5I

Deflections and Camber Loss in Heat-Curved GirdersMARVIN H. HILTON

ABSTRÀCT

To check the camber loss in heat-curvedgirders, a 140-ft, simpty supported span wasinstrumented iluring the constructÍon of abridge. The span was composed of four steelplate girders that have radii of curvaturevarying fro¡n 802.51 ft on the insíde to834.51 ft on the outside of the alignmentcurvature. cirder deflection and camberloss wêre measured before and after con-struction of the briclge deck. Sone loss inca¡nber from construction loading occurredshortly after placenent of the concretedeck. The amount of loss, however, was onlyone-fourth of that deternined fro¡¡ theÀASHTO equatÍon for predicting such loss.In addition, no significant canber losseswere caused by service loading over a 6.5-nonth period subseguent to construction.

The construct.ion of a nu¡nber of curved girderbridges during the past few years has given rise toat least one question relating to the fabrication ofthe steel girders. This involves the requirementthat additional canber be provided in steel girdersthat are to be heat curved. This additional canberis to al1oe, for subsequent losses frotn the dissipa-tion of residual stresses irnposed by the heat-curv-íng process during fabrication of the girders. TheAÀSIITO specifications suggest that âpproxítnaèely 50percent of the camber loss relating to the heat-curving process occurs during construction of thebridge, and an additional 50 percent occurs after afew months under service loading (1). Therefore,the increase in ca¡nber should be included in bridgeforming duríng construction, and after eonstructionis compì.ete the bridge profile should be higher thanthe plan grade between the supports. If the addi-tional camber ís lost as suggested by the AASHTOspecifications, then the final profile should be at-tained after several nonths of traffic loading.

Many bridge engineers and steel fabricators, how-ever, question whether the additional canber is nec-essåry. The fabrícators would prefer that they notbe required to provide the additional eamber inheat-curved girders because, in ¡nost cases, this addsto the time and expense of fabrication. To deter-nine the nature of the deflections and canber lossin a heat-curved girder bridge, one bridge sas in-strumented and measurements were taken both duringand after construction. The camber losses neasureddo not ínclude those that nay have occurred betereenthe steel fabrication plant and the job site, orthose that nay have occurred before placenent of theinstrumentation on the structure.

STRUCTURE STUDIED

À curved girder bridge consisting of three simplysupported spans, two of them relatively short at 36and 18 ft, and the third 140 ft, was studied duringits construction. All the tneasurements, however,were confined to the 140-ft span. A general view ofthe curvature of the steel gírders is shown inFigure l.

FIGURE I View showing curvature in the girders and design ofdiaphragms and lateral cross bracing.

The bridge has four steel-plate girders spaced at10 ft, 8 in. on center. The girders of the 140-ftspan are connected by truss-tlT)e diaphragms, andlateral cross bracing is used on the exterior bays,as illustrated in Fígure 1. The glrders r+ere fabri-cated from 4588 steel and were heat treated to ob-tain the requíred degree of curvature. They arecurved on radii varying fro¡¡ 802.5I ft on the insiileto 834.51 ft on the out,side of the alignment curvâ-ture. On the centerline of the bridge the alignmentis equal to a 7-degree highway curve.

INSTRT'I.{ENTATION, TESTS, AND PROCEDUF.ES

Girder and Bearing Deflection Instrunentation

Because some of the deftection increnents to be tnea-sured were expected to be on the order of hundre¿lthsof an inch, a high preclsion, ¡nodífied Wild N-IIIlevel was selected for use. The level, which is¡narked in 0.001-in. incrernents, was rnounted on atrivet set in stationary bronze lugs on the top ofthe pier cap at the north end of the span. The lineof sight of the level was thus stightly below thebotton flanges of the girders. Special design

52

scales vrere instaLled at the nidspan points of eachgirder and adjuste¿l vertically to intersect the lineof sight of the level. To meâsure and account forpossible dead-Ioaal deflections of the bridge bear-ings, dial gauges were set as close as possible tothe centerline of bearing of each girder.

Thernal Instrunentation

Thernocouples were placeal on the top and bottonflanges at the ¡nitlspan of the glrders. They werealso placed at the quarter-span points of the giril-ers and at selecte¿l positions on the web of theg irders.

During placement of the concrete deck and parapetwêlls a 24-channel temperature recor.lle-f -s.çanned eachgauge every 12 ¡nin. Other tenperature neasuretnentswere taken before the concrete vras placed and aftereach phase of the construction was complete¿l to de-termine the effect of solar radiation on the deflec-tlon of the girders.

Tests on Plastic Concrete

Tests of the plastic concrete were restricted to themeasurerTìent of properties that would have the nostdlrect influence on the girdet deflections duringdeck placenent. These included the times of initialand fínal set, unlt weight, and temperature of theconcrete.

Procedures

The instru¡nentation was installed on the test spanwhile construction was in progress, an¿l initialreadings were taken on all systems as soon as theinstallation vras cornplete. Subsequent neasurementswêre taken cluring a full day after each major stageof construction to deter¡nine the effects of cliffer-ential thermal contlitions. With the exception ofbrief tlelays during deck placenent for taking mea-surements, the contractorrs normal procedureg wereused during constructlon.

Àfter construction was completed, the posíéionsof the deflection rods and scaleE were narked on thegirders to establísh their horizontal and verticalpositíon. Initial readings nere then taken on thevertical position of the girders, and the therno-couples were scanned to obtain data that were usedto establish the dÍfferential tenperature condl-tions. these data were then used as the basis fortneasurements of the long-tern loss in camber afterthe bridge had bêen put into service. The gaugeswere then tlisrnantled and later installed after thererìoval of the forning and painting of the struc-triral steet.

RESULTS

lhernallv Induced Deflections in Steel Sectíon

With the forming for the deck in p1ace, the l-owerportion of the steel girders are shielded from thesun. Consequently, the top flanges of the glrdersare expose¿l to solar raaliation, whereas the lowerportion is exposed to only the ambient air tenpera-ture. Because the alignnent of the bridge is in agenerally southerly to northerly direction, in theearly morning the sun strikes the web and lowerflange of the eastern girder and ln late afternoonit strikes the web and lower flange of the westernglrder. The effect ls a net thernal differentialbetween the upper and lower flanges that ilevelops aninternal moment over the cross section of eachgirder (2). The internal ¡noment causes the girderto deflect upward by an amount relating to the in-

Transportation Research Record 950

tensity of the solar radiation, time of day, and soforth. The ¿lifferential temperatures shown in Fig-ure 2 were recorcled at eight times from 7:30 a.m. to3:20 p.¡n. on a typical sunny day in early August.At 7:30 a.n. the lower flanges were war¡ner than theupper flanges for all the girclers, probably becausethey were somewhat protected fron the eletnents ¿lur-ing the night. Ilowever, with ti¡ne the upper flangesheated up. By 3:00 p.m. a maximum temperature dif-ferential of 36oF'was recorded on each of the twocenter gírdérs.

The deflections Èhat correspond to each of thereported differential ternperatures are shown in Fig-ure 3. The initial reference elevations of thegirders were recordeal at 7:30 a.n. As can be notedfro¡n these data, the rnaxinum upyrard nitlspan ileflec-tions of the girders were on the order of I.25 in.at 3:00 p.n. These ¿lata indicate that the thernaleffects on girder deflections must be taken into ac-count if there is an attempt to rneasure deflectionsthat tesult frorn loading and from sustaine¿l lossesof camber caused by deail weighè or service loads.

To determine the thermal gradients through thedepth of the girders, thernocouples were placeil onthe vrebs of girders 5, 7, and 8. One hras located atnid-depth of the web and another approxinately 2 in.below the lower slile of the top flange. The thernalgradients for girder 7 (Figure 4) indicate that thetênperature increase caused by solar radiation onthe top flange was transnitted downward through theweb. Thus any calculations perforned to deter¡ninethermal deflections nust consider that the upperportion of the web above the neutral axis partici-pates in the ¿levelopment of the forces and ¡nonents.In some instances, as the data in Figure 4 suggest,a portion of the web belo\r the neutral axis waswarner than the lower flanges of the girders.

For the bridge tested ln this study, the plategirder design incorporates changes in the nornent ofinertia at points of íncreasing flange plate thlck-ness. This. in additlon to the action of the rigiddiaphragn connections beÈrdeen the giders, creates acomplex systen. The rigid diaphragm connectionscause the thernally related deflections to be dis-tributed across the width of the span, as indicatedby the data in Figure 3. Because the 3:00 p.m.thernal deflection data e¡ere nore unifornly distrib-uted across the span width, theoretical calculationshrere nade to determine the agreernent with the fieltlresuLts. The calculated deflections were base¿l onthe following relationship:

F= AEq^T (l)

where

F = force developed by expansion of Èhe heatedsteel,

A = area of the section above the neutral axis,E = modulus of elasticíty of steel,o = thermal coefficient of expansion for steel,

andAT = difference in tenperature betneen the upper

and lower flanges.

Because the internal ¡nomenÈ ln the girder is de-veloped by the proaluct of the force and the distanceto the neutral axis, the deflection (¿) is

A = (Aa^TdL'?)/sI (z)

where

d = distance from the force center to the neutralaxis,

L = length of span, andI = noment of inertia.

IIIIú

l0rl0 a.m.

,o

âotJd!oÉotr

8iq0 a.n.

7:35 å.n.

Plus differentialMinus diffe¡ential

Girder Nunber

- top flange warmer

- botton fÌange warmer

llest

1.50

É

!11ItÀÐ

Éo

oo

0aÉóeI!

=

12¡00 m

ll:20 å.n.

G-8

East

FIGURE 2 Temperature differential between top and bottom flanges of curvedgirder span with deck forming in placet before deck placement.

I I IG-6

TI

_l_

¡. oo

0.75

0.50

0.25

0

ciPder ñuber West

FIGURE 3 Upward deflections at midrpan of curved girder span resulting from solarradiation; deck forming shielded lower portion of girders from eun.

7 | 30 a,n. Refe

7:30 a.Þ.

54

G_7 600 7 0o 80o 90oTemperature, oF.

Transportation Research Record 950

I000 1100 1200

the concrete haal been place¿l on the span anal thetemperature on the top flanges began to drop rela-tive to that on the lower flanges. By 2224 p.rn. thetemperature differential betr.¡een the flanges wasslight, and the span was, for all practical pur-poses, in a thernally neutral state.

Figure 5 shows the deflections of the girders atthe various stages of concrete placement. These de-flections existed at the stage of concrete placementindicated on the graph and incluile any amount eausedby lhermal differentíal-s. At 11:25 a.m., approxi-mately 5 hr after the beginning of placement, all ofLhe concrete eras in the forms. At that timê, how-ever, the top flanges were warmer than the lower, soit could be expecteil that a counter-¿leflection up-vrard exísted. Therefore, additional deflection ¡nea-surernents were taken at 2:45 and 3:20 p.n., when thespan was close to a thernally neutral position. Aswould be expected, the downward deflection wasgreater at these tines, although the dead load onthe girders renained unchanged fron that which hadexísted at 1I:25 a.m. Àpplying the corrections pre-vÍously díscussed to account for the initial thernaldífferentials yieLded the final thermally neutraldead-load deflections that resultetl fro¡n the vreightof the concrete deck. These final values are shownby the lower curve in Figure 5 and are reported ínTable 1.

Before calculating the thernal corrections forthe deflection data, it was necessary to considerthe setting time of the concrete. ThÍs is an inpor-tant consideration because once the concrete beginsto set, sone degree of conposite action between theconcrete and steel begins. To determine the timesof initial and final set, t¡{o sanples--one at thebeginning and one nidway through the placernent oper-ation--were tested by using ASTI4 C403-68 proce-dures. It was found that the time of final set $râsapproxirnately 5:45 p.n. for the first concreteplaced on the span. For the concrete located in themiclspan region, the final set occurred at 10:30p.m. Based on these data, no composite actionbetween the steel gÍrders and concrete could be ex-pected at 3:20 p.n., when the last cleflection nea-surements were recorded. Accordingly¡ aII caLcula-tions to determine thermal corrections to the gírderdeflections that occur during ileck placenent arebased on the section modulus of the steel actiononly. Corrections to the deflections rneasured sub-sequent to the final set of the concrete, as dis-cussed later, must be calculateal based on sone de-gree of conposite action betr,¡een the girders and theconcrete deck.

SÕne slight rnovenents of the bearing assenblies¿lid occur during the placement of the concretedeck. The average final deflections, or settle-ments, in the bearÍngs at the north an¿l south endsof the span are given ln Table l. As would be ex-pected, the placernent of the concrete caused so¡nedownward settlement of the bearings. These average

FIGURE 4 Thermal gradients through the depth of girder 7 caused by solarradiation; deck forming fur place.

By using the nidspan propertles of the sÈeel sec-tion, the thermal ¿leflections calculated fron Equa-tion 2 ¡rere within less than I percent of the ther-mal deflections ¡neasured ín the field at 3:00 p.m.in early August. Thus Equation 2 gives a reasonablysatisfactory estimate of the defLections caused bydifferential temperatures that arè relatively uni-forn across the width of the span.

Dead-Load Deflections ín Steel Section

Reinforcing-Stee1 Placernent

The first deadweight loading on the span (excludingthe deck forming) was the reinforcing stee1. Tem-perature neasurements and deflection readings takenon the girders before placenent of the ¿leck concreter¡¡ere compared with the initial" readings taken ap-proxinately 12 days earlíer. The thernal ëlifferen-tials were the sane for these two periods except fora 0.5oF difference on two of the girders. By usingEquation 2 and applying a correctíon to the measureddeflections for thosê tr,ro girders, the ther¡nal dif-ferentials were neutralized. The resulting deflec-tions thus reflected only the downward movenentcaused by the deadweight of the reinforcing steel.The nidspan dead-Ioad deflections that result fromthe weight of the reinforcing steel were on theorder of 0.15625 in. (Table 1).

TABLE I l\{idspan Dead-Load Deflections of Steel Girders Causedby Placement of Deck Reinforcing Steel and Concrete

Midspan Dead-Load Deflection (in.) by cirder

Loading G-'l G-6G-8 G-.5

Reinforcing steeÌ 0.144Concrete 2.494Steel plus concrete 2.638Bearing settlement - 0.01 8

0.1 652.5682.'7 33

- 0.007

2.',l26

3.7 5+l

0.1 7l2.6622.833

- 0.012

2.82t

o.2092.6902.899

- 0.002

2.897Total

Plan valuesDifference

2.620

3.625+l

3.25 3.37 5+0.437 5 +0.46875

Note: Thermally neutral deflections.

Concrete Deck Placement

Concrete was placed on the 140-ft span beginning at6:30 a.rn. on August 21. At the beginning of thedeck place¡nent the temperature on the steel girdersindicated thät they were not in a therr¡ally neutralposition. Beeause the lower flanges vrere vrarrnerthan the top flanges, the girders were initially de-flected downward. As the day r.rent by, the tenpera-ture differential between the top and botton flangeschanged. By 10:00 a.m. the upper flanges \derewarner thân the J.ower flanges, but by l1:J.5 a.n. all

HÍ1ton

values are thus deducted fron the girder deflectionsmeasured on conpletion of the placement of the con-crete deck.

The total measured deflectÍons of the curvedgirders caused by the weight of the reinforcingsteel ând concrete are given ín Table 1 and arelower than those given in the bridge plans. fn ad-dition, the rneasured defLections wère progressivelyIarger fro¡n the inside girder to the outside girder¡whereas the plan iteflections alternate fron lower tohigher values betvreen gírdèrs. This suggests thãtthe díaphragm action between the girders tends toeven out thê actual deflection patterns. It is in-teresting to note that the average of the neasureddeflections ís 2.766 in. Theoretical calculationsthat include deflections from shear forces at thediaphragms yield an average deflection of 2.77 ín.Thus, based on the average deflection, which tendsto allo}r for diaphrâgm action between girders, there\das excelÌent agreement between the measure¿l andtheoretical dead-Ioa¿l deflections.

fwo additional deflection neasurements were re-corded the day after the deck was placed. By thistime the heat of hydration of the concrete was caus-ing the top flanges of the girders to be jrarner thanthe lower flanges. Tenperature differentials on theorder of 17o to 24oF existed at 10:00 a.rn. on August22, and it was expecte¿l that the girders would be ata higher elevation at midspan than they had been at2:45 p.n. the day before. The L0:00 a.n. data inFigure 6 show this to be the case, as the deflec-tions were at that t.ime less than the therrnally neu-tral final deflections for the previous day. Thethermal deflections were calculated by using Equa-tion 2 and are shov¡n in the upper portion of Figure6. ay applying these as corrections to the measureddata of August 22, t_}]e thernally neutral defLectionsshown by the lower curve in Figure 6 were withln0.01 in. or less of those measured on the previousday. Therefore, no deflections resulting from cam-ber loss in the steel girilers occurred aluring thefirst day after the deck was placed.

55

East Girder Number llést

FIGURE 5 Downward deflections at midspan caused by placement of concrete deck.

¿

!gd3ç3ooqo'¡oo

ooÊdA

IoE

Thernally Induced Deflections and Short-TernCamber Loss in Composite Section

As discussed earlier, the data for 2zL5 p.n. on theday the concrete deck $ras cornplete¿l best represent athermalJ.y neutrå1 conditÍon of the span understudy. Therefore, these deflections and thernaldata $rere used ag a new base reference for the com-parison of the deflections resuttíng frorn subseguentthernalr dead-loading, or other conditions. Nine-teen days after conpletion of the deck adclitlonaltemperature-deflection data were recorded to ¿teter-mlne their order of rnagnitude under the new condi-tion of the concrete deck and steel girders actlngas a cornposite section. Unlike the thernaL effectsdiscusseil earlier for t'he steel sectlon onLy, thetop flanges of the girders were then protected fronthe sun, whereas the re¡¡aining portion of the glrd-ers was exposed to anbient conditions as well as todirect sotar radiation on the east side of thebrídge in the morning and on the v¡est side in theevening. fn addition, because of the composite ac-tion of the deck ancl girders, the monent of lnertiaand locatíon of the neutral axis cliffer fron thoseof the steel section only. consequently, therrnaldeflection ¿lata were coltected during a day ln earlySeptenber for two purposes: (a) to obtain data thatcould be used for rnaking thernal- corrections to allsubsequent deflection measurements that noulal be re-corded, and (b) to determine if any loss of carnberin the heât-curved girders had occurred in the 19-day period since the application of the sustalnealdead loadlng of the concrete deck and reinforcings teel.

The results of these neasurenents, given in Fig-ures 7 and 8, show the net thermal differentials be-tween the top and botton flanges of the steel andthe deflections that result fro¡n the thermal loads,respectiveLy. These data irere recorded at seventines during the day, srith thê first ¡neasurenent be-íng used as a reference. Therefore, for the thermaldata shown in Figure 7, the net tenperâtr¡re differ-

6: 30 a.n. Reference

2:45 p.m.

Final Defl.ection(Thermalty Neutral-)

Tenperature Differential, oF.

+23ôl0:00 a.n. 8,/22

(Calculated The¡na1)

Girder llunber

2:45 p.m. 8/21 and10:00 a.n. 8/22

(Thermall.y ¡;eutraL )

56

ential betseen the top and bottom flanges of eachgirder is the algebrâic dlfference bethreen the dif-ferential at 8!30 a.n. and that at the tine of thesubsequent rneasurement. In all cases measuretnentstaken subsequent to the 8:30 a.n. reference indi-catedl that the exposed lower portion of the steelgirders lras warmer than the top flanges within theconcrete deck. Net temperature dlfferentlals on theorder of llo to 14oF developed downward deflecÈionsof the conposite girdleis on the order of 0.25 in. ornore, as shown ln Flgure 8.

Because of the uneven distribution of the tenper-

Transportation Research Record 950

aturês measureil on the lower flange and web of eachgirder, it vras difficult to use Equation 2 to calcu-Late the therrnal ¿leflections of the composite sec-tion. Al"though the calculateil thernal deflectionserere reasonably close to those measufed, the ter¡Per-ature varlation within the web of each girder madeít virtualLy inpossible to assumer with a reasonabledegree of confldence, that the true effects \rere be-ing reflected in the câlculations. Therefore, theexperirnental datâ were useal for making thernal cor-rections to the composite section deflections. Todeter¡nine the dleflections that occurreil between thè

Ê

o

oo

oo

d

II'ÅE

FIGURE 6 Deflections of girders I day after deck placement, showing effect ofdifferential temperatures resulting from heat of hydration of concrete.

Girder Nunber llest

FIGURE 7 Temperature differentials between top and bottom flanges incomposite section 19 days after deck placement.

d

oIo

oo

PdI

ots

I0:¡15 a.m.l-I:45 a.

Minus differential - botton flange warner.

Hilton

completion of the deck and 19 days lâter, the de-flections that existecl at 2:45 p.m. on August 21were used as a base for cornparison with those mea-sured at 3:30 p.m. on September 9. The former data\rere setected because they were nearly thermallyneutral. The latter data, however' indicated thatthe lower flanges were apProxinately 12oF warmerthan the upper flanges. ny using the 3:30 p.m. dif-ferential temperatures fron Figure 7 and the corre-sponding cleftectíons fro¡n Figure Ir thermal correc-tions were calculatecl by proportioning. Because thedífferentiâl tenperatures were nearly the sane foreach set of datar only a snâII reduction in the 3:30p.¡n. thernal deflections had to be maile. Àfter cal-culating the corrections for the thermally induceddeflections and subtracting thesê algebraically fromthe ¡neasured changes in deflections occurring be-tr'reen August 21 and September 9, deflections ranginqfron 0.243 in. on girder 6 to 0.313 in. on girder 8

still remained. These renaining deflections re-ported in Table 2 are thus a loss of canber in thesteel girders that occurred sonetime during the 19-day period.

TABLE 2 Deflections and Camber Loss 19 Days

After Deck Replacement

Deflection and Camber Measurement (in.)

57

Girder llunberG-?

FIGURE B Dorvnward de{lections at midspan caused by differential temperatures

between top and bottom flanges of steel girders in composite section 19 days afterdeck placement.

É -0.

hd33 -0.o

o.dvo,9 -0.oAçrlÀIõ

E

a camber loss on the order of 0.25 in. for all fourg irders.

Dead-Load Deflectíons in Co¡nposite Section

Twenty-two tlays after Èhe deck vtas completed con-crete v¡as placeal for the last of the two parapetwalls. The wa1ls \{ere place¿l on different daystthus allowing for the rneasurenent of the steelgirder deflections resulting fron the weight placeclfirst on the east and then on the west sides of thebr idge.

The dead-load deflections of the gírders from theweight of both walls are given in Table 3. The netdeflection after correction for ¿lifferential tenper-atures \ras about the same for each girder' that is'approxinately 0.5 in. Conpared with the valuesgiven on the bridge pl-ans, the actual deflectiÕnswere lower on all girders except nunber 8, which was0.125 in. higher.

TABLE 3 Midspan Dead-Load Deflections of Steel

Gilders Caused by Placement of Parapet Walls

Midspan Dead-Load Deflection (in.) byGirder

Loading G-5G-6

Total The¡malGirder Measured DeflectionsNo. Deflectionsâ (corrections)

RemaininsDeflectio;b(camber loss)

0.3s 1 0.4120.183 0.094

0.s34 0.506

West wallEast wâll

Total

Plan valuesDiffe¡ence

0.0480.429

0.477

0.5

0.r690.293

o.462

G-5

G-7G-8

- 0.505- 0.504-0.501- 0.5 l0

-0.226-0.263- 0_201- o.t97

- 0.279-0.241- 0.300- 0.3 l3

0.625 0.625 0.75f0. I 5625 +0. I 25 +0.25

aDifference between 2:45 p.m. August 21, and 3:30 p m. September.9 (19 days)."AJgebraic d¡fference between measured and thermal deflections.

The camber lossr which ranges between 0.25 in.for girder 6 to 0.3125 in. for girder I' probablyoccurred within the first few days subsequent toplacement of the deck. this is substantiated by aset of deflectíon tneasurernents taken 5 days subse-quent to the placenent of the deck, which in¿licated

Note: Thermally neut¡al deflections.

Long-Term Camber Losses

with both the east and vrest parapet walls placedtthe dead loading on the test span was essentiallyconplete. Therefore, it was once again necessary tomonitor the tenperature-¿leflection characteristicsof the completed span. To allor¡ the east parapet¡ra1I concrete Èo gain sufficient stfength to be rep-resentative of that whích would be effective over

Reference 8:30 a.n.

3:30 p.m.

58

the next several ¡nonths,4 days were allowecl toelapse before the ther¡nal deflection data were re-corded. These final temperature-¿leflection datawere recorded in nicl-September, but are not reportedhere because they were similar to those data re-corded on Septernber 9. In general, however, a naxi-¡nun downward deflection on the order of 0.21 in. wasèaused by a 10oF therrnâI difference between the up-per and loÍrer flanges. Thus, for reasonably unifornilifferentiaL thdrmal conditions, a deflection of0.021 in. per degree F could be expecteil.

At the sarne time that the ilata just discussedgrere collected, initíal readings for the measurementof long-term camber loss were recorded for eachgirder. Based on the thermal deflection data, cor-reqtions were applied to these Ínitial readings toobtain a thernally neutral basis for subsequent con-par isons.

On October IO, 24 days after the initial camberreadings were taken, the bridge was opened to traf-fic. On Àpril 29 of the following year, 202 daysafter the bridge was placed in service and 226 daysafter the initial long-term camber readings $rèrerecorded, the final ca¡nber measurements gJere re-corded. By using the thermal data that were re-corded simultaneously, the final readings were cor-rected to obtain the thernally neutral position ofthe girders. Vlíth the exception of girder 5, theinitial and final readings were virtually the sane.For girders 6 , 'l , and I there !¡as a 0.01- to0.02-in. increase ín canber. Because a clifferenceof this order of magnitude is weII within the ex-pecteal experimental error involvecl in reinstallingthe deflection scales, it is reasonable to conclutlethat there was no long-tern camber loss of any prac-tical consequence in either of these girders. AL-though these data indicate that girder 5 experiencedan increase in ca¡nber of 0.I3 in., it is not likelythat this was the case. It is more likely that thisresult can be attributed to experinental error, aI-though it is higher than expected. Therefore, ít isconcluded that there rras no camber loss of any prac-tical signifícance in the span during the 226-dayperiod, which included 202 days under serviceload ing.

CAICULATED VERSUS ACTUAL CAIqBER LOSS

OF HEAT-CURVED GIRDERS

Vlhen bridge gírders are to be heat treated to obtainhorizontal curvature, the current AASHTO specifica-t;ions for highway bridges require that an additionalamount of camber be includecl in then iluring fabrica-tíon to compensate for possible losses during ser-vice as residual stresses dissipate (3). The anountof camber (inclucling that v¡hich would be needed tooffset anticipated ilead-Ioad ileflections) is givenin the specification as

A = (ADL/^m) [A* + (o.o2L2Fy/EYo)l

where

ADt = camber (in.) at any point along the length Lcalculated by usual procedures to compensatefor deflection causecl by dead loads or anyother specified loads,

A,n = maxinun value of A¡¡ (in.) within the lengÈhL,

E = no¿lulus of elasticity (ksi) ¡Fv = specifled minimu¡n yield point (ksi) of the- girder fl-ânge,Yo = distance fron the neutral axis to the ex-

treme outer fiber (in.) (¡naximum distancefor nonsymrnetrical sections), ancl

Transportation Research Record 950

L = span length (in.) for sínple spans or thedistance between a sinple end support andthe ¿lead-loacl contraflexure point forcontinuous spans.

[NoÈe¡ Part of the canber loss is attributab].e toconstruction loads and wil-I occur during construc-tion of the bridge; total cârnber loss will be com-plete aftêr several months of in-service loads.Therefore, a portion of the canber increase (approx-inately 50 percent) should be included in the bridgeprofile. Carnber losses of this nature (but gener-ally snaller ín magnitude) are also known to occurin straight bea¡ns and girders.l

Actually, onl-y the second portion of the AASHTOformula pertains to the additional canber allonancefor heat curving. This part of the relationshlp waspresented by Brockênbrough (3) in 1970 as

A. = o.o2L2FylEYo Ø)

where ôr is the residual deflection to be offseÈby an increase in vertical canber at Èhe point ofnaxi¡num dead-load canber.

Because the test structure is a simple span, themaximum dead-Ioatl ca¡nber is at nidspan. In addi-tion, the flange plate thickness changes at certainpoints along the length of the girder, which resultsin a nonsymrnetrical section. Noting that the speci-fications assurne that 50 percent of the ca¡nber lossoccurs during constructíon and the remainder occursunder service loailing, the values for additionalcanber were calculated fron Equation 4. For theconstruction loading, the steel section Yo wasused, and for the service loading the compositesection Yo was used. This resulted in separatecalculations for the construction and the serviceloadings. The calculateil ca¡nber loss values areconpared ¡¡ith the rûeasured values in Table 4.

The canber losses câlculated for the constructionloads ranged fron 1.16 to 1.20 in., with an averageof 1.19 in. for the four girders. The measured can-ber losses ranged fron 0.24 to 0.31 ln.r with an av-erage of 0.28 in.' only 24 percent of that predictedby the for¡nula. The camber losses calculated forthe service loads ranged from 0.90 to 0.95 in., withan average of 0.92 ln. for the four gírders. Asdiscussed earlier, no service load ca¡nber loss was¿letecte¿l in the fíeld.

The total canber loss calculated for the fourgirders ranged from 2.09 to 2.11 in., with an aver-age of 2.10 in. The total canber losses neasuredwere only those classified as constructlon lossesand averaged 0.28 in., only about L3 percent of theaverage of those calculated for the four girders.

It should be note¿l that the radii of curvature ofthe four gírders comprising the test span hreregreater than 800 ft, whereas those investigateil byBrockenbrough were curved to radii in the 200- to500-ft range (3). The shorter radii of curvaturevrere developetl by applying heat to a greater portionof the flange width. The relative residual verticalcurvature renaining after loading v¡as also greaterin the shorter radii girclers. Of the five girdersinvestigated by Brockenbrough, all had radii of cur-vature less than 300 ft when curveil vrith type 3 heat(one-quarter of the flange width heated) an¿l lessthan 470 ft when curveil with tlÞe 2 heat (one-sixthof the flange v¡idth heated). Brockenbroughts rela-tionship for the increase in vertical canber (Equâ-tion 4) would thus appear to be applicable to gircl-ers heat curve¿l to consi¿lerably shorter ra¿lii thanthose tested in this study. Becausê the degree ofheating and the radíus of curvature appear to be re-Iated, residual stresses and thus loss of catnber

(3)

Hilton

TABLE 4 Calculated Versus Actual Camber Loss of Heat'Curved Girders

59

Span Radius ofGirder Length CurvatureNo. (fÐ (ft)

SteelSection Yo(in.)

Construction LoadingCanber Loss (in.)

CaÌculated Actual

CompositeSection Yo(in.)

Service LoadingCamber Loss (in,)

Calculated Actual

G-5G-6G-7G-8Avg

138.45 834.51138.5 8 823.84138.72 813.18I 38.9 r 802.5 I

4t.l39.940.340.4

1.16t.20l.l91.19t.t9

0.280.240.300.310.28

49.6s2.252.553.3

0.950.910.910.90o.92

00000

Note: 4588 sleel; yield of 50 ksi. E = 29,000 ksi.

would probably be greêter in girders curved toshorter raalii.

The results of this stu¿ly suggest that the AASHTO

speciflcations relationship (Equation 4) night notbe applicable to girders heat curve¿l to radii of 800ft or greater. Consítlering the magnitude of differ-ence between the camber losses measured on the teststructure and those calculatedr Equation 4 nay notbe conpletely applicable to girders heat curvedl torâdii in the 500- to 800-ft range. In aililition' theresults suggest that the radius of curvature mightbe a factor in calculating the potential camber lossin heat-curved girders.

ST'¡iI!,TÀRY OF CONCI,USIONS

1. The results of thê study suggest that the re-tatíonship given for the calculations of the potenrtial camber loss in heat-curveil girders IarticleI-7-]-4 (c)

' AASHTo stândard specífications for High-way Bridges (À) I may not be applicable to girdersthat have radii of curvature greater than 800 ft.

2. some canber loss from construction loadingoccurred shortly after placement of the concretedeck. The amount of carnber 1oss, however, was sig-nificantly less than that which woulcl be Predictedfron the specifications. The camber loss from con-struction loads vras approxirnately one-fourth (24percent) of that determined from the AASHTO equation.

3. There was no significanÈ camber loss causedby service loading after the bridge had been in ser-vice for approxinately 6.5 rnonths.

4. The average total canber toss, including bothconstruction and service loailingr was approxirnately13 percent of that predicteil by the AASHTO equation.

5. Considering the magnitude of the dlfferencesbetrdeen the camber losses measured on the teststructure and those calculated, the AÀSnTO equationrnight not be completely applicable to gírders heatcurved to radii in the 500- to 800-ft range.

6. Because the amount of heat apPlled to thegirders ís related to the degree of curvature re-quired, the results suggest that the radius of cur-vature night be a variable that should be considereclin calculating potential canber losses.

ACKNOIII,EDGI¡TENT

The author thanks the Virginia DePartment of lligh-ways and Transportation for sponsoring this re-search. The help of Larry Ichterr graduate assis-tant, and Jímnry French¡ technician supervlsor, inconducting the field study is appreciated.

REFERENCES

1. Standartl Specifications for Highway Bridges.ÀÀSHTO, Ifashington. D.C.' 1977.

2. M.H. Hilton. À Study of Girder Deflections Dur-íng Bridge Deck Construction. Virginla llighvtayResearch Council, Charlottesviller June 197I.

3. R.t. Brockenbrough. Crlteria for Heat CurvingSteel Beans anil Girders. ASCEr Journal of thestructural Division' vol.96, No. sT10' oct.1970.

Publication of thís pøper sponsored by C,ommittee on Steel Bridges.

The opinions, fíndings, and conclusions ¡n the papet ate those oÍ the authorand not neccssarily those of the sponsoring agency.