7
Building and Environment 37 (2002) 1361 – 1367 www.elsevier.com/locate/buildenv Inuence of steel bres on strength and ductility of normal and lightweight high strength concrete R.V. Balendran , F.P. Zhou, A. Nadeem, A.Y.T. Leung Department of Building and Construction, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon Tong, Hong Kong Received 19 June 2001; accepted 19 November 2001 Abstract This paper presents the results of a series of experiments conducted to investigate the eectiveness of bre inclusion in the improvement of mechanical performance of concrete with regard to concrete type and specimen size. Lightweight aggregate concrete and limestone aggregate concrete with and without steel bres were used in the study. The compressive strength of the concrete mixes varied between 90 and 115 MPa and the bre content was 1% by volume. Splitting tests on prisms and three-point bending test on notched beams were carried out on specimens of varying sizes to examine the size eect on splitting strength, exural strength and toughness. The experimental ndings indicate that the low volume of bre has little eect on compressive strength but improve remarkably splitting tensile strength, exural strength and toughness. The increase in splitting tensile strength, exural strength and toughness index for lightweight concrete seems much higher than that of normal aggregate concrete. The size eect on prism splitting tensile strength is not signicant beyond a critical (transition) size. There are apparent size eects on exural strength and toughness index. As the specimen size increases, splitting and exural strengths appear to decrease, and fracture behaviour tends to be more brittle. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fibre-reinforced concrete; High strength concrete; Lightweight concrete; Toughness; Size eect; Energy absorption 1. Introduction Fibre reinforcement can increase greatly the energy adsorption and impact strength of concrete. If a high vol- ume of steel bre (say 5 –20%) is incorporated, strength and ductility in compression can also be improved [1]. Fibre-reinforced concrete has found many applications in tunnel, wall cladding, bridge decks and pavements etc. [1– 4]. It can also be used as a promising repair material for rehabilitation and strengthening of existing concrete structures [1]. With the rapid development in concrete technology, con- crete of strength over 100 MPa can be easily produced with ordinary materials and conventional mix methods [3]. High strength normal or high strength lightweight concrete oers more options for the design of tall buildings and long-span bridges [5,6]. The main concern with high strength concrete is the increasing brittleness with the increasing strength [7]. Corresponding author. Tel.: +852-2788-7682; fax: +852-2788-7612. E-mail address: [email protected] (R.V. Balendran). Therefore, it becomes a more acute problem to improve the ductility of high strength concrete. Most accumulated expe- rience in normal strength bre-reinforced concrete may well be applicable to high strength concrete but the eectiveness of bre reinforcement in high strength concrete may be dif- ferent and thus needs to be investigated. Most of the research on bre-reinforced concrete is fo- cused on bre type, geometry, aspect ratio and volume con- tent. A few researchers have also investigated the eects of concrete type (normal and lightweight) and grade (normal and high strength) [8–10]. According to fracture mechanics of plain concrete, fail- ure behaviour of concrete structures tends to be more brittle with increasing size [11,23]. As a result, there is size eect on exural and shear strength. In the case of bre-reinforced concrete, if the bre volume content is high enough (say more than 3% for steel bre) to produce a very ductile con- crete, size eect probably is negligible. But for a concrete with low volume bre content, the behaviour may still ex- hibit size eect [12,13]. Although most bre-reinforced con- crete used in practice belongs to the latter type, there is lit- tle work done to investigate the size eect [1]. Therefore, it 0360-1323/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII:S0360-1323(01)00109-3

Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

Embed Size (px)

Citation preview

Page 1: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

Building and Environment 37 (2002) 1361–1367www.elsevier.com/locate/buildenv

In uence of steel "bres on strength and ductility of normal andlightweight high strength concrete

R.V. Balendran ∗, F.P. Zhou, A. Nadeem, A.Y.T. LeungDepartment of Building and Construction, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon Tong, Hong Kong

Received 19 June 2001; accepted 19 November 2001

Abstract

This paper presents the results of a series of experiments conducted to investigate the e5ectiveness of "bre inclusion in the improvementof mechanical performance of concrete with regard to concrete type and specimen size. Lightweight aggregate concrete and limestoneaggregate concrete with and without steel "bres were used in the study. The compressive strength of the concrete mixes varied between90 and 115 MPa and the "bre content was 1% by volume. Splitting tests on prisms and three-point bending test on notched beams werecarried out on specimens of varying sizes to examine the size e5ect on splitting strength, exural strength and toughness.The experimental "ndings indicate that the low volume of "bre has little e5ect on compressive strength but improve remarkably

splitting tensile strength, exural strength and toughness. The increase in splitting tensile strength, exural strength and toughness indexfor lightweight concrete seems much higher than that of normal aggregate concrete.The size e5ect on prism splitting tensile strength is not signi"cant beyond a critical (transition) size. There are apparent size e5ects

on exural strength and toughness index. As the specimen size increases, splitting and exural strengths appear to decrease, and fracturebehaviour tends to be more brittle. ? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Fibre-reinforced concrete; High strength concrete; Lightweight concrete; Toughness; Size e5ect; Energy absorption

1. Introduction

Fibre reinforcement can increase greatly the energyadsorption and impact strength of concrete. If a high vol-ume of steel "bre (say 5–20%) is incorporated, strengthand ductility in compression can also be improved [1].Fibre-reinforced concrete has found many applications intunnel, wall cladding, bridge decks and pavements etc.[1–4]. It can also be used as a promising repair materialfor rehabilitation and strengthening of existing concretestructures [1].With the rapid development in concrete technology, con-

crete of strength over 100 MPa can be easily produced withordinary materials and conventional mix methods [3]. Highstrength normal or high strength lightweight concrete o5ersmore options for the design of tall buildings and long-spanbridges [5,6].The main concern with high strength concrete is the

increasing brittleness with the increasing strength [7].

∗ Corresponding author. Tel.: +852-2788-7682; fax: +852-2788-7612.E-mail address: [email protected] (R.V. Balendran).

Therefore, it becomes a more acute problem to improve theductility of high strength concrete. Most accumulated expe-rience in normal strength "bre-reinforced concrete may wellbe applicable to high strength concrete but the e5ectivenessof "bre reinforcement in high strength concrete may be dif-ferent and thus needs to be investigated.Most of the research on "bre-reinforced concrete is fo-

cused on "bre type, geometry, aspect ratio and volume con-tent. A few researchers have also investigated the e5ects ofconcrete type (normal and lightweight) and grade (normaland high strength) [8–10].According to fracture mechanics of plain concrete, fail-

ure behaviour of concrete structures tends to be more brittlewith increasing size [11,23]. As a result, there is size e5ecton exural and shear strength. In the case of "bre-reinforcedconcrete, if the "bre volume content is high enough (saymore than 3% for steel "bre) to produce a very ductile con-crete, size e5ect probably is negligible. But for a concretewith low volume "bre content, the behaviour may still ex-hibit size e5ect [12,13]. Although most "bre-reinforced con-crete used in practice belongs to the latter type, there is lit-tle work done to investigate the size e5ect [1]. Therefore, it

0360-1323/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S0360 -1323(01)00109 -3

Page 2: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

1362 R.V. Balendran et al. / Building and Environment 37 (2002) 1361–1367

Table 1Test methods and specimen size

Test type Specimen Dimensions (mm) Parameters

Compression (basic test) Cube 100× 100× 100 Compressive strengthSplitting (basic test) Cylinder �100× 200 Cylinder splitting

tensile strengthSplitting Prism 76× 76× 100 Prism splitting

100× 100× 100 tensile strength150× 150× 100200× 200× 100

Four-point bending (basic test) Beam 150× 100× 450× 640a Modulus of ruptureand toughness indices

Three-point bending Beam (notched) 50× 100× 200× 300a Flexural strength(notch ratio 0.3) 100× 100× 400× 500a and toughness indices

200× 100× 800× 840a

aDimensions are height, width, span and length of beams.

is important to examine the e5ectiveness of "bre reinforce-ment in high strength concrete elements of varying sizes.In view of the research needs discussed above, the ex-

perimental program was designed to evaluate to what ex-tent splitting tensile strength, exural strength and ductilityof concrete are improved by the incorporation of the samevolume of steel "bre, with regard to concrete type and spec-imen size.

2. Experimental details

2.1. Testing program

It was intended to study the e5ectiveness of steel "bre inthe improvement of strength and ductility of high strengthconcrete. The in uencing variables concerned were concretetype (normal and lightweight aggregate concrete) and spec-imen size.Test type and specimen dimensions used in the study are

shown in Table 1. In addition to the basic tests for the deter-mination of compressive strength and modulus of rupture,splitting tests on prismatic specimens and three-point bend-ing tests on notched beams were carried out to investigatethe improvement in splitting strength and exural strengthand exural toughness.In the three-point bending tests on notched beams, crack

mouth opening displacement (CMOD) was used as thefeed-back control variable to ensure stable tests. In mea-suring exural toughness, the extraneous deformations con-tributed from the supports and testing machine needs to beexcluded from the measured de ection otherwise the exu-ral toughness will be a5ected [14]. Therefore, a special testset-up was used to eliminate the extraneous deformationsand to ensure the measurement of the load-line de ectioncaused only by beam deformations. The de ection was mea-sured by a LVDT transducer. Load–de ection curves wereused to evaluate exural strength and toughness indices.

Table 2Concrete mixes (W=C + S = 0:29, S=C + S = 10%)

Material LSP LSF LTGP LTGF(Kg=m3) (Kg=m3) (Kg=m3) (Kg=m3)

Cement 443 443 443 443Silica fume 49 49 49 49Water (free) 143 143 143 143Sand 660 660 660 660Limestone 1105 1105 0 0Lytaga 0 0 646 646Steel "bre 0 72 0 72

aA commercial lightweight aggregate of sintered pulverised fuel ash:LSP: Limestone, plain concrete, LSF: limestone, "bre concrete, LTGP:lightweight aggregate, plain concrete, LTGF: lightweight aggregate, "breconcrete.

Splitting tests were performed on prismatic specimenssimilar to the standard cylinder splitting tests. Only ultimateloads were recorded in the tests and splitting tensile strengthwas evaluated.

2.2. Materials and mix proportions

The mix proportions are given in Table 2. Four mixesnamely, plain limestone concrete, "bre-reinforced limestoneconcrete, plain lightweight concrete and "bre-reinforcedlightweight concrete were used. In all the mixes the volumefractions of cement, silica fume, coarse aggregates, sandand free water were kept constant. The amount of steel "brewas 1% by volume of concrete.Water–binder (cement + silica fume) ratio [W=(C + S)]

was 0.29 and silica fume replacement rate [S=(C + S)]was 10%. Silica fume is usually added to improve cementpaste=aggregate bonds and also the bond between "bre andconcrete. The active ingredient amount of the superplasti-cizer was changed from 0.5% to 1.5% by weight of cementand silica fume (C + S) content to maintain appropriateworkability for di5erent concretes.

Page 3: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

R.V. Balendran et al. / Building and Environment 37 (2002) 1361–1367 1363

Cement used was ordinary Portland cement. The super-plasticizer used was Conplast 430, of sulphated naphthaleneformaldehyde condensate type, in 40% water solution. Sil-ica fume was in the form of slurry of 50% concentration.Coarse aggregates are crushed limestone and Lytag (sinteredpulverised fuel ash). The maximum size of crushed lime-stone and Lytag was 10 and 6 mm, respectively. Steel "breswere round and straight and were 0:25 mm in diameter and15 mm in length.

2.3. Specimen preparation

In mixing, cement, sand and coarse aggregates were gen-erally blended "rst and silica fume, superplasticizer and wa-ter were then added. In the case of lightweight concrete,lightweight aggregates (Lytag) were "rst mixed with enoughwater for the short-term absorption for half an hour beforeblending with cement and sand. Steel "bres were spread inthe mixer carefully to achieve a uniform distribution of the"bres in the concrete.The specimens were demoulded after one day and stored

in a water tank at 20◦C until testing at the age of 28 days.Notches were introduced in the middle section for the beamsused for three-point bending tests by a diamond saw justbefore testing. For each test 6 specimens were used and themean was used in the analysis. The standard deviations weresmall (¡ 2%).

3. Results and discussion

The experimental test series was carried out to investigatethe e5ectiveness of steel "bre in the improvement of strengthand toughness with regard to concrete type and specimensize.

3.1. Basic properties

The basic properties of the four concrete mixes are givenin Table 3. Owing to the small "bre content (1% by volume,about 3% by weight), the density and compressive strengthof "bre-reinforced concretes are about the same as those ofthe plain counterparts.Cylinder splitting tensile strength and modulus of rup-

ture are increased for both normal and lightweight concrete

Table 3Basic properties

Concrete Density Compressive Modulus of Cylinder splitting(Kg=m3) strength rupture tensile strength

(MPa) (MPa) (MPa)

LSP 2430 113 4.6 4.5LSF 2470 115 6.3 10.5LTGP 2015 90 1.7 3.3LTGF 2030 91 6.0 6.2

Table 4Flexural strength and prism splitting tensile strength

Concrete Flexural strength Prism splitting tensile(MPa) strength (MPa)

S50 M100 L200 S76 M100 M150 L200

LSP 7.9 5.6 4.9 4.1 5.4 5.9 5.4LSF 11.3 6.1 5.6 9.6 7.2 6.6 5.4LTGP 5.9 3.3 2.7 3.6 3.2 3.9 4.4LTGF 11.3 9.3 7.9 8.2 8.5 5.6 5.7

by the introduction of steel "bre. Cylinder splitting tensilestrength of "bre-reinforced concrete is about twice as highas that of plain concrete for both normal and lightweightconcretes. But in the case of modulus of rupture, there is a2.5-fold increase for lightweight concrete and only a smallerincrease was observed for normal weight concrete.

3.2. Prism splitting tensile strength

Splitting tensile strength of a prismatic specimen can beevaluated from the following equation:

fsp =2P�h2

;

where P is ultimate load and h is height of the prismaticspecimen.Tensile strengths evaluated from splitting tests on pris-

matic specimens are included in Table 4 and plotted in Fig. 1.The "gure shows that, for the plain concrete mixes, there isno obvious size e5ect on prism splitting tensile strength. Asreported on splitting tests on cylinders by Bazant et al. [15]and Hasegawa et al. [16], there is no size e5ect on cylindersplitting tensile strength when the size of specimen exceedsa critical size (or a transition size). This transition size be-comes smaller with the increasing strength of a material.Also Fig. 1 shows that, for "bre-reinforced concrete, there issize e5ect on the prism splitting strength with smaller sizesup to 150 mm. The size e5ect is not signi"cant between 150and 200 mm and the critical (transition size) appears to be150 mm.The increase in splitting tensile strength for normal

weight concrete is 134%, 33%, 12% and 0% for specimensizes 76, 100, 150 and 200 mm, respectively. In the case oflightweight concrete, the corresponding strength increase is127%, 165%, 44% and 29%, respectively. In general, prismsplitting tensile strength of lightweight aggregate concreteis improved more than normal weight concrete.Balaguru and Foden [9] studied "bre-reinforced concrete

with various "ne lightweight aggregate fractions. Theyfound that the improvement in splitting tensile strength ismore signi"cant for concrete with higher volume lightweightaggregate and is consistent with the results of the presentstudy.

Page 4: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

1364 R.V. Balendran et al. / Building and Environment 37 (2002) 1361–1367

Fig. 1. E5ects of "bre and size on prism splitting tensile strength;(a) Normal weight concrete, (b) Lightweight concrete.

Generally speaking, the improvement of splitting strengthwith similar volume and type of "bre is more e5ective forlightweight concrete than for normal weight concrete. There-fore, in order to achieve similar increase in tensile strengthfor "bre-reinforced normal weight concrete, a higher vol-ume of "bre or better "bre=concrete bond using hooked end"bre is needed.

3.3. Flexural strength

The exural strength of a notched beam subjected tothree-point bending is calculated from the following expres-sion:

ff =3PS

2b(h− a)2 ;

where P is ultimate load, and S, b, h and a are span, thick-ness, height and notch depth. a= h=3 and S=h= 4.Flexural strengths of notched beams determined by

three-point bending tests are shown in Table 4. The e5ects

Fig. 2. E5ects of "bre and size on exural strength; (a) Normal weightconcrete, (b) Lightweight concrete.

of steel "bre and specimen size on exural strength of nor-mal and lightweight concrete specimens are depicted inFig. 2.As can be observed, exural strength decreases as the

specimen size becomes larger. It is already well establishedthat exural strength of concrete is size dependent. Themore brittle a concrete is, the more profound the size e5ectbecomes. Lightweight concrete of similar mix compositiontends to be more brittle than normal weight concrete andthus the size e5ect is expected to be more prominent. Theexperimental results seem to indicate such a trend. Whenthe specimen size increases from 50 to 100 mm, and from100 to 200 mm, the decrease in strength is 44% and 18%for lightweight concrete but only 29% and 12% for normalweight concrete.There is also size e5ect on exural strength of both normal

and lightweight "bre-reinforced concrete. The size e5ect isless as the incorporation of "bre improves the ductility ofthe materials.

Page 5: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

R.V. Balendran et al. / Building and Environment 37 (2002) 1361–1367 1365

Fig. 3. De"nition of toughness indices according to the testing methodASTM C1018 (1989).

The increase in exural strength due to the addition of "-bre in normal weight concrete is 43%, 9% and 14% for spec-imen size 50, 100 and 200 mm, respectively. For lightweightconcrete, the strength increase is 91%, 182% and 260% forspecimen size 50, 100 and 200 mm, respectively. It is ob-vious that the addition of "bre in normal weight concreteresults in a much less increase in exural strength thanin lightweight concrete. The study on exural strength of"bre-reinforced lightweight "ne aggregate concrete by Bal-aguru and Foden [9] indicates similar trends.It is very diOcult to reach a de"nitive conclusion about

the size e5ect on exural strength improvement of "bre. Itall depends on how the tensile stress–strain relationship ofconcrete will be modi"ed by the addition of "bre. Accord-ing to theoretical analysis by Hillerborg [12,13], strengthincrease rate should be higher for large specimen size. Thepresent results seem to support his prediction.It is likely that "bre-reinforcement enhances both uniaxial

tensile strength and fracture energy so that it can improve exural strength to a much greater extent for lightweightconcrete. Regarding normal weight concrete, the moderateincrease in exural strength may be mainly attributed to theimprovement in fracture energy.

3.4. Toughness index

Toughness is generally de"ned as energy adsorptioncapacity. There are a number of di5erent standards for

Table 5Toughness indices in three-point bending tests on notched beams

Concrete Toughness indices

I5 I10 I30

S50 M100 L200 S50 M100 L200 S50 M100 L200

LSF 5.0 4.7 4.3 10.0 9.1 7.0 31 26 17LTGF 6.6 6.5 6.6 16.0 16.1 16.3 60 63 60

Table 6Toughness indices in four-point bending tests on notched beams

Concrete Toughness indices

I5 I10 I30

LSF 5.0 10.0 28LTGF 6.2 15.0 55

measuring toughness of "bre-reinforced concrete such asASTM C1018 [17–20]. In addition, there are some othermethods proposed by some researchers, e.g. toughness indexproposed by Barr et al. [21], fracture energy proposed byHillerborg [12,13], Gopalaratnam et al. [14].In the present work, the toughness indices suggested in

ASTM C 1018 are used because of its wide acceptance anduse for design and construction although some limitationsexist in this method [18,22].The schematic illustration of the method and calculations

is shown in Fig. 3. The indices I5; I10 and I30 are calcu-lated as ratios of the area under the load–de ection curveup to 3, 5.5 and 15.5 times the "rst crack de ection, dividedby the area up to the "rst crack de ection, respectively. Foran elastic brittle material, all indices should be 1. But for anelastic–ideal plastic material, I5; I10 and I30 should equalto 5, 10 and 30, respectively.The toughness indices for di5erent mixes in three-point

bending and four-point bending tests are given in Tables 5and 6, respectively. The comparison between normal andlightweight concrete is shown in Fig. 4. It is observed thattoughness indices are higher for lightweight concrete thanfor normal weight concrete.Toughness indices of lightweight concrete are not very

sensitive to the specimen size in contrary to size e5ect ob-served on exural strength. Toughness indices are muchgreater than the corresponding values for elastic–ideal plas-tic behaviour, which indicate some type of strain hardeningbehaviour compared to softening behaviour.In the case of normal weight concrete, toughness indices

are smaller or close to the corresponding values for elastic–ideal plastic state. On the other hand, toughness indices be-come smaller when the specimen size increases. Therefore,"bre e5ectiveness on toughness decreases for large speci-mens for normal weight concrete.Balaguru et al. [8] studied the e5ects of matrix strength

on exural toughness and found that toughness indices were

Page 6: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

1366 R.V. Balendran et al. / Building and Environment 37 (2002) 1361–1367

Fig. 4. Toughness indices of "bre-reinforced concretes in bending;(a) Normal weight concrete, (b) Lightweight concrete.

lower for high strength concrete than normal strength con-crete. They also observed the post-peak load drops muchfaster in high strength "bre concrete than normal strength"bre concrete.Therefore, to achieve similar ductility for high strength

concrete, a higher volume "bre or a "bre of higher strengthand better properties such as hooked end "bre should beused.

4. Concluding remarks

The following concluding remarks can be made from thisstudy.

• Low volume of steel "bre increases cylinder splitting ten-sile strength and modulus of rupture, although it has littlee5ect on compressive strength.

• The e5ectiveness of "bre reinforcement depends on theproperties of the concerned concrete matrix. With thesame type and volume of "bre, the improvement in

splitting tensile strength and exural strength is muchmore for lightweight concrete than for normal weightconcrete.

• There is no size e5ect on prism splitting tensile strengthof normal weight and lightweight aggregate plain con-crete. In the case of "bre-reinforced concrete (both nor-mal and lightweight), size e5ect is not signi"cant whenthe size of specimen exceeds a critical (transition) size of150 mm.

• Toughness indices of lightweight "bre-reinforced con-crete are not very sensitive to the specimen size. On theother hand, for "bre-reinforced normal weight concrete,toughness indices become smaller when the specimen sizeincreases. The size e5ect on toughness need to be con-sidered in designing ductile behaviour of "bre-reinforcedstructures. Further research is needed to examine size ef-fect on toughness.

Acknowledgements

The work described in this paper was supported by a grantfrom City University of Hong Kong (Project No.7000737).

References

[1] Naaman AE, Reinhardt HW. High performance "bre reinforcedcement and composites 2. Proceedings of the Second internationalRILEM Workshop, London: E & FN Spon, 1996.

[2] Shah SP, Skarendahl A. Steel "ber concrete. USA: Elsevier AppliedScience Publishers Ltd, 1986.

[3] Balaguru P, Narahari R, Patel M. Flexural toughness of steel "berreinforced concrete. ACI Materials Journal 1992a;89(6):541–6.

[4] Daniel JI, Shah SP. 1994. Fiber reinforced concrete: developmentsand innovations. SP-142, American Concrete Institute.

[5] Malier Y. High performance concrete: from material to structure.London: E and FN Spon, 1992.

[6] Clarke JL. Structural lightweight aggregate concrete. UK: BlackieAcademic and Professional, 1994.

[7] Zhou FP, Barr BIG, Lydon FD. Fracture mechanical propertiesof high strength concrete with varying silica fume contents andaggregates. Cement and Concrete Research 1994;25(3):543–52.

[8] Balaguru P, Shah SP. Fiber reinforced cement composites. USA:Magraw Hill, 1992b.

[9] Balaguru P, Foden A. Properties of "ber reinforced structurallightweight concrete. ACI Materials Journal 1996;93(1):63–78.

[10] Wafa FF, Ashour SA. Mechanical properties of high-strength "berreinforced concrete. ACI Materials Journal 1992;89(5):449–55.

[11] Mihashi H, Okamura H, Bazant ZP. Size e5ect in concrete structures.UK: E and FN Spon, 1994.

[12] Hillerborg A. Analysis of fracture by means of the "ctitious Crackmodel, particularly for "bre reinforced concrete. International Journalof Cement Composites 1984;2:177–84.

[13] Hillerborg A. Determination and signi"cance of the fracturetoughness of steel "bre concrete. In: Shah SP, Skarendahl A, editors.Steel "ber concrete. USA: Elsevier Applied Science Publishers Ltd,1986.

[14] Gopalaratnam VS, Shah SP, Batson G, Criswell M, RamakrishnanV, Wecharatana M. Fracture toughness of "ber reinforced concrete.ACI Materials Journal 1991;88(4):339–53.

Page 7: Influence of steel fibres on strength and ductility of normal and lightweight high strength concrete

R.V. Balendran et al. / Building and Environment 37 (2002) 1361–1367 1367

[15] Bazant ZP, Kazemi MT, Hasegawa T, Mazars J. Size e5ect inBrazilian split-cylinder tests: measurements and fracture analysis.ACI Materials Journal 1991;88(3):325–33.

[16] Hasegawa T, Shioya T, Okada T. 1985. Size e5ect on splitting tensilestrength of concrete, Proceedings of the Japan Concrete InstituteSeventh Conference, pp. 309–12.

[17] Johnston CD. De"nition and measurement of exural toughnessparameters for "ber reinforced concrete. ASTM, Cement, Concreteand aggregates, CCAGDP 1982;4(2):53–60.

[18] ASTM C1018. Standard test method for exural toughness and "rstcrack strength of "ber reinforced concrete. ASTM Standards forConcrete and Mineral Aggregates, V.04.02, Standard DesignationC1018, 1989. 7pp.

[19] ACI Committee 544. Measurement of properties of "ber reinforcedconcrete. ACI Materials Journal 1988;85(6):583–93.

[20] Japan Concrete Institute. Method of test for exural strength and exural toughness of "ber reinforced concrete (Standard SF4). JCIStandards for Test Methods of Fiber Reinforced Concrete, 1983. pp.45–51.

[21] Barr BIG, Hasso EBD. A study of toughness indices. Magazine ofConcrete Research 1985;37(132):162–74.

[22] Mindess S, Chen L, Morgan DR. Determination of the "rst crackstrength and exural toughness of steel "ber reinforced concrete.Advanced Cement Based Materials 1994;1(5):201–8.

[23] Hillerborg A, Modeer M, Peterson PE. Analysis of crack formationand crack growth in concrete by means of fracture mechanics and"nite elements. Cement and Concrete Research 1976;6:773–82.