TECHNICAL REPORT STANDARD TITLE PAGE

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

~-r;;;--.. -a~d-S~-ht-it-lo-----------''------------------+-::-5-. -,:R:-e-po_r_t ;::Da_t_e---------------···

CREEP AND-SHRINKAGE OF CONCRETE BASED ON MAJOR VARIABLES ENCOUNTERED IN THE STATE OF TEXAS

1-:-· August , J 9 7 3 -------6. Perfonnirig Organization Code

" -·-- ·····• --- ------------------- ------ - -- --· --··· ----------·--Leonard L. Ingram and Howard L. Furr

?. P .. rforn11nu OrgoniJot1on NomfJ ond_ Addr~-;.";

Texas Transportation Institute Texas A & M University College Station, Texas 77843

8. P,rlorm111g Organization Report No.

Research Report 170-lF ·-- ·-- --- r-ro·. Work Unit No.

11. Contract or Gront No.

Research Studv No. 2-5-72-170 13. Type of Report and Period Co-vered . ------ -~-------~--~---- -----......--------------------1

12. Sponsoring Agency Nome and Addres.

Texas Highway Department 11th & Brazos A us tin, Texas 78701

Final - September 1971 August 1973

14. Sponsoring Agency Code

--~----·----·----------------------'--------------------1 15. Supplementary Notes

Research performed in cooperation with DOT, FHWA. Research Study Encountered in

Title: "Creep and Shrinkage of Concrete Based on Major Variables the State of Texas. ir

16. Ab•troct

The effects of creep and shrinkage strains in concrete are dependent on variables such as materials, stress level, and environment. In this investigation, creep and shrinkage strains as functions of time were determined for four different concretes from four different geographical areas of Texas (Dallas, San Antonio, Odessa, Lufkin). These four locations were chosen to represent four major areas of Texas for climate and aggregate for producing concrete. The concretes were made of materials commonly used in the respective areas. They were made, cured, and stored in those areas.

Standard 6 x 12 in. cylinders were used to determine strength and the stress-strain relationship, and prisms, 3 x 3 x 16 in., were used to detetmine creep and shrinkage strains. Duplicate sets of specimens were made at each place of fabrication. Each set contained 4 non-loaded prisms for shrinkage strains, 4 loaded prisms for compressive creep strains, and 18 cylinders. One set of specimens were stored in a protected area near the place of fabrication and the other set was stored at laboratory conditions, 73°F and 50 percent relative humidity.

The specimens were cured alongside pretensioned prestressed bridge beams cast at the same time as the test specimens. The curing time in the molds ranged from approximately 20 hours to 42 hours. (continued on back side)

17. Key Words 18. Distribution Statement concrete, shrinkage, creep,

compressive stress, modulus of elastic-ity, concrete strength.

19. Security Classif. (of this report) 20. Security Clossif. (of this page) 21. No. of Pages 22. Price

Unclassified Unclassified 49

Form DOT F 1700.7 IB·69l

Hyperbolic functions of unit creep with time were developed for the concrete tested from each of the four geographical area. Those functions are suitable for design purposes for computing prestress loss and camber in pre­tensioned prestressed concrete beams.

CREEP AND SHRINKAGE OF CONCRETE BASED ON MAJOR VARIABLES ENCOUNTERED

IN THE STATE OF TEXAS

by

Leonard L. Ingram, P.E. Former Assistant Research Engineer

and Howard L. Furr, P.E.

Research Engineer

Research Report 170-lF

Creep and Shrinkage of Concrete Based on Major Variables Encountered in the State of Texas

Research Study Number 2-5-72-170

Sponsored by the Texas Highway Department in cooperation with the

U. S. Department of Transportation Federal .Highway Administration

August, 1973

TEXAS TRANSPORTATION INSTITUTE Texas A&M University

College Station, Texas

Technical Reports Canter Texas Transportation Institute

-----~-------------~--~----~-~----------------. --- ·-------~-----

DISCLAIMER

The contents of this report reflect the views of the authors

who are responsible for the facts and the accuracy of the data presented

herein. The contents do not necessarily reflect the official views or

policies of the Federal Highway Administration. This report does not

constitute a standard, specification, or regulation.

ii

ACKNOWLEDGEMENTS

The assistance and cooperation of a number of persons of the Texas

Highway Department and commercial concrete fabricators were most helpful

in the development of information contained in this report. Mr. H. D.

Butler, THD D-5, was particularly helpful in planning the tests and in

providing contact with other THD personnel. Personnel of Texas Highway

Districts 6, 11, 15, and 18 provided help in fabrication of specimens

and in making space available for storage of specimens. The concrete

fabricators, Spann, Inc. (Dallas, Texas), Featherlite Structural Concrete

(Odessa, Texas), McDonough Brothers, Inc. (San Antonio, Texas), and Lufkin

Concrete Company (Lufkin, Texas) were helpful in preparing and curing test

specimens. The help of each of these is acknowledged with thanks.

Much of the information developed in this research project was used

by the primary author in his thesis for the Master of Science Degree in

Civil Engineering at Texas A&M University. The thesis, "Creep and

Shrinkage of Concrete Typical of Four Geographical Areas of Texas,n by

Leonard tee Ingram, August 1973 is on file in the library of that University.

That author extends his slncere thanks to the Texas Highway Department,

Federal Highway Administration, and Texas Transportation Institute for

permission to publish the material in his thesis.

iii

-~--- --- ------ --------- -----~----~ -----

ABSTRACT

The effects of creep and shrinkage strains in concrete are dependent

on variables such as materials, stress level, and environment. In this

investigation, creep and shrinkage strains as functions of time were

determined for four different concretes from four different geographical

areas of Texas .. (Dallas, San Antonio, Odessa, Lufkin). These four locations

were chosen to represent four major areas of Texas for climate and aggregate

for producing concrete. The concretes were made of mat~rials commonly used

in the respective areas. They were made, cured, and stored in those areas.

Standard 6 x 12 in. cylinders were used to determine strength and the

stress-strain relationship, and prisms, 3 x 3 x 16 in., were used to

determine creep and shrinkage strains. Duplicate sets of specimens were

made at. each place of fabrication. Each set contained 4 non-loaded prisms

for shrinkage strains, 4 loaded prisms for compressive creep strains, and

18 cylinders. One set of specimens was stored in a protected area near the

place of fabrication and the other set was stored at laboratory conditions,

73°F and 50 percent relative humidity.

The specimens were cured alongside pretensioned prestressed bridge

beams cast at the same time as the test specimens. The curing time in the

molds ranged from approximately 20 hours to 42 hours.

Hyperbolic functions of unit creep with time were developed for the

concrete tested from each of the four geographical area. Those functions

are suitable for design purposes for computing prestress loss and camber

in pretensioned prestressed concrete beams.

Key Words: concrete, shrinkage, creep, compressive stress, modulus of elasticity, concrete strength.

iv

SUMMARY

Shrinkage and creep of prestressed concrete are major factors in

camber and loss of prestress in prestressed bridge beams. The concrete,

conditions of curing, and climatic conditions to which the member is ex­

posed in service influence creep and shrinkage. The State of Texas has

areas that differ in climate, and aggregates for concrete differ through

the state,

In this research studies were made of concretes in four different

geographical areas of the state to determine the creep and shrinkage of

a highway bridge concrete assumed to be typical of the area in which it

was made. T:ests were made on concretes sheltered, but otherwise exposed,

in the four areas, and on companion specimens stored under constant

temperature and relative humidity.

Specimens were 3 in, square in section by 16 in. long. The concretes

were made and stored at, or near, Dallas, Odessa, San Antonio, and Lufkin,

Texas. Strain data were collected from non-loaded specimens and from

specimens under sustained stresses of 1000 psi and 2000 psi over a period

of almost two years.

It was found that shrinkage of laboratory stored specimens was greater

than that of field stores specimens. Field shrinkages at 500 day age were

300, 510, 360; and 280 microinches per inch respectively for Dallas, Odessa,

San Antonio, and Lufkin concretes stored in the field. Corresponding

values for laboratory storage were 480, 620, 480, and 430. Creep from

field stored specimens was generally a little greater than that of laboratory

stored specimens.

v

·~--- -------------·---·----·-

Unit creep curves and unit creep functions were produced for the

four materials. The hyperbolic functions of unit creep and of shrinkage

with respect to time are particularly useful to a designer in computing

prestress loss and camber at any time in the life of a bridge beam.

A prestressed concrete beam, THD Type B, was used as a subject

for comparing camber predictions based on creep and shrinkage functions

developed in an earlier study with those developed in this study (1).

The earlier study was made in Houston, Texas on concrete produced, cured,

and stored in that city. It was found that the camber based on the creep

and shrinkage functions of the Houston tests was approximately one-half as

much as that found by using some of the functions of the present study.

vi

IMPLEMENTATION

Prestress loss and camber of prestressed beams may be computed from

the information developed in the study. The materials should be the

same as those reported and the environment of curing, storage, and service

should be the same as that of the tests. The creep and shrinkage properties

reported here will have to be modified if conditions or materials other than

those of the tests· are used.

In computing prestress loss and camber of prestressed beams the com­

puter program developed in Ref. 1. may be used. The modulus of elasticity

and the functions for creep and shrinkage of the particular material and

area of service should be taken from Tables 3 and 6 of this report. The

·computer program referred to will require input data on· the beam and slab,

initial stresses, and materials. It gives information on camber, stresses

and prestress loss at any age specified.

If the comptuer is not used, the creep coefficients of Table 4, or

creep and shrinkage functions of Table 6 may be used in pencil and paper

computations for camber and prestress loss.

vii

INTRODUCTION

The collection and use of creep and shrinkage data for use in the

design of prestressed concrete highway bridges is the subject of the

study reported here. The creep behavior of concrete under sustained

stress, such as that of a prestressed beam, is dependent in a large

measure on the aggregates used in the concrete and the humidity under

which it serves in the structure. The designer must know the properties

of the material used in the design in order to determine the creep and

shrinkage effects in the structure. Loss of prestress is dependent on

both creep and shrinkage, and beam camber is dependent on creep. Elastic

strains and other influences are important, but this study is concerned

primarily with creep and shrinkage.

An earlier study (1) investigated creep and shrinkage of prestressed

concrete bridge beams in Houston, Texas. The study reported here is an

extension of that work in that the behavior of other concretes in other

parts of the state is determined. It seeks to determine creep and shrinkage

of concretes made of natural aggregates typically used in four different

areas of the state under climatic conditions of those four areas. The

areas are chosen to represent different climatic conditions. The data

collected are intended for use in the design of highway concrete structures

in the areas studied when they are made of the aggregates typical of those

ar·eas.

Data from field tests are of primary interest here, but laboratory

tests were made for purposes of comparing field and laboratory creep and

shrinkage. If laboratory data are in good agreement with field data, the

simpler laboratory tests could be used in future studies of this kind.

1

The problem of predicting the short time and long time deformational

behavior of a given concrete structure has been the subject of about 1500

research papers published since the turn of the century. In modern bridge

design, where a smooth riding surface is a necessity, the deformational

behavior of the structure must be taken into account. Such deformation is

due in part to shrinkage and creep of the concrete in the piers, beams,

and deck slab of the bridge.

In prestressed concrete bridge beams, camber (upward deflection)

occurs with the release of the prestressing force. That initial beam

deflection is·. caused by elastic strain of the materials. Creep of the

conc~ete, a time dependent strain which is only partially reversible,

causes this upward deflection to grow with time. Elastic, shrinkage,

and creep strains in the concrete cause, and are accbmpanied by, elastic

strains of the prestressing steel which reduce the prestressing force.

The effects of creep and shrinkage strains in prestressed concrete bridge

structures are dependent on such variables as materials, stress level,

environment and other factors which are generally of lesser importance.

Economy requires that materials used in the fabrication of concrete

bridge beams be taken from sources as near to the use area as is practical.

This is particularly true for sand and gravel which make up the bulk of the

concrete. These materials differ from place to place, but variations within

·relatively small areas are not so great as those found over wider areas. The

differences in the composition of materials as well as differences in

climatic conditions contribute to differences in the behavior of concrete.

All of these are of concern in a study of creep and shrinkage.

2

TEST LOCATIONS

There are Home twelve prestressing plants that produce prestressed

concrete beams for the Texas Highway Department. Of thes1", four plants

were selected to represent four geographical areas of the state. The

locations of those four plants are shown in Fiqure 1, climatological

data for the locations were taken from U. S. Department of Commerce

records (2).

A brief statement about each test follows:

Dallas, located in north central Texas, has hot summers with maximum

temperatures of 100°F or higher and relatively mild winters with minimum

0 temperature of about 20 F. The relative humidity at Dallas varies from

approximately 75 percent at 6:00 a.m. to approximately 50 percent at

6:00 p.m.

San Antonio, located in south central Texas, has relatively hot

summers with maximum temperatures of approximately 95°F. Minimum tern-

0 0 peratures during winter months generally range between 20 F and 30 F.

The relative humidity in the San Antonio area generally varies between

approximately 80 percent at 6:00 a.m. and approximately 55 percent at

6:00 p.m.

Odessa, located on the high plains of Texas, has hot summers with

maximum temperatures in excess of 100°F. Minimum temperatures generally

are in a range of 0°F to 20°F. The relative humidity at Odessa varies

from approximately 70 percent at 6:00 a.m. to approximately 35 percent

at 6:00 p.m.

Lufkin, located in east Texas, has relatively hot summers with

maximum temperatures of approximately 100°F. Minimum temperatures for

3

• Dallas

• Odessa

• Lufkin ~

• San Antonio

Figure 1 Location of Prestressing Plants

. 0 Lufkin generally are on the order of 20 F. The relative humidity in

the Lufkin area is generally high, some 70 percent to 95 percent.

TEST SPECIMENS

Specimens consisted of cylinders and prisms of plain concrete. Table

1 gives the schedule of prismatic specimens. Specimens are described below:

1. Cylinders: Standard cylinders, 6 x 12 in., were cast in steel

molds and compacted by rodding. They were used to determine the

concrete strength and stress-strain relationship.

2. Prisms: Plain concrete prisms, 3 x 3 x 16 in., were cast to

determine shrinkage versus time and unit creep versus time. Steel

molds were used with brass inserts 10 in. apart attached to two

opposite 3 x 16 in. faces for later installation of gaging points.

A set of specimens consisted of 4 loaded prisms, 4 non-loaded prisms,

and 18 cylinders. Of the loaded prisms, two were loaded to 1000 psi and

two were loaded to 2000 psi sustained compressive stress. They were axially

loaded parallel to the long axes by a hydraulic jack and the load was

sustained by means of heavy helical springs. During the loading operation,

the load was monitored with a load cell. Figure 2 (a), (b), and (c) show

the concrete prism, gage insert, and steel frame for loading the prisms.

The 4 non-loaded prisms were monitored for shrinkage strains. It was

assumed that the shrinkage of the loaded prisms was the same as the shrinkage

of the non-loaded prisms.

Two sets of specimens were made at each plant location. One set was c ..

stored in open air under protective cover near the place of fabrication and

5

·----~·--~ --~-- --. ··- -

0'\

steel form

screw

DE ~.

I. --r-1 0

10"1 I

I I ~~~

a. concrete prism

E .. b .• Gage Insert for attachment to ins;i.de of

face mold. A stainless steel gage· point· is inserted in place of the screw after the concrete is removed from the mold.

II I I 11 ---- Load Ce 11

fti I ':iM Hydraulic Jack

olll ~6" square plate (typical)

II I I II

II I , LJl---Prism

II I O

Steel helical spring

c. Method for loading

Figure 2 Prism, Gage Insert, and Method of Loading

TABLE 1. SCHEDULE OF TEST SPECIMENS FOR CREEP AND SHRINKAGE

(All specimens are 3 in. x 3 in. in section by 16 in. long)

Source Environment Specimen Number of Specimens Date of of Number Cast

Material Test Shrinkage Creep

1000 2000 psi psi

Dallas Field 1 - 8 4 2 2 9/20/71

Laboratory 9 - 16 4 2 2 9/20/71

Odessa Field 1 - 8 4 2 2 10/20/71

Laboratory 9 - 16 4 2 2 10/20/71

San Field 1 - 8 4 2 2 11/29/71 Antonio

Laboratory 9 - 16 4 2 2 11/29/71

Lufkin Field 1 - 8 4 2 2 1/27/72

Laboratory 9 - 16 4 2 2 1/27/72

7

Date Loaded

9/21/71

9/21/71

10/21/71

10/21/71

11/30/71

11/30/71

1/29/72

1/29/72

the companion set was stored in the laboratory at 73°F, 50 percent

relative humidity.

MATERIALS

Materials typical of the area where the specimens were made were

used at each prestressing plant. Only normal weight concretes were

studied. Table 2 gives information on materials and the mix proportions

used at each plartt. The batches were designed by the Texas Highway

Department for material used in prestressed concrete beams for bridges

in the Texas Highway System.

CURING AND STORAGE CONDITIONS

The curing of the test specimens was the same as for pretensioned

prestressed concrete beams fabricated to meet Texas Highway Department

specifications. At San Antonio, the concrete was cured 24 hours under a

wet mat. It was then covered with an impervious mat for an additional

three days. The plants at Odessa and Dallas utilized steam curing for

approximately 15 hours followed by three days under an impervious mat~

The plant at Lufkin utilized steam curing for 42 hours, to gain release

strength, and three days under impervious covering.

Specimens stored in the field at each site were protected from rain

and direct sunlight. The field stored specimens made at San Antonio were

stored at Boerne, Texas approximately twenty miles from the fabricator

because of a lack of suitable storage space near the fabricator. Those

8

\0

TABLE 2. Materials and Mix, Pounds per Cubic Yard of Concrete

(From information provided by Texas Highway Department)

Cement * Aggregate

Fine

Coarse

Source

Water

Dallas

705 lb Type III

1,219 lb limestone and siliceous sand

1,824 lb crushed limestone; 3/4 in. max. size

Bridgeport

253 lb

* Saturated, surface dry

Odessa

7 52 lb Type III

9 2 6 lb limes·tone and siliceous sand

1,882 lb siliceous and limestone gravel; 3/4 in. max. size

Hoban pit, Pecos

273 lb

San Antonio

658 lb Type III

1,177 lb 70% limestone sand, 30% siliceous sand

1,861 lb lime­stone gravel; 1 in. max. size

Bexar Co., 12 mi. N. San Antonio on IH 10

31.6 lb

Lufkin

705 lb Type III

1,130 lb siliceous sand

1, 777 lb crushed limestone; 1 in. max. size

Angelina Co,, 2 mi. W of Lufkin on State Route 94.

279 lb

specimens stored in the laboratory were subjected to controlled conditions

of essentially 73°F temperature and 50 percent relative humidity.

The creep specimens were loaded at the fabrication site at es­

sentially the same time that prestress was transferred to the concrete.

This was at the end of the initial curing period and prior to the second

phase of curing, that under impervious mat.

10

INSTRUMENTATION

The strength and modulus of elasticity were determined from standard

compression tests on 6 x 12 in. cylinders. The ultimate strength of the

cylinder was determined before the creep and shrinkage specimens were de-

molded. At the Lufkin location, the specimens remained in the molds for

42 hours before the required strength was obtained. At the other three

locations the specimens were demolded approximately 20 hours after casting.

Subsequent eompression tests were made in the laboratory. Four Ames dial

-4 gages with read.ings to 1 x 10 in. were mounted 90 degrees apart on the

compressometer from which strains were read during the loading of the

compression cylinders.

Brass inserts were attached to the steel molds by screws before cast-

ing the concrete. After removing the forms, stainless steel heads were

screwed tightly into the inserts. Each gage reading reflected the relative

position of the reference points drilled into these heads. The first

strain reading minus the standard invar bar reading was taken as the datum

to which all other strains were referred. Special precautions were taken

to see that the first reading was verified because that reading served as

the datum to which all subsequent strains were referred.

Strain measurements from the 3 x 3 x 16 in. prisms were made with a

multi-position 10 in. mechanical gage from which readings were taken from

-4 an attached dial gage reading to 1 x 10 in. The standard (reference)

readings were taken from an invar bar at each time a gage reading was recorded.

11

--~------~-------

The specimens were gaged on two opposite 3 x 16 in. faces and the

strain at any time was determined by averaging the strains from the two

opposite faces. Initial readings were made on each prism as soon as

possible after demolding. Readings from the creep specimens were taken

immediately before and after loading in the creep frames. Thereafter,

readings were taken each day for three to seven days, then weekly until

the end of one month, and monthly for the remaining period. One set of

the specimens was transferred to the laboratory on the day of loading with

one exception. That exception, the Odessa concrete, require more time

for transfer from the casting yard to the laboratory because of the long

travel distance.

12

RESULTS OF TESTS

This section presents the results of the tests described in the

prevJous section. The measured strains, relative humidity, temperature,

and mechanical properties data are presented in tables and graphs that

follow.

Mechanical Properties

Eighteen standard 6 x 12 in. cylinders were prepared with each set

of shrinkage and creep specimens. Those cylinders were used for deter­

mining the concrete strength and modulus of elasticity at release, 7, 28,

90, and 180 day ages. The cylinders were stored with each set of shrinkage

and creep prisms until testing.

The materials for the four concretes included in these tests satisfied

the Texas Highway Department specifications for normal weight prestressed

concrete. The strength and modulus data, average slope of the stress­

strain curve between 500 psi and 2500 psi, for the concretes are presented

in Table 3. Within that stress range the slope of any one diagram was al­

most constant. The strength and modulus of elasticity for each location

was about the same for field storage as for laboratory storage. It is

interesting to note that the modulus of elasticity of the Odessa concrete

was lower than that of the concrete from the other three areas.

Elastic strains may be found by dividing the stress by the modulus

of the elasticity at release.

13

Concrete ·from

Dallas

Odessa

San Antonio

Lufkin

*Average of 2

TABLE 3. Concrete Compressive Strength and Modulus of Elasticity

Storage Conditi.ons Field* Laboratory*

Age, Strength Modulus Strength Modulus Days f', psi E , ksi f', psi E , ksi c c c ·c

release 7;080 5,200

7 7,400 5, 710 8,230 5,400

28 8,490 5,270 9,015 5,310

90 8,970 5,4~0 8, 710 5,370

180 8,800 5,310 8,650 5,340

release 5,050 3,260

7 8,380 4,180 8,130 4,650

28 8,740 4,020 8,530 4,350

90 8,900 4,320 8;530 4,820

180 8,660 3,660 8,600 4,270

release 5,250 4,220

7 7,560 5,370 8,020 5,650

28 8;710 5,400 8,500 5,680

90 9,270 5,250 8,320 5,430

180 8,710 5,850 8,500 5,480

release 5,760 4,440

7 6, 710 5,320 7,080 5,050

28 6,770 5,130 6,840 5,020

90 7,530 4,740 7,960 4,400

180 7,420 4,520 1,350 4,550

cylinders 14

... ,

SHRINKAGE

Shrinkage strains are shown graphically in Figure 3 and certain

tabular information is found in Table 4. All of the four concretes. show

considerably more shrinkage in laboratory environment (73°F; 50% RH) than

under field conditions. The Odessa material has much higher shrinka~e in

both field and laboratory than any of the other three. Dallas and San

Antonio material have the same laboratory shrinkage, but the latter shows

more field shrinkage than the· former. Since the laboratory reduces all

materials to the same environmental conditions the difference between the

field shrinkage of the Dallas and San Antonio material would indicate that

the humidity in the vicinity of San Antonio was lower than that at Dallas

during the period of the test. The data presented in Figure 4 at first

sight would not.support that conclusion, 'l'he temperatures and relative

humidities shown in Figure 4 represent the conditions only at the time

that; strain readings were taken from the specimens. Those readings were

taken at one·month intervals and the points plotted in Figure 4 should not

be taken to represent the continuous trend of temperature and relative

humidity. They are, at best, indicators of seasonal variations and cannot

be interpret~d as prevailing conditions at the field storage sites and

should not be used to interpret the effect of climate on shrinkage.

The ratios of field shrinkage to laboratory shrinkage for the four

concretes in the small specimens of these tests indicate that the field

conditions at Odessa combine to produce shrinkage strains more nearly the

same as its laboratory strains than any of the other concretes. The ratios

shown in the table might be used to convert laboratory shrinkage strains of

15

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1 ~----... ---·---.. _ .... ! i

l .f;'>

·- "' '• -I' • ~---.1116- ~-....._

IOOOpsi ----""1:-- --. 1---....a..-l ... ~--~- .... -- ---~· I .... I LUFKIN --LABORATORY STORAGE I

i --- OPEN AIR STORAGE

I .A

~RINK~§..E~ =

! A. ... -r- ~. :-.--.:\ ----+------- ..... -- --- ~---.t.-...J-t.. ..... - ' '

... -- ----- - ---- L__---~-·- ----------- - --- -----j__,

0 50 100 150 200 250 300 ~0 400 450 500

AGE- DAYS AFTER LOADING

· FIGURE 3- CONTINUED

550 600

2600

2400

2200

2000

1000

~ ~ 1600 0::: .5 t- CD 1400 w,

0 ...... ::::;.1200 00

1000

800

600

400

200

T l .i I I ' ~ I 1 • " .... - --- !------.J ------

. ---I ... ~ i -· ·- ... i

__ !_ ---..~~'

.. -- /· T ~--, - l .... .,. .. I ,,_ .. ,"' 2000ps~L I i

I"' "' ~ : ~ !

I .. ~ p-~. ' I ~- .... ~ I I ! I --.· .... -- I ... ..;,_ .... _ ~ ;." ~ 1tooopsi.·1 7\ - ·~· --b.---- -"' --":- ""' : -v -.. / ,,--j_'""'- . .. '

~T -- I f/ ____ ...

' ,t--""4 1-' . i

~ ....... 1-' ; " .

. I

f.v- ~;-· ODESSA i ! ..... - LABORATORY STORAGE I

.-f/ ---- OPEN AIR STORAGE ; I

l J 650~- !SHRINKAGE I \. 7' .,. .A 20+T

__ "'-lloc.":. .:::_ - 1-c:-::: - -::;1...: ~- l --... _ ~:: ............. ~ F-=--:.r---: i------ ~~-_,. --· -- ~ ... - ""fi. -~-~ -+-- -- -· _.

--::~ ' , ...... ,...,..,...' --& i

~r ...... \ 525T i ...

IO+T l ' ,. ! I I i ' I ' -- --- j ___ ____,____f____ __ ----- --0

0 50 100 150 200 250 300 . 350 400 450 500 550 600 650 AGE -DAYS AFTER LOADING

FIGURE 3 - CONTINUED

1'-' \0

e TEMPERATURE

• RELATIVE Hl.NIDITY

I I

' r· 1. 100 J>-----+----1

so~ • . . ·. . . • r • I I I

60 =·i~ l 0 * ~ : ~~ : t ·~ :; ~ :- ~ ~ 4 ! 0 3 cr

0 0

: .. .. 40' • I 8 •

... .. ... 20

0 50 100 150 200 250 300 350 400 450 500 550 600 650 /JGE-OAYS

~0.---,---.---r---.---,---,---~----------------.-----~----,------

!ODESSA I ~ TEMPERATURE 00 ~

... 0 " 80 0

" ...

U : r:. I. ~I · I ·1 : ·I . i ! ~ · i : : . . . -cs o ~~·

200 300 350 500 550 400. 600 650 /JGE-DI!.YS

~~ ~!!;! 120 ! 1 . . ' ~~ I I I ! i il ' ' a <li 100 ... ... . I ~ : t-iil Pl. ... 0 ... ,

a:ao.- o ".. . 0 0 0 - .. '

•e • I • • 60 0 • T i0 . •

00 .a 0 .. e ,

iil

40 l:ioERNE 0 TEMPERATURE I ... 0 I ... ... ... • RELATIVE HUMIDITY

20 0 50 100 150 200 250 300 350 400 450 500 550 600 650

~-DAYS

120

100 0 0

0

_a - 0 I '-'! o "' ' ; . • 80 L ' I I ' ... i 0 "'i .. " p I •

40 ~g• "' I : ! ., '

0 TEMPERATURE 60~~--t·--~+~~---~~·~i-+---11 ___ ... __ ·~·"'~--r----t----r·~=Y~•n_ .. ~~J • RELATIVE HUMIDITY

5o 100 150 200 250 ~ 350 400 450 500 550 600 PGE:-DAYS

FIGURE 4- TEMPERATURES AND RELATIVE HUMIDITIES AT TIME OF READING AT FIELD LOCATIONS

650

specimens of the size used in these tests to what might be expected of

them in the field.

Hansen and Mattock (3) have reported a linear relationship between

shrinkage strain and the ratio of the volume of a specimen to its surface·.

area for specimens of various sizes and shapes stored under laboratory

conditions. This would lead to a greater shrinkage in the small specimens

of these tests than would be realized in a full size prestressed beam of

normal shape and dimensions such as is used in bridge design. The tests

performed on field concrete and reported in Ref. 1, however, showed greater

shrinkage in a short length of a full size beam section than was found in

the 3 in. x 3 in. x 16 in. specimens in storage in open air at Houston,

Texas. The local daily and seasonal climatic changes seem to have con­

siderable bearing on shrinkage behavior •. Until more information is developed

on the relationship-between field and laboratory strains, the ratios shown

in Table 4 might be used as indicators, at least, of what might be expected

in the field if laboratory behavior is known. From the experience gained

in the present series of tests and those reported in Ref. 1, it appears that

field strains from the small specimens can be used for design purposes for

full size prestressed concrete bridge beams.

The shrinkage =unctions shown in,Table 4 are intended for use ia

computing camber and prestress losses in prestressed beams. They are

explained later in the section entitled Functions for Creep and Shrinkage.

20

TABLE 4. Shrfnkage and Unit Creep at 500 Day Age and Continuous Shrinkage-Time Functions

Shrinkage

Field Storage Laboratory Storage Ratio: Source Shrinkage Function Shrinkage Function Field to

... 6 -6 Laboratory (10 in./in.) (10 in./in.) Shrinkage

Dallas 300 315 T 480 500 T 0.62 20 + T 1.5 + T

Odessa 510 525 T 620 650 T 0.82 10 + T 20 + T

San Antonio 360 380 T 480 500 T 0.75 25 + T 20 + T

Lufkin 280 290 T 430 450 T 0.65 25 + T 25 + T

Creep (lo-6in./in./ksi) ·

. Ratio: Field to

Source Field Storage Laboratory Storage Laboratory Creep

Dallas 390 340 1.14

Odessa 630 500 1.26

San Arttonio 360 370 .97

Lufkin 430 360 1.20

Creep Coefficients creep strain t elastic strain

Dallas 1.81

Odessa 1.70

San Antonio 1.60

Lufkin 1.89

21

CreeE of SEecimens

Creep curves .shown in Figure 5 are derived from measured strains ·shown

in Figure 3. Elastic strains and shrinkage are subtracted from the total

measured strains of Figure 3 to produce the creep curves. The periodic

variations seen in Figure 3 are primarily seasonal changes, and when they

are taken away, the curves of Figure 5 are smoothed out very much.

The ratio of sustained stress to ultimate strength for all the concretes

ranged from a minimum of about 12 percent to a maximum of about 40 percent.

Various experimental results show substantial evidence of a nearly linear

relationship between creep and applied stress (4). An upper limit for the

stress-strain ratio somewhere in the rather wide range of 30 and 75 percent

has been suggested. The stress-strength ratios in these tests, using the

strengths shown in Table 3, fall within that range.

Among the field tests, the San Antonio material shows a consistent

linear relationship of creep to stress in that the 2000 psi creep is twice

that of the 1000 psi concrete, Figure 5 and Table 5. No other material,

field or laboratory stored, shows such good linearity. The ratios of creep

shown in Table 5 for Dallas, Odessa, and Lufkin concretes would suggest

that the sustained stresses in those materials did not bear the 2 to 1

ratio either from the beginning or that the ratio was reduced during the

test period.

During the test there was never any question about the initial stress

value because of the care that was taken in applying the initial load. When

the specimens had been under load for approximately four months, the loads

on all field specimens were checked. At that time, far more than one-half

22

N w

a.. c: w ·-w ........ 0:: c: u ·-U>

I 0

1400

1200

1000

800

600

400

200

0

-1400

1200

1000

800

600

400

200

0

,;,

1 I ! !. ~ ! : ! J I I! l ! . I ~ ! I

I !I ~ I I ; : ' ' 1 : j ' i j ' I I . I ' I I

i i ' \. I '• t I I' i I . . ' : t I

I \ i :, i I ' i i

! ! I ' '2000psi I I ' ~ ~- , •- - , i 1 l '. /1 , --'--~~;:--=-- "' . -· . LJ I .. , - : . ' I - - ~ I j' j' . . . , "'f-.;.... --,.- . .- -• ' ' . i : _ _, _- ; - I I i I - - I ;: II r: I L ~ - I 1 .

• I . . ' - r---e - 1- I - ·-.--.---~--~ -- .... ~ :A ! ' -~~--'- " .. .:. i

7 ,..,. . -~-~ 1 • • -LA. BORA10RY STORIIGE' I Pal ~- l 1 ·

· 1" -. - ~ ~ • 1000 psi l · SAN ANTONIO -~-oPEN AIR STORAGE ~---- I I . I . .

0 50 100 150 200 250 300 350 400 450 500 550 600 650 AGE- DAYS AFTER LOADING

I

I IL, -• I J ~ I -a - ~- --.---11;- ... I 1 l

-- _.. .I ! _ ... - , ! I I

- • I . J,-B - 2000 PSI j · . 1 ..

... ..r-1. .J:L .. j - i __ ... __ • ""e , ----+-- .... _ _._- r _ _ ... - ~I _. _____ ,-.. -~- -'-. . . . '

,. ~ ! I ! -" _,--r : - : ; l' ~ -=---:::.<~ _\ ' ' l !

I ~r" ' jiOOOpsi ' ' LABORA10RYSTORAGE ' ~ . ! OOESSA ---OPEN AIR STORAGE I -7 !

0 50 100 150 200 250 300 350 400 450 500 550 600 650 AGE- DAYS AFTER LOADING

FIGURE 5- CREEP vs. TIME

a. c w'= w c:

....., 0:: ·­

.j::o. u tO

6

1000

800

600

400

200

0

.:::; 1000

800

600

400

200

0

I I

1 1 !

I I '

-- L •. i: _ ...... - i !

-,--. . -~- I 1 ·r ! i

: __ ..... i"' --,;---1 r-.;oo~;ii I t:1 J r-1 ' ~ ~

1r.L . I I I

~ i ~ ! ~ l , ... =---- I

~ --- - ~

~;WFKI~ - - i

r---.. - -·--- I

IOOOpsi- - LABORAlORY STORAGE I

I i

~, J ' ---FIELD STORAGE -~ !

i I l I 0 50 100 150 200. 250 300 350 400 450 500 550 600 650

AGE-DAYS AFTER LOADING

i

2000 psi ~ ------ .IIi------- ____ ... ------ r-- _ .... _- _ _._ ---l

-·-- . ~ ~- - "" . . !

~-'CJ

1000 psi I I --· -~....-"" ~ ..._ - .e-----~4 .... _ ... ·----- ... - -·- -i ... -- ...

·-~ :b- _ _. __ - ...;.-...:-

"' . -

~

~-~ ' , .. DALLAS LABORATORY STORAGE ' -~ I

~- ---FIELD STORAGE ! 0 50 100 150 200 250 300 350 400 450 500 550 600 650

AGE-DAYS AFTER LOADING

FIGURE 5 -CONTINUED

of the creep at termination had developed. The helical springs used in

the loading frames have spring rates of 10,000 and 18,000 pounds per inch,

respectively, for the 1000 psi and 2000 psi specimens. The computed stress

loss in the 1000 psi specimens was about 2 percent of the initial and 2.2

percent in the 2000 psi specimens. The load check indicated losses of ap­

proximately 20 psi in both the 1000 psi and the 2000 psi specimens, the

discrepancy being due to imprecise portable measuring equipment. Adjust­

ments were made as nearly as possible to meet the theoretical losses.

The load adjustments discussed above fail to account for the low

ratios of 2000 psi creep to 1000 psi creep for Odessa and Lufkin laboratory

stored concretes. The corresponding ratios for the other specimens, both

field and laboratory, approach the expected value of 2, although none reach

it. All data and procedures have been studied in an effort to exPlain the

unusual behavior of the Lufkin and Odessa laboratory materials. The

possibility of friction having developed between the horizontal bearing

plate, that separates the specimen from the spring, and the vertical tension

ties was suggested. Test frames were inspected for that possibility, but

they were not broken down because to do so would have destroyed the test.

No conclusive reason has been found to explain the trouble.

The 1000 psi field values agree well with the corresponding l~boratory

values. On the basis of the data appearing here, one could develop creep

data from 1000 psi specimens, which are relatively easy to handle, and use

it for unit creep values to be used in design.

Unit creep curves, creep divided by unit stress, are shown in Figures

6 and 7. The same information is shown in both the figures; it is just

arranged in a different way for comparison of values. Figure 6 shows the

field stored concretes in one set of curves and the laboratory cured

25

N 0\

800 I r I I • J ,, I ! ! I ! I 600 • l ' ' I I'OOOpsin ! r - i i_

400 J .,. . . - -. ___ ;.. __ -:·· -..---- - -- - -...o=--..:.---re- - · : 1

200 ~ =--- . \ ' . i . 1~ r i ; \ I \_____L:4.40 T DALLAS FIELD !t:_ ~ l l2000psi+----:-l i 1 60+ T

0 0 50 100 150 200 250 3>0 350 400

I 450 500 550 600 650

AGE-DAYS AFTER' LOADING

800.-----.---~.-----,------,-----,----~------------.-----.------r-----.------------

n.·;;; w-"' w ....... a:c: u:;:::

] 600 t . 1

. i i . . . . - --- ___ ,;._-±.--.:. -400 OOOpsi! · · -~- -~- -- -- --- - ---- · 1 ~ -- ·, - - ' ! ' 200~..;.. .l \ I' i 365T !DALLAS-LABORATORY

- · · · . ~ · 40 +T · ~ I · . 2000--E..l. I I ' 0 ..________ .

0 50 100 -150 zoo 250 300 350 400 450 !

500 550 600 AGE -DAYS AFTER LOADING

t- .s 800 -w ~g 600

1000 psi-r\ I j 1 -"ll-o

I - --i

400 l . -

I i 675T i

I

--.;i:::::: ~ I

\ 40±1:-:--i

i

==-------' ~ ~ i

I ~ !'""" I l

!

zooo . ' :ODESSA FIELD !?'/ i

' •' 200

00 500 600 250 300 350 400 550 450 150 200 50 100 AGE-DAYS AFTER LOADING

800 1000 psi+--. 1 , , . . _L_ ~ . ! I ! l : I I :

1 . \ . . • I

I 4 . . · :::y - ::1:': __ ._.,. -,._-.::--- ------1------~-------r- - -r- ---- I ~ ~~~:- ,-.. \ ~ I 1 . i ! -- I - --;--· r- p \ 525 T ! ' !

2000 psi- L_ ___ ~_+!___1_ fDESSAjLABORtTORY 1

600

400

200

00 600 250 300 350 400 AGE..:_DAYS AFTER LOADING

450 500 550 50 100 150 200

FIGURE 6- CREEP CURVES FOR THE FOUR CONCRETES

650

~

~

650

650

N "-J

600

400

200

0 0

600

400

~ 200

~ 00

a..:::­w UJ w.x 0:: ': 600 u.s .

......... !:::: c. 400 z ~-::::> 0 200 -

0 0

-

i ~-~-L~

50 100 150 200 250 300 350 400 AGE-DAYS AFTER.LOADING

I 385T : i ! ' l 1

I 25+T0 ., i i i

2000psi ..A.--- J_ . ..;. __ ..;._~ -· . '. -I

"', (') i ;,..- . "! 0 :"' I ---~ 1000 psi::::. I I SAN tNTONIOt LABORATORY

i j

50 100 150 200 250 300 ·350 400 AGE-DAYS AFTER LOADING

1000 psi I

i

! !

50 100 150 200 250 300 350 400 AGE-DAYS AFTER LOADING

' I

I

450 500 550 600

-~ - ---~ "' r'-' <:J ~_,

I I ___ L ___

450 500 550 600

I I

450 500 550 600

600.-----.-~----------,---~.------.--~--.-----,------.------.-~~,---~-.--~~

~~ ~ t t i : 400 1 11000 p~ ·~ c · 1::-___ :_.-:j ____ ~-~-!---~- .. :--w-~ 1 '

2ool ~~~ .. I II ·-~~! I I 1 I I I i :

00 150 250 300 350 400 450 500 550 600

AGE -DAYS AFTER LOADING

FIGURE 6- CONTINUED

N 00

8oo .-- I ~ , . 6oo I ' i '

l I , I I . "

400 . -- _-:::i;::::---: ,_ ---r-- . - ---, --'==- -=---=-- ------ 1- _.._ - -

I .-.- ·- - -· -~-- -~- , r 200 =--~ ~--~- ' . I ~ DALLAS FIELD IOOOps~ --LABORATORY 1000 psil if'r ---FIELD 2000psi ----LABORATORY 2000psil 0 . 0 50 100 150 200 250 300 350 400 450

AGE.-DAYS AFTER LOADING

800 i

600 ---- -- -- -\

. 400 - ---- ---- ----

200 ~

a. ~ 0 0 ttl~ 0::: ·-OE !::: <0 800 Zb :;).:=,

600

400

----

50 100 250

I l l

---::

__ _j_

200 250 300 350 400 450 500 550 AGE-DAYS AFTER LOADING

I ! ~ ~ l ! l i I

l I I I i ' I ~- I I -r -- ____ ,_ __

I --~----- i

C_ SAN ANTONIO r FIELD 1000 8 2000psi I I i

L_ __ ___l__ '( ---LABQBATQRY IOQ_QJl2000 osi L__ ___ ~i ____ ---~ --·--

200

0 0 50 100 150 200 250 300 350 400 450 500 550

AGE -DAYS AFTER LOADING

800

600 I T T i ' I

i J l -1 ·--i· - = -----=-:::-~ +' . . T -- ---- ----- -,..... .... ~ ---- ----t----1 --- --v LUFKIN - RELD 1000 6 2000 psi--LABORATORY_ 2000 ~

--LABORATORY 1000 psi -----" ~--- ~~ i

400

200

0 0 50 100 150 . 200 250 300 350 400 450 500 550

AGE-DAYS AFTER LOADING

FIGURE 7- CREEP CURVES FOR 1000 AN 0 2000 psi STRESS

I

600

'

--

600

;

600

650

'

650

!

i

650

TABLE 5. Ratio at 2000 psi Creep to 1000 psi Creep at 500 Day Age

2000 psi Creep • 1000 psi Creep Material Field Storage Laboratory Storage

Dallas 1.62 1.65

Odessa 1.80 1.38

San Antonio 1.93 2.00

Lufkin 1.84 1.48

Average 1.80 1.63

concretes in another set of curves. This is done for each source of material.

Figure 7 shows one set of curves for each location. That one set consists of

the two field curves and two laboratory curves. 'l'he scales of the unit creep

curves are reduced so much, when total creep is divided by unit stress, that

the differences seen in previous curves appear to be greatly reduced. Such

an effect is generally seen when data are reduced for design applications,

and it has the effect of minimizing differences in measured data.

The expression of creep as a function of unit stress and of time is

useful to the designer in predicting camber of beams and in estimating pre-

stress losses. Such information can be taken from curves, such as those

shown in Figure 6, or it can be expressed mathematically. The latter ex-

pression is mote useful in design and it becomes especially so when designs

are automated by means of the computer. The mathematical expression becomes

simpler if a linear relationship between creep and stress is used. Such

29

a relationship is assured in the San Antonio material of these tests. The

average of the ratios of 2000 psi creep to 1000 psi creep is seen to be 1. 80

for the four field concretes, Table 6, and the corresponding iaboratory

material ratio of 1.63 would be raised considerably if the Lufkin and Odessa

2000 psi laboratory values were discounted.

Figure 8 shows three of the four creep curves for laboratory

stored specimens to be about the same, even though the specimens were made

from different materials. It is also interesting to note from these curves

that the creep curves obtained from the field stores specimens is very

nearly the same as for laboratory stored specimens. Mix designs, Table 2,

are similar, as would be expected because of highway specifications, and

differences seen in creep and shrinkage would probably be due primarily to

the different aggregates used in the different locations. The Odessa

concrete contained the highest cement content, however, the paste content

for the four mix designs is very nearly the same, approximately 30 percent.

Consider the average unit creep observed in the laboratoryfor the

four different concretes. At 500 days age, values of approximately 340,

500, 370, and 395 (10-6 in./in./ksi) are noted from Figure 6 average curves

for the respective locations, Dallas, Odessa, San Antonio, and Lufkin. For

these specimens in the laboratory, the temperature and relative humidity

were the same, the stress levelsT·r;rere essentially constant, and the;paste

content of the mixes was approximately the same. From these conditions then,

it could be reasoned that the aggregates in the mixes would be responsible

for the differences in the magnitude of creep. Neville (4) states that of

30

w ......

'i·

800 I I [i.

r ! li !I

li I _.L--+---j -- -·----· ~-:---- I. l J 1: f, - . i ..... ' 60Q

400 . ....--- ...... - -::::=-:- . ......_-:::;::..:::-- __ ..... -- -t --- --- 1-------~:------~---- !-·

' f !: ~ / ---200 ~·

0 0

--oDESSA L~~N , il --DALLAS ---SAN ANTONI FIELD-1000 psi;

- -- . ll ' 50. 100 150 200 2 50 300 350 400 450 500

AGE-DAYS AFTER LOADING

800 I I I !

-~~ -~ - - r--:___.--f---1------r--- t=_ -= - - -- - -- i ......... - - ---- -

I - -' ,' ..... -I"""

600

400

200

Q. = 0 ~ --oDESSA

DALLAS LUFKIN LABORA

1TORY tpoo psi -- SAN ANTONtO

LL1 -= 0 w, 5~ !::: {D- 800 Zb :::::>_

........ 600

400

200

50 100 150 200 250 300 350 400 450 500 AGE-DAYS AFTER LOADING

I -- ----------- 1---- -- ---- -- -::;_.:..-:-. --- =----·= - --- ·==~---F , --------

-+-- l -1-- !' I

r I -l -- ·: I

I I I 550 600 650

---

550 600 650

- -

~ --- r---oDESSA LUFKIN FIELD 2000psi. -DALLAS ---SAN ANTONIO _ I ___ - .___ -- L- - _,__ -- -- ---0

0 50 100 150 200 250 300 350 400 450 . 500 550 600 650

AGE- DAYS AFTER LOADING

800

! I I

; I

600

- - ---- - ------ ------1-----:=l=~-- ------ -- - -·--_..,.:::::'! --::::;::= t=-.::.==:= t:=.--==--=-=------ - I

-=----ODESSA LUFKIN LABORATORY ~000 PSI ~('~ 1-"

i ~ DALLAS --- SAN. ANTONIO . i

400

200

0 0 550 600 650 450 500 150 200 250 300 350 400 50 100

AGE-DAYS AFTER LOADING

FrGURE 8- CREEP CURVES FOR THE FOUR LOCATIONS

all the physical properties of aggregate which influence creep of concrete,

the modulus of elasticity of the aggregate is probably the most important

factor. The higher the modulus the greater restraint offered by the aggregate

to the potential creep of the paste. It is seen in Table 3 that the Odessa

concrete had a lower modulus of elasticity than the other concretes. This

means that more strain, or deformation, occurred per unit of stress for

the Odessa concrete than for the other concretes. It is probable that the

Odessa aggregate had a lower modulus of elasticity than the other aggregates

thus making it an important factor influencing the creep of that concrete.

!t is not possible to distinguish separate effects of temperature or

relative humidity from the limited weather data. It is noted, however, that.

~he total effect is of primary interest. Now,if a comparison of creep values

at ·sao days is made between specimens from the same concrete, but different

storage environments, it should be possible to see the effect of the environ-

ment on the creep of that concrete. It is seen from Table 4 that the creep

values from a varying environment of the field are greater than the creep

values at a constant environment of the laboratory. Storage location had

little effect on creep values of the San Antonio concrete which indicates

that the environment of the field storage location was about the same as the

laboratory. In contrast, it is seen that the creeps from field stored concrete

at Dallas, Lufkin, and Odessa locations were increased approximately 15, 19,

and 26 percent respectively, over companion laboratory stored specimens.

Hansen and Mattock (3) recognized that a changing humidity, as encountered

in the field, will cause greater creep than will a constant condition of

humidity.

32

The creep coefficient of a concrete, ratio of creep to elastic strain,

gives the designer useful information about long term behavior of the material

under load when its elastic behavior is known. The coefficients shown in

Table 4 were found from data in Tables 3 and 6. The modulus of elasticity

of the materials at release were used to determine elastic strains, and these

strains are relatively high because of the low moduli at the very early age

of release.

Functions for Creep ~ Shrinkage

Several methods have been proposed for the prediction of creep and

shrinkage for design. Reference 5 contains an excellent discussion on

prediction of creep and shrinkage.

Hyperbolic functions are easily developed to represent measured creep

and shrinka~e data and they readily lend themselves to computer applications.

Such functions have been selected to represent the data collected for this

report. The functions have the following form:

where

e:oo sh

T

A

e: cr

e: = sh

= shrinkage strain,

= maximum shrinkage strain to which e:sh

approaches asymptotically,

= time in days since measurements began,

= constant, approximately the time required for

e:sh to reach one half e:~h ,

= e:oo T cr

B + T

33

(1)

(2)

where

e = unit creep strain, cr

goo = maximum unit creep strain to which e cr cr approaches asymptotically,

T • time in days since application of load,

B • constant, approximately the time required

for e to reach one half e cr · cr

The functions have been developed for both shrinkage and creep curves

in the form of equations (1) and (2) and are summarized in Table 6. The

hyperbolic functions show the similarity in creeps of the Dallas, San Antonio,

and Lufkin concretes and that similarity can be seen in the curves. However,

there is enough difference in the curves as to affect the results of computed

camber based on these functions for shrinkage and creep. Sinno (6) stated

that unit creep strains influence camber growth directly and need to be

estimated within± 35 x 10-6 in./in. to have an accuracy of± 0.1 in. of

maximum computed camber.

The step-by-step method used in References 1 and 6 has been

used with creep and shrinkage functions of Table 6 to make predictions of

maximum camber. The beam used for the predictions is a 56 ft long simply

supported Texas Highway Department Type B beam with thirty-two 7/16 in•

diameter prestressing strands tensioned to 18.9 kips per strand. No ex-

ternal load is applied to the beam. Those predicted maximum cambers are

shown in Figure 9. It is seen from that figure that the camber predictions

34

~

3.0 ! I I

' I I [ I ' I i I I i l I ' I ___ ..j. _____ - __ ...., - - ·r- -2.0

1.0 ~ l l J--- FIELD. DATA USED FOR PREDICTIONS I f ' v I DALILASI- LABORATORY DATA USED FOR PREDICTIONS J I i l

50 100 150 200 250 300 350 400 .AGE-DAYS AFTER LOADING

450 500 550 600 00

3.0 I

~--~- -----. ----- ·----- -----l-----+--- --1----- ----- ----..f

~ 2.0

c I.Q

0: 0 0 LLI m ::E <(

u 3.0

2.0

-----

50 100

~ ----- ---1.0 -r

0 0 50 100

3.0

2 . .0

1.0 ~-...

0 0 50 100

I

I : 1--- FIELD DATA USED FOR PREDICTIONS l i

oo~rsA 1·- LABORATORY DATA USED FOR PREDICTIONS I I 150 200' 250 300 . 350 400

AGE -DAYS AFTER LOADING 450 500 55.0 GOO

!--~ FIELD DATA USED FOR PREDICTIONS )r-S~N ANT,IO l- LABORATORY DATA USED FOR PREDICTIONS.

150 . 200 250 300 350 400 450 500 550 600 AGE- DAYS AFTER LOADING

I 1 ! - --- _ _. - -I r--- FIELD DATA USED FOR PREDICTIONS l

LUFiKIN 1- LABORATORY DATA USED FOR PREDICTIONS! l 150 200 250 300 350 400 450 500 550 600

AGE-DAYS AFTER LOADING

FIGURE 9 - PREDICTED CAMBER OF. THO TYPE B • 56 FOOT SPAN PRE­STRESSED. BEAM USING METHOD OF REFERENCE 6

will vary depending upon the creep and shrinkage functions used. Camber

predictions based on laboratory data were practically the same as those

based on field storage for the San Antonio concrete. Similar comparisons

of predicted cambers at Odessa, Dallas, and Lufkin show that the cambers

based on functions from field data are approximately 13, 12, and 10 per-

cent respectively greater than cambers based on functions from laboratory

data.

TABLE 6. Summary of Functions for Shrinkage and Creep

Concrete Producer FIELD DATA LABORATORY DATA

Location shrinkage Creep Shrinkage Creep

Dallas 315 T* 440 T 500 T 365 T 20 + T 60 + T 15 + T 40 + T

Odessa 525 T 675 T 650 T 525 T 10 + T 40 + T 20 + T 25 + T

San Antonio 380 T 400 T 500 T 385 T 25 + T 50 + T 20 + T 25 + T

Lufkin 290 T 460 T 450 T 430 T 25 + T 50 + T 25 + T 45 + T

** Houston 350.T 225 T

6 + T 15 + T

* T - Time in days

** Data from Reference 1. Beam L3-5

36

;\

~

('·

The difference in material and cyclic differences of relative humidity

and temperature at the various locations determine values of parameters in

the parabolic functions which appear in the creep and shrinkage functions

used in making the camber predictions. The range, minimum to maximum values

from Figure 9, of the mid-span camber presented in Figure 10 reflects those

differences. Also shown in Figure 10 is the predicted and measured camber

for beam L3-5 of Reference 1; · a 56 ft long Texas Highway Department Type

B beam. It can be seen from Figure 10 that the use of creep and shrinkage

data developed in Houston, Texas to predict camber for a similar beam made

artd stored at any of the locations reported here could underestimate the

camber by as much as lOOpercent. Thus it is seen that materials and

environment can have a great influence on camber prediction of prestressed

concrete. bridge beams. The designer should have information on the particular

materials used in the design as well as the behavior of concretes in the area

of installation in order to make close predictions of the service behavior

of the structure.

37

-c 3.0

-2.0

a::: w

.w m 1.0 QO ~

<:( (.) 0

0 50

MID-SPAN CAMBER FOR BEAM l3-5, REFERENCE 6, IN HOUSTON,TEXAS ENVIRONMENT ......... BOTH MEASURED AND PREDICTED

100 150. 500 200 250 300 350 400 450 550 600

AGE DAYS

FIGURE 10 - RANGE OF CAMBERS FROM FIGURE 9

'.>

CONCLUSIONS

This research was undertaken to determine the influence of materials

and environment, typical of four geographical areas of Texas, on creep and

shrinkage of plain concrete. Tests on specimens designed for collection of

time dependent Strains of loaded and non-loaded concretes were collected to

reach the objective of this research. The shrinkage strains were measured

for non-loaded 3 x 3 x 16 in. prisms. The total strains,· measured from.

prisms loaded parallel to their axis, were used to determine the creep

strains by subtracting the elastic and shrinkage strains and dividing by

the applied stress.

Duplicate sets of specimens cast at Dallas, Odessa, San Antonio, and

Lufkin were made and cured alongside pretensioned prestressed beams fab­

ricated for the Texas Highway Department. One set was stored near the

place of fabrication and the other set stored in the laboratory at 73°F,

SO percent relative humidity for the duration of the test.

Conclusions

On the basis of test conditions and results reported herein, the

following conclusions may be made:

1. Climatic conditions under which concrete is stored influences

both creep and shrinkage.

a. Shrinkage of specimens stored in open air at (or near) place

of fabrication was not as great as that of companion specimens

stored in the laboratory under conditions of constant tem­

perature and relative humidity according to these ratios:

39

Place

Dallas

Odessa

·San Antonio

Lufkin

Ratio: Field shrinkage/Laboratory shrinkage (at 500 day age)

0.62

0.82

0.75

0.65

b. Creep of specimens stored in open air at (or near) place of

fabrication was greater in three out of four cases, than that

of companion specimens stored in the laboratory under conditions

of constant temperature and relative humidity according to these

ratios:

Place Ratio: Field creep/Laboratory (at 500 day age)

creep

Dallas 1.14

Odessa 1.26

San Antonio 0.97

Lufkin 1.20

2. Computations for camber of prestressed beams, using the method

discussed in this report, should be based on creep and shrinkage

data from concrete made from the same materials and stored in the

same area as the structure of which the beams are to be an integral

part.

3. Shrinkage and unit creep may be expressed as hyperbolic functions

of time.

40

Recommendations

In computations for prestress loss and camber of prestressed beams,

creep and shrinkage should bedetermined as nearly as practicable for the

concrete and location of the structure. Information on the materials used

in the concretes of this study is contained in Tables 2 and 3 of the report,

and the locations are given 'for sources of the materials. For those

locations and materials the final (old age) shrinkage and creep values

should be those found in the study, namely: -~-

Dallas Odessa San Lufkin . -6 Antonio

Shrinkage (10 in. /in.) 315 525 380 290 -6

440 675 400 460 Unit creep (10 in./ in. /ksi)

The functions developed for shrinkage and creep of the materials in

the locations of the field tests may be used with the prestress loss and

camber computer program repotted in Reference 1. Those functions are:

San Dallas Odessa Antonio Lu_fkin

' -6 315 T 380 T 290 'l' Shrinkage (10 in./in.) 525 T 20 + T 10 + T 25 + T 25 + T

-6 440_T 675 T 400 T 460 T Unit creep (10 in./in./ksi) 60 + T 40 + T 50 + T 50 + T

In all cases, T is the time in days of age, assuming that measurements

began at one day age at time of prestressing.

c

41

REFERENCES

1. Furr, Howard L•, Sinno, Raouf, and Ingram, Leonard L., "Prestress Loss and Creep Camber in a Highway Bridge with Reinforced Concrete Slab on Pretensioned Concrete Beams," Research Report 69-3 (Final) Texas Transportation Institute, Texas A&M University, Coliege Station, Texas, October 1968.

2. u.s. Department of Connnerce, Climatological Data, National Oceanic and Atmospheric Administration, Environmental Data Service, National Climatic Center, Federal Building, Asheville, North Carolina 28801

3. Hansen, Torben C. and Mattock, Alan H., "Influence of Size and Shape of Member·ort the Shrinkage and Creep of Concrete," J. ACI February, 19~6 Proc. Vol. 63, pp. 267-290.

4. Neville, A. M., "Hardened Concrete: Physical and Mechanical Aspects," American Concrete Institute, Monograph No. 6, 1971.

5. Designing for Effects of Creep, Shrinkage, Temperature in Concrete Structures, American Concrete Institute, Special Publication No. 27, 1971, 430 pp.

6. Sinno, Raouf, "The Time;..Dependent Deflections of Prestressed Concrete Bridge Girders,'i Dissertation, Texas A&M University, 1968.

42

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