Truck Load Distribution Behaviorof the Bridge Street Bridge,Southfield, Michigan

Nabil F. Grace, Ph.D., P.E.Professor and ChairmanCivil Engineering DepartmentLawrence Technological UniversitySouthfield, Michigan

John J. Roller, P.E., S.E.Principal Structural Engineer

Construction TechnologyLaboratories, Inc.

Skokie, Illinois

Frederick C. Navarre, RE.Chief Structural EngineerHubbell, Roth & Clark, Inc.Bloomfield Hills, Michigan

Richard B. Nacey, P.E.Senior Project EngineerHubbell, Roth & Clark, Inc.Bloomfield Hills, Michigan

Wayne Bonus, P.E.Administrative Engineer

City of SouthfieldSouthfield, Michigan

I

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This paper presents the major results and detailsfrom a structural load test performed on StructureB of the Bridge Street Bridge Deployment Projectin South field, Michigan. Structure B is the firstprestressed concrete bridge in the United Statesto be almost entirely reinforced with carbonfiber reinforced polymer. The measured strainsand deflections from various bridge span loadconfigurations were analyzed for evaluating loaddistribution behavior. In addition, data from alaboratory test of a full-scale prototype double-teetest beam conducted prior to bridge construction

were compared with data obtained from the fieldload test of Structure B. Static loads were appliedto each of the three spans of Structure B usingloaded dump trucks to generate specific positivelane bending moments. Based on the results fromthe static load test of Structure B, it is concludedthat the three spans of the bridge exhibit similarload distribution behavior. As determined from themeasured strain response in the beams, the actualdistribution of the applied loads within each span in

As a result of extensive researchefforts, fibrous composite materials are now being used in

the construction of innovative civilengineering structures throughout theworld.’ These structures include bridgebeams, girders, and slabs containingspecial reinforcing elements.2-3 Onenotable example of this emerging technology in North America is the BridgeStreet Bridge Deployment Project inSouthfield, Michigan.4

This project includes the first prestressed concrete bridge in the UnitedStates to be almost entirely reinforcedwith carbon fiber reinforced poiymer (CFRP). The findings of severalresearch investigations conducted atLawrence Technological University,Southfield, Michigan, and funded bythe National Science Foundation, formulated the technical basis for the implementation of this technology. 5-10

The Bridge Street Bridge Deployment Project (see Figs. la and ib, andFig. 2) consists of two parallel, independent bridges (Structures A and B)over the Rouge River in the City ofSouthfield, Michigan. Both structureswere designed to accommodate twotraffic lanes and incorporated three68.9 ft (21 m) long, 27.9 ft (8.5 m) widespans skewed at an angle of 15 degreesrelative to the substructure. StructureA incorporates five equally spacedconventional prestressed AASHTO I-beams in each of the three spans.

Structure B consists of 12 double-tee beams (four beams per span), eachincorporating internal pretensionedLeadlineTM tendons and external post-tensioned carbon fiber composite cable

general conforms with the provisions contained inthe AASHTO Specifications.

Fig. 1 a. Southward view of Bridge Street Bridge, Southfied, Michigan. CFRPstructure, Structure B, is on the right.

March-April 2005 77

(CFCCTM)tendons. Fig. 3 shows a section through the superstructure. Specific construction details related to theproject can be found elsewhere.4Thispaper presents the major findings anddetails related to a field load test conducted on Structure B after completionof construction.

BRIDGE DESIGN DETAIlSHubbell, Roth & Clark, Inc. (HRC),

Bloomfield Hills, Michigan, was responsible for the design of the BridgeStreet Bridge Deployment Project.Bridge Structures A and B were designed for two traffic lanes using provisions of both the AASHTO Standard

Specifications for Highway Bridges’1and LRFD Bridge Design Specifications.12 As shown in Fig. 3, the superstructure dead loads for Structure Bincluded the double-tee beams, composite CFRP-reinforced concrete topping, surfacing mixture, pedestriansidewalk, concrete barrier, and thebridge parapet and railing. Live loaddesign was based on Michigan MS-23(AASHTO HS25) truck loading.

During the design phase, values forthe live load distribution factor wereinvestigated using provisions of bothsets of AASHTO bridge specifications.The typical derivation of the LRFDlive load distribution factor is basedon the longitudinal stiffness parameter, K, calculated using the momentof inertia of the full composite sectionof each double-tee beam, resulting herein a value of approximately 0.63 lanesper beam. Likewise, distribution factor calculations performed using theprovisions of Section 3.23.4 of theAASHTO Standard Specificationsresulted in a similar value of approximately 0.64 lanes per beam.

Within the provisions of Section4.6.2.2 of the AASHTO LRFD Specifications, HRC considered the momentof inertia of the beam webs alone to cal-

Intermediate pier support (typ.) Six instrumented DT beams\ of Structure B shown shaded

Sidewalk slab Structure B/1,

.6

Fig. 2. Plan view of Bridge Street Bridge.

Fig lb. Side view of Structure B.

21,314mm (South span) 20,349mm (Middle span) 21429 mm (North span)

A \ ,J

B F r

- G c

< 0 H \ I \ H IIA,ei )— Concrete barber wall

Ej \ \

Sidewalk slab

\

Structure A

\\

Each instrumented DT beam incorporated the following

- 10 internal gages for measuring concrete strains and temperatures mid- and quarter-span sections.

- 3 external displacement transducers for measuring detections at mid- and quarter-upan locations.

- 4 load cells for measuring force levels in each of the external post-tensioned tendons. Note: 1 mm = 0.00328 ft 1lJ

Abutment Jback wall

78 PCI JOURNAL

Fig. 3. Section view through superstructure of Structure B looking south.

Note: 1 mm = 0.00328 ft

culate an alternate value of the longitudinal stiffness parameter, Kg, resultingin a distribution factor of 0.81 lanes perbeam. The nominal ratio of this alternative distribution factor was noted tobe about 1.3. Calculations showing thedesign live load distribution factors areshown in Appendix A.

The Michigan MS-23 truck loadingresulted in a maximum live load perlane plus impact bending moment equalto 1496 kip-ft (2028 kN-m). SinceStructure B was to be the first bridge toincorporate prestressed concrete beamsmade using CFRP exclusively as theprimary reinforcement, a conservativeapproach was appropriate to establishthe design live load. Therefore, eachdouble-tee beam was designed for alive load plus impact (LL+1) momentequal to 1197 kip-ft (1622 kN-m), orapproximately 1.3 times the typical design value.

For most design conditions, the fullcomposite beam section is typically

used in the determination of the longitudinal beam stiffness. Therefore,for evaluating the load distributionbehavior of Structure B, comparisonsare made with the live load distributionfactor equal to 0.6 lanes per beam. Asindicated in Appendix A, the live loaddistribution factors calculated using thevarious AASHTO provisions rangedfrom 0.63 (LRFD Specifications) to0.64 (Standard Specifications).

CONSTRUCTION

Prestressed Systems Incorporated inWindsor, Ontario, Canada, fabricated12 double-tee beams for Structure B ofthe Bridge Street Bridge DeploymentProject. The double-tee beams wereeach cast with seven diaphragms to enhance transverse stiffness, house transverse post-tensioned CFRP tendons,and provide deviator-bearing elementsfor the draped longitudinal post-tensioned CFRP tendons. A cross-section-

al view of a typical double-tee beam cutnear midspan is shown in Fig. 4. Eachbeam incorporated 60 internal 0.39 in.(10 mm) diameter LeadlineTM CFRPpretensioning tendons (30 in eachbeam stem).

In addition to the Leadline tendons,each beam also incorporated fourdraped longitudinal external 1.58 in.(40 mm) diameter post-tensioningCFCC tendons. Other longitudinaland transverse non-prestressed reinforcement in the beam flange and diaphragms were also made of CFRP. Theepoxy-coated stainless steel stirrupsused for shear reinforcement in eachbeam stem were the only internal metallic reinforcement components incorporated in the beams.

After fabrication in Canada, the 12double-tee beams were transported tothe bridge site. Each of the three bridgespans of Structure B incorporated fourdouble-tee beams erected side-by-side,as shown in Figs. 2 and 3. Each double-

Four side-by-side DT beamsin each bridge span (typ.)

Draped external CFCC tendons

March-April 2005 79

2120mm

Fig. 4. Cross section of typical double-tee beam near midspan.

tee beam had five intermediate transverse diaphragms (P2 through D6) andtwo end transverse diaphragms (Dl andD7). Additional CFCC tendons wereinstalled in the transverse diaphragmsand were used to post-tension the fourbeams in each span together.

After erection, a 3 in. (76 mm) minimum thick concrete topping reinforcedwith NEFMACTMgrids was placed overeach span. The concrete topping wasdiscontinuous over the supports and anchored to the double-tee beams by thehooked stirrup ends that protruded fromthe top flange. A 1.5 in. (38 mm) thicklatex-modified surfacing mixture wasadded over the concrete topping withinthe 20 ft (6.1 m) wide clear roadwaybounded by the pedestrian sidewalkalong the west side of the bridge andconcrete barrier on the east side.

INSTRUMENTATIONDuring fabrication, six of the 12

double-tee beams for Structure B wereinstrumented with various sensors tomeasure concrete strains, beam deflections, and force levels in the externalCFCC post-tensioned tendons. The six

double-tee beams selected for instrumentation are shown in Fig. 2 (BeamsC, G, J, K, L, and M).

Once the double-tee beams wereerected at the bridge site, additionalsensors were installed throughoutStructure B during the various stagesof construction. All sensors were connected to a dedicated on-site data acquisition system used to monitor thelong-term behavior of the bridge. Instrumentation of the bridge beams andinstallation of the data acquisition system was performed by ConstructionTechnology Laboratories, Inc. (CTL),of Skokie, Illinois.

INSPECTION ANDLOAD TESTING

After construction was complete,CTL conducted a visual inspection andstatic load test. Visual inspection wasdone to document the size and locationof any concrete cracks visible to the unaided eye both before and after the loadtest. The objective of the static load testwas to evaluate structural performance

under live load conditions approximating design service load levels.

Visual Inspection

Before conducting the static load test,an initial visual inspection of StructureB was conducted to document the as-built condition. The visual inspectionincluded the top and underside of thesuperstructure. With the exception ofthe beam diaphragms that providedanchorage for the external longitudinalpost-tensioning tendons (D2 and D6),there were no structural cracks foundduring the inspection. After the staticload test was completed, there were noapparent new cracks and no discern-able difference observed in the existingdiaphragm cracks.

Static Load Test Details

After the initial visual inspection wascompleted, a static load test was conducted on November 28, 2001. Staticloads were applied to each span (individually) using two identical tandemrear-axle dump trucks provided by theCity of Southfleld. The specified empty

Epoxy-coated, stainless

- 10-mm diameter CFRPreinforcement

EaC

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A

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0

150mm

Thirty 10-mm diameter

prestressed LeadlineCFRP tendons ineach beam stem

280mm

Four 40-mm diameter external drapedpost-tensioned CFCC tendons

Transverse diaphragm

Note 1 mm = 0.00328 ft

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Right Front

6,850 lb (#649)7,000 lb (#650)

I:

Left Forward10,950 lb (#649)

10,600 lb (#650)

Note: 1 lb = 4.445 N

Fig. 5. Dump truck configuration and measured wheel loads.

gross weight of each dump truck was26,700 lb (119 kN). Prior to the test,each dump truck was filled with granular material to achieve a total target vehicle weight of 58,000 lb (258 kN).

After filling, the actual weight ofeach truck was measured by the chiefweigh master for the Road Commissionfor Oakland County. During this exercise, portable scales, accurate to within±1 percent of reading, were used tomeasure the load distributed to each of

the three axles. Details and measuredaxle loads for both dump trucks (TruckNos. 649 and 650) are shown in Fig. 5.The filled weights of both trucks werewithin 450 lb (2.0 kN) of the 58,000 lb(258 kN) target weight.

The load test consisted of four different stages of loading. Each loading stageconsisted of positioning the two dumptrucks back to back in one lane nearmidspan, as shown in Fig. 6. The firsttwo load stages consisted of positioning

Fig. 6. Typical truck orientation used foreach load stage.

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7,200 lb (#649)

7,550 lb (#650)

Left Back

10,950 lb (#649)

10,600 lb (#650)

March-April 2005 81

20400 mm

Fig. 7. Truck positions for Load Stage 1: Maximum positive moment in west lane of north span.

FF F F FF

/— F\ F FI F’ Sidewalk slab and deck fascia F FF Beam A\ FFF

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Fig. 8. Truck positions for Load Stage 2: Maximum positive moment in west lane of south span.

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opposite directions in each lanespaced 2,591 mm apart and

2591 mm

1,295 mm from mid-span centerline.

Note: 1 mm = 0.00328 ft N

20,286 mm

South span length

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Rearmost axle of trucks facingopposite directions in each lane

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spaced 2,591 mm apart and1,295 mm from mid-span centerline.

Note: 1 mm = 0.00328 ft N

82 PCI JOURNAL

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the two loaded dump trucks in the westlane of the north and south spans (individually) to generate maximum positivebending moment at mid-length.

Truck positions for the first two loading stages are shown in Figs. 7 and 8.The third and fourth load stages consisted of positioning the two loadeddump trucks in the east lane of the northand middle spans (individually) to generate maximum positive bending moment at mid-length. Truck positions forthe third and fourth loading stages areshown in Figs. 9 and 10, respectively.

During each load stage, the rearmostaxles of the two dump trucks werespaced approximately 8.5 ft (2.59 m)apart and 4.25 ft (1.30 m) from themidspan centerline. This loading configuration produced a lane bendingmoment at midspan equal to approximately 90 percent of the 1496 kip-ft

(2028 kN-m) design service live loadmoment (including impact). The resulting midspan lane bending moments inthe north, middle, and south spans were1364, 1309, and 1355 kip-ft (1850,1774, and 1836 kN-m), respectively.

During the load test, the existingbridge instrumentation and data acquisition system were used to measure theresponse to the applied loads. For eachstage of loading, instrument readingswere taken before moving the trucksonto the span (initial reading). Immediately after the trucks were moved intothe required positions, a second set ofinstrument readings was taken.

The trucks remained in the requiredpositions for a period of approximatelyfive minutes, after which a third set ofinstrument readings was taken. Thetrucks were then moved off the bridge,and a fourth and final set of instrument

readings were taken approximately fiveminutes after the load was removed.This protocol was followed for each ofthe four load stages.

Static Load Test Results

The response of Structure B to the applied static loads was evaluated basedprimarily on measured concrete strainsand deflection data at the midspan ofeach instrumented beam. Therefore,although the instrumentation array included more than 450 individual sensors, the discussion of measured datafrom the load test presented in thispaper is limited to concrete strains anddeflections measured at midspan. Deflection measurements, taken manuallyat midspan during the load test usingprecision surveying equipment, corroborated the measured strain data.

As noted in Fig. 2, every beam inthe north span (3, K, L, and M) and thethird beam from the west in each ofthe south and middle spans (C and G),was fabricated to include a full compliment of instrumentation. During eachload stage, measured data were collected for the instrumented beams inthe span being loaded. Measured straindata from each of the four load stagesare presented in Figs. 11 and 12. Thereported data from the four load stagesrepresent the measured response due tothe application of the truck loads, anddo not include the effects of the preexisting dead loads.

Measured midspan strain profilespresented in Fig. 11 indicate that theapplied load was effectively distributed to all four beams in the north span.Average measured strains near the webbottom at midspan of the four beamsranged from 23 to 45 microstrain, anddecreased from west to east. In addition, the measured midspan strain profile for Beam C is nearly identical tothe strain profile for the correspondingnorth span beam (Beam L). This observation indicates that the north andsouth spans exhibited similar load distribution behavior.

Measured midspan strain profilespresented in Fig. 12 indicate that theapplied load was effectively distributed to all four beams in the north span.Average measured strains near the webbottom at midspan of the four beams

Load Stage Strain location: midspan @ bottom of web

DTbeam J K L M

1 45 34 30 23

% Total strain 34.1 25.8 22.7 17.4

DTbeam C2 Concrete 29stranuE

LoadStagel J K L M

LoadStage2 A B C D

Top surface of concrete topping

Tension (+)

Compression C-)

Load Stages 1 & 2 ConcreteStrain Distribution

BeamJ

Beam K

— — — BeamL

Beam M

— -BeamC

Bottom surface of beam web

-50 -50 -40 -30 -20 -10

Average Measured Concrete Strains, Microstrain

0 10 20 30 40

Fig. 11. Load Stages 1 and 2: Measured responses for Beams ito M and C.

50 60

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in the north span ranged from 15 to51 microstrain, decreased from eastto west, and were consistent with thecorresponding measured deflections.Measured strain data from this loadstage were similar to the data fromLoad Stage 1. The additional stiffnesscontributed by the sidewalk installedover Beam J most likely accounted forthe slight variation occurring betweenthe peak strains measured during LoadStages 1 and 3.

It is also observed that the measuredmidspan strain profile for Beam G(see Fig. 12) is almost identical to thestrain profile for the correspondingnorth span beam (Beam L). This observation indicates that the north andmiddle spans also exhibited similarload distribution behavior.

LOAD DISTRIBUTIONBEHAVIOR

The load distribution behavior ofStructure B was evaluated by comparing the measured strain response duringthe truck load test to the load distribution factors derived from the AASHTOdesign provisions. In addition, datafrom a structural load test performedon a single prototype double-tee beamincorporating details identical to thoseof the bridge beams was used for making further comparisons with the truckload test data from Structure B.

Measured Strain Response DuringTruck Load Test

The measured data from Load Stages 1 to 4 indicate that all three spansexhibit very similar load distributionbehavior. As shown in Fig. 13, themaximum measured strain responseduring the load test was obtained whenthe trucks were positioned in the eastlane of Structure B (Load Stage 3). Itis very likely that the east lane loadingcondition represented the worst-casescenario for bending stresses to occurdue to the greater eccentricity of theload from the center of the bridge andthe absence of the sidewalk along thisside of the bridge.

A comparison of the average measured concrete strains in the web bottom of Beams I to M during Load S tag-

es 1 and 3 can be used to provide anindication of the load distribution in thenorth bridge span. Such a comparisonis shown in Fig. 14 for the combinedeffects of Load Stages I and 3. Basedon the magnitude of the average measured bottom web strains, the cumulative percentages of the applied laneloads distributed to each of the fourbeams in the north span (Beams J, K,L, and M) would be 46.3, 43.7, 51.2,and 58.9 percent, respectively.

Using this rationale, it can be theorized that no more than 60 percent ofthe total lane live load would be distributed to any individual beam. Thispercentage is in good agreement withthe AASHTO distribution factor of0.60 lanes per beam resulting from thecondition where the full composite section is used in the calculation of longitudinal stiffness.

Comparison of Measured Strains inStructure B and Prototype Beam

The truck configuration used duringthe load test of Structure B produced alane bending moment at midspan equalto approximately 90 percent of the design service moment (LL+I). This percentage corresponds to an applied lanebending moment of approximately1346 kip-ft (1825 kN-m). Prior to fabrication of the bridge beams for Structure B, a single prototype double-teebeam was fabricated by the precasterand shipped to CTL for testing.13”4

During fabrication, strain gauge instrumentation was installed by CTL atthree different sections along the lengthof the prototype double-tee beam, atthe locations shown in Fig. 15. Theconfiguration of the strain gauge instrumentation installed in the prototype

Load Stage Strain location: midspan @ bottom of web

DTbeam J K L M

15 22 35 51

%Total strain 12.2 17.9 28.5 41.5

DTbeam G“ Concrete

strain_iir

Load Stage 3

LoadStage4 E F G H

Compression (-)

Load Stages 3 & 4 ConcreteStrain Distribution

BeamJ

Beam KBeamL

— BeamMBeamG

Bottom surface of beam web

-60 -50 40 -30 -20 -10 0 10 20 30 40 50 60

Average Measured Concrete Strains, microstrain

Fig. 12. Load Stages 3 and 4: Measured responses for Beams J to M and C.

March-April 2005 85

Fig. 13. Average measured strain at bottom of double-tee web, north span.

beam was identical to that used in theinstrumented double-tee beams incorporated in Structure B.

The prototype beam was testedwith the concrete topping applied, butwithout any transverse post-tensioning applied through diaphragms. Themeasured response from the prototypedouble-tee beam at a load corresponding to the moment applied per laneduring the load test of Structure B isshown in Fig. 15.

The data presented in Fig. 15 represent the measured single-beam response to the lane bending moment applied during the load test of Structure B.The single-beam response reflects thecondition where there is no distribution of the lane load to adjacent beams.Under this condition, the average measured bottom web strain is equal to251 microstrain.

As shown in Fig. 14, the maximumcombined strain response due to theloading of both lanes of the north spanof Structure B (Load Stages 1 plus 3)was 74 microstrain. Therefore, the combined strain response measured in BeamM of the north span during Load Stages1 and 3 was equal to approximately

30 percent of the response measured inthe prototype double-tee beam.

Based on this result, it is apparentthat the longitudinal stiffness of thecompleted bridge structure is considerably greater than the sum of the stiffness contribution from the four beamsin each span. The overall effectivenessof the structural system used in Structure B has resulted in live load distribution capabilities that are consistentwith the distribution factors derivedfrom the provisions of the AASHTOStandard and LRFD Specifications.

CONCLUSIONSBased on the results from the load test

of Structure B, it is concluded that:1. The applied loads per lane were

effectively distributed to all four beamsof each bridge span.

2. The three spans of Structure B exhibit similar load distribution behavior.

3. The actual load distribution behavior is consistent with the distributionfactors derived from the provisions ofthe AASHTO Specifications.

4. Based on the measured data fromthe truck load test of Structure B, it isconcluded that the provisions of the

AASHTO Standard or LRFD Specifications can be used to predict the loaddistribution behavior of bridge superstructure configurations similar to thatof Structure B.

ACKNOWLEDGMENTSThe success of this project is due to

the energy and talent of many people,each of whom played a significant role.These include various researchers, designers, manufacturers, suppliers, andbuilders. The project benefited fromthe congressional support of MichiganRepresentatives Joseph Knollenbergand Sander Levin. The site construction was funded in the 1998 fiscal yearthrough the Federal Highway Administration (FHWA) as one of the TEA-2 1High Priority Projects. Further fundingfor instrumentation and monitoring wasprovided under the Innovative BridgeResearch and Construction Program ofTEA-21.

The Bridge Street Industrial ParkSubdivision property owners approvedthe formation of a Special AssessmentDistrict, created by the City of South-field, which contributed to the fundingof the project. In addition, the project

North Span Middle Span South Span

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86 PCI JOURNAL

Fig. 14. Load distribution based on combined percentage of strain, north span.

Measured concrete strain, ue

. MidspanLocation . Measured deflection, mm

East Middle West AveDT testbeam Topping -139 -223 -211 -191

Flange -131 -128 -140 -133

C.G. of tendons 115 113 114 12.49

Bottom of web 258 243 251

Fig. 15. Measured double-tee test beam response at 90 percent of design lane moment (LL+ I).

Load Stage 3

North Span Middle Span South Span

Load Stage I >.-

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Load Stage DT beam strain distribution,_percent

J K L M Total

1 34.1 25.8 22.7 17.4 100

3 12.2 17.9 28.5 41.5 100

Sum 46.3 43.7 51.2 58.9

Note: 1 in. = 25.4mm

__ __

Strain gage (typ.)

Top surface of concrete topping

compression ( - )

DT Test Beamconcrete Strain Distribution

Tension(+)

Bottom surface of beam web

-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300

Average Measured Concrete Strain, microstrainConcrete Strain gage locations at midspan

March-April 2005 87

was awarded a Michigan StrategicFund Grant from the Michigan Economic Development Corporation.

Furthermore, the National ScienceFoundation funded the original researchupon which the project design conceptwas based and the analytical analysispresented in earlier publications. Final

ly, the Mayor of the City of Southfield,the City Council, and the City Administration are commended for their vision of the future and their courage toventure into this exciting new technology in bridge construction.

REFERENCES1. ACI Committee 440, “State-of-

the-Art Report on Fiber ReinforcedPlastic Reinforcement for ConcreteStructures,” ACT 440R-96, AmericanConcrete Institute, Farmington Hills,MI, 1996, 153 pp.

2. Rizkalla, S. H., “A New Generationof Civil Engineering Structures andBridges,” Proceedings of the ThirdInternational Symposium on NonMetallic (FRPRC) Reinforcement forConcrete Structures, Sapporo, Japan,V. 1, October 1997, pp. 113-128.

3. Fam, A. Z., Rizkalla, S. H., and Tadros,G., “Behavior of CFRP Prestressing

and Shear Reinforcements for ConcreteHighway Bridges,” AC! StructuralJournal, V. 94, No. 1, January-February1997, pp. 77-86.

4. Grace, N. F., Navarre, F. C., Nacey,R. B., Bonus, W., and Collavino, L.,“Design-Construction of Bridge StreetBridge — First CFRP Bridge in the UnitedStates,” PCI JOURNAL, V. 47, No. 5,September-October 2002, pp. 20-35.

5. Grace, N. F., Abdel-Sayed, G., Sakia,S., and Wahba, J., “Finite ElementAnalysis of Bridge Street Bridge, Cityof Southfield, Michigan,” LawrenceTechnological University ResearchProject No. 36, Report Submitted toHubbell, Roth & Clark, Inc., ConsultingEngineers, 1997, Bloomfield Hills, MI.

6. Grace, N. F., and Abdel-Sayed, G.,“Behavior of Externally Draped CFRPTendons in Prestressed ConcreteBridges,” PCI JOURNAL, V. 43, No. 5,September-October 1998, pp. 88-101.

7. Grace, N. F., and Abdel-Sayed, G.,“Behavior of Carbon Fiber ReinforcedPrestressed Concrete Skew Bridge,”ACI Structural Journal, V. 97, No. 1,January-February 2000, pp. 26-34.

8. Grace, N. F, “Response of ContinuousCFRP Prestressed Concrete BridgesUnder Static and Repeated Loadings,”PCI JOURNAL, V.45, No.6, November-December 2000, pp. 84-102.

9. Grace, N. F., “Transfer Length ofCFRP/CFCC Strands for Double-TGirders,” PCI JOURNAL, V. 45, No. 5,September-October 2000, pp. 110-126.

10. Grace, N. F., Enomoto, T., and Yagi,K., “Behavior of CFCC and CFRPLeadline Prestressing Systems in BridgeConstruction,” PCI JOURNAL, V. 47,No. 3, May-June 2002, pp. 90-103.

11. AASHTO, Standard Specificationsfor Highway Bridges, SixteenthEdition, American Association of StateHighway and Transportation Officials,Washington, DC, 1996.

12. AASHTO, AASHTO LRFD BridgeDesign Specifications, First Edition,American Association of StateHighway and Transportation Officials,Washington, DC, 1994.

13. Roller, J. J., and Elremaily, A. F.,“Instrumentation and Structural Testingof Full-Scale Double-Tee Beam, BridgeStreet Bridge, City of Southfield,Michigan,” Final Report to the Cityof Southfield, Michigan, ConstructionTechnology Laboratories, Inc., April13, 2001, 46 pp.

14. Grace, N. F., Enomoto, T., AbdelSayed, G., Yagi, K., and Collavino, L.,“Experimental Study and Analysis ofa Full-Scale CFRP/CFCC Double-TeeBridge Beam,” PCI JOURNAL, V. 48,No. 4, July-August 2003, pp. 120-139.

Table Al. Evaluation of load fraction based on AASHTO Standard Specifications.11Stems FlangeParameter Sum1 2 Bottom Top

Width, b (in.) 42 42 84 84 —

Thickness, t (in.) 11.5 11.5 — 6 3 —

Jcomponents (Eq. AI.5) (in.4) 20,615 20,615 6758 739 48,727Modulus of elasticity ratio, ii 1.17 1.17 — 1.17 1.0 —

Cross-sectional area, A (sq in.) 483 483 504 252 1722nA (sq in.) 565.11 565.11 589.68 252 1971.9

Distance to centoid of cross-sectional21 21 45 49 5 —components_from extreme bottom_fiber,_y_(in.)

hA)’ (in.3) 11,867.31 11,867.31 26,535.6 12,474 62,744.22Distance to cenlioid of whole section

3182 31.82 31.82 31.82 —from extreme bottom_fiber,y_(in.)d= y —Y I (in.) 10.82 10.82 13.18 17.68 —

Ad2 (in.3) 66,158.78 66,158.78 102,434.73 78,770.77 313,523Moment of inertia of sectional component

83,071.17 83,071.17 1769 189 168.1 00.34about its own axis,_I,

I=(I,,+AcP-)— 481,623.34

Poisson’s ratio, v 0.16

K(Eq.Al.4) 3.386

C(Eq. A1.3) 1.450<5

NL 2

D (Eq. A 1.2) 5.456

S(ft) 7.0

Load fraction, S/D (Eq. All) 1.283

88 PCI JOURNAL

APPENDIX A - LOAD DISTRIBUTION FACTORSThe typical derivations of load distribution factors based

on AASHTO Standard Specifications (Section 3.23.4.3)11

and AASHTO LRFD Specifications (Section 4.6.2.2)12 arepresented below:(a) AASHTO Standard Specifications, Section 3.23.4.3

From Eq. (3-1 1):

in which

Loadfraction=-- (Al.!)D

C=K(

K=[(1 +v)+1

J=2[f(l —0.63 whereb> t (Al.5)

S = spacing between beams (ft)

NL = number of lanesW = overall width of bridgeI = moment of inertia of cross sectionJ = Saint-Venant torsion constantv = Poisson’s ratioEvaluation of the various parameters to calculate the load

fraction is presented in Table Al. It should be noted that Eq.Al.l would provide a distribution factor per wheel load, perdouble-tee beam.

ASD distribution factors: ASD distribution factors (S/D)per truck load, per double-tee beam for interior and fasciabeam can be expressed in terms of AASHTO distribution factors (per wheel load, per double-tee beam).

(i) ASD distribution factor (S/D) for interior beam

=0.5 x(S/D) (per Eq. Al.l) (A1.6)

(ii) ASD distribution factor for fascia beam (exterior beam)can be obtained from Eqs. A1.7 and Al.8, as givenbelow:

S(A1.7)

D 4+0.255

S/D for exterior beams, per truck load, per double-teebeam

where

= 0.5 x (S/D) (obtained from Eq. A 1.7) (A 1.8)

0I/ S \o,i /5\02r Kg(A1.9)Factor = 0.07 5

+ L 12 Lt]

Kg=n(I+Aeg2) (A1.10)

Kg = longitudinal stiffness parameter (in.4)n = ratio of modulus of elasticity of girder to slabtç = slab thickness (in.)S = center-to-center spacing between adjacent

beams (ft)L = span of beam (ft)Note that the term (I + Ae) is the moment of inertia of

the section about its axis passing through the centroid of thesection.

The values of the distribution factor parameters considering (1) the center-to-center spacing of the composite beam asa whole and (2) the spacing between the webs of the double-tee beam are presented in Table A2.

Table A2. Computation of load distribution factors for the double-tee (DT) beam.

where

D = (5.75 — 0.5 ‘1L) + 0.7NL (1 — 0.2C)2 (Al .2)

(Al .3) (b) AASHTO LRFD Specifications, Section 4.6.2.2.2bIt should be noted that for typical cross sections (Table

4.6.2.2.1.1), distribution factors for two or more design-load-(A 1.4) ed lanes could be determined using Eqs. Al .9 and A 1.10:

Load distribution factor based on Load distribution factor based onspacing between composite beams as a whole spacing between webs of the DT beam

Parameter Value Parameter ValueII 1.17 ii 1.17

Flange top thickness, in. 3 Web width, b, in. I 1.5

Flange bottom thickness, in. 6 Web height, Ii, in. 42

Distance to centroid of flange4 653

Web cross-sectional area.565 1 I

from extreme compression fiber, in. . ,iA, sq in.

fl!Q in.4 481,623.34 Moment of inertia of web. a!, in.4 83.071. 1

nA. sq in. 1971.9 Flange thickness, t, in. 9

e, in. 14.527 e, in. 25.347

K, in.4 (Eq. Al.I0) 897,760.8 K, in.4 446,137.6

S, ft 7 L, ft 66.93

L, ft 66.93 S, ft 4

t, in. 9 1, in. 9

LRFD distribution factor,0 627

LRFD distribution factor,0 404

per truck load, per DT beam (Eq. Al .9) per truck load, per web, Eq. Al .9LRFD distribution factor, 0 808per truck load,_per_DT_beam

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