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Prediction of Creep, Shrinkage, and Temperature Effects in Concrete StructuresChapter 1 - General1.1 ScopeThis report presents a unified approach to predicting the effect of moisture changes, sustainedloading, and temperature on reinforced and prestressed concrete structures. Material response,factors affecting the structural response, and the response of structures in which the timechange of stress is either negligible or significant are discussed. This code is not intended for the analysis of creep recovery due to unloading, and they apply primarily to an isothermal andrelatively uniform environment.1.2 Nature of the ProblemFactors such as the non homogeneous nature of concrete properties caused by the stages of construction properties caused by the stages of construction, the histories of water content,temperature and loading on the structure and their effect on the material response are difficult toquantify even for structures that have been in service for years.1.3 Definitions of TermsThe time-dependent deformations of concrete, either under or in an unloaded specimen,should be considered as two aspects of a single physical phenomenon (creep and shrinkage is

considered separate for convenient).1.3.1 ShrinkageShrinkage, after hardening of concrete, is the decrease with time of concrete volume withoutstress attribute to actions external to the concrete. The converse of shrinkage is swellage whichdetonates volumetric increase due to moisture. Three type of shrinkage is consider:a) Drying shrinkage is due to moisture loss in the concreteb) Autogenous shrinkage is caused by the hydration of cementc) Carbonation shrinkage results as the various cement hydration products are carbonated inthe presence of CO21.3.2 CreepThe time-dependent increase of strain in hardened concrete subjected to sustained stress isdefined as creep. The above definition treats the initial instantaneous strain, the creep strain,

and the shrinkage as additive, even though they affect each other. The creep definition lumpstogether the basic creep and the drying creep.Initial Instantaneous StrainInstantaneous stress is a porduct of both elastic and inelastic instantanous changes in strain, aswell as short term criip strain (10 - 100 min).a) Basic creep occurs under conditions of no moisture movement to or from the environmentb) Drying creep is the additional creep caused by dryingsigma-t is creep per unit stressv-t is ratio of creep strain to initial strainEci is the concrete initial modulus of Elasticitysigma-t = v-t * Eci1.3.3. RelaxationRelaxation is gradual reduction of stress with time under sustained strain.1.3.4. Modulus of ElasticityThe static modulus of elasticity (secant modulus) is the linearized instantaneous (1 to 5 minutes)stress-strain relationship.1.3.5. Contraction and ExpansionConcrete contraction or expansion is the algebraic sum of volume changes occurring as theresult of thermal variations caused by heat of hydration of cement and ambient temperaturechange.

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Chapter 2 - Material Response2.1 IntroductionIt is important to consider appropriate water content, temperature, and loading histories inpredicting concrete response parameters.2.2 Strength and Elastic Properties2.2.1. Concrete compressive strength versus timePredicting Compressive Strength:

a = days

= constant

= 28-day strengtht = age of concrete in days

2.2.2. Modulus of Rupture, direct tensile strength, and modulus of elasticity

2.3 Theory for predicting creep and shrinkage of concreteThe General Equations for predicting Creep and Shrinkage is:

d = days (in days) = constant for a given member and size

= ultimate creep coefficient

f = days (in days) = constant for a given member and size

= ultimate shrinkage strain

- The increase in creep after, say 100 to 200 days is usually more pronounced thanshrinkage. In percent of ultimate value, shrinkage usually increases more rapidly duringthe first few months.

- It was found that no consistent distinction in the ultimate shrinkage strain was appparent for moist and stream cured concrete.

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2.4 Recommended creep and shrinkage equations for standard condition2.4.1 Predicting Shrinkage

a.) Initial Moist Curing (see ACI 209R-35 Table 2.5.3)

(for shrinkage of concrete moist cured during a period of time other than 7 days)b.) Relative Humidity (see ACI 209R-35 Table 2.5.4)

(for ambient relative humidity 40 < < 80)

(for ambient relative humidity 80 < < 100)c.) Member Size (see ACI 209R-36 Table 2.5.5.2)

(the volume-surface ratio of the member)d.) Temperature (Typically Ignored)

The effects of temperature variation is small and often could be ignored. The effect of temperature is usually is two-fold. First, they directly influence the time-ratio. Second,they also affect the rate of aging of the concrete, i.e. the change of material propertiesdue to progress of cement hydration.

e.) Concrete Composition (Typically Ignored)Concrete correction factor exist, but since concrete mix characteristic are unknown atthe design stage and have to be estimated, the correction factor is usually ignored.

(average suggested value)

(shrinkage strain after 7 days of moist cured)

(shrinkage strain after 3 days of steam cured)

(see ACI 209R-6 for Table 2.4.1)

Note: should not be taken less than 0.2. Also, use if

concrete is under seasonal wetting and drying cycles and if concrete is under sustained drying conditions. 2.4.2 Predicting Creep

a.) Age of Loading (Creep Only)For loading age other that standard 7 days for moist cured and 3 days for steam cured

concrete, use loading age correction factors. Creep correction factor must be used whencomputing the ultimate creep coefficient of the present beam corresponding to the age when theslab is cast.a.2) Differential Shrinkage (Calculating Shrinkage from Time Other than 7 days)

e(100 - 28) = e (100-7) - e(28-7)a.3) Initial Moist Cured

For shirnkage of concrete moist cured during a period of time other than 7 days, use the

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shrinkage factor in Table 2.5.3.b.) Relative Humidity (see ACI 209R-35 Table 2.5.4)

(for ambient relative humidity > 40)c.) Member Size (see ACI 209R-36 Table 2.5.5.2)

1.) Influence the time-ratio2.) affects the ultimate crep coefficient and ultimate shrinkage strain

(the volume-surface ratio of the member)d.) Temperature (Typically Ignored)

See Shrinkagee.) Concrete Composition

See Shrinkage

(average suggested value for creep coefficient)

(creep coefficient for a loading age of 7 days)

(see ACI 209R-6 for Table 2.4.1)

Chapter 3 - Factors Affecting the Structural - Assumptions and Methods of Analysis3.1 Introduction3.2 Principle Facts and Assumption3.3 Simplified Methods of Creep Analysis3.3.1 Cases in which the gradual time change of stress due to creep and shrinkage is smalland has little effect. In this case the creep strain is accounted for with sufficient accuracy by anelastic analysis in which the actual concrete modulus at the time of initial laoding si repace withthe so-called effective modulus:

3.3.2 Cases in which the gradual time change of stress due to creep and shrinkage issignificant.