- Open Access
Shear Tests for Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) Beams with Shear Reinforcement
- Woo-Young Lim^{1} and
- Sung-Gul Hong^{2}Email author
https://doi.org/10.1007/s40069-016-0145-8
© The Author(s) 2016
- Received: 17 March 2016
- Accepted: 26 April 2016
- Published: 26 May 2016
Abstract
One of the primary concerns about the design aspects is that how to deal with the shear reinforcement in the ultra-high performance fiber reinforced concrete (UHPFRC) beam. This study aims to investigate the shear behavior of UHPFRC rectangular cross sectional beams with fiber volume fraction of 1.5 % considering a spacing of shear reinforcement. Shear tests for simply supported UHPFRC beams were performed. Test results showed that the steel fibers substantially improved of the shear resistance of the UHPFRC beams. Also, shear reinforcement had a synergetic effect on enhancement of ductility. Even though the spacing of shear reinforcement exceeds the spacing limit recommended by current design codes (ACI 318-14), shear strength of UHPFRC beam was noticeably greater than current design codes. Therefore, the spacing limit of 0.75d can be allowed for UHPFRC beams.
Keywords
- spacing limit
- shear reinforcement
- ultra-high performance fiber-reinforced concrete (UHPFRC)
- shear strength
- shear test
- failure modes
1 Introduction
Recently, the steel fiber-reinforced concrete (SFRC) has been widely used as structural material due to its remarkable mechanical properties compared to conventional concrete. Through the numerous experimental studies, it turns out that the addition of steel fibers can improve the structural capability of concrete (Fanella and Naaman 1985; Sharma 1986; Narayanan and Darwish 1987; Wafa and Ashour 1992; Ashour et al. 1992; Ezeldin and Balaguru 1997; Kwak et al. 2002). Even though SFRC has many advantages as structural material, some limitations still exist in the construction of the large-scale structures that requires very high compressive and tensile strength.
To overcome these limitations, ultra-high performance fiber-reinforced concrete (UHPFRC) has been developed. The UHPFRC has a compressive strength of about 150–200 MPa and a tensile strength of 10 MPa or more (Rossi et al. 2005; Farhat et al. 2007; Wille et al. 2011a, b; Park et al. 2012). In addition, shear resistance of UHPFRC beam is outstanding. Previous research on shear tests for UHPFRC beam has focused on the I-shaped beam or girder without shear reinforcement because UHPFRC can reduce a web thickness of the beam due to its great compressive and tensile strength. According to Baby et al. (2014), the presence of shear reinforcement has increased the shear capacity of the beams. Voo et al. (2010) found that a significant distribution of shear cracking occurs prior to the formation of the critical failure crack. Due to its superior mechanical properties, the UHPFRC has been successfully applied in the construction of bridges and also used for retrofitting and strengthening existing concrete structures in building structures (Alaee and Karihaloo 2003; Meda et al. 2014).
One of the primary concerns about the design aspects is that how to deal with the shear reinforcement in the UHPFRC beams. The formation of inclined shear cracking might lead directly to critical failure without warning. To avoid sudden failure in beams, shear reinforcement is required in a proper spacing so that the shear reinforcement should intersect with the diagonal shear cracks, even when shear reinforcement is not necessary according to the computation. Current design codes for reinforced concrete (RC) beams (ACI 318-14 2015; EC2 2004; CSA A23.3-04 2004; AASHTO-LRFD 2004; MC2010 2012) requires a minimum shear reinforcement in beams to ensure adequate reserve shear strength and to prevent possible sudden shear failure, when the factored shear force (V _{ u }) exceeds 0.5ϕV _{ c }. Here, ϕ is the strength reduction factor for shear and V _{ c } is the shear strength provided by concrete. Also, a spacing limit of shear reinforcement is served in design codes (ACI 318-14 2014; CSA A23.3-04 2004).
For SFRC beams, ACI 544 (1988) reported that the steel fibers show potential advantages as shear reinforcement. Previous studies have identified the synergetic effect of fiber volume fraction and presence of shear reinforcement on shear behavior of beams (Mansur et al. 1986; Narayanan 1987; Li et al. 1992; Khuntia et al. 1999; Noghabai 2000). They found that the combination of steel fibers and shear reinforcement depicted slow and controlled cracking and better distribution of tensile cracks, and minimized the penetration of shear cracks into the compression zone. According to Parra-Montesinos (2006), SFRC beams that contained fiber volume fraction (V _{ f }) more than 0.75 % exhibited a shear stress at failure greater than the conservative lower bound value of 0.3√f _{ c } ^{′}. Also, the use of a minimum V _{ f } of 0.75 % has been recommended by ACI Subcommittee 318-F.
However, the effect of shear reinforcement in a rectangular UHPFRC beam section has not been recognized even though the design shear strength for the UHPFRC structural member is obtained by summing the shear strengths provided by cement matrix, steel fibers, and shear reinforcement (JSCE 2004; K-UHPC 2012; AGFC 2013). Especially, a spacing limit of shear reinforcement have not been provided due to the lack of previous test data. Thus, it is necessary to investigate the shear behaviour of the UHPFRC beams regarding the spacing of shear reinforcement because the rectangular beam section in building structures might require sufficient beam width to provide the shear reinforcement.
In this study, shear tests for simply supported rectangular UHPFRC beam sections with and without shear reinforcement were performed to characterize the shear behavior depending on the spacing of shear reinforcement. Also, the shear contribution for the spacing of shear reinforcement is discussed.
2 Current Design Guidelines for Shear
2.1 Shear Strength
The JSCE (2004) and K-UHPC (2012) design guidelines provide the shear strength of UHPFRC beam with or without shear reinforcement.
In AFGC design guidelines (2013), shear strength of UHPFRC members is computed by summing (V _{ d } = V _{ c } + V _{ fb } + V _{ s }) of the shear strength provided by cement matrices; steel fibers; and shear reinforcements in the same manner as other design recommendations assuming the web shear failure.
2.2 Minimum Shear Reinforcement
Minimum shear reinforcement for RC beam in current design codes.
Design codes | Minimum shear reinforcement |
---|---|
ACI 318-14 (2014) | \( \rho_{{v,{\rm min}}} = 0.062{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \ge {{0.35}/{{f_{yt}}}} \) |
EC2 (2004) | \( \rho_{{v,{\rm min}}} = 0.08{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \) |
CSA A23.3-04 (2004) | \( \rho_{{v,{\rm min}}} = 0.06{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \) |
AASHTO-LRFD (2004) | \( \rho_{{v,{\rm min}}} = 0.083{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \) |
MC2010 (2012) | \( \rho_{{v,{\rm min}}} = 0.08{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \) |
For fiber-reinforced concrete beams, when compressive strength (f _{ c } ^{′}) is not exceeding 40 MPa, an overall height (h) not > 600 mm, and the factored shear force not larger than ϕ0.17√f _{ c } ^{′} b _{ w } d, the minimum shear reinforcement would not be required. Parra-Montesinos (2006) suggested that shear strength of FRC with hooked or crimped steel fibers exhibits greater than 0.29√f _{ c } ^{′} b _{ w } d.
2.3 Spacing Limits for Shear Reinforcement
ACI 318-14 (2014) prescribes the spacing limitation of shear reinforcement in Section 9.7.6.2.2. Spacing of shear reinforcement installed perpendicular to the axis of the member should not exceed d/2 in beams nor 600 mm. Where shear strength contributed by shear reinforcement (V _{ s }) exceeds 0.33√f _{ c } ^{′} b _{ w } d, maximum spacing should be reduced by one-half. EC2 suggests the spacing limits as 0.75d or 600 mm. In Section 11.3.8.1 of CSA A23.3-04 (2004), the spacing of shear reinforcement shall not exceed 0.7d _{ v } (d _{ v } = max (0.9d, 0.72h)) or 600 mm in case of beams with an overall thickness greater than 750 mm. According to MC2010 (Section 7.13.5.2), shear reinforcement generally is provided in their spacing not exceed 0.75d or 500 mm. However, current design guidelines for UHPFRC members does not provide the spacing limits for shear reinforcement.
3 Experimental Program
3.1 Specimen Description
Test variables.
Specimens | f _{ ct } (MPa) | V _{ f } (%) | a/d | ρ _{ l } (%) | ρ _{ v } (%) | f _{ y } (MPa) | f _{ yv } (MPa) | s (mm) | M _{ n } (kN-m) | V _{ @Mn } (kN) | V _{ n } (kN) | V _{ @Mn } /V _{ n } |
---|---|---|---|---|---|---|---|---|---|---|---|---|
SB1 | 11.5 | 1.5 | 3 | 0.78 | – | 617.7 | 537.5 | – | 338.3 | 512.6 | 347.6 | 1.47 |
SB2 | 11.5 | 1.5 | 3 | 0.78 | 0.6 | 617.7 | 537.5 | 165 | 338.3 | 512.6 | 449.8 | 1.14 |
SB3 | 11.5 | 1.5 | 3 | 0.78 | 0.9 | 617.7 | 537.5 | 110 | 338.3 | 512.6 | 501.0 | 1.02 |
SB4 | 11.5 | 1.5 | 3 | 0.78 | 1.4 | 617.7 | 537.5 | 66 | 338.3 | 512.6 | 603.2 | 0.85 |
The SB1 specimen is a control test specimen without shear reinforcement. (see Fig. 1b) This specimen was designed as the specimen failed by diagonal tension failure (V _{ @Mn } > V _{ n }). The SB2, SB3, and SB4 specimen has shear reinforcement with a spacing of 0.75d (165 mm), 0.5d (110 mm) and 0.3d (66 mm), respectively (Figs. 1c to 1e). Here, the spacing of 0.5d is a spacing limit provided in ACI 318-14 (2014). In SB3 and SB4 specimens, shear reinforcements were provided at a spacing. Thus, the shear reinforcement ratios of SB2, SB3, and SB4 specimens were 0.6, 0.9 and 1.4 %, respectively.
3.2 Test Set-Up and Instrumentation
Strains of the longitudinal and shear reinforcing bars was measured by using strain gauges during the tests. The location of the strain gauges is presented in Fig. 1. Strain distribution of concrete was obtained at top, mid-height, and bottom of the beam using strain gauges.
4 Material Properties
4.1 Materials and Mix Design of UHPFRC
Mix proportion (weight ratio).
Water-binder ratio | Cement | Zirconium | Filler | Fine aggregate | Water-reducing admixture |
---|---|---|---|---|---|
0.2 | 1.0 | 0.25 | 0.3 | 1.1 | 0.02 |
Two different straight-shaped steel fibers with a diameter of 0.2 mm are used to produce the UHPFRC containing steel fibers. According to Park et al. (2012), the overall shape of tensile stress–strain curves of the UHPFRC was substantially dependent on the type of macro fibers. The addition of micro fibers had an effect on the strain hardening and multiple cracking behaviors. For each batch, UHPFRC includes both steel fibers with different lengths of 16 and 19 mm. The fibers had a yield strength of 2500 MPa. Test specimens were produced after adding in a volume of 1.5 % of the total mix volume.
4.2 Compressive Behavior of UHPFRC
The UHPFRC showed a linear-elastic behavior until the end of the test. After reaching the peak strength, a brittle failure occurred as shown in Fig. 3b. However, a post-peak behavior was not observed in all of the test specimens. The average compressive strength (σ _{ cu }) and ultimate strain (ε _{ cu }) were determined to be 166.9 MPa and 0.0041 mm/mm, respectively. The modulus of elasticity (E _{ c }) was a value of 41.1 GPa, where it was calculated using ultimate stress and strain corresponding to ultimate stress under stress–strain relationship in accordance to AFGC design recommendations (2013).
4.3 Tensile Behavior of UHPFRC
Test specimens are loaded with 100 kN actuator by displacement control. During the test, a loading speed is 0.3 mm/min. The tensile stress was computed with the load divided by an effective cross-sectional area of the specimen, which is equal to (75 – 2 × 12.5) × 25 mm = 1250 mm^{2}. The effective cross-sectional area is defined as the area considering the width except for the overall notch length.
Figure 4b shows tensile strength-crack opening relationship of the notched specimens. Crack opening was measured using clip gauges with a capacity of 10 mm installing at both notches. As shown in Fig. 4b, after reaching the peak tensile stress, the stress gradually decreased as increasing the crack opening. The significant variation of the peak tensile stress is because the non-uniform distribution of the steel fibers at the notch tip. Test results showed that the average tensile stress (f _{ ct }) was 11.5 MPa.
4.4 Tensile Behavior of Reinforcing Bars
Uniaxial tension tests for D29 (d _{ b } = 29 mm, f _{ y } = 600 MPa) and D10 (d _{ b } = 10 mm, f _{ yt } = 400 MPa) reinforcing bars were also carried out in accordance with ASTM A370-14 (2014). The average tensile stresses of longitudinal (D29) and shear (D10) reinforcement were 617.7 and 537.5 MPa, respectively.
5 Test Results
5.1 Damage and Crack Patterns
In case of SB2 specimen, a diagonal tension failure as well as the compression failure of concrete occurred and shear reinforcement yielded prior to the yielding of longitudinal reinforcement. In this specimen, the compression failure and the yielding of longitudinal reinforcement occurred almost simultaneously. The specimen SB3 adopted the minimum shear reinforcement (s = 0.5d) in accordance with ACI 318-14 (2014) showed a compression failure of concrete at the compression zone occurred prior to shear failure. The inclined shear cracks were developed subsequently after the flexural yielding of longitudinal reinforcing bars. For SB4 specimen installing the shear reinforcement at the spacing of 0.3d, flexural failure occurred without observation of critical shear cracks due to the excessive amount of shear reinforcement. After the compression failure of concrete, the yielding of longitudinal and shear reinforcement was followed. Test results indicated that if the minimum shear reinforcement is installed at a spacing of 0.5d presented in ACI 318-14 (2014), the flexural failure may occur prior to shear failure. On the other hand, for beams with the spacing which is greater than minimum values in current design codes, the yielding of shear reinforcement might be observed prior to the yielding of flexural reinforcement and compression failure.
5.2 Load–Displacement Relationship
Summary of test results.
Specimens | Failure mode | At initial cracking | At yielding | At peak | At failure | V _{ test } (MPa) | \( \frac{{v_{test}}}{{\sqrt {f_{cf}}}} \) (MPa) | μ (Δ _{ failure }/Δ _{ y }) | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Δ _{ cr } (mm) | V _{ cr } (kN) | Δ _{ y } (mm) | V _{ y } (kN) | Δ _{ @Vpeak } (mm) | V _{ peak } (kN) | Δ _{ failure } (mm) | V _{ failure } (kN) | |||||
SB1 | S | 2.1 | 339.7 | 6.7 | 347.8 | 8.2 | 475.8 | 26.4 | 172.0 | 14.4 | 1.12 | 2.04 |
SB2 | SY | 1.1 | 150.2 | 7.1 | 479.1 | 11.1 | 537.3 | 15.3 | 408.9 | 16.3 | 1.26 | 2.15 |
SB3 | C | 3.6 | 555.6 | 7.3 | 359.8 | 11.8 | 551.7 | 16.3 | 441.0 | 16.7 | 1.29 | 2.23 |
SB4 | F | 1.2 | 190.5 | 7.3 | 296.1 | 10.9 | 567.0 | 16.0 | 436.1 | 17.2 | 1.33 | 2.19 |
As shown in Fig. 6, the peak load of the beams with shear reinforcement was greater than the beams without shear reinforcement. However, initial stiffness was very similar regardless of the presence of shear reinforcement and their spacing. For the control specimen (SB1), non-linear behavior showed after reaching the yielding point due to the yielding of longitudinal reinforcing bars and flexural cracks. Eventually the load suddenly dropped due to the diagonal tension failure after reaching the peak load. In case of the specimen SB2, SB3, and SB4, the strength was maintained almost being constantly at the peak strength, and then the strength dropped abruptly due to the compression failure at the compression zone without critical shear cracks even though several inclined cracks occurred. Unlike the control specimen, the strength gradually decreased due to the shear reinforcement after the compression failure of concrete. However, the peak strength of the beams with shear reinforcement was very similar. These results indicated that the shear reinforcement ratio might not influence on the peak strength of UHPFRC beams with shear reinforcement.
Shear reinforcement also had an effect on improvement of deformation capacity. Ductility (μ) of beams with shear reinforcement also appeared to be somewhat higher than the control specimen. The ductility of the control specimen was 2.04 and in case of the specimens with shear reinforcement (SB2, SB3, and SB4) were between 2.15 and 2.23.
5.3 Strain Response
6 Discussion of Test Results
6.1 Effect of Shear Reinforcement on Shear Strength
Shear contributions of UHPFRC.
Specimens | s (mm) | V _{ c } (kN) | V _{ fb } (kN) | V _{ s } (kN) | V _{ test } (kN) | \( \frac{{V_{test}}}{{V_{c}}} \) | \( \frac{{V_{test}}}{{V_{fb}}} \) | \( \frac{{V_{test}}}{{V_{s}}} \) | \( \frac{{V_{test}}}{{V_{c} + V_{fb}}} \) | \( \frac{{V_{test}}}{{V_{fb} + V_{s}}} \) | \( \frac{{V_{test}}}{{V_{c} + V_{fb} + V_{s}}} \) |
---|---|---|---|---|---|---|---|---|---|---|---|
SB1 | – | 76.7 | 270.9 | – | 475.8 | 6.20 | 1.76 | – | 1.37 | 1.76 | 1.37 |
SB2 | 0.75d | 76.7 | 270.9 | 102.2 | 537.3 | 7.01 | 1.98 | 5.26 | 1.55 | 1.44 | 1.19 |
SB3 | 0.5d | 76.7 | 270.9 | 153.4 | 551.7 | 7.19 | 2.04 | 3.60 | 1.59 | 1.30 | 1.10 |
SB4 | 0.3d | 76.7 | 270.9 | 255.6 | 567.0 | 7.39 | 2.09 | 2.22 | 1.63 | 1.08 | 0.94 |
From these results, it is found that the steel fibers irregularly distributed on the diagonal cracked section play a key role to restrain the shear crack along with the shear reinforcement.
6.2 Evaluation of Shear Strength
Existing shear strength models.
Authors | Shear strength models |
---|---|
Sharma (1986) | \( v_{u} = kf_{t}^{\prime} \left({d/a} \right)^{0.25} \) where k = 2/3; a/d is the shear span-to-depth ratio; f _{ t } ′ = 0.17√f _{ cf }, if the tensile strength is unknown, and f _{ cf } is the concrete cylinder compressive strength |
Narayanan et al. (1987) | \( v_{u} = e\left[{0.24f_{spfc} + 80\rho \frac{d}{a}} \right] + v_{b} \) where f _{ spfc } is the computed split-cylinder strength of fiber concrete (= f _{ cuf }/(20 − √F) + 0.7 + 1.0√F); ρ is the longitudinal reinforcement ratio; F is the fiber factor (=(L _{ f }/D _{ f })V _{ f } d _{ f }; e is the arch action factor, 1.0 for a/d > 2.8 and 2.8d/a for a/d ≤ 2.8; f _{ cuf } is the cube strength of fiber concrete; V _{ f } is the fiber volume fraction; d _{ f } is a bond factor, 0.5 for round fibers, 0.75 for crimped fibers, and 1.0 for indented fibers; v _{ b } is equal to the equations of 0.41τF, and τ is the average fiber matrix interfacial bond stress, taken as 4.15 MPa |
Ashour et al. (1992) | For a/d ≥ 2.5 \( v_{u} = \left({2.11\sqrt[3]{{f_{cf}}} + 7F} \right)\left({\rho \frac{d}{a}} \right)^{1/3} \) |
Kwak et al. (2002) | \( v_{u} = 3.7ef_{spfc}^{2/3} \left({\rho \frac{d}{a}} \right)^{1/3} + 0.8v_{b} \) where e is the arch action factor, 1 for a/d > 3.4, and 3.4d/a for a/d ≤ 3.4 |
Sharma (1986) investigated the effect of steel fibers on shear strength performing seven SFRC beams with a compressive strength of about 45 MPa. From their shear tests, it is found that steel fibers are effective in increasing the shear strength and SFRC beams have a high post-cracking strength. Narayanan and Darwish (1987) carried out shear tests for forty-nine SFRC rectangular cross-sectional beams with a compressive strength of 40–79.5 MPa regarding shear span to depth ratio (a/d), longitudinal and shear reinforcement, presence of shear reinforcement, and the fiber factor (F = (L/D)ρ _{ f } d _{ f }). Based on the observations of first cracks in shear, empirical shear strength equation was suggested for the evaluation of cracking shear strength. Ashour et al. (1992) tested eighteen HSFRC beams (f _{ c } ^{′} = 93 MPa) with or without shear reinforcement. Test variables were shear span-to-depth (a/d), longitudinal reinforcement ratio, fiber volume fraction. They found that shear strength of beams increase with an increase of fiber volume fraction and a decrease in a/d. On the basis of test results, predictions of shear strength for high-strength SFRC beams without shear reinforcement. ACI 544 (1997) adopted the shear strength equations proposed by Sharma (1986) based on the test results. The proposed equations follows the method of ACI 318 for calculating the contribution of stirrups to the shear capacity, to which is added the resisting force of the concrete calculated from the shear stress. Kwak et al. (2002) performed twelve four-point shear tests for normal—(30.8 MPa) and high-strength (68. 6 MPa) SFRC beams without shear reinforcement considering fiber volume fraction (V _{ f } = 0, 0.5, 0.75 %) and shear span to depth ratio (a/d = 2, 3, and 4). Shear strength equations for shear cracking was proposed to improve the accuracy of existing procedures suggested by Narayanan and Darwish (1987).
Comparison between the predicted strength and test data.
6.3 Steel Fibers as Shear Reinforcement
According to ACI 318-14 (2014), when the normalized shear strength (v _{ test }/√f _{ c } ^{′}) defined as divided the average shear stress by the square root of the compressive strength is greater than 0.29√f _{ c } ^{′} (MPa), the steel fibers can use as the shear reinforcement for SFRC beam (f _{ c } ^{′} ≤ 40 MPa, d ≤ 600 mm). Parra-Montesinos found that the shear strength of SFRC beam strength was larger than 0.3√f _{ c } ^{′} (MPa) when fiber content (V _{ f }) is equal to or greater than 0.75 %.
These results indicate that if the rectangular beam contains UHPFRC with fiber volume fraction of 1.5 %, shear reinforcement need not be provided.
6.4 Spacing Limit of Shear Reinforcement for UHPFRC Beam
As aforementioned, current design codes for reinforced concrete beam provide the spacing limit of shear reinforcement as 0.5d in ACI 318-14 (2014) when the factored shear force Vu exceeds 0.5ϕV _{ c }. Also, CSA A23.3-04 (2004) suggests its distance as 0.7d _{ v }, where d _{ v } is a maximum value between 0.9d and 0.72h. To investigate the effect of spacing limit, this study considered the distance of 0.75d, 0.5d, and 0.3d.
Test results showed that even though the spacing of shear reinforcement exceeds the spacing limit recommended by ACI 318-14 (2014), shear strength of UHPFRC beam was substantially greater than current design codes. Based on the test results, it is concluded that the spacing limit of 0.75d can be allowed for UHPFRC beams.
7 Summary and Conclusions
- 1.
Compression and direct tension tests were carried out to investigate the material properties of UHFRC. The UHPFRC used in this study showed a linear-elastic behavior until the end of the test and a brittle failure occurred after reaching the peak strength, not observing a post-peak behavior in all of the test specimens. The average compressive strength was 166.9 MPa and the modulus of elasticity was about 41.1 GPa. Also, tensile strength of UHPFRC obtained using direct tension tests was determined to be about 11.5 MPa.
- 2.
The steel fibers substantially contributes to enhancement of the shear resistance of UHPFRC beams. The shear strength of the beams with shear reinforcement was larger than that of control specimen and was improved about 13–19 %. In addition, the steel fibers in UHPFRC beam play a key role to restrain the shear crack along with the shear reinforcement.
- 3.
Shear reinforcement also had an effect on improvement of deformation capacity. The ductility of beams with shear reinforcement also appeared to be higher than the control specimen. The ductility of the control specimen was 2.04 and in case of the specimens with shear reinforcement (SB2, SB3, and SB4) were between 2.15 and 2.23.
- 4.
The AFGC recommendations (2013) showed a relatively accurate evaluations of UHPFRC beams with and without shear reinforcement compared to the existing shear strength equations for SFRC beams.
- 5.
Even though the spacing of shear reinforcement exceeds the spacing limit suggested by current design code (ACI 318-14), shear strength of UHPFRC beam was substantially greater than current design codes. Therefore, the spacing limit of 0.75d can be allowed for UHPFRC beams.
Declarations
Acknowledgments
This research was supported by a grant (13SCIPA02) from Smart Civil Infrastructure Research Program funded by Ministry of Land, Infrastructure and Transport (MOLIT) of Korean government and Korea Agency for Infrastructure Technology Advancement (KAIA).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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