Experimental and theoretical investigation of the shear resistance of steel fibre reinforced prestressed concrete X-beams Part I: Experimental work

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1 Materials and Structures/Matériaux et Constructions, Vol. 35, November 2002, pp Experimental and theoretical investigation of the shear resistance of steel fibre reinforced prestressed concrete X-beams Part I: Experimental work K. S. Elliott 1, C. H. Peaston 2 and K. A. Paine 3 (1) University of Nottingham, UK (2) Arup Research, Formerly at University of Nottingham, UK (3) University of Dundee, Formerly at University of Nottingham, UK Paper received: July 30, 2001; Paper accepted: October 31, 2001 A B S T R A C T This is the first part of two papers on the experimental (Part I) and theoretical (Part II) resistance of steel fibre reinforced precast concrete beams. Short steel fibres have been introduced into prestressed concrete X beams in order to study their behaviour under shear loads. The X beams, which have circular web profiles, were chosen to represent longitudinal sections from 215 mm deep prestressed precast hollow cored floor units, which are known to fail in shear in a brittle manner. No shear links were used. Round hooked end high strength steel (HS), and thin amorphous metal (AM) fibres were used in volume fractions up to 2.0%. The maximum flexural strength of fibre reinforced concrete (FRC) was N/mm 2, some 50% greater than plain concrete. In the plain concrete beams the ratio η of the ultimate shear resistance to the cracking resistance was 1.0, as expected. For the fibre beams η = 1.43 to 1.52 for the HS fibres and η = 1.23 for the AM fibres. Theoretical and empirical equations were developed using modified FRC principal tensile stress methods to predict ultimate shear strength and are given in Part II. R É S U M É Il s agit de la première partie d un article sur la résistance des poutres en béton préfabriqué renforcé de fibres d acier, présentant les expériences (partie I) et la théorie (partie II). De courtes fibres d acier ont été utilisées dans des poutres X précontraintes pour étudier leur comportement sous l action de forces de cisaillement. Les poutres X, qui ont des âmes de profil circulaire, ont été choisies pour représenter des sections longitudinales des dalles alvéolées précontraintes de 215 mm d épaisseur, qui sont connues pour leur mode de rupture cassant sous l action des efforts tranchants. L armature de cisaillement n a pas été utilisée. Des crochets ronds en acier à haute adhérence et de minces fibres métalliques amorphes ont été utilisés jusqu à des fractions de 2% du volume. La résistance à la tension maximale sous l effet de flexion du béton de fibres d acier était de 10,28 N/mm 2, soit 50% de plus que pour le béton normal. Pour les poutres en béton normal, le rapport η entre la résistance ultime au cisaillement et la résistance à la fissuration était de 1,0, comme prévu. Pour les poutres en fibres d acier ce rapport était entre 1,43 et 1,52 pour l acier à haute adhérence et 1,23 pour les fibres métalliques amorphes. Des équations théoriques et empiriques ont été développées à l aide de méthodes de contrainte de tension principale du béton de fibres d acier modifiées pour la prédiction de la résistance ultime au cisaillement ; celles-ci sont données dans la deuxième partie. 1. INTRODUCTION Prestressed precast concrete X beams were developed in the 1950 s when advances in long line slip-forming and extrusion techniques were combined with the favourable properties of pretensioning strand and/or wire, which could be stretched without excessive losses over a distance of about 100 m. The favourable section properties of the X shape, shown in Fig. 1, were that the second moment of area is maximised with respect to the cross sectional area within the limitations imposed by the manufacturing techniques. In other words, the flanges are as large as pos- sible and the web is as narrow as possible. The curved profile to the web enabled concrete to be fully compacted at the bottom flange, and avoided stress concentrations due to the absence of sharp corners, etc. When hollow cored floor slabs (hcs) were similarly developed using long line production the formers making the hollow cores were originally circular or oval (Fig. 2). Depths vary from 150 mm to 500 mm, although the most common depths are 200 to 250 mm for spans of up to about 12 m. In spite of the fact that the hcs is a wide slab, typically 1200 mm in width, its behaviour in plane bending (i.e. symmetrically stressed with no torsion) may /02 RILEM 519

2 Materials and Structures/Matériaux et Constructions, Vol. 35, November 2002 Fig. 1 Cross section of X-beam. The cross-section represents a longitudinal section from a typical hollow cored floor unit. be approximated to a number of X sections with an additional lateral restraint to the concrete in compression at the top of the slab. However, as this is rarely critical in the design of such units, the ultimate bending performance of the hcs may be taken as the sum of a series of X beams. Unfortunately the situation in shear is not the same. Because of the absence of shear reinforcement in the hcs, shear failure is by web-tension propagating at the narrowest part of the web, which also happens to coincide with the geometric centroid of the section. Shear failures are brittle and develop rapidly by a single crack into a shear-bond failure along the line of the pretensioning bars. They are notoriously difficult to predict and codes of practice impose several partial safety factors on the ultimate shear capacity. At a shear failure the webs are all highly stressed, and because the width of individual webs is unequal, varying by more than 15% in some cases, once a shear failure occurs in the critical web it propagates rapidly throughout the unit. Thus, the shear capacity of the hcs is not the same as the shear capacity of its component X sections, unless of course web widths are all exactly equal. A further deleterious feature of the X section is that because flexural cracking propagates more rapidly through the curved web than it would otherwise do in a rectangular section, tension stiffening is not as effective and the transition between a flexurally uncracked and flexurally cracked section is rapid. In EC2, clause [1] the power term applied to the ratio of the applied stress to the cracking stress is equal to 2. Flexural tests carried on hcs with narrow webs have found this power function to be closer to 5 or 6. Consequently the combined shear and flexural stresses near to the bottom of the web are large, giving rise to non-arrested shear cracking not experienced in a rectangular section. Therefore in order to study the shear behaviour of hcs, it was thought necessary to use X sections of similar profile to a single web in an extruded unit manufactured using the Spiroll machine, shown in Fig. 3. This machine produces hcs with much narrower webs, typically 30 mm wide, than mm in comparative slipformed units. X sections may be produced either by sin- Fig. 2 Typical profile of hollow cored floor units. Fig. 3 Looking inside a Spiroll concreting machine, showing rotating helical augers around which the concrete is extruded towards the right hand side of the picture. 520

3 Elliott, Peaston, Paine Fig. 4 Details of hooked end and flat fibres. gle casting or by longitudinal sawing of the hcs the latter having the advantage that the concrete has been produced as for a hcs. The outer webs are different to the inner ones because of the edge profile, and are not included in the study. The greatest cause for concern for hcs or X sections in shear is not necessarily their shear capacity, as this is considered to be satisfactory for most building applications, but the lack of ductility post failure. In spite of various attempts to increase the shear resistance and ductility of the hcs, e.g. cast insitu reinforced concrete in broken out cores, no practical solution compatible with the sophisticated manufacturing methods has been successful. The use of short steel fibres in concrete is well established and, if dispersed correctly in adequate numbers, is known to increase the post-cracking tensile performance of plain concrete [2, 3]. One of the most successful types of fibre is the hooked end high tensile wire fibre of 30 to 50 mm in length and around 0.5 mm diameter, Fig. 4. If such fibres could be successfully introduced into the hollow core extrusion or slip-forming machines, and be properly distributed throughout the webs of the units, the fibres should improve both the shear resistance and ductility of these units in shear failure. This paper reports on: a) the development of a fibre reinforced concrete mix, b) shear tests carried out on 200 mm deep X section beams laboratory cast in moulds. The X beams were all pretensioned according to standard practice. Shear loads were applied at a shear distance of 2.0 and 2.8 times the effective depth of the beams. Results are disseminated and corroborated with previous work on fibre reinforced concrete in shear. This work is reported in full by Paine [4]. 2. EXPERIMENTAL TESTING 2.1 FRC mix and casting of X beams A main requirement was that the mix should achieve a compressive cube strength of around 35 N/mm 2 so that detensioning and stripping of the mould could take place within 24 hours. The target 28 day cube strength was Table 1 Schedule of X-beam V f % a/d = 2.0 a/d = 2.8 Reference beams 0 PB1A PB1B PB5A PB5B HS Fibres 0.5 PB2A PB2B PB6A PB6B 1.0 PB3A PB3B PB7A PB7B 1.5 PB4A PB4B PB8A PB8B AM Fibres PB 9A PB 10A Table 2 Mix proportions used for plain mix Mix proportions kg/m 3 Water 185 Rapid hardening Portland cement 460 Silica Fume 25 Natural sand fine aggregate mm crushed limestone 965 Superplasticizer added at between 0.8 and 1.5% by mass of Portland cement. around 80 N/mm 2. Two types of fibre shown in Fig. 4 were investigated: hooked-end steel wire (HS) fibres and amorphous metal (AM) fibres. HS fibres were used since they are currently regarded as the most efficient type of fibre, whilst AM fibres were included in the test programme at a later date due to fabrication concerns raised by the hollow core manufacturer. The HS fibres, made of drawn wire of tensile strength 1100 N/mm 2, were 30 mm long x nominal diameter of 0.5 mm. The AM fibres, which were ribbon-shaped and produced by quenching a jet of molten metal on a rotating water-cooled wheel, were 30 mm long x 1.6 mm wide x 50 µm thick. Their tensile strength is quoted as 1900 N/mm 2. The schedule of beams is given in Table 1. The volume of fibre, V f, is based on the volume of concrete (not the total concrete plus fibres volume). Mix proportions are given in Table 2. The cement used was Portland cement of Grade 42.5R conforming to BS 12 [5]. Pulverised-fuel ash (PFA) to BS 3892: Part 1 [6] was used at between 17% and 23% of the total cement content by mass. The aggregate comprised crushed limestone in mm and 10-5 mm fractions and sand to Zone M (medium grading) of BS 882 [7]. Difficulties in mixing beams with increasing fibre contents were overcome by using increasingly higher dosages of superplasticizer. Previous research using the Baron-Lesage Method [8] had shown that the superplasticizer requirements for 2% HS fibres were comparable to 0.5% AM fibres, with sand/aggregate and water/ cement ratios about constant. Therefore the superplasticiser proportion was increased to for the 0.56% AM fibre mix (equal to that used for 2% HS fibres) and was taken as equal to that used for 1% HS fibres for the 521

4 Materials and Structures/Matériaux et Constructions, Vol. 35, November 2002 Table 3[a] Concrete workability and strengths for HS FRC beams tested at a/d = 2.0 Detension Test Age Test Age 28 days V f Beam Slump f ci f cu f ct,sp f cu (%) (mm) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) 0 PB1A PB1B PB2A PB2B PB3A PB3B PB4A PB4B Table 3[b] Concrete workability and strengths for HS FRC beams tested at a/d = 2.8 Detension Test Age Test Age 28 days V f Beam Slump f ci f cu f ct,sp f cu (%) (mm) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) 0 PB5A PB5B PB6A PB6B PB7A PB7B PB8A PB8B Table 3[c] Concrete workability and strengths for AM FRC beams tested at a/d = 2.8 Detension Test Age Test Age 28 days V f Beam Slump f ci f cu f ct,sp f cu (%) (mm) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) 0.28 PB PB % AM fibre mix. The mixing procedure was as follows: 1. Mix dry ingredients (including HS fibres). 2. After 2 minutes, add 1/2 water. 3. Continue mixing and add 1/2 of AM fibres. 4. Add rest of water and superplasticiser. 5. Continue mixing and add rest of AM fibres. For control purposes, eight cubes (100 mm), three prisms (100 x 100 x 500 mm) and two cylinders (150 mm diameter x 300 mm) were cast and cured in accordance with BS 1881 [9]. 2.2 Workability and material properties Slump Although slump, as a measure of workability is not appropriate to FRC mixes the test was used here as a quality control check on the relative consistency of each Fig. 5 Relationship between splitting tensile strength and V f. mix, as recommended by ACI Committee 544 [10]. Results are presented in Table 3. The effect of the different concentrations of superplasticiser used to counteract the mixing problems at high fibre contents was more noticeable on the HS fibre mix. An increase in dosage from to increased the slump from 15 mm to 40 mm at V f = 0.5%; and from 5 mm to 40 mm for an increased dosage from to at V f = 1% Compressive cube strength, f cu The results of cube tests, carried out in accordance with BS 1881, Part 116 [9], are shown in Table 3. Addition of HS fibres in most cases increased f cu with a maximum of 90 N/mm 2 achieved for V f = 1.5%. However in cases where compaction was difficult much lower strengths were achieved, e.g. 76 N/mm 2 for PB8A. Additional amounts of superplasticizer had no noticeable effect on f cu at 28 days, but does reduce the 24-hour strength Splitting tensile strength, f ct,sp Splitting tensile tests were performed on 150 mm diameter x 300 mm long cylinders in accordance with BS 1881, Part 117 [9]. The ultimate cylinder splitting strength f ct,sp are given in Table 3 and Fig. 5. The linear relationship between f ct,sp and V f is given as: f ct,sp = 0.48 f + AV cu where A = 237 for HS fibres and 335 for AM fibres. f Flexural strength f fl Flexural strengths were obtained using 100 x 100 mm cross section prisms of l = 300 mm span tested in third point bending according to JCI-SF 4 [11]. It was possible to record the peak load (viz. modulus of rupture) and post-cracking loads. Results for the modulus of rupture f fl are given in Table 4. The equivalent flexural strength f fl,eq,150 is based on the average strength up to a deflection of l/150 [11]. Typical load vs mid-span deflection curves are shown in Fig. 6. An important result is that there is a considerable post cracking capacity only in the HS fibre specimens. Fig. 7 shows that for average values of f fl,cr and f fl a critical V f in flexure is about 0.8 %. The relationships (1) 522

5 Elliott, Peaston, Paine Table 4 Flexural strength for plain, HS fibre and AM fibre mixes Vf Beam f fl,cr f fl,ult f fl,eq,150 f fl,eq,300 (%) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) 0 PB1A PB1B PB2A PB2B PB3A PB3B PB7A PB7B PB4A PB4B PB8A PB8B PB PB Fig. 6 Load vs mid-span deflection in flexural prism tests. between f fl,eq,150 and f fl,eq,300 with V f are shown in Fig. 8. The increases in strength with increasing V f are matrix independent. Comparison of the AM and HS fibre results show that the former gives greater first cracking and ultimate strengths. This is attributable to the shape of the AM fibres which, for the same V f, have eight times the surface area of an HS fibre. Micro-cracks are therefore bound together more effectively before crack localisation, leading to the higher strengths. The critical V f is between 0.28% and 0.56%. Theoretically it can be calculated as approximately 0.30% [12] assuming the critical V f in flexure to be 0.41 times that in tension [13]. Empirical approximations for f fl for HS fibres are: ffl, cr = 0. 7 f cu + 140Vf (2) f fl,ult = f fl,cr V f 0.8 (3) f fl,ult = f fl,cr (V f -0.8) V f > Beam prestressing and casting Two-metre-long beams were prestressed as shown in Fig. 1. Two types of prestressing wires both of nominal 7 mm diameter and conforming to BS 5896 [14] were used. Three wires were used - two bottom wires indented with Belgian indentations and a top wire kept plain to enable easy fixing of strain gauges. Electrical resistance strain gauges were placed on the plain wire at distances of 250 mm, 500 mm and 750 mm from one end. Fig. 7 Variation of ultimate flexural strength with V f. Fig. 8 Variation of equivalent flexural strength with V f. 523

6 Materials and Structures/Matériaux et Constructions, Vol. 35, November 2002 Table 5[a] Shear Test Results a/d = 2.0 V f Fibre Beam σ cp V cr Average V ult Average v ult (%) type (N/mm 2 ) (kn) V cr (kn) (kn) V ult (kn) (N/mm 2 ) 0 PB1A PB1A PB1B PB1B HS PB2A PB2A PB2B PB2B HS PB3A PB3A PB3B PB3B HS PB4A PB4B PB4B to half the height of the beam from the edge of the bearing [15]. At this point the prestress in the plain beams is about 0.7 of the full available prestress. At V f = 0.5%, 1.0% and 1.5% the values are 0.65, 0.45 and 0.25, respectively. The corresponding transfer lengths are 510 mm, 650 mm and more than 750 mm, respectively. The results show that the poor quality of transfer, as a result of adding fibres, reduces the effectiveness of prestress. This will have an effect on the shear, bearing and flexural strength. In order to improve the performance in shear the fibres first have to overcome the deficiencies created by their own addition to the mix. 2.4 Fibre orientation and distribution Table 5[b] Shear Test Results a/d = 2.8 V f Fibre Beam σ cp V cr Average V ult Average v ult (%) type (N/mm 2 ) (kn) V cr (kn) (kn) V ult (kn) (N/mm 2 ) 0 PB5A PB5A PB5B PB5B HS PB6A PB6A PB6A PB6B HS PB7A PB7A PB7B PB7B HS PB8A PB8A PB8B AM PB9A PB9B AM PB10A PB10B For all calculation of v ult, Ib/S is taken as 6082 mm 2, where I and S are the second and first moment of area at the centroidal axis. Each wire was stressed to 45 kn, approximately 0.75 f pu, but immediately after release there was relaxation in the grips of the jack which reduced the stress to about 0.6 f pu. Relaxation over the next 24 hour period resulted in a further 3% loss. At detensioning there was a further 6% loss, according to the strains measured in the gauge at 750 mm from the end of the beam. The final stress was about 0.55 f pu. The addition of fibres significantly increases the transfer length. The theoretical critical location for shear is at 207 mm from the end of the beam - a distance equal 524 Fibre orientation was investigated by sawing the web into a number of roughly 40 mm cubic sections so that the fibres in each of the orthogonal directions were exposed. An orientation factor, the average ratio of the projected fibre length in each direction to the actual fibre length, was then calculated where a value of 0.41 would indicate random orientation [16]. The average fibre orientation factor calculated varied between 0.38 and 0.45, and it was observed that there was no variation in orientation factor through the depth of the slabs. It can, therefore, be inferred that laboratory casting of these X-beams had no effect on the orientation of the fibres, and that an orientation factor (η θ ) of 0.41 is suitable for use in these beams. 3. SHEAR TESTS 3.1 Testing arrangement Shear tests were carried out at the same a/d ratio on both ends of each beam - the tests are referred to as Test PBxx - 1 and Test PBxx - 2 in Table 5 and as shown in Fig. 9. Deflections were measured using electrical resistance linear potentiometers (LP) that were placed at the mid-span (Test 1 only), the load-point and at a position close to the support. Principal concrete strains were measured by 45 gauge rosettes. Load was applied by a manually operated hydraulic jack and controlled with a 200 kn electrical resistance load cell. During the test wire slip (or end draw-in) was measured using a depth gauge. Small crack widths were measured using a hand-held microscope and larger crack widths using a steel rule.

7 Elliott, Peaston, Paine Fig. 9 General arrangement of shear tests. crack propagated at 40 to 45 to the horizontal and formed at mm from the face of the bearing, passing through the centre and thinnest part of the web. At a/d = 2.8 the critical crack propagated at an inclination of about 30 and formed at a distance of 150 mm from the face of the bearing. After cracking the load carrying capacity of the plain concrete beams reduced in an almost instantaneous failure. The FRC beams, however, sustained additional load being able to resist the cracking load due to the ability of fibres to cross the shear crack and resist crack propagation and widening. Shear load and def lections for the FRC beams are shown in Fig. 12. With increasingly higher fibre volumes the post-cracking shear capacity and ductility increases. FRC beams tested at a/d = 2.0 failed due to the propagation and widening of the main shear crack due to fibre pull-out and fibre breaking, in addition to some degree of concrete crushing in the compressive zone. In many cases a vertical crack developed at the bottom and intersected the diagonal crack, bringing with it the ultimate failure load. The FRC beams tested at a/d = 2.8 failed at a lower shear load than above due to flexural cracks forming in the region of highest bending moment. Fig. 10 Web shear failure for fibre reinforced X-beams. Fig. 11 Shear load and deflections for plain beams. (a) at a/d = 2.0, (b) at a/d = General behaviour of test beams All beams failed by web shear tension as shown in Fig. 10. For the plain beams, shear load and vertical deflections (measured at a position directly under the load) are shown in Fig. 11. At a/d = 2.0 the critical shear Shear capacity The results are given in Table 5. The shear capacity V cr at first crack indicates the load at which diagonal cracking first occurred, and the ultimate shear capacity V ult refers to the highest value of shear the beam withstood. For the plain beams V cr = V ult (see Fig. 11). The average shear capacity at a/d = 2.0 is V cr = 43 kn, and at a/d = 2.8 is V cr = 34 kn. The variation in V cr with V f is shown in Fig. 13. Fibres have little effect on V cr because the direct tensile strength of concrete f t is little affected by low fibre volumes theoretically a V f of 1% increases f t by about 5% even when the fibres are perfectly aligned in the direction of the stress. The variation in V ult with V f is shown in Fig. 14. Using V f = 1.5% (HS fibres) there is a 43% to 52% increase in V ult with respect to plain beams. The increase using 0.56% (AM fibres) at a/d = 2.8 is only 23%. With both fibre types at a/d = 2.8 there is a tendency for the fibre influence to diminish at increasing fibre volumes. For the HS fibres the difference between the capacities at a/d = 2.0 and a/d = 2.8 at both cracking and ultimate, remains effectively constant at between 25-35% for V f < 1%. This suggests that the fibre reinforcement mechanism is essentially the same at both a/d ratios and that enhanced

8 Materials and Structures/Matériaux et Constructions, Vol. 35, November 2002 Fig. 12 Shear load and deflections. (a) HS fibre FRC beams at a/d = 2.0, (b) HS fibre FRC beams at a/d = 2.8. (c) AM fibre FRC beams at a/d = 2.8. Fig. 13 Variation of cracking shear strength V cr with V f. Fig. 14 Variation of ultimate shear strength V ult with V f. shear capacity at lower a/d ratios is independent of fibre addition. The reason for the higher shear capacity at a/d = 2.0 is because of the increasing effect of compressive strut action closer to the support, and the favourable effect of the support pressure occurring above a line drawn at 45 from the edge of the support [15]. 526

9 Elliott, Peaston, Paine Fig. 15 Shear force vs diagonal crack width for a/d = 2.0. Short steel hooked end (HS) and amorphous metal (AM) fibres have been introduced in quantities of upto 1.5% by volume into 2 m long x 215 mm deep prestressed concrete X beams. The beams represent a single web from a longitudinal section of a precast concrete hollow cored floor unit that does not contain shear links. The FRC beams were tested under shear loads acting at 2.0 to 2.8 times the effective depth. The prestress at the centroid varied from σ cpx = 4.3 to 6.1 N/mm 2. Concrete cube strengths were between f cu = 67 and 82 N/mm 2. The objectives of the 34 tests were to determine the improvement which fibre reinforcement gives over plain prestressed concrete, and, coupled with the flexural strength properties obtained from standard 4-point bend tests, to develop empirical design equations to predict ultimate shear strength (given in Part II). The main conclusions are: 1. Using 4-point bend tests, the maximum tensile flexural strength of FRC was N/mm 2, some 50% greater than plain concrete. These are much greater than comparable code values of around 3.2 N/mm 2. The maximum equivalent flexural strength f fl,eq300 at a deflection of span/300 was 8.48 N/mm Shear failures were by diagonal shear-tension cracking, accompanied by large ductility in the FRC beams only. 3. The average ultimate shear capacity V ult of the FRC beams was upto 1.52 times the capacity of the plain beam, resulting in a maximum shear stress of 9.1 N/mm 2 in the webs. 4. The maximum shear capacity at cracking was only 1.14 times the cracking capacity of the plain beams. 3.4 Crack widths Fig. 15 shows shear load and the maximum diagonal shear crack width for a/d = 2.0 (results for a/d = 2.8 are of the same nature). The maximum load is achieved whilst the crack widths are still small. With increasing V f the crack width at maximum load increases, being about 2 mm at V f = 1.5% and 1 mm at V f = 0.5%. This shows that the ability of fibres to provide additional post-cracking capacity occurs during the early stages of failure when crack widths are small. When plain beams first crack there is an immediate reduction in load simultaneous with a large crack opening (about 1 mm). At a crack width of 4 mm, for a/d = 2.8, the load in the plain beams is about 0.25 V cr whereas in the FRC beams at V f = 1.5% it is 1.4 V cr, and at V f = 0.5% it is 0.95 V cr. When the crack width in the FRC beams attains 0.3 mm (the serviceability limit for crack width in BS 8110, [17]) the shear load is V ult. This shows that even within the serviceability limits for crack width much of the additional capacity due to fibres can be utilised. 4. CONCLUSIONS REFERENCES [1] Eurocode 2: Design of Concrete Structures Part 1: General Rules and Rules for Buildings, EN (2001). [2] Narayanan, R. and Kareem-Palanjian, A. S., Effect of fibre addition on concrete strengths, Indian Concrete Journal 58 (4) (1984) [3] Nanni, A., Splitting tension test for fiber reinforced concrete, ACI Materials Journal 85 (4) (1988) [4] Paine, K. A., Steel fibre reinforced concrete for prestressed hollow core slabs, Ph. D Thesis, University of Nottingham, UK (1998). [5] BS 12, Specification for Portland Cements, British Standards Institution (1991). [6] BS 3892, Part 1, Specification for Pulverized-Fuel Ash for use with Portland Cement, British Standards Institution, London (1993). [7] BS 882, Specification for Aggregates from Natural Sources for Concrete, British Standards Institution, London (1992). [8] Rossi, P., Mechanical behaviour of metal-fiber reinforced concretes, Cement and Concrete Composites 14 (1992) [9] BS 1881, Methods of Testing Concrete, British Standards Institution, London (1983). [10] American Concrete Institute, Committee 544, Measurement of properties of fiber reinforced concrete, ACI 544.2R-88, ACI Materials Journal 85 (6) (1988) [11] Japan Concrete Institute, Method of Test for Flexural Strength and Flexural Toughness of Fiber Reinforced Concrete, JCI Standard SF4, JCI Standards for Test Methods of Fiber Reinforced Concrete (1983) [12] Bentur, A. and Mindess, S., Fibre Reinforced Cementitious Composites (Elsevier Applied Science 1990). [13] Lanu, M., Testing fibre-reinforced concrete in some structural applications, Report No. 237, Technical Research Centre of Finland, Espoo, Finland (1995). [14] BS 5896, Specification for High Tensile Steel Wire and Strand for the Prestressing of Concrete, British Standards Institution, London (1980). [15] Girhammar, U.-A., Design principles for simply-supported prestressed hollow core slabs, Structural Engineering Review 4 (4) (1992) [16] Peaston, C. H., Elliott, K. S. and Paine, K. A., Steel fiber reinforcement for extruded prestressed hollow core slabs, in ACI SP 182 Structural Applications of Fiber Reinforced Concrete (1999) [17] BS 8110, Structural Use of Concrete, Part 1, Code of Practice for Design and Construction, British Standards Institution, London (1985). 527