Creep and Shrinkage Properties of Lightweight Concrete Used in ...

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"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


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


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


. 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


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


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


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


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


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


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)


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)


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.)


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.)


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


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


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---


20 40 60 80 100


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)


20 40 60 80 100


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


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


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


Figure A23--Shrinkage correction factor for average relative humidity after Jones

Creep and Shrinkage Properties of Lightweight Concrete Used in ...

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