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The Institution of Engineers,
Malaysia
Universiti
Teknologi MARAUniversiti Malaya
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12thInternational Conference on Concrete Engineering and Technology
1214 August 2014
Steel Fibre Reinforced Concrete - From Research to Practice
Stephen J. Foster
Professor, Head of School, School of Civil and Environmental Engineering, UNSW Australia, NSW,
Australia. Email: [email protected]
Abstract
After 50 years of research in the development and placement of fibres in reinforced concrete, the
concept has matured to the stage where it is finding increasing use in practice. Design rules for
steel fibre reinforced concrete (SFRC) available in Europe, and elsewhere, are enabling engineersto use these new generation materials, on their own or in combination with conventional
reinforcing and prestressing. In Australia, work is underway on standards development of SFRC
for structural applications; the rationale behind standards rules for development of structural
application in SFRC is presented.
1. Introduction
Romualdi and Batson (1963) demonstrated that the tensile strength and crack resistance of concrete
can be improved by providing suitably arranged and closely spaced wire reinforcement. The
concept has matured to the stage where it is finding increasing use in practice. Banthia and Trottier
(1994) remarked that steel fibres are used as shear reinforcement in reinforced concrete (RC)
structural elements, for blast resistance in structures, as shotcrete in tunnel linings, for use in slopestabilisation works and to limit early age shrinkage cracking in large concrete pavements.
By adding fibres to a concrete mix the objective is to bridge discrete cracks providing for some
control to the fracture process and increase the fracture energy. Since the early work, the pullout
mechanism of discontinuous fibres embedded in a variety of cementitious materials has been
studied by numerous researchers; however, after more than 50 years of research into steel fibre
reinforced concrete (SFRC) there remain few national standards that deal with the design of SFRC
structures and bridges in a comprehensive way. An early adopter of SFRC in standardization is that
of the New Zealand Standard NZS 3101 (2006), which largely used the recommendations of the
RILEM Technical Committee 162 as reported in Schntgen and Vandewalle (2003). In the NZ
Standard, the post-cracking strength of the SFRC is determined by use of deflection controlled tests
on prisms cast with the fibre to be used. This data is then converted to a stress versus crack openingdisplacement (-COD) relationship using a prescribed methodology. Models for strength and
service design in regards to flexure, shear and axial forces are included.
ACI-318 (2008) introduced a limited allowance for hooked or crimped steel fibres to be used as
minimum shear reinforcement in beams and slabs that are not greater than 600 mm in depth and
with concrete strengths not exceeding 40 MPa. The dosage of fibres required is typically 60 kg/m3,
a volume fraction of 0.75 per cent of the concrete.
In Europe a number of national guidelines and technical rules have been established for the design
of SFRC structural elements, including the German technical rule for design with SFRC, which
have been progressively advanced since 2005; the latest version is the DafStb Directive for SFRC
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(2012). Another major source from which design guidance may be found is the fib Model Code
(2013), which represents much of the current thinking on the topic from Europe and elsewhere.
In January 2014 the Draft for Public Comment Australian Standard for the design of Concrete
bridges was released (DR AS5100.5); this is the first standard in Australia to include proceduresfor the design of steel fibre reinforced concrete structures. This paper provides the background for
the development of the design rules for draft Australian Standard for Concrete Bridges (DR
AS5100.52013), including determination of core materials properties, design models for strength
and serviceability and on quality control deliverables.
2. Fibre Dispersion
Htut (2010) conducted X-ray imaging on seven dog-bone shape specimens subjected to uniaxial
tension action (Foster et al, 2013). It was observed that cracks initialise from areas with poor fibre
dispersion and that fibre dispersion plays a significant role in crack initialization and, consequently,
on the tensile strength. As was observed by Markovic et al. (2004), Htut found that the crack path
follows the easiest propagation route and is often near the end of fibres or around them (Figures 1
and 2). Consequently, many of the end-hooked fibres fail to engage and do not deform during the
fracture process.
(a)
(b)
Figure 1. X-ray images showing crack formation during a uniaxial tension test: (a) 0.5% fibres;
(b) 1.5% fibres.
Figure 2. Crack propagation during a uniaxial tension test: (a) 0.5% fibres.
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The dispersion of fibres in the matrix and deformation of the end-hooks significantly influences the
tensile behaviour of a SFRC composite. In the development of material models for design, this
observation needs consideration. Eleven 30 mm thick dog-bone shaped specimens with randomly
distributed 25 mm long by 0.3 mm diameter end hooked fibres and volume percentages of between
0.5% and 2% were cast and X-ray imaged prior to tensile testing (Htut, 2010, Foster et al., 2013).The images were then analysed for fibre concentration over various regions (Figure 3). Each
sample image was filtered to distinguish the fibres from the background image (Figure 4). A
particle analysis was then undertaken to determine the area of fibres in the image (white area in
Figure 4b) with the fibre dispersion/distribution factor (Ffd) defined as the ratio of white area to the
total sample area.
The median value of Ffdfor samples taken within one dog-bone specimen represents the average
fibre volume fraction,f. This data is plotted in Figure 5 for the dog-bone shaped specimens for the
different, known, fibre volumetric ratios (ffrom 0.5% to 2.0%).
Figure 3. Sampling locations for fibre dispersion analysis on a 25 mm 25 mm grid
(a) (b)
Figure 4. Example of 50 mm square sample; (a) original image before filtering and colour
inversion, and (b) digital image after filtering.
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Fibre Dispersion Factor (Ffd)
0.000
0.005
0.010
0.015
0.020
0.025
FibreVolumetricR
atio(f)
126 136fd
ffd
FF
Figure 5. Median fibre dispersion factor versus fibre volume concentration for the 30 mm thick
specimens.
From the fibre dispersion data, the standard deviation for the test series was = 0.27f and,
considering the fibres to be normally distributed, the 75thand 90
thpercentiles are 75 0.82 f
and 90 0.65 f , respectively.
3. Fibre-crack Interaction
Figure 6 shows the results and X-ray images for tensile stress versus crack opening displacement (COD) for a specimen with 1% of 25 mm long by 0.3 mm diameter hooked-end fibres tested by Htut
(2010). For tensile strength properties obtained from direct tensile testing of unnotched specimens of
reasonable size, the influence of fibre dispersion is directly considered in the resulting materialsrelationship. That is the dominant crack forms where the local fibre concentration is its lowest across a
section and where near the end of a fibre, deflects around it. When specimens have a dominant notch,
however, the crack path forms at the notch and the impact of fibre dispersion is negated (Markovic et
al., 2004). Consequently, fibres have a higher possibility of being fully deformed in the notched section
tests and, thus, higher tensile strengths and ductility are observed.
The digital X-ray images taken during the uniaxial tension test of the dog-bone specimens are used
to highlight the importance of fibre dispersion on the crack formation/initiation and propagation
processes. To validate the findings, further digital image analysis was undertaken to determine the
fibre dispersion along the crack path of the dog-bone shaped specimens containing fibre volume
concentrations of 0.5%, 1.0% and 1.5%. A typical X-ray image around the crack path is shown in
Figure 7a. Digital image analysis was undertaken on a sample size of 12.5 mm square (Figure 7b).The plot of fibre volume ratio versus fibre dispersion ratio is presented in Figure 8.
The result shows that the cracks are likely to form or propagate along the path of least resistance. The
fibre volume concentration along the crack path was found to be average through the 75th percentile
characteristic value. This confirms the conclusion that fibre dispersion contributes significantly to the
fracture process in uniaxial tension and this observation needs to be taken into consideration during the
development of behavioural models.
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(a)
(b)
Figure 6. Tensile strength of SFRC with 1.0% of 25 mm hooked-end steel fibres: (a) stress versesCOD; (b) X-ray images showing the crack path (Htut, 2010).
For the case of models based on indirect tests (i.e. prism bending tests), less favoured by those working
in the field of fracture but more favoured by industry, the influence of fibre dispersion is unclear. In this
case crack initiation is dominated by the tensile stresses at, or near, the extreme tensile fibre in the high
moment region. The results will be influenced by the type of test, 3- or 4-point bending and by whether
the specimen is unnotched or notched. For models based on this approach and applied to structural
design, it is suggested that the influences of fibre dispersion be treated as for direct tension tests with a
dominant notch.
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(a)
(b)
Figure 7. Digital X-ray image along the crack path: (a) before the image analysis and (b) after the
image analysis.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Fibre Dispersion Factor(Ffd)
0.000
0.005
0.010
0.015
0.020
0.025
FibreVolumetricRatio
f) Mean
75th %ile Characteristic
90th %ile Characteristic
126 136fd
ffd
F
F
Figure 8. Fibre volume ratio versus average fibre dispersion along the crack path.
In the case of physical-mechanical models built from single fibre pull-out observations, fibre
dispersion needs some consideration when applied to design. For the case of one-way shear in
beams, for example, where sections are large and many failure paths are possible, the influence of
variations of fibre dispersion cannot be ignored in the development of reliable design models.
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4. Materials Properties and Testing
The most fundamental property of SFRC is its post cracking residual tensile strength. For this strength a
value corresponding to a crack opening displacement (COD) of 1.5 mm in a direct tensile test is adopted
(denoted as 1.5f
, where the prime indicates a characteristic value). To assist designers and suppliersalike, a series standard strength grades are proposed; these are 1.5f values of 0.4 MPa, 0.6 MPa,
0.8 MPa, 1.2 MPa, 1.6 MPa and 2.0 MPa. In the determination of characteristic values for materials
properties the Standard, as currently written, suggests that the population may be treated as normally
distributed and a confidence level of 75% shall be used such that 95% of the population exceeds the
characteristic value. The assumption of normal distribution requires some consideration; a log normal
distribution may be more representative and removes potential for the negative strengths.
The residual direct tensile strength (refer Figure 9) may be determined by a direct tension test
(Figure 10) or by a combination of matched direct and indirect testing for a particular mix design.
In the latter case, the relationship between the direct and indirect tensile strength is obtained once
and, provided that the mix design does not change within set parameters of fibre type and content,
water to cementitious material ratio, maximum aggregate particle size and compressive strength,
may be used for any project. In this case, the relationship between 1.5f and the flexural strength is
determined as:
1.5 1 ,4 ,4R Rf k k f (1)
where k1is the boundary (or wall) influence factor and kR,4is a reference factor that provides the
relationship between ,4Rf and 1.5f . In Equation (1), ,4Rf is determined from 3-point notched
bending test, conducted in accordance with EN 14651 (2007):
4,4
2sp
3
2R
F Lf
bh
(2)
where bis the width of the specimen in mm, hsp is the distance between tip of the notch and the top
of cross section in mm, L is the span in mm and F4 the load recorded at a crack mouth opening
displacement (CMOD) of 3.5 mm.
cr
0
fct
0.5 mm 1.5 mm
f0.5f1.5
Crack formation
PP
COD
Figure 9. Classification of SFRC according to DR AS5100.5: (a) Strain softening SFRC (b) Strain
hardening SFRC.
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125
R145
125
ALL DIMENSIONS 5 mm
Epoxy glue
(optional)
125
25
Universal
joint
215
125
Figure 10. Testing arrangement for determining the direct tensile strength.
The reference factor kR,4is determined as:
,4 1.5 4,R m R mk f f (3)
wheref1.5mis the mean residual tensile strength that corresponds to a crack opening displacement of
1.5 mm and fR4,m is the mean residual flexural tensile strength corresponding to a CMOD of 3.5
mm. With the relationship between the residual (direct) tensile strength and the residual flexural
strength established for a given mix, control testing undertaken at the time of construction may be
undertaken using the more simple flexural strength testing procedure.
The factor k1(in Equation 1) is applied to the direct tension tests to adjust for the wall (boundary)
effect and is adapted from Lee et al. (2011) for a square cross-section:
11
10.94 0.6 f
kl b
(4)
where lfif the length of the fibres.
As no standardised test currently exists for the establishment of direct tension, the literature on
fracture was reviewed and the testing arrangement described in Figure 10 was adopted. The
arrangement, adapted from that of van Vliet and van Mier (2000), was selected based on: (1) the
ease of casting; and (2) stress concentrations that determine a predetermined crack path are
reduced, while the failure occurs in a reasonably defined region. While the research of Van Vlietand Van Mier was for plain concrete in tension, Markovic (2004) and Htut (2010) adopted a similar
shape for SFRC and showed consistent results. While the end support conditions and boundary
rotation effect are important for the brittle response of unreinforced concrete (Van Mier et al.,
1995), they become less important for the more ductile post matrix cracking response of SFRC
(that is, from the response point after matrix cracking) at the average measured COD of interest
(1.5 mm) and where the quasi-brittle response of the matrix has no influence. To this end, one fixedend and one rotating end is used to assist with alignment of the specimen in the testing machine.
Alternatively, the characteristic residual tensile strength, 1.5f , may be obtained from:
1.5 R,4 R,20.4 0.07f f f (5)
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where ,2Rf and ,4Rf are determined from testing of 3-point notched prisms, in flexure, conducted in
accordance with EN 14651 (2007). Equation (5) is adapted from Amin et al. (2013).
5.
Design for Strength
Design for combined bending and axial compressionFor strength in bending and axial compression, the simplified stress blocks shown in Figure 11 are
adopted. In this case the contribution of the fibres is taken to be plastic with a constant stress of
1.5f applied to the section on the tensile side of the neutral axis. Forces and moments are resolved
using equilibrium and compatibility in the usual way.
Cc
Cs
Ts
Tf
N.A.
dn
Dd
f'1.5
f2 c'
b
dn
do
Figure 11. Design for combined bending and axial compression.
Design for flexural shearOne of the main areas where it is considered that fibres may play a contribution to design practice
is in the realm of shear; either as total or partial replacement for steel ligatures. The model adopted
for the AS5100.5 draft is based on the simplified modified compression field approach (Bentz et
al., 2006) and is adapted from the alternative model presented in the fibModel Code (2013). Theshear models developed in thefibcode are based on the Level of Approximation (LoA) approach
(Muttoni and Fernndez Ruiz, 2012). With this methodology, design rules are developed based on
sound physical-mechanical models with varying levels of simplification. That is, a Level Imodel is
based on simplification of the Level IImodel that, in turn, is based on simplification of a Level III
model, etc. In the approach of the AS5100.5 draft, a Level Imodel is adapted from the Level II
model presented in thefibModel Code (see Figure 12).
w
V
Vu
wcrit
Vuf
Load-wrelationship
Vuc
Contribution of fibres
Contribution
of matrix
Vus
Contribution
of stirrups
(a) Level II approximation
w
V
uf
w = 1.5 mmuf
V
Load-wrelationship
V +V +Vuc
Contribution of fibres
Contribution
of matrix
Contribution
of stirrups
us
wuc
uf
V +Vuc us
(b) Level I approximation
Figure 12. (a) Coupling (LoA I) and (b) decoupling (LoA II) of Vucand Vuf.
It is shown in Foster (2010) that the concrete (Vuc) and fibres (Vuf ) components to the shear strength
of a beam are coupled through their common crack width (Figure 12a). In this respect the fibmodel
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is simplified by assuming a crack width at ultimate for the fibres component of wuf= 1.5 mm and
the concrete, ligatures and fibres components are decoupled (Figure 12b).
The design shear strength of a beam is then Vu, with = 0.7 and:
Vu= Vuc+ Vuf+ Vus (6)
where Vuc is determined using the simplified modified compression field model and Vus is the
contributions of the ligatures (Figure 13). The fibre component is:
1.5 cotuf f v minV k b z f (7)
where kfis a factor to account for the variance in fibre distribution and is taken as kf= 0.8 (refer
Foster et al., 2013), z is the internal lever arm between the centroids of the flexural tensile and
flexural compressive stress resultants, taken as z= 0.9do, where dois as shown in Figure 11, and
minis the minimum strut angle calculated from:
min= 29+ 7000x (8a)
wu= 0.2 + 1000x= 1.5 mm (8b)
where xis the longitudinal straining of the web measured at the mid-height of the effective shearsection (seefibModel Code, 2013).
The minimum strut angle for the fibres component, min, is determined as 38 degrees andcot(min) = 1.28. Multiplying the factors gives:
0.7uf v oV k b d f (9a)
k= cotv1.28 (9b)
C
T
k f b1.5
V
V + Vuf
z
1
1
f v
v
us
A fst sy
'
Figure 13. Design for combined bending and axial compression.
where vis the angle between the axis of the concrete compression strut and the longitudinal axis ofthe member (Figure 13).
The model is validated using the data set presented in Foster (2010), with the results presented in
Figure 14. The set consists of 180 SFRC reinforced concrete beams that failed in shear (Set A), and
115 (Set B) with the restrictions a/d fcm< 70 MPa (a is the shear span and d is the
effective depth). As the residual tensile strength was not measured in any of the tests in the data set,
the tensile strength was calculated using the VEMI Model (Voo and Foster, 2004, Foster et al.,
2006). Further details for the data set and the tensile strength model are given in Foster (2010).
Figure 14 shows the AS5100.5 approach to be sufficiently with a one percentile value in the
exponential-to-model ratio of 0.87, which suggests that the strength reduction factor () of 0.7 issufficiently conservative.
For beams that require shear reinforcement, the minimum contribution provided by the transverse
reinforcement (fibres and ligatures) is:
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min
max 0.1 , 0.6us uf c v oV V f b d (10)
For the initial implementation, a conservative approach is adopted such that the maximum
contribution of the fibres component to the shear strength, Vuf, is limited to the maximum of that
given by Equation (10) with Vustaken as zero and 30 per cent of Vu.
6.
Design for Service
Introduction
For service design, steel fibres assist in the control of cracking and deflections. For design it is assumed
that a uniform tension is taken by the fibres equivalent to a stress in the concrete of 1.51.1f . In the
determination of the minimum longitudinal reinforcement needed for bending, the draft standard
ignores the beneficial influence of the fibres; thus localisation of cracking due to the fibres crossing a
crack is avoided. In this case, the effect of the fibres is to produce more closely spaced, and finer,
cracks. A test on tension stiffening for SFRC undertaken by Amin et al. (2014) is shown in Figure 15.
This test was conducted on a 150 mm square section of 1.0 metre length, with an N20 reinforcing barand 25 kg/m3of double end-hooked Dramix
5D-65/60-BG fibres. The fibres were 0.9 mm in diameter
and 60 mm long. At a COD of 1.5 mm, dog-bone tests gave a mean residual tensile strength of 0.69
MPa. The results of the test, shown in Figure 15, indicate the model adopted to be somewhat
conservative.
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
a/d
0.0
0.5
1.0
1.5
2.0
2.5
Vu
.exp/Vu.model
= 0.7
Set A
n = 180
0.0 200.0 400.0 600.0 800.0
D (mm)
0.0
0.5
1.0
1.5
2.0
2.5
Vu.exp/Vu.model
= 0.7
Set B
n = 115
ave. = 1.27
COV = 0.17
Figure 14. Comparison of Draft AS5100.5 Level I approximation for the fibres component (data
described in Foster, 2010).
dD
dn
st
o o
st
Tf
Ts
C
Section Strains at
moment,M
Stresses Forces
d /3n
1.1f'1.5
(D+
d
)/2
n
Figure 15. Strain and stress distribution on a cracked section subjected to in-service bending.
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Crack control
The rules for the control of cracking are derived from NZS3101:Part 2 (2006) and the fibModel
Code (2013). The minimum amount of longitudinal reinforcement required to obtain controlled
crack formation is:
.min . 1.5.max
1.1 0.0ctst c p ct ef s
AA k k k f f
f (11)
whereAst.minis the area of reinforcement required within the tensile zone (in mm2), ifAst.minis zero
only steel fibres are necessary to control cracking; Actis the area of concrete on the tensile side of
the elastic centroidal axis (in mm2); fs.max is the maximum stress permitted in the reinforcement
immediately after formation of the crack, given in earlier sections of the standard;fct.efis the greater
of 0.6 ,cmf where fcm is the mean compressive strength of the concrete, and 3.0 MPa. The
coefficients k kc and kp are adjustments for shrinkage and temperature, the nature of the stress
distribution immediately prior to cracking and for the level of prestress on the section, respectively.
Deflections
The short-term deflection of an SFRC member is calculated using the model described in
Figure 15; the tension stiffening component is taken to be 1.51.1f through the depth of the tensile
zone. This model is then used to determine the effective second moment of areaIef.
Long-term deflections due to shrinkage and creep are calculated separately using the material data
specified elsewhere in the Standard, and with the principles of mechanics.
7. Quality Assurance
While quality assurance is fundamental in the delivery and placement of SFRC, in general, it is
paramount in cases where life safety is the essential criteria. While placement and distribution of bars
is easily observed before placement of the concrete, this is not the case with SFRC. The principles ofreliability need to be applied taking due account of the variability of the placed product and good site
control is necessary to ensure the desired distribution of fibres, within the bounds of usualvariabilities, and for no cold joint connections.
The draft Standard sets controls on quality at three stages; quality of materials and mixing
processes, factory and routine production control and determination on the fibre content and
distribution at site. The requirements for production process and finished product inspection are
demonstrated in Table 1 and the criteria for acceptance for dosage in Table 2.
Table 1. Continuous production control
Subject Inspection/Test Purpose Frequency
Production process inspection
Fibre content-
record
Record the quantity
added
To check the content Every batch
Fibre content in
the fresh
concrete
Testing according to
EN 14721 (2007)
Conformity with the target
dosage and verify
homogeneous distribution
of the steel fibres in the mix
Beginning of each
day and /50 m
manual dosing
/150 m automatic
dosing
Concrete mix Visual check Correct mixing with correct
fibre type and even fibre
distribution without balling
Daily
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Finished product inspection
Steel fibre
ConcretePerformance
Check limit of
proportionality, and post-
crack flexural strength in
accordance to EN 14651
(2007)
Check performance level
of the specification
Two beams every
other day ofproduction
Table 2. Criteria for acceptance of steel fibre dosage
Test control Test control Criteria
Each sample Each partial test 0.80 of the specified target
dosage
Average of three samples
from the batch
Each test 0.85 of the specified target
dosage
Continuous control: average
of > three tests
Continuous control: average
of > three tests0.90 of the specified target
dosage
8.
Conclusions
While the tensile and fracture behaviour of steel fibre reinforced concrete have been researched for
nearly five decades, their use in structures has been limited by a lack of design models and
standardisation. With design rules for SFRC introduced in some national concrete structures
standards, and also in the fib Model Code 2010, it could be expected that more use will be made of
this higher performance material in building and bridge structures for the carrying of tensile
stresses. In 2014 the Draft for Public Comment Australian Standard for the design of Concrete
bridges was released (DR AS5100.5, 2014); this is the first standard in Australia, and one of thefew national standards in the world, to include design procedures for steel fibre reinforced concrete
in a comprehensive way. This paper provided some the background for the development of the
design rules, including the determination of the materials properties, design models for strength and
serviceability and on quality control measures.
9. References
ACI-318 (2008),Building Code Requirements for Structural Concrete and Commentary, American
Concrete Industry, Farmington Hills, Michigan, USA.
Amin, A., Foster, S.J., and Muttoni, A. (2013), Evaluation of the Tensile Strength of SFRC as
Derived from Inverse Analysis of Notched Bending Tests, Proceedings of the 8th
International Conference on Fracture Mechanics Concrete and Concrete Structures
(FramCoS-8), J.G.M. Van Mier, G. Ruiz,C. Andrade, R.C. Yu and X.X. Zhang (Eds),Toledo, Spain, March 10-14, pp 1049-1057.
Banthia, N. and Trottier, J. F. (1994). Concrete reinforced with deformed steel fibres, Part I: Bond-
slip mechanisms. ACI Materials Journal. 91(5): 435-446.
Bentz, E.C., Vecchio, F.J., and Collins, M.P. (2006), The simplified MCFT for calculating the
shear strength of reinforced concrete elements. ACI Structural Journal, Vol. 103, No. 4, pp.
614-624.
DAfStB (2012) Richtlinie Stahlfaserbeton (Directive for SFRC). Deutscher Ausschuss fur
Stahlbeton, Germany - (In German).
DR AS 5100.5 (2014), Draft for Public Comment Australian Standard, Bridge Design Part 5:
Concrete, Standards Australia, Sydney.
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EN 14651 (2007) Test Method for Metallic Fibre Concrete- Measuring the Flexural Tensile
Strength (Limit of Proportionality, Residual). European Committee for Standardization.
EN 14721 (2007) and hardened concrete, European Committee for Standardization.
fib Model Code (2013), fib Model Code for code for concrete structures 2010, FdrationInternationale du Bton (), Lausanne, Switzerland, published Ernst & Sohn, Berlin
Germany.
Foster, S.J. (2010), Design of FRC beams for shear using the VEM and the draft Model Code
approach, Bulletin No 57, Fdration Internationale du Bton (fib), Lausanne, Switzerland,
pp. 195-210.
Foster, S.J., Ng, T.S., and Htut, T.N.S. (2013), High Performance Fibre Reinforced Concrete:
Fundamental Behaviour and Modelling, Proceedings of the 8th International Conference on
Fracture Mechanics Concrete and Concrete Structures (FramCoS-8), J.G.M. Van Mier, G.
Ruiz,C. Andrade, R.C. Yu and X.X. Zhang (Eds), Toledo, Spain, March 10-14, pp 69-78.
Foster, S.J., Voo, Y.L., and Chong K.T. (2006).Analysis of Steel Fiber Reinforced Concrete Beams
Failing in Shear: Variable Engagement Model, Chapter 5, Finite Element Analysis of
Reinforced Concrete Structures, Lowes, L., and Filippou, F. (Eds.), ACI SP-237.Htut, T.N.S. (2010). Fracture Processes in Steel Fibre Reinforced Concrete. PhD Thesis, School of
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