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
time-dependent concrete properties and
accurate prediction methods was demonstrated by Branson and Kripanarayanan1 1 ) who showed that loss of prestress and camber in non-composite and
composite structures could be predicted
twice as accurately when experimentally determined material parameters
were used, as compared to predictions
made using material properties esti-
PCI Journal/May-June 1972
mated from general relationships.
The prediction equations developed
in References 2, 3 and 4, and included
in the analysis of prestressed concrete
structures reported in Reference 1, form
the basis of this work. It will be shown
that using the methods described in this
paper, prediction accuracy that previously required almost 4 months of testing can be obtained with only 28 days
of creep and shrinkage test data.
29
800
760
600
/ -O
Branson
500
^^"
/t
Ross
400
300
200
100
80
160
240
320
t days
400
480
560
Fig. 1. Predicted creep comparing Ross equation with Branson Eq. (1)
Previous proposals
for creep prediction
Creep prediction methods that might
be useful to the design engineer can be
divided into two general categories:
(1) the creep-time relationship is expressed in the form of an equation, and
usually requires that one or more empirical constants be determined experimentally, and (2) creep is expressed by
a standard curve which can be modified by a number of factors to allow for
various mix and storage conditions. The
latter prediction method does not require experimental data but is usually
less accurate than using an empirical
equation based on actual measurements.
In Category 1, about a dozen exponential or hyperbolic equations have
been suggested. Most exponential equations, which have the practical disadvantage of not approaching a finite
limit, are - of doubtful value to the design engineer because they are unwieldly and/or require extended periods of
3Q
data collection. Such equations have
been proposed by Thomas( a ), McHenry(6), Saliger( 7 ), Shank( 8 ), and
Troxell, et al(9).
A number of simpler hyperbolic
equations, which do approach a finite
limit, have also been suggested. Those
used most often are the equations of
Ross (10)
c—a
+ bt °-
and Lorman(")
mt
c— n+t owhere c = creep, t = time, o' = stress,
and a, b, m and n are experimentally
determined empirical constants.
Methods using standard creep curves
can be represented by those suggested
by Jones, et al( 12 ), and Wagner(13).
Jones used a standard curve, valid for
specific mix and storage parameters,
which can be corrected for other conditions by using a set of correction factors. Wagner's method differs only in
that standard values of ultimate specific
30
25
20
a 15
L)
0
O
P
10
5
0
0
15
10
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.
The literature is rather sparse in the
area of shrinkage prediction, although a
number of complex methods have been
suggested( 14,15 ). However, since the
methods developed in this paper have
their basis in the creep prediction methods already discussed, further analysis
of available shrinkage methods will be
omitted.
In an attempt to increase the accuracy of creep and shrinkage prediction,
Meyers, et al(' 6 , combined the methods of Ross and Jones. Although some
improvements were made, it was noted
that this method, as well as others, predicted ultimate creep fairly well, but
did not adequately represent the deformation behavior of the material early in
its life.
This difficulty was overcome by
Branson, et al 2,3 '4 ), who proposed the
following standard prediction equations
Ct
to
d +to C u
PCI Journal/May-June 1972
(1)
( E85)t =
f t' t ^ (Esh)u
(2)
where
Ct = creep coefficient, defined as
ratio of creep strain to initial strain, at any time t
(e3n,)t = shrinkage strain at any time
t
C u = ultimate shrinkage coefficient
(esh),, = ultimate shrinkage strain
c, d, e, f = empirical constants
It is interesting to note that in addition
to developing the well known creep
equation, Ross suggested a shrinkage
equation similar to Eq. (2) in 1937(10).
Comparisons with measured data
show that the form of the creep prediction in Eq. (1) is more representative of
the full range of creep behavior than
the form originally suggested by Ross.
Such a comparison is made in Fig. 1.
Because the Branson equation is more
representative of the full range of creep
behavior, it can be used in an accurate
31
Moist cured and steam cured concretes
100
•
4)
q
80
Eq. ( 3 )
•
O,
■_..O
rO
U
o
a
•
60
♦
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)
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
•
U 20
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 28day data. It can also be shown that Eq.
(2) accurately represents the full range
of shrinkage vs. time behavior(2.3.4).
It is significant that accurate prediction can be obtained with 28-day data
in light of information presented by Neville and Meyers( 17 ). The accuracy of
any method can be evaluated in terms
of an error coefficient M(17).
M= VCi—
Cti)2/n
CCI
where C t = creep after one year predicted from measured
creep after t weeks under
load
Cd = actual creep after i years
under load
n = number of specimens or
experimental sets for
which creep was observed
at time t
32
It can be seen from Fig. 2 that for most
available methods, in order to predict
creep to within an error coefficient of
10 percent, 20 weeks of data is required.
Prediction equations
after Branson,
et alr=.2""
To solve Eq. (1) and (2) for C,, and
(€,h)t, three unknowns must be evaluated in each case (d, c and C. are unknown for Eq. (1), and for Eq. , (2), e, f
and (E 8h)„ are unknown). Of the three
unknowns, two from each equation are
empirical constants while C,, and
(e8n,),, are material properties.
In order to determine the empirical
constants d and c, creep data from References 12, 16 and 18-21 were normalized with respect to C,, and plotted in
Fig. 3. In most cases, three data points
a. Moist cured concrete
100ҟ
•
0
60
w
4
N
4J
WN
40
20
0
(4a)
0
•
Nor. Wt.
Sand-Lt.Wt All-Lt.Wt.
I,Moist 0(12,1) (20, 1) x(123) (2,3) •(12,21) (19, 1)
(20,2)
•III,Moist D(20, 1) (18, 1)
• (20,2)
(22,3)
0ҟ
160ҟ
320
480ҟ
640ҟ
800
Time after initial shrinkage considered in days
b. Steam cured concrete
100
y
r.
N
1
•.p
+ 80
o
a
d
60
D
0
•
F. (4b)
X40
W
20
W
N
0
Nor.Wt.
All-Lt.Wt.
Type I,Steam 0 (20, 1)
• (20, 2)
Type III,Steam o (20, 1) (21, 8) ■ (20, 2) (21,42)
0ҟ
16oҟ
320ҟ
480ҟ
640ҟ
800
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
C..
Ci28
Specimen
designation Experimental Predicted
V
0365
Experimental
C730
Experimental
C730
Predicted
V365
C; 65
y730
C,3
4
6
8
12
16
20
24
0.97
1.15
0.92
0.82
0.82
0.64
0.73
2.28
2.70
2.16
1.93
1.93
1.50
1.72
1.82
2.06
2.03
1.66
1.55
1.30
1.37
1.77
2.09
1.67
1.50
1.50
1.16
1.33
1.86
2.17
2.14
1.71
1.69
1.44
1.52
1.91
2.26
1.81
1.62
1.62
1.26
1.44
0.973
1.015
0.823
0.904
0.968
0.892
0.971
1.027
1.041
0.845
0.947
0.959
0.875
0.947
71
72
73
74
1.37
1.25
1.20
1.28
3.22
2.94
2.82
3.01
2.46
2.36
2.75
2.46
2.50
2.28
2.18
2.33
2.73
2.61
2.31
2.62
2.70
2.46
2.36
2.52
1.016
0.966
0.793
0.947
0.989
0.943
0.793
0.962
6N6
6N28
6S2
6S7
6S28
10N6
10N28
10S2
1057
10528
8N6
8N28
8S7
8S28
6M5
6M28
6R7
6R28
1OM5
10M28
1082
10R7
10828
8M5
8M28
8R2
8R7
8R28
6R2
1.90
1.52
1.10
1.04
0.95
1.04
0.75
0.65
0.72
0.66
1.73
1.88
1.41
1.35
1.51
1.10
0.74
0.60
0.93
0.92
0.68
0.66
0.63
1.57
1.73
1.09
1.13
1.08
0.90
4.47
3.58
2.59
2.45
2.24
2.45
1.76
1.53
1.69
1.55
4.07
4.43
3.32
3.18
3.56
2.59
1.74
1.41
2.18
2.16
1.60
1.55
1.48
3.70
4.07
2.56
2.66
2.54
2.12
3.45
3.01
2.21
2.20
2.20
1.79
1.59
1.30
1.34
1.43
3.02
3.40
2.45
2.59
2.78
2.48
1.70
1.54
1.84
1.93
1.34
1.33
1.40
2.96
3.00
2.10
2.32
2.34
1.80
3.46
2.78
2.01
1.90
1.74
1.90
1.36
1.18
1.31
1.20
3.16
3.36
2.58
2.48
2.76
2.00
1.35
1.09
1.69
1.67
1.24
1.20
1.15
2.87
3.15
1.98
2.06
1.97
1.64
3.72
3.32
2.53.
2.52
2.51
1.94
1.74
1.45
1.50
1.62
3.19
3.70
2.74
2.95
3.01
2.67
1.93
1.78
1.97
2.12
1.49
1.46
1.56
3.19
3.23
2.34
2.55
2.64
2.00
3.75
2.99
2.17
2.06
1.88
2.06
1.48
1.28
1.42
1.30
3.42
3.72
2.78
2.67
2.98
2.16
1.46
1.18
1.83
1.81
1.34
1.30
1.24
3.10
3.42
2.14
2.23
2.13
1.78
1.003
0.924
0.910
0.864
0.791
1.061
0.855
0.908
0.978
0.839
1.046
0.988
1.053
0.958
0.993
0.806
0.853
0.708
0.918
0.865
0.925
0.902
0.821
0.970
1.05
0.943
0.888
0.842
0.911
1.008
0.901
0.818
0.817
0.749
1.062
0.851
0.883
0.947
0.802
1.072
1.005
1.015
0.905
0.990
0.809
0.756
0.663
0.929
0.854
0.899
0.890
0.795
0.972
1.059
0.914
0.875
0.807
0.890
C28
_. C^a
Cu = 280.6 +280.6 0.025
10
**'C
are shown for a particular specimen
category and time. They represent the
upper and lower limits and average
values of these data. Only one data
point is shown for a specific time when
the spread between upper and lower
values is small. Eq. (3) was derived by
fitting a curve to the average values of
the data.
to.s
C t = 10 + t0.6 Cc
(3)
Eq. (3) can be used for both moist and
steam cured concrete.
Similarly Eqs. (4a) and (4b) were
developed from shrinkage data plotted
in Fig. 4.
34
r3 5
Predicted
365 0.6 XCu
36s = 10 13650.6
t
(e8n)t =
35 + t
(E'h)t
(moist cured) (4a)
(steam cured) (4b)
- t (Esn)u
55
Using the basic Eqs. (3), (4a) and
(4b), general prediction equations can
be supplied to the designer by specifying average values C. and (€ 8h). This
was done in Reference 1 where it was
shown that loss of prestress and camber
could be predicted to within ± 30 percent of actual results using average
values of C,u and (e8h)u. Keeton(28)
and Pauw( 23 ) have also used Eqs. (3),
(4a) and (4b) to predict structural response with an adequate degree of ac-
Table 2. Determination of error coefficient
Predicted, Experimental,
365 days
365 days
Ct
C;
1.82
2.06
2.03
1.66
1.55
1.30
1.37
2.46
2.36
2.73
2.46
3.45
3.01
2.21
2.20
2.20
1.79
1.59
1.30
1.34
1.43
3.02
3.40
2.45
2.59
2.78
2.48
1.70
1.54
1.84
1.93
1.34
1.33
1.40
2.96
3.00
2.10
2.32
2.34
1.80
1.77
2.09
1.67
1.50
1.50
1.16
1.33
2.50
2.28
2.18
2.33
3.46
2.78
2.01
1.90
1.74
1.90
1.36
1.18
1.31
1.20
3.16
3.36
2.58
2.48
2.76
2.00
1.35
1.09
1.69
1.67
1.24
1.20
1.15
2.87
3.15
1.98
2.06
1.47
1.64
(Cr - C1)
365
(C1 - G) 2
365
Predicted,
730 days
Ct
Experimental,
730 days
C,
0.05
0.03
0.36
0.16
0.05
0.14
0.04
0.04
0.08
0.57
0.13
0.01
0.23
0.20
0.30
0.46
0.11
0.23
0.12
0.03
0.23
0.14
0.04
0.13
0.11
0.02
0.48
0.35
0.45
0.15
0.26
0.10
0.13
0.25
0.09
0.15
0.12
0.26
0.37
0.16
0.0025
0.0009
0.1296
0.0256
0.0025
0.0196
0.0016
0.0016
0.0064
0.3249
0.0169
0.0001
0.0529
0.0400
0.0900
0.2116
0.0121
0.0529
0.0144
0.0009
0.0529
0.0196
0.0016
0.0169
0.0121
0.0004
0.2304
0.1225
0.2025
0.0225
0.0676
0.0100
0.0169
0.0625
0.0081
0.0225
0.0144
0.0676
0.1369
0.0256
1.91
2.26
1.81
1.62
1.62
1.26
1.44
2.70
2.46
2.36
2.52
3.75
2.99
2.17
2.06
1.88
2.06
1.48
1.28
1.42
1.30
3.42
3.72
2.78
2.67
2.98
2.16
1.46
1.18
1.83
1.81
1.34
1.30
1.24
3.10
3.42
2.14
2.23
2.13
1.78
1.86
2.17
2.14
1.71
1.69
1.44
1.52
2.73
2.61
2.31
2.62
3.72
3.32
2.53
2.52
2.51
1.94
1.74
1.45
1.50
1.62
3.19
3.70
2.74
2.95
3.01
2.67
1.93
1.78
1.97
2.12
1.49
1.46
1.56
3.19
3.23
2.34
2.55
2.64
2.00
84.66
(C `
- C;)2 =V5.299 x 10- 2 = 0.23
n
C;/n = 84.66/40 = 2.12
M
x
0.23 100 =10.85% (365 day analysis)
2.12
curacy. It is not difficult to see that superior results could be obtained if
methods were available to more accurately predict the material parameters
C. and (e$h)^,..
(C t - C1)2
730
0.05
0.09
0.33
0.09
0.07
0.18
0.08
0.03
0.15
0.05
0.10
0.03
0.33
0.36
0.46
0.63
0.12
0.26
0.17
0.08
0.32
0.23
0.02
0.04
0.28
0.03
0.51
0.47
0.60
0.14
0.31
0.15
0.16
0.32
0.09
0.19
0.20
0.32
0.51
0.22
0.0025
0.0081
0.1089
0.0081
0.0049
0.0324
0.0064
0.0009
0.0225
0.0025
0.0100
0.0090
0.1089
0.1296
0.2116
0.3969
0.0144
0.0676
0.0289
0.0064
0.1024
0.0529
0.0004
0.0016
0.0784
0.0009
0.2601
0.2209
0.3600
0.0196
0.0961
0.0225
0.0256
0.1024
0.0081
0.0361
0.0400
0.1024
0.2601
0.0484
3.0894
(C1 - C1) 2 - 3.0894 = 0.0772
40
nҟ
(C`
= V7.72 X 102=0.278
n
C;/n = 91.17/40 = 2.28
M = 0.278 >_!- = 12.20% (730 day analysis)
2.28
sumed to accurately represent the
creep-time relationship, it can be seen
that only one point on an experimental
creep-time curve is required to solve
the equation for Cu; i.e., if Ct at any
time is known then Eq. (3) becomes
Creep prediction from
28-day data
If the general form of Eq. (3) is as-
730
91.17
2.1195
(C1 - C1) 2 _
- 2.1195 = 0.05299
40
n
(C1- C,)
to.6
Cu
= Cc -
[10 + t u.sl
(5)
and C. can be evaluated, thereby giv-
PCI Journal/May-June 1972ҟ
35
Table 3. Details of concrete mixes and mixing procedure
Ingredients
for 1 cu. yd.
Idealite
Cement (Type I)
705 lb.
Coarse
aggregate
820 lb.
60%-3/4 to 5/16 in.
40%-5/16 in. to No. 8
Haydite
by Hydraulic Press Brick
705 lb.
Haydite
by Buildex
Haydite
by Carter-Waters
611 lb.
658 lb.
20 ft. 3 = 825 lb.
22.5 ft. 3 = 977 lb.
23.5 ft. ҟ
= 1318 lb.
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.
415 lb.
Darex-7/8 oz./sack
WRDA-50 oz.
—
350 lb.
—
Admixtures
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
a function of time.
The accuracy of the method can be
evaluated from Table 1. Shown are land 2-year creep coefficients predicted
from ` measured 28-day creep coefficients and experimental 1- and 2-year
creep coefficients (experimental data
from References 12, 16 and 18-21). The
ultimate creep coefficient C u was estimated by substituting Ct at 28 days
into Eq. (5). The data show that 53 per
cent of the calculated values are within
10 percent, and 83 percent of the calculated values are within 20 percent of
the one-year observed values. Similar
figures for 2-year data are 50 percent
of the calculated values within 10 per
cent, and 80 percent within 20 per
cent of the observed values. In both
cases over 90 percent of the calculated
values are within 30 percent of the observed values. It should be noted that a
30 percent variation in material properties represents a significantly lower
variation in comparing calculated structural deformations and actual structural
deformations.
An additional measure of the accuracy of the method is indicated by the
error coefficient M. The average error
coefficients for I-year and 2-year prediction for the 40 sets of data analyzed
36
are calculated in Table 2. It can be
seen, from Fig. 2, that to obtain an
error coefficient of 10 percent Neville
and Meyers(' 7 ) indicate that the tests
should be carried out for about 20
weeks. Using the prediction method developed herein similar accuracy can be
obtained with only 28 days (4 weeks)
of data collection; if greater than 28day results are obtained, increased accuracy can be expected.
It is obvious from the above development that C„ can be estimated if C t at
any time is known. The creep coefficient Ct at 28 days is recommended
here for two reasons:
1. Strength and elastic properties are
evaluated based on 28-day tests;
it was deemed desirable to maintain this standard time interval.
2. The accuracy obtained using less
than 28-day data was considered
unsatisfactory.
Experimental
verification of 28-day
creep prediction
method
The 28-day creep prediction method
and the general form of the creep-time
relationship suggested in Eq. (3) were
Table 4. Concrete properties
Idealite
Property
by H.P.B.
Haydite
by Bldx.
byC-W
-1
1-3
IS*
H-1
B-4
CW-4
6,700
8,250
9,350
6,150
8,750
5,600
5,800
6,100
5,150
5,900
-
3,650
4,500
-
3,450
4,750
-
124
123
125
124
122
113
113
105
103
115
113
4
%
Measured entrained airҟ
2
in.
Slump,ҟ
6
2'h
-
2^
2
1'h
3.68
3.20
3.33
3.55
3.04
3.10
3.32
2.93
3.05
3.84
2.45
2.84
2.21
2.84
4.08
-
3.38
3.06
3.28
3.00
2.51
2.84
2.51
2.88
3.10
2.70
4.35
3.28
3.38
4.23
3.47
-
-
-
20-50
(range)
Relative humidity,ҟ
39
percentҟ(avg.)
25-50
40
21-50
40:
7-48
28
10-48
32
10-48
32
(range)
79-84
Temperature, deg. Fҟ
83
(avg.)
80-84
82
78-85
82
75-87
82
77-87
83
77-87
83
f-7 daysҟ psi
f'-14 daysҟ Psi
f-28 daysҟ psi
pcf
Unit weight (wet) ҟ
pcf
Unit weight (dry)ҟ
E-7 days, psi X 10-6
secant @ 0.5 f
initial tangent
33 w 1
E6-14 days, psi x 10 -6
secant @ 0.5
initial tangent
33 w3 fl
Ee 28 days, psi x 10 -6
secant @ 0.5 f'
initial tangent
33 w3 f1
2.66
2.44
* Group I-S specimens were steam cured, all others were moist cured,
further verified by an experimental program at the University of Iowa. Four
sand-lightweight concrete mixes, made
with four different commercial aggregates, were tested. Each mix was subjected to three different stress levels.
Details of the concrete mixes are shown
in Table 3, and the material properties
are given in Table 4. The data were reduced and a plot similar to Fig. 3 prepared. Then Eq. (6) was derived in the
same manner as Eq. (3).
t0.fi
Ct
10.5 + t o.s C u
(6)
A slight variation in the constant d
(10.5 vs. 10) was obtained in the study
of the University of Iowa experimental
data. However, in order to be consistent, Eq. (3) with a constant of d = 10
was used in all calculations dealing
with University of Iowa data. It should
be noted that Eq. (1) has been used
PCI Journal/May-June 1972 successfully with the constant d varying
from 6 to 12. Using Eq. (3), a continuous creep time equation was developed
from 28-day data for each of the four
mixes. Figs. 5 through 8 compare these
equations to measured data. The data
indicate that 90 percent of all calculated values of Ct are within 10 per
cent, and 97 percent of all calculated
values are within 15 percent of the observed values.
Shrinkage prediction
from 28-day data
The techniques described in the section
on creep prediction from 28-day data
can also be used to obtain a continuous
equation for shrinkage as a function of
time; i.e., if (Esh)t at any time is
known, then Eq. (4a) becomes
(Esh)u = (Esh)t -
t
L 35-Ft
(7)
37
00
cm
00
U
rni.
2.
2.0
1.
1.6
U
1.
31
i
ii
c00
P O
1.2
.8
6
__^ Ct -- 0.6(2.
--.4
100
Fig. 5.
200
300
t days
Mix 01-1
40(
0
100
t. 6
Ct = 10 0 + t•^ (2.41)
200
t days
Fig. 7. Mix CW-4
300
400
^Q
A
C A.
O
2
07
U
to
2.0
2.
1.6
1.
1.2
1,
.8
--- Ct = 0
10. 6+ (2. 03)
CS
O
.4
0
Ar
0
100
200
t days
Fig. 6. Mix B-4
300.
400
--- Ct = 10.o + t6 (1.77)
100
300
2^Odays
Fig. 8. Mixes I-1 and I-3
400
O
O
C
O
4`
0'
N
M
0
O H
I+ HH
Y y O1
I
1
w x
W
41
I
I
H M
O
M
^'
M
^
^
M
+
'
b
O4.
N
^
ri
C
O
N
b
H
O Y qN
O
o
O
O
N
k1
O
O
^O
O
O
O
O
^f1
W
O
o
O
o
O
O
N
M
ui/uc 9- 01
O
O
O
O
^O
O
O
111
o
O
W
O
O
N
O
O
M
ut/ui - oi
X us a
O
O
O
x ^S3
0
0
0
0
I0
O
4.
O
yl t
M
' N
M
I
II
o
et'
1
II
I
ro
u
o
N
N
N
0
O
C
0
O
O
0
O
O
«1
O
O
V^
O
O
M
O
O
O
O
N
ui/u2 9 _pi x 4 3
s
O
O
O
O
to
O
O
d^
O
O
M
O
O
N
O
O
OO
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
Specimen
designation
q
(Esh)28
Experimental
(Esh)u
*
Predicted
(E
s1 365
(E s1
365
Q
(Esh^73o
(Esh)730
Experimental
Predicted
Experimental
Predicted
5
(E1)65
(e11)33
(Es11 ) 365
(Esh)73o
6
422
948
888
881
918
905
0.992
0.986
71
72
73
74
363
362
361
361
816
815
813
813
887
843
814
789
758
758
756
756
955
915
865
840
779
779
776
776
0.856
0.899
0.929
0.958
0.816
0.851
0.897
0.924
6N6
10N6
8N6
6M5
10M5
8M5
354
345
490
470
385
370
796
776
1105
1058
866
834
790
660
730
765
695
660
740
721
1029
982
805
775
880
685
745
830
710
675
760
740
1055
1010
826
795
0.937
1.092
1.410
1.284
1.158
1.174
0.864
1.080
1.416
1.217
1.163
1.178
* (Esh) ° — (E 88 8 — (0.445
35 + 28
and ( E ~ , ) , can be evaluated.
Summary and
The general accuracy of the method
conclusions
can be evaluated from Table 5. Shown
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, usprediction) 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
15 percent for
concrete, 45 percent of the calculated the methods are
creep
prediction
and
?
30 percent for
values are within 10 percent, and 82
shrinkage
prediction.
percent within 20 percent of the oneFrom these results it can be conyear observed values; for two-year
data, 27 percent of the calculated val- cluded that:
1. The general form of Eq. ( 3 ) is
ues are within 10 percent, and 82 per
representative of the creep-time
cent within 20 percent of the obfunction.
served values. In both cases all calcu2. The general form of Eqs. (4a) and
lated values are within 30 percent of
(4b) are representative of the
observed values.
shrinkage-time function.
Since the shrinkage data were more
For a concrete made with a given aglimited than the creep data, an error coefficient calculation was not made. It is gregate, the 28-day experimental proworth 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 rereasonable 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 Appendix.
cussed herein is acceptable.
It is therefore recommended that
Eqs. (3), (4a) and (4b) be used in conjunction with 28-day experimental programs to determine the long-time creep
and
shrinkage behavior of concrete.
Experimental
This type of experimental program
verification of 28-day
could be used to great advantage in
shrinkage
prediction
connection with precast, prestressed
members. If it is not feasible to carry
nzethod
out even a 28-day
pro. experimental
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
Commission Research Project HR-136,
initiated in February 1968. The authors thank Prestressed Concrete of Iowa,
Inc.; Idealite Co., Denver, Colorado;
Hydraulic Press Brick Co., Brooklyn,
Indiana; Carter-Waters Corp., Kansas
City, Missouri; and Buildex, Inc., Ottawa, Kansas, for their assistance.
References
1. Branson, D. E. and Kripanarayanan, K. M., "Loss of Prestress,
Camber and Deflection of NonComposite and Composite Prestressed Concrete Structures," Journal of the Prestressed Concrete Institute, Vol. 16, No. 5, SeptemberOctober 1971, pp. 22-52.
2. Branson, D. E., Meyers, B. L. and
Kripanarayanan, K. M., "Time-Dependent Deformation of Non-Composite and Composite Sand-Lightweight Prestressed Concrete Structures," Iowa Highway Commission
Research Report No. 69-1, Project
No. HR-137, Phase 1 Report, University of Iowa, Iowa City, 1969.
Also a condensed paper, Report
No. 70-1, presented at the 40th
Annual Meeting, Highway Research Board, Washington, D.C.,
January 1970, and published in
Highway Research Record, No.
324, Symposium on Concrete Deformation, 1970, pp. 15-43.
3. Branson, D. E. and Christiason,
M. L., "Time-Dependent Concrete
Properties Related to Design—
Strength and Elastic Properties,
Creep and Shrinkage," ACI Special
Publication SP-27, Creep, Shrinkage and Temperature Effects in
Concrete Structures, American
Concrete Institute, Detroit, Mich.,
1971.
4. Subcommittee II, ACI Committee
209, "Prediction of Creep, Shrink42
age and Temperature Effects in
Concrete Structures," ACI Special
Publication SP-27, Creep, Shrinkage and Temperature Effects in
Concrete Structures, American
Concrete Institute, Detroit, Mich.,
1971.
5. Thomes, F. C., "A Conception of
Creep of Unreinforced Concrete,
and an Estimation of the Limiting
Values," Structural Engineer, Vol.
11, No. 2, 1933.
6. McHenry, D., "A New Aspect of
Creep and its Application to Design," ASTM Proceedings, Vol. 43,
1943.
7. Saliger, R., "Die Neue Theorie des
Stahlbetons," Vienna, 1947.
8. Shank, J. R., "The Plastic Flow of
Concrete," Bulletin No. 91, Ohio
State University Engineering Experiment Station, Columbus, 1935.
9. Troxell, G. E., Raphael, J. M. and
Davis, R. E., "Long-Time Creep
and Shrinkage Tests of Plain and
Reinforced Concrete," ASTM Proceedings, Vol. 58, 1958, pp. 1-20.
10. Ross, A. D., "Concrete Creep
Data," Structural Engineer, Vol.
15, No. 8, August 1937, pp. 314326.
11. Lorman, W. R., "The Theory of
Concrete Creep," ASTM Proceedings, Vol. 40, 1940, pp. 1082-1102.
12. Jones, T. R., Hirsch, T. J. and
Stephenson, H. K., "The Physical
Properties of Structural Quality
Lightweight Aggregate Concrete,"
Texas Transportation Institute,
Texas A & M University, College
Station, Texas, 1959.
13. Wagner 0., "Daskriechen Unbewehrten Betons," Deutcher Ausschuss fur Stahlbeton, Bulletin No.
131, Berlin, 1958.
14. Wallo, E. M. and Kesler, C. E.,
"Prediction of Creep in Structural
Concrete," Bulletin 498, University
of Illinois Engineering Experiment
Station.
15. Hilsdorf, H. K., "Prediction of
Shrinkage and Creep Coefficients
for Structural Concrete," U.S.—Japan Joint Seminar on Research and
Basic Properties of Various Concretes, Tokyo, Japan, 1968.
Meyers, B. L., Branson, D. E. and
Anderson, G. H., "Creep and
Shrinkage Properties of Lightweight Concrete Used in the State
of Iowa," Iowa Highway Commission Research Report, Project No.
HR-136, Phase 1 Report, University of Iowa, Iowa City, 1968.
17 Neville, A. M. and Meyers, B. L.,
"Creep of Concrete Influencing
Factors and Prediction," ACI Special Publication SP-9, Creep of
Concrete, American Concrete Institute, Detroit, Mich., 1964.
18. Hansen, T. C. and Mattock, A. H.,
"The Influence of Size and Shape
of Member on the Shrinkage and
Creep of Concrete," ACI Journal,
Proceedings, Vol. 63, No. 2, February 1966. pp. 267-289.
19. Pfeifer, D. W., "Sand Replacement
in Structural Lightweight Concrete
—Creep and Shrinkage Studies,"
ACI Journal, Proceedings, Vol. 65,
No. 2, February 1968, pp. 131-142.
20. Hanson, J. A., "Prestress Loss as
Affected by Type of Curing," Journal of the Prestressed Concrete Institute, Vol. 9, No. 2, 1964, pp. 6993.
21. Reichart, T. W., "Creep and Drying Shrinkage of Lightweight and
Normal Weight Concrete," NBS
Monograph 74, U.S. Department
PCI Journal/May-June 1972
of Commerce, National Bureau of
Standards, Washington, D.C.,
March 1964, 30 pp.
22. Keeton, J. R., "Study of Creep in
Concrete, Phases 1-5," Technical
Reports No. R 33-I, II and III, U.S.
Naval Civil Engineering Laboratory, Port Hueneme, California,
1965.
23. Pauw, A., private communication.
24. Meyers, B. L., Hope, B. B., Lorman, W. R., Mills, R. H. and
Roll, F., "The Effects of Concrete
Constituents, Environment, and
Stress on the Creep of Concrete,"
ACI Committee 209, Subcommittee I Report, ACI Special Publication SP-27, Creep, Shrinkage and
Temperature Effects in Concrete
Structures, American Concrete Institute, Detroit, Mich., 1971.
25. Schumann, C. G., "Creep and
Shrinkage Properties of Lightweight Aggregate Concrete Used
in the State of Iowa," M.S. Thesis,
University of Iowa, Iowa City,
1970.
26. Meyers, B. L., Branson, D. E.,
Schumann, C. G. and Christiason,
M. L., "The Prediction of Creep
and Shrinkage Properties of Concrete," Iowa Highway Commission
Research Report, Project No. HR136, University of Iowa, Iowa City,
1970.
27. Keeton, J. R., "Creep and Shrinkage of Reinforced Thin-Shell Concrete," Technical Report R 704,
U.S. Naval Civil Engineering Laboratory, Port Hueneme, California,
November 1970, pp. 1-58.
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:
Ct
t
(3)
X 800 X 10 - 6 (moist cured)
(4a)
t
x 730 x 10- 6 (steam cured)
— 55—+
t
(4b)
(Sn
Et
=
( Esh
t
to.6
x 2.35
10 + ta•6
35 + 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
Shrinkage (C.F.)H = 1.40 — 0.010 H when 40%
Shrinkage (C.F.)H = 3.00 — 0.030 H when 80%
Minimum thickness
of
(A3)
40%
H
80%
H
100%
(A4)
(A5)
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:
Creep Correction
Condition
28 day loading
70 percent humidity
8 in. (20 cm) min. thickness
2.5 in. (6 cm) slump
8 sacks/cu. yd. (448 kg/m3)
cement content
60 percent fines
7 percent air content
Shrinkage Correction
Eq. (Al) : 0.85
Eq. (A3) : 0.80
Eq. (A6) : 0.96
Eq. (A10): 0.99
Eq. (A5) : 0.70
Eq. (A8) : 0.94
Eq. (All): 0.99
Eq. (Al2): 1.00
Eq. (Al4): 1.02
Eq. (A18): 1.09
Eq. (A13): 1.02
Eq. (A16): 1.02
Eq. (A19): 1.01
Standard values at 365 clays:
_
C365
365 0.60
10 -{- 3650.60 X 2.35 = 1.82
365
(Es'ti 30 -
35 + 365
X 800 x 10- 6 = 730
X
10- o in./in.
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