Shear rehabilitation of G-girder bridges in Albertausing fibre reinforced polymer sheets

Christophe Deniaud and J.J. Roger Cheng

Abstract: Many bridges were built in Alberta after World War II with type G-girder precast concrete elements. Today,there are approximately 1500 G-girder bridges still in service all over the province. These bridges are typical shortspan (approximately 6 m long), simply supported, and without shear keys between girders. Structural deficiency of theG-girders, especially in shear, plus the economic constraints of the government demand that an economical and effi-cient method for rehabilitation of these bridges be developed. A research program at the University of Alberta, in col-laboration with Alberta Transportation and Utilities and ISIS Canada, has been established to study the feasibility ofusing fibre reinforced polymers (FRP) to rehabilitate concrete bridge girders deficient in shear. This paper will addressthe structural deficiency of the G-girders and present eight full-scale test results from four G-girders removed from ex-isting bridges. Carbon and glass FRP sheets and two repair schemes were used in the rehabilitation. Three commonlyused shear strength evaluation methods, strut-and-tie model, modified compression field theory, and grid analysis, areinvestigated. The loads predicted by these three methods are in good agreement with the experimental results. Theshear contribution of the FRP sheets at any angle can be accurately accounted for in the analysis. All three methodsare found to be consistent.

Key words: analysis, beams, bridges, composite materials, design, fibre reinforced polymers, rehabilitation, reinforcedconcrete, shear strengthening.

Rsum : De nombreux ponts ont t construits en Alberta aprs la deuxime guerre mondiale avec des lments depoutres de bton prfabriques de type G. Aujourdhui, il y a environ 1500 ponts avec poutres de type G encore enservice travers la province. Ces ponts sont typiquement de courte porte (approximativement 6 m de long), sur appuissimples, et sans clef de cisaillement entre les poutres. La dficience structurale des poutres de type G, particulirementen cisaillement, plus les contraintes conomiques du gouvernement requirent quune mthode conomique et efficacepour la rhabilitation de ces ponts soit dveloppe. Un programme de recherche lUniversit de lAlberta, en collabo-ration avec le dpartement des transports et services publics de lAlberta et ISIS Canada, a t tabli afin dtudier lafaisabilit de lutilisation de polymres renforcs de fibres (PRF) pour rhabiliter des poutres de pont en bton qui sontdficientes en cisaillement. Cet article aborde le sujet de la dficience structurale de poutres de type G et prsente lesrsultats de huit tests en grandeur nature sur quatre poutres de type G prleves sur des pont existants. Des feuilles depolymre renforcs de fibre de verre et de carbone et deux schmas de rparations ont t utiliss pour la rhabilita-tion. Trois mthodes dvaluation de la rsistance en cisaillement communment utilises, le modle bielles-et-tendons,la thorie modific du champ de compression, et lanalyse par grillage, sont examines. Les chargements prdis par cestrois mthodes correspondent assez bien avec les rsultats exprimentaux. La contribution pour le cisaillement desfeuilles de PRF nimporte quel angle peut tre considre prcisment dans lanalyse. Ces trois mthodes apparais-sent consistantes entre elles.

Mots cls : analyse, poutres, ponts, matriaux composites, conception, polymres renforcs de fibres, rhabilitation, b-ton arm, renforcement au cisaillement.

[Traduit par la Rdaction] Deniaud and Cheng 971

Introduction

The type G-girders shown in Fig. 1 have been used exten-sively in Alberta for short span highway bridges constructedin the 1950s and 1960s. Today, approximately 1500 of thesebridges are still in service across the province. The bridgesare typically simply supported with no shear keys betweenthe girders. The G-girders were found to be deficient inshear based on current code requirements and evaluationspecifications (CAN/CSA S6 1988). The deficiency ismainly due to an increase in allowable truck loads over the

Can. J. Civ. Eng. 27: 960971 (2000) 2000 NRC Canada

960

Received August 3, 1999.Revised manuscript accepted March 1, 2000.

C. Deniaud and J.J.R. Cheng.1 Department of Civil andEnvironmental Engineering, University of Alberta, Edmonton,AB T6G 2G7, Canada.

Written discussion of this article is welcomed and will bereceived by the Editor until February 28, 2001.1Author to whom all correspondence should be addressed(e-mail: rcheng@civil.ualberta.ca).

last 40 years as well as a better understanding of shear be-havior in reinforced concrete members since the early 1970s.Overall, the design shear requirement has increased by 40%and the applied loads have also increased by about 45% overthe last 40 years. Combination of these two effects plus theaging of the bridges results in shear deficiency problems fortype G-girder bridges. Finding a reliable and economicaltechnique to rehabilitate and strengthen these girders is amajor concern for Alberta Transportation and Utilities(AT&U). A research program to assess these needs is car-ried out at the University of Alberta in collaboration withAT&U and ISIS Canada. A series of full-scale tests wereconducted using G-girders removed from existing bridges.A preliminary investigation of type G-girders conducted at

the University of Alberta in 1997 (Alexander and Cheng1997) indicated that type G-girders must be loaded eccentri-cally about the centroid of the cross section in order to failthe girders in combination of shear and torsion. They alsoshowed that the end panel is the weakest part of the girderunder eccentric loading. Special considerations are thereforerequired to reinforce not only the inner faces of the legs butalso the end diaphragm.The objective of the current series of tests is to establish a

comparison between the use of glass and carbon fibre rein-forced polymer (FRP) sheets with various sheet configura-tions, as a shear repair technique. The end diaphragm wasalso reinforced using composite sheets. A 9.5 mm thick steelplate was bonded along the bottom faces of the girders toavoid flexural failure.

The following three commonly used shear strength evalu-ation methods were also investigated: (i) the strut-and-tiemodel, (ii) the modified compression field theory (MCFT),and (iii) the grid analysis. The shear capacities predicted us-ing these methods were compared with the experimental re-sults.

Experimental program

Test specimensA total of eight tests were conducted on four G-girders.

Each end of the 6.1 m long girders was tested separatelywith different shear strengthening details, as shown in Ta-ble 1. Two types of G-girders, three with round end dia-phragms and one with square end panels, were used in thisseries, as shown in Fig. 1.Prior to application of the steel plates and composite

sheets, the concrete surfaces of the specimens were preparedusing a grinder to remove any bumps. The steel plates weresandblasted and then glued to the underside of each leg us-ing Sikadur 31 Hi Mod epoxy provided by Sika Inc. Toavoid sharp corners, putty was used to round the corners ofthe girders. Figure 2 shows a typical surface preparation ofthe end diaphragm. Fibre reinforced polymer sheets werethen applied on the inner face of each girder. One end of thesheet extended underneath the flange and the other end ex-tended on top of the steel plate or the end panel, as shown inFig. 3. At least 100 mm of development length was providedfor the FRP sheets.The two types of uniaxial FRP sheets used were carbon fi-

ber, Replark Type 20 from Mitsubishi Canada Ltd., andglass fiber, SEH51 from Fyfe LLC Ltd. The two repair con-figurations used were 250 mm wide vertical sheets or250 mm wide diagonal sheets at 45. A 50 mm spacing be-tween sheets was used in all the specimens. The round endpanels were strengthened using 50 mm wide bands appliedvertically whereas the square end panel (G4 West) wasstrengthened with horizontal carbon sheets. Table 1 providesa full description of the various specimen parameters andboth repair schemes are presented in Fig. 4.

Test setup and instrumentationTo provide an eccentric loading, a stiff steel beam was

used to distribute the load from the MTS 6000 testing ma-chine to the top of one leg of the girder, as shown in Fig. 5.The load applied to the top of the girder is computed using

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Deniaud and Cheng 961

Fig. 1. Typical type G-girder: (a) cross-section dimensions;(b) round diaphragm; and (c) square diaphragm.

GirderSteelplate

FRP repairscheme

G1 East Yes NoneG1 West No NoneG2 East Yes Vertical carbonG2 West Yes Inclined carbonG3 East Yes Vertical glassG3 West Yes Inclined glassG4 East* No NoneG4 West* Yes Inclined carbon*Square end diaphragm.

Table 1. Test matrix.

the four load cells located at each support or by subtractingthe steel beam support reaction from the MTS 6000 load.The terminology used in the testing program, Close, Far,Unloaded and Loaded, is described in Fig. 5.The side of each leg of the girders was instrumented with

several sets of Demec gauges while electrical strain gaugeswere applied on the steel plate. Eight cable displacementtransducers were used along each leg to record vertical de-

flections, and four Linear Variable Differential Transformers(LVDTs) were installed at two stirrup locations of interest.An additional LVDT was used to record the Far Unloadedsupport, which was lifting up during each test.After the first end of each girder was tested, the girder

was repaired with external stirrups prior to testing the sec-ond end. The external stirrups consisted of two HSS steeltubes with tie rods on both ends.

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962 Can. J. Civ. Eng. Vol. 27, 2000

Fig. 2. Surface preparation in the end panel.

Fig. 3. Typical end diaphragm layout.

Experimental results

Material propertiesCoupon tests were carried out in accordance with ASTM

Standard A-370 (1996) to determine the material propertiesof the steel components of each girder: the steel plate usedas external reinforcement, the 28.6 mm diameter longitudi-nal reinforcing bars, and the 9.5 mm diameter stirrup bars.Table 2 gives the steel coupon test results.For each type of FRP used, coupon specimens were made

at the same time as the bands were being bonded to the gird-ers. Material properties for the two composites are given inTable 3. It should be noted that premature failure was ob-served for the glass fibre coupons.Concrete strength was determined by 100 mm diameter

cores drilled from each girder, in accordance with the ASTMStandard C-42 (1994). Three cores were taken in each girderat three different locations. Core specimens were soaked forat least 48 h prior to testing. Correction factors developed byBartlett and MacGregor (1994) were used to find the equiva-lent in situ strength presented in Table 4.

Girder testsThe girder test results are summarized in Table 4. Figure 6

shows the load vs. deflection curves at the point load loca-tion for all tests with round end diaphragms, while the re-sults of the two tests with square end diaphragms arepresented in Fig. 7.

General behaviorWhen the girders are eccentrically loaded over one leg as

described in Fig. 5, about 70 to 75% of the total load wascarried by the Close Loaded support reaction and 20 to 25%went to the Far Loaded support. The remainder of the load,no more than 7%, was carried by the Close Unloaded sup-port. The Far Unloaded support was lifting up in all cases.From the observations, the load-sharing path was not signifi-cantly affected by the external steel plate or FRP strengthen-ing. Furthermore, the loaded leg carried the majority of theshear load.

Failure modeThe failure mode observed in all the tests except Girder 2

East and Girder 3 West was shear cracks in the end dia-phragm induced by the torsion applied in the end panel.Testing of Girder 2 East was terminated prematurely andGirder 3 West failed in shear in the Loaded leg with nocrack in the end panel. The test results of Girder 3 West arethe most promising for shear rehabilitation of this type ofgirder, as explained in the following sections. All the test re-sults showed that FRP sheets helped to hold flexural rein-forcement in place. No debonding of the steel plate wasobserved when composite materials were used. This tech-nique proved to be very efficient in avoiding premature fail-ure due to steel plate debonding.

End panels cracks For the control test with the steelplate (Girder 1 East), the crack in the end panel was inclinedat about 60 to 70 from the soffit of the diaphragm. The50 mm wide sheets applied vertically at the end panel pre-vented any horizontal cracks. The crack path in the dia-

phragm then became vertical, which was now the weakestorientation. This behavior was clearly observed in Girder 2West. Girder 3 East exhibited similar behavior, but the crackin the end panel was initiated by the peeling-off of a bandunderneath the diaphragm.For Girder 3 West, peeling did not occur, since the woven

glass fabric used has fibres at both 0 and 90, with a ratioof 80 and 20%, respectively. This material is stronger per-pendicular to the main fibre orientation when compared withthe uniaxial carbon fibre. Although only 50 mm wide bandswere used, horizontal tension can still be mobilized in thisproduct. It partially explains why the end panel did not failin this case. Unfortunately, no strain in the horizontal direc-tion was measured to confirm this hypothesis.For the square end panel specimen, Girder 4 West, the

carbon sheets were applied horizontally in the end panel.Therefore, the crack, which was running vertically along theClose Unloaded corner, was covered by FRP. Although ver-tical cracks can still develop because of the sharp corner, thehorizontal fibres are extremely effective. Twisting of thefibres can be seen in Fig. 8. In this case, the horizontalsheets were long enough to provide good anchorage and toavoid peeling off.

Shear span cracks Two major inclined cracks were usu-ally observed in each shear span. The first was initiated atthe support location and the second started to open up about500 mm away from the support sloping toward the loadpoint. These cracks were initially oriented at about 45.However the ultimate crack orientation decreased to approxi-mately 30.The steel plate alone did not affect the inclination and ini-

tiation of these cracks. However, the failure crack was closerto the beam without FRP, when compared with the failurecrack of the girder strengthened by composites. For the latter

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Deniaud and Cheng 963

Fig. 4. Repair schemes used: (a) cross section dimensions;(b) vertical sheets; and (c) inclined sheets at 45.

case, the failure crack was initiated at the leg-to-end paneljoint, then widened and propagated toward the point load.The failure crack was therefore shifted away from the sup-port face when the FRP was used, as shown in Fig. 9.

Maximum loadThe overall comparison of the total load applied on the

girders (Table 4) shows that the external steel plate increasesthe capacity of the girder by 35%. This large increase is dueto the significant stiffness the plate adds to the bottom of thelegs. Deflection of the legs is reduced and the plate acts tohold the concrete in place, thereby allowing greater sheartransfer to occur.The effect of FRP can be found by superposition and is

equal to 5 and 12% for the vertical and inclined glass sheets,respectively. It should be noted that, although the total loadfor Girder 2 East increased by only 24%, the test wasstopped prematurely. With the square end panel and an as-sumption of the same percentage contribution from the ex-ternal steel plate, the presence of carbon sheets increased theapplied load by 17%. Although the difference in load in-crease between girders with inclined and vertical sheets isnot large, the repair scheme using inclined sheets improvedthe performance, as shown in Figs. 6 and 7. This phenome-non can be attributed to the absence of cracking in the gapbetween the sheets when the fibres are inclined and the pres-ence of vertical cracks between vertical sheets observed dur-ing the test.

Strains in fibre reinforced polymer and steel platesFlexural capacity was not an issue when steel plate was

used, since the steel plate did not yield in any of the tests.The strain values recorded in the FRP sheets for each testwere relatively small compared with the maximum deforma-tion that these materials can sustain. The maximum strain re-corded was 0.18%, whereas the maximum elongation for theFRP sheets typically exceeds 1%.

The measured strains for the inclined sheets were similarin magnitude in both legs. For the vertical sheets, however,the sheet on the loaded leg sustained twice the strains mea-sured in the sheet on the unloaded leg. Therefore, it appearsthat the inclined repair scheme distributes the stress andstrain more evenly to both legs. Torsion in the end panel istherefore reduced because the angle of rotation is reducedbetween two legs.

Test specimen models

Three commonly used shear design methods, strut-and-tie,MCFT, and grid analysis, were used to evaluate the shear ca-pacity of the tested specimens. The development of the testspecimen models using these three methods and the discus-sion of predicted behavior and strength are summarized be-low along with the test results.

General assumptionsIn all cases the shear force was assumed to be carried by

the loaded leg only as observed during testing. The bendingmoments were shared between the two legs. The bendingcontribution of the unloaded leg varied from test to test and

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964 Can. J. Civ. Eng. Vol. 27, 2000

Fig. 5. Test set-up.

Bar diameter(mm)

Yieldstress fy(MPa)

ElasticmodulusE (MPa)

UltimatestrengthFu (MPa)

Steel plate 327 202 000 502Girder 2 28.6 (#9 Imp) 306 203 000 494

9.5 (#3 Imp) 311 186 000 455Girder 3 28.6 (#9 Imp) 263 191 000 414

9.5 (#3 Imp) 302 252 000 423Girder 4 28.6 (#9 Imp) 267 194 000 448

9.5 (#3 Imp) 336 203 000 511

Table 2. Steel coupon tests.

decreased with the loading level. Therefore, the L/U(Loaded/Unloaded) ratio from the experimental results at theultimate was used and is reported in Table 5. No FRP strainmeasurements were recorded at the ultimate. Since the FRPbehaves linearly when stressed, a linear extrapolation wasused from the last two Demec records to evaluate the maxi-mum FRP strains at the ultimate load, as listed in Table 5.

Strut-and-tie modelThe loaded leg of the specimen was modeled as shown in

Fig. 10. Vertical ties were located at the stirrup locations.The longitudinal bent bar was also introduced into the

model. The 300 mm lever arm between the bottom tie andthe top chord was used in all cases.The effect of load sharing in flexure was accounted for by

increasing the area of the bottom steel tie according to theL/U ratio given in Table 5. It was also assumed that the con-crete stresses in any strut were not critical. The truss wasloaded until the first tie reached its elastic limit based on thematerial properties of the steel. The yielded tie was then re-moved and a new strut-and-tie model was created. This pro-cess was repeated until the truss model collapsed because ofyielding of all of the ties. The total applied load was thesummation of all load increments for each mechanism. The

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Deniaud and Cheng 965

FRP nameType offibres Test source

Ultimatestrength(MPa)

Modulus ofelasticity(MPa)

Thickness(mm)

Replark type 20 Carbon Fibre strength* 3400 230 000 0.11Coupon specimens 422 44 800 0.70

SEH41 Glass Fibre strength Coupon specimens 106 17 700 1.80

*Manufacture specified properties.Premature failure.

Table 3. Fiber reinforced polymers material properties.

GirderIn situ fc(MPa)

Max. loadon girder(kN)

Increase(%) Failure mode

G1 East 45.9 382 35.5 Torsion in the end paneland plate debonding

G1 West 45.9 282 0.0 Torsion in end panelG2 East 46.2 350 24.1 Shear in loaded legG2 West 46.2 412 46.1 Torsion in end panel/partial

concrete crushingG3 East 42.8 394 39.4 Torsion in end panelG3 West 42.8 415 47.2 Shear in loaded legG4 East* 32.5 259 0.0 Torsion in Close Unloaded

corner

G4 West* 32.5 395 52.5 Torsion in Close Unloadedcorner

*Square end diaphragm.

Table 4. Girder test results.

Fig. 6. Load vs. point load deflection curves for specimens withround end diaphragm.

Fig. 7. Load vs. point load deflection curves for specimens withsquare end diaphragm.

effect of the composite sheets was included by increasingthe load level required to yield the vertical ties, as shown be-low:

[1] P A f E t sy sv yy y FRP FRP= + ewhere Asv, fvy, and s are the area, the yield strength, and thespacing of the stirrups, respectively. ey is the yield strain ofthe stirrups. EFRP and tFRP are the elastic tensile modulus andthe thickness of the sheets, respectively. Equation [1] is ap-plied to the case when the fibres are parallel to the stirrups.

Modified compression field theoryThis variable angle truss method was developed by Col-

lins and Mitchell (1987) and is the basis of the generalmethod described in CSA-A23.3 (1994). A computer pro-gram was created to include the contribution of the FRPsheets. The procedure requires iteration to converge to theappropriate solution. The solution technique is describedbriefly below, detailed information on the method can befound in Collins and Mitchell (1987).The method starts with estimation of the inclination angle,

q; the stirrup stress, fv; the FRP sheet stress, sFRP; and a cho-sen value for the principal tensile strain, e1. The shear load isthen calculated including the contribution of the FRP sheetsas follows:[2] V v d b vd b v b= + +s v w v w FRP wwhere

vA f

b sssv v

w

=tan q

vf= 1

tan q

vAb sFRPFRP FRP

w FRP= +

s aq

a asintan

sin cos2

dv and dFRP are the height of the stirrups and the FRP sheets,respectively; bw is the width of the web; AFRP and sFRP arethe FRP sheet area and bands spacing, respectively; a is theangle of the fibres with respect to the longitudinal axis of the

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966 Can. J. Civ. Eng. Vol. 27, 2000

Fig. 8. Twisting of carbon fibres in Close Unloaded corner(Girder 4 West).

Fig. 9. Typical shear crack patterns.

GirderL/U ratioat ultimate

emaxme

V/M ratio(m)

G1W 1.62 1.147G1E 3.95 0.889G2E 2.11 1502 1.045G2W 8.29 1783 0.795G3E 4.07 2267 0.883G3W 2.34 3907 1.012G4E 3.99 0.887G4W 4.50 1409 0.867

Table 5. Parameters used for the analysis ofthe test specimens.

Fig. 10. Strut-and-tie scheme.

section. Once the compression stress f2 is found to be lesserthan f2max, the principal strain e2 is computed. The longitudi-nal strain ex, vertical strain et , and composite strain eFRP arefound by strain transformation. The stirrup stress fv and theFRP stress sFRP are re-calculated from the calculated strainsuntil they agree with the initial estimated values. Finally, aplane section analysis with the strain at d set to ex is pre-formed to check the equilibrium of the axial load on themember.This procedure is repeated for a specific moment by in-

creasing e1 until the shear load drops, the fibres fail, or theconcrete strut crushes. By repeating this procedure for dif-ferent moments, the complete shear moment interaction dia-gram can be developed. For this study, the maximum shearload was computed for the specified V/M ratio (which is afunction of the L/U ratio) of each test (Table 5).

Grid analysisIn this approach, the girder was modeled using beam ele-

ments. Two longitudinal beams spaced 660 mm apart repre-sented the two legs, while two and seven transverse beamswere used for the end panel and flange elements, respec-tively. The spacing between two consecutive transversebeams was 750 mm except for the first transverse elementclose to each end panel element where 660 mm spacing wasused.

Material and section propertiesThe material properties of the girder were computed from

the experimental data. The weight of the girder was obtainedby summing the four reactions from the load cells in eachsupport. The compression strength fc from the concretecores was used to estimate the modulus of elasticity (CSA-A23.3-94) as follows:

[3] E fc c c1.5

= +

( )3000 6900

2300g

where gc is the density of the concrete. The shear modulusof the concrete was computed assuming an isotropic elasticmaterial with Poissons ratio nc = 0.2.Section properties for each element were also evaluated.

The moment of inertia of the leg elements was calculated us-ing the transformed section method (CSA-A23.3 1994) toaccount for cracking from service loads after 30 years of ser-vices.The St. Venant torsional constant J was estimated using

the membrane analogy by the finite differences method

(Oden and Ripperger 1981). The cross section of the ele-ments was discretized by a 2D mesh into a spreadsheet andseveral iterations were performed until convergence for anypoint of the grid where the stress function was evaluated.Material and section properties are summarized in Table 6.

Cracking torque of the diaphragmThe cracking moment in the end panel was estimated

from the stress function calculations. The shearing stressescan be computed as well as the principal stresses at any dis-crete point of the grid. The maximum principal tensile stresswas then compared to the direct cracking strength of theconcrete as predicted based on Collins and Mitchell (1987)[4] f fcr c0.33=

The cracking torque in the end panel can then be evaluatedby linear interpolation.The shearing stress was found to be maximum along the

inner face of the end diaphragm for the control specimens.When composite sheets are applied, the maximum shearingstress was shifted to the exterior face of the girder.

Flexural strength of the legThe flexural strength of each individual leg was computed

by a combination of two strength calculations. The firstmethod assumes a triangular compression zone as shown inFig. 11 to compute the flexural strength MrT. The secondmethod uses a rectangular compression block to obtain MrR.The former method accounts for unsymmetrical beam sec-tion (i.e., inverted L-shape when considering only half thehat-shaped G girder) and the later describes symmetricalbeam section behavior.The flexural strength MrR occurs at L/U ratio (see Table 5)

equals one, whereas the flexural strength MrT is assumed tooccur when L/U reaches infinity. To obtain the flexuralstrength of the specimen, an exponential decay relationshipwas adopted here between the flexural strength of the loadedleg and the L/U ratio. Based on this assumption, the flexuralstrength of each test can be determined and is reported inTable 7.

Shear strength of the legThe shear strength of the leg is the summation of the three

contributing components: concrete, steel stirrups, and FRPsheets:

[5] V V V Vf c s FRP= + + 2000 NRC Canada

Deniaud and Cheng 967

Densitygc(kg/m3)

Leg with two 28.6 mm bars

Leg with three 28.6 mm bars Diaphragm

J106 mm4Girder

Ec(MPa)

Gc(MPa)

Icr106 mm4

J106 mm4

Icr106 mm4

J106 mm4

G1W 2084 25 239 10 516 932.2 137.9 1108.8 181.3 7742.1G1E 2084 25 239 10 516 1663.8 231.6 1765.3 288.0 7742.1G2 2111 25 792 10 747 1639.1 231.6 1740.4 288.0 7742.1G3 1942 22 109 9 212 1820.6 231.6 1922.1 288.0 7742.1G4E 2197 24 002 10 001 967.9 137.9 1148.8 181.3 1373.2G4W 2197 24 002 10 001 1722.1 231.6 1823.8 288.0 1373.2

Table 6. Material and section properties of the girder elements.

Concrete shear strength Vc The modified Zsuttys T-section formula along with the concrete shear strength(1968) was used in calculating Vc[6] V v b d hc c leg f= +( )2where

v f da

c c w2.137=

r1 3/

bleg is the web width of one leg only and hf is the height ofthe flange; rw is the longitudinal reinforcement ratio, d anda are the effective depth and shear span, respectively.

Stirrups shear strength Vs The stirrup contribution wascomputed by the simplified equation given in CSA-A23.3(1994) Standard

[7] V A f ds

ssv vy=

Fibre reinforced polymer sheets shear strength VFRP Theshear friction formulation in CSA-A23.3 (1994) is used herewith some modifications for VFRP[8] VFRP = (vr vc)Acv sinafwhere

v k f Er c v FRP f= +s r e amax coss r e a= v FRP fE max sin

rv vfcv

= AA

k = 0.6 for concrete placed monolithically, emax is the maxi-mum extrapolated strain (reported in Table 5) of the sheets,af is the angle between the shear friction reinforcement andthe shear plane, and Avf and Acv are the area of shear frictionreinforcement and concrete section resisting shear transfer,respectively. For consistency with the stirrups and concreteshear contribution previously defined, a shear plane of 45was assumed. Since the FRP sheets were glued only on theinner face, half of the concrete web was assumed to transfershear stresses, as shown in Fig. 12. The shear strength calcu-lations are summarized in Table 7 for each test.The elastic grid analysis was conducted using the com-

mercial package SAP90. The boundary conditions of thegrid model were such that the Far Unloaded support wasable to lift up. The maximum load applied on the top of thegirder was obtained when one of the elements reached its as-sumed capacity (see Table 7). Because the end diaphragmoften failed first, a second elastic analysis was performedwith the end diaphragm element removed. The maximumapplied load was then given by the failure of one of theloaded leg element.

Discussion

GeneralThe ultimate load predictions from each method along

with the test results are presented in Table 8. A typical com-parison of the load vs. deflection curve for Girder 3 Westamong the three design methods investigated, along with thetest results, is shown in Fig. 13. The ratio of Loaded overUnloaded leg deflection at the load point location was about1.5 at the beginning, which is equivalent to 60% and 40%load sharing in bending for the Loaded and Unloaded leg,respectively. This value increased significantly at ultimate. Itindicated that the girder no longer behaved linearly and as awhole inverted U section. This behavior is difficult to assessfully with the methods presented. A more sophisticated anal-ysis, such as the finite element method, could be performed.The FRP stiffness per unit widths (EFRP times tFRP) pro-

vided by the glass and carbon fibres are almost identical at31.9 and 31.4 kN/mm, respectively. However, the fibres ori-ented at 45 were found to perform better than the verticalsheets. In the former case, the concrete cracks were almostat right angles to the principal orientation of the fibres. Thecomposite sheets were therefore very effective in controllingthe crack widths. This effect is evident in the shear strengthsof the girder elements in the grid method (see Table 7).The strut-and-tie model is known to be a lower bound so-

lution. The predicted results, as shown in Table 8, are con- 2000 NRC Canada

968 Can. J. Civ. Eng. Vol. 27, 2000

Fig. 11. Geometry for the triangular stress block.

DiaphragmTcr(kN m)

Leg with two 28.6 mm

Leg with three 28.6 mm

GirderMr(kN m)

Vr(kN)

Mr(kN m)

Vr(kN)

G1W 49.1 130.4 168.7 181.2 153.4G1E 49.1 267.6 200.1 308.6 178.0G2E 55.7 284.4 213.0 332.3 194.2G2W 55.7 272.0 235.3 312.9 216.4G3E 53.6 258.8 222.1 296.7 203.8G3W 53.6 264.2 266.3 305.0 248.0G4E 14.3 120.3 161.8 163.6 144.0G4W 14.3 249.5 210.2 282.3 188.8

Table 7. Strength of the girder elements.

Fig. 12. Shear friction assumptions with FRP sheets.

servative except for Girder 2 East, which was stoppedprematurely.The MCFT method considers only a rectangular concrete

stress block when computing the bending moment for the T-beam section, which can only lead to an approximation ofthe capacity of the leg under an eccentric loading. The ap-proximation can be improved, however, by using a triangularstress block as shown in Fig. 11.The grid analysis can accommodate various loading con-

ditions or combinations. The initial stage of the load deflec-tion curve can be predicted with reasonable accuracy, asshown in Fig. 13. However, the flexural strength of the ele-ment must be evaluated with care, since the load sharing be-tween the two legs varies with the position of the appliedload. Since this method is limited to elastic analysis, assess-ing the cracking moment in the end panel of the girder be-comes difficult. Girder 3 West, for example, did not fail inthe diaphragm, but the analysis predicts end panel cracking.The maximum load is then governed by flexural failure ofthe leg element rather than shear failure. However, if one ig-nores the cracking at the end diaphragm in the grid analysis,the predicted shear capacity of the leg element is at almostthe same load level as the previous prediction based on flex-ural failure.The shear friction approach used to evaluate the contribu-

tion of the composite sheets gives simple but reasonable re-sults. The Canadian standard CSA-A23.3 (1994), however,presents two methods that yield a range of shear strength.More research should be undertaken to refine or specify apreferred method between these two formulations when ap-plied to composites.

Comparison of the modelsThe predictions for each method are presented in Table 8.

A ratio Ptest over Ppred ranges from 1.11 to 1.69 (excludingGirder 2 East, which was stopped prematurely) with a meanratio of 1.33 and a coefficient of variation 11.0% for all ofthree methods. Because of the complex loading with combi-nation of bending, shear, and torsion, it is unreasonable toexpect better accuracy with the assumptions and simplifica-tions necessary for the analysis. However, the three methodsare consistent with each other and in most cases yield simi-lar ultimate loads. Most of the predictions are conservativeand therefore can be used for the design of strengthening el-ements.

A good correlation between the MCFT and the strut-and-tie model was found for almost all tests except Girder 1East. In this test, the girder was strengthened only by a steelplate that gave a heavy longitudinal reinforcement. The stir-rups spacing of 380 mm was too large to assume uniformconcrete struts, as is assumed in the MCFT method (Collinsand Mitchell 1987).A truss at 45 was assumed for the shear friction evalua-

tion. A variable angle truss can also be used as long as otherstrength evaluations are consistent. On the other hand, theMCFT can accommodate variable truss angle but requirescomputerized codes and software support.Evaluating the material and cross-sectional properties of

the girder is a critical factor to achieve reliable predictions.However, it can sometimes be difficult to evaluate theseproperties from existing structures.

Summary and conclusions

This series of tests has investigated the benefit of usingFRP sheets in the shear rehabilitation of type G-girders. Atotal of eight tests were performed on four type G-girders re-moved from existing bridges. Carbon and glass FRP sheetsand two repair configurations were used in the rehabilitation.All of the girders were loaded eccentrically about the cen-troid of the cross section in order to fail the girders in com-bination of shear and torsion. Three commonly used shearstrength evaluation methods, strut-and-tie model, MCFT, andgrid analysis, were investigated.

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Testresults(kN)

MethodsStrut-and-tie MCFT Grid analysis

Girder (kN) Ptest/Ppred (kN) Ptest/Ppred (kN) Ptest/PpredG1W 281.9 230.2 1.225 210.6 1.339 195.9 1.439G2E 351.0 409.5 0.857 393.3 0.892 281.1 1.248G2W 412.6 313.4 1.316 320.1 1.289 310.5 1.329G3E 393.0 319.1 1.232 330.4 1.190 293.1 1.341G3W 414.8 364.6 1.138 373.8 1.110 340.6 1.218G4E 259.0 172.6 1.501 171.1 1.514 179.5 1.443G4W 395.7 315.7 1.254 313.7 1.261 277.4 1.427G1E 383.1 331.7 1.155 226.3 1.693 264.1 1.451

Table 8. Ultimate point load predictions.

Fig. 13. Typical point load deflection comparisons (Girder 3 West).

The steel plate used to increase the flexural strength of thegirders was found to provide significant increase in the shearcapacity. The FRP sheets contributed to the increase of thetotal shear capacity of the girders by 5 to 17%. For the tworepair schemes investigated, the inclined sheets were foundto be more effective than the vertical sheets. The woven fab-ric glass materials performed better than the unidirectionalcarbon FRP sheets. The end panel was the weakest part ofthe girders under eccentric loading because it did not containsteel reinforcement. The vertical bands of FRP sheets ap-plied in the inner face of the round end diaphragm were noteffective, except for one case in which woven glass fibre wasused. Better results were obtained when the horizontal sheetswere used in the square end diaphragm. The FRP sheets didnot fully develop their maximum capacity throughout thetests. Therefore, the maximum strength of the fibres was nota design criterion in this type of application.The three shear evaluation methods presented in this study

were consistent with each other. The test-to-predicted ratiosbased on these three methods ranged from 1.11 to 1.69 witha mean ratio of 1.33 and a coefficient of variation of 11.0%.The shear contribution of composite sheets at any angle canbe accurately accounted for in the analysis. The strut-and-tiemodel and the MCFT are limited to the prediction of the ul-timate shear capacity of the girders, while the grid analysisprovides the complete load deflection curves with accuracylimited to the elastic range. Most of the predictions based onthese three design methods are conservative and thereforecan be used to design the shear rehabilitation of concretegirders using externally bonded FRP sheets.

Acknowledgements

This work was supported by ISIS (Intelligent Sensing forInnovative Structures) Canada, a participant in the Networkof Centres of Excellence. The G-girders tested were donatedby AT&U. Fibre reinforced polymer materials were suppliedby Mitsubishi Canada Ltd., Fyfe LLC Ltd., and Sika CanadaInc. The authors would also like to acknowledge the techni-cal support from Fyfe LLC Ltd. and technicians at the I.F.Morrison Structures Laboratory, University of Alberta.

References

Alexander, J., and Cheng, J.J.R. 1997. Shear rehabilitation of G-girder bridges using CFRP sheets. Structural Engineering ReportNo. 218, Department of Civil and Environmental Engineering,University of Alberta, Edmonton, Alta.

ASTM. 1994. Standard test method for obtaining and testingdrilled cores and sawed beams of concrete. ASTM C-42, AnnualBook of ASTM Standards, Philadelphia, Pa., pp. 2427.

ASTM. 1996. Standard test methods and definitions for mechanicaltesting of steel products. ASTM A-370, Annual Book of ASTMStandards, Philadelphia, Pa., pp. 164200.

Bartlett, F.M., and MacGregor, J.G. 1994. Assessment of concretestrength in existing structures. Structural Engineering ReportNo. 198, Department of Civil and Environmental Engineering,University of Alberta, Edmonton, Alta.

Collins, M.P., and Mitchell, D. 1987. Prestressed concrete basics.1st ed. Canadian Prestressed Concrete Institute, Ottawa, Ont.

CSA. 1988. Design of highway bridges. Standard CAN/CSA-S6,Canadian Standards Association, Rexdale, Ont.

CSA. 1994. Design of concrete structures. Standard A23.3-94, Ca-nadian Standards Association, Rexdale, Ont.

Oden, J.T., and Ripperger, E.A. 1981. Mechanics of elastic struc-tures. 2nd ed. McGraw Hill,

Zsutty, T.C. 1968. Beam shear strength prediction by analysis ofexisting data. American Concrete Institute Structural Journal,65: 943951.

List of symbols

a shear spanAcv area of the concrete section resisting shear transfer

AFRP FRP sheet areaAsv vertical steel areaAvf area of shear friction reinforcementbleg width of one leg for a hat-shaped beambw minimum effective web width within depth dd effective beam depth (distance from extreme compres-

sion fibre to centroid of tension reinforcement)dFRP FRP sheet height along the side of the beam webdv distance between the resultant of the tensile and com-

pressive forces due to flexureE modulus of elasticity of steelEc modulus of elasticity of concrete

EFRP elastic tensile modulus of the FRP sheets in the princi-pal direction of the fibres

f1 concrete principal tension stressf2 concrete principal compression stress

f2max limiting compressive stress in concrete strutfc compressive strength of concretefcr cracking strength of concretefv stirrups stressfvy yield strength of stirrupsfy yield strength of steelFu ultimate strength of steelGc shear modulus of concreteh beam heighthf flange heightJ St. Venant torsion constantM moment occurring simultaneously with V

M rR resisting moment with the rectangular stress blockM rT resisting moment with the triangular stress block

s stirrup spacingsFRP FRP sheet bands spacingTcr diaphragm cracking torquetFRP thickness of the FRP sheet

V total shear loadVc shear load resistance attributed to the concrete

VFRP shear load resistance provided by the FRP sheetsVr total shear load resistanceVs shear load resistance provided by the stirrupsv concrete shear stressvc concrete shear strength

vFRP FRP shear stressvr shear stress resistance of the shear planevs stirrup shear stressa angle between the principal direction of the FRP sheets

and the longitudinal axis of the beama f angle between the principal direction of the FRP sheets

and the shear planegc density of concrete

eFRP FRP strain in the principal direction of the fibres

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emax extrapolated maximum FRP strain in the principal direc-tion of the fibres at ultimate

et vertical strainex longitudinal strain of flexural tension chord of the mem-

berey yield strain of the steel stirrupse1 principal tensile strain in cracked concrete

e2 principal compressive strain in cracked concreteq crack angle w.r.t. the longitudinal axis of the beam

nc concrete Poissons ratio (= 0.2)rv = Avf/Acvrw longitudinal reinforcement ratios effective normal stress

sFRP FRP stresses in the principal direction of the fibres