450
A1-1.0 A2-1.0
A1-2.0 A2-2.0
400
Load (kN)
350
A1( =1.34%)
300 250 200 150
A2( =2.68%)
100 50 0 0
2.5
5
7.5 10 12.5 Displacement (mm)
15
17.5
Fig. 4. Load-displacement response of the beam series A1 (with 1 layer of reinforcement) and A2 (with 2 layers of reinforcements).
4. Influence of type of steel fibres Four reinforced HPSCC beams with different longitudinal reinforcement ratios and shear span-depth ratios of 2.0 and 3.5 were casted and tested, as shown in Table 4. The aim of the beam design is to analyze the influence of type of steel fibres on shear failure modes of the HPSCC beams at different shear span-depth ratios (a/d). The dimensions and geometry of the beams are shown in Fig. 6. In this section, the influence of the type of steel fibre on shear failures for the four beams with different a/d and longitudinal reinforcement ratio (ρ) will be discussed. The HPSCC design for Mix D with the compressive strength of 120 MPa, described in Section 2, was
Table 3 HPSCC beam specimens' descriptions and the labels. Beam
Longitudinal reinforcement
d, mm
a, mm
a/d
L1, mm
Steel fibre
L, mm
ρ (%)
A1-1.0 A1-2.0 NF-A1-2.0 A2-1.0 A2-2.0 NF-A2-2.0
2D16 2D16 2D16 4D16 4D16 4D16
280 280 280 255 255 255
280 540 540 255 510 510
1.0 2.0 2.0 1.0 2.0 2.0
300 300 300 300 300 300
✓ ✓ – ✓ ✓ –
1140 1680 1680 1140 1620 1620
1.34 1.34 1.34 2.68 2.68 2.68
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Fig. 5. Crack patterns at shear failure for the beam series A1 (with 1 layer of reinforcement) and A2 (with 2 layers of reinforcements). Table 4 HPSCC beam specimens' descriptions. Beam
Longitudinal reinforcement
d, mm
a, mm
a/d
L1, mm
L, mm
Hooked steel fibre
Straight steel fibre
ρ (%)
B1 B2 B3
2D16 4D12 2D12
280 220 220
540 765 765
2.0 3.5 3.5
300 300 300
1680 2130 2130
X
X X
1.34 1.88 0.94
X
Fig. 6. HPSCC beam (a) Elevation view of the specimens, (b) cross-section view of specimen B1, (c) cross-section view of specimen B2 and (d) cross-section view of specimen B3. (All dimensions in mm). 289
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300
B1 (HSF)
B1 (SSF)
200
Load (kN)
Load (kN)
250
150 100 50 0 0
2.5
5
7.5 10 12.5 Displacement (mm)
15
17.5
20
B2 (SSF, As=1.88%)
100 90 80 70 60 50 40 30 20 10 0 0
Fig. 7. Load-Displacement of B1 with SSF and HSF.
5
10
B3 (HSF, As=0.94%)
15 20 25 Displacement (mm)
30
35
40
Fig. 9. Load-Displacement of B2 and B3 specimens.
used for the fabrication of all beam specimens. The load-displacements for specimen B1 with straight steel fibres (SSF) and hooked steel fibres (HSF) and a/d = 2.0 are shown in Fig. 7. The two beams had the same design parameters, namely the aspect ratio, length, effective depth, reinforcement size and mixture design. As shown in the figure, beam B1 cast with HSF fails under the shear load of 278 kN, whereas the beam with SSF fails at the ultimate load of 198 kN. Also, with respect to the deflection capability, specimen B1 with HSF exhibited a slightly greater value compared to the beam with SSF. As can be observed from Fig. 8, specimen B1 with HSF failed due to shear cracks and concrete crush induced at the compression zone under the loading point, whereas specimen B1 with SSF failed mainly due to the shear cracks and large number of crack openings. Fig. 9 presents the load-deflection response of specimens B2 and B3 with a/d = 3.5, but with different longitudinal reinforcement ratios of ρ =1.88% and ρ = 0.94%, respectively. Specimen B2 had one layer of reinforcement and HSF in its matrix. On the other hand, specimen B3 had two layers of reinforcement and SSF in the matrix. However, specimen B2, with one layer of reinforcement, has a greater ultimate shear load compared to specimen B3, with 2 layers of reinforcement. It can be concluded that this increase in the shear strength by approximately 29% is due to the superior shear resistance of the HSF used in the specimen B3. As opposed to the insignificant influence of type of steel fibre on hardened flexural properties presented in Section 2, the results of bending tests here demonstrate that the beams B1 and B3 with HSF exhibit greater flexural strength due to the stronger bonding of the hooked steel fibre inside the concrete, which increases the splitting and post-cracking tensile strength of the beams more significantly compared to the beams with SSF. As a consequence, the specimens B1 and B3 with HSF exhibit higher flexural strength and their fracture behaviour tends to be more ductile. The concrete crush and failure modes of specimens B2 and B3 are displayed in Fig. 10. As shown in the figure, both specimens exhibited similar failure patterns with vertical concrete cracks across the height of beams; however, a greater amount of concrete crack openings occurred in specimen B2 with SSF.
5. Influence of longitudinal reinforcement ratio on deformation capacity of HPSCC beams In this study, three reinforced HPSCC concrete beams with different longitudinal reinforcement ratios and shear link spacing (d/2) were cast and studied, as indicated in Table 5. There was also a beam without steel fibre as a control in order to compare and investigate the confinement and shear resistance of steel fibre in HPSCC concrete beams. The aspect ratio of all the beams was 3.0. The design specifications for experimented beams are summarized in Table 5. The displacement ductility ratio in the table is calculated from the load-displacement curve of the beams as shown in Fig. 11 based on the method adopted by [22,23]. As shown in Fig. 12, the steel fibre beam with a ρ = 1.8% longitudinal reinforcement ratio (d/2- ρ1.8) shows the highest load capacity among all beams, with a strength of 106 kN, whereas the non-fibre beam with a ρ = 1.19% longitudinal reinforcement (NF-d/2-ρ1.19) had the lowest strength of 63.69 kN and the lowest ductility of 2.1 as shown in Table 5. Furthermore, as the figure indicates, the deformation capacity is shown to decrease by increasing the longitudinal reinforcement ratio, i.e. the beam with 1.19% reinforcement ratio fails due to the fracture of reinforcement at the displacement of 42 mm, whereas the corresponding beam with 1.8% reinforcement ratio fails at the displacement of 13 mm. This is due to the fact that by increasing the reinforcement ratio, the neutral axis moves towards the extreme tensile fibre, resulting in a lower net tensile strain, and deformation capacity when the concrete crushes. In addition, the steel fibre beam with a ρ = 1.2% (Beam d/2-ρ1.2) displayed a greater ductility of 5.7 versus the ductility of 3.2 for the beam with a higher amount of longitudinal reinforcement ratio (d/2ρ1.8). This is because of a greater number of concrete cracks and damage appeared in beam d/2- ρ1.8 before failure, as shown in Fig. 13(b) and (c). This underlines the existence of a specific correlation between amount of steel fibre and longitudinal reinforcement in order to achieve a higher ductility and deformation capacity in HPSCC beams, and this
Fig. 8. Failure modes of B1 specimen with a) SSF and b) HSF. 290
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Fig. 10. Flexural failures of specimens a) B2 and b) B3.
topic needs further studies in the future. The failure modes of the three beams are shown in Fig. 13. However, the non-fibre beam displayed a brittle failure with diagonal shear cracks and spalling of the concrete, whereas the steel fibre beams failed mainly due to formation of flexural cracks accompanied with fracture of the reinforcements. Fracture of reinforcement was observed for both steel fibre beams with ρ = 1.19% and 1.8%, whereas the non-fibre control beam failed due to concrete crush. 6. Influence of transverse reinforcement distance on deformation capacity of HPSCC beams Three beams with transverse link spacings of d/2 and d/4 were tested, as shown in Table 6. All beams had the longitudinal reinforcement ratio of ρ = 1.5%. The results of the load-displacement testing of the beams are presented in Fig. 14. As shown in the figure, the non-fibre beams NF-d/2-ρ1.5 and NF-d/4-ρ1.5 with transverse reinforcement distances of d/2 and d/4, respectively show approximately similar strengths of 80 kN and 83 kN. NF-d/2-ρ1.5 exhibited an undesirable low ductility of 1.2 due to the lack of transverse shear resistance. Moreover, the beam specimen with steel fibre and shear link spacing of d/2 shows the highest ultimate load capacity among all beams; however, it shows a lower ductility compared to the corresponding non-fibre beam with d/4 link spacing. This implies that transverse reinforcement spacing has a significant influence on ductility and deformation capacity of these beams. As shown in Fig. 15, the non-fibre beam with d/2 shear link spacing failed due to concrete crush at the compression zone under the load points followed by diagonal shear cracks. On the other hand, the nonfibre beam with d/4 shear link spacing showed a ductile behavior accompanied with flexural cracks between the supports. The steel fibre beam with d/2 shear link spacing also failed due to flexural cracks with fewer cracks compared to the other two beams. As is shown, flexural failure by crushing is highly unlikely due to the toughness and residual strength of HPSCC in compression. It is therefore necessary to provide a sufficient amount of steel fibre and shear reinforcement to achieve both high ultimate strength and ductility, and take advantage of the compressive behaviour of the HPSCC material.
approaches developed for conventional high performance fibre reinforced concrete contained fine and coarse aggregates. The results are presented as follows.
7. Comparison with existing studies
7.1. Flexural strength
In this section, in order to evaluate the shear and flexural performance of reinforced HPSCC in this study, the experimental results for samples B1, B2 and B3 are compared with existing theoretical
Fig. 16 shows the assumed and simplified stress distribution and strain diagram of reinforced fibrous concrete (RFC) beams [24] and fibrous ultra-high performance reinforced concrete (FUHPRC) beams
Fig. 11. Displacement ductility for reinforced concrete structural elements [22,23].
Fig. 12. Influence of longitudinal reinforcement ratio on load-displacement of HPSCC beams with and without fibre.
Table 5 Beam design specifications for the beams with different longitudinal reinforcement ratios. Beam
Longitudinal reinforcement
ρ (%)
d, mm
a, mm
a/d
Link spacing, mm
L, mm
Steel fibre
Strength, kN
Ductility, mm/mm
NF-d/2- ρ1.2 d/2- ρ1.2 d/2- ρ1.8
2D16 2D16 4D14
1.19 1.19 1.83
260 260 260
800 800 800
3 3 3
d/2 = 125 d/2 = 125 d/2 = 125
2200 2200 2200
– ✓ ✓
64 89 106
2.1 5.7 3.2
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Fig. 13. Failure modes of the UHSSC beams with different longitudinal reinforcement ratios.
[25]. With the completion of compressive and tensile strength blocks, the process of flexural analysis of the beams can be carried out using the principles of force equilibrium and strain compatibility. The neutral-axis depth (c) can be derived from the equilibrium condition in the cross section.
c=
As f y + σt bh 0.85fcf′ β1 b + σt b
(1)
where, As (mm2) and fy (MPa) is the area and yield strength of tensile steel bars, respectively; σt is the ultimate tensile strength of steel reinforced HPSCC concrete (MPa); fcf′ is the compressive strength of steel reinforced HPSCC concrete (MPa); b is the beam width (mm); and h is the beam depth (mm). However, the analytical flexural capacity is then derived, as nominal moment capacity, by equation developed by [24] and confirmed by [25,26] as follows:
a σ b (h − c )(h + c − a) Mn = As f y ⎛d − ⎞ + t 2⎠ 2 ⎝
Fig. 14. Influence of transverse reinforcement on load- displacement of the HPSCC beams.
λ is concrete stress block parameter, (equal to 0.86 for fc′ ≥ 55 MPa [27]); and β1 is the concrete stress block parameter, (equal to 0.65 for fc′ ≥ 55 (MPa) [27]). The theoretical equations shown above have been applied to analyze the flexural capacity of steel reinforced HPSCC beams. Table 7 shows the comparison of experimental moments with theoretical calculated moments for different beams and types of steel fibres cases. As
(2)
where, a is the depth of the equivalent compressive block (mm) calculated by
a=
As f y + σt bh λfcf′ b + σt b
;
Table 6 Beam design specifications for the beams with different transverse link spacing. Beam
Longitudinal reinforcement
ρ (%)
d, mm
a, mm
a/d
Link spacing, mm
L, mm
Steel fibre
Strength, kN
Ductility, mm/mm
NF-d/4-ρ1.5 d/2- ρ1.5 NF-d/2- ρ1.5
2D18 2D18 2D18
1.5 1.5 1.5
260 260 260
800 800 800
3 3 3
d/4 = 62.5 d/2 = 125 d/2 = 125
2200 2200 2200
– ✓ –
80 96 83 kN
3.4 2.0 1.2
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Fig. 15. Failure modes of the beams with different link spacing.
concrete and a/d ≥ 2.5 or a/d < 2.5. Shin et al. [5] proposed the following equations (Eqs. (3) & (4)) to calculate the ultimate shear strength (stress) of HSFRC beams.
can be seen in the table, the ratios of theoretical to the experimental values varies from 0.95 to 1.21. This ratio for the beam with hooked steel fibre (beam B3) is 0.95, whereas for the beams B2 and B3 with straight steel fibre are 1.16 and 1.21, respectively, which implies that the beam with hooked steel fibre attained approximately similar flexural strength to the corresponding conventional high performance fibre reinforced concrete beam, whereas both beams with straight steel fibre exhibited slightly lower flexural strengths.
νu = 0.22fsp +
217ρw d + 0.34F For a/d < 3 a
(3)
νu = 0.19fsp +
93ρw d + 0.34F a
(4)
For a/d ≥ 3
where 7.2. Shear strength
fsp is the splitting tensile strength of fibrous concrete, MPa. F is average fibre-matrix interfacial bond stress expressed as F = (Lf/ Df)Vf Bf where, Df = fibre diameter, mm, Lf = fibre length, mm, Vf = volume fraction of steel fibres, Bf = bond factor = 0.5 for round fibres. ρw = flexural reinforcement ratio, %.
The same specimens used for flexural comparison, were used to analytically predict the shear strength and compare the results with the experimental results. Various studies revealed some empirical formula to predict the shear strength capacity of high strength fibre reinforced concrete (HSFRC) beam with up to 100 MPa compressive strength of
Fig. 16. Strain-stress distributions and design assumptions for the analysis of steel reinforced RFC beams [24,25]. 293
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Table 7 Comparison of theoretical and experimental flexural moments of tested beams. Beam
Rebar
Type of steel fibre
As (mm2)
d mm
σt (MPa)
f'cf (MPa)
c (mm)
a (mm)
Cal. flexural moment Mn, kN·m
Exp. flexural moment Mn, kN·m
Ratio Cal./Exp.
B1 B2 B3
2D16 4D12 2D12
Straight Straight Hooked
402.12 452.39 226.19
280 220 220
10.25 10.25 9.9
120.56 120.56 106.53
53.09 54.72 51.42
35.81 36.92 34.83
66.5 62.7 50.4
54.85 53.85 53.03
1.21 1.16 0.95
Table 8 Experimental and analytical results of steel reinforced HPSCC beams. Specimen
B1 B2 B3
Experimental Shear strength, Vtest, MPa
24.6 35.3 27.5
Analytical shear strength, MPa
Vtest/Vcalc
Shin et al. [5]
Ashour et al. [28]
Khuntia et al. [30]
Eq. (3)
Eq. (5)
Eq. (6)
Eq. (4)
22
13.5 24 20
3-
For a/d < 2.5 (5)
where, τ = 4.15 MPa, a = shear span (mm), d = depth of tension steel in section(mm), and fcf′ is the compressive strength of cylinder fibrous concrete (MPa). Khunita et al. [29] made an attempt to determine a formula for predicting the shear strength of FRC and HSFRC beams as shown in Eqs. (6) and (7).
νu = (0.167 + 0.25F ) fcf,
For a/d ≥ 3
d νu = ⎛0.167 ∗ 2.5 ∗ + 0.25F ⎞ fcf, a ⎝ ⎠
(6) 4-
For a/d ≤ 2.5
Eq. (3)
17.5
1.1
19.4 15.6
Ashour et al. [28] have presented the ultimate shear strength as in Eq. (5):
⎡ 2.5 a ⎤ νu, MPa = ⎢ a + 0.41τF ⎛2.5 − ⎞ ⎥ d⎠ ⎝ ⎣ d ⎦
Eq. (7)
(7)
The results of the comparison between the existing experimental results and the predicted shear strength based for steel reinforced HPSCC beams with a/d ≤ 2.5 or a/d > 3 are presented in Table 8. As can be seen in the table, the ratios of experimental to theoretical results varies from 1.1 to 1.83, which indicates that the reinforced HPSCC beams in this study exhibited greater shear strengths compared to the conventional high performance fibre reinforced concrete beams.
5-
8. Conclusions
6-
Based on the experimental results reported in this paper, the following conclusions can be drawn: 71- The experimental results of the beam specimens without transverse shear reinforcement demonstrated that the beams with HSF had a greater ultimate load and deformation capacity. Moreover, the results showed that specimen B3 with HSF and a lower longitudinal reinforcement ratio (ρ = 0.94%) displayed greater shear strength and deformation capacity. Also, it was shown that the influence of type of steel fibre is more pronounced than the influence of longitudinal reinforcement ratio in HPSCC beams subjected to shear loads. 2- Moreover, increasing the longitudinal reinforcement increased the strength of the beams and reduced the deformation capacity. In other words, the specimen with longitudinal reinforcement ratio of 1.19% exhibited considerably higher ductility compared to the corresponding specimen with 1.83%. This shows that there is a particular correlation between longitudinal reinforcement ratio and
Eq. (4)
Eq. (5)
Eq. (6)
1.82 1.48 1.38
Eq. (7) 1.4
1.82 1.76
steel fibre in order to achieve a greater ductility and deformation capacity in HPSCC beams. However, this correlation requires further studies to obtain the optimum strength and deformation capacity. Also, the influence of the transverse reinforcement distance on failure modes and deformation capacity of HPSCC beams with and without fibres was investigated. When comparing the steel fibre beam with d/2 shear link spacing and the corresponding non-fibre beam, it became clear that the presence of steel fibre in the beams increases the stiffness, strength and slightly increases the ductility. However, the non-fibre beams with a shear link spacing of d/4 showed the greatest ductility among all specimens, including the steel fibre beam with d/2 shear link spacing, which indicates that the transverse reinforcement has a greater influence than steel fibre on ductility of HPSCC beams. The ultimate flexural capacity of reinforced HPSCC beams in this study were approximately in good agreement with the results obtained by existing theoretical flexural strength equations developed for the conventional high performance fibre reinforced concrete beams; however, it was shown that the reinforced HPSCC beams exhibit higher strength against shear. The experimental results presented in this paper showed that reinforced HPSCC beams attains high shear and flexural deformation capacities through proper selection of reinforcement ratio. Reinforced HPSCC members can be designed for very high levels of deformation and sufficient ductility. A structural design can take full advantage of the high material ductility and toughness of HPSCCs in compression and shear by using a careful selection of the type of steel fibre along with longitudinal and transverse reinforcement ratios. To obtain an adequate flexural and shear strengths, a lower longitudinal reinforcement ratio (ρ = 1.19% in this study) is recommended for HPSCC. Moreover, when using HPSCC, if adequate shear reinforcement is not provided, too high longitudinal reinforcement ratio causes significant shear demands, which can lower the deformation capacity and ductility.
Acknowledgment The authors wish to acknowledge the financial support received from the Universiti Teknologi PETRONAS Malaysia under grant number YUTP 015LC0-056. References [1] Ganesan N, Indira P, Abraham R. Steel fibre reinforced high performance concrete
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An experimental investigation on the shear and flexural behavior of steel reinforced HPSCC beams
T
⁎
Ehsan Nikbakhta, , Amin Al-Fakiha, Chieng Chew Huia, Lee Yuan Jakea, Mst. Sadia Mahzabinb a b
Department of Civil & Environmental Engineering, Universiti Teknologi Petronas, 32610, Bandar Seri Iskandar, Malaysia Department of Civil Engineering, Universiti Tunku Abdul Rahman (UTAR), 43000 Kajang, Malaysia
A R T I C LE I N FO
A B S T R A C T
Keywords: High performance concrete (HPC) Self-compacting Steel fibre Shear and flexural strength
High-Performance Self-Compacting Concrete (HPSCC) has experienced increasing demand over the past few years due to its enhanced mechanical properties and high bonding strength. These attributes make it preferable for use in structures, such as tall multi-story buildings, where high workability, strength and bending capacity are required. The objective of the present study is to investigate the shear and flexural behavior of HPSCC beams with no coarse aggregate and compressive strength of above 100 MPa. The influence of different types of steel fibre on the mechanical properties and failure modes of reinforced HPSCC beams were studied. In addition, the influence of the beam's span to effective depth ratio (a/d), longitudinal and transverse reinforcement ratios on the behavior of the HPSCC beams was studied. The results showed that the influence of the type of steel fibre is more significant than the influence of longitudinal reinforcement ratio. Moreover, the ultimate load and deformation capacity of HPSCC beams increased considerably for the beam specimens with steel fibre. However, it was shown that the non-fibre beams with d/4 shear link spacing had a higher ductility compared to the counterpart steel fibre beams with d/2 shear link spacing and with the same amount of longitudinal reinforcement ratio.
1. Introduction Conventional concrete performs well under compression and depending on its mixture design, it can have a compressive strength up to 40 MPa. However, it is very brittle and fails under flexural and sudden loading [1–3]. To suppress these flaws presented by the conventional ordinary Portland cement (OPC) concrete, high performance concrete (HPC) that has enhanced mechanical properties and durability was developed [4,5]. The superior mechanical properties of HPC are mainly due to the increasing in the bonding between particles, the use of different types of fibres, such as steel, and a low water-cement ratio in the mixture design. The constituents of HPC contribute most efficiently to different structural requirements, including strength, toughness, energy absorption capacity, durability, corrosion resistance and damage tolerance, when subjected to large deformations in reinforced structural members [6–8]. Recently, a different type of high performance concrete has been developed, namely engineered cementitious concrete (ECC). In particular, the HPC with high compact admixtures and without coarse aggregates has self-compacting capability, which means that it is able to compact itself under the influence of gravity with its own weight and without additional vibration. High-performance self-compacting
⁎
concrete (HPSCC) possesses higher fresh and mechanical properties due to the more compact microstructure. The microstructure is a result of the mixture design that uses a low water-to-binder ratio (W/B) and high-range water reducing agent [9–14]. Because of the enhanced fresh and mechanical properties of HPSCC, there has been increased interest in recent years on the application of it to structural members, particularly for use in congested reinforced concrete structural members. Often two types of steel fibres are used in the mixture design, namely straight and twisted. Moreover, studies have proved that the use of twisted steel fibres enhances the post-cracking tensile strength and strain capacity compared to straight and short steel fibres [15]. On the other hand, Shin and Mitchell [16] stated that despite all the great advantages that the steel fibres bring to the mixture, it can also become a problem because they may create a nonhomogeneous mixture and reduce the workability. Structural performance of reinforced concrete (RC) members cast with conventional self-compacting concrete under shear and flexural monotonic loads have been investigated in the past by other researchers [2,17–19]. It has been shown that due to the lower amount of coarse aggregates in conventional self-compacting concrete, the aggregate interlock is lower than that of vibrated concrete [20,21]. However,
Corresponding author. E-mail addresses: [email protected] (E. Nikbakht), [email protected] (A. Al-Fakih).
https://doi.org/10.1016/j.istruc.2019.01.018 Received 15 November 2018; Received in revised form 22 January 2019; Accepted 22 January 2019 Available online 29 January 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Constituent
Compressive strenght (MPa)
Table 1 HPSCC mix design used in this study. Mix design
3
Portland cement, kg/m Fly ash, kg/m3 Silica fume, kg/m3 Water, kg/m3 River sand, kg/m3 Superplasticizer, kg/m3 Steel fibre, kg/m3 Quartz sand, kg/m3 Water/binder ratio
A
B
C
D
600 450 50 194.45 480 21 117 154.35 0.185
700 450 78.75 194.45 480 21 117 154.35 0.169
700 450 78.75 194.25 480 21 – 154.35 0.169
600 450 78.75 194.45 480 21 117 154.35 0.185
128.27
120.56
120 99.45
100
120
120.5
106.53
97.66
80 60 40 20 0 Mix A SSF
Mix A HSF
Mix B SSF
Mix B HSF
Mix D SSF
Mix D HSF
Mix C
Mix Designs Fig. 1. Comparison of compressive strength with non-fibre (Mix C), SSF and HSF samples.
HPSCC members that have high strength, improved bonding capability and enhanced mechanical properties are more viable for the structural applications where higher strength and workability are required. To date, there are several studies conducted on behavior of high-performance fibre-reinforced cementitious composite (HPFRCC) elements. There has been limited research on shear and flexural behavior of steel reinforced HPSCC members with no coarse aggregate and compressive strength of above 100 MPa. This study investigates the mechanical properties and structural behavior of HPSCC with different mixture designs and steel fibres, including hooked and straight types. Also, the influence of the type of steel fibre is studied in various beams with different shear span-to-effective depth ratio (a/d) and longitudinal reinforcement ratio. Moreover, the influence of longitudinal and transverse shear reinforcement ratios on deformation capacity, ultimate strength and failure modes of HPSCC beams are investigated.
Flexural strength (MPa)
Mix C
Mix B, HSF
Mix B, SSF 19.25
18.03
18.9
15.12 14.26
16.13 9.13
8.55 5.52
7
14
21
28
Days
2. Mechanical properties
Fig. 2. Flexural strength of the samples with Mix B with HSF, Mix B with SSF and Mix C with no fibres.
In this study, four different mixture designs were used, as shown in Table 1. Mix C, without steel fibres, was used as a control mixture to compare with other mixture designs that contained steel fibres. Mix A, B and D were cast with straight and hooked steel fibres to study the impact of the different types on the mechanical properties of HPSCC samples. The characteristics of the straight steel fibre (SSF) and hooked steel fibre (HSF) used in this study are summarized in Table 2. After 28 days of curing, the mixtures containing the SSF presented a greater compressive strength compared to those with HSF, as shown in Fig. 1. The results show that the compressive strength provided by the SSF is greater than that of the HSF by 22.47% in Mix A and by 11.64% in Mix B. The lower compressive strength of the cube samples with hooked steel fibre is due to the formation of higher number of voids at the interfaces of fibres in the concrete matrix due to their hooked ending shape, which makes them less compact compared to the samples with straight steel fibre. In addition, Fig. 2 shows the flexural strength of the samples after 7, 14 and 28 days of curing. As can be seen, Mix C, (without steel fibres) has the lowest flexural strength compared to other samples because of its highly brittle nature. However, Mix B with SSF shows almost similar flexural strength compared to Mix B with HSF, with 19.25 MPa versus 18.9 MPa, respectively.
3. Influence of shear span to effective depth ratio (a/d) Six HPSCC beams with different longitudinal reinforcement ratios and shear span-depth ratios of 1.0 and 2.0 are shown in Fig. 3 for both casted and experimented cases. The beam specimens without transverse reinforcement were designed so that they fail in shear. There are two beam series, namely A1 and A2, with shear span/ effective depth ratios (a/d) of 1.0 and 2.0, respectively, as indicated in Table 3. Series A1 contains one layer of reinforcements with diameter of 16 mm (ρ = 1.34%), and A2 contains two layers of longitudinal reinforcements in the beams (ρ = 2.68%). As shown in the table, there are also 2 beams without steel fibre (NF) as a control beams in order to evaluate the performance of the HPSCC beams with steel fibres. The labelling of the beams is also shown in Table 3. For instance, for the A1–1.0 specimen, A1 represents the beam with 1 layer of reinforcement and 1.0 represents the aspect ratio of the beam (shear span/effective depth ratio). Testing under stress-control has been performed for all test specimens under a constant loading rate of 1.5kN/s until failure. The results of the experimental tests in this section are presented as follows. Fig. 4 compares the load-displacement responses for all six beams with different longitudinal reinforcement and aspect ratios. As can be seen, the specimens with the steel fibres show higher strength and deformation capacity before the failure. Moreover, the control beam without the steel fibres, beam NF-A2-2.0 with two layers of reinforcements (ρ = 2.68%), exhibited a sudden failure with the lowest load among other specimens at only 70 kN applied load. This is due to the fact that too high reinforcement ratio in this specimen causes significant shear demands while adequate shear reinforcement is not provided. Whereas, the same beam but with steel fibre (A2-2.0) shows the highest
Table 2 Properties of steel fibre used in this study. Straight steel fibre
Hooked steel fibre
Specification: WSF0220 Diameter: 0.2 ± 0.05 mm Length: 20 ± 1 mm Aspect ratio (L/D): 100 Tensile strength: > 2300 MPa
Specification: C-GSF0325 Diameter: 0.3 ± 0.05 mm Length: 25 ± 1 mm Aspect Ratio (L/D): 83 Tensile Strength: > 2300 MPa
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Fig. 3. HPSCC beam (a) Elevation view of the specimens, (b) cross-section view of specimen A1 and (c) cross-section view of the specimen A2. (All dimensions in mm).
NF-A1-2.0 NF-A2-2.0
500
strength among all the specimens at 440 kN, which proves that steel fibre in this specimen also provides adequate transverse shear strength and consequently increases the ultimate strength of the beam. However, this difference of the ultimate strength is considerably less for the lower longitudinal reinforcement ratio case (A1). The beam A1-2.0 displayed a 280 kN ultimate load versus 220 kN for beam NF-A1-2.0. As can be seen from Fig. 4, the results also show that raising of reinforcement ratio in the specimens with aspect ratio of 2.0 has an increasing effect on ductility and deformation capacity, i.e. A1-2.0 displays considerably higher ductility and deformation capacity compared to A2-2.0. Whereas, this increasing effect is insignificant for the beams with aspect ratio of 1.0., i.e. A1-1.0 and A2-1.0 show approximately similar ductility and deformation capacity at the failure. Moreover, the results show that increasing the longitudinal reinforcement ratio in the beams with a higher aspect ratio increased the stiffness and strength of the beams more significantly. Specifically, the beam A2–2.0 (ρ = 2.68%) exhibited a higher amount of strength compared to the corresponding beam with one layer of reinforcements, A1-2.0 by about 170 kN. On the other hand, the difference between the load carrying capacity of the beams A1-1.0 and A2-1.0 both with a/ d = 1.0 is insignificant. Fig. 5 compares the failure modes of the specimens, where it can be seen that all specimens failed due to major diagonal shear cracks. A sudden failure accompanied with concrete spalling occurred in both non-fibre beams. The beams with steel fibre mainly failed due to concrete crush at the compression zone under the loading point position and extension of shear cracks across the specimens. It is clear from the results that increasing the reinforcement ratio in the specimens with the same a/d had a little effect on concrete crack patterns and failure modes, as shown in Fig. 5.
450
A1-1.0 A2-1.0
A1-2.0 A2-2.0
400
Load (kN)
350
A1( =1.34%)
300 250 200 150
A2( =2.68%)
100 50 0 0
2.5
5
7.5 10 12.5 Displacement (mm)
15
17.5
Fig. 4. Load-displacement response of the beam series A1 (with 1 layer of reinforcement) and A2 (with 2 layers of reinforcements).
4. Influence of type of steel fibres Four reinforced HPSCC beams with different longitudinal reinforcement ratios and shear span-depth ratios of 2.0 and 3.5 were casted and tested, as shown in Table 4. The aim of the beam design is to analyze the influence of type of steel fibres on shear failure modes of the HPSCC beams at different shear span-depth ratios (a/d). The dimensions and geometry of the beams are shown in Fig. 6. In this section, the influence of the type of steel fibre on shear failures for the four beams with different a/d and longitudinal reinforcement ratio (ρ) will be discussed. The HPSCC design for Mix D with the compressive strength of 120 MPa, described in Section 2, was
Table 3 HPSCC beam specimens' descriptions and the labels. Beam
Longitudinal reinforcement
d, mm
a, mm
a/d
L1, mm
Steel fibre
L, mm
ρ (%)
A1-1.0 A1-2.0 NF-A1-2.0 A2-1.0 A2-2.0 NF-A2-2.0
2D16 2D16 2D16 4D16 4D16 4D16
280 280 280 255 255 255
280 540 540 255 510 510
1.0 2.0 2.0 1.0 2.0 2.0
300 300 300 300 300 300
✓ ✓ – ✓ ✓ –
1140 1680 1680 1140 1620 1620
1.34 1.34 1.34 2.68 2.68 2.68
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Fig. 5. Crack patterns at shear failure for the beam series A1 (with 1 layer of reinforcement) and A2 (with 2 layers of reinforcements). Table 4 HPSCC beam specimens' descriptions. Beam
Longitudinal reinforcement
d, mm
a, mm
a/d
L1, mm
L, mm
Hooked steel fibre
Straight steel fibre
ρ (%)
B1 B2 B3
2D16 4D12 2D12
280 220 220
540 765 765
2.0 3.5 3.5
300 300 300
1680 2130 2130
X
X X
1.34 1.88 0.94
X
Fig. 6. HPSCC beam (a) Elevation view of the specimens, (b) cross-section view of specimen B1, (c) cross-section view of specimen B2 and (d) cross-section view of specimen B3. (All dimensions in mm). 289
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300
B1 (HSF)
B1 (SSF)
200
Load (kN)
Load (kN)
250
150 100 50 0 0
2.5
5
7.5 10 12.5 Displacement (mm)
15
17.5
20
B2 (SSF, As=1.88%)
100 90 80 70 60 50 40 30 20 10 0 0
Fig. 7. Load-Displacement of B1 with SSF and HSF.
5
10
B3 (HSF, As=0.94%)
15 20 25 Displacement (mm)
30
35
40
Fig. 9. Load-Displacement of B2 and B3 specimens.
used for the fabrication of all beam specimens. The load-displacements for specimen B1 with straight steel fibres (SSF) and hooked steel fibres (HSF) and a/d = 2.0 are shown in Fig. 7. The two beams had the same design parameters, namely the aspect ratio, length, effective depth, reinforcement size and mixture design. As shown in the figure, beam B1 cast with HSF fails under the shear load of 278 kN, whereas the beam with SSF fails at the ultimate load of 198 kN. Also, with respect to the deflection capability, specimen B1 with HSF exhibited a slightly greater value compared to the beam with SSF. As can be observed from Fig. 8, specimen B1 with HSF failed due to shear cracks and concrete crush induced at the compression zone under the loading point, whereas specimen B1 with SSF failed mainly due to the shear cracks and large number of crack openings. Fig. 9 presents the load-deflection response of specimens B2 and B3 with a/d = 3.5, but with different longitudinal reinforcement ratios of ρ =1.88% and ρ = 0.94%, respectively. Specimen B2 had one layer of reinforcement and HSF in its matrix. On the other hand, specimen B3 had two layers of reinforcement and SSF in the matrix. However, specimen B2, with one layer of reinforcement, has a greater ultimate shear load compared to specimen B3, with 2 layers of reinforcement. It can be concluded that this increase in the shear strength by approximately 29% is due to the superior shear resistance of the HSF used in the specimen B3. As opposed to the insignificant influence of type of steel fibre on hardened flexural properties presented in Section 2, the results of bending tests here demonstrate that the beams B1 and B3 with HSF exhibit greater flexural strength due to the stronger bonding of the hooked steel fibre inside the concrete, which increases the splitting and post-cracking tensile strength of the beams more significantly compared to the beams with SSF. As a consequence, the specimens B1 and B3 with HSF exhibit higher flexural strength and their fracture behaviour tends to be more ductile. The concrete crush and failure modes of specimens B2 and B3 are displayed in Fig. 10. As shown in the figure, both specimens exhibited similar failure patterns with vertical concrete cracks across the height of beams; however, a greater amount of concrete crack openings occurred in specimen B2 with SSF.
5. Influence of longitudinal reinforcement ratio on deformation capacity of HPSCC beams In this study, three reinforced HPSCC concrete beams with different longitudinal reinforcement ratios and shear link spacing (d/2) were cast and studied, as indicated in Table 5. There was also a beam without steel fibre as a control in order to compare and investigate the confinement and shear resistance of steel fibre in HPSCC concrete beams. The aspect ratio of all the beams was 3.0. The design specifications for experimented beams are summarized in Table 5. The displacement ductility ratio in the table is calculated from the load-displacement curve of the beams as shown in Fig. 11 based on the method adopted by [22,23]. As shown in Fig. 12, the steel fibre beam with a ρ = 1.8% longitudinal reinforcement ratio (d/2- ρ1.8) shows the highest load capacity among all beams, with a strength of 106 kN, whereas the non-fibre beam with a ρ = 1.19% longitudinal reinforcement (NF-d/2-ρ1.19) had the lowest strength of 63.69 kN and the lowest ductility of 2.1 as shown in Table 5. Furthermore, as the figure indicates, the deformation capacity is shown to decrease by increasing the longitudinal reinforcement ratio, i.e. the beam with 1.19% reinforcement ratio fails due to the fracture of reinforcement at the displacement of 42 mm, whereas the corresponding beam with 1.8% reinforcement ratio fails at the displacement of 13 mm. This is due to the fact that by increasing the reinforcement ratio, the neutral axis moves towards the extreme tensile fibre, resulting in a lower net tensile strain, and deformation capacity when the concrete crushes. In addition, the steel fibre beam with a ρ = 1.2% (Beam d/2-ρ1.2) displayed a greater ductility of 5.7 versus the ductility of 3.2 for the beam with a higher amount of longitudinal reinforcement ratio (d/2ρ1.8). This is because of a greater number of concrete cracks and damage appeared in beam d/2- ρ1.8 before failure, as shown in Fig. 13(b) and (c). This underlines the existence of a specific correlation between amount of steel fibre and longitudinal reinforcement in order to achieve a higher ductility and deformation capacity in HPSCC beams, and this
Fig. 8. Failure modes of B1 specimen with a) SSF and b) HSF. 290
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Fig. 10. Flexural failures of specimens a) B2 and b) B3.
topic needs further studies in the future. The failure modes of the three beams are shown in Fig. 13. However, the non-fibre beam displayed a brittle failure with diagonal shear cracks and spalling of the concrete, whereas the steel fibre beams failed mainly due to formation of flexural cracks accompanied with fracture of the reinforcements. Fracture of reinforcement was observed for both steel fibre beams with ρ = 1.19% and 1.8%, whereas the non-fibre control beam failed due to concrete crush. 6. Influence of transverse reinforcement distance on deformation capacity of HPSCC beams Three beams with transverse link spacings of d/2 and d/4 were tested, as shown in Table 6. All beams had the longitudinal reinforcement ratio of ρ = 1.5%. The results of the load-displacement testing of the beams are presented in Fig. 14. As shown in the figure, the non-fibre beams NF-d/2-ρ1.5 and NF-d/4-ρ1.5 with transverse reinforcement distances of d/2 and d/4, respectively show approximately similar strengths of 80 kN and 83 kN. NF-d/2-ρ1.5 exhibited an undesirable low ductility of 1.2 due to the lack of transverse shear resistance. Moreover, the beam specimen with steel fibre and shear link spacing of d/2 shows the highest ultimate load capacity among all beams; however, it shows a lower ductility compared to the corresponding non-fibre beam with d/4 link spacing. This implies that transverse reinforcement spacing has a significant influence on ductility and deformation capacity of these beams. As shown in Fig. 15, the non-fibre beam with d/2 shear link spacing failed due to concrete crush at the compression zone under the load points followed by diagonal shear cracks. On the other hand, the nonfibre beam with d/4 shear link spacing showed a ductile behavior accompanied with flexural cracks between the supports. The steel fibre beam with d/2 shear link spacing also failed due to flexural cracks with fewer cracks compared to the other two beams. As is shown, flexural failure by crushing is highly unlikely due to the toughness and residual strength of HPSCC in compression. It is therefore necessary to provide a sufficient amount of steel fibre and shear reinforcement to achieve both high ultimate strength and ductility, and take advantage of the compressive behaviour of the HPSCC material.
approaches developed for conventional high performance fibre reinforced concrete contained fine and coarse aggregates. The results are presented as follows.
7. Comparison with existing studies
7.1. Flexural strength
In this section, in order to evaluate the shear and flexural performance of reinforced HPSCC in this study, the experimental results for samples B1, B2 and B3 are compared with existing theoretical
Fig. 16 shows the assumed and simplified stress distribution and strain diagram of reinforced fibrous concrete (RFC) beams [24] and fibrous ultra-high performance reinforced concrete (FUHPRC) beams
Fig. 11. Displacement ductility for reinforced concrete structural elements [22,23].
Fig. 12. Influence of longitudinal reinforcement ratio on load-displacement of HPSCC beams with and without fibre.
Table 5 Beam design specifications for the beams with different longitudinal reinforcement ratios. Beam
Longitudinal reinforcement
ρ (%)
d, mm
a, mm
a/d
Link spacing, mm
L, mm
Steel fibre
Strength, kN
Ductility, mm/mm
NF-d/2- ρ1.2 d/2- ρ1.2 d/2- ρ1.8
2D16 2D16 4D14
1.19 1.19 1.83
260 260 260
800 800 800
3 3 3
d/2 = 125 d/2 = 125 d/2 = 125
2200 2200 2200
– ✓ ✓
64 89 106
2.1 5.7 3.2
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Fig. 13. Failure modes of the UHSSC beams with different longitudinal reinforcement ratios.
[25]. With the completion of compressive and tensile strength blocks, the process of flexural analysis of the beams can be carried out using the principles of force equilibrium and strain compatibility. The neutral-axis depth (c) can be derived from the equilibrium condition in the cross section.
c=
As f y + σt bh 0.85fcf′ β1 b + σt b
(1)
where, As (mm2) and fy (MPa) is the area and yield strength of tensile steel bars, respectively; σt is the ultimate tensile strength of steel reinforced HPSCC concrete (MPa); fcf′ is the compressive strength of steel reinforced HPSCC concrete (MPa); b is the beam width (mm); and h is the beam depth (mm). However, the analytical flexural capacity is then derived, as nominal moment capacity, by equation developed by [24] and confirmed by [25,26] as follows:
a σ b (h − c )(h + c − a) Mn = As f y ⎛d − ⎞ + t 2⎠ 2 ⎝
Fig. 14. Influence of transverse reinforcement on load- displacement of the HPSCC beams.
λ is concrete stress block parameter, (equal to 0.86 for fc′ ≥ 55 MPa [27]); and β1 is the concrete stress block parameter, (equal to 0.65 for fc′ ≥ 55 (MPa) [27]). The theoretical equations shown above have been applied to analyze the flexural capacity of steel reinforced HPSCC beams. Table 7 shows the comparison of experimental moments with theoretical calculated moments for different beams and types of steel fibres cases. As
(2)
where, a is the depth of the equivalent compressive block (mm) calculated by
a=
As f y + σt bh λfcf′ b + σt b
;
Table 6 Beam design specifications for the beams with different transverse link spacing. Beam
Longitudinal reinforcement
ρ (%)
d, mm
a, mm
a/d
Link spacing, mm
L, mm
Steel fibre
Strength, kN
Ductility, mm/mm
NF-d/4-ρ1.5 d/2- ρ1.5 NF-d/2- ρ1.5
2D18 2D18 2D18
1.5 1.5 1.5
260 260 260
800 800 800
3 3 3
d/4 = 62.5 d/2 = 125 d/2 = 125
2200 2200 2200
– ✓ –
80 96 83 kN
3.4 2.0 1.2
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Fig. 15. Failure modes of the beams with different link spacing.
concrete and a/d ≥ 2.5 or a/d < 2.5. Shin et al. [5] proposed the following equations (Eqs. (3) & (4)) to calculate the ultimate shear strength (stress) of HSFRC beams.
can be seen in the table, the ratios of theoretical to the experimental values varies from 0.95 to 1.21. This ratio for the beam with hooked steel fibre (beam B3) is 0.95, whereas for the beams B2 and B3 with straight steel fibre are 1.16 and 1.21, respectively, which implies that the beam with hooked steel fibre attained approximately similar flexural strength to the corresponding conventional high performance fibre reinforced concrete beam, whereas both beams with straight steel fibre exhibited slightly lower flexural strengths.
νu = 0.22fsp +
217ρw d + 0.34F For a/d < 3 a
(3)
νu = 0.19fsp +
93ρw d + 0.34F a
(4)
For a/d ≥ 3
where 7.2. Shear strength
fsp is the splitting tensile strength of fibrous concrete, MPa. F is average fibre-matrix interfacial bond stress expressed as F = (Lf/ Df)Vf Bf where, Df = fibre diameter, mm, Lf = fibre length, mm, Vf = volume fraction of steel fibres, Bf = bond factor = 0.5 for round fibres. ρw = flexural reinforcement ratio, %.
The same specimens used for flexural comparison, were used to analytically predict the shear strength and compare the results with the experimental results. Various studies revealed some empirical formula to predict the shear strength capacity of high strength fibre reinforced concrete (HSFRC) beam with up to 100 MPa compressive strength of
Fig. 16. Strain-stress distributions and design assumptions for the analysis of steel reinforced RFC beams [24,25]. 293
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Table 7 Comparison of theoretical and experimental flexural moments of tested beams. Beam
Rebar
Type of steel fibre
As (mm2)
d mm
σt (MPa)
f'cf (MPa)
c (mm)
a (mm)
Cal. flexural moment Mn, kN·m
Exp. flexural moment Mn, kN·m
Ratio Cal./Exp.
B1 B2 B3
2D16 4D12 2D12
Straight Straight Hooked
402.12 452.39 226.19
280 220 220
10.25 10.25 9.9
120.56 120.56 106.53
53.09 54.72 51.42
35.81 36.92 34.83
66.5 62.7 50.4
54.85 53.85 53.03
1.21 1.16 0.95
Table 8 Experimental and analytical results of steel reinforced HPSCC beams. Specimen
B1 B2 B3
Experimental Shear strength, Vtest, MPa
24.6 35.3 27.5
Analytical shear strength, MPa
Vtest/Vcalc
Shin et al. [5]
Ashour et al. [28]
Khuntia et al. [30]
Eq. (3)
Eq. (5)
Eq. (6)
Eq. (4)
22
13.5 24 20
3-
For a/d < 2.5 (5)
where, τ = 4.15 MPa, a = shear span (mm), d = depth of tension steel in section(mm), and fcf′ is the compressive strength of cylinder fibrous concrete (MPa). Khunita et al. [29] made an attempt to determine a formula for predicting the shear strength of FRC and HSFRC beams as shown in Eqs. (6) and (7).
νu = (0.167 + 0.25F ) fcf,
For a/d ≥ 3
d νu = ⎛0.167 ∗ 2.5 ∗ + 0.25F ⎞ fcf, a ⎝ ⎠
(6) 4-
For a/d ≤ 2.5
Eq. (3)
17.5
1.1
19.4 15.6
Ashour et al. [28] have presented the ultimate shear strength as in Eq. (5):
⎡ 2.5 a ⎤ νu, MPa = ⎢ a + 0.41τF ⎛2.5 − ⎞ ⎥ d⎠ ⎝ ⎣ d ⎦
Eq. (7)
(7)
The results of the comparison between the existing experimental results and the predicted shear strength based for steel reinforced HPSCC beams with a/d ≤ 2.5 or a/d > 3 are presented in Table 8. As can be seen in the table, the ratios of experimental to theoretical results varies from 1.1 to 1.83, which indicates that the reinforced HPSCC beams in this study exhibited greater shear strengths compared to the conventional high performance fibre reinforced concrete beams.
5-
8. Conclusions
6-
Based on the experimental results reported in this paper, the following conclusions can be drawn: 71- The experimental results of the beam specimens without transverse shear reinforcement demonstrated that the beams with HSF had a greater ultimate load and deformation capacity. Moreover, the results showed that specimen B3 with HSF and a lower longitudinal reinforcement ratio (ρ = 0.94%) displayed greater shear strength and deformation capacity. Also, it was shown that the influence of type of steel fibre is more pronounced than the influence of longitudinal reinforcement ratio in HPSCC beams subjected to shear loads. 2- Moreover, increasing the longitudinal reinforcement increased the strength of the beams and reduced the deformation capacity. In other words, the specimen with longitudinal reinforcement ratio of 1.19% exhibited considerably higher ductility compared to the corresponding specimen with 1.83%. This shows that there is a particular correlation between longitudinal reinforcement ratio and
Eq. (4)
Eq. (5)
Eq. (6)
1.82 1.48 1.38
Eq. (7) 1.4
1.82 1.76
steel fibre in order to achieve a greater ductility and deformation capacity in HPSCC beams. However, this correlation requires further studies to obtain the optimum strength and deformation capacity. Also, the influence of the transverse reinforcement distance on failure modes and deformation capacity of HPSCC beams with and without fibres was investigated. When comparing the steel fibre beam with d/2 shear link spacing and the corresponding non-fibre beam, it became clear that the presence of steel fibre in the beams increases the stiffness, strength and slightly increases the ductility. However, the non-fibre beams with a shear link spacing of d/4 showed the greatest ductility among all specimens, including the steel fibre beam with d/2 shear link spacing, which indicates that the transverse reinforcement has a greater influence than steel fibre on ductility of HPSCC beams. The ultimate flexural capacity of reinforced HPSCC beams in this study were approximately in good agreement with the results obtained by existing theoretical flexural strength equations developed for the conventional high performance fibre reinforced concrete beams; however, it was shown that the reinforced HPSCC beams exhibit higher strength against shear. The experimental results presented in this paper showed that reinforced HPSCC beams attains high shear and flexural deformation capacities through proper selection of reinforcement ratio. Reinforced HPSCC members can be designed for very high levels of deformation and sufficient ductility. A structural design can take full advantage of the high material ductility and toughness of HPSCCs in compression and shear by using a careful selection of the type of steel fibre along with longitudinal and transverse reinforcement ratios. To obtain an adequate flexural and shear strengths, a lower longitudinal reinforcement ratio (ρ = 1.19% in this study) is recommended for HPSCC. Moreover, when using HPSCC, if adequate shear reinforcement is not provided, too high longitudinal reinforcement ratio causes significant shear demands, which can lower the deformation capacity and ductility.
Acknowledgment The authors wish to acknowledge the financial support received from the Universiti Teknologi PETRONAS Malaysia under grant number YUTP 015LC0-056. References [1] Ganesan N, Indira P, Abraham R. Steel fibre reinforced high performance concrete
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