1. Steel Fibre Reinforced Concrete - From Research to Practice

8/10/2019 1. Steel Fibre Reinforced Concrete - From Research to Practice

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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

Civil and Environmental Engineeering, The University of New South Wales: 389pp.

Lee, S.C., Cho, J. and Vecchio, F.J. (2011), Diverse embedment model for steel fibre reinforced

concrete in tension: model development. ACI Materials Journal Vol. 108, No. 5, pp. 516-

525.

Markovic, I., Walraven, J.C. and Van Mier, J.G.M. (2004), Tensile behaviour of high performance

hybrid fibre concrete, Proceedings of the 5th International Conference on Fracture

Mechanics of Concrete & Concrete Structures (FraMCoS-5), April 12-16 Vale, Colorado,

USA, pp. 1113-1120.

Muttoni A., and Fernndez Ruiz M. (2012), The levels-of-approximation approach in MC 2010:

application to punching shear provisions. Structural Concrete, Vol. 13, No. 1, pp. 32-41.

NZS 3101: Part 2 (2006), Concrete Structures Standard Part 2 Commentary on the design of

concrete structures, Standards New Zealand.

Romualdi, J.P., and Batson. G.B. (1963). Behaviour of reinforced concrete beams with closely

spaced reinforcement. Proc., ACI Journal. 60(6): 775-789.

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Documents

1. Steel Fibre Reinforced Concrete - From Research to Practice