Experimental investigation of steel fiber reinforced concrete box

Materials and Structures (2006) 39:491–499 DOI 10.1617/s11527-006-9095-y

Experimental investigation of steel fiber reinforced concrete box beams under bending Fatih Altun · Tefaruk Haktanir · Kamuran Ari

Received: 1 June 2005 / Accepted: 2 December 2005 C RILEM 2006

Abstract Reduction of dead weight of a reinforcedconcrete (RC) structure without too much concession in its load carrying capacity has always been an attractive study subject because it engenders (1) a decrease in dimensions of the members, (2) a decrease in the reinforcement steel, and (3) a decrease in lateral inertia forces during severe earthquakes. In this study, nine RC beams of outer dimensions of 300 × 300 × 2000 mm, six of which are box beams, designed and produced using a C20 class steel fiber concrete, (SFRC) with the commonly used steel fiber type of Dramix-RC-80/0.60BN at a dosage of 30 kg/m3 , are tested under bending. The mechanical behaviours of all these nine beams under bending are recorded from the beginning of the test till the ultimate failure of the tensile reinforcement in a two-point beam-loading setup. The proportions of (1) loss in ultimate load versus reduction in dead weight and (2) (ultimate experimental load)/(ultimate theoretical load) of the SFRC box beams are determined for two different box thicknesses. Dimensionless behaviour relationships of all the SFRC beams are determined, and the experimentally obtained relationship between the ratio of (actual ultimate load)/(theoretical ultimate load) and the ratio of (wall thickness)/(beam height) for the SFRC box beams is expressed diagrammatically.

F. Altun · T. Haktanir · K. Ari Erciyes University, Faculty of Engineering, Department of Civil Engineering, 38039 Kayseri, Turkey

Résumé La réduction de poids mort d’une structure (RC) renforcer-concrète sans trop de concession de sa capacité de charge de charge a toujours e´ té un sujet attrayant d’étude parce qu’elle engendre (1) une diminution des dimensions des membres, (2) une diminution de l’acier de renfort, et (3) une diminution des forces latérales d’inertie pendant des tremblements de terre graves. Dans cette e´ tude, neuf faisceaux de RC des dimensions externes de 300 × 300 × 2000 le millimètre, dont six sont des faisceaux de boˆıte, conçues et produites en utilisant un béton en acier de fibre de la classe C20, (SFRC) avec le type en acier généralement utilisé de fibre de Dramix-RC-80/0.60-BN a` un dosage de 30 kg/m3 , sont examinés sous le recourbement. Les comportements mécaniques de tous ces neuf faisceaux sous le recourbement sont enregistrés du commencement de l’essai jusqu’à l’échec final du renfort de tension dans une installation de faisceau-chargement de deuxpoint. Les proportions (1) de perte dans la charge finale contre la réduction du poids mort et (2) (charge théorique expérimentale finale de load)/(ultimate) des faisceaux de boˆıte de SFRC sont déterminées pour deux e´ paisseurs différentes de boˆıte. Des rapports sans dimensions de comportement de tous les faisceaux de SFRC sont déterminés, et le rapport expérimentalement obtenu entre le rapport de (charge finale finale réelle de load)/(theoretical) et le rapport de (taille de mur thickness)/(beam) pour les faisceaux de boˆıte de SFRC est exprimé schématiquement.

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Mots-clés: En acier renforcé de fibres, faisceaux de boˆıte, comportement Keywords Steel fiber reinforced, box beams, behaviour

1. Introduction Because of the known reasons, the foremost of which is its being the material with the lowest (cost)/(strength) ratio, structural concrete is still the most widely used construction material. However, brittleness and a much lower tensile strength than its compressive strength are two disadvantages of concrete. The addition of steel fibers (SFs) to concrete to counter these negative features to some extent is being practiced in the recent years. Steel fiber addition to RC appreciably increases its toughness, the energy absorption capacity, among other contributions like: more ductile behaviour prior to the ultimate failure, reduced cracking, and improved durability. Steel fiber reinforced concrete (SFRC) has been used at an increasing rate in various applications like: mine and tunnel linings, slabs and floors (especially those large slabs of factories on which there are great moving loads), rock slope stabilization, repair mortars, shell domes, refractory linings, dam constructions, composite metal decks, aqueduct rehabilitations, seismic retrofittings, repair and rehabilitation of marine structures, fire protection coatings, concrete pipes, and even conventional RC frames because of improved toughness against dynamic loads as reported by Ocean Heidelberg Cement Group [1]. Yet, concrete having a relatively high specific gravity of more than 2 causes the magnitude of the service loads carried by a RC structure to be only about as much as its own dead weight. This results in a rather bulky and too heavy structure transferring too great loads to the foundation, which eventually may cause soil bearing pressure problems. An expensive foundation unit, which may further be coupled by an extra cost of rehabilitation of the foundation soil, may have to be designed. Hence, such practices as usage of lightweight structural concrete and reduction of dead weight of normal concrete by designing mechanically suitable cross-sectional forms like boxes, I beams, and U beams have long been carried out with the purpose of decreasing the overall dead weight of a RC structure.

Materials and Structures (2006) 39:491–499

The parts close to its neutral axis of a RC beam under bending are subjected to small stresses even at high loads. So, beams of efficient cross-sections like I shapes are often produced with steel and pre-cast RC elements, which work efficaciously against loads with the advantage of lessening dead weights. Reduction in dead weight is especially important in regions prone to severe earthquakes, and for large-span beams like those crossing over wide bridges (span length >15 m) for which dead weight of the beam itself becomes significant. Culverts and some transverse beams perpendicular to the main girders on bridges are two examples for RC box beams. RC box beams, either pre-cast with or without pre-tensioning or cast-in-place, are also used as the main spanning units [2–4]. RC box beams have been frequently used as bridge girders in the USA, the first examples being the bridges on the Illinois highway built in 1950s [5]. Later, usage of RC box beams became widespread in many countries especially towards the late 1970s. RC box beams applications in industrial buildings began around mid 1990s [5]. RC box beams are designed and constructed in two distinct manners. In the first one, a high strength concrete is used so that the concrete in the relatively smaller compression zone of the box beam can resist the acting compression stresses. The study by Myers et al. [6], is a typical example for this approach. In another study, Dupont et al. [7], investigated SFRC beams and concluded that a SF dosage of 30–40 kg/m3 was the minimum for an improved crack reduction. In the second one, along with forming a hollow part inside the box section, the dimensions of the crosssection are enlarged forming a box beam whose outer dimensions are greater than a conventional rectangular beam. Recupero et al. [8], performed a finite element analysis to the RC-box beams and RC-I beams. The measured ultimate loads on test beams used in their experiments were found to be close to the loads computed by their finite-element model. Alkhrdaji et al. [9], produced and tested in laboratory two box-culvert type of RC elements having a wall thickness of 150 mm under bending. The experimental ultimate load turned out to be about 10% smaller than that given by the finite-element computations. So far, studies on either RC box beams or SFRC rectangular beams have been reported in the relevant literature, but studies on SFRC box beams of similar theme


are lacking. Presently, a guide for a best SF dosage for SFRC beams does not exist, and a comprehensive study aiming to determine the smallest amount of SF dosage yet having a satisfactory mechanical performance in the SFRC beams is not available, either. In this study, we have used an ordinary class of structural concrete and those steel fibers, which are widespread for most applications of SFR concrete. First, we have performed the relevant tests on standard cylindrical specimens with different SF dosages which guided us to choose an minimum SFs dosage. Next, we have observed that the toughness indices of that SFR concrete with the chosen SF dosage were within acceptable ranges by testing the standard 150 × 150 × 750 mm dimension prisms in a displacement-controlled ring. Next, we have designed and produced three groups of SFRC beams as tension failure with the same outer dimensions of 300 × 300 × 2000 mm, the first group being full prisms while the other two groups having hollow parts of 100 × 100 mm and 200 × 200 mm dimensions right in the middle. All these beams are tested in a two-point beam-loading setup with the objective of determining in a comparative way the mechanical behaviour of full prismatic SFRC beams and SFRC box beams under bending. The proportional reductions in,

r dead weight, r effective concrete and steel cross-sectional areas, and r moment of inertia versus the ultimate bendingmoment capacity of tension failure SFRC box beams are determined. By computing the ratios of experimental ultimate load to the theoretical ultimate load for all the three different cases of SFRC beams, investigation of the efficiency of wall thickness relative to the outer dimension of the beam cross-section has been the objective of the study.

2. Experimental studies C20 class of concrete was used in producing all the full and box SFRC beams. Deliberately this average class concrete was chosen because it was common for RC buildings. Indented steel bars of S420 class, were used as reinforcement steel, and all the beams were designed so that the tensile reinforcement bars would yield first far ahead of any prospective shear or compression failure. The ratio of cross-sectional area of tensile steel to the total area was about 0.004 for all the

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three types of beams produced. This quantity of steel was slightly greater than the minimum value prescribed for flexural reinforcement by the ACI 318M-02 [10]. The stirrups were placed so as to provide strong shear resistance. We used the Dramix-RC-80/0.60-BN type of steel fibers, which are of 0.75 mm length, yielding an aspect ratio of 80. The experiments were of three stages: (1) tests on cylindrical concrete samples of 150 × 300 mm dimensions, (2) tests on standard 150 × 150 × 750 mm prisms, and (3) simple bending experiments on the beams. 2.1. Tests on concrete samples The concrete mixtures for the C20 class used in the study were obtained from a commercial ready-mixed concrete plant. Five C20 batches with the same recipe and with SF dosages of 0 kg/m3 , 30 kg/m3 , 40 kg/m3 , 50 kg/m3 , and 60 kg/m3 were produced and 6 cylindrical samples of 150 × 300 mm (= 6 × 12 inch) dimensions were properly taken from each batch. The SFs were added to the trans-mixer truck at a rate of 20 kg/min, and the drum was rotated at high speed for 5 min afterwards [11]. All the cylindrical samples were kept at room temperature in the materials laboratory, while being covered by burlap, and water was splashed over them regularly every day. When the samples were 28 days old, each of them was subjected to compression test in a universal compression machine with a standard compresso-meter mounted on it at a load rate of about 0.25 N/mm2 per second, and the loads (in kN) and deformations (in 10–2 mm) were accurately recorded at 20 kN load increments up to the final crushing. The toughness of each concrete type was computed as the total area under the curve averaging the experimentally obtained plots of load versus compressive shrinkage, which could be interpreted as ability of plain concrete to absorb energy under direct compression. The results of these tests are summarized in both Table 1 and Fig. 1. The average compressive strength and elasticity modulus for a SF dosage of 30 kg/m3 turned out to be 22.5 N/mm2 and 27500 N/mm2 , respectively, which are reasonable values for a C20 class of concrete. The toughnesses of all the SFR concretes of different SF dosages are close to each other, and on the average they are a little more than two-fold of that of the reference concrete with no SFs. Although the toughness of 40 kg/m3 SF dosage concrete was a little greater than that of 30 kg/m3 SF dosage concrete, taking into

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Table 1 Mechanical properties measured on the cylindrical concrete samples Sample ID No

Steel fibers dosage (kg/m3 )

Average ultimate load (N)

Average compressive strength (N/mm2 )

Decrease in compressive strength (%)

(N/mm2 ) Elasticitymodulus

(kN.mm) Toughness

No SFs SFC-30 SFC-40 SFC-50 SFC-60

0 30 40 50 60

432 000 397 000 385 000 377 000 399 000

24.46 22.48 21.80 21.34 22.59

– 8.80 12.20 14.60 8.30

29 500 27 500 26 500 26 500 26 000

202 446 522 415 474

Fig. 1 Experimentally determined average stress – strain relationships of five different C20 classes of concrete with five different steel-fiber dosages from no SFs up to 60 kg/m3 .

consideration compressive strength, elasticity modulus, and cost of SFs, as well as toughness, the lowest SF dosage of 30 kg/m3 was chosen for the SFR concrete to be used further in the study [12]. Nine SFRC beams with outer dimensions of 300 × 300 × 2000 mm, and three prisms of dimensions of 150 × 150 × 750 mm were produced using SFR concrete with a SF dosage of 30 kg/m3 . All the nine SFRC beams and SFR concrete prisms were kept side by side on the floor of the materials laboratory, and all of them were splashed with water daily while being covered up under burlap for a period of 28 days. Each one of the three 150 × 150 × 750 mm prisms was subjected to the standard two-point-loading experiment at a rate of 1 mm/min of mid-section deflection in accordance with ASTM C1018-92 [13] in the displacement-controlled prism-loading frame as specified in ASTM C1018-92. An instant of one of these tests is shown in Fig. 2. As will be reported in Section 3 below, the results of these tests turned out to be within acceptable ranges, and the study proceeded to the final stage.

Fig. 2 Prismatic beams loading setup.

2.2. Tests on SFRC beams and SFRC box beams Three of the SFRC beams were full beams of squareprism cross-sections, and these were denoted as B1, B2, B3. Three of the SFRC beams had a central hollow part of 100 × 100 mm dimensions of their cross-sections, and the last three had a hollow part of 200 × 200 mm


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loading case. The ultimate single load to be countered by such a simply-supported beam is: Pu = 3Mu /L

Fig. 3 (a) Cross-sectional views (b) the reinforcement placed in the moulds of all the SFRC beams produced before concreting.

dimensions, and these six box beams were denoted as BB1, BB2, BB3, BB4, BB5, BB6. The distance from the centre of the reinforcement steel bar to the inner face of the form was 15 mm for all the beams. Figure 3a shows the cross-sectional view of three different types of SFRC beams and photographs in Fig. 3b shows the reinforcement cages and the moulds before concreting. The erection reinforcement is 2φ8. The ultimate bending moment denoted by Mu , which was reached at the instant of plastic yielding of the tensile steel, was computed by the conventional ultimatestrength approach, and the single load before branching into two equal loads applied on the beam was computed by its known relationship to Mu , acting on the middle portion of the beam between the two loading units [11]. The design of flexural reinforcements was done for this Fig. 4 Stress and strain distribution across beam depth.

(1)

where, Mu is the expected ultimate mid-section bending moment to be resisted, Pu is the calculated maximum load, and L = 1800 mm is the span length between restraints. The compressive and tensile stress distributions in a cross-section of an original RC box beams prior to the ultimate failure and the equivalent compressive stress block were calculated, as adopted by the conventional ultimate-load approach. The internal stress distribution and the stress block diagram in box beams are shown in Fig. 4. where a is rectangular stress block depth, c parabolic stress block depth, ε s steel strain, ε c concrete strain, h is the depth of beams, d’ concrete cover and As is tension steel area. Based on this model, the equilibrium of internal resisting forces gives: Fc = Fs

(2)

And hence, the ultimate resisting moment is: Mu = ρbd 2 f sc (1 − 0.59ρ f sc / f cc )

(3)

where, ρ is the ratio between the cross-section area of the tensile steel and the concrete “effective” area (b × d), b is the width of the beam, d is the net height between the tensile and the compression steel bars, fsc is the characteristic tensile strength of steel, and fcc is the characteristic compressive strength of concrete. The ultimate loads were computed to be 131.2 kN for the full beams (Fig. 3), 118.6 kN for the box beams with a wall thickness of e = 100 mm, and 83.9 kN for the box beams having a wall thickness of e = 50 mm.

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Fig. 5 Loading configuration of the SFRC beams and box beams.

In these computations, the characteristic mechanical properties of both C20 concrete and S420 steel were used. All the nine beams were subjected to bending experiments in a two-point beam-loading setup as shown in Fig. 5. The mid-span displacements were accurately read at every 5 kN load increments using a strain gauge up to and including the plastic yield of the tensile steel until full rupture of these tensile reinforcement bars and the data were stored in computer files.

3. Evaluation of the experimental results Because of micro-cracks and other interstices in concrete, the transfer of shear stresses within concrete is irregular. The steel fibers, when homogeneously dispersed, act like small bridges and help for a better distribution of tensile and shear stresses. Therefore, the cracks in SFR concrete are smaller in size and they are spread more evenly. As seen in Table 1, although the compressive strength of concrete seems to decrease with increasing SF dosage, the average strengths are still a little greater than 20 N/mm2 , the characteristic strength of C20, which means all the tested SFA concretes are of C20 class. As it has been explained in the first paragraph of Section 2.1, the SF dosage of 30 kg/m3 is considered as the appropriate dosage. According to ASTM C-1018 [13], both the elastic and the ensuing plastic behaviour of SFC are depicted concisely by the toughness indices of I5 , I10 , and I20 , which are equal to the ratios of the areas under the load– mid-section deflection curve up to 3 times, 5.5 times, and 10.5 times of the deflection to the first crack to the area up to the first crack [13]. The acceptable ranges for these indices particularly for the SFC are given in ASTM C-1018 as: 1 < I5 < 6, 1 < I10 < 12, and 1 < I20


< 25. The average values for the load to the first crack and the ultimate load, and the toughness indices of I5 and I10 , we obtained from the standard experiments on three 150 × 150 × 750 mm prisms produced with a SF dosage of 30 kg/m3 turned out to be: 8.8 kN, 15.6 kN, I5 = 5.9, I10 = 9.3, respectively, which were all within the acceptable ranges [13]. The ‘displacement ductility’ is defined as the ratio of ‘at yield’ to ‘at-ultimate state’ deflections. The results of the bending experiments on all the three full and six box SFRC beams are given in Table 2. Accordingly, along with toughnesses the way we computed, the displacement ductility’s of the beams tested also are presented in Table 2. The small toughnesses observed on the thinnest-walled box beams are probably due to the torsional effects resulting from slenderness of wall thickness and stress concentrations at the sharp corners of these thin-walled box beams. Alternatively, the “normalize” toughness values with respect to the capacity for three full and six box SFRC beams are given in Table 2. The past experience of the authors and results of similar experimental studies indicate that almost always the experimentally measured ultimate loads in bending setups turn out to be greater than those yielded by the theoretical ultimate-strength calculations. The reasons for this difference enlisted below:

r The actual stress distributions close to the ultimate r

r

resistance is probably wider than the simple rectangular distribution assumption. The actual strengths close to the ultimate loading are greater than 0.85 × (characteristic strength) taken in the computations. In our computations, as similarly done by RC designers, we took as the ultimate concrete strength 20 MPa, whereas the actual ultimate strength we observed on our cylindrical concrete samples was about 24 MPa. Similarly, we took 420 MPa for the ultimate strength of the S420 type of reinforcement steel, whereas the actual ultimate strength before rupture measured experimentally was observed to be 425 MPA. These differences, especially those in concrete strengths, should be the major contributor to the large experimental/theoretical ratios.

As can be seen from Table 2, the ratio of (experimental ultimate load)/(theoretical ultimate load) was about 1.56 for the full beams, 1.71 for the box beams for which the ratio of (net beam width)/(beam height),

6.9

7.4

6.1

0.0049

0.0046

0.0016

29813 28147 28925 27189 26750 27454 8968 9375 9970 1.54 1.54 1.60 1.75 1.80 1.57 1.86 1.64 1.71 83.9 2.5 Wall thickness = 50 mm

210 + 18

4.0 Wall thickness = 100 mm

212 + 11

118.6

201.9 202.3 210.0 208.1 214.0 186.0 156.0 138.0 143.9 131.2 4.5 Full beam

B1 B2 B3 BB 1 BB 2 BB 3 BB 4 BB 5 BB 6

312

Tensile steel Type of beam (mm) Beam No

Weight of beam (kN)

Table 2 Results of the bending experiments of all the SFRC beams

Theoretical ultimate load (kN)

Measured ultimate load (kN)

Experimental ultimate load/theoretical ultimate load

Toughness (kN.mm)

Normalize toughness average

Displacement ductility average


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Fig. 6 The relationship of (experimental ultimate load)/(theoretical ultimate load) versus the ratio of (net wall thickness)/(outer beam height), 2 e/h, experimentally determined herein.

2 e/h, was 0.67, and 1.74 for the box beams for which the ratio of (net beam width)/(beam height), 2 e/h, was 0.33. These numerical values are diagrammatically shown in Fig. 6, which suggests that a SFRC box beam whose net wall thickness ratio is around 0.33 should be the optimum from the standpoint of the load-carrying capacity in proportion to its total cross-sectional area and moment of inertia. The diagrammatic appearance of the average values presented in Table 2 can be seen in Fig. 6. The first point is the average of a rather thin-walled box-beam, for which 2 e/h is 0.33, the one in the middle is for box beams of a 2 e/h of 0.67, and the third one is for the full beams; and hence, the relationship depicted in Fig. 6 covers a rather wide range. This figure can assist box-beam designers as a preliminary tool. After having computed the theoretical ultimate load of a SFRC box beam by the conventional ultimate load approach for ordinary RC beams, Fig. 6 can be seen as a design aid in rationally assessing the actual ultimate load to be resisted by that box beam. Moreover, Fig. 6 can also be used for predicting the appropriate wall thickness of the SFRC box beam versus the desired ultimate load to be carried by it. As mentioned before, Fig. 6 is valid for reasonably tension failure SFRC box beams. As seen in Table 2, for a decrease of 11% in dead weight and a decrease of 10% in tensile steel, a drop of only 1% in the experimental ultimate load occurred for the thicker wall SFRC box beams (2 e/h = 0.67), and for a decrease of 44% in dead weight

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Fig. 7 The relationships of loads versus mid-section displacements for all the RC beams tested.

and a decrease of 39% in tensile steel, a drop of 29% in the experimental ultimate load occurred for the thinner wall SFRC box beams (2 e/h = 0.33). Both these results clearly indicate that box beams with some hollow parts around their neutral axes work efficiently against bending. For the thinner SFRC box beams, 2 e/h = 0.33, the loss in ultimate load resistance (29%) is smaller than both gains in mass of concrete (44%) and amount of tensile steel reinforcement (39%). The reduced transverse earthquake loads due to reduced weights of the box beams of a prospective structure may inflict smaller loads and bending moments on those box beams, which may remain in proportion to their slightly smaller load-carrying capacities. Stripping of the tensile steel bars did not occur, meaning there was no bond-strength problem even in the thin-walled SFRC box beams. The relationship of the measured loads versus midsection displacements for all the nine beams is given in Fig. 7. The three-dimensional relationship of the measured loads versus the mid-section displacements and the cross-sectional moments of inertia for these beams is given in Fig. 8. The total areas under these curves, which are interpreted as their toughnesses, are computed to be 29000 N.m, 27000 N.m, and 9500 N.m, for the full SFRC beams (2 e/h = 1.0), the SFRC box beams with 2 e/h = 0.67, and the SFRC box beams with 2 e/h = 0.33, respectively. While 27000 N.m is fairly close to 29000 N.m, the toughness of the thinner-walled SFRC box beams is 7.4% smaller than 29000 N.m, which may be


Fig. 8 The relationships of loads versus (mid-section displacements) and (cross-sectional moment of inertias) for all the RC beams tested.

interpreted as the ductility of too thin-walled SFRC box beams being low. The relative loss in toughness of the thin-walled SFRC box beams is measured to be greater than the relative loss in the ultimate load resisted by them. The cross-sectional moment of inertias of the box beams with 2 e/h = 0.67 and 2 e/h = 0.33 are 1.2% and 20% smaller than that of the full beams, respectively. Despite a considerable loss in moment of inertia as compared to the full beam of the same outer dimensions, the ratio of (experimental ultimate load)/(theoretical ultimate load) of the thin-walled box beams with 2 e/h = 0.33 is measured to be 14% greater than that of the full beams. 4. Discussions and conclusions Standard compression experiments with cylindrical samples of 150 × 300 mm dimensions and flexural experiments with prisms of 150 × 150 × 750 mm dimensions revealed that toughness of steel fiber reinforced (SFR) concrete with a steel fiber type of Dramix-RC80/0.60-BN at a dosage of 30 kg/m3 increases more than two-fold as compared to plain concrete of the same recipe while the compressive strength and elasticity modulus of the SFRC are slightly smaller. As can be seen from Table 2, although the ultimate load-carrying capacity of the thin-walled SFRC box beams is 29% less than that of the full RCBs, the weight of the former is 44% smaller than that of the latter.


This reduction in dead weight will show up as reduced static moments and reduced earthquake loads on all the structural members, and hence the thin-walled SFRC box beams may be subjected to reduced external effects and they can be used instead of the heavier full beams, especially for large-span types of structures, like bridges. As mentioned before, the gain in dead weight by preferring box beams over full beams will be especially more pronounced for large-span beams. It is believed that if (1) high-strength concrete is used instead of a medium-strength concrete, and/or (2) hollow parts are produced as tapered from inside at the corners of the bends, which should be practicable with the help of a suitable inner mould, such negative effects as the unaccounted-for torsional stresses and stress accumulations at corners will be countered to some extent and the ratios of

r (experimental ultimate load)/(theoretical ultimate load) and

r (ultimate load of box beam)/(ultimate load of full beam of the same outer dimensions) may increase with thin-walled box beams. An experimental curve is obtained for the relationship between the ratio of (actual ultimate load)/(theoretical ultimate load) and the ratio of (wall thickness)/(beam height) for the SFRC box beams. References 1. Ocean Concrete Products (1999) Ocean Heidelberg Cement Group, Steel Fibre Reinforcement (Working Together to Build Our Communities Report, USA).

499 2. Bridge Analysis Report, Prepared for City of Reno via Nevada Department of Transportation Agreement (N: SA1500\Deliverables, USA, 2001) P206-99-015. 3. Bridge Design Manual (2001) (Texas Department of Transportation all rights reserved, USA, 512. 4. Subject CIV3222 (2000) Bridge design and assessment Review of Behaviour and Design of Reinforced Concrete Members in Flexure’ (Department of Civil Engineering, Monash University, Edition Date: 9). 5. Elliott KS (1996) Multi-Strorey Precast Concrete Framed Structures, Composite Construction, Chapter 6, (Published, England). 6. Myers JJ, Carrasquillo RL (1999) Mix Proportioning for High-Strength HPC Bridge Beams. American Concrete Institute Convention, Detroit, MI, Special Publication 189:37– 54. 7. Dupont D, Vandewalle L (2002) ‘Bending Capacity of Steel Fibre Reinforced Concrete (SFRC) Beams’ International Congress on Challenges of Concrete Construction, Dundee) pp. 81–90. 8. Recupero A, D’Aveni A, Ghersi A (2003) N-M-V Interaction Domains for Box and I Shaped Reinforced Concrete Members. Structures Journal, 100(1):113–119. 9. Alkhrdaji T, Nanni A (2001) ‘Design, Construction, and Field-Testing of an RC Box Culvert Bridge Reinforced with Glass FRP Bars’, Non-Metallic Reinforcement for Concrete Structrues-FRPRCS-5, Cambridge, July 16–18, pp. 1055– 1064. 10. ACI Committee (2002) 318, Building Code Requirements for Structural Concrete (ACI 318M-02) and commentary (318RM-02)’ (American Concrete Institute). 11. Vandewalle L, RILEM TC162-TDF (2000) Test and design methods for steel fibre reinforced concrete. Materials and structures 33 (January–February) pp. 3–5. 12. Altun F, Haktanir T (2004) A Comparative experimental investigation of steel fiber added reinforced concrete beams. Materials De Construcción 54(276):5–15. 13. ASTM C1018-92 (1992) Standart Test Method for Flexural Toughness and First-Crack Strength of FibreReinforced Concrete (American Society for Testing and Materials).