CRACK WIDTH ANALYSIS OF STEEL FIBERS REINFORCED CONCRETE BEAMS

Radi poboljšanja svojstava betonskih elemenata i konstrukcija, sprovedena su brojna istraživanja s dodacima organskih i neorganskih vlakana betonskim mješavinama. Sa ovim dodacima, poboljšana su svojstva kao što su čvrstoća pri zatezanju, čvrstoća pri savijanju, žilavost, dinamička čvrstoća i tako dalje. U posljednje vrijeme, beton ojačan vlaknima (Fiber Reinforced Concrete – FRC) ima široku primjenu kod različitih konstrukcija i konstruktivnih elemenata kao što su: tunelske cijevi, prefabrikovani segmenti, prskani beton, industrijski podovi, željeznički pragovi i tako dalje. Jedna od najpopularnih vlakana u upotrebi jesu čelična vlakna, te se takav beton zove beton ojačan čeličnim vlaknima (Steel Fiber Reinforced Concrete – SFRC). Dodavajući čelična vlakna mješavini betona, svojstva betonskih elemenata prije stvaranja pukotina neće se bitno mijenjati, ali se vrlo mijenja postpukotinsko ponašanje takvih elemenata [7]. U slučaju krtih materijala kao što je beton, pukotine se javljaju za relativno niske vrijednosti opterećenja (savijanje). Ovo se može objasniti činjenicom da krti materijali imaju veoma nisku mogućnost apsorbovanja energije, što je rezultat malih deformacija koje mogu podnijeti [2]. Prisustvo čeličnih vlakana poboljšava apsorpciju totalne energije, gdje vlakna apsorbuju energiju deformisanjem i čupanjem.


INTRODUCTION
In order to improve the properties of concrete elements and constructions, numerous studies have been carried out with the addition of organic and inorganic fibers to concrete mixtures.With these additions properties such as tensile strength, flexural strength, toughness, dynamic strength etc. have been improved.Recently, Fiber Reinforced Concrete (FRC) is widely used in various constructions and constructive elements such as: tunnel linings, prefabricated segments, shotcrete, industrial floors, railway sleepers and so on.One of the most popular fibers are steel fibers, and such concrete is called Steel Fiber Reinforced Concrete (SFRC).By adding steel fibers to a concrete mixture, the properties of concrete elements before cracking will change insignificantly, but the postcracking behaviour of such elements considerably changes [7].
For brittle materials such as concrete, cracks occur for relatively low loading values (bending).This can be explained by the fact that brittle materials have very low ability to absorb energy, which is the result of small deformations that they can bear [2].The presence of steel fibers improves the absorption of total energy, where the fibers absorb energy by deforming and pulling out.

Materijali
U eksperimentalnom istraživanju korištene su dvije vrste betona -beton obične čvrstoće (OSC) -C30/37 i beton visoke čvrstoće (HSC) -C60/70 (tabela 1).Obe vrste betona spravljane su sa 0,45% čeličnih vlakana i bez njih.Korištena čelična vlakna su tipa IRI 50/30 Obviously, the crack appearance is inevitable.Steel fibers cannot prevent the crack formation, but they can reduce it.Studies show that there is a high influence of steel fiber addition to a concrete mixture to the crack width in concrete elements.Crack width reduction depends on the type of steel fibers and quantity (percentage) in mixture.But even with a small percentage of steel fibers, the crack width reduction was noticed [17,7].
Klepša et al. [10] investigated the crack width and spacing for beams of ordinary concrete and concrete with the addition of 30 kg/m 3 of steel fibers.After the appearance of large cracks, the crack width for beams of ordinary concrete were increased about ten times.Šalna and Marčiukaitis [16] conducted the study of influence of steel fibers for concrete beams with different spans.The beams consisted of 1.0, 1.5 and 2.0% of steel fibers and it has been shown that beams with 2.0% steel fibers have almost 3 times lower crack width compared to beams with 1.0% fibers for average load.Furthermore, it has been shown that beams with 2.0% steel fibers have 32% greater load capacity compared to beams with 1.0% steel fibers.Vasanelli et al. [17] investigated the influence of the fiber type and quantity on the crack width of reinforced concrete beams.Beams containing 0.6% of steel fibers showed 42% less cracks width compared to beams without fibers for characteristic force.Dupont and Vandewalle [7] investigated the effect of the steel fibers addition of different quantities and main reinforcement profiles to the crack width of reinforced concrete beams.It has been shown that by increasing the amount of steel fibers the crack width is reduced, and the results are more pronounced for smaller profiles of the main reinforcement, as expected.The average reduction of the crack width for beams with a maximum of 60 kg/m 3 of fibers for the mean values of bending moments is about 70% compared to the beams without fibers.Crack width analysis is still in focus of research, a s the behaviour of concrete elements is insufficiently explored [5,9].
In this paper the experimental results and analysis of crack width and crack formation in concrete beams with steel fibers are presented.Calculation of crack ultimate limit state (cracking) has the purpose to limit the crack width of concrete elements, with the aim to prevent deterioration of concrete structures, which is often a result of corrosion due to the flow of liquids and gases through large cracks in concrete elements.The effect of the steel fibers addition to the crack width of reinforced concrete beams loaded with a short-term ultimate static load with a single unload cycle was analysed.The beams were made of two types of concrete: ordinary strength concrete (OSC) -C30/37 and high strength concrete (HSC) -C60/70, with and without 0.45% of steel fibers.
The physical -mechanical properties of all concrete mixtures were previously tested: compressive strength, splitting tensile strength, bending tensile strength and modulus of elasticity [13,14].Properties were tested for the concrete age of t=35-40 days and t=420-430 days.Compressive strength and splitting tensile strength were tested on cube samples 15x15 cm.Bending tensile strength was tested on prismatic samples 10x10x40 cm, and modulus of elasticity on cylinder samples 15/30 cm.

Beams
In total 16 beams were tested.All beams are in cross section 15x28 cm and length 300 cm (figure 1).The beams are divided into four series: A, F, G, H. Series A and G are t=35-40 days of age, while F and G series were t=420-430 days.Furthermore, all series are divided into 4 subgroups (1,2,3,4), where subgroups 1 and 2 represent ordinary strength concrete, and subgroups 3 and 4 high strength concrete.The beams' overview is presented in table 3. The beams are reinforced with longitudinal reinforcement S500 and stirrups class 240, as presented in figure 1.The chosen beams dimensions and reinforcement (longitudinal, stirrups and fibers) correspond to the application in practice.The beams layout with measuring devices prior to testing, as well as loading is shown in figure 2. Slika 1. Prikaz grede sa armaturom (mjere u cm) Figure 1
In the beams test with ultimate short-term load with one unloading cycle, beams were loaded with two concentrated forces at a distance of 80 cm, and 100 cm from bearings (figure 1).The beams are loaded with a constant load with the value of one force FG=4.00 kN, which is the constant in the test period.On that force, exploitation load was added FQ=7.60 kN.Total force in that moment is F G+Q=11.6 kN.Last loading level for which measurements were carried out (ultimate) was FU=20.60 kN, after which the force was added to failure.
The crack width was measured in the centre of the beams on three or more places on both sides, depending on crack formation.The measurement was performed with a microscope of accuracy of 0.05 mm.The measurement procedure is shown in figure 3. Due to precision, the final measurement was performed in AutoCAD software.

RESEARCH RESULTS AND ANALYSIS
The crack width and crack propagation were measured and analyzed on a total of 16 reinforced concrete beams, with and without 0.45% of steel fibers.The effect of steel fibers and the concrete age on the crack width was investigated.In table 4 average crack width results from measuring points for all subgroups and three loading levels are presented.Na gredi G4, prva pukotina pojavila se nakon ciklusa rasterećenja, te je stoga t a greda izuzeta iz daljnje analize.Prikaz razvoja pukotina za jednu karakterističnu armirano-betonsku gredu sa čeličnim vlaknima može se videti na slici 4.
For beam G4, first crack appeared after the unloading cycle, therefore this beam was excluded from further analysis.Crack development for one characteristic beam is shown in figure 4.
When defining the effects of steel fibers to the crack width for the beams' age t=35-40 days, series A and G were compared, and for the age t=420-430 days that are F and H series.The average crack width and the analysis of the fiber addition effect are given in tables 5 and 6.Diagram of the relation force (F) -crack width (w) is shown on figures 5 and 6.
Sa slika 5 i 6 može se vidjeti da je razvoj pukotina OSC i FROSC greda u početku ispitivanja izjednačen; međutim, dostizanjem nivoa ultimnog opterećenja (nešto ispod i iznad FU vrijednosti), razlika u razvoju pukotina je očigledna (za obe ispitane starosti betona).Od tog trenutka, FROSC grede imaju mnogo manje širine pukotina od OSC greda.Kod greda starosti t=35-40 dana, približavajući se sili F U , razlika širine pukotina According to the results shown in the tables and in the figures, it can be concluded that the addition of steel fibers reduces the crack width both for ordinary concrete and for high strength concrete.For the exploitation load level average crack width for concrete beams of t=35-40 days age are lower for FROSC compared to OSC for 31%, and for ultimate load level the difference is 90%.FRHSC beams age t=35-40 days for exploitation load level have 43% lower crack width values compared to HSC beams of the same age, while for ultimate load level the difference is 64%.For concrete beams of age t=420-430 days a slightly different behavior was noticed.For exploitation load level average crack width of FROSC beams are 36% lower compared to OSC beams, but for ultimate load level the difference is only 16%.FRHSC beams have significant crack width values reduction for exploitation load level compared to HSC beams of 99%, while for ultimate load level the difference is 43%.
From the figures 5 and 6 it can be seen that crack development for OSC and FROSC beams at the beginning of the test is equal, however by reaching the ultimate load level (slightly below and above FU) the difference in the crack development is obvious (for both concrete age).From that point FROSC beams have significantly lower crack width values compared to OSC beams.For the beams of age t=35-40 days, by approaching the FU force, difference in the crack width is razvija se postepeno, dok se kod greda starosti t=420-430 dana razlika pojavljuje relativno naglo.Za grede betona visoke čvrstoće primjećeno je nešto drugačije ponašanje.Od početka eksperimenta, širine pukotina greda sa čeličnim vlaknima znatno su niže (~50%), a dostizanjem ultimnog nivoa opterećenja, razlika se samo povećava.
developing gradually, but for beams of age t=420-430 days the difference occurs relatively rapidly.From the beginning of the experiment crack width are lower for steel reinforced concrete beams (~50%), and by reaching the ultimate load level the difference is only increasing.
The addition of steel fibers ultimately fails to significantly affect the crack width of reinforced concrete beams due to their age.Average crack width of FROSC beams for exploitation load level are lower for beams of age t=420-430 days compared to beams of age t=35-40 days for 27%, while for FRHSC beams the difference is only 3%.For ultimate load level average crack width of FROSC beams is 7% greater for beams of age t=420-430 days, and for FRHSC beams the difference is 3%.
From the figures 7 and 8 it can be seen that the concrete age affects the crack width of OSC and HSC beams only after reaching the ultimate load level.Slightly lower values of the crack width for concrete age of t = 420-430 days are noticeable.For beams with steel fibers no significant difference was observed in crack formation at the beginning of the test.By exceeding the ultimate load level, beams of age t=420-430 days shows significantly lower values of the cracks width.

ACI building code metod
ACI building code 318 [1] za proračun širine pukotina predlaže empirijsku formulu: where: σs -stress in reinforcement on crack, β1 -coefficient that takes into account the reinforcement bond, β2 -coefficient that takes into account the effect of load duration or load repetition, σsr -stress in tensed reinforcement calculated at the beginning of crack section under load conditions that cause the first crack, Es -Youngs' modulus of elasticity for reinforcement.
where: βb -ratio of distance between neutral axis and tension face to distance between neutral axis and reinforcing steel, σs -stress in the reinforcement, dc -distance between reinforcements' center and lower edge of the element, Ae -effective concrete area.

RILEM TC162-TDF method
For calculation the crack width of steel fiber reinforced concrete RILEM (fr.Réunion Internationale des Laboratoires et Experts des Matériaux, systèmes de construction et ouvrages -en.International Union of Laboratories and Experts in Construction Materials, Systems and Structures) proposed the application of the EN 1992:2004 method.Method of calculation presented in EN 1992:2004 is corrected by supplementing the formula for mean crack distance calculation [12].Furthermore, stress in the tensile reinforcement should be calculated considering that steel fibers that are "bridging" the crack will take residual tensile stresses (σfb) uniformly by the crack height.The modified expression for the mean crack distance is given by: 12 50 500,25 gdje je: k1 -koeficijent koji uzima u obzir svojstva spoja armature; k2 -koeficijent koji uzima u obzir formu raspodjele deformacije; ρr -efektivni odnos armature (As1/Ac,eff); Φ -poluprečnik čeličnog vlakna; L -dužina čeličnog vlakna.
The great disadvantage of this method is not taking into consideration the percentage, i.e. the amount of steel fibers embedded in the concrete elements.Also, the determination of residual stress due to the addition of steel fibers is questionable.

ACI building code method
Committee 544 [3] suggests adding tensile force which is taken by fiber reinforced concrete for crack width calculation of concrete element with steel fibers.The fiber contribution is in constant tensile stress σf in cracked part of the element: gdje je: lf i df -geometrijske karakteristike vlakna; Vf -procenat vlakana; Fbe -efektivnost veze čeličnih vlakana i betona where: lf i df -geometrical characteristics of fibers, Vf -fiber percentage, Fbe -effectiveness of bond between steel fibers and (varira između 1.0 i 1.2, zavisno od osobina vlakna).concrete (ranging from 1.0 and 1.2 depending on the fiber characteristics).

CONCLUSION
Based on the results and analysis for final (ultimate) load level after one unloading cycle for which measurement was taken for all the beams, effect of steel fiber addition to crack formation and crack width of concrete beams is as follows: − For ordinary concrete beams (age t=35-40 days) average crack width reduction of FROSC beams compared to OSC beams is 90%; − For high strength concrete beams (age t=35-40 days) average crack width reduction of FRHSC beams compared to HSC beams is 64%; − For ordinary concrete beams (age t=420-430 days) average crack width reduction of FROSC beams compared to OSC beams is 16%; − For high strength concrete beams (age t=420-430 days) average crack width reduction of FRHSC beams compared to HSC beams is 43%; The concrete age fails to significantly affect crack width reduction for beams with steel fibers (from 3% to 7%).
The aim of this paper is primarily to present the experimental results of the measured crack width in reinforced concrete beams with real dimensions (15/28/300 cm), for two concrete ages (t=35-40 and t=420-430 days), for which there is a little recorded data.The paper complements the database of the subject matter.Also, theoretic basis for calculating crack width of reinforced concrete beams by EN 1992:2004 and ACI building code method is given, as well as method for calculating crack width of reinforced concrete beams with steel fibers by RILEM TC162-TDF and ACI building code method.
The theoretical basis presented is the foundation for future research with the purpose of comparing the measured crack widths obtained by experiment with empirical formula given in standards and recommendations.
This paper has opened many issues in the field of defining the behavior of elements and constructions of fiber reinforced concrete with steel fibers over time, for the purpose of its increasingly frequent application as a constructive material in engineering practice.

Merima SAHINAGIC-ISOVIC Marko CECEZ
Fibre reinforced concrete in recent years has grown from experimental material to a practical usable material, due to its positive properties such as increased tensile strength, bending strength, toughness etc.However, still there are many unanswered questions that are the subject of many research.In this paper results and analysis of crack width of concrete beams with steel fibres are presented.This analysis considers influence of steel fibre addition on the crack width of reinforced concrete beams (dimensions 15/28/300 cm) loaded up to fracture during shot-term ultimate static load with one unloading cycle.Concrete beams were made of two types of concrete: ordinary strength concrete (OSC) -C30/37 and high strength concrete (HSC) -C60/70, with and without 0.45% of steel fibres.The results indicate that there is a significant influence of fibre addition on crack width, especially for ordinary concrete.At the end, empirical calculations of the concrete elements' crack width with steel fibres according to the recommendations of RILEM and ACI building code are given.Key words: concrete, steel fibres, static load, crack width

Table 7 .
Concrete age effect for the beams without steel fibers

Table 8 .
Concrete age effect for the beams with steel fibers