Design of TransverselyPrestressed Concrete

Bridge Decks

Randall W. PostonAssociateSchupack Suarez Engineers, Inc.Norwalk, Connecticut

by

J R

4

John E. BreenThe Nasser I. Al-Rashid Chair

in Civil EngineeringDepartment of Civil EngineeringThe University of Texas at AustinAustin. Texas

Ramon L.CarrasquilloAssociate ProfessorDepartment of Civil EngineeringThe University of Texas at AustinAustin. Texas

68

SynopsisPrestressing of bridge decks is a

concept with potential benefits in botheconomy and improved durability.This paper summarizes the major de-sign related observations and conclu-sions from an extensive experimentaland analytical study conducted to de-velop criteria for design of durableprestressed bridge decks.

General provisions for design ofprestressed composite girder-slabbridge decks are presented. Althoughthe experimental research and testingwas directed at cast-in-place post-

tensioned decks on precast concretegirders. these provisions are valid forprestressed decks on steel girdersand panelized deck systems on eitherconcrete or steel girders.

The design provisions are pre-sented in the form of suggestedAASHTO Bridge Design Specificationchanges based on a synthesis of thefindings from both the durability andstructural phases of the study. Anexample showing the practical appli-cation of the proposed recommenda-tions is included.

CONTENTSSynopsis.......................................... 69Introduction...................................... 70Transverse Prestressing Effects ..................... 70Serviceability. Strength and Structural Integrity ......... 87DurabilityConsiderations ............................ 91OtherApplications ................................. 93Suggested Requirements for

Transversely Prestressed Bridge Decks ............. 93Suggested Specification Provisions ................... 94CostAnalyses .................................... 97Prototype Transversely Prestressed Bridge Deck ....... 98Conclusions....................................... 99DesignRecommendations .......................... 100References........................................ 101

Appendix— Design Example ........................ 102Acknowledgments.................................. 109

PCI JOURNAL'September-October 1989 69

INTRODUCTION

T his paper is the last of a three-partseries summarizing a study con-

ducted at the Ferguson Structural Engi-neering Laboratory at The University ofTexas at Austin investigating the use ofprestressing as a method of improvingbridge deck design_ The first paper'summarized the results from the dur-ability phase of the research programwhich emphasized the experimental in-vestigation of post-tensioned concretespecimens subjected to aggressive de-icing salt exposure. In the second pa-per,2 a summary of a series of interre-lated physical tests and computeranalyses which were conducted to pro-vide necessary information for de-velopment of design criteria far pre-stressed concrete bridge decks was pre-sented.

The durability phase of the program'-'studied the effect of concrete qualityand cover on corrosion, the relationshipbetween prestressing and chloride ionpenetration in cracked and uncrackedconcrete, and the specific detailing re-clnirements necessary to reduce the riskof corrosion. In the experimental pro-

gram of the structural phase,2.1.5 an ap-proximately half=scale slab and girderbridge model utilizing transversepost-tensioning was tested to determinetransverse prestress distribution in thedeck slab considering the effects of vari-ables such as presence of diaphragms,lateral girder stiffness, and tendon pin-file as well as to investigate its behaviorunder vertical wheel loads. An exten-sive series of two- and three.-dimen-sional linear elastic finite element corn-puter analyses were then used togeneralize the results considering theeffect of slat) thickness, diaphragm stillness, and bridge skew. 2 4 6,'

In this paper the findings from thestructural and durability studies aretranslated into specific design recorn-mcndations and suggested AASHTOBridge Design Specification provisions.The overall research project primarilyaddressed prestressing of compositecast-in-place bridge decks over multiplegirders although a limited analyticalstudy of the transverse prestressing ef-fects in box girder bridges was also in-cli led,''•6,7

TRANSVERSE PRESTRESSING EFFECTSOne of the principal concerns identi-

fied at the beginning of the researchstudy was the influence of the lateral re-straint of girders on transverse prestressdistribution in the deck. As shown inFig. 1, the basic question is how much ofthe edge prestressing would he effectivein the interior regions of the deck. Theresults from the finite element analysisof the slab-girder bridge without dia-phragms presented in an earlier papersindicate that the transverse stress dis-tribution in a composite slab-girderbridge deck is not affected significantlyby the lateral stiffness of the girders ifthe girders rest on flexible neoprenepads, as is the usual case.

In box-girder and in slab-girderbridges with fixed support conditions,there is a restraint problem from the gir-clers which needs to be considered.However, for slab-girder bridges currentpractice is to almost exclusively useflexible neoprene hearings, with occa-sional use of'steel rocker hearings. Bothof these bearings should allow for suf-ficient relative girder movement duringtransverse prestressing. This findingsuggests that the lateral stiffness effectsof girders in composite slab-girderbridges wil] not have to be consideredin design although the effect of the re-straint of the webs must he consideredin box-girder bridges,•'•°.7

70

longitudnal direction

trarsrv^rN directkxr T^^

Bridge Dock TS

Transww" Prestre«!ng

GirderDiaphragm

(a) Girder - Slab Bridge

rS

Bridge DecJcT5 ?

Web

(b) I- Cell Box Girder Bridge

(C)2-Cell Box Girder Bridge

Fig. 1. Regions of uncertainty of transverse prestress distrioution.(a) Girder-slab bridge; (b) 1-cell box girder bridge; (c) 2-cell box girder bridge.

w

PCI JOURNAL/September-October 1989 71

In contrast to girder restraint consid-erations in slab-girder bridges, theanalytical and experimental results pre-sented previously' clearly indicate thatthere are significant reductions in trans-verse slab prestress in both slab-girderbridges and box-girder bridges becauseof the presence of diaphragms. There-fore, the effect of diaphragms on theprestress distribution in a transverselyprestressed bridge deck must be con-sidered in design.

For practical design considerationsthere are two methods which can beused to compensate for diaphragm re-straining effects. The first method in-volves prestressing the diaphragms witha supplementary force equal to the forceattracted by them clue to transverse pre-stressing of the deck. This would permitapproximately equal shortening in theslab and diaphragms. Consequently, thedeck transverse prestress distributionwould be relatively unaffected by thediaphragms. Thus, the prestress forcethat is applied to the diaphragms toovercome the restraining effects will besome factor times the transverse pre-stress force applied to the slab.

The second method which can beused to compensate for diaphragm re-straining effects involves amplifying thetransverse prestressing in the slab byusing more closely spaced tendons inregions near the diaphragms. To use thismethod in design, two things need to beknown. They are.

1. What amplification of the prestressforce is required to overcome the re-straining effects; and

2. Over what area should the force beapplied.

The following recommendations forthe analysis of transverse prestressingrestraint effects in slab-girder bridgesassume that a bridge deck basically be-haves compositely as an elastic slabcontinuous over the supporting girders.

To illustrate Eq. (1), if the designtransverse prestress is 200 psi (1.38MPa) in an 8 in. (20.3 cm) slab, then thetransverse slab prestress force per unitedge length, Fs , would be 19,200 lbs perft (280 kN/m), and the diaphragm forcerequired to compensate for restrainingeffects would be 1.6 times 19,200 lbs(85.4 kN), which is about 30,700 lbs (137kN). This basic equation [Eq. (1)1 is ap-plicable for both end and interior dia-phragms. For this basic equation, thebridge slab thickness is assumed to be 8in. (20.3 cm), the bridge skew 0 degrees,the diaphragm spacing 25 ft (7.6 m), andthe diaphragm stiffness corresponds tothat of standard concrete diaphragms

Bridge With No DiaphragmsFur it mruskew or skew bridge which

will not include diaphragms, or for thosecases in which the diaphragms will notbe present at the time of transverse pre-stressing, the transverse prestress dis-tribution for design purposes can be as-siimed to be equal to the applied edgeprestress less appropriate friction lossesand time effects.

Compensating for DiaphragmRestraining Effects by Prestressingthe Diaphragms

The basic diaphragm prestress forcerequired to compensate for the dia-phragm restraining effects is given byEq. (1):

P,= I.6Fs (1)

wherePpb = basic prestress force applied to

the diaphragms to compensatefor diaphragm restraining ef-fects

1.6 = factor to account for presence ofdiaphragms (unit of length is ft)(factor would he 0.49 if metricunit is meter)

Fs = transverse slab prestress forceper unit edge length requiredto resist effects of structuralloads assuming no diaphragmrestraining effects

72

Table 1. Comparison between diaphragm prestress forcerequired to compensate for diaphragm restraining effectsdetermined by proposed basic equation and that computedby finite element analysis.

P1, IFs

End diaphragm Interior diaphragm

Finite Pro- Finite Pro-

Strand Diaphragm element posed clement posed

profile case analysis I Eq. (1)] analysis I Eq. (1)]

Straight .A,11 1.4 1.6 1.55 1.6

Straight End onh 1.4 1.6 —Draped All 1.55 1.6 1.75 1.6

Draped End on IN 1.55 1.6 — —

Assuut{^ttuns lorcoi nparison:Distance between interior diaphragms = 25 ft (7,6m).Slab thickness = 8 in. (20.3 cm).Standard concrete diaphragms: A = 160 in.' (1032 cm5).Skew angle = 0 degrees.

[approximately 160 in. 2 (1032 cm2 ) I.Modifications to this basic equation willbe required as suggested below for slabthickness, diaphragm stiffness, bridgelength, and bridge skew.

Table I presents comparisons be-tween the diaphragm prestress force re-quired to compensate for diaphragm ef-fects determined by Eq. (1) and thatdetermined by a finite element analysis,The comparisons are presented in termsof the ratio of P. to F. In general, theconstant value of 1.6 is a reasonably con-servative assessment of the valuesdetermined by finite element analysis.While the study basically considereddiaphragms in skewed bridges as havinga squared off arrangement, the recom-mendations made should be conserva-tive for structures using skewed inter-mediate diaphragms.

Correction for Slab Thickness — Asthe slab thickness decreases, the rela-tive restraint due to the diaphragms in-creases and hence the diaphragm forceincreases. The basic equation I Eq. (1) 1is modified fur the effect of slab thick-ness, as:

Pn = C 1 1.6 Fs (2)

where Ci is the correction factor for slabthickness.

The proposed slab thickness correc-tion factor is:

C, = Bit (3)

where t is the slab thickness, in, (1 in. _2,54 cm).

Table 2 presents a comparison be-tween the diaphragm prestress force re-quired to overcome diaphragm re-straining effects predicted by Eq. (2)and that computed by finite elementanalysis for varying slab thickness. Thecomparisons are in terms of the ratio ofPa to Fs. The proposed slab thicknessmodification results in very reasonableand generally conservative estimates ofthe required diaphragm prestress forcein all cases. Exceptionally good agree-ment exists for the interior diaphragmcases.

Correction for Diaphragm Stiffness -Current trends in bridge constructionindicate that fewer diaphragms arebeing used, especially in the interior re-gions of bridges. If diaphragins arc used,current practice calls for standard con-crete diaphragms with an area of about

PCI JOURNAL September-October 1 989 73

Table 2. Comparison between diaphragm prestress forcerequired to compensate for diaphragm restraining effectsdetermined by proposed basic equation modified for slabthickness and that computed by finite element analysis.

ta, ll.,

End diaphragm Interior diaphragm5l`il

Finite Pro- Finite Pro-thick-ness Diaphragm element posed element posed(in.) case analysis I Eq. (2)1 analysis (Eq. (2)1

6 All 1.9 2.1 2.1 2.16 End only 1.8 2.1 - -8 All 1.4 1.6 1.55 1.1i8 End only 1,4 1.6 - --

10 All 1,1 1.3 1.25 1,310 End only 1.1 1.3 - -

Assumptions for coinI)isL uiuu l ciweeit inte[irrr11i: l iragst, 25 f (7.6 in)Standard concrete diaphragms: A = 160 in, ? (1032 cros).Skew angle = 0 degrees.Straight strand profile.

Table 3. Comparison between diaphragm prestress force required to compensate fordiaphragm restraining effects determined by proposed basic equation modified fordiaphragm stiffness and that computed by finite element analysis.

Cross- Pn /I's

sectionaldiaphragm

End diaphnigm Interior diaphragm

Finite Finitestuffiest(EA) Strand Diaphragm element Proposed element Proposed

(k-in?!in t) profile case analysis I Eq. (4)) analysis I Eel. (4)1

320,000 Straight All 0-8 0.8 0.8 0.8Straight End only 0.8 0.8 - -Draped All 1.0 0.9 1.0 0.8Draped End only 1.0 0.8 - -

640,000* Straight All 1.4 1.6 1.55 1.6(Standard Straight End only 1.4 1.6 - -concrete Draped All 1.55 1.6 1.7.5 1.6

diaphragms; Draped End only 1.55 1.6 - -A = 160 in 2 )

960,000 Straight All 2.2 2.4 1.7 2.4Straight End only 2.2 2.4 - -Draped All 2.0 2.4 2.4 2.4Draped Eiidonly 2.2 2.4 -

Assumptions for comparison:Distance between inlrriurdiuphragms = 25 ft (7.Fi at).Slab thivkuess = S in, {20.1 cm),Skew angle = 0 degrees,*Concrete modulus assumed = .ft$X) ksi (279411 \I Pa).

Metric conversion factor:1 kip4.45 kN.

(1 kip-in. Ylin? = 4.45 kNcm2/cm2).

74

Table 4. Comparison between diaphragm prestress forcerequired to compensate for diaphragm restraining effectsdetermined by proposed basic equation modified for spacingbetween interior diaphragms and that computed by finiteelement analysis.

P,2 lFs*

End diapbragni 1 sterior diaphragm

Finite Pro- Finite Pro-Spacing betweeninteriordiaphragtns element posed clement posed

(ft) analysis j Eq. (6)1 analysis I Eq. (6)1

18 1.9 2.2 2.4 2.221 1.7 1.9 2.0 1.925 1.4 1.6 1.55 1.628 1.25 1.1 1.4 1.4

*ALipIicable4irih h)rI ri IKexwith inlrriiiriti,q)111a;nis.

Assumptions for comparison;Slab tlsiekness = S in. {2x1.3 (m).Standard concrete dieiphral;ms;A dill in? (11138 eni° S.Skew angle — U dv gree s.Strai)zht strand profile.

160 in .2 (1032 cnl^). For this case, thebasic equation I Eq. (1) 1 does not needmodification. However, if nonstandardconcrete diaphragms or if steel dia-phragms similar to those used for steelgirder bridges are called for in design,the following modification to the basicratio is proposed:

Pn = CX 1-6 Fs (4)

where CK is the correction factor for dia-phragm stiffness,

The correction factor for diaphragmstiffness is defined as follows:

(2 = (EA), /640,000 (5)

whereE = modulus of elasticity of the dia-

phragm materials, ksi (1 ksi =6.894 M Pa), and

A = effective diaphragm cross-sec-tional area resisting axial defor-mations, in. 2 (1 in.2 = 6.45 cm2)

The term (EA), represents the effec-tive cross-sectional diaphragm axialstiffness.

Table 3 presents a comparison be-

tween the diaphragm prestress force re-quired to overcome diaphragm re-straining effects predicted by Eq. (4)and that predicted by finite elementanalysis for varying diaphragm stiffness.The comparisons are again based onratios of PD to F. The proposed modifi-cation for diaphragm stiffness roughlyapproximates that obtained by finiteelement analysis and is generally con-servative.

Correction for Interior DiaphragmSpacing — The number of interior clia-phragm locations varies with bridgelength. Current practice indicates thatfor bridge lengths up to 55 ft (16.8 m),one line of interior diaphragms at mid-span is used. From 55 to 95 ft (16.8 to29.0 in), two lines of interior diaphragmsat third points are used. For bridgelengths greater than 95 ft (29.0 m), threediaphragm lines at quarter points areused. Thus, the spacing between dia-phragms in bridges which includeinterior diaphragms varies from about 18to 32 ft (5.5 to 9.8 m). As the distancebetween interior diaphragms decreases,the restraining force in both end and

PCI JOURNAUSeplember-October 1989 75

interior diaphragms increases and hencethe force required to overcome dia-phragm restraining effects increases. Toaccount for the interior diaphragmspacing effect (i.e., bridge length effect),the following equation is proposed:

PD =CL I.6FS (6)

where CL is the correction factor for thestiffness effect due to interior diaphragmspacing.

If no interior diaphragms are used,this correction is not required. To de-termine CL, the following equation isproposed:

CL = 25/Se(7)

where Sp is the spacing between interiordiaphragms or between end and interiordiaphragms, ft (1 11= 0.305 m).

Table 4 presents a comparison be-tween the proposed diaphragm pre-stress force modified for spacing be-tween interior diaphragms and thatcomputed by finite element analysis.Again, the comparisons are made interms of the ratio of PD to Fs. In general,the values calculated by Eq. (6) are rea-sonably close to those determined by fi-nite element analysis.

Correction for Bridge Skew Angle -The results from finite element analysesindicate that as the skew angle of thebridge increases from zero degrees, therestraining force in the diaphragm dueto transverse prestressing decreases.This implies that the diaphragm pre-stress force required to overcome re-straining effects also decreases. It wouldbe conservative to ignore any decreasein diaphragm force for bridges withskew. However, detailing considera-tions suggest that prestressing dia-phragms on a skew bridge is probablynot practical. Thus, the factor (Csx) tocorrect the basic equation for effects ofskew will be taken as 1.0 in the pro-posed design recommendations and noother numerical table is required.

Multiple Corrections — It is proposed

that the correction factors be multipliedas illustrated by Eq. (8) for multiple cor-rections to the basic equation;

P„ = C,CxCL Csn 1.6 Fs(8)

A parametric study with a mix of vari-ables revealed that Eq. (8) could be asmuch as 20 percent unconservative ifmore than two of the correction factorsused had a value less than 1. Thereforein using Eq. (8) no more than two cor-rection factors with values less than onecan be used. However, the two lowestcorrection factors may be used. Table 5compares the results obtained for Eq. (8)and those obtained by finite elementanalysis for several cases with a mix ofvariables. It appears that the proposedsimplified procedure for determiningthe diaphragm prestress force requiredto overcome the restraining effectsshould produce reasonable yet con-servative results.

The development of the equationsutilized in this method assumes that theprestress force was applied at the cen-troid oF the diaphragm cross section. Inpractice, this may not always be possi-ble. If the height of the diaphragm issmall compared to the total height of th€bridge superstructure, the exact locationof the diaphragm tendon may not affectthe stresses in the slab significantly. Theopposite is true, however, when thediaphragm height is nearly equal to thatof the superstructure. Regardless of theheight of the diaphragm, the prestress-ing force should never be located suchthat it may induce tension stress in thediaphragm.

Taking into consideration the aboveconstraints, a reasonable allowable ec-centricity of the diaphragm prestressforce is '/s the distance to the kern pointof the diaphragm, or '112 the height of thediaphragm. [f the prestress eccentricityin the diaphragms exceeds this amount,a more detailed anal ysis of the effect onthe stresses in the bridge deck should becarried out.

76

Table 5. Comparison between diaphragm prestress force calculated by Eq. (8) and thatdetermined by finite element analysis for a mix of variables.

CaseBridge

variablesCorrection

factorsProposed[ Eq. (8)J

Finiteclementanalysis

1 Bridge length= 75 ft Cr, = 1 (0.77)(0.5)1.6= 0.62 0_59Diaphragm spacing = 25 ft *Csx = 0.77 Limit imposed that onlyU = 40 degrees C, = 0.8 two correction factorsSlab thickness = 10 in. CX = (1.5 can be taken less than 1(EA), = 320,000 kip-in?/in

2 Bridge length = (1011 C 1.25 (1.25)(1.23)(1.5)(1.6) = 3-69 2.49

1)iaphragm spacing= 20 ft C, = 1.23i= u degrees *C£K = ISlab thickness = 6.5 in. Cx = 1.5(L A)o = 960,000 kip-in?/in?

3 Bridge length = 76 tt Cr, = 1 ((.94)(1.14)(1.6) = 1.71 1.71= 0.94

H = 20 degrees C, = 1.14Slab thickness = 7 in. Cx = I(FA)„ = 640,000 kip-in.2lin.2

4 Bridge length= 76 ft C' = 1 (0.89)(1.6) = 1.42 1.33Diaphragm spacing = 25 ft CX = l

H = 0 degrees C, = 0.89Slab thickness = 9 in. "Csx = 1

= 640.000 kip-in.211n?

Correctioti for I>ri:I , skc%v.Not included in actual ,k'sign recon niencl awns.

Metric conversion factors: 1 ft — 0.305 m; I in. — 2.54 cm; 1 kip — 4.45 kN.

Compensating for Diaphragm

Restraining Effects by Applying

Extra Prestressing in the Slab in

Regions Near the Diaphragms

The results from the laboratory modelbridge tests revealed that applying extraprestressing in the form of more closelyspaced tendons in a 4 ft (1.2 m) regionaround the diaphragms was a viable andexpeditious method to overcome the re-straining effects of the diaphragms.'a Inthe case of the model bridge tested, thetendon spacing was conservatively cutin half from that used in nondiaphragmslab regions. This resulted in twice theprestressing force per unit edge lengthin the diaphragm regions as compared tonondiaphragm regions. however, the re-

sults from the experimental tests as wellas from the finite element studies re-vealed that a somewhat lower value ofprestressing force in diaphragm regionswould have been adequate.

For design, two equations are pro-posed for determining the amplifiedprestress force required in diaphragmregions. For U to 10 degree skewbridges, Eq. (9) is proposed:

F = 1.6 F5(9)

whereF,. = amplified transverse slab pre-

stress force per unit edge lengthapplied in regions near dia-phragms in order to compensatefor diaphragm restraining effects

PCI JOURNALISeptember-October 1989 77

Oft. 4ft_.I I_Oft.^ Off.

DiaphropmstN

Girders

L (feet) —'-1

Fig. 2. Diaphragm amplified prestress regions for a nonskew bridge (1 ft = 0.305 m).

F5 = tranverse slat) prestress force perunit edge length required to re-sist effects of structural loads as-suming no diaphragm restrainingeffects

This amplified prestressing would heapplied over an edge length of 4 ft (1.2m) centered on the diaphragms, Forbridges with greater than 10 degreeskew, Eq. (10) is proposed:

Fe = 1.2F3 (10)

Thus, for bridges with greater than 10degree skew, less amplified prestressforce per unit edge length would be re-quired; however, it will need to heapplied over a wider region of the slabthan the 4 ft (1.2 m) edge strip used withnon skew bridges.

The slab edge length over which thisamplified prestressing force must beapplied is given by Eq. (11):

x – tl tan 0 + 4 =: (L + W tan 0)/N (11)

wherex = slab edge length at diaphragms

over which Fe will be required, ft(1 ft= 0.305 in)

W= width of bridge slab, ft (1 ft =0,305 in)

0 = bridge skew angle as measuredbetween the transverse edge ofthe deck slab and the normal tothe Iongitudinal edge of thedeck slab, degrees (see Fig. 3)

L = span length, ft (1 ft = 0.305 m)N = number of diaphragm lines per

span (i.e., four for a span withtwo sets of interior diaphragms,and two for a span with only enddiaphragms)

The limit of (L + W tan 0)/N is im-posed to ensure that the diaphragm re-gions do not overlap, This implies thatfor some skew bridges, the amplified

78

Fig. 3. Diaphragm amplified prestress regions for a skew bridge (1 tt – 0.3U5 m).

prestress force Fe may he required alongthe entire edge length of the bridge. Fora bridge with no skew, the diaphragmamplified prestress region is 4 ft (1.2 m)wide, which was the equivalent clis-tance used for the laboratory bridgemodel?-a Figs. 2 and 3 show in shadingthe diaphragm amplified prestress re-gions for a bridge with no skew and withskew, respectively.

To examine the applicability of Eqs.(9) through (11), finite element analyseswere used to examine the effects of therecommended prestress distributions ofthe prototype bridge of Ref. 2 for skewangles varying from 0 to 60 degrees.Figs. 4 and 5 present typical stress con-tours from the analysis for the cases ofbridge skew of 10 and 40 degrees, re-spectively. The contours represent per-centages of the stress induced along theslab edge by F. Ideally, it would liedesirable to have a uniform stress dis-

tribution in the slab with all stress equalto the stress induced by Fr.

This is clearly not possible in practice.However, in all cases studied, the re-sults indicate that a substantial portionof the deck area is between 95 and 120percent, which suggests a reasonablyuniform prestress distribution. Thereare a few hot' spots up to 1511 percentbut this is not a problem with the lowlevels of slab prestress usually used.Thus, the use of' Eqs. (9) through (11)resulted in reasonable, yet generallyconservative slat) prestress distributionsfor the wide range of' skew anglesexamined for the study bridge. The pre-stress distributions which result fromthe use of these equations should bereasonably unifi rni and generally con-servative.

Prestress LossesPrestress losses such as friction losses

PCI JOUPNALJSeptember-October 1989 79

Fig. 4. Transverse stress contours for study bridge with 10 degreeskew; amplified prestressing force applied in diaphragm regions;F 5 produces edge stress - 100 percent (1 ft = 0.305 m).

in post-tensioning result in less com-pression to resist imposed loads andmust be considered in design. Rallss re-ported a tendon force loss clue to frictionof 30 percent for a post-tensioning sys-tem consisting of closely draped ten-dons in a full-depth test slab simulatingdraping for continuity over long longi-tudinal girders. This reduction is on thesame order as that produced by the re-straining effect of diaphragms. How-ever, no additional rules are requiredsince the loss of prestress is adequatelycovered in the current AASHTO Speci-fieations,M Section 9.16.

Secondary Moment Effects

Draped tendons or any unsymmetrical

placement of prestressing about thecentroid of a bridge deck results in sec-ondary moments in continuous trans-verse bridge slabs which are verticallyrestrained. The effect is to increase slabstresses due to prestressing at some lo-cations and decrease these stresses atothers. Thus, there is less effectivecompression at the locations where thestresses decrease due to secondary mo-ments. In general, this secondary mo-ment effect will probably not be verysignificant fur thin transversely pre-stressed bridge decks. Draped tendonsare probably not cost effective sinceonly small eccentricities are possiblewithin thin slabs. However, for thosecases in which secondary moments canexist, the effects can be considered

80

Fig. 5. Transverse stress contours for study bridge with40 degree skew; amplified prestressing force appliedalong entire length of bridge; F, produces edge stress =100 percent (1 ft = 0.305 m).

using conventional continuous elasticbeam theory

Maximum Tendon SpacingThe maximum spacing of transverse

tendons is governed by two effects.First, if the tendons are spaced too farapart, shear lag in the slab will result ina nonuniform stress distribution in theinterior regions. Second, the larger thetendon spacing, the larger the area of in-

effectively stressed slab near the deckedge.

The shear lag effect seems to be welladdressed by ACI provisions 10 for pre-stressed slab systems. The maximumallowable tendon spacing is the lesser of8 times the slab thickness or 5 ft (1.5 m).This provision was set considering theload to be uniformly applied. However,it is believed that with adequate bondeddistribution reinforcement, the ACI

PCI JOURNALSepternber-October 1989 81

FACE Q:-TRANSVERSE P OFPRESTRESS CURS .'

TENDON

TENDONANCHORAGE

:;T GIRDER

Y

(o) SECTION AT DECK EDGE

y +$2P

ACTUALCAPACITY DUETO PRESTRESS (0.85)5 0

A55UMEbCAPACITY DUE

TO PRESTRE55^

Q 1t n ^2 1

Q LIVE LOAD ANDSLAB DEAD LOAD

0GIRDER TENDON SLABFLANGE ANCHORAGE EDGE

TRANSVERSE DISTANCE

(b) TRANSVERSE MOMENT PROFILE BETWEEN TENDONS

Fig. 6. Development of maximum tendon spacing (1 ft = 0.305 m).

spacing limitations should also be ap-pEicahle to slabs under concentratedloads. It is, therefore, recommended thatthe ACI maximum tendon spacing limitsbe adopted as an upper limit for trans-versely prestressed bridge decks.

In addition to the shear lag considera-tion, a tendon spacing Limit based onachieving an effective prestressingstress distribution at the deck edges

should be adopted. As discussed in aprevious paper, there is a distributionarea between post-tensioning strandsalong the deck edge in which the pre-stressing forces are not effective. Eitherthe load must be kept off these areas, orresistance to the load most be providedby some other means. The positiontaken here is that it is preferable to pre-vent load application over these areas

82

rather than providing passive rein-forcement for local strengthening_ Thisis because use of conventional rein-forcement to carry service live loadswould entail cracking of the concretenear the curb, where ponded watercreates an especially corrosive en-vironrnent.

Moments in the deck near the slabedge may be induced by either verticalloads or lateral rail impact loads, Onlythe vertical loads are considered in es-tablishing the maximum transverse pre-stressing tendon spacing.

Fig. 6a shows a section through a deckat the longitudinal edge. A concentratedwheel load is located 1 ft (0.305 m) fromthe face of the guardrail, in accordancewith AASHTO design specifications."The distance from the edge of the deckto the bearing side of the tendonanchorage plate is represented as a,while y is the transverse distance fromthe deck edge to the inside face of thecurb or rail. Fig. 6b shows the momentcapacity and moment due to loadingacross this section, taken at midpointbetween two tendons.

Referring to Fig. 6h, with the slabdead load moment of such small mag-nitude at the point of applied liveload, the limiting acceptable designwould be for the applied concentratedload to be located where the slab mo-ment capacity due to prestressing alonereaches zero. It can be shown that fordesign purposes,' a reasonable limit forthe tendon spacing to ensure an eflec-tive prestress distribution at the deckedges for resisting applied concentratedlive load is given by Eq. (12):

S 3(y—a+ 12) (in.) (12)

whereS = tendon spacing, in. (1 in. = 2.54

cm)y = transverse distance for the

deck edge angle to inside face ofcurb or rail, in. (1 in. = 2.54 cm)

a — distance from deck edge to the

Table 6. Maximum tendonspacings from Eq. (12).

Value of (I (in.)

10y {tipper

Iin.) 0 5 limit)

0 .3621 66 54 39 24

12 72* 57 4218 90 75* 60

*Other limits will control maximumspacing.Note: 1 in. = 2.54 cm.

bearing side of the tendon an-chorage plate, in. (1 in. = 2.54cm)

The exact system of prestressing to beused will generally not be known at thetime ofdesign. A practical limit value fora should be recommended for thosecases where the prestressing system isnot known. From manufacturers' litera-ture on bearing plates and pocket for-mers for tendon anchorages, it is foundthat the distance a may vary from zero,for anchorage plates bearing against thedeck edge and covered by the railingconcrete to 10 k in. (26.() cm), for a 1%in. (3.5 cin) diameter threaded bar with aflat anchor plate. To account for allpossibilities, the practical limit of ashould be set at approximately thehigher value. For simplicity of applica-tion, it is recommended that the tipperlimit of he set at 10 in. (25.4 cm). Table6 gives the maximum tendon spacingsfor various values of y and a as calcu-lated using Eq. (13).

The maximum transverse prestressingtendon spacing allowed, then, should bethe maximum given by the ACI limits of8 times the slab thickness or 5 ft (1.5 m),or Eq. (12).

Tendon Layout for Skewed Bridges

On a nonskew bridge, the transversetendons may be distributed at the

PCI JOURNAL/September-October 1989 83

PRESTRESSINGTENONS

DEAD END ANCHORAGE

- STRESSING END ANCHORAGE

(a) TENDON ANCHORAGE TYPES FOR SKEWED BRIDGES

SHORT LENGTHTENDONS

GIRDERS

.'\ -- -

PROBLEM AREA FORSTRUCTURAL INTEGRITY

(b) PROBLEMS AT ACUTE CORNERS OF DECK

Fig. 7. Details of skewed bridge wkh perpendicular prestressing tendons.

specified spacings in the various Zonesalong the entire bridge length. How-ever, on a skewed bridge, complicationsarise near the abutments and expansionjoints. In these regions, the use of ten-dons placed perpendicular to the girdersresults in varying tendon lengths. Inaddition, tendon anchorages would berequired along the transverse edge ofthe deck.

It is generally not recommended thattendons he placed on a skew in theseinstances. The transverse prestressing

force available to resist slab moments isreduced from the applied prestressingby the cosine of the skew angle. Thisamounts to nearly a 15 percent reduc-tion for a bridge with a 30 degree skew,and thus would require the use of moreprestressing steel. Furthermore, the ef-fective transverse stress distribution inthe slab is affected by the application ofthe post-tensioning k rtes on skew. Be-cause of this reduced efficiency, the useof skewed tendons should generally heavoided wherever possible.

84

rL GIRDERTRANSVERSE PRESTRESS I 1 I IITYP.)

DECK TENDONS

END DIAPHRAGM

CLOSELY SPACEDANCHORAGE

AREA200 ^o

?ter V^ /

^i Sn S ^+--^^ II

Sn = S COSiOn)

DEAD END ANCHORAGE9 -- STRESSING END ANCHORAGE

Fig. 6. Tendon layout for skewed decks.

For perpendicular tendons to be usedon skewed bridges, several complica-tions must he dealt with. Tendonanchorages along the transverse deckedge, required on a skewed bridge withperpendicular tendons, do not present aproblem since dead end anchorages maybe used and the tendons stressed fromthe longitudinal deck edge, as shown inFig. 7a. The two major difficulties in thissituation are at the acute corners of thedeck, as illustrated in Fig. 7b. There therequired tendon lengths become soshort that losses due to anchorage seat-ing are extreme. Tendon lengths shorterthan, say, 12 ft (3.7 m) may be impracti-cal since elongation during tensioningwould be less than 1 in, (2.5 cm). In

addition, the structural integrity of theextreme corner region is hard to main-tain with transverse prestressing, espe-cially for bridges with high skew angles,since it extends longitudinally beyondthe end of the girder.

To avoid these problems, it is recom-mended that a fan arrangement of pre-stressing tendons be used at the acutecorners of a skewed bridge deck asshown in Fig. 8. The tendons should beas long as possible to minimize wedgeseating losses, and in any event, no lessthan say 12 ft (3.7 m) unless special pre-cautions are taken to ensure adequateprestress after losses. 'l'he advantages ofthis tendon arrangement are that it pro-vides a load path directly to the support,

PCI JOUFRNALSeptember-October 1989 $5

avoids high concrete stresses in thelongitudinal direction due to live load, al-lows the use of longer prestressing ten-dons, and avoids closely spaced anchor-ages. When utilizing such a pattern, careshould be taken not to extend the deadend oft he tendons so far into the slab asto approach a frilly skewed tendon lay-out.

The spacing of the fn tendons mustbe carefully detailed to account for thereduced spacing for these tendons, S. ,equal to the spacing for perpendiculartendons, S. multiplied by the cosine ofthe skew angle of the tendon. The re-sulting spacing is measured along theexterior girder.

At the transverse deck edge where fantendon anchorages are spaced closelytogether (see Fig. 8), an integral enddiaphragm should he provided to with-stand the high compression stresses. II'such a diaphragrrr is not used, ananalysis, such as by the finite elementmethod, should be made to determinethe stresses at that location.

For those cases in which the slat) iscontinuous over interior bridge bent lo-cations, it is expected that all anchorageswould be along the longitudinal edgesofthe slab.

Jacking Sequenceif all strands in a transversely pre-

stressed bridge deck are stressedsimultaneously, then there would not beany stress losses in the strands due toelastic shortening of the slab. However,stressing all tendons simultaneously isimpractical. Successive stressing of ten-dons results in stress losses in all previ-ously stressed tendons due to elastic

shortening of the concrete slab. Maxi-mum tendon stress losses would occurfor each tendon post-tensioned indi-vidually. For the laboratory modelbridge,"' the maximum stress loss due tojacking sequence was calculated to be 3percent. Railss reported the maximumstress loss as 3.8 percent, which is closeto the calculated value, The cflect ofjacking sequence is insignificant whencompared to other effects such as slabstress reductions due to the presence ofdiaphragms.

Variable Slab ThicknessThere are cases in which a variable

thickness or haunched slab might beused in a bridge deck. For purposes ofdetermining transverse prestressingdiaphragm restraint effects in thesecases, it would he reasonable yet con-servative to use the minimum slabthickness. As slab thickness decreases,the diaphragm restraining effects in-crease. Thus, using the minimum slabthickness would result in a highercalculated force required to overcomerestrain irig effects.

Minimum Value of CompressionFor most structural bridge applica-

tions envisioned, there is no need tospecify a minimum desired value ofcompression which should be inducedby the transverse prestressing, andhence no specific design recommenda-tions will be proposed. However,should a unique occasion arise in whichthe deck slab may be extra thick, a rea-sonable minimum target value of com-pression which should he induced is150 psi (1.0 MPa).

86

SERVICEABILITY, STRENGTH ANDSTRUCTURAL INTEGRITY

Besides the effect of lateral restrainton transverse prestress distribution,other design considerations for durablepost-tensioned bridges were also eval-uated in the overall study. The struc-tural design implications of serviceabil-ity, strength arid structural integrity arediscussed in the following sections.

Crack Control

From the viewpoint of corrosion risk,cracks urntit be limited whether causedby structural loads or other factors suchas temperature and shrinkage stresses inconcrete. 1•3 Current crack controlrecommendations are assumed to be ad-equate in limiting nonstructural crack-ing.

Shrinkage and Temperature Rein -forcement — The provisions of the cur-rent AASHTO Specificationsh are as-sumed to be adequate with regard tominimizing concrete cracking due toshrinkage and temperature stresses.However, as written, these provisionsimply that for a transversely prestressedbridge deck, the prestressing would beadequate as temperature and shrinkagereinforcement. This is not true, espe-cially for a deck with unhonded ten-dons. It is recommended that the mini-mum temperature and shrinkage re-quirement for reinforced concrete in theAASHTO Specification Section 8.20 bemet in the form of bonded auxiliarynon pre stressed reinforcement at bothtop and bottom slat surfaces in both thetransverse and longitudinal direction ofall transversely prestressed bridgedecks.

Allowable Tension Stresses — Thedurability study results r •3 indicated thatcorrosion risk was reduced for crackwidths limited to about 0.002 in. (0.05mm) by the use of prestressing. How-ever, even though little corrosion oc-

curred for small crack widths, the CI-levels at the reinforcement level at cracklocations exceeded the chloride corro-sion threshold. On the other hand, inuntracked concrete, (lie Cl levels atreinforcement depth were below thethreshold. This suggests that the pru-dent approach would be to eliminatecracking altogether under normal load-ing conditions. 'l'hus, for a transverselyprestressed bridge deck which is ex-posed to chlorides in service, anycracking would constitute a damagelimit state. It is implicit that such a"crack free" design can only ensure cor-rosion protection if adequate thicknessof concrete cover, adequate concretequality and adequate compaction existso that the "untracked" concrete pro-vides the necessary barrier to inhibit thecorrosion mechanism.

Using a limit state design philosophyand considering the statistical disper-sion of concrete cracking strength aswell as potential fatigue problems" andlikelihood of overloads on a bridge, theproposed design recommendation is tolimit the extreme fiber deck slab tensilestresses under lull service load to 2 J,The value 2 T];' seems to be a reason-ably conservative tension limit, yet hassignificant economic advantages over azero tensile stress limit.

Bonded Transverse Reinforcement —When unhonded transverse prestressing

is used, supplementary bonded rein-forcement is needed to control crackingunder overloads, and to ensure overallstructural integrity. The amount of suchbonded reinforcing, A A , in the trans-verse direction recommended for eachslab surface per foot width of deck fol-lows from ACT :318 rettuireunents:r"

AB = 0,024 t (in.) (1 m. 4 = 6.45 cm )where t is the overall thickness of deck(in.) (1 in. = 2.54 cm).

PCI JOURNAL September-October 1989 87

This amount of bonded transversereinforcement should he placed in boththe top and bottom of the deck whenunbonded transverse prestressing isused and distributed uniformly.

If bonded transverse prestressing isused, supplementary transverse nonpre-stressed bonded reinforcement need beprovided only for temperature andshrinkage control as previously de-scribed.

Bonded Longitudinal DistributionReinforcement — As discussed in acompanion paper, 2 the longitudinalmoment in a typical composite I-beamand slab bridge deck due to concen-trated wheel loads is approximatelyone-quarter of the transverse slah mo-ment at that location, For typical bridgedecks, this level of moment results inconcrete tensile stresses on the bottomof the deck of less than 2 ,, f , . Such lowstress values are much less than the ten-sile strength of the concrete. However,in case the concrete does becomecracked, and because of the possibilityof overloads, some longitudinal rein-forcement must be provided to resistthese moments. The amount of rein-forcement required will be governed byeither the design moment or the mini-mum reinforcing requirements to en-sure ductile failure.

In view of the low values of longi-tudinal moment in the slab due to awheel load determined in the laboratorystudy,' determination of the longitud-inal distribution reinforcing in the bot-tom of the slab should be made by directdesign. The design longitudinal mo-ment should be one-quarter of the trans-verse live load plus impact moment, andthe amount of reinforcement shouldconform to the minimum requirementsof AASHTO Section 8.17.1. 11 However,to expedite the design process, a designvalue of (0.03) t (sq in, per ft width ofdeck) (1 in. = 2.54 cm; 1 ft = 0.:305 m) forlongitudinal reinforcement in slab-girder bridges appears adequate if amore exact determination is not desired.

For the reinforcing arrangementshown in Fig. 9, the maximum spacingof the longitudinal distribution bars al-lowed by AASHTO requirements forflexural reinforcement distribution(AASHTO Section 8.16.8.4) is 9.8 in.(24.9 cm). This is overly restrictive inthis case since the longitudinal tensilestresses in uncracked concrete on thebottom of the slab are less than 2 7TInstead, a maximum spacing of 12 in.(30.5 cm) is recommended for longi-tudinal distribution reinforcing, whichprovides nearly three bars in the cone ofload influence beneath a 20 in. (51 cm)wide wheel.

Transverse Cracking —A transverselyprestressed bridge deck designed in ac-cordance with the recommendations fortransverse prestressing presented in thispaper should be free of deck cracks run-ning in the longitudinal direction. Thegreat advantage of the absence of thesecracks is that one mechanism by whichcorrosion of the reinforcement andfreeze-thaw deterioration of the con-crete takes place is eliminated. How-ever, if slab cracking should occur run-ning in the transverse direction across thedeck and thus parallel to the transverseprestressing, the potential for substan-tial early deck deterioration will still hepresent and the highly stressed tendonsmay be exposed to corrosion attack. In'Texas, the Texas State Department ofIiighways and Public Transportation(TSD1IPT) reports that the primarycracking in their bridge decks occurs inthe transverse direction, and conse-quently, transverse prestressing wouldnot be particularly beneficial. This is thereason that as the study progressed, theneed for minimum levels of longitudinaldeck prestressing was also evaluated.

For slab and girder bridges, the twomost promising methods for dealingwith transverse cracking in the deck arethe use of epoxy-coated reinforcementand longitudinal post-tensioning of thebridge deck. Because adequately thick,high quality, uncracked concrete pro-

88

TRANSVERSE LONGITUDINAL TOPPRESTRESSING TEMPERATURE a SHRINKAGE

TENDONS REINFORCING

.Q_• 4 .4J.

t !9',DQ d a•' rt I"ow 2 11

depending onexposure

LONGITUDINAL TRANSVERSE SUPPLEMENTARYDISTRIBUTION BONDED REINFORCINGREINFORCING

Fig. 9. Transverse section of deck showing depth to longitudinal distributionreinforcing (1 in 2 54 cm).

tects the reinforcement against corro-sion, resists freeze-thaw deterioration,and has a low susceptibility to fatigue,longitudinal post-tensioning of thebridge deck is the more promisingmethod. If a deck is not longitudinallypost-tensioned, epoxy-coated rein-forcement and bonded transverse pre-stressing should be used as a minimumlevel of protection. When epoxy-coatedreinforcement is used, all reinforcing lo-cated within 4 in, (10.2 cm) of concretesurfaces exposed to an aggressive en-vironment should be coated.

Longitudinally post-tensioning abridge superstructure is a viable methodof preventing transverse cracking inbridge decks. The ACI Building Code1)recommends that if post-tensioning isused to counteract temperature andshrinkage stresses, a minimum averagecompressive stress of 1{0) psi (0.69 MPa)due to the effective prestress (after los-ses) on gross concrete area should beprovided.

Several possibilities exist for longi-tudinally post-tensioning slab and gir-der bridge superstructures to eliminate

transverse temperature and shrinkagecracking in the deck. These include:longitudinal post-tensioning of only theslab for the full length of the bridge;longitudinal post-tensioning of only theslab in the end quarters of a span inconjunction with using shored con-struction; and designing pretensionedgirders for construction loads only, thenpost-tensioning the completed structurefor the full design loads plus the desiredcompression in the deck.

Regardless of the particular longi-tudinal prestressing scheme used, thesame protection provided for transverseprestressing tendons and anchoragesmust also be provided for longitudinaltendons. The minimum bonded nonpre-stressed temperature and shrinkagereinforcement should still he providedwhen the deck is longitudinally post-tensioned. Also, girders for a bridgeusing this method of construction musthe designed to accept the additionalstress the longitudinal post-tensioningimposed. Details for designing thelongitudinal post-tensioning for simpleand continuous span bridges as well as

PCI JOURNAL/September-October 1989 89

detailed design examples may be foundin Ref. 6.

Deflection ControlThe use of prestressing generally de-

creases live load deflections and thusIive load deflection problems should notbe a concern for a transversely pre-stressed bridge deck. A companion pa-per2 shows that live load deflections of atransversely prestressed deck slab arenegligible. However, at the start of thepresent study, there was also concern farcamber and deflection effects fromtransverse prestressing. Ralls5 reportedthat the maximum upward camber anddownward deflection was less than 0.01in. (0.25 mm) due to prestressing themodel bridge deck. This value repre-sents a camber or deflection to slab spanratio of about 0.02 percent. Thus, thesesmall deflections are of no practical con-cern,

Ultimate StrengthIn a companion paper,2 it was shown

that the experimental results of both thisstudy and others conclusively confirmthat the failure mode of the interior por-tion of a deck slab is punching shear.Most current practices (except for theOntario slab design procedure) calculatethe ultimate capacity of the bridge deckassuming one-way flexural behavior.This ignores in-plane forces (archingaction) and redistribution of load in thelongitudinal direction. This will nor-mally result in an underestimation ofstrength by a factor of at least 6 in inter-ior regions where membrane action isable to develop. A lower and more rea-sonable value will be found elsewhere,such as for the deck overhangs. if asimplified shear strength analysis ofslabs including arching effects wereavailable, the use of simple middepthtendons for transversely prestressedbridge decks could be expedited. In theabsence of such a method, however, it isrecommended that the current proce-

dure for checking the deck strength beused for transversely prestressed bridgedecks.

Bonded Versus Unbonded Tendons1I cre are both advantages and disad-

vantages in using either an unbonded ora bonded post-tensioning system. Theresults from the durability study' s indi-cated that both an unbonded tendoncompletely surrounded by grease withan integral plastic duct, and a bondedtendon completely surrounded by groutwith a rigid galvanized duct providedadequate corrosion protection in thelength between anchorages. The un-bonded tendon surrounded 1w greaseand a plastic duct is more vulcierablc tocorrosive attack if the plastic duct is notcoin pletely assembled and joined toprotected anchorages or is damagedbefore concrete is cast. The bondedsystem seems to have an additionalcorrosion protection because moisturemust penetrate the concrete cover, duct,and the grout before corrosion canoccur. In both systems, it is necessary tomaintain continuous protection wherethe duct quid anchors join.

The ultimate strength behavior of un-bonded and bonded prestressing sys-tems also has important design implica-tions, The principal difference in thetendon behavior is the steel stress atfail ti re. Since the tendon is free to slip inan unbonded system, the strain is moreor less equalized along its length, andthe strain at the critical section is less-ened. Consequently, when the concretecrushing stress is reached, stress in thesteel is often far below its ultimatestrength. Thus, for the same amount ofprestressing steel in an minbonded and abonded member, the ultimate strengthof the bonded member will be 10 to 30percent greater.9

In comparing the cost of an unbondedsingle-strand system to that of a groutedsingle-strand system, it is usuall y foundthat the unbonded system is less expen-

90

sive. The additional cost with use of abonded system is a result of the costof grouting hardware and the cost ofgrouting labor operations. However,these costs are basically constantwhether there is a single or whetherthere are multiple tendons. Thus, thecost of multiple tendons in a single ductwith a single pair of anchorages ap-proaches the cost of several unbondedsingle tendons with the associated sev-eral pairs of anchorages. From a coststandpoint, a grouted multistrand sys-tem can be just as economical as an un-bonded single-strand system.

Anchorage DesignAnchoring a prestress tendon at the

edge of the thin bridge deck induceslarge bursting and spilling stresseswhich could lead to substantial crackingor even violent failure of the concrete atthe anchorage zone. To control thesestresses, sufficient amounts of concreteand confining reinforcement must heprovided. Currently, there are severalmethods available for the design of pre-stress tendon anchorage zones. How-ever, none of these methods semi ade-quate for the analysis of multipleanchorages in thin slabs. It is, therefore,recommended that provisions be in-

eluded in the project specifications re-quiring the contractor to show by someappropriate means that the proposedanchorage detail is adequate prior to itsapproval for use.

Railing AttachmentAs has been discussed, there are areas

along the sides of a transversely pre-stressed bridge deck which are ineffec-tively stressed since the post-tensioningis applied at discrete locations and ten-don anchorages are often recessed intothe edge of the slab. Traffic rails withcontinuous attachment to the bridgedeck such as conclete barriers, as well asrailing utilizing posts anchored directlyto the deck, can impose concentratedstresses and transverse moments nearthe slab edge where moment capacitydue to prestressing is not present. It is,therefore, recommended that decks withtraffic railings located within a distanceequal to the spacing of the transversetendons from the slab edge should beprovided with nonprestressed rein-forcement adequate to resist lateralrailing impact loads. This reinforcementshould provide the full required mo-ment capacity for a transverse distancefrom the deck edge equal to the tendonspacing.

DURABILITY CONSIDERATIONSThe design implications for improv-

ing the durability of bridge decks withthe use of transverse prestressing arediscussed in the following sections.

Concrete Cover andConcrete Quality

Even though deck prestressing shouldreduce cracks in a bridge deck, there isstill a risk of corrosion due to the long-term exposure of chlorides which pene-trate slowly through uncrackeci con-crete. The durability study results'•-'

indicate that the combination of a 2 in.(5.1 cm) clear cover and a water-cementratio (wfe) of 0.45 was adequate for cor-rosion protection in uncracked concreteto resist the aggressive exposure of therelatively short durations (5 to 7 months)accelerated tests. However, Weed'2found that in actual construction thedepth of cover over bridge deck steelwas approximately normally distributedwith a mean value close to the specifiedvalue, bait with a standard deviation ofapproximately 3/r in, (1 cm) k r a 2 in. (5.1cm) cover. This implies that about 15

PCI JOURNAL/September-October 1989 91

percent of the steel could he expected tohave a cover less than 1% in. (4.1 can).The durability study results indicatethat at this depth the Cl- levels wouldbe greater than the corrosion chloridethreshold, and thus would be at a highcorrosion risk,

The current AASHTO Section9.25.1.2° value is 2 in. (5.1 cm) whendeicers are used. This is very marginalas a practical all-inclusive requirement.Setting a minimum clear cover value of2.5 in. (6.4 cm) would ensure that moststeel would have at least a 2 in. (5.1 cm)cover, which would he at an acceptablecorrosion risk. Therefore, it is proposedthat a minimum 2.5 in. (6.4 cm) coverover all top reinforcement with a maxi-mum water-cement ratio of 0.45 be usedfor transversely prestressed bridgedecks exposed to chlorides in service.

This combination is in completeagreement with the provisions for rein-forced concrete slabs in the current ACIBuilding Code.1° The current AASHTOSection 9.25.1 recommendation of I in.(2.5 cm) for concrete cover under bottomslab reinforcement is assumed to be ad-equate when the chloride exposure islimited to the top of the bridge deck.However, if there is any threat of saltexposure at the bottom slab surfaces,such as would occur in a marine envi-ronment, 2.5 in. (6.4 cm) of bottom coveris also recommended.

Protection of Prestressing

The consequences of corrosion of theprestressing steel in a transversely pre-stressed bridge deck would be quite se-vere. It is recommended that prestress-ing tendons be protected by an impene-trable harrier which extends the Fulllength between anchorages and isphysically attached to the anchorages.This would completely eliminate anymoisture path to the tendons betweenanchorages. A duct with completegrouting would provide the best protec-tion against corrosion; however, a rug-

ged grease-filled plastic duct could alsoprovide adequate protection as long asno defects exist in the duct. The mostcurrent information on appropriate ma-terials for corrosion protection of post-tensioning tendons is found in Refs. 13to 16. It is essential that the duct beexamined for any damage after the ten-don is placed and before the concrete iscast. Any damage must be repaired byappropriate measures.

Anchorage Protection

Maintaining a minimum 2.5 in. (6.4cm) concrete cover around all surfaces ofan anchorage would normally provideadequate corrosion protection. How-ever, a minimum 2.5 in. (6.4 cm) coverover the prestressing ducts will likelyresult in less concrete cover over someareas of the anchorage. For the durabil-ity specimens'-3 with a concrete cover of2 in. (5.1 cm) over the prestressing, only34'4 in. (1.9 cm) of cover was providedover the top anchorage surfaces. Theheavy corrosion which resulted in someof these anchorages clearly suggests thatreliance on positive measures other thanconcrete cover must be used for anchor-age corrosion protection.

In unbonded post-tensioning, theanchorage is critical throughout the ern-tire life of the structure. Therefore, it isproposed that the anchorage must hecompletely sealed against moisture.This sealing can be achieved with theuse of a suitable coating material such asan epoxy-resin compound, or a speciallymade covering of plastic or other suit-able materials which completely encap-sulates the anchorage, jaws, and strandextensions. Providing a physical barrierto moisture around the anchorages aswell as the prestressing tendon effec-tively results in an "electrically iso-lated" tendon which will be at low riskto corrosion, as suggested by Schu-pack.16

It is also proposed that externalanchorages shall not be used even if

92

protected by an auxiliary protective bar-rier. All protected anchorage compo-nents, including the strand extensions,must be surrounded by not less than 1'/zin, (3.8 cm) of concrete or mortar.

After stressing the tendons and seal-ing the anchorages, stressing pocketsshould be filled with a suitable chlor-ide-free mortar with low shrinkageproperties. As was done for the durabil-ity specimens, it is recommended thatthe pocket be painted with an epoxy-resin bond agent to improve adhesion of

the fresh mortar to the hardened con-crete.

CI ContentThe durability study test results'-e

indicate that in order to minimize therisk of corrosion, the maximum watersoluble CF content in concrete byweight of cement should he limited to0.06 percent, The limit on CI- contentwould be verified by trial mix on testsamples.

OTHER APPLICATIONSAlthough the emphasis of the experi-

mental testing program was for cast-in-place post-tensioned decks on precastconcrete girders, the general findings ofthe study are appropriate for other ap-plications. Specifically, the proposedrecommendations are equally valid forprestressed concrete decks on steel gir-ders.

Likewise, the use of precast stay-in-place panels with subsequent pre-stressing of the deck is not precludedfrom the general design procedureswhich were derived. The use of precastpanelized systems could shorten erec-tion time. The use of this type of systemmay be particularly attractive for re-decking of an existing bridge.

SUGGESTED REQUIREMENTS FORTRANSVERSELY PRESTRESSED BRIDGE DECKS

Because the AASHTO Specificationssare minimum requirements for bridgedesign, some of the ideas included inthis paper are not fully represented inthe suggested provisions. Specifically,neither longitudinal post-tensioning ofthe deck nor epoxy-coated reinforce-ment are expressly required. In addi-tion, design details for continuousbridges and tendon placement inskewed slabs have been omitted. Guid-ance for designing the longitudinal pre-stressing and details for continuousbridges may be found irk Ref. 7.

The proposed design recommenda-tions follow the limit states design con-cept. When a structure becomes unfit for

its intended use, it is said to havereached a limit state." There are ba-sically three limit states for a trans-versely prestressed bridge deck that areconsidered by the proposed designrecommendations. They are:

1. Ultimate limit state which mightbe evidenced by a flexural failure or apunching shear failure;

2. Damage limit state in the form ofpremature or excessive cracking whichmight allow penetration of corrosiveagents;

3. Durability limit state in the form ofunacceptable corrosion of reinforcingsteel and deterioration of concretewhich would impair the performance

PCI JOURNAL./September-October 1989 93

and integrity of the prestressed bridgedeck.

The proposed AASHTO provisionsassume that all other portions of theAASHTO Specifications" are applicable.

Some of the provisions could be directlyincluded in existing sections of theAASHTO Specifications, while otherswould require the formation of newsections.

SUGGESTED SPECIFICATION PROVISIONSMetric Conversion FactorsI in. – 2.54 cnir; 1 ft = 0.305 iii; 1000 psi= h.%4 ciPa; I kip = 4.45 kN. Fs

1.0 Notationa = distance from slab edge to the

bearing side of transverse ten-don anchorage, in.

An = area of bonded nonprestressedtransverse reinforcement perfoot width of slab, in.2

AL = area of bonded nonprestressedlongitudinal distribution rein-forcement per foot width ofslab, in.2

CK = correction factor of diaphragmstiffness

= correction factor for diaphragmspacing; applied only wheninterior diaphragms are pres-ent

Cr = correction factor for bridgedeck thickness

(EA)D = cross-sectional diaphragmstifliness where E is the mod-ulus of elasticity of diaphragmmaterial (ksi) and A is thecross-sectional area of dia-phragm resisting axial defor-mation in.2

fr = specified compressive strengthof concrete, psi

VT,' = square root of specified com-pressive strength of concrete,psi

F, = amplified transverse slab pre-stress force per unit edgelength required to overcomeweb restraining effects in hox-girder bridges and diaphragm

L

NPD

SDtWU

0

restraining effects in slab-girder bridges

= transverse slab prestress forceper unit edge length requiredto resist effects of structuralloads assuming no restraininge ffhcts

= longitudinal span length of thesuperstructure, ft

= number of line of diaphragms= prestress force required in dia-

phragms to overcome dia-phragm restraining effects inslab-girder bridges, units offorce

= interior diaphragm spacing, ft= bridge deck slab thickness, in.= bridge slab width, ft

distance from slab edge to in-side face of railing or barrierwall, in.

= bridge skew angle as measuredbetween the transverse edge ofthe deck slab and the normal tothe longitudinal bridge cen-terline, degrees

1.1 ScopeThese provisions shall apply for decks

of composite slab-girder bridges and ofbox-girder bridges which utilize trans-verse prestressing.

1.2 Design Assumption

The bridge deck shall be designed as-suming that it behaves as an elastic slabcontinuous over the supporting girdersin a slab-girder bridge and as an elastic

94

slat) continuous over the webs in a box-girder bridge.

1.3 Transverse PrestressingEffects

1.3.1 Box Girder Bridges

1.3.1.1 Transverse prestressing shallbe considered effective in all regions oftop slabs of box-girder bridges only ifdiaphragms are not present at the timeof transverse prestressing or if the dia-phragms are transversely prestressed toa level consistent with the deck pre-stressing.

1.3.1.2 Design of a bridge deck whichutilizes transverse prestressing shalltake into account the influence of webrestraint, losses in prestressing, and sec-ondary slab moments on transverse pre-stress distribution, The effects of trans-verse prestress on transverse momentsand shears in the webs and soffits of thebox-girder section shall he consideredin the analysis.

1.3.1.3 In lieu of a more exactanalysis, the restraining effect of webson transverse prestress distribution maybe accounted for in accordance with theapproximate procedure presented inSection 1.3.1.4.

1.3.1.4 The amplified transverse pre-stress force per unit edge length re-quired at all slat) locations to overcomeweb restraining effects shall he not lessThan:One-Cell Box Section:

F= 1.1F (1.3.1.4-1)

Fe = 1.15F5(1.3.1.4-2)

Three (or greater)-Cell Box Section:

F,= 1.4F (1.3.1.4-

1.3.2 Slab-Girder Bridges1.3.2.1 Design ofa bridge deck which

utilizes transverse prestressing shalltake into account the influence of dia-

phragn restraints, losses in prestressing,and secondary slab moments on trans-verse prestress distribution. The influ-ence of diaphragms needs to he consid-ered only if the diaphragms will be in-place at the time of transverse pre-stressing.

1.3.2.2 In lieu of a more exactanalysis, the effect of diaphragms ontransverse prestress distribution may beaccounted for in accordance with theapproximate procedures presented ineither Section 1.3.2.3 or Section 1.3.2.4.

1.3.2.3 The prestress force requiredin the diaphragms ofnonskew bridges toovercome diaphragm restraining effectsshall be not less than:

P1,= C,CR CL 1.6 F5 (1.3.2.3-1)

whereCr = 8/i (1.3.2.3-2)Cg = (EA), /640,000 (1.3.2.3-3)CL = 25/Se (1.3.2.3-4)

No more than two values for C, C3,and CL, shall be taken less than 1 in Eq.(1.3.2.3-1). In Eq. (1.3.2.3-1), Fs shall becomputed for a 1 ft length of slab.

Unless an analysis is carried out in ac-cordance with Section 1.3.2.2, the pre-stress force calculated by Eq. (1.3.2.3-1)shall he applied at a distance not ex-ceeding 1/12 the height of the dia-phragm from the centroid of the dia-phragrn.

1.3.2.4 The amplified transverse pre-stressing force per each 1 ft edge lengthof slab in the diaphragm regions re-quired to overcome diaphragm re-straining effects shall be not less than:For bridges with8 10 degrees:

Fe = 1.6F3 (1.3.2.4-1)

For bridges with 0> 10 degrees:

Fe = 1.2 Fs (1.3.2.4-2)

The amplified transverse prestressforce per unit edge length required byEqs. (1.3.2.4-1) or (1.3.2.4-2) shall be ap-plied along the slab edge with a uniform

PCI JOU RNAL^ Se ptember-October 1989 95

distribution at diaphragm locations foran edge length of:

x W tang+ Oft{ (L+ Wtano)/N

(1.3.2.4-3)

where W and I are in units of feet. Forend diaphragm regions, x shall be mea-sured from the transverse slab edge onnonskew bridges, and from the acuteslab corner on skewed bridges. For in-termediate diaphragm regions, thelength x shall be considered centeredover the intersection of the longitudinalbridge centerline and the overall cen-terline of that set of diaphragms.

1.4 Maximum Transverse TendonSpacing

The maximum spacing of individualtransverse tendons or groups of tendonsshall not exceed eight times the deckslab thickness, 5 ft, nor 3 (y – a + 12).Without more precise information, thevalue ofa may be taken as 10 in.

1.5 Stresses at Service Loads AfterLosses Have Occurred

The tensile concrete stress ire pre-compressed tensile zones of trans-versely prestressed bridge decks afterall allowances for losses shall not exceed2v'f,.

1.6 Minimum BondedReinforcement

For a transversely prestressed bridgedeck which utilizes unbonded con-struction, the minimum area of top andbottom uniformly distributed supple-mentary bonded reinforcement per footwidth of slab in the transverse directionshall be computed by:

A5 = 0,024 t (1.6-1)

1.7 Distribution Reinforcement forSlab-Girder Bridges

1.7.1 For slab and girder bridges,

bonded longitudinal distribution rein-forcement in the bottom of a trans-versely prestressed bridge deck shall beprovided to resist at least 1/4 the maxi-mum design transverse live load plusimpact slab moment.

1.7.2 The requirements of Section1.7.1 may be considered satisfied if dis-tribution reinforcement is provided inaccordance with the following formula:

A,_- (4.03)t (1.7.2-1)

1.7.3 The specified amount of distri-bution reinforcement shall be uniformlyspaced between girder flanges. Individ-ual bars shall not be spaced farther apartthan 12 in.

1.8 Shrinkage and TemperatureReinforcement

1.8.1 For all transversely prestressedbridge decks, reinforcement for shrink-age and temperature stresses shall beprovided near the top and bottom slabsurfaces not otherwise reinforced withsufficient bonded nonprestressed rein-forcement, in accordance with AASHTO8.20.

1.8.2 Prestressing tendons used tocontrol shrinkage and temperaturestresses in the longitudinal directionshall be proportioned to provide aminimum average compressive stress of100 psi in the slab after all losses. Use ofsuch tendons does not negate the re-quirements of Section 1.8.1.

1.9 Tendon Anchorage ZonesPost-tensioning anchorages and sup-

porting concrete in transversely pre-stressed bridge decks shall be designedto resist bursting, splitting, and spallingstresses induced by the maximum ten-don jacking force, for strength of con-crete at time of prestressing. Adequacyof the anchorage zone design shall bedemonstrated prior to its acceptance foruse.

96

1.10 Traffic RailingsTransversely prestressed bridge

decks with traffic railings located withina distance equal to the spacing of thetransverse tensions from the slab edgeshall he provided with nonprestressedreinforcing to resist transverse railingloads. The full moment capacity re-quired shall he provided for a distancefrom the slab edge equal to the tendonspacing.

1.11 Special ExposureRequirements

1.11.1 For corrosion protection oftransversely prestressed bridge decksexposed to deicing salts, marine envi-ronments or any other corrosive envi-ronments, the maximum water-cementratio of concrete shall not exceed 0.45.

1.11.2 For corrosion protection oftransversely prestressed bridge decksexposed to chlorides in service, thetnaximuni water soluble chloride ionconcentrations in test samples of hard-ened concrete taken from a trial mixshall not exceed 0.06 percent by weightof cement.

1.11.3 For corrosion protection, the

minimum clear concrete cover over allreinforcement in a transversely pre-stressed bridge (leek directly exposed tochlorides in service shall he 2'/2 in.

1.11.4 For corrosion protection, allanchorages, prestressing, and strandextensions shall be fully encapsulatedby a durable protective harrier whichprevents the penetration of moisture.Protective measures for unhondedsingle strands shall conform to "Specifi-cation for Unhonded Single StrandTendons" (P1'I, 1984, Ref 15).

1.11.5 After placement of prestress-.ing tendons and anchorages and of con-ventional reinforcement and beforeconcrete is cast, any damage to the pro-tective barrier surrounding the tendonsand anchorages shall he repaired.

1.1 1.6 All anchorage components in-cluding strand extensions shall he cov-ered by not less than 1 1/2 in. of concreteor mortar as measured from any exposedsurface.

1.11.7 Stressing pockets shall hefilled with a suitable chloride-free low-shrinkage mortar_ Before placing themortar, the sides of the pocket shall bepainted with a suitable resin bond agentto improve adhesion.

COST ANALYSESA primary criterion for selecting a

particrilarstructural system is most oftencost. The costs considered are the initialconstruction cost and the life c ycle costof the system. The bridge of the designexample presented in the Appendix wasconstructed in "Texas as a conventionallyreinforced deck, and thus, a more directcost comparison between prestressedand conventionally reinforced deckscould be made.

Based primarily on average 1984Texas State Department of Highway andPublic Transportation (TSDHPT) bidtabulations, initial cost estimates fir theexample bridge in the Appendix are

summarized in Table 7 for four con-struction options. The costs associatedwith the post-tensioning in the trans-versely and longitudinally prestressedoptions were obtained from a post-ten-sionint; supplier. It is evident fromTable 7 that any type of design whichincorporates features which should ap-preciahly increase the durability ofbridge (leeks increases the constructioncost somewhat. However, the increasein cost is fairly close for the differentconstruction options designed to in-crease durability.

i he construction cost increase for thedesigns with enhanced durability fea-

PCI JOURNAL^September-October 1989 97

Table 7. Initial cost figures for example bridge of Appendix.

Conven- Trans-tionalh verse Frans-.

rein- pre- verseforced stressed and

Conven- w/top wltop longitu-tionall_v bars bars .linalh

rein- epoxy epoxy pre-Cost forced coated coated stressed

Total deck cost (S) 13,000 15,200 15,900Unit deck cost

($/fP) 6.57 7.68 7.83 8.03Normalized deck cost 1.00 1.17 1.19 1.22Total unit bridge

cost ($/ft2 ) 25.00 26.11 26.26 26.46Normalized bridge

cost 1.00 1.04 1,05 1.06

Metric conversion factor: 1 ft x = 0.09.3 ail.

tures on the simple span bridge of theAppendix ranges from 17 to 22 percentof the deck cost, or 4 to 6 percent of thetotal bridge cost. If life cycle costs areconsidered, the cost of bridge decksconstructed with features for increaseddurability is less than that for a conven-tionally reinforced deck assuming a 5 to

10 year longer service life. The amountof savings could be 20 percent or morefor the simple span bridge example inthe Appendix' Between the three con-stniction options for increased durabil-ity, the uk cycle cost is fairly uniform,and thus, cost competitive with eachother.

PROTOTYPE TRANSVERSELYPRESTRESSED BRIDGE DECK

In 1986, the Texas State Departmentof Highway and Public Transportation(TSDHPT) constructed a trial trans-versely post-tensioned slab and girderbridge using single strand unhondedtendons in LaGrange, Texas, Comparedto their vast experience with conven-tionally reinforced deck slabs, theyfound the construction process for thistrial bridge both time and labor inten-sive.

The use of single strand tendons re-sulted in a very large number ofstressing operations. Repeated handlingof the stressing rams along the edge of

the bridge was burdensome and timeconsuming.

The contractor's actual costs weregreater than anticipated. This in partwas most likely due to the unfamiliarityof the construction crew to this newmethod and relatively little indoctrina-tion provided to the constructor, con-structor's crew and inspecting fieldforces. Another disadvantage noted bythe TSDHPT was that their choice ofusing unhanded tendons instead ofbonded tendons most likely precludedthe future widening of this particularbridge.

98

CONCLUSIONSPremature deterioration of concrete

bridge decks has become a major prob-lem in the last 20 years. The primarycauses of this deterioration are corrosionof the reinforcing steel and freeze-thawaction. This investigation focused on theapplication of prestressing to bridgedecks for the prevention of concretecracking, thereby sealing out chloridesand water which initiate reinforcing cor-rosion and concrete deterioration. It isimplicit that such a "crack free" designcan only ensure corrosion protection ifadequate thickness of concrete cover,adequate concrete quality and adequatecompaction exist so that the "un-cracked" concrete provides the neces-sary barrier to inhibit the corrosionmechanism. The primary objectives ofthe research program were to determinethe effect of major variables on corrosionprotection in concrete slabs, evaluatethe structural effects of prestressingbridge decks, and develop design rec-ommendations for the implementationof prestressing for bridge ducks.

The major conclusions from the studyare as follows:

1. A desirable approach for tfie designof concrete bridge decks exposed to ag-gressive environments is to minimizecracking under normal loading condi-tions through the use of prestressing.This is supported by the results of thedurability study'•$ which show thatwhile proper concrete cover, quality andcompaction are absolutely essential toensure durability of uncracked concrete,concrete quality and cover have littleeffect on chloride penetration in crackedconcrete. The test specimens showedthat even in such high quality slabs, cor-rosion ofreinforcemernt in slabs initiatesafter cracking occurred. The corrosionthen occurs primarily at crack locations.Prestressing, however, reduces the po-tential for corrosion and possiblyfreeze-thaw damage by limiting thepenetration of chlorides, moisture, and

oxygen through the cracks commonlyassociated with reinforced concrete, aslong as adequate concrete quality andcover are provided.

2. Transverse prestressing of a slab-girder bridge can effectively developcompressive stresses in the slab tocounteract tensile stresses that occurdue to live loads, as demonstrated by thelateral post-tensioning stress distribu-tion tests 2'4 The same was found to hethe case for box-girder bridges throughanalytical studies. The desired trans-verse stress distribution in a trans-versely prestressed deck is mainly af-fected by the restraining actions of thediaphragms. These restraints may beeffectively compensated for by pre-stressing the slab before diaphragms areinstalled, increasing the amount oftransverse prestressing in the deck nearthe diaphragms, or post-tensioning thediaphragms themselves.

3. A prestressed bridge deck requiresapproximately the same level of designeffort, should need less maintenance,and should have a longer service lifethan a conventionally reinforced slabwith uncoated reinforcing steel. Sinceconstruction forces will probably beunfamiliar with slab prestressing tech-niques, initial uses of such systems willrequire extra indoctrination for con-struction and inspector field forces. Ex-cept for such added costs on initial proj-ects, initial construction cost of a pre-stressed deck should be competitivewith that of a conventionally reinforceddeck with coated steel and will increasethe total construction cost of the bridgeapproximately 5 to 10 percent.

4. A prestressed deck designed in ac-cordance with the recommendationspresented in this paper and theAASIITO slab live load moments"should exhibit essentially linear elasticbehavior through factored load levels.'If a more "exact" method is used to de-termine the slab live load moments, the

PCk JOURNAL/September-October 1989 99

deck should still behave elastically be-yond service load levels. Failure of aprestressed deck is expected to be bypunching shear at a rnfraimum factor ofsafety against live load plus impact of

seven. This high factor of safety suggeststhat excluding the effects of compres-sive mein Inane forces in the stnuctiuralanalysis may lead to excessively conser-vative deck designs.

DESIGN RECOMMENDATIONSThe concept of prestressing bridge

decks has been shown to be viable aswell as advantageous, The design rec-ommendations and suggested AASHTOSpecification provisions found in thispaper should give ample guidance forthe design of prestressed bridge decks.For brevity, detailed recommendatonsconcerning design of longitudinal pre-stressing and continuous span bridgeshave been omitted from this paper, butmay be found in Ref. 7.

It is recommended that for highwaybridges located in areas where exposureto deicing salts and freeze-thaw condi-tions are expected, as in a marine envi-ronment, a prestressed bridge deck fol-lowing the recommendations presentedin this paper should be considered as aviable option. Such decks should pref-erably be prestressed in both the longi-

tudinal and transverse directions. Ifonlytransverse prestressing is utilized, how-ever, the nonprestressed reinforcementin the top of the deck should be epoxy-coated.

For maximum effectiveness in corro-sion resistance of prestressed decksutilizing post-tensioning, the post-ten-sioning tendon system must be com-pletely encapsulated in a corrosion re-sistant barrier. This requires carefulplacement and inspection. Overallstructural integrity must be ensured byprovision of an adequate amount of aux-iliary bonded reinforcement if un-bonded tendons are utilized. Thus, theprovision of both an adequate corrosionharrier and improved structural integrityindicate that grouted, bonded tendonsare highly preferable for deck pre-stressing.

11

REFERENCES1, Poston, R. W., Carrasquillo, fl. I., and

Breen, J. E., "Durability of Post-Ten-sioned Bridge Decks," ACI MaterialsJournal, V. 87, No. 4, July-August 1987,pp. 315-326.

2. Poston, R. W., Phipps, A. R., Almustafa,R. A., Breen, J. E., and Carrasquillo,R. L., "Effects of Transverse Prestressingin Bridge Decks," Journal of StructuralEngineering, ASCE, V. 114, No. 4, April1988, pp. 743-764.

3. Poston, R. W., Carrasquillo, R. L., andBreen, J. E., "Durability of PrestressedBridge Decks," Report 316-1, Center forTransportation Research, The Universityof Texas at Austin, July 1985, 176 pp.

4. Phipps, A. R., Almustala, R. A., Rails,M. L., Poston, R. W., Breen, J. E., andCarrasquillo, R. L., "Structural Effects ofTransverse Prestressing in BridgeDecks," Report 3I6-2, Center for Trans-portation Research, The University ofTexas at Austin, July 1985, 246 pp.

5. Rails, M. L., "Stress Distribution in aTransverse Prestressed Slab-GirderBridge Deck," MS Thesis, The Univer-sity of Texas at Austin, May, 1983.

6. Almustafa, R., "The Analysis of Trans-verse Prestressing Effects in BridgeDecks," PhD Dissertation, The Univer-sity of Texas at Austin, December 1983.

7. Poston, R. W., Phipps, A. R., Breen, J. E.,and Carrasquillo, R. L., "Design Proce-dures for Prestressed Concrete BridgeDecks," Report 316-3F, Center forTransportation Research, The Universityof Texas at Austin, November 1985, 192PP.

8. American Association of State Highwayand Transportation Officials, StandardSpecifications for Highway Bridges,13th Edition, 1983.

9. Lin, T. Y., and Burns, N. H., Design of

Prestressed Concrete Structures, 3rdEdition, John Wiley & Sons, New York,1981.

10. ACT Committee 318, "Building CodeRequirements for Reinforced Concrete(ACI 318-83)," American Concrete In-stitute, Detroit, Michigan, 1983.

11. Overman, T. R., Breen, J. E., and Frank,K. H., "Fatigue Behaviorof PretensionedConcrete Girders," Report 300-2F,Center for Transportation Research, TheUniversity of Texas at Austin, 382 pp.

12. Weed, M. R., "Recommended Depth ofCover for Bridge Deck Steel," Trans-portation Research Record No. 500,Transportation Research Board, 1974.

13. Ad Hoc Committee of the FIP Commis-sion on Prestressing Steels and Systems,"Tentative Recommendations for theCorrosion Protection of Unbonded Ten-dons," PCI JOURNAL, V. 28, No. 1, Jan-uary-February 1983, pp. 40-49.

14. Etienne, C., Binnekamp, D., Copier, W.,Hendricks, R., and Smit, C., "CorrosionProtection of Unbonded Tendons,"HERON, V. 26, No. 3, 1981.

15. PTI Committee, "Specification for Un-bonded Single Strand Tendons," Ad-HocCommittee for Unbonded Single StrandTendons, Post-Tensioning Institute,Phoenix, Arizona, October 1984.

16. Schupack, M., "Protecting Post-Ten-sioning Tendons in Concrete Struc-tures," Civil Engineering, ASCE, De-cember 1982, pp. 43 -45.

17. MacGregor, J. C., "Safety and Limit StateDesign for Reinforced Concrete," Cana-dian Journal of Civil Engineering, V. 3,No. 4, 1976.

Note: The full text of Refs. 3, 4 and 7 can beobtained through the National Technical In-formation Service, Springfield, VA 22161.

PCI JOURNAL/September-October 1989 101

APPENDIX -DESIGN EXAMPLE

Metric conversion factors: 1 in. = 2.54cm; 1 ft = 0.305 m; 1000 psi – 6.894MPa; 1 kip = 4.45 kN.

Throughout the design example, ref-erences to the provisions proposed inthis paper are prefixed by a "P" for"Proposed Specification Provisions,"while those cited from the currentAASHTO Specification" are so desig-n4ted.

Fig. Al shows the major features ofthe bridge for which a post-tensionedbridge deck is to be designed. The spanis 55 ft long and skewed approximately21 degrees. The bridge deck is to besupported on five prestressed concretegirders. Diaphragms are provided onlyat the supports.

The use of an unbonded monostranclprestressing system of the transverseprestressing of this deck would requirevery close strand spacing. Not only isthis inefficient, but the strand layout atthe acute corners of the deck becomescluttered. The shorter length tendonsneeded in the slat) corners also makemultistrand systems unattractive be-cause of high seating losses. The mostadvantageous prestressing system forthis deck is, therefore, high strengththreaded bars. Insufficient room isavailable in a thin slab for two layers ofthreaded bar tendons, so middepth ten-dons will he used. Other prestressingsystems could be used with minorchanges.

Materials selected tur this design in-elude concrete with a compressivestrength of 4 ksi, Grade 60 nonpre-stressed reinforcement, 1 in. diameterGrade 150 bonded threaded rods fortransverse prestressing, and V2 in. diam-eter Grade 270 seven-wire extrusioncoated unhonded strand for longitudinalprestressing of the.. deck.

The minimum deck thickness neededwith middepth transverse tendons and

longitudinal prestressing in the top ofthe slab is 8 in., as shown in Fig. A2. The2 1/2 in. concrete cover on top surface isrequired by P.1.11.3.

Slab Loads - The effective transverseslab span, S, is calculated as (AASHTO3.24.1.2):

S = clear span= girder spacing — girder top flange

widthFor a Texas Type 54 girder, the top

flange is 16 in. wide.S=7.5-16/12= 6.167 ftDead load consists of the 8-in, slab

and a 2-in, asphalt overlay. The uniformdead load per ft width on the deck, W,is then:

WD = (0.150)8/12+ (0.140)2112= 0.123 kip/itlft

The corresponding dead load mo-ment, MDL, , for the continuous slab is:

MnL = Ova S -/ 10(0.123)(6.167)2/10

= 0.49 k i p-Ri ftThe transverse slab live load moment

per ft width of slab including impact,MLL+! , is (AASHTO 3.24.3.1):11LL+1 _ (Impact factor) I (S + 2)1321 P

(Continuity factor)where

Impact factor= 1.3 (AASHTO 3.8.2)P = load on one rear wheel group of

trick= 16 kips for HS20 design loading

(AASHTO :3.24.3)Continuity factor = 0.8 (AASHTO

3.24.3.1)rLha,+, _ (1.3)1(6.167+2)1321 16 (0.8)

4.247 kip-ft/ ftTotal service load moment in the

deck, :Lis , is then:8 = !41DL + :WLL +1

= 0.469 + 4.247= 4.716 kip-ft/fl

Transverse Prestress Design — The,allowable extreme fiber concretestresses, f and f, are:

102

6.03 j 53.00•

6.03

1

TYPE 54 GIRDERS 20 38 41"

- . BRIDGE

-ENO DIAPHRAGMS ^y p

iiiJii

1

Fig. Al. Plan of example bridge.

TEMPERATURE AND

SHRINKAGE LONGITUDINAL DECK

REINFORCING PCSTTENSION ING

i•

.. d . Q a'. x

•o 'o 4 Q 5

o ° -a .! .p rL TRANS.TENDON

I ..

LONGITUDINAL I •• THREADED

DISTRIBUTION ROD WITI SHEATHING

REINFORCING {TRANSVERSE SLABPOSTTEN SION ING 1

tz _ z + + _ 4

1 = 2(4) = 8"

Fig. A2. Transverse section of deck showing determination of deckthickness for design example.

PCI JOURNAUSeptember-October 1989 103

(a) Compression_ (0.4) f, (AASHTO 9.15.2.2)

(0.4)4= 1.60 ksi

(b) Tensionf = 2 ^ (P-1.5)

= 2.4000/1000= 0.126 ks iCross section area, A, and section

modulus, S', of a 1-ft wide strip of slabare calculated as:

A = 8(12) = 96 in.2/ftS' = 2t 2 = 2(8)2= 128 iri,3/ft

The required transverse prestress slabforce per unit edge length, F2 , is thenfirst found if governed by tensionstresses.

f, = Fs /A - ?t1s /S'-0.126 = F2/96- 1(4.716)121/128Fs = 30.35 kips per ftAssuming tensile stress controls,

check the compression stress:f= Fs/A+^ W,/S'

= 30.35196+ [(4.716)12]1128= 0.758 ksi < 1.6 ksi = f (ok)

This deck will require amplified pre-stressing in the slab at the bridge ends tocompensate for the restraint of the dia-phragms, The required transverse slabprestress force per unit edge length inthese areas, F, , is found as:

F, = 1.2F2(P-1.3.2.4)= 1.2 (30.35)= 36.42

This amount of transverse prestress-ing roust be applied for an edge distanceat each end of the bridge ofx, where:

x-_ Wtan0+ 4<_ (L+ W tan0)/NV

(P-1.3.2.4)W tan 0 + 4 = 36 tan (21°) + 4

= 17.8 ft(L + W tan fl)/N =155+ 36 tan(21 °)1l2

= 34.4 ftUsex117.8ftTo determine the transverse tendon

spacing, the effective force per tendonafter all losses must be known. Initialstress for the threaded bars, To , is(0.8)J during jacking and should notexceed (0.7)J after seating of the an-chorage, where .f$ is the ultimatestrength of the prestressing steel

(AASHTO 9.15.1)..If the tendon were jacked to (0.8) f,

the stress at the jacking end would be:To= 0.8(150)= 120ksiFor a straight tendon, the stress at the

far end of the tendon, T, is calculatedby:

T1 = Ioe H^ ? (AASHTO 9.16.1)where

h = wobble coefficient= 0.0003 (AASHTO 9.16.1)

L' = length of tendon, ftT, = (120) e ru.i103M))

= 118.7 ksiThis must be no greater, however,

than 0.7f .(0.7 .f, = (0.7) 150

105.0 ksi < 118.7 ksiTherefore, T 105.0 ksi.

Prestress losses due to concrete creepand shrinkage and steel relaxation mayhe estimated as 22 ksi (AASHTO9.16.2.2). Thus, the final effective stressin the prestressing tendon, 1',, is:

T,= ls- 22 1(}5 - 22 = 83.0 ksiA 1-in, diameter high strength

threaded bar has a cross-sectional area of0.85 sq in. The effective prestressingforce per tendon, Fr , is then:

Fr = 7,A = (83.0) 0.85 = 70.555 kipswhere A, is the area of prestressing steelfor one tendon, in.2

The spacing of the transverse tendonsmay now be calculated,(a) Non-diaphragm regions:

Spacing = FTIFS = 70.55130.35= 2.32 ft = 27.9 in. (use 28 in.)

(b) Diaphragm regions:Spacing = FT /F, = 70.55136.42

= 1.94 ft 23.2 in. (use 23 in.)Maximum spacing of the tendons

must be checked (P-1.4).Spacing . 8 t = 8(8) = 64 in.

5ft= 60 in.3(j - t+ 12)

The distance from the slab edge to theinside face of the rail, q, is 12 in. Frommanufacturers' literature, the distancefor a ]-in, diameter threaded rod with aplate anchorage is H 35 in. Thus:

104

Spacing c 3(12- 8.25 + 2) = 47.3 in.Since the maximum design spacing of

28 in. is less than 47 in., the design ten-don spacings meet the requirements.

Concrete stresses have also beenchecked for the conditions at the time ofinitial tendon stressing and were withinacceptable limits (AASHTO 9.15.2.1).This step, however, is omitted here forbrevity.

Supplementary Bonded Reinforce-ment — Since the threaded bars will hegrouted after stressing, supplementarybonded reinforcing is not required (P1.6).

Ultimate Moment Check — The fac-tored transverse slab moment, t1 iscalculated as (AASHTO 3.22):

:11 t = (load factor) x I (dead loadcoefficient) x :VD,,+ (live load coefficient) x MILL+rl

= 1.3[1.0(0.469)+ 1.67(4.25)1= 9.83 kip-ft/ft

Nominal flexural strength of the deck,is calculated by the formula

(AASI ITO 9.17.2):

M,, =A;f d1 1-0.6(P )/JfIwhere

A; = area of prestressing steel, in.zd = distance from extreme compres-

sive fiber to centroid of pre-stressing force, in.

f * = average stress in prestressingdusteel at ultimate load, ksi

p* = ratio of prestressing steel = AB I

hd where b is width of section

For bonded tendons:f a = f (1 - 0.5 (1>'.f )I.fc

(AASHTO 9.17.4.1)The nondiaphragm area of the (leek is

critical for strength requirement since ithas less prestressing steel. For a 1-ftwide strip of slat) in the nondiaphragmnregion:

A; = 12/28(0.85) = 0.364 in./Iid = 4 in.; b = 12 in.p* = A; i/nd = 0.364/I 12(4)1

= 0.00759f ̂ = 150(1-0.51(0.00759)1501/4)

_ (128.7 ksi

.t4 = (0.3664)128.7(4) { 1 - 0.6[ (0.00759)128.7114}

= 160.0 kip-in./ft (= 13.33 kip-It/ft)l0

For post-tensioned cast-in-placemembers, rb = 0.95 (AASHTO 9.14):

13.33: 9.8310.95 = 10.35 kip-Rift (ok)Reinforcing Limits — The maximum

steel allowed is such that:p*fs„!f,' - 0.30 (AASHTO9.18.1)(0.00759)128.7/4= 0,24z 0.3 (ok)The minimum amount of reinforce-

ment must he able to develop an ulti-mate flexural capacity of at least 1.2times the cracking momen t, Welt , basedon a tensile stress of 7.5 f,' (AASHTO9.18.2.1).

f= :u('R !S'(7,5 4(HIi) i10(H1- ,Lic,1128M,, = 60.72 kip-inift

= 5,O6 kip-ft/ftM; 1.2%1

th .M, = (0.95) 13.33= 12.7 kip-ft/ft

1.2.%4,, = 1.2 (5.06)= 6.07 kip-ft/lt (ok)

Distribution Reinforcement — Lon-gitudinal distribution reinforcement inthe bottom (lithe slab is taken as:

AL . (0.03)t (P-1.7.2)AL (0.03) 8 = 0.24 in. 2/ ftSpacing of these bars must he Iess

than 12 in. (P 1.7.3).Use #4 bars spacesd at 10 in. (AL =

0.24 in.2/ft).

Shrinkage and TemperatureReinforcement

Nonpresiressed Reinforcement — RyP-1.8.1, bonded nonprestressed steelwill be needed in both directions in thetop of the slab, and in the transverse di-rection in the bottom of the slab. Use #4bars spaced at 18 in. (0.133 in. alft) in allthese location".,

Longitudinal Deck Prestressing -Since this deck is considered as exposedto a corrosive environment, and also toprotect the concrete from freeze-thaw

PCI JOURNAUSeptember-October 1989 105

IRS- D"_

4' UNBONDED •1PS_ TENDONS 1 0 HS. THREADED ROD

TRANSVERSE

REIN► FOR LATERALRAIL LOADS

ar 2-2

2" OVERLAY

WITH SHEATHING {MIDDEPTHII TRANSVERSE SLAB

POSTTEHSIONING )TENDON I^ +I 1 2=" CL.

ANCHORAGE B J l 1 1

2 SPA aT 7 * - 6" - IS' -Q

t-ig. A4. Transverse section of deck for design example.

106

ANCHOR PLAfE GROUT TUBE

MIN.

MORTARANCHORAGE Q {')'

IMPERMEABLEDUCT

PLUG p "

EPDXY RESIN __ _

BONDERAPPL,IEU BEFOREMORTAR - L^

GROUTEDTENDON

•I

y

lam. Q 2" TOP

_ BOTTOM . _ . 0

IMPERMEABLE PROTECTIVE

TENDON COATING OR CAPE%TENSION

Fig. A5. Vertical section through slab showing special detailing requirements at tendonanchorages. As detailed, this would be an electrically isolated tendon which is a patentedconcept (see Ref. 16).

deterioration, it is desirable to preventtransverse cracking of the slab. Lon-gitudinal prestressing of the deck willtherefore be used. A minimum averagecompressive stress in the slab of 100 psimust be provided to counteract lon-gitudinal tensile stresses (P-1.8.2).

Neglecting girder haunches and thedifference in modulus of elasticity be-tween the slab and girders, the compos-ite, section properties for one girder arefound to be:

A= 1213in.2I = 476,5(1) in.'+Y r - 17.19 in.h i = 44.81 in.Ignoring any compression in the slab

due to composite dead loads, the longi-tudinal prestress force, PL , required toobtain 100 psi at the slab middepth is

PCI JOURNAL/September-October 1989

determined in these calculations:From Fig. A2, it can be seen that the

center of the longitudinal prestressing isIocated 2.88 in, below the top of theslab. The eccentricity of the longitudi-nal prestressing tendon, e, is then:

e = sr - 2.88 = 17.19 - 2.88 = 14.31 in.ecf= PJJA+PL I

where c is the distance from the corn-posite neutral axis to the center of theslab.

0.10= PE 11213 + I (14.:31) (17.19 -4 )1476,5001

PL = 81.93 kips/girder= 81.93!7.5 = 10.92 kip/ft width

The effective force per strand must befound to determine the tendon spacing.The maximum tendon stress at thejacking end during stressing is:

107

To = (Q.8) fa = (0.8) 270 = 216 ksiand from AASHTO Section 9.16.1 thestress at the far end of the tendon is:

fr=where

fc = 0.002 k/ft for extrusion coatedstrand

['S = (216)e-10.0'2 ' 55" = 193.5 ksiBit

"1s (0.7) .f' = 0.7 (270) = 189 ksiSince

(0.7)}8 < 7x , let Tx = 189 ksiLosses from all other sources are

taken as 32 ksi (AASHTO 9.16.2.2), sothat the final effective stress iii the Ion-gitudinal tendons is:

T,= Ti.– 32= 189– 32= 157 ksi

The effective prestress force per ten-don for a V -in, seven-wire strand withan area ofO.153sg in, isthen:

FT = TTA,= 157(0.153)= 24.0 kips

Spacing of the longitudinal tendonsmay now be calculated.

Spacing = I-T IP, = 24.0/10.9.2= 2 .20 ft (= 24.4 in.)

Use 26 in. (17 strands total).

The effect of the longitudinal deck pre-stressing on the precast girders must beaccounted for. The tensile stress in thebottom of the girder due to the longitu-dinal deck prestressing is calculated as:f =PL /A – (FL eyb)iif= 81.93/1213– l81.93(14.31)44.811/

476,500=– 0.043 ksi

This additional tensile stress in thebottom of the precast girders may be

easily accommodated by slightly low-ering the pretensioned strand eccen-tricity, increasing the concrete strength,or adding two more pretensionedstrands.

Final Details — Other details of thetransversely prestressed deck designwhich must he addressed are the tendonlayout at the skewed ends of the deck,reinforcing for lateral railing loads, andcorrosion protection of the tendons andanchorages.

A fan tendon arrangement will beused at the acute corners of the (leek.The spacing of the tendons on skewmust be reduced by the cosine of theskew angle. In this instance, the re-duced spacing is found as:

Fan tendon spacing = (diaphragm re-gion spacing)cos0

= 23cos(21°)= 21.5 in.

Use 21 in. as shown in Fig. A3.By 1-1.10, nonprestressed reinforce-

ment will have to be provided at the slablongitudinal edges to resist the momentfrom lateral railing loads. Since the cal-culations rertnired to find the amount ofreinforcement needed are the same asfor a conventional slab, they will beomitted here.

Corrosion protection of the pre-stressing tendons and anchorages is re-quired by P 1.11. A detail For these pro-tective measures is shown together witha plan and section view of the trans-versely prestressed deck design in Figs.A3 through A5.

NOTE: Discussion of this paper is invited. Please submityour comments to PCI Headquarters by June 1, 1990.

108

ACKNOWLEDGMENTS

This paper is based on results of Proj-ect 316, "The Application of TransversePrestressing to Bridge Decks," con-ducted for the Texas State Departmentof Highways and Public Transportationin cooperation with the Federal HighwayAdministration by The University ofTexas at Austin Center for Transporta-tion Research at the Phil M. FergusonStructural Engineering Laboratory.

The contents of this paper reflect the

views of the authors and do not neces-sarily reflect the views or policies of thesponsoring agencies. The authors wishto acknowledge the major contributionA. R. Phipps made to this study, espe-cially the synthesis of research data intodesign recommendations. The authorsalso thank R. A. Almustafa, R. MoraAbaca, and M. L. Rails fir their majorcontributions to the overall researchprogram.

PCI JOURNALSeptember-October 1989 109