Research ArticleFlexural and Shear Behavior of FRP Strengthened AASHTOType Concrete Bridge Girders
Nur Yazdani1 Farzia Haque2 and Istiaque Hasan3
1Civil Engineering Department University of Texas at Arlington Arlington TX USA2Bridge Division Texas Department of Transportation Dallas District Dallas TX USA3Pennoni Associates Philadelphia PA USA
Correspondence should be addressed to Nur Yazdani yazdaniutaedu
Received 29 July 2016 Accepted 19 October 2016
Academic Editor Claudio Mazzotti
Copyright copy 2016 Nur Yazdani et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Fiber-reinforced polymers (FRP) are being increasingly used for the repair and strengthening of deteriorated or unsafe concretestructures including structurally deficient concrete highway bridges The behavior of FRP strengthened concrete bridge girdersincluding failure modes failure loads and deflections can be determined using an analytical finite element modeling approach asoutlined in this paper The differences in flexural versus shear FRP strengthening and comparison with available design guidelinesare also beneficial to design professionals In this paper a common AASHTO type prestressed concrete bridge girder with FRPwrapping was analyzed using the ANSYS FEM software and the ACI analytical approach Both flexural and shear FRP applicationsincluding vertical and inclined shear strengthening were examined Results showed that FRP wrapping can significantly benefitconcrete bridge girders in terms of flexureshear capacity increase deflection reduction and crack control The FRP strength wasunderutilized in the section selected herein which could be addressed through decrease of the amount of FRP and prestressing steelused thereby increasing the section ductility The ACI approach produced comparable results to the FEM and can be effectivelyand conveniently used in design
1 Introduction
Fiber-reinforced polymers (FRP) are recent innovations instructural engineering as compared to concrete steel andwoodThesematerials have certain advantages over the tradi-tional materials such as high stiffness-to-weight andstrength-to-weight ratios corrosion resistance and con-structability Civil engineering applications of FRP sheetsinclude rehabilitation or restoration of the strength of adeteriorated structural member retrofitting or strengtheninga sound structural member to resist increased loads andcorrection of design or construction errors FRP wrappingis increasingly being used with structural members made ofreinforced concrete prestressed concrete and masonry
One area in which FRP sheets are being used quitefrequently in recent years is the strengthening of structurallydeficient or damaged concrete bridges As is widely known asignificant percentage of the bridges in the US is structurallydeficient Deficiency in bridges can be caused by design
flaws deterioration due to environmental impact increasein service loads and accidental vehicular impacts [1] Tradi-tional techniques to strengthen structural members includeexternally bonded steel plates steel or concrete jackets andexternal posttensioning (ACI) [2] Labor and equipmentcosts to install FRP systems are often lower than traditionaltechniques and installation is easier in areas with limitedaccess FRP systems also provide better aesthetics in manycases
FRP wrapping of concrete bridge girders and columnscan improve flexural shear corrosion seismic and impactresistance (Figure 1) A state-of-the-art report by ACI Com-mittee 440 [2] provides guidance for the selection designand installation of FRP wrapping systems for externallystrengthening concrete structures based on experimentalresearch analytical work and field applications The ACIreport outlines design procedure for flexure shear and axialforce and combined axial and bending forces which are con-sidered to be conservative ACI 440 also mentions areas that
Hindawi Publishing CorporationJournal of EngineeringVolume 2016 Article ID 5201910 10 pageshttpdxdoiorg10115520165201910
2 Journal of Engineering
Figure 1 FRP Flexural and shear strengthening
Figure 2 AASHTO type bridge girders with composite deck
require additional research including theoretical modelingof FRP strengthened structures Besides experimental andfield tests finite element models (FEM) of FRP strengthenedstructural members are an alternate and economic avenue todetermine their behavior
The objective of this study [3] was to model a prestressedconcrete AASHTO type IV bridge girder using the finiteelement software ANSYS [4] to analyze flexural and shearstrengthening with FRP and to compare the results obtainedwith ACI 440 provisions AASHTO type IV bridge girdersare popular for moderate spans (24 to 36m) and are widelyused in the USA (Figure 2) This study provides importantinformation on the FEM procedure for FRP strengthenedprestressed concrete girders The results obtained are veryhelpful to designers and researchers in understanding practi-cal and cost-effective design procedure for flexure and shearstrengthening of prestressed concrete bridge girderswith FRPwrapping
Experimental and analytical studies of Carbon FRP(CFRP) retrofitted prestressed concrete girders showed thatthe use of CFRP can result in increased moment and shearresisting capacities Di Ludovico et al [5] investigated fiveprestressed concrete I-shaped girders which were designedaccording to ANAS (Italian Transportation Institute) Oneof them was undamaged two of them were predamagedand two of them were CFRP retrofitted Four-point loadingusing two hydraulic jacks was applied up to theoreticalyielding It was suggested that fiber debonding between thegirder and CFRP may take place in the undamaged girderwhich has to be prevented to restore full flexural capacity Itwas found that the U-shaped CFRP laminates experienced
1 strain before debonding Cementitious mortar had tobe placed between concrete and the repair zone to ensureperfect bonding Both stiffness and flexural moment capacityof girders increased due to CFRP wrapping Cerullo et al[6] conducted an investigation on a real decommissionedbridge girder repaired with externally bonded CFRP Repairof one AASHTO type III concrete girder was carried outfrom a damaged bridge Before CFRP application cracks onthe damaged girder were mapped and flexural behavior wasexamined by elastic load test The shear strength deficiencyof the girder was found by investigating the crack patternand spalling of concrete Horizontal cracks caused by flexuralloading could successfully be repaired using CFRP TheCanadian Standards Association (CSA) code was found tobe conservative for design The CFRP retrofitting took onlythree days which was found to be very convenient Pettyet al [7] tested eight simply supported I-shaped 42-year-old prestressed concrete bridge girders retrofitted with CFRPfor ultimate shear capacity A single concentrated load wasapplied near the critical shear load location Only 54 of thetensile capacity of CFRP could be utilized due to the variationin cross section of the girder The strut-and-tie model wasfound to be effective in predicting the shear capacity of thegirders The AASHTO LRFD method was found to be moreaccurate than the ACI approach for shear capacity predictionof bridge girders The girder shear capacity increased by 36due to the vertical U-shaped strips
Several design guides standards and manufacturersquosguidelines are available worldwide for the design and analysisof FRP strengthening systems for concrete structures Someof these provisions are based on theoretical models whileothers are based on experimental work [8] In the USA theprimary designanalysis source is the guidelines publishedby Committee 440 of the American Concrete InstituteIn ACI 440 the design recommendations are based onlimit state method and strengthserviceability requirementsAdditional load factors are applied to the contribution of theFRP reinforcement These factors were determined based onstatistical evaluation of variability in mechanical propertiespredicted versus full-scale test results and field evaluationsThe following failure modes are considered (1) crushing ofconcrete before yielding of the reinforcing steel (2) yieldingof tension steel followed by rupture of the FRP laminate (3)yielding of the tension steel followed by concrete crushing(4) sheartension delamination of the concrete cover and(5) debonding of the FRP from the concrete substrate [8]Although Mode 2 is preferred in order to fully utilize thestrengths of both the prestressing steel and the FRP laminatelaboratory testing to date has only shown this mode as apossibility for beams with proper detailing In most casesMode 4 has controlled the failures Additional informationon this failure mode is available in the literature [9ndash12]
2 Materials and Methods
ANSYS Parametric Design Language (APDL) 145 was usedherein to model a typical AASHTO type IV I-girder ANSYSis capable of predicting the nonlinear behavior of FRP
Journal of Engineering 3
strengthened prestressed girders A simply supported typicalinterior girder with a span of 24m was considered
Three types of ANSYS elements were used in the modelThe Solid 65 element was used to create 3D models ofconcrete This element is capable of simulating concretecracking in tension and crushing in compression It haseight nodes and three degrees of freedom at each nodetranslations in the nodal 119909 119910 and 119911 directions This elementis also capable of simulating plastic deformation and creepLink 180 element (uniaxial tension-compression) was usedto model the prestressing steel and shear reinforcementsIt has two nodes with three degrees of freedom at eachnode translations in the nodal 119909 119910 and 119911 directions Thiselement is capable of rotation large deflection and largestrain FRPwrappingwasmodeled using the Shell 41 elementThis element has four nodes and three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsShell 41 is a 3D element having membrane stiffness but nobending stiffness and has variable thickness stress stiffeningand large deflection options
Four sets of FEM real constants (constitutive properties)were used Set 1 for the Solid 65 elements had the smearedreinforcement material numbers volume ratio and orienta-tion angle entered as zero as reinforcementwasmodeledwithLink 180 elements Set 2 was used for the Link 180 elementto represent longitudinal prestressing steel Set 3 was usedfor Link 180 element to represent the stirrups and Set 4 wasused for Shell 41 elements to model the epoxy adhesive Set5 was used for the FRP modeling with Shell 41 elementsOther parameters such as element 119909-axis rotation elasticfoundation stiffness and added mass were entered as zeroas they were not applicable for this model
The material properties were defined by five models forconcrete mild steel rebar prestressed steel epoxy and FRPParameters needed to define the material models are shownin Table 1
Material Model 1 was defined for concrete The Solid65 element requires linear isotropic and multilinear isotropicconcrete material properties The multilinear isotropic mate-rial uses theVonMises failure criterion alongwith theWillamand Warnke [13] model to define the concrete failure Theconcrete compressive uniaxial stress-strain relationship wasobtained using the following equations fromMacGregor [14]
where 119864119888 is modulus of elasticity 119891 is stress at any strain 120576and 120576∘ is strain at the ultimate compressive strength 1198911015840119888
The multilinear relationship requires the first point ofthe curve to be defined by the user and satisfy HookersquosLaw The curve is used to help with convergence of thenonlinear solution algorithm Figure 3(a) shows the concretestress-strain relationship based onMacGregor [14] Linearity
Table 1 Material models [9] and properties for FEM
Model 1 concrete (linear and trilinear isotropic)Density 2400 kgm3
Modulus of elasticity 34GPaInitial modulus of elasticity 30GPa28-day compressive strength 48MPaInitial compressive strength 34MPaPoissonrsquos ratio 02Open crack shear transfer coefficient 03Closed crack shear transfer coefficient 1Uniaxial cracking stress 433MPaUniaxial crushing stress minus1
Model 2 shear steel (bilinear isotropic)Modulus of elasticity 1999GPaPoissonrsquos ratio 03Yield strength 414MPa
Model 3 prestressing steel (linear isotropic)Modulus of elasticity 193053MPaUltimate tensile strength 1862MPaPoissonrsquos ratio 03
Model 4 epoxy (linear isotropic)Modulus of elasticity 2758MPaPoissonrsquos ratio 04
Model 5 CFRP (linear orthotropic)Modulus of elasticity (primary direction) 62053MPaOther modulus of elasticity 4826MPaUltimate tensile strength 931MPaPoissonrsquos ratio 022Shear modulus 3266MPa
changes at 03 1198911015840119888 and at a point defined by 1198911015840119888 and 120576∘ = 0003indicating traditional crushing strain for unconfined con-crete The intermediate points were calculated using (1) Theshear transfer coefficients for open and closed cracks weredetermined using Wolanski [15] as a basis The uniaxialcracking stress was based on the modulus of rupture 119891119903 asshown in the following equation [16]
119891119903 = 75radic1198911015840119888 (2)
The other variables in the concrete model were left todefault
Vertical or inclined U-stirrups of 95mm diameter werespaced at 457mm center throughout the span MaterialModel 2 for shear steel was bilinear isotropic requiring theyield stress and the tangent modulus of the steel to be defined(Table 1) The prestressing steel consisted of 28 tendonsthat were 12mm in diameter The tendons were arranged intwo layers in the bottom flange of the girder as shown inFigure 4(a) They were lumped and modeled as concentratedat the center of the 28 tendons connecting the nodes at127mm from the bottom surface of the girder MaterialModel 3 for prestressing steel as shown in Figure 3(b) was
4 Journal of Engineering
0
10
20
30
40
50
60
0 0002 0004
Stre
ss (M
Pa)
Strain (a) Concrete
0
500
1000
1500
2000
0 002 004
Stre
ss (M
Pa)
Strain (b) Prestressing steel
0
200
400
600
800
1000
0 001 002
Stre
ss (M
Pa)
Strain(c) FRP
Figure 3 Material stress-strain curves for FEM
508
152
229203
660
203
229
584
152
203
1371
strands28ndash12mm dia
(a) Actual
279
775
317
1371
660
203
508
(b) Modified (c) Meshed
Figure 4 Girder cross sections (mm)
Journal of Engineering 5
(a) Concrete (b) Stirrup and prestressing steel
(c) Flexural FRP (d) Shear FRP
Figure 5 Concrete steel and FRP models
multilinear isotropic following the VonMises failure criteriausing the following [15]
120576119901119904 le 0008119891119901119904 = 193053120576119901119904 (MPa) 120576119901119904 gt 0008119891119901119904 = [268 minus 0075120576119901119904 minus 00065] times 01450377lt 098119891119901119906 (MPa)
(3)
where 120576119901119904 is strain in prestressing steel and 119891119901119904 is stress inprestressing steel
The assumed thickness of epoxy adhesive was 051mmMaterialModel 4 for the epoxywas linear isotropic (Table 1)The one-layer CFRP sheet thickness was assumed as 1mmand was represented with Model 5 with linear orthotropicproperties as shown in Figure 3(c) The assumed values forthe CFRP and epoxy are common and can be found at manu-facturerrsquos websites
AASHTO type IV girder section is not quite adaptable forFEMmeshing and reinforcement modeling Therefore someconversion was made with the converted shape having thesame area and height as the original girder and almost thesamemoment of inertia Figure 4 shows the actual convertedand FEM meshed girder sections and Table 2 shows thecomparison of the cross-sectional properties The area wasmeshed with 76mmmesh size based on the nodes needed
Table 2 Original and transformed girder sections
Original TransformedArea mm2 709031 709031Gross moment of inertia m4 01085 01094Distance to centroid from top mm 628 627Height mm 1300 1300
to model reinforcement and the aspect ratio for the elementsThe meshed area with 140 nodes was extruded for the 24mspan length as shown in Figure 5(a)The volume was dividedinto 53 elements along the longitudinal direction to allowfor modeling of the stirrups The prestressing steel model isshown in Figure 5(b) A two-layered section was used for theepoxy and FRP models (Figures 5(c) and 5(d))
Five different girders with FRP and load configurationswere investigated herein through separate modeling Con-figurations 1 and 2 (controls) were girders without any FRPapplication and flexural or shear failure mode respectivelyConfiguration 3 assumed one layer of FRP for flexuralstrengthening throughout the bottom of the girder bottomflange Configuration 4 for shear strengthening involvedvertical U-wrap FRP throughout the girder span whileConfiguration 5 hadU-wrap FRP as 45-degree inclined stripsthroughout the spanThe shear cracks in beams are developedby diagonal tension Therefore it is expected that the 45-degree U-wraps will be more efficient in arresting the shearcracks as the orientation of the fiber is perpendicular to thecrack in this configuration
6 Journal of Engineering
24m
P
(a) Flexural load24m
P
(b) Shear load
Figure 6 Load configurations on span
minus0879Eminus03
0077391
0155662
0233932
0312202
0390472
0468743
0547013
0625283
07
Figure 7 Camber due to prestress flexural strengthening
For the FRP strengthened and control girders the flexuraland shear designs were based on the AASHTO LRFD BridgeSpecifications [17] and ACI 440 provisions [2]
21 Nonlinear Analysis The 24m simple span was simulatedwith a three-point loading setup For Configurations 1 and 3the point loadwas applied atmid-span formaximumbendingmoment effect as shown in Figure 6(a) For Configurations2 4 and 5 the point load was applied adjacent to thesupport formaximum shear force effect (Figure 6(b)) A staticanalysis approach was utilized herein with simple supportdisplacement constraints provided at the nodes at the twoends In the first load step only initial prestrain was appliedPrestressing was defined using ANSYS Command Window[4] The initial strain was determined from the effective pre-stress and the modulus of elasticity of prestressing steel Theapplied prestress was 690MPa selected herein to facilitateconvergenceThe camber of themodel girder due to prestressis shown in Figure 7 In the second load step the self-weightof the girder was applied The FEM was set up to examinethree different girder behaviors initial cracking yielding ofthe prestressing steel and flexuralshear failure of the girderThe FRP strengthened beam design was developed in orderto avoid the Mode 4 [2] cover delamination failure in orderto concentrate on fully achieving the tensile strength of theFRP composite fabric
22 Analytical Calculations Hand calculation was usedherein to determine the expected theoretical capacities ofthe girders The analysis is based on the steel and concretestrengths and the cross-sectional properties and steel layout(both prestressed and regular) Provisions from theAASHTOLRFD were utilized for the strength analysis of the con-trol girder [17 Chapter 5] AASHTO LRFD Specifications
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Load
P (k
N)
Centerline deflection (mm)
Figure 8 Load-deflection curve for control unstrengthened girder
currently do not include provisions for the strength deter-mination of FRP strengthened bridge members Thereforeprovisions from theACI 440 guidelineswere used to calculateflexural strengths for the FRP-reinforced girders [2 Chapter10] No load factors or resistance factors were applied Basedon the theoretical flexural capacities equivalent three-pointconcentrated loads (Figure 6) were calculated from staticsThe analytical and FEM load capacities for each girder arecompared in Section 3
3 Results and Discussion
FEM results are presented herein in the form of the valuesof the equivalent concentrated applied load corresponding tothe various loading stages
31 Unstrengthened (Control) Girder for Flexure (Configura-tion 1) The flexural load-deflection curve for the controlgirder showed seven distinct points effective prestress addi-tion of self-weight zero deflection decompression initialcracking steel yielding and failure (Figure 8) Hand calcu-lations were used herein to validate the FEM results hereinas shown in Table 3 Initial prestress application stage initialflexural cracks cracking at yielding load and cracking atflexural capacity are shown in Figure 9 Nonconvergence ofthe nonlinear algorithm occurred at a load of 1003 kN indi-cating flexural failure The excessive cracking that occurred
Journal of Engineering 7
(a) Prestress and self-weight (b) Initial cracking
(c) At prestress yielding (d) At flexural capacity
Figure 9 Cracking stages control girder
Table 3 Flexural FEM and hand calculation results control girder
Parameter FEM Hand calculationsDeflection due toprestress mm
minus18 minus18Deflection atapplication ofself-weight mm
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
Figure 2 AASHTO type bridge girders with composite deck
require additional research including theoretical modelingof FRP strengthened structures Besides experimental andfield tests finite element models (FEM) of FRP strengthenedstructural members are an alternate and economic avenue todetermine their behavior
The objective of this study [3] was to model a prestressedconcrete AASHTO type IV bridge girder using the finiteelement software ANSYS [4] to analyze flexural and shearstrengthening with FRP and to compare the results obtainedwith ACI 440 provisions AASHTO type IV bridge girdersare popular for moderate spans (24 to 36m) and are widelyused in the USA (Figure 2) This study provides importantinformation on the FEM procedure for FRP strengthenedprestressed concrete girders The results obtained are veryhelpful to designers and researchers in understanding practi-cal and cost-effective design procedure for flexure and shearstrengthening of prestressed concrete bridge girderswith FRPwrapping
Experimental and analytical studies of Carbon FRP(CFRP) retrofitted prestressed concrete girders showed thatthe use of CFRP can result in increased moment and shearresisting capacities Di Ludovico et al [5] investigated fiveprestressed concrete I-shaped girders which were designedaccording to ANAS (Italian Transportation Institute) Oneof them was undamaged two of them were predamagedand two of them were CFRP retrofitted Four-point loadingusing two hydraulic jacks was applied up to theoreticalyielding It was suggested that fiber debonding between thegirder and CFRP may take place in the undamaged girderwhich has to be prevented to restore full flexural capacity Itwas found that the U-shaped CFRP laminates experienced
1 strain before debonding Cementitious mortar had tobe placed between concrete and the repair zone to ensureperfect bonding Both stiffness and flexural moment capacityof girders increased due to CFRP wrapping Cerullo et al[6] conducted an investigation on a real decommissionedbridge girder repaired with externally bonded CFRP Repairof one AASHTO type III concrete girder was carried outfrom a damaged bridge Before CFRP application cracks onthe damaged girder were mapped and flexural behavior wasexamined by elastic load test The shear strength deficiencyof the girder was found by investigating the crack patternand spalling of concrete Horizontal cracks caused by flexuralloading could successfully be repaired using CFRP TheCanadian Standards Association (CSA) code was found tobe conservative for design The CFRP retrofitting took onlythree days which was found to be very convenient Pettyet al [7] tested eight simply supported I-shaped 42-year-old prestressed concrete bridge girders retrofitted with CFRPfor ultimate shear capacity A single concentrated load wasapplied near the critical shear load location Only 54 of thetensile capacity of CFRP could be utilized due to the variationin cross section of the girder The strut-and-tie model wasfound to be effective in predicting the shear capacity of thegirders The AASHTO LRFD method was found to be moreaccurate than the ACI approach for shear capacity predictionof bridge girders The girder shear capacity increased by 36due to the vertical U-shaped strips
Several design guides standards and manufacturersquosguidelines are available worldwide for the design and analysisof FRP strengthening systems for concrete structures Someof these provisions are based on theoretical models whileothers are based on experimental work [8] In the USA theprimary designanalysis source is the guidelines publishedby Committee 440 of the American Concrete InstituteIn ACI 440 the design recommendations are based onlimit state method and strengthserviceability requirementsAdditional load factors are applied to the contribution of theFRP reinforcement These factors were determined based onstatistical evaluation of variability in mechanical propertiespredicted versus full-scale test results and field evaluationsThe following failure modes are considered (1) crushing ofconcrete before yielding of the reinforcing steel (2) yieldingof tension steel followed by rupture of the FRP laminate (3)yielding of the tension steel followed by concrete crushing(4) sheartension delamination of the concrete cover and(5) debonding of the FRP from the concrete substrate [8]Although Mode 2 is preferred in order to fully utilize thestrengths of both the prestressing steel and the FRP laminatelaboratory testing to date has only shown this mode as apossibility for beams with proper detailing In most casesMode 4 has controlled the failures Additional informationon this failure mode is available in the literature [9ndash12]
2 Materials and Methods
ANSYS Parametric Design Language (APDL) 145 was usedherein to model a typical AASHTO type IV I-girder ANSYSis capable of predicting the nonlinear behavior of FRP
Journal of Engineering 3
strengthened prestressed girders A simply supported typicalinterior girder with a span of 24m was considered
Three types of ANSYS elements were used in the modelThe Solid 65 element was used to create 3D models ofconcrete This element is capable of simulating concretecracking in tension and crushing in compression It haseight nodes and three degrees of freedom at each nodetranslations in the nodal 119909 119910 and 119911 directions This elementis also capable of simulating plastic deformation and creepLink 180 element (uniaxial tension-compression) was usedto model the prestressing steel and shear reinforcementsIt has two nodes with three degrees of freedom at eachnode translations in the nodal 119909 119910 and 119911 directions Thiselement is capable of rotation large deflection and largestrain FRPwrappingwasmodeled using the Shell 41 elementThis element has four nodes and three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsShell 41 is a 3D element having membrane stiffness but nobending stiffness and has variable thickness stress stiffeningand large deflection options
Four sets of FEM real constants (constitutive properties)were used Set 1 for the Solid 65 elements had the smearedreinforcement material numbers volume ratio and orienta-tion angle entered as zero as reinforcementwasmodeledwithLink 180 elements Set 2 was used for the Link 180 elementto represent longitudinal prestressing steel Set 3 was usedfor Link 180 element to represent the stirrups and Set 4 wasused for Shell 41 elements to model the epoxy adhesive Set5 was used for the FRP modeling with Shell 41 elementsOther parameters such as element 119909-axis rotation elasticfoundation stiffness and added mass were entered as zeroas they were not applicable for this model
The material properties were defined by five models forconcrete mild steel rebar prestressed steel epoxy and FRPParameters needed to define the material models are shownin Table 1
Material Model 1 was defined for concrete The Solid65 element requires linear isotropic and multilinear isotropicconcrete material properties The multilinear isotropic mate-rial uses theVonMises failure criterion alongwith theWillamand Warnke [13] model to define the concrete failure Theconcrete compressive uniaxial stress-strain relationship wasobtained using the following equations fromMacGregor [14]
where 119864119888 is modulus of elasticity 119891 is stress at any strain 120576and 120576∘ is strain at the ultimate compressive strength 1198911015840119888
The multilinear relationship requires the first point ofthe curve to be defined by the user and satisfy HookersquosLaw The curve is used to help with convergence of thenonlinear solution algorithm Figure 3(a) shows the concretestress-strain relationship based onMacGregor [14] Linearity
Table 1 Material models [9] and properties for FEM
Model 1 concrete (linear and trilinear isotropic)Density 2400 kgm3
Modulus of elasticity 34GPaInitial modulus of elasticity 30GPa28-day compressive strength 48MPaInitial compressive strength 34MPaPoissonrsquos ratio 02Open crack shear transfer coefficient 03Closed crack shear transfer coefficient 1Uniaxial cracking stress 433MPaUniaxial crushing stress minus1
Model 2 shear steel (bilinear isotropic)Modulus of elasticity 1999GPaPoissonrsquos ratio 03Yield strength 414MPa
Model 3 prestressing steel (linear isotropic)Modulus of elasticity 193053MPaUltimate tensile strength 1862MPaPoissonrsquos ratio 03
Model 4 epoxy (linear isotropic)Modulus of elasticity 2758MPaPoissonrsquos ratio 04
Model 5 CFRP (linear orthotropic)Modulus of elasticity (primary direction) 62053MPaOther modulus of elasticity 4826MPaUltimate tensile strength 931MPaPoissonrsquos ratio 022Shear modulus 3266MPa
changes at 03 1198911015840119888 and at a point defined by 1198911015840119888 and 120576∘ = 0003indicating traditional crushing strain for unconfined con-crete The intermediate points were calculated using (1) Theshear transfer coefficients for open and closed cracks weredetermined using Wolanski [15] as a basis The uniaxialcracking stress was based on the modulus of rupture 119891119903 asshown in the following equation [16]
119891119903 = 75radic1198911015840119888 (2)
The other variables in the concrete model were left todefault
Vertical or inclined U-stirrups of 95mm diameter werespaced at 457mm center throughout the span MaterialModel 2 for shear steel was bilinear isotropic requiring theyield stress and the tangent modulus of the steel to be defined(Table 1) The prestressing steel consisted of 28 tendonsthat were 12mm in diameter The tendons were arranged intwo layers in the bottom flange of the girder as shown inFigure 4(a) They were lumped and modeled as concentratedat the center of the 28 tendons connecting the nodes at127mm from the bottom surface of the girder MaterialModel 3 for prestressing steel as shown in Figure 3(b) was
4 Journal of Engineering
0
10
20
30
40
50
60
0 0002 0004
Stre
ss (M
Pa)
Strain (a) Concrete
0
500
1000
1500
2000
0 002 004
Stre
ss (M
Pa)
Strain (b) Prestressing steel
0
200
400
600
800
1000
0 001 002
Stre
ss (M
Pa)
Strain(c) FRP
Figure 3 Material stress-strain curves for FEM
508
152
229203
660
203
229
584
152
203
1371
strands28ndash12mm dia
(a) Actual
279
775
317
1371
660
203
508
(b) Modified (c) Meshed
Figure 4 Girder cross sections (mm)
Journal of Engineering 5
(a) Concrete (b) Stirrup and prestressing steel
(c) Flexural FRP (d) Shear FRP
Figure 5 Concrete steel and FRP models
multilinear isotropic following the VonMises failure criteriausing the following [15]
120576119901119904 le 0008119891119901119904 = 193053120576119901119904 (MPa) 120576119901119904 gt 0008119891119901119904 = [268 minus 0075120576119901119904 minus 00065] times 01450377lt 098119891119901119906 (MPa)
(3)
where 120576119901119904 is strain in prestressing steel and 119891119901119904 is stress inprestressing steel
The assumed thickness of epoxy adhesive was 051mmMaterialModel 4 for the epoxywas linear isotropic (Table 1)The one-layer CFRP sheet thickness was assumed as 1mmand was represented with Model 5 with linear orthotropicproperties as shown in Figure 3(c) The assumed values forthe CFRP and epoxy are common and can be found at manu-facturerrsquos websites
AASHTO type IV girder section is not quite adaptable forFEMmeshing and reinforcement modeling Therefore someconversion was made with the converted shape having thesame area and height as the original girder and almost thesamemoment of inertia Figure 4 shows the actual convertedand FEM meshed girder sections and Table 2 shows thecomparison of the cross-sectional properties The area wasmeshed with 76mmmesh size based on the nodes needed
Table 2 Original and transformed girder sections
Original TransformedArea mm2 709031 709031Gross moment of inertia m4 01085 01094Distance to centroid from top mm 628 627Height mm 1300 1300
to model reinforcement and the aspect ratio for the elementsThe meshed area with 140 nodes was extruded for the 24mspan length as shown in Figure 5(a)The volume was dividedinto 53 elements along the longitudinal direction to allowfor modeling of the stirrups The prestressing steel model isshown in Figure 5(b) A two-layered section was used for theepoxy and FRP models (Figures 5(c) and 5(d))
Five different girders with FRP and load configurationswere investigated herein through separate modeling Con-figurations 1 and 2 (controls) were girders without any FRPapplication and flexural or shear failure mode respectivelyConfiguration 3 assumed one layer of FRP for flexuralstrengthening throughout the bottom of the girder bottomflange Configuration 4 for shear strengthening involvedvertical U-wrap FRP throughout the girder span whileConfiguration 5 hadU-wrap FRP as 45-degree inclined stripsthroughout the spanThe shear cracks in beams are developedby diagonal tension Therefore it is expected that the 45-degree U-wraps will be more efficient in arresting the shearcracks as the orientation of the fiber is perpendicular to thecrack in this configuration
6 Journal of Engineering
24m
P
(a) Flexural load24m
P
(b) Shear load
Figure 6 Load configurations on span
minus0879Eminus03
0077391
0155662
0233932
0312202
0390472
0468743
0547013
0625283
07
Figure 7 Camber due to prestress flexural strengthening
For the FRP strengthened and control girders the flexuraland shear designs were based on the AASHTO LRFD BridgeSpecifications [17] and ACI 440 provisions [2]
21 Nonlinear Analysis The 24m simple span was simulatedwith a three-point loading setup For Configurations 1 and 3the point loadwas applied atmid-span formaximumbendingmoment effect as shown in Figure 6(a) For Configurations2 4 and 5 the point load was applied adjacent to thesupport formaximum shear force effect (Figure 6(b)) A staticanalysis approach was utilized herein with simple supportdisplacement constraints provided at the nodes at the twoends In the first load step only initial prestrain was appliedPrestressing was defined using ANSYS Command Window[4] The initial strain was determined from the effective pre-stress and the modulus of elasticity of prestressing steel Theapplied prestress was 690MPa selected herein to facilitateconvergenceThe camber of themodel girder due to prestressis shown in Figure 7 In the second load step the self-weightof the girder was applied The FEM was set up to examinethree different girder behaviors initial cracking yielding ofthe prestressing steel and flexuralshear failure of the girderThe FRP strengthened beam design was developed in orderto avoid the Mode 4 [2] cover delamination failure in orderto concentrate on fully achieving the tensile strength of theFRP composite fabric
22 Analytical Calculations Hand calculation was usedherein to determine the expected theoretical capacities ofthe girders The analysis is based on the steel and concretestrengths and the cross-sectional properties and steel layout(both prestressed and regular) Provisions from theAASHTOLRFD were utilized for the strength analysis of the con-trol girder [17 Chapter 5] AASHTO LRFD Specifications
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Load
P (k
N)
Centerline deflection (mm)
Figure 8 Load-deflection curve for control unstrengthened girder
currently do not include provisions for the strength deter-mination of FRP strengthened bridge members Thereforeprovisions from theACI 440 guidelineswere used to calculateflexural strengths for the FRP-reinforced girders [2 Chapter10] No load factors or resistance factors were applied Basedon the theoretical flexural capacities equivalent three-pointconcentrated loads (Figure 6) were calculated from staticsThe analytical and FEM load capacities for each girder arecompared in Section 3
3 Results and Discussion
FEM results are presented herein in the form of the valuesof the equivalent concentrated applied load corresponding tothe various loading stages
31 Unstrengthened (Control) Girder for Flexure (Configura-tion 1) The flexural load-deflection curve for the controlgirder showed seven distinct points effective prestress addi-tion of self-weight zero deflection decompression initialcracking steel yielding and failure (Figure 8) Hand calcu-lations were used herein to validate the FEM results hereinas shown in Table 3 Initial prestress application stage initialflexural cracks cracking at yielding load and cracking atflexural capacity are shown in Figure 9 Nonconvergence ofthe nonlinear algorithm occurred at a load of 1003 kN indi-cating flexural failure The excessive cracking that occurred
Journal of Engineering 7
(a) Prestress and self-weight (b) Initial cracking
(c) At prestress yielding (d) At flexural capacity
Figure 9 Cracking stages control girder
Table 3 Flexural FEM and hand calculation results control girder
Parameter FEM Hand calculationsDeflection due toprestress mm
minus18 minus18Deflection atapplication ofself-weight mm
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
strengthened prestressed girders A simply supported typicalinterior girder with a span of 24m was considered
Three types of ANSYS elements were used in the modelThe Solid 65 element was used to create 3D models ofconcrete This element is capable of simulating concretecracking in tension and crushing in compression It haseight nodes and three degrees of freedom at each nodetranslations in the nodal 119909 119910 and 119911 directions This elementis also capable of simulating plastic deformation and creepLink 180 element (uniaxial tension-compression) was usedto model the prestressing steel and shear reinforcementsIt has two nodes with three degrees of freedom at eachnode translations in the nodal 119909 119910 and 119911 directions Thiselement is capable of rotation large deflection and largestrain FRPwrappingwasmodeled using the Shell 41 elementThis element has four nodes and three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsShell 41 is a 3D element having membrane stiffness but nobending stiffness and has variable thickness stress stiffeningand large deflection options
Four sets of FEM real constants (constitutive properties)were used Set 1 for the Solid 65 elements had the smearedreinforcement material numbers volume ratio and orienta-tion angle entered as zero as reinforcementwasmodeledwithLink 180 elements Set 2 was used for the Link 180 elementto represent longitudinal prestressing steel Set 3 was usedfor Link 180 element to represent the stirrups and Set 4 wasused for Shell 41 elements to model the epoxy adhesive Set5 was used for the FRP modeling with Shell 41 elementsOther parameters such as element 119909-axis rotation elasticfoundation stiffness and added mass were entered as zeroas they were not applicable for this model
The material properties were defined by five models forconcrete mild steel rebar prestressed steel epoxy and FRPParameters needed to define the material models are shownin Table 1
Material Model 1 was defined for concrete The Solid65 element requires linear isotropic and multilinear isotropicconcrete material properties The multilinear isotropic mate-rial uses theVonMises failure criterion alongwith theWillamand Warnke [13] model to define the concrete failure Theconcrete compressive uniaxial stress-strain relationship wasobtained using the following equations fromMacGregor [14]
where 119864119888 is modulus of elasticity 119891 is stress at any strain 120576and 120576∘ is strain at the ultimate compressive strength 1198911015840119888
The multilinear relationship requires the first point ofthe curve to be defined by the user and satisfy HookersquosLaw The curve is used to help with convergence of thenonlinear solution algorithm Figure 3(a) shows the concretestress-strain relationship based onMacGregor [14] Linearity
Table 1 Material models [9] and properties for FEM
Model 1 concrete (linear and trilinear isotropic)Density 2400 kgm3
Modulus of elasticity 34GPaInitial modulus of elasticity 30GPa28-day compressive strength 48MPaInitial compressive strength 34MPaPoissonrsquos ratio 02Open crack shear transfer coefficient 03Closed crack shear transfer coefficient 1Uniaxial cracking stress 433MPaUniaxial crushing stress minus1
Model 2 shear steel (bilinear isotropic)Modulus of elasticity 1999GPaPoissonrsquos ratio 03Yield strength 414MPa
Model 3 prestressing steel (linear isotropic)Modulus of elasticity 193053MPaUltimate tensile strength 1862MPaPoissonrsquos ratio 03
Model 4 epoxy (linear isotropic)Modulus of elasticity 2758MPaPoissonrsquos ratio 04
Model 5 CFRP (linear orthotropic)Modulus of elasticity (primary direction) 62053MPaOther modulus of elasticity 4826MPaUltimate tensile strength 931MPaPoissonrsquos ratio 022Shear modulus 3266MPa
changes at 03 1198911015840119888 and at a point defined by 1198911015840119888 and 120576∘ = 0003indicating traditional crushing strain for unconfined con-crete The intermediate points were calculated using (1) Theshear transfer coefficients for open and closed cracks weredetermined using Wolanski [15] as a basis The uniaxialcracking stress was based on the modulus of rupture 119891119903 asshown in the following equation [16]
119891119903 = 75radic1198911015840119888 (2)
The other variables in the concrete model were left todefault
Vertical or inclined U-stirrups of 95mm diameter werespaced at 457mm center throughout the span MaterialModel 2 for shear steel was bilinear isotropic requiring theyield stress and the tangent modulus of the steel to be defined(Table 1) The prestressing steel consisted of 28 tendonsthat were 12mm in diameter The tendons were arranged intwo layers in the bottom flange of the girder as shown inFigure 4(a) They were lumped and modeled as concentratedat the center of the 28 tendons connecting the nodes at127mm from the bottom surface of the girder MaterialModel 3 for prestressing steel as shown in Figure 3(b) was
4 Journal of Engineering
0
10
20
30
40
50
60
0 0002 0004
Stre
ss (M
Pa)
Strain (a) Concrete
0
500
1000
1500
2000
0 002 004
Stre
ss (M
Pa)
Strain (b) Prestressing steel
0
200
400
600
800
1000
0 001 002
Stre
ss (M
Pa)
Strain(c) FRP
Figure 3 Material stress-strain curves for FEM
508
152
229203
660
203
229
584
152
203
1371
strands28ndash12mm dia
(a) Actual
279
775
317
1371
660
203
508
(b) Modified (c) Meshed
Figure 4 Girder cross sections (mm)
Journal of Engineering 5
(a) Concrete (b) Stirrup and prestressing steel
(c) Flexural FRP (d) Shear FRP
Figure 5 Concrete steel and FRP models
multilinear isotropic following the VonMises failure criteriausing the following [15]
120576119901119904 le 0008119891119901119904 = 193053120576119901119904 (MPa) 120576119901119904 gt 0008119891119901119904 = [268 minus 0075120576119901119904 minus 00065] times 01450377lt 098119891119901119906 (MPa)
(3)
where 120576119901119904 is strain in prestressing steel and 119891119901119904 is stress inprestressing steel
The assumed thickness of epoxy adhesive was 051mmMaterialModel 4 for the epoxywas linear isotropic (Table 1)The one-layer CFRP sheet thickness was assumed as 1mmand was represented with Model 5 with linear orthotropicproperties as shown in Figure 3(c) The assumed values forthe CFRP and epoxy are common and can be found at manu-facturerrsquos websites
AASHTO type IV girder section is not quite adaptable forFEMmeshing and reinforcement modeling Therefore someconversion was made with the converted shape having thesame area and height as the original girder and almost thesamemoment of inertia Figure 4 shows the actual convertedand FEM meshed girder sections and Table 2 shows thecomparison of the cross-sectional properties The area wasmeshed with 76mmmesh size based on the nodes needed
Table 2 Original and transformed girder sections
Original TransformedArea mm2 709031 709031Gross moment of inertia m4 01085 01094Distance to centroid from top mm 628 627Height mm 1300 1300
to model reinforcement and the aspect ratio for the elementsThe meshed area with 140 nodes was extruded for the 24mspan length as shown in Figure 5(a)The volume was dividedinto 53 elements along the longitudinal direction to allowfor modeling of the stirrups The prestressing steel model isshown in Figure 5(b) A two-layered section was used for theepoxy and FRP models (Figures 5(c) and 5(d))
Five different girders with FRP and load configurationswere investigated herein through separate modeling Con-figurations 1 and 2 (controls) were girders without any FRPapplication and flexural or shear failure mode respectivelyConfiguration 3 assumed one layer of FRP for flexuralstrengthening throughout the bottom of the girder bottomflange Configuration 4 for shear strengthening involvedvertical U-wrap FRP throughout the girder span whileConfiguration 5 hadU-wrap FRP as 45-degree inclined stripsthroughout the spanThe shear cracks in beams are developedby diagonal tension Therefore it is expected that the 45-degree U-wraps will be more efficient in arresting the shearcracks as the orientation of the fiber is perpendicular to thecrack in this configuration
6 Journal of Engineering
24m
P
(a) Flexural load24m
P
(b) Shear load
Figure 6 Load configurations on span
minus0879Eminus03
0077391
0155662
0233932
0312202
0390472
0468743
0547013
0625283
07
Figure 7 Camber due to prestress flexural strengthening
For the FRP strengthened and control girders the flexuraland shear designs were based on the AASHTO LRFD BridgeSpecifications [17] and ACI 440 provisions [2]
21 Nonlinear Analysis The 24m simple span was simulatedwith a three-point loading setup For Configurations 1 and 3the point loadwas applied atmid-span formaximumbendingmoment effect as shown in Figure 6(a) For Configurations2 4 and 5 the point load was applied adjacent to thesupport formaximum shear force effect (Figure 6(b)) A staticanalysis approach was utilized herein with simple supportdisplacement constraints provided at the nodes at the twoends In the first load step only initial prestrain was appliedPrestressing was defined using ANSYS Command Window[4] The initial strain was determined from the effective pre-stress and the modulus of elasticity of prestressing steel Theapplied prestress was 690MPa selected herein to facilitateconvergenceThe camber of themodel girder due to prestressis shown in Figure 7 In the second load step the self-weightof the girder was applied The FEM was set up to examinethree different girder behaviors initial cracking yielding ofthe prestressing steel and flexuralshear failure of the girderThe FRP strengthened beam design was developed in orderto avoid the Mode 4 [2] cover delamination failure in orderto concentrate on fully achieving the tensile strength of theFRP composite fabric
22 Analytical Calculations Hand calculation was usedherein to determine the expected theoretical capacities ofthe girders The analysis is based on the steel and concretestrengths and the cross-sectional properties and steel layout(both prestressed and regular) Provisions from theAASHTOLRFD were utilized for the strength analysis of the con-trol girder [17 Chapter 5] AASHTO LRFD Specifications
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Load
P (k
N)
Centerline deflection (mm)
Figure 8 Load-deflection curve for control unstrengthened girder
currently do not include provisions for the strength deter-mination of FRP strengthened bridge members Thereforeprovisions from theACI 440 guidelineswere used to calculateflexural strengths for the FRP-reinforced girders [2 Chapter10] No load factors or resistance factors were applied Basedon the theoretical flexural capacities equivalent three-pointconcentrated loads (Figure 6) were calculated from staticsThe analytical and FEM load capacities for each girder arecompared in Section 3
3 Results and Discussion
FEM results are presented herein in the form of the valuesof the equivalent concentrated applied load corresponding tothe various loading stages
31 Unstrengthened (Control) Girder for Flexure (Configura-tion 1) The flexural load-deflection curve for the controlgirder showed seven distinct points effective prestress addi-tion of self-weight zero deflection decompression initialcracking steel yielding and failure (Figure 8) Hand calcu-lations were used herein to validate the FEM results hereinas shown in Table 3 Initial prestress application stage initialflexural cracks cracking at yielding load and cracking atflexural capacity are shown in Figure 9 Nonconvergence ofthe nonlinear algorithm occurred at a load of 1003 kN indi-cating flexural failure The excessive cracking that occurred
Journal of Engineering 7
(a) Prestress and self-weight (b) Initial cracking
(c) At prestress yielding (d) At flexural capacity
Figure 9 Cracking stages control girder
Table 3 Flexural FEM and hand calculation results control girder
Parameter FEM Hand calculationsDeflection due toprestress mm
minus18 minus18Deflection atapplication ofself-weight mm
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
multilinear isotropic following the VonMises failure criteriausing the following [15]
120576119901119904 le 0008119891119901119904 = 193053120576119901119904 (MPa) 120576119901119904 gt 0008119891119901119904 = [268 minus 0075120576119901119904 minus 00065] times 01450377lt 098119891119901119906 (MPa)
(3)
where 120576119901119904 is strain in prestressing steel and 119891119901119904 is stress inprestressing steel
The assumed thickness of epoxy adhesive was 051mmMaterialModel 4 for the epoxywas linear isotropic (Table 1)The one-layer CFRP sheet thickness was assumed as 1mmand was represented with Model 5 with linear orthotropicproperties as shown in Figure 3(c) The assumed values forthe CFRP and epoxy are common and can be found at manu-facturerrsquos websites
AASHTO type IV girder section is not quite adaptable forFEMmeshing and reinforcement modeling Therefore someconversion was made with the converted shape having thesame area and height as the original girder and almost thesamemoment of inertia Figure 4 shows the actual convertedand FEM meshed girder sections and Table 2 shows thecomparison of the cross-sectional properties The area wasmeshed with 76mmmesh size based on the nodes needed
Table 2 Original and transformed girder sections
Original TransformedArea mm2 709031 709031Gross moment of inertia m4 01085 01094Distance to centroid from top mm 628 627Height mm 1300 1300
to model reinforcement and the aspect ratio for the elementsThe meshed area with 140 nodes was extruded for the 24mspan length as shown in Figure 5(a)The volume was dividedinto 53 elements along the longitudinal direction to allowfor modeling of the stirrups The prestressing steel model isshown in Figure 5(b) A two-layered section was used for theepoxy and FRP models (Figures 5(c) and 5(d))
Five different girders with FRP and load configurationswere investigated herein through separate modeling Con-figurations 1 and 2 (controls) were girders without any FRPapplication and flexural or shear failure mode respectivelyConfiguration 3 assumed one layer of FRP for flexuralstrengthening throughout the bottom of the girder bottomflange Configuration 4 for shear strengthening involvedvertical U-wrap FRP throughout the girder span whileConfiguration 5 hadU-wrap FRP as 45-degree inclined stripsthroughout the spanThe shear cracks in beams are developedby diagonal tension Therefore it is expected that the 45-degree U-wraps will be more efficient in arresting the shearcracks as the orientation of the fiber is perpendicular to thecrack in this configuration
6 Journal of Engineering
24m
P
(a) Flexural load24m
P
(b) Shear load
Figure 6 Load configurations on span
minus0879Eminus03
0077391
0155662
0233932
0312202
0390472
0468743
0547013
0625283
07
Figure 7 Camber due to prestress flexural strengthening
For the FRP strengthened and control girders the flexuraland shear designs were based on the AASHTO LRFD BridgeSpecifications [17] and ACI 440 provisions [2]
21 Nonlinear Analysis The 24m simple span was simulatedwith a three-point loading setup For Configurations 1 and 3the point loadwas applied atmid-span formaximumbendingmoment effect as shown in Figure 6(a) For Configurations2 4 and 5 the point load was applied adjacent to thesupport formaximum shear force effect (Figure 6(b)) A staticanalysis approach was utilized herein with simple supportdisplacement constraints provided at the nodes at the twoends In the first load step only initial prestrain was appliedPrestressing was defined using ANSYS Command Window[4] The initial strain was determined from the effective pre-stress and the modulus of elasticity of prestressing steel Theapplied prestress was 690MPa selected herein to facilitateconvergenceThe camber of themodel girder due to prestressis shown in Figure 7 In the second load step the self-weightof the girder was applied The FEM was set up to examinethree different girder behaviors initial cracking yielding ofthe prestressing steel and flexuralshear failure of the girderThe FRP strengthened beam design was developed in orderto avoid the Mode 4 [2] cover delamination failure in orderto concentrate on fully achieving the tensile strength of theFRP composite fabric
22 Analytical Calculations Hand calculation was usedherein to determine the expected theoretical capacities ofthe girders The analysis is based on the steel and concretestrengths and the cross-sectional properties and steel layout(both prestressed and regular) Provisions from theAASHTOLRFD were utilized for the strength analysis of the con-trol girder [17 Chapter 5] AASHTO LRFD Specifications
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Load
P (k
N)
Centerline deflection (mm)
Figure 8 Load-deflection curve for control unstrengthened girder
currently do not include provisions for the strength deter-mination of FRP strengthened bridge members Thereforeprovisions from theACI 440 guidelineswere used to calculateflexural strengths for the FRP-reinforced girders [2 Chapter10] No load factors or resistance factors were applied Basedon the theoretical flexural capacities equivalent three-pointconcentrated loads (Figure 6) were calculated from staticsThe analytical and FEM load capacities for each girder arecompared in Section 3
3 Results and Discussion
FEM results are presented herein in the form of the valuesof the equivalent concentrated applied load corresponding tothe various loading stages
31 Unstrengthened (Control) Girder for Flexure (Configura-tion 1) The flexural load-deflection curve for the controlgirder showed seven distinct points effective prestress addi-tion of self-weight zero deflection decompression initialcracking steel yielding and failure (Figure 8) Hand calcu-lations were used herein to validate the FEM results hereinas shown in Table 3 Initial prestress application stage initialflexural cracks cracking at yielding load and cracking atflexural capacity are shown in Figure 9 Nonconvergence ofthe nonlinear algorithm occurred at a load of 1003 kN indi-cating flexural failure The excessive cracking that occurred
Journal of Engineering 7
(a) Prestress and self-weight (b) Initial cracking
(c) At prestress yielding (d) At flexural capacity
Figure 9 Cracking stages control girder
Table 3 Flexural FEM and hand calculation results control girder
Parameter FEM Hand calculationsDeflection due toprestress mm
minus18 minus18Deflection atapplication ofself-weight mm
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
multilinear isotropic following the VonMises failure criteriausing the following [15]
120576119901119904 le 0008119891119901119904 = 193053120576119901119904 (MPa) 120576119901119904 gt 0008119891119901119904 = [268 minus 0075120576119901119904 minus 00065] times 01450377lt 098119891119901119906 (MPa)
(3)
where 120576119901119904 is strain in prestressing steel and 119891119901119904 is stress inprestressing steel
The assumed thickness of epoxy adhesive was 051mmMaterialModel 4 for the epoxywas linear isotropic (Table 1)The one-layer CFRP sheet thickness was assumed as 1mmand was represented with Model 5 with linear orthotropicproperties as shown in Figure 3(c) The assumed values forthe CFRP and epoxy are common and can be found at manu-facturerrsquos websites
AASHTO type IV girder section is not quite adaptable forFEMmeshing and reinforcement modeling Therefore someconversion was made with the converted shape having thesame area and height as the original girder and almost thesamemoment of inertia Figure 4 shows the actual convertedand FEM meshed girder sections and Table 2 shows thecomparison of the cross-sectional properties The area wasmeshed with 76mmmesh size based on the nodes needed
Table 2 Original and transformed girder sections
Original TransformedArea mm2 709031 709031Gross moment of inertia m4 01085 01094Distance to centroid from top mm 628 627Height mm 1300 1300
to model reinforcement and the aspect ratio for the elementsThe meshed area with 140 nodes was extruded for the 24mspan length as shown in Figure 5(a)The volume was dividedinto 53 elements along the longitudinal direction to allowfor modeling of the stirrups The prestressing steel model isshown in Figure 5(b) A two-layered section was used for theepoxy and FRP models (Figures 5(c) and 5(d))
Five different girders with FRP and load configurationswere investigated herein through separate modeling Con-figurations 1 and 2 (controls) were girders without any FRPapplication and flexural or shear failure mode respectivelyConfiguration 3 assumed one layer of FRP for flexuralstrengthening throughout the bottom of the girder bottomflange Configuration 4 for shear strengthening involvedvertical U-wrap FRP throughout the girder span whileConfiguration 5 hadU-wrap FRP as 45-degree inclined stripsthroughout the spanThe shear cracks in beams are developedby diagonal tension Therefore it is expected that the 45-degree U-wraps will be more efficient in arresting the shearcracks as the orientation of the fiber is perpendicular to thecrack in this configuration
6 Journal of Engineering
24m
P
(a) Flexural load24m
P
(b) Shear load
Figure 6 Load configurations on span
minus0879Eminus03
0077391
0155662
0233932
0312202
0390472
0468743
0547013
0625283
07
Figure 7 Camber due to prestress flexural strengthening
For the FRP strengthened and control girders the flexuraland shear designs were based on the AASHTO LRFD BridgeSpecifications [17] and ACI 440 provisions [2]
21 Nonlinear Analysis The 24m simple span was simulatedwith a three-point loading setup For Configurations 1 and 3the point loadwas applied atmid-span formaximumbendingmoment effect as shown in Figure 6(a) For Configurations2 4 and 5 the point load was applied adjacent to thesupport formaximum shear force effect (Figure 6(b)) A staticanalysis approach was utilized herein with simple supportdisplacement constraints provided at the nodes at the twoends In the first load step only initial prestrain was appliedPrestressing was defined using ANSYS Command Window[4] The initial strain was determined from the effective pre-stress and the modulus of elasticity of prestressing steel Theapplied prestress was 690MPa selected herein to facilitateconvergenceThe camber of themodel girder due to prestressis shown in Figure 7 In the second load step the self-weightof the girder was applied The FEM was set up to examinethree different girder behaviors initial cracking yielding ofthe prestressing steel and flexuralshear failure of the girderThe FRP strengthened beam design was developed in orderto avoid the Mode 4 [2] cover delamination failure in orderto concentrate on fully achieving the tensile strength of theFRP composite fabric
22 Analytical Calculations Hand calculation was usedherein to determine the expected theoretical capacities ofthe girders The analysis is based on the steel and concretestrengths and the cross-sectional properties and steel layout(both prestressed and regular) Provisions from theAASHTOLRFD were utilized for the strength analysis of the con-trol girder [17 Chapter 5] AASHTO LRFD Specifications
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Load
P (k
N)
Centerline deflection (mm)
Figure 8 Load-deflection curve for control unstrengthened girder
currently do not include provisions for the strength deter-mination of FRP strengthened bridge members Thereforeprovisions from theACI 440 guidelineswere used to calculateflexural strengths for the FRP-reinforced girders [2 Chapter10] No load factors or resistance factors were applied Basedon the theoretical flexural capacities equivalent three-pointconcentrated loads (Figure 6) were calculated from staticsThe analytical and FEM load capacities for each girder arecompared in Section 3
3 Results and Discussion
FEM results are presented herein in the form of the valuesof the equivalent concentrated applied load corresponding tothe various loading stages
31 Unstrengthened (Control) Girder for Flexure (Configura-tion 1) The flexural load-deflection curve for the controlgirder showed seven distinct points effective prestress addi-tion of self-weight zero deflection decompression initialcracking steel yielding and failure (Figure 8) Hand calcu-lations were used herein to validate the FEM results hereinas shown in Table 3 Initial prestress application stage initialflexural cracks cracking at yielding load and cracking atflexural capacity are shown in Figure 9 Nonconvergence ofthe nonlinear algorithm occurred at a load of 1003 kN indi-cating flexural failure The excessive cracking that occurred
Journal of Engineering 7
(a) Prestress and self-weight (b) Initial cracking
(c) At prestress yielding (d) At flexural capacity
Figure 9 Cracking stages control girder
Table 3 Flexural FEM and hand calculation results control girder
Parameter FEM Hand calculationsDeflection due toprestress mm
minus18 minus18Deflection atapplication ofself-weight mm
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
Figure 7 Camber due to prestress flexural strengthening
For the FRP strengthened and control girders the flexuraland shear designs were based on the AASHTO LRFD BridgeSpecifications [17] and ACI 440 provisions [2]
21 Nonlinear Analysis The 24m simple span was simulatedwith a three-point loading setup For Configurations 1 and 3the point loadwas applied atmid-span formaximumbendingmoment effect as shown in Figure 6(a) For Configurations2 4 and 5 the point load was applied adjacent to thesupport formaximum shear force effect (Figure 6(b)) A staticanalysis approach was utilized herein with simple supportdisplacement constraints provided at the nodes at the twoends In the first load step only initial prestrain was appliedPrestressing was defined using ANSYS Command Window[4] The initial strain was determined from the effective pre-stress and the modulus of elasticity of prestressing steel Theapplied prestress was 690MPa selected herein to facilitateconvergenceThe camber of themodel girder due to prestressis shown in Figure 7 In the second load step the self-weightof the girder was applied The FEM was set up to examinethree different girder behaviors initial cracking yielding ofthe prestressing steel and flexuralshear failure of the girderThe FRP strengthened beam design was developed in orderto avoid the Mode 4 [2] cover delamination failure in orderto concentrate on fully achieving the tensile strength of theFRP composite fabric
22 Analytical Calculations Hand calculation was usedherein to determine the expected theoretical capacities ofthe girders The analysis is based on the steel and concretestrengths and the cross-sectional properties and steel layout(both prestressed and regular) Provisions from theAASHTOLRFD were utilized for the strength analysis of the con-trol girder [17 Chapter 5] AASHTO LRFD Specifications
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Load
P (k
N)
Centerline deflection (mm)
Figure 8 Load-deflection curve for control unstrengthened girder
currently do not include provisions for the strength deter-mination of FRP strengthened bridge members Thereforeprovisions from theACI 440 guidelineswere used to calculateflexural strengths for the FRP-reinforced girders [2 Chapter10] No load factors or resistance factors were applied Basedon the theoretical flexural capacities equivalent three-pointconcentrated loads (Figure 6) were calculated from staticsThe analytical and FEM load capacities for each girder arecompared in Section 3
3 Results and Discussion
FEM results are presented herein in the form of the valuesof the equivalent concentrated applied load corresponding tothe various loading stages
31 Unstrengthened (Control) Girder for Flexure (Configura-tion 1) The flexural load-deflection curve for the controlgirder showed seven distinct points effective prestress addi-tion of self-weight zero deflection decompression initialcracking steel yielding and failure (Figure 8) Hand calcu-lations were used herein to validate the FEM results hereinas shown in Table 3 Initial prestress application stage initialflexural cracks cracking at yielding load and cracking atflexural capacity are shown in Figure 9 Nonconvergence ofthe nonlinear algorithm occurred at a load of 1003 kN indi-cating flexural failure The excessive cracking that occurred
Journal of Engineering 7
(a) Prestress and self-weight (b) Initial cracking
(c) At prestress yielding (d) At flexural capacity
Figure 9 Cracking stages control girder
Table 3 Flexural FEM and hand calculation results control girder
Parameter FEM Hand calculationsDeflection due toprestress mm
minus18 minus18Deflection atapplication ofself-weight mm
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
at this load stage throughout the entire span is evident inFigure 9(c) The FEM was validated by comparing variousparameters with hand calculations and strain compatibilityapproach Table 3 shows sample calculations for Configura-tion 1 girder The corresponding loads and deflections valueswere close in general validating the results from the FEM
32 Flexural Strengthening (Configuration 3) In the flexuralFEM the point load was applied at mid-span as shownin Figure 6(a) The load-deflection curve for this girder isshown in Figure 10 and various cracking stages are shownin Figure 11 The cracking yielding and flexural failureloads increased by 1765 514 and 38 respectively dueto FRP flexural strengthening as compared to the controlunstrengthened girder (Table 4) The maximum deflectionat the failure load decreased by 35 due to FRP wrappingand localized cracking at the girder ends due to the factthat prestress was reduced The height of the flexural cracksand the area of concrete subjected to flexural cracks alsodiminished as compared to the control girder
The analytical procedure from ACI 440-2R [2] was usedherein to predict the flexural capacity of the strengthenedgirder corresponding well with the FEM prediction Thedetailed equations are quite few and are readily available fromthe reference The ACI 440 prediction was close to that from
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 10 Load-deflection curve for flexurally strengthened girder
the FEM The effective failure strain prediction from ACI440 was 0008786 again close to the FEM output as was themaximum FRP stress (Table 4) The flexural failure mode ofthe girder was governed by yielding of the prestressing steelfollowed by concrete crushing and FRP rupture as per theFEM and ACI 440 This may be inferred from the fact thatthe tensile strength of the FRP (931MPa) was greater than theactual failure stress in the FRP (531MPa) FRP strengtheningcaused 38 and 24 increases in the flexural load capacity ofthe girder according to the FEM and the ACI 440 approachrespectively
33 Shear Strengthening (Configurations 2 4 and 5) For theshear strengthening configurations the point load in the FEMwas applied at 107m (critical shear location according toAASHTO) from the girder end at one side (Figure 6(b)) toprovide critical shear force effect on the girder The load-displacement curve is presented in Figure 12 and pertinentresults are presented in Table 5 Because of the lowmaximumbending moment near mid-span due to mostly self-weightflexural failure did not control over shear failure in thisFEMThe crack progression in the shear strengthened girdersshowed reduction in the height of the shear cracks ascompared to the control girder The ultimate shear capacity
8 Journal of Engineering
(a) Prestress and self-weight (b) Initial cracking
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
FEM outputs ACI 440 predictionsLoad levels Control girder Strengthened girderCracking load kN 242 284 NAYielding load kN 778 818 NAFailure load kN 1003 1387 1248Deflection at cracking mm 155 193 NADeflection at flexural failure mm 279 181 NAFRP strain at flexural failure NA 00095 00088Maximum FRP stress MPa NA 531 545
Table 5 Shear strengthening results
Control girder Strengthened girder (vertical FRP wrap) Strengthened girder (45∘ FRP wrap)FEM ACI 440 FEM ACI 440
Failure load kN 1227 1575 1795 1968 2207FRP strain at failure NA 00018 0002 0002 0002
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
Load
P (k
N)
Centerline deflection (mm)
Figure 12 Load-deflection curve for shear strengthened girder
of the vertical U-wrapped FRP strengthened girder was about15 greater from the ACI 440 provisions as compared to theFEM resultsThe FEM stress in the prestressing steel at failurewas 435MPa much below the yielding capacity as expectedin a shear failure situation The maximum vertical U-wrapFRP strain at failure was 00018 from the FEM and 0002 fromACI 440 calculations again showing that the shear failure
was caused by stirrup yielding and not FRP rupture Theshear load capacity increased by about 13 due to the verticalwrapping The ACI 440 shear capacity prediction was about14 greater than the FEM output
The influence of a 45-degree shear U-wrap FRP onthe girder capacity is also presented in Table 5 The shearfailure load capacity of the girder with the inclined FRPorientation increased by about 25over that from the verticalorientation and about 38 over the control girder shearcapacity
It is noted that 57 of the FRP tensile strength was usedin flexural strengthening while 74was used in case of shearstrengtheningThis is because the FRP rupture mode did notcontrol the girder failures herein and the FRP strength wasnot fully utilized FRP application reduced concrete crackingand girder deflection
FRP strengthening effectively increased the girder loadcarrying capacity and reduced cracking and deflections Theprestressing steel strain at the nominal strength should bechecked to maintain sufficient degree of ductility accordingto ACI 440 [2] Adequate ductility is achieved if the strain inthe prestressing steel at the nominal strength is at least 0013 abit higher than 0011 from the FEM for flexural strengtheningTo address this the flexural strength reduction factor has tobe decreased to 077 in design according to ACI 440 Toincrease the girder ductility the prestressing steel and the FRP
Journal of Engineering 9
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
areas could be reduced compared to the levels used in thisstudy
4 Conclusions
The following conclusions may be made based on the resultsfrom this study
(1) An AASHTO type IV prestressed concrete bridgegirder was successfully modeled using finite elementsoftware ANSYS for both flexural and shear FRPstrengthening The approach is simpler and moreeconomic than full scale experimental testing
(2) The FEM results are accurate based on the valida-tion of the results with hand calculations Valida-tion parameters included camber due to the initialprestress and after application of the self-weight ofthe girder zero deflection decompression initialcracking and failure loads
(3) Excellent contributions from the FRP flexuralstrengthening to the bridge girder were evident forcracking yielding and flexural capacity loads Theflexural failure load increased by almost 38 dueto FRP wrapping and the maximum deflectiondecreased by 35 Tension cracks at the girder endsreduced due to FRP and the heightextent of flexuralcracks diminished
(4) The analytical procedure from ACI 440 [2] yieldedcomparable results to the FEM output for flexuralFRP strengthening in terms of the FRP strain FRPstress and failure loadThe ACI 440 predictions wereslightly conservative as compared to the FEM results
(5) Prestress steel yielding was the dominant failuremode for both the ACI 440 and FEM simulationsfollowed by concrete crushing About 57 of theFRP tensile strength was utilized at flexural failureThe amounts of FRP and prestressing steel could bedecreased within the design constraints to increasethe prestressing steel strain and girder ductility
(6) The FRP shear wrapping also contributed well to thegirder shear capacity The FEM results showed thatthe shear capacity increased by about 13 due tovertical shear wrapping and 38 due to inclined shearwrapping respectively The prestressing steel stresswas well below yielding at failure as expected
(7) The yielding of stirrups was the dominant failuremode in shear as demonstrated by both the FEMand the ACI 440 outputs The ACI 440 provisionshowever were found to be a bit on the nonconserva-tive side for shear strengthening as compared to theFEM outputs The FRP strains at failure from the twoapproaches were comparable
(8) Both FEM and ACI 440 analytical techniques maybe effectively used to predict the flexural and shearbehavior of CFRP strengthenedAASHTO type bridgegirders
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
References
[1] D A Brighton Finite element analysis of an intentionallydamaged prestressed reinforced concrete beam repaired withcarbon fiber reinforced polymers [MS thesis] University ofToledo 2011
[2] ACI (American Concrete Institute) Committee 440 ldquoGuide forthe design and construction of externally bonded FRP systemsfor strengthening concrete structuresrdquo ACI 4402R-08 ACI(American Concrete Institute) Farmington Hills Mich USA2008
[3] F Haque Enhancing effectiveness of AASHTO type prestressedconcrete bridge girder through fiber reinforced polymer strength-ening [MS thesis] University of Texas at Arlington ArlingtonTex USA 2014
[4] ANSYS ANSYS Parametric Design Language (Version 145)ANSYS Canonsburg Pa USA 2012
[5] M Di Ludovico A Prota G Manfredi and E Cosenza ldquoFRPstrengthening of full-scale PC girdersrdquo Journal of Composites forConstruction vol 14 no 5 pp 510ndash520 2010
[6] D Cerullo K Sennah H Azimi C Lam A Fam and BTharmabala ldquoExperimental study on full-scale pretensionedbridge girder damaged by vehicle impact and repaired withfiber-reinforced polymer technologyrdquo Journal of Composites forConstruction vol 17 no 5 pp 662ndash672 2013
[7] D A Petty P J Barr G P Osborn M W Halling andT R Brackus ldquoCarbon fiber shear retrofit of forty-two-year-old AASHTO I-shaped girdersrdquo Journal of Composites forConstruction vol 15 no 5 pp 773ndash781 2011
[8] M Mohanamurthy and N Yazdani ldquoFlexural strength predic-tion in FRP strengthened concrete bridge girdersrdquo EuropeanJournal of Advances in Engineering and Technology vol 2 no3 pp 59ndash68 2015
[9] D Bruno F Greco S L Feudo and P N Blasi ldquoMulti-layermodeling of edge debonding in strengthened beams usinginterface stresses and fracture energiesrdquo Engineering Structuresvol 109 pp 26ndash42 2016
[10] O Rabinovitch ldquoDebonding analysis of fiber-reinforced-polymer strengthened beams cohesive zone modeling versus alinear elastic fracture mechanics approachrdquo Engineering Frac-ture Mechanics vol 75 no 10 pp 2842ndash2859 2008
[11] J G Teng J W Zhang and S T Smith ldquoInterfacial stresses inreinforced concrete beams bonded with a soffit plate A FiniteElement StudyrdquoConstruction and BuildingMaterials vol 16 no1 pp 1ndash14 2002
[12] M J Mathews and S R Swanson ldquoCharacterization of theinterlaminar fracture toughness of a laminated carbonepoxycompositerdquo Composites Science and Technology vol 67 no 7-8pp 1489ndash1498 2007
[13] K J Willam and E P Warnke ldquoConstitutive model for triaxialbehavior of concreterdquo in Proceedings of the Seminar on ConcreteStructures Subjected to Triaxial Stresses International Associa-tion of Bridge and Structural Engineering Conference BergamoItaly 1974
[14] J G MacGregor Reinforced Concrete Mechanics and DesignPrentice Hall Englewood Cliffs NJ USA 1992
10 Journal of Engineering
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
[15] A J Wolanski Flexural behavior of reinforced and prestressedconcrete beams using finite element analysis [MS thesis] Mar-quette University Milwaukee Wis USA 2004
[16] American Concrete Institute (ACI) ldquoBuilding code require-ments for structural concreterdquo ACI 318-14 American ConcreteInstitute (ACI) Farmington Hills Mich USA 2014
[17] AASHTO (American Association of State Highway andTransportation Officials) LRFD Bridge Design SpecificationsAASHTO (American Association of State Highway and Trans-portation Officials) Washington DC USA 7th edition 2014
![CFRP [Wet-preg]](https://static.documents.pub/doc/80x56/546e6828b4af9faa268b4674/cfrp-wet-preg.jpg)
