Acta Scientiarum. Technology
ISSN: 1806-2563
Universidade Estadual de Maringá
Brasil
de Oliveira Júnior, Luiz Álvaro; de Lima Araújo, Daniel; Dias Toledo Filho, Romildo; de
Moraes Rego Fairbairn, Eduardo; Souza de Andrade, Moacir Alexandre
Tension stiffening of steel-fiber-reinforced concrete
Acta Scientiarum. Technology, vol. 38, núm. 4, octubre-diciembre, 2016, pp. 456-463
Universidade Estadual de Maringá
Maringá, Brasil
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Acta Scientiarum http://www.uem.br/acta ISSN printed: 1806-2563 ISSN on-line: 1807-8664 Doi: 10.4025/actascitechnol.v38i4.28077
Acta Scientiarum. Technology Maringá, v. 38, n. 4, p. 455-463, Oct.-Dec., 2016
Tension stiffening of steel-fiber-reinforced concrete
Luiz Álvaro de Oliveira Júnior1, Daniel de Lima Araújo2*, Romildo Dias Toledo Filho3, Eduardo de Moraes Rego Fairbairn3 and Moacir Alexandre Souza de Andrade4
1Escola de Engenharia, Pontifícia Universidade Católica de Goiás, Goiânia, Goiás, Brazil. 2Escola de Engenharia Civil e Ambiental, Universidade Federal de Goiás, Rua Universitária, 1488, 74605-220, Goiânia, Goiás, Brazil. 3Programa de Pós-Graduação em Engenharia Civil, Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil. 4Departamento de Apoio e Controle Técnico, Furnas Centrais Elétrica S.A., Aparecida de Goiânia, Goiás, Brazil. *Author for correspondence. E-mail: [email protected]
ABSTRACT. In this paper, the mechanical behavior of steel-fiber-reinforced concrete was investigated to analyze the influence of steel fibers on tension stiffening. Using tension tests, the tension stiffening coefficient was evaluated through the load versus strain responses obtained from strain gages fixed to reinforcement steels. Moreover, an empirical model is proposed to estimate the tension stiffening coefficient of steel-fiber-reinforced concrete from reinforcement strains. From the test results, it was verified that the addition of steel fibers to concrete reduced the reinforcement steel strains and the crack width and increased the stiffness of cracked concrete, mainly in concretes reinforced with high volumes of fibers. Keywords: tension tests, empirical model, crack width.
Análise do regime pós-fissuração do concreto armado reforçado com fibras de aço
RESUMO. Neste trabalho foi investigada a influência das fibras de aço no regime pós-fissuração do concreto armado submetido à tração. Para isso, foram ensaiados tirantes de concreto armado, dos quais foi obtido o parâmetro de endurecimento do concreto no regime pós-fissuração por meio de extensômetros colados nas barras de aço. Dos ensaios é proposto um modelo empírico para estimativa do parâmetro de endurecimento do concreto reforçado com fibras de aço. Os resultados mostram que a adição de fibras de aço ao concreto reduziu a deformação da armadura e a abertura das fissuras nos tirantes após a fissuração do concreto, com consequente aumento da rigidez do tirante quando comparada ao concreto sem adição de fibras. Esse efeito foi tanto mais acentuado quanto maior era o volume de fibras adicionado ao concreto. Palavras-chave: tirante de concreto, modelo empírico, abertura de fissura.
Introduction
Tension stiffening reflects the ability of concrete to carry tension between cracks, which increases the rigidity of a reinforced concrete member before the reinforcement yields. This effect is primarily due to the mobilization of bonds at the steel–concrete interface. The tension stiffening is affected by the reinforcement ratio, the distribution and diameter of reinforcement bars, the concrete shrinkage, and the brittleness of the matrix. There are several empirical relationships to evaluate tension stiffening (Fields & Bischoff, 2004). For all relationships, the decrease of stiffness in a cracked member can be taken into account using a modified relationship for the load–strain response of the reinforcement steel (Figure 1a), using an average stress–strain response for concrete in the post-cracking range (Figure 1b), or both (Belarbi & Hsu, 1994). There are also some analytical models based on the bond-slip between
concrete and reinforcement steel (Floegl & Mang, 1982; Gupta & Maestrini, 1990; Wu, Yoshikawa, & Tanabe, 1991; Choi & Cheung, 1996).
Figure 1a shows a typical load–strain response of a tension specimen and of a bare steel bar. In this figure, the contribution of concrete to the tension response is given by the difference between the strains in the tension specimen and the bare steel bar. The tension specimen response is initially linearly elastic with uniform stresses in the concrete and steel along the length of the member until the tensile strength of the concrete is reached. In Figure 1b, after the first crack (C1), the average tensile stress in the concrete decreases with increasing strain, which reduces the tension stiffening as the load increases (Fields & Bischoff, 2004). New cracks (C2, C3, and C4) arise as the load increases, further reducing the distance between them until this distance is more than twice the anchorage length. At the end of the cracking stage,
456 Oliveira Júnior et al.
Acta Scientiarum. Technology Maringá, v. 38, n. 4, p. 455-463, Oct.-Dec., 2016
the cracking becomes stable and no new cracks will form. During the stabilized cracking stage, the crack widths increase while the tensile stress and the tension stiffening decrease. However, the tension stiffening decreases more slowly due to the loss of bonding, which is due to internal micro-cracking near the interface between the steel and concrete (Fields & Bischoff, 2004). When the reinforcement steel yields, the transfer of tensile stresses at the steel-concrete interface is damaged, which makes it difficult to transfer loads after the yielding load of the reinforcement steel is reached.
Figure 1. a) Typical load–strain response from a tension test and; b) reduction of the average tensile stress in concrete by tension stiffening.
Concrete shrinkage negatively influences the tension stiffening once it causes an initial shortening of the member, which induces compressive stress in the reinforcement steel. To maintain equilibrium, the reinforcement steel induces tensile stress in the concrete, which reduces the cracking load (Lorrain,
Maurel, & Seffo, 1998; Bischoff, 2001). In addition, high-strength concretes present larger shrinkage, and larger reductions of tension stiffening are expected when shrinkage is ignored.
In fiber-reinforced concrete, fibers improve the mechanical properties of the matrix due to the bridge effect through the cracks after cracking of the matrix. Furthermore, fibers improve the tenacity and ductility of the matrix by controlling the cracking process and increasing the tensile and bond strengths between the steel and concrete. The improvement of the bond strength and the ability to transfer tensile stress through the cracks should increase the tension stiffening of fiber-reinforced concrete (Abrishami & Mitchell, 1997; Yang, Walraven, & Den Uijl, 2009; Deluce & Vecchio, 2013; Lee, Cho, & Vecchio, 2013). Fibers also control splitting cracks and cracking caused by shrinkage. Fibers with a high modulus of elasticity are more efficient in limiting the shrinkage of the matrix because of the greater difference between the modulus of elasticity of the fiber and that of the matrix (Zhang & Li, 2001).
This paper aims to show the influence of steel fibers on the tension stiffening effect and proposes an empiric model for predicting the tension stiffening coefficient from the fiber content. In addition, this paper shows that the partial substitution of cement for less reactive materials, such as fly ash, is a possible strategy to reduce the consumption of cement because no changes in the tension stiffening of concrete due to mineral additions were observed.
Material and methods
Twenty-six tension tests of plain and steel-fiber-reinforced concrete (SFRC), with and without mineral additions (silica fume and fly ash), were performed. One tension specimen was produced for plain concretes with and without mineral additions, but two were produced for the fiber-reinforced concrete. The variables analyzed were the fiber aspect ratio and fiber content. The specimens were stored in a humid chamber in which the temperature was kept at approximately 23ºC and the humidity was approximately 95%. Thus, there was no need to determine concrete shrinkage because the specimens were removed from the humid chamber only 12 hours before the tests.
Materials
In the production of the concretes, the following materials were used: blast furnace slag Portland cement, natural sand, coarse aggregate with a
Tension
Acta Sci
maximusuperplwith m10% sireplaceDramixbecauseBN (cais 80) sfibers w1,000 MThe fo(58.87 (117.75a high even wThus, twas decwhich wobtaine
Theminerawith mcementfiber coplain csteel fibecauseThe wofibers othese taSFRC w
Table 1(kg m-3).
Material
Cement Natural saCoarse aggWater Steel fiberSuperplastWorkabilit
Table 2(kg m-3).
Material
Cement Silica fumFly ash Natural saCoarse aggWater Steel fiberSuperplastWorkabilit
n stiffening of S
entiarum. Techn
um size of lasticizer adm
mineral additioilica fume toment of 30%x® RC 65/60 e its aspect ratialled F80 is thsteel fibers witwere 60 mm loMPa and a moollowing fiberkg m-3), 1.00
5 kg m-3). Howaspect ratio to
when using a hthe greatest vocreased from was possible bed for each type compositionl additions is
mineral additiot and aggregatontent as a reoncrete compibers. Howevee a low volumorkability of frobtained from ables. A slightwas observed.
. Composition o
Plain concre
439.05 and 870.10 gregate 870.10
173.50 r 0.00 ticizer 3.29 ty (mm) 210
2. Composition
Plain concre
261.46 e 31.74
100.43 and 871.53 gregate 871.53
172.28 r 0.00 ticizer 3.27 ty (mm) 220
FRC
nology
25 mm, stemixture (1.0%)ons were proo provide wo
% of the cemeBN (called F
io is 65) and Dhis paper becauth hooked endong and had a odulus of elastr contents w
0% (78.50 kg wever, the addo fresh concrethigh amount oolume fraction1.50% to 1.25
because the reipe of fiber was n of the copresented in
ons in Table 2tes in the mixesult of the a
position due ter, this adjus
me fraction offresh concrete
slump tests ist decrease in t
of concretes witho
eteSteel fiber-
Dramix RC 65/600.75% 1.00% 1.5425.68 428.69 423849.37 857.38 84849.37 857.38 84167.24 168.82 1658.87 78.50 1174.25 4.29 4135 130 8
of concretes wi
eteSteel fiber-
Dramix RC 65/600.75% 1.00% 1.5260.84 259.40 2531.67 31.49 31
100.19 99.64 98869.46 864.66 85869.46 864.66 85171.20 170.25 1658.87 78.50 1174.35 4.32 4190 150 6
el fibers, an). The concr
oduced by addorkability andent with flyF65 in this pa
Dramix® RC 80use its aspect rds were used. Ttensile strengtticity of 200 G
were used: 0.7m-3), and 1.5
ition of fiber wte is very difficof superplasticin of the F80 f% (98.13 kg mnforcement invery similar. oncretes withTable 1 and
2. The amounxtures varied wadjustment ofo the addition
stment was smf fibers was uwith and with
s also presentethe workability
out mineral addi
-reinforced concrete0 BN Dramix RC 80/650% 0.75% 1.00% 13.01 424.68 429.61 46.02 849.37 859.21 86.02 849.37 859.21 86.58 167.24 169.18 17.75 58.88 78.50 9.23 4.25 4.3085 40 120
ith mineral addi
-reinforced concrete0 BN Dramix RC 80/650% 0.75% 1.00% 16.53 257.09 259.40 2
1.15 31.,21 31.49 38.54 98.75 99.64 95.11 856.95 864.66 85.11 856.95 864.66 88.37 168.73 170.25 17.75 58.88 78.50 9.28 4.28 4.3260 140 130
d a retes ding by ash. aper 0/60 ratio The
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v. 38, n. 4, p. 45
e the concretesile tests weretests, cylindri
mm and heigh, four-point bermine the tostrength of th
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55-463, Oct.-Dec
s, compressione carried outical specimens
hts of 300 mmbending tests
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are cross-sectioe 800 mm in lgle bar oftrength of 49410 GPa. Thesure the ra, that is, to avoonce the spec
ition.
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as 1000 mmand was positens to leave 10allow a loadgages were fixtension spec
ed in Figure 2e of the tea bare bar, the
457
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458 Oliveira Júnior et al.
Acta Scientiarum. Technology Maringá, v. 38, n. 4, p. 455-463, Oct.-Dec., 2016
length, test setup, and measuring and evaluation techniques were used in both cases. The strain of the bare bar was measured by three electrical strain gages fixed to the same position of the tension specimens.
Testing procedure
The tension tests were carried out under displacement control in an electrical-mechanical universal testing machine with a capacity of 300 kN (see Figure 3). The rate of the displacements used during all tests was 0.3 mm min-1. The reinforcement steel strains were measured by three strain gages spaced 102 mm apart. The first strain gage was placed at 92 mm from the superior end of a concrete prism of 800 mm. The steel strains were measured at each 5 kN load increment.
Figure 3. Test setup.
Results and discussion
Concrete properties
The mechanical properties of concretes without mineral additions are given in Table 3 and concretes with mineral additions are given in Table 4.
These tables show that the mechanical properties of the SFRC were positively affected by the presence of fibers. The compressive strength (fcm) had a maximum increase of 28%. The flexure (fctm,f) and
splitting (fctm) tensile strengths were also affected by fibers, and these properties increased as the fiber content increased. The same is true for the toughness factor. By comparing the results in Tables 3 and 4, it can also be observed that the mechanical properties of the SFRC were reduced by the 30% replacement of the cement by fly ash.
Table 3. Mechanical properties of concretes without mineral additions.
Vf (%) Plain concrete
Steel fiber-reinforced concrete Dramix RC 65/60 BN Dramix RC 80/60 BN 0.75% (0.49)A
1.00% (0.65)A
1.50% (0.98)A
0.75% (0.60)A
1.00% (0.80)A
1.25% (1.00)a
fcm, MPa 44.37 56.90 45.48 52.17 52.31 51.80 56.37fctm, MPa 4.20 6.15 6.12 8.28 6.46 6.85 7.75 fctm,f, MPa – 8.14 8.80 9.22 9.10 9.50 7.01 Toughness factor, MPa – 7.13 7.91 8.25 7.35 7.95 5.56
Table 4. Mechanical properties of concretes with mineral additions.
Vf (%) Plain concrete
Steel fiber-reinforced concrete Dramix RC 65/60 BN Dramix RC 80/60 BN 0.75% (0.49)A
1.00% (0.65)A
1.50% (0.98)A
0.75% (0.60)A
1.00% (0.80)A
1.25% (1.00)A
fcm, MPa 41.40 44.37 42.63 49.90 43.20 42.05 45.00 fctm, MPa 4.25 4.73 6.48 7.09 6.15 5.96 5.85 fctm,f, MPa – 6.85 6.87 9.84 8.20 9.34 8.93 Toughness factor, MPa – 5.81 6.33 8.90 7.34 8.20 7.26
Crack width
The crack patterns in tension specimens were observed during tension tests. The plain concrete specimens showed a small number of transverse cracks. With the addition of steel fibers, multiple cracks were observed, which demonstrated that the best control of the cracking process was provided by the fibers.
Figure 4 shows how the average main crack width (wm) varied as the load increased. The values presented in these figures refer to the mean of measurements carried out at several points of the crack (mainly in corners), which means that the crack width was not uniform along its path. The same figure shows the maximum limit of cracking recommended by the American Concrete Institute (ACI, 2005) for concretes without fibers, which in this case was 0.329 mm. A significant reduction in the crack width due to the addition of fibers was observed, and this reduction increased as the amount of fiber increased. In some cases, this reduction reached 75% compared to the crack width in the tension specimen made of plain concrete. Comparing the crack width to the maximum limit prescribed by the ACI 224R, it was noted that in tension specimens made of SFRC this limit was
Tension
Acta Sci
reachedreinforc
Figure 4without m
Load–st
Theevaluatmechanaspect rwas obsgreater specimthis loa(Figureaffectedfor boreinforcwas higsteel inwas veradditionwith mwere siminerasubstitureducin
n stiffening of S
entiarum. Techn
d for loads ncement or, in
4. Average mainmineral additions.
train relation
e load–strain e the influenical behavior ratio and the fserved that spe
tensile loadsens of tad increased aes 5 and 6), ald by the fiber aoth fibers, thcement steel igher than the
n the plain conrified for mixtns. Furthermo
mineral additioimilar to the rl additions, ution of cemenng the tensile s
FRC
nology
near the yieldsome cases, w
n crack widths i.
relation wasence of steelof tension spefiber content wecimens of thes for a given the plain as the fiber colthough it wasaspect ratio. It
hat the yieldiin the SFRC tyielding load
ncrete tension tures with andore, the respoons had loweresponses of c
which sugnt by fly ash isstrength of SFR
ding load ofas not reached
in tension specim
s determinedl fibers on
ecimens. The fwere evaluatede SFRC suppo
strain level tconcrete,
ontent increas not significat was also verifing load oftension specim
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wherβ - T
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steel
m,sεΔtensio
Maringá,
e 5. Influence ofn of a tension spe
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load–strain imen by aption, sεΔ is th
he bare steel bension specim
he same difsured in the fation 1.
máx,s
sεΔ
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re: Tension stiffeni- Difference i
and the tensio
máx - Differenc
on specimens
v. 38, n. 4, p. 45
f the F65 fiber cocimen.
stiffening cte ( β ) can berelationship
pplying Equahe difference
bar and the smen at the sam
fference betwfirst crack (Fig
ing coefficientin strain betw
on specimen; ce between stra
when the first
55-463, Oct.-Dec
ontent on the load
coefficient ofe determined
of the teation 1. In between the
strain of the bme load, and Δween strainsgure 1a), acco
t (dimensionleween reinforce
ains of steel ba
t crack appears
459
c., 2016
d–strain
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ension this
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460
Acta Scientiarum
Figure 6. Influenrelation of a tensio
The strainembedded in have uniformfrom the averglued to tsimplificationsignificant (F& Vallini, 20applied to tconcrete (Figby comparinequations avatension stiffen[1], Collins aInstitute of InternationaleFields and stabilized crackcomparison sstiffening obtwith and wagreement wanalytical equ
m. Technology
nce of the F80 fibon specimen.
n along the lthe concrete
m distributionraged value othe bar. Aln, the errorsischer & Li, 205). This metension speciure 7), and itsg these resuailable in thening, that is: nd Mitchell (Japan (AIJ,
e du Béton Bischoff
king stage with showed that tained from b
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ethodology wimens made s viability was
ults with the e literature toBelarbi and H1991) [2], Arc1986) [3], F(FIB, 2012)(2004) [5]
long-term loadthe values o
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he load–strain
e steel bar assumed to s obtained train gages s was a were not
i, Mihashi, as initially
of plain s evaluated
analytical o evaluate
Hsu (1994) chitectural Fédération [4], and for a
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M
Figure 7. Complain concreteequations prese
Proposed emstiffening coe
To estimSFRC, ananalysis wparameters:( IR ) obtain( D/L ) by ththe tensionapproaches,average curvversus the sused withoupresence ofsignificantlyconcrete. Liindividual avobtain the cdescribes ththe reinforceregression msteel fibers o
Maringá, v. 38, n.
mparison of thee obtained fromented in the literat
pirical model toefficient for SFR
mate the tensioempiric mo
was proposedstrains ( ε ) an
ned by multiplhe fiber contenn stiffening p
refer to Fieldsves of the tenstrain bar obtut making anyf mineral addity change theinear regressio
average curvescoefficients ofhe experimenement index sh
model to accouon tension stiff
Oliveir
. 4, p. 455-463, O
tension stiffeningm the tests with
ture.
o estimate the teC
on stiffening cdel based on
d using thend the reinforclying the fiber
nt ( fV ). For anparameters ans and Bischoffnsion stiffeninained from thy distinction rtions because tension stiffe
ons were perobtained fromthe linear mo
ntal behavior. hould be inclu
unt for the inflffening.
ra Júnior et al.
Oct.-Dec., 2016
g coefficients of h the analytical
ension
oefficient for n regression e following cement index r aspect ratio n overview of nd modeling f (2004). The ng coefficient he tests were regarding the they did not
ening of the rformed over m the tests to odel that best
For SFRC, uded in the fluence of the
Tension
Acta Sci
Figuconcretobtainegood agpropose
=β 00.1
Figure 8coefficien
Figuslopes othe fibEquatioestimatSFRC. coeffici
001.=β
Figure reinforce
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entiarum. Techn
ure 8 shows te and comped from the greement betwed model, whi
(−+ 184.42100
8. Proposed modnt for plain concre
ure 9 shows of the linear reber reinforcemon 3, whichting the tensIn this case, t
ient is also lim
( 76774200 . +−+
9. Correlation bement index.
ure 10 showed model an
n stiffening for
FRC
nology
the proposedares it to thtests. This co
ween the averaich is given by
)ε±15.5304 for
del to estimate tete.
the correlatiegression modment index, wh represents sion stiffeningthe maximum
mited to 1.00.
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between tension
ws a comparisnd the exper concretes rei
model for pe average cuomparison shage curve andEquation 2.
r Vf = 0.00%
the tension stiffe
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the modelg coefficienttension stiffen
00
stiffening and
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Maringá,
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e 10. Influence on stiffening coeffi
igure 11 shoosed modelon stiffening fs. A good agreand the proporete reinforce%, the SFRC w
wed an increficient with inc
v. 38, n. 4, p. 45
eement betweeosed model wcreases, the creases. Mores of 1.50%, th
not show anyncreases sudd
with this fiber plastic behaviess than 1.50%coefficient wits observed, but observed for
of the F65 fiber cient.
ows a compaand an exp
for concretes reement betweeosed model wd with an F6with an F80 coease in the creasing concre
55-463, Oct.-Dec
en the experimwas observed. A
tension stiffeover, for conhe tension stiffy decrease. Odenly as the
content, the or in tension
%, a decreaseth an increaseut this decreasplain concrete
content on the
arison betweeperimental avreinforced witen the experim
was found. Lik65 fiber conteontent of 1.25%
tension stiffete strain. Thu
461
c., 2016
mental As the ffening ncretes ffening
On the strain
SFRC n. For in the of the se was e.
average
n the verage th F80 mental ke the ent of % also
ffening us, the
4
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f
w
p
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462
Acta Scientiarum
SFRC also stension. For decrease in thincreasing codecrease was plain concrete
Figure 11. Influtension stiffening
Comparingfibers, a similaconcretes reinindex of the fwith a greateruse a lower fibindex remainsreinforcementplastic behavio
The hardeoccurred for contents, thatfibers. In bothfibers was appwas also obsersignificantly c
m. Technology
shows an elafiber contentshe tension stioncrete strainalso much les
e.
uence of the F80 coefficient.
g the results oar behavior in nforced with fibers is observr aspect ratio aber content bes constant. In t index greateror in tension. ening after the
the speciment is, 1.50% F6h cases, the reiproximately thrved that the mchange the te
astic-plastic bs of less thaniffening coeffi
n was found,ss than that ob
fiber content on
obtained for bothe tension stithe same reinved. Thus, if are used, it is ecause the reinaddition, SFR
r than 0.60 sh
first crack of ns with the la65 fibers and inforcement inhe same (RI =mineral additioension stiffeni
ehavior in n 1.25%, a ficient with , but this bserved for
n the average
oth types of iffening for nforcement steel fibers possible to
nforcement RCs with a how elastic-
f the matrix argest fiber 1.25% F80 ndex of the = 1.00). It ons did not ing of the
M
SFRC, whisubstitution
Conclusion
The follothe experim
1. Thereduction dgreater reducases, this raverage cracplain concre
2. SFRCcompared toof fibers toimprove thmembers. Findex greatetension was
3. No iSFRC was ois suggestedcement by ftensile behproperties waddition of f
4. Thecalculationmembers suThus, the ecoefficient sthe FIB (201concrete, cawidth forstructures re
Acknowledg
The auEducation(Capes – Bresearch andElétricas S.Aand technici
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Received on June 5, 2015. Accepted on March 15, 2016.
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