Research ArticleIncreasing the Capacity of Existing Bridges byUsing Unbonded Prestressing Technology A Case Study

Antonino Recupero1 Nino Spinella1 Piero Colajanni2 and Cosimo D Scilipoti3

1 Dipartimento di Ingegneria Civile Informatica Edile Ambientale e Matematica Applicata Universita di MessinaContrada di Dio Villaggio S Agata 98166 Messina Italy

2 Dipartimento di Ingegneria Civile Ambientale Aerospaziale e dei Materiali (DICAM) Universita di PalermoViale delle Scienze 90128 Palermo Italy

3 RampS Engineering S R L Via S Francesco di Paola 264 Barcellona PG 98051 Messina Italy

Correspondence should be addressed to Nino Spinella nspinellaunimeit

Received 6 February 2014 Revised 20 June 2014 Accepted 29 June 2014 Published 23 July 2014

Academic Editor Andreas Kappos

Copyright copy 2014 Antonino Recupero et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

External posttensioning or unbonded prestressing was found to be a powerful tool for retrofitting and for increasing the lifeextension of existing structures Since the 1950s this technique of reinforcement was applied with success to bridge structuresin many countries and was found to provide an efficient and economic solution for a wide range of bridge types and conditionsUnbonded prestressing is defined as a system in which the post-tensioning tendons or bars are located outside the concrete cross-section and the prestressing forces are transmitted to the girder through the end anchorages deviators or saddles In response tothe demand for a faster and more efficient transportation system there was a steady increase in the weight and volume of trafficthroughout the world Besides increases in legal vehicle loads the overloading of vehicles is a common problem and it must alsobe considered when designing or assessing bridges As a result many bridges are now required to carry loads significantly greaterthan their original design loads and their deck results still deteriorated by cracking of concrete corrosion of rebars snapping oftendons and so forth In the following a case study about a railway bridge retrofitted by external posttensioning technique will beillustrated

1 Introduction

In Europe the motorway and railway networks were builtabout 30 to 40 years ago [1] they have a large number ofprestressed concrete bridges and viaducts Many reinforcedconcrete bridges in highway systems are deteriorated andordistressed to such a degree that structural strengthening ofthe bridge or reducing the allowable truck loading on thebridge by load posting is necessary to extend the service lifeof the bridge [2] Besides inmotorway networks over the lastfew decades there was a rapid increase in traffic volume andweight of heavy vehicles and contemporarily therewas a rapidincrease in transit speed on railway networks Many bridgeswhich were built with now obsolete design standards are

not able to carry on the recent traffic requirements and theyrequire either weight or speed restriction the strengtheningor even the total replacement [2]

Various methods for the rehabilitation of bridges arecurrently available including the addition of structural rein-forcement components as steel rebar or reinforced concrete(RC) jackets and bonded steel plates

Two methods are currently proving to be very usefulin increasing the cross-section capacity of the bridge beamthe strengthening by fibres reinforced polymer (FRP) orfiber reinforced cementitious mortar (FRCM) [3ndash10] and thereinforcement with external tendons

The effect of FRP or FRCM sheets and external pre-stressing tendons on the strength of RC beams has largely

Hindawi Publishing CorporationAdvances in Civil EngineeringVolume 2014 Article ID 840902 10 pageshttpdxdoiorg1011552014840902

2 Advances in Civil Engineering

been investigated [11] with success However in some casesexternal bonded FRP or FRCM could not be sufficient tostrengthen the main girder of bridge

In addition their use is characterized by elevated costspoor resistance to fire and difficulties in maintenance espe-cially for bridge decks

External prestressing tendons bear the applied load thusimproving the load-carrying capacity and effectively extend-ing the service life of the structure [12] The use of externalunbonded reinforcement offers the potential of providing amore cost effective and less disruptive solution to the problemof strengthening RC beams

The external tendons are easily inspected and poor work-manship or corrosion of external reinforcement can be eas-ily checked and monitored They are also compatible withprinciples of conservation which require that a structure bereturned to its original condition after any interventions

Several owners also require that operations of bridgeretrofitting occur with minimal disruption to traffic flowFor this reason the technique of externally posttensioning isgrowing in popularity thanks to the speed of installation andthe minimal disturbance to traffic flow

The goal of this work is to describe themethod of externalposttensioning as a means of retrofitting bridges which havebeen found to be understrengthThe paper shows the princi-ples of external posttensioning and presents as a case studythe retrofitting of a single span bridge in Novara (North ofItaly) During the construction of the railway line Turin-Novara the Consortium CAVTOMI required to use theroad bridge namely Terdoppio for the transit of the railwaytrains to place the equipment of the railway line Thereforethe traffic loads would be increased and reinforcement wasnecessary In particular the external tendons system waschosen to be used In this case to provide the space for theanchoring of the external cables a demolition of existing gratewalls was needed But the retrofittingmethod is applicable formultispan bridge also depending on boundary conditionsFor example Bertagnoli et al [13] have illustrated a similarretrofitting application on a multispan bridge realizing somehousing pockets for the external cables on the side web of thelateral beams However different solutions can be pursuedas function of costs and feasibility of the intervention whichshould be assessed on a case-by-case basis

Moreover the prestressed concrete (PC) beam of Ter-doppio bridge was numerically analyzed at the ultimate limitstate (ULS) to compare the load capacity of reinforced beamevaluated by a handy sectionalmethodwith a nonlinear finiteelement analysis (NLFEA) At this aim theVecTor2 finite ele-ment software which is based on the Modified CompressionField Theory (MCFT) [14] was used

The MCFT is a smeared rotating crack model The keyassumption the MFCT uses to simplify is that the principalstrain directions coincide with the principal stress directionsThis assumption has recently been removed by Vecchio[15] which has introduced the disturbed stress field model(DSFM) The DSFM explicitly incorporates rigid slippingalong crack surfaces into the compatibility relations for theelement allowing for a divergence of the angles of inclination

Existing cables

(a)

Demolition of existing grate-wall

(b)

Realization of new deck

(c)

Realization of new grate-wall

Realization of external prestressing tendons

(d)

Figure 1 Longitudinal section of (a) existing bridge (b) demolitionof gravel-grate walls and elimination of road superstructure (c)realization of a new deck and (d) realization of new gravel-gratewalls and a system of external prestressing

of average principal stress and apparent average principalstrain in the concrete

In addition MCFT and DSFM have been recentlyextended to the case of FRC elements [16ndash18] proving theirgeneral capacity to reproduce the response of structuralmembers with different mechanical and load conditions

2 A Case Study The Terdoppio Bridge

21 Need of Rehabilitation for the Terdoppio Bridge In 2006during the works for the construction of the railway lineTurin-Novara the Consortium CAVTOMI (ie the generalcontractor) needed to use the Terdoppio road bridge forthe transit of the railway cars This single span bridge(Figure 1(a)) was provisionally used as bypass of the existingprincipal line that was under replacement

The road bridge on the river Terdoppio was built in theearly 70s and it is constituted by a deck of six prestressed andprefabricated beams and six diaphragms which were castedin situ Preliminary analyses pointed out that the existingstructure was not fit to allow the transit of the carriage railwayand it was therefore necessary to adjust or replace it

The two solutions were also estimated from the economicpoint of view The owner chose to make the reinforcementand the adjustment of the bridge The rehabilitation wasprojected and then was developed in the way less intrusive aspossibleTheminimum interference on the existing structure

Advances in Civil Engineering 3

152506700 5700 2850

CL

Inclined cables Straight cables

(a)

500

280

700600600 1160

5800

1160116011601160

100

100

1400

100

15095

0

(b)

Figure 2 (a) Longitudinal and (b) transversal scheme of existing bridge

as imposed by the company was planned by the followingphases

(i) demolition of gravel-grate walls and removal of roadsuperstructure and concrete milling of the existingsurface deck both steps have accounted for aroundthe 12 of total intervention costs (Figure 1(b))

(ii) realization of a new deck of 250mm thickness on theexisting deck the new deck is able to bear the newrailway local loads it is linked to the original structureby steel connectors (Figure 1(c))

(iii) realization of a system of external prestressing with 10cables 80610158401015840 strands anchored close to the supportdiaphragms and with metallic deviator on interme-diate diaphragms there is realization of new gravel-grate walls (Figure 1(d))

The phase of planning of adjustment was preceded by awide campaign of nondestructive investigations that allowedthe best calibration of the subsequent choices In the planningof the system of rehabilitation the combined effect of existingbonded prestressing and new unbonded external prestressingwas taken into account

22 Geometrical and Mechanical Investigation of TerdoppioBridge The Terdoppio bridge is a classical typology of ldquoGril-lage Bridgerdquo The single span of bridge is 305m (Figure 2)The beams have a cross-section with a height equal to 14mand theywere prestressedwith the pretensionmethodwith 38strands (119860

119901= 93mm2 for each) The tensile strength at ULS

is119891119905= 1750MPaThe strands present a polygonal layout with

a horizontal central part large of 6mThe original design was recovered for accurate calibra-

tion obtaining also information about the load tests per-formed on the structure during construction For integratingthese data it was chosen to program a campaign of nonde-structive in situ tests and particularly some core borings on

the existing deck were also integrated by SONinc-REBound(SONREB) tests on concrete beams and diaphragms

Relationships proposed in literature about SONREBoffered an indirect estimation of concrete strength (119891cm) indifferent parts of bridge structure

For the concrete of existing beams following the seriesof destructive and nondestructive tests it was reasonable toassume a class C3545 typical of the prefabrication industryof that period In existing deck slab by analyzing the resultsof nondestructive and destructive tests on specimens it wasreasonable to assume for the concrete a class C2025

The check phase based on data provided by the prelim-inary tests emphasized that the existing structure was notsuitable to allow the transit of the railway coaches as requiredby the national code specifications

In fact the authoritiesrsquo specifications require the passageof the following

(1) a testing train for high-speed bridges that were inconstruction it is composed of 24 axles each of 210 kNcapacity for a total of 5040 kN this train could easilybe packed in the ballast field and it had to crossthe Terdoppio bridge for reaching the railway line inconstruction

(2) an equivalent train to the LM71 reduced to the 83as required by the ITALFERR Manual Code [19] forrailway bridges classified as Category B

(3) a train of coaches that bear the ballast (Figure 3) witha total load for each coach equal to 800 kN on 4 axles

Therefore the bridge needed the rehabilitation or thereplacement

23 Scheme of Rehabilitation Proposed Different hypothesesof adjustment have attentively been valued

(1) assemblage of a metallic structure of inclined-legframe typology under the existing structure

4 Advances in Civil Engineering

200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN

520

19001800

5201080

72001100012040

18001900

Figure 3 Multiple coaches for ballast train

Figure 4 Anchor heads and antispalling reinforcement

(2) reinforcement of principal beams with FRP plates onthe bottom face of the beams [20]

(3) reinforcement of principal beams with a system ofunbonded prestressing external to cross-section ofbeams

After awealthy debatewith the contractor and Italian rail-way authorities the third proposal for economic motivationwas chosen Moreover for avoiding excessive costs only apartial rehabilitation of the bridge was selected by allowingtotally the transit of the train equivalent to the LM71 to reduceto the 83 and of the train that bears the ballast (Figure 3)and the load of a testing train (for High-Speed bridges) withreduction to 60The total recharge up to 100 of the testingtrain would have happened after the transit on the bridge

It was decided therefore to apply a system of externalprestressing with 10 external cables of 8 strands 0610158401015840 whichdeparting from the diaphragms of extremity already recon-structed for lodging the prestress anchorage were deviatedby the first intermediary diaphragm (those posed at 34 ofspan) It was chosen to have steel deviator arrangements ondiaphragms

For rationalizing the operations of adjustment the fol-lowing executive phases were selected

(1) removal of road superstructure and concrete millingof the existing surface slab

(2) assemblage of the connectors for the integrative newslab

(3) positioning of the bars of reinforcement and thecasting of integrative slab

(4) demolition of top part of abutment and setup of theplan of work on altitude of existing bearings

(5) positioning of the anchor heads and the antispallingreinforcement the casting of integrative diaphragm(Figure 4)

(6) installation of the metallic saddles of deviation under34 diaphragms using rebar and epoxy resin to con-nect the two components (Figures 5 and 6)

(7) lodging of the integrative external cables and theirprestressing up to nominal force

(8) casting of new top part of abutments and reconstruc-tion of their backfills

(9) positioning of the joints between deck and abutments(10) placing of ballast and rails(11) final testing with the trains used in design phases

(Figure 3)For each phase of construction the corresponding check

calculations were performed The new slab with a thicknessof 250mm was necessary to bear greater local loads thanprevious It was casted with concrete of class C3545The newslab increased the total height of transversal sections of beamswith a notable improvement in terms of stiffness and loadcapacity

3 Numerical Model

31 Numerical Analyses of Strengthened Beams Theproposedrehabilitation scheme for the Terdoppio bridge was investi-gated with deep attention to evaluate the new bearing load

Advances in Civil Engineering 5

(a) (b)

Figure 5 (a) View of external prestressing (b) metallic saddle of deviation

Metal profileRebar

Rebar

Continuous welding Continuous weldingTendon

(a) (b)

Epoxy resin

Existing diaphragm

Metal profile

Tendons

Figure 6 Details of connection between existing bridge and metallic saddle of deviation

of each beam At this aim several numerical analyses werecarried out to obtain precious information about the tensionand strain fields at different load stages

First a linear-elastic calculation was performed to knowthe force that the deck was expected to undertake at servicelimit state (SLS) and the stress distribution along the heightof the beam cross-section

Second a simple sectionalmodelwas used to calculate thecapacity of strengthened beam at ULS It allowed consideringjust the principal geometrical and mechanical parametersproviding an easy control of results Finally a NLFEA wasperformed at ULS using the software VecTor2 [21] whichimplements the MCFT originally proposed by Vecchio andCollins [14] and its upgrading [15]

32 Beam Setup As described in Scheme of RehabilitationProposed section the reinforcement of primary beams was

carried out with a new system of unbonded prestressingdisposed externally to the cross-section of beam (Figure 7)

Two groups of bonded strandswere originally used for theRC beamThe first was characterized by strands with straightaxis along the beam the second group was placed with avariable slope of strands as shown in Figure 6(a) Each strandwas 0510158401015840 in equivalent diameter while the yield and ultimatestrength of steel were 119891

119901(1)119896= 1575MPa and 119891

119905= 1750MPa

respectivelyThe slab on the beams had a thickness of 200mm and

rebar along two orthogonal directions in its plane was usedAlong the longitudinal direction the flexural reinforcementwas provided by 21206018mm+ 112060112mm on the top (for thebending moment close to support) and 41206018mm on thebottom (for the bending moment at half span) for each widthof slab pertaining to considered beam (=1160mm) In thetransversal direction 512060112mmm was used both on the topand on the bottom of slab

6 Advances in Civil Engineering

Existing slab New slab

Existing cables

(a) (b)

External cables

CL

1400

280

700 100

150

100

100500

950

Figure 7 (a) Longitudinal and (b) transversal rehabilitation scheme of beam

328

kN

2331kN

2NpSLS

328

kN

2NpS

LSsin

(1205722)

q = 215 kNm

120572 = 8∘

23kN

Figure 8 Concentrated forces equivalent to external prestressing actions at support and deviation of external cable sections

The shear reinforcement was variable along the beamStirrups with two legs 1206018mm and 12060110mm spacing 250mmwere used for the region between the support and 525m1206018mm spacing 250mm for the region between 525m and1025m and 1206018mm and 1206016mm spacing 250mm for theregion between 1025m and 1525m The beam was of length305m and it is symmetrically loaded and reinforced

As previously mentioned the concrete for the beam ischaracterized by a cylindrical strength 119891cm = 35MPa whilethe concrete for the existing top slab has a cylindrical strength119891cm = 20MPa

For the rehabilitation of bridge the primary beams havebeen retrofitted with a new deck of 250mm thickness (119891cm =35MPa) which was linked to the existing slab by steelconnectors and a system of two external prestressing cables80610158401015840 strands for each beamThe axial force for each externalprestressing cable at SLS was 119873

119901SLS = 1177 kN thus theequivalent balances vertical load was equal to 215 kNm(Figure 8)

33 Linear-Elastic Analysis at SLS The reinforcement of thebeam by the external tendons system has modified the stressregime of the structural element These modifications wereallowed to carry the new loads

The structure after the reinforcement is composed bytwo parts of concrete casted in different times If as a result

of the external loads and the prestressing the beam remainsfully compressed (or with tensile tension values less thanelastic limit) then it is possible to apply the principle of super-positionTherefore total forces are due by sumof prestressingand external load This assumption is no longer valid whenconcrete is cracked (ie at failure)

Three steps with different effects were taken into account(1) dead load prestressing and prestress losses (2) dead loaddue to the just casted new deck and (3) the cross-section ofthe beam composed by the new deck also

The effects in the three different stages were evaluatedseparately and then subsequently summed

In Figure 9 the stress shape along the depth for a cross-section at the midspan of the beam is shown The beam issubjected to compression stress only

34 Sectional Analysis at ULS Several simple models weredeveloped by the same authors to handily evaluate the shearstrength of RC and fibrous reinforced concrete (FRC) beams[22ndash27] However the expected failure mode of beam takeninto account allows obtaining the ultimate load by a sectionalcalculation

The external forces to apply at the beam to take intoaccount the actions of external prestressing cables are eval-uated by simple geometric considerations as shown inFigure 8

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

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2 Advances in Civil Engineering

been investigated [11] with success However in some casesexternal bonded FRP or FRCM could not be sufficient tostrengthen the main girder of bridge

In addition their use is characterized by elevated costspoor resistance to fire and difficulties in maintenance espe-cially for bridge decks

External prestressing tendons bear the applied load thusimproving the load-carrying capacity and effectively extend-ing the service life of the structure [12] The use of externalunbonded reinforcement offers the potential of providing amore cost effective and less disruptive solution to the problemof strengthening RC beams

The external tendons are easily inspected and poor work-manship or corrosion of external reinforcement can be eas-ily checked and monitored They are also compatible withprinciples of conservation which require that a structure bereturned to its original condition after any interventions

Several owners also require that operations of bridgeretrofitting occur with minimal disruption to traffic flowFor this reason the technique of externally posttensioning isgrowing in popularity thanks to the speed of installation andthe minimal disturbance to traffic flow

The goal of this work is to describe themethod of externalposttensioning as a means of retrofitting bridges which havebeen found to be understrengthThe paper shows the princi-ples of external posttensioning and presents as a case studythe retrofitting of a single span bridge in Novara (North ofItaly) During the construction of the railway line Turin-Novara the Consortium CAVTOMI required to use theroad bridge namely Terdoppio for the transit of the railwaytrains to place the equipment of the railway line Thereforethe traffic loads would be increased and reinforcement wasnecessary In particular the external tendons system waschosen to be used In this case to provide the space for theanchoring of the external cables a demolition of existing gratewalls was needed But the retrofittingmethod is applicable formultispan bridge also depending on boundary conditionsFor example Bertagnoli et al [13] have illustrated a similarretrofitting application on a multispan bridge realizing somehousing pockets for the external cables on the side web of thelateral beams However different solutions can be pursuedas function of costs and feasibility of the intervention whichshould be assessed on a case-by-case basis

Moreover the prestressed concrete (PC) beam of Ter-doppio bridge was numerically analyzed at the ultimate limitstate (ULS) to compare the load capacity of reinforced beamevaluated by a handy sectionalmethodwith a nonlinear finiteelement analysis (NLFEA) At this aim theVecTor2 finite ele-ment software which is based on the Modified CompressionField Theory (MCFT) [14] was used

The MCFT is a smeared rotating crack model The keyassumption the MFCT uses to simplify is that the principalstrain directions coincide with the principal stress directionsThis assumption has recently been removed by Vecchio[15] which has introduced the disturbed stress field model(DSFM) The DSFM explicitly incorporates rigid slippingalong crack surfaces into the compatibility relations for theelement allowing for a divergence of the angles of inclination

Existing cables

(a)

Demolition of existing grate-wall

(b)

Realization of new deck

(c)

Realization of new grate-wall

Realization of external prestressing tendons

(d)

Figure 1 Longitudinal section of (a) existing bridge (b) demolitionof gravel-grate walls and elimination of road superstructure (c)realization of a new deck and (d) realization of new gravel-gratewalls and a system of external prestressing

of average principal stress and apparent average principalstrain in the concrete

In addition MCFT and DSFM have been recentlyextended to the case of FRC elements [16ndash18] proving theirgeneral capacity to reproduce the response of structuralmembers with different mechanical and load conditions

2 A Case Study The Terdoppio Bridge

21 Need of Rehabilitation for the Terdoppio Bridge In 2006during the works for the construction of the railway lineTurin-Novara the Consortium CAVTOMI (ie the generalcontractor) needed to use the Terdoppio road bridge forthe transit of the railway cars This single span bridge(Figure 1(a)) was provisionally used as bypass of the existingprincipal line that was under replacement

The road bridge on the river Terdoppio was built in theearly 70s and it is constituted by a deck of six prestressed andprefabricated beams and six diaphragms which were castedin situ Preliminary analyses pointed out that the existingstructure was not fit to allow the transit of the carriage railwayand it was therefore necessary to adjust or replace it

The two solutions were also estimated from the economicpoint of view The owner chose to make the reinforcementand the adjustment of the bridge The rehabilitation wasprojected and then was developed in the way less intrusive aspossibleTheminimum interference on the existing structure

Advances in Civil Engineering 3

152506700 5700 2850

CL

Inclined cables Straight cables

(a)

500

280

700600600 1160

5800

1160116011601160

100

100

1400

100

15095

0

(b)

Figure 2 (a) Longitudinal and (b) transversal scheme of existing bridge

as imposed by the company was planned by the followingphases

(i) demolition of gravel-grate walls and removal of roadsuperstructure and concrete milling of the existingsurface deck both steps have accounted for aroundthe 12 of total intervention costs (Figure 1(b))

(ii) realization of a new deck of 250mm thickness on theexisting deck the new deck is able to bear the newrailway local loads it is linked to the original structureby steel connectors (Figure 1(c))

(iii) realization of a system of external prestressing with 10cables 80610158401015840 strands anchored close to the supportdiaphragms and with metallic deviator on interme-diate diaphragms there is realization of new gravel-grate walls (Figure 1(d))

The phase of planning of adjustment was preceded by awide campaign of nondestructive investigations that allowedthe best calibration of the subsequent choices In the planningof the system of rehabilitation the combined effect of existingbonded prestressing and new unbonded external prestressingwas taken into account

22 Geometrical and Mechanical Investigation of TerdoppioBridge The Terdoppio bridge is a classical typology of ldquoGril-lage Bridgerdquo The single span of bridge is 305m (Figure 2)The beams have a cross-section with a height equal to 14mand theywere prestressedwith the pretensionmethodwith 38strands (119860

119901= 93mm2 for each) The tensile strength at ULS

is119891119905= 1750MPaThe strands present a polygonal layout with

a horizontal central part large of 6mThe original design was recovered for accurate calibra-

tion obtaining also information about the load tests per-formed on the structure during construction For integratingthese data it was chosen to program a campaign of nonde-structive in situ tests and particularly some core borings on

the existing deck were also integrated by SONinc-REBound(SONREB) tests on concrete beams and diaphragms

Relationships proposed in literature about SONREBoffered an indirect estimation of concrete strength (119891cm) indifferent parts of bridge structure

For the concrete of existing beams following the seriesof destructive and nondestructive tests it was reasonable toassume a class C3545 typical of the prefabrication industryof that period In existing deck slab by analyzing the resultsof nondestructive and destructive tests on specimens it wasreasonable to assume for the concrete a class C2025

The check phase based on data provided by the prelim-inary tests emphasized that the existing structure was notsuitable to allow the transit of the railway coaches as requiredby the national code specifications

In fact the authoritiesrsquo specifications require the passageof the following

(1) a testing train for high-speed bridges that were inconstruction it is composed of 24 axles each of 210 kNcapacity for a total of 5040 kN this train could easilybe packed in the ballast field and it had to crossthe Terdoppio bridge for reaching the railway line inconstruction

(2) an equivalent train to the LM71 reduced to the 83as required by the ITALFERR Manual Code [19] forrailway bridges classified as Category B

(3) a train of coaches that bear the ballast (Figure 3) witha total load for each coach equal to 800 kN on 4 axles

Therefore the bridge needed the rehabilitation or thereplacement

23 Scheme of Rehabilitation Proposed Different hypothesesof adjustment have attentively been valued

(1) assemblage of a metallic structure of inclined-legframe typology under the existing structure

4 Advances in Civil Engineering

200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN

520

19001800

5201080

72001100012040

18001900

Figure 3 Multiple coaches for ballast train

Figure 4 Anchor heads and antispalling reinforcement

(2) reinforcement of principal beams with FRP plates onthe bottom face of the beams [20]

(3) reinforcement of principal beams with a system ofunbonded prestressing external to cross-section ofbeams

After awealthy debatewith the contractor and Italian rail-way authorities the third proposal for economic motivationwas chosen Moreover for avoiding excessive costs only apartial rehabilitation of the bridge was selected by allowingtotally the transit of the train equivalent to the LM71 to reduceto the 83 and of the train that bears the ballast (Figure 3)and the load of a testing train (for High-Speed bridges) withreduction to 60The total recharge up to 100 of the testingtrain would have happened after the transit on the bridge

It was decided therefore to apply a system of externalprestressing with 10 external cables of 8 strands 0610158401015840 whichdeparting from the diaphragms of extremity already recon-structed for lodging the prestress anchorage were deviatedby the first intermediary diaphragm (those posed at 34 ofspan) It was chosen to have steel deviator arrangements ondiaphragms

For rationalizing the operations of adjustment the fol-lowing executive phases were selected

(1) removal of road superstructure and concrete millingof the existing surface slab

(2) assemblage of the connectors for the integrative newslab

(3) positioning of the bars of reinforcement and thecasting of integrative slab

(4) demolition of top part of abutment and setup of theplan of work on altitude of existing bearings

(5) positioning of the anchor heads and the antispallingreinforcement the casting of integrative diaphragm(Figure 4)

(6) installation of the metallic saddles of deviation under34 diaphragms using rebar and epoxy resin to con-nect the two components (Figures 5 and 6)

(7) lodging of the integrative external cables and theirprestressing up to nominal force

(8) casting of new top part of abutments and reconstruc-tion of their backfills

(9) positioning of the joints between deck and abutments(10) placing of ballast and rails(11) final testing with the trains used in design phases

(Figure 3)For each phase of construction the corresponding check

calculations were performed The new slab with a thicknessof 250mm was necessary to bear greater local loads thanprevious It was casted with concrete of class C3545The newslab increased the total height of transversal sections of beamswith a notable improvement in terms of stiffness and loadcapacity

3 Numerical Model

31 Numerical Analyses of Strengthened Beams Theproposedrehabilitation scheme for the Terdoppio bridge was investi-gated with deep attention to evaluate the new bearing load

Advances in Civil Engineering 5

(a) (b)

Figure 5 (a) View of external prestressing (b) metallic saddle of deviation

Metal profileRebar

Rebar

Continuous welding Continuous weldingTendon

(a) (b)

Epoxy resin

Existing diaphragm

Metal profile

Tendons

Figure 6 Details of connection between existing bridge and metallic saddle of deviation

of each beam At this aim several numerical analyses werecarried out to obtain precious information about the tensionand strain fields at different load stages

First a linear-elastic calculation was performed to knowthe force that the deck was expected to undertake at servicelimit state (SLS) and the stress distribution along the heightof the beam cross-section

Second a simple sectionalmodelwas used to calculate thecapacity of strengthened beam at ULS It allowed consideringjust the principal geometrical and mechanical parametersproviding an easy control of results Finally a NLFEA wasperformed at ULS using the software VecTor2 [21] whichimplements the MCFT originally proposed by Vecchio andCollins [14] and its upgrading [15]

32 Beam Setup As described in Scheme of RehabilitationProposed section the reinforcement of primary beams was

carried out with a new system of unbonded prestressingdisposed externally to the cross-section of beam (Figure 7)

Two groups of bonded strandswere originally used for theRC beamThe first was characterized by strands with straightaxis along the beam the second group was placed with avariable slope of strands as shown in Figure 6(a) Each strandwas 0510158401015840 in equivalent diameter while the yield and ultimatestrength of steel were 119891

119901(1)119896= 1575MPa and 119891

119905= 1750MPa

respectivelyThe slab on the beams had a thickness of 200mm and

rebar along two orthogonal directions in its plane was usedAlong the longitudinal direction the flexural reinforcementwas provided by 21206018mm+ 112060112mm on the top (for thebending moment close to support) and 41206018mm on thebottom (for the bending moment at half span) for each widthof slab pertaining to considered beam (=1160mm) In thetransversal direction 512060112mmm was used both on the topand on the bottom of slab

6 Advances in Civil Engineering

Existing slab New slab

Existing cables

(a) (b)

External cables

CL

1400

280

700 100

150

100

100500

950

Figure 7 (a) Longitudinal and (b) transversal rehabilitation scheme of beam

328

kN

2331kN

2NpSLS

328

kN

2NpS

LSsin

(1205722)

q = 215 kNm

120572 = 8∘

23kN

Figure 8 Concentrated forces equivalent to external prestressing actions at support and deviation of external cable sections

The shear reinforcement was variable along the beamStirrups with two legs 1206018mm and 12060110mm spacing 250mmwere used for the region between the support and 525m1206018mm spacing 250mm for the region between 525m and1025m and 1206018mm and 1206016mm spacing 250mm for theregion between 1025m and 1525m The beam was of length305m and it is symmetrically loaded and reinforced

As previously mentioned the concrete for the beam ischaracterized by a cylindrical strength 119891cm = 35MPa whilethe concrete for the existing top slab has a cylindrical strength119891cm = 20MPa

For the rehabilitation of bridge the primary beams havebeen retrofitted with a new deck of 250mm thickness (119891cm =35MPa) which was linked to the existing slab by steelconnectors and a system of two external prestressing cables80610158401015840 strands for each beamThe axial force for each externalprestressing cable at SLS was 119873

119901SLS = 1177 kN thus theequivalent balances vertical load was equal to 215 kNm(Figure 8)

33 Linear-Elastic Analysis at SLS The reinforcement of thebeam by the external tendons system has modified the stressregime of the structural element These modifications wereallowed to carry the new loads

The structure after the reinforcement is composed bytwo parts of concrete casted in different times If as a result

of the external loads and the prestressing the beam remainsfully compressed (or with tensile tension values less thanelastic limit) then it is possible to apply the principle of super-positionTherefore total forces are due by sumof prestressingand external load This assumption is no longer valid whenconcrete is cracked (ie at failure)

Three steps with different effects were taken into account(1) dead load prestressing and prestress losses (2) dead loaddue to the just casted new deck and (3) the cross-section ofthe beam composed by the new deck also

The effects in the three different stages were evaluatedseparately and then subsequently summed

In Figure 9 the stress shape along the depth for a cross-section at the midspan of the beam is shown The beam issubjected to compression stress only

34 Sectional Analysis at ULS Several simple models weredeveloped by the same authors to handily evaluate the shearstrength of RC and fibrous reinforced concrete (FRC) beams[22ndash27] However the expected failure mode of beam takeninto account allows obtaining the ultimate load by a sectionalcalculation

The external forces to apply at the beam to take intoaccount the actions of external prestressing cables are eval-uated by simple geometric considerations as shown inFigure 8

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Civil Engineering 3

152506700 5700 2850

CL

Inclined cables Straight cables

(a)

500

280

700600600 1160

5800

1160116011601160

100

100

1400

100

15095

0

(b)

Figure 2 (a) Longitudinal and (b) transversal scheme of existing bridge

as imposed by the company was planned by the followingphases

(i) demolition of gravel-grate walls and removal of roadsuperstructure and concrete milling of the existingsurface deck both steps have accounted for aroundthe 12 of total intervention costs (Figure 1(b))

(ii) realization of a new deck of 250mm thickness on theexisting deck the new deck is able to bear the newrailway local loads it is linked to the original structureby steel connectors (Figure 1(c))

(iii) realization of a system of external prestressing with 10cables 80610158401015840 strands anchored close to the supportdiaphragms and with metallic deviator on interme-diate diaphragms there is realization of new gravel-grate walls (Figure 1(d))

The phase of planning of adjustment was preceded by awide campaign of nondestructive investigations that allowedthe best calibration of the subsequent choices In the planningof the system of rehabilitation the combined effect of existingbonded prestressing and new unbonded external prestressingwas taken into account

22 Geometrical and Mechanical Investigation of TerdoppioBridge The Terdoppio bridge is a classical typology of ldquoGril-lage Bridgerdquo The single span of bridge is 305m (Figure 2)The beams have a cross-section with a height equal to 14mand theywere prestressedwith the pretensionmethodwith 38strands (119860

119901= 93mm2 for each) The tensile strength at ULS

is119891119905= 1750MPaThe strands present a polygonal layout with

a horizontal central part large of 6mThe original design was recovered for accurate calibra-

tion obtaining also information about the load tests per-formed on the structure during construction For integratingthese data it was chosen to program a campaign of nonde-structive in situ tests and particularly some core borings on

the existing deck were also integrated by SONinc-REBound(SONREB) tests on concrete beams and diaphragms

Relationships proposed in literature about SONREBoffered an indirect estimation of concrete strength (119891cm) indifferent parts of bridge structure

For the concrete of existing beams following the seriesof destructive and nondestructive tests it was reasonable toassume a class C3545 typical of the prefabrication industryof that period In existing deck slab by analyzing the resultsof nondestructive and destructive tests on specimens it wasreasonable to assume for the concrete a class C2025

The check phase based on data provided by the prelim-inary tests emphasized that the existing structure was notsuitable to allow the transit of the railway coaches as requiredby the national code specifications

In fact the authoritiesrsquo specifications require the passageof the following

(1) a testing train for high-speed bridges that were inconstruction it is composed of 24 axles each of 210 kNcapacity for a total of 5040 kN this train could easilybe packed in the ballast field and it had to crossthe Terdoppio bridge for reaching the railway line inconstruction

(2) an equivalent train to the LM71 reduced to the 83as required by the ITALFERR Manual Code [19] forrailway bridges classified as Category B

(3) a train of coaches that bear the ballast (Figure 3) witha total load for each coach equal to 800 kN on 4 axles

Therefore the bridge needed the rehabilitation or thereplacement

23 Scheme of Rehabilitation Proposed Different hypothesesof adjustment have attentively been valued

(1) assemblage of a metallic structure of inclined-legframe typology under the existing structure

4 Advances in Civil Engineering

200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN

520

19001800

5201080

72001100012040

18001900

Figure 3 Multiple coaches for ballast train

Figure 4 Anchor heads and antispalling reinforcement

(2) reinforcement of principal beams with FRP plates onthe bottom face of the beams [20]

(3) reinforcement of principal beams with a system ofunbonded prestressing external to cross-section ofbeams

After awealthy debatewith the contractor and Italian rail-way authorities the third proposal for economic motivationwas chosen Moreover for avoiding excessive costs only apartial rehabilitation of the bridge was selected by allowingtotally the transit of the train equivalent to the LM71 to reduceto the 83 and of the train that bears the ballast (Figure 3)and the load of a testing train (for High-Speed bridges) withreduction to 60The total recharge up to 100 of the testingtrain would have happened after the transit on the bridge

It was decided therefore to apply a system of externalprestressing with 10 external cables of 8 strands 0610158401015840 whichdeparting from the diaphragms of extremity already recon-structed for lodging the prestress anchorage were deviatedby the first intermediary diaphragm (those posed at 34 ofspan) It was chosen to have steel deviator arrangements ondiaphragms

For rationalizing the operations of adjustment the fol-lowing executive phases were selected

(1) removal of road superstructure and concrete millingof the existing surface slab

(2) assemblage of the connectors for the integrative newslab

(3) positioning of the bars of reinforcement and thecasting of integrative slab

(4) demolition of top part of abutment and setup of theplan of work on altitude of existing bearings

(5) positioning of the anchor heads and the antispallingreinforcement the casting of integrative diaphragm(Figure 4)

(6) installation of the metallic saddles of deviation under34 diaphragms using rebar and epoxy resin to con-nect the two components (Figures 5 and 6)

(7) lodging of the integrative external cables and theirprestressing up to nominal force

(8) casting of new top part of abutments and reconstruc-tion of their backfills

(9) positioning of the joints between deck and abutments(10) placing of ballast and rails(11) final testing with the trains used in design phases

(Figure 3)For each phase of construction the corresponding check

calculations were performed The new slab with a thicknessof 250mm was necessary to bear greater local loads thanprevious It was casted with concrete of class C3545The newslab increased the total height of transversal sections of beamswith a notable improvement in terms of stiffness and loadcapacity

3 Numerical Model

31 Numerical Analyses of Strengthened Beams Theproposedrehabilitation scheme for the Terdoppio bridge was investi-gated with deep attention to evaluate the new bearing load

Advances in Civil Engineering 5

(a) (b)

Figure 5 (a) View of external prestressing (b) metallic saddle of deviation

Metal profileRebar

Rebar

Continuous welding Continuous weldingTendon

(a) (b)

Epoxy resin

Existing diaphragm

Metal profile

Tendons

Figure 6 Details of connection between existing bridge and metallic saddle of deviation

of each beam At this aim several numerical analyses werecarried out to obtain precious information about the tensionand strain fields at different load stages

First a linear-elastic calculation was performed to knowthe force that the deck was expected to undertake at servicelimit state (SLS) and the stress distribution along the heightof the beam cross-section

Second a simple sectionalmodelwas used to calculate thecapacity of strengthened beam at ULS It allowed consideringjust the principal geometrical and mechanical parametersproviding an easy control of results Finally a NLFEA wasperformed at ULS using the software VecTor2 [21] whichimplements the MCFT originally proposed by Vecchio andCollins [14] and its upgrading [15]

32 Beam Setup As described in Scheme of RehabilitationProposed section the reinforcement of primary beams was

carried out with a new system of unbonded prestressingdisposed externally to the cross-section of beam (Figure 7)

Two groups of bonded strandswere originally used for theRC beamThe first was characterized by strands with straightaxis along the beam the second group was placed with avariable slope of strands as shown in Figure 6(a) Each strandwas 0510158401015840 in equivalent diameter while the yield and ultimatestrength of steel were 119891

119901(1)119896= 1575MPa and 119891

119905= 1750MPa

respectivelyThe slab on the beams had a thickness of 200mm and

rebar along two orthogonal directions in its plane was usedAlong the longitudinal direction the flexural reinforcementwas provided by 21206018mm+ 112060112mm on the top (for thebending moment close to support) and 41206018mm on thebottom (for the bending moment at half span) for each widthof slab pertaining to considered beam (=1160mm) In thetransversal direction 512060112mmm was used both on the topand on the bottom of slab

6 Advances in Civil Engineering

Existing slab New slab

Existing cables

(a) (b)

External cables

CL

1400

280

700 100

150

100

100500

950

Figure 7 (a) Longitudinal and (b) transversal rehabilitation scheme of beam

328

kN

2331kN

2NpSLS

328

kN

2NpS

LSsin

(1205722)

q = 215 kNm

120572 = 8∘

23kN

Figure 8 Concentrated forces equivalent to external prestressing actions at support and deviation of external cable sections

The shear reinforcement was variable along the beamStirrups with two legs 1206018mm and 12060110mm spacing 250mmwere used for the region between the support and 525m1206018mm spacing 250mm for the region between 525m and1025m and 1206018mm and 1206016mm spacing 250mm for theregion between 1025m and 1525m The beam was of length305m and it is symmetrically loaded and reinforced

As previously mentioned the concrete for the beam ischaracterized by a cylindrical strength 119891cm = 35MPa whilethe concrete for the existing top slab has a cylindrical strength119891cm = 20MPa

For the rehabilitation of bridge the primary beams havebeen retrofitted with a new deck of 250mm thickness (119891cm =35MPa) which was linked to the existing slab by steelconnectors and a system of two external prestressing cables80610158401015840 strands for each beamThe axial force for each externalprestressing cable at SLS was 119873

119901SLS = 1177 kN thus theequivalent balances vertical load was equal to 215 kNm(Figure 8)

33 Linear-Elastic Analysis at SLS The reinforcement of thebeam by the external tendons system has modified the stressregime of the structural element These modifications wereallowed to carry the new loads

The structure after the reinforcement is composed bytwo parts of concrete casted in different times If as a result

of the external loads and the prestressing the beam remainsfully compressed (or with tensile tension values less thanelastic limit) then it is possible to apply the principle of super-positionTherefore total forces are due by sumof prestressingand external load This assumption is no longer valid whenconcrete is cracked (ie at failure)

Three steps with different effects were taken into account(1) dead load prestressing and prestress losses (2) dead loaddue to the just casted new deck and (3) the cross-section ofthe beam composed by the new deck also

The effects in the three different stages were evaluatedseparately and then subsequently summed

In Figure 9 the stress shape along the depth for a cross-section at the midspan of the beam is shown The beam issubjected to compression stress only

34 Sectional Analysis at ULS Several simple models weredeveloped by the same authors to handily evaluate the shearstrength of RC and fibrous reinforced concrete (FRC) beams[22ndash27] However the expected failure mode of beam takeninto account allows obtaining the ultimate load by a sectionalcalculation

The external forces to apply at the beam to take intoaccount the actions of external prestressing cables are eval-uated by simple geometric considerations as shown inFigure 8

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Advances in Civil Engineering

200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN 200 kN

520

19001800

5201080

72001100012040

18001900

Figure 3 Multiple coaches for ballast train

Figure 4 Anchor heads and antispalling reinforcement

(2) reinforcement of principal beams with FRP plates onthe bottom face of the beams [20]

(3) reinforcement of principal beams with a system ofunbonded prestressing external to cross-section ofbeams

After awealthy debatewith the contractor and Italian rail-way authorities the third proposal for economic motivationwas chosen Moreover for avoiding excessive costs only apartial rehabilitation of the bridge was selected by allowingtotally the transit of the train equivalent to the LM71 to reduceto the 83 and of the train that bears the ballast (Figure 3)and the load of a testing train (for High-Speed bridges) withreduction to 60The total recharge up to 100 of the testingtrain would have happened after the transit on the bridge

It was decided therefore to apply a system of externalprestressing with 10 external cables of 8 strands 0610158401015840 whichdeparting from the diaphragms of extremity already recon-structed for lodging the prestress anchorage were deviatedby the first intermediary diaphragm (those posed at 34 ofspan) It was chosen to have steel deviator arrangements ondiaphragms

For rationalizing the operations of adjustment the fol-lowing executive phases were selected

(1) removal of road superstructure and concrete millingof the existing surface slab

(2) assemblage of the connectors for the integrative newslab

(3) positioning of the bars of reinforcement and thecasting of integrative slab

(4) demolition of top part of abutment and setup of theplan of work on altitude of existing bearings

(5) positioning of the anchor heads and the antispallingreinforcement the casting of integrative diaphragm(Figure 4)

(6) installation of the metallic saddles of deviation under34 diaphragms using rebar and epoxy resin to con-nect the two components (Figures 5 and 6)

(7) lodging of the integrative external cables and theirprestressing up to nominal force

(8) casting of new top part of abutments and reconstruc-tion of their backfills

(9) positioning of the joints between deck and abutments(10) placing of ballast and rails(11) final testing with the trains used in design phases

(Figure 3)For each phase of construction the corresponding check

calculations were performed The new slab with a thicknessof 250mm was necessary to bear greater local loads thanprevious It was casted with concrete of class C3545The newslab increased the total height of transversal sections of beamswith a notable improvement in terms of stiffness and loadcapacity

3 Numerical Model

31 Numerical Analyses of Strengthened Beams Theproposedrehabilitation scheme for the Terdoppio bridge was investi-gated with deep attention to evaluate the new bearing load

Advances in Civil Engineering 5

(a) (b)

Figure 5 (a) View of external prestressing (b) metallic saddle of deviation

Metal profileRebar

Rebar

Continuous welding Continuous weldingTendon

(a) (b)

Epoxy resin

Existing diaphragm

Metal profile

Tendons

Figure 6 Details of connection between existing bridge and metallic saddle of deviation

of each beam At this aim several numerical analyses werecarried out to obtain precious information about the tensionand strain fields at different load stages

First a linear-elastic calculation was performed to knowthe force that the deck was expected to undertake at servicelimit state (SLS) and the stress distribution along the heightof the beam cross-section

Second a simple sectionalmodelwas used to calculate thecapacity of strengthened beam at ULS It allowed consideringjust the principal geometrical and mechanical parametersproviding an easy control of results Finally a NLFEA wasperformed at ULS using the software VecTor2 [21] whichimplements the MCFT originally proposed by Vecchio andCollins [14] and its upgrading [15]

32 Beam Setup As described in Scheme of RehabilitationProposed section the reinforcement of primary beams was

carried out with a new system of unbonded prestressingdisposed externally to the cross-section of beam (Figure 7)

Two groups of bonded strandswere originally used for theRC beamThe first was characterized by strands with straightaxis along the beam the second group was placed with avariable slope of strands as shown in Figure 6(a) Each strandwas 0510158401015840 in equivalent diameter while the yield and ultimatestrength of steel were 119891

119901(1)119896= 1575MPa and 119891

119905= 1750MPa

respectivelyThe slab on the beams had a thickness of 200mm and

rebar along two orthogonal directions in its plane was usedAlong the longitudinal direction the flexural reinforcementwas provided by 21206018mm+ 112060112mm on the top (for thebending moment close to support) and 41206018mm on thebottom (for the bending moment at half span) for each widthof slab pertaining to considered beam (=1160mm) In thetransversal direction 512060112mmm was used both on the topand on the bottom of slab

6 Advances in Civil Engineering

Existing slab New slab

Existing cables

(a) (b)

External cables

CL

1400

280

700 100

150

100

100500

950

Figure 7 (a) Longitudinal and (b) transversal rehabilitation scheme of beam

328

kN

2331kN

2NpSLS

328

kN

2NpS

LSsin

(1205722)

q = 215 kNm

120572 = 8∘

23kN

Figure 8 Concentrated forces equivalent to external prestressing actions at support and deviation of external cable sections

The shear reinforcement was variable along the beamStirrups with two legs 1206018mm and 12060110mm spacing 250mmwere used for the region between the support and 525m1206018mm spacing 250mm for the region between 525m and1025m and 1206018mm and 1206016mm spacing 250mm for theregion between 1025m and 1525m The beam was of length305m and it is symmetrically loaded and reinforced

As previously mentioned the concrete for the beam ischaracterized by a cylindrical strength 119891cm = 35MPa whilethe concrete for the existing top slab has a cylindrical strength119891cm = 20MPa

For the rehabilitation of bridge the primary beams havebeen retrofitted with a new deck of 250mm thickness (119891cm =35MPa) which was linked to the existing slab by steelconnectors and a system of two external prestressing cables80610158401015840 strands for each beamThe axial force for each externalprestressing cable at SLS was 119873

119901SLS = 1177 kN thus theequivalent balances vertical load was equal to 215 kNm(Figure 8)

33 Linear-Elastic Analysis at SLS The reinforcement of thebeam by the external tendons system has modified the stressregime of the structural element These modifications wereallowed to carry the new loads

The structure after the reinforcement is composed bytwo parts of concrete casted in different times If as a result

of the external loads and the prestressing the beam remainsfully compressed (or with tensile tension values less thanelastic limit) then it is possible to apply the principle of super-positionTherefore total forces are due by sumof prestressingand external load This assumption is no longer valid whenconcrete is cracked (ie at failure)

Three steps with different effects were taken into account(1) dead load prestressing and prestress losses (2) dead loaddue to the just casted new deck and (3) the cross-section ofthe beam composed by the new deck also

The effects in the three different stages were evaluatedseparately and then subsequently summed

In Figure 9 the stress shape along the depth for a cross-section at the midspan of the beam is shown The beam issubjected to compression stress only

34 Sectional Analysis at ULS Several simple models weredeveloped by the same authors to handily evaluate the shearstrength of RC and fibrous reinforced concrete (FRC) beams[22ndash27] However the expected failure mode of beam takeninto account allows obtaining the ultimate load by a sectionalcalculation

The external forces to apply at the beam to take intoaccount the actions of external prestressing cables are eval-uated by simple geometric considerations as shown inFigure 8

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

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International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Advances in Civil Engineering 5

(a) (b)

Figure 5 (a) View of external prestressing (b) metallic saddle of deviation

Metal profileRebar

Rebar

Continuous welding Continuous weldingTendon

(a) (b)

Epoxy resin

Existing diaphragm

Metal profile

Tendons

Figure 6 Details of connection between existing bridge and metallic saddle of deviation

of each beam At this aim several numerical analyses werecarried out to obtain precious information about the tensionand strain fields at different load stages

First a linear-elastic calculation was performed to knowthe force that the deck was expected to undertake at servicelimit state (SLS) and the stress distribution along the heightof the beam cross-section

Second a simple sectionalmodelwas used to calculate thecapacity of strengthened beam at ULS It allowed consideringjust the principal geometrical and mechanical parametersproviding an easy control of results Finally a NLFEA wasperformed at ULS using the software VecTor2 [21] whichimplements the MCFT originally proposed by Vecchio andCollins [14] and its upgrading [15]

32 Beam Setup As described in Scheme of RehabilitationProposed section the reinforcement of primary beams was

carried out with a new system of unbonded prestressingdisposed externally to the cross-section of beam (Figure 7)

Two groups of bonded strandswere originally used for theRC beamThe first was characterized by strands with straightaxis along the beam the second group was placed with avariable slope of strands as shown in Figure 6(a) Each strandwas 0510158401015840 in equivalent diameter while the yield and ultimatestrength of steel were 119891

119901(1)119896= 1575MPa and 119891

119905= 1750MPa

respectivelyThe slab on the beams had a thickness of 200mm and

rebar along two orthogonal directions in its plane was usedAlong the longitudinal direction the flexural reinforcementwas provided by 21206018mm+ 112060112mm on the top (for thebending moment close to support) and 41206018mm on thebottom (for the bending moment at half span) for each widthof slab pertaining to considered beam (=1160mm) In thetransversal direction 512060112mmm was used both on the topand on the bottom of slab

6 Advances in Civil Engineering

Existing slab New slab

Existing cables

(a) (b)

External cables

CL

1400

280

700 100

150

100

100500

950

Figure 7 (a) Longitudinal and (b) transversal rehabilitation scheme of beam

328

kN

2331kN

2NpSLS

328

kN

2NpS

LSsin

(1205722)

q = 215 kNm

120572 = 8∘

23kN

Figure 8 Concentrated forces equivalent to external prestressing actions at support and deviation of external cable sections

The shear reinforcement was variable along the beamStirrups with two legs 1206018mm and 12060110mm spacing 250mmwere used for the region between the support and 525m1206018mm spacing 250mm for the region between 525m and1025m and 1206018mm and 1206016mm spacing 250mm for theregion between 1025m and 1525m The beam was of length305m and it is symmetrically loaded and reinforced

As previously mentioned the concrete for the beam ischaracterized by a cylindrical strength 119891cm = 35MPa whilethe concrete for the existing top slab has a cylindrical strength119891cm = 20MPa

For the rehabilitation of bridge the primary beams havebeen retrofitted with a new deck of 250mm thickness (119891cm =35MPa) which was linked to the existing slab by steelconnectors and a system of two external prestressing cables80610158401015840 strands for each beamThe axial force for each externalprestressing cable at SLS was 119873

119901SLS = 1177 kN thus theequivalent balances vertical load was equal to 215 kNm(Figure 8)

33 Linear-Elastic Analysis at SLS The reinforcement of thebeam by the external tendons system has modified the stressregime of the structural element These modifications wereallowed to carry the new loads

The structure after the reinforcement is composed bytwo parts of concrete casted in different times If as a result

of the external loads and the prestressing the beam remainsfully compressed (or with tensile tension values less thanelastic limit) then it is possible to apply the principle of super-positionTherefore total forces are due by sumof prestressingand external load This assumption is no longer valid whenconcrete is cracked (ie at failure)

Three steps with different effects were taken into account(1) dead load prestressing and prestress losses (2) dead loaddue to the just casted new deck and (3) the cross-section ofthe beam composed by the new deck also

The effects in the three different stages were evaluatedseparately and then subsequently summed

In Figure 9 the stress shape along the depth for a cross-section at the midspan of the beam is shown The beam issubjected to compression stress only

34 Sectional Analysis at ULS Several simple models weredeveloped by the same authors to handily evaluate the shearstrength of RC and fibrous reinforced concrete (FRC) beams[22ndash27] However the expected failure mode of beam takeninto account allows obtaining the ultimate load by a sectionalcalculation

The external forces to apply at the beam to take intoaccount the actions of external prestressing cables are eval-uated by simple geometric considerations as shown inFigure 8

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Advances in Civil Engineering

Existing slab New slab

Existing cables

(a) (b)

External cables

CL

1400

280

700 100

150

100

100500

950

Figure 7 (a) Longitudinal and (b) transversal rehabilitation scheme of beam

328

kN

2331kN

2NpSLS

328

kN

2NpS

LSsin

(1205722)

q = 215 kNm

120572 = 8∘

23kN

Figure 8 Concentrated forces equivalent to external prestressing actions at support and deviation of external cable sections

The shear reinforcement was variable along the beamStirrups with two legs 1206018mm and 12060110mm spacing 250mmwere used for the region between the support and 525m1206018mm spacing 250mm for the region between 525m and1025m and 1206018mm and 1206016mm spacing 250mm for theregion between 1025m and 1525m The beam was of length305m and it is symmetrically loaded and reinforced

As previously mentioned the concrete for the beam ischaracterized by a cylindrical strength 119891cm = 35MPa whilethe concrete for the existing top slab has a cylindrical strength119891cm = 20MPa

For the rehabilitation of bridge the primary beams havebeen retrofitted with a new deck of 250mm thickness (119891cm =35MPa) which was linked to the existing slab by steelconnectors and a system of two external prestressing cables80610158401015840 strands for each beamThe axial force for each externalprestressing cable at SLS was 119873

119901SLS = 1177 kN thus theequivalent balances vertical load was equal to 215 kNm(Figure 8)

33 Linear-Elastic Analysis at SLS The reinforcement of thebeam by the external tendons system has modified the stressregime of the structural element These modifications wereallowed to carry the new loads

The structure after the reinforcement is composed bytwo parts of concrete casted in different times If as a result

of the external loads and the prestressing the beam remainsfully compressed (or with tensile tension values less thanelastic limit) then it is possible to apply the principle of super-positionTherefore total forces are due by sumof prestressingand external load This assumption is no longer valid whenconcrete is cracked (ie at failure)

Three steps with different effects were taken into account(1) dead load prestressing and prestress losses (2) dead loaddue to the just casted new deck and (3) the cross-section ofthe beam composed by the new deck also

The effects in the three different stages were evaluatedseparately and then subsequently summed

In Figure 9 the stress shape along the depth for a cross-section at the midspan of the beam is shown The beam issubjected to compression stress only

34 Sectional Analysis at ULS Several simple models weredeveloped by the same authors to handily evaluate the shearstrength of RC and fibrous reinforced concrete (FRC) beams[22ndash27] However the expected failure mode of beam takeninto account allows obtaining the ultimate load by a sectionalcalculation

The external forces to apply at the beam to take intoaccount the actions of external prestressing cables are eval-uated by simple geometric considerations as shown inFigure 8

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Civil Engineering 7

New deck Compression stresss = 250mm

594MPa960MPa964MPa

08MPa

69MPa

62MPa

119MPa

Figure 9 Stress diagram at midspan cross-section of beam

Figure 10 showed the free-body midspan cross-sectionof beam where 119909

119888is the distance between the top com-

pressed part of beam and the neutral axis 1198601199011= 24 times 93 =

2232mm2 and 1198601199012= 14 times 93 = 1302mm2 are the area

of equivalent inclined and straight cable respectively and119873119901SLS = 1177 kN is the axial force for each external pres-

tressed cableAssuming the stress-block distribution for compressed

concrete the equilibrium along the longitudinal axis of beamallows obtaining the position of neutral axis

08119909119888119891cm119861 = 1198601199011119891119901(1)119896 + 1198601199012119891119901(1)119896 + 2119873119901SLS cos120572 (1)

The distance between the top compressed part of beam andthe neutral axis is 242mmThebending equilibrium equationallows obtaining the flexural strength of beam

119872119906= minus08119909119888

208119909119888119891cm119861 + 1198891198862119873119901SLS cos120572

+ 1198891198871198601199012119891119901(1)119896+ 1198891198881198601199011119891119901(1)119896

(2)

obtaining119872119906= 13013 kNm

Having known the flexural strength of beam the loadbearing of beam is evaluable writing a simple equation ofequilibrium between the external forces and the reaction ofsupport The equivalent force of external distributed load isapplied at a distance from the support equal to 1198714 = 763mwhile the actions due to the external prestressing cables arerepresented by concentrated forces applied in the pole 119860 andat distance 119871

119901= 640m from the support (Figure 8)

35 TheModified Compression FieldTheory (MCFT) Severalanalytical formulations have been suggested to reproduce theresponse of RC structural elements subject to different loadconditions adopting models based on several constitutivelaws and mechanical theories [14 28 29]

Between these the MCFT represents a general model forthe load-deformation behaviour of two-dimensional cracked

reinforced concrete subjected to shear and flexure It modelsconcrete considering concrete stresses in the principal direc-tions summed with reinforcing stresses assumed to be onlyaxial The concrete stress-strain behaviour in compressionand tension was derived originally from tests performed byVecchio and Collins [30]

36 Nonlinear Analyses at ULS Figure 11 shows the meshgenerated for the beam taken into account Thanks to thecomplete symmetry only half beam was modelled and suita-bly restrained to the symmetrical axis

The mesh was composed of four-node triangular andrectangular elements with variable thickness to representthe concrete and two-node truss bars with uniform cross-sectional area for rebar and bonded cables The colours indi-cate areas with different reinforcement percentage The finiteelement size was chosen adopting the cover as vertical sizeand a ratio between sides of rectangular element close toone The action induced by external prestressed cables wasmodelled as concentrate nodal forces on steel plates with auniform thickness and fully connected to concrete providingregions without rotations (Figure 12)

Perfect steel-to-concrete bond has been assumed for bothrebars and inclined and straight cables For the latter a pre-strain has been considered to take into account the prestress-ing action It was determinate considering a Young modulusfor the steel of cables equal to 186GPa and an axial force at SLSfor each tendon equal to about 1000MPa (including the forcedegradation due to shrinkage and creep) thus a prestrainequal to 56mmm has been used

The software VecTor2 allows managing many parametersconcerning mechanical characteristics of materials and thoseconstitutive laws The numerical analyses were carried outassuming the default values for each parameter and specifi-cally taking the Hognestad parabola for concrete an elastic-plastic law for steel rebars and finally the known Ramberg-Osgood formulation for prestressing steel [21]

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Advances in Civil Engineering

B fcm

08

2NpSLScos120572

da

db dc

xc

xc

Ap1fp(1)k

Ap2fp(1)k

Figure 10 Free-body forces diagram at midspan cross-section of beam

Stress (conc)Enter job title f2 Displacement factor = 100

minus8544 to minus8180

minus8180 to minus7816

to minus7453to minus7089

to minus6725to minus6362

to minus5998

to minus5634

to minus5271to minus4907

to minus4543

to minus4180

to minus3816to minus3452

to minus3089

to minus2725

to minus2362to minus1998

to minus1634

to minus1271

to minus907

to minus543

to minus180

to minus184

Figure 11 Finite element model of half beam

NLFEAs were performed assigning three different loadcases the statical self-weight on all concrete elements thestatically external prestressing forces and the monotonicallyincreasing displacement on the node located in the middle ofthe top steel transfer plate placed at 1198714 from the supportThe total load has been computed as twice the reaction forceat the support Thus the displacement controlled procedureshave been able to reproduce the postpeak branch of the load-displacement curve

Figure 13 illustrates the load-displacement numericalcurve evaluated in the midspan cross-section of beam Theload capacity at ULS provided by the NLFEA is equal to1883 kN value close to that obtained by sectional analysisThelarge postpeak branch shows a flexural failure with a constantincrement of strength and awide deflection atmidspan cross-section of beam has been obtained

The NLFEA provided also interesting information aboutthe crack pattern and stress fields at ULS (Figure 14)

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Civil Engineering 9

X

Y

2231000

324600

minus327600

11500

Figure 12 Concentrate nodal forces on steel plates due to external prestressing cables

0 20 40 60

0 400 800 1200 1600

120575 (mm)

P(k

N)

2000

1600

1200

800

400

0

400

300

200

100

0

P(k

ip)

P-120575

120575 (in)

Figure 13 Load-displacement numerical curve

Figure 14 Crack pattern of beam at failure

The crack pattern at ULS confirmed the flexural crisis ofstructural member with large vertical cracks in the midspanof beam In the shear span region cracks are inclined withrespect to the longitudinal axis and slightly wider

The stress fields of concrete are clearly compatible withthe crack pattern described above thus the compressionstress level at beam crisis is less than cylindrical strengthof concrete and when the bonded cables strain reaches themaximum value available then beam fails

4 Conclusions

An application of external prestressing retrofitting has beenpresented The structure element analyzed was an existingsingle span bridge for which it was necessary to improve theload capacity allowing the transit of larger loads as trains

An in situ campaign of tests has allowed an accuratedesign with optimized choices which have been described

The design of retrofitting for the considered case of studythe Terdoppio bridge was investigated by several numericalanalyses which have provided precious information aboutthe load capacity and stress and strain fields at different loadstages

The linear-elastic analysis provided information about thestress shape along the cross-section of the beam confirmingthat the beam was subjected to compression only

The sectional model has allowed calculating the flexuralcapacity of strengthened beam considering few parametersto obtain accurate values of strength and an easy control ofresults

In addition the sophisticated FEM software VecTor2which implements the well-known MCFT has been usedto perform different NLFEAs Numerical results have beenreported and discussed showing the ability of the theoreticalmodel adopted to provide a response of the beam analyzedsubjected to transversal load in agreement with the valuesobtained by the sectional method

Furthermore interesting information has been providedby the NLFEAs about the crack pattern and stress fields ofstructural member considered at each stage of load predict-ing a large ductile branch at failure as expected in designphase

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Advances in Civil Engineering

References

[1] A F Daly and W Witarnawan ldquoStrengthening of bridge usingexternal post-tensioningrdquo in Proceedings of the Conference ofEastern Asia Society for Transportation (EASTS rsquo97) SeoulRepublic of Korea October 1997

[2] A Daly and W Witarnawan ldquoA method for increasing thecapacity of short and medium span bridgesrdquo in Proceedings ofthe 10th REAAA Conference Tokyo Japan September 2000

[3] F Seible ldquoAdvanced composites materials for bridges in the21st centuryrdquo in Proceedings of the 2nd International Conferenceon Advanced Composite Materials in Bridges and Structures(ACMBS rsquo96) pp 17ndash30 Montreal Canada 1996

[4] J M Stallings J W Tedesco M El-Mihilmy andMMcCauleyldquoField performance of FRP bridge repairsrdquo Journal of BridgeEngineering vol 5 no 2 pp 107ndash113 2000

[5] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[6] P Casadei N Galati G Boschetto K Y Tan A Nanni andG Galecki ldquoStrengthening of impacted prestressed concretebridge I-girder using prestressed near surface mounted C-FRPbarsrdquo inProceedings of the 2nd International Congress FederationInternationale du Beton Naples Italy June 2006

[7] G Campione P Colajanni L La Mendola and N SpinellaldquoDuctility of reinforced concrete members externally wrappedwith fiber-reinforced polymer sheetsrdquo Journal of Composites forConstruction vol 11 no 3 pp 279ndash290 2007

[8] P Colajanni F de Domenico N Maugeri A Recupero NSpinella and G Mantegazza ldquoExperimental results of RC col-umns strengthenedwith fibre reinforced cementitiousmortarsrdquoin Proceedings of 3rd International Conference on ConcreteRepair Rehabilitation and Retrofitting (ICCRRR rsquo12) P MoyoEd pp 1137ndash1143 CRC Press Cape Town South Africa 2012

[9] P Colajanni F De Domenico A Recupero and N SpinellaldquoConcrete columns confined with fibre reinforced cementitiousmortars experimentation and modellingrdquo Construction andBuilding Materials vol 52 pp 375ndash384 2014

[10] P Colajanni M Papia and N Spinella ldquoStress-strain lawfor confined concrete with hardening or softening behaviorrdquoAdvances in Civil Engineering vol 2013 Article ID 804904 11pages 2013

[11] M H Harajli ldquoStrengthening of concrete beams by externalprestressingrdquo PCI Journal vol 38 no 6 pp 76ndash78 1993

[12] J Choi ldquoComparative study of effective stresses of concretebeams strengthened using carbon-fibre-reinforced polymerand external prestressing tendonsrdquo Structure and InfrastructureEngineering vol 10 no 6 pp 753ndash766 2014

[13] G Bertagnoli V I Carbone L Giordano and G MancinildquoRepair and strengthening of damaged prestressed structuresrdquoinDurability of Post-Tensioning Tendons vol 15 of FIB Bullettinpp 139ndash153 2001

[14] F J Vecchio and M P Collins ldquoThe modified compressionfield theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[15] F J Vecchio ldquoDisturbed stress field model for reinforced con-crete formulationrdquoASCE Journal of Structural Engineering vol126 no 9 pp 1070ndash1077 2000

[16] F Minelli and F J Vecchio ldquoCompression field modeling offiber-reinforced concrete members under shear loadingrdquo ACIStructural Journal vol 103 no 2 pp 244ndash252 2006

[17] P Colajanni L la Mendola S Priolo and N Spinella ldquoExperi-mental tests andFEMmodel for SFRCbeamsunder flexural andshear loadsrdquo in Proceedings of the Seismic Engineering Interna-tional Conference Commemorating the 1908 Messina and ReggioCalabria Earthquake (MERCEA rsquo08) vol 1020 pp 872ndash879Reggio Calabria Italy July 2008

[18] N Spinella P Colajanni and L La Mendola ldquoNonlinear anal-ysis of beams reinforced in shear with stirrups and steel fibersrdquoACI Structural Journal vol 109 no 1 pp 53ndash64 2012

[19] Italferr Sovraccarichi per il Calcolo dei Ponti FerroviarimdashIstru-zioni per la Progettazione lrsquoesecuzione ed il Collaudo ISCPS-OM2298-261995 1995

[20] A R Marı Bernat A Cladera E Oller and J M BairanGarcia ldquoShear design of FRP reinforced concrete beamswithouttransverse reinforcementrdquo Composites B Engineering vol 57pp 228ndash241 2014

[21] P S Wong and F J Vecchio ldquoVecTor2 and FormWorks userrsquosmanualrdquo Tech Rep Department of Civil Engineering Univer-sity of Toronto Toronto Canada 2002

[22] A Recupero A DrsquoAveni and A Ghersi ldquoBending moment-shear force interaction domains for prestressed concretebeamsrdquo ASCE Journal of Structural Engineering vol 131 no 9pp 1413ndash1421 2005

[23] P Colajanni A Recupero and N Spinella ldquoShear strengthprediction by modified plasticity theory for sfrc beamsrdquo inSeismic Engineering International Conference Commemoratingthe 1908 Messina and Reggio Calabria Earthquake (MERCEArsquo08) vol 1020 no 1 pp 888ndash895 2008

[24] N Spinella P Colajanni and A Recupero ldquoSimple plasticmodel for shear critical SFRC beamsrdquo Journal of StructuralEngineering vol 136 no 4 pp 390ndash400 2010

[25] P Colajanni A Recupero and N Spinella ldquoGeneralization ofshear truss model to the case of SFRC beams with stirrupsrdquoComputers and Concrete vol 9 no 3 pp 227ndash244 2012

[26] N Spinella ldquoShear strength of full-scale steel fibre-reinforcedconcrete beams without stirrupsrdquo Computers and Concrete vol11 no 5 pp 365ndash382 2013

[27] P Colajanni A Recupero and N Spinella ldquoDesign procedurefor prestressed concrete beamsrdquo Computers amp Concrete vol 13no 2 pp 1ndash16 2014

[28] J M B Garcia and A R M Bernat ldquoShear-bending-torsioninteraction in structural concrete members a nonlinear cou-pled sectional approachrdquo Archives of Computational Methods inEngineering vol 14 no 3 pp 249ndash278 2007

[29] G Bertagnoli G Mancini A Recupero and N SpinellaldquoRotating compression field model for reinforced concretebeams under prevalent shear actionsrdquo Structural Concrete vol12 no 3 pp 178ndash186 2011

[30] F J Vecchio andM P Collins ldquoResponse of reinforced concreteto in plane shear and normal stressrdquo Tech Rep Departmentof Civil Engineering University of Toronto Toronto Canada1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of