1、ACI 209R-92(Reapproved 2008)Prediction of Creep, Shrinkage,and Temperature Effects inConcrete StructuresReported by ACI Committee 209James A. Rhodes? Domingo J. Carreira+Chairman, Committee 209 Chairman, Subcommittee IIJames J. BeaudoinDan E. Brauson*tBruce R. GambleH.G. GeymayerBrij B. GoyaltBrian
2、B. HopeJohn R. Keeton tClyde E. KeslerWilliam R. LormanJack A. Means?Bernard L Meyers l -R.H. MillsK.W. NasserA.M. NevilleFrederic Roll?John Tim us kMichael A. WardCorresponding Members: John W. Dougill, H.K. HilsdorfCommittee members voting on the 1992 revisions:Marwan A. DayeChairmanAkthem Al-Mana
3、seerJames J. BeaudoiuDan E. BransonDomingo J. CarreiraJenn-Chuan ChemMenashi D. CohenRobert L DayChung C. Fu 1Satyendra K. GhoshBrij B. GoyalWill HansenStacy K. HirataJoe HutererHesham MarzoukBernard L. MeyersKarim W. NasserMikael PJ. OlsenBaldev R. SethKwok-Nam ShiuLiiia Panula$* Member of Subcommi
4、ttee II, which prepared this reportt Member of Subcommittee IIS=-=dThis report reviews the methods for predicting creep, shrinkage and temperature effects in concrete structures. It presents the designer with a unifiedand digested approach to the problem of volume changes in concrete. Theindividual
5、chapters have been written in such a way that they can be usedalmost independently from the rest of the report.The report is generally consistent with ACI 318 and includes materialindicated in the Code, but not specifically defined therein.Keywords: beams (supports); buckling; camber; composite cons
6、truction (concreteto concrete); compressiv e strength; concretes; concrete slabs; cracking (fraoturing); creep properties; curing; deflection; flat concrete plates; flexural strength;girders; lightweight-aggregate concretes; modulus of elasticity; moments of inertia;precast concrete; prestressed con
7、crete: prestress loss; reinforced concrete: shoring;shrinkage; strains; stress relaxation; structural design; temperature; thermalexpansion; two-way slabs: volume change; warpage.ACI Committee Reports, Guides, Standard Practices, andCommentaries are intended for guidance in designing, plan-ning, exe
8、cuting, or inspecting construction and in preparingspecifications. References to these documents shall not bemade in the Project Documents. If items found in thesedocuments are desired to be a part of the Project Docu-ments, they should be phrased in mandatory language andincorporated into the Proje
9、ct Documents.JCONTENTSChapter 1-General, pg. 209R-2l.l-Scope1.2-Nature of the problem1.3-Definitions o f termsChapter 2-Material response, pg. 209R-42.1 -Introduction2.2-Strength and elastic properties2.3-Theory for predicting creep and shrinkage of con-crete2.4-Recommended creep and shrinkage equat
10、ionsfor standard conditionsThe 1992 revisions became effective Mar. 1, 1992. The revisions consisted ofminor editorial changes and typographical corrections.Copyright 8 1982 American Concrete Institute.All rights reserved including rights of reproduction and use in any form or byany means, including
11、 the making of copies by any photo process, or by any elec-tronic or mechanical device, printed or written or oral, or recording for sound orvisual reproduction or for use in any knowledge or retrieval system or device,unless permission in writing is obtained from the copyright proprietors.209R-2 AC
12、I COMMITTEE REPORT2.5-Correction factors for conditions other than thestandard concrete composition2.6-Correction factors for concrete composition2.7-Example2.8-Other methods for prediction of creep andshrinkage2.9-Thermal expansion coefficient of concrete2.10-Standards cited in this reportChapter 3
13、-Factors affeating the structural response -assumptions and methods of analysis, pg. 209R-123.1-Introduction3.2-Principal facts and assumptions3.3-Simplified methods of creep analysis3.4-Effect of cracking in reinforced and prestressedmembers3.5-Effective compression steel in flexural members3.6-Def
14、lections due to warping3.7-Interdependency between steel relaxation, creepand shrinkage of concreteChapter 4-Response of structures in which time -change of stresses due to creep, shrinkage and tem-perature is negligible, pg. 209R-164.1-Introduction4.2-Deflections of reinforced concrete beam and sla
15、b4.3-Deflection of composite precast reinforced beamsin shored and unshored constructions4.4-Loss of prestress and camber in noncompositeprestressed beams4.5-Loss of prestress and camber of composite pre-cast and prestressed-beams unshored and shoredconstructions4.6-Example4.7-Deflection of reinforc
16、ed concrete flat plates andtwo-way slabs4.8-Time-dependent shear deflection of reinforcedconcrete beams4.9-Comparison of measured and computed deflec-tions, cambers and prestress losses using pro-cedures in this chapterChapter 5-Response of structures with signigicant timechange of stress, pg. 209R-
17、225.l-Scope5.2-Concrete aging and the age-adjusted effectivemodulus method5.3-Stress relaxation after a sudden imposed defor-mation5.4-Stress relaxation after a slowly-imposed defor-mation5.5-Effect of a change in statical system5.6-Creep buckling deflections of an eccentricallycompressed member5.7-
18、Two cantilevers of unequal age connecte d at timet by a hinge 5.8 loss of compression in slab anddeflection of a steel-concrete composite beam5.9-Other cases5.10-ExampleAcknowledgements, pg. 209R-25References, pg. 209R-25Notation, pg. 209R-29Tables, pg. 209R-32CHAPTER l-GENERALl.l-ScopeThis report p
19、resents a unified approach to predictingthe effect of moisture changes, sustained loading, andtemperature on reinforced and prestressed concretestructures. Material response, factors affecting the struc-tural response, and the response of structures in whichthe time change of stress is either neglig
20、ible or significantare discussed.Simplified methods are used to predict the materialresponse and to analyze the structural response underservice conditions. While these methods yield reasonablygood results, a close correlation between the predicteddeflections, cambers, prestress losses, etc., and th
21、emeasurements from field structures should not be ex-pected. The degree of correlation can be improved if theprediction of the material response is based on test datafor the actual materials used, under environmental andloading conditions similar to those expected in the fieldstructures.These direct
22、 solution methods predict the response be-havior at an arbitrary time step with a computational ef-fort corresponding to that of an elastic solution. Theyhave been reasonably well substantiated for laboratoryconditions and are intended for structures designed usingthe ACI 318 Code. They are not inte
23、nded for the analy-sis of creep recovery due to unloading, and they applyprimarily to an isothermal and relatively uniform en-vironment .Special structures, such as nuclear reactor vessels andcontainments, bridges or shells of record spans, or largeocean structures, may require further consideration
24、swhich are not within the scope of this report. For struc-tures in which considerable extrapolation of th e state-of-the-art in design and construction techniques is achieved,long-term tests on models may be essential to provide asound basis for analyzing serviceability response. Refer-ence 109 desc
25、ribes models and modeling techniques ofconcrete structures. For mass-produced concrete mem-bers, actual size tests and service inspection data willresult in more accurate predictions. In every case, usingtest data to supplement the procedures in this report willresult in an improved prediction of se
26、rvice performance.PREDICTION OF CREEP 209R-31.2-Nature of the problemSimplified methods for analyzing service performanceare justified because the prediction and control of time-dependent deformations and their effects on concretestructures are exceedingly complex when compared withthe methods for a
27、nalysis and design of strength perfor-mance. Methods for predicting service performance in-volve a relatively large number of significant factors thatare difficult to accurately evaluate. Factors such as thenonhomogeneous nature of concrete properties caused bythe stages of construction, the histori
28、es of water content,temperature and loading on the structure and their effecton the material response are difficult to quantify even forstructures that have been in service for years.The problem is essentially a statistical one becausemost of the contributing factors and actual results are in-herent
29、ly random variables with coefficients of variationsof the order of 15 to 20 percent at best. However, as inthe case of strength analysis and design, the methods forpredicting serviceability are primarily deterministic innature. In some cases, and in spite of the simplifyingassumptions, lengthy proce
30、dures are required to accountfor the most pertinent factors.According to a survey by ACI Committee 209, mostdesigners would be willing to check the deformations oftheir structures if a satisfactory correlation between com-puted results and the behavior of actual structures couldbe shown. Such correl
31、ations have been established forlaboratory structures, but not for actual structures. Sinceconcrete characteristics are strongly dependent on en-vironmental conditions, load history, etc., a poorer cor-relation is normally found between laboratory and fieldservice performances than between laborator
32、y and fieldstrength performances.With the above limitations in mind, systematic designprocedures are presented which lend themselves to acomputer solution by providing continuous time functionsfor predicting the initial and time-dependent averageresponse (including ultimate values in time) of struct
33、uralmembers of different weight concretes.The procedures in this report for predictin g time-dependent material response and structural service per-formance represent a simplified approach for designpurposes. They are not definitive or based on statisticalresults by any means . Probabilisitic method
34、s are neededto accurately estimate the variability of all factors in-volved.1.3-Definitions of termsThe following terms are defined for general use in thisreport. It should be noted that separability of creep andshrinkage is considered to be strictly a matter of defin-ition and convenience. The time
35、-dependent deformationsof concrete, either under load or in an unloaded speci-men, should be considered as two aspects of a singlecomplex physical phenomenon.881.3.1 ShrinkageShrinkage, after hardening of concrete, is the decreasewith time of concrete volume. The decrease is clue tochanges in the mo
36、isture content of the concrete andphysico-chemical changes, which occur without stress at-tributable to actions external to the concrete. The con-verse of shrinkage is swellage which denotes volumetricincrease due to moisture gain in the hardened concrete.Shrinkage is conveniently expressed as a dim
37、ensionlessstrain (in./in. or m/m) under steady conditions of relativehumidity and temperature.The above definition includes drying shrinkage , auto-genous shrinkage, and carbonation shrinkage.a)Drying shrinkage is due to moisture loss in theconcreteb) Autogenous shrinkage is caused by the hydrationo
38、f cementc)Carbonation shrinkage results as the variouscement hydration products are carbonated in thepresence of CO,Recommended values in Chapter 2 for shrinkagestrain (E i.e., strength, elastic modulus, creep, shrink-the ultimate (in time) compressive strength of concrete,age and coefficient of the
39、rmal expansion.df,), is reached.g2The equations recommended in this chapter are sim-The ranges of g andp in Eqs. (2-l) and (2-2) for theplified expressions representing average laboratory datanormal weight, sand lightweight, and all lighweight con-obtained under steady environmental and loading con-
40、cretes (using both moist and steam curing, and Types Iditions. They may be used if specific material responseand III cement) given in References 6 and 7 (some 88specimens) are: a = 0.05 to 9.25, fi = 0.67 to 0.98.parameters are not available for local materials andenvironmental conditions.The coasta
41、nts a andfl are functions of both the typeExperimental determination of the response para-of cement used and the type of curing employed. The usemeters using the standard referenced throughout thisof normal weight, sand lighweight, or all-lightweightegate does not appear to affect these constantsrep
42、ort and listed in Section 2.10 is recommended if an significantly. Typical values recommended in Referencesaccurate prediction of structural service response is 7 are given in Table 2.2.1. Values for the time-ratio,desired. No prediction method can yield better resultsthan testing actual materials u
43、nder environmental and)*f) or I)/=),/ in Eqs. (2-l) and (2-2) aregiven also in Table 2.2.1.PREDICTION OF CREEP 209R-5“Moist cured conditions“ refer to those in ASTM C132 and C 511. Temperatures other tha n 73.4 f 3 F (23f 1.7 C) and r elative humidities less than 35 percent mayresult in values diffe
44、rent than those predicted when usingthe constant on Table 2.2.1 for moist curing. The effectof concrete temperature on the compressive and flexuralstrength development of normal weight concr etes madewith different types of cement with and withoutaccelerating admixtures at various temperatures betwe
45、en25 F (-3.9 C)and 120 F (48.9 ( C) were studied in Ref-erence 90.Constants in Table 2.2.1 are not applicable to con-cretes, such as mass concrete, containing Type II or TypeV cements or containing blends of portland cement andpozzolanic materials. In those cases, strength gains areslower and may co
46、ntinue over periods well beyond oneyear age.“Steam cured” means curing with saturated steam atatmospheric pressure at temperatures below 212 F (100C).Experimental data from References 1-6 are comparedin Reference 7 and all these data fall within about 20percent of the average values given by Eqs. (2
47、-l) and(2-2) for constants n and / ? in Table 2.2.1. The tem-perature and cycle employed in steam curing may sub-stantially affect the stren gth-time ratio in the early daysfollowing curing.1*72.2.2 Modulus of rupture, direct tensile strength andmodulus of elasticityEqs. (2-3), (2-4),and (2-5) are c
48、onsidered satisfactoryin most cases for computing averag e values for modulusof rupture, f, direct tensile strength, ft, and secant mod-ulus of elasticity at 0.4(f,), E, respectively of differentweight concretes.14-12f, = (Q.J = 800x 10 in./in . (m/m) versus 803 x lOA for moist cured con-crete, and
49、730 x lOA versus 788 x 10e6 for steam curedconcrete.The creepsurements7,18and shrinkage data, based on 20-year mea-for normal weight concrete with an initialtime of 28 days, are roughly comparable with Eqs. (2-8)to (2-10). Some differences are to be found because ofthe different initial times, stress levels, curing conditions,and other variables.However, subsequent work” with 479 creep datapoints and 356 shrinkage data points resulted in the sameaverage for v, = 2.35, but a new average for (EJ, =780 x 10-6in./in . (m/m), for both moist and steam curedconcrete. It
