Shrinkage and Creep

In Prestressed Concrete
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UNITED STATES DEPARTMENT OF COMMERCE • Alexander B. Trowbridge, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Shrinkage and Creep in Prestressed Concrete

Perry H. Petersen and David Watstein

Building Research Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C.

Building Science Series 13

Issued: March 22, 1968

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CONTENTS

Page

1. Introduction 1

2. Materials 1

2. 1. Concrete 1

2. 2. Steel reinforcement 2

3. Specimens 3

4. Procedure in making observations 4

5. Efficiency of stress transfer, steel to concrete 4

6. Basis of computations 6

7. Test results 7

8. Analysis and discussion 7

9. Sunnnary 11

10. References 12

n
Shrinkage and Creep in Prestressed Concrete

Perry H. Petersen* and David Watstein**

The loss of prestress resulting from creep and shrinkage in concrete was investigated

for concrete specimens made with Type I Portland cement and with Type III Portland

cement. The primary variables in this study were

:

1. Relative humidity at which the concrete was maintained while under observation.

I 2. Age of the concrete at the time it was prestressed.

3. Ratio of prestress to strength ; variation of this parameter required that the ratio of reinforcement be a variable.

4. Mass ratio factor defined as the ratio of the cross-section area of concrete specimen

to its surface area per unit length.

Forty-nine sets of specimens were fabricated and tested ; each .set consisted of a

prestressed specimen and an otherwise identical companion specimen without reinforce- ment. The length changes with time were observed at intervals up to an age of 500 days.

These observations were made for concretes subjected to different levels of prestress, and

for concretes prestressed at different ages. Length changes in nonreinforced companion

specimens were also obtained. Thus this study is concerned with elastic deformation

occurring at time of stress transfer, shrinkage or swelling, and creep.

Key Words : Creep, relaxation, prestressed concrete, shrinkage, loss of prestress, variable

prestress.

* Present address : Master Builders, 2490 Lee Blvd., Cleveland, Ohio 44118 •Present address: Structural Clay Products Institute, McLean, Va. 22101

1. Introduction

The advantages of prestressed concrete over

' conventional reinforced concrete are well known

and have been amply demonstrated by nimierous

I projects both in tlie Ignited States and abroad. As

! IS true of all relatively new materials, however, some properties of prestressed concrete remain to be fully explored. One of these is that loss of

j prestress in pretensioned concrete elements wherein the steel wire or cable is prestressd beforehand

and the concrete is placed around the steel and

bonded to it. Many investigators have studied the

strains in concrete subjected to constant stress, and in one instance, observations were continued

past the 20-year mark One investigator was

concerned in part with stress relaxation in concrete at constant strain [2]. Thus it may be that new data reported herein have much significant

value to the researcher as well as to the designer

1 and engineer inasmuch as this study encompasses

creep in the concrete coupled with the loss of

jj prestress in bonded wires.

This investigation was carried out at the Na1 Figures in brackets indicate the literature references at the end of this paper.

tional Bureau of Standards with concrete speci- mens made with normal (Type I) Portland ce- ment and with high-early strength (Type III)

Portland cement. Loss of prestress with age was

obtained from the observed strains for different

intensities of prestress. The study was carried out

with symmetrically reinforced test specimens of

various sizes havnig different ratios of cross- sectional area to surface area per unit of length,

herein designated as mass ratio.

2. Materials

2. 1. Concrete

The concrete was proportioned 1 :1.5 :2.0 by dry

weight of cement, sand and pea gravel. A normal

Type I cement and a Type III cement meeting

the requirements of federal specifications for their

resi)ective types were used. The sieve analysis, absorption, and specific gravities were determined

for the sand and the pea gravel; these data are given in table 1.
Table 1. Sieve analyses, absorptions and specific

gravities of concrete aggregates

U. S. standard sieve sizes

14 inI in- No. 4... No. 8_.. No. 16-

_

No. 30-. No. 50.. No. 100- No. 200.

.\bsorption, percent by weight Bulk specific gravity, saturated surface dry

Gravel

percent

passing

99.0

98.7

31. 1 6.0 3.0

2.0

1.3

1.1 2.6

The conciete was mixed in a 6-cu ft rotary

drum mixer for about 4 minutes and then placed

in the wood forms and vibrated in ^ilfice. After

several hours, the top was screeded level and the

concrete covered witli wetted burlap. The forms

were removed at 2 days and the specimens were

stored under wet burlap until time for transfer

of prestress.

The water-cement ratios, slump, and the compressive strengths of the concretes m the various

specimens are j)-iven in table 2.

Table 2. Watcr-cemctit ratio, slump, compressiv e strength and modulus of elasticity of concretes

Type I cement concretes

Set No.

1 through 6

21 through 26-..

73, 74

71, 72

101 through 106.

121 through 126.

Water- cement ratio by weight

0.53

.52

.55 .57

.53

.51

Compressive strength of 6- by 12-in cylinders

Slump

7.5 7.0

7.2

7.2

7.2 7.6

7 day

100%RH >

3360 3600

3960 3770

4450

3230

28 day

100%RH I

5200

5150

5710

5960

5990 5470

28 day 50%RH '

• 5530

» 5740 •5640

1 year 100%RH

7500

7020 6910 6950

8270

7360

1 year 50% RH '

psi

b 6150

» 5550

I- 6220

» 5180

b 7000

» 4840

Modulus

of elasticity

3,690,000(28 da) 2,720,000(7 da) 3,770,000(28 da) 2,850,000(7 da) 3,860,000(28 da)

2,800,000(7 da)

Type III strength cement concretes

Set No.

42 through 45...

41, 46

61, 62

63

141 through 146.

161 through 166.

Water- cement ratio by weight

0.54

.54

.57

.57 .56

..55

Compressive strength of 6- by 12-in cylinders

Slur

5.5

5.5 6.0 6.0

5.5

5.7

3 dav 100%RH I

3800

3770

3920 3370

3330 3490

12 dav 100% RH I

5600 5810

5140

5580 4970

5910

12 day 50%RH >

: 5600

'5476'

'5926"

1 year 100%RH

5730

7760

6760

6800

7200

8340

1 year 50%RH

psi

d 5700

« 6170

d 6390

« 6370

<i 6230

' 6480

Modulus

of elasticity '

psi 3,400,000(12 da) 2,670,000(3 da)

3,330,000(12 da) 3,170,000(3 da) 3,270,000(12 da)

2,390,000(3 da)

» Cured at 100%, RH first 7 days,

b Cured at 100% RH first 28 days.

« Cured at 100% RH first 3 days,

i Cured at 1007o RH first 12 days.

* The modulus was the secant value obtained at the age corresponding to transfer of prestress for a stress level equal to the average initial prestress.

' Storage condition after initial moist cure.

2. 2. Steel Reinforcement

The reinforcement consisted of steel spring wire

0.1125 inches in diameter having a modulus of

elasticity of 28,000,000 psi and a tensile strength

of 233,000 psi.

F'iGURE la. View of prestressing unit shoiving a close-up

of the wires and spacers.

In fabricating the smallest specimens, the six

square molds were placed in line on a common

axis, and external anchorages were used in ten- sioning the four wires extending through the

molds in series. Steel spreaders were used to obtain the necessary alinement of the four wires

in the prisms of three different sizes. However, in

larger prisms requiring 16, 48, or 64 wires, one,

tliree, or four symmetrically placed self-contained

units were used. These were designed by the late

II. Schorer, Borsari Tank Co., New York City. A

short section of a unit is shown in tigures la and

lb. Each unit consisted of two groups of eight

wires each, wound over a center member in a

clockwi.se and counter-clockwise direction, respectively, so as to balance the torsional moments. The

individual wires were held in position by stamped

2
Figure lb. Complete self-contained fahrieated IG-wire

prcstrcssini/ unit .52 in lonr/ and hydraulic jack.

spacer discs loouted ai regular intervals. The core of the unit consisted of a precisely centered l/o-in

diameter cold-diawn and heat-tieated steel rod

which served as the temporary compression member. It was enclosed within a ]iaper tube to j^revent

bond to the concrete thereby facilitating subsequent removal of the rod. All wires in one unit were connected rigidly at one end to a gripping

member while at the other end, the wires were held

by a loading device which permitted them to be

stressed in tension while the comi:)ressive reaction was borne by the center rod.

3. Specimens

A list of sets of specimens is given in table eS for those made with Ty])e I cement, and in table

4 for those made with Type III cement. In all, there were 49 sets of i)risms, each set consisting of

a pair of identical specimens, excejit that one of

each set was reinforced and one was no<. The unreinforced specimens served as coiitrols to determine the strinkage or swelling. In addition, 6- by

12-in. cylinders were made from each batch of concrete for determination of compressive strength

and elastic properties at the required ages; these

stress-free cylinders were cured and stored under

the same environmental conditions as the prisms.

Specimens were ari'anged in groups identified by

numerals given in tables 3 and 4. The molds for

reinforced specimens of a given group were ar- ranged in line and the specimens were cast around

the same set of tensioned wires. Specimens in a given group but cast on diffei'ent dates are further

identified by letters following the group numbers.

The specimens were in the form of square prisms

in the smaller sizes, anti octagonal or hexagonal

))risms in the larger sizes. The niunber of wires,

dimensions of the s])ecimens, gage lengths, type

of cement, and curing conditions subsequent to

]irestressing are all given in table 3 and 4. Mass

ratio ts used here and elsewhere in this paper is defined as the ratio of the net cross-sectional area

of concrete to the surface area of the specimen per

unit of length. All the specimens were wet cured

up until the age at whicli the prestress force was

transferred to the concrete. The ends of prisms were coated with asphalt to eliminate moisture

ti'ansfer at the ends.

The wires were pretensioned at least a week

in advance of placing concrete so as to eliminate

as far as possible all effects of creep of steel or readjustment of the pretensioned units that might

Table 3. Specimens made from Type I cement concrete

Group

No. Set No. Shape

Gross

area of concrete

Net

area of concrete

Mass

ratio No.of wires

Ratio

of rein- forcement Length

Gage

length

.\ge of concrete

at time of transfer of prestress

Relative humidity •

sq in sq in Percent in in Days Percent

1 Octag. _ 17.22 16.69 1. 14 16 0.94 67 20 28 100

2 do 17.37 16.84 1.15 16 .94 67 20 28 50

3 do 10.73 10.20 0.90 16 1.53 52 20 28 100

4 do 10.55 10.02 .89 16 1.56 52 20 28 50

5 do 7.45 6.92 .75 16 2.25 45 20 28 100

6 do 7.25 6.72 .74 16 2.31 45 20 28 50

2 21 Octag _ _. 17.44 16.91 1. 15 16 0.93 67 20 7 100

2 22 do 17.52 16.99 1.15 16 .93 67 20 7 50

2 23 do___ 10.97 10.44 0.91 16 1.50 52 20 7 100

2 24 do 10.61 10.08 .90 16 1.55 52 20 7 50

2 25 do 7.55 7.02 .75 16 2.21 45 20 7 100

2 26 do 7.25 6.72 .74 16 2.31 45 20 7 50 SB 71 Hex 31.91 30.32 1.52 48 1.55 72 20 7 50 5B 72 do 31.70 30.11 1.51 48 1.56 72 20 7 100 5A 73 do .30.87 29.28 1 .49 48 1.60 72 20 28 50

5.\ 74 do 31.70 30. 11 1.51 48 1.56 72 20 28 100

6 101 Square. . 4.08 4.04 0.,50 4 0.97 32 10 28 100

6 102 do 4.14 4. 10 .i)0 4 .96 32 10 28 50

6 103 do 2.54 2.50 .39 4 1.56 32 10 28 100

6 104 do 2.53 2.49 .39 4 1.57 32 10 28 50

6 105 do.-^ 1.76 1.72 .32 4 2.26 32 10 28 100

6 106 do 1.79 1.75 .32 4 2.22 32 10 28 50

7 121 Square . _ _ 4.09 4.05 .50 4 0.97 32 10 7 100

7 122 do. 4.18 4. 14 .50 4 .95 32 10 7 50

7 123 do 2.50 2.46 .39 4 1.59 32 10 7 100

7 124 do 2.48 2.44 ..39 4 1.60 32 10 7 50

7 125 do 1 .74 1.70 .32 4 2.28 32 10 7 100

7 126 do 1.72 1.68 .32 4 2.31 32 10 50

" storage conditions after transfer of prestress.

3
Table 4. Specimens made from Type III cement concrete

Group

No. oet INC. Shape

Gross

area of concrete

Net

£ir6£l of concrete

Mass

ratio No.

of wires

Ratio forcement LengthGage

1 ength

Age of concrete

2lXi tjiine of

tir&iiisfer of prestress

Relative humidity *

so in sq in Percent in in Days Percent 3B 41 Octag 10 43 9 90 U QQoy 16 1 58 52 20 3 100 3A 42 do 17 60 17 07 1 15 16 0 92 67 20 12 3A 43 "do 10 97 10.44 u

0

1

16 1 50 52 20 1 o lUU 3A 44 ; ^ 1 ; I do

I

10 79 10 26 90 16 1 53 52 20 12 50 3A 45 do 7 60 7 03 76 16 2 21 45 20 12 50 SB 10 14 g 61 ooQQ 16 1 63 52 20 ou 4A a 1 r\ 40 69 38 57 1 75 64 1 62 96 20 12 1 An 4A do 41 27 39 15 1 76 64 1 60 96 20 1

2

ou

415 Do _ - UO - ^ 41 27 39 15 1 64 1 60 96 20 ou

8 141 Square. - - - 4 13 4 09 0 50 4 0 96 32 10 12 100

QO 4 08 4 04 50 4 97 32 10 12 50

8 143 ao 2 53 2 49 39 1 57 32 10 1 o1 z

1 Tin lUU 8 144 do 2 56 2 52 39 1 55 32 10 12 ou

8 145 "do 1 80 1 76 33 2 21 32 10 12 1lUU 8 146

~ At\ 1 73 1 69 33 4 2 30 32 10 12 ou

9 161 Square _ _ 4 06 4 02 50 4 0 98 32 10 3 100

9 162 do 3 95 3 91 50 4 1 00 32 10 3 50

9 163 do 2 47 2 43 39 4 1 61 32 10 3 100

9 164 do 2 45 2 41 39 4 1 62 32 10 3 50

9 165 do 1 75 1 71 33 4 2 27 32 10 3 100

9 166 do 1 79 1 75 33 4 2 22 32 10 3 50

» Storage conditions after transfer of prestress.

tend to decrease the initial tension in the reinforcement. An initial steel tensile stress of 125,000

psi on eacli wire was recorded at the time the

prestress was transferred to the concrete, except

for specimens in sets No. 1-6, inclusive, for which

the steel tensile stress was 119,000 psi. The wires were thoroughly cleaned with solvent before placing concrete in order to facilitate bonding

throughout their length.

The gage lines in the prismatic specimens were

either 5, 10, or 20 in. long. The gage points consisted of l/2-iii- \o\\g 1/4-20 flat-headed brass screws embedded in the concrete surface merely by having the flat top surfaces lightly glued to the inside

of the form faces prior to concreting. Upon re- moval of the forms, the flat surfaces were cleaned

and gage lines established by drilling holes suit- able for accommodating 5-, 10, or 20-in. Whitte- more strain gages, this drilling being done during

the period of moist curing with wetted burlap.

4. Procedure in Making Observations

When each of the prisms had reached the age

at which the prestress was to be transferred to the concrete, initial readings were taken using the

appropriate Whittemore strain gage (5-, 10-, or

20-in.). Then immediately upon the transfer of

prestress further readings were taken, and these were continued at regular intervals of time up to an age of 500 days. Readings were taken on the

nonstressed specimens every time they Mere made

on the prestressed ones.

5. Efficiency of Stress Transfer, Steel to

Concrete

In order to validate the basis upon which all the

computations were made, it was necessary to determine that the change in strain gage readings on

the concrete at midlength of prisms was indeed

indicative and equal to that occurring in the embedded steel. The sets of specimens smallest in cross section were only 32 in. long. With these

specimens in particular, it was especially questionable whether sufficient length had been allowed to | fully develop the required anchorage outside of

the center 10-in. gage length in order to assure

{ that the concrete and steel did not slip relative

(o each other within that gage length. To check the

develoj)nient of bond between the wires and the

concrete, 5-in gage lines were installed throughout

the length on two faces of several of the shorter

specimens; see flgure 2, specimen No. 162. Figures 3a and 3b graphically depict strain

observations made along the length of Type I cement specimens ; figures ia and 4b are concerned

with the Type III cement specimens. Since it was

Figure 2. Smaller specimens depicting detailed 5-in gage length on specimen No. 162 and typical center- spaced 10-in gage length on specimens No. 150 and

166.

4
impractical to determine strain at the extreme end

of each specimen, values for shrinkage or swelling

from the nonstressed companion specimens were assumed to apply; this assumption introduces a

slight error at the ends due to the restraint by the

steel wii'es and their time-delay efl'ect on strain

and stress. First to be considered, figures 4a and

4b depict essentially a constant value of strain

along the center 15 in of each specimen. Further

consideration of the curves indicates that the constant deformation may indeed be applicable for more than the indicated 15-in gage line; note that

the second gage line in from each end includes

strains which occur within 6 in of the end of the

specimen. Assuredly, the specimens made with

Type III cement in all cases developed full bond

within 81/2 of the end if not in a lesser distance.

This conclusion is born out by G. Marshall [3]

-2000 X 10"*

<§) I DAY

STRESS TRANSFER AT 7 DAYS

STRESS TRANSFER AT 28 DAYS

(a)

rl— 5"

. .|. 5"-4— 5—J— 5" - I - 5 —I— 5'—jl"-^ DISTANCE ALONG TEST SPECIMEN

(a) Specimens cured at 50 percent RH.

who measured development lengths in highly

stressed wires 0.08 inches in diameter.

Figures 3a and 3b do not give the same assur- ance for specimens made with Type I cement.

Here the specimens loaded at 28 days indicate that

the required anchorage is developed in 6 to 8 in

of length one day after stress transfer, whereas

the required length increases with age up to 500

days. As mentioned joreviously, the strains are those based on gage lines 5 in long. It is clear that

if the gage were shorter, the average strain indicated by each gage could be more nearly indicative of the true strain at the midpoint of each gage

line. It is therefore reasonable to suppose that the

length of the constant strain zone near the midsection of the specimens is longer than indicated

in figures 3a and 3b since the points showing the

"breaks'' must of necessity lie below a smooth

-2000X10"' n

1 1

1

1 r

/ \— @ 500 DAYS

@ 1 DAY

STRESS TRANSFER AT 3 DAYS

• STRESS TRANSFER AT 12 DAYS

(0)

"L— 5"— 5" »|- S •!• 5" > ! • 5 —L-5"—Jr DISTANCE ALONG TEST SPECIMEN

(a) Specimens cured at 50 percent RH.

-8ooxicr« @ 500 DAYS

DISTANCE ALONG TEST SPECIMEN Figure 3. Variation of compressive strain on surface of concrete along the length of 32-in specimens made with

Type I cement. Times on graphs indicate age after stress transfer.

(b) Specimens cured at 100 percent RH.

DISTANCE ALONG TEST SPECIMEN Figure 4. Variation of compressive strain on surface of concrete along the length of 32-in specimens made ivith Type III cement. Times on graphs indicate age after stress transfer.

(b) Specimens cured at 100 percent RH.

6
curve based on a very large number of short gages. Therefore, it seems probable that the center 10-in

gage length does represent true strains of fully

bonded concrete and steel. Also, whereas these

prestressed wires were 0.1125 inches in diameter

and stressed to 1'25,()00 psi, another investigator

[3] has shown that 0.08-in wires prestressed to 200,000 psi developed end anchorage in less than

5 in initially, and in 7.5 in of length one year after

stress transfer.

6. Basis of Coinputations

Immediately prior to transfer of the prestress

load to the concrete, a check was made as pre- viously mentioned to be certain that the magnitude of stress in the steel wires had not changed

fi'om the original level. With this assurance, initial strain gage readings Avere made on all the speci- mens in the group prestressed with the same unit.

ITpon release of presti'ess to the concrete, any

change in gage length on the concrete was as- sumed to denote the same change in length in the steel. Thus, it was simple to compute the

residual total load still imposed by the steel wires,

and fi'om this, the concrete compressive stress based on net area of concrete. Whereas the deformation in the steel was taken

as purely elastic, the deformation in the concrete was assumed to consist of three parts

:

a. Elastic deformation

b. Shrinkage or swelling deformation.

c. Creep or plastic flow. The elastic deformation upon transfer of the

prestress to the concretes was assumed to follow

closely the stress-strain curves obtained on the

6- by r2-in cylinders. Stress-strain curves were

actually obtained on five sets of cylinders repre- senting ages of 7 days, 28 days, and 1 year for

each concrete made with Type I cement, and 3

days, 12 days, and 1 year for each conci-ete made

with Type III cement. Cylinders cured at relative

humidities of both 50 and 100 percent were in- cluded in each set for all but the earliest ages for

each concrete. The graphs in figures 5 and 6 illustrate the

method by which the strain in the concrete was

analyzed. The straight line in figure 5 passing

through points A and B was constructed to represent the relationship between the observed strain

ec and the residual stress in the concrete computed

from the remaining tensile force in the prestressing unit. Point A was obtained from the strain on the surface of concrete observed immediately

after stress transfer and the stress in the concrete computed from the remaining tension in the steel at that time; point 1^ was obtained from the observed total strain at some chosen age of speci- men and the similarly computed residual stress in the concrete. The value of e. is equal to the summation of elastic strain, creep, and shrinkage or swelling in the concrete.

Although Washa and Fluck [4] reported an

increase in the moduli of elasticity associated with

sustained loading, the authors made use of the

moduli of previously unloaded specimens in analyzing their test results. In order to determine

the magnitude of elastic strain included in tc, stress-strain curves were plotted, as in figure 6, for several ages, covering at intervals the entire

range of ages in the creep measurements. When

a particular specimen was being analyzed, the

residual stresses were computed at ages for which

the stress-strain curves wei-e available. These val- ues of I'esidiuil stresses were then entered on the

stress axis of figure 6 and points on the corresj)0)iding stress-strain curves were plotted. These

points formed the locus of a generalized stress- strain curve (fig. 6) which permitted a determinatio}! of the elastic strain in a specimen at any

age. The creep could thus be computed from the

observed value of total defoi'mation, the elastic

TOTAL OBSERVED STRAIN IN CONCRETE

Figure 5. .4. schematic 7-clationship between total observed

strain and the residual stress in the concrete.

(rzo

ELASTIC STRAIN IN CONCRETE

Figure 6. Sclicmatic diagram, illustrating method for determination of the generalized stress-strain curve.

6
strain at any age, and the observed shrinkage or

swelling at that age. The shrinkage or swelling of the concrete is determined by measuring tlie unstressed companion specimens. The creep strain is then computed by substracting the elastic strain and the

shrinkage from e, ,• in case of swelling, the deformation is added to €,..

7. Test Results

Data pertinent to the concrete specimens made

with Type I cement are given in table 5 and 6

;

those with the Type III cement in tables 7 and

8. P]ach table is divided into the two ages at which

the prestress forces were transferred to the concrete. Creep, shrinkage or swelling, initial concrete prestress (allowing for elastic deformation

only), and subsequent stress in the concrete at ages 1, 10, 100, and 500 days (reckoned from the

time of transfer of prestress) were all determined

as previously outlined. Also given is the prestressstrength ratio defined as the ratio of initial prestress at time of transfer of prestress to the actual

strength of the concrete at that same age; see table 6 and 8.

8. Analysis and Discussion

Figure 7 depicts on semilog paper the data obtained on 6 of the 14 sets of specimens made with

Type I cement and in which stress transfer was

accomplished at age 28 days. Three of these (Nos.

1, 3, and 5) were stored at 100 percent relative

humidity (RH), the other three (Nos. 2, 4, and 6)

TIME UNDER STRESS, DAYS

a( 50 percent R.ll. The top curves show the resi- dual stress up to an age of 500 days. The center curves depict shrinkage of the 50 percent RH

sj)ecimens and the swelling which occurred in the

100 percent RH specimens. The lower curves indi- cate the amount of creep. Figure 8 indicated cor- responding data for comparative specimens

loaded at 7 days of age. In comparing the 7-day

and 28-day data; it is readily noted that loss of

stress and ci'eep are higher for the 7-day speci- mens. The primary reason for this behavior

is that the concrete prestress-strength ratio is greater in tlie 7-day specimens than in the 28-day

specimens. This relationship is also true of the

3-day and 12-day release specimens made with

Type III cement (data not shown graphically).

Other investigators [56] observed a roughly linear

relationship between creep and prestress-strength

ratio. The loss of prestress as indicated by the top

set of curves for a limited number of specimens

in figures 7 and 8 can be depicted better by the re- lationships indicated in figures 9 and 10. The

graphs in these figures are of particular interest

inasmuch as they include all specimens. Figure 9

inchides all the specimens of Type I cement (stress

transfer at 7 and 28 days), while figures 10 shows

all si)ecimens of Type III cement (stress transfer

at 3 and 12 days). In both these figures the loss of

prestress after 500 days has been plotted against

the prestress-strength ratio. Inasmuch as the loss of prestress plotted in

figures 9 and 10 was obtained on the basis of the

2400

2000

1600

1200

-200

-400

-600 -800

-1000

1

1

21—22_

1

- SWELLING

1 ____2!iliJS_—

1 1

_ SHRINKAGE

1 1

TIME UNDER STRESS, DAYS

Figure 7. Typical curves for residual stress, shrinkage

or swelling and creep versus time under stress, for Type I cement concretes and stress transfer at 28 days.

Figure 8. Typical curves for residual stress, shrinkage or swelling and creep versus time under stress, for Type I cement concretes and stress transfer at 7 days.
Table 5. Values of creep and shrinkage or swelling for specimens

made of Type I cement concrete

Creep Shrinkage or swelling ' Set Rclflti V6 No. ratio h u mid i t- V

1 day 10 day 100 day 500 day 1 day in10 Aday luu aay 500 day

PcrC€77

1

Microinches per inch i*j iCTomcti €s per men

Prestrcss transferred at 28 days

101 0.50 100 22 82 200 305 + 14 4-17 ~\-50 + 102 102 .50 50 40 203 500 580 — 122 47Q — / ou — 820

103 .39 100 30 110 280 420 + 18 1 og 1 CO

-f- Oo + 100

104 .39 50 94 348 720 840 — 145 -500 -710 — 755

105 !32 100 11 150 380 590 + 18 +30 +50 + 100

106 !33 50 90 410 780 910 -150 -520 -720 -780

1 1.14 100 45 140 258 340 + 10 +40 +83 + 133

2 1.15 50 54 150 420 575 -70 — ZoU -780

3 0.90 100 64 190 370 517 0 + 14 1 OA -f-oU + 130

4 .89 50 64 200 570 750 — 90 290 — oou — 780

5 . 75 100 67 250 500 675 + 13 1 -^o 1 OA -TOU + 130

6 [74 50 70 265 775 968 — 90 — Qon OZV) — D# U — 740

73 1 . 49 50 50 180 475 680 — 47 — I/O — OOU — 755

74 1 .51 100 20 104 270 440 +4 -f- lo -J- OO +75

Prestress transferred at 7 days

121 0.50 100 50 210 380 460 + 10 1 25 + 132 122 .50 50 128 380 690 780 — 100 — o\j\) — oyo — 760

123 .39 100 110 365 618 745 + 12 25 + 120

124 .39 50 240 600 907 1015 — 130 -445 -670 — 718

125 !32 100 115 500 800 933 +25 +30 +75 + 108

126 .32 50 260 775 1158 1270 - 130 -440 -600 -658

21 1.15 100 102 283 465 560 + 18 + 35 + 100 + 150 22 1.15 50 103 295 580 714 -65 -233 -735 -867

23 0.91 100 170 400 685 850 + 15 +30 + 105 + 160 24 .90 50 255 570 985 1130 -80 -290 -790 -903

25 .75 100 382 754 1100 1286 + 12 + 29 + 102 + 145 26 .74 50 356 830 1365 15.30 -90 -330 - 763 -845

71 1.52 50 185 507 940 1150 -58 -200 -655 -870

72 1.51 100 120 405 680 830 + 1 + 15 +50 + 100

' Swelling is indicated by positive values.

Table 7. Values of creep, and shrinkage or swelling for specimens made of Type III cement concrete

Set No. Mass

ratio Relative humidity

Percent

Creep

1 day 10 day 100 day 500 day

Microinches per inch

Prestress transferred at 12 days

Shrinkage or swelling •

1 day 10 day 100 day 500 day

Microinches per inch

141 0.50 100 6 130 283 400 +51 +62 + 102 + 150

142 .50 50 70 235 483 566 -95 -366 -652 -720

143 .39 100 38 198 413 570 +52 +58 +97 + 126

144 .39 50 no 375 664 765 - 112 -385 -560 -610

145 .33 100 5 195 470 700 +51 +57 + 100 + 130 146 .33 50 19 297 570 705 - 119 -350 -515 -550

42 1.15 50 53 148 320 435 -43 -216 -650 -790

43 0.91 100 45 147 315 445 + 19 +40 + 72 + 106 44 .90 50 100 288 625 758 -62 -280 -693 -795

45 .76 50 130 356 790 945 -81 -343 -740 -812

61 1.75 100 124 256 450 667 + 14 + 17 +37 +70

62 1.76 50 66 243 580 798 -50 - 145 -480 -735

Prestress transferred at 3 days

161 0.50 100 1.36 322 490 560 +37 +62 + 111 + 135

162 .50 50 184 4.36 716 802 - 114 -410 -754 -830

163 .39 100 260 575 844 960 +22 +43 + 88 + 117

164 .39 50 297 703 1020 1115 - 136 -422 -650 -728

165 .33 100 209 677 980 1125 +43 +65 + 110 + 130

166 .33 50 430 890 1200 1345 -138 -440 -642 -740

41 .89 100 213 543 770 890 +30 +54 + 112 + 146 46 .88 50 340 668 1000 1128 -100 -300 -750 -852

63 1.78 50 250 470 781 970 -52 -130 -512 -752

' Swelling is indicated by positive values.

8
Table 6. Compressive strength, initial and residual prestress, and unit creep strain"

for Type I cement concrete

Strength Stress Residual stress in concrete Ratio: Loss of Unit creep Set Mass Relative at at initial prestress strain, /i» No. ratio humidity prestress prestress prestress to at 500

transfer transfer 1 day 10 day 100 day 500 day comp. str. day

Percent psi psi psi psi psi psi Percent Percent 10— Vps>

Prestress transferred at age 28 days

101 0.50 100 5990 1 155 1 152 1140 1120 1 1 10 19 .

3

3.9 0. 264

102 . 50 50 5990 1 140 1100 970 820 780 19.0 31.6 . 509

103 . 39 100 5990 1790 1790 1766 1730 1680 29 .

8

6.

1

. 235

104 . 39 50 5990 1800 1650 1480 1200 1150 30.

0

36.

1

. 467

105 . 32 100 5990 2480 2480 2430 2350 2250 41.4 9 .

3

. 238

106 .33 50 5990 2440 2320 1970 1620 1530 40.7 37.3 .373

1 1.14 100 5200 1064 1060 1050 1040 1025 20.5 3.7 .320

2 1.15 50 5200 1057 1030 960 790 720 20.3 32.0 .544

3 0.90 100 5200 1664 1645 1620 1.580 1540 .32.0 7.4 .311

4 . 89 50 5200 1692 1630 1500 1210 1085 32 .

5

35 .

8

.443

5 .75 100 5200 2325 2305 2240 21.55 2100 44 . 7 9 .

7

. 290

6 . 74 50 5200 2382 2280 2050 1575 1425 45 .

8

40.

1

. 406

73 1 .49 50 5710 1828 1790 1680 1400 1 230 32 .

0

32 .

8

. 372

74 1.51 100 5710 1783 1780 1750 1710 1675 31.2 6.

1

. 247

Prestress transferred at 7 days

121 0. 50 100 3230 1131 1120 1100 1080 1070 35 .

0

.5 .

4

. 407

122 .50 50 3230 1106 1060 930 775 735 34 .

2

33 .

5

. 705

123 .39 100 3230 1750 1725 1650 1602 1575 54 .

3

10.0 .426

124 . 39 50 32.30 1762 1650 1380 1160 1085 54 .

7

38. .5 . 576

I 125 . 32 100 3230 2338 2310 2200 2110 ZUDO 72 .

3

11.7 . 399

126 .32 50 3230 2362 2200 1815 1.500 1400 73.3 40.7 .538

21 1 . 15 100 3600 1082 1068 1038 1020 1010 30.0 6. 7 .518

22 l]l5 50 3600 1080 1050 970 775 705 3o!o 34 .' 7 1661 23 0.91 100 3600 1660 1630 1552 1505 1480 46.

1

10.8 .521

24 .90 50 3600 1710 1610 1420 1060 955 47.5 44. 1 .661 25 .75 100 3600 2280 2130 2000 1900 1850 63.4 18.9 .564 26 .74 50 3600 2300 2120 1800 1285 11.50 64.0 50.0 .665

71 1.52 50 3770 1715 16.10 1490 1130 960 45 .

5

44. 1 .671 72 1.51 100 3770 1720 1690 1620 1560 1520 45.6 11.6 .483

' /I is defined as unit creep strain at 500 da>-s ba?ed on stress at time of transfer.

Table 8. Compressive strcmith, initial and residual prestress, and

unit creep strain" for Type III cement concrete

Strength Stress Residual stress in concrete Ratio: Loss of Unit creep

\ Set Mass Relative at at initial prestress strain, »

" No. ratio humidity prestress prestress prestress to at 500

1

,j transfer transfer 1 day 10 day 100 day 500 day comp. str. day

Percent psi psi psi psi psi psi Percent Percent lO-'/psi

Prestress :ransferred fIt age 12 Days

141 0.50 100 4970 1132 1136 1118 1099 1080 22.8 4.6 0.353

142 .50 50 4970 1145 1102 1000 860 825 23.0 27.9 .494

1 143 .39 100 4970 1767 1772 17.30 1670 1630 35.6 7.8 ..323

1 144 .39 50 4970 1748 1670 1490 1290 1230 35.2 29.6 .438

I 145 .33 100 4970 2363 2363 2305 2236 2136 47.7 9.6 .296

l! 146 ,33 50 4970 2450 2277 2085 1890 1800 49.4 26.5 .288

i 42 1.15 50 5600 1090 1065 998 845 783 19.4 28.2 .399

1 43 0.91 100 5600 1703 1690 1650 1600 1565 30.4 8.

1

.261 44 .90 50 5600 1724 1660 1500 1210 1110 30.8 35.6 .440 45 .76 50 5600 2275 2160 1880 1440 1325 40.6 41.7 .415

61 1.75 100 5140 1830 1805 1760 1700 1635 35.6 10.7 .364 62 1.76 50 5140 1800 1760 1650 1390 1190 35.0 33.9 .443

Prestress ransferred a t age 3 Da,\ s

, 161 0.50 100 3490 1132 1115 1085 1061 1048 32.4 7.4 .495

162 .50 50 3490 11,55 1087 960 796 750 33. 1 35. 1 .694

163 .39 100 3490 1737 1677 1595 1530 1490 49.8 14.2 .553

1 164 .39 50 3490 17,50 1603 1355 11.50 1070 50.2 38.8 .637

11 165 .33 100 3490 2267 2235 2110 2012 1945 65.0 14.2 .496

! 166 ..33 50 3490 2233 2020 1660 1410 1295 64.0 42.0 .602

41 .89 100 3770 1722 1685 1605 1540 1510 45.6 12.3 .517

1 46 .88 50 3770 1682 1570 1365 1050 950 44.5 43.5 .670

i: 63 1.78 50 3370 17(iO 1670 1550 1290 1140 52.2 35 .

3

.551

'ilia defined as unit creep .strain at ,500 days based on stress at time of transfer.

9
0.2 0.3 0.4 0.5 PRESTRESS - STRENGTH RATIO

Figure 9. Loss of prestress at 500 days versus prestress- strcnyth ratio; Type I cement concretes.

• 12 DAY TRANSFER O 3 DAY TRANSFER o

MAINTAI AFTER

o

NED AT 5 STRESS0 % RH rRANSFER •

•

•

C o —

O

< —

MAINTAir ED AT 10 0 % RH

PRESTRESS - STRENGTH RATIO

Figure 10. Loss of prestrcss at 500 days versus prestress- strength ratio; Type III cement concretes.

total observed time-dependent deformation in concrete, a portion of the loss of prestress represents that due to drying shrinkage. Although it is not known how the drying shrinkage of concrete

is alTected by the stress level, it is generally as- sumed that it is independent of the magnitude of

the compressive stress. This assumption was also

made here and the curves shown in figures 9 and

10 were faired through the experimental points

so as to give intercepts of an 18-percent loss and

a 3-percent gain for specimens subjected to 50

percent RH and 100 percent RH, respectively.

Thus, it was assumed that as the prestress-strength

ratio approaches zero, the loss of prestress in specimens maintained at 50 percent RH would ap- proach 18 percent, i.e., the loss associated with a drying shrinkage of 800 X 10"'' in/in. Similarly,

for specimens maintained at 100 percent RH the

ffain in prestress would be of the oi'der of 3 percent, corresponding to a swelling of concrete of

about 130 X 10-« in/in.

The influence of mass ratio on shrinkage seems

to change considerably with drying time. This

relationship may be noted in figure 11 wherein

>500 DAYS

• 7 DAYS MOIST-CURE O 28 DAYS MOIST-CURE

.8 1.0 1.2 1.4 1.6 1.8 MASS RATIO

(a) Type I cement concretes.

1 1 1 1 1 1 1

1 —o|\_^ 1 DAY OF DRYING —

^^^^^^ 10 DAYS

O

100 DAYS

£—

0 '

0 ^ ""^

iOO DAYS — • 3 DAYS MOIST O 12 DAYS MOIST

1 1 1

CURE

CURE

1 1

(b)

1 1 1

MASS RATIO

(b) Type III cement concretes.

FiGiTRE 11. fihrinkaye versus mass ratio after drying for

1, 10, 100 and 500 days at 50 percent RH.

shrinkage at 50 percent RH for given periods of

drying are plotted against mass ratios; each of

the two cements and the two ages at which drying was initiated are separately plotted in figures 11a

and lib. There appears to be a marked difference,

up to the observed age of 500 days, between the

Type I cement concrete specimens wet-cured for

28 days and those cured for only 7 days. Also, it appears that at 1 and 10 days of drying the large

specimei\ had less shrinkage than did the smaller

10
Mi

specimens. However, at 500 days, the 28-day cured

Type I cement specimens all shrank about the same amount independently of mass ratio; this was also the case for specimens wet-cured for 7 days, and having mass ratios in excess of 0.7. Creep per unit of stress has been variously

called : unit creep, creep under unit of stress, unitary-deferred deformation, unit creep strain and

the" like [7] and [8]. Lorman [9] employs in his

study a term m defined or designated as "the creep

coefficient in millionths of an inch per inch per psi

which is assumed to be numerically equal to the

ultimate creep strain per unit of stress." There

are indications by Lorman and others that this

ni is constant up to some ratio of stress-to-strength

of concrete; all of these studies have been con- cerned with creep under constant stress. The

breakover point beyond which m, increases appreciably has been variously given as being in the

range of 1500 psi stress [9], at stress-strength

ratios of 0.20 to 0.26 [10], or as high as 0.50 [2]. In this report, stress was not maintained constant

but was allowed to decrease as creep and shrinkage

took place. AVith considerable shrinkage and creep

occurring in some instances, the stress level decreased appreciably. Because all the specimens

were under a stress which varied with time, an

alternate definition of unit creep strain designated as fi will be introduced. It is defined as the

creep occurring at 500 days per unit of stress, the

stress being the initial prestress at the time of

transfer. Values of /i, unit creep strain at 500 days as defined above, are plotted against the prestressstrengtli ratios in figures 12 and 13. It appears to be reasonable to assume that these plots are

straight lines; these were obtained by method of

least squares. The S])ecimens subjected to 50 per- cent RII (Type I and Type III cements alike) exhibit a decrease in ix with an increase in prestressstrength ratio. For constant stress conditions, it would be ex})ected that fx would remain essentially constant for all stress-strength values up to the

breakover point and then increase. For the conditions of these tests there was no indication of a

bi-eakover jwint u}) to the maximum i)restressstrength ratio of 0.7 used in this investigation.

Figures 14 and 15 indicate the relationshii) be- tween unit creep strain at 500 days and mass

ratio; the straiglit lines shown were obtained by

method of least squares. In general, /x increases

slightly with an increase in mass ratio for all specimens and botli storage conditions (50% and

100%KII). Also this effect of mass ratio on /x apl)ears less marked tlian the effect of the prestressstrengtli ratio. Inge Lyse [11] reported that in an atmosphere

of 50 j)ercent KH, a sustained stress of about 25

percent of the initial concrete strength will result

in creep nearly equal to the shrinkage under the same ambient conditions. It is assumed that the

temperature was at about 70°F. He also related

that Mamillan [12] equated creep at a 15 percent

stress-strength ratio to the amount of shrinkage

at 85 percent KM, and creep at a 85 percent stress with shrinkage at 15 percent RH. Again these

two investigators were concerned with constant

stress. In this study, creep computed for the four

var'iables (2 cements, 2 ages of stress transfer)

approximately equals shrinkage (at 50% RH)

for stress-strength ratios ranging from 32 to 36

percent. True, tliese ratio values are higher than

file aforementioned 25 percent value established

by Lyse. This relationship should be so since the

concrete stress in this instance diminished with

time because of creep and shrinkage.

9. Summary

This study involved creep and shrinkage oc- curring in prestressed si)ecimens in which the steel reinforcement was bonded to the concrete. Thus,

any change in linear dimension caused a change to occur in the amount of prestress force to wliich the concrete was subject. CVeep and shrinkage in the

concrete superimposed upon elastic deformation

PRESTRESS - STRENGTH

RATIO Figure 12. Unit Creep Strain at 500 days versus prestnss-streiifftli ratio for Type I eement concretes.

PRESTRESS - STRENGTH

RATIO

FiGURK 13. Vnit Creep Strain at 500 days versus prestress-stre)i(/th ratio for Type III cement concretes.

11
Figure 14. Unit Creep Strain at 500 days versus mass

ratio for Type I cement concretes.

=1 .2

1

1 * 1 '

1 '

1

' 1 ' 1 1 1

•

• —-

•

o

3 DAY - 100 % R.H. • — 0

,o nilY-50 % R.*i

A

12 DAY - 100 % R.H. - ^

1 , 1 1 , 1 ,1,1,1,

MASS RATIO

FiGXTRE 15. Unit Creep Strai^i at ,500 days versus mass

ratio for Type III cement concretes.

of concrete and reinforcement caused a relaxation

of tlie initial prestress force. Several items of note are

:

1. Wires 0.1125 inches in diameter, tensioned to 125,000 psi initial prestress, require an embedment

for anchorage of less than 10 inches in length

when used in good quality normal portland ce- ment concrete witli an age of release of prestress

as early as 7 days, or when used in high-early

strength cement concrete as early as 3 days. The

required length of embedment seemed independent of cure of concrete, wet or dry.

2. Early shrinkage of nonstressed specimens

exposed to 70°^". and 50 percent EH seemed to be

dependent upon the mass ratio. Small cross- sectional specimens exhibited more rapid shrinkage at an earlier age than the larger S2:)ecimens,

but the larger specimens ai)peared to approach

the shrinkage values of smaller ones at ages of

about 500 days.

3. Loss of prestress in these specimens having

bonded tendons appears to vary linearly with the

ratio of initial concrete prestress to initial strength, regardless of strength of concrete or age

of release of prestress. There is little difference in the percentage of loss of prestress between speci- mens of normal jiortlancl cement and those made

with high-early strength cement when storage

conditions are the same.

4. Unit creep strain (i.e., creep strain at 500

days divided by initial concrete prestress) was

found to be dependent upon moisture conditions

during storage. Greater creep per psi of stress

occui'S at 50 i)ercent RH than at 100 percent RH.

5. Unit creep strain at 500 days appears to be almost independent of the prestress-strength

ratio for specimens stored at 100 percent RH.

However, for specimens stored at 50 percent RH

Unit Creep Strain at 500 days appears to decrease

linearly with increasing prestress-strength ratios.

6. The mass ratio hacl little significant effect on the unit creep strain at 500 days.

10. References

[1] G. E. Troxell, .J. M. Raphael and R. E. Davis,

Long-Time Creep and Shrinkage Tests of Plain

and Reinforced Concrete, ASTM Proc. 58, 1101

(19.j8). [2] Tien S. Chang and Clyde E. Kesler, Correlation of Sonic Properties of Concrete with Creep and Relaxation, ASTM Proc. 56. 1257 (1956).

[3] G. Marshall, End Anchorage and Bond Stress in Prestressed Concrete, Magazine of Concrete Research, No. 3 (Dec. 1949).

[4] G. W. Washa and P. G. Fhicli, Effect of Sustained

Ijoading on Compressive Strength and Modulus

of Elasticity of Concrete, ACI Proc. 46, 693-700, (May 19.50). [5] T. W. Reichard, Creep and Drying Shrinkage of Lightweight and Normal Weight Concretes, NBS

Monograph 74 (Mar. 1964),

[6] .T. R. Keeton, Time-Dependent Deformations of

I'lain Concrete, Highway Research Board Proceedings, 39, 310-335. (1960).

[7] Review of Literature on Creep in Concrete, Miscel- laneous Paper 6-132, Corps of Engineers, U.S. Army (June 1955).

[8] R. Dutron, Creep in Concretes, RILEM Bulletin

34 (1957).

[9] W. R. Lorman, The Theory of Concrete Creep,

ASTM Proc. 40, 1082 (1940).

[10] Frendenthal and Roll, Creej) and Creep Recovery

of Concrete under High Compressive Stress, ACI

Proc. 54, nil (June 19.58). [11] Inge Lyse, Shrinkage and Creep of Concrete, ACI

Proc. 56, 775 (Feb. 1960).

[12] M. Mamillan. Etude sur le Fluage du Beton, Annales Institute Technique du Batiment et des Travaux Publics (Paris), 134, 221-233 (February

1959).

i^r U.S. Government Printing Office: 1968 0—284-587

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