strengthening of flat slabs with post-tensioning using anchorages by bonding

7/28/2019 Strengthening of flat slabs with post-tensioning using anchorages by bonding

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Engineering Structures 33 (2011) 20252043

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Engineering Structures

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Strengthening of flat slabs with post-tensioning using anchorages by bonding

Duarte M.V. Faria , Vlter J.G. Lcio, A. Pinho RamosDepartment of Civil Engineering, Faculdade de Cincias e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

a r t i c l e i n f o

Article history:Received 23 September 2010Received in revised form25 February 2011Accepted 28 February 2011Available online 29 March 2011

Keywords:Post-tensioningStrengtheningFlat slabsPunching

a b s t r a c t

This work aims to study a new flat slab strengthening technique based on post-tensioning with

anchorages by bonding using an epoxy adhesive. The main advantages of this technique over thetraditional prestress strengthening systems that use mechanical anchorages are that it does not needexternal permanent anchorages, meaning that the forces are introduced into the concrete graduallyinstead of being localized, thereby preserving aesthetics and useable space. The seven tested slab modelsshow that this technique meets its objective as it is able to reduce reinforcement strains at service loadsby up to 80% if the strengthening technique is applied in two directions and slab deformations by up to70%, consequently makingcrack widths smaller. It can alsoincrease punching load capacity by as much as51% when compared to non-strengthened slabs. The results are compared with the EC2 (2004) [20], ACI318-08 (2008) [23] and MC2010 (2010) [ 21] provisions. The main conclusions are that this strengtheningtechnique is effective regarding ultimate and serviceability states and that it represents an advance in RCslab strengthening techniques.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

The most common strengthening techniques used in slabsare related to increasing punching and/or flexural capacity anddeformation control. The most widely used are the introductionof additional longitudinal reinforcement, with or without asection increase [1], strengthening by means of epoxy-bondedsteel plates [24 ] or fibre reinforced polymers (FRP) [ 57 ],strengthening by replacing concrete with a higher grade concreteor fibre reinforced concretes [ 8,9], strengthening using concretecollars [ 10] or steel collars [8,10] and strengthening by introducingnew shear reinforcements [ 8,1014 ]. These techniques are knownas passive since the strengthening systemis only mobilized whennew deformations appear.

Active techniques reduce the existing deformations, crackingand stresses caused by bending and punching. Little researchhas been carried out on these techniques where steel strandsare used, although they have already been used in practicalapplications [ 15,16]. More recently the use of prestressed FRPhas become more popular as studies are being developed.The traditional active technique using prestressing steel strandsand external permanent anchorages allows strengthening toflexure and punching simultaneously; deformation and cracking

Corresponding author. Tel.: +351 962821685; fax: +351 212 948 398.E-mail addresses: [email protected] (D.M.V. Faria), [email protected]

(V.J.G. Lcio),[email protected] (A.P. Ramos).

behaviour also improves. However, it also has some disadvantagesthat must be taken into account when deciding which techniqueto use. The technique described here sets out to eliminate some of the disadvantages of the traditional prestressing techniques.

This paper describes the experimental research conductedon a new reinforced concrete slab strengthening technique andpresents the results obtained. This strengthening system consistsof introducing post-tensioning using anchorages formed bybonding a prestressing steel strand to the concrete, using an epoxyadhesive agent for the purpose. Compared with the traditionalstrengthening using external prestressing, this technique does notneed external permanent anchorages; it does not compromiseaesthetics and useable space and, whereas in the traditionaltechnique the anchorage forces are localized, in this system theanchorage forces are introduced gradually through bonding. Thisrepresents newknowledge anddevelopments in thefieldof RCslabstrengthening.

2. The system

2.1. Construction stages

The strengthening system proposed here consists of intro-ducing post-tensioning using anchorages formed by bonding aprestressing steel strand and the concrete. The strengthening pro-cedure is based on the following stages ( Fig. 1): drilling the slab(Fig. 1(a)) and setting up the strands (Fig. 1(b)), prestressing the

0141-0296/$ see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2011.02.039
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2026 D.M.V. Faria et al. / Engineering Structures 33 (2011) 20252043

Nomenclature

Suffices

i Individual0 At the stage before transfer of prestress

initial and ini Initial, after transferfinal and fin Final, at maximum load in test y and z Directions of reinforcement

Notation

cp Average normal concrete stresses Reinforcement ratio of bar reinforcement

P Prestress load variation Bond stress max Average value for maximum bond stress trans Average value for allowable transmission bond

stressd Average effective depth f ccm Concrete compression strength on 150

150

150 mm 3 cubes f ck characteristic concrete compression strength on150 300 mm

2 cylinders f cm concrete compression strength measured on 150 300 mm 2 cylinders f t Ultimate strength of reinforcement f y Yield strength of reinforcementh Slab depthP Prestress/strand loadu Length of the perimeter control ( u = c + 4 d inEC2,u = c + 4d in ACI 318-08, u = c + d inMC2010)c Column side dimensionV Load applied to the slab

V dev Vertical component of prestress forces crossing thecontrol perimeterV eff Effective punching loadV exp Experimental punching loadV Rm Mean value of punching resistanceE s Modulus of elasticity of steelF trans B Transmitted force at BF tB Force at the top in BF bB Force at the base in B

steel with temporary anchorages (Fig. 1(c)), injecting with a bond-ing agent ( Fig. 1(d)), releasing the provisional anchorages andtransferring the prestress forces to the concrete (Fig. 1(e)).

Although the system represented in Fig. 1 is unidirectional, itcan be bidirectional and have several strands on each column side,as long as certain restrictions (mentioned below) are respectedregarding the prestress forces for effective punching calculation,which are limited by geometrical considerations (Section 6.2). If theproblem is in the roof slab then steel strands maybe positionedabove the column. Deviators are only supported near the centre,above/close to the column and act as cantilevers.

2.2. Equipment

Specific equipment is needed to apply the prestress. Most of this equipment is not required once the bonding agent has beencured and it can be reused in other prestressing operations. This

equipment consists of a strut capable of sustaining the horizontalcomponent of the prestress force, two actuators at the ends of the

strut and a deviator, positioned at the top of the slab. Only thedeviator stays in the structure and thus must be embedded in theslab finishing.

Steel struts, steel mechanical actuators and steel deviatorswere developed and built as described below. The steel strut wasdesigned to be used in different lengths and to adjust to severalprestress profiles. The strut is divided into two sections, one of which may be inserted into the other; it is adjusted by meansof a thread and two screws used as a set. Fig. 2 illustrates theequipment.

As Fig. 2 shows, there are two parts in each end of the strutthat connect to the mechanical actuators, described below. Theseparts give the strands the desired slope and are connected to thestrut with bolts, for easier assembly The actuators are also shownin Fig. 2. These mechanical actuators are activated using a wrenchand three bolts.This mechanical systemallows theprestress forcesto be maintained without loss while the epoxy adhesive is cured.The deviators give the appropriate curvature to the strand and arepositioned above the slab, as shown in Fig. 2.

2.3. General considerations

As mentioned before this system allows strengthening to flex-ure and punching simultaneously and promotes an improvementregarding deformation and cracking behaviour. Normally theseproblems exist in slabs with relatively high slenderness and/orlackof reinforcement, or slabs with poor quality concrete due to con-struction and/or design errors. Relating to its installation we maysay that two men took in average 2.5 h to drill the holes, assemblethe system including the prestressing of the strands and injectingthe bonding agent. As the steel struts are divided in two parts it isnot difficult to lift them up, making its installation easy.

3. Background considerations

The bond between the steel strands and the concrete isimportant to this strengthening technique. An experimentalprogramme of pull-out and push-in tests was developed tostudy it. These two types of test are designed to simulate thebond behaviour that may be found in the present strengtheningtechnique. Pull-out tests simulate the behaviour of a strand whenits tension is increased by loading on the slab; push-in testssimulate the behaviour of the strand when the prestress forcethat is applied before injecting the hole with the bonding agent(the bonding agent used was HILTIs HIT-RE 500) is transferredto the concrete by bonding. This experimental programme andits results have already been presented [1719 ], and so, in thismanuscript only a synopsis of the tests and its results is presentedfor better understating of the following developments.

Pull-out tests consist in pulling out the strands sealed with

the bonding agent in a concrete block (Fig. 3). Five tests wereperformed for each embedment length, which were 100, 150and 200 mm long. The experimental results from some pull-outtests are presented in Fig. 4. These figures show the relationshipbetween the pull-out force and slip.

The push-in tests consisted in drilling a hole through a concreteblock from one side to another and then inserting a high strengthsteel strand. Afterwards the strand was tensioned, with the helpof a mechanical actuator, that allows the load to be maintainedwhile the adhesive is injected and cured. After curing of thebonding agent the strands were de-stressed in the base end, andthe load difference between both sides was borne by bond (Fig. 5).Afterwards the strand was pulled-out from the top side. Forces ineach end were measured with load cells and slip was measured

with the help of four displacement transducers diametricallyopposed (two in each end of the strand). In each test, forces and


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D.M.V. Faria et al. / Engineering Structures 33 (2011) 20252043 2027

a b

c d

e

Fig. 1. System description.

Fig. 2. Equipment used to apply the prestress, (left) adjustable strut, (top right) assembled mechanical actuator and (bottom right) deviators.

displacements were measured continuously, making it possible todetermine the forces and slips in each side (base and top), at anytime. In the Fig. 6 the load evolution at both ends is shown. Afterthe strand insertion in the hole, it was stressed until it reachedthe desired load (in this case about 170 kN), represented by point A. At this point the load at the top and in the base are equal.The epoxy adhesive was then injected and cured. At this stagethe tension in the strand was reduced at the base end and bondstresses developed along the embedment length. As the base forcedecreases, it reaches a point (point B) where the top force alsostarts to drop. Point B stands for the maximum transmitted force(F trans B = F tB F bB) that a determined embedment length is ableto transmit by bonding without losses at the top end. This is theforce to keep in mind regarding the maximum force that maybe installed in the strands used in the strengthening technique

described before, varying with the effective embedment lengthavailable in the slab.

From these tests it was possible to obtain for severalbonded lengths, maximum pull-out and transmittable loads. Theseexperimental results were compared with theoretical resultsregarding maximum pull-out and transmittable loads and alsodraw-in results. Theoretical results were obtained by solving thegoverning equation of the bond phenomenon adopting a non-linear local bond/slip law derived from pull-out tests with a shortembedment length. Based on the results it is concluded thatit is reasonable to assume an average constant bond stress inboth cases, making it more user-friendly, since maximum pull-out loads and transmittable loads increase approximately linearlywith the increase of the embedment length hef . Therefore, thedetermined average values for pull-out and push-in bond stressesused to determine maximum pull-out and transmittable loads areof 12.0 MPa and 5.2 MPa, respectively. These tests make it possible

to quantify the maximum allowable initial force to install in thestrand, taking into account the drilled length available and the


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Fig. 3. Pull-out test.

1050 15 20 25 30

PO-H1-100 PO-H3-100 PO-H4-100

75.0

62.5

50.0

L o a

d ( k N )

25.0

12.5

0.0

37.5

Slip (mm)

Fig. 4. Pull-out test results.

maximum force that can be supported by the strand anchorage.These forces are obtained by the product of the respective averagebond stress, trans or max , with the bonded area considering the

strand diameter. In [ 19] were also provided design values for transand max .

Long-term tests were also performed. These tests were verysimilar to push-in tests and consisted in measuring the loss forcein bonded strands for 16 months. Tests showed that the average

losses were of 13% and that most of the losses take place in thefirst two months [ 19].


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Fig. 5. Push-in test.

A

B

B a s e

F o r c e

( k N )

Top Force (kN)

0.00.0

25.0

25.0

50.0

50.0

75.0

75.0

100.0

100.0

125.0

125.0

150.0

150.0

175.0

175.0

200.0

200.0

Fig. 6. Push-in test results.


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TOP VIEW

Fig. 7. Test geometry.

4. Experimental work

4.1. Models and tests

The experimental work consisted of testing seven slabs tofailure by punching. These slabs measured 2300 2300 mm

2;slabs DF1DF3 were 100 mm thick, and slabs DF4DF7 were120 mm thick. Slabs DF1 and DF4 were reference slabs forcomparison purposes, while all others were strengthened. SlabDF7 was strengthened bidirectionally while the others were only

strengthened unidirectionally. The punching load was applied bya hydraulic jack positioned under the slab, via a central 200 200 mm 2 steel plate. Eight points on the top of the slab wereconnected to the strong floor of the laboratory using strands andspreader beams. Fig. 7 shows a plan and elevation of the testarrangement, including the strands drawn for slab DF7, the onlyspecimen with strands in both directions. Fig. 8 is a photo of thesame slab.

The models simulated the area near a column of an interiorslab panel up to the zero moment lines. The bottom reinforcementof the slab consisted of 6 mm rebars every 200 mm, in bothorthogonal directions. In slabs DF1DF3 the top reinforcementconsisted of 10 mm rebars every 60 mm and in slabs DF4DF710 mm rebars every 75 mm were used, in both orthogonal

directions. The slab thickness ( h), average effective depths ( d) andtop flexural reinforcement ratios ( ) are presented in Table 1 . In

Fig. 8. Slab DF7 top view.

the strengthened slabs, except DF7, the prestress direction wasthe direction of the rebars at smaller effective depth. Tests wereintended to simulate slabs with relatively high slenderness, sincethese are the kind of slabs prone to be strengthened with thistechnique and in laboratory it was chosen to use models that were

able to reproduce such slenderness. This study was not directed tostudy size effect since EC2 [ 20] and MC2010 [ 21] present different


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Fig. 9. Detailed prestress profile, for slabs DF2 and DF3.

Table 1Geometric and material properties.

Model DF1 DF2 DF3 DF4 DF5 DF6 DF7

ha (mm) 100 100 100 120 120 120 120db (mm) 69 67 67 88 85 84 89 c (%) 1.91 1.97 1.97 1.20 1.24 1.26 1.19 f ccm (MPa) 31.0 33.0 31.5 24.7 26.0 26.3 27.0 f cm (MPa) 24.8 26.4 25.2 19.8 20.8 21.0 21.6

6 f y (MPa) 537 656 f t (MPa) 541 637

10 f y (MPa) 561 678 f t (MPa) 537 648a Model depth.b Average effective depth of bar reinforcement.c Average reinforcement ratio.

approaches to study punching behaviour, where size effectis takeninto account, and it may be used in the present study.

Concerning reinforcement ratios, our study indented to exam-inesome slabs with a high reinforcement ratio,sinceslabs with rel-atively high slenderness are commonly constructed with a higherreinforcement ratio, thus simulating more accurately a real case.

The strands were positioned 50 mm from the column sides anda radiusof 2500 mmwas adopted forthe deviator,and thereforeforthe strands. The slope of the strands in the embedded portion wasabout 1 / 5 (11 .3) , as shown in Fig. 9. In the experimental tests thedeviators were just seated on the slabs and were not covered by ascreed. Nevertheless, in an real strengthening situation, deviatorsmust be covered, but this screed (slab finishing) main purpose isto provide protection to deviators and strands and not to providebond.

After the holes were drilled, surveys of the real hole lengthsand positioning were carried out to determine the real slopesand lengths available for bonding. These values are important tocompute the effective vertical prestress forces and the effectivebonded length. It is important to mention that the holes weredrilled from the top of the models, as would be done in practice.Analysing these measurements it was found that the averagelength of the damaged concrete on the bottom of the slab due todrilling (bottom end in Fig.9)isabout103mmwhileonthetopendit is about 170 mm, meaning that there is a considerable reductionin relation to the complete hole length of about 500 mm. Damageon the top face of the slab was greater because the vibrationinduced when the drilling begins is higher than when drillingreaches the bottom of the slab. Regarding damage caused bydrilling,both damages (atthe topand at thebottom) areimportant,since in none of them the strand is completely involved/confinedand surrounded by the bonding agent.

The holes were 18 mm in diameter and were made using anelectro-pneumatic rotary impact drill with carbide tipped bits.

These holes were afterwards cleaned by blowing air throughand brushing. The strands were cleaned of rust, grease and dust,

inserted into the holes and tensioned using the temporary strutsand mechanical actuators. This tensioning was done gradually andfrom both ends, in order to avoid different forces in both strandends. After this, the epoxy adhesive was injected into the concretehole from bottom to top, avoiding the formation of air bubbles.The injection process followed the procedure described in [18,19],

for the push-in tests. It used an injection system that mixes anepoxy resin with a hardener in a mixingnozzle. After themixing anexothermic reaction takes place to form a polymer matrix, whichbecomes the bonding agent.

The reference slabs DF1 and DF4 were tested by applying avertical load in the centre of the slab. In the strengthened slabs,before the prestress operation and while the bonding agent wascuring, the vertical load was kept constant at about 40% of thepunching failure load of the respective reference slabs. Only afterthe release of the provisional equipment (Fig. 1) was the verticalload increased up to slab failure. All the failures were by punching.

4.2. Monitoring

Four load cells were used ( Fig. 7) to measure the verticalload applied to the models, one on each spreader beam. Up tonine displacement transducers were used to measure the verticaldisplacement of the top surface of the slabs during the tests. Inmodel DF1 only the displacement transducers 15 were used andthedisplacement transducers 8 and9 were only used in modelDF7.Strain gauges were glued to the top reinforcement of the models(Fig. 10) and were placed perpendicular to the strengtheningdirection in strengthened slabs, except in DF7, to correspond tothe rebarsat greater effective depth. The strains in each monitoredrebar were measured using a pair of diametrically opposed straingauges in order to eliminate deviations in the measurements,i.e. those due to flexure of the rebars. The strains were computedfrom the average of the values obtained in each pair of straingauges.

The forces in each prestressing strand were measured witha load cell during the prestressing operation while using thetemporary strut ( Fig. 7) and with a pair of strain gauges foreach strand during the loading of the slab. During the prestressoperation it was possible to correlate the force measured in theload cells with the strains measured in the strain gauges. After therelease of the provisional anchorages and transfer of the prestressforces to the concrete (Fig. 1(e)), the forces in the strands werecomputed using the relation obtained in the first stage. Fig. 10shows the positioning of the strain gauges andof the displacementtransducers.

4.3. Materials properties

Compression tests on cubes of 150 150 150 mm3

( f ccm )were carried out on the same day as the test of the corresponding


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STRAIN GAUGES

Fig. 10. Displacement transducers (top left), reinforcing bars strain gauges (top right), and strands strain gauges (bottom).

slab. The results are listed in Table 1 , together with cylinder

compression strengths ( f cm ) calculated as 0 .80 f ccm . The yield andultimate strengths of the reinforcement are also included.The strands used were 15.2 mm diameter with a 139 .5 mm 2

cross section, having273 kNof maximum force and246 kNof proof force at 0.1%, and a modulus of elasticity of 197.4 GPa.

The epoxy adhesive was also tested for its flexural andcompressive resistance. Briefly the results from flexural andcompressive testing showed that the average elastic tensilestrength was 49.1 MPaand the average yield compressive strengthwas 108.8 MPa.

5. Discussion of the results

Punching is characterized by brittle behaviour at failure witha sudden drop in resistance just after the peak load and it wasregistered in all slabs. Fig. 11 shows photos of several models afterpunching failure.

5.1. Load/evolution of strand forces

As explained in Section 4.2 a load cell was placed at one end of each strand. A pair of strain gauges was also glued to each strand(Fig. 10) and so it was possible to compute the load in each strandduring tests. The force/strain measurement relation was approxi-mately linear within the test range, making it easy to correlate thestrain measurement with the strand load during the tests.

While the vertical load was kept constant at about 40% of

the punching failure load of the respective reference slabs, theprestress was applied to the slab. Initial prestress forces were

determined based on previous research results relating to push-

in tests and on the effective bonded length (Section 4.1), applyingthe uniform bond model with the average bond stresses referredto earlier trans (Section 3). From the observation of Table 2 it maybe seen that maximum initial bond stress ( i,0) was only slightlyhigher that the average value of 5.2 MPa (Section 3) in some cases.

Fig. 12 presents the relationship between the strains and thestrand forces during prestressing (on the left) and those betweenthestrandforces andthe applied loads in thetests to failure (on theright). The later graphs start from the situation when the strandswere locked off against the temporary frames, i.e. that at the endof the graphs on the left. At this point, there is an instant loss of force in the strands which is associated with the elastic shorteningof the slab, since at transfer of prestress by bonding to the slab,the horizontal component of prestress force induces compressionstresses in theslab, causing slab shortening. This elastic shorteningimplies also a reduction of the prestress forces. Compressionstresses were computed based on the scheme presented in Fig. 13.Compression stresses are computed based on an average widthobtainedwiththewidth between assumed points of prestressforceapplication in the middle of the bonded length ( lprestress appl . ) andin a width crossing the column axe ( lslab axe ) considering a forcedegradation at 45 . Applying this methodology an average instantprestressloss of 13kN is computed,that is very close to theaverageregistered loss of 12 kN, although with some scatter. After thisoperation, the slab is loaded until failure and the evolution of strand forces is approximately linear.

Table 2 presents the results for strand loads and the corre-sponding installed bond stresses in each stage. It also shows pre-stress forces losses and gains, respectively, for the transmission

andloading stages. Theload increase until failure in each strandav-erages 28.8 kN, corresponding to a strand stress increase of about


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Fig. 11. Models appearance after punching failure.

Table 2Strand loads and bond stresses for different test stages.

Model Strands P i,0 a (kN) i,0 b (MPa) P i, initia lc (kN) i, initia ld (MPa) P i, initia l e (kN) P i, final f (kN) i, fina lg (MPa) P f , finalh (kN)

DF2 S1* 64.8 4.86 48.0 3.60 16.8 84.3 6.32 36.3

S2 62.1 4.48 40.5 2.93 21.6 76.7 5.54 36.3

DF3 S1 55.0 5.66 50.5 5.20 4.5 78.1 8.04 27.6S2 63.0 5.63 52.0 4.65 11.0 78.6 7.03 26.6

DF5 S1 73.6 4.86 58.3 4.58 15.3 76.1 5.97 17.8S2 75.8 4.48 59.4 4.05 16.4 97.6 6.66 38.2

DF6 S1 64.2 5.66 53.9 4.76 10.3 79.0 6.98 25.1S2 74.9 5.63 74.3 4.11 0.6 96.7 5.34 22.4

DF7

S1 66.9 4.86 55.3 4.53 11.6 67.2 5.72 11.8S2 65.2 4.48 51.5 4.33 13.7 62.7 5.46 11.2S3 75.7 5.66 46.4 3.67 29.3 33.3 2.40 13.1S4 77.2 5.63 33.0 2.53 44.2 33.0 2.30 0.0

a Initial prestress load in each strand.b Bond stress corresponding to P i, 0 .c Prestress load after transmission in each strand.d Bond stress corresponding to P i, initial .e Instant prestress load loss in each strand =P i,0 P i, initial .f Prestress load at punching failures in each strand.g Bond stress corresponding to P i, final .h Prestress load increase until punching failure in each strand

=P

i, final P

i, initial.

* S stands for strand.


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Fig. 12. Force/strain relationships for strands during prestressing (left) and slab load/strand force relationships during tests (right).

205MPa,not takinginto account thestrands from model DF7, sincethere was a problem during thebonding agent injection, that com-promised the intended bond behavior (Fig. 12). Also, bond stresses( i, final ) in this stage (punching failure) are far from the maximumvalue obtained in pull-out tests of 12.0 MPa (Section 3).

5.2. Load/displacement results

This section presents the results obtained from the analysisof vertical displacements of the slabs. The displacements are

presented as averages of pairs of values measured by symmetricaldisplacement transducers, in relation to the centre of the slabs(transducer D3 Fig. 10).

Fig. 14 shows displacements for slabs DF1 andDF4 measured atthe several displacement transducers. In the graphs, for example,D1 and D5 represent the average of the values registered bydisplacement transducers 1 and 5, relative to D3. For slab DF1between a load of about 5 kN to about 50 kN the development

of flexural crack occurs and beyond this load cracking stabilizes.For model DF4 these loads are about 20 kN70 kN, respectively.


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Fig. 12. (continued )

Fig.13. Scheme of load degradation and widths for compressive stress calculation.

These results are mainly to be compared with the results obtainedin the corresponding strengthened models. Fig. 15 shows theevolution of the displacements of strengthened slab models DF2,

DF3, and DF5DF7. A considerable decrease in displacements maybe observed at loads of about 80 kN when the prestress wasapplied. This decrease is more visible in the prestress direction,corresponding to the alignment of D1 with D5, than in theorthogonal direction, except in DF7 where the prestress in bothdirections affected both directions displacements.

As an example, in DF2 themaximum displacement fell by about35% after the prestress was transmitted to the slab. After thestrengthening there was a slight increase in slab stiffness causedby the prestress application. It is also important to note that whenthe prestress is applied with the help of the temporary steel strutthe force application point is close to the struts ends, while whenthe prestress is transferred to the slab and the temporary strut isremoved, the application point of that force moves to the interior

of the slab. Some of the initial decrease of displacements is lost, asmay be observed in Fig. 15.

Fig. 14. Displacement evolution with load for models DF1 and DF4.

Displacement reduction and consequent crack width reductionis considerable for all models, meaning that this system is effec-tive regarding serviceability limit states. Table 3 presents the max-

imum displacements measured for different load steps ( V ), in allmodels. Table 4 presents the prestress forces and corresponding


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Fig. 15. Displacement evolution with load for models DF2, DF3, DF5DF7.

Table 3Maximum displacements (mm).

Model V = 150 kN V = 180 kN V = 210 kN V = 240 kN V = 270 kN V = 290 kN V = 315 kN(1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2)DF1 9.5 12.1 DF2 4.6 4.7 6.4 6.3 8.1 8.0 10.0 9.7 12.3 11.9 DF3 4.1 5.1 5.5 6.6 7.6 8.4 9.7 10.5 DF4 6.3 5.2 8.4 7.2 DF5 2.8 3.7 4.2 5.2 5.7 6.8 7.4 8.6 9.4 10.7 11.1 12.6 DF6 2.1 3.3 3.4 4.9 5.2 6.7 6.9 8.4 8.9 10.5 10.5 12.2 DF7 1.7 1.9 2.4 2.5 3.6 4.0 5.2 5.6 6.9 7.4 8.1 8.6 10.1 10.7

(1) Direction parallel to strands.(2) Direction perpendicular to strands.

deviation forces after the transmissionstage (initial) andat punch-ing failure (final). V dev , ini is computed based on the initial prestressload (P initial = P i, initial from Table 2 ) and on the measurements of thereal slope of thedrilled holes (Section 4.1). Since themodels de-formed during the tests, leading to larger vertical deviation of the

strands and to an increase in their load (at punching failure desig-nated as P final = P i, final from Table 2 ), thedeviation forcesare alsoexpected to increase. As the displacements of the slab and the evo-lution of forces in the strands were controlled during the tests, itwaspossibleto compute thefinalvertical deviationforces ( V dev , fin).


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Table 4Initial prestress load and corresponding deviation forces.

Model P initia la (kN) P finalb (kN) Variation (%) V dev , ini c (kN) V dev , fin d (kN) Variation (%)

DF2 88.40 160.98 82.1 30.60 61.30 100DF3 102.50 156.70 48.9 37.90 63.10 66.5DF5 117.70 173.70 47.6 49.90 79.60 59.5DF6 128.20 175.74 37.1 57.40 84.40 47.0DF7 186.16 196.13 5.4 74.50 84.90 14.0

a Initial prestress load.b Final prestress load.c Initial deviation forces.d Final deviation forces.

Fig. 16. Strain evolution with load for models DF1 and DF4.

Comparing model DF1 with models DF2 and DF3, the averagedecrease in displacements is about 50%, for load steps of 150 and180 kN. Comparing models DF5 and DF6 with model DF4, thatreduction is about 55% in the prestress direction and 30% in theother direction. Formodel DF7these reductions average about 70%

and 65%, respectively, compared with model DF4.

5.3. Load/strain results

This section presents the results obtained from the analysis of strains in the longitudinal reinforcing bars of the slabs. The strainspresented below are the averages from the pairs of gauges shownin Fig. 10. The yield strain of the main bars was approximately2.7 .

Fig. 16 shows that in the reference slabs only the steel barpositioned closest to the column starts to yield at a load of about155 kN in model DF1.

All strengthened models registered a decrease of strains duringthe prestress operation ( Fig. 17). This decrease would have been

bigger if the strain gauges had been positioned in the samedirection as the prestress direction. In model DF7 the prestress

effects were more visible, since there was also prestress in thedirection of the instrumented rebars. In this model a considerabledecrease in rebar strains can be seen, leading to smaller strainvalues at punching failure than in the other models. This decreasereaches about 80% when compared with slab DF4 for load steps of 150 and 180 kN.

6. Punching loads

6.1. Punching load capacity

All the slabs failed by punching and their ultimate loads ( V exp ),including self-weight, are given in Table 5 .

An analysis showing the effect of prestress on the punchingcapacity is presented in this section. To make allowance for thevariations of slab depths, ratios of bar reinforcement and concretestrength, the experimental ultimate loads were divided by resis-tances calculated by EC2s [20] expression for the characteristicstrength of ordinary rc slabs, but with the characteristic concretestrengths replaced by theactualmean strengths ( Table 1 ) andwiththe limit on the depth factor k ignoredsee Eq. (1). The resultingratios of strength were divided by the ratios for slabs DF1 (for the100 mmslabs) and DF4 (for the 120 mmslabs) to isolate the effectsof the strengthening. The results obtained are shown in Fig. 18.

It is clear that the strengthening was effective with averageincreases of punching load being 40% for slabs DF2 and DF3 ascompared with DF1 and 51% for DF5DF7 when compared to DF4.

6.2. Comparison of experimental results and code provisions

The resistance without punching shear reinforcement, us-ing EC2 [20] was calculated with the following expression(Eqs. (1)(4) ) :

V Rm = 0.18 k (100 f cm )1/ 3

+ k1 cp u d (1) = y z 0.02 (2)

cp = cpy + cpz

2(3)

d =d y + d z

2. (4)

The limitation of the parameter k = 1 + 200 / d in EC2 [20]to a maximum of 2 was neglected and k1 = 0.1. In the quantifi-cation of punching resistance the mean values for the compressiveresistance of concrete were used and the partial safety coefficientwas neglected. Reinforcement ratio values are calculated takinginto account a slab width equal to the column width plus 3 d foreach side.

Deviationforces arecomputedbasedon theworkofRamos[ 22],whoproposedthat their calculation shouldbe basedon theverticalcomponents of prestress forces in the strands running within

distances of 0 .5d p from the column sides ( d p is the prestressstrand effective depth). In Fig. 19 is presented pictures of saw cuts


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Fig. 17. Strain evolution with load for models DF2, DF3, DF5DF7.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

Fig. 18. Relative punching strengths for slabs DF13 and slabs DF47.

of slabs in both orthogonal directions. It is possible to observe

that the punching failure angle is higher in a cut perpendicularto the strengthening direction. Actually, the punching failure

surface approximatelyintersectsthe baseof thedeviators. Allotherstrengthened slabs exhibited a similar behaviour.

For the calculation of the resistance without punching shear re-

inforcement and without any prestress effect, using ACI 318-08[23], the relevant expression for square columns, with side lengthsless than 4 d is Eq. (5):

V Rm =4 f cm u d

12. (5)

In prestressed slabs the following expression is used (Eq. (6)):

V Rm = 0.29 f cm +0.3 cp u d +V dev . (6)According to ACI 318-08 [23], Eq. (6) is applicable when f ck 35 MPa (corresponding to an approximate value of f cm 43 MPa),with bidirectional prestress and when the average compressive

stress in concrete in each direction due to prestress is between 0.9

and 3.5 MPa. Though this expression is not strictly applicable tomost of the models presented here, it was nevertheless used to


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Table 5Comparison between effective experimental loads and code provisions taking into account the initial deviation forces.

Model P initia l a (kN) V dev , inib (kN) V exp c (kN) Code V ef f d (kN) V Rme (kN) V eff / V Rm

DF1 0.00 0.00 190.72 EC2* 190.72 202.58 0.94

ACI 318* 190.72 137.79 1.38

DF2 88.40 30.60 272.94 EC2* 242.34 204.82 1.18

ACI 318* 272.94 156.01 1.75

DF3 102.50 37.90 254.64EC2* 216.74 202.22 1.07ACI 318* 254.64 161.55 1.58

DF4 0.00 0.00 199.00 EC2* 199.00 217.41 0.92

ACI 318* 199.00 167.49 1.18

DF5 117.70 49.90 295.00 EC2* 245.10 219.15 1.12

ACI 318* 295.00 202.50 1.46

DF6 128.20 57.40 292.72 EC2* 235.32 217.97 1.08

ACI 318* 292.72 209.31 1.40

DF7 186.16 74.50 319.52 EC2* 245.02 235.02 1.04

ACI 318* 319.52 245.18 1.30a Initial prestress load.b Initial deviation forces.c Experimental punching load.d V eff effective punching load: EC2 V eff = V exp V dev , ini ; ACI 318-08 V eff = V exp .e Predicted failure load.* Taking into account the assumption described in Section 6.

estimate the ACI 318-08 [ 23] predicted punching load. Deviationforces are computed based on the vertical component of prestressforces crossing the control perimeter defined in ACI 318-08 [ 23].

In both codes cp was computed based on Fig. 13, consideringthe width at the face of the column along the perpendiculardirection of the strands and on the slab depth.

Table 5 gives a comparison between experimental loads andthe predicted values obtained using EC2 [ 20] and ACI 318-08 [23],taking into account the initial deviation forces.

For the reference slabs DF1 and DF4, EC2 [ 20] leads toexpected mean punching resistances very close to those obtainedexperimentally, with an average ratio V eff / V Rm of 0.93, slightlyagainst safety. ACI 318-08 [23] provides more conservative results,

since the experimental punching loads reached between 18% and38% above the average prediction, with an average V eff / V Rm of 1.28.With regard to the strengthened models EC2 [20] gives an averageV eff / V Rm of 1.10 and ACI 318-08 [ 23] the ratio is 1.50. So, bothEC2[20]andACI318-08[ 23] is somewhatconservativewhen usingthe initial deviation forces.

Table 6 presents a comparison between experimental loadsand the predicted values obtained using EC2 [20] and ACI 318-08[23], taking into account the final deviation forces (Section 5.2and Table 4 ). Using this methodology, mean punching resistancesare closer to the experimental value, leading to a reduction of conservatism in both EC2 [ 20] and ACI 318-08 [23]. With respectto the strengthened models, the mean V eff / V Rm for EC2 [20] isreduced to 0.96 (with a COV of 0.04) and for ACI 318-08 [ 23] itbecomes about 1.29 (with a COV of 0.07). Regarding EC2 resultsit is important to remind that it was ignored the limitation of theparameter k = 1 + 200 / d to a maximum of 2 and so all theresults are on the safe side.

Recently,it waspublished thefirstdraft of MC2010[ 21]. Punch-ing design recommendations in MC2010 [ 21] present a new de-sign philosophy based on the critical shear crack theory describedin [24,25], for slabs without andwith transverse reinforcement, re-spectively. In MC2010 [ 21] the design expressions are presented,while in [24] are presented the expressions for the average valuesEq. (7) that can be compared with the experimental results.

V Rmu d f cm =

3/ 4

1 +15 dd g 0+d g

(7)

where is theslab rotation, d g is themaximum aggregatesize andd g 0 is a reference size equal to 16 mm. The rotation of the slab may

be obtained by Eq. (8).

= 1.5 r sd

f yE s

msdmrd

1.5

. (8)

If the slab is prestressed may be obtained using Eq. (9):

= 1.5 r sd

f yE s

msd mPdmRd mPd

1.5

(9)

where msd is the average moment per unit length for calculationof the flexural reinforcement in the support strip and can beapproximated for inner columns without moment transfer asV / 8 (V is the punching load); mRd is the design average flexuralstrength per unit length in the support strip; mPd is the averagedecompression moment in the support strip due to prestressingand r s indicates the position where the radial bending moment iszero with respect to the column axis.

Combining Eq. (7) that describes the failure criterion withEq. (8) or Eq. (9) that describes the loaddeflection behaviour andsetting V Rm equal to V , it is possible to obtain iteratively thepunching strength. In Table 7 is presented the results for V Rmfor each tested slab. MC2010 [21] states that deviation forcesfrom strands applied inside the basic control perimeter could bededucted to the column reaction.

In Table 7 is presented values for V Rm according to Eq. (7),using Eq. (8) (without considering the prestress effect in the slabrotation) and using Eq. (9) with the initial and final prestress

forces (from Table 4 ), since MC2010 [21] mentions that punchingload should be computed based on the maximum slab rotation of both orthogonal directions and since most slabs are strengthenedin one direction. This comparison was also performed in slabDF7. Experimental values of slab rotation were obtained usingmaximum displacements of the slab ( Figs. 14 and 15) assumingthat this rotation concentrates near the column faces. Fromthe observation of Table 7 is possible to verify that the betterapproximation of the computed V Rm with the experimentaleffective punching load is obtained when using Eq. (9) with finalprestress forces and deviation angle, as had happened with othercodes. Table 7 shows that using Eq. (9) when computing V Rm of prestressed slabs gives better results than using Eq. (8), althoughmost slabs are only strengthened in one direction.

In Table 8 is presented a comparison between values for d(corresponding to the V Rm values presented in Table 7 ) computed


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Fig. 19. Slabs saw cut in both directions.

using Eq. (8) (without considering the prestress effect in the slabrotation)and applying Eq. (9) using initial andfinalprestress forceswith experimental values. From the obtained results it is possibleto find that values calculated for d using Eq. (9) are closer to theregistered ones for the strengthened models.

The introduction of deviation forces originated by the strandsrelieve the effective punching load near the column, as these actin opposite direction of the gravity loads. Additionally, there isan introduction of compression stresses that causes a decreasein crack opening, proportional to d presented in Table 8 . Byits observation is possible to see that those measured valuesare smaller in the prestressed direction, and that in slab DF7crack opening is almost the same in both directions. Nevertheless,comparing for example slab DF1 with slabs DF2 and DF3, it is seenthat although these last slabs are only prestressed in one direction,crack opening in the other direction also decreases (assuming thatslab rotation of slab DF1 is similar in both directions) meaning that

prestress has also an influence in the non-prestressed direction.Regarding DF4 it would be expectable that crack opening was

higher when compared to slabs DF5DF7, and this may be dueto experimental results scatter also noticed by Muttoni [ 24].Observing results presented in Table 3 and Figs. 14 and 15, itwas registered a decrease in displacement of strengthened slabsin relation to their reference slabs for the same load levels.Concerning steel strains and observing Figs. 16 and 17 it is possibleto see a decrease in steel strains in all strengthened slabs with aconsiderable decrease in slab DF7.

In Fig. 20 is presented the relation between normalizedpunching load V eff ud f cm

and crack opening d. It is clear that thereis a tendency of a decrease in normalized punching load with crackopening. In this figure is also clear that DF4 results are slightly outof the range of the remaining ones.

In all codes comparison, strands were not considered in thecalculation of flexural reinforcement ratio since these are notbonded in the punching area. The bonded portion of the strands

is positioned far from the punching failure surface and with aslope. As deviators are only supported near the centre and act as


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Table 6Comparison between effective experimental loads and code provisions taking into account the final deviation forces and strands final forces.

Model P final ,pun a (kN) V dev , fin b (kN) V exp c (kN) Code V ef f d (kN) V Rme (kN) V eff / V Rm

DF1 0.00 0.00 190.72 EC2* 190.72 202.58 0.94

ACI 318* 190.72 137.79 1.38

DF2 160.98 61.30 272.94 EC2* 211.64 207.43 1.02

ACI 318* 272.94 191.80 1.42

DF3 156.70 63.10 254.64EC2* 191.54 204.02 0.94ACI 318* 254.64 190.27 1.34

DF4 0.00 0.00 199.00 EC2* 199.00 217.41 0.92

ACI 318* 199.00 167.49 1.18

DF5 173.70 79.60 295.00 EC2* 215.40 221.58 0.97

ACI 318* 295.00 236.63 1.25

DF6 175.74 84.40 292.72 EC2* 208.32 219.99 0.95

ACI 318* 292.72 240.01 1.22

DF7 196.13 84.90 319.52 EC2* 234.62 235.49 1.00

ACI 318* 319.52 256.41 1.25a Final prestress load.b Final deviation forces.c Experimental punching load.d V eff effective punching load: EC2 V eff = V exp V dev , fin ; ACI 318-08 V eff = V exp .e Predicted failure load.* Taking into account the assumption described in Section 6.

Table 7Comparison between effective experimental loads and MC2010 code provisions taking into account the initial and final strand deviation and compression forces.

Model V eff (kN) usingV dev , ini

V eff (kN) usingV dev , fin

V Rm (kN) usingEq. (8)

V eff / V Rm V Rm (kN) using Eq. (9),with initial prestress

V eff / V Rm V Rm (kN) using Eq. (9),with final prestress

V eff / V Rm

DF1 190.72 190.72 156.41 1.22 1.22 156.41 1.22 156.41 1.22DF2 242.34 211.64 154.77 1.57 1.37 160.94 1.51 168.20 1.26DF3 216.74 191.54 151.85 1.43 1.26 159.76 1.36 165.83 1.16DF4 199.00 199.00 180.57 1.10 1.10 180.57 1.10 180.57 1.10DF5 245.10 215.40 176.45 1.39 1.22 186.45 1.31 193.70 1.11DF6 235.32 208.32 174.68 1.35 1.19 186.40 1.26 193.22 1.08DF7 245.02 234.62 189.34 1.29 1.24 204.96 1.20 207.61 1.13

Average 1.40 a 1.26 a Average 1.28 b Average 1.15 c

COV 0.07a 0.05 a COV 0.10b COV 0.16c

a Values are for strengthened slabs only; for slabs DF1 and DF4 the average relation is 1.16 with a COV of 0.07.b

Values for all slabs; if only strengthened slabs are considered the average relation obtained is of 1.33 with a COV of 0.09.c Values for all slabs; if only strengthened slabs are considered the average relation obtained is of 1.15 with a COV of 0.06.

Table 8Comparison between the experimental and computed product d of the slab computed based on MC2010 expressions for .

Model Experimental d (mm) d usingEq. (8)

Exp./Computed d using Eq. (9) withinitial prestress

Exp./Computed d Eq. (9) withfinal prestress

Exp./Computed

Strands 1 and 2direction

Oppositedirection

DF1 1.33 1.44 0.92 1.44 1.44 0.92 DF2 1.17 1.18 1.46 0.80 0.81 1.32 0.88 0.89 1.18 0.99 1.00DF3 1.10 1.15 1.45 0.76 0.79 1.27 0.86 0.90 1.15 0.96 1.00DF4 1.27 1.14 1.60 0.79 0.71 1.60 1.60 0.79 0.71DF5 1.45 1.63 1.62 0.90 1.01 1.42 1.03 1.15 1.28 1.13 1.27DF6 1.33 1.53 1.62 0.82 0.94 1.39 0.96 1.10 1.26 1.05 1.21DF7 1.47 1.44 1.64 0.89 0.88 1.35 1.09 1.07 1.31 1.12 1.10

Average 0.83 a 0.88a Average 0.96 1.02 Average 1.05 b 1.12 bCOV 0.07a 0.10a COV 0.10 0.12 COV 0.07b 0.11 b

a Values are for strengthened slabs only. For slabs DF1 and DF4 the average relation is 0.81 with a COV of 0.11.b Values are for strengthened slabs only. If all slabs are considered the average relation is 1.02 with a COV of 0.15.

cantilevers, only the slope of the strands in the straight portion isused in the calculation of deviation forces.

7. Design guidelines

Regarding the design of a slab strengthened with the systemproposed, and having in account the results of code comparisonpresented in the last section, both EC2 [ 20] and MC2010 [21]may be used. If the initial prestress and deviation forces are used

both codes provide safe estimates of the punching load and thisis the suggested philosophy of design. Nevertheless it is possible

to estimate the strand force increment taking into account theslab rotation. As seen before, MC2010 [ 21] provides an expressionfor the calculation of (Eqs. (8) and (9)) as a function of slabpunching load, and assuming that this is the slab rotation of the slab that takes place between the transmission phase failure(this is close to reality as in most cases prestress will be chosento reverse almost all if not all existing slab deformations), it ispossible to estimate strand force increment and therefore finalcompression and deviation forces from prestress. The increase of

strands length ( l) in the unbonded portion of the strand, foreach side of the column, can be assumed to be proportional to the


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0.45

0.50

0.55

0.60

0.65

1.00 1.20 1.40 1.60 1.80

Fig. 20. Normalized punching loads versus crack opening.

Fig. 21. Predicted and measured load increase versus strand length increment.

slab rotation , taking into account the strands effective depthd

p and the depth of the compression zone in the concrete crosssection ( l ( d p x)). This increase in strands length iscomposed of two portions: one that is the elastic elongation of the strand and the other that is the slip of the bonded portionof strand for a determined strand force. The slip of the bondedportion is dependentof thestrandforce (P > P i, initial ) , on the initialtransmitted force (P i, initial ) , on the bonded length and on the bondbehaviour, andmaybe computed based on the results andanalysispresented by Faria et al. [ 19] and resumed in Section 3 of thismanuscript. The elastic elongation may be computed by the elastictheory and is dependent on the unbonded length of the strand. Acomparison of the experimental results and the computed valuesis presented in Fig. 21 where is presented the theoretical relationbetween strand load and the increase of strands length l forthe several strengthened slabs and also the experimental results

(where for l = 0, P = P i, initial ). It may be observed thatthe theoretical results are always higher that the experimentalresults. This may beascribed to thefact that thetheoreticalanalysisdoes not take into account that the strand effective depth variesalong its development towards the centre of the slab. Using thecomputedvalues presentedin Table 8 usingEq. (9), thatare inferiorto the experimental ones, the theoretical values for force increasewould actually be closer to the experimental ones. By doing soit is possible to estimate maximum prestress force installed inthe strand and thereby compare it to the maximum allowed forcelimited by the maximum bond capacity and yielding of the strand.

8. Conclusions

This paper describes the experimental research conductedon a new reinforced concrete slab strengthening technique and

presents the results obtained. This active strengthening techniqueenables the simultaneous solving of the several deficiencies withrespect to the traditional technique of external prestressing withexternal anchorages. Compared with the traditional strengtheningusing external prestressing, this method does not require externalanchorages thus improving the aesthetics of the repaired slab andmaintaining the clear headroom below it.

An experimental programme was developed to study theefficiency of the proposed strengthening technique when used tostrengthen flat slabs.

This technique reduced theslabsdeflectionsat service loads upto 70% as compared with unstrengthened slabs, and reduced crackwidths significantly.

The experimental research carried out also shows that therewasa decrease in theaverage strains of thereinforcingbars,mainlyin the bidirectional strengthened slab.

The load capacity of the strengthened slabs washigher than thereference slabs. The increments in load capacity varied between36% and 54%.

The calculation of the vertical deviation forces above thecolumns, using the initial deviation forces led to punchingresistances lower than those obtained experimentally. Whenthe final vertical deviation forces were used, conservatism wasdiminished. Both EC2 [20] and MC2010 [21] provided a betteragreement between the predicted and the experimental results,whereas ACI 318-08 [23] was somewhat conservative.

Regarding all said before it maybe stated that the experimentalresults indicate that the system is effective with respect toserviceability and ultimate behaviour.

It was given guidelines for the correct estimation of maximuminstalled force in the strands due to slab rotation.

Acknowledgements

This work received support from the Fundao para a Cinciae Tecnologia-Ministrio da Cincia, Tecnologia e Ensino Superior

through scholarship number SFRH/BD/37538/2007 and ProjectPTDC/ECM/114492/2009. We would like to thank Concremat formakingthe slab modelsand HILTI Portugal whosuppliedthe epoxyadhesive (HILTI HIT-RE 500) and all the equipment related toadhesives and drilling.

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