Influence of Flexure-ShearCracking on StrandDevelopment Length inPrestressed Concrete MembersRobert J. Peterman, Ph.D., P.E.

Assistant ProfessorKansas State University*

Department of Civil EngineeringManhattan, Kansas

*rormerly Post-Doctoral ResearchAssociate at Purdue University

Julio A. Ramirez, Ph.D., P.E.Professor and Assistant Head forGraduate StudiesDepartment of Civil EngineeringPurdue UniversityWest Lafayette, Indiana

Jan Olek, Ph.D., P.E.Associate Professor

Department of Civil EngineeringPurdue University

West Lafayette, Indiana

In this study, 18 development length tests werecarried out on single strand rectangular andmultiple strand T-shaped semi-lightweight beamshaving design compressive strengths of 7000 psi(48 MPa). In the rectangular beam tests, the designmoment capacity was exceeded in all specimens.However, in the T-beam tests, bond failures atloads below the design capacity occurred in somespecimens immediately after the formation of aflexure-shear crack near the loading point.Additional T-beam tests showed that the bondfailure associated with flexure-shear crackingcould be prevented by increasing the transversereinforcement near the point of maximummoment. The shift in the tension force that occurswhen flexural cracks turn diagonally needs to beconsidered when determining if sufficientanchorage of strands is provided. Therefore, theauthors recommend that the current AASHTO andAC! requirements for strand development shouldbe enforced at a “critical section” that is located adistance cJ from the point of maximum momenttowards the free end of the strand, where d is thedistance from the extreme compression fiber tothe centroid of the prestressed reinforcement.

76 PCI JOURNAL

The use of higher concretestrengths has reduced the cost ofbridge structures by increasing

the maximum span lengths that can bebridged using standard girder crosssections. However, with longer spanlengths the self weight of the prestressed concrete sections has becomean increasingly larger portion of thetotal design load for the bridge. Therefore, in order to reduce the dead loadof the concrete girder, lightweight aggregate is often used in the concretemix.

In the state of Indiana, lightweightaggregate (consisting mostly of expanded shale) has been used to produce semi-lightweight (SLW) prestressed concrete for selected projectssince 1991. The SLW concrete used inthese projects has weighed around 130lb per cu ft (2080 kg/rn3) compared to145 lb per cu ft (2320 kg/rn3) for normal weight concrete. The SLW concrete is obtained by partially replacingthe gravel or limestone coarse aggregate with a lightweight substitute.

PROBLEM STATEMENTIn a recent study sponsored by the

Federal Highway Administration(FHWA),’ the applicability of the current AASHTO2equation for calculating development lengths of prestressing strands in pretensioned lightweightconcrete beams was evaluated. Theunit weight of the concrete was lessthan 120 lb per cu ft (1920 kg/rn3) indicating that the coarse aggregate hadbeen replaced in full with alightweight ingredient. In the FHWAstudy, the current AASHTO development length equation was found to beunconservative for estimating development lengths in girders whenlightweight concrete was used.

In view of these findings, the applicability of the current AASHTO development length equation for strandsin SLW concrete girders was alsoquestioned. Therefore, the researchpresented in this paper, which was cosponsored by the Indiana Departmentof Transportation (INDOT) and theFHWA, focused on determining thedevelopment length of prestressedstrand when SLW concrete is used.This was necessary in order to determine the adequacy of existing struc

IIIIIIr

tures and to provide recommendationsfor the design of future projects usingSLW concrete.

All of the SLW prestressed girderbridges built in Indiana prior to thisstudy had a concrete design strengthof 7000 psi (48 MPa) and are reinforced with 1/2 in. special (13.3 mm)diameter strand. Therefore, this studyfocused primarily on the developmentlength determination of ‘/2 in. special(13.3 mm) prestressing strand in SLWmembers with a similar concrete design strength.

BACKGROUND

Discussed below is background information on validation of prestressingstrand, assessment of strand surfacecondition, and review of existingstrand transfer and developmentlength equations.

Strand Validation(Moustafa Test Method)

Logan,3 in a special report publishedin the March-April 1997 PCI JOURNAL, concluded that there is a significant difference in bond performance inpretensioned concrete beams amongstrands produced by different strandmanufacturers. The report recommended that all 0.5 in. (12.7 mm) diameter strand used in pretensioned applications be required to have aminimum average pullout capacity of36 kips (160 kN), with a standard deviation of 10 percent for a six-sample

group, when embedded 18 in. (460mm) in concrete test blocks. This testprocedure has become known as theMoustafa method, named after Dr.Saad Moustafa who first conductedpullout tests on similar specimens inthe l970s.4

The first task of this study presentedherein, therefore, involved the fabrication and testing of a similar pulloutspecimen to determine if the strandused in this study would meet the minimum average pullout capacity recommended by Logan. Following discussions with Logan, the transversereinforcement used in the pulloutspecimens in this study was modifiedfrom that shown in Ref. 3 to provide atransverse tie next to each strand (seeFig. 1). Since ‘/2 in. special strand hasa nominal diameter of 0.522 in. (13.3mm) instead of 0.5 in. (12.7 mm), thecorresponding minimum average pullout capacity for the ‘/2 in. specialstrand (assuming a similar averagebond stress at ultimate load) is 37.6kips (167 kN).

The girders for all of the semi-lightweight (SLW) girder bridges inIndiana were manufactured at CSRHydro-Conduit, Lafayette, Indiana.During the last ten years, Hydro-Conduit has used strand primarily fromtwo suppliers. Therefore, at the outsetof this experimental program, it wasdecided that the test specimens wouldbe fabricated using prestressing steelfrom those same two suppliers. References to strand supplied from these

-

U

Strands#4 Bars x 76” Long

#3 Ties(4 Total)2” Bond Break

1.

4” 9 Spaces @8=72”6’ 12”(#3 Tie Spacings) .;

__________

24”6 8-“

Note: 1” = 25.4 mm.

2’Clear r1

U 6”

Fig. 1. Details of Moustafa pullout specimen used in this study.

September-October 2000 77

companies will be denoted by the letters “A” and “B” throughout thispaper. Therefore, the pullout specimenused to “validate” the strands in thisstudy contained nine strands fromeach strand supplier.

Surface Condition Assessment

Many observers have noted differences in appearance, color, and drawing lubricant residue of strand fromdifferent manufacturers. Therefore, attempts were made to document theinitial surface condition of the strandused in this study. Visual appearanceof the strand, in terms of color andsigns of weathering, were noted forthe strand used in the pullout andbeam specimens.

In addition, every piece of strandused in the pullout specimen waswiped with a white paper towel priorto tying it into the reinforcing bar cageto remove residue and aid in the visualassessment of the initial surface condition. This process was also performedby Logan3 prior to casting his pulloutspecimens.

Transfer and Development Lengths

The “transfer length” is defined asthe distance required to transfer thefully effective prestress force in thestrand to the concrete. The transferlength is not a quantity specified in either the ACT Building Code5 or theAASHTO Specifications.2However,both codes suggest a transfer length of50 strand diameters when checkingshear provisions. The ACI Commentary to the Building Code (Section12.9) provides a formula for calculating the transfer length that is based onthe expression for development length.

According to this formula, the transfer length (Li) is given by:

=-

(1)

where fse is the effective stress (ksi) inthe strand after all losses, and db is thenominal diameter of the strand ininches.

The “development length” is thebond length required to anchor thestrand as it resists external loads on

the member.6As external loads are applied to a flexural member, the member resists the increased moment demand through increased internaltensile and compressive forces. Theincreased tension in the strand isachieved through anchorage to the surrounding concrete.

In the current specifications, it is assumed that the development length isequal to the length required to transferthe effective prestress force (transferlength) plus an additional length required to develop the increase in strandtension produced by the external loaddemand. This additional length required to develop the maximum stressin the strand is often referred to as the“flexural bond length.” The development length is specified by both theACI and AASHTO Codes as:

Ld =(fpsfse) db

where f is the stress in theprestressed strand at nominal strengthof the member (in ksi), and fse and dbare the same as in Eq. (1).

Transfer lengths affect structural design considerations in two ways.First, current code provisions for sheardesign of prestressed concrete members are based on the amount of precompression in the member. Since theeffective prestress has been observedto vary approximately linearly fromzero at the end of the member to be

fully effective at the end of the transfer zone,6 significant deviations in theactual transfer length from the codesuggested 50 strand diameters couldlead to inadequate estimates of themember’s shear strength.

The transfer length can also have asignificant impact on the flexural behavior of prestressed concrete members. Kaufman and Ramirez,7and Russell and Burns,6 have found thatanchorage failures were likely whendiagonal shear cracking propagatedthrough the transfer zone of a pretensioned strand. Beams with debondedstrands are especially susceptible tothis phenomenon. Therefore, the valueof the transfer length is important indetermining whether flexural crackswill likely propagate into this zoneprior to the member reaching its nominal capacity.

In practice, development length re(2) quirements are typically checked,

rather than designed for. When a prestressed concrete member is designed,required longitudinal reinforcementquantities are based on service loadstresses as well as calculations ofnominal capacities. Both the ACT andAASHTO Codes prescribe reinforcement ratio limits to ensure that ductility is provided through ample yieldingof the prestressed reinforcement at ultimate loads.

Thus, for flexural considerations,the designer calculates a nominalmoment capacity of the prestressedsection by estimating a final level of

Fig. 2. Whittemore points mounted on transfer length specimen.

78 PCI JOURNAL

Table 1. Single-strand beam parameters.stress that will be achieved by thestrand (f). Based on the estimate off5 the designer calculates a development length (La) by Eq. (2). Acheck is then made to ensure that thestrand will have a large enough embedment length (Le) in the concreteto obtain the estimated stress atnominal capacity (J).

The embedment length is defined asthe bonded length of the prestressedstrand from the beginning of bond tothe critical section. In most design applications, and in the literature, thecritical section is interpreted as thepoint of maximum moment.6ACT Section 12.10.2 states that “critical sections for development of reinforcement in flexural members are at pointsof maximum stress and at pointswithin the span where adjacent reinforcement terminates...” Both the ACTand AASHTO Codes imply that if theembedment length is greater than thedevelopment length (Le > Ld), then thebeam should be able to reach its nominal moment capacity in the absence ofshear failure.

Conversely, if the embedmentlength is less than the developmentlength (Le < La), then bond failuremay occur prior to the beam reaching its nominal moment capacity andthe design is unsatisfactory. However, research has shown that bondfailures may still occur when (Le >Ld) if web shear cracking occurs andpropagates into the transfer zone.Russell and Burns6 recommendeddesign procedures which take thisinto consideration when normalweight concrete is used.

TEST PROGRAMWhile considerable research has

been published on the experimentaldetermination of transfer and development lengths in members utilizingnormal weight concrete, with emphasis on structural behavior and implications for design, similar work formembers made of semi-lightweightconcrete is essentially absent fromthe literature. Therefore, the initialobjective of this experimental program was to determine the transferand development length of prestressed strand in semi-lightweightgirders, and to assess the adequacy of

Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; I psi = 0.006895 MPa.

current code provisions for the designof such members.

Measurement of Transfer Lengths

Transfer lengths were experimentally determined by measuring concrete surface strains at the ends of testspecimens. Stainless-steel points weresecured to the specimens at 2 in. (51mm) spacings prior to detensioningthe strands. The points were mountedusing a five-minute epoxy and werelocated at the depth of the strand.

Distances were measured betweenpoints using a Whittemore gauge thathad a 10 in. (254 mm) gauge lengthand had a differential reading capability of 1/i000 in. (0.00254 mm), with aperceived accuracy of twice thisamount. Therefore, the resolution ofthe gauge was about 20 ire. Surfacestrain readings were taken prior to detensioning, immediately after detensioning, and periodically during thefirst month after stripping.

Two specimens were fabricatedspecifically for measuring transferlengths. These specimens had a crosssection that measured 4 x 6 in. (100 x150 mm) and contained two concentricstrands. One of the specimens contained “A” strands while the otherspecimen contained “B” strands. Whittemore readings were taken on bothsides and at both ends of each specimen, which was approximately 7 ft10’/2 in. (2400 mm) long. Fig. 2 showsthe Whittemore points mounted on oneof the transfer length specimens.

Evaluation of Development Lengths

Development lengths must be evaluated, rather than determined, in experimental programs. This is typically doneusing test specimens that are loadedsuch that the maximum moment occursat the point in the beam where the provided embedment length Le is equal tothe calculated development length L.

This point is commonly referred to asthe “critical section.”

Development length evaluation inthis experimental program consisted oftesting six single-strand specimens andsix multiple-strand specimens. Thespecimens in this investigation hadfully-bonded straight strands and weretested by applying loads from a hydraulic actuator that was located at adistance Ld from the end of the specimen. Loads were applied incrementallyuntil failure of the members occurred.

Interpretation of the test results isstraightforward. A flexural failure indicates that the embedment length isadequate to develop the strand, while abond failure indicates that the embedment length is not sufficient and thatthe actual development length is largerthan the calculated value.

Calculation of DevelopmentLengths for Test Specimens

The ACT and AASHTO development length equation [Eq. (2)] considers the development length to be afunction of three variables, namely:

fse effective stress in strand after alllosses (ksi)

db: nominal diameter of strand ininches

f5: stress in strand at nominalstrength of member (ksi)

Thus, the code-prescribed development length is not a single value thatcan be evaluated for a given strand. Instead, it is a function of both the strandproperties and the properties of themember in which it is cast. Interestingly, for a given strand size and member geometry, the development lengthmay be calculated to be different valuesby different designers, depending onthe assumptions which are made in calculating fse and f. From Eq. (2), it canbe seen that the calculated developmentlength is largest whenf is maximizedandfe is minimized.

Number of Strand Embedment Concrete Strandbeams producer length strength size

3 A_ 6ftl’/2in. psi /2 ispeciaI

3 B 6 ft 1/2 in. 7000 psi ‘/2 in. special

September-October 2000 79

Test at “Short” End

Fig. 3. Cross section of single-stranddevelopment length beams. Fig. 4. Loading arrangement for the single-strand beams.

In other words, if the designer overestimates f while underestimating(i.e., by overestimating prestresslosses), then the calculated development length will be “longest.” Whilethere may be other implications on design (i.e., member sizing, stress andcamber calculations, etc.), the result ofcalculating excessively long development lengths (in terms of actual bondperformance) is conservative since itwill result in longer required embedment lengths.

However, the opposite case may notbe true. If the designer underestimatesf while at the same time overestimating fse (by underestimating prestresslosses), then the calculated development length will be minimized. Thiscalculation will, in turn, lead to shorterrequired embedment lengths and lessconservative designs (since bond failure could occur if the actual development length is larger than the providedembedment length).

Since this research was aimed atevaluating the validity of the currentcode equations for developmentlengths when semi-lightweight concrete is used, it was determined thatthe “worst-case” scenario should betested. With this in mind, the experimental tests in this study were designed so that the “shortest” development lengths that might realistically becalculated by designers would betested.

As noted above, the “shortest” development lengths are calculated when

f is minimized and fse is maximized.The stress in the strand at nominalstrength of the member, f, is typically estimated by either direct calculation from code equations or by astrain compatibility analysis. Whilethe strain compatibility analysis isgenerally considered to be more accurate, especially when more than onelayer of steel is provided, the codeequations typically yield a lower estimate off.

Using the ACT Code,5 the stress inthe strand at member nominal capacitymay be estimated by the equations inSection 18.7.2 of the Code. For members with bonded prestressing tendonsand no compression reinforcement, theformula forf reduces to:

l’ F f11fPs=fPu{1[P “ii

where

f = specified tensile strength ofprestressed tendons in ksifactor for the type of prestressing tendon used (= 0.28 forlow-relaxation strand)

f3j = factor used to enable ultimateflexural capacity calculationsto be made by representing theconcrete in compression by anequivalent rectangular stressblock

pt,, = ratio of prestressed reinforcement = AIbd, where isthe area of the prestressed re

Six single-strand developmentlength specimens were fabricated andtested in this investigation. The purpose of the single-strand specimenswas to provide an economical meansto conduct multiple developmentlength tests with the same concreteand strand supplier combinations.Table 1 lists the concrete and strandparameters of the single-strand testbeams.

The single-strand beams were usedfor two development length tests each— one test per end. Shear reinforcement was provided only in the central

2 Layers of Mesh (Center Region Only)

1/2-Special (13.3 mm)270 ksi (1860 MPa) Strand

Test at “Long” End

5-6(4725 mm)

inforcement in the tensionzone, b is the width of thecompression face of the member, and d is the distance fromthe extreme compression fiberto the centroid of the prestressed reinforcement

= specified compressive strengthof concrete in ksi

Thus, in order to test the most severe condition, the stress in thestrand at nominal capacity of the testspecimens was calculated using Eq.(3). In addition, the effective prestress after all losses, f, was calculated by assuming only 8 percenttotal losses. This value was also usedby Logan3 and is a practical minimum value that might be calculatedby design engineers.

(3) Single-StrandDevelopment Length Specimens

80 PCI JOURNAL

portion of the beams to ensure that thisregion would be intact after the firstend of the beam was tested. The central portion of the beam was part ofthe loaded span for the testing of bothends of the single-strand beams.

The shear reinforcement in the center region of the beams was purposefully not centered in the beam. Thiswas done to provide the ability to increase the embedment length at oneend of the test specimens in the eventthat initial beam tests based on the calculated development lengths wouldexperience bond failure.

The nomenclature used for the single-strand specimens is the following:“[Concrete Strength & Type]- [StrandTypej-[Beam # within Seriesj[TestEnd]”

Thus, the name “7SLW-A-2L”would refer to a test specimen utilizing 7000 psi Semi-LightWeight concrete that had a single /2 in. special(13.3 mm) strand produced by Manufacturer “A”, and was the test at the“Long” end of specimen number(of 3). The “long” end refers to thebeam end with the greatest distance tothe shear reinforcement located in thecentral region.

Although all of the developmentlength beams in this study containedsemi-lightweight concrete, the studywas carried out concurrently with another study that utilized normalweight concrete. Therefore, the term“SLW” was (unnecessarily) used inthe naming of all specimens in thisstudy. All of the test data presented inthis paper are from prestressed beamswith a design concrete strength of7000 psi (48 MPa).

The single-strand specimens had a rectangular cross section measuring 8 x 12 in.(200 x 305 mm), and contained a singleprestressing strand located at a depth dof 10 in. (255 mm) (see Fig. 3). Thewidth of 8 in. (200 mm) was slightlylarger than the 6’12 in. (165 mm) widthused by Logan3 for his single-strandspecimens, in order to minimize thedepth of concrete in compression andmaximize the strain in the prestressedstrand at the ultimate flexural capacityof the specimens. The increased specimen width was needed because /2 in.special (13.3 mm) diameter strandswere tested in this study, whereas

Logan tested specimens containing ‘/2in. (12.7 nmi) diameter strands.

Using the 8 in. (200 mm) width, thestrain in the strands at nominal flexuralcapacity of the test beams in Table 1was estimated at 2.7 percent based on astrain compatibility analysis. Althoughthis value was lower than the 3.5 percent value recommended by Buckner9for minimum strand strains in development length specimens, it was largerthan the 2.0 percent value calculatedby Logan for his single-strand beamsthat failed by strand rupture.

Fig. 4 shows the loading arrangements corresponding to the 7000 psi(48 MPa) singlëstrand rectangularbeams. Loads were incrementally applied to the beams using a hydraulicram powered by an electronically controlled power unit. Values of load, deflection at the applied load, and strandslip at the beam end were recordedthroughout the entire loading sequenceof all 12 tests (two tests per beam forsix beams). Fig. 5 shows the test setupused for the single-strand beam tests.

Fig. 5.Test setup forsingle-strandbeams.

Multiple-StrandDevelopment Length Specimens

The purpose of the single-strandspecimens in this investigation was toprovide an inexpensive means to conduct numerous development lengthtests on beams having the same concrete and strand supplier combination. To study the effect of multiplestrands (at close spacing) on development length, full-scale specimenscontaining multiple strands weretested in addition to the six single-strand specimens. These specimenswere designed based on the analysisof test data from the single-strandrectangular specimens.

Results from tests on single-strandspecimens indicated that the currentACT and AASHTO equations wereappropriate for use with semi-lightweight concrete. Therefore, thefirst group of three multiple strandspecimens was designed with an embedment length based on the currentcode provisions. These specimenseach contained five bottom strands

September-October 2000 81

and had a T-shaped cross section withan overall depth of 21 in. (535 mm)and a compression flange width of 36in. (915 mm) (see Fig. 6).

Two of the three T-beam specimenscontained 1/2 in. special (13.3 mm) diameter “A” strands while the third T

beam had a similar strand pattern bututilized “B” strands. All three Tbeams had a design compressivestrength of 7000 psi (48 MPa). Thisinitial group of three specimens werecast at the same time and in the sameprestressing bed (see Fig. 7).

This was enabled by splicing all fivestrands in the span between the bulkheads of the beams using “A” and “B”strands (see Fig. 8). Splicing of thestrands ensured that all beams had thesame initial tension in the strands.These beams are referred to as TBeam Al, T-Beam A2, and T-Beam B(see Table 2).

Unlike the single-strand specimens,which were each tested at both ends,the multiple-strand T-beams were designed with a length that was approximately equal to twice the calculateddevelopment length, so that a pointload applied at midspan would effectively test the anchorage at both endssimultaneously. The actual length ofthe T-beams was 6 in. (150 mm)longer than twice the calculated development length, because the load wasapplied to the beam through a 6 in.(150 mm) wide steel plate.

This beam length increase ensuredthat the length of embedment of thestrand (from the free end of the beam tothe edge of the loading plate) coincidedwith the development length calculatedbased on the principles discussed earlierin this paper. Fig. 9 shows the dimensions and loading arrangement for themulti-strand T-beams.

Design of shear reinforcement usingboth the AASHTO and ACI Code provisions showed that #4 (13 mm) stirrups at 15 in. (305 mm) spacingswould provide sufficient shear reinforcement for all T-beams in thisstudy. However, the transverse reinforcement provided in T-beams Al,A2, and B was #4 (13 mm) stirrups at6 in. (150 mm) spacings, or more thantwice the code-required amount. Fig.10 shows the vertical stirrup spacingfor the first group of three T-beams.

The T-beams were tested in the Kettelhut Structural Engineering Laboratory at Purdue University. Loads wereincrementally applied to the beamsthrough a 6 in. wide x 24 in. long (150x 610 mm) steel plate using a 220 kip(978 kN) capacity MTS hydraulic actuator. Values of load, midspan deflection, and strand slip for all five strandsat both ends of the beam wererecorded during the testing of each Tbeam. Figs. 11 and 12 show the testsetup and strand slip measuring deviceused for the multi-strand T-beams.

(1) 1/2-Special (13.3 mm) strand to controlstresses @ release. This strand was bonded only

emberends and was cut prior to testing.

Fig. 6. Cross section of multi-strand T-beams.

Fig. 7. The T-beams were cast end-to-end so that the strand jacking force for eachbeam was identical.

82 PCI JOURNAL

Importance of Stirrup Spacing onLongitudinal Steel Stress

The results of the developmentlength tests will be presented later inthis paper. However, some of the findings are mentioned at this point because they affected the fabrication ofthe second group of three T-beamspecimens.

T-Beam B experienced bond failureprior to reaching the nominal momentcapacity. A careful review of a videotape of this load test (in slow motion)showed that an inclined flexure-shearcrack occurred immediately prior tostrand slip and subsequent web-shearcracking. It has been observed° thatthe initiation of inclined cracks in sim

ply supported beams will cause an increase in the tension demand closer tothe support.

The ACT Code accounts for this tension force shift in flexural memberswith non-prestressed reinforcement(ACI 12.10.3) by requiring that longitudinal bars in tension be extended fora distance equal to the effective depthof the member beyond the point wherethey are required to resist flexure.

The behavior of T-Beam B suggested that this shift in tension demand in the prestressed reinforcementresulted in a bond failure. This observed behavior also suggests that the“critical section” for prestressed concrete members referred to in ACI12.9.1 may not correspond to the location of the maximum moment, butrather a section at some distancecloser to the free end of the strand.This hypothesis is discussed in the following paragraphs.

Fig. 13 shows an idealized bilinearrepresentation of the stress capacity inbonded prestressed tendons versus thedistance from the free end of thestrand. For the T-beam specimens, development length tests were conductedso that the maximum stress in thestrands (f) was produced at a distance from the end of the beam thatwas equal to the ACI prescribed development length Ld.

In Fig. 13, the stress in the prestressed concrete strand must liebelow the bilinear curve at all locations in order for bond requirements tobe satisfied. Note that at a distance (x)closer to the free end from the devel

opment length (Ld), the maximum permissible stress in the strand is equal to(f2-4f).

Fig. 14 (from MacGregor10)showsthe internal forces in a cracked beamwithout stirrups. For wide cracks, theaggregate interlocking force V0 disap

Fig. 8.Splicing of “A” and“B” strands betweenT-Beams.

pears, along with Vd, V, and Ci’, andT2 = T1. In other words, the inclinedcrack has made the tensile force atPoint C a function of the moment atSection A-B-D-E,’° and Point C cannow be assumed to be the “criticalsection.”

Table 2. Multi-strand T-beam parameters.

Strand Embedment Concrete StrandT-beam producer length strength size

Al A 6 ft 11/2 in 7000 psi ‘/2 in special

‘‘ A2 ‘‘ A 6ftl’/2in. 7000psi V2in.special

B B 6 ft 1’/2 in. 7000 /2 in. special

Note: I in. = 25.4 mm; 1 ft = 0.305 m; 1 psi = 0.006895 MPa.

Fig. 9. Loading arrangement for multi-strand T-beams.

12-6” (3800 mm) Longitudinal Bar I111111111 liii 1111111 liii III

3” jj 24 Spaces @6(152 mzn)= 12-0” (3650 mm)(75 mm) (75 mm)Fig. 10. Spacing of transverse reinforcement for T-Beams Al, A2, and B.

September-October 2000 83

ends of the I-beams.

For a beam without stirrups, havingits nominal moment capacity (and corresponding stress f) demanded at adistance (Ld) from the free end of thestrand, the onset of flexure-shearcracking will produce a strand stress(at the crack location) that lies abovethe bilinear curve in Fig. 13. If theACT expression for strand development length represents the actuallength required to develop the strandstress (J) corresponding to nominalcapacity for the beam, then inclinedcracking may lead to bond failure.

Fig. 15 (from MacGregor10)showsthe internal forces in a cracked beamwith stirrups. In this case, the presenceof stirrups will ensure that there willalways be a compression force C] anda shear force V acting on the part ofthe beam below the crack, and therefore T2 will be less than T1. However,even though the tension force at PointC will be less than the tension at Section A-B-D-E, the strand stress maystill lie above the bilinear curve in Fig.13 and failure by bond can still occur.

The ACT Commentary to Section12.10.3 notes that “A diagonal tensioncrack in a flexural member withoutstirrups may shift the location of thecalculated tensile stress approximatelya distance d towards a point of zeromoment. When stirrups are provided,this effect is less severe, although stillpresent to some extent.” Thus, if aflexure-shear crack forms, some degree of shift in the location of maximum tensile stress will occur.

Fig. 13 illustrates that a change instrand stress of (4/) equal to (xldb) ksi

must occur over the distance x fromthe point of maximum moment so thatthe strand stress (at distance x from themaximum moment) will not lie abovethe bilinear curve. Therefore, when aninclined crack occurs, extending fromthe point of maximum moment to apoint “x” closer to the free end of thestrand, a reduction in strand stress of(x/db) ksi must occur over the horizontal projection of the crack to preclude

bond failure. This can be accomplished by providing extra transversereinforcement across the crack.

The amount of required transversereinforcement to cause the appropriatereduction in strand stress may be estimated using the model in Fig. 16. Thismodel, which assumes the inclinedcrack can be represented by a linearcrack, is the basis for the calculationof required transverse reinforcement

Fig. 11. Test setup for development length evaluation of Fig. 12. LVDT’s were used to measure the strand slip at bothT-beams.

I;

I(fp —f,)d,

From Figure, f, f,Af

Slope f—f = 1x

— Therefore, 4f (SIope)x) = —(fp,f,.)db 4

Fig. 13. Bilinear variation of steel stress with distance from free end of strand.

84 PCI JOURNAL

A

Fig. 16. Calculation of transverse reinforcement required to reduce the tension force across an inclined crack by the amount T.

D

Vay)Ø Va

Vdt7

T2 = = = -=. = =E

Fig. 14. Internal forces in a cracked beam without stirrups. Fig. 15. Internal forces in a cracked beam with stirrups.

•1“

v,c.z

r2 =

Left Free-Body Diaeram

jd

Rieht Free-Body Diagram

T, =7; —AT

Model Assumptions:

• The flexure-shear crack can be represented by a linear crack as shown.• Dowel action is conservatively ignored.• The weight of the beam is negligible.• The line of action of the sum of all aggregate-interlock forces (J’,) passes approximately through

point 0. Therefore, the moment due to this force about point 0 is small and can be ignored.

The force in the stirrups crossing the crack can be determined by summing moments about point 0.

M,,=0 Solving... V= 2A,,jd

Therefore, Afrv= 2A,jd

_

Assuming all stirrups crossing the crack are yielding, then the force in the stirrups (Vs) is equal to the totalarea of the stirrups (A.,) multiplied the yield stress (f;.,).

For the 7000 psi (48 MPa) T-beams...

A2AJd

A,,., = (5)(0.167) = 0.835 sq in.a = /Jjc = 0.987 in. --from flexural analysis of sectionjd=d-a/2 19—(0.987)/2 18.51 in.f., = 60 ksici,, = 0.522 in. -- for 1/2-Special strand

2(0.835)(l 8.5 1)=0.99 sq in.(640 sq mm)A,

= (60)(0.522)

Therefore, using #4 (13mm) stirrups (A = 0.40 in2/stirrup), 3 stirrups are required to cross the crack.

September-October 2000 85

(also in Fig. 16). This calculation indicates that, for T-Beam B, at least three#4 (13 mm) stirrups would haveneeded to cross the diagonal crack inorder to cause the appropriate reduction in strand stress and preclude possible bond failure. A post-failure inspection of T-Beam B indicated thatonly one (or perhaps two) stirrupcrossed the inclined crack that preceded failure.

Second Group ofAdditional Three T-Beams

Based on the observed behavior(flexure-shear cracking followed bybond failure) of T-Beam B, three additional 7 ksi (48 MPa) T-beam specimens were fabricated and tested inthis experimental program. These Tbeams each contained strand fromProducer “B” and were identical inlength, cross section, and longitudinalreinforcement to the other three Tbeams presented in this paper. However, the three additional specimens

differed from the original three Tbeams in the amount of transverse reinforcement near midspan. Fig. 17shows the varying amounts of transverse reinforcement used in the additional three T-beams.

One T-beam had #4 (13 mm) stirrups at 6 in. (152 mm) on centerthroughout its entire length. The stirrup spacing in this beam was identicalto the spacing in T-Beam B (thatfailed by bond). A second T-beam had#4 (13 mm) stirrups at 3 in. (75 mm)on center in the middle portion andwas used to test the hypothesis ex

plained in the previous paragraphs,namely, that increased stirrup spacingcan reduce the tension shift that supposedly resulted in bond failure of TBeam B.

The third additional T-beam had #4(13 mm) stirrups at 15 in. (375 mm)on center in the middle portion of thebeam. This corresponded to the ACICode-required amount of transversereinforcement for shear. The additional three T-beams were cast end-to-end, as in Fig. 7, which ensured thatthey each had identical levels of pre

The reinforcement in the flanges ofthe additional T-beams was similar tothat in the original three T-beams.Table 3 lists the parameters of the additional three T-beams.

TEST RESULTSPresented below is a summary of

the strand pullout, strand surface condition, strand transfer length, and single-strand and multi-strand development length test results.

Pullout Test Results

The pullout specimen was cast andtested at two days and at four days. Thestrands were pulled out of the blockusing a hydraulic ram furnished byCSR Hydro-Conduit. The load wasrecorded using a load cell that wasplaced between two steel plates. Thelower plate had two steel angles weldedto the bottom side to allow the samecontact area with the concrete blockthat was specified by Logan.3 Fig. 18shows the load cell configuration usedto detennine the pullout values.

The maximum load occurring duringa given pullout test was stored automatically by a data acquisition system.Also, the load at “first slip” was ob

-- 12-6’ (3800 mm) Longitudinal Bar

III I liii 11111111111111111 U3” 3”24 Spaces @ 6” (152 mm) = 12-0” (3650 mm)

4.I•(75 mm) (75 mm)

Vertical Stirrup Spacing For T-Beam B-6”

12-6” (3800 mm) Longitudinal Bar

111111 IIIIIIIIIIIIIIIIIIIIIIIIIIIII 1111113” 5 Spaces @ 28 Spaces @ 3” (75 mm) 5 Spaces @ 3”

(75 mm) 6” (155 mm) 6” (155 mm) (75 mm)

Vertical Stirrup Spacing For T-Beam B-3

stress.

12-6” (3800 mm) Longitudinal Bar

1111111111 I I 1111111

1114 Spa. 1 6 Spaces 15” (375 mm) Spa. @1114’ 6” 6” ‘; (155mm) (155mm)

3” (75 mm) 3” (75 mm)

Vertical Stirrup Spacing For T-Beam B-15”

Fig. 17. Vertical stirrup detailing for the three additional T-beams.

Table 3. Parameters of additional three T-beams.

T-beam Strand Embedment Concrete Strandname producer length strength size

B-3” B 6 ft 1V2 in. 7000 psi 1/2 in. special

B-6” B 6 ft 1’/z in. 7000 psi f in. special

B-15” B 6 ft 1/2 in. 7000 psi /2 in. special

Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; 1 psi = 0.006895 MPa.

86 PCI JOURNAL

Fig. 18.Load cell arrangement used to

measure pullout force..

tamed by placing a small piece of tapeon the strand at the point where it entered the concrete. As soon as a motionof the tape was detected, the corresponding value of load was recorded.

Tables 4 and 5 show the pulloutloads and “first slip” values, whileFig. 19 shows the positioning of thestrands in the pullout specimen. As indicated, the average pullout capacityfor each strand type tested exceededthe minimum value of 37.6 kips (167kN), indicating that the bond qualityof both strands was acceptable. Tables4 and 5 show that the pullout and first-slip values were slightly higher at fourdays than at two days, as expected,due to the higher concrete strength andpresumed higher modulus of elasticity.These tables also show that, althoughboth strands had similar ultimate pullout capacities, the “B” strand began toslip at a significantly lower load.

Surface ConditionAssessment Results

From the beginning of this study itwas noted by several observers thatthe two 1/2 in. special (13.3 mm)strands used had a markedly differentappearance. The “A” strand had abluish hue about it that might best bedescribed as a “gun-steel blue” color.The “B” strand, on the other hand, hada yellow/brassy tint.

Prior to casting the pullout specimens, the strand samples were wipedwith a paper towel to remove residueand help assist in the visual assessment. Fig. 20 shows the towels used towipe the strands for the pullout specimen. This figure shows there is a distinct difference between the residue on

the strands. The towels from the “B”strands have considerably more noticeable residue than those corresponding to the “A” strands.

In performing the towel wipes, itwas noted that it was easier to wipe

the “B” strands than the “A” strands,as there was much more of a tendency to bind or tear the towels onthe “A” strands when applying equalpressure. In general, the residue corresponding to the “A” strands wasbrown or rust colored while theresidue corresponding to the “B”strands was black. The chemicalcomposition of this residue was notdetermined.

It should be noted that all “towelwipes” in this study were performedby the same person. Also, the twostrand rolls in this study (one roll of“A” strand and one roll of “B” strand)were placed indoors when they werereceived from the producers in an attempt to minimize weathering duringthe course of the study. Both strandrolls were received at the precastingplant during the summer of 1997.

two days (concrete compressiveTable 4. Results from pullout tests atstrength was 4800 psi).

Strand “A” Strand “B”---.-...--.-- —-.------

Strand Max. pullout Load at Strand - Max. pullout Load at

designation force (Ib) first slip (Ib) designation force (Ib) first slip (Ib)

A-9 36,450 31,300 B-9 38,450 20,800

A-8 37,300 29,500 B-8 38,000 16,200

A-7 41,000 32,000 B-7 38,800 15,100

A-6 41,000 36,000 B-6 37,800 19,100

Average 38,940 32,200 Average 38,260 17,800

Std. Dev. 2,080 2,380 Std. Dev. 390 2,270

Note: 1 lb = 4.448 N; 1 psi = 0.006895 MPa.

Table 5. Results from pullout tests at four days (concrete compressivestrength was 5200 psi).

Strand “A” Strand “B”

Strand Max. pullout Load at Strand Max. pullout Load at

designation force (Ib) first slip (ib) designation force (Ib) first slip (lb)---.--- -.---

A-S 39,350 33,800 B-S 42,700 20,900

A-4 41,450 31,600 B-4 38.000 19,200

A-3 43,200 36,700 B-3 40,550 23,200

A-2 42,450 41,600 B-2 38.550 22,000

A-i 41,100 37.200 B-I 37,450 . 22,900

Average 41,510 36,180 Average 39.450 21,640

Std. Dev. 1.3 10 3,390 Std. Dev. - 1,933 1,460

Note: 1 lb = 4.448 N; 1 psi = 0.006895 MPa.

September-October 2000 87

Transfer LengthMeasurement Results

Values of surface strains were mea

sured on specimens similar to those in

Fig. 2. The transfer length can then be

inferred directly from the recorded

values of strain. For a concentrically

prestressed member supported along

the entire length, such as the one in

Fig. 2, the member will be under sim

pie axial loading when the prestress

force is transferred to the concrete.

Thus, the compressive stresses (and

hence strains) in the member will vary

from zero at the free end to a near-

constant value corresponding to the

“P/A” stress. The length it takes forthe strand to bond to the concrete and

“transfer” the full tension in the ten

don to the concrete is called the trans

fer length.

Fig. 21 shows the results of surface

strain measurements taken for the

7000 psi (48 MPa) SLW transfer-

length specimen with two ‘/2 in. spe

cial (13.3 mm) “B” strands. Results

from the specimen containing “A”

strands were similar. Measurements

were taken immediately after transfer

of prestress, and at 3, 14, 36, and 66

—— I—-

— I—.— At Transfer of Prestress I

—U— 3 Days After Transfer

—*- 14 Days After Transfer -

—.— 36 Days After Transfer

ysAfterTransfer,

‘•...._ I

Fig. 21. Surface strains for ‘/2 in-Special (13.3 mm) “B” strand in transfer-length specimens. Note: 1 in. = 25.4 mm.

88

A-I0

B-20

A-30

B-40

A-50

8-60

A-70

B-80

0

B-I

A-90

0

A-2

Fig. 19. Positioning of strands in pullout specimen.

0

B-30

A-40

B-50

A-60

B-70

A-S0

B-9

Fig. 20. Towels used to wipe strands before placing them in pullout specimen.

0 20 40 60 80 1000

-200

-400

-600

_________________________________

-800

______

-1000

-1200

-1400

-1600

-1800

Distance Along Beam (in.)

PCI JOURNAL

Table 6. Results from the single-strand rectangular beam tests.days thereafter. The vertical dashedlines are drawn at the approximatebreaks between the “sloping” portionof the curves where strains are increasing and at the “flat” portion corresponding to the region under constant stress of P/A. The distance fromthe end of the transfer length specimento the dashed line is the transferlength.

Results from both transfer lengthspecimens indicated that the measuredtransfer lengths were less than 50strand diameters (the amount suggested by both AASHTO and ACTwhen checking shear provisions) except in the case of one end wheresplitting of the concrete was noted. Inthis case, the measured transfer lengthwas close to 70 strand diameters.

Single-StrandDevelopment LengthTest Results

A total of twelve single-strand development length tests were conductedin this study (six beams tested at bothends). As discussed previously, thesingle-strand beam specimens provided a cost effective means of conducting several load tests. The failureloads and deflections corresponding tothe maximum sustained load areshown in Table 6.

Table 6 shows the test results for thesingle-strand rectangular beams containing “A” and “B” strands. Thistable lists the maximum moment inthe beams, occurring at a distance Ldfrom the end of the beam and determined from the measured values ofapplied load. In every case, the maximum moment exceeded the AASHTOnominal moment capacity (Ma), indicating the beams’ strands were adequately developed at the point of maximum moment (which occurred at adistance equal to the code-prescribeddevelopment length Ld from the beamend).

This finding is consistent with theresults from measurements of strandend-slip during testing, which revealedthat slip did not occur in all but onespecimen, namely, 7SLW-A-1S. Inthis specimen. a strand slip of 0.051in. (1.3 mm) was recorded on the datascan prior to failure. However, thisminimal slip occurred after the nomi

nal moment capacity had been exceeded by over 10 percent.

Table 6 also indicates that all failures occurred after considerable deflections had occurred. Each of the7000 psi (48 MPa) beams deflectedmore than l’/2 in. (40 mm) in a 15 ft3 in. (4.65 m) span prior to reachingits ultimate capacity. Nine of thetwelve beams failed in flexure whenthe strands ruptured. The other threespecimens failed in shear.

While these shear failures occurredwhen the shear stress on the section(V/bd) was less than 92 psi (631MPa), or 1.1 they occurred wellafter yielding of the prestressing steelhad occurred and after considerableductility had been exhibited. It is possible that when the prestressing steelyielded, the effects of dowel action diminished and the lightly reinforcedbeams (without stirrups) became susceptible to shear.

Tn summary, test results from thetwelve single-strand developmentlength specimens indicated that thecode-required development lengthswere sufficient to develop the capacityof a single prestressed strand in amember cast with 7000 psi (48 MPa)semi-lightweight (SLW) concrete.Therefore, as previously mentioned,

the T-beam specimens containingmultiple strands were also designedusing the ACT and AASHTO development length expressions.

Development LengthTest Results on Multi-StrandT-Beams

Table 7 summarizes the test data, including the failure load, deflectioncorresponding to the maximum sustained load, and maximum momentfor each T-beam. The first group ofthree T-beam specimens cast, namely,T-Beams Al, A2 and B were identicalin detail. Table 7 shows that both Tbeams containing “A” strands (Al andA2) exceeded the AASHTO nominalmoment capacity for the section andfailed by strand rupture. Thus, theAASHTO and ACT developmentlength expressions were conservativefor these beams.

Both of these failures were ductile,as midspan deflections exceeded 1 3/tin. (36 mm) prior to the ultimate capacity being attained. T-Beam B hadessentially the same ultimate capacityas T-Beam Al of 120.5 kips (536 kN).Interestingly, though, this load corresponded to a much lower deflectionfor the B beam [0.82 in. versus 2.02

Max. load Max. moment* Deflection at max.Beam (Ib) (kip-ft) load (in.)

7SLW-A-1 S 10,740

7SLW-A-IL 10,370

40.0

39.8

Failure mode

7SLW-A-2S

7SLWA-2L

2.1 Shear

3.1 Shear

10,600 39.5 2.7- — ——---—

— _ff_____________ -— —-

10,000 38.5 >3.0

7SLW-A-3S 10,540 39.2

7SLW-A-3L

7SLW-B- IS

Flexure — Strand rupture

Flexure — Strand rupture

10,350

11,000

39.8

2.6

2.4

7SLW-B-IL 10,680

7SLW-B-2S 10,980

40.9 2.2

40.9 >3.0

Flexure — Strand rupture

Flexure — Strand rupture

Flexure — Strand rupture

Flexure — Strand rupture

7SLW-B-2L

7SLW-B-3S 11,180

7SLW-B-3L 10,350

40.8 1.7 Flexure Strand rupture

10,530 40.4 2.6 Shear, then Strand rupture

41.5

39.7

2.0

2.9

Note: 1 lb=4.448 N; I kip-ft= 1.357 kN-m; 1 in. = 25.4 mm.*AASHTO Nominal Moment capacity (M,) = 34.6 kip-ft (J = 260 ksi).

Flexure — Strand rupture

Flexure — Strand rupture

September-October 2000 89

Table 7. Results from the multi-strand T-beam tests.

Note: 1 lb =4.448 N; I kip-ft= 1.357 kN-m; 1 in. =25.4 mm.*AASHTO Nominal Moment Capacity (LVI,,) = 340.3 kip-ft.

in. (20 mm versus 51 mm)] and itfailed by bond, as the strands slippedwith respect to the surrounding concrete and pulled in from the end of thebeam (see Fig. 22).

After reviewing videotape of thefailure of T-Beam B, the investigators

Fig. 22.Strands pulled infrom the ends of

T-Beam B.

noted that a flexure-shear crack developed just prior to collapse (seeFig. 23). This observation led to thehypothesis that the flexure-shearcrack caused an increase in tensionnearer the beam end and effectivelyshifted the “critical section” from the

section at the point load to the placewhere the flexure-shear crack intersected the strand. This was discussedearlier in this paper.

It is important to note that the cracking that occurred in T-Beam B prior tofailure was not dissimilar to the crackpatterns that developed in T-BeamsAl and A2, yet significantly differentmodes of failure occurred. It is likely(based partly on pullout specimen behavior and towel-wipe tests) that thebond quality of the “A” strand maycause it to develop over a shorter distance than the equivalent-sized “B”strand.

If this were true, then a flexureshear crack which shifts the tensiondemand closer to the support may notbe critical in the case where “A”strand was used. In general, this tension shift would only lead to suddencollapse upon cracking if the actualdistance required to develop a strandlies between the point of maximummoment and the point where the diagonal crack intersects the strand.

In order to test the hypothesis outlined above, three additional 7000 psi(48 MPa) T-beam specimens utilizing1/2 in. special (13.3 mm) “B” strandwere fabricated and tested, each having the same dimensions and test configuration as the original three Tbeams. Table 7 shows the results fromthe additional three 7000 psi (48 MPa)T-beam tests.

T-Beam B-6” was tested first. Thisbeam had a constant 6 in. (152 mm)stirrup spacing which was identical tothat in T-Beam B. As Table 7 indicates, T-Beam B-6” failed bybond/shear at a load of 110.0 kips(489.2 kN), corresponding to 97.6 percent of the AASHTO nominal momentcapacity for the section. Strand slipdata showed that all strands had smallvalues of slip prior to reaching themaximum sustained load.

At the time of failure, the load washeld constant and crack patterns werebeing recorded. Therefore, it is likelythat additional slip of the strands occurred during the time period whenthe load was held constant (but end-slip readings were not continuouslyrecorded). While it cannot be proven,it is plausible that additional slip of thestrands resulted in a reduced prestress

MaximumT-beam load (kips)

Al 120.5

A2 124.0

B

Maximum Deflection atmoment* max. load (in.) Failure mode

362.9 2.02 Flexure — Strand rupture

373.1 1.42 Flexure — Strand rupture

120.5

B-3”

362.9

129.9

0.82

390.5 1.39

Bond

B-6” 110.0 332.0

B-iS” 302.6

0.31

Flexure — Strand rupture

0.24

Bond/Web shear failure

Bond/Web shear failure

Fig. 23.

_______

Flexure-shearcracking, and

subsequent splitting .in T-Beam B.

90 PCI JOURNAL

force and, therefore, a loss in shear capacity. Fig. 24 shows the failurecracks for T-Beam B-6”.

T-Beam B-3” was the next beamtested. This beam had #4 (13 mm)stirrups at 3 in. (75 mm) on center inthe middle portion of the beam. Table7 shows that this beam failed bystrand rupture at a load of 129.9 kips(577.7 kN). This load corresponded toa maximum moment in the beam thatwas 14.7 percent larger than theAASHTO nominal moment capacityfor the section.

Review of strand-slip data for thisbeam showed that slip was essentiallyzero at the time of failure. Nine of theten ends measured had a recorded slipat failure that was less than 0.001 in.(0.03 mm). The other strand had arecorded slip of 0.046 in. (0.12 mm).

T-Beam B-3” had the same strandand concrete batch used in T-BeamB-6”, which experienced bond failureat a load of only 110.0 kips (489.2kN). In other words, with stirrupsspaced at 3 in. (75 mm) on center, TBeam B-3” was able to withstand anapplied load that was 18.1 percentlarger than the failure load for TBeam B-6”. Fig. 25 shows the failurecrack and corresponding strand rupture for T-Beam B-3”.

T-Beam B-15” was the last beamtested in the series. This beam had astirrup spacing in the central regionof the beam of 15 in. (375 mm),which corresponded to the AASHTOand ACT Code minimum amount required for shear. As expected, thisbeam experienced bond/shear failureat only 100.0 kips (444.9 kN), thelowest load for all the 7000 psi (48MPa) T-beam specimens tested (seeTable 7). Fig. 26 shows the shear failure that occurred after strand slip initiated in the member.

In summary, both of the 7000 psi(48 MPa) T-beams containing “A”strand (Al and A2) experienced flexural failures (by strand rupture). Eachhad #4 (13 mm) stirrups at 6 in. (152mm) throughout the entire length ofthe beam. Three of the four T-beamsutilizing “B” strand (B, B-6”, and B-15”) experienced bond failure and, intwo cases (believed subsequent), shearfailure when loaded at a distance fromthe end of the beam equal to the

Fig. 24.Failure ofT-Beam B-6.

Fig. 25.Failureoccurred bystrand rupturein T-BeamB-3”.

Fig. 26. Failure of T-Beam B-i 5”.

September-October 2000 91

When the same combinations ofstrand and concrete were tested in themulti-stranded T-beams, however, theresults were mixed. In particular, thecombination of 1/2 in. special (13.3mm) “B” strands and a 7000 psi (48MPa) concrete mix resulted in bondfailures for three of the four T-beamspecimens tested. Two other T-beamspecimens, which had the same concrete mix and the same diameter “A”strands, resulted in flexural failures bystrand rupture.

The review of the failure of T-beamB in this study showed that the bondfailure was preceded by a flexure

This study has yielded credible evi- shear crack. It is postulated that the

dence that there is an interaction be- onset of cracking resulted in a shift of

tween the shear carried by a pre- the maximum tensile stress (i.e., the

stressed concrete member near the critical section) in the strand from the

point of maximum moment and the point of maximum moment towards

length required to sufficiently anchor the free end of the strand.

the longitudinal reinforcement. Al- Although similar crack patternsthough the findings of this study were were noted for the T-beams containingmade in the context of tests on mem- the 1/2 in. special (13.3 mm) “A”bers with semi-lightweight concrete, strands, that failed by strand rupture, itwhich typically have a lower modulus is surmised that the actual develop-of rupture and would thus be more ment length for the “A” strand maysusceptible to flexure-shear cracking, have been considerably less than thethe principles discussed herein should code value that was tested. In thisalso be applicable for members cast case, then, a shift in the “critical secwith normal weight concrete. tion” would still result in an embed-

Measurements of concrete surface ment length (to the critical section)strains indicated that the transfer that is larger than the actual develop-lengths associated with both “A” and ment length for the strand, and col“B” strand in 7000 psi (48 MPa) SLW lapse would not occur.

concrete were less than the AASHTO On the other hand, if the actual deand ACT Codes’ assumed 50 strand di- velopment length of the “B” strandameters in the absence of longitudinal was close to the code-determinedsplitting at transfer. In the end where value that was tested, then a shift insplitting occurred, the measured trans- the critical section could lead to colfer length was close to 70 strand diam- lapse. The above hypothesis is consiseters. These measurements also tent with the earlier slip measured forshowed that the transfer lengths re- the “B” strand in the Moustafa pulloutmained essentially unchanged during specimen tests.the first 60 days following transfer of To test this theory, three additionalprestress. T-beam specimens, containing the

Tests on single-stranded rectangular same concrete mix and strand combibeams and multiple-stranded T-beams nation as T-Beam B, were fabricatedrevealed that the length required to de- and tested. Each of these additional Tvelop the tensile capacity of a strand beams had different amounts of transin concrete is, in some cases, depen- verse reinforcement near midspan. Fordent on the member geometry and the T-beam with the largest amount ofloading configuration. Strand rupture transverse reinforcement at the point(associated with flexural failure) oc- of maximum moment, namely, Tcurred for both “A” and “B” strands Beam B-3”, bond failure was prewhen cast in single-strand rectangular vented (presumably by minimizing thespecimens containing 7000 psi (48 shift in the location of the critical secMPa) concrete. tion) and the mode of failure was flex-

CONCWSIONSBased on the work carried out in

this investigation, the following conclusions can be drawn:

1. Both of the 1/2 in. special (13.3mm) strands used in this study metthe requirement for minimum average pullout force (37.6 kips) according to the Moustafa procedure.Therefore, according to the Moustafatest, both strands had acceptablebond characteristics.

2. Twelve load tests on rectangularsingle-strand beams indicated that theAASHTO and ACT developmentlengths of:

Ld = (f - fse) db

provided sufficient embedment todevelop the full capacity of a singlestrand in the SLW concrete mixesused.

3. The onset of flexure-shear cracking resulted in a shift of the maximumtensile stress (i.e., the critical section)in the strand from the point of maximum moment towards the free end ofthe strand.

RECOMMENDATIONSThe following recommendations are

made based on the results of thisstudy.

1. Since a shift in the location of thecritical section may occur due to flexure-shear cracking, the authors recommend that the current AASHTO andACI requirements for strand development length be enforced at a criticalsection that is located a distance dfrom the point of maximum moment

AASHTO and ACT developmentlengths.

These failures occurred suddenly,and without much warning, at significantly smaller deflections (see Table7). Flexural failure (by strand rupture)was achieved in a T-beam using “B”strand when #4 (13 mm) stirrups wereprovided at 3 in. (75 mm) centers inthe middle portion of the beam. Thisspacing provided a stirrup area thatwas five times greater than the amountrequired by the AASHTO and ACTshear provisions.

MAJOR FINDINGS

ure by strand rupture.The amount of transverse reinforce

ment required to prevent bond failurerepresents between 2.5 to 5 times theamount required by shear design(Note: T-Beam B-6” failed by bondwhile T-Beam B-3” failed by strandrupture). While such increases in theamount of transverse reinforcementare not practical for most design situations, the designer must consider thatthe critical section may shift in theevent of inclined cracking.

92 PCI JOURNAL

towards the free end of the strand,where d1, is the distance from the extreme compression fiber to the centroid of the prestressed reinforcement.

2. For beam sections other than thepoint of maximum moment, strandanchorage should be provided so thatthe required prestress force at a givensection may be theoretically “developed” (based on linear interpolationof Fig. 13 or equivalent) at a sectionlocated a distance d from the point ofinterest towards the free end of thestrand.

3. In place of the above recommendations, the designer may elect to provide enough transverse reinforcementto minimize the shift in tensile demand that will occur in the event ofdiagonal cracking. The amount of required transverse reinforcing steelmay be calculated using the modelpresented in Fig. 16.

Discussion

Recommendations 1 and 2 may appear to be too conservative at firstglance. However, the implications formost design situations will be small. Forshallow members, the effective depth isclearly small, so checking developmentlength requirements at a small distanceof d from the current point will not beovertaxing on design. For larger members with fully bonded strands, the issueof development length is seldom a critical factor in design.

The implications for the design ofmembers containing blanketed strandsis beyond the scope of this work.However, the more stringent development check would certainly be conservative. Since the termination of blanketing is usually staggered, then a shiftin the location of maximum tensilestress may not be as critical as in thisstudy due to the inherent redundancyprovided by strands with differentdebonded regions.

Finally, the recommendation tocheck development length requirements at a distance d from the pointof interest towards the free end ofthe strand is based on the assumption that the initiating crack willhave an orientation of 45 degreeswith respect to the longitudinalmember axis. While more sophisticated models may be used to estimate the most likely crack angle(considering beam geometry and reinforcing ratios), the authors believethe simple and conservative assumption of 45 degrees is highly desirablefrom a design viewpoint.

NEED FORADDITIONAL RESEARCHSince this study involved only

bonded strand in SLW concrete, additional research would be beneficial toquantify the:

1. Effect of flexure-shear crackingon members with unbonded tendons.

2. Effect of different concretemixes, and corresponding aggregateinterlock, on the tension shift noted inthis study. The model used to calculaterequired transverse reinforcement(Fig. 16) in this paper conservativelyignored the role of aggregate interlockby assuming the resultant force passedthrough the point about which moments were summed.

ACKNOWLEDGMENTSAppreciation is expressed to the In

diana Department of Transportation(INDOT) and the Federal HighwayAdministration (FHWA) for providingfunding for this research. Specifically,INDOT personnel Tommy Nantungand Hasmukh Patel and FHWA personnel Tom Saad were key resourcepersons within these organizations.

The authors would also like tothank the personnel at CSR HydroConduit, Inc., for their support inmeeting the difficult scheduling demands of this project. Specifically,the assistance given by WilliamYoder and Rick Yoder is especiallyappreciated. In addition, the authorsare appreciative of Jon Jonsson andDr. Prasad Rangaraju for their manyhours of service in the design of theSEW concrete mix and fabrication ofthe test specimens.

Finally, the authors want to thankthe PCI JOURNAL reviewers for theirvaluable and constructive comments.

September-October 2000 93

REFERENCES

1. Zena, D., Albrecht, P., and Lane, S., “Investigation of Transferand Development Length of Lightweight Prestressed ConcreteMembers,” Federal Highway Administration (EisenhowerGrants for Research Fellowships) Preliminary Report, February 1995, 271 pp.

2. AASHTO, Standard Specifications for Highway Bridges, Sixteenth Edition, as amended by the 1998 Interim Revisions,American Association of State Highway and TransportationOfficials, Washington, DC, 1998.

3. Logan, D., “Acceptance Criteria for Bond Quality of Strandfor Pretensioned Prestressed Concrete Applications,” PCIJOURNAL, V. 42, No. 2, March-April 1997, pp. 52-79.

4. Moustafa, S., “Pull-Out Strength of Strand and Lifting Loops,”Concrete Technology Associates Technical Bulletin, 74-B5,May 1974. Available from the Precast/Prestressed Concrete Institute, Chicago, IL.

5. ACT Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACT 31 8R-99),” American Concrete Institute, Farmington Hills, MI,1999.

6. Russell, B., and Burns, N., “Design Guidelines for Transfer,Development and Debonding of Large Diameter SevenWire Strands in Pretensioned Concrete Girders,” Texas Department of Transportation in cooperation with FederalHighway Administration Research Report 1210-SF, January1993, 286 pp.

7. Kaufman, M. K., and Ramirez, J. A., “Reevaluation of the Ultimate Shear Behavior of High Strength Concrete PrestressedI-Beams,” ACI Structural Journal, V. 85, No. 3, May-June1988, pp. 295-303.

8. Peterman, R. J., Ramirez, J. A., and Olek, J., “Evaluation ofStrand Transfer and Development Lengths in PretensionedGirders with Semi-Lightweight Concrete,” Final Report, JointHighway Research Program FHWAIIN/JTRP-99/3, Washington, DC, August 1999, 183 pp.

9. Buckner, D., “A Review of Strand Development Length forPretensioned Concrete Members,” PCI JOURNAL, V. 40, No.2, March-April 1995, pp. 84-105.

10. MacGregor, J., Reinforced Concrete: Mechanics and Design(Third Edition), Prentice Hall, NJ, 1997, pp. 180-195.

APPENDIX — NOTATION

a = depth of equivalent rectangular stress block= area of prestressed reinforcment in tension zone= area of total shear reinforcement crossing crack

b width of compression face of member [calculation ofin Eq. (3)1; also, horizontal distance from beam re

action force to section of interest (see Fig. 16)C1 = resultant compressive force in concrete above inclined

crack (see Figs. 14, 15, 16)C = resultant compressive force in concrete below inclined

crack (see Figs. 14, 15, 16)

db = nominal diameter of strand (in.)d = distance from extreme compression fiber to centroid

of prestressed reinforcement

f = specified compressive strength of concrete (ksi)= stress in strand at nominal strength of member (ksi)

f = specified tensile strength of prestressed tendons (ksi)fse = effective stress in strand after all losses (ksi)

= yield strength of shear reinforcementjd = “lever arm” between resultant tension and compres

sion forces at nominal flexural capacity of sectionLd = development lengthLe = embedment lengthL = transfer lengthR = vertical reaction force at end of simply supported

beam (see Fig. 16)

Va = resultant of all aggregate interlock forces along inclined crack

V = horizontal component of aggregate interlock forcesalong inclined crack

Vay = vertical component of aggregate interlock forcesalong inclined crack

V = force in stirrups crossing crack == resultant shear force in concrete above inclined crack

(seeFigs. 14,15,16)V = resultant shear force in concrete below inclined crack

(seeFigs. 14,15,16)x = horizontal projection of inclined crack

13i = factor used to enable ultimate flexural capacity calculations to be made by representing the concrete incompression by an equivalent rectangular stress block

4f = change in strand stress along horizontal projection ofinclined crack

= change in prestress force along horizontal projectionof inclined crack

= factor for type of prestressing tendon used (= 0.28 forlow-relaxation strand)

p, = ratio of prestressed reinforcement = A/bd

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