Shear Tests for Ultra-High Performance Fiber

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International Journal of Concrete Structures and Materials

Vol.10, No.2, pp.177188, June 2016

DOI 10.1007/s40069-016-0145-8

ISSN 1976-0485 / eISSN 2234-1315

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Web End = Shear Tests for Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) Beams with Shear Reinforcement

Woo-Young Lim1), and Sung-Gul Hong2),*

(Received March 17, 2016, Accepted April 26, 2016, Published online May 26, 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 ber reinforced concrete (UHPFRC) beam. This study aims to investigate the shear behavior of UHPFRC rectangular cross sectional beams with ber 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 bers 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 ber-reinforced concrete (UHPFRC), shear strength, shear test, failure modes.

1. Introduction

Recently, the steel ber-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 bers 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 ber-reinforced concrete (UHPFRC) has been developed. The UHPFRC has a compressive strength of about 150200 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 signicant 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 retrotting 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 (Vu) exceeds 0.5/Vc. Here, /

is the strength reduction factor for shear and Vc 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 bers show potential advantages as shear reinforcement. Previous studies have identied the synergetic effect of ber 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).

1)Institute of Engineering Research, Seoul National University, Seoul 08826, Korea.

2)Department of Architecture and Architectural Engineering, Seoul National University, Seoul 08826, Korea.

*Corresponding Author; E-mail: [email protected] Copyright The Author(s) 2016. This article is published with open access at Springerlink.com

177

They found that the combination of steel bers 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 ber volume fraction (Vf) more than 0.75 %

exhibited a shear stress at failure greater than the conservative lower bound value of 0.3Hfc0. Also, the use of a minimum Vf 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 bers, 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 sufcient 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 StrengthThe JSCE (2004) and K-UHPC (2012) design guidelines provide the shear strength of UHPFRC beam with or without shear reinforcement.

The design shear strength (Vd) is obtained by summation of the shear strength provided by cement matrix, steel ber, and shear reinforcement as follows:

Vd Vc Vfb Vs 1

where Vc, Vfb, and Vs are shear strength provided by cement matrix, steel bers, and shear reinforcement, respectively.

The shear strength provided by cement matrix is obtained as given:

Vc /b0:18

where fvd is the design average tensile strength in the direction perpendicular to diagonal tensile crack; bu is the angle occurring between axial direction and diagonal tensile crack plane. This angle shall be larger than 30. The value of z is distance from the position of the resultant of the compressive stresses to the centroid of tensile steel (mm), generally d/1.15.

In these guidelines, the design average tensile strength in the direction perpendicular to diagonal tensile crack can be expressed as Eq. (4) since the material reduction factor considers the orientation of the steel bers. Thus, the value of fvd is obtained as follows:

fvd

1 wv

Z wv

0 /crk w

1 wv

Z wv

0 rdwdw 4

where wv = max (wu, 0.3 mm); wu is the ultimate crack width corresponding to peak stress on the outer ber; /c is

material reduction factor (= 0.8); rk(w) is the tension softening curve; and rd(w) is equal to /crk(w).

Shear strength by the shear reinforcement is provided in K-UHPC recommendations (2012) and it can be determined as follows:

Vs /b

Avfyt sin as cos as

s d 5

where Av is the cross sectional area of shear reinforcement; fyt is the design yield strength of shear reinforcement; as is the angle between longitudinal axis of beam and shear reinforcement; and s is the spacing of shear reinforcement. It should be noted that JSCE guidelines does not provide this term.

In AFGC design guidelines (2013), shear strength of UHPFRC members is computed by summing (Vd = Vc ? Vfb ? Vs) of the shear strength provided by cement matrices; steel bers; and shear reinforcements in the same manner as other design recommendations assuming the web shear failure.

For a reinforced section, the term of shear strength provided by cement matrices is given by:

0:21 ccf cE k

f 0c

bwd 6

where ccf is the partial safety factor on bers and is assumed to be a value of 1.3; cE is a safety coefcient; ccfcE is equal to1.5, k is determined by 1 ? 3rcp/fc0 for rcp C 0; and 1 ? 0.7

rcp/fc0c,0.05 for rcp \ 0; rcp is calculated by the equation of Ned/Ac; Ned is the axial force in the cross section due to prestressing; and Ac is the area of concrete cross section.

The part of shear strength provided by the ber is determined as follows:

Vfb

f 0c

bwd 2

where /b is the member reduction factor and is recommended as 0.77, fc0 is the compressive strength, bw is the beam width, and d is the effective depth of the beam.

The shear strength by steel bers can be determined as follows:

Vfb /b

AfvrRd;f

tan h 7 where Afv is the area of ber effect and is assumed to be bwz for rectangular section; z is the inner lever arm and is

178 | International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016)

fvd

tan bu

bwz 3

approximately equal to 0.9d; and h is the angle between the principal compression stress and the beam axis, which a minimum value of 30 is recommended; and rRd,f is residual

tensile strength and can be computed as follows:

rRd;f

shear strength of FRC with hooked or crimped steel bers exhibits greater than 0.29Hfc0bwd.

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 (Vs) exceeds 0.33Hfc0bwd, maximum spacing should be reduced by one-half. EC2 suggests the spacing limits as0.75d or 600 mm. In Section 11.3.8.1 of CSA A23.3-04 (2004), the spacing of shear reinforcement shall not exceed0.7dv (dv = 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 DescriptionTest specimens which had a same dimension were designed in accordance with K-UHPC (2012) guidelines as shown in Fig. 1. As shown in Table 2, primary test parameter is the spacing (s) of shear reinforcement. Figure 1a shows the cross-section of the test specimens. Rectangular cross-sectional specimens had a dimension (bw 9 h) of

150 9 290 mm, where, bw is the beam width and h is the overall height of the beam. The effective depth (d) of the beam is 220 mm and the shear span to depth ratio (a/d) is3.0. Concrete cover is 30 mm. To induce shear failure, four D29 (db = 29 mm) high-strength reinforcements (fy = 600 MPa) were used, where db is a diameter of reinforcing bars and fy is a design yield strength of reinforcement. The longitudinal reinforcement ratio (q) is equal to the value of 0.078. Shear reinforcement [D10 (db = 10 mm),

fyt = 400 MPa] was designed in accordance with ACI 318-14 (2014). Therefore, the moment capacities (Mn) of all

specimens were 338.3 kN m and shear strength corresponding to moment capacity was 512.6 kN.

The SB1 specimen is a control test specimen without shear reinforcement. (see Fig. 1b) This specimen was designed as

Table 1 Minimum shear reinforcement for RC beam in current design codes.

Design codes Minimum shear reinforcement

ACI 318-14 (2014) qv;min 0:062

f 0c

1 Kccf

1 wlim

Z wlim

0 rf w

dw; where wlim

max wu; wmax

where K is the ber orientation factor assuming to be a value of 1.25; rf(w) is a function of the tensile stress and crack width; and wmax is the maximum crack width.

The shear strength by the vertical shear reinforcement is as follows:

Avs zfyt cot h 9

Meanwhile, ACI 544 (1988) provides shear strength for ber-reinforced concrete proposed by Sharma (1986) as follows:

Vcf

3 fct

0:25

d a

bwd 10

where fct is splitting tensile strength of FRC.

2.2 Minimum Shear ReinforcementCurrent design provisions (ACI 318-14 2014; EC2 2004; CSA A23.3-04 2004; AASHTO-LRFD 2004; MC2010 2012) for reinforced concrete (RC) beam provide the minimum and maximum shear reinforcement as shown in Table 1. According to Section 9.6.3 of ACI 318-14 (2015), a minimum area of shear reinforcement should be provided in beams where the factored shear force (Vu) exceeds 0.5/cVc.

In Section 9.2.2 of EC2 (2004), when design shear force (Vd) is higher than design shear resistance (Vdc) provided by concrete (Vd [ Vdc), sufcient shear reinforcement should be provided in order that shear resistance (VRd) is larger than design shear force (Vd B VRd).

For ber-reinforced concrete beams, when compressive strength (fc0) is not exceeding 40 MPa, an overall height (h) not [ 600 mm, and the factored shear force not larger than /0.17Hfc0bwd, the minimum shear reinforcement would not be required. Parra-Montesinos (2006) suggested that

=fyt 0:35=fyt

EC2 (2004) qv;min 0:08

f 0c

=fyt

CSA A23.3-04 (2004) qv;min 0:06

f 0c

=fyt

AASHTO-LRFD (2004) qv;min 0:083

f 0c

=fyt

MC2010 (2012) qv;min 0:08

f 0c

fc0 is the compressive strength of concrete (in MPa) and fyt is the design yield strength of shear reinforcement (in MPa).

International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016) | 179

D10 (SD400)

290

4D29 (SD600)

44,5

44,5 150

B1 specimen B2, B3, and B4 specimens

(a)

300 1320 300

4D29 (SD600)

290

L3, L4

L5, L6 D10@165 (SD400)

290

L1, L2

L5, L6

L3, L4

L1, L2

1920

(b)

(c)

300 1320 300

L1, L2

300 1320 300

L1, L2

L3, L4

L5, L6 D10@66 (SD400)

290

D10@110 (SD400)

290

L5, L6

L3, L4

1920

(d) (e)

Fig. 1 Details of the test specimens (unit: mm). a Cross section, b SB1 specimen, c SB2 specimen (s = 0.75d), d SB3 specimen

(s = 0.5d), e SB4 specimen (s = 0.3d).

Table 2 Test variables.

Specimens fct (MPa) Vf (%) a/d ql (%) qv (%) fy (MPa) fyv (MPa) s (mm) Mn (kN-

V@Mn

(kN)

Vn (kN) V@Mn/Vn

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 fct is measured tensile strength obtained using direct tension test; Vf is ber volume fraction; a/d is the shear span-to-depth ratio; ql is the

longitudinal reinforcement ratio (As/bwd); qv is the shear reinforcement ratio (Asv/bws); As is the area of the longitudinal reinforcement; Asv is

the area of the shear reinforcement; fy is measured yield strength of longitudinal reinforcement; fyv is measured yield strength of shear

reinforcement; s is the spacing of shear reinforcement; Mn is the exural moment strength; V@Mn is the shear force at exural moment strength;

Vn is the shear strength determined in accordance with JSCE and K-UHPC recommendations.

P 660 300

300 660

330 330

the specimen failed by diagonal tension failure (V@Mn [ Vn). 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 were0.6, 0.9 and 1.4 %, respectively.

3.2 Test Set-Up and InstrumentationFigure 2 shows the test set-up and instrumentation. Simply supported beams were loaded with a capacity of 1000 kN actuator by displacement control. Deection of the beam

was measured using three Linear Vertical Displacement Transducers (LVDTs). One is installed at the mid-span of the beam and others are at one-half distance (330 mm) of both sides with respect to mid-span.

135

C4 C5 C6

C1 C2 C3

C7 C8 C9

Strain

gauges

290

/ 2

P / 2

LV1 3

Fig. 2 Test set up (unit: mm).

180 | International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016)

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 UHPFRCThe UHPFRC is a kind of reactive powder concrete that coarse aggregates were not included. Fine aggregates consist of sand with a diameter of \ 0.5 mm, which is the largest component of the UHPFRC. Portland cement is used as the binder, and the ller material is crushed quartz with an average diameter of 10 lm and a density of 2600 kg/m3. The

workability provided by the low water-to-cement ratio of the concrete is maintained by the addition of a high-performance water reducing agent, a polycarboxylate superplasticizer with a density of 1060 kg/m3. In Table 3, the proportions of the components are shown in terms of weight ratios.

Two different straight-shaped steel bers with a diameter of 0.2 mm are used to produce the UHPFRC containing steel bers. According to Park et al. (2012), the overall shape of tensile stressstrain curves of the UHPFRC was substantially dependent on the type of macro bers. The addition of micro bers had an effect on the strain hardening and multiple cracking behaviors. For each batch, UHPFRC includes both steel bers with different lengths of 16 and 19 mm. The bers 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 Compression tests for cylindrical test specimens with a diameter of 100 mm and a height of 200 mm were performed to obtain the compressive strength of UHPFRC in accordance with ASTM C39/C39M (2005). Figure 3a shows stressstrain curves of the test specimens with a ber volume fraction of 1.5 %. Compressive strength was measured using universal testing machine controlling by displacement and axial strain (ec) was obtained using two strain gauges on the opposite surface of the test specimen. Loading rate was0.3 mm/min during the tests. The cylindrical test specimens were produced with each batch simultaneously and were cured by steam curing at a temperature above 90 C for 48 h, and then they cured at room temperature for 60 days until testing.

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 (rcu) and ultimate strain (ecu)

were determined to be 166.9 MPa and 0.0041 mm/mm, respectively. The modulus of elasticity (Ec) was a value of41.1 GPa, where it was calculated using ultimate stress and strain corresponding to ultimate stress under stressstrain relationship in accordance to AFGC design recommendations (2013).

4.3 Tensile Behavior of UHPFRCThe tensile strength of UHPFRC was obtained using direct tension tests for dog-bone shaped specimens in accordance with K-UHPC (2012) guidelines as shown in Fig. 4a. Test specimens had an overall width of 125 mm, a height of 300 mm, and a thickness of 25 mm, but an effective width and a height are 75 and 150 mm, respectively. To induce critical crack at the center of the specimen, notches were installed at both sides of the specimen. The length (a0) and

width of the notches was 12.5 and 2 mm, respectively.

Test specimens are loaded with 100 kN actuator by displacement control. During the test, a loading speed is0.3 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 9 12.5) 9 25 mm = 1250 mm2.

The effective cross-sectional area is dened 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 signicant variation of the peak tensile stress is because the non-uniform distribution of the steel bers at the notch tip. Test results showed that the average tensile stress (fct) was 11.5 MPa.

4.4 Tensile Behavior of Reinforcing Bars Uniaxial tension tests for D29 (db = 29 mm,

fy = 600 MPa) and D10 (db = 10 mm, fyt = 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 PatternsThe amount of shear reinforcement greatly affected the damage and crack patterns for UHPFRC rectangular cross-sectional beams (Vf = 1.5 %). Figure 5 shows damage and

Table 3 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

International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016) | 181

Compressive strength (MPa)

200

0 0.000 0.002 0.004 0.006

150

C1 C2 C3 C4 C5 C6

100

Axial strain (mm/mm)

(a)

(b)

Fig. 3 Uniaxial compression test for UHPFRC. a Stressstrain curves, b failure mode.

125

Tensile strength (MPa)

100 kN Actuator

Clip gauges

Test specimen

notch

Strain gauges

300 2

G1G2

0 0 2 4 6 8

Crack opening (mm)

(a) (b)

Fig. 4 Direct tensile test for UHPFRC. a Dog-bone shaped specimen, b stressstrain curves.

SB1

SB2 (s=0.75d)

SB3 (s=0.5d)

SB4 (s=0.3d)

Fig. 5 Damage and crack patterns at the end of the test.

182 | International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016)

crack patters at the end of the tests. For control specimen SB1 which does not contain the shear reinforcement, exural cracks initiated at the bottom of beam at the mid-span, and then the diagonal cracks occurred at the end of the exural cracks. Finally the diagonal tension failure occurred after the yielding of longitudinal reinforcing bars. In this specimen,

compression failure at the compression zone was also observed with shear cracks.

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 exural yielding of longitudinal reinforcing bars. For SB4 specimen installing the shear reinforcement at the spacing of0.3d, exural 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 exural 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 exural reinforcement and compression failure.

5.2 LoadDisplacement RelationshipFigure 6a shows the loaddisplacement relationship of test specimens. Here, the displacement is a deection measured at the mid-span of the beam. Figure 6b depicts denition of yielding point and ductility. The value of Vy is the yield strength, Vpeak is the peak shear strength, Vfailure is the strength at failure, Dy, D@Vpeak and Dfailure are the displace

ment corresponding to the strength of Vy, Vpeak and Vfailure,

respectively. The displacement at failure is dened as the deection when the load dropped to 80 % of the peak load. The secant stiffness at a point of two-third of the measured peak strength is used to idealize the elastoplastic curve that passes through the peak point of the loaddisplacement curve, and the displacement at an intersecting point between the two lines is used to determine the yield point on the curve (Pan and Moehle 1989). The ultimate shear strengths of the UHPFRC beams are reported in Table 4 in terms of the average shear stress which is dened as the peak shear force divided by the beam width and effective depth (vu = Vu/bwd). The ductility (l) is dened as the ability of the structure or parts of it to sustain large deformations beyond the yield point, which is obtained in terms of displacements, as the maximum displacement (Vfailure) divided

with the yield displacement (Dy).

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 exural 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 inuence on the peak strength of UHPFRC beams with shear reinforcement.

Shear reinforcement also had an effect on improvement of deformation capacity. Ductility (l) of beams with shear reinforcement also appeared to be somewhat higher than the control specimen. The ductility of the control specimen was2.04 and in case of the specimens with shear reinforcement (SB2, SB3, and SB4) were between 2.15 and 2.23.

5.3 Strain ResponseFigure 7 shows the strain response of the test specimens. To measure the strains, strain gauges were used. Flexural yielding and shear yielding are dened as the point when the strain of the reinforcing bars reaches a yield strain (=0.002). Also, a concrete failure is dened as a failure at the compression zone of the beam, that is, the compressive strain at the extreme ber of the beam reaches an ultimate limit state of the UHPFRC. To dene the ultimate state of the UHPFRC, the ultimate strain determined using material tests was used. Material tests showed that the ultimate strain of UHPFRC was between 0.003 and 0.0032. The specimen SB1 shows the diagonal tension failure after exural yielding. In this specimen, the exural yielding occurred prior to concrete failure. For SB2 specimen installed shear reinforcement at the spacing of 0.75d, shear reinforcement yielded before exural yielding and concrete failure. In case of the SB3 specimen, a exural-shear failure occurred. The strain of shear reinforcement reaches the yield strain after exural yielding and concrete failure. On the other hand, the SB4 specimen which is over-reinforced beam shows that shear yielding occurred before the exural yielding, but after concrete compressive failure. As shown in Fig. 5, the ultimate failure mode was the compressive concrete failure. In this study, a critical shear crack was not observed during the tests.

1400

SB1

SB2

SB3

SB4

Strength

1200

Peak

1000

peak

Load (kN)

SB2

Failure

800

V V

600

peak

Yielding

0.8

failure peak

400

SB1 SB3

SB4

Ductility

200

failure

0 0 10 20 30 40 50

(a) (b)

Displacement (mm)

failure

Displacement

Fig. 6 Loaddisplacement relationship and denition of yielding point. a Loaddisplacement relationship, b denition of yielding

point and ductility.

International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016) | 183

Table 4 Summary of test results.

Specimens Failure

mode

At initial cracking At yielding At peak At failure Vtest

(MPa)

vtest fcf

Dcr (mm) Vcr (kN) Dy (mm) Vy (kN) D@Vpeak

(mm)

Vpeak (kN) Dfailure

(mm)

Vfailure (kN)

(MPa)

(Dfailure/ Dy)

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 Vcr is the initial cracking strength; Vy, Vpeak, and Vfailure are the yield strength, peak strength, shear strength at failure, respectively. Dcr, Dy,

D@Vpeak, and Dfailure are the measured displacement corresponding to the strength of Vcr, Vy, Vpeak, and Vfailure at the mid-span of the test

specimen, respectively. l is the ductility obtained by the equations of Dfailure/Dy. It should be note that S means the diagonal tension failure; SY is the shear yielding; C is the compression failure of concrete; F is the exural yielding.

1400

0 0.000 0.002 0.004 0.006 0.008

1400

0 0.000 0.002 0.004 0.006 0.008

1200

Longitudinal rebar (L1)

At maximum

Longitudinalrebar (L4) At maximum

At yielding

Longitudinal rebar yielding Stirrup yieldingConcrete crushing

1000

Concrete (C1)

Stirrup (S2)

Load (kN)

800

At yielding

Reinforcing bar yielding

Concrete crushing

Concrete (C1)

Load (kN)

600

400

200

Strain (mm/mm)

(a)

(b)

1400

0 0.000 0.002 0.004 0.006 0.008

1400

0 0.000 0.002 0.004 0.006 0.008

1200

Longitudinal rebar yielding Stirrup yielding

Concrete crushing

1000

At maximum

At yielding

Longitudinalrebar (L2) At maximum

At yielding

Longitudinal rebar yielding Stirrup yieldingConcrete crushing

1200

1000

Stirrup (S3)

Stirrup (S2)

Load (kN)

800

600

Concrete (C7)

600

Concrete (C7)

400

200

Longitudinal rebar (L1)

200

Strain (mm/mm)

Fig. 7 Measured strain values of concrete, longitudinal and shear reinforcement. a SB1, b SB2 (s = 0.75d), c SB3 (s = 0.5d),

d SB4 (s = 0.3d).

6. Discussion of Test Results

6.1 Effect of Shear Reinforcement on Shear Strength

The ultimate shear strength of the UHPFRC beams was dependent on the presence of shear reinforcement. The shear strength of the beams with shear reinforcement was larger than that of control specimen and was improved about 1319 %. However, the effect of the amount of shear reinforcement was insignicant. Although the area of shear reinforcement increases about 55.6 % with respect to the current design codes, the increase of shear strength was only about 2.6 % (in case of SB3 and SB4). In addition, provided that the amount of shear reinforcement decreases about37.5 % regarding the minimum shear reinforcement, deterioration of the shear strength was in about 2.6 %. These

results indicated that the steel bers substantially contribute to enhancement of the shear resistance of UHPFRC beams. The shear contributions of UHPFRC are reported in Table 5, where the shear resistances (Vc, Vfb, and Vs) are obtained using AFGC recommendations. As shown in Table 5, current design guidelines had some conservatism to the test results. Among the component of shear resistance for the beams, shear strength provided by steel bers was determined to be the greatest value regardless of shear reinforcement. Especially, in case of the control specimen, the shear strength was more largely affected by the shear contribution of steel bers (Vtest/Vfb = 1.76) than cement matrix

(Vtest/Vc = 6.2). On the other hand, in case of the specimens

with shear reinforcement, the shear resistances were affected by shear contributions by steel bers and shear reinforcement. As increasing the amount of shear reinforcement,

184 | International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016)

Table 5 Shear contributions of UHPFRC.

Specimens s (mm) Vc (kN) Vfb (kN) Vs (kN) Vtest (kN) Vtest

Vtest Vfb

Vtest Vs

Vtest Vc Vfb

Vtest Vfb Vs

VtestVc Vfb Vs

SB1 76.7 270.9 475.8 6.20 1.76 1.37 1.76 1.37SB2 0.75d 76.7 270.9 102.2 537.3 7.01 1.98 5.26 1.55 1.44 1.19SB3 0.5d 76.7 270.9 153.4 551.7 7.19 2.04 3.60 1.59 1.30 1.10SB4 0.3d 76.7 270.9 255.6 567.0 7.39 2.09 2.22 1.63 1.08 0.94s is the spacing of shear reinforcement; d is the effective depth; Vc, Vfb, and Vs are shear strength provided by cement matrices, steel ber and

shear reinforcement obtained in accordance with AFGC design guidelines (2013); and Vtest is the peak shear force determined from the tests.

shear contribution provided by shear reinforcement decreased. However, if the spacing of shear reinforcement is0.75d (qv = 0.9 %), the effect of shear resistance provided by shear reinforcement decreased while the shear contribution by steel bers increased. If the shear reinforcement provides in about 1.4 % (s = 0.3d), the shear contributions by steel bers and shear reinforcement was very similar (Vtest/Vfb = 2.09 and Vtest/Vs = 2.22) even though the shear

resistance is larger than test results. On the contrary to this, in case of the UHPFRC beam with a shear reinforcement ratio of 0.6 %, the effect of the shear reinforcement was less signicant than other reinforced beams.

From these results, it is found that the steel bers 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 StrengthThe shear strength predictions of FRC beams were evaluated as to whether or not they are applicable to UHPFRC beams. For comparisons, the existing shear strength models for SFRC beams proposed by Sharma (1986), Narayanan et al. (1987), Ashour (1992), ACI 544 (1997), Kwak et al. (2002) were used. They are summarized in Table 6.

Sharma (1986) investigated the effect of steel bers on shear strength performing seven SFRC beams with a compressive strength of about 45 MPa. From their shear tests, it is found that steel bers 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 4079.5 MPa regarding shear span to depth ratio (a/d), longitudinal and shear reinforcement, presence of shear reinforcement, and the ber factor (F = (L/D)qfdf). Based on the observations of rst cracks in shear, empirical shear strength equation was suggested for the evaluation of cracking shear strength. Ashour et al. (1992) tested eighteen HSFRC beams (fc0 = 93 MPa) with or without shear reinforcement. Test variables were shear span-to-depth (a/d), longitudinal reinforcement ratio, ber volume fraction. They found that shear strength of beams increase with an increase of ber 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

Table 6 Existing shear strength models.

Authors Shear strength models

Sharma (1986) vu kf 0t d=a

0:25where k = 2/3; a/d is the shear span-to-depth ratio; ft0 = 0.17Hfcf, if

the tensile strength is unknown, and fcf is the concrete cylinder

compressive strength Narayanan et al. (1987) vu e 0:24fspfc 80q da

where fspfc is the computed split-cylinder strength of ber concrete

(= fcuf/(20 - HF) ? 0.7 ? 1.0HF); q is the longitudinal

reinforcement ratio; F is the ber factor (=(Lf/Df)Vfdf; e is the arch action factor, 1.0 for a/d [ 2.8 and 2.8d/a for a/d B 2.8; fcuf is the cube strength of ber concrete; Vf is the ber volume fraction; df is a

bond factor, 0.5 for round bers, 0.75 for crimped bers, and 1.0 for

indented bers; vb is equal to the equations of 0.41sF, and s is the

average ber matrix interfacial bond stress, taken as 4.15 MPa Ashour et al. (1992) For a/d C 2.5 vu 2:11

fcf

1=3

3 7F

q da

Kwak et al. (2002) vu 3:7ef 2=3spfc q da

1=30:8v

where e is the arch action factor, 1 for a/d [ 3.4, and 3.4d/a for a/

d B 3.4

International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016) | 185

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 ber volume fraction (Vf = 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).

As shown in Table 7, the existing shear strength equations for SFRC beams were very conservative compared to the experimental data. This means that they would be unreasonable to predict the shear strength of the UHPFRC beams with a compressive strength more than 160 MPa. On the other hand, AFGC recommendations (2013) showed a relatively accurate evaluations of UHPFRC beams with and without shear reinforcement.

6.3 Steel Fibers as Shear Reinforcement According to ACI 318-14 (2014), when the normalized shear strength (vtest/Hfc0) dened as divided the average

shear stress by the square root of the compressive strength is greater than 0.29Hfc0 (MPa), the steel bers can use as the shear reinforcement for SFRC beam (fc0 B 40 MPa,

d B 600 mm). Parra-Montesinos found that the shear strength of SFRC beam strength was larger than 0.3Hfc0

(MPa) when ber content (Vf) is equal to or greater than0.75 %.

Normalized shear strengths were evaluated whether or not

current design codes are applicable to UHPFRC beams with shear reinforcement. As reported in Table 4, normalized shear strengths of all the specimens with Vf = 1.5 % were larger than 1.12Hfc0 (MPa) regardless of the presence of shear reinforcement and its spacing as shown in Fig. 8.

These results indicate that if the rectangular beam contains UHPFRC with ber 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 0.5/Vc. Also, CSA A23.3-04 (2004) suggests its distance as 0.7dv, where dv 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

In this study, shear tests on simply supported UHPFRC rectangular beam sections with and without shear reinforcement were carried out to investigate the shear behaviour considering the spacing of shear reinforcement. The main test parameter was the spacing of shear reinforcement. Findings obtained through the experiments are as follows:

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.

2.0

f V

' 166.9MPa; 1.5%

= =

1.5

v test/ f' c

SB1 SB2 SB3 SB4

1.0

v f

/ 1.12

test c

(UHPFRC)

0.5

v f

/ 0.29

test c

(FRC, ACI 318)

0.0

Specimens

Fig. 8 Lower bound of normalized shear strength for

UHPFRC.

Table 7 Comparison between the predicted strength and test data.

Specimens Sharma (1986) Narayanan and

Darwish (1987)

Ashour et al. (1992) Kwak et al. (2002) AFGC (2013)

SB1 2.79 3.71 6.30 3.12 1.37 SB2 2.09 2.56 3.58 2.27 1.19 SB3 2.28 2.86 4.18 2.49 1.10 SB4 2.46 3.15 4.83 2.71 0.94 Mean 2.41 3.07 4.72 2.65 1.15 SD 0.30 0.49 1.17 0.36 0.08

186 | International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016)

American Association of State Highway and Transportation

Ofcials. (2004). AASHTO LRFD Bridge Design Specication (3rd ed.). Washington, DC: AASHTO.

Ashour, S. A., Hasanain, G. S., & Wafa, F. F. (1992). Shear behavior of high-strength ber reinforced concrete beams. ACI Structural Journal, 89(2), 176184.

Association Franaise du Gnil Civil (AFGC). (2013). Btons brsultra-hautes performances, Association Franaise du Gnil Civil.

ASTM A370-14. (2014). Standard test methods and denitions for mechanical testing of steel products. West Conshohocken, PA: ASTM International.

ASTM C39/C39M-05. (2005). Standard test method for compressive strength of cylindrical concrete specimens. West Conshohocken, PA: ASTM International.

Baby, F., Marchand, P., & Toutlemonde, F. (2014). Shear behavior of ultrahigh performance ber-reinforced concrete beams. I: Experimental investigation. Journal of Structural Engineering ASCE, 140(5), 04013111.

CSA A23.3-04. (2004). Design of concrete structures. Rexdale,

ON: Canadian Standard Association.

EN 1992-1-1. (2004). Eurocode 2: Design of Concrete StructuresPart 1-1: General Rules and Rules for Buildings. British Standards Institution.

Ezeldin, S., & Balaguru, P. N. (1997). Normal- and high-strength ber-reinforced concrete under compression. ACI Material Journal, 94(4), 286290.

Fanella, D. A., & Naaman, A. E. (1985). Stressstrain properties of ber reinforced mortar in compression. ACI Journal, 82(4), 475483.

Farhat, F. A., Nicolaides, D., Kanellopoulos, A., & Karihaloo,B. L. (2007). High performance ber-reinforced cementitious composite (CARDIFRC)performance and application to retrotting. Engineering Fracture Mechanics, 74, 151167.

Japan Society of Civil Engineers (JSCE). (2004). Recommendations for Design and Construction of Ultra-High Strength Fiber Reinforced Concrete Structures, draft. Khuntia, M., Stojadinovic, B., & Goel, S. C. (1999). Shear strength of normal and high-strength ber reinforced concrete beams without stirrups. ACI Structural Journal, 96(2), 282289.

Korea Concrete Institute. (2012). Design recommendations for ultra-high performance concrete (K-UHPC), KCI-M-12-003, Korea (in Korean).

Kwak, Y. K., Eberhard, M. O., Kim, W. S., & Kim, J. B.

(2002). Shear strength of steel ber-reinforced concrete beams without stirrups. ACI Structural Journal, 99(4), 530538.

Li, V. C., Ward, R., & Hamza, A. M. (1992). Steel and synthetic bers as shear reinforcement. ACI Materials Journal, 89(5), 499508.

Mansur, M. A., Ong, K. C. G., & Paramsivam, P. (1986). Shear strength of brous concrete beams without stirrups. Journal of Structural Engineering ASCE, 112(9), 20662079. MC2010. (2012). b Model Code for Concrete Structures 2010, fdration internationale du bton, Lausanne, Switzerland: Ernst & Sohn.

International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016) | 187

2. The steel bers 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 1319 %. In addition, the steel bers 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.

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 Access

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =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.

References

ACI Committee 318. (2014). Building Code Requirements for Structural Concrete (ACI 318M-14) and Commentary (318R-14). Farmington Hills, MI: American Concrete Institute.

ACI Committee 544. (1988). Design considerations for steel ber reinforced concrete. ACI Structural Journal, 85(5), 118.

Alaee, F. J., & Karihaloo, B. L. (2003). Retrotting of reinforced-concrete beams with CARDIFRC. Journal of Composites for Construction ASCE, 7(3), 174186.

Meda, A., Mostosi, S., & Riva, P. (2014). Sehar strengthening of reinforced concrete beam with high-performance ber-reinforced cementitious composite jacketing. ACI Structural Journal, 111(5), 10591067.

Narayanan, R., & Darwish, I. Y. S. (1987). Use of steel bers as shear reinforcement. ACI Structural Journal, 84(3), 216227.

Noghabai, K. (2000). Beams of brous concrete in shear and bending: Experiment and model. Journal of Structural Engineering ASCE, 126(2), 243251.

Pan, A., & Moehle, J. P. (1989). Lateral displacement ductility of reinforced concrete at plates. ACI Structural Journal, 86(3), 250258.

Park, S. H., Kim, D. J., Ryu, G. S., & Koh, K. T. (2012). Tensile

Behavior of ultra high performance hybrid ber reinforced concrete. Cement and Concrete Composites, 34, 172184. Parra-Montesinos, G. J. (2006). Shear strength of beams with deformed steel bers. Concrete International, 28(11), 5766.

Rossi, P., Arca, A., Parant, E., & Fakhri, P. (2005). Bending and compressive behaviors of a new cement composite. Cement and Concrete Research, 35, 2733.

Sharma, A. K. (1986). Shear strength of steel ber reinforced concrete beams. ACI Journal, 83(4), 624628.

Voo, Y. L., Poon, W. K., & Foster, S. J. (2010). Sheear strength of steel ber-reinforced ultrahigh-performance concrete beams without stirrups. Journal of Structural Engineering ASCE, 136(11), 13931400.

Wafa, F. F., & Ashour, S. A. (1992). Mechanical properties of high-strength ber reinforced concrete. ACI Materials Journal, 89(5), 440455.

Wille, K., Kim, D. J., & Naaman, A. E. (2011a). Strain hardening UHP-FRC with low ber contents. Materials and Structures, 44, 583598.

Wille, K., Naaman, A. E., & Parra-Montesinos, G. J. (2011b). Ultra-high performance concrete with compressive strength exceeding 150 MPa (22 ksi): A simpler way. ACI Materials Journal, 108(6), 4654.

188 | International Journal of Concrete Structures and Materials (Vol.10, No.2, June 2016)

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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.

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Title

Shear Tests for Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) Beams with Shear Reinforcement

Author

Lim, Woo-young; Hong, Sung-gul

Pages

177-188

Publication year

2016

Publication date

May 2016

Publisher

Springer Nature B.V.

ISSN

19760485

e-ISSN

22341315

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/s40069-016-0145-8

ProQuest document ID

1797073025

The Author(s) 2016

Shear Tests for Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) Beams with Shear Reinforcement

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