creep and shrinkage properties of lightweight concrete used in
TRANSCRIPT
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II TAl Io9r 68-2
D ,
"CREEP AND SHRIN)(AGE PROPERTIES OF LIGHTWEIGHT CONCRETE tJSED IN THE STATE OF IOWA''
PHASE 1
by
B.L. Meyers
D. E. Branson
G. H. Anderson . "
Progress Report for Period Febmary 1968 to October 1968
Department of Civil Engineering The University of Iowa
Iowa City
October 1968
Iowa Department of Transportation Library 800 Lincoln Way Ames, Iowa 50010
II
f· ((.
"CREEP AND SHRINKAGE PROPER TIES OF LIGHTWEIGHT
CONCRETE USED IN THE STATE OF IOWA"
PHASE 1
By
B. L. Meyers
D. E. Branson
G. H. Anderson
Progress Report for Period February 1968 to October 1968
Department of Civil Engineering University of Iowa
Iowa City
October 1968
;'
ABSTRACT
In February of 1968 a cooperative research project by the
Iowa State Highway Commission (Project No. HR-136) and the
University of Iowa, Iowa City, Iowa was initiated in order to
determine experim.entally the creep and shrinkage characteristics
of lightweight-aggregate concrete used in the State of Iowa. This
report is concerned with Phase 1 of the Project as described in
the Prospectus for the project submitted in November of 1967:
"The State Highway Commission is planning to conduct pilot studies in prestressed-lightweight structures fabricated with materials that are proposed for use in bridge structures in the near future. Thus, Phase will have as its immediate objective, investigating the materials to be used in the above mentioned pilot studies. " (1)
The work described in this report was also carried out in con-
junction with a second cooperative project: "Time-Dependent
Camber and Deflection of Non-Composite and Composite Light-
weight-Prestressed Concrete Beams" (Project No. HR-137 ). (2, 3)
The specimens investigated in Project HR-136 were pre-
pared using Idealite coarse and medium lightweight aggregate,
·natural sand, and Type 1 Portland Cement. The major variables
considered were, level of stress, age at time of loading, and
storage conditions, including moist curing and steam curing. In
addition, methods for predicting creep and shrinkage were analyzed
l
and design recommendations are presented.
The data presented herein includes inforination obtained
from the first 3 to 4 months of the Phase 1 testing program.
This phase is being continued and more complete inforrn.ation
will be presented in the final report to be submitted upon com -
pletion of cooperative program HR -136. The final. report will
also include data obtained from similar investigations to be
carried out on other lightweight aggregates available in the
State of Iowa.
All work described in this· report was carried out in the
University of Iowa Structures Laboratory, Iowa City, Iowa
under the direction of Dr. Bernard L. Meyers and Dr. Dan E.
Branson.
11
Chapter
1.
2.
3.
4.
TABLE OF CONTENTS
List of Tables
List of Figures
Notation
INTRODUCTION
1.1 Statement of the problem
1.2 Objective and scope
1.3 Nature of creep and shrinkage
REVIEW OF LITERATURE
2.i General remarks
2.2 Relevant influence factors
2.3 Predi~tion of creep
DESCRIPTION OF EXPERIMENTAL PROCEDURE
3.1 Description of mix and specimens
3.2 Preparation of specimens
3. 3 Compressive ·strength test
3. 4 Description of loading procedu.re
3.5 Calibration of loading jack
3.6 Measurement of strains
3.7 Temperature and humidity
PRESENTATION OF EXPERIMENTAL RESULTS
4.1 Interpretation of data
4.2 Age of concrete at loading
iii
Page
v
vi
ix
1
1
1
2
4
4
4
9
11
11
13
13
13
16
16
18
20
20
20
Chapter
5.
TABLE OF CONTENTS (cont.)
4.3 Level of applied stress
4.4 Methods of curing
DISCUSSION OF EXPERIMENTAL RESULTS
Page
21
22
25
5.1 Comparison of predicted creep with actual creep 25
5.2 Development of a "standard" creep curve 28
5.3 · Procedure for estimating creep
5.4 Comparison of predicted with actual shrinkage
6. SUMMARY AND CONCLUSIONS
LIST OF REFERENCES
APPENDIX
iv
31
37
41
43
46
Table
1
2
Al
LIST OF TABLES
DETAILS OF CONCRETE MIX AND MIXING PROCEDURE FOR SANDLIGHTWEIG~T CONCRETE USED IN PRESTRESSED BEAMS
CONCRETE PROPERTIES
EXPERIMENTAL CREEP AND SHRINKAGE DATA
v
Page
12
15
47
Figure
1
2
3
4
5
6
7
8
LIST OF FIGURES
Stress-strain curves
Calibration curve
Temperature versus time
Relative humidity versus time
Comparative creep strains for specimens loaded at 7 and 14 days with a stress-strength ratio of 0.25 versus time after loading
Comparative creep strains at three levels of applied stress
Normalized creep strains
Comparative shrinkage strains of unloaded companion specimens with initial readings taken at 7 days of age
9 Comparison of prediction methods with· actual creep for group A specimens ioaded at 7 days of age with a stress-
Page
14
17
19
19
21
23
23
24
strength ratio of 0.25 27
10 Comparison of prediction methods with actual creep for group D specimens loaded at 7 days of age with a stress-strength ratio of 0.25 27
11 Comparison of predl.ction methods with actual creep for group A specimens loaded at 14 days of age with a stress-strength ra·tio of 0. 25 29
12 Comparison of prediction methods with actual creep for group D specimens loaded at 14 days of age with a stress-strength ratio of 0.25 29
13
14
15
"Standard" curve for estimating creep of concrete made with Idealite expanded shale
Modified correction factor for cement content
Modified correction factor for relative humi~ity
vi
30
32
32
LIST OF FIGURES (cont.)
Figure
16 Comparison of estimated with actual creep for group A specimens loaded at 7 days of age using the modified
Page
Jones method for prediction 34
17 Comparison of estimated with actual creep for group D specimens loaded· at 7 days of age using the modified Jones method for prediction 35
18 Comparision of estimated with actual creep for groups A and D specimens loaded at 14 days of age with a stressstrength ratio of 0.25 using the modified Jones method for prediction 36
19 Comparison of predicted with actual shrinkage for group A specimens 39
20 Comparision of predicted with actual shrinkage for group D specimens 39
Al Additive definition of creep strain 50
A2 Creep constants according to Ross for group A specimens 51
A3 Creep constants according to Ross for group D specimens 51
A4 Creep correction factor for air content after Jones 52
AS Creep correction factor for cement content after Jones 52
A6 Creep correct~on factor for slump after Jones 53
A7 Creep correction factor for percent fines after Jones 53
AB Creep correction factor for average relative humidity after Jones 54
A9 Creep correction factor for minimum member thickness after Jones 54
AlO Creep correction factor for age at loading after Jones 55
All Range of creep in expanded clay and shale concrete _./
stressed at 1000 psi after Jones 55
vii
LIST OF FIGURES (cont.)
Figure Page
Al2 Comparison of prediction methods with actual c.reep for group A specimens loaded at 7 days of age with a stress-strength ratio of 0.30 56
Al3 Comparison of prediction methods with actual creep for group A specimens loaded at 7 days of age with a stress-strength ratio of 0.20 56
Al4 Comparison of prediction methods with actual creep for group D specimens loaded at 7 days of age with a stress-strength ratio of 0.35 57
Al5 Average of creep constants according to Ross for groups A and D specimens 57
\
Al6 Shrinkage constants according to modified Ross method 58
Al7 "Standard" curve for·estimating :shrinkage of concrete made with expanded clay and.shale aggregate after Jones 59
Al8 Shrinkage correction factor for cement content after Jones 59
Al9 Shrinkage correction factor for air content after Jones 60
A20 Shrinkage correction factor for slump after Jones 60
A21 Shrinkage correction factor lor percent fines after Jones 61
A22 Shrinkage correction factor for minimum thickness of member after Jones 61
A23 Shrinkage correction factor for average relative humidity after Jones 62
viii
a,b
c
d,e
E c
f'c
f'c m
sh
t
w
Esh
(J
NOTATION
constants used for Ross creep prediction
creep strain from experimental data used in Ross creep prediction
constants used for modified Ross shrinkage prediction
elastic modulus of concrete at 28 days
compressive strength of concrete at 28 days
compressive strength of cdncrete at m days
shrinkage strain from experimental data used in modified Ross shrinkage prediction
time
unit weight of concrete
creep strain at any time
initial strain due to applied load
initial strain due to applied load on creep curve number n
drying shrinkage of an unloaded specimen at any time
total time-~ependent deformation measured on a loaded drying specimen at any time
applied stress
ix
1
Chapter 1
INTRODUCTION
1.1--Statement of the problem
The increasing use of lightweight concrete as a structural
material demands a thorough understanding of all its properties,
expecially creep and shrinkage. Although creep and shrinkage are
not unique properties of concrete, none of the other principal
structural materials exhibit as significant time-dependent deforma
tions under normal sustained loads and ambient conditions.
Technological advances in design methods and construction
techniques have rh.~de it desirable to design and construct longer
span concrete structures. Additional improvement can be attained by
utilizing prestressing methods and composite construction in light~
weight-aggregate concrete structures. This type of construction has
had limited use because the material ·response of lightweight aggre
gate concrete is not well understood. ·Thus, it is necessary to
·investigate the affect of various parameters on the creep and shrink
age characteristics of a given lightweight-aggregate concrete in
order to use it effectively in construction.
1.2--0bjective and scope
The objective of this_investigation is to determine experi
lmentally the long-time creep and shrinkage characteristics of a
lightweightaaggregate concrete. The program includes the investigation
of creep_ and shrinkage of lightweight Idealite aggregate concrete
2
made with 100 percent sand substitution for the fine aggregate portion
of the mix. In general the following parameters are considered:
1. Age of concrete at time of loading (included specimens loaded at 7 and 14 days of age).
2. Level of applied sustained stress (included specimens loaded with a stress-strength ratio of 0.20 to 0.35 of the short-time ultimate strength).
3. Methods of curing (all specimens were moist cured at 100 percent relative humidity or atmospheric steam cured until a minimum strength of 4500 psi was attained).
An experimental investigation of this nature will supply the designer
with sufficient basic material so that lightweight structures can be
designed with confidence. The above research can also be used to
supplement structural research in the area of camber and deflection
by supplying material properties that can be used in the development
of new design methods.
1.3--Nature of creep and.shrinkage
This investigation is limited to creep caused by uniaxial
compression. The word "creep" as used in this investigation is
defined by the joint ACI-ASCE, Conunittee 323 report: "the inelastic
deformation dependent on time and resulting solely from the presence
of stress and a function thereof.'.'
Drying shrinkage deformations of concrete result from loss
of moisture to the ambient relative humidity. The word "shrinkage" I
,as used in this investigation is .as defined by the joint ACI-ASCE,
Committee 323 report: "the contraction of concrete due to drying
and chemical changes dependent on time, but not on the stresses
L_ __
J
induced by external loading."
Creep and shrinkage are often considered to be additive
in nature(l). This results in assuming the overall increase in strain
of a stressed and drying specimen to consist of shrinkage (equal in
magnitude to that of a companion unstressed specimen) and of a change
in strain (creep) due to stress. The assumption of the additive.
character of creep and shrinkage has the merit of simplicity, but is
not valid. Creep and shrinkage are not independent phenomena, and
can not be superposed. In fact, the affect of shrinkage on creep is
to increase the magnitude of creep. However, creep and shrinkage
occur simultaneously in most structures and from a practical stand
point, treatment of the two as additive is more convenient. This
investigation will also consider creep as a deformation in excess of
shrinkage since the available data were obtained on the assumption
of the additive properties of creep and shrinkage.
4
Chapter 2
REVIEW OF LITERATURE
2.1--General remarks
There is a large volume of literature pertaining to the
causes and effects of time-dependent deformations in concrete. A
number of creep theories and mechanisms of creep in concrete have
been reviewed by Neville(2
) a~d Ali and Kesler(J). Meyers and
Neville(l) have reviewed infl~encing factors and prediction of creep.
The shrinkage studies by Pickett(4 ) are notable. The work
of Davis, et al. (S) in classifying the three forms of water in con
crete is acknowledged. Of interest is Neville's(2) statement that
the free water portion is gradually reduced by evaporation and by the
continuous hydration of cement. ?tudies by Hanson and Mattock ( 6)
indicate that the size and shape, among other variables, influence
the shrinkage and creep of concrete.
The remainder of this review will consider only the influ-
encing factors and. prediction of creep and shrinkage as related to
this investigation.
2.2--Relevant influence factors
The germane influencing factors affecting creep and.shrink-
age are aggregate properties, age of concrete, level of stress, methods I
of curing, and storage conditions.
I
5
Aggregate properties
Experimental work by Rutledge and Neville (7) has indicated
that the modulus of ~lasticity is probably the most important physi
cal property of an aggregate. Work by Reichart(S) indicates that
there appears to be a correlation between shrinkage and the modulus
of elasticity of the concrete. Since the modulus of concrete is an
index of the strength of the aggregate used an increase in the modu-
lus of elasticity increases the restraint offered by the aggregate
to creep.
In general, aggregates with higher porosity exhibit lower
modulus of elasticity. Earlier studies by Neville( 2) established
that ba~ic creep is associated with moisture movement within the con-
crete system. The higher the absorption of aggregates, the greater
the amount of water required, thereby increasing the creep related
to moisture movement.
Sustained load tests by Shideler(g) on concretes made with
eight different types of lightweight aggregates indicate that, although
the aggregates were similar in appearance and method of processing, a
wide range of creep values were exhibited. Therefore, it is advisable
that individual processors of lightweight aggregates for structural
concrete obtain reliable experimental time-dependent deformation data.
The fine aggregate portion of lightweight aggregate mixes
lmay be either fine lightweight aggregate or sand. Generally, light-
weight aggregate mixes contain a greater quantity of fines than normal
weight concrete. The percentage and the type of fine aggregate used
I
affects.the creep and shrinkage of the concrete. From the investi
gations of Pfeifer and Hanson(lO) and Pfeifer(ll) in which varying
quantities of sand were substituted for lightweight fines in mixes
6
prepared with a number of different coarse aggregates, the following
conclusions were made: (a) the water-cement contents required de-
creased with increasing natural sand content, (b) creep and shrink-
age were reduced as increasing amounts of sand fines were used,
(c) the improved properties obtained by the use of natural sand sub-
stitution are gained only at the expense of an incre~se in concrete
unit weight.
Age of concrete
The rate of creep decreases as the degree of hydration
and development of strength increases. (12)
Studies by Illston show
that concrete matures continually with time, i.e., ·the strength of
concrete increases with time. Therefore, the rate of creep for a
specimen loaded 14 days after casting would be less than that for a
specimen loaded at seven days after casting.
Level of stress
Creep, applied load, and strength of mortar are interre
lated (l3). It has been shown that creep is approximately proportional
to the ratio of applied stress to ultimate strength at the time of
load application, regardless of the type of cement. The relationship
appears to be independent of service exposure conditions.
'•·1
I
7
Experimental results have also indicated that the creep
of concrete is directly proportional to the.applied stress provided
the applied stress does not exceed certain upper bounds. Meyers
and Neville(l) have suggested that such proportionality exists
within the working stress range of concrete. Other studies, by
Freudenthal and Roll(l4), have found the proportionality limit to
be between 20 and 26 percent of ·the ultimate strength.
Methods of curing
The most common method of curing concrete is moist curing
at'lOO percent relative humidity. Steam curing has a distinct advan-
tage when used to cure lightweight-concrete prestressed members.
Steam curing accelerates the hydration of cement, thereby increasing
the early strength of concrete. Although it may be assumed that the
creep of lightweight concrete is greater than that of most normal
weight concretes, it should also be noted that relatively wide vari~
ations ·are encountered in the creep and shrinkage· of both materials.
Shideler(9) has presented data for high strength light-
weight and normal weight concretes ~ured under moist curing and atmos-
pheric steam conditions. The results show that steam curing at
160 degrees F. , as compared with moist curing at 7 4 d·egrees F. , reduces
the creep of concrete as much as 50 percent.
A d . (15) h . . d d ccor ing to Hanson , atmosp eric steam curing re uce
the creep of 6 by 12-inch long laboratory.cylinders containing Type I
cement by factors of 20 to 30 percent of that of specimens moist cured
I
8
for six days. Also, the corresponding reduction of shr{nkage by
steam curing was reported to be 10 to 30 percent for mixes moist
cured for six days. The beneficial reduction in creep and shrinkage
is due to more rapid hydration of cement and to drying after the
concrete has been removed from the steam atmosphere.
Storage conditions
Creep is affected by the ambient relative humidity, if
drying takes place while the specimen is under load. Tests by Troxell,
Raphael, and Davis(l6
) show that creep at 50 percent relative humidity
may be two to three times gre~ter than that at 100 percent relative
humidity for concrete loaded at 28 days. Lyse(l7) reported that creep
at 100 percent relative humidity is about 40 percent of .tile creep
observed at 50 percent relative humidity. Neville(lJ) concludes that
the magnitude of creep is independent of the relative humidity of the
surrounding medium if the concrete has reached hygral equilibrium
prior to loading. Therefore, it appears that the process of drying
while the concrete is subject to sustained load is a factor in creep
while ambient humidity is not. Thus, for concrete loaded at later
ages, creep becomes independent of ambient relative humidity; Alter-
nating the ambient relative humidity between two limits tends to
increase creep in comparison to the creep observed at constant humidity
conditions. Th . b ... f. db H (lS) dP.k (l9 ). is o servation is con irme y ansen an ic ett .
The temperature surrounding the concrete also affects creep
and shrinkage. · · d 1 d(ZO) · d. The investigation of Ross an Eng an in icates
9
that creep increases with an increase in temperature, the increase
~eing more pronounced in the range of 68 to 180 degrees F. than for
temperatures up to 280 degrees F. This broad. pattern was observed
both for concrete stored in air and for concrete under simulated
d . . f . Th (2l) d . · 1 con itions o- mass curing. euer note s1m1 ar ~emperature
influences on creep; i.e., for semi-dry and wet concretes, creep
values at 120 degrees F. were two to three times greater than at 60
degrees F .. at the end of a thre~-day loading period. In general, the
increase in temperature may be considered to decrease the gel viscos-
ity and to initiate moisture movement and loss to the surrounding
medium.
2.3--Prediction of creep
Several investigators have expressed creep-time relations
in the form of an equation, a "standard" creep curve, or a "standard"
ultimate specific creep value. Most of the equat'ions developed are
of the exponential or hyperbolic form. The "standard" creep curve
and the "standard" ultimate specific creep values are usually obtained
from mix design parameters.
One of the earlier exponential analysis of creep prediction
is presented by Troxell, Raphael, and Davis(l6). The hyperbolic
R (22) (23)
equation proposed by .ass and developed in more detail by Lorman
is relatively simple to apply and fairly accurate. Meyers and
Neville(l) have shown further application of the above equations and
graphical representations of actual ve~sus predicted values of creep.
10
1 This relationship will be used in Chapter 5 to pr~dict the creep
of Idealite concrete.
(24) Wagner developed a prediction method utilizing "stan-
<lard" ultimate specific creep values. Correction coefficients are
provided for concrete'made from different mixes and stored at various
relative humidites. Age of loading, and size of member are considered.
Correlation of predicted with actual creep values are not good with
this method and it will not be used in this report.
A similar approach was used by Jones, Hirsch, and Stephen-
(25) son . A "standard" creep curve containing basic creep values car-
responding to age of concrete is presented. The "standard" values of
creep are then modified for a particular air content, cement type and
content, slump, percent fines, relative humidity of storage, thickness
of the member, and age of loading. Their studies indicated that the
creep of structural lightweight concrete under a sustained compressive
stress is about the same as the creep of the conventional normal
weight concrete. This method will also be used in this report.
If no creep data is available, creep can not be predicted
by an equation such as that of Ross. Thus, the methods of Jones or
Wagner may be ~sed to obtain an approximate value for.creep. In the
case of reinforced concrete members, this predicted value of creep is
usually reasonable for design purposes. It has clearly been demon
strated by Meyers and Pauw(26 ) that the deflection of these members
is not as sensitive to creep·as has been· thought in the past.
,-11
Chapter 3
DESCRIPTION OF EXPERIMENTAL PROCEDURE
3.1--Description of mix and specimens
The mix used in the experimental investigation described in
this study was designed for use in the construction of structural
lightweight prestressed concrete bridge girders. One hundred percent
sand substitution was used for the fine lightwe.ight aggregate portion
of the mix. Commercially processed Idealite was used for the medium
and coarse lightweight aggregate portion of the mix. Idealite is a
"coated", hard-shelled, expanded shale lightweight aggregate pro\iuced
by the rotary kiln process. Table 1 shows the mix 'objectives, ingre
dients, and mixing procedure used for prestressed beams and cylinders
made in the structures laboratory at The University of Iowa.
Specimens were required for compressive strength,· creep, and
shrinkage. All specimens were cast in 6-inch diameter by 12-inch
long cylindrical molds. The concrete in the laboratory mix was cast
in three layers each rodded 25 times. The investigation consisted of
four groups of specimens made from the above mix proportions. Groups
A, B, and C were made in the structures laboratory and cured for four
days at 100 percent relative humidity. Group D specimens were supplied
by the contractor and steam cured until a minimum compressive strength
of 4500 psi was attained. All group D sepcimens were horizontally
cast and steam cured in the field by the contractor.
Table 1
DETAILS OF CONCRETE MIX AND MIXING PROCEDURE FQR SANDLIGHTWEIGHT CONCRETE USED IN PRESTRESSED BEAMS
MIX DESIGN OBJECTIVES
MIX
Concrete Quantity
Concrete Strength at 28 Days
Unit Weight in Plastic State
Air Entrainment
INGREDIENTS
Cement (Type I)
Sand
Idealite Aggregate (Contains 60% of 3/4" to 5/16" and 40% of 5/16" to 118)
Water
Dar ex @ 7/8 oz. per sack
WRDA (Used instead of 31. 5 oz. of Pozzolith)
MIXING PROCEDURE
l~ cu. yds.
5000 psi
(120 to 123) pcf
(5 ± 1) %
1058 lbs.
2093 lbs.
1230 lbs.
52.5 gals ..
9.75 oz.
75.0 oz.
1. Proportion and batch sand and Idealite
2. Add 26 gallons of water
3. Mix for approximately. two minutes
4. Proportion and batch the cement
5. Add six gallons of water
6. Add Darex AEA in 3 gallons of water
7. Add WRDA with the remaining water while adjusting to a 2~" slump
12
13
3.2--Preparation of specimens
All specimens were capped five days after casting with a
sulfur base capping compound. Stainless steel gage points were glued
to the creep and shrinkage specimens with steel epoxy. Three gage
lines were spaced uniformly around each cylinder. All specimens,
including those to be loaded at 14 days of age, were stored in the
creep laborato.ry after removal from the curing room.
3.3--Compressive strength test
The compressive strength was determined for the field and
laboratory mixes at ages 7, 14, and 28 days. Three cylinders were
used in each determination. Stress-strain data was obtained for
group C at ages 7 and 28 days, and for group D at 7 days of age.
Stress-strain curves for the above groups are presented in Figure 1.
The concrete properties of compressive strength, unit weight, measure
of air entrainment, slump, and modulus of elasti~ity are shown in
Table 2.
3.4--Description of loading procedure
Three specimens were stacked vertically in standard ASTM
design creep racks and loaded to the desired stress with a calibrated
hydraulic jack. The creep racks were loaded and leveled prior to
loading the specimens~ A ball seat was used at the bottom of the loading
frame in order to assure a concentrically applied load.
All creep racks were spring loaded with nested railroad
springs. The spring capacity for each spring was determined using a
14
4
,,...... . p
•rl
O" (JJ 3 -Cf)
p. •rl ~ '--'
CIJ (JJ (JJ
H .1-J 2 (/)
0 5 10 15 20 25
Strain (in.fin. x 10-4)
Figure 1 -- Stress-strain curves
----------
15
Table 2
CONCRETE PROPERTIES
Group Group Group Group Property A B c D
·----·--.= = ==--::=~=-==--==~==---===::;.;c=.=
f'c (7 days) psi 6700 ssoo 61SO S600
f'c (28 days) psi 93SO 81SO 87SO 6100
Unit Wt. (Wet) pcf 124.0 124.0 12S.O
Unit Wt. (Dry-7d) pcf 123.0 123.S 123.S 122.0
Meas. Air Entrain. % 4.0 6.0 6.0
Slump in 2.0 2.S 2.S
1Modulus of Elasti...: psi x a. 3.20 a. 3.04 city at 7 Days 106 b. 3.33 b. 3.10
(3. 68) (3.3S) c. (3. SS) c. (3.32)
1Modulus of Elasti- psi x a. 3.28 city at 28 Days 106 b. 3.38
( 4. 3S) (4.09) c. (4.23) c. (3.47)
1The modulus of elasticity values are as follows: a. Measured secant (to O.S f 'c) modulus of elasticity. b. Measured initial tangent modulus of elasticity. c. All values in parentheses are computed using E = 33/w3f 'c
E in psi, w in pcf, and f 'c . in psi. c c
16
Riehle-hydraulic testing machine. Theoretically, the loss in applied
stress from micro-deformations will be very small provided the spring
capacity is not exceeded. The creep racks were checked periodically
with the hydraulic jack, and the level of applied stress corrected
if necessary. Generally the loss in stress was from one to three
percent of the original applied stress.
3.5--Calibration of loading jack
The hydraulic loading jack was calibrated in a Riehle
hydraulic testing machine. The calibration curve is shown in Figure
2. The smallest increment on the hydraulic jack is 0.100 kip with
a maximum compressive loading of 60 kips. The smallest increment on
the hydraulic testing machine is 0.500 kip with a maximum compressive
loading of 300 kips.
3.6--Measurement of strains
A Whittemore mechanical strain gage (gage length = 10 inches)
was used to measure all deformations. Each time readings were taken,
a temperature correction factor was recorded. These corrections were
obtained from a mild steel standard bar stored under ambient condi
tions in the creep laboratory. The coefficient of expansion for
steel and ~oncrete are approximately equal to 0.0000065 in./ deg. F.
All strain gage readings were recorded to the nearest 0.0001 inch.
A total of nine strain readings were recorded for each creep rack.
17
80
----- -
60 ,....._
fJl p..
•r-1 ~ '-"
/ v /
'"Cl Cll 0 rl
Q)
i:: ·r-1 ,.d CJ 40 Cll s OD i::
·r-1 .µ fJl Q) .µ
Q)
rl ,.d Q)
·r-1 tZ
20
--- v /
v ,/
-
v I I
I I I ,.,/
/ I
I I I
IV
0 I/ 0 20 40 60
Hydraulic jack load (kips)
Figure 2--Calibration curve
L ____ _
18
3.7--Temperature and humidity
The ambient creep laboratory temperature varied from 84
degrees F. to 78 degrees F., with an average temperature of 81.1.
degrees F. The ambient relative humidity varied from 55 percent to
20 percent, with an average value of 29.7 percent relative humidity.
All values of temperature and humidity recorded during the test
period are presented in Figures 3 and 4.
85
80
• 7 5 p.. s (I).
H 70
March April
Figure 3--Temperature versus time
60
,......_ iN! 50 .........
:>.. .µ ·rl '"O 40 ·rl s ;::l .c . 30 M
(I) p::;
.20
.March April
Figure 4--Relative humidity versus time
19
May June
May June
20
Chapter. 4
PRESENTATION OF EXPERIMENTAL RESULTS
4.1--Interpretation of data·
At any time, the total deformation of a structural con
crete member is equal to the algebraic sum of the elastic deforma
tion, the creep deformation, and the shrinkage deformation.
Figure Al shows graphically the method employed in this investiga
tion to isolate elastic, creep, and shrinkage strains in concrete.
The creep and shrinkage data for specimens in groups A through D
are recorded in Table AL Only the data from groups A and D wi·ll
be used in the pres.entation and discussion of experimental re·sults,
since only limited data was obtained in groups B and C for use in
evaluating beam tests.
4.2--Age of concrete at loading
Creep strains decrease as the age at time of loading is
increased for concrete. The observed strains as measured with a
Whittemore strain gage in this investigation are shown in Figure 5.
The relative magnitude of creep reduction with age at time of
loading for group A (moist cured) concrete is approximately the same
as for group D (steam cured) concrete. However, the ratio of creep
reduction to total creep strain is greater for the steam cured con
crete than the moist cured concrete.
. i:l
•.-4 -. i:l ·.-4 I 0 H c.J
·.-4
5
p.. (lJ (lJ
H u
600
400
200 -
0 0
486 µ-in.fin. 554 µ-in.fin. 477 µ-in.fin . 471 µ-in. /in.
21
- L\- _____ ~-1-i b----- _y·
20
__ - n,_- - - - - Group D
40
Loaded at 7 days of age
Loaded at 14 days of age
60 80
Time after loading (days)
100
Figure 5--Comparative creep strains for specimens leaded at 7 and 14 days with a stress-strength ratio of 0.25 versus time after loading
4.3--Level of applied stress
It has been suggested that the creep of concrete is directly
proportional to the applied stress within the working stress range of
cqncrete(l). A comparison of three levels of applied stress was made
with group A specimens. The results of this comparison are presented
in Figure 6. Note that Figure 6 verifies the assumption that creep
is approximately proportional to the applied sustained stress. ,
Figure 7 shows the normalized creep strains (creep strain/
applied stress) for groups A and D. The data points are fairly close
together for each group. Theoretically, all the data points should
22
·coincide for a particular mix. The deviation between group A and D
may be attributed to the different methods of curing. Note that the
points plotted for normalized creep at different levels of applied
stress (Figure 7) show less scatter for steam cured concrete than
moist cured concrete.
4.4--Methods of curing
In this investigation two methods of curing concrete were
employed (steam curing and moist curing). Previous investigation
has in·dicated that steam cured lightweight concrete (Type I cement)
. (15) exhibits 20 to 30 percent less creep than moi~t cured concrete .
Figure 5 shows a comparison of the two methods of curing for speci-
mens loaded at 7 and 14 days after casting. Group D specimens
(steam cured) exhibit approximately 25 percent less creep strain than
group A specimens (moist cured). It appears that the methods of
curing are independent of the influence on creep at various ages of
loading.
Companion shrinkage specimens exhibited the same general.
behavior. Figure 8 shows the comparative shrinkage strains for group
A and group D specimens. The experimental results indicate that
steam cured specimens exhibit 40 percent less creep than group A
(moist cured) specimens. The magnitude of shrinkage in groups A and
D appear higher than the average values of shrinkage obtained from
unloaded specimens in other investigations. This is attributed to
the low ambient relative humidity (about 30 percent) in the creep
laboratory during the test period.
23
600 ......... . p
·rl -. p ·rl I 0 400 H CJ
•rl s .........
p ·rl
cO 525 p-in./in. H c. .µ
200 c :-1 486 µ-in.fin. CJ)
p. 17 402 p-in./in. E:. Q) 13 Q)
H u
.0
0 20 40 ·60 80 100
Time after loading (days)
Figure 6--Comparative creep -strains at three levels of applied stress
CJ) CJ) Q)
H .µ ......... CJ) <.O
I "O 0 Q) r-i
•rl r-i x p. p. =::: '°--N p •
·rl p (1j •rl H I .µ 0 00 H
CJ p. ·rl Q) s Q) ,_,_,
H u
0.30
0.20
0.10
D Group A~- -B- - - -0 ----o-- .I ----
D- -- - - _ •u- - - - - ...,. - ·I _, ~ ---6 - ~ _/
o ,,, - - -r. Group n ..ts ...-- ... 0
,,,"' 0.-'lt o ............. ....~J--- .
~/ / / "
I /
I " I
~
g Moist cured (Group A)
f Steam cured (Group D)
0 J...._ ________ _J_ __________ ....._ ________ __. __________ _._~~~~--'
0 20 40 60 80 100
Figure 7--Normalized creep strains
1
2
3
,......_ 0
p "M ......... . p
"M I 0 ,.... (.)
"M s '-'
aJ bO ct1 ~ p "M H .c Cf)
600
400
200
0 0 20 40
Group D~
60
Time (days)
0 Hoist cured
• Steam cured
80
Figure 8--Comparative shrinkage strains of unloaded companion specimens with initial readings taken at 7 days of age
24
100
25
Chapter 5
DISCUSSION OF EXPERIMENTAL RESULTS
5.1--Comparison of predicted creep with actual creep
A number of creep prediction methods have been described
in the review of literature. However, only the methods developed by
Ross(22
) and Jones et al. C25) will be used in this investigation .to
compare predicted creep with actual creep. The Ross expression is
convenient to apply and seems to have good accuracy if sufficient
creep data are available. The Ross hyperbolic expression for creep is
t
a+ bt (1)
where 'a' and 'b' are constants and 't' is the time in days after
application of load. A plot of t/c versus t is a linear function,
and the constants (a and b) can easily be evaluated from such a plot
(Figures A2 and A3). Note that the actual creep data from laboratory
specimens were used in obtaining the constants. Ultimate creep is
given by the expression
1 Ee oo = b (2)
However, if no creep data is available it is necessary to
use less accurate methods to predict creep. The best of these methods
1
was developed by Jones et al. C25
) which employs a "standard" creep
curve modified by correction factors for various design parameters.
The factors considered are air co.ntent, cement type and content,
I
26
slump, percent fines, relative humidity of storage, thickness of
member, and age at loading. The above correction factors are shown
in Figures A.4 through AlO. In this investigation it was also neces-
sary to modify the "standard" values so as to consi1der the type of
aggregate investigated. For the expanded shale aggregate used in
this investigation, the lower curve shown in Figure All seems to fit
the data best.
In addition, the Jones method was developed for all-light-
weight concrete; thus a correction factor is required for 100 percent
sand substitution for the fine aggregate portion of groups A and D
specimens. Previous investigations indicated a reduction in creep
from 0 to 30 percent for 5000 psi concrete cast with 100 percent
. (11) natural sand . The correction factor used in this investigation
is a 20 percent reduction from 100 percent sand substitution.
For group D specimens it is also necessary to evaluate a
correction factor for steam curing. Laboratory tests have indicated
a 20 to 50 percent reduction in creep for steam cured concrete made
. (8 9 15) with Type I cement ' ' . The correction factor for steam curing
used in this investigation is a 25 percent reduction. Thus, group D
specimens will have a 45 percent reduction in creep strains as com-
pared to the predicted creep values using the standard Jones method.
The results of the above discussion, pertaining to creep
prediction methods, are shown in Figure 9 and 10. For clarity, only
the specimens loaded with a stress-strength ratio of 0.25 and loadeµ
at seven days are shown in Figures 9 and 10. Data for the remaining
' \
27
600
E: • ,....., 11 . 486 µ-in.fin. 1
p ·rl -. p
400 ·rl I 0 H (.)
·rl s O Actual '-'
p ·rl
6 Ross (General) (1j
H 200 .µ UJ
D Jones (Lightweight)
p.. Q) Q)
H u
0 0 20. 40 60 80 100
Time after loading (days)
Figure 9--Comparison of prediction methods with actual creep for group A specimens loaded at 7 days of age with a stressstrength ratio of 0.25
400
E: • 11 477 µ-in.fin.
,......_ . p p
·rl •rl m-....... H . 0 Actual .µ p 200 UJ •rl
I p.. 0 h. Ross (General) QJ H Q) (.)
H ·rl
1
u s 0 Jones (Lightweight) '-'
0 0 20 40 60 80 100
Time after loading (days)
. Figure 10--Comparison of prediction methods with actual creep for group D specimens loaded at 7 days of age with a stressstrength ratio of 0.25
28
specimens are presented in Figures Al2 through Al4. Note that the
Ross predicted creep values show good accuracy as compared to the
actual creep strains. Similar results are shown in Figures 11 and
12 where comparisons for specimens loaded at 14 days are plotted.
From these results, it seems a more accurate "standard" creep curve
is r~quired in order to apply the Jones et al. method of creep pre-
diction accurately to the material: in this study.
5.2--Development of a "standard" creep curve
A "standard" creep curve for the concrete mix used in this
investigation was developed by averaging the "Ross" constants
(including all levels of applied stress and curing methods). This
average curve of Ross constants (a and b) is shown in Figure A.15.
The resulting expression is
t (3) Ee 0.0305 + 0.00206t
where Ee is the cr.eep strain obtained at any time for an average
applied stress of 1700 psi. The expression (equation 3) represents
the "standardli creep curve based on the material properties for the
concrete mixes in this investigation. This curve is presented in
Figure 13. The new "standard" curve developed for the mix under
investigation can be used successfully to predict the creep of Idealite
I
concrete with slightly modified Jones correction factors.
The modified correction factors are obtained by normalizing
the Jones data with respect to average mix properties use.d in this
investigation. For example, the mix in this investigation contained
'•/
29
600 1
554 µ-in.fin. ,,....... . p
"M -. p "M 400
A- ---~-- - - - - - - - - -
I 0 H cJ
"M s ........ p 0 Actual
"M ctl H .µ 6 Ross (General) 200 l1J
p. Q) 0 Jones (Light-Q)
H weight) u
0 20 40 60 80 100
Time after loading (days)
Figure 11--Comparison of prediction methods with actual creep for group A specimens loaded at 14 days of age with a stressstrength ratio of 0;25
400
,,....... Eil 471 µ-in. /in. .
·P p "M •M ctl-H . .µ p 200 l1l "M
I 0 Actual p. 0 Q) H Q) CJ H "M 6 Ross (General) u s ........
0 Jones (Lightweight) 0
0 20 40 60 80 100
Time after loading (days)
Figure 12--Comparison of prediction methods with actual creep for group D specimens loaded at 14 days of age with a stressstrength ratio of 0.25
. r::
·r-l -. r:: •r-l I
600
e 400 C)
·r-l s .._,
r:: ·r-l cd H -1-1
rJJ 200 p.. (j) (j)
H u
0
Jd L-e-JO
f ¢
I I I I
0 100
-- - ...,, .... .....
I
EC = ["standard" creep J [correction factors] (at 1700 psi)
i
i 200 300 400 500 . 600 700
Time after loading (days)
Figure 13--"Standard" curve for estimating creep of concrete made with Idealite expanded shale
I I I
I
w 0
31
7~ bags of cement, the Jones correction factor for cement content is
based on an average 6 bag mix. The modified correction factor for
the mix under investigation is LO for a mix containing 7~ bags of
cement per cubic yard (see Figure 14).
It was als.o necessary to modify the average relative humi-
dity correction factor (Figure 15). The average relative humidity
for the mix under investigation was about 30 percent, as opposed to
an average relative humidity of .60 percent for the Jones investigation
(see Figure AS). Further modification is not required since the
remaining factors derived were either based on global averages or
have the same average value as the mixes in this investigation.
· 5.3--Procedure for estimating creep
The procedure for estimating creep is, first select a
"standard" creep value for the age under consideration from the curve
in Figure 13. To adjust this value for the seven variables select
the appropriate correction factors (see Figure 14,15,A4,A6,A7,A9 and
AlO). For example: given the following information; an expanded
shale aggregate concrete member with 7 sacks of cement per cubic yard,
3 inch slump, 4 percent air content, 60 percent fines (less than
114 sieve), a least lateral dimension of 9 inches, exposed to an aver-
age relative humidity of 40 percent, and loaded at 7 days of age at
2000 psi, calculate the 1 year creep. First, a "standard" creep value I
1at 1700 psi. is chos.en from the "standard" curve on Figure 13 at 365 days
of age. This value is approximately 465 micro-in.fin. From Figures 14,
I
32
1. 2
H 0 .µ C)
ct! 4-i
p. ()) 1.0 ())
H u
0.8 6 8 10
Sacks of cement per c. y.
Figure 14--Modified correction factor for cement content
1.0 \ \
0.8 ,-.. H
0 .µ
\ \.
\~ C)
ct! 4-i
p. 0.6 ()) ())
H u
~~ ~
0.4 ~~ ~ ~
......._.
0.2 20 40 60 80 100
Average relative humidity in percent
Figure 15--Modified correction factor for relative humidity
_,
33
15, A4, A6, A7, A9, and AlO the following corrections are obtained:
7 sacks,cubic yard factor 1.12 (Fig. 14)
3 inch slump II 1.17 (Fig. A6)
4 percent air " 0.97 (Fig. A4)
60 percent fines II 1.10 (Fig. A7)
9 inch thickness " 0.87 (Fig. AS)
60 percent humidity II 0.83 (Fig. 15)
Loaded at 7 days of II 1.17 (Fig. AlO) age (Type I cement)
Stress factor 2000/1700 = 1.18
Now, multiply these factors times the "standard" creep valu.e to
obtain an estimate of final creep for one year.
Creep at 2000 psi • [0.00046~ [1.12 x 1.17 x 0.97 x 1.10 x
0.87 x 0.83 x 1.17 x 1.1~
0.000648 in./in.
In order that confidence may be gained in the application of the above
procedure for estimating a reasonable value for creep, Figures 16, 17
and 18 are plotted. Note the comparison of the estimated creep with
actual creep. In general the procedure of estimating creep with the
"standard" curve (Figure 13) increases in accuracy with an increase
lin time after load application.
11 I
I
I I
. i::
·r-l -. i:: ·r-l I 0 H (.)
•r-l s '-'
E. 11
E.
600 12
E. 13
400
200
0
34
525 µ-in.fin. 486 µ-in.fin. 402 µ-in.fin.
2
3
-•-.&-•-Estimated
0 8 0 Actual
20 40 60 80 100
Time after loading (days)
Figure 16--Comparison of estimated with actual creep for group A specimens loaded at 7 days of age using the modified Jones method for prediction
-..r
I I
600
,,....._ . i:: ·ri -. i:: •ri I 400 0 !-I (J
·ri s '-"
i:: ·ri
c1) !-I 200 .µ (J)
p.. QJ QJ !-I u
Ei = 619 µ-in.fin. Ei 1= 477 µ-in.fin.
2
0
...... ... .... /
~/
20
-----
40
35
0.35 f'c~-----..-....--- 1 -,_---....... --0.25 f'c ~---A----.,_ ____ _
--- 2
-8--A- Estimated
0 1'.2. Actual
60 80 100
Time after loading (days)
Figure 17--Comparison of estimated with actual creep for group D specimens loaded at 7 days of age using the modified Jones method for prediction
-·
36
600 ......... Ei 554 µ-in.fin. . i:: E. 1 471 µ-in.fin.
Group A~ ·r-i 12 - - - - -.- --. - -p .....-·r-i -- 1 I 0 0 H
400 u •r-i 2 5 p -·r-i (\j H .µ U)
P.,· 200 QJ
-e- -A- Estimated QJ H
8 Actual u 0
0 20 40 60 80 100
Time after loading (days)
Figure 18--Comparison of estimated with actual creep for groups A and D specimens loaded at ~4. days of age with a stress-s_trength ratio of 0.25 using the modified Jones method for prediction
I
J7
5.4--Comparison of predicted with actual shrinkage
In order to obtain predicted values of shrinkage, the methods
of Ross and Jones et al. are applied in a manner similar to that used
in obtaining creep predictions. A modified Ross expression for shrink-
age is
t (4) Ssh e + dt
where 'e' and 'd' are constants and 't' is the time in days after
exposure to ambient storage conditions. Note in equation 1 that the
dependent variable was creep strain (sc); while in equation 4 the
dependent variable is shrinkage strain (Ssh) in micro-inches per inch.
A plot of t/sh versus t for groups A and D is shown in Figure Al6,
the constants 'e' and 'd' can easily be evaluated from the figure.
The actual shrinkage data was employed to obtain these constants.
Ultimate shrinkage is given by the expression
Ssh o.> 1
-d- . (5)
As in the case of creep prediction, if laboratory data is
not available it is necessary to.employ less accurate methods to
predict shrinkage. The most accurate of these methods was also
developed by Jones et al. <25 ), and employs a "standard" curve
(Figure Al7). The "standard" shrinkage value is modified for various
design parameters. The factors considered are cement content, air
content, slump, percent fines, thickness of member, and relative
humidity of storage. The above correction factors for shrinkage
are shown in Figures Al8 through A23.
38
In addition, the Jones method was developed for all-
lightweight concrete; thus an additional correction factor is required
for 100 percent sand substitution for the fine aggregate portion of
groups A and D specimens. Previous investigations indicated a reduc-
tion in shrinkage from 3 to 40 percent for 5000 psi concrete cast with
(10 11) 100 percent natural sand ' . The correction factor used in this
analysis is a 15 percent reduction for 100 percent sand substitution.
For group D specimens it is also necessary to consider an
additional correction factor for steam curing. Laboratory tests have
indicated 10 to 40 percent reduction in shrinkage for steam cured
d . h ( 8 ' 9 ' 15) concrete ma e wit Type I cement . The correction factor for
steam curing used in this analysis is 20 percent reduction. Thus,
group D specimens will have a 35 percent reduction in shrinkage strains
as compared to the predicted creep values using the standard Jones
method.
The results of the above discussion pertaining to shrinkage
prediction by the Ross and Jones et al. methods is presented in
Figur~s 19 and 20. Note that for the two groups the Jones method is
least accurate. Since only limited data was obtained in this study,
the Jones method will not be further modified.
The Ross·method yields very good results for both test
groups. It is recommended that the modified Ross expression be used
to predict shrinkage strains (see equation 4 and Figure Al6). Accu-
rate results from 60 days of shri~kage data are indicated in Figure 20.
The following is a summary of the modified Ross method for predicting
. 0
·rl -. 600
-~· 400 I 0 H (.)
·rl
-5 (]) b£) ctl
~ •rl H
..c Cf.l
200
39
o Actual
~ Ross (General)
D Jones (Lightweight)
0 20 40 60 80 100
Time (days)
Figure 19--Comparison of predicted with actual shrinkage for group A specimens
. 0 ·rl -. 0 ·rl I 0 H (.)
·rl s ..__,
400
(]) bO . 200 ctl ~ 0
·rl H
..c Cf.l
0 Actual
~ Ross (General)
D Jones (Lightweight)
0 20 40 60 80 100
Time (days)
Figure 20--Comparison of predicted with actual.shrinkage for group D specimens
shrinkage for any material:
1. From a limited (say 60 days) amount of shrinkage data plot t/sh versus t similar to Figure Al6, giving greater weight to larger values of t.
· 2. Obtain the 'e' and 'd' constants from the figure plotted in step 1.
3. Substitute the 'e' and 'd' constants into equation 4, thus obtaining the general shrinkage expression for any time 't' in days.
40
4. Ultimate shrinkage may be obtained from equation 5.
For Idealite lightweight conrete (group A, moist cured) the general
shrinkage expression is
t (6) Esh 0.04 + 0.0017t
For Idealite aggregate lightweight concrete (group D, steam cured)
the general shrinkage expression is
t (7) Esh 0.15 + 0.0025t
In the case of shrinkage prediction, it was not possible to obtain
an average set of 'e' and 'd·' constants for moist and steam curing
due to the limited amount of available shrinkage data.
41
~ Chapter 6
SUMMARY AND CONCLUSIONS
In this investigation a comprehensive study was ma.de of
the creep and shrinkage characteristics of a lightweight "Idealite"
aggregate concrete. A literature survey of the various parameters
affecting creep and shrinkage of concrete pertinent to this study
is presented in Chapter 2. One hundred percent sand substitution
was employed for the fine lightweight aggregate portion of the mix.
Other parameters discussed were age of concrete, level of stress,
methods of curing, and storage conditions.
The affects of the above parameters were determined in
the experimental investigation and are discussed in Chapt~r 3.
Note that the method of loading and measurement of time-dependent
deformations was identical for all specimens.
Based on the an·alytical findings in Chapters 4 and 5, the
following conclusions can be made:
1. Creep strains decrease as the age of loading is in
creased for the lightweight concrete under investigation (see .
Figure 5).
2. Creep of lightweight concrete is proportional to the
applied stress within· the working stress ranges (.20 - .35 f'c)
observed in this research (see Figure 6).
3. Steam cured specimens loaded at 7 and 14 days exhibit a
decrease in creep strains of approximately 25 percent as compared to
moist cured specimens loaded at the same times (see Figure 5).
4. Companion unloaded steam cured shrinkage specimens
exhibit a reduction in shrinkage strains of about 40 percent (see
Figure 8) .as compared to unloaded moist cured specimens.
42
5. The Ross method of creep predictions gives excellent
results (see Figures 9, 10, 11 and 12). However, this method requires
experimental creep data.
6. The standard Jones et al. method of creep prediction is
less accurate than the Ross method (see Figures 9, 10, 11 and 12).
However, the Jones method has the advantage of being independent of
existing creep data.
7. The Ross predictions were averaged (at all levels of
applied stress and ages at loading, see equation 3) to obtain a
"standard" creep curve (see Figure 13) to be used in a modified Jones
If!ethod of estimating long-time dependent deformations. Improved
accuracy was attained by this procedure (see Figures 16, 17 and 18).
In general, the method of creep prediction using the modified Jones
method increases in accuracy with an increase in time after load
application.
8. ·Similar procedures were employed to formulate a method
for shrinkage prediction. Although it was shown that the Jones method
is applicable (see Figures 19 and 20), because of limited data the
following Ross type expressions ·(equations 6 and 7) are recommended
in lieu of the modified Jones method. A plot of the Ross expressions
is also presented in Figures 19 and 20.
43
LIST OF REFERENCES
44
LIST OF REFERENCES
1. Meyers, B. L., and Neville, A. M., "Creep of Concrete: Influencing Factors and Prediction," Symposium on Creep of Concrete, ACI Special Publication No. 9, Detroit, Michigan, 1964.
2. Neville, A. M., ''Theories of Creep in Concrete," ACI Journal, Proceedings V. 52, No. 1, September 1955, pp. 47-57 .
. 3. Kesler, C. E. , and Ali, I. , "Mechanisms of Creep," Symposium on Creep of Concrete, ACI Publication SP-9, 1964, pp. 35-63.
4. Pickett, G., "Shrinkage Stress in Concrete," ACI Journal, Proceedings V. 42, No. 3, January-February 1946, pp. 165-204, 361-400.
5. Davis, R. E., Davis, H. E., and Hamilton, J. S., "Plastic Flow of Concrete under' Sustained Stress," Proceedings, ASTM, V. 34, Part II, 1934, pp. 354-386.
6. Hanson, T. C., and Mattock, A.H., "Influence of Size and Shape of Member on the Shrinkage and Creep of Concrete," ACI Journal_, Proceedings V. 63, No. 2, February 1966, pp. 267-289.
7. Rutledge, S. E., and Neville, A. M., "The Influence of Cement Paste Content on Creep of Lightweight Aggregate Concrete," Magazine of Concrete Research V. 18, No. 55, June 1966, pp. 69-74.
8. Reichart, T. W., "Creep and Drying Shrinkage of Lightweight and Normal-Weight Concretes," NBS. Nomograph 7 4, U. S. Department of Cornmernce, Natio~al Bureau of Standards, U. S. Government Printing Office, Washington, D. C., March 1964.
9. Shideler, J. J., "Lightweight Aggregate Concrete for Structural Use," ACI Journal, Proceedings V. 54, No. 4, October 1957, pp. 299-328.
10. Pfeifer, D. W.,· and Hanson, J. A., "Sand Replacement in Structural Lightweight Concrete-Sintering Grate Aggregates," ACI Journal, Proceedings V. 64, No. 3, March 1967, pp. 121-127.
11. Pfeifer, D. W., "Sand Replacement in Structural Lightweight Concrete-Creep and Shrinkage Studies," ACI Journal, Proceedings V. 65, No. 2, February 1968, pp. 131-139.
12. Illston, J.M., "The Components of Strain in Concrete under Sustained Compressive Stress," Magazine of Concrete Research V. 17, No. 50, March 1965, pp. 21-28.
13. Neville, A. M., "Role of Cement in the Creep of Mortar," ACI Journal, Proceedings V. 55, No. 9, March 1959, pp. 963-984.
4c' _)
14. Freudenthal, A. M., and Roll, F., "Creep and Creep-Recovery of Concrete under High Compressive Stress," ACI Journal, Proceedings V. 54, No. 12, June 1958, pp~ 1111-1142.
15. Hanson, J. A., "Prestress Loss as Affected by Type of Curing," PCI Journal V. 9, No. 2, April 1964, pp. 69-93.
16. Troxell, G. E., Raphael, I. M., and Davis, R. E., "Long-time Creep and Shrinkage Tests of Plain and Reinforced Concrete," _Proceedings, ASTM, V. 58, 1958, pp. 1101-1120.
17. Lyse, I.; "Shrinkage and Creep of Concrete," ACI Journal, Proceedings V. 56, No. 8, February 1960, pp. 775-782.
18. Hansen, T. C., "Creep of Concrete - A Discussion of Some Fundamental Problems," Bulletin No. 33, Swedish Cement and Concrete Research Institute, September 1958, pp. 48.
19. Pickett, G., "The Effect of Moisture Content on the Creep of Concrete under a Sustained Load, :i ACI Journal, Proceedings V. 38, No. 6, February 1942°, pp. 333-355.
20. Ross, A. D., and England, G. L., "Reinforced Concrete under Thermal Gradients," Magazine of Concrete Research V. 14, No. 40, March 1962, pp. 5-12.
21. Theuer, A. U., "Effect of Temperature on the Stress-Deformation of Concrete," Journal of Research, National Bureau of Standards, V. 18, No. 2, 1937, pp. 195-204.
22. Ross, A. M., "Concrete Creep Data," The Structural Engineer, V. 15, No. 8, August 1937, pp. 314-326.
23. Lorman, W. R., "The Theory of Concrete Creep," Proceedings, ASTM, Vo. 40, 1940, pp. 1082-1102.
24. Wagner, O., "Das Kriechen unbewehrten Betons," Deutscher Ausschuss fur Stahlbeton, Bulletin No. 131, Berlin, 1958.
25." 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, August 1959.
26. Meyers, B. L., and Pauw, A., "Effect of Creep and Shrinkage on the Behavior of Reinforced Concrete Members," Symposium on Creep of Concrete, ACI Publication SP-9, 1964, pp. 129-158.
46
APPENDIX
47
Table Al
EXPERIMENTAL CREEP AND SHRINKAGE DATA
Description Time after Total Creep Shrinkage of loading strain strain strain
specimens (days) (µ-in. /in.) (µ-in. /in.) (µ-in. /in.)
Grou.e A 0 525 0 0 loaded at 1 675 150 0 7 days of 2 720 173 22 age with a 5 865 246 94 stress- 8 948 292 131 strength 15 1080 332 223 ratio of 26 1213 394 294 0.30 42 1350 433 392 f'c 7 = 6700 psi 63 1430 483 422
77 1511 550 436 90 1555 565 465
Grou.e A 0 486 0 0 loaded at 1 613 127 0 7 days of 2 675 167 22 age with a 5 813 233 94 stress- 8 890 273 131 strength 15 1030 321 223 ratio of 26 1160 380 294 0.25 42 1300 422 392 f'c = 6700 psi 63 1355 447 422 7
77 1401 479 436 90 1445 494 ·465
Group A 0 402 0 0 loaded at 1 497 95 0 7 days of 2 566 142 22 age with a 5 671 175 94 stress- 8 738 205 131 strength 15 857 232 223 ratio of 26 980 284 294 0.20 42 1110 316 392 f'c = 6700 7 psi
~···
48
Table Al (cont.)
Description Time after Total Creep Shrinkage of loading strain strain strain
specimens (days) (µ-in./in.)(µ-in./in.) (p-in. /in.)
=-==-::=::=-.;~=-·=====-= ·=·~~--=-=-:~--=-~--=-===-~:===~.::
GrouE A 0 554 0 0 loaded at 1 655 96 5 14 days of 2 690 114 22 age with a 8 852 205 93 stress- 19 1000 284 162 strength 35 1152 375 223 ratio of 56 1241 395 292 0.25 70 1276 415 307
f 'c 14 = 8230 psi 83 1340 451 335
GrouE B 0 374 0 0 loaded at 1 508 104 30 7 days of 7 718 247 97 age with a 14 913 281 258 stress- 28 1098 352 372 strength 42 1180 376 430 ratio of 56 1248 412 462 0.25 60 1332 462 496 f'c = 5500 psi 75 1375 476 525
7
Grou12 c 0 506 0 0
loaded at 1 605 94 5 7 days of 3 711 167 38 age with a 7 839 216 117 stress- 21 1040 301 232 strength 35 1201 371 324 ratio of 49 .1316 446 364 0.30 64 1415 479 430 f'c = 6150 psi ' 7
49
Table Al (cont.)
Description Time after Total Creep Shrinkage of loading strain strain strain
specimens (days) (µ-in./in.)(µ-in./in.) (p-in. /in.)
-====:·:;..=.==;:-.. ;::.:;: .:..:..-=.- ==--;;.--==-==:::=:.=...-::-=--=~--::- ...:::=-=-==--~= :--....::....::.~ -=:-=:-.::==.:.::::.-.:..:..==:-..:.::.::;~~-=.::=:..:.c::. --
Grou.e D 0 6.9 0 0 loaded at 1 737 110 s 7 days of 3 780 149 12 age with a 7 874 230 25 stress- 18 1061 354 88 strength 32 1160 . 408 133 ratio of 46 1228 442 167 0.35 60 1320 483 218 f'c = 5600 psi 75 1420 546 255
7
Grou12 D 0 477 0 0 loaded at 1 571 86 8 7 days of 3 605 116 12 age with a 7 683 181 25 stress- 18 810 245 88 strength 32 903 293 133 ratio of 46 955 311 167 0.25 60 1035 340 218 f'c = 5600 psi 75 1100 368 255 . 7
Grou12 D 0 471 0 0 loaded at 1 551 57 23 14 days of 3 603 99 33 age with a 7 641 130 40 stress- 19 745 187 87 strength 26 797 217 109 ratio of 39 875 262 142 0.25 53 955 291 193 f 'c 14 = 5800 psi 68 1005 307 227
Time
a. Shrinkage of an unloaded specimen
Time
b. Creep of a loaded specimen
i:: ·r-1 cu ~ .µ u:i
Time
c. Creep and shrinkage as additive strains
Figure Al--Additive definition of creep strain
/ /
7
, , /
[/ /
c c
c sh
E'. ]_
1
50
c t
1,
51
0.30 a a b 0.20 f'c 0.028 0. 0023 7 0.25 f'c14 0.028 0.0020 0.25 f'c 0.026 0.0019 0.20 f 1c7--'-
7 0.30 f'c 7 0.020 0. 0017
0.20
u ....._ .µ
0.10 0.25 7
0 0 20 40 60 80
t (days)
Figure A2--Creep constants according to Ross for group A specimens
u ....._ .µ
0.30
0.20
0.10
0
0.25 0.25
- 0. 35
0 20
_a_ 0.056 0.030 0.025
b 0.0025 0.0024 0.0016
40
t (days)
0.25
60 80
.. Figure A3--Creep constants according to Ross for group D specimens
100
100
1.6
I v
1.4 H 0 .µ tJ Ill
,__ __ ,_ __ __, ___ L--- ---l---..4----l
.__ ___ _..__. ····--+----!--- +-+/-~ v 4-! 1. 2 p. Q) Q)
H u
..... -·- --;·-------· ------ --+~--I
.'/ __ 1. 0 ~ ----t-----~·- -t---+-----1
I---- - --·- ---+---+----+--!--___,
0.8 0 4 8 12
Air content in percent
Figure A4--Creep correction factor for air content after Jones
1.2
H 0 .µ tJ Ill
4-! 1.0 p.
Q) Q)
H u
0.8 2 4 6 8 10
Sacks of cement per c. y.
Figure A5--Creep correction factor for cement content after Jones
-J
H 0 .µ CJ ctl
4-1
p. (J) (J)
1-1 u
1.6
1. 4 >---
1. 2
1.0
0.8
0.6 0
- v / v·
/
/ v
~v I
I I
-··-
2 4 6
Slump in inches
Figure A6--Creep correction factor for slump after Jones
1.2 /
v H 0 .µ CJ ctl
1.0 4-1
p.
/
-~ ~
L---.._.
(J) (J)
H u
0.8 30 40 60 80 100
Percent fines by weight ~ #4 sieve
..
Figure A7--Creep correction factor for percent fines after Jones
53
1-l 1.0 0 .µ tJ
. ell 4-l
p. Cl) Cl) 0.8 1-l u
40 60 80 100
Average relative humidity in percent
Figure A8--Creep correction factor for average relative humidity after Jones
1-l 0 .µ tJ 1.0 ell
4-l
p. Cl) Cl)
1-l 0.8 u 0 4 8 12
Minimum thickness of member in inches
16
Figure A9--Creep correction factor for minimum member thickness after Jones
54
n
•r-1 (/) p.
0 0 0 .--i
. i::
·r-1 -. i:: ·r-1 I ;:l'
1. 4
1.2
1.0
.~ 0.8 p. Cl) Cl) !-l· u
0.6
SS
Type III cement
Type I cement
0 10 20 30 40 50
Age in loading in days
Figure AlO--Creep correction factor for age at loading after Jones
1200
H 0 .µ 800 c.J c1j ~
p. Cl) Cl)
H u 400
0 0 80 160 240 320 400 480
Age in·days
Figure All--Range of creep in expanded clay and shale concrete stressed at 1000 psi after Jones
. i:::
·.-l -. i::: ·.-l I 0 1-l ()
·.-l s '-'
p.. QJ QJ H u
600
400
200
. I
I
' I
0
525 µ-in.fin.
1'-------- - - ----u
0 Actual
Ross (General)
56
6---
D Jones (Lightweight)
20 40 60 80 100
Time after loading (days)
Figure Al2--Comparison of prediction methods with actual creep for group A specimens loaded at 7 days of age with a stressstrength ratio of 0.30
. i:::
•.-l -. i::: •.-l I 0 1-l ()
•.-l s '-'
i:::
400
·@ 200 1-l .µ en
p.. QJ QJ 1-l u
0
402 µ-in.fin.
-- ------- 1
0 Actual
6 Ross (General)
D Jones (Lightweight)
20 40 60 80 100
Time after loading (days)
Figure Al3--Comparison of prediction methods with actual creep for group A specimens loaded at 7 days of age with a stressstrength ratio of 0.20
57
600 E: •
11 619 µ-in.fin. 1
,........ . p
·i-l -. p 400 ·i-l
I 0 H C)
•i-l s 0 Actual '-'
p •i-l D.. Ross (Generai) e 200 .µ UJ D Jones (Lightweight) p. Q) Q)
H u
0 20 40 60 80 100
Time after loading (days)
Figure Al4--Comparison of prediction methods with actual creep for group D specimens loaded at· 7 days of age with a stressstrength ratio of .0.35
C) -.µ
0.20
0.10
..
0 .....,."--~~~~-'-~~~~~.._~~~~~-'-~~~~~.,._~~~~---' sd 0 20 40 60 100
t (days)
Figure Al5--Average of creep constants according to· Ross for groups A and D specimens
58
0.60
0.50
0.40
.c 0.0025 ~ o.30 .µ
0.20
0. 0017
0.10 -e 0.15
0.04
0 20 40 60 80 100
t (days)
Figure Al6--Shrinkage constants according to modified Ross method
59
. J:l 1200 "M
---- -->--------· ----. J:l -- ------- ------~-- ---- -- ---"M I ;1
J:l 800 -·
"M
QJ b[) Cll ~ J:l 400 "M H ..c Cf)
0
--r- -~-- -r--
I/ .....---~
E: = ,,standard" shrinkage x
/ sh correction factor
' ------· ---r--- _____ T ___ I 0 80 160 240 320 400 480
Age in days
Figure Al7--"Standard" curve for estimating shrinkage of concrete made with expanded clay and shale aggregate after Jones
1.2 ----
/ QJ b[) Cll H ~ 0
1.0 J:l .µ "M (.) H Cll
v /
--~ i--..c 44 Cf)
·-
0.8 2 4 6 8
Sacks of cement per c. y.
Figure Al8--Shrinkage correction factor for cement content after Jones
60
1. 2 1-1 0 .µ (.)
cO 44
(!) 1.0 bO cO ~ p
~ ~ --!.----
L,..--v--
.,,....-"M 1-1
..c (/) 0.8
0 4 6 8
Air content in percent
Figure Al9--Shrinkage correction f~ctor for air content after Jones
1. 2 1-1 0 .µ (.) nl
44
(!) 1.0 bO cO ~ p
"M 1-1
..c 0.8 (/)
0 2 .4 6
Slump in inches
Figure A20--Shrinkage correction factor for slump after Jones
H 0
1.2
t; 1.0 ct!
lH
(!)
bO ct!
~ 0.8 H
...c: Cf.l
0.6
61
!---->---+--;-----~ ----- ----
30 40 50 60 70
Percent fines by weight < 114 sieve
Figure A21--Shrinkage correction factor for percent fines after Jones
1--1 0 .µ tJ
.ct! lH
1.0
0.8
(!) 0.6 bO ct!
~ ·ri
1--1 ...c: Cf.l
0.4
0.2 0 4
·+---t---· -···
., '
' ' ··-········--
8 12
Continuous Drying
16
Minimum thickness in inches
' '
20
Figure A22--Shrinkage correction factor for minimum thickness of member after Jones
62
1. 2
H ~ ~
0 .µ CJ ctl 'H 0.8 Q) b.O ctl
~ •r-1 H
..c: 0.4 Cl)
-............ --
"" --t--
"" --·--------- ---- ----
~
"' ~ ' "' - -- ----
0 ~ 50 60 70 80 90 100
Average relative humidity in percent
Figure A23--Shrinkage correction factor for average relative humidity after Jones