Engineering Structures 33 (2011) 3597–3609

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Engineering Structures

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Shear failure analysis on ultra-high performance concrete beams reinforced withhigh strength steelJun Xia a, Kevin R. Mackie a,∗, Muhammad A. Saleem b, Amir Mirmiran b

a University of Central Florida, The Department of Civil, Environmental, and Construction Engineering, 4000 Central Florida Blvd. Orlando, FL, 32816-2450, USAb Florida International University, The Department of Civil and Environmental Engineering, 10555 West Flagler Street, Miami, FL, 33174, USA

a r t i c l e i n f o

Article history:Received 18 March 2010Received in revised form7 March 2011Accepted 27 June 2011Available online 20 August 2011

Keywords:Bond strengthPassive reinforcementShear reinforcementDowel actionMoment–shear interaction

a b s t r a c t

A new deck system for moveable bridges was developed that makes use of ultra-high performanceconcrete (UHPC) reinforced with high strength steel (HSS) rebar to achieve the light weight and highstrength requirements in moveable bridge applications. However, the typical deck strips of this decksystem failed predominantly due to shear cracks in simply supported beam proof tests. This paperinvestigates the mechanism of the deck strip shear failure experimentally and analytically. Experimentalstudies were performed at several scales, including material characterization, bond strength tests, small-scale prism tests, and full-scale beam tests. Specimens with traditional shear strengthening techniqueswere also tested. Several existing formulas were utilized to predict the shear strength, and the resultswere compared to the experimental results. The accuracy and limitations of these formulas are discussed.The shear failure of UHPC–HSS beams is not characterized by brittle response or catastrophic loadreduction as with normal reinforced concrete. Therefore, this particular shear failure mode is regardedas acceptable. However, the additional shear resistance caused by the localized deformation of thelongitudinal reinforcement is not recommended to be considered for design capacity formulas.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Ultra-high performance concrete (UHPC) is a fiber-reinforcedconcrete (FRC) with high compressive strength cement matrix andhigh tensile strength fibers. It exhibits the strain hardening effectin uniaxial tension tests due to the existence of the fibers with vol-ume fraction at about 2%. According to the classification methodintroduced by Naaman and Reinhardt [1], UHPC can be regardedas one kind of high performance fiber-reinforced cement compos-ite (HPFRCC). Several UHPC products are commercially availableworldwide, and Ductal r⃝ is one widely available in the US. Thema-terial properties of Ductal r⃝ were fully investigated byGraybeal [2].The high strength and gooddurabilitywere confirmedbased on theexperimental results. Compressive strengths as high as 221 MPaare ensured by applying a heat treatment process, which is recom-mended by Lafarge, the manufacturer of the UHPC material usedin this paper; otherwise, lower strengths will result. The benefitsof this recommended heat treatment process were also confirmedby Graybeal [2]. The tensile strength was experimentally investi-gated by Chanvillard and Rigaud [3] using both uniaxial and four-point bending tests. The ultimate tensile strength from the direct

∗ Corresponding author. Tel.: +1 407 823 2857.E-mail address: kmackie@mail.ucf.edu (K.R. Mackie).

0141-0296/$ – see front matter© 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2011.06.023

tension test was found to be around 10.8 MPa, while the equiva-lent strength obtain from the flexural test was usually higher dueto the scale effect. The fibers blended in the UHPCmatrix provide abridging effect across themicro cracks and thus increase the tensilestrength and ductility. The punching shear resistance of the UHPCslabwas investigated byHarris and Roberts-Wollmann [4], and theminimumdeck thickness to prevent the punching shear failure un-der the factored wheel load (165 kN) for a 200 mm by 500 mmpatch is predicted to be 25 mm. In Europe, Ductal r⃝ has been in-vestigated by Toutlemonde [5] to build a full depth waffle shapebridge deck system. In US, the Pi-girder and two-way waffle shapefull depth deck system are currently being investigated in Iowastate [6–9] under the research projects sponsored by the FederalHighway Administration (FHWA).

The term high strength steel (HSS) used in this paper refers tostructural steel material that has a minimum yielding stress over517MPa (75 ksi). Several types of Grade 75 stainless steel rebar arecommercially available [10] that meet the requirement of ASTMA955 [11]. Although the superior corrosion resistance of stainlesssteel rebars makes them the best choice for deck applications, thematerial cost is usually several times higher than that of normalGrade 60 carbon steel rebar. High strength microcomposite steelrebar (MMFX2) is an uncoated, high strength rebar made froma low carbon, chromium alloy steel. It meets the requirementof ASTM A1035 [12] for Grade 100 rebar with yielding stress of690 MPa and ultimate strength as high as 1200 MPa. Although

3598 J. Xia et al. / Engineering Structures 33 (2011) 3597–3609

the corrosion resistance of MMFX2 rebar is not as good as that ofstainless steel rebar according to Clemeña [13], it is much betterthan that of carbon steel rebar. MMFX2 rebars were used in thisresearch for their superior strength and ductility.

The structural behavior of UHPC beams reinforced with passiveHSS rebar is affected by the bond strength between the twomaterials. Although no exact information was found in theliterature on this topic, several related works are mentioned hereto give a lower bound estimation of the bond strength between thetwo.Holschemacher [14] investigated the bond strength between apure UHPCmatrix and ribbed Grade 60 carbon steel rebar by usingpull-out specimens. The local bond stress was around 40–70 MPafor US #3 rebars with 45 mm concrete cover. Some of thespecimenswith 25mmcover failed in concrete splitting. The UHPCused in the test had no fibers in the mix design, and none of thespecimens were subjected to heat treatment. Lubbers performedanchorage tests on UHPC (Ductal r⃝) [15]. Low relaxation, 12 mmdiameter, 1862 MPa prestressing strands were embedded in UHPCwith a minimum bond length of 305 mm and no prestress forceapplied. All strands that fractured during the pullout test showedthe existence of the high bond strength. Normal strength concretebeam splice tests performed by Ansley [16] on US #6 and US #8MMFX2 rebars show that the bond length required to yield therebar is 45 times the rebar diameter. After yielding, the nonlinearductile response of the rebar material reduced the bond strengthand changed the commonly brittle splice failure to a gradual andmore ductile failure.

Advanced construction materials, such as UHPC and HSS,provide an opportunity to help rehabilitate infrastructure systemsthat are either structurally deficient or obsolete. In particular,a deck system utilizing ultra-high performance concrete (UHPC)with only passive HSS longitudinal reinforcement was proposedfor use on moveable bridges [17] to replace the existing opengrid steel deck system. The original grid deck system has severalshortcomings: the riding surface is less skid resistant when wet;traffic-induced vibration causes noise and sensations of poorridership [18]; and the steel deck is corrosion and damage prone,and costly tomaintain. The replacement deck system has stringentacceptance criteria on the overall depth, self weight, and capabilityto meet the AASHTO LRFD code [19] requirements, which preventthe use of conventional reinforced concrete. Several light-weightdeck systems made of fiber-reinforced plastic (FRP) [20] oraluminum [21] were proposed, while their application in thefield are still under investigation. The combination of UHPC andHSS rebar provides a solution with a light-weight, high strengthdeck system that was experimentally proven to meet the crucialrequirements [17]. However, one of the remaining concerns aboutthe new UHPC–HSS deck system is its shear type failure mode.Although the ultimate load of all the simply supported T-sectiondeck strips, which were originally designed based on the flexuralstrength criterion [17], exceeded the expected load demand, thespecimens all failed with widened shear cracks similar to normalstrength reinforced concrete. However, the shear failure of theUHPC–HSS beam was not abrupt or catastrophic. It was observedfrom the experiment that along with the widening of the shearcracks, the longitudinal rebar at the crack location bent locallywhile the concrete in the compression zone either stayed intactor gradually crushed. The high ductility of this failure mode isattributed to the high strength, high ductility, and self-compactingproperty of theUHPCmaterial,which causes the considerable bondstrength between the HSS rebar and UHPC. More investigation ofthis type of shear failure is necessary to determine if it should beavoided or be accepted in design practice.

The objective of this paper is to further investigate themechanism of the shear failure mode of UHPC beams with passiveHSS rebars via both experimental and analytical investigations.

Experimentally, mechanical tests at different scale levels wereperformed. Thematerial level tests were performed to confirm thematerial properties. A series of bond tests based on a compressionmechanism were performed to obtain the estimate of the bondstrength between HSS rebar and UHPC blocks with concrete coverapproximately equal to the rebar diameter. Small-scale beamswith different end anchorage types were tested. The full-scale T-section beam tests had similar specimen geometry and loadingconfigurations as in the previous research [17]. For the purposeof this study, additional specimens were tested with transversereinforcement either by adding single-leg stirrups or by bendingup the longitudinal rebar. Another two specimens were testedwith different longitudinal reinforcement in an attempt to achieveflexural failure. Analytically, although there are quite a few shearstrength design formulas [22–27] in the literature, for most ofthem, UHPC is out of the applicable range due to the ultra-highcompressive strength. The only off-the-shelf equation for sheardesign with UHPC is from the ‘‘Ultra-High Performance Fibre-Reinforced Concretes—Interim Recommendations’’ published byAssociation Franccaise de Génie Civil (AFGC) [27]. It has been usedto predict the shear strength of prestressed bridge girders [28].Dowel action contribution is not included in the French codeformula but is believed by Reineck [25] and He and Kwan [26]to be an important shear transfer mechanism in beams withoutshear reinforcement. Their ‘toothmodel’ is used to check the shearcapacity controlled by the interfacial bond strength. A deformablestrut and tie model was also proposed based on the observeddeformation shape of the specimens. The predictions based on thethree analytical methods were compared with the experimentalresults and their accuracy and limitations were discussed. Inaddition, moment and shear interaction is discussed in this studyand the difference between UHPC and normal strength concretewere presented. The analytical approaches used by Choi et al. [29]and Choi and Park [30] were adopted to investigate the maximumshear capacity under the influence of external moment.

Shear-induced deformation and failure is very important in thedesign of reinforced concrete flexuralmemberswithout transversereinforcement. Modified compression field theory (MCFT) wasused by Vecchio to predict the shear responses of reinforcedconcrete [31]. The moment–shear interaction was considered atthe material level under the principal stress domain. It was foundthat although the shear resistance generally decreases with theincrease of the moment, for T-sections, the shear resistance mayincrease with slightly increased external moment. Application ofMCFT to UHPC members is dependent on the further investigationon the material responses under multi-dimensional stress states,and this limits its application in this paper. Equation 11-5 inthe ACI 318-08 code [22] reflects the fact that shear strengthdecreases when the moment capacity is fully utilized. The sameconclusion was drawn by Muttoni and Ruiz [23] for rectangularsections based on the assumptions that the shear failure wasdirectly related to the critical shear crack width. Choi et al. [29]and Choi and Park [30] claimed that only the top concrete portionin compressionprovides the shear resistance of the sectionwithoutshear reinforcement. In addition, the allowable shear contributionis dependent on the normal stress caused by the external axialload and the moment. By checking the principal tensile andcompressive stresses, the maximum allowable shear stress of allsection layers can be obtained. Therefore, the maximum allowableshear force of the section can be estimated with respect to theexternal moment level and the resisting stresses distributed alongthe section height. Although shear–moment interaction alwaysexists at the section level, the impact may not be significant at thecomponent level. By comparing the load capacity of the flexuralmember to its plastic load capacity calculated based on the idealflexural failure, Imam et al. [32] found that the influence of shear

J. Xia et al. / Engineering Structures 33 (2011) 3597–3609 3599

Table 1Matrix of experimental program.

Test category Description Quantities Concrete batch

Materialcharacterization

UHPC cylinder compression test 3 eachbatch

1

UHPC uniaxial tension test 3 eachbatch

1

MMFX2 rebar uniaxial tension test 2 eachsize

N/A

Bond test Compression bond test 13 1Small-scale beam test Rectangular prism reinforced with MMFX2 rebar 2 1Full-scale beam test T-beam reinforced with various types and sizes of rebar, some with different shear strengthening

reinforcement6 2 and 3

was only significant at medium span-to-depth ratios (a/d) forfiber-reinforced concrete, which is true also for normal strengthreinforced concrete according to Kani [33]. When the span-to-depth ratio is small, the arch effect will be activated and the loadcan be directly transferred to the supports. On the other hand, thelarger the span-to-depth ratio is, the less critical the shear demandwill be when compared to the moment demand.

2. Experimental investigation

2.1. Methods

Experimental investigationswere performed in four categories:material characterization, bond strength, small-scale prisms, andfull-scale T-section beams to quantify the factors that can influencethe shear capacity of the beams and to obtain the shear failuremode and capacities directly. The specimen matrix is summarizedin Table 1. None of the specimens mentioned in the table wereheat treated after casting; however, the influence of lack of heattreatment is discussed with the experimental results.

The cylinder compression tests were based on ASTM C39 [34]using a universal testing machine (UTM). The cylinders frombatch 2 and batch 3 were tested at the Florida Department ofTransportation’s Structural Materials Laboratory with fine endgrinding, while those from batch 1 were tested in the University ofCentral Florida laboratory with limited end surface treatment. Theuniaxial tension test of UHPC using dog-bone coupon specimenswas carried out on an MTS 50 kN UTM machine. The rebaruniaxial testwas carried out following theASTME8 [35] procedure.Detailed procedures and results of these material characterizationtests were reported elsewhere [17], and the correspondingproperties are summarized in this paper.

The compression bond specimens were made by casting UHPCaroundMMFX2 rebar in a PVCpipe. Rigid foamwas used to stop theUHPC flow and small diameter PVC tubes were used to maintainthe designated bond length and cover size. The specimen sketchis shown in Fig. 1. The specimens were loaded in the UTM with asteel cap and neoprene pad on top of the rebar portion extendingout from the specimens. The surrounding PVC pipes were removedbefore the loading to avoid potential confinement effects. The bondlength and the cover size are summarized in Table 2. The test isdesignated as a compression bond test because the concrete is incompression (as well as portions of the rebar); therefore, it is nota true representation of the stress state in a reinforced flexuralmember.

Two small-scale reinforced prisms were cast for preliminaryexperimentation. Both of them were reinforced with one US #3MMFX2 rebar. In the first specimen, the rebar was bent to forma 90° hook at both ends (Prism-H) while the other one was castwith a straight bar protruding from the specimen ends (Prism-U).The bottom and side covers for both specimens were set equal tothe diameter of the rebar itself, which is approximately 10 mm.Three strain gaugeswere attached to each prismwith the locations

Fig. 1. Specimen sketch of the compression bond test.

Table 2Bond length and cover for each test group.

MMFX2 rebarsize

Bond length(×db)

Cover size(mm)

Quantities

2 13.2 3US #3 4 13.2 3

8 13.2 3US #4 2 11.7 2US #6 2 14.2 2

shown in Fig. 2. Two strain gauges were used on the rebar tocapture the strain variation along the prism, while the third gagewas mounted on the top surface of the concrete in the mid-span.Deflections on both sides of the prisms were measured by linearpotential meters that were mounted to an aluminum referenceframe fixed between the supports. The third-point bending fixtureis shown in Fig. 2. The specimens were measured before the testsand the average height and width of specimen Prism-U is 63.8 and39.4 mm, respectively; for specimen Prism-H, the values are 69.0and 40.6 mm. The cover for both specimens was approximately9.5 mm, which equals the diameter of the rebar.

The full-scale beam specimen design drawings are shown inFig. 3 with specific section dimensions. This full-scale beam was atypical deck strip portion of a continuous deck panel. The deck stripwas tested as a simply supported beam reacting on the steel girdersthat are typically spaced 1219 mm apart on moveable bridges. Thetotal length of the beam is 1372 mm, allowing for constructionof the end anchorage. The test results for the single-span single-unit deck strip without any end anchorage (1T1S-U) and with the180° hook anchorage (1T1S-H2) were reported elsewhere [17].Four more deck strips were cast: the specimen with normal Grade60 single-leg US #2 shear stirrups (1T1S-S), the specimen withtapered section and normal US #7 rebar (1T1S-T), the specimenwith reduced reinforcement ratio by using two US #4 MMFX2rebars (1T1S-R), and the specimen with multiple longitudinalreinforcement with two of them bent up at the shear criticallocations (1T1S-B). To allow for comparison, the details for all sixspecimens are summarized in Table 3. The loading configurationand the instrumentation plan were similar for all specimens, andare shown in Fig. 4. Special rebar layouts for those using multiple

3600 J. Xia et al. / Engineering Structures 33 (2011) 3597–3609

a b

Fig. 2. The small reinforced prism and loading configuration. (a) Setup sketch, (b) instrumentation.

a b c

Fig. 3. The T-section beam dimensions. (a) Transverse direction normal section, (b) transverse direction taper section, and (c) longitudinal direction section.

a b

c d

Fig. 4. The T-section beam instrumentation plan. (a) Front view without bent bar, (b) front view with bent bar, (c) top view, and (d) bottom view.

Table 3T-section beam configuration summary.

Specimen Flexural reinforcement Rebar end anchorage Rebar area (mm2) Shear reinforcement

1T1S-H2 1 US #7, MMFX2 180 hook 387 No1T1S-U 1 US #7, MMFX2 N/A 387 No1T1S-T 1 US #7, Grade 60 180 hook 387 No1T1S-S 1 US #7, MMFX2 180 hook 387 1 leg US #2 Grade 60 stirrups1T1S-R 2 US #4, MMFX2 180 hook 258 No1T1S-B 1 US #4 and 2 US #3, MMFX2 180 hook 271 Bend up the 2 US #3 rebar at shear crack locations

longitudinal rebars are shown in Fig. 4. All full-scale experimentswere conducted at the Titan America Structures and ConstructionTesting Laboratory at Florida International University.

2.2. Results

The concrete properties of UHPC for three separate batches areshown in Table 4. The relatively low compressive strength for batch1 was due to the fact that the specimens were tested without

perfect end grinding. The bond test results are summarized inTable 5. Although the load and table movement were recordedduring the test, only themaximum load capacities were of interest.All of the specimens failed due to longitudinal concrete splitting.A single specimen contained a casting imperfection, as shownin Fig. 5, with smaller cover width along the specimen lengththat caused failure with lower than average bond strength. Therebar stress exceeded the 690 MPa yielding stress for the US #3rebar with bond length as low as eight times the bar diameter.

J. Xia et al. / Engineering Structures 33 (2011) 3597–3609 3601

Fig. 5. The failure mode and weakening of the full section.

Table 4Tested UHPC properties.

Batch Average 28days fcu (MPa)

Average first crackstrength (MPa)

Average ultimate tensilestrength (MPa)

1 124 7.9 102 193 – –3 193 – –

Meanwhile the average bond strengths for different bond lengthswere very close. Some of the specimens were cut in half verticallyafter testing for inspection purposes, and it was found that someportions of the UHPC contact surface still matched the ribs of thedeformed MMFX2 rebar. This implies that the self-consolidatingconcrete and rebar were tightly bonded due to the dense UHPCmatrix [36], and the bond failure is not due to the crushing ofthe concrete between the ribs. The compression bond test causedcompressive stress in the UHPC, as well as in portions of the rebar,and this may overestimate the bond strength in a flexural memberin which the bottom UHPC portion was in tension. Although moreexperiments are needed to obtain the complete understanding ofthe bond behavior between the twomaterials, the tests performedin this study provide an easy and economic way for bond strengthestimation when a small concrete cover is used.

The test results on the two small-scale reinforced prisms areshown in Fig. 6. The slight difference in the specimen dimensionsexplains the different initial slopes of the load versus deflection

curves in Fig. 6. The rebar portions near the supports weresignificantly engaged after reaching a load level around 12 kN forboth specimens, as shown in the load versus rebar strain (SG1)curves in Fig. 6. Prism-U failed at around 26 kN due to bond failure,and thus the shear crack completely opened, as shown in Fig. 7a.It was observed that the rebar bent locally at the crack location,which caused compression in the rebar as measured in SG1. Thespecimen Prism-H failed at a load level around 39 kN and did nothave one primary shear crack, but rather several distributed smallshear cracks developed, as shown in Fig. 7b. The strain reading(SG1) for this specimen kept increasing with degraded stiffnessdue to the existence of the end hooks. However, the steel hookat one end of the prism failed due to concrete splitting, as shownin Fig. 8a, and caused the load drop. In order to check the bondcondition after testing, the prisms were cut transversely along thelength. One typical section that was 25 mm away from the shearcrack tip is shown in Fig. 8b. The rebar was tightly bondedwith theconcrete, and no sign of bond failure exists. Because the middleportion of Prism-H still remained intact, a 140 mm long middleportion (Prism-S) was cut from Prism-H and tested with a smallershear span of 127 mm. Prism-S failed of shear at around 55 kNwith higher compressive strain on the top UHPC portion and lowertensile strain on the rebar, as shown in Fig. 9. Therefore, it wasconcluded that themoment in the longer-span specimen did affectthe ultimate shear strength.

All full-scale specimens failed with diagonal shear cracks thatpropagated to the support region. The crack widths and strain re-sponses were different for each specimen. Therefore, for compar-ison, the test results were divided into two groups with specimen1T1S-H2 as the benchmark. Test results for the specimens utiliz-ing US #7 rebar as longitudinal reinforcement (1T1S-H2/U/T/S) areshown in Figs. 10 and 11. Meanwhile, test results for specimens1T1S-H2/R/B are shown in Figs. 12 and 13.

The load versus displacement curves in Fig. 10 have similarinitial slopes due to the same longitudinal rebar size. However, thecurves diverge at higher load levels due to the different rebar typeand end anchorage conditions. All three specimens with MMFX2rebar showed a gradual stiffness transition point on the load versusstrain (SG1) plot in Fig. 10, while the transition is more abruptfor the specimen with normal Grade 60 rebar. Strain readingsfrom SG1 (mounted on the top surface of the concrete betweenthe support and the loading region) reflect how much load wasbeing transferred by the concrete compression zone. The slopechange of the load versus SG1 curve is indicative of a change inload distribution. This transition point occurred much earlier inspecimen 1T1S-R and was not clearly exhibited in specimen 1T1S-S. The shear cracks were observed to appear initially at load levelsthat correspond directly to these transition points (zone) during

Table 5Bond test results.

Rebarsize

Bond length×db

Ultimateload (kN)

Bond area(mm2)

Average bondstrength (MPa)

Rebarstress (MPa)

Statistics

µ(MPa) σ (MPa)

US #3 2 12.94 570 22.69 182.36 26.6 2.52 15.11 26.5 212.912 17.53 30.74 247.114 27.95 1140 24.52 393.834 28.49 24.99 401.554 32.6 28.6 459.398 62.75 2280 27.52 884.258 61.34 26.9 864.398 47.13 20.67a 664.17

US #4 2 24.28 1014 23.96 188.23 23.5 –2 23.32 23.01 180.78

US #6 2 43.28 2280 18.98 152.44 18.4 –2 40.78 17.89 143.69

a Specimen shown in Fig. 5.

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a

b

c

Fig. 6. Load–strain and load–displacement results from the small-scale prisms.(a) Load versus displacement for both specimens, (b) load versus strain plot forPrism-U, and (c) load versus strain plot for Prism-H.

the experiments. The behaviors after the transition point weredifferent for specimen 1T1S-H2/T/S depending on the existence oftransverse reinforcement. While stiffness degradation of the SG1curve was observed for specimens 1R1S-H2 and 1T1S-T in Fig. 10,the curve for specimen 1T1S-S continued with approximately thesame slope.

From the experiment, it was seen that, after the shear crackopened, the rebar portion at the crack location was forced to bendand then the two portions beside the diagonal cracks rotated alongwith the pullout of the rebar. The structural responses for all sixspecimens at transition and ultimate load level are summarizedin Table 6 with the failure mode categorized based on the loadversus SG1 responses. Type I failure is defined as failure due to thecrushing of top concrete between the support and loading edge.Specimens 1T1S-H2/T/B belong to this type as their SG1 values atfailure were all close to the crushing strain of UHPC of −0.0035.Type II failure is defined as failure due to crushing of top concretein the mid-span. This failure mode is actually the flexural failure

a

b

Fig. 7. Failure modes for the two small-scale prisms. (a) Failure mode for Prism-Uand (b) failure mode for Prism-H.

mode, and was only achieved by specimen 1T1S-S due to theexistence of the shear reinforcement. Type III failure is defined asshear-bond failure for which the crushing of the concrete betweenthe support and loading edge does not lead to the ultimate failurestate. Specimens 1T1S-U and 1T1S-R belong to this failure modedue to the lack of end anchorage and the closely placed end hooksfor the two US #4 rebars, respectively. Regarding the influencedue to the lack of heat treatment, it is believed that the increasedcompressive strength of UHPCwill help increase the shear strengthfor those specimens that failed due to concrete crushing (Type Iand II). For a failure Type III specimen, the positive impact from theheat treatment is primarily on helping increase the bond strengthbetween the UHPC and the MMFX2 rebar.

Reducing the flexural reinforcement ratio as presented in thispaper did not change the ultimate shear failure mode. Specimenswith small flexural reinforcement ratio (1T1S-B/R) still failed withwidened shear cracks. The high bond strength and the relativelysmall cover ensured that the flexural crack could not widenwithout total interfacial bond failure. At the mid-span of thebeam, where the interfacial stress is small, this failure is onlyachievable if the rebar experiences significant radial contractionwhen approaching the ultimate tensile strength. The opening offlexural cracks was observed during the experiment on specimen1T1S-T, which is reinforced with normal Grade 60 rebar thatyielded during the test. However, even under these circumstances,the flexural cracks closed after the longitudinal rebar began strainhardening. This was followed by the same opening of the diagonalshear cracks as seen in the other specimens. For the specificspecimen configurations presented in this paper, the addition ofshear stirrups will avoid the opening of shear cracks; however,this is cumbersome for precast decks consisting of hundreds oftypical deck strips. Therefore, the ductile shear failure assured bythe sufficient end anchorageswas regarded as an acceptable failuremode for UHPC beams with passive HSS reinforcement.

J. Xia et al. / Engineering Structures 33 (2011) 3597–3609 3603

Table 6Corresponding responses at the transition point and ultimate point.

Transition point Ultimate pointLoad (kN) SG0 (µε) Load (kN) SG1 (µε) SG0 (µε) Failure type

1T1S-H2 133 5000 209 Around −3500 9600 Type I1T1S-U 67 N/A 147 <−3500 N/A Type III1T1S-S 133 4500 213 −2000 11000 Type II1T1S-T 111 3000 156 Around −3500 >20000 Type I1T1S-R 62 2500 156 <−3500 8190 Type III1T1S-B N/A N/A 156 −3000 9770 Type I

a b

Fig. 8. Failure modes for Prism-H. (a) Splitting at the anchorage end block and (b) good bond after failure.

a b

Fig. 9. Test results of specimen with small shear span. (a) Load versus strain plot and (b) failure mode with slippage of rebar.

3. Analytical work

3.1. Methods

For conventional concrete, the shear failure is prevented bychoosing an adequate section size and by providing enough trans-verse shear reinforcement. Therefore, the ultimate load capacity ofthe beam is determined by the flexural response with rebar yield-ing criteria. For UHPC beams with passive reinforcement, if theshear failure was regarding as the acceptable failure mode, spec-ifying the design equation to estimate the ultimate shear capacityis essential. Due to the ultra-high compressive strength of UHPC,most of the widely used shear design equations cannot be applieddirectly without experimental verification. In this paper, three de-sign methods were chosen that were either proposed for use onUHPC or do not directly involve the compressive strength of theconcrete material. Two of them were obtained from the literatureand the third one was proposed by the authors. The details of eachmethod are discussed as follows.

3.1.1. French code formulaThe equation from French code [27] is very similar to the

conventional shear design equations, which contains the shearresistance contributions from concrete, transverse reinforcement,and fibers, as shown in Eq. (1):

Vu = VRb + Va + Vf . (1)

The contribution from the concrete portion can be expressed as

VRb =1γE

0.21γb

kfcb0d. (2)

Here, fc is the compressive strength of UHPC, and k is a factorthat considers the prestressing effects within the concrete and isequal to 1 for beams without prestressing or post-stressing. TermγEγb = 1.5 was introduced to consider the uncertainty associatedwith UHPC. Parameters d and b0 are the structural depth andwidth of the web, respectively. The final form of Eq. (2) withoutconsideration of the resistance factor is similar to its counterpartin the ACI concrete design code, Equation 11-3 [22]. The only

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a b

c d

Fig. 10. Test results of 1T1S specimen with US #7 rebar. (a) Load versus displacement, (b) load versus rebar strain, (c) load versus concrete strain at loading edge, and(d) load versus rebar strain at mid-span.

a b

c d

Fig. 11. Failure mode of the four 1T1S specimens. (a) 1T1S-S, (b) 1T1S-H2, (c) 1T1S-T, and (d) 1T1S-U.

difference is the coefficient, which equals 0.17 in the ACI equationwhen MPa and mm units are adopted. All formulas in this paperadopt these two basic units except those terms specified explicitly.

The contribution from the reinforcing fibers can be expressed as

Vf =SσP

γbf tan(βu). (3)

J. Xia et al. / Engineering Structures 33 (2011) 3597–3609 3605

a b

c d

Fig. 12. Test results of 1T1S specimens compared to shear strengthened specimens. (a) Load versus displacement, (b) load versus rebar strain, (c) load versus strain atloading edge, and (d) load versus strain at mid-span.

a b

Fig. 13. Failure mode of the two strengthened 1T1S specimens. (a) 1T1S-B and (b) 1T1S-R.

Here, S = b0z is the resistance area of fibers calculated bymultiplying the width of web b0 by the lever arm z between thetensile and compressive resultant forces. It is assumed that z =

0.9d for rectangular sections [27], and that this is a conservativeassumption for T-sections. Parameter βu represents the angle ofthe struts of compressed concrete from the neutral fiber of thebeam. Partial safety factor γbf was introduced to account for anymanufacturer defects that influence the tensile property of UHPC.It equals 1.3 for the case of fundamental combinations and 1.05 forthe case of accidental combinations.

The average post-crack residual tensile strength σP can becalculated as

σP =1K

1wlim

∫ wlim

0σ(w)dw. (4)

Variable σP is determined by the maximum crack width wlimand the stress versus crack width relation σ(w). The maximum

crack width limit of 0.3 mm is recommended in the French code.If it is assumed that the stress versus crack width relation is lin-ear up to the maximum crack width of 0.3 mm, then σP can beapproximately estimated as the average of the stress level corre-sponding to zero crack width and a crack width limit of 0.3 mm.The anisotropy of fiber orientation distribution is not considered(K = 1).

3.1.2. Ultimate shear stress limited by the interfacial shear strengthThe ‘tooth model’ summarized by Reineck [25] allows the

estimation of the shear strength based on the interfacial bondstrength between the concrete and the rebar. It is assumedthat the beam can be divided into segments that are connectedonly at the top compression region, as shown in Fig. 14a. Themoment equilibrium of the segment results in the followingequation:∆T · z = V · Scr . (5)

3606 J. Xia et al. / Engineering Structures 33 (2011) 3597–3609

a b

Fig. 14. ‘Tooth’ model and load transfer through struts and ties [25]: (a) Tooth Model, (b) Strut and tie model.

Here, V is the nominal shear resistance including all thecontributions from concrete, fibers, and the dowel action of thelongitudinal rebar. Scr is the width of the segments, determined bythe crack spacing. The net tensile force ∆T accumulated from theinterfacial stress for individual segments can be expressed as1T = τπdsScr . (6)

Here, τ is the interfacial bond stress and πdsScr is the calculatedbond area. By inserting Eq. (6) into Eq. (5) as proposed by Reineck,an equation capable of predicting the ultimate shear strengthbased on the bond strength was obtained asVu,τ = τuπdsz. (7)

Eq. (7) is suitable to use on UHPC because concrete crushing isnot the intended failure mode; therefore there is no term directlyrelated to the compressive strength of the concrete material.Although the average flexural crack spacing of UHPC is muchsmaller than that of normal concrete, the crack spacing term Scrcancels out in the derivation process and does not affect the resultsin Eq. (7). By obtaining the interfacial bond strength from thecompression out specimens, the ultimate shear strength whenthe bond failure happens can be predicted. Reineck also pointedout that the shear force contribution from the uncracked concretepotion can be estimated as

Vcu =23cτπds =

23czVu. (8)

Here, c is the height of the uncracked portion, and z is the leverarm between the tensile and compressive resultant forces. ForUHPC, the ratio c/z is usually even smaller due to the high modu-lus of elasticity of UHPCwhen compared to normal concrete,whichmeans that the shear strength contribution from the concrete com-pression zone is only a small portion of the total shear resistance.In other words, the concrete in the compression zone only experi-ences very small shear effects before the interfacial bond fails.

3.1.3. Deformable strut and tie model for ultimate shear capacityestimations

Reineck [25] also proposed a strut and tiemodel for a beamwithno shear reinforcement, as shown in Fig. 14b. Based on that, theauthors proposed a deformable strut and tie model as shown inFig. 15 to consider the load transfer after the failure of the tensiontie between points B and C. This tensile force can be provided bythe concrete due to the existence of the interfacial bond strengthor can be provided by the transverse reinforcement (shear stirrupsor bent up rebars). The absence or break of the tension tie betweenpoints B and C will cause the collapse of the primary strut andtie model and activate other secondary load transfer mechanisms,such as the dowel action of the longitudinal rebar in the caseof normal concrete. However, for normal strength concrete, thesecondary load transfermechanism is usually not sufficient to holdthe existing load and thus the sudden load drop takes place. In thecase of UHPC–HSS beams, the opening of the shear cracks triggers

a

b

c

Fig. 15. Deformable strut and tie model. (a) Struts and ties, (b) deformation andgeometry, and (c) internal force equilibrium at nodes.

the contribution of the bridging fibers and causes a graduallyweakened tension tie between points B and C, thus preventingthe abrupt and catastrophic failure. Furthermore, the rebar atthe cracking location was not only deformed in shear, but alsobent significantly. The interaction between rebar and concrete canincrease the shear resistance even after the opening of the shearcracks under the combined contribution from bridging fibers andthe secondary load transfer mechanism. The following equations,based on the force equilibrium, demonstrate the relationshipbetween theultimate shear force that is transferred by the concretecompression region andby the concrete–rebar interactionwhen allthe fibers have pulled out at the shear cracks.V = Fc2 + Fc sin(θc)Fc2 = Fs sin(θd)Fc cos(θc) − Fs cos(θd) = NL.

(9)

Here, θc and θd are two angles related to the deformation shapewith the relationship

tan(θc) + tan(θd) = d/L1. (10)

J. Xia et al. / Engineering Structures 33 (2011) 3597–3609 3607

Parameters NL and NV are the external forces provided bythe support. Parameters Fci and Fsi are the internal forces of theconcrete struts and steel ties at different regions. The externalshear force V is of interest. Two extreme cases can be representedby the same model. When the angle θd equals zero, force Fc2equals zero as well, and all load is transferred through the concretecompression zone. When the angle θc equals zero, dowel forceFc2 equals the full external shear force V , and only a portionof the load is transferred through the top compression region(technically, load transferred equals Fc3, which is the horizontalcompression force transfer by the top portion of UHPC at the mid-span). Between the two extreme cases, the load is distributedbetween the two mechanisms. If it is assumed the support cannotprovide any lateral resistance (NL = 0), then the ultimate shearforce Vu limited by the maximum steel tie force when Fs = Fs,u is

Vu = Fs,u cos(θd)dL1

. (11)

Eq. (11) can be used to predict the ultimate shear strength basedon the longitudinal rebar stress being close to the support withoutconsidering how the load is being transferred.

3.1.4. Ultimate shear strength equations considering moment–shearinteraction

The investigation approach of Choi et al. [29] and Choi andPark [30] was adopted in this paper to investigate the moment–shear interaction of UHPC–HSS beams. However, due to the lack ofauthoritative information on the biaxial principal stress interactionfor UHPCmaterial, four σ1, σ2 interactionmodels were introduced,as shown in Eq. (12). Of these, Eq. (12a) is the numerical expressionof themodel adopted by Choi and the rest are the assumed possibleinteractions. By specifyingmaterial properties of Ec = 55GPa, fc =

−193 MPa, and ft = 10.4 MPa, the corresponding normal stressversus maximum shear stress relations based on the fourassumptions are shown in Fig. 16a.

σ1 ≤ ft and σ2 ≥ fc (12a)σ1fc + σ2ft − ft fc = 0 (12b)

σ12

ft2+

σ22

fc2= 1 (12c)

(σ1 − ft)2

ft2+

(σ2 − fc)2

fc2= 1. (12d)

To predict the ultimate shear strength of the T-sectionsdiscussed in this paper, a moment-curvature analysis was firstperformed. An elastic–plastic stress–strain relation with yieldingstress of 10.3 MPa was used for the tensile behavior of UHPC,and the linear stress versus strain relation was used for thecompression side up to the crushing strain of −0.0035. Afterreaching the crushing strain, the stress of UHPCwas set to decreaselinearly until reaching zero at a strain level of −0.01. A nonlinearstress–strain relation was adopted based on the experimentalresults of MMFX2 steel rebar. The normal stresses for all layerswere recorded during the analysis for each curvature increment,and themaximumallowable shear stress distributionwas obtainedbased on the four principal stress interaction assumptions. Theultimate shear force for the section was obtained by accumulatingthe shear resistance contribution from all layers. Theoretically, thiscurvature-dependent shear resistance would be checked againstthe external shear demand at all locations along the simplysupported beam. However, the section at the edge of the loadingpad was determined to be the critical section, and the shear spanlength of 356 mm was used to convert the moment-curvaturerelation derived previously to the curvature versus flexural loadcapacity curve. By plotting the converted demand curve alongwith

a

b

Fig. 16. Biaxial stresses relationship. (a) Normal and maximum shear stresses and(b) distribution of maximum shear stress along the section height.

the shear strength curves, the intersections of the curves wereinterpreted aswhen the shear begins to interferewith themomentcapacity for the critical section. While the full flange width of theT-section was included in the flexural analysis, only the portionequal to the web thickness plus two times the flange thicknesswas taken into account in the shear strength calculation. Similaranalysis procedures were repeated for the rectangular section forthe small prisms.

3.2. Results

The shear resistances for the small-scale and full-scale beamspecimens were estimated based on Eqs. (2) and (3). The resultsare summarized in Table 7, based on the following assumptions.The design safety factors γE , γb, and γbf were set to 1.0, and theangle βu was assumed to be 45°. A linear stress versus crack widthresponse was assumed for crack widths up to 0.3 mm. Therefore,the average post-crack strength can be estimated as σP = 9 MPa,based on the material characterization tests.

The shear strength prediction from the French code at amaximum crack width equal to 0.3 mm matches the test resultfor the small prism, while the predictions for the T-section beamwere significantly lower than the test results. The reason forthe underestimation is because the predicted shear strength wasactually corresponding to the shear crack width of 0.3 mm andthus it cannot consider the secondary contribution. The shearresistance contribution from this secondary effect is considerablefor a UHPC beam with passive high strength reinforcement. Theequation may also neglect the contribution of the flanges ofthe T-section specimen by using only the width of the web incalculating the shear resistance area after cracking. This equationalso neglected the shear–moment interaction. The existence ofmoment is believed to have an adverse effect on the shear capacity,and thus a reduction factor is usually introduced, such as thoseproposed by Muttoni and Ruiz [23].

Shear strength estimation based on the interfacial stress limitswas obtained from Eqs. (7) and (8). The maximum bond strengthsfrom the compression test were used as the interfacial stress

3608 J. Xia et al. / Engineering Structures 33 (2011) 3597–3609

Table 7Estimated shear strength using Eqs. (2) and (3).

fcj (MPa) b0 (mm) d (mm) VRb (kN) S (mm2) σP (MPa) Vf (kN) Vu (kN) Pu (kN) Ptest (kN)

Prism-H 124.1 38.1 50.8 4.5 1742 9 15.7 20.2 40.4 401T1S-H2 193.1 50.8 101.6 15.1 4645 9 41.8 56.9 113.7 209

limits. Assuming that parameter z equals 0.9d, the estimated shearstrengths were 36 and 117 kN, respectively, for the small-scaleprism and the full-scale T-section beam specimens. Both values arelower than the experimental results, but close to those estimatedbased on the French code. The shear strength predicted under thismethod corresponds to the statewhen the interfacial bond failed atthe shear crack location. Themethod also underestimated the post-crack shear resistance due to the neglect of the secondary effects.

The shear strength based on Eq. (11), assuming that θc angleequals zero, is listed in Table 8. For the small-scale prismspecimens, the rebar stresses were calculated based on the rebarstrain measured close to the support during the test. For thefull-scale T-section beam specimens, the rebar stresses wereestimated based on the strain results of the rebar at mid-span. Forthose specimens without any recorded rebar strain (1T1S-U), theyielding stress of the specific longitudinal reinforcement was usedin the calculation. Most of the estimated shear strengths are closeto the test results, except for Prism-S, due to the small shear span.The comparisons show the strut and tiemodel can account for loadtransfer at the final stage of the specimens with large shear spans(L1/d > 2) if the stress within the longitudinal rebar is available.If the end anchorage of the longitudinal reinforcement is ensured,using a rebar yielding stress of 690 MPa in Eq. (11) can lead to aconservative estimation of the ultimate shear strength of a UHPCbeam with passive longitudinal HSS rebar.

The results for the moment–shear interaction are presented asfollows. For T-sections, the distribution of maximum shear stressalong the section height are shown in Fig. 16b at several curvaturelevels (different κ value) for assumption equation (12c). The shearforces versus curvature for all assumptions are shown in Fig. 17a.It was seen that the intersections of the curves lay between 40 and70 kN, which is much lower than the flexural load capacity. Theinteractions explain the existence of the transition point/zone onthe experimental load versus displacement curves. Plastic hingeswere developed at the critical sections after the concrete portionreached the ultimate shear strength. The fiber contribution andthe secondary load transfer mechanism were activated thereafter.The parabolic model in Eq. (12c) introduced the interaction in theprincipal stress domain, and its prediction of the shear capacitywas close to the model used by Choi. The parabolic model iseasier to implement without explicit checking of the tensile orcompressive failuremodes. The linear and hyperbolic assumptionsoverestimated the impact of the moment, and thus caused alower sectional ultimate shear resistance. A similar conclusionwasalso found for the small-scale prisms, as shown in Fig. 17b. Byplotting the moment and shear resistance, the moment and shearinteraction curve can be obtained for the particular T-section, asshown in Fig. 18. When compared to the corresponding curves fornormal strength concrete, itwas found that the shear strength ratiofor UHPCwas higher, and the increase of moment can be beneficialto the shear strength. It should be noticed that because onlythe influence of moment on the shear strength was considered,the curves derived in this study were more in the sense of aninteraction envelope.

4. Conclusion

Based on the experimental and analytical work presented, itwas concluded that, for UHPC beams reinforced with passive

a

b

Fig. 17. Shear strength versus load capacity based on the flexural strength forcritical section: (a) T-section, full-scale beamand (b) rectangular section small-scaleprism.

Fig. 18. The moment and shear interaction curves compared to the existinginteraction rules for normal strength concrete.

HSS rebar, shear failure is more critical if there is no transversereinforcement. The actual flexural load capacity based on theultimate tensile strength of HSS rebar is much higher than thedesign value which was predicted on the nominal yielding stressof HSS based on the 0.2% offset rule. To avoid the dominationof shear failure in UHPC–HSS beams, a considerable amountof shear reinforcement was required to increase the shearresistance to be higher than the actual flexural capacity. However,adding transverse reinforcement may not be practical and is noteconomical.

Ductile shear failure with higher post-crack shear resistancewas recommended as an acceptable failure mode due to the ex-istence of bridging fibers and the secondary load transfer mech-anism due to concrete and rebar interaction. From experimental

J. Xia et al. / Engineering Structures 33 (2011) 3597–3609 3609

Table 8Shear resistance based on deformable strut and tie model.

Specimens fs (MPa) As (mm2) Fs (kN) L1/d 2Vu (kN) Pu_test (kN) Error (%)

Prism-U 414 71 29 2.5 23.2 27 −12.00Prism-H 690 71 49 2.27 43.1 39 10.13Prism-S 240 71 17 1.14 29.9 55 −45.731T1S-U 690 387 267 3.5 152.7 147 3.941T1S-T 621 387 240 3.5 137.3 158 −13.201T1S-R 897 258 231 3.5 132.1 156 −15.631T1S-H2 1000 387 387 3.5 221.4 208 6.41

observations, this shear failure is not abrupt or catastrophic. Ifthere was no transverse reinforcement, the additional post-crackshear resistance was provided by the bending and shear defor-mation of the rebar along with the opening of the shear cracks. Iftransverse reinforcement existed, the shear crack was restrainedand parallel shear cracks developed until the concrete on the topface crushed. For either case, there were noticeable deformationsand frequent noise of cracking before the final load drop. How-ever, for beams without transverse reinforcement, only a portionof the post-crack shear resistance contributed by the fibers is rec-ommended to be considered by the French code. The purpose ofthis practice is to make sure that the maximum shear crack widthis less than 0.3 mm. Based on the comparison in this paper, if reli-able end anchorage of the longitudinal reinforcement exists, theactual ultimate load capacity of UHPC–HSS beams can be muchhigher than the prediction based on the French code. In case of pre-cast UHPC–HSS bridge decks developed based on the research pre-sented, the 180° beam end anchoragewas used in the system-leveldeck panel specimens. Experimental results show the new decksystem as a viable alternative to the open grid steel deck systemfrom a load capacity point of view with acceptable shear failuremode.

Acknowledgments

This study was sponsored by Florida Departmenrt of Trans-portation (FDOT) under the contract No. BD015 RPWO # 22 withMr. Marcus Ansley as the project manager. The authors are pleasedto acknowledge the support of Mr. Charles Ishee at the FDOTStructural Materials Laboratory for testing the UHPC cylinders. La-farge North American andMMFX Technologies Corporation are ac-knowledged for providing thematerials tested in this research. Theauthors acknowledge Dr. Lei Zhao for his contribution on initiatingthis research project. The views and findings reported here, how-ever, are those of the writers alone, and not necessarily the viewsof the sponsoring agency.

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