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Title no. 110-S22

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 110, No. 2, March-April 2013.MS No. S-2011-115.R2 received March 5, 2012, and reviewed under Institute

publication policies. Copyright 2013, American Concrete Institute. All rightreserved, including the making of copies unless permission is obtained from th

copyright proprietors. Pertinent discussion including authors closure, if any, will bepublished in the January-February 2014ACI Structural Journal if the discussion isreceived by September 1, 2013.

Experimental Investigation on Reinorced Ultra-High-

Perormance Fiber-Reinorced Concrete Composite Beams

Subjected to Combined Bending and Shearby Talayeh Noshiravani and Eugen Brhwiler

An experimental study on a series o composite beams combininga 250 mm (9.84 in.) deep reinorced concrete (RC) element anda 50 mm (1.97 in.) thick reinorced ultra-high-perormance ber-reinorced concrete (R-UHPFRC) element is presented. The speci-mens are tested in a cantilever-beam setup with the R-UHPFRCelement acting as an additional tensile reinorcement. The testparameters include the span length and the ratio and type o thesteel reinorcing bars, including stirrups. Most o the beams ail infexure at a orce that is 2.0 to 2.8 times higher than the resistance

o the reerence RC beams. The medium-span cantilevers witha low stirrup content ailure along a fexure-shear crack. Near-interace concrete cracking sotens the bond between the elementsand enhances the member deormation capacity. The R-UHPFRCelement contributes signicantly to the shear resistance.

Keywords: composite beams; debonding; deormation capacity; fexure-shear resistance; ultra-high-perormance ber-reinorced concrete.

INTRODUCTIONThe addition o a thin overlay o ultra-high-perormance

ber-reinorced concrete (UHPFRC) to reinorced concrete(RC) members is an emerging technique or durable design,protection, and strengthening o concrete structures.1

UHPFRC belongs to the amily o ultra-high-strengthcementitious composites. Due to its compact matrix, thematerial is quasi-impermeable. The homogenous distributiono ne and discontinuous steel bers in the matrix providesthe materials notably high tensile resistance and ductility.As illustrated in Fig. 1(a), the UHPFRC behavior in directtension is maniested in three phases o elastic strain hard-ening due to multiple microcracking and strain sotening dueto localization o deormations at an individual macrocrack.The member geometry, presence o reinorcing bars, andUHPFRC casting procedure have a strong infuence on theber orientation and, thus, the tensile behavior.

A thin layer o UHPFRC reinorced with small-diameter

steel reinorcing bars can be used as a protective fexuralreinorcement on RC members (Fig. 1(b)). Cast-in-place orglued reinorced UHPFRC (R-UHPFRC) layers on fexuralRC elements create composite members with an enhancedload-bearing behavior.2,3 From hereater, R-UHPFRCRCcomposite members are reerred to as RU-RC members.For foor slabs and bridge decks, Habel et al.3 recommendan R-UHPFRC-to-RC height ratio between 10 and 20%with an R-UHPFRC thickness between 30 and 100 mm(1.81 and 3.94 in.). This design recommendation ensuresthe optimum interaction between the two elements andtheir contribution to the member resistance. It also allowsor an economic use o UHPFRC.

Closely spaced steel reinorcing bars in the R-UHPFRClayer provide in-plane continuity that ensures the layers

Fig. 1(a) Constitutive law o UHPFRC in tension3; and(b) cross section o RU-RC slab strip cross section.

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Talayeh Noshiravani is an Engineer at Zilch + Mller Ingenieure, Munich, Germany.She received her BASc rom the University o Waterloo, ON, Canada; her MASc

rom the University o Toronto, ON, Canada; and her PhD rom the cole Polytech-nique Fdrale de Lausanne (EPFL), Lausanne, Switzerland. Her research interestsinclude applications o ultra-high-perormance ber-reinorced concrete (UHPFRC)in structural design and strengthening projects, evaluation o load-bearing capacityo existing structures, and experimental investigations on the behavior o structures.

Eugen Brhwiler is a Proessor o structural engineering and the Head o the Labora-tory o Maintenance and Saety o Structures (MCS) at the EPFL. He received his civilengineering and doctoral degrees rom the Swiss Federal Institutes o Technology in

Zurich in 1983 and Lausanne in 1988. His research interests include UHPFRC or therehabilitation o structures, reliability and saety o structures, remaining atigue lie anddynamic behavior o existing bridges, monitoring, and nondestructive testing methods.

composite action with the RC element.3-5 Thus, RU-RCmembers can be designed without any mechanical device orstirrups connecting the two elements. Research on the fex-ural resistance and load-bearing behavior o RU-RC beamsand slab strips has shown the monolithic behavior o the twoelements up to the maximum bending resistance.2,3,5 Thus,

RU-RC members with bonded reinorcement can be designedbased on the plane-sections hypothesis. Oesterlee5 recom-mends using high-strength ribbed or smooth reinorcing barsin RU-RC members to provide a high fexural strength or ahigh rotation capacity, respectively.

An inadequate shear resistance may determine themember response o RC beams or slabs that are strength-ened with additional fexural reinorcement only.6,7 Thereis currently insucient test data on the shear behavior oRU-RC members. A conservative approach is to assume thatonly the RC element in the composite member carries theshear orces. This is particularly problematic when the RCelements shear resistance and rotation capacity limit the

fexural strengthening o RU-RC members without the addi-tion o any shear reinorcement.

To improve the understanding o the response o RU-RCmembers and their shear strength, an experimental programinvolving RU-RC beams was carried out.8 The beamswere subjected to quasi-static loading. The test parametersincluded shear span-depth ratio (a/d), the amount o trans-verse and longitudinal reinorcement, and the strength andbond condition o the R-UHPFRC reinorcing bars. Theresults are compared to the ailure criterion o the CriticalShear Crack Theory (CSCT) or beams.9

RESEARCH SIGNIFICANCEChanges in the service conditions and the state o existing

structures may necessitate strengthening interventions. Flex-ural strengthening o existing slabs and bridge decks mayrequire additional shear reinorcement, thus increasing theintervention costs. RU-RC members oer a cost-eective,durable, and low-impact solution in strengthening proj-ects. RU-RC composite members shall also be used in newstructures. Can an R-UHPFRC layer contribute to memberresistance and prevent the need or shear strengthening?This research aims to provide a better understanding o thefexure-shear behavior o RU-RC beams and the contribu-

tions o R-UHPFRC reinorcement to the member resistance.

EXPERIMENTAL INVESTIGATIONTest specimens and parameters

To predict the resistance o RU-RC members, it is impor-tant to consider the shear resistance mechanisms in theRC element and the infuence o the R-UHPFRC layer onthese mechanisms. Previous research has shown the infu-ence o the a/d, the ratio o the longitudinal reinorcementrl, the bond condition o the reinorcing bars, the transversereinorcement ratio rv, and the stirrup spacing s on the shearstrength o RC beams.6,10 These parameters infuence themechanisms o shear resistance and the fow o stresses

carried by the concrete and steel components (Appendixes Aand B*).6-21 The aorementioned parameters are used in theexperimental program exploring the structural response oRU-RC members.

The experimental program involves 12 RU-RC beams,two UHPFRC-RC composite beams, and three reerence RCbeams. Equations (1) to (3) calculate the eective depth othe composite section d, rv, and the mechanical reinorce-ment ratios wi. In Eq. (1) and (3), i stands or each tensilelongitudinal reinorcementnamely, UHPFRC or tensilesteel reinorcing bars in the RC or R-UHPFRC sections(subscripts U, st, or sU, respectively); di is the distancebetween the neutral axis o each reinorcement and theextreme compressive ber; andi is the reinorcement elasticlimit strength.

(1)

(2)

(3)

*

The Appendixes are available at www.concrete.org in PDF ormat as an addendumto the published paper. They are also available in hard copy rom ACI headquarters ora ee equal to the cost o reproduction plus handling at the time o the request.

Table 1Cantilever beam tests

Beam a, mm s, mm a/drv,%

wst,%

wU,%

wsU,%

AsUsteelgrade*

L0

1000

200 4.2 0.34 8.1 0 0

L1400

4.0 0.17 8.1 3.9 0

L2 3.8 0.17 8.1 3.9 9.2 Inox

L3 200 3.8 0.34 8.1 3.9 9.2 Inox

MN0

800

2003.4 0.34 8.1 0 0

MN1 3.1 0.34 8.1 3.9 6.7 11MSn30

MN2 3.1 0.34 8.1 3.9 9.1 ETG88

MN3 250 3.0 0.15 16.8 3.9 9.2 Inox

MW0

400

3.4 0.17 8.1 0 0

MW1 3.2 0.17 8.1 3.9 0

MW2 3.1 0.17 8.1 3.9 6.7 11MSn30

MW3 3.1 0.17 8.1 3.9 6.9 Inox

MW4 3.1 0.17 8.1 3.9 7.3 B500 B

MW5 3.1 0.17 8.1 3.9 9.1 ETG88

MW6 3.0 0.09 16.8 3.9 9.2 Inox

SN1600

200 2.3 0.34 8.1 3.9 6.7 11MSn30

SW1 400 2.3 0.17 8.1 3.9 6.7 11MSn30*Steel grade o 8 mm (0.3 in.) diameter reinorcing bars in R-UHPFRC.Note: 1 mm = 0.0394 in.

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The test parameters or each beam are listed in Table 1.The beam names distinguish between the beams with a long(L), medium (M), or short (S) cantilever span. The speci-mens with a medium and short span are urther dieren-tiated according to their narrow (N) or wide (W) stirrupspacing. The names o the reerence RC beams end with0. The composite beams are numbered according to theincreasing reinorcement content. With the exception oBeams MN3 and MW6, all other specimens were undamagedend segments cut rom longer beams that were previouslytested in our-point bending by Oesterlee5 and Noshiravani.8

The specimen cross sections and reinorcement detailingare shown in Fig. 2(a). All composite specimens havea 250 mm (9.84 in.) deep RC element covered with a 50 mm(1.97 in.) thick layer o UHPFRC. The reerence RC beamshave a depth o 265 mm (10.43 in.). The widths o all beamsare 150 mm (5.90 in.). The RC elements in all o the beams,except Beams MN3 and MW6, have the same reinorcementdetailing. Beams MN3 and MW6 have a higher ratio olongitudinal reinorcement but a lower rv than the rest o thebeams. The R-UHPFRC layers have three or our reinorcingbars with a diameter o 8 mm (0.32 in.). The longitudinalreinorcing bars are anchored beyond the supports withwelded cross reinorcing bars.

Material propertiesCommercial ready mixed concrete (C30/37) with an

aggregate size o 16 mm (0.63 in.) was used to cast the RCelements. The average values o the concrete properties inTable 2 are based on the standardized tests during the beamtests or concrete ages between 126 and 246 days.

The specimens were cast with a UHPFRC mixturenamed HIFCOM 13 developed at the cole PolytechniqueFdrale de Lausanne.5 The average UHPFRC tensile prop-erties in Table 2 are rom direct tension tests carried outby Oesterlee.5 The mixture design and the results o direct

tensile tests on dogbone specimens are provided in AppendixB. Furthermore, the UHPFRCs average cylinder compres-sive strengthUc is 160 MPa (23.2 ksi) or UHPFRC o ageso 90 and 210 days. The compressive behavior o UHPFRCup to this strength is almost linear. The tested UHPFRCmodulus o ruptureUrwas 51.0 MPa (7.40 ksi) or the sameUHPFRC age.

The steel properties in Table 2 are the average valuesrom the standardized tensile tests on three randomsamples. The tensile response o the tested reinorcing barsis provided in Appendix C. The tested bond strengths othe ribbed and smooth reinorcing bars are 44 and 5 MPa(6.38 and 0.725 ksi) at a slip o 0.80 and 0.01 mm (0.031 and

0.0004 in.), respectively.5

Test setup and procedureThe cantilever-beam test setup is illustrated in Fig. 2(b).

The xed end is provided by an end pin support, attached toan isolated steel rame, and an intermediate roller support,placed on a massive concrete block. The external verticalprestressing between the supports prevents a shear ailureoutside the cantilever span. The tests are displacement-controlled. The displacement is applied with a hydraulicjack attached to a second isolated steel rame.

The ollowing parameters were measured automaticallyduring each test: orces, beam defections, support displace-

ments, and the deormations across the concrete interacezone and along the UHPFRC layer and the steel reinorcing

Fig. 2Specimens and test setup. (Note: 1 mm = 0.0394 in.)

Table 2Mean values o tested material properties5

Concrete

Ec, GPa c,cube, MPa c, MPa ct, MPa

29.9 47.4 41.6 3.80

UHPFRC

Elastic Strain hardening Strain sotening

EU, GPa Ut,el, MPa eUt,u Ut,u, MPa wU, mm Ut,S, MPa

48.8 10.2 0.003 12.53.0 4.0

6.5 0

Steel

Steel grade Es, GPa f, mmsy,MPa esu, %

su,MPa su/sy Surace

210

6 626 3.70 655 1.05 Ribbed

B500 B 8* 516 4.90 589 1.14 Ribbed

11MSn30 8 566 5.20 595 1.05 Smooth

Inox 8 710 2.20 906 1.27 Ribbed

ETG88 8 703 7.70 902 1.28 Smooth

B500 B 10 594 4.30 653 1.10 Ribbed

B500 B 12 571 5.00 640 1.12 Ribbed

B500 B 14 565 9.79 663 1.17 Ribbed*Stirrups and R-UHPFRC reinorcing bars.R-UHPFRC reinorcing bars only.Yield plateau ends at strain o 2%.Notes: 1 GPa = 1000 MPa = 145.0 ksi; 1 mm = 0.0394 in.

bars. Furthermore, beam deormations and crack openingswere measured manually at chosen stages o displacement.

EXPERIMENTAL RESULTS AND DISCUSSIONObserved member response and ailure modes

Figures 3 and 4 illustrate the orce-defection responsesand the ully developed crack patterns o the beams at the

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end o the test. The variable D is the measured beam defec-tion at the jack with respect to the strong foor. The beamsare divided into two groups according to their ailure alonga fexural or a fexure-shear collapse crack that is used todene the ailure mode. The plots show the beam responseeither up to the rst rupture o the tensile reinorcing bars orup to the maximum jack displacement. The ne dotted linesinterrupting the continuity o the plots indicate the suddendrops o resistance, during which no measurements couldbe taken. The fexural ailure o Beam SW1 ollows the ulldevelopment o a web-shear crack in the RC element. As

illustrated in Fig. 4(a), the rotation o the RU-RC beams atfexure-shear ailure is comparable to that o their reerenceRC beam.

The crack patterns in the gures were only traced on oneside o the beam. Nevertheless, the patterns were very similaron the two vertical aces o the beams. The crack outline ontop o the UHPFRC across the width o the member onlyvaried slightly due to the heterogeneity o the material.

Figure 4(c) shows the crack pattern and manual crackwidth measurements at the last displacement stage beorethe ultimate resistance o the beams. In this gure, the jackorce is given with respect to the ultimate orce Vu. The webdeormation in the composite beams with a fexure-shear

ailure localize at one or two diagonal cracks (Fig. 4(c)). Thebeams rotate about the crack tip close to the roller support.

Between approximately 80% and 90% o the respectiveultimate resistance o each beam, the crack widths o thefexure-shear collapse cracks in the RU-RC beams are largerthan their reerence RC specimen. In Beams MW3 to MW6,the fexure-shear collapse crack crosses only one stirrupclose to the crack tip at the support, whereas it crosses twostirrups in Beam MN3.

Table 3 summarizes the important results o each test at

the ultimate resistance (that is, peak). It lists the measuredangle o the collapse crack (qc), the maximum defection othe cantilever span at peak (Du), the calculated beam rota-tion (yu = Du/a), the peak orce Vu, and the ultimate moment(Mu = Vua). The table also provides the moment resistance othe beams in the our-point bending tests (MR,4p) perormedby Oesterlee.5 The latter value is corrected or the dier-ence in the moment due to the dead load in each test setup.Table 3 also provides the ratios oMu toMR,4p and toMR,RC.The latter is the bending moment resistance o the reerenceRC beams or the RC elements when there is no RC beam.

TheMu/MR,4p ratios greater than 1.0 can be explained by thelarger variability o the UHPFRC tensile strength along the

1.8 m (5.91 t) long region o constant moment in the our-point bending test setup instead o the support region in the

Fig. 3Beams ailing in fexure: (a) orce-defection responses;

and (b) ully developed crack patterns at end o test. Fig. 4Beams ailing in fexure shear: (a) orce-defectionresponses; (b) ully developed crack patterns at end o test;and (c) crack widths. (Note: 0.4 mm 1/64 in.)

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cantilever beams. The highMu/MR,RCratios in the last columnindicate the eectiveness o the strengthening method.

Table 3 also indicates the ailure mode o each beam: fex-ural (F) and fexure-shear (FS) ailure. All o the RU-RCbeams with long and short cantilever spans had a fexural

ailure. Among the medium-span beams, the beams withrv = 0.34% and those with rv = 0.17% and a wsU< 6.9% alsoailed in fexure.

The rest o the medium-span beams with rv 0.17% ailedin a sudden manner due to the crushing o the concrete ahead othe diagonal fexure-shear collapse crack. Nevertheless, mosto these beams reached their maximum bending resistance.The resistances o the RC beams indicate that the fexure-shear ailure o Beam MW0 occurred ater the yielding othe longitudinal reinorcing bars. Similar to Beam MW0, theultimate resistance o Beams MW3 to MW5 and MN3 coin-cide with the yielding o their R-UHPFRC reinorcing bars.This indicates that the ailure o the composite beams along

the fexure-shear collapse crack is close to its maximumbending resistance.Beam MW6, with the same ratio o longitudinal reinorce-

ment as MN3, ails at a orce that is 67% o the resistanceo MN3. Beam MW6 represents a clear case o a fexure-shear ailure and is used as a reerence or classiying theailure mode o the other beams with an analogous pre-peakresponse. Moreover, it is important to note that the diagonalcollapse cracks in the composite beams appear at an averageorce o 76.1 kN (17.1 kips). This orce is 1.7 times the ulti-mate resistance o the reerence RC beam (MW0).

Increasing the mechanical ratio o the longitudinalreinorcement in the RC element is expected to reduce the

member rotation capacity. Nevertheless, while the ultimateresistance o Beams MW3 to MW5 is 2.1 to 2.3 times higher

than their reerence beam MW0, their rotation at ultimatelimit is between 90 and 100% o the latter.

Increasing the transverse reinorcement content byreducing the stirrup spacing has a positive infuence onboth the ultimate resistance and the rotation capacity othe beams. The stirrups crossing the fexure-shear collapsecrack o Beam MN3 increase the ultimate resistance by1.34 to 1.50 times that o the rest o the beams with a fexure-shear ailure. Its rotation at peak is 1.67 times higher thanBeam MW6, with wider stirrup spacing.

In Fig. 3(a), the maximum bending resistance o thebeams with ribbed or smooth reinorcing bars coincides withthe yield limit o the reinorcing bars. The infuence o thesurace characteristics o the R-UHPFRC reinorcing barsdepends on the properties o UHPFRCnamely, its tensilestrength and strain sotening behavior. Due to the highbond strength, the members with either ribbed or smoothreinorcing bars in the R-UHPFRC element have the sameorce-defection response up to the sotening o UHPFRC.

For beams with ribbed reinorcing bars, the yield o the steelcoincides with the start o the strain sotening, while theyield o the smooth reinorcing bars may occur at the sametime (or example, Beams MN1, MW2, and SW1) or wellater the initiation o the UHPFRC sotening (or example,Beams MN2 and SN1).

Flexure-shear versus fexural ailureThe examples o Beams MW2 and MW4 are used to

illustrate the response o a beam ailing in fexure versusone that ails in fexure-shear. These beams are similarexcept or the surace characteristics and slightly dierentstrengths o their R-UHPFRC reinorcing bars. For each

beam, Fig. 5 shows: 1) the orce-displacement response;2) the deormed shape; 3) the sequential snapshots o the

Table 3Summary o test results up to ultimate resistance

Beam ID* Failure qc, degrees Du, mm Vu, kN yu, rad Mu, kNm MR,4p, kNm Mu/MR,4p Mu/MR,RC

L0 02BRCV Flexural 90 40.5 34.4 0.041 34.4 32.6 1.05 1.00

L1 04BRCU0 Flexural 90 13.8 43.4 0.014 43.4 34.8 1.25 1.25

L2 12B4x70R0 Flexural 73 39.0 96.5 0.039 96.5 82.4 1.17 2.77

L3 12B4x70RV Flexural 65 30.9 92.9 0.031 92.9 82.4 1.13 2.67

MN0 01BRCV Flexural 76 35.1 44.4 0.043 35.5 32.1 1.11 1.00

MN1 09B4x50SV Flexural 90 15.0 96.8 0.019 77.4 63.4 1.22 2.22MN2 14B4x70SV Flexural 90 35.5 92.7 0.044 74.2 72.9 1.02 2.13

MN3 18S4x70RV Flexure-shear 22 21.0 134.7 0.026 107.8 1.00 1.96

MW0 01BRC0 Flexure-shear 28 16.3 43.2 0.020 34.6 32.0 1.08 1.00

MW1 03BRCU0 Flexural 70 10.8 58.9 0.014 47.1 37.0 1.27 1.35

MW2 10B4x50S0 Flexural 50 15.0 104.7 0.019 83.8 63.5 1.32 2.41

MW3 11B3x70R0 Flexure-shear 30 16.3 91.7 0.020 73.4 70.2 1.05 2.11

MW4 07B4x50R0 Flexure-shear 30 14.3 90.7 0.018 72.6 69.2 1.05 2.08

MW5 14B4x70S0 Flexure-shear 35 14.3 99.6 0.018 79.7 72.9 1.09 2.29

MW6 18S4x70R0 Flexure-shear 34 12.6 90.9 0.016 72.7 0.67 1.32

SN1 10B4x50SV Flexural 90 12.4 115.0 0.021 69.0 63.7 1.08 1.98

SW1 09B4x50S0 Flexural 30; 90 13.8; 16.1 124.4; 122.0 0.023; 0.027 74.6; 73.2 63.4 1.16 2.14; 2.10*Beam ID used by Oesterlee.5Ratio with respect to maximum bending resistance that is approximately resistance o MN3.Ratio with respect to maximum bending resistance o RC element that is 55.0 kNm (40.4 kip-t).Notes: 1 mm = 0.0394 in.; 1 kN = 0.224 kips; 1 kNm = 0.735 kip-t.

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crack pattern with maximum measured crack widths; and 4)the corresponding plots o the manual strain measurementstaken along the UHPFRC top and bottom bers at indicatedorce levels.

Beam MW2, with smooth R-UHPFRC reinorcing bars,ailed in fexure and MW4, with ribbed reinorcing bars,ailed in fexure-shear. The bending moment resistance oBeam MW2 is 15% higher than the maximum resistance oBeam MW4. At this resistance, the dierence oDu o thebeams is less than 5%. The orce-defection responses oboth beams up to a orce o approximately 75 kN (16.9 kips)are the same.

At 76 kN (17.1 kips), Beam MW2 had only a ew fexuralcracks in the RC element and a UHPFRC macrocrack that

began to orm approximately 300 mm (11.8 in.) rom theroller support. In contrast, in Beam MW4, a diagonal cracksuddenly appeared, causing the orce to drop by 10%.

The fexure-shear crack in Beam MW4 developed downto the level o the compressive longitudinal reinorcing bars;with it, a series o inclined near-interace debonding cracksappeared. Extending 650 mm (25.6 in.) away rom theroller, these cracks initiated as fexural cracks and rapidlyrotated toward the collapse crack (Fig. 4(c)), reducing thebeam stiness. Meanwhile, the tensile strains along thebottom UHPFRC ber increased. The double curvature othe R-UHPFRC element in Beam MW4 became obvious in

the strain plot showing the increase o the bottom ber strainmeasurements with respect to the top ber strains. Beyond

Fig. 5Beam MW2 versus MW4: (a) orce-defection response; (b) deormed shape; and (c) crack widths and UHPFRCextreme-ber strains. (Note: Crack widths are in units o mm; 1 mm = 0.039 in.; 0.4 mm 1/64 in.; 1 kN = 0.224 kips.)

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this orce, the stiness o MW4 reduced and the dier-ence between the orces resisted by each beam increasedrom 10 to 15%.

Up to 84 kN (18.9 kips), more inclined fexural cracksdeveloped in both beams. The measured crack widthsin Beam MW2 were smaller than in MW4. At this orce,the near-interace concrete in Beam MW2 also began tocrack similarly to Beam MW4. The interace-zone cracksin the latter continued to grow as a series o smeared fatcracks. The strain diagrams show the strain hardening othe R-UHPFRC element along the cracked interace zone.The increased strains and orce in the R-UHPFRC elementsalong the cracked interace zone are indicators o the changeo the fow o stresses in the RC element.

Beyond 84 kN (18.9 kips), the collapse crack ineach beam opened. The angles o the fexural collapsecrack in Beam MW2 and the fexure-shear crack inBeam MW4 were 50 and 30 degrees rom the longitudinalaxis, respectively. Beam MW2 ailed due to the rupture othe smooth reinorcing bars in the R-UHPFRC element. Incontrast, Beam MW4 ailed due to the concrete crushingahead o the tip o the fexure-shear collapse crack that sepa-rated the RC element into two segments, causing the verticaldrop o the segment below the jack (Fig. 5(b)).

Cracking behaviorCollapse cracksThere are three main dierences

between the nal crack pattern o the beams ailing infexure and those ailing in fexure-shear: 1) the angle o thecollapse crack in the RC element (qc); 2) the location andangle o UHPFRC macrocracks; and 3) the intermediate-crack-induced debonding (ICD) zone.

The angles o the fexure collapse cracks in Fig. 3(b)are between 50 and 90 degrees rom the longitudinal axis,whereas the angles o the fexure-shear collapse cracks inFig. 4(b) vary rom 22 to 35 degrees. The latter coincide

with the principal compressive stress eld in concrete alongwhich the diagonal cracks grow.

Both the longitudinal and transverse reinorcement infu-ence the crack widths and spacing in the composite beams.The UHPFRC element without reinorcing bars decreasesthe number o cracks and crack widths in the RC element. Incomposite RU-RC beams, fexural cracks are more smearedthan those in the RC and the UHPFRC-RC beams. The crackpatterns o Beam L2 (wsU 9.2%) versus L1 with wsU= 0%show that beams with a higher longitudinal reinorcementratio in the R-UHPFRC element have more smeared fexuralcracks with smaller openings.

In beams with wide stirrup spacing, the smeared cracking

in the RC elements is interrupted by discrete fexure-shearcracks that compete with fexural cracks to become thecollapse crack (Fig. 4(c)). In the members with s = 400 mm(15.7 in.), fexure-shear ailure occurs at one single diagonalcrack. Stirrups control the opening and development odiagonal cracks in the RC element. The infuence o stir-rups on the cracking behavior is illustrated in the dierencebetween the crack patterns o Beam MN1 versus MW2 orBeam MN3 versus MW6.

The horizontal crack spacing in the beams with largerstirrup spacing is more irregular and generally smallerthan the beams with smaller stirrup spacingor example,Beam L2 versus L3. As the internal orces increase and

secondary fexural cracks appear, the crack spacing in theRC element reduces. The crack spacing reduced in the near-

interace concrete cracks that appeared subsequent to theormation o a long fexure-shear crack. The average o themeasured spacing o these smeared cracks is approximatelyequal to or less than the thickness o the R-UHPFRC layer.

ICDThe stiness o RU-RC composite members

depends on the bond between the two elements. Indeed,in pure fexure, near-interace concrete cracks causingthe debonding between the elements only begin once theUHPFRC strain sotening occurs.3,5 The debonding is attrib-uted to the deormation incompatibility between the twoelements. The eect o this debonding on the behavior oRU-RC members is small enough to be neglected.2,3 Never-theless, the results o the tests presented herein show that,in the presence o bending and high shear stresses, the near-interace concrete cracking prior to the maximum bendingresistance and the UHPFRC strain sotening infuencesthe bond between the RC and its R-UHPFRC overlay, asobserved in Beam MW4 (Fig. 5(c)).

As shown in Fig. 6, the widening o fexure-shear cracksinduces vertical prying stresses at the crack mouth thatprovoke ICD o the two elements. ICD is classied as oneo the ailure modes o RC members with thin external fex-ural reinorcement, such as ber-reinorced polymer (FRP)strips.22 Compared to its FRP or steel counterparts, however,an R-UHPFRC tensile reinorcement layer has a signi-cantly higher bending stiness and an out-o-plane resis-tance that can counteract the prying stresses.

Figure 6 illustrates the ormation o the ICD zone asobserved in the pre-peak response o the specimens presentedherein. ICD is primarily maniested as closely spaced fex-ural cracks that are initially vertical but rapidly change direc-tion toward the long diagonal cracks. The angles o the ICD

cracks in the specimens range between 5 and 15 degrees romthe longitudinal axis. Close to the maximum resistance, theangle o the smeared cracks decreases. The ICD may be seenas a volume o concrete sotening with increasing deorma-tion. The ormation o the ICD zone is due to the geometricalcompatibility between the R-UHPFRC and RC elements.By reducing the shear stresses transerred between the twoelements, ICD decreases the member stiness and allows orthe ormation o dierent stress transer mechanisms.

The ICD zone approximately corresponds to the concretelayer between the R-UHPFRCRC interace and the center-line o the RC tensile reinorcement. On the beam prole,the ICD zone begins at the mouth o diagonal cracks and

extends horizontally with increasing defection. The initia-tion o ICD cracks as fexural cracks suggests that the

Fig. 6Intermediate-crack-induced debonding (ICD).

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applied moment in the composite section at the oreront othe ICD zone is close to the cracking momentMcr. The latteris dened as the moment causing the concrete stress at theinterace ber to exceed the tensile strength o concrete.

Structural response o RU-RC composite beamsGeneral member responseFigure 7 illustrates the

general structural responses o the beams with a fexural orfexure-shear ailure and distinguishes between the variouscracking states in the member. Irrespective o the ailuremode, the general response o the beams can be divided intothe pre- and post-peak regimes. In the pre-peak regime, thecracking behavior and the ICD determine the member rota-tion capacity. The maximum orce and the collapse crackdene the ailure mode.

The ailure o RU-RC members depends on the soteningo the R-UHPFRC element at the mouth o a fexural orfexure-shear crack competing to become the collapse crack.

Above fexural cracks, the UHPFRC is mainly in tension. TheR-UHPFRC element at the mouth o fexure-shear cracks issubjected to combined tensile and bending stresses. Inclinedfexural cracks induce both longitudinal and vertical tensilestresses in the UHPFRC, thus causing the macrocracks inUHPFRC to orm at an angle less than 90 degrees rom thelongitudinal axis. The sotening o the UHPFRC determineswhich crack becomes the collapse crack.

Contribution o R-UHPFRC element to member resis-tanceThe maximum resistance o RU-RC members isdened by the member moment resistance. The contribu-tion o the R-UHPFRC element to the member resistancestrongly depends on the tensile properties o the UHPFRC.

The addition o tensile longitudinal reinorcement in theR-UHPFRC element increases the beams bending resis-

tance. In addition to resisting tensile stresses in the longi-tudinal (in-plane) direction, the UHPFRC layer can alsoresist vertical (out-o-plane) tensile stresses. Inclined fex-ural cracks can activate the tensile resistance o the layerin the vertical direction. The UHPFRC macrocrack along adiagonal crack appears at a distance o d/tanqc away romthe center o rotation. The vertical component o the tensileorce in the UHPFRC away rom the center o rotation canincrease the member capacity. This increase in resistancecan be seen by comparing the orce-defection response oBeam MW2 (qc = 50 degrees) with Beams MN1 and MN2(qc = 90 degrees).

The test results urther show the contribution o theR-UHPFRC element to the member resistance. The responseo Beam SW1 demonstrates that the out-o-plane resistanceo UHPFRC prevents the ailure o the composite memberater the appearance o the diagonal web-shear crack inthe RC element. Instead, ollowing the rupture o the RCelement, the R-UHPFRC layer transers the out-o-planestresses rom the bearing plate under the jack to the intacttrapezoidal segment o the RU-RC beam over the roller.This composite segment unctions as a tapered beam thatultimately ails in fexure at approximately the same orcelevel. Note that low shear resistance o concrete supportingthe UHPFRC layer makes it impossible or the R-UHPFRCbelow the steel bearing plate to ail in shear. Indeed, thethickness o the layer and UHPFRCs resistance to verticaltensile stresses provide it a high enough shear resistance thatthe layer over the RC beam can only ail in bending.

In the case o Beams MW3 to MW6 and MN3, whichailed in combined fexure and shear, the R-UHPFRClayer over the ICD zone bends in double curvature; thus, itcarries a constant shear orce. Member resistance decreaseswith widening o the diagonal cracks. The reduction is dueto the decreased contribution o aggregate interlock alongthe diagonal cracks. Assuming that the contribution o the

RC element is a unction o beam rotation due to the diag-onal crack opening, the additional resistance o the beamscompared to their RC elements is due to the contributiono the R-UHPFRC element to the member shear resistance.

The contribution o the R-UHPFRC layer can be quanti-ed in the case o Beams MW3 to MW5 with respect to theresistance o Beam MW0. At a given rotation, the resistanceo the latter beam indicates the contributions o concrete andsteel in the RC element. The dierence between the resis-tance o each RU-RC beam and their reerence RC beamis the contribution o the R-UHPFRC element in combinedtension and bending.

Pre-peak rotation capacityIt is generally expected that

additional tensile fexural reinorcement will reduce therotation capacity o RC elements, whether ailing in fexureor shear. This is not the case or all the beams in the testprogram described herein.

The ICD in the pre-peak regime increases the rotationcapacity o the composite members. Among the beamsailing in fexure, the infuence o the ICD on the rota-tion capacity can be seen by comparing the behavior othe RU-RC beams with reerence to that o the UHPFRC-RC beams. As shown in Fig. 3(a), the rotations o BeamsMN1 and MW2 at peak are 1.4 and 1.3 times the rotation oMW1, respectively, and the rotations o Beams L2 and L3 atpeak are 2.8 and 2.2 times the rotation o L1, respectively.

In the case o the composite beams with a fexure-shearailure, the rotation o the RU-RC members at ailure is

Fig. 7Typical response o beams.

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between 90 and 100% o yu o their reerence RC beam(MW0). In the latter beams, the ICD increases the memberrotation and at the same time reduces the contribution o theR-UHPFRC element to the shear resistance.

By controlling the opening o the diagonal cracks, thestirrups indirectly control the opening o interace cracksand thus the progress o the ICD. The infuence o the stir-rups depends on the level o the shear orce. For example,in the beams with the maximum shear span, the low stirrup

content allowed opening o the diagonal cracks and the ICD;thereore, Beam L2 has a higher rotation capacity than L3.This is not the case or Beams MW2 and MN1 with a =800 mm (31.5 in.). The low content o well-spaced stirrupsin Beam MN3 allowed the opening o the two fexure-shearcracks and a longer ICD zone, thus increasing the rotationcapacity in comparison with Beam MW6.

Post-peak responseThe post-peak regime o RU-RCmembers is distinguished by the signicantly high residualresistanceRres o the member. The response varies dependingon the resistance o the UHPFRC with respect to its steelreinorcing bars, as well as the slip between the two in thesotening phase o the UHPFRC.

The residual resistance in the post-peak regime is themaximum resistance ater the end o the contribution o theUHPFRC section to the member resistance. While the post-peak resistance is not o interest in a resistance-based designo structural elements, it is advantageous in displacement-based design, where the plastic redistribution capacity ostructural members is needed or the plastic rotation demands.

In members with a fexural ailure, the post-peak responsebegins with the yielding o the steel reinorcing bars atthe end o the strain-hardening phase o UHPFRC. Thisresponse is characterized by the gradual reduction o abeams resistance R down to a yield plateau. This deni-tion does not apply i the yield plateau directly ollows the

ascending branch o the cracked-elastic structural response,such as the response o Beams SN1 or MN2. The behavior othese beams is due to the low strength o the UHPFRC withrespect to its smooth reinorcing bars, the slip between thesmooth reinorcing bars and the UHPFRC, and the yieldingo the reinorcing bars as the UHPFRC sotens.

The beams ailing in combined fexure and shear havea sudden drop in resistance due to the development o thefexure-shear collapse crack into the compression zone overthe roller and crushing o concrete. Up to the peak resistance,the UHPFRC is in strain hardening. In the post-peak regime,Beam MW6 maintains 87% o its resistance, whereas theother beams with less longitudinal reinorcement in their

RC elements lose 40 to 54% o their resistance. While theorce-defection plots o Beams MW6 and MN3 (with ahigher wst) gradually decrease, the plots o Beams MW3 toMW5 remain at an approximately constant resistance. Thehigher amount o reinorcement in the RC element impliesthat a higher portion o the orce is carried by the beamaction corresponding to the reinorcement in the RC element.The reduced strain in the R-UHPFRC element prior to themaximum resistance allows the layer to contribute more tothe post-peak resistance o the member.

As the contribution o the UHPFRC to the post-peak resis-tance diminishes, the dowel and the membrane actions o thereinorcing bars continue to resist the downward movement

o the jack. The resistance o these mechanisms can be deter-mined using the models or RC members.21

COMPARISON WITH EXISTING SHEAR MODELSFOR RC ELEMENTS

The experimental results provided in this paper show thatthe RU-RC members have a higher ultimate resistance at arotation level that is approximately equal to yu o their reer-ence RC beam with a similar crack pattern. Moreover, theRU-RC beams have slightly larger crack widths. Given theproposed height ratio o the RC and R-UHPFRC elementsby Habel et al.,3 it is reasonable to assume that the shearstresses are mainly carried by the stress elds in the RC webThe web shear resistance depends on the degree o deorma-tion, crack width, crack spacing, and size o the member.

The behavior o RU-RC beams with ICD cannot be evalu-ated based on the analysis o the monolithic compositesection. ICD separates the components o the compositetension chord (that is, the RC reinorcing bars and theR-UHPFRC element) and changes the angle o the compres-sive stresses in the web. To account or the nonlinearityintroduced by ICD, the response o RU-RC beams shouldbe analyzed based on an integral approach ocused on themember response. A comprehensive approach is to combinethe equilibrium o stresses in a member with the geometricalcompatibility and the material stress-strain relationships.

To compare the shear resistance o the composite beamsto RC beams with equal bending resistance, the memberresponse is compared to the ailure criterion o the CSCTor beams without shear reinorcement.9 This theory takesan integral approach ocusing directly on the memberresponse.23 The CSCT uses the member rotationyas an inte-gral parameter to relate the shear strength to the opening oa discrete fexure-shear crack along which the web deorma-tions concentrate. Equation (4) is the general CSCT expres-sion or calculating the shear resistance VCSCT o beams,which explicitly accounts or aggregate interlock along thefexure-shear crack where shear ailure happens. Variablesdg0 and dg are the reerence aggregate size o 16 mm (5/8 in.)

and the actual concrete aggregate size.23 The constantsC1 and C2 are actors related to the shear strength at whichthe critical fexure-shear crack appears and the decay oconcrete contribution along the crack as it opens. For theailure criterion o beams developing plastic strains, C1 andC2 are 1/6 and 2 in the equation with SI units (MPa and mm)or 2 and 2 in the equation with U.S. customary units (psi andin.), respectively.9

(4)

Figure 8 shows the shear orce-rotation plots o thecomposite beams with a fexure-shear ailure versus theCSCT ailure criterion calculated or the minimum andmaximum values od. The fexure-shear collapse cracks oall o the composite beams appear at a higher shear orcethan in the reerence RC beam. The ailure criterion orBeam MN3 is the cumulative sum o the CSCT criterionand the orce in the stirrups crossing the diagonal cracks.As shown in Fig. 8(b), the stirrups crossing the crack beginto yield ater the appearance o the second diagonal crack.

The resistance beyond the ailure criteria is due to thecontributions o the R-UHPFRC element. First, the distribu-

tion o stresses in the RU-RC element increases the shearorce required or the development o the fexure-shear

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crack. Second, the ICD reduces the angle o the compressivestresses carried by concrete in the oreront o the fexure-shear crack. Third, the R-UHPFRC element carries part othe shear stresses in bending. In addition to these mecha-nisms, stirrups increase the member resistance and rotationcapacity by carrying part o the stresses across the crack, aswell as by controlling the opening o crack widths in the RCelement and the ICD progress.

CONCLUSIONSThe ollowing conclusions were reached:1. RU-RC members have a signicantly higher stiness

and ultimate resistance than their RC elements alone. Theexperiments show that the additional R-UHPFRC reinorce-ment can increase the ultimate resistance to up to 2.77 timesthat o the RC beam.

2. Both the in-plane and out-o-plane resistance oR-UHPFRC elements contribute to the member shear resis-tance. According to the models or RC beams, the specimens

with the wide stirrup spacing should have ailed in shear ata much lower resistance. The presence o the R-UHPFRCelement allowed most o these specimens to reach theirmaximum bending moment at similar rotations as their reer-ence RC beams. Hence, the addition o a tensile R-UHPFRCreinorcement can be used as an eective shear strength-ening method.

3. The response o RU-RC members is strongly infu-enced by the ormation o the ICD zone that sotens theconnection between the R-UHPFRC and RC elements, thusincreasing the deormation capacity. As the ICD progresses,the plane section theory no longer holds or the compositemember; however, it still remains valid or each individual

element with bonded reinorcement. The ICD zone is morepronounced in members that carry higher shear stresses

that is, members with higher ratios o ribbed longitudinalreinorcement in the R-UHPFRC element.

4. The R-UHPFRC element contributes to the resistanceo RU-RC members by three dierent means. First, thebending resistance o the R-UHPFRC elements allows theelement to carry a part o the shear stresses introduced intothe element by the prying action o RC segments ormedby diagonal fexure-shear cracks. Second, the R-UHPFRCelements restrain the widening o a fexure-shear collapsecrack in the RC element, thus improving the contribution oconcrete to the shear resistance. Third, the ICD zone betweenthe elements changes the stress elds in the member andreduces the intensity o the stresses that need to be carriedacross the fexure-shear collapse cracks.

5. For the RU-RC members with a fexure-shear ailure,the defection is between 80 and 90% o their matching RCspecimen. This is especially important considering that thefexure-shear resistances o these RU-RC beams are 2.0 to2.3 times that o the latter. The measured crack widths indi-cate that concrete carries only a minor part o the shearstresses. The increase in rotation capacity is due to theormation o the ICD zone.

6. Existing models or RC members cannot be used to

determine the shear resistance and deormation capacity oRU-RC members. There is a need or a new analytical modelthat accounts or the contribution o the R-UHPFRC elementto the member shear resistance.

ACKNOWLEDGMENTSThis study was unded by CTI Project 7787.1 EPRP-IW. The UHPFRC

ingredients and the steel reinorcing bars were donated by HOLCIM andSwiss Steel. Their support is greatly appreciated.

NOTATIONSubscript notation ollows standard notationA = areaAsv = stirrup area at stirrup spacing s

a = shear spana/d = shear span-depth ratiob = beam widthC = compression orce; however, in CSCT equation, C1 and C2

designate constantsd = eective depthdg = concrete aggregate sizedg0 = reerence aggregate size o 16 mm (5/8 in.)di = depth o reinorcement i with respect to extreme compressive

concrete berdv = vertical lever armEc = Youngs modulus o elasticity o concreteEs = Youngs modulus o elasticity o steelEU = Youngs modulus o elasticity o UHPFRCEU,H = stiness o UHPFRC in strain-hardening phaseEU,S = stiness o UHPFRC in strain-sotening phaseF = orcec = concrete cylinder compressive strengthc,cube = concrete cube compressive strengthct = concrete tensile strengthi = elastic limit strength o reinorcement i (that is,sy orUt,el)sy = steel yield stresssu = steel tensile strengthUc = UHPFRC average compressive strengthUr = UHPFRC modulus o ruptureUt,el = UHPFRC elastic tensile strengthUt,S = UHPFRC tensile-sotening resistanceUt,u = UHPFRC maximum tensile strengthM = momentMcr = cracking momentMR,RC = moment resistance o reerence RC beams or RC elementsMR,4p = moment resistance rom our-point bending testsR = resistance

Rres = residual resistances = stirrup spacing

Fig. 8Shear-rotation curves o RU-RC beams with fexure-shear ailure versus ailure criterion according to CSCT.(Note: 1 mm = 0.0394 in.)

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T = tension orceV = shear orce or orce acting at end o cantilever spanVCSCT = shear resistance based on CSCTw = crack widthx = position or vector component along x-axis, with axis origin at

roller supportD = beam displacement at jack with respect to strong foore = strainesu = steel strain at ultimate strengthesy = steel strain at yield stresseUt,u = UHPFRC tensile strain at maximum tensile strength

qc = measured angle o collapse crack in concreterl = ratio o longitudinal reinorcementrv = ratio o transverse reinorcement in RC elements = stresswi = mechanical reinorcement ratio o reinorcement iy = beam rotation

Subscriptsc = concretei = steel or UHPFRC reinorcementst = tensile reinorcing bars in RC elementsU = reinorcing bars in R-UHPFRC elementU = UHPFRCu = maximum or ultimate resistance; strength; resistance at peakz = vertical component o crack width

REFERENCES1. Brhwiler, E., and Denari, E., Rehabilitation o Concrete Structures

Using Ultra-High Perormance Fibre Reinorced Concrete, The SecondInternational Symposium on Ultra High Perormance Concrete (UHPC),Kassel, Germany, 2008, 902 pp.

2. Alaee, F. J., and Karihaloo, B. L., Retrotting o Reinorced ConcreteBeams with CARDIFRC,Journal o Composites or Construction, ASCE,V. 7, No. 3, 2003, pp. 174-186.

3. Habel, K.; Denari, E.; and Brhwiler, E., Structural Response oElements Combining Ultra High-Perormance Fiber-Reinorced Concretesand Reinorced Concrete, Journal o Structural Engineering, ASCE,V. 132, No. 11, 2006, pp. 1793-1800.

4. Wuest, J., Comportement structural des btons de bres ultra peror-mants en traction dans des lments composs, doctoral thesis, colePolytechnique Fdrale de Lausanne, Lausanne, Switzerland, 2007, 244 pp.(in French)

5. Oesterlee, C., Structural Response o Reinorced UHPFRC and RCComposite Members, doctoral thesis, cole Polytechnique Fdrale deLausanne, Lausanne, Switzerland, 2010, 136 pp.

6. Kani, G. N. J., Basic Facts Concerning Shear Failure, ACI J OURNAL,Proceedings V. 63, No. 6, June 1966, pp. 675-692.

7. Muttoni, A., and Schwartz, J., Behaviour o Beams and Punchingin Slabs without Shear Reinorcement, Proceedings o the IABSE Collo-quium, V. 62, 1991, pp. 703-708.

8. Noshiravani, T., Fracture Test o R-UHPFRCRC Composite BeamsSubjected to Combined Bending and Shear, PhD thesis, cole Polytech-nique Fdrale de Lausanne, Lausanne, Switzerland, 2011, 326 pp.

9. Vaz Rodrigues, R.; Muttoni, A.; and Fernndez Ruiz, M., Infuenceo Shear on Rotation Capacity o Reinorced Concrete Members withoutShear Reinorcement, ACI Structural Journal, V. 107, No. 5, Sept.-Oct.2010, pp. 516-525.

10. Leonhardt, F., and Walther, R., Schubversuche an eineldrigen Stahl-betonbalken mit und ohne Schubbewehrung zur Ermittlung der Schubtrag-higkeit und der oberen Schubspannungsgrenze, Ernst & Sohn, Berlin,Germany, 1962, 68 pp. (in German)

11. Collins, M. P.; Bentz, E. C.; and Sherwood, E. G., Where is Shear

Reinorcement Required? Review o Research Results and Design Proce-dures,ACI Structural Journal, V. 105, No. 5, Sept.-Oct. 2008, pp. 590-600

12. Walraven, J. C., Fundamental Analysis o Aggregate Inter-lock, Journal o Structural Engineering, ASCE, V. 107, No. 11, 1981,pp. 2245-2270.

13. Vecchio, F. J., and Collins, M. P., The Modied Compression-Field Theory or Reinorced Concrete Elements Subjected to Shear, ACIJOURNAL, Proceedings V. 83, No. 2, Mar.-Apr. 1986, pp. 219-231.

14. Rossi, P.; Brhwiler, E.; Chhuy, S.; Yenq, Y.-S.; and Shah, S. P.,Fracture Properties o Concrete as Determined by Means o WedgeSplitting Tests and Tapered Double Cantilever Beam Tests, FractureMechanics Test Methods or Concrete: Report o Technical Committee89-FMT Fracture Mechanics o Concrete, Test Methods, RILEM, Chapmanand Hall, London, UK, 1991, pp. 87-128.

15. Mihaylov, B. I.; Bentz, E. C.; and Collins, M. P., Behavior o LargeDeep Beams Subjected to Monotonic and Reversed Cyclic Shear, ACI

Structural Journal, V. 107, No. 6, Nov.-Dec. 2010, pp. 726-734.16. Kani, M.; Huggins, M.; and Wittkopp, R., Kani on Shear in ReinorcedConcrete, University o Toronto Press, Toronto, ON, Canada, 1979, 225 pp.

17. Paulay, T.; Park, R.; and Philips, M. H., Horizontal Construc-tion Joints in Cast-In-Place Reinorced Concrete, Shear in ReinorcedConcrete, SP-42, American Concrete Institute, Farmington Hills, MI, 1974,pp. 599-616.

18. Zilch, K.; Schmidhuber, C.; and Niedermeier, R.,Bauteilversuche zurQuerkratbiegung an mittels Klebearmierung verstrkten Bauteilen: [Forsc-hungsbericht], Stuttgart: Fraunhoer-IRB-Verl., 2000, 160 pp. (in German)

19. Muttoni, A., Punching Shear Strength o Reinorced Concrete Slabswithout Transverse Reinorcement,ACI Structural Journal, V. 105, No. 4,July-Aug. 2008, pp. 440-450.

20. Stoel, P., Zur Beurteilung der Tragsicherheit bestehender Stahlbet-onbauten, doctoral thesis, Swiss Federal Institute o Technology in ZurichZurich, Switzerland, 2000, 186 pp. (in German)

21. Mirzaei, Y., Post-Punching Behavior o Reinorced Concrete Slabs,doctoral thesis, cole Polytechnique Fdrale de Lausanne, Lausanne,Switzerland, 2010, 140 pp.

22. Teng, J. G.; Chen, J. F.; Smith, S. T.; and Lam, L., Behaviour andStrength o FRP-Strenghtened RC Structures: A State-o-the-Art Review,Proceedings o the Institution o Civil Engineers Structures & Buildings ,V. 156, Institution o Civil Engineers, London, UK, 2003, pp. 51-62.

23. Muttoni, A., and Fernndez Ruiz, M., Shear Strength o Memberswithout Transverse Reinorcement as Function o Critical Shear CrackWidth,ACI Structural Journal, V. 105, No. 2, Mar.-Apr. 2008, pp. 163-172.

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NOTES:

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APPENDIXES

APPENDIX A SHEAR RESISTANCE MECHANISMS IN RC MEMBERS

The mechanisms of shear resistance in RC members depend on the stresses carried by both

concrete and steel.

The primary shear resistance mechanism in RC members is the inclined compression stress

field in concrete. Strut action carries the stresses in beams with smooth rebars or in beams with

deformed rebars and a/d of less than approximately 2.5. The tensile force along the longitudinal

reinforcement of these beams is constant. The strength of the strut depends on the concrete

compressive strength and the reinforcement detailing.

Beam action resists the shear forces in members with bonded longitudinal reinforcement and

a/d>2.5. In these members, the tension in the longitudinal reinforcement changes along the member.

Upon yielding of the longitudinal rebars, the tensile force becomes constant; thus, strut action

replaces beam action in carrying the shear stresses.9

The change in the tensile force is made possible by the web stresses that are carried by the

shear reinforcement anchored into the longitudinal tension chord and the aggregate interlock along

crack lips.11

Aggregate interlock depends on the crack width, compressive stresses across the crack,

shear displacement, and concrete quality.12, 13

The vertical and longitudinal reinforcement crossing

the cracks control their opening and enhance aggregate interlock. The roughness of the crack lips

depends on the strength of concrete and the size and strength of its aggregates.13, 14

Cracks that pass

through the aggregates are smooth and reduce aggregate interlock. This is often the case of high-

strength concretes or mixes with low-strength aggregates.

Beam versus strut action in RC beams with ribbed and smooth rebars are shown in Fig. B-1.

10,

15Aggregate interlock (AI) and dowel action (DA) of the rebars at flexural cracks resist the bending

of the concrete segments between the cracks that is caused by the bond stresses between concrete

and rebars along the base of the segment.16

A similar phenomenon occurs between the flexure-shear

cracks in an RC element with glued tensile steel plates, except that dowel action (mainly the

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34

contribution of the rebars bending at a crack) is replaced with the out-of-plane bending of the steel

plates.17, 18

Fig. A-1 (a) Beam versus (b) strut action in RC beams subjected to point loads.10, 15

The localization of web deformations at a flexure-shear crack and the interference of this

crack with the compression stress field in the web cause the flexure-shear failure of RC members.7

Flexure-shear failure occurs along the collapse or so-called critical crack and determines the

member resistance and rotation capacity.7, 19, 20

Following a flexure-shear failure, the dowel action

of the longitudinal rebars embedded in concrete and the membrane action of the tensile

reinforcement continue to provide residual resistance.21

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35

Appendix B UHPFRC mix HIFCOM 135

Table B-1 Mix design (1 kg/m3=0.062 lbm/ft3 and 1 mm=0.0394 in).

CEM III B cement 1277.4 kg/m3

silica fume 95.8 kg/m3sand 664.6 kg/m3

Steel fibers

length=13 mm;Diameter= 0.16 mm

235.5 kg/m3

that is 3% by volume

Superplasticiser 42.3 kg/m3

Water 0.155 kg/m3

Fig. B-1 Tensile behavior of plain UHPFRC from horizontally cast dog-bone specimens (1

MPa=145.0 psi; 1 mm=0.0394 in).

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36

Appendix C Results of tensile tests on steel rebars

Fig. C-1 Stress-strain curves of steel rebars.