High-strength concrete applications to prestressed bridge girders

Construction and Building Materials, Vol. 12, Nos 2]3, pp. 105]113, 1998Q 1998 Elsevier Science Ltd

Printed in Great Britain. All rights reserved0950]0618r98 $19.00 q 0.00

( )PII:S0950–0618 97 00012-3

High-strength concrete applications toprestressed bridge girders

Catherine FrenchU†, Alireza Mokhtarzadeh‡, Tess Ahlborn‡ and Roberto LeonU

UDepartment of Civil and Mineral Engineering, University of Minnesota, 500 PillsburyDr. S.E., Minneapolis, MN 55455-0220, USA‡Graduate Research Assistant, Department of Civil and Mineral Engineering,University of Minnesota, 500 PillsburyDr. S.E., Minneapolis, MN 55455-0220, USA

Received 20 May 1994; revised 11 October 1994; accepted 11 October 1994

This paper focuses on recent research conducted at the University of Minnesota on applications ofhigh-strength concrete to prestressed bridge girders. The research comprised production of

(high-strength concrete with a variety of cementitious materials Portland cement, microsilica and fly)ash in different proportions, and made with six different types of coarse aggregate. Some specimens

( )were moist-cured in saturated limewater at 738F 238C ; others were heat-cured in an environmental( )chamber at 1208 or 1508F 508 or 658C to simulate the accelerated curing technique used by

precast/prestressed plants. The hardened concrete specimens were tested for compressive strength,(modulus of elasticity, tensile strength, modulus of rupture, shrinkage, creep, absorption potential as

)an indicator of permeability and freeze-thaw durability. In addition, a parametric study was conductedto determine the viability of using high-strength concrete in prestressed bridge girders. Two long spanprestressed bridge girders have been constructed to investigate transfer lengths, prestress losses,fatigue performance, shear and ultimate strength of girders cast with high-strength concrete. Q 1998Elsevier Science Ltd. All rights reserved.

Keywords: high-strength concrete; Portland cement; microsilica

Introduction

Given the variability in physical properties and avail-ability of concrete-making materials in different re-gions, the definition of high-strength concrete varieswith location. In general, it is defined as concrete witha uniaxial compressive strength greater than what isordinarily obtained in a region. Despite all the compli-cations which may arise from defining high-strengthconcrete, concrete made with normal-weight aggregateswith 28-day uniaxial compressive strength as de-

Ž .termined by a standard 6=12 in. 150=300 mm testŽ .specimen in excess of 6 000 psi 41 MPa is generally

referred to as high-strength concrete.Empirical equations used to predict properties of

concrete or to design structural members have beenbased on tests of concrete made with traditional mate-rials having compressive strengths less than approxi-

Ž .mately 6 000 psi 41 MPa . Extrapolation of these em-

†Corresponding author. Tel.: q1 612 6255522; fax: q1 612 6267750

pirical equations to materials of higher strength anddifferent microstructure is unjustified and may be dan-gerous. Increasing use of high-strength concrete hasmade it necessary to review our codes and designspecifications for their applicability to high-strengthconcrete. In a 1987 report produced by American Con-

Ž .crete Institute ACI Committee-363-High-StrengthConcrete4, numerous research needs were identifiedfor high-strength concrete, many of which emphasizedthe need for information on mechanical properties ofhigh-strength concrete with which to modify codes andspecifications to accommodate the new material char-acteristics. In 1993, American Concrete InstituteCommittee 363 presented a revised summary of currenthigh-strength concrete research5. Other recent state-of-the-art reports on high-strength concrete includeones published by an FIP-CEB working group onhigh-strength concrete and the British Cement Associ-ation11,20. Production, utilization and performance ofhigh-strength concrete has been a topic of discussion inmany national and international symposia in recent

105

High-strength concrete applications to prestressed bridge girders: C. French et al.106

years12 ] 14. Although there has been much recent re-search conducted regarding high-strength concrete,several issues still remain unanswered. In addition,much of the research has been directed toward cast-in-place applications, very little information is availableregarding the production and behavior of high-strengthconcrete for precast prestressed applications.

This paper focuses on the high-strength concretematerials research currently being conducted at theUniversity of Minnesota and the application of thisresearch to the prestressed bridge girder industry. Byutilizing high-strength concrete in prestressed bridgegirder systems, economy may be achieved by increasedgirder lengths or spacings. Increased girder lengthsenable greater underpass clearance widths or replace-ment of deeper girder sections with shallower sections.Wider girder spacings eliminate girder lines therebyreducing fabrication, transportation and erection costs.The materials research will be described first, followedby the application of this research to prestressed bridgegirder systems.

Materials research

The objective of the materials research underway atthe University of Minnesota is to document the effectsof mix materials, proportions, curing conditions, ageand test procedures on the mechanical properties,creep, shrinkage, absorption potential and durability ofhigh-strength concrete. Mechanical properties underinvestigation include: compressive strength, modulus ofelasticity, modulus of rupture and splitting tensilestrength. Recommendations for refinements in existingtesting practices are also sought through this investiga-tion.

Approximately 150 mixes totaling over 7 000 speci-mens have been cast over a period of three years. Mixvariables include total cementitious material contents

Ž 3.of 750, 850 and 950 pcy 445, 505 and 565 kgrm anduse of ASTM Class C fly ash and microsilica at replace-ments levels of 0, 10, 20, 30% and 0, 7.5, 10, 15%,respectively. The water-cementitious materials ratio wasmaintained at 0.30 for the major portion of this study.Six types of coarse aggregate were investigated: bothhigh and low absorptive limestone, round and partiallycrushed glacial gravel and two sources of granite. Othermix variables investigated in this study include: type of

Ž .cement ASTM Type I and III , brand of cement, typeŽ .of microsilica dry densified and slurry , type and brand

of water-reducing admixture, coarse to fine aggregateratio, aggregate gradation and maximum aggregate sizeŽ . wŽ .x1r2 in. and 3r4 in. 13 mm and 19 mm .

Ž .Effect of mold size 4=8 in. and 6=12 in. cylinderswŽ .x100=200 mm and 150=300 mm cylinders , mold

Ž .material steel and single-use plastic , specimen endŽ .condition capped, ground, unbonded neoprene cap ,

Ž .age 1, 7, 14, 28, 56, 182, 365 days and curing conditionŽ Ž .heat at 1208 and 1508F 508 and 658C , heat followed

.by limited moist, moist, limited moist and air-curedwere also investigated. The heat-cured process wasintended to simulate the curing process typical of pre-cast-prestressed manufacturers. After casting, the cylin-ders were kept at room temperature for approximately3 h. The temperature was increased to 1208r1508FŽ .508r658C over a period of 2.5 h, held constant for 12h and decreased to room temperature over a period of2 h. The moist-curing process was accomplished with alime-water bath.

All compression tests, splitting tensile strength testsand modulus of rupture tests were conducted using anMTS Model 810 Material Testing System. The system

Žhas a dual capacity of 120 000 or 600 000 pounds 534.or 2 670 kN , tension or compression and can be pro-

grammed to operate in either load or displacementcontrol modes.

Compressive strength, Young’s modulus of elasticityand splitting tensile strength were measured on both

Ž . Ž4=8 in. 100=200 mm and standard 6=12 in. 150.=300 mm specimens. Modulus of rupture of high-

strength concrete beams was determined using two-Ž .point loading of 6=6=2.4 in. 150=150=600 mm

Ž .beams with 18 in. 450 mm clear span. Creep andŽ .shrinkage specimens were 4=10 in. 100=250 mm

cylinders. A major portion of this study representsmaterials and procedures that are considered to berepresentative of what is being used in the precast-pre-stressed industry. Comparative relationships will beestablished to correlate test results from standardprocedures with those of alternative methods.

Results of materials research

The following represent some of the materials researchresults obtained from the data gathered to date.

Effect of specimen size, mold material and end condition

An initial pilot study was conducted to correlate theeffects of specimen size, mold material and end condi-tion with other available research findings. Comparisonof compressive strength test results indicate that, on

Ž .average, 4=8 in. 100=200 mm cylinders tested 6%Ž .higher than companion 6=12 in. 150=300 mm

cylinders. This finding correlated well with results fromfour other reported studies15,16,18,21. On average, 6=12

Ž .in. 150=300 mm cylinders cast in heavy-gaugereusable steel molds tested 2.5% higher than those castin single-use plastic molds. This result was consistentwith that reported by Carrasquillo et al.9 for concretecompacted by manual rodding. Compressive strength

Ž .tests of 4=8 in. 100=200 mm high-strength con-Žcrete cylinders with alternative end conditions high-

strength capping compound, neoprene caps and grind-.ing were compared. The compressive strengths of

cylinders with ground ends and cylinders tested withunbonded neoprene caps were only 1% higher than thecompressive strengths of cylinders capped with a high-

High-strength concrete applications to prestressed bridge girders: C. French et al. 107

strength capping compound up to strengths of 15 000Ž .psi 103 MPa . For the remainder of the study, con-

crete was compacted by the manual rodding method inŽ . Ž .4=8 in. 100=200 mm and 6=12 in. 150=300 mm

single-use plastic molds; high-strength capping com-pound was used for the end preparation.

( )Effect of aggregate reference mixes

The reference mix composition defined for the studyŽ 3.had a total cementitious content of 750 pcy 445 kgrm

and contained 0% fly ash and microsilica. To investi-gate the effect of aggregate on strength, tests wereconducted in which the aggregates particles were sepa-rated by sieves and recombined to provide a standardgradation in addition to conducting tests using theas-received gradation. Comparing the test results ofconcrete made from two different sources of limestone

Ž .with different absorption characteristics 1.5% vs. 2.9%in otherwise identical mixes, there was no significantdifference in 28-day compressive strengths observed.Further studies are being conducted to evaluate thecreep and shrinkage characteristics and freezerthawdurability of these two aggregates with dissimilar ab-sorption characteristics.

In comparing the compressive strengths of concretefabricated with limestone versus glacial gravel, concretemade with limestone had higher compressive strengthsŽ .Figure 1 . Limestone particles exhibited a superiorbond characteristic with cement paste and the plane offracture in limestone concrete crossed most of thecoarse aggregate particles. In contrast, round gravelparticles showed poor bond with the cement paste and,except for small-sized particles, the plane of fracturepassed around coarse aggregate particles. Compressivestrength of the mixes utilizing crushed glacial graveland granite were between those of limestone and roundgravel mixes. Failure in the rounded glacial gravelmixes appeared to occur between the aggregate andthe cement paste; whereas; the failure of the crushedgranite gravel mix was attributed to the flaky physicalnature of the aggregate. Mineralogical characteristicsof the specific granites used are suspected to be thereason for the relatively poor performance of high-

strength concretes made with granite. Further investi-gations are underway to study these observations.

Effect of total cementitious content and composition

In general, use of excessive Portland cement in anyconcrete mix design should be avoided. High-perfor-mance concrete is not only a function of strength, itrequires achievement of adequate workability and ser-viceability. Excess cement, which is sometimes used inproduction of high-strength concrete, results in moreexpensive concrete and causes larger volume change,higher temperature gradient between inside and out-side of members and possible unwanted cracking. Forthe three cementitious contents investigated, 750, 850

Ž 3.and 950 pcy 445, 505 and 565 kgrm no significantoverall advantage was observed to justify the use ofhigher cement contents. The total cementitious content

Ž 3.of 750 pcy 445 kgrm was selected for the majorportion of this study.

As observed in other studies8,23, the replacement ofcement by weight with fly ash resulted in decreased

Žcompressive strengths observed at early ages up to.approx. 180 days in comparison with strengths ob-

Žtained with the reference mixes no addition of fly ash.or microsilica for the moist-cured specimens. Nearly

all heat-cured specimens containing fly ash exhibitedŽ .lower compressive strengths at all ages to 365 days .

Fly ash differs from other pozzolans which usuallyincrease the water requirement of concrete mixes. Re-placement of cement by weight with fly ash reduced theamount of superplasticizer required for a given slump.Other benefits of using fly ash in the mixes includedreduced bleeding and segregation and improved fin-ishability of concrete; however, the literature containssome data to the contrary 23.

The replacement of cement by weight with microsil-Ž .ica SF improved the strength of concrete compared

with the reference mix at all ages for all types ofaggregate. The beneficial effect of moisture in thecuring process of microsilica concrete is evident inFigures 2 and 3. The required amount of superplasti-cizer for a given slump increased when cement wasreplaced with a dry-densified form of microsilica on a

Ž .Figure 1 Compressive strength of reference concrete}effect of aggregate 4=8 in. 100=200 mm cylinders


one-to-one weight basis. The inclusion of dry-densifiedform of microsilica increased cohesiveness and reducedsegregation and bleeding of fresh concrete. The in-creased cohesiveness required a higher slump to matchthe workability of the reference mixes.

As shown in Figure 2, a microsilica content of 7.5%by weight of cement significantly improved the com-pressive strength of high-strength concrete made withround gravel compared with the strengths observed forthe reference mixes. This was attributed to improvedbond between the round gravel aggregate and thecement paste. More aggregate fractures were noted inthe round gravel mixes containing microsilica than inthose round gravel mixes without microsilica. Becauseaggregate fracture was already achieved in compressivetests of the limestone reference mixes, the addition ofmicrosilica had much less of an effect on the strength

Ž .of the limestone mixes Figure 3 . The compressivestrength of concrete made with limestone was limited

Ž .to approximately 15 000 psi 103 MPa for 4=8 in.Ž .100=200 mm cylinders. This limit was reached whenthe plane of failure passed through almost all of thecoarse aggregate particles.

Replacement by weight of ASTM C150 Type IIIPortland cement with 10% fly ash and 7.5% microsilicahad the same effect, more or less, as that observedusing the 7.5 microsilica replacement percent by weight

of cement through 28 days. This effect is shown inFigure 4 for the glacial gravel mix. This combination offly ash and microsilica has advantages of economy andimproved workability through the incorporation of flyash, while the strength enhancement is provided by theaddition of microsilica.

Effect of curing condition

Heat curing improved the strengths of the mixes atearly ages. On average, heat-cured samples containingmicrosilica gained approximately 85% of their 28-daycompressive strength during the first 24 h. For refer-ence mixes and mixes containing fly ash this percentagewas approximately 75%. At approximately 28 days, thestrengths of the heat-cured and moist-cured specimenswere nearly equal. At later ages, the strengths of thecontinuously moist-cured specimens surpassed those ofthe heat-cured specimens. This effect was particularlysignificant for the mixes containing microsilica. Addi-tional studies are currently in progress on specimenssubjected to moisture for a period of one or three daysfollowing the heat-curing process.

Modulus of elasticity

Figure 5 shows a comparison of the modulus of elas-Ž .ticity measured on 6=12 in. 150=300 mm moist-

Ž .Figure 2 Compressive strength of glacial gravel concrete}effect of microsilica 4=8 in. 100=200 mm cylinders

Ž .Figure 3 Compressive strength of limestone concrete}effect of microsilica 4=8 in. 100=200 mm cylinders


Ž .Figure 4 Compressive strength of glacial gravel concrete}effect of FArSF 4=8 in. 100=200 mm cylinders

cured cylinders relative to the relations given in ACIŽ X .E s57 0006f psi and proposed by ACI 363:c c

E s40 0006f X q1.0=106 psic c

for 3 000 psi- f X -12 000 psic

Ž XE s3 3206f q6 900 MPac c

X .for 21 MPa- f -83 MPac

It is clear that, for high-strength concrete, the ACI318-953 equation overestimates the measured modulusof elasticity. The latter relation slightly overestimatedthe modulus of elasticity measured in this investigation.Heat-cured samples gave slightly lower modulus ofelasticity results compared with the moist-cured cylin-ders. Of additional interest is the change of modulus of

Želasticity with time shown in Figure 6 for the heat-.cured specimens . The initial modulus of elasticity is

important to the precast prestressed industry for inves-

Figure 5 Modulus of elasticity at 28 days

Ž .Figure 6 Comparison of 1-day vs. 28-day modulus of elasticity heat-cured


tigating effects such as elastic shortening. The resultsobtained from this study indicate that the initial modu-lus of elasticity is approximately 97% of the 28-daymodulus of elasticity. The highly dense cement pasteand the improved cement paste-aggregate bond, neces-sary to attain high-strength concrete, make high-strength concrete behave like an ideal composite mate-rial. Significant influence of coarse aggregate elasticproperties on elastic properties of high-strength con-crete has also been reported by other studies1,6,7.

Tensile strength of concrete

Data obtained for modulus of rupture and split cylin-der strength ranged between ACI 318-89 Code equa-tions and ACI High-Strength Committee 363 proposed

Ž .equations Figures 7 and 8 .

Modulus of rupture:

f 9 s7.56f 9 psi for normal strengthr c

concreteACI 318: Ž f 9 s0.626f 9 MPa for normal strengthr c

.concrete

f 9 s11.76f 9 psi for 3 000 psi- f 9r c c

-12 000 psiACI 363: Ž f 9 s0.946f 9 MPa for 21 MPa- f 9r c c

.-83 MPa

Splitting tensile strength:

The type of curing significantly affected the modulus ofrupture test results as evinced with the moist-curedsamples exhibiting higher flexural tensile strengths. Thiscan be explained as follows. Drying shrinkage stain in

Žheat-cured beams maximum on the surfaces of the. Žbeam are added to the flexural tensile strain maxi-

.mum on the outermost fibers during two point loadingof the beams causing the heat-cured beams to break at

Ža lower load. The moist-cured samples moist up to the.time of test did not suffer from shrinkage strain,

therefore a higher load was needed to break the

moist-cured beams. The type of curing did not affectthe splitting tensile strength of high-strength concretesamples. The reason is that during the splitting tensilestrength test the elements along the diagonal plane

Žinside the concrete with the least amount of shrinkage.strain are under tension and therefore pre-existing

Ž .shrinkage strain mostly on the surface does not inter-fere with the test result.

High-strength prestressed bridge girder research

A parametric study was conducted using LEAP soft-ware17 to determine the effect of increased concretestrength on maximum achievable girder span lengthsand spacings for a series of Minnesota Department of

Ž .Transportation MnDOT prestressed I-girder sections.The constants and variables are shown in Figure 9.Sample results are shown in Figure 10 for a MnDOT

Ž .81 I-girder which is 81 in. 2.06 m deep. The figureshows the required number of strands for a given

Ž . wŽ .xgirder spacing 4, 7 or 10 ft. 1.22, 2.13 or 3.05 m andŽ .concrete strength 7 000, 10 000, 12 000 or 15 000 psi

wŽ .x48, 69, 83, or 103 MPa to maximize the span length.As evident in the figure, wider girder spacings require agreater number of strands to achieve the same lengthas more closely spaced girders because wider spacedgirders must carry a greater proportion of the bridgedead and live loads. The compressive strengths at re-lease near the hold-down points tend to control thewider spaced girder designs because these girders mustbe fabricated with a large amount of prestress force tocarry the large loads at later ages. Girder self-weight isa significant portion of the maximum load the closelyspaced girders are required to carry. Consequently, the28-day nominal strengths tend to control the narrowerspaced girders.

At a given span length, the use of higher strengthconcrete has the effect of enabling a slight reduction inthe required amount of strands. This is a result of theincrease in allowable stresses provided by higherstrength concrete. Typical 28-day nominal concretestrengths currently produced by the precast-prestressed

Figure 7 Modulus of rupture


Figure 8 Splitting tensile strength

Figure 9 Prestressed bridge girder parametric study constants andvariables

Figure 10 Span length vs. number of required strands

Ž .10industry are on the order of 6 000 psi 41 MPa .Figure 10 shows that significant increases in span lengthmay be achieved by using higher strength concrete. For

Ž .example for the 81 I-girder section at a 4 ft. 1.22 mŽ .spacing using 0.6 in. 15 mm diameter strands, the

maximum span length may be increased by 16% goingŽ .from a nominal concrete strength of 7 000 psi 48 MPa

Ž .to 10 000 psi 69 MPa .A limit to the effectiveness of high-strength concrete

is also illustrated in Figure 10. The use of high-strength

Figure 11 Comparison of bridges cast with normal and high-strengthconcrete

concrete requires the addition of reinforcement to in-crease the maximum span lengths. As more reinforce-ment is added in the section, it it less effective due toits reduced eccentricity. Consequently, for high-strengthconcrete to be fully effective, it requires larger diame-ter higher strength reinforcement to enable its fullpotential. Another issue found to control the design of

Ž Ž . .the 81 I-girder spaced 4 ft. 1.22 m on center was theflexural moment capacity rather than the allowablestresses. If high-strength concrete is used in the bridgedeck, the span length of the 81 I-girder fabricated with

Ž .12 000 psi 83 MPa concrete may be increased furtherby 25%.

Figure 11 provides an indication of the economywhich may be achieved through the use of high-strength

Ž .concrete. The figure shows the case of a 160-ft. 48.8 mbridge fabricated with 81 I-girders of two different

Ž . wŽconcrete strengths 7 000 or 10 000 psi 48 or 69.xMPa . The use of the higher strength concrete enables

Ž . wŽa 75% increase in girder spacing from 4 to 7 ft. 1.2.xto 2.1 m . The widely spaced girders require a greater

Žnumber of strands per girder 48 compared with 32.required for the closely spaced girders because of the

increased proportion of the loads each girder mustcarry. The total number of strands required for thewidely spaced girder is lower, however, because of thereduced number of girder lines. In addition, the re-duced number of girder lines corresponds with savingsin fabrication, transportation and erection costs.

There are many questions associated with the use ofhigh-strength concrete in prestressed bridge girder sys-tems. Current ACI3 and AASHTO2 design provisionsare based on empirical relationships developed from


Figure 12 High-strength prestressed bridge girder test variables

isolated tests of specimens with concrete strengths notŽ .exceeding 8 000 psi 55 MPa . A limited number of

recent tests19,22 indicate that relationships for transferand development lengths of strands in high-strengthconcrete, as well as prestress losses versus time, varyfrom relationships based on tests of normal strengthconcrete specimens.

To investigate issues such as transfer lengths, longterm prestress losses, fatigue, ultimate flexure and shearstrengths, two long-span high-strength prestressedbridge girders were instrumented and constructed inAugust 1993 to be tested as part of the University ofMinnesota study. The girders were cast with variationson two mix designs developed through the materialsresearch program. One of the girders was cast with alimestone mix, the other was cast with a glacial gravelmix that incorporated 7.5% replacement of cement byweight with microsilica.

The girders are 45 I-girder sections. They are 45 in.Ž . Ž .1.14 m deep fabricated with forty-six 0.6 in. 15 mm

Ž .diameter 270 000 psi 1 860 MPa low-relaxation strands.The nominal 28-day concrete compressive strength was

Ž .10 500 psi 72 MPa . To best take advantage of 28-dayconcrete compressive strength, the span length of the

Ž .girder was maximized to 132.75 ft. 40.45 m . This spanlength represents a 48% increase over the maximum

Žspan length achieved using conventional 7 000 psi 48. Ž .MPa concrete fabricated with 0.5 in. 12.7 mm diame-

ter strands. Instrumentation was placed to obtain infor-mation on prestress losses, creep and shrinkage, trans-fer lengths of the strands, camber, strand stress rangesunder fatigue loading, compressive stress distributionat ultimate, cracking and ultimate flexure and shearstrengths. In addition to the effect of mix composition,

Žthe effects of stirrup configuration a conventional ‘U’stirrup and modified ‘U’ with leg extensions for im-

.proved anchorage and strand draping versus debond-Ž .ing are under investigation Figure 12 .

Actual concrete strengths achieved in the field wereabove specifications. A 28-day compressive strength of

Ž .12 000 psi 83 MPa was targeted to achieve the re-Žquired design compressive strengths of 8 925 psi 62

. Ž .MPa at release and 10 500 psi 72 MPa at 28-days.The glacial gravel with microsilica mix achieved a

Ž .strength of 10 420 psi 71.0 MPa in 18 hours andŽ .continued to increase to 11 100 psi 78 MPa by 28

days. The limestone mix surpassed the required releaseŽ .at 24 h with a strength of 9 200 psi 64 MPa . The

strength then continued to increase well above theŽdesign requirement to a strength of 12 100 psi 83.4

.MPa at 28 days. Both mixes showed good workabilityand consolidation during placement and no modifica-tions were made to standard construction techniquesfollowed by the precast manufacturer.

A concrete deck slab has been cast on each girder.Fatigue, ultimate flexure and shear tests are planned tocommence in the summer of 1994.

Summary

Research is currently underway at the University ofMinnesota to document the effects of material compo-sition, age and curing on the mechanical properties anddurability of high-strength concrete. Over 7 000 speci-mens have been cast to date. Two long-span pre-stressed bridge girders have been cast using high-strength concrete. Variables include the mix composi-tion, stirrup configuration and strand draping versusdebonding in the end regions.

This research investigation has been conducted un-der the joint sponsorship of the Minnesota PrestressAssociation, Minnesota Department of Transportation,University of Minnesota } Center for TransportationStudies and National Science Foundation Grant No.BCS-8451536. The authors also wish to acknowledgethe generous donations of materials and equipment byLehigh Cement Company, Holnam, Inc., National Min-erals Corporation, J.L. Shiely Company, EdwardKraemer & Sons, Inc., Meridian Aggregates, W.R.Grace & Co., Cormix and Elk River Concrete Products.The views expressed herein are those of the authorsand do not necessarily reflect the views of the sponsors.

Appendix 1

Conversion factors

1 in s25.4 mm1 ft. s0.3048 m1 lb. s0.454 kg1 lb. s4.448 N1 psi s0.006895 MPa1 ksi s6.895 MPa1 pcy s0.5933 kgrm3

t8 s1.8t8 q32F c

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High-strength concrete applications to prestressed bridge girders