research article live-load testing application using a wireless … · 2019. 7. 31. · interstate...

Research ArticleLive-Load Testing Application Using a Wireless SensorSystem and Finite-Element Model Analysis of an IntegralAbutment Concrete Girder Bridge

Robert W Fausett Paul J Barr and Marvin W Halling

Department of Civil and Environmental Engineering Utah State University 4110 Old Main Hill Logan UT 84322 USA

Correspondence should be addressed to Paul J Barr paulbarrusuedu

Received 3 July 2014 Revised 15 September 2014 Accepted 3 October 2014 Published 23 October 2014

Academic Editor Eugenio Martinelli

Copyright copy 2014 Robert W Fausett 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

As part of an investigation on the performance of integral abutment bridges a single-span integral abutment prestressed concretegirder bridge near Perry Utah was instrumented for live-load testingThe live-load test included driving trucks at 224ms (5mph)along predetermined load paths and measuring the corresponding strain and deflection The measured data was used to validatea finite-element model (FEM) of the bridge The model showed that the integral abutments were behaving as 94 of a fixed-fixedsupport Live-load distribution factors were obtained using this validated model and compared to those calculated in accordanceto recommended procedures provided in the AASHTO LRFD Bridge Design Specifications (2010) The results indicated that if thebridge was considered simply supported the AASHTO LRFD Specification distribution factors were conservative (in comparisonto the FEM results) These conservative distribution factors along with the initial simply supported design assumption resulted ina very conservative bridge design In addition a parametric study was conducted by modifying various bridge properties of thevalidated bridge model one at a time in order to investigate the influence that individual changes in span length deck thicknessedge distance skew and fixity had on live-load distributionThe results showed that the bridge properties with the largest influenceon bridge live-load distribution were fixity skew and changes in edge distance

1 Introduction

The concept of integral abutment bridges has been imple-mented since 1938 when the Teens Run Bridge was construct-ed near Eureka Ohio [1] Integral abutment bridges are con-structed without movable transverse deck joints at the piersor abutments and can be designed and constructed as eithersingle ormultispan bridgesThe elimination of the deck jointsis appealing to bridge owners due to their costlymaintenanceHowever this design philosophy subjects the superstructureand abutment to secondary stresses due to the continuityof the bridge from bridge settlement backfill and changesin temperature Although these stresses are not ideal themaintenance cost developed by utilizing movable deck jointsis much more significant than the design requirements andconstruction cost developed from the secondary stresses ofthe integral abutments [1] Paraschos and Made [2] provide

the results of a survey of the status problems and cost thatstates have experienced using integral abutment bridges Asa result of these benefits more and more Departments ofTransportation (DOTs) are constructing bridges using inte-gral abutment design principles However due to the uncer-tainty of the degree-of-fixity of the integral abutment engi-neers typically conservatively design for bending accordingto simply supported assumptions

Finite-element analysis has been a practical tool utilizedin many studies of integral abutment bridges The developedmodel provides an accurate representation of the in situbridge which can then be evaluated in detail using differentload locations and bridge characteristics to quantify thebridge response In previous studies finite-element modelshave been created either as a replication of an actual bridge oras a representation of a general bridge type (ie integral abut-ment and box girder) In all of these studies simulated loads

Hindawi Publishing CorporationJournal of SensorsVolume 2014 Article ID 859486 11 pageshttpdxdoiorg1011552014859486

2 Journal of Sensors

were applied to the finite-element models that were similar tothe vehicle traffic on the bridge and the overall performanceof the bridge as well as the distribution factors load ratingsstress fatigue and thermal effects was quantified Examplesof these studies include Jauregui and Barr [3] Mourad andTabsh [4] Dicleli and Erhan [5] Hodson et al [6] Lahovich[7] Cai et al [8] Kalaycı et al [9] and Kim et al [10] Otherstudies involving the determination of distribution factors forother types of bridges include Ebeido and Kennedy [11] Ryanand Hindi [12] and Song et al [13]

The finite element and integral abutment bridge studieshave been conducted with and without using validatedmodels with live-load data Live-load distribution factors(LLDFs) have been calculated for integral abutment bridgesusing theoretical bridge models such as a study conductedby Dicleli and Erhan [5] which investigated the accuracy oflive-load distribution formulas for single-span prestressedconcrete and integral abutment bridge girders Mourad andTabsh [4] investigated deck slab stresses for integral abutmentbridges using two separate bridge models differing in girdercross sections slab thicknesses and pile spacings Lahovich[7] developed live-load distribution factors for an integralabutment bridge using a ldquobridge in a backpackrdquo and the fold-ed plate girder bridge in order to quantify the response ofeach of the bridges under various types of loading LLDFshave also been quantified for bridges using validated finite-element models based on measured live-load data such asthe study conducted by Hodson et al [6] The researchers forthis study investigated the live-load behavior of an integralabutment bridge The integral abutments were found to addconsiderable restraint to the structure making the AASHTOLRFD live-load distribution factors conservative Kalaycıet al [9] also utilized a validated finite-element bridge modelof a concrete deck on steel I-girders in order to determine theLLDFs of two integral abutment bridges in the State of Ver-mont While single-span integral abutment bridges are morecommonly constructed few studies have been performedusing finite-elementmodels validated from live-load test dataon a single-span prestressed integral abutment and concretegirder bridge to determine LLDFs

As part of a study to determine the overall behavior ofintegral abutment bridges researchers at Utah State Univer-sity performed live-load testing on a single-span prestressedconcrete girder and integral abutment bridge near Perry UTThe setup of this test involved attaching strain gauges anddeflectometers at various locations on the bridge The live-load test consisted of slowly driving trucks across the bridgealong predetermined load paths as well as parking trucksat different locations on the bridge The data collected fromthese tests was used to create and validate a finite-elementmodel (FEM) of the bridge The model was developed usingthe same dimensions and characteristics as the actual bridgeBoundary conditions due to the stiffness of the integral abut-ments were altered until the FEM and live-load data resultedin a strong correlation Live-load distribution factors werethen obtained using this validated model and compared tothose calculated in accordance to procedures recommendedin the AASHTO LRFD Bridge Design Specifications [14]

Figure 1 Perry Bridge (structure number 1F 205) elevation viewduring testing

The AASHTO LRFD and finite-element distribution factorswere used to obtain a load rating of the bridge

Subsequent to the live-load study a live-load distributionparametric investigation was conducted by incrementallymodifying the validated model for changes in span lengthdeck thickness edge distance skew and fixity Distributionfactors were calculated for each change in individual bridgeproperty and compared with the corresponding calculateddistribution factors obtained from the procedures in theAASHTO LRFD Specifications [14] The results showed thatthe bridge properties with the largest influence on the live-load distribution were changes in fixity skew and edge dis-tance Changes in these parameters showed that the AASH-TO LRFD Specifications were between 10 nonconservativeand 56 conservative depending on girder position loadingand fixity The parameter with the least amount of influenceon live-load distribution was the deck thickness providinga range between 4 and 19 nonconservative Dependingon which bridge property was modified both increases anddecreases in conservatism were exhibited

2 Bridge Description

The Perry Bridge (structure number 1F 205) as shown inFigure 1 was constructed in 1976 The superstructure wasdesigned as a single-span prestressed concrete bridge Thebridge is located 805 km (50 miles) north of Salt Lake CityUT It carries two lanes of northbound traffic as part ofInterstate 1584 traveling over Cannery Road in the town ofPerry UTThe bridge has a clear span length of 244m (80 ft)and an overall length of 251m (825 ft) The bridge clearanceis 468m (153 ft) The bridge incurs an average daily traffic(ADT) of approximately 22000 vehicles 29 percent of whichare trucks The bridge was designed with no skew but has asuperelevation of 2

The deck has a width of 134m (444 ft) measured fromoutside to outside of the barriers The roadway width is123m (405 ft) wide measured from the inside of the barrierswith a shoulder width of 160m (525 ft) and 343m (113 ft)on the western and eastern sides respectively The twotraffic lanes are 366m (12 ft) wide These dimensions areshown in Figure 2 The deck is comprised of concrete that is

Journal of Sensors 3

S1 S2 S3 S4 S5

S6 S7 S8 S9 S10

053m 366m

132m

160m

269m

343m

269m269m269m 132m134m

134m123m

366m 053m

ShoulderLeft laneRight lane

Figure 2 Bridge cross-sectional view at Section AA with dimensions and strain gauge placements

203mm (8 in) thick with an additional 152 to 203mm (6 to8 in) asphalt overlayThedeck concrete had a specified comp-ressive strength of 241MPa (3500 psi) and was reinforcedwith number 16 (number 5) bars of Grade 420 (Grade 60)billet-steel The top reinforcing mat was constructed with508mm (2 in) of cover The concrete barriers were 085m(28 ft) tall and were cast with a cold joint along both sides ofthe bridgeThe barriers are reinforced with number 13 (num-ber 4) bars of Grade 420 (Grade 60) steel with a specifiedcover of at least 381mm (15 in)

The five precast girders supporting the deck are AASHTOType IV bridge girders that are 251m (825 ft) long and 137m(45 ft) tall The girders have a center-to-center spacing of269m (88 ft) The 56-day specified compressive strength ofthe girder concrete was 345MPa (5000 psi) The girder wasprestressed with sixteen-127 cm (05 in) diameter and seven-wired strand that had an ultimate stress of 1860MPa (270 ksi)The jacking stress was 1400MPa (2025 ksi) The shear rein-forcement was provided with number 16 (number 5) barsof Grade 420 (Grade 60) steel The girders were prestressedusing a harped strand profile Both harping points are located975m (32 ft) from the girder ends and the centroid of thestrands at the harping point is 103mm (406 in) from thebottom of the girder At the girder ends the centroid of theprestressing strands is located at 340mm (134 in) from thebottom of the girder The final prestressing force for eachgirder after losses was calculated to be 3370 kN (757 kips)

The supports of the Perry Bridge superstructure weredesigned as integral abutments and are 076m (25 ft) thickand 320m (105 ft) tall The integral abutments traverse theentire width of the bridge At each abutment the girder issupported on a 127mm (05 in) elastomeric bearing padThese pads transfer the vertical load from the girders to fiveconcrete drilled piles which each have a maximum allowabledesign load of 356 kN (80 kips)Wingwalls were cast adjacentto both abutment ends and have a total length of 472m(155 ft) a width of 030m (1 ft) and varied height between061m (2 ft) near the abutment and 290m (95 ft) towards thecenter of the bridge

At the time of testing the bridge superstructure was infairly good condition The girders did not show any signs ofcracking The wing walls on the east side of the bridge had

a vertical crack at the connection of the approach slab andend of the bridge

3 Live-Load Test

The live-load test was conducted by driving a truck or acombination of trucks along predetermined load paths andmeasuring the corresponding strain displacement and tem-perature using a wireless sensor system that was attached tothe bridge superstructure The sensors were attached at twocross-sectional locations along the bridge These sensorsinclude ten wireless surface mounted strain sensors and fivevertical displacement sensors

A wireless data acquisition system from Bridge Diagnos-tic Inc was used to record changes in strains during thelive-load test The system utilized four-channel nodes towirelessly transmit gauge readings along the length of thebridge to a central station by way of a broadband systemThestrain gauges were connected utilizing intelliducer sensorsthat automatically identified the gauge number All sensorreadings were monitored simultaneously during the test at arate of 40Hz The wireless strain sensors (sensors S1 throughS10) were attached at the top of the girder web and on thebottom flange of each girder at 131m (43 ft) as measuredfrom the south end of the bridge as shown as Cross SectionAA in Figure 2 The cross section location for the straininstrumentation was selected at 091m (3 ft) from midspandue to the possible influence of the intermediate diaphragmat the midspan

Displacement transducers were used to measure changesin deflection during testing The displacement transducersconsisted of a base plate that was fixed to the bridge with anattached cantilevered plate The cantilevered plate had fourstrain gauges wired in a full-bridge configuration attachednear the base of the cantilever plate and a wire attached atthe tip The wire extended from the tip of the cantileverplate to a fixed location below the bridge The wire was thentensioned so that the tip of the cantilevered plate deflected38mm (15 in) downward The change in strain from thefour gauges was used to determine the changes in verticaldeflection of the transducer to within 0025mm (0001 in)Because the diaphragm would theoretically have no effect


106m

D3


LP3 658mLP2

627m607mLP5 333m

D5D1

LP1

D2 D4

LP4

Figure 3 Bridge cross-sectional view at Section BB with deflectometer placements and load paths

0254m

185m

137m

0254m

546m409m

203m

WA =WB = 765kN

734kNWA =WB = 765kN

734kNWA =WB = 760kN

761kN

0584m

Figure 4 Truck A and B weights and dimensions

on the displacement the deflection equipment (sensors D1through D5) was attached on the bottom flange of eachof the girders at midspan The displacement sensors werealso monitored wirelessly using the four-channel nodes andthe intelliducer The location of the displacement sensors isprovided as Cross Section BB of Figure 3

Multiple live-load tests were performedusing a controlledlane closure by means of a slowdown that provided traffic-free periods on the bridge This was accomplished by havinga highway patrol car slowly drive down the middle of bothlanes of the highway beginning 366 km (228 miles) fromthe bridge This slowdown allowed for windows of time offour to fiveminutes of uninterrupted testingDuring this timeperiod the trucks were positioned and the live-load tests onone load path were completed

Two similar heavily loaded tandem rear axle dump truckswere used to apply the live-load Truck A had a gross vehicleweight (GVW) of 223 kN (501 kips) while Truck B had aGVW of 229 kN (515 kips) The distance between the frontaxle and middle axle was 409m (134 ft) while the distancebetween the middle axle and back axle was 137m (449 ft)Both trucks had front axle tire spacings of 203m (666 ft)andmiddle and back axle spacings of 185m (607 ft) Truck Aand Truck B had front axle weights of 761 kN (171 kips) and760 kN (171 kips) respectively Their middle and back axleshad weights of 734 kN (165 kips) and 765 kN (172 kips)respectively The researchers had planned on two different

trucks but these were the only ones available at the time oftesting A footprint of Trucks A and B is shown in Figure 4

Five static or pseudostatic (truck driving at 224ms(5mph)) load cases using different load pathswere conductedin all The drivers tried to maintain the constant velocitythroughout the test Slight variations occurred but nothingthat induced dynamic strains Because different trucks werenot available at the time of testing dynamic testing at higherspeeds was not performed The strains displacements andcorresponding truck positions were recorded at a frequencyof 50Hz The lateral truck position of each load path wasmarked along the entire longitudinal length of the bridgeThelateral position of each load path is provided in Figure 3mea-suring from the east side of the bridge to the driverrsquos side fronttire Load Case 1 featured both Trucks A and B statically posi-tioned back-to-back at the midspan of Load Path 1 This loadcase was intended to maximize the exterior girder responseLoad Case 1 was replicated three times Load Case 2 hadtwo trucks positioned side-by-side This configuration wasintended to maximize the loading on the first interior girderFor this case Truck A followed Load Path 1 while Truck Bfollowed Load Path 2 Both trucks were driven along theirrespective load paths at approximately 224ms (5mph)Thistest was replicated twice Load Case 3 featured both trucksslowly driving along the center of the highway traffic lanes(left and right lanes of Figure 3) Truck A followed Load Path3while TruckB followedLoadPath 4This testwas performed


three times Load Case 4 had Truck B following Truck A inseries psuedostatically along Load Path 1This was performedin order to maximize the load on the exterior girderThis testwas replicated twice Load Case 5 was performed twice andfeatured Truck A psuedostatically driving along Load Path 5

The longitudinal truck position was monitored duringthe pseudostatic load cases using an autoclicker which wasmounted on the driver side tire of Truck A The autoclickerwhich was also monitored placed an electronic marker in thedata file at each wheel revolution Using the data markers andthe known circumference of the tire the exact location of thetruck was determined as it traversed the length of the bridge

Before using the data collected from the live-load testan analysis was required to determine whether or not thedata was acceptable for use Two analyses were conducted toensure accurate data First multiple tests were performed foreach load casewhich allowed for a direct comparison betweentwo sets of what should be identical data In all cases themeasured data between the multiple runs for each load casewas within 1The second analysis that was conducted on thelive-load data was a strain versus deflection analysis for eachgauge in order tomake sure all of the gaugeswere reading cor-rectlyThis analysiswas effective because strain anddeflectionare proportional In order tomake this comparison the strainand the deflection were plotted for all five girders for multiplepositionsThis analysis was completed for multiple load casesand compared to hand calculations when two gauges weredissimilar to identify discrepancies

Figure 5 shows an influence line for the bottom strain ofGirder 2 as the truck was driven along Load Case 5 Whenthe truck was at either end of the bridge the bottom strainat Section AA for Girder 2 was very small As the truck waspositioned closer to themidspan the bottom strain increasedAmaximum recorded strain for this girder and load case wasnearly 11microstrains Although themagnitudes varied thesetrends were typical for other girders and load cases Figure 6shows the deflection measurements for all five girders forLoad Case 2 For this particular figure the data is when thetruck was at the midspan of the bridge Figure 6 shows thatGirder 3 experienced the largest deflection This is due to thelateral position of the truck The adjacent girders (Girders 2and 4) experienced a smaller deflection Girder 5 which wasthe furthest from the load experienced the least deflectionThese trends were also similar for other load cases

4 Finite-Element Analysis

A finite-element model of the Perry Bridge was createdusing SAP2000 v1500 [15] All structural elements of thebridge model were created using eight-node solid elementsThese elements have three transitional degrees-of-freedomat each node Various cross-sectional dimensions were useddepending on the structural member

The majority of the deck solids elements were 203mm times203mm times 305mm (810158401015840 times 810158401015840 times 1210158401015840) rectangles The dimen-sions of the solid elements for the girder varied due to thegirder shape but in all instances the aspect ratios were keptbetween 15 and 3The jersey barrier element dimensions also

0 20 40 60 80 100

02468

101214

0 5 10 15 20 25 30

Position (ft)

Mic

rostr

ain

Position (m)

LL dataModel data

Figure 5 Microstrain comparison at midspan between live-loadand FEM data for Load Case 5 Girder 2

1 2 3 4 5Girder number

ModelLL data

minus00195minus00175minus00155minus00135minus00115minus00095minus00075minus00055minus00035minus00015

minus05minus045minus04

minus035minus03minus025minus02minus015minus01minus005

0

Defl

ectio

n (m

m)

Defl

ectio

n (in

)

Figure 6 Deflection comparison near midspan between live-loadand FEM data for Load Case 2 all girders

Figure 7 3D FEM view of the Perry Bridge using solid elements

varied due to its shape but had aspect ratios between 15 and2 In all 19316 joints and 10752 solids were utilized to developthe FEM Figure 7 shows a 3D view of the barrier deck andgirder elements for the Perry Bridge FEM

In order to validate the accuracy of the finite-elementmodel the measured strains and deflections from the live-load test were compared to the corresponding calculatedstrains and deflections of the model Nodes were created forthe FEM in the same respective locations as the strain gaugesand deflectometers on the actual bridge This allowed fora direct comparison with the measured results The mate-rial properties including the specified concrete compressive


strength and therefore the modulus of elasticity for the deckgirder and barrier elements were initially assigned to thematerial properties in the FEM based on the specified bridgeplans These properties were increased by approximately 10during the validation process to allow for higher in situ valuesthan the specified ones The properties were kept constantthroughout the validation process Transitional springs wereapplied at the girder ends of the bridge The springs wereplaced at the bottom along the height of the girder end and atdeck nodes The magnitude of the springs was systematicallyincreased during the validation process to represent the fixityof the integral abutment of the actual bridge The final springstiffness was determined when a trend line with an overallslope as close to 10 as possible between the bridgemodel dataand the bridge live-load data was achieved The final bound-ary conditions for the bridge were nearly fixed-fixed withtransitional springs restraining movement on all but the top80 of the middle girder as well as no transitional restraintson the middle of the deck This variation in transverse fixityis believed to have been caused by the additional stiffnesscreated by the wing walls on the edge beams The overallrotational restraint is attributed to the stiffness of the integralabutments

Figure 5 provides an influence line comparison betweenthe measured live-load and the calculated FEM data ofGirder 2 for Load Case 5 The live-load data was monitoredcontinuously while the truck was driven along the bridgeThe FEM data was determined discretely with the truckpositioned every five feet As shown a strong correlationbetween the bridge model and live-load data was achievedboth in terms of magnitude as well as trend Figure 6 alsoprovides a comparison between the live-load and FEM datashowing the lateral deflection distribution of the bridge forall five girders for the truck at the midspan of Load Case 2For this figure the live-load deflection data for Girder 3 wasneglected due to a faulty deflectometer Based on the resultsa strong correlation between the two sets of data was alsoachieved for the deflection data

A comparison between the live-load data and FEMmicrostrains was also performed for other truck positionsand load cases For this comparison a trend line wascalculated and found to have a slope of 112 with a coefficientof correlation determined to be over 095 suggesting a strongcorrelation between the two sets of data Deflection com-parisons showed an even stronger correlation with a trendline slope calculated to be 106 and a correlation coefficientof 099 These correlations are provided in Figures 8 and 9respectively

In order to determine the degree-of-fixity of the PerryBridge the sum of all of the girder midspan moments wasobtained from the validated FEM and subsequently com-pared to themidspan girder moments of two single girders ofthe same bridge length but one with simply supported endsand the other with fixed-fixed supports For this analysis theAASHTO HS-20 truck was applied at various longitudinaland transverse positions on themodel and the correspondinglongitudinal position on the single girders Based on thecomparisons of the results the approximate percent fixity ofthe Perry Bridge was determined to be 94 based on a linear

0

5

10

15

20

25

0 5 10 15 20 25

Live

-load

mic

rostr

ains

FEM mictrostrains

minus5minus5

y = 11217x + 04541

R2 = 09519

Figure 8 Live-load microstrain versus model microstrain nearmidspan for all girders

000

001

0 001

Live

-load

dat

a defl

ectio

n (in

)y = 10591x minus 8E minus 05

R2 = 099

minus005

minus004

minus003

minus002

minus001

minus005 minus004 minus003 minus002 minus001

Model deflection (in)

Figure 9 Live-load deflection versus model deflection at midspanfor all girders

interpolation Because of the uncertainty in fixity during theinitial design phase the Perry Bridge was originally designedassuming simply supported end conditions The actual fixityresults in a very conservative midspan moment design andcan provide cost savings if taken into account

5 Live-Load Distribution Factors

After the FEM was validated with the live-load data it wasthen used to determine live-load distribution factors forthe Perry Bridge The FEM distribution factors were thencompared to those calculated using recommended proce-dures in the AASHTO LRFD Bridge Design Specifications[14] Distribution factors are used to simplify the designprocess The maximum moment caused by a truck (or laneof traffic) is first estimated by treating the bridge as a beamA designer then obtains the design moments for each girderby multiplying the maximum moment by a factor which isusually referred to as the live-load distribution factor Theequations provided in theAASHTOSpecifications are depen-dent on the girder location (interior or exterior) skew anglespan length deck thickness overhang length girder spacingand girder stiffness However distribution factors calculatedin accordance to the AASHTO Specifications do not takeinto account possible continuity due to the different types


Table 1 Comparison of distribution factors for single and two loaded lanes cases

Number of lanes loaded Girder case AASHTO LRFD (1) SS FEM (2) difference= (1 minus 2)(1)

Fixed FEM(3)

difference= (1 minus 3)(1)

Continuity= (3 minus 2)(3)

Single lane Interior 054 012 78 028 47 58Exterior 087 031 64 074 15 58

Two lanes Interior 076 019 75 046 39 58Exterior 080 036 55 086 minus8 58

of abutments available for bridge construction The currentdistribution factor equations were developed assuming thatthe bridge was simply supported

To obtain more accurate distribution factors using thevalidated FEM AASHTO HS20-44 truck loads were appliedto the model This truck has a loading of 356 kN (8 kips)on the front axle and 142 kN (32 kips) on the middle andback axles For calculation of the distribution factors all axlesare separated by a longitudinal distance of 427m (14 ft) Thetransverse distance between the wheel spacing for all axles is183m (6 ft)

In order to maximize the moment based on the positionof the truck on the bridge in the longitudinal direction aresultant force analysis was conducted and the location ofthe middle axle of the truck was determined to be at 071m(233 ft) off the center of the bridge In order to maximizethe interior and exterior girder moments for both single andmultiple lane loadings in the transverse direction all possi-ble lateral truck positions were evaluated by incrementallymoving the truck (or trucks for the multiple lane cases)laterally across the width of the bridge For each lateral loadcase all five girder moments were obtained The maximumFEM single and multiple lane moments were calculated forboth the interior and exterior girders The distribution factorwas then obtained by placing a single HS-20 truck on anindividual girder at the same longitudinal location as theFEMThis girder was evaluated as both simply supported andfixed The distribution factors for the bridge could then becalculated for single lane or two lanes loadings dependingon which multipresence factor was applied The distributionfactor could then be determined using

DF = 119872FEM119872SSFFtimesMPF (1)

whereDF=distribution factor119872FEM =maximumFEMgird-er moment119872SSFF = maximum girder moment of a simplysupported or fixed-fixed girder and MPF = multipresencefactor (one lane = 12 two lanes = 10)

The AASHTO LRFD Specifications [14] provide equa-tions to calculate the distribution factors for an interior girderwith one lane and multiple loaded lanes In addition anequation is provided to obtain the exterior girder distributionfactor with two or more design lanes loaded For the exteriorgirder case with one design lane loaded the code specifiesthat the lever rule be used to determine the distribution fac-tor

Once all of the distribution factors had been calculatedin accordance to the AASHTO LRFD Specifications [14] and

the FEM the percent difference was obtained in order toquantify the accuracy of the current code procedures inpredicting the load distribution of a concrete girder bridgewith integral abutments In all cases when the simply sup-ported single girder (119872SS) was used the AASHTO LRFDSpecification distribution factors were overly conservativeThis is primarily due to the fixity of the actual bridge Themaximum percent difference was 78 conservative for thesingle loaded lane case for an interior girder However thegoverning design case was the exterior girder with two loadedlanes which was 55 conservative All girder cases are givenin Table 1

The distribution factor was also calculated based on thefixed boundary condition (119872FF) of the single girder resultingin a more realistic end condition and allowing for a moredirect comparison of the accuracy of the code distributionfactorsThe results in Table 1 show that themaximumpercentdifference between the FEM and fixed-fixed distributionfactors was 47 conservative However for the single lanecase the exterior girder controlled the designwith the highestdistribution factor that was only 15 conservative Aftercomparing all the single and multiple loaded lane cases itwas determined that the critical loading condition was forthe exterior girder when trucks were applied in two lanesIn this case the AASHTO LRFD Distribution factor was 8unconservative in comparison to the FEMdistribution factor

By comparing the distribution factors for the Perry Bridgewith simply supported and fixed-fixed end conditions theeffect of continuity can also be determined The distributionfactor obtained using the simply supportedmoment containserrors from both the distribution factor calculation andthe effect of fixity Because the Perry Bridge was found tobe 94 fixed most of the error due to fixity is removedthrough calculating the distribution factor using fixed-fixedboundary conditions Therefore the difference between thetwo distribution factors would leave the effect of continuityThe results in Table 1 show that the effect of continuity is 58

6 Parametric Study

In order to quantify the effect that different bridge propertieshave on the magnitude of the live-load distribution factor aparametric study was conducted Bridge properties that arecurrently influenced in the calculation of the distributionfactors in the AASHTO LRFD Bridge Design Specifications[14] are span length deck thickness edge distance and skewEach bridge property was investigated for this study In orderto evaluate the influence of an individual bridge property


various FEMs were created and loaded with the AASHTOHS20-44 truck at the longitudinal position for maximummoment All possible lateral positionswere evaluated in orderto maximize the moments in each girder Except for theparametric study dealing with the effect of fixity each of theFEMs was simply supported

For each of the parametric FEMs the bridge was devel-oped using the same properties as the original Perry BridgeFEMThe bridge property being investigated was then incre-mentally modified and all other properties were kept con-stant Distribution factors were calculated for all girders foreach incremental change and then compared to the calculateddistribution factors in accordance to the AASHTO LRFDSpecifications By evaluating differences in the magnitude ofthe distribution factors from the baseline bridge the generaltrends were able to provide insight into how changes tothe individual bridge properties affected the live-load dis-tribution For each bridge property parametric study exceptfor fixity a distribution factor ratio (FEMAASHTO distri-bution factor) was provided and plotted as a function ofthe corresponding change in the individual bridge propertyThe ratio of the FEM distribution factor to the AASHTOLRFD distribution factor shows the range in conservatismor unconservatism of the AASHTO empirical relationshipsRatios below one indicate that for that particular bridgeproperty the distribution factor calculated according to theAASHTO LRFD Specification is conservative Converselyratios above one show that the distribution factor is non-conservative as compared to the FEM For all parametricstudies the two lanes loaded exterior girder had the largestdistribution factor and therefore governed the design

7 Effects of Span Length

As the span length increases longitudinally the bridgebecomesmore flexibleThis reduction in stiffness reduces theload distribution of the cross section The effect of changesin span length was evaluated at intervals of 91m (30 ft)beginning at 152m (50 ft) and ending at 610m (200 ft)Theselengthswere chosen to encompass span lengths of typical pre-cast girder bridge lengths allowed by the distribution factorequations in the AASHTO LRFD Specifications [14] Afterobtaining the controlling distribution factors the percentdifferences between the FEM and AASHTO LRFD Spec-ifications were found to be between 25 nonconservativeand 8 conservative depending on the span length At aspan length of 152m (50 ft) the FEM distribution factorwas 8 conservative but as the span length is increased theAASHTO LRFD Specifications became nonconservative andthe nonconservatism increased with increasing span lengthFigure 10 provides the distribution factor ratio for variousspan lengths for the exterior girder with two lanes loadedThis region of nonconservatism has been observed by otherresearchers that is [5 6]

The solitary casewherewith an increase in span length theAASHTO LRFD Specifications become more conservative isfor the single lane loaded exterior girder This is primarilydue to this case being calculated using the lever rule which is

50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)

Figure 10 FEM distribution factorAASHTO Distribution Factorversus length of span for the case with exterior girder two lanesloaded

6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)

Figure 11 FEM distribution factorAASHTO Distribution Factorversus deck thickness for the case with exterior girder two lanesloaded

not a function of span length but only of edge distance skewand spacing

8 Effects of Deck Thickness

The effect of deck thickness was evaluated by calculatingthe distribution factors for deck thicknesses of 015m (6 in)020m (8 in) 025m (10 in) and 030m (12 in) Increasingthe deck thickness increases the transverse bending stiffnessThis leads to an increase in the ratio of transverse-to-lon-gitudinal stiffness which in turn implies a more uniformdistribution of girder moments and a lower live-load dis-tribution factor After obtaining the distribution factors forthe various load cases the controlling distribution factor wasobtained from the exterior two lanes loaded case Basedon these results the AASHTO LRFD Specifications weredetermined to be between 4 and 19 nonconservative Asthe deck thickness increases the AASHTO LRFD Specifica-tions become more and more nonconservative as shown inFigure 11 This implies that the relationships in the AASHTOLRFD Specification overpredict the influence that increasesin slab thickness has on the live-load distribution Similarto the study for increases in span length all cases becomemore nonconservative except for the exterior girder singlelane loaded caseThis is due to the lack of the lever rule takinginto account the deck thickness


9 Effects of Skew

Changes in skew were evaluated every 15 degrees from 0 to60 degrees After obtaining the distribution factors for allgirders for a particular skew angle the controlling girder wasdetermined The AASHTO LRFD Specifications were foundto be between 10 nonconservative and 56 conservativefor the two lanes loaded exterior girder As the skew angleincreases the AASHTO LRFD Specifications become moreconservative This trend occurs for all load cases becauseskew affects the lever rule the AASHTO LRFD Specificationequations and the FEM

10 Effects of Edge Distance

The effect of edge distance was evaluated for distances of046m (15 ft) 076m (25 ft) 11m (35 ft) 14m (45 ft) and17m (55 ft)This rangewas chosen to includemost of the val-ues allowed in the AASHTO LRFD Specifications After eval-uating all of the load cases the AASHTO distribution factorfor the exterior girder two lanes loaded case was determinedto be between 24 nonconservative and 17 conservativeFor the initial condition of 046m (15 ft) theAASHTOLRFDSpecifications are nonconservative but as the edge distanceincreases the AASHTO LRFD Specifications became con-servative at an edge distance of 107m (35 ft) as shown inFigure 12 This is also the case for the single loaded exteriorgirder The single and multiple loaded interior girder casesare approximately constant for any change in edge distance

11 Load Rating

Two separate types of load ratings are determined in order todefine the load capacity of a bridge the inventory rating andthe operating rating The inventory rating when multipliedby the controlling bending moment caused by a HS20-44truck specifies the maximum live-load that the bridge cansafely sustain for an undetermined length of time The oper-ating rating when multiplied by the same moment specifiesthe largest live-load that the bridge is allowed to sustain underthe AASHTO LRFD Specification [14] The load ratings aredetermined by

RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)

RF = bridge load rating (operating or inventory) 119877119899=

nominal flexure capacity 120574119863=dead load factor (13) 120574

119871= live-

load factor (13 for operating 217 for inventory)119863=nominaldead load effect (composite and non-composite dead load)119871 = nominal live-load effect (caused by HS20-44 truck) and119868 = live-load impact factor (1524(119871 + 38))

The operating and inventory load ratings were calculatedfor the Perry Bridge based on the controlling distributionfactors from the AASHTO LRFD Specifications the simplysupported FEM and the fixed-fixed FEM These ratingsare provided in Table 2 The AASHTO LRFD Specificationcontrolling distribution factor was 087 based on the singlelane loaded exterior girder caseThe controlling distribution

15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)

Figure 12 FEM distribution factorAASHTO Distribution Factorversus edge distance for the case with exterior girder two lanesloaded

Table 2 Load ratings using the AASHTO and FEM results

Fixity Distribution factor Load ratingsInventory Operating

AASHTO SS 087 047 078AASHTO FF 087 219 365FEM FF 074 257 429

factor for the simply supported FEM and fixed-fixed FEMwere 036 and 086 respectively Both the controlling dis-tribution factors for the FEMs were the two lanes loadedexterior girder case As shown according to the AASHTOLRFD Specifications and simply supported FEM this bridgeshould not be capable of bearing the load of the HS20-44because their load ratings fall below one The load ratingsprovided by the fixed-fixed FEM however would allow thistype of loading which shows that fixity needs to be taken intoaccount In addition the analysis shows that the AASHTOLRFD Specifications ratings are more than twice as conserv-ative as the simply supported FEM ratings Hodson et al[6] also found that the AASHTO LRFD Specifications wereoverly conservative in determining load ratings of bridges

12 Summary and Conclusions

As part of an investigation into the behavior of integralabutment bridges a live-load test was conducted on a bridgein Perry UT A finite-element model (FEM) was created withthe same bridge parameters and validated with the live-loadtest data The bridge distribution factors determined fromvalidated FEMwere then compared to calculated distributionfactors using equations recommended in theAASHTOLRFDBridgeDesign Specifications Parametric studies on the influ-ence of changes in span length deck thickness edge distanceskew and fixity on live-load distributionwere also conductedThe results of the research lead to the following conclusions

(i) Due to the integral abutment support system thePerry Bridge does not act as a simply supported bridgebut instead was determined to be 94 fixed In orderto provide more adequately sized and economicalbridges the AASHTO LRFD Specification equationsneed to be adjusted to take into account the fixity of abridge


(ii) The live-load test data led to a subsequent finite-element model derived of solid elements with aspectratios no greater than 3 A trend line and correlationcoefficient were used to determine the extent to whichthe two sets of data were correlated The trend linefor the strain comparison had a slope of 112 witha coefficient of correlation determined to be over095The deflection comparison had an even strongercorrelation with a trend line slope of 106 and acorrelation coefficient of 099

(iii) The comparison between the FEM distribution factorfrom the live-load test and the AASHTO LRFD Spec-ifications distribution factor was taken for both asimply supported FEM and a fixed-fixed FEM Foreach the controlling case was the two lanes loadedexterior girder The simply supported FEM as com-pared to the AASHTO LRFD Specification had a per-cent difference of 55 on the conservative side Thefixed-fixed FEM as compared to the AASHTO LRFDSpecification had a percent difference of 8 on thenonconservative side This indicates that the bridgefalls somewhere in between the simply supported andfixed-fixed cases

(iv) The effect of continuity of the bridge was determinedto be 58 through determining the percent differ-ence for the distribution factors obtained with sim-ply supported boundary conditions and fixed-fixedboundary conditions Because the Perry Bridge isnearly fixed-fixed and both distribution factors showthe error in the distribution factor calculation thedifference between the two distribution factors showsthe effect of continuity

(v) The results of the parametric study indicated that thebridge properties with the largest influence on bridgelive-load distributionwere fixity skew and changes inedge distance The change in fixity caused the LLDFsto vary from 088 for a simply supported bridge to035 for a fixed-fixed bridge The skew and changesin edge distance showed the AASHTO LRFD Specifi-cations to be between 10 nonconservative and 56conservative and between 24 nonconservative and17 conservative respectively

(vi) The results of the parametric study also indicated thatthe bridge properties with the smallest influence weredeck thickness and span length The AASHTO LRFDSpecifications were determined to be between 4 and19 conservative for the deck thickness and between25 nonconservative and 8 conservative for thespan length

(vii) Load ratings were determined for the fixed-fixedFEM and the AASHTO LRFD Specifications basedupon using both simply supported and fixed-fixedmoments For the AASHTO LRFD Specificationsusing simply supported moments as in regular designstandards the inventory and operating load rat-ings were determined to be 047 and 078 respec-tively When using the fixed-fixed moments for

the AASHTO LRFD Specifications the inventoryand operating load ratings increased to 219 and 365respectively For the fixed-fixed FEM the inventoryand operating load ratings were determined to be 257and 429 respectivelyThis shows that if a bridge lacksa sufficient load rating determining the fixity of thebridge has a large effect in increasing the load ratingIn addition a model study provides an even moreaccurate and larger load rating that would prevent abridge from being labeled as structurally deficient

Conflict of Interests

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

Acknowledgments

This publication was supported by a subcontract from Rut-gers University Center for Advanced Infrastructure andTransportation (CAIT) under DTFH61-08-C-00005 fromthe US Department of Transportation Federal HighwayAdministration (USDOT-FHWA) Any opinions findingsand conclusions or recommendations expressed in this pub-lication are those of the authors and do not necessarily reflectthe views of Rutgers University or those of the US Depart-ment of Transportation Federal Highway Administration

References

[1] M Burke ldquoIntegral bridgesrdquo in Integral and Semi-IntegralBridges pp 1ndash19 Wiley-Blackwell Chichester UK 2009

[2] A Paraschos and A M Made ldquoIntegral Abutment Bridgesmdashasurvey on the status of use problems and costs associated withintegral abutment bridgesrdquo Better Roads pp 1ndash9 February 2011

[3] D V Jauregui and P J Barr ldquoNondestructive evaluation of theI-40 bridge over the Rio Grande Riverrdquo Journal of Performanceof Constructed Facilities vol 18 no 4 pp 195ndash204 2004

[4] S Mourad and S W Tabsh ldquoDeck slab stresses in integral abut-ment bridgesrdquo Journal of Bridge Engineering vol 4 no 2 pp125ndash130 1999

[5] M Dicleli and S Erhan ldquoLive load distribution formulas forsingle-span prestressed concrete integral abutment bridge gird-ersrdquo Journal of Bridge Engineering vol 14 no 6 pp 472ndash4862009

[6] D J Hodson P J Barr andMWHalling ldquoLive-load analysis ofposttensioned box-girder bridgesrdquo Journal of Bridge Engineer-ing vol 17 no 4 pp 644ndash651 2012

[7] A Lahovich New technologies in short span bridges a studyof three innovative systems [MS thesis] University of Mas-sachusetts Amherst Amherst Mass USA 2012

[8] H Cai O Abudayyeh I Abdel-Qader U Attanayake JBarbera and E Almaita ldquoBridge deck load testing using sensorsand optical survey equipmentrdquo Advances in Civil Engineeringvol 2012 Article ID 493983 11 pages 2012

[9] E Kalaycı S A Civjan S F Brena and C A Allen ldquoLoad test-ing andmodeling of two integral abutment bridges in VermontUSrdquo Structural Engineering International vol 21 no 2 pp 181ndash188 2011


[10] E-K Kim H Oh and J Sim ldquoSemiempirical methodology forestimating the service life of concrete deck panels strengthenedwith fiber-reinforced polymerrdquoMathematical Problems in Engi-neering vol 2014 Article ID 273693 13 pages 2014

[11] T Ebeido and J B Kennedy ldquoShear distribution in simply sup-ported skew composite bridgesrdquo Canadian journal of civil engi-neering vol 22 no 6 pp 1143ndash1154 1995

[12] D Ryan and R Hindi ldquoLive load distribution factors for cast-in-place concrete box girder bridgesrdquo in Proceedings of theStructures Congress Crossing Borders April 2008

[13] S-T Song Y H Chai and S E Hida ldquoLive-load distributionfactors for concrete box-girder bridgesrdquo Journal of BridgeEngineering vol 8 no 5 pp 273ndash280 2003

[14] AASHTO AASHTO LRFD Bridge Design Specifications Amer-ican Association of State Highway and Transportation OfficialsWashington DC USA 5th edition 2010

[15] Computers and Structures Inc SAP2000 v 1500 BerkeleyCalif USA 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



were applied to the finite-element models that were similar tothe vehicle traffic on the bridge and the overall performanceof the bridge as well as the distribution factors load ratingsstress fatigue and thermal effects was quantified Examplesof these studies include Jauregui and Barr [3] Mourad andTabsh [4] Dicleli and Erhan [5] Hodson et al [6] Lahovich[7] Cai et al [8] Kalaycı et al [9] and Kim et al [10] Otherstudies involving the determination of distribution factors forother types of bridges include Ebeido and Kennedy [11] Ryanand Hindi [12] and Song et al [13]

The finite element and integral abutment bridge studieshave been conducted with and without using validatedmodels with live-load data Live-load distribution factors(LLDFs) have been calculated for integral abutment bridgesusing theoretical bridge models such as a study conductedby Dicleli and Erhan [5] which investigated the accuracy oflive-load distribution formulas for single-span prestressedconcrete and integral abutment bridge girders Mourad andTabsh [4] investigated deck slab stresses for integral abutmentbridges using two separate bridge models differing in girdercross sections slab thicknesses and pile spacings Lahovich[7] developed live-load distribution factors for an integralabutment bridge using a ldquobridge in a backpackrdquo and the fold-ed plate girder bridge in order to quantify the response ofeach of the bridges under various types of loading LLDFshave also been quantified for bridges using validated finite-element models based on measured live-load data such asthe study conducted by Hodson et al [6] The researchers forthis study investigated the live-load behavior of an integralabutment bridge The integral abutments were found to addconsiderable restraint to the structure making the AASHTOLRFD live-load distribution factors conservative Kalaycıet al [9] also utilized a validated finite-element bridge modelof a concrete deck on steel I-girders in order to determine theLLDFs of two integral abutment bridges in the State of Ver-mont While single-span integral abutment bridges are morecommonly constructed few studies have been performedusing finite-elementmodels validated from live-load test dataon a single-span prestressed integral abutment and concretegirder bridge to determine LLDFs

As part of a study to determine the overall behavior ofintegral abutment bridges researchers at Utah State Univer-sity performed live-load testing on a single-span prestressedconcrete girder and integral abutment bridge near Perry UTThe setup of this test involved attaching strain gauges anddeflectometers at various locations on the bridge The live-load test consisted of slowly driving trucks across the bridgealong predetermined load paths as well as parking trucksat different locations on the bridge The data collected fromthese tests was used to create and validate a finite-elementmodel (FEM) of the bridge The model was developed usingthe same dimensions and characteristics as the actual bridgeBoundary conditions due to the stiffness of the integral abut-ments were altered until the FEM and live-load data resultedin a strong correlation Live-load distribution factors werethen obtained using this validated model and compared tothose calculated in accordance to procedures recommendedin the AASHTO LRFD Bridge Design Specifications [14]

Figure 1 Perry Bridge (structure number 1F 205) elevation viewduring testing

The AASHTO LRFD and finite-element distribution factorswere used to obtain a load rating of the bridge

Subsequent to the live-load study a live-load distributionparametric investigation was conducted by incrementallymodifying the validated model for changes in span lengthdeck thickness edge distance skew and fixity Distributionfactors were calculated for each change in individual bridgeproperty and compared with the corresponding calculateddistribution factors obtained from the procedures in theAASHTO LRFD Specifications [14] The results showed thatthe bridge properties with the largest influence on the live-load distribution were changes in fixity skew and edge dis-tance Changes in these parameters showed that the AASH-TO LRFD Specifications were between 10 nonconservativeand 56 conservative depending on girder position loadingand fixity The parameter with the least amount of influenceon live-load distribution was the deck thickness providinga range between 4 and 19 nonconservative Dependingon which bridge property was modified both increases anddecreases in conservatism were exhibited

2 Bridge Description

The Perry Bridge (structure number 1F 205) as shown inFigure 1 was constructed in 1976 The superstructure wasdesigned as a single-span prestressed concrete bridge Thebridge is located 805 km (50 miles) north of Salt Lake CityUT It carries two lanes of northbound traffic as part ofInterstate 1584 traveling over Cannery Road in the town ofPerry UTThe bridge has a clear span length of 244m (80 ft)and an overall length of 251m (825 ft) The bridge clearanceis 468m (153 ft) The bridge incurs an average daily traffic(ADT) of approximately 22000 vehicles 29 percent of whichare trucks The bridge was designed with no skew but has asuperelevation of 2

The deck has a width of 134m (444 ft) measured fromoutside to outside of the barriers The roadway width is123m (405 ft) wide measured from the inside of the barrierswith a shoulder width of 160m (525 ft) and 343m (113 ft)on the western and eastern sides respectively The twotraffic lanes are 366m (12 ft) wide These dimensions areshown in Figure 2 The deck is comprised of concrete that is


S1 S2 S3 S4 S5

S6 S7 S8 S9 S10

053m 366m

132m

160m

269m

343m

269m269m269m 132m134m

134m123m

366m 053m








3 Live-Load Test





106m

D3


LP3 658mLP2

627m607mLP5 333m

D5D1

LP1

D2 D4

LP4


0254m

185m

137m

0254m

546m409m

203m

WA =WB = 765kN

734kNWA =WB = 765kN

734kNWA =WB = 760kN

761kN

0584m















0 20 40 60 80 100

02468

101214

0 5 10 15 20 25 30

Position (ft)

Mic

rostr

ain

Position (m)

LL dataModel data



ModelLL data




0

Defl

ectio

n (m

m)

Defl

ectio

n (in

)










0

5

10

15

20

25

0 5 10 15 20 25

Live

-load

mic

rostr

ains

FEM mictrostrains

minus5minus5

y = 11217x + 04541

R2 = 09519


000

001

0 001

Live

-load

dat

a defl

ectio

n (in


R2 = 099

minus005

minus004

minus003

minus002

minus001










Fixed FEM(3)















6 Parametric Study








50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S1 S2 S3 S4 S5

S6 S7 S8 S9 S10

053m 366m

132m

160m

269m

343m

269m269m269m 132m134m

134m123m

366m 053m








3 Live-Load Test





106m

D3


LP3 658mLP2

627m607mLP5 333m

D5D1

LP1

D2 D4

LP4


0254m

185m

137m

0254m

546m409m

203m

WA =WB = 765kN

734kNWA =WB = 765kN

734kNWA =WB = 760kN

761kN

0584m















0 20 40 60 80 100

02468

101214

0 5 10 15 20 25 30

Position (ft)

Mic

rostr

ain

Position (m)

LL dataModel data



ModelLL data




0

Defl

ectio

n (m

m)

Defl

ectio

n (in

)










0

5

10

15

20

25

0 5 10 15 20 25

Live

-load

mic

rostr

ains

FEM mictrostrains

minus5minus5

y = 11217x + 04541

R2 = 09519


000

001

0 001

Live

-load

dat

a defl

ectio

n (in


R2 = 099

minus005

minus004

minus003

minus002

minus001










Fixed FEM(3)















6 Parametric Study








50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










106m

D3


LP3 658mLP2

627m607mLP5 333m

D5D1

LP1

D2 D4

LP4


0254m

185m

137m

0254m

546m409m

203m

WA =WB = 765kN

734kNWA =WB = 765kN

734kNWA =WB = 760kN

761kN

0584m















0 20 40 60 80 100

02468

101214

0 5 10 15 20 25 30

Position (ft)

Mic

rostr

ain

Position (m)

LL dataModel data



ModelLL data




0

Defl

ectio

n (m

m)

Defl

ectio

n (in

)










0

5

10

15

20

25

0 5 10 15 20 25

Live

-load

mic

rostr

ains

FEM mictrostrains

minus5minus5

y = 11217x + 04541

R2 = 09519


000

001

0 001

Live

-load

dat

a defl

ectio

n (in


R2 = 099

minus005

minus004

minus003

minus002

minus001










Fixed FEM(3)















6 Parametric Study








50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















0 20 40 60 80 100

02468

101214

0 5 10 15 20 25 30

Position (ft)

Mic

rostr

ain

Position (m)

LL dataModel data



ModelLL data




0

Defl

ectio

n (m

m)

Defl

ectio

n (in

)










0

5

10

15

20

25

0 5 10 15 20 25

Live

-load

mic

rostr

ains

FEM mictrostrains

minus5minus5

y = 11217x + 04541

R2 = 09519


000

001

0 001

Live

-load

dat

a defl

ectio

n (in


R2 = 099

minus005

minus004

minus003

minus002

minus001










Fixed FEM(3)















6 Parametric Study








50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














0

5

10

15

20

25

0 5 10 15 20 25

Live

-load

mic

rostr

ains

FEM mictrostrains

minus5minus5

y = 11217x + 04541

R2 = 09519


000

001

0 001

Live

-load

dat

a defl

ectio

n (in


R2 = 099

minus005

minus004

minus003

minus002

minus001










Fixed FEM(3)















6 Parametric Study








50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Fixed FEM(3)















6 Parametric Study








50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















50 100 150 200

00000200040006000800100012001400

15 25 35 45 55 65

Length of span (ft)

FEM

DF

AA

SHTO

DF

Length of span (m)


6 7 8 9 10 11 12

1020104010601080110011201140116011801200

150 170 190 210 230 250 270 290 310

Deck thickness (in)

FEM

DF

AA

SHTO

DF

Deck thickness (mm)






9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










9 Effects of Skew




11 Load Rating


RF =119877119899minus 120574119863119863

120574119871119871 (1 + 119868)

(2)



119871= live-



15 2 25 3 35 4 45 5 55

00000200040006000800100012001400

045 065 085 105 125 145 165

Edge distance (ft)

FEM

DF

AA

SHTO

DF

Edge distance (m)



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article live-load testing application using a wireless … · 2019. 7. 31. · interstate...

Documents