a comprehensive experimental study

Cracking behavior in reinforced concrete members with steel fibers: Acomprehensive experimental study

Giuseppe Tiberti, Fausto Minelli ⁎, Giovanni Plizzari

University of Brescia, DICATAM— Department of Civil Engineering, Architecture, Land, Environment and Mathematics, Italy

a b s t r a c ta r t i c l e i n f o

Article history:

Received 28 December 2013

Accepted 24 October 2014

Available online xxxx

Keywords:

Tensile properties (C)

Fracture toughness (C)

Durability (C)

Fiber reinforcement (E)

Crack control

The addition of fibers in concrete determines a cracking phenomenon characterized by narrower andmore close-

ly spaced cracks, with respect to similar members without fibers. Fiber Reinforced Concrete (FRC) may signifi-

cantly improve the tension stiffening into the undamaged portions of concrete among cracks, and, in addition,

may provide noticeable residual stresses at a crack due to the bridging effect provided by its enhanced toughness.

This paper aims at further investigating the ability of fibers in controlling cracks by discussing more than ninety

tension tests on Reinforced Concrete (RC) prisms, carried out at the University of Brescia, having different sizes,

reinforcement ratios, amount of fibers and concrete strengths. In particular the influence of FRC in reducing the

crack spacing and the crack width is evaluated as a function of the FRC toughness.

Finally, the most recent available models for predicting the crack spacing of FRC composites are evaluated and

critically discussed.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The employment of Fiber Reinforced Concrete (FRC) is becoming

more andmore prominent as numerous researches have demonstrated

its effectiveness in many structural applications, both with reference to

Serviceability Limit States (SLS) and Ultimate Limit States (ULS). More-

over, a number of physical, semi-empirical and empirical models have

been recently developed toward the formulation of appropriate design

procedures useful for practitioners, especially for strain-softeningmate-

rials. The recent inclusion of FRC in the fibModel Code 2010 [1], referred

to as MC2010 in the following, in national codes as well as the organi-

zation of conferences devoted to FRC [2–4] confirms this positive

development.

FRC has been particularly used in structural elements when crack

propagation control is of primary importance, i.e. in precast tunnel seg-

ments [5] or in beamswhere little or no shear reinforcement is provided

[6]. In several of these applications, the reinforcement generally consists

of a combination of conventional rebars and fibers [7]. In the case of

rather tough FRC, a total substitution of the secondary or web reinforce-

ment could be also achieved [8].

If the addition of fibers in a classical beam, having longitudinal rein-

forcement, does not necessarily provide benefits in terms of flexural

bearing capacity and, especially, ductility at ultimate limits states

(ULS) [9], there is a general consensus that FRC significantly improves

the behavior at SLS, with respect to crack and deflection control. In ser-

vice conditions, steel-to-concrete bond allows the transfer of tensile

stresses from the rebar to the surrounding concrete (between cracks),

which stiffens the response of a Reinforced Concrete (RC) member sub-

jected to tension; this stiffening effect is referred to as “tension stiffen-

ing”. Several authors already studied this mechanism in traditional RC

elements [10–12], generally made of Normal Strength Concrete (NSC).

In fibrous RC elements, the transfer of non negligible residual stresses

at crack provides an additional significant mechanism that influences

the member response. The combination of these two mechanisms

(tension stiffening and the post-cracking residual stresses provided by

fibers at any crack, referred to as “residual strength” or “tension soften-

ing” in the following) results in a different crack pattern, characterized

by a reduced crack spacing and crack width. In addition, the collapse

mode and the ductility of FRC elements may also be affected by stress

concentrations due to enhanced bond and the residual tensile stress at

a crack [9].

A number of research studies have been carried out so far on the ten-

sile behavior of FRC members since late 90s. Mitchell and Abrishami

[13] presented one of the first studies; more recently, Bischoff [14,15]

performed monotonic and cyclic tests and included shrinkage effects

in the analysis. Noghabai [16] proposed an analytical model describing

the behavior of tie-elements based on the observation of experimental

tests. Physical analytical models predicting the behavior of FRC tension

members were also recently proposed by other researches [17,18].

However, none of the experimental studies mentioned were broad

enough to clearly identify the influence of the FRC toughness, which is

a performance based parameter useful for designers and depends on

the fiber content, material, combination, volume fraction and aspect

Cement and Concrete Research 68 (2015) 24–34

⁎ Corresponding author at: DICATAM— Department of Civil Engineering, Architecture,

Land, Environment and Mathematics, University of Brescia, Via Branze, 43, 25123 Brescia,

Italy. Tel.: +39 030 3711 223.

E-mail address: [email protected] (F. Minelli).

http://dx.doi.org/10.1016/j.cemconres.2014.10.011

0008-8846/© 2014 Elsevier Ltd. All rights reserved.

Contents lists available at ScienceDirect

Cement and Concrete Research

j ourna l homepage: ht tp : / /ees.e lsev ie r .com/CEMCON/defau l t .asp

ratio. Moreover, none of these studies have been comprehensive in

terms of the number of specimens tested or in the parameters

considered.

The present paper describes themain results obtained from 97 tests

on tension-ties to the aim of evaluating crack formation and develop-

ment in FRC structures. Tests were carried out by varying numerous pa-

rameters, i.e. the element size, the reinforcement ratio, the bar diameter,

the concrete cover, thefiber volume fraction, thefiber geometry and the

FRC toughness.

Preliminary results on a first experimental phase (52 tests) are al-

ready published in [19]. In a second phase, further 45 tests were carried

out with the principal aims to improve the range of parameters studied

(e.g. new longitudinal steel ratios, diameter over reinforcement ratio

were included) and to obtain a more reliable crack pattern together

with amore accurate crack spacing evaluation. Different from the previ-

ous experimental program [19], special attention was devoted to speci-

men curing in order to avoid shrinkage phenomena resulting in a more

reliable reading of specimen average strains. This allowed a more deep

investigation of crack formation and development in tie-elements, com-

pared to the first phase.

The global research work herein presented is a part of a joint re-

search project with the University of Toronto, who tested similar mem-

bers made of HSC [20], allowing for the investigation of the influence of

concrete strength on crack control [21].

This paper will mainly focus on a comprehensive description of the

tests carried out at the University of Brescia in the two previously men-

tioned stages, with emphasis on the influence of fibers in terms of crack

formation and development: the crack initiation, the crack formation

stage, the crack spacing and its progression will be evaluated. The re-

sults will be also compared against the formulations proposed by CEB

Model Code 1978 [22], fib MC 2010 [1] and RILEM TC 162-TDF [23].

In addition, this experimentation aims to provide a useful database,

linking the experimental evidence (crack spacing and mean crack

width) to the performance parameter required byMC2010 (i.e. the cod-

ified residual strengths of the corresponding FRC materials). Moreover,

these experiments might also be useful toward the development of

improved formulations for crack spacing, crack width and tension stiff-

ening behavior in FRC elements.

2. Experimental investigation

Unlike previous researches [13–16], valuable but rather limited in

the parameters being investigated, the experimental program was de-

signed so that a comprehensive database of uni-axial tension tests of

Reinforced Concrete (RC) and Steel Fiber Reinforced Concrete (SFRC)

members containing one central steel rebar could be obtained. These fi-

brous and non-fibrous members will be identified as RC and SFRC ten-

sile ties, respectively. The following key-parameters were investigated:

- Mean value of concrete cylinder compressive strength (fcm) from

27 MPa to 47 MPa;

- Element size: square prism having side from 50 to 200 mm;

- Clear concrete cover: from 20 to 85 mm;

- Effective reinforcing ratio, ρeff: from 0.98 to 3.26%;

- Rebar diameter ϕ: 10, 20 and 30 mm;

- ϕ/ρeff ratio: from 306 to 2043 mm;

- Specimen length: from 950 to 1500 mm;

- Volume fraction of fibers Vf: 0, 0.5 and 1.0%.

Note that the effective reinforcement ratio (ρeff) is the rebar area

over the area of concrete in tension surrounding the reinforcement: in

the present samples, ρ = ρeff.

2.1. Uni-axial tension RC and SFRC test specimen configurations

A total number of 97 RC prismatic members were cast. The research

was developed in two phases. In thefirst stage, 52 specimens having the

geometry shown in Fig. 1a were cast and tested. Each specimen was

950 mm long and five square cross sections were selected: 50, 80,

100, 150 and 200 mm in size. Reinforcing bars having a diameter of

10, 20 and 30 mm (B450C steel, according to European standard EN

10080 [24]), corresponding to a reinforcement ratio (ρ) varying from

1.25% to 3.26%, were employed.

In a second phase, the same reinforcing bar diameters were used,

whereas four square cross sections (one less) were selected (80, 120,

180 and 200 mm in size) and a reinforcement ratio from 0.98% to

2.23% was adopted. The specimens having a rebar diameter of 20 and

30 mm were longer with respect to those of the previous phase

(1500mm vs. 950mm): in fact, the average crack spacing could be bet-

ter evaluated in longer elements as the number of expected cracks is

higher. Members with a rebar diameter of 10 mm were 1000 mm

long. Geometry and reinforcement details of specimens of the second

phase are depicted in Fig. 1b. Note that, in the 2nd phase, holed steel

plates were welded at both the rebar ends and a different test set-up

was used, as explained in the next paragraph. The properties of the re-

inforcing bars used in tie elements are reported in Table 1.

Principal aim of the 2nd phase was to investigate with more details

members having large rebar diameter (e.g. 30 mm), enabling to im-

prove the range of the significant parameter ϕ/ρeff under investiga-

tion. Moreover, a wider number of experiments together with the

adoption of a better curing procedure allow amore in-depth evaluation

of the crack formation and development. The concrete cover was, in all

cases, at least 2–3 times the bar diameter to prevent splitting phenom-

ena during the tests [13,25].

All sampleswere castwith the same concretematrix designed to ob-

tain a normal strength concrete (NSC), C30/37 according to Eurocode 2

[26]. The samebasicmix designwas used for all batches [19], i.e. cement

content of 400 kg/m3; water to cement ratio of 0.47; sand (0–4 mm)

610 kg/m3; coarse aggregate (4–10 mm) 1132 kg/m3; superplasticizer

3.3 l/m3. With fibers, the amount of aggregate lowers up to a small 4%.

Different dosages and two types of steel fibers, the macro fiber 30/

0.62 and the micro fiber 13/0.20, were utilized. Table 2 summarizes

the main characteristics of the two fibers employed. Note that the

fiber designation denotes the fiber length as the first number and the

fiber diameter as the second (both in millimeters).

The micro fibers were only used in addition to macro fibers, deter-

mining a hybrid system that can help bothwith regard to early cracking

(controlled by micro fibers) and for diffused macro-cracking (mainly

controlled by macro fibers). Based on the different combinations of

type of fiber and dosage, member dimension and steel reinforcement

ratio, 7 test series were investigated corresponding to two RC and five

SFRC series, as summarized in Table 3. For each series, Table 3 reports

thematerial identification (batch ID), the volume fraction of steel fibers

and fiber designations.

Each combination of fiber reinforcement, member dimension and

steel reinforcement ratio defines a specific set of tests, whose repetitions

and notations are listed in Table 4, in which the entire experimental

program is reported in detail. Three specimens were in general tested

for each material combination. Note that Table 4 reports the mean ex-

perimental crack spacing srm. The mean crack spacing of a single speci-

men was evaluated by measuring the distance between visible cracks

on the surface. Furthermore, themean crack spacing of each set of sam-

ples (srm) was calculated as the mean value of the measured mean

values of each single specimen.

2.2. Material properties

A number of tests were conducted in order to determine themateri-

al properties. Standard tests on 150 mm cubes were carried out for the

determination of the concrete compressive strength. The tensile

strengths (direct tension test) were measured from ϕcyl 80·210 mm

cylinders (first phase) and ϕcyl 150·300 mm cylinders (second phase).

Young modulus (secant static modulus in compression according to

25G. Tiberti et al. / Cement and Concrete Research 68 (2015) 24–34

UNI 6556 [27]), was determined on the same cylinders (before

performing direct tensile tests) by carrying out three loading cycles

with a maximum stress equal to 1/3 of concrete compressive strength,

fcm. The stabilized secant modulus of elasticity was calculated in the

unloading branch of the third cycle by considering a lower bound refer-

ence stress equal to 1/10 fcm. Table 3 reports themain values of cylindri-

cal compressive/tensile strengths and young modulus for the 7

materials tested: the former was determined from the experimental

cubic strength by adopting the relationship fcm = 0.83·fcm,cube.

In addition, among many standards available for the material char-

acterization [28], all SFRC materials were characterized according to

the European Standard EN 14651 [29] and MC2010 [1], which require

that three point bending tests (3PBT) be performed on small notched

beams (150·150·550 mm). Typical experimental curves, concerning

the nominal stress vs. Crack Mouth Opening Displacement (CMOD)

are depicted in Fig. 2, for SFRC 0.5M and SFRC 1M series (2nd phase).

Based on these curves, the residual strengths fR,j (evaluated at 4 differ-

ent CMODvalues, i.e. 0.5, 1.5, 2.5 and 3.5mm [29]), and the flexural ten-

sile strength (limit of proportionality) fL were calculated, as listed in

Table 5 (mean values).

In a more recent and reliable philosophy, well acknowledged by the

most recent guidelines and documents on FRC (one above all, the MC

2010 [1]), the FRC toughness (i.e. the fR,j parameters) is the most

comprehensive parameter that should be evaluated for a better repre-

sentation of the mechanical behavior of FRC. The toughness is a reliable

parameter representing the post-cracking behavior of any FRC compos-

ite that, on the contrary, would not be accurately described by using the

fiber geometry and content themselves.

The following discussion will be based more on the influence on

cracking of the residual strengths fR,j rather than on the classical param-

eters being investigated, i.e. the fiber length, aspect ratio and content Vf.

2.3. Set-up and instrumentation

In the first phase (samples having a length of 950 mm) tests were

performed by means of a hydraulic universal servo-controlled (closed-

loop) testing machine, under stroke control (by clamping both the

rebar ends), by monitoring the specimen behavior up to the onset of

the rebar strain-hardening. The deformation rate varied from 0.1 to

0.2 mm/min up to the rebar yield; then the rate was progressively in-

creased up to 1 mm/min, the latter beyond an average member strain

of approximately 2%.

Referring to the first phase of research, all specimens without fibers

(RC) and SFRC series 1M were stored in a fog room (R.H. N 95%; T =

20 ± 2 °C) until 2 or 3 days before testing; then they were air dried in

the laboratory. All the other specimenswere moist cured with wet bur-

lap under plastic sheet until 2 or 3 days before testing, since it was not

possible, for space restriction, using the same fog room. For these latter

specimens, shrinkage effects were not likely totally controlled, even

though themember response could be corrected by taking into account

the effect of the initial shrinkage strain, as proposed by Bischoff [30];

however, it was confirmed that shrinkage does not significantly

Bar diameter

10

Bar diameter

20

Bar diameter

30

50

50

80

80

150

15

0

11

50

100

10

0

150 200

15

0

20

0

Reinforcement

b

(a) (b)

Variation of the

specimen side, b

Variation of the longitudinal

steel ratio =3.26% to 1.25%

Variatio

n o

f the

rebar d

iameter

80

80

Variation of the longitudinal

steel ratio =2.23% to 0.98%

200

20

0

120

12

0

180

18

0

180

18

0

Variation of the

specimen side, b

30

03

00

b

1st phase 2nd phase

L=

15

00

(L

=1

00

0 f

or

10

bar

)

Fig. 1. Geometry and reinforcement details of specimens (1st (a) and 2nd (b) phases). Measures given in mm.

Table 1

Properties of steel reinforcing bars.

Rebar As (mm2) ϕ (mm) Es (GPa) fy (MPa) εsh (×10−3) fult (MPa)

ϕ10 78 10 204 522 29.7 624

ϕ20 314 20 192 515 20.2 605

ϕ30-1a 707 30 192 554 15.8 672

ϕ30-2a 707 30 189 484 17.9 604

a The ϕ30 bars came from two different production heats.

Table 2

Characteristics of fibers employed.

Fiber ID Type of steel Shape fuf [MPa] Lf [mm] ϕf [mm] Lf/ϕf [–]

30/0.62 Carbon Hooked-end 1270 30 0.62 48.39

13/0.20 High carbon Straight 2000 13 0.20 65.00

26 G. Tiberti et al. / Cement and Concrete Research 68 (2015) 24–34

influence the final crack pattern and the crack spacing (the main scope

of this paper), whereas it does influence the first cracking load.

In the second phase (longer specimens), tests were carried out by

means of a steel reacting frame conveniently modified for the scope

(Fig. 3). Two steel plates, with bolt-holes previously machined, were

welded at the ends of the specimen (see Fig. 1b), which was connected

by pins in vertical position to the strong floor and to the steel frame

(both acting as reacting system, Fig. 3). The upper end of the specimen

was connected to an electromechanical screw jack,with amaximumca-

pacity of 1500 kN.Note that these plates and the correspondingwelding

did not change the behavior of the bare bar as preliminary verified

through uni-axial tests on the welding joint.

Tests were carried out under stroke control and by assuming the

same load-procedure of the first phase. In the fog room, shrinkage

strains were measured by means of free shrinkage prisms: since the

measured strains were negligible (around 20–25 micro-strains), no-

shrinkage offset strains were herein applied.

A typical instrumented specimen is shown in Fig. 4a: four Linear

Variable Differential Transformers (LVDTs, one for each side), were

employed to measure the mean deformation of the specimen over a

length ranging from 900 mm to 1400 mm, the former in the 950/

1000mm long specimens, and the latter for the remaining experiments

(Fig. 4b).

3. Results and discussion

3.1. Typical tensile tie behavior

The diagrams reported in Fig. 5a and in Fig. 5b provide typical axial

load vs. average tensile member strain (the average strain of the rebar

Table 3

Mechanical properties of concrete and fiber contents.

Batch ID Days after casting fcm [MPa] fctm [MPa] Ec [GPa] Fibers 30/0.62 [%]vol. Fibers 13/0.20 [%]vol Vf,tot [%]vol

1st phase 0 Plain 34 40.5

(5.01%)

3.71

(4.44%)

29.5

(11.04%)

– – –

0.5M 42 39.7

(8.38%)

3.37

(14.65%)

23.7

(19.52%)

0.5 – 0.5

1M 58 36.4

(9.36%)

3.50

(2.86%)

30.7

(8.31%)

1 – 1

1M + m 116 43.3

(11.78%)

2.81

(12.75%)

27.5

(17.16%)

0.5 0.5 1

2nd phase 0 Plain 43 47.2

(4.91%)

3.50

(9.68%)

33.9

(3.54%)

– – –

0.5M 36 40.8

(8.48%)

3.35

(7.31%)

32.6

(4.24%)

0.5 – 0.5

1M 120 27.4

(10.66%)

2.85

(13.54%)

27.8

(9.05%)

1 – 1

Relative standard deviation was reported in round brackets.

Table 4

Experimental program, specimen notation and mean crack spacing (srm).

Phase Rebar Batch ID b [mm] Length, L [mm] Reinf. ratio (%) Clear cover, c [mm] Specimen ID Spec. # srm [mm]

1st phase ϕ10 0 Plain 50 950 3.26 20 N 50/10 — 0 3 120

0.5M N 50/10 — 0.5M 3 59

1M N 50/10 — 1M 3 61

1M + m N 50/10 — 1 M + m 3 50

ϕ10 0 Plain 80 950 1.25 35 N 80/10 — 0 2 150

0.5M N 80/10 — 0.5M 3 109

1M N 80/10 — 1M 3 94

1M + m N 80/10 — 1M + m 3 96

ϕ20 0 Plain 100 950 3.24 40 N 100/20 — 0 3 147

0.5M N 100/20 — 0.5M 3 112

1M N 100/20 — 1M 3 113

1M + m N 100/20 — 1M + m 3 87

ϕ20 0 Plain 150 950 1.42 65 N 150/20 — 0 3 213

0.5M N 150/20 — 0.5M 3 105

1M N 150/20 — 1M 3 160

1M + m N 150/20 — 1M + m 3 135

ϕ30 0 Plain 150 950 3.24 60 N 150/30 — 0 3 212

ϕ30 0 Plain 200 950 1.80 85 N 200/30 — 0 2 278

2nd phase ϕ10 0 Plain 80 1000 1.25 35 N 80/10 — 0 3 144

0.5M N 80/10 — 0.5M 3 105

1M N 80/10 — 1M 3 102

ϕ20 0 Plain 120 1500 2.23 50 N 120/20 — 0 3 170

0.5M N 120/20 — 0.5M 3 151

1M N 120/20 — 1M 3 127

ϕ20 0 Plain 180 1500 0.98 80 N 180/20 — 0 3 358

0.5M N 180/20 — 0.5M 3 234

1M N 180/20 — 1M 3 223

ϕ30 0 Plain 180 1500 2.23 75 N 180/30 — 0 3 232

0.5M N 180/30 — 0.5M 3 198

1M N 180/30 — 1M 3 145

ϕ30 0 Plain 200 1500 1.80 85 N 200/30 — 0 3 310

0.5M N 200/30 — 0.5M 3 220

1M N 200/30 — 1M 3 197


embedded in a prismatic tie, εsm) plots of SFRC andRC specimens, for re-

bars having a diameter of 20 mm and 30mm (2nd phase), respectively.

The average member strain εsm was calculated as the mean elongation

of the 4 LVDTs, divided by the length of the base measurement. In

both the diagrams, a comparison between one typical RC (plain) and

corresponding SFRC member is provided. In addition, the response of

the corresponding bare bar is reported.

Even though tests were conducted well beyond, the results are

plotted up to a maximum average strain of 5·10−3, in order to properly

describe the tensile behavior at SLS, where the crack and deformation

control are of main importance, and also to assess the behavior at first

yielding.

The diagrams indicate that fibrous and non-fibrous samples present

approximately the same load at first cracking since fibers generally do

not affect the concrete tensile strength, at least for volume fractions

lower than 1% and in the case of strain-softening material (note that

the tensile strength of these two series is rather similar, as reported in

Table 3).

In control samples it emerges that, after first cracking, the force

generally drops down as soon as a new crack forms. This phenomenon

is less clear in FRC specimens since fibers ensure a residual strength

through cracks (“tension softening” effect in this case), which smoothly

reduces the saw-tooth steeply phenomenon detected in the experimen-

tal curves. The phase where no new cracks occur, and those existing

widen, is denoted as the “stabilized crack stage”: it takes place for

εsm = 0.85·10−3 and 1.45·10−3 in series N 120/20 and N 200/30, re-

spectively (Fig. 5). Considering the entire sets of tests, the stabilized

crack stage forms in the range of εsm = 0.5–1.5·10−3.

One should notice that there is no clear evidence about a possible re-

lationship between strain at crack stabilized stage and SFRC toughness,

differently from onewould expect: the higher number of cracks report-

ed in SFRC elements, in fact, form in the same range of average strains as

in RC elements.

3.2. Benefits of fibrous reinforcement in combination with rebars

The typical responses of FRC tensile ties reported in Fig. 5 enable to

emphasize one of the two main advantages related to the combination

of rebars and fibers; that is the global stiffness increase caused by the

transmission of noticeable residual stress across cracks. This tendency

can be recognized also during the crack formation stage but it is espe-

cially clear during the stabilized crack stage: in fact, as schematically

depicted in Fig. 5a, the difference in tensile resistance at a particular

stain level, denoted by ΔN, illustrates the role of fibers. Hence, the ten-

sion stiffening increases with respect to that of RC samples.

In the same way, by referring to a certain axial member load, a

considerable reduction of the averagemember strain (tension stiffening

strain, denoted as Δεsm in Fig. 5b) occurs. This phenomenon is rather

crucial in design, with significant influence on the crack width

calculation.

3.3. Evolution of the mean crack spacing

A significant aspect investigated concerns the crack pattern and its

evolution in terms ofmean crack spacing (srm). The latterwas calculated

for each specimen as the mean distance between cracks. Furthermore,

for each set of samples, srmwas calculated by averaging srm of each sin-

gle specimen.

In Fig. 6a and b, the evolution of themean crack spacing srm is plotted

as a function of the average strain up to the end of the crack formation

stage for specimens N 120/20 and N 200/30 (2nd phase), respectively.

From this plot, the reduction of the mean crack spacing, which rep-

resents the second main advantage due to the addition of fibers, can

be clearly noticed. The residual post-cracking strength provided by

steel fibers (at any crack) contributes to the reduction of the transmis-

sion length (lt) necessary to transfer tensile stresses in concrete through

bond. This effect can be considerable even if it is assumed, as a first ap-

proximation, that the bond stresses between rebar and surrounding

concrete are not affected by fibers, assumption currently also supported

byMC2010 [1]. Nevertheless, Plizzari [31] has demonstrated that, in the

case of splitting, fibers improve the bond (τbm) whereas, if the pull-out

occurs, fiber contribution on bond tends to be negligible [25,32].

Comparing responses at a specific value of average strain, as the

FRC toughness increases, the mean crack spacing decreases; this ten-

dency is consistent for a given average strain and it also applies, as ex-

pected, once the stabilized crack stage is reached. Furthermore, this

trend is more pronounced in N 200/30 specimens (Fig. 6b), since the

3PBT - EN - 14651

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

CMOD [mm]

Nom

inal

stre

ss

N [

MP

a]

SFRC 0.5M

SFRC 1M

σ

Fig. 2. Experimental results of 3PBT SFRC notched beams according to EN 14651 (SFRC

series of 2nd phase).

Table 5

Residual strengths of the SFRCs according to EN 14651.

Fracture parameters of the SFRCs according to EN-14651

Batch ID fLm [MPa] fR1m [MPa] fR2m [MPa] fR3m [MPa] fR4m [MPa]

1st phase 0.5M 5.46

(2.06%)

5.00

(1.94%)

4.55

(3.97%)

4.05

(5.98%)

3.46

(9.45%)

1M 4.81

(6.03%)

5.09

(3.12%)

4.12

(6.38%)

3.42

(4.80%)

3.01

(11.74%)

1M + m 5.97

(9.46%)

6.30

(19.02%)

5.35

(22.35%)

4.35

(18.35%)

3.54

(12.00%)

2nd phase 0.5M 4.60

(6.61%)

4.12

(18.86%)

4.07

(17.24%)

3.35

(13.19%)

2.69

(16.28%)

1M 4.64

(8.54%)

5.43

(13.86%)

4.89

(16.73%)

4.36

(15.59%)

3.86

(15.57%)

Relative standard deviation was reported in round brackets.


longitudinal rebar steel ratio (ρ) is lower and tension softening is more

prominent.

3.4. Evolution of the tension stiffening strain

It is now rather clear that, in general, the expectedmean crackwidth

of a SFRCmember diminishes because of the post-cracking toughness of

SFRC, involving two important contributions: a reduction of both the av-

erage member strain (εsm) and the mean crack spacing (srm).

The former aspect has been investigated in the diagrams reported in

Fig. 7a/b for series N 120/20 and N 200/30, respectively. The average

member strain of fibrous and non-fibrous tensile ties (εsm) is provided

as a function of the bare bar strain εs. Consider first a range of strains

up to 2.4·10−3, corresponding to the stabilized crack stage up to the

onset of yielding. By referring to a given applied force, represented by

Fig. 3. Schematic of a specimen 1500 mm long, of the reacting frame and of the test set-up (measures given in mm).

Base ofmeasurement

4 LVDTs,one for each sideof the specimen

b

b

Steel reinforcing

LVDT

L=

95

0/1

00

0 (

1st

/2nd p

has

e),

1500 (

2nd p

has

e)

90

0 (

1st

/2n

d p

has

e), 1

40

0 (

2n

d p

has

e) central bar

(a) (b)

Fig. 4. Typical configuration of the tensile tie during test (a) and instrumentation (b). Measures given in mm.


a certain bare bar strain (εs), in RC elements the average member strain

εsm is lower (tension-stiffening strain). Moreover, in presence of fibers a

further reduction can be seen (Fig. 7a/b). From this plot, a reduction of

about 20% is noted between SFRC 0.5M and RC series. This reduction

strictly depends on the FRC toughness, without any influence of the ten-

sile strength, which, as already mentioned, is similar in the two series

herein considered, as well depicted by the elastic ranges of the two

plots.

3.5. Main factors influencing the mean crack spacing: ϕ/ρeff and FRC

toughness

In Fig. 8a the mean crack spacing (srm) is plotted versus the key

parameter ϕ/ρeff, which is generally included in many building codes

for the prediction of srm. In particular, the experimental results are plot-

ted for reference RC members, SFRC members with a volume fraction

Vf = 0.5% and 1.0% (the latter includes macro fibers, macro + micro fi-

bers according to the batches 1M and 1M + m, presented in Table 3).

The diagrams reported in Fig. 8a confirm the tendency previously ob-

served in Fig. 6: for the same value of ϕ/ρeff, the use of fibers results in

a considerable reduction of themean crack spacing due to the enhanced

material toughness. In comparisonwith RC samples, the globalmean re-

ductions of srm equals to 30% for SFRC with Vf = 0.5% and 37% for SFRC

with Vf = 1% (24% higher).

Since several formulations proposed in the literature or in design

codes define the crack spacing to be linearly proportional to the

parameter ϕ/ρeff, a linear regression was utilized in order to evaluate

the dispersion of results. As depicted in Fig. 8a, the coefficient of corre-

lation R2 is equal to 0.92 for RC (plain control) samples whereas it

results 0.75 and 0.93 for SFRCmemberswith Vf of 0.5% and 1.0%, respec-

tively. Basically, a possible linear relationship between srm and ϕ/ρeffcould be reliable, even though, for SFRC, that should be considered

with the addition of a further built-in parameter taking into account

the post-cracking residual strength provided by fibers.

Among the fracture parameters fR,j suggested by EN 14651 [29], fR1mseems to better capture the experimental tendency, as the ratio be-

tween fR1m (Vf = 0.5%) and fR1m (Vf = 1.0%) is 22% (Table 5). In fact,

fR1m defines the residual post-cracking SFRC strength at CMOD =

0.5mm, corresponding to crack width ranges typical of crack formation

at stabilized crack stages.

Besides the mean crack spacing, also the minimum crack spacing

was evaluated by measuring the minimum distance between visible

cracks on the surface (at stabilized crack stage). Furthermore, the min-

imum crack spacing of each set of samples (srmin) was calculated as

the mean value of the measured minimum values of each single speci-

men. The latter can be a significant parameter since it can be considered

approximately equal to the transmission length (lt), as well underlined

by Borosnyói and Balázs [12]. In Fig. 8b, srm is reported as a function of

theminimum crack spacing (srmin). A linear regressionwas also applied

in this case. The corresponding coefficient of correlations R2 and equa-

tions are plotted in Fig. 8b, from which quite high values of R2 (ranging

for 0.86 to 0.92) can be noticed in all cases. This suggests an almost

Specimens 120x120 - 20 - = 2.23%

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5

Average member strain, sm [‰]

Ax

ial

forc

e [k

N]

Bare bar 20

N 120/20 - 0

N 120/20 - 0.5M

N

Specimens 200x200 - 30 - = 1.80%

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5


Ax

ial

forc

e [k

N]

Bare bar 30

N 200/30 - 0

N 200/30 - 0.5M

sm

(a) (b)

Fig. 5. Typical response of fibrous and non-fibrous N 120/20 (a) and N 200/30 tie elements (b).

Specimens 120x120 - 20 - = 2.23%

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Crack

sp

aci

ng [

mm

]

RC

SFRC 0.5M

SFRC 1M

Final crack spacing

Specimens 200x200 - 30 - = 1.80%

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Crack

sp

aci

ng [

mm

]

RC

SFRC 0.5M

SFRC 1M

Final crack spacing

(a) (b)

Fig. 6. Evolution of the mean crack spacing of fibrous and non-fibrous series: N 120/20 (a) and N 200/30 tie elements (b).


constant ratio between srm/srmin, varying from 1.18 (RC series) to

1.4 ÷ 1.45 (SFRC series). The latter couple of values are quite close to

the expected ratio in presence of a mean crack spacing equal to 1.5 lt,

which is the case of amember having infinite length [25]. The estimated

ratio for plain series is not far from 1.3·srmin (=lt), which corresponds

to the value suggested by Bigaj van Vliet [25] in order to take into ac-

count the limited member length.

Further experimental evidences can be globally found looking at

all diagrams abovementioned and at the mean crack spacing values

reported in Table 4. Firstly, for a given bar diameter, an increase in

reinforcement ratio ρeff decreases the mean crack spacing of both

SFRC and RC samples. However, the rate of decrease is rather lower

in SFRC than in RC, especially in the case of ϕ = 20 mm (Table 4): in

fact, for the minimum ρeff = 0.98%, the ratio srm,RC/srm,SFRC 0.5M = 1.53

whereas, for the highest ρeff = 3.24%, the ratio srm,RC/srm,SFRC 0.5M =

1.31. Therefore, SFRC results more effective in controlling the cracking

phenomenon for lower reinforcement ratios, as already notices in

Fig. 6a and b.

Moreover, for a given reinforcement ratio, an increase in the rebar

diameter increases the mean crack spacings of both SFRC and non-

fibrous concrete (with similar trend).

In addition, the combination of micro and macro fibers enhances

micro-cracking control, as also depicted by notched beam tests, which

show fairly higher values of residual post-cracking stresses, especially

for fR1m (Table 5). Furthermore, with higher reinforcement ratios, the

adoption ofmicrofibers (in addition tomacro-fibers) is slightlymore ef-

fective as they are especially efficient at early-cracking stages.

Finally, for the same type of fibers (macro), Vf=1% is not significant-

ly more efficient than Vf =0.5% in terms of crack spacing, especially for

high reinforcement ratios. This is also due to fairly similar fracture prop-

erties (Table 5), which are probably due to higher porosity in the SFRC

elements with 1% of fibers even if no direct measurements were done.

Fig. 9 reports themean crack spacing vs. fR1m plot for the SFRC spec-

imens, for 4 different ranges of ϕ/ρ parameters. Results concerning all

SFRC specimens are herein plotted. The graph strongly confirms that

an increase in the residual strength fR1m leads to a significant decrease

of crack spacing. Four linear regression lines are also reported,with sim-

ilar slopes for ϕ/ρ b 1500.

This graph further proves that the cracking behavior in SFRC com-

posites can be properly described and modeled by using fR1m, which is

a suitable parameter related to SLS. Nevertheless, this possible trend

should be better confirmedwith future research based on experimental

campaigns specifically designed for evaluating a larger range of the re-

sidual strength fR1m values (higher values of fR1m should be especially

investigated).

3.6. Discussion of crack spacing formulations

A number of crack spacing formulations for RC members can be

found in literature or in building codes. In this section, the following

0

0.5

1

1.5

2

2.5

3

0.0 0.4 0.8 1.2 1.6 2.0 2.4

Bare bar strain, s [‰]

Av

era

ge

mem

ber

str

ain

, sm

[‰]

0

0.5

1

1.5

2

2.5

3

0.0 0.4 0.8 1.2 1.6 2.0 2.4

Bare bar strain, s [‰]

Av

era

ge

mem

ber

str

ain

, sm

[‰]

(a) (b)

Fig. 7. Evolution of the tension-stiffening strain of fibrous and non-fibrous series: N 120/20 (a) and N 200/30 tie elements (b).

Mean crack spacing vs. / eff

R2 = 0.92

R2 = 0.75

R2 = 0.93

0

50

100

150

200

250

300

350

400

0 500 1000 1500 2000 2500

/ eff [mm]

Mea

n c

rack

sp

aci

ng [

mm

]

RC

SFRC Vf=0.5%

SFRC Vf=1%

100x100 20

120x120 20

180x180 30

200x200 30

180x180 20

150x150 20

50x50 10

80x80 10

150x150 30

Mean crack spacing vs. minimum crack

spacing

srm = 1.18srmin

R2 = 0.92

srm= 1.40srmin

R2 = 0.91srm = 1.45srmin

R2 = 0.86

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350

Minimum crack spacing [mm]

Mea

n c

rack

sp

aci

ng

[m

m]

RC

SFRC Vf=0.5%

SFRC Vf=1%

(a) (b)

Fig. 8. Crack spacing vs. ϕ/ρeff non-fibrous series/fibrous series: mean crack spacing (a), minimum crack spacing (b).


formulationswill be considered and compared against the experimental

results herein reported:

- MC 1978 22½ ";

- MC 2010 1½ ":

MC 1978 introduced the following models for the evaluation of the

expected crack width wk and mean crack spacing srm [mm]:

wk ¼ 1:7 $wm ¼ 1:7 $ εsm $ srm ð1Þ

srm ¼ 2 $ cþs

10

! "

þ k1 $ k2 $ϕ

ρeff:

ð2Þ

The coefficients k1 and k2 depend on the rebar bond properties and

the distribution of tensile stress within the section, respectively. In

this case, it was assumed k1 = 0.4 (deformed bars) and k2 = 0.25

(pure tension).

The starting point of theMC 2010 [1] approach is the introduction of

the design crack width (wd), which corresponds to the maximum crack

width (wmax) defined as follows:

wd ¼ wmax ¼ 2 $ εsm $ ls;max: ð3Þ

Recalling Eq. (1) [22], this expression can be derived:

srm ¼ 1:17 $ ls;max ¼ 1:17 $ k $ cþ1

4$ϕ

ρeff

$fctmτbm

# $

: ð4Þ

Referring to RCmembers, plots of the mean crack spacing predicted

byMC 1978 andMC 2010 against those observed from experiments are

presented in Fig. 10a and b, respectively. Good agreement can be seen

with experimental data (mean percentage error — MPE, around 24%

for both formulations).

Regarding SFRC elements, one of the earliest introducedmodels and

most frequently used was proposed by RILEM committee TC 162-TDF

[23]. This approach modifies the Eurocode 2 [33] expression for non-

fibrous concrete with a factor related to the fiber aspect ratio:

srm ¼ 50þ 0:25 $ K1 $ K2

ϕ

ρs;eff

!

$50

L f=ϕ f

' (

ð5Þ

where Lf/ϕf is the fiber aspect ratio and the term in round brackets 50/

(Lf/ϕf) should be not greater than 1.0. This expressionwas applied by as-

sumingK1 equal to 0.8 (for deformed reinforcing bars) and K2 equal to 1

(elements under pure tension). The comparison between Eq. (5) and

the experimental results is presented in Fig. 11a. Unlike the rather

good fitting of Fig. 10, the prediction of this relationship is rather poor

(MPE about 100%), which was reasonably expected since this approach

takes into account only thefiber aspect ratio and does not explicitly con-

sider the mechanical properties of the SFRC composite.

More recently, MC 2010 [1] proposed a different relationship, in

which the influence of fibers is taken into account bymeans of a reduc-

tion of the introduction length (ls,max, generally assumed for RC ele-

ments as for Eq. (4)), according to the factor fFtsm, which includes the

FRC toughness at SLS (fFtsm=0.45 fR1m). Accordingly, the following ex-

pression can be derived:

srm ¼ 1:17 $ ls;max ¼ 1:17 $ k $ cþ1

4$ϕ

ρeff$fctm−fFtsmð Þ

τbm

# $

¼ 1:17 $ k $ cþ1

4$ϕ

ρeff$fctm−0:45 $ fR1mð Þ

τbm

# $

: ð6Þ

Eq. (6) has been applied based on the residual strengths (mean

values) reported in Table 5. The factor k was assumed equal to 1,

while the bond stress (τbm) over the concrete tensile strength (fctm)

ratio was assumed equal to 1.8 even for SFRC specimens [1]. The predic-

tions of Eq. (6) are reported in Fig. 11b. A quite good agreement with

test results emerges (MPE = 28%), even though in the 5% of samples

(all belonging to 1M + m series; see Table 3) the term in the round

Mean crack spacing vs. fR1m - SFRC series

Vf<1%

0

50

100

150

200

250

300

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

fR1m [MPa]

Mea

n c

rack

sp

aci

ng

[m

m]

/ <500

500< / <1000

1000< / <1500

/ >1500

Fig. 9.Mean crack spacing vs. fR1m.

Prediction of the mean c.spacing- RC series

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500

Mean crack spacing (predicted)[mm]

Mea

n c

rack

sp

aci

ng

(m

easu

red

)[m

m]

MC1978

MPE=24.7%

Prediction of the mean c.spacing- RC series

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500


Mea

n c

rack

sp

aci

ng

(m

easu

red

)[m

m]

MC2010,

Final draft

MPE=24.0%

(a) (b)

Fig. 10. Crack spacing prediction for non-fibrous series: MC1978 (a), MC2010 (b).


brackets (Eq. (6)) does not have any physical meaning as it results neg-

ative (i.e. fFtsm=0.45 fR1m N fctm). In those cases, a positive value of srm is

still obtained as it is coincidentally balanced by the effect of the concrete

cover k·c. Based on the experimental results presented herein, Eq. (6)

reasonably includes the parameter fR1m, which is representative of the

member behavior at SLS. However, enhanced crack spacing formula-

tions can be obtained by using the broad experimental results herein

reported.

4. Conclusions

In the present paper, a broad experimental study was presented

aiming at evaluating the cracking behavior of RC and SFRC ties, with

special focus on the enhancement of crack control due to the addition

of fibers. A series of 97 tension tests have been carried out, correspond-

ing to 31 RC samples and 66 SFRC specimens.

Based on the results and on the discussion presented, the following

main conclusions emerge:

1- SFRCpositively influences thebehavior of tension-ties at SLS, by de-

termining closely spaced cracks and, therefore, reducing crack

width, due to two main aspects: tension-stiffening increases and

mean crack spacing (srm) reduces with respect to RC members. A

crack spacing reduction of around 30% was seen in SFRC elements

with Vf = 0.5% and of 37% with Vf = 1%.

2- The stabilized crack stage does not seem to be influenced by the en-

hanced toughness provided by SFRC materials: a higher number of

cracks form, without a clear indication that the crack stabilized

stage develops later or earlier than in non-fibrous elements.

3- Considering the different specimen length between SFRC and RC

ties, the ratio between the mean crack spacing (srm) andminimum

crack spacing (srmin) is likely not influenced by fibers.

4- An increase in reinforcement ratio ρ decreases the mean crack

spacing of both SFRC and RC elements, but the rate of decrease is

rather lower in SFRC than in RC. SFRC results more effective in con-

trolling the cracking phenomenon for lower reinforcement ratios.

5- For a given reinforcement ratio, an increase in the conventional re-

inforcing bar diameter increases the mean crack spacing of both

SFRC and non-fibrous concrete (with similar trend).

6- Mixingmicro andmacro fibers enhancesmicro-cracking control, as

also depicted by notched beam tests, which show fairly higher

values of residual post-cracking stresses;

7- For the same type of fibers (macro), Vf =1% does not result signif-

icantly more efficient than Vf = 0.5% in terms of crack spacing,

especially for high reinforcement ratios. This is mainly due to fairly

similar fracture properties;

8- SFRC stiffens the post-cracking response of RCmembers and can be

effective in diminishing the deflections of the structures (this is a

key-point for SLS design).

9- The crack spacing reduction can be analytically well modeled by

using the fracture parameter fR1m, as currently included in MC

2010; fR1m, in fact, is the performance parameter for SFRC design

at SLS. The MC 2010 model for predicting srm in SFRC elements

generally predicts with sufficient accuracy the experimentally ob-

served data on RC and SFRC series, even though refinement is prob-

ably necessary for FRC composites having fFtsm = 0.45 fR1m N fctm.

10- A useful database, linking the tension stiffening test results (crack

spacing, mean crack width, tension stiffening strain, etc.) to the

codified residual strengths (fR,j) of the corresponding SFRC mate-

rials in accordance to MC2010 is now available.

List of symbols

As cross-sectional area of conventional steel reinforcing bar in

tension;

b tensile tie side;

c clear concrete cover;

CMOD Crack Mouth Opening Displacement;

Ec concrete elastic modulus;

Es steel elastic modulus;

fcm mean value of cylindrical compressive concrete strength;

fcm,cube mean value of cubic compressive concrete strength;

fctm mean value of tensile concrete strength;

fftsm serviceability residual strength (post-cracking strength for

serviceability crack opening);

fL limit of proportionality;

fLm mean value of limit of proportionality;

fR,j residual flexural tensile strength of fiber reinforced concrete

corresponding to CMOD= CMODj;

fR,jm mean value of residual flexural tensile strength of fiber rein-

forced concrete corresponding to CMOD= CMODj;

fuf mean value of ultimate tensile strength of fibers;

fult mean value of ultimate strength of reinforcing steel in tension;

fy mean value of yield strength of reinforcing steel in tension;

k empirical parameter to take into account the influence of the

concrete cover according to MC 2010;

k1 factor accounting for effect of bond characteristics of conven-

tional reinforcing bars on cracking behavior according to MC

1978;

0

50

100

150

200

250

300

0 50 100 150 200 250 300


Mea

n c

rack

sp

aci

ng

(m

ea

sured

)[m

m]

0

50

100

150

200

250

300

0 50 100 150 200 250 300


Mea

n c

rack

sp

aci

ng

(m

easu

red

)[m

m]

(a) (b)

Fig. 11. Crack spacing prediction for fibrous series, RILEM TC-162 DCF (a), MC2010 (b).


K1 factor accounting for effect of bond characteristics of conven-

tional reinforcing bars on cracking behavior according to

RILEM TC 162-TDF;

k2 factor accounting for strain gradient effects on cracking be-

havior according to MC 1978;

K2 factor accounting for strain gradient effects on cracking be-

havior according to RILEM TC 162-TDF;

L tensile tie specimen length;

Lf fiber length;

Lf/ϕf fiber aspect ratio;

ls,max transmission length (introduction length) according to

MC2010 notation;

lt transmission length;

s rebar spacing;

srm mean value of crack spacing;

srmin minimum crack spacing;

Vf volume fraction of fibers;

wd design crack width according to MC2010 notation;

wk expected crack width according to MC1978 notation;

wm mean value of crack width;

wmax maximum crack width;

ΔN difference in terms of load response between tensile ties for a

given average member strain;

Δεsm difference in terms of deformation response between tensile

ties for a given load;

εs bare bar strain;

εsh strain at onset of strain-hardening behavior of steel;

εsm average tensile member strain (average strain of the rebar

embedded in a prismatic tie);

ϕ conventional reinforcing bar (rebar) diameter;

ϕcyl diameter of cylindrical concrete sample;

ϕf fiber diameter;

ρ longitudinal reinforcing ratio;

ρeff effective longitudinal reinforcing ratio;

τbm mean value of bond stress between concrete and rebar.

Acknowledgments

A special acknowledgment goes to M.Sc. Eng. Giovanni Bocchi,

Matteo Campanelli, Massimo Ferrari, Marco Franceschini, Emanuele

Maffetti, Ivan Pedrali, Matteo Romelli, Daniel Sandoval Peña and Luca

Schioppetti, and to the technicians Eng. Luca Cominoli and Mr. Andrea

Delbarba for their valuable support in performing the tests and in the

data processing. The Authors are also grateful to the company Alfa Acciai

SpA (Brescia, Italy) for supplying all rebars for the experimental program.

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[24] UNI EN10080, Steel for the Reinforcement of Concrete—Weldable Reinforcing Steel,2005. (25 pp.).

[25] A. Bigaj van Vliet, Bond of Deformed Reinforcing Steel Bars Embedded in Steel FiberReinforcedConcrete— State of theArt, Technical report, TU-Delft, October 2001, p. 65.

[26] Eurocode 2 EN 1992-1-1, Design of Concrete Structures, General Rules and Rules forBuildings, 2005.

[27] UNI 6556, Testing Concrete. Determination of Secant Modulus of Elasticity in Com-pression, 1976. (3 pp.).

[28] F. Minelli, G.A. Plizzari, A new round panel test for the characterization of fiber rein-forced concrete: a broad experimental study, ASTM J. Test. Eval. (ISSN: 1945-7553)39 (5) (September 2011) 889–897.

[29] EN 14651, Test Method for Metallic Fibre Concrete—Measuring the Flexural TensileStrength (Limit of Proportionally (LOP), Residual), European Committee for Stan-dardization 2005. (18 pp.).

[30] P.H. Bischoff, Effect of shrinkage on tension stiffening and cracking in reinforcedconcrete, Can. J. Civ. Eng. 28 (3) (2001) 363–374.

[31] G.A. Plizzari, Bond and splitting crack development in normal and high strengthfiber reinforced concrete, in: N.P. Jones, R.G. Ghanemed (Eds.), Proceedingsof 13th ASCE Engineering Mechanics Division Conference, The Johns HopkinsUniversity, June 13–16 1999 (Available on CD).

[32] M.H. Harajli, M.E. Mabsout, Evaluation of bond strength of steel reinforcing bars inplain and fiber-reinforced concrete, ACI Struct. J. 99 (4) (July–August 2002).

[33] Comité Européen de Normalisation, Eurocode 2: Design of Concrete Structures, Gen-eral Rules and Rules for Buildings, European Prestandard ENV 1992-1-1Dec 1991.

Giuseppe Tiberti is an Assistant Professor of Structural Engineering, University of Brescia,Italy. He received his Ph.D. in Materials for Engineering in 2009 and his MSc in 2004, bothfrom the University of Brescia. His interests include tunnel linings made by precast seg-ments in fiber reinforced concrete, concrete pavements, fiber reinforced concrete andnonlinear analyses of reinforced concrete structures.

Fausto Minelli is an Assistant Professor of Structural Engineering, University of Brescia,Italy. His interests include shear behavior of lightly transverse reinforced beams, high per-formance concrete,fiber reinforced concrete andnonlinear analyses of reinforced concretestructures. He is member of fib Task Group 4.2 “Ultimate limit states models” and fib TaskGroup 8.3 “Fiber Reinforced Concrete”.

GiovanniA. Plizzari is a Professor of Structural Engineering, University of Brescia, Italy. Hisresearch interests include material properties and structural applications of high-performance concrete, fiber reinforced concrete, concrete pavements, fatigue and fractureof concrete, and steel-to-concrete interaction in reinforced concrete structures. He is amember of ACI Committees 544 (Fiber-Reinforced Concrete) and of fib Task Group 8.3“Fiber Reinforced Concrete”.


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