A comparative study of flexural and shear behavior of ultra-high-performance fiber-reinforced concrete beams

Abstract

In this research, the flexural and shear behavior of five locally developed ultra-high-performance fiber-reinforced concrete beams was experimentally investigated. Four-point loading tests were carried out on concrete specimens which were further compared with five normal-strength concrete beams constructed at the laboratory. The objective of this study is to assess the flexural and shear behavior of ultra-high-performance fiber-reinforced concrete beams and compare them with that of normal-strength beams and available equations in the literature. Results indicate underestimation of shear (up to 2.71 times) and moment capacities (minimum 1.27 times, maximum 3.55 times) by most of the equations in beams with low-reinforcement ratios. Finally, results reveal that the experimental flexural and shear capacities of ultra-high-performance fiber-reinforced concrete specimens are up to 3.5 times greater than their normal-strength counterpart specimens.

Keywords

bending (flexural) failure normal-strength concrete shear failure ultra-high-performance fiber-reinforced concrete

Introduction

Vulnerability of the aging infrastructure to durability concerns has in recent years led to a growing interest in advanced materials such as the ultra-high-performance fiber-reinforced concrete (UHPFRC) with its higher compressive and tensile strengths, ductility, and durability (Graybeal, 2006). UHPFRC is defined by its compressive strength of above 150 MPa and its internal fiber reinforcement to guarantee non-brittle behavior as per the Association Française de Génie Civil (De travail BFFUP, AFGC Groupe, 2002).

Graybeal (2008) and Chen and Graybeal (2011) conducted experimental and numerical studies on flexural behavior of full-scale prestressed ultra-high performance concrete (UHPC) I- and Pi-girders. Yang et al. (2011) studied the effects of placing methods and steel fiber ratios of less than 0.02 on the behavior of UHPFRC and reported multi-cracking and localized macrocrack. Numerical investigations on flexural behavior of UHPC beams with straight steel fibers of various lengths and volumetric contents (Yoo et al., 2016) showed the effect of long fibers on improving flexural performance, while their orientation does not compare well to short fibers. Negligible effect of fiber length on initial and descending slopes of the flexural load–cracking mouth opening displacement (CMOD) curve was also observed. Yoo et al. (2017) also reported better flexural performance of long fibers; however, the use of long and short hybrid fibers deteriorated cracking behavior in some cases. In testing the flexural behavior of full-scale UHPC girders, Graybeal (2008) observed higher capacities than their conventional counterparts with similar cross-sections.

The underlying criterion sought in UHPC construction is to achieve a homogeneous high-density mix design by means of reducing fine cracks. The outstanding performance of UHPC as compared to NHC or even high-strength concrete is mostly attributed to its much denser hardened cement matrix with almost no capillaries (Graybeal, 2008). UHPC is generally made with the addition of microsilica, reduction of water-to-cement ratio to less than 0.2, application of superplasticizers, optimization of grain-size distribution to achieve maximum density, addition of a particular amount of steel fiber to improve ductility, and providing better curing conditions (Richard and Cheyrezy, 1995; Sobolev, 2004; Wille et al., 2011).

Pourbaba et al. (2018a) introduced a new mix design for UHPFRCs using the indigenous fine materials, and investigated the age-dependent properties of UHPFRC specimens. Another mix design was also introduced by Khaloo et al. (2017). Khalil and Tayfur (2013) conducted some research on bending capacity of UHPC beams. They tested 11 UHPC beams with different fiber contents and shapes. Results revealed that steel fibers significantly contribute to the increase in bending capacity up to 27% and 23% for specimens with 1% waved and hooked steel fibers, respectively. Owing to the well-established fact that the behavior of UHPC, when exposed to high creep strains and/or service loads in structural elements, is unpredictable to an extent, Barbos (2015) conducted experiments on the behavior of UHPC subjected to long-term loads; a 70% reduction of creep coefficient was reported with the use of 2.55% steel fiber content. Yang et al. (2010) conducted a comparative analysis of the bending behavior of UHPCs and design code requirements. Based on their study, the layout and orientation of fibers were influenced by the concreting method. Another observation was the ductile post-cracking behavior of UHPC, meanwhile keeping crack widths within reasonable limits.

This study aims to experimentally investigate the flexural and shear behavior of UHPCs and compare them with design equations. Also, in order to interpret results easily and make an analogy, normal-strength beams with similar dimensions to UHPCs were constructed and tested under similar conditions.

Experimental program

In this study, the generic UHPC mix developed by Pourbaba et al. (2018a) was used, with similar material contents to the proprietary commercial product Ductal^® (Table 1) and with a water-to-cement ratio of 0.184. Chemical and physical properties of microsilica are presented in Table 2. A mixture of water and ice was used to avoid overheating. Polycarboxylate ether-based superplasticizers were used (Wille et al., 2011). Straight fibers were used with a length of 13 mm, a diameter of 0.16 mm, a density of 7.8–8.0 g/cm³, and a tensile strength of 2700 MPa. Fine river sand with a maximum size of 1.1 mm was used, well within the range of standard sand’s continuous curve. Table 3 presents chemical composition of quartz powder also used in this study. Use of natural pozzolans provides several benefits; it reduces hydration temperature, increases ultimate capacity, decreases permeability, increases strength against sulfate invasion, and, finally, reduces the alkaline activity of silica. Finally, AIII reinforcing bars (DIN 488-1, 1984) were used with yield and ultimate strengths of 400 and 600 MPa, respectively.

Table 1.

Mix design of ultra-high performance concrete (UHPC) (Pourbaba et al., 2018a).

Materials	Mix proportions (kg/m³)
Portland cement	695
Fine sand	992
Microsilica	228
Quartz powder	206
Superplasticizer	60
Steel fiber	151
Water	167

Table 2.

Chemical and mechanical properties of microsilica.

Property	%	Mechanical properties
SiO₂	85	–
Fe₂O₃	2	–
CaO	1.5	–
Al₂O₃	1	–
MgO	2	–
C	3	–
Loss on ignition (LOI)	3.5	–
Moisture	1	–
Size	–	Less than 1 µm
Shape	–	Solid spherical particles
Specific surface area (m²/kg)	–	14,000–20,000
Density of a batch (kg/m³)	–	200–300
Specific weight (kg/m³)		400–600

Table 3.

Chemical composition of quartz powder.

Property	%
SiO₂	21.16
Fe₂O₃	3.9
CaO	63.52
Al₂O₃	4.22
MgO	1.52
K₂O	0.59
Na₂O	0.4
Loss on ignition (LOI)	1.32

Five UHPC (B1–B5) and five normal-strength concrete (NSC) beams (B′1–B′5) of the same size were prepared (Table 4 and Figures 1 to 3). Reinforcement ratios were chosen to ensure the beams are not shear-critical. The mix procedure followed recommendations of Wille et al. (2011) and Russell and Graybeal (2013). Three 100-mm cubic samples were taken from each mix for the compressive strength tests after 28 days of submersion in water tank under laboratory conditions. As per De Larrard et al. (1994), a conversion factor of 0.95 was used to obtain the cylindrical compressive strength of UHPFRC. The average compressive strengths of UHPFRC and NSC were 135 and 32 MPa, respectively.

Table 4.

Test matrix.

UHPC beams	NSC beams	Dimensions (mm)	Longitudinal reinforcement	Reinforcement ratio
B1	B′1	558 × 152 × 76	3 Φ 6	0.96
B2	B′2	558 × 152 × 76	3 Φ 8	1.74
B3	B′3	558 × 152 × 76	3 Φ 10	2.77
B4	B′4	558 × 127 × 203	3 Φ 8	0.64
B5	B′5	558 × 127 × 203	3 Φ 10	1.01

UHPC: ultra-high performance concrete; NSC: normal-strength concrete.

Figure 1.

Cross-section of test specimens (units: mm).

Figure 2.

Concrete molds before casting.

Figure 3.

Concrete molds after casting.

All specimens were tested in four-point bending, as shown in Figures 4 and 5. The load was applied in increments of 10 kN. Linear variable differential transformers (LVDTs) were used to measure mid-span displacement. Loading and crack propagation of specimens B1 to B5 are shown in Figures 6 to 10. Failure modes of shallow and deep UHPC and NSC beams are shown in Figures 11 to 14.

Figure 4.

Loading of specimens in the laboratory.

Figure 5.

Schematic loading pattern of beams (units: mm).

Figure 6.

Loading pattern and propagation of cracks in specimen B1.

Figure 7.

Loading pattern and propagation of cracks in specimen B2.

Figure 8.

Loading pattern and propagation of cracks in specimen B3.

Figure 9.

Loading pattern and propagation of cracks in specimen B4.

Figure 10.

Loading pattern and propagation of cracks in specimen B5.

Figure 11.

Failure of specimens B1 to B3.

Figure 12.

Failure of specimens B1 and B5.

Figure 13.

Failure of specimens B′1 to B′3.

Figure 14.

Failure of specimens B′3 and B′5.

Theoretical bending and shear capacity

UHPC beams

Based on the research by Khalil and Tayfur (2013) and Oh (1992), the nominal bending capacity of UHPC beams is calculated as follows

M_{n} = A_{s} F_{y} (d - \frac{a}{2}) + σ_{t} b (h - c) \frac{(h + c - a)}{2}

(1)

where c = depth of neutral axis, calculated as

c = \frac{(A_{s} F_{y} + σ_{t} bh)}{(0.85 f_{cf}' β_{1} b + σ_{t} b)}

(2)

The tensile capacity of a fiber-reinforced concrete regardless of the stresses sustained by the concrete is calculated as

σ_{t} = 2 η_{0} η_{b} η_{l} V_{f} τ_{f} (\frac{l_{f}}{d_{f}})

(3)

where $η_{0} =$ fiber orientation factor, equal to 0.41 for concrete with uniform fiber dispersion; $η_{b} =$ bond efficiency factor between steel fibers and concrete, equal to 1 and 1.2 for straight and waved or hooked fibers, respectively; and $η_{l}$ accounts for fiber length, calculated as

η_{l} = 1 - \frac{\tanh (\frac{β . l_{f}}{2})}{\frac{β . l_{f}}{2}}

(4)

where $l_{f} =$ fiber length, which is 13 mm in this study, and $β$ calculated as

β = \sqrt{\frac{2 π G_{m}}{E_{f} A_{f} \ln (\frac{s}{r_{f}})}}

(5)

where $G_{m}$ = shear modulus of concrete (21 GPa), $E_{f}$ = elastic modulus of steel (200 GPa), $A_{f}$ = cross-sectional area of steel fiber (0.02 mm²), s = average spacing between steel fibers

s = 25 \sqrt{\frac{l_{f}}{V_{f} d_{f}}}

(6)

where $d_{f}$ = diameter (0.16 mm), $r_{f}$ = radius (0.08 mm), and $V_{f}$ = volumetric fraction of steel fibers, which can be determined as 1.92, based on the mass content and volumetric fraction of steel fibers as 7.8 g/cm³ and 7.02%, respectively. $τ_{f}$ is the bond stress between steel fibers and concrete, calculated as

τ_{f} = 0.66 \sqrt{f_{c}'}

(7)

c = \frac{a}{β_{1}}

(8)

where a = depth of the equivalent rectangular stress block which is schematically depicted in Figure 15 and $β_{1}$ = 0.65 for concrete strength of 135 MPa in this study, and typically decreases linearly at a rate of 0.07 for every 7 MPa increase in concrete strength above 30 MPa, but shall not be taken less than 0.65. Similarly, based on the work by Henager and Doherty (1976), ACI 544.4R-88 (1988) proposed a method for the calculation of the flexural capacity of fiber-reinforced concretes (FRCs) with a rectangular section

M_{n} = A_{s} F_{y} (d - \frac{a}{2}) + σ_{tu} b (h - e) \frac{(h + e - a)}{2}

(9)

e = \frac{(ε_{s} (fibers) + 0.003) c}{0.003}

(10)

σ_{tu} = \frac{0.00772 ρ_{f} F_{be} l}{d_{f}}

(11)

Figure 15.

Modified strain–stress–force distribution of reinforced UHPC beam (Henager and Doherty, 1976; Khalil and Tayfur, 2013; Hossain, 2014).

Furthermore, another method for the calculation of the flexural capacity has been proposed by the Federal Highway Administration (Aaleti et al., 2013); an approach based on equilibrium and strain compatibility concepts is provided and the flexural capacity of UHPC is calculated based on whether the maximum tensile or compressive strain limit is reached. At maximum tensile strain, the following equation is proposed

M_{n} = f_{tu} b (h - c) (\frac{3 h - c}{6}) + ρ_{s} f_{y} bh (d - \frac{c}{3})

(12)

c = (\frac{ρ_{s} f_{y} + f_{tu}}{f_{tu} + 0.0035 E_{UHPC} (\frac{c}{h - c})}) h

(13)

where the modulus of elasticity is calculated below, as proposed by Haber et al. (2018), although alternative formulae available in the literature may be used

E_{UHPC} = 3775 \sqrt{f_{c}'}

(14)

and $f_{tu}$ is calculated below as proposed by Wille et al. (2014)

f_{tu} = 7.5 + \frac{α τ V_{f} l_{f}}{d_{f}}

(15)

where $α τ$ = 0.03 for straight fibers, and accounts for the group effect of fibers, fiber orientation, and bond behavior before and after cracking. Imam et al. (1995) proposed a modified method of ACI 544.4R-88 (1988) for the flexural capacity and ultimate shear strength, $v_{u}$ , of steel fibers

M_{fl} = \frac{1}{2} ρ f_{y} b d^{2} (2 - η) + 0.83 Fb d^{2} (0.75 - η) (2.15 + η)

(16)

η = \frac{a}{d} = \frac{ρ f_{y} + 2.32 F}{0.85 f_{c}' + 3.08 F}

(17)

F = (\frac{L_{f}}{d_{f}}) V_{f} D_{f}

(18)

It was also reported by Imam et al. (1995) that based on the studies performed on steel fiber–reinforced concrete (SFRC) beams without stirrup, a beam may fail in shear prior to reaching its flexural capacity. Therefore, and in spite of the fact that the UHPFRC beams in this study have failed in bending rather than shear, consideration of shear–flexure interaction may also be useful since there are reports in the literature where SFRC beams have failed in shear and not flexure (Amin and Foster, 2016; Aoude et al., 2012; Conforti et al., 2013; Dinh et al., 2010; Rosenbusch and Teutsch, 2003). In this regard, Imam et al. (1995) proposed an equation to estimate the relative flexural capacity of SFRCs without stirrups

M_{u} = 0.6 b d^{2} ψ \sqrt[3]{ω} [f_{c}'^{0.44} (\frac{a'}{d}) + 275 \sqrt{\frac{ω}{{(\frac{a'}{d})}^{3}}}]

(19)

ω = ρ (1 + 4 F)

(20)

ψ = \frac{1 + \sqrt{(\frac{5.08}{d_{a}})}}{\sqrt{1 + (\frac{d}{25 d_{a}})}}

(21)

where $d_{a}$ = maximum aggregate size, which is 1 and 15 mm for UHPC and NSC, respectively, and $a ’$ is the shear span.

Imam et al. (1995) carried out statistical analyses based on test results of 16 high-strength beams with and without fibers as well as available data in the literature to propose the following equation for the shear strength of high-strength SFRC

V_{u} = 0.6 bd ψ \sqrt[3]{ω} [f_{c}'^{0.44} + 275 \sqrt{\frac{ω}{{(\frac{a'}{d})}^{5}}}]

(22)

RILEM TC 162-TDF (2003) proposed a formula for the shear capacity of SFRC

V_{u} = V_{cd} + V_{fd} + V_{wd}

(23)

V_{cd} = [0.12 k {(100 ρ f_{c}')}^{1 / 3} + 0.15 σ_{cp}] b_{w} d

(24)

V_{fd} = 0.7 k_{f} k τ_{f} b_{w} d

(25)

k = 1 + \sqrt{\frac{200}{d}} \leq 2.0

(26)

τ_{fd} = 0.12 f_{Rk, 4}

(27)

where $σ_{cp}$ = zero as no axial force acts on the cross-section; $f_{Rk, 4}$ = 18 MPa, based on previous work by the authors (Pourbaba et al., 2018b); $k_{f}$ = factor that accounts for the contribution of flanges in a T-section to shear resistance; and $τ_{fd}$ = design value of the increase in shear strength due to steel fibers.

NSC beams

Analyzing the fracture and failure modes of NSC beams reveals that they fail in shear. In line with the aim of this study to make comparable values of moment and shear capacities between two beam types, both moment and shear capacity values were determined according to ACI 318-14 (2014) and the safety factors for both cases were determined based on $M_{\exp} / M_{n}$ and $V_{\exp} / V_{n}$ ratios. Nominal moment capacity of NSC beams is given as (ACI 318-14)

M_{n} = ρ f_{y} b d^{2} (1 - 0.59 ρ \frac{f_{y}}{f_{c}'})

(28)

where $M_{n}$ = nominal bending capacity of the beam, b = width of the beam, d = depth of tension steel, $ρ$ = reinforcement ratio, $f_{y}$ = yield strength of steel (400 MPa), and $f_{c}'$ = compressive strength of concrete. The nominal shear capacity of NSC beams is given as (ACI 318-14)

V_{c} = (\sqrt{f_{c}'} + 120 ρ_{w} \frac{V_{u} d}{M_{u}}) \frac{b_{w} d}{7} \leq 0.3 \sqrt{f_{c}'} b_{w} d

(29)

where $V_{c}$ = nominal shear strength, $V_{u}$ = factored shear force, $M_{u}$ = factored moment, $M_{n}$ = nominal flexural strength, $b_{w}$ = width of the web, $V_{wd}$ = shear strength of the transverse steel, and $ρ_{w}$ = reinforcement ratio with respect to the web. $V_{c}$ shall be taken less than 1.0 to limit $V_{c}$ in the proximity of bending moments’ contra flexure points. If the minimum value was taken, $M_{u}$ would be equivalent to $V_{u} d$ . Imam et al. (1995) also proposed an equation for the ultimate shear strength of NSC beams

V_{u} = 0.54 bd ψ \sqrt[3]{ρ} [\sqrt{f_{c}'} + 249 \sqrt{\frac{ρ}{{(\frac{a'}{d})}^{5}}}]

(30)

Discussions of results

In specimens B1–B3, flexural cracks were developed within the maximum bending region and were propagated toward upper parts of the beam up to failure. In specimens B4 and B5, despite the increased height, the dominant failure mode was flexure. In normal-strength beams, cracks were initially developed at regions near to the support where shear forces were notable. Subsequently, inclined cracks were developed within mid-parts of the beam until failure. Near failure, spalling of concrete occurred and reinforcements were completely exposed. According to Figure 16, in small UHPFRC specimens, an increase in reinforcement ratio led to an increase in peak load values and a decrease in displacement values. This observation was not totally true for NSC beams or beams with a larger cross-section (Figures 17 to 19).

Figure 16.

Force-displacement curves of specimens B1–B3.

Figure 17.

Force-displacement curves of specimens B4–B5.

Figure 18.

Force-displacement curves of specimens B′1–B′3.

Figure 19.

Force-displacement curves of specimens B′4–B′5.

Table 5 summarizes the experimental and theoretical values of moment and shear capacities of UHPFRC specimens. It can be seen that the model proposed by Khalil and Tayfur (2013) and Oh (1992) give better results than the other proposed equations; in all the models, the ratios of experimental values to predictions by equations are significant (up to 3.55 times) for low-reinforcement ratios (i.e. specimen B4). In small specimens, no particular trend was observed for the discussed ratios when the reinforcement ratio increased from 0.96% to 1.74%. However, the converse was true when the reinforcement ratio increased from 1.74% to 2.77%. The difference between the predictions of $M_{u}$ and $V_{u}$ (proposed by Imam et al. (1995)) and RILEM TC 162-TDF (2003) and the experimental values increase with the increase in the reinforcement ratio for small specimens. It is also worth mentioning that Imam et al. (1995) investigated SFRC beams with shear span to effective depth, $(a' / d)$ ratios greater than 1.5, reinforcement ratios greater than 1.87%, and fiber ratios less than the 1.5% by volume. It can be seen that in specimens B4 and B5 where the $(a' / d)$ ratio is less than unity, overestimations up to 51% between theoretical and experimental values are observed. This can also be further clarified by equations (19) and (22), where the power of $(a' / d)$ is 3 and 5, respectively. Moreover, the direct correlation of the moment capacity and shear capacity with $d^{2}$ and d, respectively, justifies the significantly different moment and shear capacities in relation to corresponding experimental values and that the effect of $(a' / d)$ is overestimated.

Table 5.

Experimental and theoretical moment and shear capacities in ultra-high-performance fiber-reinforced concrete specimens.

Specimen ID	Present study		Khalil and Tayfur (2013), Oh (1992)	ACI 544.4R-88 (1988)	Aaleti et al. (2013)	Imam et al. (1995)		RILEM TC 162-TDF (2003)		Experimental-to-theoretical ratios^a
Specimen ID	$M_{\exp} (kN . m)$	$V_{\exp} (kN)$	$M_{n} (kN . m)$	$M_{n} (kN . m)$	$M_{n} (kN . m)$	$M_{fl} (kN . m)$	$M_{u} (kN . m)$	$V_{n} (kN)$	$V_{n} (kN)$	$M_{\exp} / M_{n}$	$M_{\exp} / M_{n}$	$M_{\exp} / M_{n}$	$M_{\exp} / M_{fl}$	$M_{\exp} / M_{u}$	$V_{\exp} / V_{n}$	$V_{\exp} / V_{n}$
B1	5.56	36.57	5.40	1.94	4.72	2.43	6.66	43.78	37.42	1.03	2.87	1.18	2.29	0.83	0.84	0.98
B2	8.41	55.30	6.65	3.34	6.36	3.80	6.48	42.58	39.05	1.26	2.52	1.32	2.21	1.30	1.30	1.42
B3	10.04	64.56	7.91	4.78	8.09	4.93	5.85	38.51	38.52	1.27	2.10	1.24	2.04	1.72	1.68	1.68
B4	39.11	257.30	31.89	11.03	25.78	15.26	80.01	526.38	95.83	1.23	3.55	1.52	2.56	0.49	0.49	2.68
B5	40.91	269.14	37.34	17.00	28.55	21.07	78.31	515.22	99.17	1.10	2.41	1.43	1.94	0.52	0.52	2.71

Values in the denominator of ratios in columns 11–17 correspond to the values in columns 4–10.

Furthermore, Table 6 shows the experimental and theoretical values of NSC specimens. Similar to UHPFRC specimens, the conservative prediction of capacities with respect to low-reinforcement ratios is also observed in normal-strength specimens. With respect to shear strength, increasing the reinforcement ratio reduces the difference between experimental and theoretical values. Besides, increasing the reinforcement ratio in specimens B4 and B5 reduces the difference between experimental and theoretical values in both moment and shear capacities.

Table 6.

Experimental and theoretical moment and shear capacities in normal-strength concrete specimens.

Specimen ID	Present study		Imam et al. (1995)	ACI 318-14 (2014)		Experimental-to-theoretical ratios
Specimen ID	$M_{\exp} (kN . m)$	$V_{\exp} (kN)$	$V_{n} (kN)$	$M_{n} (kN . m)$	$V_{n} (kN)$	$V_{\exp} / V_{n}$	$M_{\exp} / M_{n}$	$V_{\exp} / M_{n}$
B′1	2.99	19.67	11.72	1.83	7.68	1.68	1.63	2.56
B′2	3.04	22.61	15.18	3.00	7.97	1.49	1.01	2.84
B′3	3.44	19.98	17.01	3.81	8.36	1.17	0.90	2.39
B′4	11.20	73.71	116.00	10.57	22.01	0.64	1.06	3.35
B′5	11.90	78.32	160.80	15.96	23.63	0.49	0.75	3.31

Furthermore, comparison of experimental values for UHPFRC and normal-strength specimens shows significant differences up to 3.5 times for both moment and shear capacities.

Moreover, Table 7 shows the peak load fracture energy of UHPFRC and NSC specimens. For the same number of reinforcements, it can be seen that in UHPFRC specimens (i.e. B2 and B4), increasing the beam depth from 76 to 203 mm increases the peak load and fracture energy values by about 3.65 and 1.03 times, respectively. The difference remains relatively the same for the peak load value (3.2 times) but differs significantly for the fracture energy (2.54 times) for a larger diameter of reinforcements (B3 and B5 specimens).

Table 7.

Peak load and fracture energy of test specimens.

Specimen	Peak load (kN)	$G_{f - total}$ (N mm)	$G_{f - post peak}$ (N/mm)
B1	73.13	982.50	85.05
B2	110.61	1169.42	101.23
B3	129.12	1067.56	92.41
B4	514.61	2374.11	92.09
B5	538.27	3782.05	146.70
B′1	39.33	166.08	14.38
B′2	45.22	166.27	14.40
B′3	39.95	103.42	8.95
B′4	147.42	1124.11	43.60
B′5	156.64	673.29	26.11
Average (B1–B3)	104.29	1073.16	92.90
Average (B4 and B5)	526.44	3078.08	119.39
Average (B′1–B′3)	41.50	145.26	12.58
Average (B′4 and B′5)	152.03	898.70	34.86

In addition, on average, UHPFRC specimens sustain higher loads and have higher fracture energies than their normal-strength counterparts by about 1.50 and 6.40 times for specimens with small cross-section and by about 2.46 and 2.42 for specimens with a large cross-section.

Conclusion

The flexural and shear behavior of UHPFRC beams was experimentally investigated and compared to NSC beams and available predictive equations in the literature. The following conclusions may be drawn from this study:

Analysis of failure modes and crack propagation patterns indicate that while UHPC beams fail in bending, the behavior of NSC beams is governed by shear.

Comparison of experimental values with theoretical ones is indicative of conservative estimation in most models with respect to low-reinforcement ratios.

Special focus should be given to deep beams with $(a' / d)$ less than 1.0 with respect to moment and shear capacities since the available models do not provide reasonable results.

The flexural and shear strengths of UHPFRC specimens are up to 3.5 times greater than their NSC counterparts.

On average, UHPFRCs sustain higher loads and have higher fracture energies than their NSC counterparts by about 1.50 and 6.40 times for small sections and by about 2.46 and 2.42 for large sections, respectively.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Masoud Pourbaba

Amir Mirmiran

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