Prediction of Creep and Shrinkage Behavior for Design from Short Term Tests

PREDICTION OF CREEP AND SHRINKAGE BEHAVIOR FOR DESIGN FROM SHORT TERM TESTS

B. L. Meyers University of Iowa Iowa City, Iowa D. E. Branson University of Iowa Iowa City, Iowa C. G. Schumann Chicago Bridge and Iron Co. Plainfield, Illinois

Presents simple empirical equations for predicting long-time creep and shrinkage properties of concrete. Prediction accuracy that previously required almost 4 months of testing can now be achieved with only 28 days of creep and shrinkage data. General constants are presented for use when the 28-day experimental program is not feasible.

The importance of having adequate mated from general relationships. time-dependent concrete properties and The prediction equations developed accurate prediction methods was de- in References 2, 3 and 4, and included monstrated by Branson and Kripanaray- in the analysis of prestressed concrete anan1 1) who showed that loss of pre- structures reported in Reference 1, form stress and camber in non-composite and the basis of this work. It will be shown composite structures could be predicted that using the methods described in this twice as accurately when experimen- paper, prediction accuracy that previ- tally determined material parameters ously required almost 4 months of test- were used, as compared to predictions ing can be obtained with only 28 days made using material properties esti- of creep and shrinkage test data.

PCI Journal/May-June 1972 29 800

760

600 Branson / -O 500 ^^" /t Ross 400

300

200

100

80 160 240 320 400 480 560 t days

Fig. 1. Predicted creep comparing Ross equation with Branson Eq. (1)

Previous proposals data collection. Such equations have been proposed by Thomas(a ), Mc- for creep prediction Henry(6), Saliger(7), Shank(8), and Creep prediction methods that might Troxell, et al(9). be useful to the design engineer can be A number of simpler hyperbolic divided into two general categories: equations, which do approach a finite (1) the creep-time relationship is ex- limit, have also been suggested. Those pressed in the form of an equation, and used most often are the equations of usually requires that one or more em- Ross (10) pirical constants be determined experi- c — a mentally, and (2) creep is expressed by + bt °- a standard curve which can be modi- and Lorman(") fied by a number of factors to allow for mt various mix and storage conditions. The c— n+t o- latter prediction method does not require experimental data but is usually where c = creep, t = time, o = stress, less accurate than using an empirical and a, b, m and n are experimentally equation based on actual measure- determined empirical constants. ments. Methods using standard creep curves In Category 1, about a dozen expo- can be represented by those suggested nential or hyperbolic equations have by Jones, et al( 12 ), and Wagner(13). been suggested. Most exponential equa- Jones used a standard curve, valid for tions, which have the practical disad- specific mix and storage parameters, vantage of not approaching a finite which can be corrected for other condi- limit, are - of doubtful value to the de- tions by using a set of correction fac- sign engineer because they are unwield- tors. Wagners method differs only in ly and/or require extended periods of that standard values of ultimate specific

3Q 30

a 15 L) 0 O P 10

0 0 10 15 20 25 3C

Actual Time Under Load - Weeks Fig. 2. Accuracy of predicting 1-year creep from short-time tests

creep are supplied in lieu of the standard creep curve. (E85)t = f t' t^ (Esh)u (2) The literature is rather sparse in the where area of shrinkage prediction, although a number of complex methods have been Ct = creep coefficient, defined as suggested( 14,15 ). However, since the ratio of creep strain to ini- methods developed in this paper have tial strain, at any time t their basis in the creep prediction meth- (e3n,)t = shrinkage strain at any time ods already discussed, further analysis t of available shrinkage methods will be Cu = ultimate shrinkage coeffi- omitted. cient In an attempt to increase the accur- (esh),, = ultimate shrinkage strain acy of creep and shrinkage prediction, c, d, e, f = empirical constants Meyers, et al( 6 , combined the meth- It is interesting to note that in addition ods of Ross and Jones. Although some to developing the well known creep improvements were made, it was noted equation, Ross suggested a shrinkage that this method, as well as others, pre- equation similar to Eq. (2) in 1937(10). dicted ultimate creep fairly well, but Comparisons with measured data did not adequately represent the defor- show that the form of the creep predic- mation behavior of the material early in tion in Eq. (1) is more representative of its life. the full range of creep behavior than This difficulty was overcome by the form originally suggested by Ross. Branson, et al 2,3'4), who proposed the Such a comparison is made in Fig. 1. following standard prediction equations Because the Branson equation is more to representative of the full range of creep Ct u (1) d +to C behavior, it can be used in an accurate

PCI Journal/May-June 1972 31 Moist cured and steam cured concretes 100 • O, • Eq. ( 3 ) rO q ■_..O 4) 80

U • o 60 a ♦ •

40 • Nor. Wt. Sand_Lt.Wt.l Al1_Zt.t. I,Moist o ( 12,1) (20,2)-O-(19,3) (2,3) ••(12,21) (2, 1) (17, 4) U 20 III,Moist C (18,7) (20,2 •(17,4) Tp.I,Steam a (18,2) ♦(17,6) T .III Steam 7(20,3) (21 V 17. 7.) (2 0 160 320 480 640 800 Time after loading in days Fig. 3. Creep coefficient as a percent of ultimate vs. time, comparing Eq. (3) with test data. Loading ages are 7 days for moist cured and 2 to 3 days for steam cured concretes. (In each set of parentheses, the numbers refer to the source of the data and the no. of specimens, respectively.)

prediction method based on only 28- It can be seen from Fig. 2 that for most day data. It can also be shown that Eq. available methods, in order to predict (2) accurately represents the full range creep to within an error coefficient of of shrinkage vs. time behavior(2.3.4). 10 percent, 20 weeks of data is re- It is significant that accurate predic- quired. tion can be obtained with 28-day data in light of information presented by Ne- Prediction equations ville and Meyers( 17). The accuracy of any method can be evaluated in terms after Branson, of an error coefficient M(17). et alr=.2"" To solve Eq. (1) and (2) for C,, and M= VCi— Cti)2/n (€,h)t, three unknowns must be evalu- CCI ated in each case (d, c and C. are un- where Ct = creep after one year pre- known for Eq. (1), and for Eq., (2), e, f dicted from measured and (E8h)„ are unknown). Of the three creep after t weeks under unknowns, two from each equation are load empirical constants while C,, and Cd = actual creep after i years (e8n,),, are material properties. under load In order to determine the empirical n = number of specimens or constants d and c, creep data from Ref- experimental sets for erences 12, 16 and 18-21 were normal- which creep was observed ized with respect to C,, and plotted in at time t Fig. 3. In most cases, three data points

32 a. Moist cured concrete 100ҟ •

0 (4a) 60

• 4 N 40 w Nor. Wt. Sand-Lt.Wt All-Lt.Wt. I,Moist 0(12,1) (20, 1) x(123) (2,3) •(12,21) (19, 1) 4J 20 (20,2) •III,Moist D(20, 1) (18, 1) • (20,2) WN (22,3) 0 0ҟ160ҟ320 480ҟ640ҟ800 Time after initial shrinkage considered in days

y100 b. Steam cured concrete r. N •.p 1 + 80 0 o • F. (4b) a D d 60

X40 W Nor.Wt. All-Lt.Wt. 20 Type I,Steam 0 (20, 1) • (20, 2) N Type III,Steam o (20, 1) (21, 8) ■ (20, 2) (21,42) W 0 0ҟ16oҟ320ҟ480ҟ640ҟ800 Time after initial shrinkage considered in days

Fig. 4. Shrinkage as a percent of ultimate vs. time. Curve a, based on Eq. (4a), is for moist cured concrete, initial shrinkage considered for 7 days; Curve b, based on Eq. (4b), is for steam cured concrete, initial shrinkage considered for 2 to 3 days. (For plotted data, the numbers in parentheses refer to data source and no. of specimens, respectively. Three data points for a specific time refer to upper and lower limits and an average value. Only one data point indicates too narrow a range to show.)

PCI Journal/May-June 1972 33

Table 1. 28-day extrapolation of creep

Specimen Ci28 C.. 0365 r3 5 C730 C730 V365 y730 designation Experimental Predicted Experimental Predicted Experimental Predicted C;65 C,3 4 0.97 2.28 1.82 1.77 1.86 1.91 0.973 1.027 6 1.15 2.70 2.06 2.09 2.17 2.26 1.015 1.041 8 0.92 2.16 2.03 1.67 2.14 1.81 0.823 0.845 12 0.82 1.93 1.66 1.50 1.71 1.62 0.904 0.947 16 0.82 1.93 1.55 1.50 1.69 1.62 0.968 0.959 20 0.64 1.50 1.30 1.16 1.44 1.26 0.892 0.875 24 0.73 1.72 1.37 1.33 1.52 1.44 0.971 0.947 71 1.37 3.22 2.46 2.50 2.73 2.70 1.016 0.989 72 1.25 2.94 2.36 2.28 2.61 2.46 0.966 0.943 73 1.20 2.82 2.75 2.18 2.31 2.36 0.793 0.793 V 74 1.28 3.01 2.46 2.33 2.62 2.52 0.947 0.962 6N6 1.90 4.47 3.45 3.46 3.72 3.75 1.003 1.008 6N28 1.52 3.58 3.01 2.78 3.32 2.99 0.924 0.901 6S2 1.10 2.59 2.21 2.01 2.53. 2.17 0.910 0.818 6S7 1.04 2.45 2.20 1.90 2.52 2.06 0.864 0.817 6S28 0.95 2.24 2.20 1.74 2.51 1.88 0.791 0.749 10N6 1.04 2.45 1.79 1.90 1.94 2.06 1.061 1.062 10N28 0.75 1.76 1.59 1.36 1.74 1.48 0.855 0.851 10S2 0.65 1.53 1.30 1.18 1.45 1.28 0.908 0.883 1057 0.72 1.69 1.34 1.31 1.50 1.42 0.978 0.947 10528 0.66 1.55 1.43 1.20 1.62 1.30 0.839 0.802 8N6 1.73 4.07 3.02 3.16 3.19 3.42 1.046 1.072 8N28 1.88 4.43 3.40 3.36 3.70 3.72 0.988 1.005 8S7 1.41 3.32 2.45 2.58 2.74 2.78 1.053 1.015 8S28 1.35 3.18 2.59 2.48 2.95 2.67 0.958 0.905 6M5 1.51 3.56 2.78 2.76 3.01 2.98 0.993 0.990 6M28 1.10 2.59 2.48 2.00 2.67 2.16 0.806 0.809 6R7 0.74 1.74 1.70 1.35 1.93 1.46 0.853 0.756 6R28 0.60 1.41 1.54 1.09 1.78 1.18 0.708 0.663 1OM5 0.93 2.18 1.84 1.69 1.97 1.83 0.918 0.929 10M28 0.92 2.16 1.93 1.67 2.12 1.81 0.865 0.854 1082 0.68 1.60 1.34 1.24 1.49 1.34 0.925 0.899 10R7 0.66 1.55 1.33 1.20 1.46 1.30 0.902 0.890 10828 0.63 1.48 1.40 1.15 1.56 1.24 0.821 0.795 8M5 1.57 3.70 2.96 2.87 3.19 3.10 0.970 0.972 8M28 1.73 4.07 3.00 3.15 3.23 3.42 1.05 1.059 8R2 1.09 2.56 2.10 1.98 2.34 2.14 0.943 0.914 8R7 1.13 2.66 2.32 2.06 2.55 2.23 0.888 0.875 8R28 1.08 2.54 2.34 1.97 2.64 2.13 0.842 0.807 6R2 0.90 2.12 1.80 1.64 2.00 1.78 0.911 0.890 0.6 XCu C28 _. C^a C 365 36s = 10 13650.6 Cu = 280.6 +280.6 0.025 10

are shown for a particular specimen t (moist cured) (4a) category and time. They represent the (e8n)t = 35 + t upper and lower limits and average values of these data. Only one data (steam cured) (4b) (E'h)t 55- t (Esn)u point is shown for a specific time when the spread between upper and lower Using the basic Eqs. (3), (4a) and values is small. Eq. (3) was derived by (4b), general prediction equations can fitting a curve to the average values of be supplied to the designer by specify- the data. ing average values C. and (€8h). This to.s was done in Reference 1 where it was shown that loss of prestress and camber Ct = 10 + t0.6 Cc (3) could be predicted to within ± 30 per- Eq. (3) can be used for both moist and cent of actual results using average steam cured concrete. values of C,u and (e8h)u. Keeton(28) Similarly Eqs. (4a) and (4b) were and Pauw( 23 ) have also used Eqs. (3), developed from shrinkage data plotted (4a) and (4b) to predict structural re- in Fig. 4. sponse with an adequate degree of ac-

34 Table 2. Determination of error coefficient

Predicted, Experimental, Predicted, Experimental, 365 days 365 days (Cr - C1) (C1 - G)2 730 days 730 days (C1- C,) (Ct - C1)2 Ct C; 365 365 Ct C, 730 730 1.77 1.82 0.05 0.0025 1.91 1.86 0.05 0.0025 2.09 2.06 0.03 0.0009 2.26 2.17 0.09 0.0081 1.67 2.03 0.36 0.1296 1.81 2.14 0.33 0.1089 1.50 1.66 0.16 0.0256 1.62 1.71 0.09 0.0081 1.50 1.55 0.05 0.0025 1.62 1.69 0.07 0.0049 1.16 1.30 0.14 0.0196 1.26 1.44 0.18 0.0324 1.33 1.37 0.04 0.0016 1.44 1.52 0.08 0.0064 2.50 2.46 0.04 0.0016 2.70 2.73 0.03 0.0009 2.28 2.36 0.08 0.0064 2.46 2.61 0.15 0.0225 2.18 2.73 0.57 0.3249 2.36 2.31 0.05 0.0025 2.33 2.46 0.13 0.0169 2.52 2.62 0.10 0.0100 3.46 3.45 0.01 0.0001 3.75 3.72 0.03 0.0090 2.78 3.01 0.23 0.0529 2.99 3.32 0.33 0.1089 2.01 2.21 0.20 0.0400 2.17 2.53 0.36 0.1296 1.90 2.20 0.30 0.0900 2.06 2.52 0.46 0.2116 1.74 2.20 0.46 0.2116 1.88 2.51 0.63 0.3969 1.90 1.79 0.11 0.0121 2.06 1.94 0.12 0.0144 1.36 1.59 0.23 0.0529 1.48 1.74 0.26 0.0676 1.18 1.30 0.12 0.0144 1.28 1.45 0.17 0.0289 1.31 1.34 0.03 0.0009 1.42 1.50 0.08 0.0064 1.20 1.43 0.23 0.0529 1.30 1.62 0.32 0.1024 3.16 3.02 0.14 0.0196 3.42 3.19 0.23 0.0529 3.36 3.40 0.04 0.0016 3.72 3.70 0.02 0.0004 2.58 2.45 0.13 0.0169 2.78 2.74 0.04 0.0016 2.48 2.59 0.11 0.0121 2.67 2.95 0.28 0.0784 2.76 2.78 0.02 0.0004 2.98 3.01 0.03 0.0009 2.00 2.48 0.48 0.2304 2.16 2.67 0.51 0.2601 1.35 1.70 0.35 0.1225 1.46 1.93 0.47 0.2209 1.09 1.54 0.45 0.2025 1.18 1.78 0.60 0.3600 1.69 1.84 0.15 0.0225 1.83 1.97 0.14 0.0196 1.67 1.93 0.26 0.0676 1.81 2.12 0.31 0.0961 1.24 1.34 0.10 0.0100 1.34 1.49 0.15 0.0225 1.20 1.33 0.13 0.0169 1.30 1.46 0.16 0.0256 1.15 1.40 0.25 0.0625 1.24 1.56 0.32 0.1024 2.87 2.96 0.09 0.0081 3.10 3.19 0.09 0.0081 3.15 3.00 0.15 0.0225 3.42 3.23 0.19 0.0361 1.98 2.10 0.12 0.0144 2.14 2.34 0.20 0.0400 2.06 2.32 0.26 0.0676 2.23 2.55 0.32 0.1024 1.47 2.34 0.37 0.1369 2.13 2.64 0.51 0.2601 1.64 1.80 0.16 0.0256 1.78 2.00 0.22 0.0484 84.66 2.1195 91.17 3.0894

(C1 - C )2 (C1 - C1)2 - 3.0894 = 0.0772 1 -_ 2.1195 = 0.05299 n 40 nҟ40

(C` (C` - C;)2 =V5.299 x 10- 2 = 0.23 = V7.72 X 102=0.278 n n C;/n = 84.66/40 = 2.12 C;/n = 91.17/40 = 2.28 M M 0.23 x 100 =10.85% (365 day analysis) = 0.278 >_!- = 12.20% (730 day analysis) 2.12 2.28 curacy. It is not difficult to see that su- sumed to accurately represent the perior results could be obtained if creep-time relationship, it can be seen methods were available to more accur- that only one point on an experimental ately predict the material parameters creep-time curve is required to solve C. and (e$h)^,.. the equation for Cu; i.e., if Ct at any time is known then Eq. (3) becomes Creep prediction from to.6 Cu = Cc - u.sl (5) 28-day data [10 + t If the general form of Eq. (3) is as- and C. can be evaluated, thereby giv-

PCI Journal/May-June 1972ҟ 35 Table 3. Details of concrete mixes and mixing procedure

Ingredients Idealite Haydite Haydite Haydite for 1 cu. yd. by Hydraulic Press Brick by Buildex by Carter-Waters Cement (Type I) 705 lb. 705 lb. 611 lb. 658 lb. Coarse 820 lb. 20 ft.3 = 825 lb. 22.5 ft.3 = 977 lb. 23.5 ft. ҟ= 1318 lb. aggregate 60%-3/4 to 5/16 in. 40%-5/16 in. to No. 8 3/4 in. to No. 4 3/4 in. to No. 4 3/16 to 1/8 in. Sand 1395 lb. 1150 lb. 1020 1 b. 816 lb. Water 292 lb. 350 lb. 350 lb. 415 lb. Admixtures Darex-7/8 oz./sack — — WRDA-50 oz.

Mixing procedure: 1. Proportion and batch sand and aggregate. 2. Add approximately one-half of required water. 3. Mix for approximately two minutes. 4. Proportion and batch cement. 5. Add admixtures along with remaining water. 6. Mix for approximately three minutes or until homogeneous mixture is obtained. ing a continuous equation for creep as are calculated in Table 2. It can be a function of time. seen, from Fig. 2, that to obtain an The accuracy of the method can be error coefficient of 10 percent Neville evaluated from Table 1. Shown are l- and Meyers( 7 ) indicate that the tests and 2-year creep coefficients predicted should be carried out for about 20 from ` measured 28-day creep coeffi- weeks. Using the prediction method de- cients and experimental 1- and 2-year veloped herein similar accuracy can be creep coefficients (experimental data obtained with only 28 days (4 weeks) from References 12, 16 and 18-21). The of data collection; if greater than 28- ultimate creep coefficient Cu was esti- day results are obtained, increased ac- mated by substituting Ct at 28 days curacy can be expected. into Eq. (5). The data show that 53 per It is obvious from the above develop- cent of the calculated values are within ment that C„ can be estimated if C t at 10 percent, and 83 percent of the cal- any time is known. The creep coeffi- culated values are within 20 percent of cient Ct at 28 days is recommended the one-year observed values. Similar here for two reasons: figures for 2-year data are 50 percent 1. Strength and elastic properties are of the calculated values within 10 per evaluated based on 28-day tests; cent, and 80 percent within 20 per it was deemed desirable to main- cent of the observed values. In both tain this standard time interval. cases over 90 percent of the calculated 2. The accuracy obtained using less values are within 30 percent of the ob- than 28-day data was considered served values. It should be noted that a unsatisfactory. 30 percent variation in material properties represents a significantly lower variation in comparing calculated struc- Experimental tural deformations and actual structural verification of 28-day deformations. creep prediction An additional measure of the accuracy of the method is indicated by the method error coefficient M. The average error The 28-day creep prediction method coefficients for I-year and 2-year pre- and the general form of the creep-time diction for the 40 sets of data analyzed relationship suggested in Eq. (3) were

36 Table 4. Concrete properties

Property Idealite Haydite by H.P.B. by Bldx. byC-W -1 1-3 IS H-1 B-4 CW-4 f-7 daysҟ psi 6,700 6,150 5,600 5,150 3,650 3,450 f-14 daysҟ Psi 8,250 - 5,800 5,900 4,500 4,750 f-28 daysҟ psi 9,350 8,750 6,100 -- - Unit weight (wet)ҟpcf 124 125 - 113 105 115 Unit weight (dry)ҟpcf 123 124 122 113 103 113 Measured entrained airҟ% 4 6 --- - Slump,ҟ in. 2 2h - 2^ 2 1h E-7 days, psi X 10-6 secant @ 0.5 f - 3.20 3.04 2.93 2.45 2.66 initial tangent - 3.33 3.10 3.05 2.84 2.84 33 w 1 3.68 3.55 3.32 3.84 2.21 2.44 E6-14 days, psi x 10 -6 secant @ 0.5 - - - 3.06 2.51 2.88 initial tangent - - - 3.28 2.84 3.10 33 w3 fl 4.08 - 3.38 3.00 2.51 2.70 Ee 28 days, psi x 10 -6 secant @ 0.5 f - 3.28 - - - - initial tangent - 3.38 - - - - 33 w3 f1 4.35 4.23 3.47 - - - Relative humidity,ҟ(range) 20-50 25-50 21-50 7-48 10-48 10-48 percentҟ(avg.) 39 40 40: 28 32 32 Temperature, deg. Fҟ(range) 79-84 80-84 78-85 75-87 77-87 77-87 (avg.) 83 82 82 82 83 83

Group I-S specimens were steam cured, all others were moist cured,

further verified by an experimental pro- successfully with the constant d varying gram at the University of Iowa. Four from 6 to 12. Using Eq. (3), a continu- sand-lightweight concrete mixes, made ous creep time equation was developed with four different commercial aggre- from 28-day data for each of the four gates, were tested. Each mix was sub- mixes. Figs. 5 through 8 compare these jected to three different stress levels. equations to measured data. The data Details of the concrete mixes are shown indicate that 90 percent of all calcu- in Table 3, and the material properties lated values of Ct are within 10 per are given in Table 4. The data were recent, and 97 percent of all calculated duced and a plot similar to Fig. 3 pre- values are within 15 percent of the ob- pared. Then Eq. (6) was derived in the served values. same manner as Eq. (3). Shrinkage prediction t0.fi u (6) from 28-day data Ct 10.5 + to.s C The techniques described in the section A slight variation in the constant d on creep prediction from 28-day data (10.5 vs. 10) was obtained in the study can also be used to obtain a continuous of the University of Iowa experimental equation for shrinkage as a function of data. However, in order to be consis- time; i.e., if (Esh)t at any time is tent, Eq. (3) with a constant of d = 10 known, then Eq. (4a) becomes was used in all calculations dealing with University of Iowa data. It should (Esh)u = (Esh)t - t (7) be noted that Eq. (1) has been used L 35-Ft

PCI Journal/May-June 1972 37

cm 2. 2.0

00 1. 1.6 U U 1. 1.2 rni. 3 1 .8 6 __^ Ct -- - - - t. 6 0.6(2. Ct = 10 0 + t•^ (2.41) .4 c00 iii 100 200 300 40( 0 100 200 300 400 t days P O t days Fig. 5. Mix 01-1 Fig. 7. Mix CW-4

^ Q C A. A O 2.0 2. 2 07 1.6 1.

U 1.2 1,

.8 to 6 CS --- Ct = 010. + (2. 03) --- Ct = t6 (1.77) O .4 10.o +

0 0 100 200 300. 400 100 300 400 Ar t days 2^Odays Fig. 6. Mix B-4 Fig. 8. Mixes I-1 and I-3 C O O O

0 4` N

H M M 0 O O H ^ M + I+ HH M M ^ Y y O 1 C II 11 ' w x ^ b W 41 b H O4. O N NO Y qN ^ I I ri

O O N o O

O O O O O o O O O O o O O O O O O O o O O O O O O O O ^O ^f1 W M N ^O 111 W M N

ui/uc 9- 01 X u s a ut/ui - oi x ^S3

0 0 0 0

O O 4. M yl t MN et1 I0II I II

I u ro o o N N N O 0 C

0 O O

O O O O O O O O O O O O O O O O O O O O O O O O «1 V^ M N to d^ M N

ui/u2 9_pi x 4 s3 UT/ui9_0i x us3

Figs. 9-12. Predicted shrinkage curves based on 28-day values compared with measured values

PCI Journal/May-June 1972 39 Table 5. 28-day extrapolation of shrinkage

* s1 365 365 Q (Esh)730 (E1)65 (e11)33 Specimen (Esh)28 (Esh)u (E 5 (E s1 (Esh^73o designation Experimental Predicted Experimental Predicted Experimental Predicted (Es11 ) 365 (Esh)73o 6 422 948 888 881 918 905 0.992 0.986 71 363 816 887 758 955 779 0.856 0.816 q 72 362 815 843 758 915 779 0.899 0.851 73 361 813 814 756 865 776 0.929 0.897 74 361 813 789 756 840 776 0.958 0.924 6N6 354 796 790 740 880 760 0.937 0.864 10N6 345 776 660 721 685 740 1.092 1.080 8N6 490 1105 730 1029 745 1055 1.410 1.416 6M5 470 1058 765 982 830 1010 1.284 1.217 10M5 385 866 695 805 710 826 1.158 1.163 8M5 370 834 660 775 675 795 1.174 1.178

(Esh)° — (E 88 8 — (0.445 35 + 28 and (E~,), can be evaluated. Summary and The general accuracy of the method can be evaluated from Table 5. Shown conclusions are one- and two-year shrinkage strains Methods to predict the long-time creep (calculated in same manner as in creep and shrinkage behavior of concrete, us- prediction) and experimental values ing 28-day data have been developed (data from References 12, 16, 18-21). and experimentally verified. It has been The data indicate that, for moist cured shown that the expected accuracies of concrete, 45 percent of the calculated the methods are * 15 percent for values are within 10 percent, and 82 creep prediction and ? 30 percent for percent within 20 percent of the one- shrinkage prediction. year observed values; for two-year From these results it can be con- data, 27 percent of the calculated val- cluded that: ues are within 10 percent, and 82 per 1. The general form of Eq. (3) is cent within 20 percent of the ob- representative of the creep-time served values. In both cases all calcu- function. lated values are within 30 percent of 2. The general form of Eqs. (4a) and observed values. (4b) are representative of the Since the shrinkage data were more shrinkage-time function. limited than the creep data, an error co- For a concrete made with a given ag- efficient calculation was not made. It is gregate, the 28-day experimental pro- worth noting, however, that in a recent gram need only be carried out once to paper, Meyers, et al(z4) suggest that for establish a creep- or shrinkage-time re- reasonable accuracy "it is desirable to lationship. Should the mix and storage conduct shrinkage tests for as long as conditions of a particular mix being possible, and 56 days (8 weeks) is con- analyzed be different from those tested sidered the minimum acceptable testing experimentally, the creep or shrinkage period." However, it is now felt that time function can be modified by the the accuracy of the 28-day method dis- correction factors shown in the Appen- cussed herein is acceptable. dix. It is therefore recommended that Eqs. (3), (4a) and (4b) be used in con- junction with 28-day experimental pro- grams to determine the long-time creep Experimental and shrinkage behavior of concrete. This type of experimental program verification of 28-day could be used to great advantage in shrinkage- - prediction connection with precast, prestressed nzethod members. If it is not feasible to carry out even a 28-day. experimental- pro- gram, suitable general constants for C,' Figs. l2 compare shrinkage and (Es,L), have heen evaluated and prediction from are presented in Referencer 1, 2, 3, 4, 28-day data and measured shrinkage 25 and 26. These are summarized in the values for four of the concrete mixes Appendix along with the corresponding tested at the University of Iowa. The standard conditions. data indicate that 72 percent of all calculated values are within 10 percent, 84 within 15 percent, and 90 percent within 30 percent of observed shrinkage values. The research reported herein was con-

PCI Journal/May-June 1972 41 ducted under Iowa State Highway age and Temperature Effects in Commission Research Project HR-136, Concrete Structures," ACI Special initiated in February 1968. The auth- Publication SP-27, Creep, Shrink- ors thank Prestressed Concrete of Iowa, age and Temperature Effects in Inc.; Idealite Co., Denver, Colorado; Concrete Structures, American Hydraulic Press Brick Co., Brooklyn, Concrete Institute, Detroit, Mich., Indiana; Carter-Waters Corp., Kansas 1971. City, Missouri; and Buildex, Inc., Ot- 5. Thomes, F. C., "A Conception of tawa, Kansas, for their assistance. Creep of Unreinforced Concrete, and an Estimation of the Limiting Values," Structural Engineer, Vol. 11, No. 2, 1933. References 6. McHenry, D., "A New Aspect of 1. Branson, D. E. and Kripanaraya- Creep and its Application to De- nan, K. M., "Loss of Prestress, sign," ASTM Proceedings, Vol. 43, Camber and Deflection of Non- 1943. Composite and Composite Pre- 7. Saliger, R., "Die Neue Theorie des stressed Concrete Structures," Jour- Stahlbetons," Vienna, 1947. nal of the Prestressed Concrete In- 8. Shank, J. R., "The Plastic Flow of stitute, Vol. 16, No. 5, September- Concrete," Bulletin No. 91, Ohio October 1971, pp. 22-52. State University Engineering Ex- 2. Branson, D. E., Meyers, B. L. and periment Station, Columbus, 1935. Kripanarayanan, K. M., "Time-De- 9. Troxell, G. E., Raphael, J. M. and pendent Deformation of Non-Com- Davis, R. E., "Long-Time Creep posite and Composite Sand-Light- and Shrinkage Tests of Plain and weight Prestressed Concrete Struc- Reinforced Concrete," ASTM Pro- tures," Iowa Highway Commission ceedings, Vol. 58, 1958, pp. 1-20. Research Report No. 69-1, Project 10. Ross, A. D., "Concrete Creep No. HR-137, Phase 1 Report, Uni- Data," Structural Engineer, Vol. versity of Iowa, Iowa City, 1969. 15, No. 8, August 1937, pp. 314- Also a condensed paper, Report 326. No. 70-1, presented at the 40th 11. Lorman, W. R., "The Theory of Annual Meeting, Highway Re- Concrete Creep," ASTM Proceed- search Board, Washington, D.C., ings, Vol. 40, 1940, pp. 1082-1102. January 1970, and published in Highway Research Record, No. 12. Jones, T. R., Hirsch, T. J. and 324, Symposium on Concrete De- Stephenson, H. K., "The Physical formation, 1970, pp. 15-43. Properties of Structural Quality Lightweight Aggregate Concrete," 3. Branson, D. E. and Christiason, M. L., "Time-Dependent Concrete Texas Transportation Institute, Properties Related to Design— Texas A M University, College Strength and Elastic Properties, Station, Texas, 1959. Creep and Shrinkage," ACI Special 13. Wagner 0., "Daskriechen Unbe- Publication SP-27, Creep, Shrink- wehrten Betons," Deutcher Auss- age and Temperature Effects in chuss fur Stahlbeton, Bulletin No. Concrete Structures, American 131, Berlin, 1958. Concrete Institute, Detroit, Mich., 14. Wallo, E. M. and Kesler, C. E., 1971. "Prediction of Creep in Structural 4. Subcommittee II, ACI Committee Concrete," Bulletin 498, University 209, "Prediction of Creep, Shrink- of Illinois Engineering Experiment

42 Station. of Commerce, National Bureau of 15. Hilsdorf, H. K., "Prediction of Standards, Washington, D.C., Shrinkage and Creep Coefficients March 1964, 30 pp. for Structural Concrete," U.S.—Ja- 22. Keeton, J. R., "Study of Creep in pan Joint Seminar on Research and Concrete, Phases 1-5," Technical Basic Properties of Various Con- Reports No. R 33-I, II and III, U.S. cretes, Tokyo, Japan, 1968. Naval Civil Engineering Labora- Meyers, B. L., Branson, D. E. and tory, Port Hueneme, California, Anderson, G. H., "Creep and 1965. Shrinkage Properties of Light- 23. Pauw, A., private communication. weight Concrete Used in the State 24. Meyers, B. L., Hope, B. B., Lor- of Iowa," Iowa Highway Commis- man, W. R., Mills, R. H. and sion Research Report, Project No. Roll, F., "The Effects of Concrete HR-136, Phase 1 Report, Univer- Constituents, Environment, and sity of Iowa, Iowa City, 1968. Stress on the Creep of Concrete," 17 Neville, A. M. and Meyers, B. L., ACI Committee 209, Subcommit- "Creep of Concrete Influencing tee I Report, ACI Special Publica- Factors and Prediction," ACI Spe- tion SP-27, Creep, Shrinkage and cial Publication SP-9, Creep of Temperature Effects in Concrete Concrete, American Concrete In- Structures, American Concrete In- stitute, Detroit, Mich., 1964. stitute, Detroit, Mich., 1971. 18. Hansen, T. C. and Mattock, A. H., 25. Schumann, C. G., "Creep and "The Influence of Size and Shape Shrinkage Properties of Light- of Member on the Shrinkage and weight Aggregate Concrete Used Creep of Concrete," ACI Journal, in the State of Iowa," M.S. Thesis, Proceedings, Vol. 63, No. 2, Febru- University of Iowa, Iowa City, ary 1966. pp. 267-289. 1970. 19. Pfeifer, D. W., "Sand Replacement 26. Meyers, B. L., Branson, D. E., in Structural Lightweight Concrete Schumann, C. G. and Christiason, —Creep and Shrinkage Studies," M. L., "The Prediction of Creep ACI Journal, Proceedings, Vol. 65, and Shrinkage Properties of Con- No. 2, February 1968, pp. 131-142. crete," Iowa Highway Commission 20. Hanson, J. A., "Prestress Loss as Research Report, Project No. HR- Affected by Type of Curing," Jour- 136, University of Iowa, Iowa City, nal of the Prestressed Concrete In- 1970. stitute, Vol. 9, No. 2, 1964, pp. 69- 27. Keeton, J. R., "Creep and Shrink- 93. age of Reinforced Thin-Shell Con- 21. Reichart, T. W., "Creep and Dry- crete," Technical Report R 704, ing Shrinkage of Lightweight and U.S. Naval Civil Engineering Lab- Normal Weight Concrete," NBS oratory, Port Hueneme, California, Monograph 74, U.S. Department November 1970, pp. 1-58.

PCI Journal/May-June 1972 43 Appendix

Standard conditions. The correction factors (C.F.) and the general values for C,, and (e85),, listed below are based on standard conditions (References 3 and 26) as follows: 4 in. (10 cm) or less slump, 40 percent ambient relative humidity, minimum thickness of member 6 in. (15 cm) or less, loading age and shrinkage from 7 days for moist cured, and loading age and shrinkage from 2 to 3 days for steam cured concrete. General values for C. and (€81,),,,. When experimental work is not possible, Eqs. (3), (4a) and (4b) can be used with general average values for C,, and as follows: to.6 x 2.35 (3) Ct 10 + ta•6

t X 800 X 10 - 6 (moist cured) (4a) (SnE t= 35 + t

t x 730 x 10- 6 (steam cured) (4b) ( Esh t — 55—+ t Correction factors Loading age, where tLA is the loading age in days: Creep (C.F.)LA = 1.25 tZAO."s for moist cured concrete (Al) Creep (C.F.)LA = 1.13 tjA•osa for steam cured concrete (A2) Humidity, where H is the ambient relative humidity in percent: Creep (C.F.)H = 1.27 — 0.0067 H when H 40% (A3) Shrinkage (C.F.)H = 1.40 — 0.010 H when 40% H 80% (A4) Shrinkage (C.F.)H = 3.00 — 0.030 H when 80% H 100% (A5)

Minimum thickness of member, where T is the minimum thickness in inches: Creep (C.F.)T = 1.14 — 0.023 T, for : 1 year loading (A6) Creep (C.F.) 3. = 1.10 — 0.017 T, for ultimate value (A7) Shrinkage (C.F.)T = 1.23 — 0.038 T, for S 1 year drying (A8) Shrinkage (C.F.)T = 1.17 - 0.029 T, for ultimate value (A9) Slump, where S is the slump in inches: Creep (C.F.)s = 0.82 + 0.067 S (A10) Shrinkage (C.F.)s = 0.89 + 0.041 S (All) Cement content, where B is the number of bags (94 lb.) of cement per cubic yard (56 kg/m3) of concrete: Creep (C.F.)B = 1.00 (Al2) Shrinkage (C.F.)B = 0.75 + 0.034 B (A13) Percent fines, where F is the percent of fine aggregate by weight:

44 Creep (C.F.)F = 0.88 + 0.0024 F (A14) Shrinkage (C.F.)p = 0.30 + 0.0140 F, for F 50% (A15) Shrinkage (C.F.)r = 0.90 + 0.0020 F, for F ? 50% (A16) Air content, where A is the air content in percent: Creep (C.F.)A = 1.00, for A 6% (A17) Creep (C.F.)A = 0.46 + 0.090 A, for A> 6% (A18) Shrinkage (C.F.)A = 0.95 + 0.0080 A (A19)

Example. The following example is for moist cured concrete:

Condition Creep Correction Shrinkage Correction 28 day loading Eq. (Al) : 0.85 - 70 percent humidity Eq. (A3) : 0.80 Eq. (A5) : 0.70 8 in. (20 cm) min. thickness Eq. (A6) : 0.96 Eq. (A8) : 0.94 2.5 in. (6 cm) slump Eq. (A10): 0.99 Eq. (All): 0.99 8 sacks/cu. yd. (448 kg/m3) cement content Eq. (Al2): 1.00 Eq. (A13): 1.02 60 percent fines Eq. (Al4): 1.02 Eq. (A16): 1.02 7 percent air content Eq. (A18): 1.09 Eq. (A19): 1.01

Standard values at 365 clays: _ 3650.60 C365 10 -{- 3650.60 X 2.35 = 1.82 365 X 800 x 10- 6 = 730 X 10- o in./in. (Esti 30 - 35 + 365 Corrected values: C365 = (1.82) (0.85 x 0.80 x 0.96 x 0.99 x 1.00 x 1.02 X 1.09) = 1.31

(e8h)356 = (730 X 10- 0) (0.70 x 0.94 X 0.99 x 1.02>< 1.02 x 1.01) 510 X 10- 6 in./in.

Discussion of this paper is invited. Please forward your discussion to PCI Headquarters by Sept. 1 to permit publication in the Sept.-Oct. 1972 issue of the PCI Journal.

PCI Journal/May-June 1972 45