Research ArticleModified PCI Multipliers for Time-Dependent Deformation ofPSC Bridges

Joo-Ha Lee 1 Kwang-Mo Lim1 and Chan-Gi Park 2

1Department of Civil and Environmental Engineering e University of Suwon Hwaseong 18323 Republic of Korea2Department of Rural Construction Engineering Kongju National University Yesan 32439 Republic of Korea

Correspondence should be addressed to Chan-Gi Park cgparkkongjuackr

Received 28 February 2018 Revised 14 May 2018 Accepted 23 May 2018 Published 10 July 2018

Academic Editor Constantin Chalioris

Copyright copy 2018 Joo-Ha Lee et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Nowadays prestressed concrete (PSC) bridges have become very common but there are still many difficulties in predicting their long-term behavior In order to predict the long-term behavior of PSC bridges it is possible to use very complex formulas developed byvarious researchers or numerical analysis through computer but many engineers are having difficulty in using such methodsMoreover the accuracy of the prediction result is not satisfactory compared to the effort On the contrary the PCI Bridge DesignManual proposes a method that can easily predict the long-term behavior using multipliers However this method does not take intoaccount various construction schedules and has some assumptions that are inadequate for the current situation in various girdersections and topping thicknesses -erefore in this study new long-time factors were developed by modifying the multipliers of thePCI Bridge Design Manual by a rational manner-is allows prediction of long-term behavior of bridges taking into account variousconstruction schedules and the characteristics of modern girder sections -e prediction results of the long-term camber anddeflection of PSC bridges using the proposed multipliers were compared with those using the basic PCI Bridge Design Manual theimproved PCI Bridge Design Manual KR C-08090 (same as ACI 318-14) and numerical analysis As a result the newly proposedmethodmakes possible to predict the long-term behavior at any time after casting and the accuracy of the prediction is also improved

1 Introduction

Recently the application of prestressed concrete (PSC)bridges has been increasing due to the development of high-strength concrete the improvement of strength and quality ofprestressing (PS) steel and the development of structuralanalysis technology using computer program -e long-termbehavior of these PSC bridges is very important because itdirectly affects the serviceability and safety of the bridge Inthe case of high-speed railway for example very small de-flection of the railway caused by the long-term deformation ofthe bridge can cause serious problems on the running abilityand safety of train -erefore it is necessary to accuratelypredict the time-dependent deformation in the design andconstruction stages and even use stage of the bridge Howeverit is very difficult to accurately calculate time-dependentdeformation of PSC bridges -e calculations should takeinto account creep and shrinkage as well as load-induced

deformation which can cause significant deformation overthe years Especially unlike nonprestressed members forprestressed members prestress forces and prestress lossesmust be considered In addition when combined withnonprestressed members the prediction of long-term be-havior becomes more difficult

Korearsquos railway design guidelines and handbooks (KRC-08090) provides a factor λ applied to initial deflection forestimating the additional long-term deflection of non-prestressed reinforced concrete members as shown in thefollowing equation

λ ξ

1 + 50ρprime (1)

where ρprime is the ratio of compressive reinforcement and ξ isthe time-dependent factor for sustained loads to be equal to20 for 5 years or more 14 for 12 months 12 for 6 monthsand 10 for 3 months

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 1391590 13 pageshttpsdoiorg10115520181391590

It should be noted that (1) of KR C-08090 [1] actuallycomes from the equation presented by ACI 318-14 [2] -eACI 318 code [2] is primarily for building applications notfor bridges Moreover both KR C-08090 [1] and ACI 318-14[2] do not provide specific design guideline such as pre-diction equations for long-term behavior of PSC members-e ACI 318-14 [2] merely suggests an abstract guidelinethat additional time-dependent deflections of PSC memberscan be calculated by considering the stresses of concrete andsteel bars under sustained load the creep and shrinkageeffects of concrete and the relaxation of PS steels

Alternatively the long-term deflection of PSC bridgescan be calculated by using the concrete creep coefficient anddrying shrinkage formulas given in various standards [3ndash5]However such formulas are somewhat complicated to use inpractice because they need to take into consideration variousparameters including concrete mix proportion and sur-rounding environment -ey also do not fully account forthe effects and losses of the prestress Moreover eventhrough these complex methods there is no guarantee ofhighly accurate predictions

Until recently many researchers have proposed variousmethods to predict the long-term behavior of PSC bridges[6ndash11] However the reliability of such predictions has not beensufficiently verified and these methods are difficult and com-plicated for designers to understand and use In addition due torecent advances in computer technology many researchers aretrying to predict and evaluate the long-term behavior of PSCbridges by numerical analysis using the finite differencemethodor finite element method [12ndash17] but for designers a simpleand clear prediction method is more preferable

On the contrary the PCI Bridge Design Manual [18]presents multipliers that can be easily used to predict long-term deformation of PSC bridges However in the PCIBridge Design Manual [18] the multipliers can be appliedonly to two points of time erection and final In practice thetiming of the girder construction of PSC bridges can varygreatly depending on the site conditions and the long-term

deflection should be checked out at any important time inaddition to the time of erection and final depending onvarious construction plans and processes Furthermoresince the PCI Bridge Design Manual [18] multipliers arebased on the 1977 Martinrsquos study [19] it is difficult to saythat they properly reflect the characteristics of various crosssections of modern PSC bridges

-erefore in this study modified PCImultipliers for long-term deflection of PSC bridges considering various con-struction schedules and cross sections of modern PSC bridgeswere proposed so that the time-dependent deformation of PSCbridges can be more easily and accurately predicted

2 PCI Bridge Design Manual Basic Multipliers

Table 1 shows the basic multipliers presented in the PCIBridge Design Manual [18] for predicting long-term cam-bers and deflections of PSC members Derivation of thesemultipliers is in [19]

In (1) for the nonprestressed concrete the base factor foradditional long-term deflection μb is 20 in the absence ofcompressive reinforcement For PSC members howeversince the elastic deflection due to member weight at therelease of the prestress not at the standard age of 28 days ismultiplied by the long-time factor the factor should becalculated considering the elastic modulus Eci at the time ofrelease not the elastic modulus Ec at 28 days as follows

μdf Eci

Ecμb (2)

Since Eci is about 85 of Ec and μb is 20 (2) would thenbecome μdf 17 As shown in Table 1 therefore themultiplier for deflection at final is 1 + μdf 27

In the PCI Bridge Design Manual [18] it is assumed thatthe period from casting to erection is about 30ndash60 days andin this period creep and drying shrinkage which are themain factors of the long-term behavior will have reachedabout 40 to 60 of the ultimate value Using the average

Table 1 PCI Bridge Design Manual basic multipliers [18]

Without composite topping With composite toppingAt erection(1) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

185 185

(2) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

180 180

Final(3) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

270 240

(4) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

245 220

(5) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 300 300

(6) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 230

2 Advances in Civil Engineering

value of 50 therefore the long-term deflection coefficientat erection is presented as the following equation

1 + μde 1 + 05μdf (3)

-e multiplier for deflection at erection would then be1 + 05(17) 185

In deriving the multiplier for the camber in the PCIBridge Design Manual [18] the prestress loss is taken intoaccount -at is the method of obtaining the long-termcamber by multiplying the long-time factor by the elasticcamber at the release of the prestress is the same as (2) butconsidering the prestress loss which is a phenomenon inwhich the prestress as a sustained load decreases over time-e long-term prestress loss is assumed to be 15 of theinitial force -erefore using μdf in (2) factor for final long-time camber can be expressed as follows

μpf μdfP

P0 (4)

-erefore the multiplier used to determine the camberdue to prestress is 1 + μpf 1 + 17(085) 245

-emultiplier for the camber due to prestress at the timeof erection is derived in the same way as (3) is derived -elong-term loss of prestress is governed by long-term be-havior factors such as creep and shrinkage of concrete So ifthese long-term behavior factors occur 50 of ultimate aterection prestress loss will also result in one-half of the long-time total loss 15 Applying this to (4) the multiplier forthe camber caused by the prestress at the time of erection canbe calculated as follows

1 + μpe 1 + μde(1minus 015 times 050) (5)

-erefore the multiplier applied to the initial upwardcamber caused by prestressing force is equal to be1 + μpe 1 + 085(0925) asymp 180

Since the long-term deflection due to the superimposedsustained dead load depends on the creep the multiplier isexpressed by the following equation using the basic factorμb 20

1 + μsdf 1 + 20 30 (6)

In addition the PCI Bridge Design Manual [18] providesmultipliers for composite members by taking into accountthe effect of increased moment of inertia due to topping Asshown in the following equations the effect of topping on

the deflection and camber is taken into account by multi-plying the difference between long-time factors at erectionand final by the ratio of noncomposite to composite mo-ments of inertia IoIc

μdfc μde + μdf minus μde( 1113857Io

Ic1113888 1113889 (7)

μpfc μpe + μpf minus μpe1113872 1113873Io

Ic1113888 1113889 (8)

Here the PCI Bridge Design Manual [18] assumes that thesection becomes composite at about the time of erection -ethickness of the topping is assumed to be 2 inches and the valueof IoIc is assumed to be 065 for commonly used members-erefore if these values are substituted in (7 and 8) themultiplier for deflection and camber of the composite memberwith topping is 240 and 220 respectively as shown in Table 1

3 PCI Bridge Design ManualImproved Multipliers

As shown in Table 2 the PCI Bridge Design Manual 2ndEdition [20] suggested an improved multiplier method pro-posed by Tadros et al [21] -is method is very similar to thebasic multiplier method described in the preceding sectionAccording to the manual however this method provides twoimprovements First it provides more accurate coefficients forcases where the reliable creep coefficient is known or high-performance concrete with a very low creep coefficient is usedSecond the prediction of the deflection caused by the prestressloss can be calculated by considering the amount of prestressloss actually occurred However it is not easy to know thecorrect creep coefficient and the actual prestress loss at thedesign stage Moreover there are many variables that must becalculated separately to derive the multiplier which is some-what inconvenient for designers to use However since theaverage value is presented it can be used effectively It is notedthat the improved multiplier method has been deleted in thecurrent PCI Bridge Design Manual 3rd Edition [18]

4 Development of Proposed Multipliers

41ModificationofPCIMultipliers forPredictionatAnyTimeAs mentioned earlier the PCI Bridge Design Manual [18]provides multipliers only for at the time of erection and final

Table 2 PCI Bridge Design Manual improved multipliers [20]

Load conditionErection time Final time

Formula Average Formula AverageInitial prestress 1 + Ca 196 1 + Cu 288Prestress loss αa(1 + χCa) 100 (1 + χCu) 232Self-weight 1 + Ca 196 1 + Cu 288Dead load on plain beam 100 100 1 + Cuprime 250Dead load on composite beam 100 100 1 + Cuprime 250Cu ultimate creep coefficient for loads applied immediately after transfer and the average value is 188 Cuprime ultimate creep coefficient for loads applied attime of erection and the average value is 150 Ca creep coefficient for loading applied immediately after transfer and strains measured at time of erectionand the average value is 096 αa time-dependent prestress loss at erection divided by total time-dependent prestress loss and the average value is 060χ Bazantrsquos aging coefficient and the average value is 070

Advances in Civil Engineering 3

Moreover it is assumed that the erection time is about 30ndash60days after casting In practice however the time of erection isvery flexible depending on the site conditions-erefore in thisstudy the multipliers applicable at any time including thevarious time of erection were suggested by considering the rateof creep and drying shrinkage It can be useful for field con-struction management and maintenance of structures if thecamber or deflection can be predicted at any time after casting

Equations (3) and (5) were modified using rt the rate ofcreep and drying shrinkage over time

1 + μdt 1 + rt times μdf (9)

1 + μpt 1 + μdt 1minus 015 times rt( 1113857 (10)

where t is the time after casting and μdt and μpt are the factorsfor time-dependent deflection and camber at the time of t

applied to initial deformation caused by member weight andprestressing force respectively μdf is 17 as in the PCI BridgeDesign Manual [18] If the time of the erection is t(e) themultiplier for the deflection and camber at erection can beexpressed by substituting t(e) in (9) and (10) as follows

1 + μdt(e) 1 + rt(e) times μdf

1 + μpt(e) 1 + μdt(e) 1minus 015 times rt(e)1113872 1113873(11)

Also the multiplier for the long-term deflection due tothe superimposed dead load at any time can be expressed bythe following equation

1 + μsdt 1 + r[tminust(s)] times μsdf (12)

where μsdt is the factor for additional long-time deflection attime t applied to initial deflection caused by superimposeddead load and t(s) is the time at which the superimposed

dead load is applied μsdf is 20 as in the PCI Bridge DesignManual [18]

-e creep and drying shrinkage predictions presented inACI 209R-92 [3] were used to calculate the rate of creep andshrinkage over time rt For creep and shrinkage understandard condition the relationship between at any time andat final is given by (13) and (14) respectively

vt t06

10 + t06vu (13)

εsh( 1113857t t

35 + tεsh( 1113857u (14)

where t time in days vt creep coefficient at any timevu ultimate creep coefficient (εsh)t shrinkage strain atany time and (εsh)u ultimate shrinkage strain

Long-term behavior is both affected by creep and dryingshrinkage at the same time -erefore rt the rate of creepand drying shrinkage over time were derived from theaverage of (13) and (14) as shown in (15) Figure 1 shows thegraphs of creep and drying shrinkage rates over time

rt 12

t06

10 + t06 +t

35 + t1113888 1113889 (15)

42 Modification of Multipliers for Composite Member Asmentioned earlier in the PCI Bridge DesignManual [18] forthe composite member the thickness of the topping is as-sumed to be 2 inches and the ratio of noncomposite tocomposite moments of inertia IoIc is 065 for all casesregardless of the shape of cross section However given thevariety of girder geometry and the recent bridge slab deck

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Tim

e-ra

tio v

alue

s for

cree

p an

d sh

rinka

ge (

)

Elapsed time (day)Creep time ratioShrinkage time ratioAverage time ratio of creep and shrinkage

Figure 1 Rate of creep and drying shrinkage over time

4 Advances in Civil Engineering

thickness the assumptions for composite members in thePCI Bridge Design Manual [18] are not likely to reflectmodern bridge characteristics -erefore in this study themultipliers for the long-term behavior of composite memberwere proposed by analyzing the representative cross sectionsof the recent bridges

Currently girder sections commonly used in single-spanrailway bridges in Korea are I girder box girder and WPC(wide flange prestressed concrete) In general a thickness ofslab placed on the girder is 280mm Figure 2 and Table 3show the details of the cross sections of I girder box girderand WPC which are the representative girder sections ac-tually used in practice Table 4 shows IoIc for all cross

sections of Figure 2 and Table 3 As shown in Table 4 thevalue of IoIc is different from 065 of the PCI Bridge DesignManual [18] IoIc was in the range of 051 to 056 and boxgirder bridges and long span bridges tend to have relativelylarge IoIc For the convenience of design this study pro-posed to use the total average value of 053 for IoIc

-e PCI Bridge Design Manual [18] assumed that thesection becomes composite at about the time of erectionbut it is not always Rather there are many cases wheretopping is not applied when the girder is erected because offield condition and construction schedules -ereforemultipliers have been proposed to enable the prediction ofdeflection and camber of the composite member at anytime t by considering the time t(c) at which the sectionbecomes composite -is can be expressed as follows using(7)ndash(10)

1 + μdtc 1 + μdt(c) + μdt minus μdt(c)1113872 1113873Io

Ic1113888 1113889

1 + μptc 1 + μpt(c) + μpt minus μpt(c)1113872 1113873Io

Ic1113888 1113889

(16)

where IoIc is 053-e factor for long-term deflection by a composite

topping should be also modified by the ratio of IoIc becausethe elastic deflection caused by the placement of the toppingto which the factor is applied is calculated using the non-composite section as follows

1 + μtt 1 + μsdtIo

Ic1113888 1113889 (17)

where μtt is the factor for additional long-term deflectioncaused by topping at any time t

As a result the multipliers of the PCI Bridge DesignManual [18] in Table 1 were revised as shown in Table 5

ed

ifg

h

b c ba

j k jl

(a)i

c b

j

da

cb

kl

m

nopq

o

g

n

he f

(b)

p

cb

m

n

q r

de

f

i j kg

lh g

k j i

o

a

(c)

Figure 2 Typical cross sections of PSC bridges (a) I girder (b) box girder (c) WPC girder

Table 3 Cross section dimension of I box and WPC girders byspan (mm)

Type I girder Box girder WPC girderSpan 25m 30m 35m 30m 35m 40m 30m 35m 40m 1000 1000 1000 1200 1200 1200 3580 3580 2650 400 400 400 220 220 220 150 150 150 200 200 200 50 50 50 100 100 100 80 150 150 660 660 660 982 1135 1514 90 120 120 2000 2400 2600 116 115 86 1520 1550 1950 1900 2300 2500 350 500 450 240 180 180 30 30 30 98 113 151 320 200 200 70 70 70 1181 1150 865 2350 2200 2600 400 350 350 730 730 370 240 350 350 50 50 50 110 110 110 200 200 200 1080 1530 1730 145 175 205 680 900 900 220 220 220 1610 1550 1280 mdash mdash mdash 250 250 250 1700 2000 2300 mdash mdash mdash 30 30 30 1450 1750 2050 mdash mdash mdash 220 220 220 135 135 135 mdash mdash mdash 760 760 760 115 115 115 mdash mdash mdash 1260 1260 1260 480 480 120 mdash mdash mdash mdash mdash mdash 250 250 250

Advances in Civil Engineering 5

5 Verification of Proposed Multipliers

In order to verify the proposed multipliers for actuallyconstructed PSC bridges the predictions of long-termcamber and deflection by the proposed multipliers werecompared with those by the basic PCI multipliers [18] theimproved PCI multipliers [20] and KR C-08090 [1] (same asACI 318-14 [2]) In addition numerical analysis was per-formed and the results were compared with the results fromother prediction methods

51 PSCBridges forVerification PSC bridges A and B whichwere recently constructed on a new line from Wonju toGangneung in Korearsquos high-speed railway were selected toverify the prediction methods Bridge A is a WPC type witha span of 388m and bridge B is constructed with an I-girdertype with a span of 34m -e cross-sectional details of thebridges at midspan are shown in Figure 3 Tables 6 and 7

show the construction history of the bridges and the elasticdeformation due to the applied load respectively

52 Numerical Analysis for Long-Term Behavior of PSCBridges Long-term behavior of the bridges A and B waspredicted using MIDAS Civil a general-purpose finite el-ement analysis program-e validity of theMIDAS Civil hasalready been confirmed through previous researches [22ndash24] In general the prediction of long-term behavior usinga finite element analysis is known to have a higher accuracythan that of the methods using a multiplier such as the PCIBridge Design Manual [18 20] although the design con-venience is poor [25ndash28] -erefore the numerical analysisresults were used to verify the newly proposed multipliers

-ematerial model was selected from the database of theMIDAS Civil program C40 and C27 were selected forthe girder and deck concrete respectively and the strandof SWPC7B empty152mm was selected for PS steel -ese

Table 4 Ratio of noncomposite to composite moments of inertia by girder type and span

Span PCI Bridge Design Manual I girder Box girder WPC girder Average25m

065

051 mdash mdash 05130m 049 054 053 05235m 052 056 050 05340m mdash 057 054 056Average 065 051 056 052 053

Table 5 Proposed multipliers

Without topping With toppingAt erection(1) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt(e) 1 + 17rt(e)

(2) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(e)(1minus 015rt(e)) 1 + 17rt(e)(1minus 015rt(e))

At certain time(3) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt 1 + 08rt(c) + 09rt

(4) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(1minus 015rt) 1 + 08rt(c)(1minus 015rt(c)) + 09rt(1minus 015 times rt)

(5) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 1 + 20r[tminust(s)] 1 + 20r[tminust(s)]

(6) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 1 + 106r[tminust(c)]

Final(7) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

270 19 + 08rt(c)

(8) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

245 1765 + 08rt(c)(1minus 015rt(c))

(9) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 300 300

(10) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 206

6 Advances in Civil Engineering

materials are the same as concrete and PS steel actually usedfor bridges A and B -e structural members of the bridgeswere modeled based on structural calculations and designdrawings of bridges A and B According to the designdrawing the strands were arranged by setting the actualcoordinates of the strand on the girder nodes using the 3-Dinput type from tendon profile option of MIDAS Civil -eCEB-FIP MC90 model [5] was used to calculate creep anddrying shrinkage of concrete For the relaxation of thetendon the Magura 45 model was used to consider thetime-dependent loss of the prestress Based on the con-struction history of the bridges A and B in Table 6construction sequence analysis was carried out After thecast of deck composite behavior of the girder and the deckwas simulated through the node connection using the rigidtype of elastic link In the same way common duct which isthe additional superimposed dead load was also simulatedfor composite behavior after its installation At the finalstage the deformation patterns of bridges A and B areshown in Figure 4 As a result the bridges A and B in themidspan showed 324mm and 393mm of camber at girdererection and 297mm and 192mm of camber at finalrespectively

53 Comparison of Predictions of Long-Term DeformationTables 8 and 9 and Figure 5 show the predictions of the long-term deformation of bridges A and B by using the proposedmultipliers the basic PCI multipliers [18] the improved PCImultipliers [20] KR C-08090 [1] and numerical analysisFor the improved PCI multipliers [20] the average values inTable 2 were used because the actual creep coefficient and theamount of the prestress loss can hardly be known

Although the values of predictions by the proposedmultipliers and KR C-08090 [1] were somewhat different

from the prediction by numerical analysis their predictiontrends of the camber over time were generally similar be-cause they provided available multipliers at any time In thecase of the basic PCI multipliers [18] however the long-term behavior after the erection was quite different fromother prediction methods because there are no applicablelong-term factors for the period between the erection andthe final

-e girder of bridge A was erected on the 30th day aftercasting while the girder of bridge B was erected on the 150thday relatively long time after casting -e basic PCI

1025 90 420 90 1025

2650

120

100

110

2670 30

00

150

2250

600

220

95 600150

2190

60600

3000

600

1040 110 695110695

(a)

400 200 4001000

2600

150

120

1950

180

200

2600

200 350350

900

(b)

Figure 3 Cross-sectional details of bridges (a) A and (b) B

Table 6 Construction history of bridges A and B

EventTime from casting (days)Bridge A Bridge B

(1) Release 1 1(2) Erection (t(e)) 30 150(3) Topping (t(c)) 240 157(4) 1st random time (t1) 270 180(5) Superimposed dead load (t(s)) 390 360(6) 2nd random time (t2) 700 1000

(7) Final 5 years ormore

5 years ormore

Table 7 Elastic camber and deflection of bridges A and B

LoadCamber (+) or deflection (minus)Bridge A Bridge B

Self-weight minus223 minus165Prestressing force +461 +353Topping minus80 minus75Superimposed dead load minus25 minus265

Advances in Civil Engineering 7

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

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value of 50 therefore the long-term deflection coefficientat erection is presented as the following equation

1 + μde 1 + 05μdf (3)

-e multiplier for deflection at erection would then be1 + 05(17) 185

In deriving the multiplier for the camber in the PCIBridge Design Manual [18] the prestress loss is taken intoaccount -at is the method of obtaining the long-termcamber by multiplying the long-time factor by the elasticcamber at the release of the prestress is the same as (2) butconsidering the prestress loss which is a phenomenon inwhich the prestress as a sustained load decreases over time-e long-term prestress loss is assumed to be 15 of theinitial force -erefore using μdf in (2) factor for final long-time camber can be expressed as follows

μpf μdfP

P0 (4)

-erefore the multiplier used to determine the camberdue to prestress is 1 + μpf 1 + 17(085) 245

-emultiplier for the camber due to prestress at the timeof erection is derived in the same way as (3) is derived -elong-term loss of prestress is governed by long-term be-havior factors such as creep and shrinkage of concrete So ifthese long-term behavior factors occur 50 of ultimate aterection prestress loss will also result in one-half of the long-time total loss 15 Applying this to (4) the multiplier forthe camber caused by the prestress at the time of erection canbe calculated as follows

1 + μpe 1 + μde(1minus 015 times 050) (5)

-erefore the multiplier applied to the initial upwardcamber caused by prestressing force is equal to be1 + μpe 1 + 085(0925) asymp 180

Since the long-term deflection due to the superimposedsustained dead load depends on the creep the multiplier isexpressed by the following equation using the basic factorμb 20

1 + μsdf 1 + 20 30 (6)

In addition the PCI Bridge Design Manual [18] providesmultipliers for composite members by taking into accountthe effect of increased moment of inertia due to topping Asshown in the following equations the effect of topping on

the deflection and camber is taken into account by multi-plying the difference between long-time factors at erectionand final by the ratio of noncomposite to composite mo-ments of inertia IoIc

μdfc μde + μdf minus μde( 1113857Io

Ic1113888 1113889 (7)

μpfc μpe + μpf minus μpe1113872 1113873Io

Ic1113888 1113889 (8)

Here the PCI Bridge Design Manual [18] assumes that thesection becomes composite at about the time of erection -ethickness of the topping is assumed to be 2 inches and the valueof IoIc is assumed to be 065 for commonly used members-erefore if these values are substituted in (7 and 8) themultiplier for deflection and camber of the composite memberwith topping is 240 and 220 respectively as shown in Table 1

3 PCI Bridge Design ManualImproved Multipliers

As shown in Table 2 the PCI Bridge Design Manual 2ndEdition [20] suggested an improved multiplier method pro-posed by Tadros et al [21] -is method is very similar to thebasic multiplier method described in the preceding sectionAccording to the manual however this method provides twoimprovements First it provides more accurate coefficients forcases where the reliable creep coefficient is known or high-performance concrete with a very low creep coefficient is usedSecond the prediction of the deflection caused by the prestressloss can be calculated by considering the amount of prestressloss actually occurred However it is not easy to know thecorrect creep coefficient and the actual prestress loss at thedesign stage Moreover there are many variables that must becalculated separately to derive the multiplier which is some-what inconvenient for designers to use However since theaverage value is presented it can be used effectively It is notedthat the improved multiplier method has been deleted in thecurrent PCI Bridge Design Manual 3rd Edition [18]

4 Development of Proposed Multipliers

41ModificationofPCIMultipliers forPredictionatAnyTimeAs mentioned earlier the PCI Bridge Design Manual [18]provides multipliers only for at the time of erection and final

Table 2 PCI Bridge Design Manual improved multipliers [20]

Load conditionErection time Final time

Formula Average Formula AverageInitial prestress 1 + Ca 196 1 + Cu 288Prestress loss αa(1 + χCa) 100 (1 + χCu) 232Self-weight 1 + Ca 196 1 + Cu 288Dead load on plain beam 100 100 1 + Cuprime 250Dead load on composite beam 100 100 1 + Cuprime 250Cu ultimate creep coefficient for loads applied immediately after transfer and the average value is 188 Cuprime ultimate creep coefficient for loads applied attime of erection and the average value is 150 Ca creep coefficient for loading applied immediately after transfer and strains measured at time of erectionand the average value is 096 αa time-dependent prestress loss at erection divided by total time-dependent prestress loss and the average value is 060χ Bazantrsquos aging coefficient and the average value is 070

Advances in Civil Engineering 3

Moreover it is assumed that the erection time is about 30ndash60days after casting In practice however the time of erection isvery flexible depending on the site conditions-erefore in thisstudy the multipliers applicable at any time including thevarious time of erection were suggested by considering the rateof creep and drying shrinkage It can be useful for field con-struction management and maintenance of structures if thecamber or deflection can be predicted at any time after casting

Equations (3) and (5) were modified using rt the rate ofcreep and drying shrinkage over time

1 + μdt 1 + rt times μdf (9)

1 + μpt 1 + μdt 1minus 015 times rt( 1113857 (10)

where t is the time after casting and μdt and μpt are the factorsfor time-dependent deflection and camber at the time of t

applied to initial deformation caused by member weight andprestressing force respectively μdf is 17 as in the PCI BridgeDesign Manual [18] If the time of the erection is t(e) themultiplier for the deflection and camber at erection can beexpressed by substituting t(e) in (9) and (10) as follows

1 + μdt(e) 1 + rt(e) times μdf

1 + μpt(e) 1 + μdt(e) 1minus 015 times rt(e)1113872 1113873(11)

Also the multiplier for the long-term deflection due tothe superimposed dead load at any time can be expressed bythe following equation

1 + μsdt 1 + r[tminust(s)] times μsdf (12)

where μsdt is the factor for additional long-time deflection attime t applied to initial deflection caused by superimposeddead load and t(s) is the time at which the superimposed

dead load is applied μsdf is 20 as in the PCI Bridge DesignManual [18]

-e creep and drying shrinkage predictions presented inACI 209R-92 [3] were used to calculate the rate of creep andshrinkage over time rt For creep and shrinkage understandard condition the relationship between at any time andat final is given by (13) and (14) respectively

vt t06

10 + t06vu (13)

εsh( 1113857t t

35 + tεsh( 1113857u (14)

where t time in days vt creep coefficient at any timevu ultimate creep coefficient (εsh)t shrinkage strain atany time and (εsh)u ultimate shrinkage strain

Long-term behavior is both affected by creep and dryingshrinkage at the same time -erefore rt the rate of creepand drying shrinkage over time were derived from theaverage of (13) and (14) as shown in (15) Figure 1 shows thegraphs of creep and drying shrinkage rates over time

rt 12

t06

10 + t06 +t

35 + t1113888 1113889 (15)

42 Modification of Multipliers for Composite Member Asmentioned earlier in the PCI Bridge DesignManual [18] forthe composite member the thickness of the topping is as-sumed to be 2 inches and the ratio of noncomposite tocomposite moments of inertia IoIc is 065 for all casesregardless of the shape of cross section However given thevariety of girder geometry and the recent bridge slab deck

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Tim

e-ra

tio v

alue

s for

cree

p an

d sh

rinka

ge (

)

Elapsed time (day)Creep time ratioShrinkage time ratioAverage time ratio of creep and shrinkage

Figure 1 Rate of creep and drying shrinkage over time

4 Advances in Civil Engineering

thickness the assumptions for composite members in thePCI Bridge Design Manual [18] are not likely to reflectmodern bridge characteristics -erefore in this study themultipliers for the long-term behavior of composite memberwere proposed by analyzing the representative cross sectionsof the recent bridges

Currently girder sections commonly used in single-spanrailway bridges in Korea are I girder box girder and WPC(wide flange prestressed concrete) In general a thickness ofslab placed on the girder is 280mm Figure 2 and Table 3show the details of the cross sections of I girder box girderand WPC which are the representative girder sections ac-tually used in practice Table 4 shows IoIc for all cross

sections of Figure 2 and Table 3 As shown in Table 4 thevalue of IoIc is different from 065 of the PCI Bridge DesignManual [18] IoIc was in the range of 051 to 056 and boxgirder bridges and long span bridges tend to have relativelylarge IoIc For the convenience of design this study pro-posed to use the total average value of 053 for IoIc

-e PCI Bridge Design Manual [18] assumed that thesection becomes composite at about the time of erectionbut it is not always Rather there are many cases wheretopping is not applied when the girder is erected because offield condition and construction schedules -ereforemultipliers have been proposed to enable the prediction ofdeflection and camber of the composite member at anytime t by considering the time t(c) at which the sectionbecomes composite -is can be expressed as follows using(7)ndash(10)

1 + μdtc 1 + μdt(c) + μdt minus μdt(c)1113872 1113873Io

Ic1113888 1113889

1 + μptc 1 + μpt(c) + μpt minus μpt(c)1113872 1113873Io

Ic1113888 1113889

(16)

where IoIc is 053-e factor for long-term deflection by a composite

topping should be also modified by the ratio of IoIc becausethe elastic deflection caused by the placement of the toppingto which the factor is applied is calculated using the non-composite section as follows

1 + μtt 1 + μsdtIo

Ic1113888 1113889 (17)

where μtt is the factor for additional long-term deflectioncaused by topping at any time t

As a result the multipliers of the PCI Bridge DesignManual [18] in Table 1 were revised as shown in Table 5

ed

ifg

h

b c ba

j k jl

(a)i

c b

j

da

cb

kl

m

nopq

o

g

n

he f

(b)

p

cb

m

n

q r

de

f

i j kg

lh g

k j i

o

a

(c)

Figure 2 Typical cross sections of PSC bridges (a) I girder (b) box girder (c) WPC girder

Table 3 Cross section dimension of I box and WPC girders byspan (mm)

Type I girder Box girder WPC girderSpan 25m 30m 35m 30m 35m 40m 30m 35m 40m 1000 1000 1000 1200 1200 1200 3580 3580 2650 400 400 400 220 220 220 150 150 150 200 200 200 50 50 50 100 100 100 80 150 150 660 660 660 982 1135 1514 90 120 120 2000 2400 2600 116 115 86 1520 1550 1950 1900 2300 2500 350 500 450 240 180 180 30 30 30 98 113 151 320 200 200 70 70 70 1181 1150 865 2350 2200 2600 400 350 350 730 730 370 240 350 350 50 50 50 110 110 110 200 200 200 1080 1530 1730 145 175 205 680 900 900 220 220 220 1610 1550 1280 mdash mdash mdash 250 250 250 1700 2000 2300 mdash mdash mdash 30 30 30 1450 1750 2050 mdash mdash mdash 220 220 220 135 135 135 mdash mdash mdash 760 760 760 115 115 115 mdash mdash mdash 1260 1260 1260 480 480 120 mdash mdash mdash mdash mdash mdash 250 250 250

Advances in Civil Engineering 5

5 Verification of Proposed Multipliers

In order to verify the proposed multipliers for actuallyconstructed PSC bridges the predictions of long-termcamber and deflection by the proposed multipliers werecompared with those by the basic PCI multipliers [18] theimproved PCI multipliers [20] and KR C-08090 [1] (same asACI 318-14 [2]) In addition numerical analysis was per-formed and the results were compared with the results fromother prediction methods

51 PSCBridges forVerification PSC bridges A and B whichwere recently constructed on a new line from Wonju toGangneung in Korearsquos high-speed railway were selected toverify the prediction methods Bridge A is a WPC type witha span of 388m and bridge B is constructed with an I-girdertype with a span of 34m -e cross-sectional details of thebridges at midspan are shown in Figure 3 Tables 6 and 7

show the construction history of the bridges and the elasticdeformation due to the applied load respectively

52 Numerical Analysis for Long-Term Behavior of PSCBridges Long-term behavior of the bridges A and B waspredicted using MIDAS Civil a general-purpose finite el-ement analysis program-e validity of theMIDAS Civil hasalready been confirmed through previous researches [22ndash24] In general the prediction of long-term behavior usinga finite element analysis is known to have a higher accuracythan that of the methods using a multiplier such as the PCIBridge Design Manual [18 20] although the design con-venience is poor [25ndash28] -erefore the numerical analysisresults were used to verify the newly proposed multipliers

-ematerial model was selected from the database of theMIDAS Civil program C40 and C27 were selected forthe girder and deck concrete respectively and the strandof SWPC7B empty152mm was selected for PS steel -ese

Table 4 Ratio of noncomposite to composite moments of inertia by girder type and span

Span PCI Bridge Design Manual I girder Box girder WPC girder Average25m

065

051 mdash mdash 05130m 049 054 053 05235m 052 056 050 05340m mdash 057 054 056Average 065 051 056 052 053

Table 5 Proposed multipliers

Without topping With toppingAt erection(1) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt(e) 1 + 17rt(e)

(2) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(e)(1minus 015rt(e)) 1 + 17rt(e)(1minus 015rt(e))

At certain time(3) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt 1 + 08rt(c) + 09rt

(4) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(1minus 015rt) 1 + 08rt(c)(1minus 015rt(c)) + 09rt(1minus 015 times rt)

(5) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 1 + 20r[tminust(s)] 1 + 20r[tminust(s)]

(6) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 1 + 106r[tminust(c)]

Final(7) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

270 19 + 08rt(c)

(8) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

245 1765 + 08rt(c)(1minus 015rt(c))

(9) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 300 300

(10) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 206

6 Advances in Civil Engineering

materials are the same as concrete and PS steel actually usedfor bridges A and B -e structural members of the bridgeswere modeled based on structural calculations and designdrawings of bridges A and B According to the designdrawing the strands were arranged by setting the actualcoordinates of the strand on the girder nodes using the 3-Dinput type from tendon profile option of MIDAS Civil -eCEB-FIP MC90 model [5] was used to calculate creep anddrying shrinkage of concrete For the relaxation of thetendon the Magura 45 model was used to consider thetime-dependent loss of the prestress Based on the con-struction history of the bridges A and B in Table 6construction sequence analysis was carried out After thecast of deck composite behavior of the girder and the deckwas simulated through the node connection using the rigidtype of elastic link In the same way common duct which isthe additional superimposed dead load was also simulatedfor composite behavior after its installation At the finalstage the deformation patterns of bridges A and B areshown in Figure 4 As a result the bridges A and B in themidspan showed 324mm and 393mm of camber at girdererection and 297mm and 192mm of camber at finalrespectively

53 Comparison of Predictions of Long-Term DeformationTables 8 and 9 and Figure 5 show the predictions of the long-term deformation of bridges A and B by using the proposedmultipliers the basic PCI multipliers [18] the improved PCImultipliers [20] KR C-08090 [1] and numerical analysisFor the improved PCI multipliers [20] the average values inTable 2 were used because the actual creep coefficient and theamount of the prestress loss can hardly be known

Although the values of predictions by the proposedmultipliers and KR C-08090 [1] were somewhat different

from the prediction by numerical analysis their predictiontrends of the camber over time were generally similar be-cause they provided available multipliers at any time In thecase of the basic PCI multipliers [18] however the long-term behavior after the erection was quite different fromother prediction methods because there are no applicablelong-term factors for the period between the erection andthe final

-e girder of bridge A was erected on the 30th day aftercasting while the girder of bridge B was erected on the 150thday relatively long time after casting -e basic PCI

1025 90 420 90 1025

2650

120

100

110

2670 30

00

150

2250

600

220

95 600150

2190

60600

3000

600

1040 110 695110695

(a)

400 200 4001000

2600

150

120

1950

180

200

2600

200 350350

900

(b)

Figure 3 Cross-sectional details of bridges (a) A and (b) B

Table 6 Construction history of bridges A and B

EventTime from casting (days)Bridge A Bridge B

(1) Release 1 1(2) Erection (t(e)) 30 150(3) Topping (t(c)) 240 157(4) 1st random time (t1) 270 180(5) Superimposed dead load (t(s)) 390 360(6) 2nd random time (t2) 700 1000

(7) Final 5 years ormore

5 years ormore

Table 7 Elastic camber and deflection of bridges A and B

LoadCamber (+) or deflection (minus)Bridge A Bridge B

Self-weight minus223 minus165Prestressing force +461 +353Topping minus80 minus75Superimposed dead load minus25 minus265

Advances in Civil Engineering 7

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

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Moreover it is assumed that the erection time is about 30ndash60days after casting In practice however the time of erection isvery flexible depending on the site conditions-erefore in thisstudy the multipliers applicable at any time including thevarious time of erection were suggested by considering the rateof creep and drying shrinkage It can be useful for field con-struction management and maintenance of structures if thecamber or deflection can be predicted at any time after casting

Equations (3) and (5) were modified using rt the rate ofcreep and drying shrinkage over time

1 + μdt 1 + rt times μdf (9)

1 + μpt 1 + μdt 1minus 015 times rt( 1113857 (10)

where t is the time after casting and μdt and μpt are the factorsfor time-dependent deflection and camber at the time of t

applied to initial deformation caused by member weight andprestressing force respectively μdf is 17 as in the PCI BridgeDesign Manual [18] If the time of the erection is t(e) themultiplier for the deflection and camber at erection can beexpressed by substituting t(e) in (9) and (10) as follows

1 + μdt(e) 1 + rt(e) times μdf

1 + μpt(e) 1 + μdt(e) 1minus 015 times rt(e)1113872 1113873(11)

Also the multiplier for the long-term deflection due tothe superimposed dead load at any time can be expressed bythe following equation

1 + μsdt 1 + r[tminust(s)] times μsdf (12)

where μsdt is the factor for additional long-time deflection attime t applied to initial deflection caused by superimposeddead load and t(s) is the time at which the superimposed

dead load is applied μsdf is 20 as in the PCI Bridge DesignManual [18]

-e creep and drying shrinkage predictions presented inACI 209R-92 [3] were used to calculate the rate of creep andshrinkage over time rt For creep and shrinkage understandard condition the relationship between at any time andat final is given by (13) and (14) respectively

vt t06

10 + t06vu (13)

εsh( 1113857t t

35 + tεsh( 1113857u (14)

where t time in days vt creep coefficient at any timevu ultimate creep coefficient (εsh)t shrinkage strain atany time and (εsh)u ultimate shrinkage strain

Long-term behavior is both affected by creep and dryingshrinkage at the same time -erefore rt the rate of creepand drying shrinkage over time were derived from theaverage of (13) and (14) as shown in (15) Figure 1 shows thegraphs of creep and drying shrinkage rates over time

rt 12

t06

10 + t06 +t

35 + t1113888 1113889 (15)

42 Modification of Multipliers for Composite Member Asmentioned earlier in the PCI Bridge DesignManual [18] forthe composite member the thickness of the topping is as-sumed to be 2 inches and the ratio of noncomposite tocomposite moments of inertia IoIc is 065 for all casesregardless of the shape of cross section However given thevariety of girder geometry and the recent bridge slab deck

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Tim

e-ra

tio v

alue

s for

cree

p an

d sh

rinka

ge (

)

Elapsed time (day)Creep time ratioShrinkage time ratioAverage time ratio of creep and shrinkage

Figure 1 Rate of creep and drying shrinkage over time

4 Advances in Civil Engineering

thickness the assumptions for composite members in thePCI Bridge Design Manual [18] are not likely to reflectmodern bridge characteristics -erefore in this study themultipliers for the long-term behavior of composite memberwere proposed by analyzing the representative cross sectionsof the recent bridges

Currently girder sections commonly used in single-spanrailway bridges in Korea are I girder box girder and WPC(wide flange prestressed concrete) In general a thickness ofslab placed on the girder is 280mm Figure 2 and Table 3show the details of the cross sections of I girder box girderand WPC which are the representative girder sections ac-tually used in practice Table 4 shows IoIc for all cross

sections of Figure 2 and Table 3 As shown in Table 4 thevalue of IoIc is different from 065 of the PCI Bridge DesignManual [18] IoIc was in the range of 051 to 056 and boxgirder bridges and long span bridges tend to have relativelylarge IoIc For the convenience of design this study pro-posed to use the total average value of 053 for IoIc

-e PCI Bridge Design Manual [18] assumed that thesection becomes composite at about the time of erectionbut it is not always Rather there are many cases wheretopping is not applied when the girder is erected because offield condition and construction schedules -ereforemultipliers have been proposed to enable the prediction ofdeflection and camber of the composite member at anytime t by considering the time t(c) at which the sectionbecomes composite -is can be expressed as follows using(7)ndash(10)

1 + μdtc 1 + μdt(c) + μdt minus μdt(c)1113872 1113873Io

Ic1113888 1113889

1 + μptc 1 + μpt(c) + μpt minus μpt(c)1113872 1113873Io

Ic1113888 1113889

(16)

where IoIc is 053-e factor for long-term deflection by a composite

topping should be also modified by the ratio of IoIc becausethe elastic deflection caused by the placement of the toppingto which the factor is applied is calculated using the non-composite section as follows

1 + μtt 1 + μsdtIo

Ic1113888 1113889 (17)

where μtt is the factor for additional long-term deflectioncaused by topping at any time t

As a result the multipliers of the PCI Bridge DesignManual [18] in Table 1 were revised as shown in Table 5

ed

ifg

h

b c ba

j k jl

(a)i

c b

j

da

cb

kl

m

nopq

o

g

n

he f

(b)

p

cb

m

n

q r

de

f

i j kg

lh g

k j i

o

a

(c)

Figure 2 Typical cross sections of PSC bridges (a) I girder (b) box girder (c) WPC girder

Table 3 Cross section dimension of I box and WPC girders byspan (mm)

Type I girder Box girder WPC girderSpan 25m 30m 35m 30m 35m 40m 30m 35m 40m 1000 1000 1000 1200 1200 1200 3580 3580 2650 400 400 400 220 220 220 150 150 150 200 200 200 50 50 50 100 100 100 80 150 150 660 660 660 982 1135 1514 90 120 120 2000 2400 2600 116 115 86 1520 1550 1950 1900 2300 2500 350 500 450 240 180 180 30 30 30 98 113 151 320 200 200 70 70 70 1181 1150 865 2350 2200 2600 400 350 350 730 730 370 240 350 350 50 50 50 110 110 110 200 200 200 1080 1530 1730 145 175 205 680 900 900 220 220 220 1610 1550 1280 mdash mdash mdash 250 250 250 1700 2000 2300 mdash mdash mdash 30 30 30 1450 1750 2050 mdash mdash mdash 220 220 220 135 135 135 mdash mdash mdash 760 760 760 115 115 115 mdash mdash mdash 1260 1260 1260 480 480 120 mdash mdash mdash mdash mdash mdash 250 250 250

Advances in Civil Engineering 5

5 Verification of Proposed Multipliers

In order to verify the proposed multipliers for actuallyconstructed PSC bridges the predictions of long-termcamber and deflection by the proposed multipliers werecompared with those by the basic PCI multipliers [18] theimproved PCI multipliers [20] and KR C-08090 [1] (same asACI 318-14 [2]) In addition numerical analysis was per-formed and the results were compared with the results fromother prediction methods

51 PSCBridges forVerification PSC bridges A and B whichwere recently constructed on a new line from Wonju toGangneung in Korearsquos high-speed railway were selected toverify the prediction methods Bridge A is a WPC type witha span of 388m and bridge B is constructed with an I-girdertype with a span of 34m -e cross-sectional details of thebridges at midspan are shown in Figure 3 Tables 6 and 7

show the construction history of the bridges and the elasticdeformation due to the applied load respectively

52 Numerical Analysis for Long-Term Behavior of PSCBridges Long-term behavior of the bridges A and B waspredicted using MIDAS Civil a general-purpose finite el-ement analysis program-e validity of theMIDAS Civil hasalready been confirmed through previous researches [22ndash24] In general the prediction of long-term behavior usinga finite element analysis is known to have a higher accuracythan that of the methods using a multiplier such as the PCIBridge Design Manual [18 20] although the design con-venience is poor [25ndash28] -erefore the numerical analysisresults were used to verify the newly proposed multipliers

-ematerial model was selected from the database of theMIDAS Civil program C40 and C27 were selected forthe girder and deck concrete respectively and the strandof SWPC7B empty152mm was selected for PS steel -ese

Table 4 Ratio of noncomposite to composite moments of inertia by girder type and span

Span PCI Bridge Design Manual I girder Box girder WPC girder Average25m

065

051 mdash mdash 05130m 049 054 053 05235m 052 056 050 05340m mdash 057 054 056Average 065 051 056 052 053

Table 5 Proposed multipliers

Without topping With toppingAt erection(1) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt(e) 1 + 17rt(e)

(2) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(e)(1minus 015rt(e)) 1 + 17rt(e)(1minus 015rt(e))

At certain time(3) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt 1 + 08rt(c) + 09rt

(4) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(1minus 015rt) 1 + 08rt(c)(1minus 015rt(c)) + 09rt(1minus 015 times rt)

(5) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 1 + 20r[tminust(s)] 1 + 20r[tminust(s)]

(6) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 1 + 106r[tminust(c)]

Final(7) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

270 19 + 08rt(c)

(8) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

245 1765 + 08rt(c)(1minus 015rt(c))

(9) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 300 300

(10) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 206

6 Advances in Civil Engineering

materials are the same as concrete and PS steel actually usedfor bridges A and B -e structural members of the bridgeswere modeled based on structural calculations and designdrawings of bridges A and B According to the designdrawing the strands were arranged by setting the actualcoordinates of the strand on the girder nodes using the 3-Dinput type from tendon profile option of MIDAS Civil -eCEB-FIP MC90 model [5] was used to calculate creep anddrying shrinkage of concrete For the relaxation of thetendon the Magura 45 model was used to consider thetime-dependent loss of the prestress Based on the con-struction history of the bridges A and B in Table 6construction sequence analysis was carried out After thecast of deck composite behavior of the girder and the deckwas simulated through the node connection using the rigidtype of elastic link In the same way common duct which isthe additional superimposed dead load was also simulatedfor composite behavior after its installation At the finalstage the deformation patterns of bridges A and B areshown in Figure 4 As a result the bridges A and B in themidspan showed 324mm and 393mm of camber at girdererection and 297mm and 192mm of camber at finalrespectively

53 Comparison of Predictions of Long-Term DeformationTables 8 and 9 and Figure 5 show the predictions of the long-term deformation of bridges A and B by using the proposedmultipliers the basic PCI multipliers [18] the improved PCImultipliers [20] KR C-08090 [1] and numerical analysisFor the improved PCI multipliers [20] the average values inTable 2 were used because the actual creep coefficient and theamount of the prestress loss can hardly be known

Although the values of predictions by the proposedmultipliers and KR C-08090 [1] were somewhat different

from the prediction by numerical analysis their predictiontrends of the camber over time were generally similar be-cause they provided available multipliers at any time In thecase of the basic PCI multipliers [18] however the long-term behavior after the erection was quite different fromother prediction methods because there are no applicablelong-term factors for the period between the erection andthe final

-e girder of bridge A was erected on the 30th day aftercasting while the girder of bridge B was erected on the 150thday relatively long time after casting -e basic PCI

1025 90 420 90 1025

2650

120

100

110

2670 30

00

150

2250

600

220

95 600150

2190

60600

3000

600

1040 110 695110695

(a)

400 200 4001000

2600

150

120

1950

180

200

2600

200 350350

900

(b)

Figure 3 Cross-sectional details of bridges (a) A and (b) B

Table 6 Construction history of bridges A and B

EventTime from casting (days)Bridge A Bridge B

(1) Release 1 1(2) Erection (t(e)) 30 150(3) Topping (t(c)) 240 157(4) 1st random time (t1) 270 180(5) Superimposed dead load (t(s)) 390 360(6) 2nd random time (t2) 700 1000

(7) Final 5 years ormore

5 years ormore

Table 7 Elastic camber and deflection of bridges A and B

LoadCamber (+) or deflection (minus)Bridge A Bridge B

Self-weight minus223 minus165Prestressing force +461 +353Topping minus80 minus75Superimposed dead load minus25 minus265

Advances in Civil Engineering 7

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

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thickness the assumptions for composite members in thePCI Bridge Design Manual [18] are not likely to reflectmodern bridge characteristics -erefore in this study themultipliers for the long-term behavior of composite memberwere proposed by analyzing the representative cross sectionsof the recent bridges

Currently girder sections commonly used in single-spanrailway bridges in Korea are I girder box girder and WPC(wide flange prestressed concrete) In general a thickness ofslab placed on the girder is 280mm Figure 2 and Table 3show the details of the cross sections of I girder box girderand WPC which are the representative girder sections ac-tually used in practice Table 4 shows IoIc for all cross

sections of Figure 2 and Table 3 As shown in Table 4 thevalue of IoIc is different from 065 of the PCI Bridge DesignManual [18] IoIc was in the range of 051 to 056 and boxgirder bridges and long span bridges tend to have relativelylarge IoIc For the convenience of design this study pro-posed to use the total average value of 053 for IoIc

-e PCI Bridge Design Manual [18] assumed that thesection becomes composite at about the time of erectionbut it is not always Rather there are many cases wheretopping is not applied when the girder is erected because offield condition and construction schedules -ereforemultipliers have been proposed to enable the prediction ofdeflection and camber of the composite member at anytime t by considering the time t(c) at which the sectionbecomes composite -is can be expressed as follows using(7)ndash(10)

1 + μdtc 1 + μdt(c) + μdt minus μdt(c)1113872 1113873Io

Ic1113888 1113889

1 + μptc 1 + μpt(c) + μpt minus μpt(c)1113872 1113873Io

Ic1113888 1113889

(16)

where IoIc is 053-e factor for long-term deflection by a composite

topping should be also modified by the ratio of IoIc becausethe elastic deflection caused by the placement of the toppingto which the factor is applied is calculated using the non-composite section as follows

1 + μtt 1 + μsdtIo

Ic1113888 1113889 (17)

where μtt is the factor for additional long-term deflectioncaused by topping at any time t

As a result the multipliers of the PCI Bridge DesignManual [18] in Table 1 were revised as shown in Table 5

ed

ifg

h

b c ba

j k jl

(a)i

c b

j

da

cb

kl

m

nopq

o

g

n

he f

(b)

p

cb

m

n

q r

de

f

i j kg

lh g

k j i

o

a

(c)

Figure 2 Typical cross sections of PSC bridges (a) I girder (b) box girder (c) WPC girder

Table 3 Cross section dimension of I box and WPC girders byspan (mm)

Type I girder Box girder WPC girderSpan 25m 30m 35m 30m 35m 40m 30m 35m 40m 1000 1000 1000 1200 1200 1200 3580 3580 2650 400 400 400 220 220 220 150 150 150 200 200 200 50 50 50 100 100 100 80 150 150 660 660 660 982 1135 1514 90 120 120 2000 2400 2600 116 115 86 1520 1550 1950 1900 2300 2500 350 500 450 240 180 180 30 30 30 98 113 151 320 200 200 70 70 70 1181 1150 865 2350 2200 2600 400 350 350 730 730 370 240 350 350 50 50 50 110 110 110 200 200 200 1080 1530 1730 145 175 205 680 900 900 220 220 220 1610 1550 1280 mdash mdash mdash 250 250 250 1700 2000 2300 mdash mdash mdash 30 30 30 1450 1750 2050 mdash mdash mdash 220 220 220 135 135 135 mdash mdash mdash 760 760 760 115 115 115 mdash mdash mdash 1260 1260 1260 480 480 120 mdash mdash mdash mdash mdash mdash 250 250 250

Advances in Civil Engineering 5

5 Verification of Proposed Multipliers

In order to verify the proposed multipliers for actuallyconstructed PSC bridges the predictions of long-termcamber and deflection by the proposed multipliers werecompared with those by the basic PCI multipliers [18] theimproved PCI multipliers [20] and KR C-08090 [1] (same asACI 318-14 [2]) In addition numerical analysis was per-formed and the results were compared with the results fromother prediction methods

51 PSCBridges forVerification PSC bridges A and B whichwere recently constructed on a new line from Wonju toGangneung in Korearsquos high-speed railway were selected toverify the prediction methods Bridge A is a WPC type witha span of 388m and bridge B is constructed with an I-girdertype with a span of 34m -e cross-sectional details of thebridges at midspan are shown in Figure 3 Tables 6 and 7

show the construction history of the bridges and the elasticdeformation due to the applied load respectively

52 Numerical Analysis for Long-Term Behavior of PSCBridges Long-term behavior of the bridges A and B waspredicted using MIDAS Civil a general-purpose finite el-ement analysis program-e validity of theMIDAS Civil hasalready been confirmed through previous researches [22ndash24] In general the prediction of long-term behavior usinga finite element analysis is known to have a higher accuracythan that of the methods using a multiplier such as the PCIBridge Design Manual [18 20] although the design con-venience is poor [25ndash28] -erefore the numerical analysisresults were used to verify the newly proposed multipliers

-ematerial model was selected from the database of theMIDAS Civil program C40 and C27 were selected forthe girder and deck concrete respectively and the strandof SWPC7B empty152mm was selected for PS steel -ese

Table 4 Ratio of noncomposite to composite moments of inertia by girder type and span

Span PCI Bridge Design Manual I girder Box girder WPC girder Average25m

065

051 mdash mdash 05130m 049 054 053 05235m 052 056 050 05340m mdash 057 054 056Average 065 051 056 052 053

Table 5 Proposed multipliers

Without topping With toppingAt erection(1) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt(e) 1 + 17rt(e)

(2) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(e)(1minus 015rt(e)) 1 + 17rt(e)(1minus 015rt(e))

At certain time(3) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt 1 + 08rt(c) + 09rt

(4) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(1minus 015rt) 1 + 08rt(c)(1minus 015rt(c)) + 09rt(1minus 015 times rt)

(5) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 1 + 20r[tminust(s)] 1 + 20r[tminust(s)]

(6) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 1 + 106r[tminust(c)]

Final(7) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

270 19 + 08rt(c)

(8) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

245 1765 + 08rt(c)(1minus 015rt(c))

(9) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 300 300

(10) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 206

6 Advances in Civil Engineering

materials are the same as concrete and PS steel actually usedfor bridges A and B -e structural members of the bridgeswere modeled based on structural calculations and designdrawings of bridges A and B According to the designdrawing the strands were arranged by setting the actualcoordinates of the strand on the girder nodes using the 3-Dinput type from tendon profile option of MIDAS Civil -eCEB-FIP MC90 model [5] was used to calculate creep anddrying shrinkage of concrete For the relaxation of thetendon the Magura 45 model was used to consider thetime-dependent loss of the prestress Based on the con-struction history of the bridges A and B in Table 6construction sequence analysis was carried out After thecast of deck composite behavior of the girder and the deckwas simulated through the node connection using the rigidtype of elastic link In the same way common duct which isthe additional superimposed dead load was also simulatedfor composite behavior after its installation At the finalstage the deformation patterns of bridges A and B areshown in Figure 4 As a result the bridges A and B in themidspan showed 324mm and 393mm of camber at girdererection and 297mm and 192mm of camber at finalrespectively

53 Comparison of Predictions of Long-Term DeformationTables 8 and 9 and Figure 5 show the predictions of the long-term deformation of bridges A and B by using the proposedmultipliers the basic PCI multipliers [18] the improved PCImultipliers [20] KR C-08090 [1] and numerical analysisFor the improved PCI multipliers [20] the average values inTable 2 were used because the actual creep coefficient and theamount of the prestress loss can hardly be known

Although the values of predictions by the proposedmultipliers and KR C-08090 [1] were somewhat different

from the prediction by numerical analysis their predictiontrends of the camber over time were generally similar be-cause they provided available multipliers at any time In thecase of the basic PCI multipliers [18] however the long-term behavior after the erection was quite different fromother prediction methods because there are no applicablelong-term factors for the period between the erection andthe final

-e girder of bridge A was erected on the 30th day aftercasting while the girder of bridge B was erected on the 150thday relatively long time after casting -e basic PCI

1025 90 420 90 1025

2650

120

100

110

2670 30

00

150

2250

600

220

95 600150

2190

60600

3000

600

1040 110 695110695

(a)

400 200 4001000

2600

150

120

1950

180

200

2600

200 350350

900

(b)

Figure 3 Cross-sectional details of bridges (a) A and (b) B

Table 6 Construction history of bridges A and B

EventTime from casting (days)Bridge A Bridge B

(1) Release 1 1(2) Erection (t(e)) 30 150(3) Topping (t(c)) 240 157(4) 1st random time (t1) 270 180(5) Superimposed dead load (t(s)) 390 360(6) 2nd random time (t2) 700 1000

(7) Final 5 years ormore

5 years ormore

Table 7 Elastic camber and deflection of bridges A and B

LoadCamber (+) or deflection (minus)Bridge A Bridge B

Self-weight minus223 minus165Prestressing force +461 +353Topping minus80 minus75Superimposed dead load minus25 minus265

Advances in Civil Engineering 7

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

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Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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wwwhindawicom Volume 2018

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5 Verification of Proposed Multipliers

In order to verify the proposed multipliers for actuallyconstructed PSC bridges the predictions of long-termcamber and deflection by the proposed multipliers werecompared with those by the basic PCI multipliers [18] theimproved PCI multipliers [20] and KR C-08090 [1] (same asACI 318-14 [2]) In addition numerical analysis was per-formed and the results were compared with the results fromother prediction methods

51 PSCBridges forVerification PSC bridges A and B whichwere recently constructed on a new line from Wonju toGangneung in Korearsquos high-speed railway were selected toverify the prediction methods Bridge A is a WPC type witha span of 388m and bridge B is constructed with an I-girdertype with a span of 34m -e cross-sectional details of thebridges at midspan are shown in Figure 3 Tables 6 and 7

show the construction history of the bridges and the elasticdeformation due to the applied load respectively

52 Numerical Analysis for Long-Term Behavior of PSCBridges Long-term behavior of the bridges A and B waspredicted using MIDAS Civil a general-purpose finite el-ement analysis program-e validity of theMIDAS Civil hasalready been confirmed through previous researches [22ndash24] In general the prediction of long-term behavior usinga finite element analysis is known to have a higher accuracythan that of the methods using a multiplier such as the PCIBridge Design Manual [18 20] although the design con-venience is poor [25ndash28] -erefore the numerical analysisresults were used to verify the newly proposed multipliers

-ematerial model was selected from the database of theMIDAS Civil program C40 and C27 were selected forthe girder and deck concrete respectively and the strandof SWPC7B empty152mm was selected for PS steel -ese

Table 4 Ratio of noncomposite to composite moments of inertia by girder type and span

Span PCI Bridge Design Manual I girder Box girder WPC girder Average25m

065

051 mdash mdash 05130m 049 054 053 05235m 052 056 050 05340m mdash 057 054 056Average 065 051 056 052 053

Table 5 Proposed multipliers

Without topping With toppingAt erection(1) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt(e) 1 + 17rt(e)

(2) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(e)(1minus 015rt(e)) 1 + 17rt(e)(1minus 015rt(e))

At certain time(3) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

1 + 17rt 1 + 08rt(c) + 09rt

(4) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

1 + 17rt(1minus 015rt) 1 + 08rt(c)(1minus 015rt(c)) + 09rt(1minus 015 times rt)

(5) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 1 + 20r[tminust(s)] 1 + 20r[tminust(s)]

(6) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 1 + 106r[tminust(c)]

Final(7) Deflection (downward) componentmdashapply to theelastic deflection due to the member weight attransfer of prestress

270 19 + 08rt(c)

(8) Camber (upward) componentmdashapply to theelastic camber due to prestress at the time of transferof prestress

245 1765 + 08rt(c)(1minus 015rt(c))

(9) Deflection (downward)mdashapply to elasticdeflection due to superimposed dead load only 300 300

(10) Deflection (downward)mdashapply to elasticdeflection caused by the composite topping mdash 206

6 Advances in Civil Engineering

materials are the same as concrete and PS steel actually usedfor bridges A and B -e structural members of the bridgeswere modeled based on structural calculations and designdrawings of bridges A and B According to the designdrawing the strands were arranged by setting the actualcoordinates of the strand on the girder nodes using the 3-Dinput type from tendon profile option of MIDAS Civil -eCEB-FIP MC90 model [5] was used to calculate creep anddrying shrinkage of concrete For the relaxation of thetendon the Magura 45 model was used to consider thetime-dependent loss of the prestress Based on the con-struction history of the bridges A and B in Table 6construction sequence analysis was carried out After thecast of deck composite behavior of the girder and the deckwas simulated through the node connection using the rigidtype of elastic link In the same way common duct which isthe additional superimposed dead load was also simulatedfor composite behavior after its installation At the finalstage the deformation patterns of bridges A and B areshown in Figure 4 As a result the bridges A and B in themidspan showed 324mm and 393mm of camber at girdererection and 297mm and 192mm of camber at finalrespectively

53 Comparison of Predictions of Long-Term DeformationTables 8 and 9 and Figure 5 show the predictions of the long-term deformation of bridges A and B by using the proposedmultipliers the basic PCI multipliers [18] the improved PCImultipliers [20] KR C-08090 [1] and numerical analysisFor the improved PCI multipliers [20] the average values inTable 2 were used because the actual creep coefficient and theamount of the prestress loss can hardly be known

Although the values of predictions by the proposedmultipliers and KR C-08090 [1] were somewhat different

from the prediction by numerical analysis their predictiontrends of the camber over time were generally similar be-cause they provided available multipliers at any time In thecase of the basic PCI multipliers [18] however the long-term behavior after the erection was quite different fromother prediction methods because there are no applicablelong-term factors for the period between the erection andthe final

-e girder of bridge A was erected on the 30th day aftercasting while the girder of bridge B was erected on the 150thday relatively long time after casting -e basic PCI

1025 90 420 90 1025

2650

120

100

110

2670 30

00

150

2250

600

220

95 600150

2190

60600

3000

600

1040 110 695110695

(a)

400 200 4001000

2600

150

120

1950

180

200

2600

200 350350

900

(b)

Figure 3 Cross-sectional details of bridges (a) A and (b) B

Table 6 Construction history of bridges A and B

EventTime from casting (days)Bridge A Bridge B

(1) Release 1 1(2) Erection (t(e)) 30 150(3) Topping (t(c)) 240 157(4) 1st random time (t1) 270 180(5) Superimposed dead load (t(s)) 390 360(6) 2nd random time (t2) 700 1000

(7) Final 5 years ormore

5 years ormore

Table 7 Elastic camber and deflection of bridges A and B

LoadCamber (+) or deflection (minus)Bridge A Bridge B

Self-weight minus223 minus165Prestressing force +461 +353Topping minus80 minus75Superimposed dead load minus25 minus265

Advances in Civil Engineering 7

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

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AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

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Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

materials are the same as concrete and PS steel actually usedfor bridges A and B -e structural members of the bridgeswere modeled based on structural calculations and designdrawings of bridges A and B According to the designdrawing the strands were arranged by setting the actualcoordinates of the strand on the girder nodes using the 3-Dinput type from tendon profile option of MIDAS Civil -eCEB-FIP MC90 model [5] was used to calculate creep anddrying shrinkage of concrete For the relaxation of thetendon the Magura 45 model was used to consider thetime-dependent loss of the prestress Based on the con-struction history of the bridges A and B in Table 6construction sequence analysis was carried out After thecast of deck composite behavior of the girder and the deckwas simulated through the node connection using the rigidtype of elastic link In the same way common duct which isthe additional superimposed dead load was also simulatedfor composite behavior after its installation At the finalstage the deformation patterns of bridges A and B areshown in Figure 4 As a result the bridges A and B in themidspan showed 324mm and 393mm of camber at girdererection and 297mm and 192mm of camber at finalrespectively

53 Comparison of Predictions of Long-Term DeformationTables 8 and 9 and Figure 5 show the predictions of the long-term deformation of bridges A and B by using the proposedmultipliers the basic PCI multipliers [18] the improved PCImultipliers [20] KR C-08090 [1] and numerical analysisFor the improved PCI multipliers [20] the average values inTable 2 were used because the actual creep coefficient and theamount of the prestress loss can hardly be known

Although the values of predictions by the proposedmultipliers and KR C-08090 [1] were somewhat different

from the prediction by numerical analysis their predictiontrends of the camber over time were generally similar be-cause they provided available multipliers at any time In thecase of the basic PCI multipliers [18] however the long-term behavior after the erection was quite different fromother prediction methods because there are no applicablelong-term factors for the period between the erection andthe final

-e girder of bridge A was erected on the 30th day aftercasting while the girder of bridge B was erected on the 150thday relatively long time after casting -e basic PCI

1025 90 420 90 1025

2650

120

100

110

2670 30

00

150

2250

600

220

95 600150

2190

60600

3000

600

1040 110 695110695

(a)

400 200 4001000

2600

150

120

1950

180

200

2600

200 350350

900

(b)

Figure 3 Cross-sectional details of bridges (a) A and (b) B

Table 6 Construction history of bridges A and B

EventTime from casting (days)Bridge A Bridge B

(1) Release 1 1(2) Erection (t(e)) 30 150(3) Topping (t(c)) 240 157(4) 1st random time (t1) 270 180(5) Superimposed dead load (t(s)) 390 360(6) 2nd random time (t2) 700 1000

(7) Final 5 years ormore

5 years ormore

Table 7 Elastic camber and deflection of bridges A and B

LoadCamber (+) or deflection (minus)Bridge A Bridge B

Self-weight minus223 minus165Prestressing force +461 +353Topping minus80 minus75Superimposed dead load minus25 minus265

Advances in Civil Engineering 7

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

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Submit your manuscripts atwwwhindawicom

multiplier method [18] calculated the long-term camberusing the same multiplier for both bridges regardless of thedifferent erection time while the new proposed method useddifferent long-term multipliers for the bridges A and B inorder to consider different creep and shrinkage rates Asa result the predictions at erection by the proposed methodwere smaller for bridge A and larger for bridge B than thoseby the basic PCI multiplier method [18] as shown inFigure 5

In terms of the long-term behavior after erection thecamber predicted by KR C-08090 [1] was generally thelargest among all prediction methods KR C-08090 [1] doesnot take into account prestress loss so it overestimates thecamber by prestress force -e predictions by the proposedmethod were larger than the predictions by numericalanalysis until about 200 days after superimposed dead loadwas applied and thereafter they were smaller than thepredictions by numerical analysis

When comparing the camber at final the predictionswere large in the order of KR C-08090 [1] numericalanalysis proposed method improved PCI multipliers [20]and basic PCI multipliers [18] for both bridges A and BNumerical analysis seems to estimate the effect of creep and

shrinkage on long-term deformation weaker than othermethods In comparison with numerical analysis for de-formation at the final difference rates of the proposedmethod basic PCI multipliers [18] improved PCI multi-pliers [20] and KR C-08090 [1] were 101 259 116and 343 for bridge A respectively and 146 331143 and 350 for bridge B respectively It is interestingto note that the proposed formula and the improved PCImultiplier method [20] show very similar prediction resultsof ultimate deformation at final

Figure 6 shows the long-term behavior predicted by theproposed multipliers for each load type In early agesa relatively large amount of camber was observed due to theprestress but as time went by the rate of increase of camberby prestress decreased sharply because the amount of creepand drying shrinkage converged and the PS steel relaxationincreased -e amount of deflection due to self-weight wassmaller than the camber due to the prestress but the ten-dency of deflection over time was very similar to that ofcamber On the contrary after the girder erection a con-siderable amount of immediate deflection and long-termdeflection due to dead loads such as topping and commonduct partially offset the camber

000000e + 000270033e + 000540066e + 000810100e + 000108013e + 001135017e + 001162020e + 001189023e + 001216027e + 001243030e + 001270033e + 001297037e + 001

MIDASCivilpostndashprocessorDisplacementYZ-direction

(a)

000000e + 000175416e + 000350832e + 000526248e + 000701664e + 001877080e + 001105250e + 001122791e + 001140333e + 001157874e + 001175416e + 001192958e + 001

MIDASCivilpostprocessorDisplacementYZ-direction

(b)

Figure 4 Analysis result of final deformation of bridges (a) A and (b) B

8 Advances in Civil Engineering

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

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AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

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Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

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Electrical and Computer Engineering

Journal of

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Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

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International Journal of

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Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Tabl

e8

Predictio

nsby

variou

smetho

dsforbridge

A(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus2

230

176

minus3929

236

minus5265

237

minus5291

241

minus5364

245

minus5453

254minus5

665

Prestress

4610

171

7887

220

10130

221

10171

223

10284

226

10420

233

10734

Topp

ing

minus800

148

minus1180

178

minus1427

192

minus1533

206minus1

648

Superimpo

sed

dead

load

minus250

266

minus664

300minus7

50

Total

2380

3957

4066

3700

3243

2771

2671

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus2

230

185

minus4126

minus4126

minus4126

240minus5

352

Prestress

4610

180

8298

8298

8298

220

10142

Topp

ing

minus800

minus800

230minus1

840

Superimpo

sed

dead

load

minus250

300minus7

50

Total

2380

4173

3373

3123

2200

Improved

PCI

BDM

Self-weigh

tminus2

230

196

minus4371

minus4371

minus4371

288minus6

422

Prestress

4610

196

9036

9036

9036

288

13277

Prestresslossminus6

92

100

minus692

minus692

minus692

232minus1

604

Topp

ing

minus800

minus800

250minus2

000

Superimpo

sed

dead

load

minus250

250minus6

25

Total

2380

3973

3173

2923

2625

KRC-08090

Self-weigh

tminus2

230

150

minus3345

227

minus5062

230

minus5129

245

minus5464

265

minus5910

300minus6

690

Prestress

4610

150

6915

227

10465

230

10603

245

11295

265

12217

300

13830

Topp

ing

minus800

150

minus1200

215

minus1720

250

minus2000

300minus2

400

Superimpo

sed

dead

load

minus250

235

minus588

300minus7

50

Total

2380

3570

4603

4274

3861

3720

3990

Num

erical

analysis

Total

2348

3237

3446

3240

2988

2894

2970

Advances in Civil Engineering 9

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Tabl

e9

Predictio

nsby

variou

smetho

dsforbridge

B(unitmm)

Metho

dLo

ad(1)

Release

Multip

lier

(2)

Erectio

nt(e)

Multip

lier

(3)

Topp

ing

(t(c))

Multip

lier

(4)1st

rand

omtim

e(t1)

Multip

lier

(5)

Superimpo

sed

dead

load

(t(s))

Multip

lier

(6)2n

drand

omtim

e(t2)

Multip

lier

(7)

Final

Prop

osed

multip

liers

Self-weigh

tminus1

650

226

minus3725

227

minus3744

229

minus3771

236

minus3886

242

minus3994

250minus4

120

Prestress

3530

212

7477

213

7508

214

7553

219

7740

224

7909

230

8102

Topp

ing

minus750

142

minus1065

183

minus1370

196

minus1470

206minus1

545

Superimpo

sed

dead

load

minus265

278

minus736

300minus7

95

Total

1880

3752

3014

2717

2218

1710

1642

PCIBridge

DesignManual

(BDM)

Self-weigh

tminus1

650

185

minus3053

minus3053

minus3053

240minus3

960

Prestress

3530

180

6354

6354

6354

220

7766

Topp

ing

minus750

minus750

230minus1

725

Superimpo

sed

dead

load

minus265

300minus7

95

Total

1880

3302

2552

2287

1286

Improved

PCI

BDM

Self-weigh

tminus1

650

196

minus3234

minus3234

minus3234

288minus4

752

Prestress

3530

196

6919

6919

6919

288

10166

Prestresslossminus5

30

100

minus530

minus530

minus530

232minus1

228

Topp

ing

minus750

minus750

250minus1

875

Superimpo

sed

dead

load

minus265

250minus6

63

Total

1880

3155

2405

2140

1648

KRC-08090

Self-weigh

tminus1

650

210

minus3465

211

minus3482

220

minus3630

240

minus3960

280

minus4620

300minus4

950

Prestress

3530

210

7413

211

7448

220

7766

240

8472

280

9884

300

10590

Topp

ing

minus750

150

minus1125

220

minus1650

275

minus2063

300minus2

250

Superimpo

sed

dead

load

minus265

265

minus702

300minus7

95

Total

1880

3948

3217

3011

2597

2499

2595

Num

erical

analysis

Total

1792

3926

2866

2536

2138

1954

1923

10 Advances in Civil Engineering

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Consequently the proposed multipliers method pro-vided not only the closest prediction values but also themost similar long-term behavior trend to the numericalanalysis

6 Conclusions

Since the current PCI Bridge Design Manual [18] providesthe long-term deformation multipliers only at erection andfinal it cannot consider various construction processesFurthermore the multipliers for the composite cross sectionare also required to be modified to reflect the characteristicsof the cross section used in modern PSC bridges -ereforein this study newmodified PCImultipliers were proposed toovercome these problems -e conclusions drawn from thisstudy are as follows

(1) -e new modified PCI multipliers were proposed byusing the rate of creep and shrinkage over timeUnlike the existing PCI Bridge Design Manual [18]method it is possible to reflect the actual girdererection time and predict the long-term deformationfor any construction schedule Moreover throughthe new method camber and deflection of PSCbridges can be predicted at any time including designstage construction stage and use stage

(2) -e ratio of noncomposite to composite moments ofinertia IoIc was 051ndash056 as a result of analyzingrepresentative cross sections used in practice byspan while the PCI Bridge Design Manual [18]suggests 065 of IoIc-erefore it is suggested to usethe average value of 053 for IoIc in order to predictthe long-term behavior of composite members

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

PS forceSelf-weight

ToppingAdditional DL

(a)

ToppingPS forceSelf-weight Additional DL

0

ndash80

ndash60

ndash40

ndash20

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 6 Predictions by the proposed multipliers for each load type (a) Bridge A (b) Bridge B

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

(a)

Proposed multiplierPCI BDMImproved PCI BDM

KR C-08090Numerical analysis

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mid

span

cam

ber (

mm

)

Time aer casting (days)

(b)

Figure 5 Comparison of various predictions for bridges (a) A and (b) B

Advances in Civil Engineering 11

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(3) In order to verify the proposed multipliers for ac-tually constructed PSC bridges the predictions oflong-term camber and deflection by the proposedmultipliers were compared with those by the basicPCI multipliers [18] improved PCI multipliers [20]KR C-08090 [1] and numerical analysis As a resultKR C-08090 [1] predictions were significantly higherthan the other predictions and the basic PCI mul-tipliers [18] did not show a reasonable tendency inthe long-term behavior between the erection timeand the final Among all methods except the pro-posed method the improved PCI multipliers [20]showed the most similar predictions to the nu-merical analysis However this improved PCImultiplier method also has limitations in finding thelong-term deflection or camber of the bridge at anytime and there are several variables such as the creepcoefficient that must be known precisely in order touse the multipliers which is inconvenient for de-signers to use However the predictions through thenewly proposed multipliers showed a reasonablelong-term behavior trend and the amount of thefinal camber was also the most similar to the nu-merical analysis result Above all the proposedmethod can make it possible for the designer topredict the long-term behavior of the bridge veryeasily according to any construction schedule

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by a grant (17RTRP-B067919-05) from Railroad Technology Research Program funded byMinistry of Land Infrastructure and Transport of Koreangovernment

References

[1] Korea Rail Network Authority Railway Design Guidelines andHandbooks Bridge Concrete Track Ends Usability Review (KRC-08090) in Korean Korea Rail Network Authority DaejeonRepublic of Korea 2014

[2] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[3] ACI Committe 209 Prediction of Creep Shrinkage andTemperature Effects in Concrete Structure American ConcreteInstitute Farmington Hill MI USA 1992

[4] AASHTO (American Association of State Highway andTransportation Officials) AASHTO LRFD Bridge DesignSpecifications AASHTO Washington DC USA 2007

[5] CEBFIP Model Code Comit Euro-International du BetonTelford Ltd London UK 1990

[6] H-G Kwak and Y-J Seo ldquoLong-term behavior of compositegirder bridgesrdquo Computers and Structures vol 74 no 5pp 583ndash599 2000

[7] H Yang ldquoUncertainty and updating of long-term predictionof prestress forces in PSC box girder bridgesrdquo Computers andStructures vol 83 no 25ndash26 pp 2137ndash2149 2005

[8] S Biswal and A Ramaswamy ldquoUncertainty based modelaveraging for prediction of long-time prestress losses inconcrete structuresrdquo Construction and Building Materialsvol 153 pp 469ndash480 2017

[9] W He and Z Zhang ldquoModeling creep fracture in rock byusing kelvin discretized virtual internal bondrdquo Advances inCivil Engineering vol 2018 Article ID 8042965 8 pages 2018

[10] Y-S Park Y-H Lee and Y Lee ldquoDescription of concretecreep under time-varying stress using parallel creep curverdquoAdvances in Materials Science and Engineering vol 2016Article ID 9370514 13 pages 2016

[11] Z Pan and S Meng ldquo-ree-level experimental approach forcreep and shrinkage of high-strength high-performanceconcreterdquo Engineering Structures vol 120 pp 23ndash36 2016

[12] H-G Kwak and Y-J Seo ldquoNumerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girderbridgesrdquo Construction and Building Materials vol 16 no 1pp 49ndash63 2002

[13] I N Robertson ldquoPrediction of vertical deflections for a long-span prestressed concrete bridge structurerdquo EngineeringStructures vol 27 no 12 pp 1820ndash1827 2005

[14] T Lou S M R Lopes and A V Lopes ldquoA finite elementmodel to simulate long-term behavior of prestressed concretegirdersrdquo Finite Elements in Analysis and Design vol 81pp 48ndash56 2014

[15] P Liu Q Xing DWang andM Oeser ldquoApplication of linearviscoelastic properties in semianalytical finite element methodwith recursive time integration to analyze asphalt pavementstructurerdquo Advances in Civil Engineering vol 2018 Article ID9045820 15 pages 2018

[16] A Sagara and I Pane ldquoA study on effects of creep andshrinkage in high strength concrete bridgesrdquo Procedia En-gineering vol 125 pp 1087ndash1093 2015

[17] H Sousa J Bento and J Figueiras ldquoConstruction assessmentand long-term prediction of prestressed concrete bridgesbased on monitoring datardquo Engineering Structures vol 52pp 26ndash37 2013

[18] PCI Bridge Design Manual Second Release PrecastPrestressed Concrete Institute Chicago IL USA 3rd edi-tion 2014

[19] L D Martin ldquoA rational method for estimating camber anddeflection of precast prestressed membersrdquo PCI Journalvol 22 no 1 pp 100ndash108 1977

[20] PCI Bridge Design Manual PrecastPrestressed ConcreteInstitute Chicago IL USA 2nd edition 2003

[21] M K Tadros A Ghali and A W Meyer ldquoPrestressed lossand deflection of precast concrete membersrdquo PCI Journalvol 30 no 1 pp 114ndash141 1985

[22] Y Zhang ldquoOrthogonal test analysis on influencing factors ofprestressed concrete small box beam camberrdquo Applied Me-chanics and Materials vol 405-408 pp 1527ndash1530 2013

[23] Y Jianjun W Xun and H Xianzheng ldquoEffects of live load onthe deflection of long-span PC continuous rigid-framehighway bridge based on midasrdquo in Proceedings of 20147th International Conference on Intelligent ComputationTechnology and Automation pp 944ndash946 Changsha China2014

12 Advances in Civil Engineering

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[24] T Grigorjeva A Juozapaitis and Z Kamaitis ldquoStatic analysisand simplified design of suspension bridges having variousrigidity of cablesrdquo Journal of Civil Engineering and Man-agement vol 16 no 3 pp 363ndash371 2011

[25] ACI Committee 435 Control of Deflection in ConcreteStructures ACI 435R-95 ACI Farmington Hills MI USA2003

[26] F B Angomas ldquoBehavior of prestressed concrete bridgegirdersrdquo All Graduate -eses and Dissertations Utah StateUniversity Logan UT USA 2009

[27] E H Gheitanbaf ldquoImproving the prediction of time-dependent effects on prestressed concrete bridgesrdquo Gradu-ate-eses and Dissertations Iowa State University Ames IAUSA 2015

[28] M K Tadros F Fawzy and K Hanna ldquoPrecast prestressedgirder camber variabilityrdquo PCI Journal vol 56 no 1pp 135ndash154 2011

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom