Prestress Losses inPretensioned High-Strength

Concrete Bridge Girders

NATIONALCOOPERATIVE HIGHWAYRESEARCH PROGRAMNCHRP

REPORT 496

TRANSPORTATION RESEARCH BOARD EXECUTIVE COMMITTEE 2003 (Membership as of March 2003)OFFICERSChair: Genevieve Giuliano, Director and Professor, School of Policy, Planning, and Development, University of Southern California,

Los AngelesVice Chair: Michael S. Townes, Executive Director, Transportation District Commission of Hampton Roads, Hampton, VA Executive Director: Robert E. Skinner, Jr., Transportation Research Board

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at Berkeley RONALD F. KIRBY, Director of Transportation Planning, Metropolitan Washington Council of GovernmentsHERBERT S. LEVINSON, Principal, Herbert S. Levinson Transportation Consultant, New Haven, CTMICHAEL D. MEYER, Professor, School of Civil and Environmental Engineering, Georgia Institute of TechnologyJEFF P. MORALES, Director of Transportation, California DOTKAM MOVASSAGHI, Secretary of Transportation, Louisiana Department of Transportation and DevelopmentCAROL A. MURRAY, Commissioner, New Hampshire DOTDAVID PLAVIN, President, Airports Council International, Washington, DCJOHN REBENSDORF, Vice President, Network and Service Planning, Union Pacific Railroad Co., Omaha, NECATHERINE L. ROSS, Executive Director, Georgia Regional Transportation AgencyJOHN M. SAMUELS, Senior Vice President-Operations Planning & Support, Norfolk Southern Corporation, Norfolk, VAPAUL P. SKOUTELAS, CEO, Port Authority of Allegheny County, Pittsburgh, PAMARTIN WACHS, Director, Institute of Transportation Studies, University of California at BerkeleyMICHAEL W. WICKHAM, Chairman and CEO, Roadway Express, Inc., Akron, OH

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NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAMTransportation Research Board Executive Committee Subcommittee for NCHRPGENEVIEVE GIULIANO, University of Southern California,

Los Angeles (Chair)E. DEAN CARLSON, Kansas DOTLESTER A. HOEL, University of VirginiaJOHN C. HORSLEY, American Association of State Highway and

Transportation Officials

MARY E. PETERS, Federal Highway Administration ROBERT E. SKINNER, JR., Transportation Research BoardMICHAEL S. TOWNES, Transportation District Commission

of Hampton Roads, Hampton, VA

T R A N S P O R T A T I O N R E S E A R C H B O A R DWASHINGTON, D.C.

2003www.TRB.org

NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM

NCHRP REPORT 496

Research Sponsored by the American Association of State Highway and Transportation Officials in Cooperation with the Federal Highway Administration

SUBJECT AREASBridges, Other Structures, and Hydraulics and Hydrology Materials and Construction

Prestress Losses inPretensioned High-Strength

Concrete Bridge Girders

MAHER K. TADROSNABIL AL-OMAISHI

University of NebraskaLincoln, NE

STEPHEN J. SEGUIRANTConcrete Technology Corporation

Tacoma, WA

AND

JAMES G. GALLTPalmer Engineering Company

Winchester, KY

NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM

Systematic, well-designed research provides the most effectiveapproach to the solution of many problems facing highwayadministrators and engineers. Often, highway problems are of localinterest and can best be studied by highway departmentsindividually or in cooperation with their state universities andothers. However, the accelerating growth of highway transportationdevelops increasingly complex problems of wide interest tohighway authorities. These problems are best studied through acoordinated program of cooperative research.

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NCHRP REPORT 496

Project D18-07 FY99

ISSN 0077-5614

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Library of Congress Control Number 2003110071

2003 Transportation Research Board

Price $19.00

NOTICEThe project that is the subject of this report was a part of the National CooperativeHighway Research Program conducted by the Transportation Research Board with theapproval of the Governing Board of the National Research Council. Such approvalreflects the Governing Boards judgment that the program concerned is of nationalimportance and appropriate with respect to both the purposes and resources of theNational Research Council.

The members of the technical committee selected to monitor this project and to reviewthis report were chosen for recognized scholarly competence and with dueconsideration for the balance of disciplines appropriate to the project. The opinions andconclusions expressed or implied are those of the research agency that performed theresearch, and, while they have been accepted as appropriate by the technical committee,they are not necessarily those of the Transportation Research Board, the NationalResearch Council, the American Association of State Highway and TransportationOfficials, or the Federal Highway Administration, U.S. Department of Transportation.

Each report is reviewed and accepted for publication by the technical committeeaccording to procedures established and monitored by the Transportation ResearchBoard Executive Committee and the Governing Board of the National ResearchCouncil.

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COOPERATIVE RESEARCH PROGRAMS STAFF FOR NCHRP REPORT 496

ROBERT J. REILLY, Director, Cooperative Research ProgramsCRAWFORD F. JENCKS, Manager, NCHRPAMIR N. HANNA, Senior Program OfficerEILEEN P. DELANEY, Managing EditorKAMI CABRAL, Associate EditorANDREA BRIERE, Associate Editor

NCHRP PROJECT D18-07 PANELField of Materials and ConstructionArea of Concrete Materials

WILLIAM N. NICKAS, Florida DOT (Chair)SALIM M. BAIG, New Jersey DOTSCOT BECKER, Wisconsin DOTSTEVEN L. ERNST, FHWAJOSE GOMEZ, Virginia DOTSHAWN P. GROSS, Villanova UniversityBIJAN KHALEGHI, Washington State DOTTOORAK ZOKAIE, Leap Software, Inc., Gold River, CA JOEY HARTMANN, FHWA Liaison RepresentativeWILLIAM WRIGHT, FHWA Liaison RepresentativeSTEPHEN F. MAHER, TRB Liaison Representative

AUTHOR ACKNOWLEDGMENTSThe research reported herein was performed under NCHRP Proj-

ect 18-07 by the University of NebraskaLincoln, the contractorfor this study, jointly with Concrete Technology Corporation,Tacoma, Washington, and Palmer Engineering, Lexington, Ken-tucky. Maher K. Tadros, Cheryl Prewett Professor of Civil Engi-neering, was the principal investigator, and Nabil Al-Omaishi,Research Assistant Professor, was a prime participant in theresearch. Other major participants in the project were Stephen J.Seguirant of Concrete Technology Corporation and James G. Galltof Palmer Engineering.

Sherif Yehia, Nick Meek, Kelvin Lein, and Wilast Amornrat-tanopong of the University of Nebraska provided assistance during

the experimental phases of the project. David Scott of New Hamp-shire Department of Transportation, Bill Augustus of NortheastConcrete Products, Robert Steffen of the University of New Hamp-shire, Kevin Pruski of Texas Department of Transportation, BursonPatton of Texas Concrete Company, Arlen Clark of Clark County,Washington, Jim Parkins of Concrete Technology Corporation, andMark Lafferty of Concrete Industries provided assistance in instru-mentation and data acquisition of instrumented bridges in Nebraska,New Hampshire, Texas, and Washington. Karen Harris of the Uni-versity of Nebraska contributed to the project administration. AudraHansen, Nipon Jongpitaksseel, Ann Kulik, Chuanbing Sun, andEmil Tadros contributed to report preparation.

This report presents guidelines to help bridge designers obtain realistic estimates ofprestress losses in high-strength pretensioned concrete bridge girders and thus achieveeconomical designs. These guidelines incorporate procedures that yield more accuratepredictions of modulus of elasticity, shrinkage, and creep of concrete and more realisticestimates of prestress losses than those provided by the procedures contained in currentspecifications. This report will be of particular interest to engineers, researchers, and oth-ers concerned with the design of pretensioned concrete bridge structures.

The use of high-strength concrete for pretensioned concrete bridge girders hasbecome accepted practice by many state highway agencies because of its engineeringand economic benefits. High-strength concrete permits longer girders and increasedgirder spacing, thus reducing total bridge cost. Design of pretensioned concrete gird-ers requires accurate estimates of prestress losses. These losses are affected by factorssuch as mix design, curing, concrete strength, and service exposure conditions.

Recent research has indicated that the current provisions used for calculating pre-stress losses in normal-strength concrete may not provide reliable estimates for high-strength concrete bridge girders. Thus, research was needed to evaluate the applicabil-ity of the current provisions for estimating prestress losses in high-strength concretebridge girders and to develop guidelines for better estimating these losses in order tohelp bridge design engineers develop economic designs for such girders.

Under NCHRP Project 18-07, Prestress Losses in Pretensioned High-Strength Con-crete Bridge Girders, the University of NebraskaLincoln was assigned the task ofdeveloping design guidelines for estimating prestress losses in pretensioned high-strengthconcrete bridge girders. To accomplish this objective, the researchers reviewed relevantdomestic and foreign literature; identified limitations on the methods currently used forestimating prestress losses; conducted laboratory tests for evaluating relevant propertiesof concrete; derived formulas for predicting modulus of elasticity, shrinkage, and creepof concrete; and developed a detailed method and an approximate method for esti-mating prestress losses in pretensioned high-strength concrete bridge girders.

The research also included (a) field measurements on seven full-scale bridge gird-ers in four states selected to represent a wide range of geographic and construction prac-tices and (b) analysis of data from earlier field measurements on 31 pretensioned gird-ers in seven states. The report gives numerical examples that illustrate the use of thesemethods and demonstrate that the methods developed in this research yield better esti-mates of prestress losses than those obtained from the current methods.

The methods developed in this research can be used to obtain realistic estimates ofprestress losses in pretensioned high-strength concrete bridge girders. These methodswill be particularly useful to highway agencies and consulting firms involved in thedesign of pretensioned concrete bridge structures and are recommended for consider-ation and adoption by AASHTO as part of the LRFD Bridge Design Specifications.

FOREWORDBy Amir N. Hanna

Staff OfficerTransportation Research

Board

1 SUMMARY

3 CHAPTER 1 IntroductionProblem Statement, 3Objectives and Scope of the Research, 3Research Approach, 3Organization of the Report, 4Applicability of Results to Highway Practice, 4

5 CHAPTER 2 Background and Literature SearchIntroduction, 5Definitions, 5Components of Prestress Losses in Pretensioned Girders, 6Factors Influencing Modulus of Elasticity, 6Factors Influencing Shrinkage, 8Factors Influencing Creep, 8Factors Influencing Relaxation of Strands, 9Time-Dependent Stress Analysis, 9Prestress Loss Calculation Methods, 10Time-Step Prestress Loss Methods, 10Refined Prestress Loss Methods, 11Lump-Sum Methods, 13

14 CHAPTER 3 Research ResultsIntroduction, 14Experimental Program, 14Modulus of Elasticity, 17Experimental Shrinkage Results, 18 Experimental Creep Results, 20 Proposed Creep and Shrinkage Correction Factors, 21Proposed Shrinkage Formula, 27Proposed Creep Formula, 28Relaxation of Prestressing Strands, 28Proposed AASHTO-LRFD Revisions, 29 Numerical Example of Material Properties Using Proposed Prediction

Formulas, 29Prestress Loss, 30Experimental Program, 30Other Experimental Data, 35Proposed Detailed Prestress Loss Method, 38Proposed Approximate Prestress Loss Method, 45Comparison of Measured and Predicted Losses, 48Comparison with Previously Reported Experimental Results, 49Numerical Examples: Comparison of Proposed Prestress Loss Prediction

Methods with AASHTO-LRFD Methods, 49

56 CHAPTER 4 Conclusions and Suggested ResearchConclusions, 56Suggested Research, 57

58 SIGN CONVENTION AND NOTATION

61 REFERENCES

63 APPENDIX A Other Methods of Shrinkage Strain Prediction

63 APPENDIX B Other Methods of Creep Coefficient Prediction

63 APPENDIX C Other Methods of Prestress Losses Prediction

63 APPENDIX D Material Testing

63 APPENDIX E Modulus of Elasticity Data

63 APPENDIX F Shrinkage Data

63 APPENDIX G Creep Data

CONTENTS

63 APPENDIX H Temperature Readings

63 APPENDIX I Strain Readings

63 APPENDIX J Specific Details of the Previous Measured Prestress Losses Experimental Data

63 APPENDIX K Prestress Loss Data

63 APPENDIX L Detailed Method Spreadsheet

63 APPENDIX M Proposed AASHTO-LRFD Revisions

The objective of this research was to develop design guidelines for estimating prestresslosses in high-strength pretensioned concrete girder bridges. The guidelines are intendedto address limitations in the current AASHTO-LRFD Bridge Design Specifications.Two main areas were identified for improvement: (a) prediction of modulus of elastic-ity, shrinkage, and creep of concrete, especially as they relate to the high-strength con-crete and (b) methods for estimating prestress losses that would account for the effects ofdifferential creep and shrinkage between precast concrete girder and cast-in-place con-crete deck and for relatively high prestress levels and low creep and shrinkage in high-strength concrete.

The research consisted of experimental and theoretical programs. The experimentalprogram consisted of measurements of properties of materials and of prestress loss inseven full-scale bridge girders in four states, representing a range of geographic con-ditions and construction practices: Nebraska, New Hampshire, Texas, and Washington.In addition, test results previously reported for 31 pretensioned girders in seven states,Connecticut, Illinois, Nebraska, Ohio, Pennsylvania, Texas, and Washington, wereincluded in the study. Additionally, relevant data reported by American Concrete Insti-tute (ACI) Committee 363 and FHWA were considered.

Formulas for prediction of modulus of elasticity, shrinkage, and creep of concretethat were consistent in form with the AASHTO-LRFD formulas were developed.These formulas produced comparable results for conventional concrete with those of theAASHTO-LRFD formulas. It was concluded that local material properties significantlyimpacted the prediction of modulus of elasticity, shrinkage, and creep. The proposedformulas produce national averages; factors are given to adjust these averages for thefour states covered in the project.

A detailed method based on pseudo-elastic analysis theory using modified age-adjusted effective modulus of elasticity of concrete is proposed for estimating prestresslosses. The method considers the effects of composite action between the precast con-crete girder and the cast-in-place concrete deck, material properties, environmental con-ditions, and construction schedule parameters available. An approximate method thatproduces reasonable estimates for commonly encountered conditions is also proposed.

SUMMARY

PRESTRESS LOSSES IN PRETENSIONED HIGH-STRENGTH CONCRETE BRIDGE GIRDERS

Both methods produced better correlation with test results than current AASHTO-LRFDmethods.

Numerical examples are given to demonstrate the proposed loss prediction methodsand to explain the recommendation that no elastic shortening losses at prestress trans-fer or elastic elongation gains at application of additional load, be considered in the cal-culation of concrete stresses, if transformed section properties are used.

2

3CHAPTER 1

INTRODUCTION

PROBLEM STATEMENT

Use of high-strength concrete for pretensioned concretebridge girders has become accepted practice by many statehighway agencies because of its technical and economicbenefits. High-strength concrete permits longer girders andincreased girder spacing, thus reducing total bridge cost.The design of pretensioned concrete girders requires accu-rate estimates of prestress losses. These losses are affectedby factors such as mix design, curing, concrete strength, andservice exposure conditions.

Recent research has indicated that the current provisionsdeveloped for calculating prestress losses in normal-strengthconcrete may not provide reliable estimates for high-strengthconcrete bridge girders. Thus, research was needed to evalu-ate the applicability of the current provisions for estimatingprestress losses in high-strength concrete bridge girders and todevelop guidelines for estimating these losses. This informa-tion will help bridge design engineers to develop economicaldesigns for such girders. This project was conducted to addressthis need.

If one underestimates prestress losses, there is a risk ofcracking the girder bottom fibers under full service loads. Onthe other hand, if prestress losses are overestimated, a higherprestress force must be provided, which will result in largeramounts of camber and shortening than is necessary. It is,therefore, important to have a reasonably accurate estimate ofprestress losses.

OBJECTIVE AND SCOPE OF THE RESEARCH

The objective of this research was to develop designguidelines for estimating prestress losses in pretensionedhigh-strength concrete bridge girders. The research waslimited to the materials and practices currently used by statehighway agencies in the design and production of prestressedconcrete bridge girders and to assess their effects on prestresslosses.

To accomplish this objective the following tasks wereperformed:

1. Relevant literature, design specifications, research find-ings, and current practices for estimating prestress losses

in pretensioned concrete bridge girders were collectedand reviewed. This information was assembled frompublished and unpublished reports, contacts with statetransportation agencies, industry organizations, and otherdomestic and foreign sources.

2. Based on the information gathered in Task 1, the appli-cable range of concrete strengths for which the currentAASHTO provisions for estimating prestress losses inpretensioned concrete bridge girders was determined.

3. Based on the information gathered in Task 1, the mate-rial properties and other factors such as curing, exposure,and loading conditions that affect prestress losses in pre-tensioned high-strength concrete girders were studied.The test methods used for determining these materialproperties were identified.

4. A detailed experimental research plan, which encom-passed the investigation of full-scale girders and associ-ated analysis, was developed for evaluating the effects ofthe material properties and other factors on the prestresslosses in pretensioned concrete bridge girders. This planaddressed concrete strength levels that are currently usedby state highway agencies and are beyond the applica-bility range of the current AASHTO Specifications.

5. The plan developed in Task 4 was executed. It includeda material testing program for the field and laboratoryand a full-scale testing of seven bridge girders in fourstates. Also, an implementation plan for putting theresults of this research into practice was suggested.

6. Design guidelines for estimating prestress losses in pre-tensioned high-strength concrete bridge girders weredeveloped based on the results of the entire researcheffort.

RESEARCH APPROACH

Time-dependent prestress loss is influenced by creep andshrinkage of concrete and stress relaxation of the prestressingstrands. As concrete shrinks, the prestressing steel shortensand loses some of its tension. Consequently, concrete creepsless than in the case of sustained constant compression; so-called creep recovery takes place. Also, as concrete creepsand shrinks, the prestressing strands relax at a slower rate thanthey would if they were stressed and kept stretched between

two fixed points; thus, the reduced relaxation is less than theintrinsic relaxation that occurs in a constant-length labora-tory test. This interaction between shrinkage and creep of con-crete and relaxation of prestressing strands is partially takeninto account in the current prediction formulas of theAASHTO-LRFD Specifications (1).

The effect of high compressive strength concrete on the pre-stress loss due to creep and shrinkage strain is not taken intoaccount in the current AASHTO-LRFD Specifications (1).The use of high-strength concrete to improve the structuralefficiency of pretensioned bridge girders has created the needfor an accurate estimation of material properties that impactthe time-dependent components of prestress losses.

Also, the current AASHTO-LRFD formulas do not con-sider the interaction between the precast pretensioned con-crete girder and the precast or cast-in-place concrete deck.The concrete deck, if used, can induce significant shrinkagedeformation that results in additional stresses, thus affectingthe magnitude of the prestress losses and the tensile stress atthe girder bottom.

ORGANIZATION OF THE REPORT

This report consists of four chapters. This chapter providesthe introduction and research approach, describes the prob-lem statement and research objective, and outlines the scopeof the study. Chapter 2 describes the findings of the literaturereview, relevant material properties, and current loss predic-tion methods. The conditions for which the current AASHTO-LRFD loss prediction methods are applicable are indicated.

4

Chapter 3 discusses the material properties that affect prestresslosses. It also covers the experimental program for materialproperties and prestress loss measurements in seven full-scalegirders located in Nebraska, New Hampshire, Texas, andWashington. The proposed formulas for prediction of mod-ulus of elasticity, shrinkage, and creep of concrete and relax-ation of prestressing strands are presented. A detailed methodand an approximate method for estimating prestress lossesin pretensioned bridge girders and numerical examples todemonstrate their use are presented in Chapter 3. Chapter 4summarizes the significant conclusions of this project andpresents suggestions for future research.

APPLICABILITY OF RESULTS TO HIGHWAY PRACTICE

The design and construction of precast prestressed concretebridge girders is impacted by the amount of prestressing thatcould be applied to the girders and the effective prestressremaining after elastic and short-term losses have developed.The findings presented in Chapters 3 and 4 on the predictionof modulus of elasticity, shrinkage, and creep of concrete andon the estimation of prestress losses could be included in theAASHTO-LRFD Specifications to provide designers of pre-stressed concrete bridges with more realistic estimates of pre-stress losses. Realistic estimates of prestress losses, especiallyfor high-strength concrete, would prevent specifying exces-sive prestress forces and should result in economical designswith realistic concrete stresses at service conditions and rela-tively moderate girder camber.

5INTRODUCTION

There are two sources of possible inaccuracies in prestresslosses calculations: (a) incorrect theory and (b) inaccurateestimate of material properties. The research team revieweddomestic and foreign literature, research findings, and exper-imental data. The literature search focused on experimentsrelated to concrete material properties and prestress losses.

The prestress losses prediction formulas are used by currentAASHTO-LRFD and AASHTO Standard Specifications (2)for considering the effects of variation in material proper-ties, especially concrete strength. The range of conditions forwhich the current AASHTO-LRFD and the AASHTO Stan-dard Specifications are applicable, was determined fromthree parametric studies. The first study assessed the vari-ability of the prestress loss component attributed to concretecreep. The second study evaluated the shrinkage componentwith consideration to type of beam cross section, concretecompressive strength, relative humidity, and amounts of pre-stressing steel. The third study compared prestress losses fora number of designs using the AASHTO-LRFD methods.

DEFINITIONS

Definitions of the significant terms used in this study aregiven below because some of the terms, such as long-termprestress loss, have no universally accepted definitions. Thismakes comparing the results of some methods misleading.

Prestress Loss

The primary purpose of calculating the effective prestressforce acting on a prestressed concrete section is to evaluateconcrete stresses and deformations under service conditions.The most representative definition of prestress loss is the lossof compressive force acting on the concrete component ofa prestressed concrete section. Creep and shrinkage causemember shortening and a loss of tension in the prestressingtendons as well as a compression force increment in nonpre-stressed reinforcement, if such reinforcement exists in a mem-ber. The sum of the reduction in tensile force in the tendonsand compression force increment in the non-prestressed re-inforcement is equal and opposite to the incremental loss ofcompression force in concrete. That force is the force neededfor concrete stress analysis.

Since this project deals with pretensioned members, whichare generally reinforced in flexure with prestressing strandsonly, loss of tension in the strands is equal and opposite to lossof compression in the concrete. Therefore, the more common,though less comprehensive, definition of prestress loss, thatis, loss of tension in the prestressing strands is adopted. Pre-stress loss is considered a positive quantity, even though it isa compression increment in the strands.

Total Loss of Prestress

Theoretically, total loss of prestress is the reduction oftension from the time strands are tensioned until the end ofservice life of the prestressed concrete member. Only thepart of that total loss that is of practical significance tobridge designers is considered in this project. Thus, the totalloss of prestress is defined as the difference in the stress inthe strands immediately before transfer to the concrete mem-ber and the stress at the end of service life of the member.

Elastic Loss (or Gain)

As the prestressing force is released from the bed and trans-ferred to the concrete member, the member undergoes short-ening and cambers upward between its two ends. The elasticloss at transfer is the tensile stress loss due to prestress com-bined with stress gain due to member weight. As an addi-tional load, for example, the deck weight, is introduced to themember, the strands elongate, and thus undergo elastic gain.As will be shown in Chapters 3 and 4, the elastic losses andgains do not have to be calculated. They can be automaticallyaccounted for when transformed section properties are used.When prestress loss prediction methods are compared, it is important to isolate elastic losses and gains and properlyaccount for them in the comparison. Elastic gain is considereda negative quantity in the total loss value.

Long-Term Losses

Long-term prestress loss is the loss due to creep and shrink-age of concrete and relaxation of steel. In this study, the elas-tic losses or gains due to applied dead and live loads are notincluded in the long-term prestress loss. Because the currentAASHTO Specifications do not include any terms for elastic

CHAPTER 2

BACKGROUND AND LITERATURE SEARCH

gain due to any of the loads applied after prestress transfer,the long-term losses given in these specifications implicitlyinclude these elastic gain increments.

COMPONENTS OF PRESTRESS LOSSES IN PRETENSIONED GIRDERS

Components of prestress losses are illustrated in Figure 1and described below.

(a) Loss due to prestressing bed anchorage seating, relax-ation between initial tensioning and transfer, andtemperature change from that of the bare strand totemperature of the strand embedded in concrete. Thiscomponent is not considered in this project.

(b) Instantaneous prestress loss at transfer due to pre-stressing force and self weight.

(c) Prestress loss between transfer and deck placement dueto shrinkage and creep of girder concrete and relaxationof prestressing strands.

(d) Instantaneous prestress gain due to deck weight on thenoncomposite section and superimposed dead loads(SIDL) on the composite section.

(e) Long-term prestress losses after deck placement dueto shrinkage and creep of girder concrete, relaxation ofprestressing strands, and deck shrinkage.

Prestress losses in pretensioned high-strength concretegirders are influenced by material properties (internal factors)and environmental conditions (external factors). Accurateprediction of prestress losses requires accurate prediction ofthe long-term properties of concrete and prestressing strands,which is a very complex process because of the uncontrollablevariables involved. The material properties that vary with timeand affect prestress losses are compressive strength, modulusof elasticity, shrinkage (stress independent), and creep (stressdependent) of concrete, and relaxation of strands.

6

The rate at which concrete properties change with timedepends on a number of factors, including type and strength ofcement, type, quality, and stiffness (i.e., modulus of elastic-ity) of aggregates, and quantity of coarse aggregates; type andamount of admixtures; water/cement ratio; size and shape ofthe girder; stress level; and environmental conditions (humid-ity and temperature). Relaxation of strands is a long-termreduction of stress when strands are subjected to an imposedstrain, and can be estimated with good accuracy.

FACTORS INFLUENCING MODULUS OF ELASTICITY

The factors that affect the determination of modulus of elas-ticity in the laboratory are the moisture content and the load-ing conditions, such as top and bottom bearing plate sizes,loading rate, and specimen shape and size. Stiffness of thecement paste, porosity and composition of the boundary zonebetween paste and aggregates, stiffness and porosity of theaggregates, and proportion of the concrete constituents are alsofactors. Both concrete strength and concrete unit weight areindirect factors in influencing the modulus of elasticity. Theyare dominantly used in prediction formulas as a way of cap-turing the fundamental underlying factors. This, in part,explains the inaccuracy in the current prediction of the modu-lus of elasticity of concrete, Ec. In early-age concrete, thestrength of the cement paste is the primary contributor to thestrength while the stiffness of the coarse aggregates is the pri-mary contributor to the modulus of elasticity.

Accurately estimating the value of Ec allows for accurateprediction of the initial camber and initial elastic prestress lossand helps improve the accuracy of the prediction of creeploss. The modulus of elasticity increases approximately withthe square root of the concrete compressive strength; empiri-cal equations have been developed to estimate the modulus ofelasticity based on the compressive strength of the concrete.

Stress in strands

TimeStrand Prestress Deck tensioning transfer placement

Anchorage seating loss

Jacking

Relaxation and temperature losses

Creep, shrinkage and relaxation

Elastic gaindue to deck placement

A

BCD

E

F

Superimposed

H

I KElastic gaindue to SIDL

Elastic gain due to live loadJ

Live load

G

Elastic shortening

dead load

Figure 1. Stress versus time in the strands in a pretensioned concrete girder.

When the unit weight of concrete, wc, is different from0.145 kcf (assumed for the normal unit weight concrete inSection C5.4.2.4 of the AASHTO-LRFD Specifications), andin the absence of more laboratory data, the modulus of elas-ticity, according to the AASHTO-LRFD (1), the ACI-318 (3),and the Precast/Prestressed Concrete Institute Bridge DesignManual (PCI-BDM) (4), is based on the compressive strengthand unit weight of concrete (AASHTO Equation 5.4.2.4-1and ACI-318 Equation 8.5.1):

The above formula is applicable to concretes with unitweights between 0.090 and 0.155 kip/ft3 (1,442 and 2,483 kg/m3). According to ACI-363 Committee Report (5 ),this formula tends to significantly overestimate the modulusof elasticity for concretes with compressive strengths over6 ksi (41 MPa). Other equations were proposed, and thefollowing formula was adopted by ACI Committee 363(ACI-363 Equation 5-1):

This formula does not account for factors other than the unitweight and compressive strength that clearly affect the valueof Ec, such as coarse aggregate content in concrete and prop-erties of the aggregates. Myers and Carrasquillo (6) showedthat elastic modulus appeared to be a function of the coarseaggregate content and type.

E w f kcf and ksi

E w f kg m and MPa

c c c

c c c

= ( ) + ( ) ( )= ( ) + ( ) ( )

0 145 1000 1265 2

86 6900 3320

1 5

1 5 3

. ( ).

.

E w f kg m and MPac c c= ( )0 043 1 5 3. .E w f kcf and ksic c c= ( )33 000 11 5, ( ).

7

The prediction of the modulus of elasticity can be consider-ably improved if the influence of the modulus of elasticity ofthe particular type of aggregate used in the concrete is takeninto account. This has been reflected in the Comit Euro-Inter-national du Beton-Fdration Internationale de la Prcontrainte(CEB-FIP) Model Code (7), which introduced the empiricalcoefficient E to reflect the strength of the aggregate used:

where: Ec = tangent modulus of elasticity at zero stress andat a concrete age of 28 days and fcm = mean compressivestrength of concrete. The values of the empirical coefficientE are 1.2 for basalt and dense limestone, 1.0 for quartzaggregates, 0.9 for limestone, and 0.7 for sandstone.

Figure 5.3 of the ACI-363 Committee Report compares val-ues for the modulus of elasticity of concrete experimentallydetermined from previous research with those predicted by theACI-318 Building Code formula and based on a dry unit weightof 0.145 kip/ft3. This chart was reproduced and is included inFigure 2, which also includes experimental data collected fromthe FHWA Showcase (8). Deviations from predicted values arehighly dependent on the properties of the coarse aggregate.

The research work at the University of Minnesota indicated,based on the use of local materials, that the AASHTO-LRFDequation overestimated the modulus of elasticity of high-strength concrete (Ahlborn [9]). Researchers at the Universityof Texas (6 ) reported all high-strength concrete mixes testedin their research had moduli of elasticity larger than thosepredicted by ACI Committee 363 formula. Huo (10) and Huoet al. (11) indicated that both the AASHTO-LRFD and the

E f ksi

E f MPa

c E cm

c E cm

= ( ) ( )= ( ) ( )

3100 1 44

21500 103

1 3

1 3

.

( )

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0Compressive Strength (ksi)

Modulus of Elasticity (ksi)

(ksi)fAASHTO-LRFD, Ec = 33,000w1.5 c'

( ) (ksi)0.145

wcf 'c 1,0001265ACI 363, Ec = 1.5

Figure 2. Modulus of elasticity versus compressive strength data obtained from ACI-363 Report (5) and FHWA Showcase (8).

ACI Committee 363 equations underestimated the modulusof elasticity of three high-strength concrete mixes studiedin that research.

The differing opinions among researchers on the predictionequations for the modulus of elasticity have raised a questionas to how to correctly predict the value of Ec for high-strengthconcrete. Although all the prediction equations for modulusof elasticity have compressive strength of concrete f c as a vari-able, other factors clearly affect the value of Ec, such as coarseaggregate content in the concrete and properties of the aggre-gates. These factors will be further explored in Chapter 3.

FACTORS INFLUENCING SHRINKAGE

Shrinkage depends on many variables, including water-to-binder ratio, moisture, relative humidity of the environment,ambient temperature, aggregate properties, and size and shapeof the structural member. It is assumed to be independent ofloading and results primarily from shrinkage of the cementpaste. Because aggregates tend to restrain the shrinkage ofthe paste, the stiffness and proportion of aggregates influenceshrinkage.

Shrinkage is conveniently expressed as a dimensionlessstrain under steady conditions of relative humidity and tem-perature. The AASHTO-LRFD formula for estimating shrink-age strain, sh, as a function of a time-development factor, ktd,and the ultimate shrinkage (at time infinity), sh, u, is:

=( ) 3 100 12H70 for H 80% ( )

k humidity factor for shrinkage

H70

for H < 80%,

hs =

=

140 11( )

k V/S ratio size correction factor

te t

tt

V S

s

V S

= ( )

=+

+

26

45

1064 94923

100 36. ( )

sh s hsk k= ( )9

k tt

after days of moist curingtd =+35

7 8( )

k tt

after days of accelerated curing

td = +55 1 3 7

( )

sh,u sh for moist curing= 510 10 66 ( )

sh,u sh for accelerated curing= 560 10 56 ( )

sh td sh,uk= ( )4

8

In these equations, t is drying time after end of curing indays, H is relative humidity of ambient air, and V/S ratio isvolume-to-surface ratio in inches. Other methods of predict-ing shrinkage strain such as the PCI-BDM, the ACI-209 (12),and the CEB-FIP are presented in Appendix A.

FACTORS INFLUENCING CREEP

The creep of concrete depends on many factors otherthan time, such as volume content of hydrated cementpaste, relative humidity, the type and volume of the aggre-gate, the age of the concrete at the time of loading, the stresslevel, the duration the concrete is stressed, and the geome-try of the member. The size and shape of a concrete mem-ber can significantly influence the rate and the magnitudeof creep. Hansen (13) observed that the rate and magnitudeof ultimate creep were substantially smaller for largermembers.

Creep in high-strength concrete is generally smaller thanin normal-strength concrete loaded to a similar stress levelbecause of the lower water-to-binder ratio of high-strengthconcrete. At any time, the creep strain can be related to theinitial elastic strain by a creep coefficient, (t, ti), which isthe ratio of creep strain to elastic strain. Creep strain willreach its ultimate value with an ultimate creep coefficient,u, at the end of the service life of the structure.

The AASHTO-LRFD creep prediction formulas are pre-sented here. Other methods, for example, the PCI-BDM, theACI-209, and the CEB-FIP are presented in Appendix B.

k loading age factor tla = = 1 0 118 19. ( )

k humidity factor for creep H120hc

= =

1 58 18. ( )

k size factor

te t

tt

.77e

c

V S -0.54V S

=

=+

+

+

26

45

1 80 12 587

170 36..

.

( )

k concrete strength factor

f with f in ksi

f

cc

=

=

+

1

0 679

16.

( )

cr f c hc lak k k k= ( )15

u cr= 3 5 14. ( )

t, t ki td u( ) = ( )13

ti = age of concrete, in days, when load is initially appliedfor accelerated curing or the age minus 6 days formoist curing.

FACTORS INFLUENCING RELAXATION OF STRANDS

If a strand is stressed and then held at constant strain, thestress decreases with time. The decrease in stress is calledintrinsic relaxation loss. The intrinsic relaxation loss is largerwith larger initial stress and higher temperature. Strands usedin current practice are low-relaxation strands, which undergoconsiderably less relaxation than stress-relieved strands. As aresult, the relaxation component of prestress loss has becomea very small one.

The intrinsic relaxation loss for stress-relieved strand 1:

The intrinsic relaxation loss for low-relaxation strand 1:

where: t is time in days from time of initial stressing, fpj (ksi),fpy (ksi) is yield strength of prestressing steel estimated at

f t40.0

ff

fpR1pi

pypj=

( )

log .. ( )24 0 0 55 22

f t10.0

ff

fpR1pi

pypj=

( )

log .. ( )24 0 0 55 21

k time-development factor t tt t

tdi

i= =

( )+ ( )

0 6

0 61020

.

.

( )

9

85% of ultimate strength for stress relieved strands and 90%for low-relaxation strands. Relaxation loss in prestressingstrands after transfer is given by the formulas:

For stress-relieved strand:

For low-relaxation strand:

where: fpES is loss due to elastic shortening, fpSR is loss dueto shrinkage, and fpCR is loss due to creep. Low-relaxationstrands are the standard product for concrete girders. In mostapplications, the relaxation loss after transfer is in the 1.8 to3.0 ksi rangea relatively small component of the total pre-stress loss.

TIME-DEPENDENT STRESS ANALYSIS

Stress-Strain Relationships

The strain that occurs upon initial loading in a concrete spec-imen subjected to a sustained axial load is the elastic strain.Additional strain then develops with time due to creep andshrinkage. Shrinkage strain is stress-independent. The ratio ofcreep strain at time t to elastic strain for a concrete specimenloaded at time ti is creep coefficient, (t, ti). Figure 3 shows

f f f f ksipR2 pES pSR pCR= +( ) ( )6 0 0 12 0 06 24. . . ( )

f f f f ksipR2 pES pSR pCR= +( ) ( )20 0 0 4 0 2 23. . . ( )

Stress

Time

Constant stress

Variable stressStress f

Strain

Time

sh c

2f

= (1+ )+ E sh

c1

f = (1+ )+ E

c

f = E

Variable stress

Constant stress

Figure 3. Creep strain for constant and variable stress conditions.

creep strain versus time for constant and variable concretestress conditions.

Age-Adjusted Effective Modulus

Elastic and creep strains of concrete can be combined andtreated as if they were elastic deformations through use of anage-adjusted effective modulus of elasticity. For constantsustained stress, the elastic-plus-creep strain is equal to (1 +) times the elastic strain. Thus, the elastic-plus-creep straincan be thought of as elastic-only strain if an effective modu-lus of elasticity is used to calculate that pseudo-elastic strain.

Therefore, the total concrete strain under long-term con-ditions is:

If the concrete stress varies with time, the elastic-plus-creep strain becomes (1 + ) where the coefficient is theaging coefficient, initially proposed by Trost (14) and furtherdeveloped by Bazant (15) and Dilger (16). It varies between0 and 1 depending on concrete stress variability and the agingprocess of the member being considered. The age-adjustedeffective modulus of elasticity of concrete is thus defined as:

The total concrete strain is:

Thus, the time-dependent analysis for the effects of allconstant sustained loads (initial prestress, self weight, deckweight, and SIDL) can be carried out using an effective elas-ticity modulus E c as defined by Equation 25, and for variablestress inducing effects (prestress loss and differential creepand shrinkage between the precast and cast-in-place compo-nents of section) using the age-adjusted effective modulusdefined by Equation 27. Tadros et al. (17, 18) demonstratedthat, for precast prestressed concrete members, the agingcoefficient ranges between 0.6 and 0.8.

Procedure for Time-Dependent Stress Analysis

The procedure presented by Dilger (16 ) may be used forcomputing time-dependent stresses in prestressed concretemembers. The analysis is based on initial strain theory often

2 28=

+fE

c

csh ( )

=+

E E1cc

( )27

1 26=

+fE

c

c

sh ( )

=

+E Ec c1

25

( )

10

employed in finite-element analysis of the effects of temper-ature change in structures.

The following three steps illustrate this analysis for simplysupported precast concrete members.

Step 1: Immediately after transfer of prestress, separate thevarious components of the cross section into free-to-deformelements to allow deformation due to creep, shrinkage, andrelaxation. Deformation of mild reinforcement is assumed tobe zero. Concrete deformation will occur due to creep andshrinkage, and prestressing steel deformation will be relatedto its relaxation.

Step 2: The deformation of each of the components isbrought to zero by applying axial force and bending momentto the concrete and axial force to the prestressing steel, usingage-adjusted concrete modulus of elasticity.

Step 3: The various components are then reconnectedassuming full bond between them to restore equilibrium. Thisis done by applying equal and opposite forces to the restrain-ing forces calculated in Step 2. These new forces are com-bined into an axial force and a bending moment introduced tothe age-adjusted equivalent transformed composite section.The deformation of the member due to this step is the totaldeformation. The stresses in the various components are thesum of the stresses obtained in Step 2 and Step 3.

PRESTRESS LOSS CALCULATION METHODS

Estimating prestress loss requires an accurate predictionof material properties and of the interaction between creepand shrinkage of concrete and the relaxation of steel. In addi-tion, prestress losses are influenced by composite action be-tween the cast-in-place concrete deck and the precast concretegirders. Use of high-strength concrete in precast prestressedconcrete allows for high levels of prestress and long spancapacities. However, experience in estimating prestress lossfor high-strength concrete is limited. Approaches for esti-mating prestress losses can be divided into the followingthree major categories, listed in descending order of complex-ity and accuracy:

(a) Time-Step methods(b) Refined methods(c) Lump-Sum methods

TIME-STEP PRESTRESS LOSS METHODS

These methods are based on a step-by-step numericalprocedure implemented in specialized computer programsfor the accurate estimation of long-term prestress losses. Thisapproach is especially useful in multi-stage bridge construc-tion such as spliced girder and segmental box girder bridges.As concrete creeps and shrinks, the prestressing strands shortenand decrease in tension. This, in turn, causes the strands to relaxless than if they were stretched between two fixed points.Hence, reduced rather than intrinsic relaxation loss takes

place. As the prestressing strand tension is decreased, con-crete creeps less, resulting in some recovery.

To account for the continuous interactions between creepand shrinkage of concrete and the relaxation of strands withtime, time will be divided into intervals; the duration of eachtime interval can be made progressively larger as the concreteage increases. The stress in the strands at the end of each inter-val equals the initial conditions at the beginning of that timeinterval minus the calculated prestress losses during the inter-val. The stresses and deformations at the beginning of aninterval are the same as those at the end of the preceding inter-val. With this time-step method, the prestress level can beestimated at any critical time of the life of the structure. Moreinformation on these methods is given in Tadros et al. (19),Abdel-Karim (20) and the PCI-BDM (4).

REFINED PRESTRESS LOSS METHODS

In these methods, individual components of prestress lossare calculated separately and the total prestress losses are thencalculated by summing up the separate components. How-ever, none of these methods accounts for composite actionbetween deck slabs and precast girders. Because the deckconcrete shrinks more and creeps less than the precast girderconcrete, prestress gain rather than prestress loss may occur.

Data representing the properties of materials, loading con-ditions, environmental conditions, and pertinent structuraldetails have been incorporated in the prediction formulasused for computing the individual prestress loss components.Over the years, several methods have been developed. Amongthese methods, are the current AASHTO-LRFD Refinedmethod (1), the AASHTO Standard Specifications method (2),and the PCI-BDM method (4).

In the eleventh edition of the AASHO (currently calledAASHTO) Specifications, total losses were estimated as asum of individual components. The provisions for prestressloss that appeared in the 1973 Specifications (21) were firstintroduced in the 1971 Interim Specifications. These provi-sions marked the first use of a rational method of estimatingloss of prestress in the AASHO/AASHTO Specifications.The following equation was introduced in the 1971 InterimSpecifications:

where: fs = total loss of prestress, ES = loss due to elasticshortening, SH = loss due to concrete shrinkage, CRC = loss

f ES SH CR CRs C S= + + + ( )29

11

due to creep of concrete, and CRS = loss due to relaxation ofprestressing steel.

Elastic Shortening Losses

Elastic shortening losses were estimated using the follow-ing equation:

where: fcgp = average concrete stress at the center of gravity ofthe prestressing steel at time of release. The coefficient 7 inthis equation was apparently an estimate of the modular ratioof Es to Eci. Losses due to elastic shortening after release ofprestressing force in the AASHTO 1977 Specifications (22)were given by:

where: Es = modulus of elasticity of prestressing steel andEci = modulus of elasticity of concrete at time of release.

Shrinkage Losses

Losses due to concrete shrinkage provided in the 1973 Spec-ifications (21) are given in Table 1. These values correspondto a value for ultimate shrinkage strain of approximately 550 106 for concrete and a modulus of elasticity of approximately28,000 ksi for prestressing tendons. A reduction factor, of 0.77was used to adjust the ultimate shrinkage strain for a V/S ratioof approximately 4 in. Correction factors for average ambientrelative humidity were applied by the PCI Committee on Pre-stress Losses (23); the final values appearing in the StandardSpecifications are shown in Table 2.

Starting with the twelfth edition in 1977, the AASHTOSpecifications (22) provisions for estimating loss of prestresshave remained essentially unchanged. The prestress lossesformula was repeated in its original form from the 1973 Spec-ifications (21), but changes in equations for estimating thecomponents were made. These changes were first introducedinto the Specifications with the 1975 Interim AASHTO Spec-ifications. Losses due to shrinkage of concrete were given by:

where: H =mean annual ambient relative humidity, in percent.This equation was developed to yield similar results as those

SH H= 17 000 150 32, ( )

ES EE

fsci

cgp= ( )31

ES fcgp= 7 30( )

Average ambient relative humidity (percent) SH losses (ksi) 100 - 75 5 75 - 25 10 25 - 0 15

TABLE 1 Shrinkage losses versus humidity in 1973 AASHO Specifications (21)

in the table contained in the 1973 Specifications, but elimi-nated the abrupt change in shrinkage loss between the threehumidity ranges given in the PCI Committee Report (23). Figure 4 depicts the shrinkage losses predicted by theAASHTO 1977 Specifications and provides a comparisonwith the 1973 Specifications.

Creep Losses

Losses due to creep of concrete in the 1973 AASHO Spec-ifications were given by:

where: fcd is the average concrete compressive stress at thecenter of gravity of the prestressing steel under full deadload. The factor 16 is approximately the product of a modu-lar ratio of 7 and an ultimate creep coefficient of 2.3.

Losses due to creep of concrete in the 1975 AASHTOInterim Specifications were:

where: fcgp is as defined for elastic shortening losses and fcds= concrete tensile stress at the center of gravity of the pre-stressing steel due to all dead loads except the self weight ofthe beam.

Relaxation Losses

The 1973 AASHO Specifications did not provide an equa-tion for estimation of relaxation losses for low-relaxation

CR f fC cgp cds= 12 7 34( )

CR fC cd= 16 33( )

12

strands; it provided the following equation for stress-relievedstrands.

The constants in the above equation can be derived ifone assumes an intrinsic relaxation loss of approximately10% of fpi, and a relaxation reduction factor of one-eighthof the combined SH, ES, and CRC values, to account for theeffects of member shortening on the intrinsic relaxation loss.The 1975 AASHTO gave the following formulas for stress-relieved and low-relaxation strands.

(a) For stress-relieved strands, losses due to relaxationwere given by:

(b) For low-relaxation strands, losses due to relaxationwere given by:

The first edition of AASHTO-LRFD Bridge Design Spec-ifications (24) was adopted and published in June 1994. Inthis edition, the refined method of estimating time-dependentlosses was basically the same as the one used in the previouslypublished AASHTO Standard Specifications. However, relax-ation loss after transfer for low-relaxation strands was takenas 30% of the relaxation loss for stress-relieved strands.

The current AASHTO-LRFD Refined Estimates methodcomputes the prestress losses in members constructed andprestressed in a single stage, relative to the stress immediatelybefore transfer, as a sum of individual loss components:

where: fpT is total loss of prestress, fpES is loss due to elas-tic shortening, fpSR is loss due to concrete shrinkage, fpCRis loss due to creep of concrete, fPR2 is loss due to relaxationn of prestressing steel.

The elastic shortening loss in pretensioned members isgiven by:

where: Ep is modulus of elasticity of prestressing strands andEci is modulus of elasticity of concrete at transfer.

f f E EpES cgp p ci= ( )39

f f f f fpT pES pSR pCR PR2= + + + ( )38

CR ES . 5 SH CRS C= +( )5 000 0 1 0 0 37, . ( )

CR ES . SH CRS c= +( )20 000 0 4 0 2 36, . ( )

CR SH ES CRS C= + +( )20 000 0 125 35, . ( )

Humidity (percent)

Shrinkage strain

Steel modulus of elasticity (ksi)

V/S ratio factor

Humidity factor

Shrinkage loss (ksi)

100 - 75 550x10-6 28,000 0.77 0.3 3.56 75 - 25 550x10-6 28,000 0.77 1.0 11.86 25 - 0 550x10-6 28,000 0.77 1.3 15.42

TABLE 2 Shrinkage loss prediction using PCI Committee method (23)

02000400060008000

1000012000140001600018000

0 20 40 60 80 100 120

RH (%)

SH Losses (psi)

1997 AASHTO1973 AASHTO

Figure 4. Losses due to concrete shrinkage.

Loss due to shrinkage of concrete is taken as a function ofthe relative humidity only, and does not take into account thevariability of shrinkage with other parameters as indicated inSection 5.4.2.3.3 of the AASHTO-LRFD. Shrinkage loss isestimated by the following equation:

where: H = mean annual ambient relative humidity.

Loss due to creep may be taken as:

where: fcdp = change in concrete stress at the center of grav-ity of the prestressing strands due to the permanent loads, withthe exception of the load acting at the time the prestressingforce is applied. Values of fcdp should be calculated at thesame section or at the sections for which fcgp is calculated.

The relaxation after transfer is:

Other methods of prestress losses prediction such as thePCI-BDM method (4), CEB-FIP Model Code method (25),Ontario Bridge Design Code method (26), ACI-ASCE Com-mittee 423 method (27), Concrete Technology Associates(CTA) method (28), Modified Rate of Creep method (29), andTadros et al. method (19) and are given in Appendix C.

LUMP-SUM METHODS

Lump-sum methods represent average conditions. Theyare useful in preliminary design, but the estimated loss shouldbe recalculated in the final design. According to the currentAASHTO-LRFD Approximate method, prestress loss forgirders with 270 ksi low-relaxation strands is given by thefollowing formulas:

f f f fpR2 pES pSR pCR= +( )6 0 0 12 0 06 42. . . ( )

f 1 f fpCR cgp cdp= 2 0 7 0 0 41. . ( )

f 1 HpSR = 7 0 0 15 40. . ( )

13

where: PPR is the partial prestress ration, which normally= 1 for precast pretensioned members. These formulasreflect trends obtained from a computerized time-stepanalysis of different beam sections for an ultimate concretecreep coefficient ranging from 1.6 to 2.4, ultimate concreteshrinkage strain ranging from 0.0004 to 0.0006, and rela-tive humidity ranging from 40% to 100%.

This procedure recognizes reduction in prestress loss forconcrete compressive strengths above 6.0 ksi. However, itdoes not recognize higher prestress levels for higher concretestrengths. It assumes, without justification, a large differencein prestress loss prediction for box girders and I-girders, andconversely no difference in loss values for vastly differentproduct types: I-girders, double tee beams, and voided slabs.

Based on a review of available information, it was evidentthat additional research is required to establish realistic esti-mates of modulus of elasticity, creep, and shrinkage of high-strength concrete. The AASHTO-LRFD provisions need tobe updated (1) to consider high-strength concrete in Sections5.4.2.3 and 5.4.2.4, (2) to improve the prestress loss calcu-lation methods of Section 5.9.5 for high-strength concrete,and (3) to link the material property formulas of Sections5.4.2.3. and 5.4.2.4 with prestress loss prediction formulasof Section 5.9.5 into one integrated approach. Both detailedand approximate estimation of prestress losses are neededin design depending on the design stage and the type ofmember.

33 1 0 15 6 6 6 8

46

( )[ ]+ ( ).( )

f PPR ksi

for Double Tees and Voided Slabs;c

33 1 0 15 6 6 6 6 45 ( )[ ]+ ( ). ( )f PPR ksi for I-Girders;c

26 4 644

+ ( )PPR ksi for Rectangular Beams and Solid Slabs; ( )

19 4 4 43+ ( )PPR ksi for Box Girders; ( )

INTRODUCTION

This chapter presents the prediction formulas of modulusof elasticity, creep, and shrinkage of high-strength concrete.The experimental basis for the proposed prediction formu-las is given. Seven bridge girders in the states of Nebraska,New Hampshire, Texas, and Washington were instrumentedfor prestress loss measurement. Two methods are proposed forthe estimation of prestress losses, a detailed method and anapproximate method. The laboratory and field measurementswere used to verify and calibrate the prediction methods.

In applying the proposed prediction methods, two alter-natives for the input material properties were used. The firstalternative was to use the measured material properties for thebridge girders that had been instrumented for prestress loss.The second alternative was to use specified and predictedmaterial values that would normally be available to designers.In the latter alternative, specified concrete strength, assumedconstruction schedule, and the corresponding estimated mod-ulus of elasticity, creep, and shrinkage were input into the lossprediction formulas. Comparisons were also given betweenmeasured loss values and those predicted by other methods inorder to demonstrate the improvements offered by the pro-posed method.

Formulas presently used by various codes for computingconcrete modulus of elasticity, shrinkage, and creep have beenempirically established based primarily on data for normal-strength concrete with compressive strength up to 6.0 ksi (30).There has been recent interest in reevaluating these formulasand extending their applicability to concrete strengths between8.0 and 12.0 ksi. Experimental work included both laboratorytests and field measurements.

This section covers the material testing program of con-crete mixes used in Nebraska, New Hampshire, Texas, andWashington for pretensioned concrete girders and presentsthe results of previously reported research. For each materialproperty, a summary of measured values is presented, fol-lowed by a proposed estimation method. A record of all datacollected in this research is given in the appendixes (which arenot published herein) for the various parameters evaluated.

EXPERIMENTAL PROGRAM

The materials testing program consisted of laboratorymaterial tests conducted at the University of Nebraska (lab-

14

oratory tests) and material tests conducted at girder produc-tion plants and at construction sites (on-site tests).

Laboratory Material Tests

The precast concrete producer in each of the four statesprovided three concrete mix designs and furnished raw ma-terials for making and testing specimens at the University ofNebraska. One of the mixes represented the concrete intendedto be used in the instrumented bridge girders. In addition, eachparticipating state highway agency arranged for shipping rawmaterials and for producing this mix in laboratories that pro-vided one mix design for the normal-strength concrete usedin bridge deck construction. Proportions of state highwayagency mixes are given in Tables 3 through 6. Additionaldetails are given in Appendix D.

Twenty-seven 4 in. by 8 in. concrete cylinders were madefor each of the three high-strength concrete mixes and for thenormal-strength concrete deck mix. For each concrete mix, aset of three cylinders was tested for concrete compressivestrength and modulus of elasticity at each of the followingages1, 3, 7, 14, 28, 56, 90, 128, and 256 days. Shrinkagemeasurements were performed using three 4 in. by 4 in. by24 in. specimens per concrete mix design. A total of 12 spec-imens were required for testing three high-strength mixes forthe girder mix and one normal-strength mix for the deck. Atotal of 48 specimens were tested.

Four 4 in. by 4 in. by 24 in. specimens were used to obtainthe creep measurements for each of the three girder mixes.Three specimens were loaded at the age of 1 day, and onespecimen was loaded at 56 days. Twelve specimens wererequired for the three high-strength concrete mixes producedfor each state. A total of 48 creep tests were performed.

On-Site Materials Testing

In addition to the laboratory specimens, similar specimenswere made and monitored in the field. They were subjected tothe same curing and environmental conditions as the bridgegirders. The on-site testing program consisted of the follow-ing. Eighteen 4 in. by 8 in. cylinders were produced at each ofthe four plants. Sets of three cylinders were tested for concretecompressive strength and modulus of elasticity at the agesof 1, 3, 7, 14, 28, and 56 days. A set of three 4 in. by 4 in. by

CHAPTER 3

RESEARCH RESULTS

15

Mix designation NE09G NE10G NE12G NE04D

Size (in.)/Type 0.75, ASTM Grade 5 0.5,

ASTM Grade 5 0.375,

ASTM Grade 5 1.5,

ASTM Grade 5 Crushed limestone

Quantity (pcy) 1530 1860 1913 883 Size/Type Nebraska 47B None Nebraska 47B Nebraska 47B

Sand and gravel Quantity (pcy) 765 None 933 2039

Size/Type ASTM C33 ASTM C33 None None Sand

Quantity (pcy) 765 990 None None Potable water Quantity (pcy) 250 240 254 263

Type III I III I Cement type Quantity (pcy) 705 750 680 658 Silica fume Quantity (pcy) None 50 None None

Type None Class C Class C None Fly ash Quantity (pcy) None 200 320 None Type Prokrete N Prokrete N WRDA 19 Prokrete N High-range water

reducer Quantity (oz/100 lb of binder) 30 30 34.2 5-14 Type Conchem SP-L Type A None Conchem SP-L

Water-reducer Quantity (oz/100 lb of binder 10-20 None4 3-5

Type None None Daratar 17 None Retarder Quantity (oz/100

lb of binder) None None 4 None Air content Amount (%) 5-7 5-7 5-7 6

Mix designation NH10G NH11G NH12G NH04D

Size (in.)/Type 0.75, ASTM Grade 5 0.75,

ASTM Grade 5 0.75,

ASTM Grade 5 1.0,

ASTM Grade 5 Crushed river gravel

Quantity (pcy) 1850 1850 1850 1805 Sand Quantity (pcy) 940 925 950 1205

Potable water Quantity (pcy) 250 250 242 250 Type II II II II Cement Quantity (pcy) 800 800 800 658

Silica fume Quantity (pcy) 56 75 100 None Type None None None Class F Fly ash Quantity (pcy) None None None 132 Type Adva Flow Adva Flow Adva Flow None High-range water

reducer Quantity (oz/cy) 51.4 53 63 None Type Mira Mira Mira Daracem 100 Water-reducer Quantity (oz/cy) 51.4 53 63 118 Type Darex II Darex II Darex II Darex II Air entraining

admixture Quantity (oz/cy) 3 3 4 10 Type DCI-S DCI-S DCI-S None Corrosion

inhibitor Quantity (oz/cy) 33 33 33 None

TABLE 3 Mix properties for Nebraska girders and deck

TABLE 4 Mix properties for New Hampshire girders and deck

24 in. shrinkage specimens were produced from the same mixdesign used for the pretensioned bridge girders; measure-ments were taken for 3 months. The results from the labora-tory tests were compared with those obtained from varioussites, to determine the effects of the various curing and envi-ronmental conditions.

Mixing and Sampling Procedures

Concrete mixing in the laboratory was done using 5.5-cfbatches in a 9-cf capacity rotary drum. ASTM C192 (31),Standard Practice for Making and Curing Concrete TestSpecimens in the Laboratory was followed for making the

16

Mix designation TX08G TX09G TX10G TX04D

Size (in.)/Type 0.75, ASTM Grade 5 0.75,

ASTM Grade 5 0.75,

ASTM Grade 5 None Crushed limestone

Quantity (pcy) 2029 2011 1975 None Size/Type None None None 1.5, River gravel

Gravel Quantity (pcy) None None None 1811

Size/Type Natural river sand Natural river sand Natural river sand Natural river sand Sand

Quantity (pcy) 1237 1340 1237 1192 Potable water Quantity (pcy) 206 192 197 244

Type III III III I Cement Quantity (pcy) 611 564 705 611 Silica fume Quantity (pcy) None None None None

Type None None None Class C Fly ash Quantity (pcy) 152 Type Rheobuild 1000 Rheobuild 1000 Rheobuild 1000 None High-range

water reducer

Quantity (oz/100 lb of binder) 27 21 29 None

Type Pozzolith 300R Pozzolith 300R Pozzolith 300R None Water-reducer Quantity (oz/100 lb of binder 3.5 3.0 3.5 None

Retarder Quantity (oz/100 lb of binder) 6 Air content Amount (%) 2 2 2 2

Mix designation WA10G WA11G WA12G WA04D

Size/Type 0.75, ASTM Grade 5 0.75,

ASTM Grade 5 0.75

ASTM Grade 5 1.0,

ASTM Grade 5 Gravel Quantity (pcy) 2010 1877 1959 1810

Size/Type Natural river sand

Natural river sand

Natural river sand

Natural river sand Sand

Quantity (pcy) 1235 1383 1204 1046 Potable water Quantity (pcy) 219 217 213 263

Type III III III I-II Cement Quantity (pcy) 705 658 752 660 Silica fume Quantity (pcy) None None 50 None

Type None None None Class F Fly ash Quantity (pcy) None None None 75 Type Advacast Advacast Advacast None High-range water

reducer Quantity (oz/100 lb of binder) 7 7 7 None Type WRDA-64 WRDA-64 WRDA-64 Pozz-80

Water-reducer Quantity (oz/100 lb of binder) 4 4 4 6

Air content Amount (%) 1.5 1.5 1.5 2

TABLE 5 Mix properties for Texas girders and deck

TABLE 6 Mix properties for Washington girders and deck

test specimens. The concrete cylinders were made accordingto ASTM C192 and cured in the laboratory curing room at anambient temperature of about 73F for 24 hours. The cylin-ders were then de-molded and returned to the curing roomuntil the test age. Creep and shrinkage specimens were cast

for each of the three girder concrete mixes. After placementand consolidation, the surface was screeded and trowel fin-ished and then covered with burlap. The forms were removedafter 24 hours. The specimens were then left to cure at a roomambient temperature of 73F.

MODULUS OF ELASTICITY

Experimental Results

The modulus of elasticity of concrete was determined inaccordance with ASTM C469 (32). At any given concrete age,the reported modulus was the average of the results of twocylinders. The applied loads and the longitudinal strains wererecorded until the applied load reached 40% of the concreteultimate strength at the age of loading.

Appendix E shows the measured compressive strength andmodulus of elasticity. Figure 5 shows modulus of elasticityversus compressive strength test results reported in the litera-ture and those produced in this study. The figure shows thehigh variability in the experimental data. This variability maybe attributed to a combination of factors including the degreeof dryness of the specimens at the time they were tested, mix-ture proportions, properties of the concrete mix ingredients,method of testing, speed of load application, equipment accu-racy, and operator experience.

Proposed Formula

The prediction formula given in both the ACI-318 and theAASHTO Specifications provided better correlation with thetest results than those obtained from the ACI-363 formula.Neither prediction method accounted for the effects of aggre-gate type on modulus of elasticity and strength. Figure 6shows the relationship between unit weight and compressivestrength. These data indicate that nearly all the high-strengthmixes included in this investigation had a unit weight lessthan 0.155 kcf. The relationship shown in the figure can be

17

represented by the following formula, which accordingly hasan upper limit of 0.155 kcf:

The unit weight formula is proposed to be incorporated intomodulus of elasticity calculation. Also, it is proposed that twofactors be included: K1 representing the difference betweennational average and local average (if tests results with localmaterials are available), and K2 representing whether anupper-bound or a lower-bound value is desired in the calcu-lations. An upper-bound value would be conservative to usefor crack control analysis and a lower-bound value would beappropriate for prestress loss and deflection calculations. Theproposed formula for modulus of elasticity is:

A correction factor K1 = 1.0 corresponds to an equal aver-age of all predicted values and all measured values of the mod-ulus of elasticity. Individual averages of data groups from eachof the participating states correspond to K1 values other thanunity, representing the effect of local material variability. Thecorrection factor K2 is based on the 90th percentile upper-bound and the 10th percentile lower-bound for each of thefour states and for the entire data bank. The K1 and K2 valuesdetermined in this research are given in Table 7. The tablealso shows that the ratio of predicted to experimental valuesis closest to unity, when the proposed Equation 48 is used, in

E K K f1000

fc 1 c c= + 33 000 0 140 482

1 5

, . ( ).

w in kcf f1000

but not greater than . kcf

cc( ) = + 0 140

0 155 47

.

( )

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0

Compressive Strength (ksi)

Modulus of Elasticity (ksi)

(ksi)f,1000f0.140 +PROPOSED, Ec = 33,000 K1K2 c

'

1.5c

'

(ksi)fw33,000AASHTO-LRFD, Ec c'1.5=

(ksi)0.145

w1,000f1265E363,ACI1.5

cc

'

c

=

Figure 5. Modulus of elasticity versus compressive strength.

comparison to the AASHTO-LRFD formula. Consider aNebraska mix with a specified compressive strength of 8.0 ksi.According to Table 7, the value of K1 = 0.975, the upper-bound K2 = 1.211 and the lower-bound K2 = 0.788. The pre-dicted average, upper-bound, and lower-bound, values of themodulus of elasticity for this concrete strength may be esti-mated as follows:

Upper-bound E

ksi

c = ( )( )

+ =33 000 0 975 1 211

0 140 81000

8 6 2751 5

, . .

. ,

.

Average E

ksi

c = ( ) +( )=

33 000 0 975 0 140 81000 8

5 182

1 5, . .

,

.

18

Figure 7 shows the measured values versus those predictedusing the proposed method. It demonstrates that the proposedmethod produces an accurate prediction of the average,lower-bound, and upper-bound, values of the modulus of elas-ticity of concrete. Appendix E contains additional compar-isons between the proposed prediction method, the AASHTO-LRFD method, and other methods. Figure 8 illustrates acomparison between test results for a set of high-strength con-crete mixes used in Washington State, with those predicted bythe proposed formula and the AASHTO-LRFD formula. Thesignificant difference between the two prediction methodsillustrates the proposed formulas ability to more accuratelyaccount for local materials and for high-strength concrete.

EXPERIMENTAL SHRINKAGE RESULTS

Shrinkage specimens were cast at the same time and curedunder the same conditions as the creep specimens. Readingswere taken in parallel with the creep tests for each mix to com-pare the time-dependent strain of loaded and unloaded speci-mens. The creep and shrinkage specimens in this project hada V/S ratio of 1.0. The specimens were at an ambient relativehumidity of 35% to 40%. Demountable mechanical (DEMEC)gages were used at a spacing of about 8 in. to measure the sur-face strains in the longitudinal direction. Five DEMEC pointswere used on each of two surfaces of each specimen. TheDEMEC points were spaced at 4 in. This allowed for 3-to-8-in. gage lengths per surface, or 6 readings per specimen.Shrinkage readings were taken daily for the first week, weeklyfor the first month, and monthly for about 1 year. Figures 9through 12 present the measured shrinkage strains of the

Lower-bound E

ksi

c = ( )( )

+ =33 000 0 975 0 788

0 140 81000

8 4 0831 5

, . .

. ,

.

w = 0.001f'c + 137.28

120

125

130

135

140

145

150

155

160

4000 6000 8000 10000 12000 14000 16000

Compressive Strength (psi)

Uni

t Wei

ght (p

cf)

Figure 6. Relationship between unit weight andcompressive strength of concrete.

Proposed K1 and K2Ratio of Predicted to

Measured

K1

90th percentile K2

10th percentile K2

Proposed AASHTO-LRFD

Nebraska NE09G, NE10G, NE12G

0.975 1.211 0.788 1.000 1.037

New Hampshire NH10G, NH11G, NH12G

0.911 1.123 0.878 1.000 1.122

Texas TX08G, TX09G, TX10G

1.321 1.115 0.886 1.000 0.768

Washington WA10G, WA11G, WA12G

1.154 1.182 0.817 1.000 0.889

All data 1.000 1.224 0.777 1.020 1.037

TABLE 7 K-values and predicted-to-measured ratios of modulus ofelasticity of concrete

01000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Measured modulus of elasticity (ksi)

Predicted modulus of elasticity (ksi)

Average

Upper Bound

Lower Bound

AASHTO-LRFD

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Measured modulus of elasticity (ksi)

Predicted modulus of elasticity (ksi)

Average

Upper Bound

Lower Bound

AASHTO-LRFD

Figure 7. Predicted versus measured values of modulus of elasticity, nationwideexperiments with wide strength range.

Figure 8. Predicted versus measured values of modulus of elasticity, Washington Statehigh-strength concrete mixes.

specimens produced in the laboratory. Appendix F containsdata for all test specimens. The ratio of estimated shrinkagestrains to measured values, with the AASHTO-LRFD and theACI-209 formulas, are also shown in Table 8. It can be seenthat the predicted shrinkage strains are generally much higherthan the measured quantities confirming the need for improvedshrinkage prediction formulas.

EXPERIMENTAL CREEP RESULTS

Creep tests were performed at the laboratory on the 12 high-strength concrete mixtures in accordance with the ASTM

20

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300

Time (days)

Shrinkage Strain (microstrains)

S1S2S3ACI 209AASHTOProposed

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Time (days)

Shrinkage Strain(microstrains)

S1S2S3ACI 209AASHTOProposed

Figure 9. Shrinkage for Nebraska mix NE09G-S.

Figure 10. Shrinkage for New Hampshire mix NH10G-S.

Standard C 512 (33). Similar to the shrinkage strain measure-ments, DEMEC mechanical strain gages were used. A totalof four specimens were cast for each mix. Three of thesespecimens were loaded at the age of 1 day, and the fourth wasloaded at the age of 56 days. The specimens were then loadedat an intensity of not more than 40% of the compressivestrength at the age of loading.

The initial strain readings were taken immediately beforeand after loading. Creep measurements were then taken dailyfor the first week, weekly for the first month and monthly forabout 1 year. The creep coefficients were calculated from themeasured total strains, elastic strains, and shrinkage strains.Figures 13 through 16 show the test results for the four mixes

of the instrumented girders. The calculated creep coefficientsof the 12 high-strength concrete mixtures are given in Appen-dix G. Table 9 shows measured-to-estimated creep ratios usingAASHTO-LRFD and ACI-209. It can be seen that the esti-mated creep coefficients are much higher than the measuredquantities. The average of estimated to measured ratios, withthe ACI-209 and the AASHTO-LRFD formulas, are 179%and 161%, respectively. It appears that the LRFD method,which includes a correction factor for concrete strength, ismore accurate than the ACI-209 method; more comparisonsare shown in the appendix.

These large differences in creep coefficients can have asubstantial effect on the long-term prestress losses estimation.

21

Similar observations were made in previous research (Huo et al. [11]), (Mokhtarzadeh [34]), (Gross [35]). It was notedthat the creep strains developed rapidly during the early agethen exhibited very little change after several months, seeFigures 13 through 16.

PROPOSED CREEP AND SHRINKAGECORRECTION FACTORS

Correction factors are u