shear behavior of unbonded post-tensioned

ACI Structural Journal/May-June 2006 409

ACI Structural Journal, V. 103, No. 3, May-June 2006.MS No. 04-309 received September 28, 2004, and reviewed under Institute publication

policies. Copyright © 2006, American Concrete Institute. All rights reserved, includingthe making of copies unless permission is obtained from the copyright proprietors. Pertinentdiscussion including author’s closure, if any, will be published in the March-April2007 ACI Structural Journal if the discussion is received by November 1, 2006.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

This work presents a study of the structural behavior of segmentalconcrete beams with external prestressing, focusing on theresponse of these structures under shear. Six tests have beenperformed on beams to evaluate their shear response and load-carrying capacity at different levels of prestressing. To obtaindesign guidelines about reinforcement detailing in such structures,the structural response under combined flexure and shear has beencarefully inspected. Moreover, to evaluate the possible benefits thatthe use of steel fiber-reinforced concrete (SFRC) could carry, testswere conducted on both conventional and SFRC elements.

Keywords: bridges; joints; strength; tension.

INTRODUCTION Prefabricated segmental concrete bridges with external

prestressing and dry joints are associated with a span-by-span construction process that is thought to be the fastestamong this type of construction process. For the constructionof each of the spans, the segments are placed one next to theother, suspended from a beam or arranged in a mobile false-work, and are assembled by means of external prestressing.In Europe, where a waterproofing layer to prevent leakage isusually applied on the top of the deck, it is not necessary toapply any epoxy resin between the joint-faces of thesegments. This was also a common practice in some states ofthe U.S. some time ago. Nevertheless, epoxy-free joints arepresently forbidden in the U.S. due to the durability problemsthat arose in some bridges. It is precisely the subject matter ofthe present work to study externally prestressed segmentalbridges with resin-free dry joints. Its most significantcharacteristic is the nonexistence of bond reinforcementcrossing the joints, neither active nor passive. The firstexample of application constructed is the Long Key Bridge.1

A more recent example can be found in Bangkok.2

For the serviceability limit state (SLS), these bridges aredesigned considering that the limit state of decompressionmust not be reached; hence a minimum compression σn =0.5 MPa (75 psi) is maintained in all sections and the jointsremain closed. When the overload increases up to theultimate limit state (ULS), joints open up significantly(Fig. 1), and the structure rapidly loses stiffness and reachesa considerable deflection. The fact that there is no passivereinforcement crossing the joints means that bendingmoments must be carried by more active reinforcement or byhigher initial stresses in the steel tendons. In simplysupported bridges, it is not the SLS of decompression thatguides the design3 but the ULS of normal stresses.

The shear transmission through open joints is a morecomplex subject. The universally accepted theory proposesthat the shear forces flow across the joint, through web andflanges, by two qualitatively and quantitatively differentmechanisms. The first mechanism takes into account the

support effect of the interlocking shear keys usuallyprovided at the joint. Just the shear keys remaining in contactare able to transfer shear across an open joint. The secondrepresents the friction force that arises when two flat andcompressed surfaces tend to slip one against the other, whichis proportional to the actual compression.4

One of the controversial issues regarding the evaluation of theshear capacity of a joint is the quantification of the compressedflat zone of the section that is susceptible to transmit shear loadsAsm. Some authors5,6 limit the section of the flange capable oftransmitting shear just to areas next to the webs.

Another issue that causes controversy among researchersis the reinforcement of the segment in the proximity of theopen joint. Some authors5,6 support the necessity ofproviding extra shear reinforcement to hang shear in thezone next to the open joint. Figure 2 graphically sketches thejustification for this reinforcement.

RESEARCH SIGNIFICANCEThough models of segmental bridges with unbonded rein-

forcement under a combination of shear and bending loads havealready been tested,7-10 the authors believe that it is the first timethat a complete experimental study of the behavior of suchsingular structures is approached, dealing specifically with thehanger reinforcement and the effective width of the shear flow.Also, it is the first time that real-scale tests have been carried outon this type of beam made of steel fiber-reinforced concrete

Title no. 103-S43

Shear Behavior of Unbonded Post-TensionedSegmental Beams with Dry Jointsby José Turmo, Gonzalo Ramos, and Ángel C. Aparicio

Fig. 1—Open joints at ultimate limit state.

ACI Structural Journal/May-June 2006410

(SFRC), and that its behavior is compared with that of similarconventional concrete beams.

THEORETICAL ANALYSISThe response of conventional concrete beams under

tangential stresses cannot be studied at a sectional level. Theformation of a strut-and-tie mechanism for shear transmissionbefore failure requires a spatial study of the shear response. In thesame manner, the structural response of segmental concretebeams with dry joints and external prestressing is too complexfor just a pure sectional analysis to evaluate the shear response.

It is known that in any beam, the shear load V, acting at asection x, is mathematically related with the exterior bendingmoment M, by Eq. (1)

(1)

After flexural cracking, the exterior bending moment M, ineach section x of the beam, is compensated by a pair of axialforces separated by a lever arm z, including a compressiveand a tensile axial force, Nc and Ns, respectively (Eq. (2))

(2)

Then, Eq. (1) can be transformed in the following manner

(3)

In conventional concrete beams, the lever arm z remainsapproximately constant between two contiguous sections, atleast during the initial loading stages. Then

(4)

and

(5)

Equation (5) represents what is traditionally known as thebeam effect, and leads to a distribution of tangential stressesalong the length and width of the transversal section aftercracking takes place shown in Fig. 3(a). Hence, it is necessary toplace stirrups to carry the tensile stresses when the web of thebeam cracks (strut-and-tie analogy). If due to any circumstancethe bond of the longitudinal reinforcement with thesurrounding concrete is lost, the reinforcement is unableto vary its stress from one section to another of the beam,which implies

(6)

and

(7)

Equation (7) is known as the arch effect, and means thatthe shear force is resisted by an inclination of the compressiveaxial force. Generally, these two mechanisms are superimposedbefore the beam fails by shear.

In a segmental structure with external prestressing, wherethere is no passive reinforcement connecting the segmentsand where the prestressing tendons contact the concrete onlyat anchor blocks and deviators, the axial force remainsessentially constant in every cross section of the beam. Thus,the transmission of the shear force relies on the arch effect.

V x( )∂M x( )

∂x----------------=

M x( ) Ns z⋅ Nc z N z⋅=⋅= =

V x( )∂M x( )

∂x---------------- ∂ N z⋅( )

∂x------------------- z ∂ N( )

∂x------------ N ∂ z( )

∂x----------⋅+⋅= = =

∂ z( )

∂x---------- 0=

V x( ) z ∂ N( )

∂x------------⋅=

∂ N( )

∂x------------ 0=

V x( ) N ∂ z( )

∂x----------⋅=

José Turmo is an assistant professor at the School of Civil Engineering of CiudadReal, University of Castilla-La Mancha, Spain. He received his BS in civil engineering andhis MS from the University of Cantabria, Spain, and his PhD from the Technical Universityof Catalonia, Barcelona, Spain. His research interests include steel and concrete structures.

Gonzalo Ramos is an associate professor at the School of Civil Engineering ofBarcelona, Technical University of Catalonia. He received his BS in civil engineeringand his MS and PhD from the Technical University of Catalonia. His researchinterests include concrete structures and construction management.

Ángel C. Aparicio is a professor at the School of Civil Engineering of Barcelona,Technical University of Catalonia. He received his BS in civil engineering andhis MS from the Technical University of Madrid, Madrid, Spain, and his PhD from theUniversity of Cantabria. His research interests include structural behavior anddurability of concrete structures.

Fig. 2—Crack patterns in vicinity of open joints and hangerreinforcement.6

Fig. 3—Normal and shear stresses in: (a) conventionalconcrete beam; and (b) in externally post-tensioned segmentalconcrete beam.


In this manner, an inseparable association of longitudinalcompressive stresses and tangential stresses takes place. Thedistribution of normal and tangential stresses in a section ofsuch structures is represented in Fig. 3(b).

EXPERIMENTAL PROGRAMTest design

Shear tests involved a total of six segmental beams with anI-shape cross section of 0.60 m (1.97 ft) in height and 7.60 m(24.93 ft) in length. Three of the beams were cast of normalconventional concrete (PC) and the other three of SFRC. Thebeams were provided with interlocking dry joints, withthree shear keys of 90 mm (3.54 in.) in height in each joint.

The tests were divided into two series: The first seriesinvolved four simply-supported beams with a span of 7.20 m(23.62 ft), consisting of three segments of varying lengthassembled together with external prestressing, to which anexternal load Q1 was applied up to failure (Fig. 4). Thefollowing nomenclature was used in these test series:

1. V1-PC-35: PC beam of mean cylinder compressivestrength fcm of 30 MPa (4350 psi) with an axial prestressingforce of 350 kN (78.7 kips);

2. V1-PC-70: PC beam of fcm = 30 MPa (4350 psi) with anaxial prestressing force of 700 kN (157.4 kips);

3. V1-SFRC-35: SFRC beam of fcm = 30 MPa (4350 psi)with an axial prestressing force of 350 kN (78.7 kips); and

4. V1-SFRC-70: SFRC beam of fcm = 30 MPa (4350 psi)with an axial prestressing force of 700 kN (157.4 kips).

The objective of V1-PC tests was to verify the behavior ofan open joint when subjected to shear loading, to quantify theinfluence of the axial prestressing force on the capacity ofthe joint and the structure, and to study the efficiency of theshear reinforcement near the joint to determine if it is necessaryto include the hanger reinforcement that is proposed by someauthors.5,6 With V1-SFRC tests, which complement V1-PCtests, the objective was to study the possibility of replacing theconventional shear reinforcement by steel fibers when usingSFRC. With this aim, the conventional reinforcement placed inV1-PC beams (Φ8 mm stirrups every 300 mm [No. 3 stirrupsevery 12 in.]) was completely removed in these beams (exceptfor the reinforcement at anchorage and deviator zones, anda few longitudinal bars placed to avoid the premature flexuralfailure of the longest segment).

The second series of tests was intended to further study theshear transmission at an open joint. Specifically, theintention was to measure the capacity of the joint and verifythe contribution of the compressed flange to transmit shearforces in structures with shear span/effective depth a/d ratioshigher than the ratios considered in the tests by Fouré.10

With this aim, two beams of 7.60 m (24.93 ft) in length and0.60 m (1.97 ft) in height were tested up to failure. Eachbeam consisted of two segments and was tested under three-point loading (Fig. 5). In each of the structures, whichconsisted of a main span of 6.00 m (16.69 ft) and a cantileverof 1.40 m (4.59 ft), the limit state of decompression wassurpassed by increasing load Q1. Once the opening of the jointwas reached, and while maintaining load Q1 constant, load Q2was applied and increased up to the failure of the beam. In thismanner, load Q2 permitted the increase of the shear force at thejoint without increasing the flexural moments.

The configuration of the V3 test was aimed to reproducethe conditions of a continuous beam in which the joints nextto the supports carry large flexural moments and shear forcesacting concomitantly. Also, tests aimed to compare theinfluence of SFRC in the case of beams with shear stirrups.Beams were conventionally reinforced, with a high shearreinforcement ratio at the joint zones of Φ16 mm stirrupsevery 200 mm (No. 6 stirrups every 8 in.).

The following nomenclature was used in this second testseries:

1. V3-PC: PC beam of fcm = 33 MPa (4786 psi), with anaxial prestressing force of 250 kN (56.2 kips); and

2. V3-SFRC: SFRC beam of fcm = 38 MPa (5511 psi), withan axial prestressing force of 250 kN (56.2 kips).

The cross section of the beam at midspan is shown inFig. 6. A more complete geometric definition and reinforcementdetails of these tests are described in works by Piernagorda11

and Turmo.12

FabricationThe formwork for the beams was fabricated from fenolic

wood panels. The geometry of the keys was configured usingstandard industry-molded steel boxes attached to the existingformwork. The reinforcement was provided by a false shopand later placed in the forms. Details of the reinforcement

Fig. 4—V1 test configuration (dimensions in mm).

Fig. 5—V3 test configuration (dimensions in mm).

412 ACI Structural Journal/May-June 2006

arrangement can be seen in Fig. 7 and 8 for V1-SFRC andV3, respectively. Note the appreciable difference betweenthe reinforcement ratios of both series.

The concrete was supplied from a concrete plant. The steelfibers were added on site to the transit mixing truck. Because theaim was to emulate the real fabrication conditions of segmentalbridges as much as possible, casting was carried out in twophases: the end segments of beam V1 (Segments D1 and D3 inFig. 4) and Segment D1 of Beam V3 (Fig. 5) were cast in the firstphase, once initially cured, the central segment of Beam V1 andSegment D2 of Beam V3 were match-cast in the second phaseagainst the first segments. Consolidation was assured by meansof internal compaction with a needle vibrator. The formworkwas removed after 48 hours.

The BBR system was used for prestressing by means of asmall hydraulic tensioning jack. Beams V1-75 were providedwith eight prestressing tendons (Ap = 1120 mm2 [1.74 in.2]),Beams V1-35 with four (Ap = 560 mm2 [0.87 in.2]), andBeams V3 with two (Ap = 280 mm2 [0.43 in.2]). Tensioningwas performed from the active side (marked with an A in Fig. 4and 5) while the beams were on the floor. Afterward, the beamswere positioned on their supports and, due to the shakingand movement of the beams, the prestressing stressessmeasured in the active and passive anchorage were equal.

MaterialsEach of the beams was cast with conventional concrete or

SFRC. The mixture proportion per cubic meter was 400 kgof cement, 825 kg of 0 to 5 mm sand, 950 kg of 5 to 12 mmgravel, 190 L of water, and a high-range water-reducingadmixture dosage of 0.9%. In the case of SFRC, 60 kg ofsteel fibers were added. The compressive strength at the dateof testing and the slump test results are summarized in Table 1.Hot-rolled deformed steel bars were used as passive reinforce-ment. This steel grade has a minimum yield strength of500 MPa (72.5 ksi), a minimum tensile strength of 550 MPa(80 ksi) and a minimum elongation of 12% for a gaugelength five times the diameter (similar to Grade 75 fromASTM A 615). Bars were supplied cut and bent and after-ward placed in the forms. Prestressing steel grade was Y1860 S7 with a nominal tensile strength of 1860 MPa (270 ksi),identical to grade 270 ksi proposed by ASTM A 416. Thenominal diameter was 15.24 mm (0.6 in.).

InstrumentationThe stress in the prestressing tendons was controlled by

means of load cells (0.5 MN nominal load). Load cells werepositioned at the active jacking end and passive dead end ofBeams V1-SFRC-35, V1-SFRC-70, and V1-PC-35. Thedeformation of the prestressing tendons was measured throughstrain gauges glued to the cables after tensioning (G).Deflections and joint openings were measured bymagnetic extensometers. With all this instrumentation, theobjective was to obtain information to determine theevolution of the magnitude of the actuating prestressingforce and its loss of eccentricity during the test (and hence,the reduction of lever arm).

With the objective of verifying the distribution ofnormal stresses across the width of the slab, strain gauges(EG) were embedded in the upper flange of the beam inthe zone next to the joint of V1-PC tests. Embeddedstrain gauges (EG) were also placed in the web of thesegment with the intention of determining the stressdistribution in the web between open joints. Two hydraulicactuators of 0.25 and 1.00 MN capacity were used for thetests, which measured the applied load through an incorporatedcell. As an example, the instrumentation setup for Beam V1-PCis shown in Fig. 9.

EXPERIMENTAL RESULTS AND DISCUSSIONTest Series V1

The response of the beams is linear up to the separationand decompression of the joints (between Segments D2 and

Fig. 7—Reinforcement of V1-SFRC beams.

Fig. 6—Cross section of beams (dimensions in mm).

Fig. 8—Reinforcement of V1-PC beams.

Table 1—Concrete propertiesPC SFRC

D1 and D3 D2 D1 and D3 D2

Slump, mm (in.) 160 (6.3) 150 (5.9) 110 (4.3) 160 (6.3)

fcm-V1, MPa (psi) 37.2 (5395) 33.9 (4917) 33.9 (4917) 34.5 (5004)

fcm-V3, MPa (psi) 40.7 (5903) 33.1 (4801) 40.0 (5801) 38.1 (5526)


D3)—the moment at which the joint opens and a drastic lossin stiffness is evidenced (Fig. 10). The decompression loadis closely related to the axial prestressing force, and its valuein each test can be deduced either from the points of changein slope of the load-deflection curves (Fig. 10) or from theload versus joint opening response (Fig. 11). Once the jointis separated and decompressed, it continues to open as loadincreases and, correspondingly, the beam deflection increasesconsiderably. The joint between Segments D1 and D2 did notopen in any of the tests.

The behavior of the prestressing force, measured at theanchorage locations along Test V1-SFRC-70, can be seen inFig. 12. This response is qualitatively similar to that obtainedfrom the other tests of Series V1. The response shows howthe prestressing force remains practically constant untilreaching the applied load QD = 0.152 MN (34.2 kips),corresponding to the decompression and separation of thejoint. The forces in the tendons remains constant and equalto the jacking forces less losses until the joints open up. Theprestressing force increases almost linearly only after the jointopens, remaining almost constant before it. The averageprestressing force at failure is 1.45 times the initial prestressingforce (from σp0 = 574 MPa [83 ksi] to σpf = 833 MPa[120 ksi]). This corresponds to the stress increase in theshort tendons (measured with Load Cell C2) to that of thelong tendons (measured with Load Cell C1). The stressincreases measured at the active anchorage jacking end coincidewith those measured at the passive anchorage dead end.

Embedded strain gauges were only included in V1-PCtests. Figure 13 shows the load-strain response from embeddedstrain gauges of the V1-PC-70 test. The comparison of the

similar behavior of Gauges EG4 and EG5, located in the topflange of the beam, indicates a progressive increase ofcompressive deformations with load. This implies that thenormal stresses are distributed fairly uniformly along theentire width of the top flange, indicating that the shear lageffect is negligible. Gauge EG2, located in the bottomflange, gradually loses its initial compression produced bythe prestressing force as the load level increases. Once theultimate limit state of decompression is reached, the curveadopts a vertical tangent, corresponding to zero deformation.

From the prefailure phase, it is worth noting that theapparent position of the neutral axis, as well as the numberof active shear keys and cracking development, are intimatelylinked to the axial prestressing force. Note that only the PCbeams were taken up to failure because the conventionalreinforcement was lacking in Beams V1-SFRC. There was afear that a brittle failure could occur, which could cause harmto both people and equipment. Thus, tests were interruptedwhen an imminent failure was intuited.

In Beam V1-PC-35, cracking only affected the upper keys(Fig. 14(b)). Subsequently to the diagonal cracking of SegmentD3, which initiates at the base of the keys and orientates at 40degrees toward the loading point, a vertical crack propagatesfollowing the position of the stirrup. Finally, a horizontal crackappears in the compressed zone, in the joint area, due to exces-sive normal stresses, and develops toward the loading pointlosing horizontality due to the combination of normal andtangential stresses. The beam fails through the flange under ashear force of Vu,exp = 0.081 MN (18.2 kips).

In Beam V1-PC-70, as a consequence of the deeper positionof the neutral axis, cracking affects the three keys (Fig. 14(d)).

Fig. 9—V1-PC test instrumentation: (a) plan top flange; and (b) elevation.

Fig. 10—Load-deflection responses of V1 tests. Fig. 11—Load versus joint opening diagrams of V1 tests.

414 ACI Structural Journal/May-June 2006

Again the reinforcement of the segment induces a bifurcation ofthe crack that develops following the layout of the shearreinforcement, perpendicular to the axis of the segment. Thiscrack, with an inclination of 70 degrees to the horizontal, finallyconcentrates the entire crack opening. Failure occurs when theshear crack reaches the compression zone, corresponding to ashear force of Vu,exp = 0.136 MN (30.6 kips).

In Beam V1-SFRC-35, only one crack appeared, at the baseof the central key. It developed with a 45-degree inclination upto the bottom of the top flange, continuing its developmentalong a horizontal plane at the web-flange interface, achievinga significant opening, as can be seen in Fig. 14(a). The test wasinterrupted before the failure of the beam, with the jointsubjected to a shear force Vu,exp = 0.074 MN (16.6 kips).

In Beam V1-SFRC-70, a large crack originated at the baseof the lower key, which developed toward the loading pointwith an angle of 30 degrees to the horizontal (Fig. 14(c)).The opening of the joint fully extended throughout the webof the segment. The deformations of the beams were significant,visually appreciable. The test was terminated before thefailure of the beam, with the joint subjected to a shear forceVu,exp = 0.126 MN (28.3 kips).

Test Series V3In the V3 series tests, load Q1 was applied at midspan as a

first step. The behavior of the beams is linear until thedecompression of the joint. At that stage, the joint opens and

a loss in stiffness occurs. Once the joint is decompressed, itcontinues to open with increasing load, and the deflection ofthe beam increases considerably. When load Q1 reached thevalue Q1 = 0.198 MN (44.5 kips), the pump of the hydraulicjack was locked off, maintaining Q1 constant for the rest ofthe test. Up to this point, no cracking was observed in theweb of the beam.

While maintaining load Q1 constant, the second actuatorintroduces two loads in the structure: 0.31Q2 at the cantileverzone, and 0.69Q2 in the span (Fig. 5).

In Beam V3-PC, cracks arise from the two upper shearkeys and advance toward the loading point (Fig. 14(f)). Theshear stirrup next to the joint intercepts these cracks and,subsequently, cracking develops following its location. Themajor cracking development localizes in the crack thatinitiates at the central key, and thus its opening becomessignificant, producing the separation of the faces of the jointsituated below it. The beam ends up failing by a combination ofnormal and tangential stresses in the upper flange, with the jointsubjected to a shear force Vu,exp = 0.134 MN (30.1 kips).

Cracking observed in Beam V3-SFRC was initiated at thetwo upper keys (Fig. 14(e)), with the first crack arising fromthe base of the upper key at a load Q2 = 0.04 MN (9 kips).Subsequently, a loss in stiffness of the structure was evident,though the presence of fibers induced a more gradual stiffnessloss than in the case of V3-PC. This crack develops at 45 degreestoward the loading point, without intercepting any stirrup. Asload increases, the beam does not react with an increasingopening of the joint, but with an increase of the crack width. Inthis way, the crack appears to be a prolongation of the openjoint. As a result of the open joint and the crack, the structuregives the impression of being separated in halves with rigid

Fig. 12—Load versus prestressing stress diagrams ofV1-SFRC-70 test.

Fig. 13—Load-strain response from embedded gauges forV1-PC-70 test.

Fig. 14—Crack patterns obtained in beam tests: (a) V1-SFRC-35; (b) V1-PC-35; (c) V1-SFRC-70; (d) V1-PC-35; (e)V3-SFRC; and (f) V3-PC.


body movement, with the rotation point in the plane of thecrack. The initial crack develops up to a point where failure inthe flange occurs by a combination of normal and tangentialstresses, at a shear force of Vu,exp = 0.132 MN (29.7 kips).

Analysis of resultsThe beam test results are summarized in Table 2, where

the maximum shear force Vu,exp at the critical joint and theaccompanying exterior moment Mu,exp acting in this jointsection are included. The axial prestressing force Pf,measured at the anchorage zone by the load cell at the timethat the maximum shear force Vu,exp was reached, is alsotabulated. The table also includes the ultimate momentMu,calc of the critical joint section. This moment has beencalculated considering the maximum eccentricity loss of theprestressing force ∆e, due to the deflection of the beammeasured throughout the tests. When interpreting the testsresults, it must be kept in mind that the V1-SFRC beamswere not tested up to failure.

From the analysis of Table 2, it seems that the failure bypure normal stresses induced by flexure at the joint plane canbe discarded. The failure security factor γf , calculated as aquotient between the actuating moment at the joint zoneMu,exp and the ultimate moment of the joint section Mu,calc,is always less than 1, with values oscillating in the interval of0.73 to 0.89. The trend observed in Table 2 seems to indicatethat apparently the beams do not fail as a result of reachingtheir capacity by normal stresses at the section of the joint.This, together with the analysis of the cracking developmentup to failure, points toward a failure caused by high normalstresses combined with tangential stresses, with a failuremechanism that is not sectional but spatial.

It was deduced from the theoretical study that, in a segmentalstructure with external prestressing and no passive reinforce-ment, the arch effect is responsible for the shear transference.This implied that the longitudinal compression stresses and theshear stresses are associated; hence, after the opening of the joint,the shear force is transferred along the entire effective width ofthe flange. These theories were verified by the results of theexperimental tests.

Precisely, one of the apparently more surprising resultsobtained in the tests is the fact that beams with very differentreinforcement arrangements present very similar load-carrying capacity. The V1-PC beams, reinforced withconventional shear stirrups, showed an ultimate shearcapacity very similar to the V1-SFRC beams, with no shearstirrups. The width of the main crack, visibly observed in thetests, indicates that the contribution of the reinforcing fibers tothe shear transference across the crack zone can be ignoredin practice, as well as any other type of mechanism of tangentialstress transference arising from the aggregate interlock effect.The shear response mechanism that assures the flow oftangential stresses in beams without shear reinforcement isthe arch effect. Only the arch effect allows justification forbeams with and without shear stirrups to have so similar a

shear load-carrying capacity. A sketch of the arch developedin the V1 tests is shown in Fig. 15.

The shear reinforcement does not seem to be effective inthese types of structures. Though this reinforcement can beuseful for crack control (noticeable from the comparison ofFig. 14(c) and (d)), the steel bars next to the open joints arenot expected to transmit shear force because they are notintended to connect any strut with any tie. The nonexistenceof a beam effect and the fact of limiting the flow of tangentialstresses to the compressed zones makes it difficult for thedevelopment of a strut-and-tie mechanism; thus, the shearstirrups have a secondary role. In fact, the crack thatdevelops between the joint and the loading point in testV1-SFRC-70 (Fig. 14(c)), where the neutral axis is locatedat the web-flange interface, does not limit the structure totransmit shear force.

It is evident that if no strut-and-tie mechanism develops,the hanger reinforcement does not seem necessary. Moreover,the crack patterns observed in the tests do not reflect the onesketched in Fig. 2, which justified the placement ofhanger reinforcement. In spite of the presence of diagonalcracking, there is no possibility for the development of a strut-and-tie mechanism beneath the keys in contact, not even locally.Because there is no conveniently anchored longitudinalreinforcement to carry the horizontal component of thecompression stresses, the compression struts cannotequilibrate in the area of the open joint.

The analysis of the cracking of the beams prior to failure,with a diagonal crack across the entire width of the flange(Fig. 14(a) and (e)) confirms that the entire flange is capableof transmitting shear forces (or, at least, was able to transmitshear force along the entire effective width). The shear forcetransference through the flange increases the transversebending; thus, proper transverse flexural reinforcement mustbe provided if the specified load-bearing capacity of thestructure is to be maintained.

Shear strength of these beams once the joint is open cannotbe predicted with the conventional formulas for evaluatingshear strength in RC and PC beams. Different codes propose

Fig. 15—Sketch of arch effect—V1 tests.

Table 2—Results of beam tests

Vu,exp,kN (kips)

Pf ,kN (kips)

Mu,exp ,kNm

(ft-kips)

Mu,calc ,kNm

(ft-kips)∆e,

mm (in.) γf

V1-PC-35 81(18)

582(131)

217(160)

247(182)

42(1.65) 0.88

V1-SFRC-35 74(17)

529(119)

195(144)

234(173)

24(0.94) 0.83

V1-PC-70 136(31)

905(203)

350(258)

394(291)

23(0.91) 0.89

V1-SFRC-70 126(28)

933(210)

326(240)

407(300)

21(0.83) 0.80

V3-PC 134(30)

309(69)

74(55)

88(65)

6(0.24) 0.84

V3-SFRC 132(30)

354(80)

74(55)

101(74)

5(0.20) 0.73

ACI Structural Journal/May-June 2006416

different formulas for evaluating the shear capacity in suchbeams. All these formulas have a common philosophy. Shearstrength is the sum of the shear stress carried by the concretetimes the area of the web and the shear carried by the stirrups.The shear capacity of the concrete comes from threemechanisms: the dowel action (zero in this beams as there isno anchored reinforcement in the joint); the aggregate interlock(that is negligible due to the opening of the joints); and theshear carried by the compressed flange (the only existingmechanism to transfer shear). The area of the web transferringshear (z × bw) has no meaning, as shown in Fig. 3(b). Sheartransferred by the stirrups can be calculated from the stirruparea crossing a crack, but cracks do not cross stirrups instrongly shear-reinforced beams, as shown very neatly inFig. 14(f). Predicting the shear crack slope can not be donewith conventional formulas. Figure 14(d) shows a crack with aslope of 70 degrees to the horizontal, when shear cracks shouldhave a slope below 45 degrees in a prestressed beam.

Hopefully, when the shear span to depth ratio increases, asit does in actual bridges, specimens fail in flexure, not in shear.This has been proved experimentally by several researchers.Among them, Ramírez-Aguilera,8 Aparicio et al.,13 and Take-bayashi et al.14 The study by Takebayashi et al. presented afull-scale test up to failure of a simply supported bridge whereno shear failure was evidenced. Very recently, Turmo et al.15

validated with these tests a FEM model that takes into accountexplicitly the shear behavior of these bridges and applied it tothe study of actual bridges and concluded that shear is not tofear in full-scale bridges.

CONCLUSIONSThe beam tests carried out allowed the authors to extract

some very interesting conclusions regarding the behavior ofstructures with dry joints. The extrapolation of these resultsto actual bridges should be done with care. Several facts,such as: a) the transverse section of the beam maintains noproportionality between the width of the flange and the heightof the section (unlike a box girder of an actual bridge); b) theratio between the width of the flange and the height of thetested beams is less than in an actual bridge; c) the use ofreal-scale keys in beams with a reduced depth; d) the geometryof the beams, with segments of different lengths; and e) theapplied point loads, which were not distributed loads, makethe direct extrapolation to actual bridges unfeasible.

Based on the research, the following conclusions can be made:1. The addition of fiber to concrete does not seem to

increase the load-carrying capacity of the beams. This isshown by test results of Beams V3;

2. The cracking that produces the failure of the structurearises from the joint. The shear failure of the beams is notsectional, like in flexure, but spatial;

3. The crack pattern that takes place at the zone next to thejoint seems to be markedly influenced by the depth of theneutral axis, or at least, by the number of keys in contact;

4. The crack pattern that justifies the placement of hangerreinforcement in the proximity of an open joint is notevident. Furthermore, the conventional shear reinforcementdoes not seem to be effective in these tests because the beamsprovided with shear stirrups resisted very similar ultimateshear forces compared to SFRC beams without anyconventional shear reinforcement (V1 series);

5. The mode of failure of the flange, with cracks goingthrough it from one side to the other, seems to discard the

theory stating that the transmission of tangential stressestakes place only in the web area;

6. The theoretical analysis and the experimental testssupport the thesis that normal and tangential stresses areassociated in these types of structures, with the flange beingcapable of transmitting tangential stresses along its entireeffective width. Thus, the flange is also taking part inresisting shear forces;

7. The increase in the transverse flexure due to the fact thatpart of the shear force is in fact transmitted through theflange should be taken into account when designing thetransverse reinforcement; and

8. Shear strength of these beams, once the joint is open,cannot be predicted with the existing formulas for evaluatingshear strength in conventional RC and PC beams.

FURTHER RESEARCHIt would be convenient to carry out tests on beams that are

actually scaled bridge models. This would permit thedetermination of the effective width of the flange to be usedin transmitting shear forces. Even if a FEM two-dimensionalmodel has been validated12 (whose complexity does not allowpresentation in this paper), it would be desirable to have a three-dimensional design model, calibrated with these six tests andwith others carried out in the future, capable of predicting theshear behavior of this type of structure. This would allowstudying the behavior up to failure with other types of loading.

ACKNOWLEDGMENTSThe authors thank J. Piernagorda for his contribution to the progress of

the research during the experimental phase. Partial funding of the researchby the Spanish Ministry of Science and Technology (Project MAT2002-00849),and by the Spanish Ministry of Public Works (Project: “Theoretical andExperimental Study of the Shear Transference in Segmental Steel FiberReinforced Concrete Beams, with External Prestressing and Dry Joints”)is greatly appreciated. One of the authors benefited from a scholarshipfrom the Spanish Ministry of Education and Culture from 2000 until 2003(Scholarship for the Formation of University Professors).

NOTATIONAp = area of prestressing steelAsm = compressed flat zone of dry joint that is susceptible to transmit

shear loadsbw = web widthe = eccentricity of prestressing steel, distance between strand and

center of masses of concrete transverse cross sectionfcm = mean concrete cylinder strength at date of testingg1 = self-weight loadM = bending momentMu,calc = ultimate expected moment of join section (flexural strength)Mu,exp = actuating moment at joint zone at failureN = axial forceNc = axial force on concreteNs = axial force on steelPf = final prestressing forceQ = external vertical loadR = vertical reaction at supportV = shearVp = shear due to prestressingVu,exp = shear at joint zone at failurez = lever arm∆e = loss of eccentricityΦ = nominal diameter of reinforcing barsγf = failure security factor, calculated as quotient between actuating

moment at joint zone at failure Mu,exp and ultimate expectedmoment of joint section, Mu,calc

σn = normal stresses acting on jointσp0 = initial prestressing stress at start of testσpf = final prestressing stress


REFERENCES1. Muller, J., “Construction of the Long Key Bridge,” Journal of the

Prestressed Concrete Institute, Nov.-Dec. 1980, pp. 97-111.2. Shafer, G., “Bangkok Blockbuster,” Civil Engineering Magazine,

V. 69, No. 1, Jan. 1999, http://www.pubs.asce.org/ceonline/0199feat.html.3. Ramos, G., “Study on Structural Behavior of Concrete Bridges with

External Prestressing,” PhD thesis, ETSICCP de Barcelona, Feb. 1994. (inSpanish)

4. Ramirez, G.; MacGregor, R.; Kreger, M. E.; Roberts-Wollmann, C.;and Breen, J., “Shear Strength of Segmental Structures,” Proceedings of theWorkshop AFPC External Prestressing in Structures, Saint-Rémy-lès-Chevreuse, June 1993, pp. 287-296.

5. Virlogeux, M., “Some Elements for a Codification of ExternalPrestressing and of Precast Segments,” Proceedings of the WorkshopAFPC External Prestressing in Structures, Saint-Rémy-lès-Chevreuse,June 1993, pp. 449-466.

6. ATEP, “Design and Construction of Bridges and Structures withExternal Prestressing,” Madrid, Sept. 1996. (in Spanish)

7. MacGregor, R. J. G., “Evaluation of Strength and Ductility of a Three-Span Externally Post-Tensioned Box Girder Bridge Model,” PhD dissertation,University of Texas at Austin, Austin, Tex., Aug. 1989.

8. Ramírez-Aguilera, G., “Behavior of Unbonded Post-TensioningSegmental Beams with Multiple Shear Keys,” master’s thesis, Universityof Texas at Austin, Austin, Tex., Jan. 1989.

9. Anllo, M., “Experimental Analysis up to Failure of ExternallyPrestressed Concrete Beams,” MSc thesis, Universitat Politècnica deCatalunya, Barcelona, Spain, 1996. (in Spanish)

10. Fouré, B.; Bouafia, Y.; Soubret, R.; and Thomas, P., “Shear Test onKeyed Joints between Precast Segments,” Proceedings of the WorkshopAFPC External Prestressing in Structures, Saint-Rémy-lès-Chevreuse,June 1993, pp. 297-319.

11. Piernagorda, J., “Shear Tests on Segmental Concrete Beams withExternal Prestressing and Dry Joints,” master’s thesis, ETS de Ingenieros deCaminos de Barcelona, June 2002. (in Spanish)

12. Turmo, J., “Flexure and Shear Behavior of Segmental ConcreteBridges with External Prestressing and Dry Joints,” PhD thesis, ETSICCPde Barcelona, July 2003, http://www.tdx.cesca.es/TDX-1030103-090157/(in Spanish)

13. Aparicio, A. C.; Ramos, G.; and Casas, J. R., “Testing of ExternallyPrestressed Concrete Beams,” Engineering Structures, V. 24, No. 2, 2001,pp. 73-84.

14. Takebayashi, T.; Deeprasertwong, K.; and Leung, Y., “A Full-ScaleDestructive Test of a Precast Segmental Box Girder Bridge with Dry Jointsand External Tendons,” Proceedings of the Institution of Civil Engineers—Structures and Buildings, Aug. 1994, pp. 297-315.

15. Turmo, J.; Ramos, G.; and Aparicio, A. C., “FEM Study on theStructural Behaviour of Segmental Concrete Bridges with UnbondedPrestressing and Dry Joints: Simply Supported Bridges,” EngineeringStructures, V. 27, No. 11, pp. 1652-1661.

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shear behavior of unbonded post-tensioned

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