Engineering Structures 72 (2014) 140–151

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Engineering Structures

journal homepage: www.elsevier .com/locate /engstruct

Loop connection with fibre-reinforced precast concrete componentsin tension

http://dx.doi.org/10.1016/j.engstruct.2014.04.0320141-0296/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +55 62 3209 6084; fax: +55 62 3209 6087.E-mail addresses: dlaraujo@ufg.br (D.L. Araújo), marinacurado@yahoo.com.br

(M.C. Curado), pfer@furnas.com.br (P.F. Rodrigues).

Daniel de Lima Araújo a,⇑, Marina Craveiro Curado a, Paulo Fernando Rodrigues b

a Civil Engineering School, Federal University of Goiás, Rua Universitária, n� 1488, Qd 86, Setor Universitário, Goiânia/GO, Postal Code 74605-220, Brazilb Furnas Centrais Eletricas, Department of Support and Technical Control, BR 153, km 1290, Aparecida de Goiânia/GO, Postal Code: 74001-970, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 June 2013Revised 10 April 2014Accepted 15 April 2014

Keywords:Precast membersTensile connectionsTensile strengthLoop barsSteel fibres

Overlapping of reinforcement bars or loops is often used to connect precast members. The precast unitshave projecting bars, usually with a full 180� hook, which are embedded in situ in concrete after erection.This paper studies a tension joint using direct overlapping loops, evaluating the influence of the additionof steel fibres to the in situ concrete. Other variables studied were the diameter of the loop bend and thepresence of transverse reinforcement in the loop. The results indicate the possibility of reducing the jointwidth between precast elements by using steel fibres. An expression based on strut and tie theory is pro-posed to calculate the connection’s strength, and it provided a good approximation to the experimentalresults.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The precast elements are fabricated in series, limiting onsitework to the assembly of elements by lifting equipment. This workstage includes the realisation of connections between theseelements so as to guarantee the transfer of actions between themand ensure the structural integrity of the complete structure. Tomaintain a rapid speed of construction, which is one of the princi-pal advantages of pre-fabrication, simple connections which can berealised within the smallest possible width should be chosen so asto also minimise the material and labour costs involved in thisstage.

In the case of connections subject to tensile loads, overlappingwith loop-shaped bent bars is a classical way to transfer this loadbetween precast elements [1,2]. However, few studies have beencarried out using this type of connection so far [3–8]. One of theadvantages of the use of this type of connection is the fact thatthe loop-shaped anchorages are capable of transferring the stressesbetween the reinforcement and the concrete over a shorter lengththan that necessary for straight bars, which allows the connectionjoint’s width to be reduced.

In straight anchorages, the transmission of forces happens viabond stresses. In loop-shaped anchorages, next to bond stresses,

radial stresses are also mobilised, which transmit to the concrete,via compression, part of the force to be anchored. Following theFIB manual [9], the radial stresses on the loop lead the inclinationof compressed struts between the opposing loops, by means ofwhich the tensile force is transferred from one element to the other(Fig. 1). The diagonal inclination generates a tensile force normal tothe loop’s plane, which should be resisted by a transversereinforcement placed inside the loop, at the two ends of the over-lapping loops, in order to avoid splitting of the concrete in theloop’s plane.

The splitting of the concrete in the loop’s plane can also beavoided by the addition to the concrete of steel fibres that will fillthe connection. The presence of steel fibres increases ductility andtensile strength and improves the concrete’s deformation proper-ties. What should also be considered is the possibility of reducingthe anchorage length due to the improvement of the bondingbetween steel and concrete provided by the addition of the steelfibres to the concrete matrix. For this reason, the use of steel fibresin this type of connection can be advantageous.

2. Research significance

The aim of this research is to study a tension joint formed by theoverlapping of reinforcement loops, evaluating the influence of theloop’s bending diameter, the presence of transverse reinforcementplaced inside the loop, and the presence of steel fibres added to theconcrete at the joint. The overlapping of reinforcement loops is

Nomenclature

Ac cross-sectional area of concrete coreAcn transverse section of the strutAt area of transverse reinforcementb width of connection (dimension parallel to the load

direction)c concrete covering perpendicular to the loopsD diameter of the bend of the loop barEc mean value of tangent modulus of elasticity of concreteEs modulus of elasticity of reinforcementFu ultimate load at connectionFt force on transverse reinforcementFT flexural toughness of concretefc mean value of concrete cylinder compressive strengthfct,sp mean value of concrete splitting tensile strengthfc,dc mean value of concrete cylinder compressive strength

obtained from stress–strain curvesfct,f mean value of concrete flexural tensile strengthfu failure strength of reinforcement

fy yield strength of reinforcementGf fracture energy of concreteh, wt dimensions‘e reinforcement’s anchorage length‘0 overlap length between the loopsNy yield load of one leg of the loop barr radius of the bend of the loop bars spacing between overlapping loopst thickness of test specimensTR toughness ratio of concreteVf fibre volumea, b, h angle; strut inclinationU mechanical ratio of transverse reinforcement/ diameter of the u-barrc,rad radial concrete stressru maximum tensile stress at loop reinforcementm effectiveness factor

D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151 141

useful when one wishes to decrease the length of the lapping ofbars. This reduction of the overlapping length is especially interest-ing for the connections between precast elements, resulting insmaller joint widths to be filled with concrete in situ. The overlap-ping length of reinforcement loops can be decreased even more bythe presence of steel fibres in the in situ concrete. Furthermore, thefibres can simplify the execution of the connection due to thereduction of the reinforcement ratio, especially for the reinforce-ment normal to the loop’s plane. There are few works in the liter-ature on this type of connection, although it is widely used [3–8].There is even less published work about the application of steelfibres in joints with overlapping of reinforcement loops.

3. Experimental programme

The experimental programme consisted of the execution of 24tensile tests on prismatic models with dimensions of360 mm � 530 mm � 150 mm, which simulated the connectionbetween precast elements, consisting of the overlapping of twosteel bars, 10 mm in diameter with a full 180� hook, which areembedded in concrete. Fig. 2 shows the dimensions of the model

Fig. 1. Transfer of forces at the loop connection: (a) radial stresses, and (b) inclinedcompressed struts between the overlapped loops [9].

that was used in the test and that consisted of three blocks sepa-rated by a joint of 15 mm. The central part was representativefor the connection and its width was kept constant and equal to110 mm. The reinforcement’s overlap length was set equal to90 mm, and the distance between the loops’ planes was 20 mm(Fig. 3). Previous studies by the authors showed that a loop-shapedreinforcement embedded in concrete with 1% steel fibres, similarto those used in this work, is capable of reaching the steel’s yieldlimit before being pulled out with an anchorage length of only90 mm. In the case of the use of 2% steel fibres, the anchoragelength can be reduced to 50 mm [10]. In this way, the overlaplength used in the tested connection, 90 mm, represented approx-imately half of what would have been recommended by the FIB [9].

Steel bars of 16 mm diameter and bent in the shape of a loopwere anchored in the end blocks. The steel bars projected out ofthe model and were attached to the test device, allowing the appli-cation of a tensile force on the connection. The end blocks wereconveniently reinforced in order to avoid the failure of these blocks

Fig. 2. Dimensions of test specimen, in millimetres, and position of strain gauges atthe connection.

Fig. 3. Detail of the connection region: (a) reinforcement’s overlap length; (b) lateral view (mm).

142 D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151

and therefore to guarantee that the failure would occur in the mod-el’s central part, which simulated the connection.

The analysed variables in the experimental programme werethe loop’s bending diameter, the presence of reinforcement trans-versal to the loop’s plane (consisting of two bars of 10 mm), andthe volume of steel fibres added to the concrete to fill up the con-nection. For the loop’s bending diameter, the values of 160 and100 mm were used, the first being the minimum value calculatedfollowing the FIB’s recommendation [9] and the second beingdefined by the minimum bending diameter of the machine usedto bend the reinforcement. The content of steel fibres used was1% (78.5 kg/m3) or 2% (157 kg/m3) of the concrete volume.

In the production of the concrete, a Portland cement with filler(CP II-F-32 according to the Brazilian standard), a silica fume, asmall aggregate of the natural sand type, and a coarse aggregatewith nominal maximum size of 12.5 mm were used, conformingto the composition shown in Table 1. In order to guarantee the nec-essary fluidity of the mixture, a synthetic superplasticizer additivebased on polycarboxylate polymer technology was used in a vari-able percentage depending on the presence and the content of steelfibres. For the concrete without fibres, a superplasticizer percent-age of 1% in relation to the equivalent cement mass was used, cor-responding to the weighted average of the masses of cement andsilica fume in relation to their densities. For the concretes withfibres, a superplasticizer content varying between 1.4% and 2%was used.

Wirand� FS7 high strength steel hooked fibres, 33 mm in lengthand 0.55 mm in diameter, were used, resulting in an aspect ratio of60. The tensile strength of the steel wire fibre is up to 1100 MPa.The length adopted for the fibres took into consideration the width

Table 1Composition of matrix for production of one cubic metre of concrete.

Material Quantity (kg/m3)

Equivalent cement 508Cement – CP II F 32a 483Water 182Silica fume 19Natural sand 729Gravel 12.5 mm 836Steel fibres Variable (1–2%)Superplasticizer additive Variable (1–2%)Water/cement relation 0.38

a According to Brazilian standard.

of the connection region, so as to avoid the preferential alignmentof the fibres in the direction of the connection’s major dimension.

The properties of the overlapping reinforcement steel weredetermined by means of direct tensile tests according to Brazilianstandard ABNT NBR ISO 6892:2002 [11], which resulted in a yieldstrength (fy) of 595 MPa and a failure strength (fu) of 655 MPa.

The models were cast in two stages. Initially, the end blockswere cast with concrete without fibres. In this stage, six cylindricaltest specimens with dimensions of 150 mm � 300 mm were castand tested to determine the compressive strength and the modulusof elasticity after 28 days of concrete casting.

The second stage consisted of the casting of the central part ofthe model with the same concrete as was used for the casting ofthe end blocks in the case of the connection without steel fibres.In the models with steel fibres, the concrete matrix was the sameas that used for the casting of the end blocks, and the superplasti-cizer was adjusted to allow the dispersion of the steel fibres. Theconcrete casting was carried out in two layers in the direction per-pendicular to the hooks’ plane. The concrete consolidation, as wellas that of the end blocks of the connection region, was carried outwith an immersion vibrator in order to avoid the alignment of thesteel fibres in a preferential plane. Twelve cylindrical test speci-mens with dimensions 150 mm � 300 mm were cast in order todetermine the compressive strength, the splitting tensile strength,the modulus of elasticity, and the stress–strain curve under com-pression of the concrete of the connection region. Three prismatictest specimens with dimensions of 100 mm � 100 mm � 400 mmwere also cast. For concrete with fibres, these prismatic specimenswere subjected to a four-point bending test in order to determinethe flexural tensile strength and the flexural toughness [12]. In theconcrete without fibres, the test specimens were sawed halfwaythrough in the middle of the span and then submitted to a three-point bending test in order to determine the flexural tensilestrength and the fracture energy [13]. All the tests were carriedout 28 days after casting of the connection.

Table 2 summarises the matrix of the test programme. Themodels’ nomenclature consists of three parts: the first part repre-sents the loop’s bending diameter, the second shows the volumeof steel fibres added to the concrete, and the third corresponds tothe presence (or not) of transverse reinforcement placed insidethe loop (CAT and SAT, respectively). All specimens were castand tested in duplicate.

The test consisted of the application of displacement until fail-ure of the test specimen, as shown in Fig. 4. The displacement rate

Table 2Matrix of test programme.

Test specimen Mixture Loop’s bending diameter (mm) Fibre volume (%) Transverse reinforcement

D100-VF0-SAT 1 100 0 AbsentD160-VF0-SAT 1 160 0 AbsentD100-VF0-CAT 2 100 0 PresentD160-VF0-CAT 2 160 0 PresentD100-VF1-SAT 3 100 1 AbsentD160-VF1-SAT 3 160 1 AbsentD100-VF1-CAT 4 100 1 PresentD160-VF1-CAT 4 160 1 PresentD100-VF2-SAT 5 100 2 AbsentD160-VF2-SAT 5 160 2 AbsentD100-VF2-CAT 6 100 2 PresentD160-VF2-CAT 6 160 2 Present

Fig. 4. Test setup: (a) front view; (b) cut A–A.

D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151 143

was kept constant during the test and was equal to 0.3 mm/min.During the test, a computer registered the values of the loadresisted by the connection, in kilonewtons, the displacement ofthe setup, in millimetres, and the deformations of the strain gaugeson reinforcement (E1, E2, E3, E4, E5, and E6 in Fig. 2). At the end ofthe test, the test specimen’s failure mode was verified, notingwhether there had been yielding of the reinforcement at themoment of failure of the connection.

Table 3Mechanical properties of the concrete (mean and standard deviation).

Vf (%) fc (MPa) Ec (GPa) fct,sp (MPa)a fc,dc (MPa)

0 62.30 ± 2.27 30.66 ± 0.57 5.59 ± 0.22 62.61 ± 1.861.94 ± 2.31 30.00 ± 0.10 6.15 ± 0.39 55.45 ± 5.6

1 70.82 ± 1.88 31.23 ± 0.45 9.17 ± 0.46 65.85 ± 2.575.39 ± 3.67 31.66 ± 0.47 9.59 ± 0.49 69.60 ± 2.8

2 77.01 ± 2.72 31.60 ± 1.23 11.69 ± 0.93 71.67 ± 1.571.91 ± 5.47 31.52 ± 0.54 10.03 ± 0.85 70.05 ± 2.0

ND: value not determined.a Splitting tension strength.b Compressive strength obtained from stress–strain curves.c Toughness ratio.d Flexural tensile strength.e Fracture energy determined by three-point bending test for the concretes without fif Flexural toughness determined by four-point bending test for the concretes with fib

4. Results and discussion

4.1. Mechanical properties of the concrete

Table 3 shows the mechanical properties of the concrete used inthe test programme. It can be noted that the influence of the steelfibres on the modulus of elasticity of concrete is negligible. In rela-tion to the compressive strength, the addition of steel fibres in the

b TR c fct,f (MPa) d Gfe (N mm/mm2) FT (MPa) f

9 0.455 4.56 ± 0.80 0.079 ± 0.045 –8 0.455 4.78 ± 0.40 0.067 ± 0.006 –7 0.546 ND – ND1 0.512 12.10 ± 0.12 – 10.45 ± 0.453 0.730 15.22 ± 1.50 – 13.71 ± 1.210 0.749 11.88 ± 1.08 – 10.77 ± 0.69

bres [13].res [12].

Fig. 5. (a) Average stress–strain curves and (b) average load-deflection response curves for concrete.

144 D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151

amounts 1% and 2% led to increases in the strength of 18% and 20%respectively compared to the concrete without fibres.

On the other hand, for average values of splitting tensilestrength, compared to concrete without fibres, increases of 60%and 85% were noted when fibres were added in the volume frac-tions of 1% and 2% respectively. The flexural tensile strength isincreased by 159% and 190% with the addition of 1% and 2% fibresrespectively.

The test to obtain the stress–strain curve allows the increase intoughness of the concrete in compression to be evaluated (Fig. 5).In this paper, the toughness is measured as the total area under thestress–strain curve up to a strain of 0.015, as this is sufficient torepresent the trend of the post-peak behaviour. This toughness iscompared to the toughness of a rigid plastic material in the formof a toughness ratio (TR), as defined by other researches [14,15].It can be noted that due to the addition of 1% and 2% steel fibresto the concrete, there were increases of the order of 16% and 63%

Table 4Results of tested specimens.

Test specimen Ultimate load atconnection: Fu (kN)

Maximum stressreinforcement (M

D100-VF0-SAT_1 56 357D100-VF0-SAT_2 71 452D160-VF0-SAT_1 67 427D160-VF0-SAT_2 72 458D100-VF0-CAT_1 75 477D100-VF0-CAT_2 72 458D160-VF0-CAT_1 82 522D160-VF0-CAT_2 72 458D100-VF1-SAT_1 94 598D100-VF1-SAT_2 80 509D160-VF1-SAT_1 85 541D160-VF1-SAT_2 78 497D100-VF1-CAT_1 108 688D100-VF1-CAT_2 101 643D160-VF1-CAT_1 104 662D160-VF1-CAT_2 105 668D100-VF2-SAT_1 107 681D100-VF2-SAT_2 103 656D160-VF2-SAT_1 107 681D160-VF2-SAT_2 107 681D100-VF2-CAT_1 103 656D100-VF2-CAT_2 106 675D160-VF2-CAT_1 105 668D160-VF2-CAT_2a 89 567

a Result not considered in the analyses;b Not calculated.

respectively in the toughness ratio of the steel fibre reinforced con-crete compared to the concrete without fibres.

Fig. 5 also shows the average load-deflection curves obtainedfrom the four-point bending test for the steel fibre reinforced con-crete. Note that in Table 3 the increase in the amount of fibres from1% to 2% influenced the flexural toughness, which showed anincrease of up to 31% with the increase in the steel fibre volume.

4.2. Connection strength

Table 4 shows the test results concerning the ultimate load andfailure mode of each test specimen. For the calculation of the max-imum stress in the reinforcement, an equal distribution of the loadbetween the two loops of the reinforcement was considered, sincethe two extensometers that were glued to the reinforcementshowed very similar strains during the whole test (Fig. 6). The fail-ure mode was defined as failure in the concrete or yielding of the

inPa)

Radial concrete stress atmaximum load, rc,rad (MPa)

Failure mode

b Failure in concreteb Failure in concreteb Failure in concreteb Failure in concreteb Failure in concreteb Failure in concreteb Failure in concreteb Failure in concrete94.0 Yield of steelb Failure in concreteb Failure in concreteb Failure in concrete108.0 Yield of steel101.0 Yield of steel65.0 Yield of steel65.6 Yield of steel107.0 Yield of steel103.0 Yield of steel66.9 Yield of steel66.9 Yield of steel103.0 Yield of steel106.0 Yield of steel65.6 Yield of steelb Failure in concrete

D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151 145

steel in function of the strain registered in the reinforcement at themoment of ultimate load. In this way, even if the concrete in theconnection failed, if this happened after the reinforcement startedyielding, the failure would be defined as being by yielding of thesteel.

In the test specimens in which the concrete in the connectionfailed, the formation of a crack typical of splitting between theloop’s planes occurred. In specimens without fibres and withouttransverse reinforcement, failure occurred abruptly because ofthe material’s fragile behaviour and because the crack was notintercepted by the reinforcement, resulting in complete separationof the test specimens (Fig. 7a).

4.2.1. Influence of the loop’s bending diameterThe reduction of the reinforcement’s bending diameter from

160 to 100 mm caused a small change in the maximum load atconnection when failure occurred in the concrete. The largestdifference between the average values for the maximum loadwas 9%, observed in the specimens without fibres and transversereinforcement. This difference is reduced by the presence of trans-verse reinforcement and steel fibres in the connection.

In specimens where the failure mode was yielding of steel, theradial concrete stress was determined. A horizontal equilibrium forone U-bar gives

rc;rad ¼p/4r

fy ð1Þ

In order to limit the bearing stresses to acceptable values, theradial stress is not greater than three times the compressivestrength when there is a larger concrete cover [9]. It is easily seen

Fig. 6. Load versus reinforcement strain for th

from Table 4 that this limit was not exceeded even at a lower bend-ing diameter, which suggested that the failure of connection wasnot due to the reduction of the diameter of the bend of the U-barbut due to the reduction of the length of the overlap.

4.2.2. Influence of the presence of transverse reinforcementThe presence of the transverse reinforcement in the connection

without fibres restricted the opening of the splitting crack, pre-venting abrupt failure of the test specimen (Fig. 7b). The test spec-imens without fibres and with transverse reinforcement showed,on average, an ultimate strength that was 13% higher than that reg-istered for the connections without fibres and without transversereinforcement. All the test specimens without steel fibres at theconnection failed in the concrete core before the reinforcementreached the steel’s yield stress.

For the test specimens with 1% steel fibres added to theconcrete, there was an average increase of 24% in the value ofthe maximum load due to the presence of the transverse reinforce-ment. The test specimens without transverse reinforcementshowed failure of the concrete core (Fig. 7c), while in the test spec-imens with transverse reinforcement, the steel of the reinforce-ment loop yields, reaching it́s the steel’s failure strength (fu) atthe end of the test (Fig. 8a). The transverse reinforcement is littlerequested near the failure of the connection, as shown by the E5and E6 reinforcement strains in Fig. 6.

4.2.3. Influence of steel fibresFor the test specimens without transverse reinforcement, the

addition of 1% steel fibres was not sufficient to guarantee theyielding of the steel of the reinforcement loop, as the failure of

e test specimens with 1% and 2% fibres.

Fig. 7. Failure mode of the connection: (a) test specimens without fibres and without transverse reinforcement; (b) test specimens without fibres and with transversereinforcement; (c) test specimens with 1% fibres and without transverse reinforcement.

146 D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151

the concrete at the connection was noted. However, the connectionshowed a stable post-peak behaviour, with gradual loss of strengthdue to the fibres (Fig. 7c and Fig. 9). Furthermore, the maximumload increased by an average of 27% due to the addition of 1% steelfibres compared to specimens without transverse reinforcementand fibres.

With the increase of the steel fibre content to 2%, the connec-tion failed due to yielding of the reinforcement loop and the factthat the steel’s failure strength (fu) was reached at the end of thetest (Fig. 8). In this case, few cracks were observed at theconnection.

In the case of test specimens containing transverse reinforce-ment and 1% steel fibres, the failure occurred by yielding of thereinforcement loop. In the test specimens with 2% steel fibresand without transverse reinforcement, failure had already hap-pened in the reinforcement loop, and as such the use of the trans-verse reinforcement did not influence the connection’s strength.

Fig. 8. Failure of the reinforcement loop in (a) test specimens with 1% fibres

5. Comparison with analytical models for loop connection

There are few analytical models for a connection with loop-shaped bent bars loaded in tension. The most recent is the paperof Joergensen and Hoang [7], which presented an experimentalprogramme to study loop connections with concrete failure. Theresults showed that the ultimate load was increased by an increasein the overlap length of the loop-shaped bars, by a decrease in thespacing between adjacent loop-shaped bars, and by an increase inthe amount of transverse reinforcement. The ultimate load was notaffected by the diameter of the loop-shaped bent bars. The paperalso presented an upper bound plasticity model that was obtainedby adopting a modified version of a m-formula originally proposedfor beam shear problems.

The Joergensen and Hoang’s analytical model was applied to theexperimental programme developed in this paper. However, it isnot able to evaluate the ultimate load of loop connections without

and transverse reinforcement and (b) in test specimens with 2% fibres.

Fig. 9. Load-displacement curve of test specimens without transversereinforcement.

D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151 147

transverse reinforcement or with steel fibres. Then, it was appliedto only four specimens tested in this paper. Eqs. (1)–(3) are thesolution proposed in this analytical model when there is concretecore failure and a P u and a P h. In this case, a is the anglebetween the yield line and the displacement vector, h is the anglebetween the diagonal yield line and the U-bar, and u is the angle offriction for concrete. Fig. 10 shows the yield lines adopted for theconnection tested in this paper. Eq. (1) was divided by four becausein the connection tested in this paper only one diagonal yield linewas formed.

Fu ¼14mfcAc

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4Um

1�Um

� �þ s

‘0

� �2s

� s‘0

0@

1A ð1Þ

m ¼ 0;88ffiffiffiffifc

p 1þ 1ffiffiffiffiffi‘0p

� �ð2Þ

U ¼ Atfy

Acfcð3Þ

In this model, Ac is the cross-sectional area of the concrete core, thatis, the shaded area shown in Fig. 10c. Since only the core is confinedby U-bars, it seems reasonable to assume that the concrete coveroutside the core does not contribute significantly to the strengthof the connection. From Fig. 10c, the expression for Ac can bededuced; that is:

Ac ¼p4

Dþ 2/ð Þ2 þ 2 b� ‘e þ ‘0 � /� D2

� �Dþ 2/ð Þ

� b Dþ 2/ð Þ ð4Þ

It can be seen that this analytical model is suitable because the fail-ure in the concrete was observed in specimens with transverse rein-forcement and without steel fibres. In fact, for a specimen with aloop bending diameter of 100 mm, the ultimate load predicted bythe analytical model was 67.6 kN. This value is only 8% lower thanthe mean value observed in the tests. In the same way, for the spec-imen with a loop bending diameter of 160 mm, the ultimate loadpredicted by the analytical model was 73.6 kN. This value is only4% lower than the mean value observed in the tests. In all cases, val-ues of s = 20 mm, b = 110 mm, ‘e = 100 mm, ‘0 = 90 mm, At = 157 -mm2, fc = 61.94 MPa, and fy = 595 MPa mm were considered. Theangle h was taken as Arctan(s/‘0), that is, 12.5�, the angle a was51.2� for D = 160 mm and 45.6� for D = 100 mm, and the angle uwas assumed to be 37�.

For specimens without transverse reinforcement or with steelfibres, other analytical models must be developed. In an attemptto provide suitable models for these cases, the analytical modeldeveloped by Hsu et al. was adopted [16]. These authors proposeda theory of shear transfer for uncracked concrete based on the trussmodel and incorporated a softened compression stress–strain rela-tion along the concrete struts. The model was based on the equilib-rium, compatibility, and stress–strain equations for a reinforcedconcrete element. For the application of the model to a shear trans-fer in the critical zone of a push-off specimen, these authorsdefined a coefficient K to describe the ratio of maximum transversestress to maximum shear stress on the shear plane. For the loopconnection presented in this paper, it was assumed that the regionbetween two U-bars, which were spaced by s, was subject to thedirect shear stress. Then, an inclined strut formed between theoverlapped loops, which, in conjunction with the tension providedby the U-bars, constituted a truss-like action (Fig. 11). This regionwas assumed to be similar to that observed in push-off specimens.The failure is due to the crushing of concrete in the compressionstruts. With this model it is possible to analyse the loop connectionwith and without transverse reinforcement.

This model was originally developed for plain concrete. Then,the constitutive law of the concrete in compression was modifiedto consider the presence of steel fibres. There are several stress–strain relations available in the literature for Steel Fibre ReinforcedConcrete (SFRC), but in this paper the model proposed by OliveiraJúnior et al. [17], which used a similar SFRC to that used in thispaper, was chosen. The general stress–strain relation in compres-sion is showed by Eq. (5), in which rc is the compressive stress,fc is the compressive strength, ec is the compressive strain, ec0 isthe peak strain, and b is a factor that considers the influence ofsteel fibres on the model. The parameters b and ec0 can be obtainedin function of the fibre volumetric fraction and the compressivestrength of concrete by Eqs. (6) and (7).

rc

fc¼

b ecec0

� �b� 1þ ec

ec0

� �b ð5Þ

b ¼ 0:0536� 0:5754Vf

� �fc ð6Þ

ec0 ¼ 0:00048þ 0:01886Vf

� �lnfc ð7Þ

The iterative procedure used to solve the nonlinear simultaneousalgebraic equations of this model, adapted from the original paper[16], is as follows:

1. Select a value for the compression strain in the direction ofthe strut (e2);

2. Assume a value of the principal tension stress (r1);3. Solve for the principal tension strain (e1) from the stress–

strain curve of the concrete. In this case, it was assumedthat the stress–strain curve was the original one fromHsu et al. [16] and the tensile stress was taken as fct = 0.9-fct,sp. Then:

e1 <fct

Ece1 ¼

r1

Ecð8Þ

e1 �fct

Ece1 ¼ 0:005

fct

r1� 1

� �2

þ fct

Ec

" #ð9Þ

4. Find the coefficient for the softening effect (k), that is,

k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:7� e1

e2

rð10Þ

Fig. 10. Failure mechanism in loop connection: (a) yield lines, (b) relative displacements in yield lines, and (c) cross-section of concrete core.

Fig. 11. Schematic representation of proposed strut and tie model for the connection with overlapping of reinforcement loops: (a) lateral view; (b) plan view.

148 D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151

5. Find the compressive stress in the concrete strut (r2) fromEq. (5). In this case, the coefficient for the softening effect(k) was introduced in the stress–strain relation in compres-sion, that is,

r2 ¼1k

fcbecec0

� �b� 1þ ec

ec0

� �b ð11Þ

6. Solve for angle b between the strut and the horizontal axis(Fig. 10), that is,

ex �fy

Escos2 b ¼ rx � r1 � qtfy

r2 � r1ð12Þ

ex <fy

Escos2 b ¼ rx � r1 � qtEse1

r2 � r1 þ qtEsðe2 � e1Þð13Þ

In these expressions, rx is the stress normal to the loop con-nection, which was take as zero because there is no stressnormal to the connection; Es is the modulus of elasticity ofreinforcement, which was taken as 210,000 MPa; and qt = At/Ac is the ratio of transverse reinforcement. In this case, thecross-sectional area of the concrete core was calculated with-out the U-bar diameter; that is,

Ac ¼p4

D2 þ 2 b� ‘e þ ‘0 � /� D2

� �D� bD ð14Þ

D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151 149

In these expressions, ex is the strain normal to the loopconnection, which is calculated by the strain compatibility;that is,

Table 5Compar

Spec

D100D160D100D160D100D160D100D160D100D160D100D160

C = conMean v

ex ¼ e2 cos2 bþ e1 sin2 b ð15Þ

7. Solve for the principal tension stress (r1); that is,

ey �fy

Esr1 ¼

r2 K sin b cos b� sin2 b� �

� q‘fy

K sin b cos bþ cos2 bð16Þ

ey<fy

Es

r1¼r2 K sinbcosb�sin2 b� �

�q‘Es e2 sin2 bþe1 cos2 b� �

K sinbcosbþcos2 bð17Þ

In these expressions, ey is the strain parallel to the loop con-nection; q‘ is the ratio of loop connection, defined as q‘ = A‘/(150 � 360 mm2), where A‘ is the total area of the U-bars. Ifthe shear stress is distributed uniformly over the rectangu-lar area ‘0t, then it is possible to assume that K = ‘0/s [16].

8. If the calculated r1 is close enough to the assumed r1 value,a set of solutions r1, r2, e1, b, and k is obtained for theselected e1 value. Otherwise, a new r1 value is calculatedand Steps 2–7 are repeated.

9. The shear stress on the shear plane can be calculated fromthe equilibrium; that is:

sxy ¼ r2 � r1ð Þ sin b cos b: ð18Þ

The load on the loop connection can be obtained by multiplyingthe shear stress from Eq. (18) by the cross-sectional area of theconcrete core without the U-bar diameter from Eq. (14).

This iterative procedure was applied to all tested specimens andthe principal results are shown in Table 5. The ultimate load of theloop connection (Fu,model) was obtained by increasing the compres-sion strain in the direction of the strut (e2) until the load on theconnection started to decrease. It was found from this table thatthe mean value of Fu,test/Fu,model was 0.97 with a standard deviationof 0.14. In 24 cases, the predicted failure mode agreed with themode observed in the tests. In the concrete core failure mode,the deformation of the U-bar (ey) was less than the yield strain ofthe steel. Thus it can be concluded that this model is able to cap-ture the experimental tendencies in a satisfactory manner.

It is important to note from this table that the principal tensionstress (r1) in all specimens was less than the tensile strength ofconcrete. This shows that the failure of the loop connection wascontrolled by the compression on the strut. In fact, the ultimate

ison of experimental results and theoretical results from modified model of Hsu e

imen r1 (MPa) r2 (MPa) ex�10�3 ey�10�3 Fu

-VF0-SAT 3.43 71.65 0.015 1.9 7-VF0-SAT 3.43 71.65 0.015 1.9 8-VF0-CAT 3.32 71.26 0.014 1.9 7-VF0-CAT 3.32 71.26 0.014 1.9 8-VF1-SAT 3.99 82.07 0.013 2.76 8-VF1-SAT 3.99 82.07 0.013 2.76 10-VF1-CAT 4.29 87.17 0.009 2.76 9-VF1-CAT 4.29 87.17 0.009 2.76 10-VF2-SAT 4.26 87.27 0.020 3.05 9-VF2-SAT 4.26 87.27 0.020 3.05 11-VF2-CAT 4.17 82.05 0.023 3.05 8-VF2-CAT 4.17 82.05 0.023 3.05 10

crete core failure; Y = yielding of steel of U-bars; r1, r2, ex, and ey are values at ualue = 0.97; standard deviation = 0.14.

load increased when the compressive strength of concreteincreased. Moreover, the compressive stress in the concrete strut(r2) is larger than the compressive strength of concrete becausethe coefficient for the softening effect was less than the unity inall tests (i.e., k = 0.87). Thus, this coefficient can represent the con-finement of the concrete core due to two bent bars.

The angle b between the strut and the horizontal axis at ulti-mate load is constant in all tests and is equal to 77.7�. This valueis in accordance with the geometry of the loop connection, thatis, b = arctan(‘0/s). Moreover, the strain normal to the loop connec-tion (ex) is small not only at the ultimate load but also along thewhole loading history. It suggested that the strength of the connec-tion was not affected by the transverse reinforcement. In fact, thestrain on the transverse reinforcement measured in tests was, ingeneral, smaller than 0.5 � 10�3 until the yield load of the loopconnection was reached (Fig. 6). This strain increases in tests onlywhen the concrete cracks, but this model is not capable of repre-senting the behaviour of cracked concrete. Thus, it is possible toconclude from this model that the ultimate load increases onlywith the increase in the compressive strength of concrete andnot with the transverse reinforcement. Moreover, since the com-pressive strength of concrete has great variability, it justifies thelarge standard deviation when the experimental results are com-pared with this model.

Another important aspect of this modified model was that theultimate load was greatly affected by the cross-sectional area ofthe concrete core and this area was affected by the position ofthe U-bars in the connection. Then, in specimens with a loopbending diameter of 160 mm, the model tended to underestimatethe ultimate load. Finally, it is important to mention that when thefailure occurred in the reinforcement in the tested specimens, thesteel’s failure strength (fu) was used in the model instead ofthe yield strength (fy).

6. Design model for loop connection with steel fibres

The analytical model proposed by Hsu et al. [16] and modifiedin this paper is not easy to use in design. Therefore, a strut andtie model was developed from the tests for estimating the tensilestrength of the loop connection with U-bars and steel fibres. Aninclined strut between the overlapping loops, conforming to theFIB manual [8] and the analytical models, can be identified fromthe tests. The reinforcement loop performs the role of the tie(Fig. 11).

Considering the equilibrium of the forces in the connection, theapplied tensile force (Fu) is directly resisted by the tie, that is,

t al. [16].

,model (kN) Failure mode Fu,test/Fu,model Fu,test/Fu,model

Observed Predicted Specimen 1 Specimen 2

6.1 C C 0.74 0.939.5 C C 0.75 0.805.7 C C 0.99 0.959.0 C C 0.92 0.817.9 Y/C C 1.07 0.913.3 C C 0.82 0.763.2 Y Y 1.16 1.089.6 Y Y 0.95 0.963.6 Y Y 1.14 1.100.0 Y Y 0.97 0.978.2 Y Y 1.17 1.203.7 Y/C Y 1.01 0.86

ltimate load.

150 D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151

Fu = Fs, where Fu is the tensile force resisted by the connection andFs is the tensile force in the tie.

From the forces’ equilibrium in node A, in the vertical direction,the compressive force in the strut can be obtained from Eq. (19).

Fs ¼ Fc cos h ð19Þ

The angles between the compressed struts and the tie can beobtained from the proper geometry of the model (Eq. (20)).

cos h ¼ ‘0ffiffiffiffiffiffiffiffiffiffiffiffiffiffis2 þ ‘2

0

q ð20Þ

where s is the spacing between the superposed loops and ‘0 is theoverlap length between the loops.

The compression force in node A can be estimated by means ofthe area and the compressive strength of the strut in this region(Eq. (21)).

Fc ¼ Acnfcn ð21Þ

where Acn is the transverse section of the strut in node A and fcn isthe effective compressive strength of the nodal region in function ofthe forces in the struts and the tie.

The transverse section of the strut in node A can be calculatedby means of Eq. (22).

Acn ¼ Dþ 2/ð Þwt ð22Þ

where D is the bend diameter, / is the diameter of the U-bars,and wt is the effective width of the inclined strut in node A(Fig. 11).

The compressive strength for a concrete within nodes can beestimated by means of Item 6.5.4 of Eurocode 2 [18]. In this case,the maximum compressive stress in compression-tension nodeswith anchored ties provided in one direction can be estimated byEq. (23).

fcn ¼ 0:85 1� fc

250

� �fc ð23Þ

where fc is the concrete’s compressive strength measured oncylindrical test specimens.

Substituting Eqs. (20)–(23) in Eq. (19) and considering thatFu = Fs, the expression for the design of the loop connection’stensile strength is given by Eq. (24).

Fu ¼ Dþ 2/ð Þwt0:85 1� fc

250

� �fc

‘0ffiffiffiffiffiffiffiffiffiffiffiffiffiffis2 þ ‘2

0

q ð24Þ

Fig. 12. Parametric analysis of the modifie

In this expression, the effective width of the strut (wt) is anunknown. It was determined from the parametric analysis of themodified analytical model of Hsu et al. [16]. By varying the benddiameter of the U-bars (D) and the spacing between the superposedloops (s), the width of the strut was calculated. It can be seen fromFig. 12 that there is a strong relation between the value of wt andthe values of D and s. Moreover, the coefficient for the softeningeffect (k) is also correlated with the spacing between the super-posed loops (s). From this analysis, Eqs. (25) and (26) are proposed.

wt ¼0:6894� 0:0022Dð Þs

k; with all dimensions in millimetres:

ð25Þ

k ¼ 0:014sþ 0:553 � 0:86; with s in millimetres: ð26Þ

This design model was applied to test specimens with concretecore failure to validate the model. The results are shown in Table 6.With the objective of comparing them with the experimentalresults, the factor (1 � fc/250) in Eq. (24) is not considered becausethe compressive strength was not varied in the tests. It can benoted that the relationship between the ultimate load observedin the experimental tests and the ultimate design load showedan average value equal to 1.03 with a standard deviation of 0.10.Thus, this design model can be used as an initial estimate of theconcrete core failure of the loop connection. When the ultimatedesign load is greater than the yield load of the U-bars, the failurewill occur in the reinforcement and not in the concrete.

An important aspect of the equilibrium of node A in Fig. 11 isthat there is a force normal to the plane of the loop connection.This force is normally resisted by the transverse reinforcement,but it was resisted by the concrete in the loop connection withouttransverse reinforcement. This force causes a tension stress normalto the plane of the loop connection, which was evaluated from theprincipal tension stress in the modified analytical model. In alltests, this tension was less than the tensile strength of concretebecause a small spacing was used between the two U-bars in theloop connection. However, it increases with increases in the ulti-mate load of the loop connection. Thus, the steel fibres have animportant role in this connection of increasing the tensile strengthof the concrete and preventing its splitting failure. In another way,they permit an increase in the ultimate load of concrete core failurewith an increase in the compressive strength of the strut when ahigh strength concrete is used.

d analytical model of Hsu et al. [16].

Table 6Comparison of experimental and design model for loop connection with concrete corefailure.

Specimen Fu,design (kN) wt (mm) Fu,test/Fu,design Fu,test/Fu,design

Specimen 1 Specimen 2

D100-VF0-SAT 67.72 10.92 0.83 1.05D160-VF0-SAT 73.01 7.85 0.92 0.99D100-VF0-CAT 67.33 10.92 1.11 1.07D160-VF0-CAT 72.59 7.85 1.13 0.99D100-VF1-SAT 76.98 10.92 1.22 1.04D160-VF1-SAT 83.00 7.85 1.02 0.94

Mean value = 1.03; standard deviation = 0.10.

D.L. Araújo et al. / Engineering Structures 72 (2014) 140–151 151

7. Conclusions

In this paper, a loop connection with steel fibres resisting a ten-sile force was studied. The width of the joint adopted in this work(110 mm) was approximately half of that recommended by the FIB[9] for loop connections without fibres. The influence of steel fibreson in situ concrete, the bending diameter of the loop, and thepresence of transverse reinforcement of the loop were evaluated.The main conclusions obtained were as follows:

– The reduction of the loop’s bending diameter from 160 to100 mm did not lead to a change in the connection’s strength,indicating the possibility of using a loop with a smaller diame-ter than the one recommended by the FIB [9].

– For the connections without fibres or with 1% fibres but withouttransverse reinforcement, concrete core failure was observed,showing that the joint’s width of 110 mm was insufficient forthe tension load transmission by the connection.

– In the connections without steel fibres, the presence of thetransverse reinforcement has little influence on the ultimateload of the connection. The major influence was the improve-ment of the connection’s post-peak behaviour, which restrictedthe opening of the crack and allowed a gradual load capacityloss.

– The addition of 2% steel fibres resulted in an increase in the ulti-mate load of the connection. In this case, the U-bars reached theyield stress of the steel, as the connection’s failure happenedthrough failure of the reinforcement. This shows that in thiscase the joint’s width was sufficient for the load transmissionby the connection.

– The modified analytical model is able to capture the experimen-tal tendencies in a satisfactory manner and shows that failure ofthis type of connection is controlled by the compressivestrength of the strut formed between two U-bars. The tensilestress normal to the connection was less than the tensilestrength of concrete due to the small spacing between the U-bars, which was twice the bar diameter in this case. So, the ulti-mate load of the connection increased with the increase in thecompressive strength of concrete. Moreover, steel fibres havean important role in this connection of increasing the tensilestrength of the concrete and prevent its splitting failure. So,they can be used for the replacement of transverse reinforce-ment to resist the tensile strength perpendicular to the loopreinforcement.

– The strut and tie model was proposed to evaluate the concretecore failure of the connection, and was validated using theexperimental results. It was in agreement with the test resultsand can be applied for a first evaluation of the connection’sstrength. The failure will happen in the U-bars when the loadof concrete core failure is greater than the yield load of thereinforcement. It should be emphasised that the design modelproposed is valid for connections with geometries similar tothose studied in this work. More studies should be carried outto extrapolate the design model to other loop connectiongeometries.

Acknowledgements

The authors wish to thank the company Furnas CentraisElétricas for the financing of this research within its Researchand Development Programme supported by ANEEL. They also wishto thank the company MC-Bauchemie Brazil for the donation of thematerials used in the research and CAPES, the Coordination for theImprovement of Higher Education Personnel, for grantingthe scholarship.

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