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It) rIf 14/ CIVIL ENGINEERING STUDIES STRUCTURAL RESEARCH SERIES NO. 141 COMMUNICATION NOT FOR PUBLICATION BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. MURPHY Issued as a Part of the SIXTH PROGRESS REPORT of the INVESTIGATION OF PRESTRESSED CONCRETE FOR HIGHWAY BRIDGES SEPTEMBER r 1957 UNIVERSITY OF ILLINOIS URBANA r ILLINOIS
112

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Page 1: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

It) :r~qA

rIf 14/ CIVIL ENGINEERING STUDIES STRUCTURAL RESEARCH SERIES NO. 141

~P~ATE COMMUNICATION

NOT FOR PUBLICATION

BEHAVIOR OF PRESTRESSED CONCRETE BEAMS

UNDER LONG-TIME LOADING

A Thesis

by

P. E. MURPHY

Issued as a Part

of the

SIXTH PROGRESS REPORT

of the

INVESTIGATION OF PRESTRESSED CONCRETE

FOR HIGHWAY BRIDGES

SEPTEMBERr 1957

UNIVERSITY OF ILLINOIS

URBANAr ILLINOIS

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BEHAVIOR OF PRESTRESSED CONCRETE BEAMS

UNDER LONG-TIME LOADING

A Thesis by

P. E. Murphy

Issued as a Part of the 5i xth Progress· Report of the

INVESTIGATION OF PRESTRESSED CONCRETE FOR HIGHWAY BRIDGES

Conducted by

THE ENGINEERING EXPERIMENT STATION

UNIVERSITY OF ~LUNO~S

In Cooperation WHh

THE. D~VISION OF H~GHWAYS STATE OF ~LUNOIS

and

U .. S. DEPARTMENT OF COMMERCE BUREAU OF PUBUC ROADS

Urbana" n linoo5

September 1957

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iii

TABLE OF :CONTENTS

I . IN JR 0 D UC T ION • . • . . .. . • • . . . . .. .. . . . .. • .. • 0 • • • • • •

II.

ilL

IV.

v.

1 . Introduction....... 0 • • • • • • • 0 • • • • • • • • • .. .. • •

2. Obiect......

3. Outline of Tests

4. Acknowledgments.

2

'3

5.. Notation. . .. . 0 0 • •. o. 0 • 0 .' • • 0 0 • • • • • 0 .. .. " .. " • • 3

MATERIALS, SPECIMENS, AND FABRiCATION·. 0 0 0 •••• 0 ......

6. Materials ........... 0 ...... 0 0 .......... 0 .•• 0 ..

5

5

7. Description of Specimens .. 0 ....... 0 ... 0 •• 0 •••• 0 • • 6

FABRICATION OF SPECIMENS .. ~ ........... 0 " 0 ............. . 8

8.. Prestressi ng Frame . • 0 0 • 0 .. .. • 0 0 • ... • .. .. .. .. .. .. 0 • • • • 8

9 . Tens ion i ng 0 f Wi res • 0 0 .. • .. .. .. 0

10. Casting and Curing of Specimens 0 .......

MEASUREMENTS AND INSTRUMENTATION 0 ••••••••

1 1 . Stra i nMeasurements .. 0 .. 0 0 0 • 0 0 • 0 0 0 • 0 .. 0 • .. • 0 0 • •

8

10

12

12

12 .. Deflection Measurements .. 0 0 0 0 0 .. 0 0 0 •• " 0 0 •• 0 0 • • 14

13.. Modulus of Elasticity of Concrete ...... 0 .. 0 0 .. 0 .... 0 0 ...

TEST PROCEDURE AND LOADING FRAME ... 0 0 0 0 • 0 •• 0

14; Test Procedure .. 0 0 ••••.• 0 " 0

15. Loadi ng Frame . 0 • 0 o· 0 .. .. " 0 "

14

16

16

18

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TABLE OF CONTENTS (Continued)

VI. PRESENTATION OF TEST RESULTS ................... .

16. Cylinder Strains.

17. Beam Deflections

18. Beam Strains. . .

VII. INTERPRETATION OF TEST RESULTS .......•...

19 .. Discussion of Measured Strains and Deflections . .

20. Description of Analysis for Deflections ...... .

21 .. Comparison of Measured and Computed Deflections

22. Beam Deflections on Basis of Beam Strains.

23. Prestress Losses. . . . . . . . . . . . . . . .

iv

Page

22

22

22

23

25

25

35

39

44·

45

VIII. SUMMARy.............................. 47

IX. BIBLIOGRAPHy............................... 49

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Table No.

1 •

2.

3.

4.

5.

6.

LIST OF TABLES

Properti es of Beams . . . . . . . . . .

Typical Sieve Analysis of Aggregates.

Properties of Concrete Mixtures ..

Test Chronology ...

Moduli of Elasticity.

Computed Stress Distribution in Beams .

Page

50

51

52

53

54

55

v

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LIST 0 F FIGURES

Figure No.

1.

2.

3.

4.

5.

6.

7.

Di mensions for Beams MU-l and MU-2.

Dimensions and Loading Arrangement for Beams ML-1 and ML-2 .

Dimensions and Loading Arrangement for the 4 by 16-in-Cylinders

Beams in P lace on the Storage Frame.

Nominal Stress Distribution in Beams.

Stress-Strai n Relationshi p for Type X Wire. . . . . . . . . . . . . . • .

P lot of Re laxation Loss versus Ti me for Type X Wire . . . . .

vi

Page

56

57

58

59

60

61

62

8. . Oi mensions of Storage Frame for Beams. . • . • . • • . . • . 63

9. Loading of a 4 by 16-in. Cylinder in the Olsen Testing Machine . . .'. 64

10. Dimensions of Prestressing Frame. . . . • • . . . . . . . • . • . . • . .. 65

11.

12.

13.

14.

15.

16.

17:.

18.

19.

20.

View of Prestressing Frame During Tensioning of Wires ...

Plot of Concrete Strength versus Time Based on 6 by 12-in. Cylinders ..

Plot of Modulus of Elasticity versus Time ...•.....

View of Beam before Release ..••.... 0 ••••

Plot of Loss in Spring Load versus Time for Beam ML-l

Plot of loss in Spring Load versus Time for Beam ML-2

Measured Total Strains for 4 by 16-in. Cylinders ...

Midspan Deflection versus Ti me for Un loaded Beams .

Midspan Deflection versus Ti me for Loaded Beams. • . . .

Comparison of Midspan Deflections for Beams versus Time.

66

67

68

69

70

71

72

73

74

75

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LIST OF FIGURES (Continued)

Figure No.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31 .

Successive Strain Distributions in Beam MU-1

Successive Strain Distributions in Beam MU-2

Successive Strain Distributions in Beam ML-1

Successive Strain Distributions in Beam ML-2

Creep Strains versus Time for Loaded Cylinders ........•...

Dimensionless Plot of Creep Straons versus Time for Loaded Cylinders.

Dimensionless Plot of Creep Strains versus Time at Different Levels of Stress . . . . ~ . . . . . . . . . . . . . . . . . . . . . . •

Comparison of Creep Strains for Loaded Cylinders versus Time.

Computed Stress Distribution in Beams .. . . 0 • 0 • • • • • • ••

Dimensionless Plot of Creep Strains for Computations versus Time.

Creep Strains for Deflections Computations versus TimeH

and Average Shrinkage Strains versus Time . . . . . . .

76

77

78

79

80

81

82

83

84

85

86

32. Measured Deflections and Computed "ExactJl Deflections for Beam MU-1 87

33. Measured Deflections and Computed "Exact" Deflections for Beam MU-2 88

34. Measured Deflections and Computed "Approxi mate ll Deflections for Beam MU- 1 . : . . . . . . . . . . . . . 0 • • • • • • • • • • • • •• 89

35. Measured Deflections and Computed "Approximate" Deflections for Beam MU-2 . . . . . . . . . . • . . . . . . . 0 • • • • • • • • • •• 90

36. Measured Deflections and Computec! "Exact" Deflections for Beam ML-1 91

37. Measured Deflections and Computed "Exact" Deflections for Beam ML-2 92

38. Measured Deflections and Computed IIApproximate" DeflecHons for Beam ML-1. . . . . . . . . . . . . . . . . . . .. ......... 93

39. Measured Deflections and Computed IIApproximate" Deflections for Beam ML-2. . . . . .. ..................... 94

vii

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Figure No.

40.

41 •

LIST 0 F FI GURES (Continued)

Measured Deflections and Deflections Based on Beam Strains for Un loaded Beams MU-1 and MU-2. . . . . . . . . . . . . . •.

Prestress Loss as Percent of Initial Prestress versus Time ...... .

vi i i

95

96

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I. INTRODUCnON

1. Introd uction

Although tests had already been performed on four prestressed post-tensioned

beams to determine the effects of time-dependent variables (l) (2), the results obtained

indi cated suffi cient di fferences between the various beams and between the computed and

actua I deflections to warrant an entirely new set of tests. This was decided with fu II

knowledge of the variable nature of time effects which precludes any exact prediction

of their magnitude. Nevertheless, it was felt that results could be obtained which would

be more uniform and agree reasonably well with analyses.

In the first set of beams, the manner of fabrication and the cur'ing and storage

conditions both seemed to introduce variables which could not be measured, but which

nonetheless affected the results. For these reasons, pretensionsng was substituted for

post-tensioning to eliminate grouting, .and beams were stored in a controlled temperature

and humidity room. The use of pretensioning is not a departure from current practice as

witnessed by the preponderant use of pretensioning today except in very large members.

It is true that controlled humidity and temperature do not represent field conditions, but

the purpose of the tests could better be served if the analyses were made on the basis of

what is known or can be measured.

2. Object

The objects of this report are: (0 presentation of the data obtained from long­

time strain and deflection readings on four prestressed concrete beams, two unloaded, and

two loaded, and strain readings on companion cyl inders, and (2) comparison of the measured

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beam deflections with those computed on the basis of certain simplifying assumptions re­

garding the creep and relaxation characteristics of steel and concrete in the beam.

3. Out I ine of Tests

2

Four beams were subiected to long-time test. Each. speci men was a pretensioned

beam 4 by 6-in. in cross-section, and spanned 6 ft. Drawings of these beams and their

loading arrangement are shown in Figs. 1 and 2.. For control purposes, each beam had

four 4 by 16-in. companion cylinders. Two of these were loaded to 2000 psi nominal

stress in compression as shown in Fig. 3; and the other two were left unloaded. Twelve,

6 by 12-in. control cylinders were cast with each beam. Ten of these were tested over

a period of28 days to follow the variation in concrete strength.

All beams contained the same amount of prestressing wire, and with the exception

of ML-l, were to have 2000 psi compressive stress at the bottom fiber immediately upon

release, and zero stress in the top fiber. The latter was obtai ned by placing the center

of gravity of the steel at the lower kern point of the concrete cross-section.. The bottom

compressive stress in ML-l was reduced somewhat to compensate for the lower tension

stress induced by loading after the transformed section becomes effective. The properties

of the specimens are given in Table 1.

After release of prestress, each beam was immediately transferred from the crane

bay of Talbot Laboratory to a controlled temperature and humidity room and placed in a

specially designed frame (Fig. 4). Here beams ML-l and ML-2 were loaded at their

third-poi nts by springs to a nominal top fiber compressive stress of 2000 psi and ] 000 psi

respectively. The nominal stress distributions for loaded and unloaded beams are graphically

presented in Fig_ 5.

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3

4. Acknowledgments

The studies reported herein were made as a part of an investigation of prestressed

concrete for highway bridges conducted in the Talbot Laboratory 'of the University of

Illinois in cooperation with the Division of Highways, State of Illinois, and the U. S.

Department of Commerce, Bureau of Public Roads.

The program of the investigation has been guided by an advisory committee

on which the following persons have served during the period covered by the work

described in this report: E. F. Kelley, E. L. Erickson and Harold Allen, representing

the Bureau of Public Roads,: W., E .. Chastain, Sr., W. J. Mackay, and C. E. Thunman i Jr.,

representing the Illinois Division of Highways; and N. M. Newmark, C. P. Siess, I. M.

Vi est, and N. Khachaturian, representing the University of Illinois.

The proiect has been under the general direction of C. P. Siess and under the

immediate supervision of M. A. Sozen, Research Associate in Civil Engineering.

Appreciation is expressed to Mr. Sozen for his help and advice in planning

the tests and preparing th is report, and to the laboratory personnel for their cooperation

and aid in carrying out the test program. In addition, C. E. Kesler, of the Department

of Theoretical and Applied Mechanics kindly permitted the use of certain facilities under

his direction during the tests.

This report was written as a thesis under the direction of Dr. Seiss, whose

assistance and encouragement are gratefully ,acknowledged.

5. Notation

Beam Constants

b = width of beam

h = overall depth of beam

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A = total area of wire reinforcement s

Notation relating to prestressing only

F. = initial prestress force I

~F = loss in prestress force

F = se effective prestress force after losses

Stresses

Concrete

£I = c 7-day cylinder strength

£I. = CI

cylinder strength at the age of loading or release of prestress

f = applied compressive stress c

~ = stress at bottom fiber due to prestressing

fcb = stresses at bottom fiber of prestressed beam after loading

f = ct stresses at top fiber of prestressed beam after loading

Steel

f . = initial prestress Sl

f = relaxation loss in steel sr

E = s

modulus of elasticity of steel

Strai ns

Concrete

E = C

E = ce

2000 E

C

compressive strain

concrete strain at level of stee I due to effective prestress force F

se

= strai n after 2000 hours

E = modulus of elasticity of concrete c

4

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5

II. MATERIALS, SPECIMENS AND FABRICATION

6. Materials

(a) Cement

Marquette Type III Portland Cement, purchased locally, was used in all beams.

(b) Aggregates

Wabash River sand and gravel were used for all beams. The maximum size of

the grave I used was 3/8 in. The maior constituents of the gravel were limestone and dolo­

mite with minor quantities of quartz., granite, gniess, etc. The sand consisted mainly of

quartz. The sand had an average fineness modulus of 3.30. Typical aggregate sieve

analyses are reported in Tabl.e 2. Tests for surface moisture content were made one day

prior to the mixing of concrete. The range in surface moisture content for the sand was

0.2 to 1. 9 percent, and 0.5 to 3.2 percent for the gravel. One percent by weight of

the surface dry aggregate was allowed for absorption of both sand and gravel.

(c) Concrete Mixes

Mixes were designed by the trial batch method. A 7-dayconcrete strength

of approximately 4500 psi and a slump of three inches were desired. Table 3 contains

the proportions of the mixes, slumps and 7-day compressive strengths for the concrete

used in each beam. The strengths are based on standard 6 by 12-in control cylinders.

(d) Reinforcing Wire

Steel designated as Type X was used as prestressing reinforcement for the beams.

This was manufactured by the American Steel and Wire Division of the United States Steel

Corporation and is designated by the manufacturer as "Hard Drawn Super-Tens Stress Relieved

Wire ll• The following steps were involved in its manufacture: hot roiling, lead patenting,

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6

cold-drawing and stress relieving. The wire was delivered in coi Is about 6 ft in diameter

and weighing approximately 300 Ib each. The following heat analysis has been furnished

by the manufacturer: 0.81~ C, 0.76~ Mn, 0.01~ P, 0.027~ Sand 0.23«.' Si.

To improve the bond characteristics, all wires were first wiped with a cloth

dipped ina hydrochloric acid solution, and then placed in the moist room for about two

weeks to rust. This operation produces a slightly pitted surface. All wires were cleaned

i ust before use wi th a wi re brush to remove loose rust.

The diameter of the wire was measured to be O. 196 in. Two wire specimens were

tested in a 120,000-lb capacity Baldwin hydraulic testing machine for the determination of

stress-strain characteristics. Strains were measured with an 8-in. extenso meter and recorded

with an automatic recording device. The extensometer had a range of about 4 percent

strain. The manufacturer's values of E = 29,400 t OOO psi and minimum f = 250,000 psi su

compared well with the average measured values of E = 30,000,000 psi and f= 264,000 su

psi. The stress-strain curve for the wire is shown on Fig . 6. Relaxation Losses at the stress

level to be used (about 56.5 percent of ultimate) were not expected to exceed 3.5 percent,

on the basis of previous relaxation tests (1). For a determination of loss in these tests, two

specimens of Type X wire were placed in the steel wire relaxation frames at levels of

approximately 51 and 55 percent. The method of measuring the loss by -vibrating the wires

has been described in a previous report (3), and wi II not be repeated here .. Relaxation

curves for the two specimens are shown on Fig. 7.

7 .. Description of Specimens

All beams tested were pretensioned beams nominally 4 by 6 in. in cross-section

and 7 1/2 ft long (Figs. 1 and 2). Each beam contained six O. 196-in. high strength :Steel

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7

wires for tension reinforcement.. Nine inches overhang were allowed at each end for

the development of the prestressing force. Bond specimens in tests reported by Janney (4)

required 10 to 13 inches for transfer length using rusted 0.197-in. wire stressed to 120,000

psi; thus, the nine inches allowed here may have been somewhat short.. The center of

gravity of steel reinforcement in all beams was 2 in. above the bottom of the beam.

Beams were designated MU-1, MU-2, ML-l, and ML-2. The letter U in­

dicates un loaded, and L indicate,;' loaded. The unloaded beams MU-l and MU-2 were

placed in the storage frame in the control room immediately 'after release of prestress,

and periodi c deflection and strain measurements were taken (Fig .. 4). Beam ML-l was

placed in the frame and loaded at its third-points but with a total load of 4000 lb.:, :Seam

ML-2 was a Iso loaded at its third-points but with a toto I load of 2000 Ib (Fig. 4).

Dimensions of the storage frame are shown on Fig. 8.

Four 4 by 16-in. cylinders were cast from the batch used in each beam to de­

termine the effects of shrinkage and creep. One cylinder was loaded through springs for

long-time creep readings (Fig. 3). A total load of 25, 130 Ib was required to produce

a uniform compressive stress of 2000 psi in the concrete. -A second cylinder was loaded

to the same lood in a 200,000-lb Olsen testing machine for about a :week (Fig. 8). The

other two cylinders were left unloaded in order to observe shrinkage strains. All concrete

strains were measured mechanically with a 10-in. Whittemore gage.

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8

I'll" FABRJCATION OF SPECIMENS

8. Prestressing. Frame

Since the beams were to be pretensioned, it was necessary to provide some sort

of prestressing frame or bed in which to tension the wire before casting the concrete. The

small size of beams and the desire to measure the instantaneous loss led to the adoption of

a portable frame which would fit around the concrete form (Fig. 10). This frame consisted

of two 3-in. standard pipes fitted to heavy end-plates by means of rings of the same inside

diameter as the pipes welded to the end plates •. The end plates were 5 bY'2 by 19 in.

They were dri lied with two rows of five. 201-in .. holes;- a smooth fit for the prestressing

wires. The holes were 3/4 in. on centers horizontally and vertically. This separation

allowed suffi ci ent room for full bond between wires whtle providing a minimum one-inch

cover on the sides and bottom of the beam.

9. Tensioning of Wires

(a) End Detai Is of Wires

Threaded connections were chosen for the following reasons: simplicity in

anchoring the wires, compact arrangement of the wires with a relatively small spacing

between them, and practically no loss of prestress when the stress in the wire is trans­

ferred from the jack to the bearing plate. The level of prestress planned (50 -55 of

ultimate) was not sufficient to overstress the wire at the threads.

Specially heat-treated, 24-threads-to-the-inch chasers in an automatic

threading machine were used to cut the threads on the end three inches of the wires.

The threads on the wires were cut to provide a medium fit with the threads in the nuts.

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9

This resulted in a thread which was slightly larg.er than a No. 10 which has a basic major

diameter ofO. 190 in. The nominal and measured diameter of the wire u.sed was 0.196 in.

The nuts were specially made in the laboratory machine shop. They were sub­

dri lied wi th a No. 16 tap dri II and tapped with a standard No. 12, 24-threads-to-the-inch

tap. This provided a full No. 12 thread in the nuts. Nuts with a No. 10 thread required

that too much material be cut from the wires to be practical. The thread cut on the wires

to fit the No. 12 thread in the nuts was sufficient to develop at least 160,000 psi in the

wires for several d~ys and was considered to be the most suitable. The nuts were 5/8 in.

long.

(b) Measurement of Tensioning Force

The tensioning force in each wire was determined by measuring the compressive

strain in aluminum dynamometers placed on the wire between the nut and the bearing plate

at the end of the beam opposite that at which the tension was applied. They consisted of

2-in. lengths of 1/2-in. aluminum rod, with 0.2-in. diameter holes drilled through their

centers. Strains were measured by means of two Type A-7, SR-4 electric strain gages

attached to opposite sides of the dynamometer and wired in series. Thus, readings were

obtained which were an average of the two gages. With this arrangement small eccen­

tricities of load did not affect the strain readings. The gages were carefully protected

against handling and moisture by a heavy wrapping of electrical pressure tape over a generous

coating of petrosene wax. The dynamometers were ca librated using the 6000-lb range of

the 120,OOO-lb Baldwin hydraulic testing machine. The calibrations of the dynamometers

were nearly the same; the strain increment necessary to measure a tensioning stress of

150,000 psi in the O. 196-in. wires was approximately 2700 millionths. The large increment

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10

of strain allowed a fairly precise measurement of stress in the wires, since the strain indicator

used had a sensitivity of 2 to 3 millionths.

(c) Tensioning Pro.cedure

The frame was assembled on two concrete block supports. The wires were slipped

through the end-plate of the form and the end-plates of the prestressing frame (Fig. 11). At

the end opposite the prestressing end dynamometers were sl ipped on the wires, then the nuts

were screwed down against them. About 3/8 in. of thread was exposed. At the prestressing

end nuts were placed on each wire, the iacking frame was positioned for either the upper

or lower row of wires. Then, the pull-rod was run through the slot in the jacking frame

and screwed onto the wire to be tensioned. The other end of the pu II-rod was run through

a 3D-ton Simplex center-hole liydraulic ram operated by a Blackhawk pump,. 'and was secured

by a large nut at the end. Immediately before tensioning, dynamometer readings were

taken on all wires. Wires were tensioned individually. Slotted shims about 5/8 in ~ in

length were used to take up the elongation of the wi re. When. the desired stress was reached I

the nut was turned down tight against the shims and the force on the iack was released at the

pump. Because of slight deformations in the frame with progressive tensioning, it was

necessary to go back and adiust the stress in the wires. All wires were stressed to within

+ 1.5 microinches of the required value:~

After tensioning the six wires in the frame, the frame was transported to the form

where the wires were placed inside the form and the end plates were positioned. The beam

was ready for costing the next morning.

10. Casting and Curing of Specimens

The concrete forms were made of heavy 2-in. nominal size boards. A preliminary

check revea led a slight verti ca I warp in the side boards. To remedy th is, c lamps were used

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11

throughout the length of the beam.

All concrete was mixed about 3 minutes in a non-ti Iting drum-type mixer of

6 cu ft capacity, and was placed in the forms and cylinder molds with the aid of a high

frequency internal vibrator. The mixing water was added after the dry materials had been

mi xed for a short ti me .

Several hours after casting, the top surface of the beam was troweled smooth

and all cylinders capped with neat cement paste. Beams and cylinders were allowed to

cure in their forms in the air of the laboratory. The beams were left in the forms until

they had reached sufficient strength to be released. Bottom fiber stress desired immediately

after release was 2000 psi. The wires were released wh'en the fiber stress was from 50% -

55 % of the concrete strength. Variation ,in concrete strength was obtained from com­

pressive tests of 10 concrete cylinders over a period of 28 days (Fig. 12). For beams MU-l,

MU-4 and ML-1, five days were required to reach the desired strength. For beam ML-2,

seven days were required. A chronology of tensioning, casting, prestressing, etc., through

final positioning of the beam in the storage frame appears in Table 4.

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12

IV. MEASUREMENTS AND INSTRUMENTATION

11. Strain Measurements

(a) Electric Strain Gages

Electric strain gages.·were used in the ·following location for each specimen:

Beams: On the dynamometer only (discussed previously in Section 9-b).

Cylinders: Two type A-7, SR-4 electric strain gages were mounted on each of

the three rods used in the cylinder loading frame and connected in series to give average

strains. These were used for strain measurements in the load-strain calibration of the rods

performed on the 120,000-lb Bladwin dydraulic testing machine. The gages were:"used only

during loading to measure the load on the cylinder, and were not depended upon for readings

after the load was applied.

All electric strains were read with a Baldwin SR-4 portable strain indicator.

Type A-7, SR-4 gages for temperature compensation were mounted on an unstressed steel

block.

(b) Mechanical Strain Gages

Strain distribution through the depth of the beam as well as creep and shrinkage

cylinder strains were measured by means of a 1 O-in. Whittemore strain gage. Measurements

on all gage lines were read twice or until readings agreed within 0.00001 in./in. There

are four gage lines on each side of the beam wi th one measurement on' each side of the

center line for the unloaded beams. For the loaded beams the four gage lines remained,.

but the two readings per line were overlapped 5 inches to insure flexural strains free of

shear distortions o layout of gage lines is shown on Figs. 1 and 2. Because of insufficient

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13

clearance between the pipes of the prestressing frame and the beam, readings on two gage

lines were in doubt before rel~ase. For this reason, two rows of gage lines with one reading

on each side of the gage line were added to the top and bottom of the beam. These were

read only before and immediately after release to obtain accurate instantaneous strains.

This Jayout is also to be seen in Figs. 1 and 2. The three 10-in. gage lines for the cylinders

were arranged symmetrically around the circumference of the cylinders (Fig. 3).

For these tests, it was decided to locate the gage plugs in the concrete flush

with the surf~~e rather than gluing them on the outside as in previous tests and thus avoid

the danger of breaking them off. Several methods were attempted but finally the following

was chosen as giving the best results: Holes 15/32 in. in diameter were drilled in the wood

forms at the desired location of the gage plugs. Just before casting, steel rods 3 in. long

and 7/16 in. in diameter were placed in the holes and extended 1/2 in. past the inside

surface of the form. These remained in place about 7 hours after pouring, long enough to

allow the initial set to take place, and then were pulled out.

One day before release of prestress, steel gage plugs 5/17 in. in diameter

and 5/16 in. deep, drilled at the center with a No. 54 drill to a depth of 1/8 in. and

reamed, were positioned in the preformed holes in the manner described in Section 14. The

same gage plugs were used on the cylinders in holes dri lied in the concrete. Gage plugs

3/8 in. in diameter and 1/4 in. deep drilled in the same manner as above were glued on

the top and bottom gage lines of the beam with. Duco cement. Th is was also done for the

4 by 16-in. cylinder loaded in the 200,OOO-lb Olsen machine. Glue was considered satis­

factory in these cases because of the short duration of their use.

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14

12. Deflection Measurements

Instantaneous and long-time deflections were measured at the mid-span of each

beam with a 0.001 Ames dial indicator. Two additional dials were installed on ML-2,

7-1/2 in. on either side of the center line. For a description of the mounting of these

gages see Section 15(a).

13. Modulus of Elasticity of Concrete

"Instantaneous" rather than lIelectric ll has been used to describe strains and

deflections in the beams at release of prestress and at loading. This was done because a

certain portion of these deflections and strains represent creep. To determine approximately

what portion of the measured change was creep and what portion elastic, two methods of

determining the modulus of elasticity were used: Compressometer readings on 6 by 12-in.

cylinders during a compression test, and loading and unloading a 4 by 16-in. cylinder to

2000 psi in the 200,OOO-lb Olsen testing machine. This was done on the day of release of

prestress. In both cases an initial tangent modulus was desired. The results were more con­

sistent for the "unloading" procedure, and these are the values shown in column (3), Table 5.

Comparison with val ues of modu Ius of elastj city obtained from measured instantaneous strai ns

at the bottom fiber of the beam at release are shown in column (6), Table 5. These are

discussed in Section20(b).

An average curve of initial tangent modulus versus time was desired for the

analysis. This was obtained by making several lIunloading ll tests over a period of time and

interpolating between them by means of a curve reflecting the increase in modulus of

elasticity with increase in concrete strength simi lar to Jensen·s expression for the modulus

of elasticity (5). Concrete strengths were measured from 6 by 12-in. cylinders. The

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15

resulting aver.a.ge modu.1i of elasticity versus time curve for beams MU-1, MU-2.,. and

ML-l are shown on Fig. 13. .. A.separate curve is shown o.n Fi9-. 13 for beam ML-2. Values

from this curve are about 15tj, less than the average curve for the other beams. Zero time

on this curve refers to the time of release of prestress.

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16

v. TEST 'PROCEDURE AND LOADING FRAMES

14. Test Procedure

The actual beams were preceded by two trial beams. in order to work O.ut an

effi ci ent procedure for prestressing, casting, re:leasi ng and storing. After this pi lot operation,

the production of the four test beams was completed in six weeks.

On the day before release of the wires, the beam and prestressing frame were

placed on two large concrete support blocks. He~e the beam was prepared for re:lease

(Fig. 14). A thick mixture of Hydrocal (high-strength gypsum cement) was forced into the

preformed gage plug recesses by means of a tube and plunger. The plaster was allowed to

harden slightly, and then the gage plugs were guided into position through a transparent

plastic template which lined the plugs up vertically and horizontally on center lines pre­

viously laid out on the beam. A standard 10-in. spacer bar was used as a final check. All

this had to be done quite rapidly, as the plaster set up in 10 to 15 minutes. This procedure

was followed for all beams. As mentioned before, the top and bottom gage plugs were

glued into place, since only a few readings were required of them. After the gage plugs

were located, the beam was placed on bearing plates. The bearing support at one end

consisted of two steel plates 4 by 4 by 3/4:in. with a machined surface and a 3/4-in. round

roller 0 One plate rested on the concrete support block, and the other bore against the

bottom of the beam. The roller was placed between them. The bearing plates at the op­

posite end were exactly the same size, but had a transverse notch in each in which a l-in.

round ro II er was fi tted to provi de hinge support. The center line of the ro II er was located

three feet from the beam center line. All bearing plates were plastered to their bearing

surfaces with Hydroca I.

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17

As soon as the beam was prepared, holes for gage plugs were dri lied in the

4 by 16-in. cylinders with the exception of that to be placed in the 200,OOO-lb Olsen

testing machine. The holes were drilled with a stationary type shop drill having vertical

travel on Iy and equipped with a 3/8-in. diameter carborundum-tipped bit. Some difficulty

was experienced here when drilling in;o gravel. Again Hydrocal was used as the cementing

agent for the gage plugs.

On the morning of release, a 4 by 16-in. cylinder was placed in the 200,OOO-lb

Olsen testing machine and loaded to 25, 120 lb, or 2000 psi stress (Fig. 9). Periodic strain

readings were taken and a close check kept on the weighing beam to keep it balanced l

especially during the first few days after loading when the creep deflections were larger.

The purpose of this cylinder was to obtain creep information 'when the cylinder was the same

age as the beam at release, to check initial creep strains of cylinders loaded in the frame,

and to obtain the modulus of elasticity (Section 13).

A single O. OOl-in. Ames dial was set up at midspan of the beam to measure

instantaneous deflection. Initial strain readings were taken on all gage lines. The nuts

were loosened slowly, about a quarter-turn each time, until the total load in the wires had

been transferred to the beam. This precaution was necessary because the stress level was

high for threaded connections. It took about 20 minutes to releaseaH the wires. ,As soon

as this was completed, center line deflection was read, and then strain readings were taken.

These readings represented instantaneous deflection and strains. Next, readings on several'

side gage lines were taken as a check on the top and bottom readings . Finally, the pre­

stressing frame was removed along with the end plates. Strains and deflections were again

read, but the changes were insignificant.

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18

The beam was then ready to be transported to the controlled temperature and

humidity room and placed in the storage frame. By means of automatic moisture, heating,

and cool ing devi ces, th is room is kept constantly at 50 percent relative humidity and

75 deg F temperature. All beams were placed in the room immediately after release, and

all control cylinders within 24 hours of release with the exception of the cylinder loaded

for a week in the 200,OOO-lb Olsen testing machine.

15. Loading Frame

(a) Beams

The loading frame consisted of longitudinal angles welded between vertical end

channels (Fig. 8). The two unloaded beams were placed in the bottom two berths. Bearing

plates and rollers exactly the same as on the concrete support blocks were again used here.

The bottom plates were welded to the frame. A. OOl-in. Ames dial was fastened to the

frame by a horizontal steel dowel bolted to the angles. The dial plunger was centered on

the beam and reacted against a small aluminum plate.

Two beams, ML-l and ML-2, were loaded on the frame by means of four 2-in.

diameter springs. To obtain a concentric load on the springs, small circular steel caps were

fitted to the springs top and bottom,and provided with a 1/2-in. diameter hole at the center.

The springs were calibrated in the 120,OOO-lb Baldwin hydraulic testing machine with the

caps on. Readings were taken wi th a direct reading compressometer equipped with a

O. OOl-in. Ames dial indicator. There are sufficient variation that a general spring constant

could not be employed, and for best results load-deflection readings were taken from

calibration curves for each spring. The springs in place rested directly on a half-round

2-3/8-in. diameter bar 10 inches long which provided a point reaction against a 1/4-in.

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19

bearing plate plastered to the beam. A total of 4000 Ib for ML-1 and 2000 Ib for ML-2

was applied by tightening down nuts on 1/2in. diameter rods bolted to the frame angles.

Some of these rods had been fitted with A-7, SR-4 strain gages, but the sensitivity of the

rods was so small compared to that of the springs that the electrical readings were used only

during loading to obtain a uniform distribution of load. The springs alone were relied on

to give final load readings.

It was anticipated in the design of the frame that there would be an upward

deflection of the angles caused by loading. To acquire a set of readings which represented

only the downward deflection of the beams relative to the ends, a 2 by 3IB-in. steel strap

supported exactly at the support points of the beam was included in each berth for a loaded

beam (Fig. 8). The strap was supported by smooth polished steel dowels to prevent twist at

the support. Ames dials attached to this strap at the center of the beam measured only

deflection of the center relative to the support points of the beam. Just before loading,

deflection gages of other beams on the frame were also read. The loading caused a

O. 0016-in. increase in the dial reading of the beam immediately below1 but had no effect

on the second beam. This gage was returned to its original reading.

The beam springs have a high spring constant and are therefore susceptible to

losses when the beam deflects. This was considered in the calculations (Figs. 15 and 16).

There was practi ca lIy no eccentri city in the loaded springs and reading on both sides of the

spring were the same obtained during calibration for that particular load.

(b) Cylinders

Cylinders in loading frames were always loaded the morning of the day followi ng

prestress release-approximately 20 hours later.

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20

The loading frame (Fig. 3) consists of the following: three 5 1/2-in. diameter

rai Iroad car springs, and three one-inch round rods threaded at each end which hold the

springs in line with the rest of the frame. The force of the compressed springs react on the

top of the cylinder through a top bearing plate, and on a bottom bearing plate beneath the

cylinder through the three rods. In loading, the hydraulic iack was placed on top of the

upper spring plate between the three rods and another plate having holes for the rods was

slipped down onto the ram of the iack. The nuts were then turned down flush wi th the

topmost p late and the three springs were compressed simu Itaneous Iy by operating the hydrau Ii c

ram which reacted against the topmost plate and upon the upper plate of the springs. The

lower nuts were then screwed down tightly against the upper spring plate and the load on

the iack transferred to the rods by releasing at the pump. The same pump and iack were

used as in the tensioning of the wires (Section 9(c) ).

Much difficulty was experienced obtaining a true concentric load. The use of

three springs makes this especially hard. A ball inserted between a 3/4-in. bearing plate

at the top of the cylinder and the top frame bearing plate proved unsatisfactory. The method

finally used was to control the loading with reference to the reading of the electric strain

gages on the rods, and then read the concrete strains with the Wh ittemore gage. If they

were not within 0.00005 in. of each other, the load on the cylinder was released, zero

readings taken, and the cylinder again loaded with the total load so proportioned between

the three rods that the difference in concrete strains was within the allowable. Then, the

final concrete and spring strain readings were taken. The reading on the springs was taken

primari Iy to check the total load on the cylinder as read by the rod strains, and also to

measure the loss of force in the springs with time. Readings indicate that a total loss of

approxi mate Iy 4 percent can be expected.

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21

Readings were taken regularly on bath beams and loaded cylinders. On the

average, this was every day for the first four days, every two days for the next four days,

every week for the next two weeks and every three weeks thereafter .

. Cylinders to measure shrinkage, two per beam, were placed in the control room

at the same time as the beams (Table 4). Readings on these were neither taken so regularly

nor so often as on the beams because of the relatively small strains invo Ived.

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VI. PRESENTATION OJ; TEST RESULTS

16. Cylinder Strains

Total strains and shrinkage strains measured from cylinders for each beam are

shown on Fig. 17. The upper curves are total strains and the lower curves are shrinkage

strains. Each point on the total strain curves represents the average of three readings

from one loaded cylinder per beam, and each point on the shrinkage curves represents

22

the average of six readings from two unloaded cylinders per beam. Curves of total strains

measured from cylinders loaded for a week in the Olsen testing machine are not shown.

Their results checked those of the cylinders loaded in the frames. Cylinders were loaded

to a unit stress of 2000 psi. - The origin of total strain readings refers to the time immedi­

ately after loading. I.nstantaneous strains are not included. The cylinders were loaded

about 20 hours after release of prestress (see Table 4). The origin of the shrinkage strain

curves indicates the initial reading taken in the controlled atmosphere room on the day of

prestressing. The time of this reading is given in Table 4.

17. Beam Deflections

P lots of measured midspan deflections versus time for the unloaded and loaded

beams up to 2000 hours are shown on Figs. 18 and 19. In all beams, the origin corresponds

to the readi ng before prestress, that is, under dead load on Iy. Upon re lease of the wires,

prestress was transferred to the beam causing an instantaneous upward deflection. . Approxi­

mately fifteen minutes were required to release-the prestress completely. The magnitude

of this deflection is indicated by the ordinate at zero time marked IIAfter Prestres~I~.

Three hours were required to remove the prestressing frame, convey the beam to

the controlled atmosphere room, and install it in the storage frame. The upward deflection

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23

caused by creep during this time was not recorded. All time deflections for unloaded beams

are referred to the reading taken immediately after positioning the beam. This is the

ordinate at zero time marked Illn Storage Frame ll on Fig. 18. The points "After Prestress U

and IIln Storage Frame" are identical on Figs. 18 and 19. The downward instantaneous"

deflection caused by the loading of ML-1 and ML-2 is shown on Fig. 19 as the difference

. between the two ordinates at zero time marked "In Storage Frame" and "After Load ll• The

time required for loadi ng was about one hour. Time deflections for the loaded beams have

as their origin the ordinate at zero time marked "After Load l1•

On Fig. 20 the observed time deflections for all beams are p lotted against the

logarithm of time. The origin is the point "In Storage Frame ll on Fig. 18 for unloaded beams,

and "After Load II on Fig. 19 for loaded beams.

18. Distribution of Strain over Depth of Beam

Beam strains were measured on four gage lines on each side of the beam. In

addition, gage I ines were added on the top and bottom of the beam just before prestressing

to obtain accurate instantaneous strains. A description of all gage lines is given in

Section 11 (b), and their layout is shown in Fig. 1 and 2. Successive strain distributions

for beams MU-1, MU-2, ML-1, and ML-2 are shown on Figs. 21, 22, 23, and 24. Each

strain is the average of four readings, two on one side of the beam and two on the other.

Strains IIBefore Prestress ll are represented by a vertical zero strain line at the left side of

the figure. Strains "After Prestress l1 were obtained from readings on the top and bottom gage

Iines o Although it was not possible to measure the creep deflections during the three hours

between releasing of wires and placing in the storage frame, it was possible to measure

the creep strains. These are the differences in strain: between the line "After Prestress"

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24

and I1ln Storage Frame". The datum line for the time strain readings for unloaded beams is

the last-named line.

Strain distributions immediately before loading for the loaded beams are given by

the line marked tlln Storage Frame", and after loading by the lines marked "After Load lf•

The latter line then becomes the datum line for time strains. Time in hours measured from

the above datum lines is marked above each strain distribution line at the top of the figures.

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25

VII. I NTERPRETATION OF TEST RESULTS

~9. Discussion of Measured Strains and Deflection

(a) Cylinder Strains

Total Strains. Measured total strains for the loaded control cylinders are shown

on Fig. 17. Cylinders were loaded nominally to 2000 psi" The actual unit load obtained

from spring readings was within 3 percent of this value. The measured strains were later

adiusted linearly to correspond to a unit load of 2000 psi. The cylinders were loaded with

steel springs as described in Section l5(b). The loss in applied load amounted to only

3 percent in 2000 hours and was neglected" The curves of Fig. 17 represent the average

of mechanical strain measurements on three 10-in. gage lines (Fig. 3). Averaging was

felt to be permissable in this case since deviation from mean readings did not exceed

7 percent in anyone case.

Because of the slowness of loading cylinders in the frames, the lIinstantaneous"

strains included a certain proportion of creep strain, depending on the time required for

loading. Thus, lIinstantaneous ll strains ranging from 600 to 900 x 10-6

were recorded. With

the exception of ML-2, which had somewhat weaker concrete (Table 3), the concrete proper­

ties of the cylinders were quite si mi lar, and they were loaded at about the same age

(Table 4). For this reason, instantaneous strains have been omitted in the plots of tota I

strains.

The creep strains for the loaded cylinders are presented on Fig. 25. Theywere

obtained by assuming that the shrinkage strains in the loaded cyl inders of a given batch

were the same as for the corresponding unloaded cylinders, and then taking the difference

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26

between the total strains for the loaded cylinders and the shrinkage strains. Creep strains

have been I inearly corrected to_ 2000 psi. Instantaneous strains, measured in a screw-type

testing machine, column (1),. Table 5, and as described_in Section 13, are compared below

with total strains at 2000 hours (instantaneous plus creep strains):

Instantaneous Tota I Strain Total Strain Beam Strain x 10° ot 2000 Hrs. x 106 Instantaneous Strai n

MU-l 650 2170 3.4

MU-2 630 1870 3.0

ML-1 650 1990 3. 1

ML-2 740 2670 3.6

The magnitudes of "instantaneous" and total strains depend on the modulus of elasticity of the

concrete at loading, creep characteristics of the concrete, the age of loading, and the unit

load app I i eel. Factors wh ich affect the creep characteristi cs of the concrete are the

water:cement ratio and the storage conditions.

In order to compare the derived creep strains qualitatively, dimensionless plots

of creep strains obtained as described above for the loaded cylinders of all beams are pre-

sented on Fig. 26. The abcissas of these plots are values of tIT expressed as a percentage,

where t is the time of an intermediate reading and T is total time or 2000 hours. The ordinates

represent the creep strain at the time.!.. as a percentage of the total creep strain at 2000houTs

under a constant load of 2000 psi. It is apparent from these curves that the creep strain

curves for the cylinders were the same qual itatively in spite of small differences in concrete :>

properti es.

The dimensionless plot of creep strains versus time, shown on Fig. 27, is a re-

production of Fig. 56 from the Fourth Progress Report (1). Curves for two different stress

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27

levels, 1000 psi and 2000 ps.i, up to 2500 hours are presented to indicate the validity of the

assumption that the variation of creep wi th applied stress wi thin these limits is linear. Creep

strains were obtained by subtracting shrinkage strains from total strains. The slight difference

in the curves is no greater than might be expected between two specimens at the same stress

level. It should be noted, however, that these cylinders were loaded about 90 days after

casting. Also the ratio f I f~i was smaller than in the pr esent tests.

Concrete strengths at time of loading of the cylinders (Table 4) are given in the

table below. They were obtained by reading the ordinate on the concrete strength curve

corresponding to the time of loading (Fig. 12). Also shown is the actual unit load on the

cylinder as measured from the springs, and the ratio of unit load to concrete strength. The

latter is a Iso shown for the uni t load corrected to 2000 psi.

Beam £I. f Cl c

f If 1 •

C Cl 2000/£1 .. Cl

MU-1

·MU-2

ML-1

ML-2

psi

3760

3930

3800

3550

psi

2050

2000

2030

1940

0.55

0.51

0.53

0.55

0.53

0.51

0 .. 53

0.56

This is consistent with current practice in which ratios of f to p .. as high as 0.60 are used. c CI

Attempting to find some relationship between creep strains at a given time and the

ratio of appl ied load to concrete strength, the best comparison was on the basis of 5-day

concrete strengths which is tabulated below. The only conclusion permissible from these data

is that for the same concrete stress a reduction in concrete strength causes an increase in

creep strain.

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28

Beam 2000

f' • Ratio Ratio of E c CI

of Strains· Concrete Strengths

x106

psi (1) (2) (3) (4)

MU-1 1520 3760 1. 13 1.01

MU-2 1240 3930 0.92 0.97

ML-l 1340 3800 1.00 1.00

ML-2 ]930 3550 1.44 ].07

Column (1) Concrete creep strain at 2000 hours for 2000 psi (2) 5-day concrete strength (3) Based on ML-1 equal to unity (4) Based on ML-1 equal to unity

Although it appears from the arithmetic plot (Fig. 25) that the creep has almost

ended, the plot of creep strains versus the logarithm of time presented on Fig. 28 indicates

that some creep can sti II be expected . However, the rate of creep of all cylinders has de~~

creased considerably at 2000 hours. Indications are that about 80 to 85 percent of the total

creep has already taken place. Other creep tests (6) have recorded only about 60 to 70 per-

cent of the total creep at 2000 hours, but for lower stresses, greater age at loading, and

norma I cement. Storage conditions were the same.

Shrinkage strains versus time are also presented on Fig. 17. Each shrinkage strain

curve represents the average' of six mechanical strain readings on two cylinders •. Deviation

from the mean did not exceed 10 percent between the three gage lines of a cylinder, nor

2 percent between the two cylinders. Within these limits, ave.raging was considered per-

missible.

Although ML-2 had the largest water:cement ratio, 0.80, it shows the least

shrinkage .. strain in Fig. 17. The explanation is that readings were not begun unti I seven days

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29

after casting (Table 4), whereas the unloaded cylinders of the other beams were first read

five days after casting. The 48-hour difference would increase the shrinkage strains of ML-2

and make them compatible with the water:cement ratios ..

The magnitude of the average shrinkag.e strains at 2000 hours is 0.00056. The

Bureau of Public Roads, in its IICriteria for Prestressed Concrete Bridges II (7) assumes a value

of 0.0002 for total shrinkage. R. W. Carlson (8) gives 0.00065 as the shrinkage at 2000

hours of 3 by 6-in. cylinders at 50 percent relative humidity and using normal cement.

Size of specimen, water:cement ratio, storage conditions, and type of cement are probably

the most important factors in obtaining a certain shrinkage strain at a given time. The

shrinkage seems to be leveling offl but at least 15 to 20 percent more is anticipated.

(b) Beam Deflections

Unloaded Beam. Deflections at mid-span for unloaded beams are compared in

Figs. 18 and 20. The instantaneous upward deflection at prestressing was the same for both

MU-1 and MU-2. At 2000 hours the time deflection of beam MU-1 is 22 percent higher

than that of beam MU-2. This compares well with a 27 percent difference in creep strains

measured from their cylinders at the same time (Fig. 25). The two deflection curves appear

to be qualitatively similar.

The following table is a presentation of the measured and computed instantaneous

deflections, the total measured deflection, and the ratio of the computed instantaneous and

total deflection:

Beam Measured Deflection

MU-l MU-2

Instantaneous

in . . 086p .0865

Total at 2000 hours

in" . 185 .167

Computed Instantaneous Ratio Deflection

in. Total/Computed

Instantaneous

0.068 2.7 0.066 2.5

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30

The computed instantaneous deflections were based an values of the modulus of

elasticity of concrete indicated by tests of cylinders d.escribed in Section 13, and given in

column ( 3), Table 5. The discrepancy between the computed and measured deflections may

be attributed to the increase in deflection due to creep during the release of the wi res.

The ratios of total to instantaneous deflection were smaller than the ratios of

total strain to instantaneous strain presented in Section 19(a). The principal reason for this

is that the strains were measured on cylf:nders creeping under a constant load whi Ie the load

in the beams· was decreasing due to prestress loss.

Although the arithmetic plots of Fig. 18 show a leveling off at 2000 hours, this

is not so apparent in the semi-logarithmic plots of Fig. 20. Here the deflection is seen to

be still increasing, but at a diminishing rate. Indications are that about 80 percent of the

total deflection has already taken place.

Loaded Beams. Deflections measured at midspan for the loaded beams are shown

on Figs. 19 and 20. The significance of the descriptive terms marked on the deflection axis

has been explained in Section 17 .. The desired stress distribution before and after loading is

given in Fig. 5. For ~am ML-l, it was intended that the stress distribution of the unloaded

beams at midspan be reversed by loading. For beam ML-2, the stress distribution was to be .

rectangular immediately after loading at midspan •. Consequently, if there were no prestress

loss in beam ML-2 there would theoretically be no angle change in the flexure span. Angle

change would occur only at the ends producing an upward deflection at midspan. In realitYI

there wou Id be a prestress loss, but computations indi cated that the beam wou Id have a

final time deflection of zero at midspan. This beam would tend to deflect upward initially

as described above, and then as prestress was lost, angle changes at the center would return

it to a final zero deflection at midspan. The loss of load in the springs was also considered.

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31

Unfortunately, the lower concrete strength produced larger prestress losses than were antici-

pated, and the large creep strains with time combined with stress conditions different from

those desired produced downward midspan deflection of 0.035 in. at 2000 hours.

The measured instantaneous deflection caused by prestressing, the instantaneous

deflection caused by loading, and the computed values for both of these are shown in the

table below. Also presented in the following table are total deflections at 2000 hours, and

the ratio of total deflection to the computed deflection caused by loading:

Beam

ML-1

ML-2

Measured Deflections

At Prestress At Load tT ota I

.0831

.0960

. 138

.0625

.254

.099

*Computed Deflections

At Prestress At Load

0.063

.078

. 116

.0665

* Based on modulus of elasticity shown in column (3), Table 5. t Measured from the time immediately before loading.

Ratio of Deflections

T ota I/Computed at Load

2.2

1 .5

The measured deflections at prestress di ffer from those of the un loaded beams. For

ML-1 this is explained by the fact that a reduced initial prestress force (Table 1) was used to

compensate for the lower bottom tensi Ie stress produced by loading and thus reach the desired

stress distribution shown in Fig. 5. This prestress force, by mistake, was actually smaller

than it was computed to be. In the case of beam ML-2, the lower modulus of elasticity and

larger creep strains resulting from a weak concrete caused a larger deflection at prestressing

than for the unloaded beams, though the initial prestress was the same.

It is noted in the table that the ratio of the deflections caused by loading for

ML-1 and ML-2 is 2.2, but that the ratio of the loads applied is 2.0/ (Table 1). The dif-

ference in the two ratios is caused mostly by creep. The concrete stress was higher at the

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extreme fiber for ML-1 than for ML-2 and the loading time was greater. Both of these

factors tend to increase the creep deflections.

32

The computed instantaneous deflections were based on values of the modulus of

elasticity indicated by tests of cylinders described in Section 13 and shown in column (3),

Table 5. The discrepancy between the computed and measured deflections caused by pre­

stressing can be attributed mostly to the increase in deflection caused by creep during release

of the wires. The agreement of the computed deflections caused by loading with the

measured deflections is better than for the deflections caused by prestress. In fact, for

ML-2, the computed deflection is slightly greater than the measured. This can perhaps be

attributed to a uhardening ll effect caused by prestressing resulting in lower deflections at

loading. In addition, the concrete stress in beam ML-2 was decreased from thpt produced

by prestressing, thus reducing the effect of creep, and approaching rrore closely the

Il e lastic ll deflection condition (free of creep) which the modulus of elasticity is supposed to

represent. A Ithough the ratio of total to instantaneous deflection for ML-1 is much less than

for the unloaded beams, the total deflection is much larger .In Fig. 20, it is seen that the

time deflections of ML-l are about 44 percent greater than those for MU-2. This is reason­

able since loss of prestress reduces the bottom fiber compressive stress and increase the angle

change.

The deflections of the loaded beams would be even greater if the load applied

were constant. As the beams deflect, the force in the springs decreases. The magnitude of

the decrease is seen in Figs. 15 and 16; 14 percent for ML-1 at 2000 hours, and 6 percent

for ML-2. These curves were derived by assuming that the curve for the loss in load would

be proportional to the deflection curve for the beam. Several spring readings were taken over

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33

a period of time to establish the correct proportion. Curves presented in Section 21 show

that the increase in deflection for a constant load of 4000 Ib on .ML-l is 28 percent. This

would raise the ratio of total deflection to computed instantaneous deflection to about the

same magnitude as those of the un loaded beams.

(c) Beam Strains

Unloaded Beams. The strain distributions through the depth of the unloaded

beams MU-l and MU-2 are shown in Figs. 21 and 22. A description of these figures has

been given in Section 18. Strain lines between gage lines 1 and 4 have been extrapolated

to the top and bottom of the beam, except for the line "After Prestress". In this case the

readings were taken on the top and bottom of the beam. Each strain reading at a gage line

is the average of four readings, two on each side of the beam. For readings on the same

side of the beam an average 3 percent deviation from mean was noted, and the same devia­

tion was noted for the opposite sides. The strain distribution is linear up to 2000 hours.

The small amount of tension indicated in the top fiber on the line "After Prestress"

was probably the resu It of a slightly greater eccentri city of the wires than that required to

place them at the lower kern point. For the strain change between IIAfter' Prestress II and

"In Storage Frame" the strain line should rotate about the point of zero strain, since three

hours was too short a time for shrinkage strains to cause any movement of the point of

rotation. This is clearly the case for MU-l, but a slight deviation is apparent for MU-2.

The strains indicated on the top fiber of the beam are shrinkage strains reduced

by a small amount of creep in tension. The table below compares the shrinkage strains

indicated by the unloaded cylinders and the strains measured at the apparent level of zero

stress in the beams:

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34

Measured Shrinkage Strain

Beam Time Beam Strain Cylinder Strain

xl00 6

Hours x10

MU-l 2081 520 530

MU-2 1914 560 580

The comparison ~s quHe goodj' indicating that the di fference ira size between the beam and

the cylinder produced little or no difference ~n shrinkage strains.

Loaded Beams. The strain- distributions through the depth of the loa ded beams

Ml-l and ML-2 are shown on Figs 0 23 and 240 A description of these figures has been given

in Section 18. In Fig. 5 is shown the desHred stress distributions for the loaded beams. The

prestress losses at the level of the steel can be obtained from the strain measurements shown

on Figs. 23 and 24. The approx~mate stress distribution can then be determined from the

effectOve prestress. This ~s done on SectSon 20(bL Strain lines between gage lines 1 and 4

have been extrapolated to the top 000 bottom of the beam except at IIAfter Prestress U where

readings were taken on the top and bottom gage lines o Each strafn reading at the gage line

as the average of four readings}' two on each side of the beam. These beams exhibited more

variance among the four readlngs than did MU-1 and MU-2. The beam ML-1 seemed to

have some torsuon in it. ComparBng readongs on the same gage line, an average 5 percent

deviation from mean was noted for both beams" while a maximum 14 percent variation

exftsted between gage lines on opposHe sides of ML-1. The torsion does not seem to have

affected the linearity of strain distribution except for gage line 2 of ML-l where a slight

deviation 'M:lS noted .

. Both beams show about the same tensile strain in the top fiber after prestressing-

60 x 10-6

. This would correspond to about 140 psi. Th~smight have been caused by the

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35

wire reinforcement being located outside the kern point of the concrete cross-section.

I t is noted on Fig. 23 that the strai ns at the bottom of the beam are much less

than the strains at the top of the unloaded beams (Figs. 21 and 22). According to the

desired stress distributions shown on Fig. 5, these should be planes of zero stress. The

explanation, however, is that wi th prestress loss an initial stress condition of zero stress

in the bottom fiber at rrudspan of a loaded beam wou Id change to one of tensi Ie stress.

These tensi Ie stresses would result in tensi Ie strains reducing the compressive strains caused

by shrinkage. This seems to be the case for beam ML-l. The computations of Section 20(b)

have attempted to establish the actual initial stress distribution in the beams.

20. Description of Analysis for Deflections

(a) Assumptions and Scope of the Analysis

Preceding these tests, a theoretical analysis was undertaken by G. McLean (3)

to predict prestress loss in a beam creeping under a constantly changing stress. Losses due

to shrinkage and steel relaxation were also considered. It is now desired to follow this

method through using the data obtained in these tests, but substituting a numerical analysis

for the a Igebrai c one proposed by McLean. Deflections for both loaded and unloaded beams

are computed on the basis of several Simplifying assumptions. This represents the llexact"

analysis. Following this, some "approximate ll methods are attempted. These methods are

not entirely valid because they neglect certain variables, but it is interesting to see the

error involved when these short-cut methods are used.

The following general assumptions were made:

(a) Creep strains are linearly proportional to the sustained stresses.

(b) Shrinkage strains are independent of stress and uniform over the depth of the beam.

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36

In addition to these assumptions, the following factors used in the exact ana lysis

were treated as described:

(a) Wire relaxation data were obtained from Fig. 7. The curve of relaxation

loss for wire No. 12 was used after release of prestress.

(b) Creep strains were corrected for ihe "elastic ll change in strain caused by

the loss in prestress. For this computation the modulus of elasticity was assumed to vary

with time according to the curve on Fig. 13.

(c) The load on the beams ML-1 and ML-2 was assumed to vary with time. The

reduction in load was made according to the curves of loss of spring load versus time shown

on Fi gs 1 5 and 16.

(d) Full transfer of prestress between supports was assumed in all calculations.

\e) Deflection calculations were started at stage IIln Storage Frame" for the

un loaded beams and at stage JlAfter Load II for the loaded beams. The stress distribution

determined at these stages in Section 20(b) and shown on Fig. 29 was used as the initial

condition in the deflection computations.

(f) Since cylinder time readings did not begin until about 15 hours after beam

readings (Table 4), a linear change in creep strains was made for the increase in concrete

strength. This amounted to a 3 percent increase in creep strains for all beams, representing

the average change in concrete strength. Although no direct relationship could be found

between the creep strains for different concrete strengths, such a change within narrow

limits was considered valid for concrete of the same mix.

(g) As shown in Section 19(a), it was not possible to establish a direct relation-

ship between a creep coefficient and the f If'. ratios of the four beams. A correlation c CI

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37

could be devised applicable only to these tests, but that would not constitute a "general

creep function lf• Instead, creep strains corrected linearly to a 2000 psi load, increased

3 percent for time of loading as explained in (f), and adjusted to be qualitatively the same

as ML-1, which represented a median, were used in the computations. The adjustment

involved 8n eliminating qualitative irregularities was very small; it did not exceed 2 percent.

The dimensionless plot resulting for all beams is shown on Fig. 30. The individual creep

curves used in the computations are shown on Fig. 31 .

. Also shown on Fig. 31 is the average shrinkage curve used in the calculations.

The difference between the actual curves was judged small enough to warrant the use of an

average curve.

The increase in deflection due to time-dependent variables was considered in

sma II interva Is of ti me. These i nterva Is were short, aboyt 50 hours, at the early stages \

of the test when creep strain rate was high, and long, about 500 hours, at the later stages

of the test when the creep strain rate was low. The computation of total deflection at the

end of each interval involved the following steps:

(1) Determine the conditions of stress at the beginning of the interval.

(2) Determine the creep strain during the interval corresponding to the stress

distribution establ ished in step (1).

(3) Compute the loss in prestress corresponding to the total change in strain

at the level of the steel and the relaxation loss during that interval.

(4) Correct the change in strain distribution obtained in step (2) for the Uelastic"

change in strains caused by the loss in prestress.

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38

(5) Obtain the angle change at the end of the interval considered from the re­

sulting strain distribution in step (4).

(6) Compute the deflection by considering the distribution of angle change

along the length of the beam.

(b) Assumed Stress Distribution in the Beams at Beginning of Computed Deflections

The desired stress distributions in the concrete for the loaded md unloaded beams

after prestressing and loading are shown on Fig. 5. . Due to losses in the initial prestress

caused by creep of concrete, elastic shortening of the concrete, and relaxation of the

steel, the actual stress distributions differed from those desired. Since strain measurements

through the depth of the beam had been taken before and after prestressing and loading, it

was possible to obtain the prestress loss from the change in strain at the level of the steel.

Strain distributions for the unloaded beams are shown on Figs. 21 and 22, and for the

loaded beams on Figs. 23 and 24. The figures have been discussed in Section 19(c).

Having obtained the prestress loss, the effective prestress and the resulting stress distribution

were determined. These values, at the stages IIAfter Prestress", IIln Storage Frame ll, and

"After Load" are shown in Table 6. The difference of three hours in the first two stages

is reflected in the strain measurements at the level of the steel for each. This difference

is about 75 xlO-6

except for beam ML-2 which shows a greater difference. This difference

IS caused by creep of ~he concrete during the three hours.

For the computations it was assumed that the center of gravity of the wires was

located at the kern point of the concrete cross-section, and therefore there was no tension

in the top fiber. This is not the actual condition, however, as the strai n distributions

shown on Figs. 21, 22, 23, and 24 indicate. In these figures, tensi Ie strains at the stage

"After Prestress" are clear~y shown on the top of the beam. The effect of this behavior

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39

on instantaneous deflections caused by prestressing WQu.ld be to increase them due to a

greater prestress moment. Time deflections for unloaded beams would be increased slightly

wh i Ie time deflections for loaded beams wou Id be slightly decreased. This is assuming that

the rate of creep is the same in both tension and 'compression. Since the magnitude of these

tensile stresses could be determined only approximately, and since their effects would be

small, they were neglected in computing deflections. A graphical representation of the

stress distributions assumed for computations taken from the values given in Table 6 is shown

on Fig. 29.

It was also possible to determine the modulus of elasticity of concrete in the

beam from measured strains extrapolated to the bottom fibers for the values of the stresses

given in column (5), Table 6. These values of modulus of elasticity are shown in column (6),

Table 5. They are lower than the values given in column (3), Table 5, which were

determined from cylinders. The difference is caused chiefly by the creep strain produced

in the 15 or 20 minutes required to release the wires.

21 .. Comparison of Measured and Computed Deflections

(a) Unloaded Beams

Plots of measured and computed deflections based on an "exact ll analysis up to

2000 hours for beams MU-l and MU-2 are shown on Figs. 32 and 33. The assumed stress

distribution in the beams at the beginning of deflection measurements are shown on Fig. 29.

Also shown on the same figures are deflection curves computed for a stress 5 percen t greater

and 5 percent less than the assumed compressive stress in the bottom fiber. ,Referring to

Figs. 32 and 33 it is seen that the computed deflection curves describe the behavior of the

beam quite well qualitatively up to 2000 hours. The computed deflections are slightly less

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40

than the measured before 300 hours and by 2000 hours have become about 14 percent greater.

This behavior is the same for both MU-l and MU-2. A comparison of the three computed

deflection curves indicates that inaccuracies in assuming the initial stress conditions are

directly reflected in the computed deflections.

From a comparison of measured and computed deflections it is noted that the

measured deflections seem to be the result of a higher stress than computed in the early

stages and a lower. stress than computed in the later stages. Computing the deflections under

a higher initial stress during the early stages of the test and under a lower initial stress

during the later stages would result in a curve having good correlation with the measured

deflections as indicated by the curves shown.

Partia I prestress at the supports due to insuffi cient transfer length wou Id tend to

reduce the measured deflections. ~owever, it is also possible that quantitive differences

between the measured and computed deflection curves might be caused by a fundamental

difference in the creep behavior of ran a~ially-Ioaded cylinder, from which the creep strains

were taken, and a prestressed beam.

The deflection curves for MU-l and MU-2 which were computed by approxi mate

analyses are shown on Figs. 34 and 35. Computations performed in Method A assumed no

prestress loss, and therefore no change in the initial stress conditions, which were the same

as rn the "exact ll analysis. This incorrect assumption gives deflections for both MU-l and

MU-2 whi ch are about 55 percent greater than the measured deflections at 2000 hours. The

deflections indicated by Method B were computed in the following manner~ The prestress

loss at any time was computed for the total strain at that time at the level of the steel

assuming a constant initial stress distribution (Fig. 29). From the effective prestress remain­

ing, the corresponding bottom fiber stress was determined. The tota I angle change was

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41

obtained assuming that creep took place under this stress up to the time considered.

"Elastic" change in strain caused by a loss in prestress was neglected. Steel relaxation was

also neglected. This method has the advantage that a deflection can be obtained at any time

by a simple computation without knowing the intermediate changes in concrete stress. The

agreement between the measured and computed deflections is quite good, indicating only

that the approximations were taken in the right direction. At 2000 hours the computed

deflection is 4 percent greater than the measured deflection.

(b) Loaded Beams

P lots of measured and computed deflections based on an "exact" analysis for beams

ML-1 and ML-2 appear on Figs. 36 and 37. The assumed stress distribution at the beginning

of the deflection measurements is shown in Fig. 29. Also shown on Figs. 26 and 37 are

deflection curves computed for a stress 5 percent greater and 5 percent less than the bottom

fiber stress assumed before loading. Referring to the curves of Fig. 36, it is seen that the

qualitative and quantitative agreement of the computed curves with the measured curves is

quite good. At 2000 hours the computed deflection for the assumed initial stress distribution

before loadi ng is on I y 8 percent greater than the measured. The si mi lari ty between these

curves and the computed curves for the unloaded beams (Figs. 32 and 33) is quite evident.

The loaded beams have the added variable of the stress distribution at the ends of

the span. This has been assumed to be the same as at the midspan before loading. However,

there were no strain measurements taken here and therefore there was no way of checking

this assumption. A partial prestress condition at the supports of a loaded beam, however,

would tend to increase the measured midspan deflections. This behavior is the reverse of

that for an unloaded beam with partial prestress at the support. The computed deflection

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42

curves shown on Fig. 36, which are based on full prestress throughout the length of the beam

do not indi cate such a condition. On the other hand, tension in the top fiber, whi ch was

neglected in the computations, would tend to decrease the measured deflections in loaded

beams.

It was noted that the deflections computed for a 5 percent increase in initial stress

before loading were about 4 percent less than those computed for the assumed initial stress,

whi Ie the deflections for a 5 percent decrease in ini tial stress were 4 percent greater than

those deflections computed for the initial stress. This is iust the reverse of the unloaded

beams, where an increase in assumed initial stress resulted in an increase in computed de­

flections.

The computed deflection curves for beam ML-2 are shown on Fig. 37. The curves

become qualitatively simi lar as 2000 hours is approached. It should be noted that the total

measured deflections are quite small - less than one .... third of the measured deflections of

ML-1. It is also to be noted in Fig. 37 that a decrease of 5 percent in the assumed initial

bottom fiber stress before loading results ina 29 percent increase in deflections at 2000 hours,

and good agreement with the measured deflections. An increase of 5 percent in the initial.

assumed bottom fiber stress before loading results in a 30 percent decrease in deflections at

2000 hours. It is quite evident from these curves that a beam having a nearly rectangular

stress distribution at midspan after loading is very sensitive to small changes in prestress or

load. The cause of the slight "hump" appearing in all computed deflection curves up to

500 hours is not fu lIy understood. It should be noted, however, that it tends to disappear

as the assumed initial stress before loading is decreased.

It should also be mentioned here that the magnitude of the creep strains of ML-2

had a large influence on the deflections. Referring to Fig_ 31, which shows the cylinder

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43

creep strains for all beams as used in computations, it is seen that the strains of ML-2 are

about 40 percent greater than those of ML-1. Using the creep strains of ML-l in computing

the deflections of ML-2 resulted in a deflect"ion less than half as large at 2000 hours than

was computed using ML-2 Is own creep strains.

The deflection curves computed by the approximate analyses for the loaded beams

are shown on Figs. 38 and 39. The procedure used for Method A and Method B was identical

to that described for the unloaded beams except that strain distributions at support and at

midspan were considered independently. In addition, deflections were computed by

Method B assuming a constant load. The deflections indicated by Method A for beam ML-1,

Fig. 38, are about 37 percent less than the measured deflections. The use of a varying load

with Method B gives very good agreement with the measured deflections. Assuming a

constant load in the computations results in deflections which are 28 percent greater at

2000 hours than those for a varying load, whi Ie the decrease in load was about 14 percent.

This difference appears to be correct not only because Method B has given good correlation

between measured and computed deflections of loaded and unloaded beams, but also because

any change in strain distribution caused by flexural stresses produces twice the angle change

of a variation in bottom compressive stress of a beam with prestress only as is done for the

5 percent deflection curves.

Approximately computed deflections are compared with the measured deflections

for beam ML-2 on Fig. 39. I t is apparent that the use of Method A gives deflections whi ch

are very much in error, and do not define the actual behavior of the beam at all. This

demonstrates the importance of considering prestress losses in a loaded beam with a nearly

rectangu lor stress distribution at midspan. The deflections computed according to Method B

Page 60: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

exhibit fairly good agreement with the measured deflections except in the early stages.

However, Method B a Iso fai Is to describe the actua I deflection behavior of the beam.

22. Beam Deflections on the Basis of Beam Strains

44

The measured deflections of beams MU-l and MU-2 are compared in Fig. 40 with

deflections obtained from the angle changes in the measured strain distributions for beams.

The method of obtaining the strain distribution through the depth of the beam by means of

measured strains has been described in Sections 18 and 19(c). Measured strain distributions

at various times for the unloaded beams are shown on Figs. 21 and 22.

The total angle change at any time was determined as the difference in strains

on gage lines 1 and 4 divided by the di stance between gage lines, 5 inches. The strai ns

were measured from the reference line flln Storage Frame" to the strain distribution line at

a given time g Deflections computed in this manner constitute an lIinternal check" and the

agreement with measured deflections should be quite good. As is seen on Fig. 40, these

deflections are less than those actually measured. For MU-1 the computed deflections are

11 percent less than the measured deflections, and for MU-2 they are 8 percent less. A

portia I prestress condi tion at the supports is not the reason for this di fference as th is wou Id

result in computed deflections greater than the measured.

Curves similar to those of Fig. 40 are not shown for the loaded beams. No strain

measurements were taken at the ends of the span and therefore the strain distribution there

had to be assumed. Although it would have been possible to substitute the strain distributions

at midspan of the unloaded beams for the end strain distributions of the loaded beams, it is

doubtful if the interpretation 'WOuld have had any va lue because of the small errors usually

involved .

Page 61: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

45

23 . Prestress Losses

The instantaneous and time prestress losses at midspan in percent of initial stress

versus time are shown on Fig. 41. The instantaneous losses were derived from strain measure-

ments on the beam in the manner described in Section 20(b) are shown in co lumn (8), Table 6.

The ti me losses were determined from the computations for deflections by the procedure out-

I ined in Section 20(a).

The variables used to compute the time loss were the creep strains, shrinkage

strains, and relaxation loss for each beam. For all practical purposes, the latter might have

been omitted. At the beginning of time readings, the stress level of the wire reinforcement

in all beams was about 48 percent of the ultimate stress. After 2000 hours this had dropped

to 35 percent. As has been shown in previous tests (1), the relaxation losses between these

levels is negligible. The losses of wire No. 12 were used in the calculations. These

amounted to 1000 psi at 2000 hours or about 2 percent of the total losses of the beams.

I n the following table are given the instantaneous prestress loss and computed

time prestress loss at 2000 hours from the curves shown on Fig. 41. The initial stresses are

shown on the curves:

Beam

Instantaneous Pres tr ess Loss

Time Loss

Total Loss

MU-1 MU-2

ksi ksi

21.7 20.8

38.4 34.7

60.1 55.5

ML-1 ML-2

ksi ksi

19.8 25.2

24.8 36.2

44.6 61.4

As is seen in the table, the instantaneous loss occurring in the first 3 hours amounted to

35 to 45 percent of the total loss. The main factors influencing the instantaneous prestress

Page 62: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

46

losses are the stress intensity, modulus of elasticity of the concrete, its creep characteristics

and age of concrete at release. Relaxation loss, the greater portion of whi ch takes place

before release, also contributes to i'le magnitude of the instantaneous prestress loss. The

main factors influencing the prestress losses with time are the initial stress distribution, the

intensity of stress, and the creep and shrinkage characteristics of the concrete, which in

turn are affected by the storage conditions.

Also shown on Fig. 41 are total prestress losses based entirely on strain measure­

ments at the level of the steel. Their magnitude is shov.n by a short horizontal line at

2000 hours. The measured losses are about 10 percent I ess than those shown in the tab le.

Some of the difference can be accounted for by the fact that relaxation losses are included

only in the measured instantaneous loss.

Page 63: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

47

VIII. SUMMARY

The object of the tests described in this report was to study the combined effects

of time-dependent variables on the behavior of prestressed concrete beams.

Four pretensioned beams were tested. They were nominally 4 by 6-in. in cross­

section and 7 ft. 6 in. long. Six O. 196-in. high strength steel wires were used for rein­

forcement. The center of gravity of the wires was at the lower kern point of the cross

section. The initial prestress was 150 ksi in three beams and 137 ksi in the other. Two

beams remained unloaded after prestressing whi Ie two beams were loaded by springs at their

third points. All beams were supported on a 6-ft span in a specially constructed storage

frame located in a controlled temperature and humidity room.

Strains through the depth of the beam were measured mechani cally over 10-in.

gage lines. Deflections were measured at midspan of all beams.

Each beam had four 4 by 16-in. control cylinders. One of these was loaded by

means of springs to 2000 psi compressive stress in a special frame, and the other was loaded

to the same stress in a screw-type testing machine. Strain measurements taken wi th a

Whittemore strain gage on three 1 O-in. gage lines provided creep strain data. The other

two companion cylinders remained unloaded to provide data on shrinkage strains.

Three beams were prestressed at 5 days, and one beam at 7 days. The effect of

creep on deflections at prestressing and loading was found to be rather large. Slight

differences in concrete properties were reflected in the comparative magnitudes of the time

deflections of the unloaded beams. The deflection versus time curves were qualitatively

simi lar, however. Comparison of measured deflections due to ti me effects for a loaded and

unloaded beam with about the same compressive stress intensity at midspan showed that the

Page 64: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

48

deflections were greater for the loaded beam.

Creep strain curves obtained from the control cylinders differed in magnitude for

each beam, but were qualitatively the same. This was also true for the shrinkage strains.

Computed deflection curves based on several simplifying assumptions regarding the

creep and shrinkage behavior of concrete, and using the measured cylinder strains, were

slightly greater than the measured deflections for the unloaded beams and varied for the

loaded beams. It was noted that any reasonable method of predicting the time deflections

based on representative curves of creep and shrinkage strains in the concrete gave good

results if the reduced concrete stress resulting from a loss of prestress was considered. Com­

puted prestress losses were found to be about 10 percent greater than those obtained from

actual strain m~asurements at the level of the steel.

Page 65: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

49

IX. BIBLIOGRAPHY

1. Fourth Progress Report of the Investigation of Prestressed Concrete for Highway Bridges, Engi neeri ng. Experi ment Station, University of Illinois, 1955.

2. Fifth Progress Report of the Investigation of Prestressed Concrete for Highway Bridges, Engineering Experiment Station, University of Illinois, 1956.

3. McLean, G., IIA Study of the Time-Dependent Variables in PrestressedConcrete", M.S. Thesis, University of Illinois, June 1954. Issued as part of the Third Progress Report of the Investigation of Prestressed Concrete for Highway Bridges.

4. Janney, J. R., IINature of Bond in Pretensioned Prestressed Concrete ll, Journal ACt,

Vol. 25, Ntay 1954.

5. .Jensen, V. P., II Ultimate Strength of Reinforced Concrete Beams as Related to the Plasticity Ratio of Concrete ll

, University of Illinois Experiment Station Bulletin 345, June 1945.

6. Davis, R. E., H. E. Davis, and J. S. Hamilton, IIPlastic Flow of Concrete Under Susta i ned Stress II, Proc. AST M, Vo I. 34, pt. ~ 1934.

7. "Criteria for Prestressed Concrete Bridges", Department of Commerce, Bureau of Public Roads, 1954.

8. Carlson, R. W., "Drying Shrinkage of Concrete as Affected by Many Factors ", Proc. ASTM, Vol. 38, pt. JL 1932.

Page 66: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

TABLE 1. PROPERTIES 0 F BEAMS

Total load Beam b h No. of Wires Wire p. Fi f . - applied

and Area As Tlpe CI Sl

at third points

in. in. sq. in. psi Ib ksi Ib

MU-1 3.96 5.94 6-0.181 X 3760 27030 149.4 0

MU-2 3.96 5.94 6-0.181 X 3930 27030 149.4 0

Ml-l 3.96 5.94 6-0.181 X 3800 24860 137.4 4000

Ml-2 3.96 5.94 6 ·0. 181 X 3550 27030 149.4 2000

~

Page 67: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

51

TABLE 2. TYPICAL SIEVE ANALYSIS OF ·AGGREGATES

Gravel Sieve Percentage Retained

3/8 11 7.2 4 84.8

GJ 8 96.4 > c t... 16 97.7 <' c 30 98.5 Q)

50 99.0 0..

100 99.4

Sand. Sieve

4 2.7 8 20. 1

-c 16 42.6 s::: c 30 71.0 V')

50 95.5 100 98.6

Fineness Modulus 3.30

Page 68: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

TABLE 3. PROPERTIES OF CONCRETE MIXES

Cement:Sand :Gravel Water :Cement Slump 7-Day Beam Compressive Stress

by weight by weight inches psi

MU-l 1 :2.98:3.35 0.76 3" 4070

MU-2 1 :2 . 99:3 . 32 . 0.74 3" 4300

ML-l 1 :2 . 97:3 . 36 0.745 2 1/2" 4170

ML-2 1:2.96:3.33 0.80 5 11 3550

. Age at Test

days

5

5

5

7

. Cement Type

III

III

III

III

t11 r-..)

Page 69: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

E o G)

ctl

MU-1

MU-2

ML-l

ML-2

Vi G) I-

~ 4-o 0> C ·c o

·Vi c ~ 4-o G) -o o

4-11-57

4-18-57

5-1-57

5-9-57

Vi I-G)

-0 0> .: c­.- >.. tiu 0-0

U e: 4- 0 o Vi

G) E - 0 o G)

Octl

4-12-57

4-19-57

5-2-57

5-10-57

* Hours after Release of Prestress (+) Hours before Re I ease of Prestress (-)

TABLE 4. TEST CHRONOLOGY

E o G)

G)ctl Vi o e: G) .-

Q) ~ ~ G)

I-4- _

o Vi G)

G) I­_ D..

04-o 0

4-17-57

4-24-57

5-7-57

5-17-57

c o

-0 G) Q) E - 0 o I-tiLL. C Q)

rn E 0 o I-

G) .E ctlv) -IC

+3.0

+3.5

+3.0

+5.~ 5

~ c ·0 D..

-0 I-

.....c: I--o -0

G) -0 o

.,9 E ~

ctl -IC

+4.5

+6.0

0> C

+= I- Vi Q) <u

-0 ..... .: c - Q) >..~ t)

u 0.: ·c.....c: e: ._ 0

"I-oJ2 -.0 G) ~ "'--0 >..0

..c.,9 ~-IC

+44.:5

- 3.5

- 4.5

- .1.6

e: Q) 0-0

0> .= c-.- >.. -oW o Q) G) ~ 0>

-~ .g e: -.­._ I-

c-C V')

-IC

- 4.0

+ 6.5

+ 7.0

+15.0

I-Q)

-0 e:

Q)

>"E U 0

I-.LL.

C C " .--.0-0 ...- Q)

>..-0 ..c 0 ~..9 -IC

+19.0

+28.5

+22.0

+14.0

01 W

Page 70: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

54

TABLE 5. MODULI 0 F ELASTI-CITY

Modulus of Elasticity Modulus of Elasticity Beam From Cylinders From Beams

E f E E f E c c c c c c

( 1) 6 ' (2) (3)6 (4) 6 (5) (g) in. Ii n. x 1 0 ' psi x 10 psi in ./in. x 10 psi 10-' • X pSI

MU-1 650 2000 3.08 800 1963 2.46

'MU-2 630 2000 3.18 790 1970 2.50

ML-1 650 2000 3.08 755 1800 2.38

ML-2 740 2000 2.70 900 1938 2. 15

Column (1) and (4) Compressive strain. (2) and (5) Stress causing compressive strain.

Page 71: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Beam

TABLE 6. COMPUTED STRESS DISTRIBUTION IN BEAMS

Stage

e ce

(1)

"After Prestress II

f sr

(2)

~F

(3)

F se

(4)

~ (5)

Stage

"In Storage Framen

s AF F

se ~ f sr

e c

(6) (7) (8) (9) (l0) 6 -- -- --- - -~___r:,

in/in x 10 psi Ib Ib psi in/in x 10 psi psi Ib Ib

525: 3400 3460 23570 - 1963

517 3400 3420 23610 -1970

610

575

3400 3925 23110 -1926

3400 3740 23290 -1938

S~age

IAfterLoad"

Flexural Stresses Fi no I Stresses

f fcb f fcb ct ct (11 ) (12) (13) (14)

psi psi psi psi

MU-1

MU-2

ML-1

ML-2

470

580

3400 3170 21590 - 1800

3500 3780 23250 - 1938

545 3400 3580 21280 -1770 -2000 +1922 -2000 +152

725 3500 4570 22460 -1875 -1000 + 954 - 1 000 -921·

Column (1), (6) Total strain at level of steel measured from before prestressing

(2), (7) Relaxation loss. (3), (8) Prestress Loss (4), (9) Effective Prestress (5), (10) Bottom Fiber compressive stress in concrete computed on basis oLgross section (11), (12) Stresses induced by loading computed on basis of transformed section.

(13) Column (11) (14) Algebraic sum of column (10) and (12)

01 01

Page 72: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Gage Lines Top and Bottom ,

4"'1 : -~=J ~ ~ , B? Gageline

10"

Plan

;; r·~~i;;:-u~·1 ~~~i;~u~ I

0 0 0 0 0 0

0 0 0

0 0 0

~ - (S) Deflection Dial

6' -0" 2 plates 4"x4"x3/4"

Elevation

~1/2"

~r-----::~~---~-=--. ------..-~ """""'1];;@1 2/;; = 5"

I.. 10" .1. 10" .. I T 1/2" End View of Beam Indicating Position of Prestressed Wires Gageline Gageline

Lay-out of Gage Plugs

Fig. 1. Dimensions for Beams MU-l and MU-2

2

~

2 plates 41X4"X 3/ 4"

0 0 0

o 0 0

..... 11-11 '3 3' 11-'

4 - -:- 4. 4 Lt . 4"

:-::t

----N\

---i ~}

IF\' r-l

1\.0

01 0.

Page 73: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

9" 2' -0"

~[

Plan

2' _0"

Springs 2 in. D

2' -0" 9"

(0[1 - ~ ~ I ~ 0 I

=1 0 0 ",I, - _I-I -------r-----.------.I

Gageline 10"

rl

~ I 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

I~ageline lQ:1

Lay-out of Gage Plugs

r":;lC\I --1

J~ ---..:

rllC\l

~

Elevation

Deflection Dial

End View of Beam Indicating Position of Prestressing Wires

Fig. 2. Dimensions and LoadinG Arranuernent for Beams ML-l and ML-2

I~

01

"

Page 74: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

1" - N. F • Bolt 111 - N. F. Nut

3-Whittemore Gage Lines Equally Spaced 1200 Apart

4" x 16" Cylinder

Fig. 3. Dimensions and Loading Arran,_,ement for the 4" x 161

' Cylinders

58

Page 75: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

I_ 2' -0" t 2' -0" 14 2' -0" ~I

114 7*'~1·7*"·1 t r A

I. 8' - 611 pi

Eleva.tion

Fig. 4. Beams in place on Storage Frame

7'1 n

W:J 2' _011

Section A-A

11l --0

Page 76: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Entire Length of Beam

r- = -2000 psJ. c

MU-l

-2000 psi

At Support After Load and at Midspan Before

Load

+

+

= -1954 psi

Load

t f =-2000 psi

c

= +1922 psi

ML-l

=-1000 psi

fb = 954 psi c

MU-2 ML-2

At Midspan

f t =-2000 psi c

f t = -1000 psi c

fb =-1000 psi c

Unloaded Beams - at Start Loaded Beams - Imr;ledia tely Before and After Loading of Time Deflections (Time Deflections beGin Immediately After Loading)

Fig. 5. Nominal stress Distribution in Beams

0-o

Page 77: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

250 ~

,.......

~ f = 264 ksi ~ su

200 I~ '/ 1\ 0.2 percent Offset

stress = 215 ksi

'r! U)

~'(j

150 U) U)

ill H +' U)

.p • .-1

I I I

§ 100

06 . 0.196 in. Diameter

j E = 30 x 1 PSl 8 in. Gage LenGtb s

50

I o I

o 1 2 3 4 5 6 7 8 Unit Strain - percent

Fig. 6. Stress - Strain Relationship for Type X Wire 0.

Page 78: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

5.0 I

4.0

'" V

.r-! U)

~

3.0 U) U)

0 H

If~ V r, I.

s:: 0

.r-! -j-J

f: 2.0 ~ :x:

cD r-l OJ

I I I I

I p::;

I I

I 1.0 I

I I I I

o 5 da

~ ~ Wire No. 11 12

~ ~

Ultimate Type X = 264 ksi

1000 2000 3000

Time in Hours

Fig. 7. Plot of Relaxation Loss Versus Time for Type X Wires

1re No. 11

rre No. 12

% Ult.

54 ._~~'a '51

4000

0-N

Page 79: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

I

2 LS 3" x 3" x 5/16"

111 ld s ~ 2 We ed on L 1 pl. 3/8" x 2" x 6' -6"

8' - h"

I" ~ •. A "I r-- ...- -

Co

Detail A

-r ---, '- 2 L

S 3" x 3" x 5/16" F--

I

..- 1 - 8 C 13.75 1 - 8 C 13.75----" r--t

r- ........, - Clip LS 3x3x5/1~

I r-

'-- 2 LO 3" X 3" X 5/16" I I I r I '-2 L S 2 1/2" x 2 1/2" x 1/4"

I I --~ '-2 L

S 2 1/2" x 2 1/2" X 1/4Jl

,.... 3.75 LA

Elevation

Note: All connections are welded.

---,

~ 3·75

I I-I I I -I I

I

(\J , ~~ -10" Long

ril 'I 2 LS

;;1 ,-j

I -r--t

o , .-l

3"x3 1' x5/16"

Fig. 8. Dimensions of Stora"e Frame for Beams

Section A-A

0-w

Page 80: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Fig. 9. Loading of 4 by 16-in. Cylinder in Olsen Testing Machine

Page 81: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

\@=::::~~==~~=====~~=~:~::~~~ ---ft. 8'-0" .. 121L

~

L..-

I I

End Plate

Elevation

L Standard 3" Pipe End Plate

~6 - O.196-in. High Strength Steel WiLes

, Plan '- Standard 311 Pipe

1911

7f;"_~ 7t"

~

tJ~ 0' OO+OO~I 0 "::;1 00 00, ~~~

~ 5 - if7 Lirill @ 3/4" c. to c. 3

. U /411 2"

End Plate

Fig. 10. Dimensions of Prestressing Frame

I I

I ,

~

L..-

0-In

Page 82: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Fig. 11. View of Prestressing Frame During Tensioning of Wires

66

Page 83: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

6000

5000

..-l 4000 U)

Pi

...c: +' ~ ~ OJ H 3000 +' U)

OJ >

..-l U) U)

OJ H

~ 2000 0 u

1000

o

ML-l -

~ MU-2 -

~ ~ /'

~ V /' A

l' / V

IV

7

~~ ~ ~ v MU-l

."

~

~ ~ ---

14 Time in Days

MU-2 - r\ ----~ ""-

'- I- ML-1

"-- ML-2

21

Fi(,. 12. Plot of Concrete Stren,:::,t.h Versus Time Based on 6 by 12-in. Cylinders

-

28

~ "J

Page 84: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

5.0

L rBeams MU-l, MU-2, and ML-l

t<"\ 4.0 I 0 rl

><

~ ~ ~ ~

V / '-

-----""..",,-- roo Beam ML-2

'H U)

,."'l

~ 3.0 'H

C.J r£l

V V ",

/ V

~ - ----- ---1---------'--- -- '--+' 'H 0 'rl +' U) 2.0 cd rl r£l fH 0

U)

;j rl ;j rd 1.0 0 ~

o 500 1000 1500 2000

Time in Hours

Fig. 13. Plot 01' Modulus of Elasticity Versus Time

~

Page 85: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Fig. 14. View of Beam Before Release

Page 86: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

84

bO 88 ~ 'M ~

-rl

~ (]) p::;

rcj

~ 92 H

r-1 cd +J 0 E-;

+J ~ (]) u 96 ~ (])

P-i

~

I , -------

100

........ .......... """..-

~ ~

~ ~

I

V l/'

V

--~

500 1000 1500

Time in Hours

Fig. 15. Plot of Loss in Spring Load Versus Time for Beam ML-l

2000

" o

Page 87: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

)2

bD 91+ s:4

'M s:4

'M

~ Q) p:;

rcj cd 0 96 H

r-l

-5 0 E-I

".."...,.,.-~ ....."

~ ~

V ~

./ ~

-t.:> ~ Q) u 98 !:-, Q)

P-l

/ V

'--------._- .. -~ '-----.... . ••• ~ '------ -~.-- .. -

100

o 500 1000 1500 2000

Time in Hours

Fig. 16. Plot o~_ Loss in Spring Load Versus Time for Beam ML-2

'J ......

Page 88: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

3000

-_._---"--- ---~.--.,- ----Beam

2400 -- ---r -;;;;2

L---I---

----L----- r MU-l

\0 1800 0 rl

>< s::

.,-j

cd ~I .p (f) 1200

~ I.---' l-------

I~ ~

l---- r ML-l

--~ r:::: ~ l--""" ~

/ ~ C::::== L.--- '- MU-2

L-:::::::=: --

~ V V ~

/. ~

# ~ V~

600 ~ ~

ML-l - 1\ MU-2

j jr-I!~ \.

r- MU-l

, '- ML 2 J..----:: ....----=

) f ~~ rL o 500 1000 150C 2000

Time in Hours

Fig. 17. Measured Total Strains for 4 by 16-in. Cylinders

;:j

Page 89: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.20

U) .15 Q)

~ u s::

'M

~ 0

'M +l .10 u Q)

.---I CH (l) (::)

q

~ U)

rcj .05 '14 ~

MU-l l I

I

~ ~ I

-~ , I

~~ r;::-~ ~ ~ ~ MU-2

I

/ ",

I

I I ,

r-+-- After Prestress = In Storage Frame, MU-l and MU-2

V Before Prestress MU-l and MU-2 I

I

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

o 500 1000 1500

Time in Hours

Fig. 18. Midspan Deflection Versus Time for Unloaded Beams

2000

'-J w

Page 90: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.10 I'-Aftel' Prestress=In Storage Frame, ML-2

I--After Prestress=In Storaue Frame, ML-l

.05

~After Load - ML-2 rd H ~~

U} ~ OJ ~ 0 rCl U ~

'r-!

r ML-2

K.- Before Pres tress, ML-l and ML-2

~ 0

'r-! ~ U OJ - .05 rl

ct-; OJ ~

~

~ I

I \ After Load, ML-l oj Pi U}

'd or-! ~ -.10

rd H

~ 0 ~

-.15

, !

'" ~ ~ ~ ~ ~ '--ML 1 \1

o 500 1000 1500 2000

Time in Hours

Fig. 19. Midspan Deflection Versus Time For Loaded Beams ~

Page 91: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.16

Ul Q)

.12 .c: 0 s:: on

s:: 0 on +-' u

.08 Q)

rl tH <U Q

s::1 a Ul 'd on ~ .04

o 1

V ~ ,~

VI ~ ~ ,~

l.iliiii

~ , , , ~ ~ ~-/ ~

i....IIIIIII ~

J~ ~ ~ ,

~ ~

~ ~ "'" ~~ ", ~ ~ ....

-'~ """

l...- I..I1II ~ ~ -III -'

--~ ~ --10 100 1000

Time in Hours

Fib- 20. Comparison of Midspan Deflections for Beams Versus Time

ML-1

MU-l

MU-2

ML-2

10000

...... (11

Page 92: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

\' " \.~ ~ -::tr-l Top of BearnJ'

\~ ~<B Time in Hours ~

Gage Line 1 \ \ '\ " ~ \. ,

~ ~ " , '\ ~ ,

~ I" '\ " ~ ~ Gage-Line 2

, ~ ~ ... ~ '-. ~

'~ ~ '\~ ~

~" \\ \ 1\ '\ '\ ~

~Before ~ [\ \ '\ '\ ~ Prestress ~

Gage Line 3 1\ \ ~ ~" ~ '" \. ' .. , "- ~'-.

After Prestress J\ 1\ ~ ~

"- '\ ~ t- C. G. of Wire Reinforcement

1\\ In Storage .,

~ '\ \. "\ t\. k' Frame

\ \ .~

~ " ~ "\ , Gage Line 4 ~

\' ", " " ~ ~Bottom of Beam ~ ~ , 300 600 900 1200 1500 1800 2100 2400

Compressive Strain x 106

Fig. 21. Successive Strain Distributions in Beam MU-1 '-I 0-

Page 93: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

----.-------~-~~--- ----~

\ \~'\.~ t-...:t Top of Beam J' l1\ r-I

Gage Line 1 ~ Time in Hours

\ , ~ ~~ ~ ~

~ ~ \

, ~' ~ ~ ~

\ '\ \ ," ~ Gage Line 2 \~ ~~ "- '- "-,

~ , '\ ~ '\ ~~

~ \ \. '\ '\ ~

rBefore Prestress " \ \ '\ ~ I\.

\\ , , ,- ~" Gage Line 3 '-\\. , "- "- " ~ " " " 1\." ,"-After \ ~ , - e.G. of Wire Prestress Reinforcement

'\\ \~ '\ " ~'\ \. ~

\' ~ storage \ '\ " ,'\ Gage Line 4

~ Frr=:ottom of Be,,:

r\.. , \ '\ '\ ~'\

300 600 900 1500 1800 2100 2400

Compressive strain x 106

Fig. 22. Successive Strain Distributions in Beam MU-2 '..I '..I

Page 94: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

GCl.ge Line 1

Gage Line 2

Gage Line 3

Gage Line 4

Ul Ul OJ H .p Ul Q)

~ OJ H o

CH OJ J:Q

H OJ .p G-I ~

In storage Frame

Top of Beam

Time in Hours

of Beam

C. G. of Wire Reinforcement

1200 1500

Compressive strain x 106

1(300

Fig. 23. Successive Strain Distributions in Beam ML-l

2100 2400

~

Page 95: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Gage Line 1 t..

1\ " (/)

(/) Q)

H +>

Gage Line 2 ~ Ul Q)

~ Q)

H 0 ~ Q) r:q

V

Gage Line 3

Gage Line 4

, '0\ \0

~ ~ ~~ Top of Beam J

~ ~ 0 \0 ~r'\ ~~ Time in Hours m Q)

l OJ i<'\ r-I

~ ~ , -P H Cf) rr.. ~ ~-- ---

~ ,

. , ~After Load ,

~ \. " 1\

f ~, \ Ul \' ~ Q) H +> (/)

Q)

~ , ~~ I

H I Q)

~ +> I

~ \ ~'\ \. \ , i

'N, ' ~ \ ~C. G. of Wire

Reinforcement

'\ \~ ~~ ,

It.. ~,

{Bottom of BeEl.l11 \\ \Nl I 500 600 900 1200 1500

6 Compressive strain x 10

1800

Fig. 24. Successive strain Distributions in Beam ML-2

2100 24DO

~

Page 96: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

2000

1600

'D 1200 0 .-1

~

~ ·rl ro ~ tJ (f) 800

/

V/ /

,~ ~ 400 V If-

o o

\ ~

"".- L ~

~

/ r,-

/

~V ~ ~ ~

~ ~

-' \ -V ~ ........... ~ ~

~ / ~ ...." ~ ,.",-

~ ~ ~ "".",,-

~

500 1000 1500 Time in Hours

Fig. 25. Creep strains Versus Time for Loaded Cylinders

r- ML-2 MJ-l - 1\

-~

I- ML-l

f- MU-2

-

-

I

-2000

00 o

Page 97: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

100

80

.~ oj H

M ~ oj

60 +> 0

E-I ct-I 0

+> s:4 OJ C)

H 40 OJ

P..

.~ ~ .r! c:3 H

+> CJJ 20

o

MU-2 ~ ~ ~

/ ~ I- MU-l

ML-~_2 /

MU-l\ 1/

J

I f

o

r ) I--ML-l

if

20 40 60

Time in Percent of Test Duration Duration of Test 2000 Hours

80

Fig. 26. Dimensionless Plot of Creep strains Versus Time for Loaded Cylinders

81

100

Page 98: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

100

80

o~ ttl H +' Cf.l

,..; cd 60 +' 0

8 Cr-I 0

+' ~ (l) C) H

40 (l)

P-4 ~ on

s:l

~

J r on :0 H +' ::I)

20

r

~

o o

~ ~ ~

~ ~

/ ~ ~ 1000 psi ~

II"" ..- 2000 psi

~ ".

~

~/ / ,

20 40 60 80

Time in Percent of Test Duration

Duration of Test 2500 Hours

Fig. 27. Dimensionless Plot of Creep Strains Versus Time at Different Levels of stress

82

-----

100

Page 99: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

2000

1500

\.0 0 r4

X

~ .r-! 1000 as H +' rJ)

500

o

/ ML-2

IJ ~,

~ ~~ MU-l

II j ML-l

~ ,.

~~ IIV MU-2

/ ~ I J~ ~

~ ,

V ~~ ~ ~ ~ ~

~~ ~ ~ , ~ ~ ~ ~ ~~

~ ~ ~ I0IlIIII ~ :::

~ -""""""' ... -I I

10 100 1000

Time in Hours

Fig. 28. Comparison of Creep Strains for Loaded Cylinders Versus Time

10000

co w

Page 100: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

Entire Length of Beam

fb = 1926 psi c Beam MU-l

b r =-1938 psi c

Beam MU-2

Unloaded Beams at Start of Time Readings

At Support After Load and Midspan Before Load

~ fb = 1770 psi

c

rb =-1875 psi c

+

+

Load

t f =-2000 psi

c

b f == 1922 psi

c

Beam ML-l

t r =-1000 psi c

fb c

954 psi

Beam ML-2

At Midspan

to' f =-200 PSl c

fb c

152 psi

rt.=-lOOO psi c

b 1 . f =-92 PSl c

Loaded Beams - Immediately Before and After Loading (Time Deflections Begin Immediately After Loadin;:;)

Fig. 29. Computed Stress Distribution in Beams ~

Page 101: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

100

80

s:: . ..-/ ttl :>-; +' U)

rl ttl 60 +' 0 E-i

tH 0

+' s:: OJ C)

~ 40 OJ III

s:: . ..-/ s:: . ..-/ ttl '-i +' U) 20

o

~ ~

V ~

/ ~

/ /

I J V

/ I r

o 20 40 60

Time in Percent of Test Duration

Duration of Test 2000 Hours

80

Fig. 30. Dimensionless Plot of Creep Strains for Computations Versus Time

85

100

Page 102: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

\.0 0 rl

~

.~ ro H

M

2000

1600

1200

800

400

o _ o

/

/ V/

J~ ~ ~ ~ ~

V V

------........

V ~ ../

/ V

---------V ,,-

~

~ ~ ~ ~ ~ ....",."..,,-

V ~ ~ ..... ~

jIIII"'"

V ~ ~ ~ ~ .....

~ ~ ~ ",..

V

......... ""'" ~ ~ ~ ~ Average Shrinkage strain

500 1000 1500

Time in Hours

Fig. 31. Creep strains for Deflection Computations Versus Ttrne, And Average Shrinkage strains Versus Time

z.n:..-2

MU-1

ML-1

MU-2

2000

ex> 0..

Page 103: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.12

Ul OJ

.09 .C: CJ ~

.r-!

I=! 0

.r-! +' CJ

.06 (l)

r-l ct--l (l) Q

~ ~ Pl Ul

rrj .r-! ~ .03

r o

For Assumed Stress +5%_ r\ For Assumed Stress _ \\

~ ~

~ ~ ~

~ ~ --~ ... - ...... --

~ - ---~ ~ ~

.--

)~ I--

~ \ Measured

-For Assumed Stress -5%

----

500 1000 150C

Time in Hours

Fig. 32. Measured Deflections and Computed "Exact" Deflections for Beam MU-1

--

,-----

~--

---

2000

ex>

"

Page 104: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.12

Ul OJ

.09 ..q u ~

.,-i

c 0

.,-i

-J-l u

.06 Q)

,-I l+-i Q)

~

Q

a CIl cd .,-i

~ .C3

o

For Assumed Stress +5% \

For Assumed Stress - ,,\ \

~ .........

::::;:: ~ -~ ---'- ~_I --~ ......... .....

~ ~ ...- ~..., -\ ~~ ~ ...-'

For Assumed Stress -5% \ ~

~,.,. .......... \ Measured

I~ ......

// II' I

500 1000 1500

Time in Hours

Fig. 33. Measured Deflections and Computed "Exact" Deflections for Beam MU-2

-- -~ I I

2000

co co

Page 105: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.12

.09

Ul OJ ~ 0 ~ .06 .r! -5:l 0 'r! -fJ 0 OJ

r-l Cr;

.06 OJ q

~

~ Ul

~

i# rd -r! ::8

·(3 J ,.

I , o

~ ,....

---~

""",,-

~ l/ I- Method A -

V-/ /

l-Method B

V ~ I

~ --,,,- -- --la- ap.---

V ~ -= ...... flllllll""fIIIIIIII .~

~ ~ Measured

~ ~ ~ ...

~

~

I

500 1000 1500

Time in Hours

FiL;,. 34. Measured Deflections and Computed "Approximate'· Deflections ~>or Beam MU-1

-

~---

-

2000

co -.0

Page 106: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.12

U] Q)

.r:l

~ .09

~ 0 'r! +-' 0 Q)

r-t .06 ~

~ § PI

~

r/ / U]

r-cJ

~ .03

-

~ 1

o f .. o

'--r- Method A

-----~

~ ",,-

V

1/ V Method B - ,

.... --- .... - ...-- ........

Vl ~--- ..... ,,-= ~

,.,,-

~ .. ..-- - M=asured.

~ ~

500 1000 1500

Time in Hours

Fig. 35. ~8.sured Deflections and Computed "Approximate" Deflections for Beam MU-2

-

-

~--

-

-

2000

--0 o

Page 107: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

o

.03 (/)

OJ ,.cl CJ

~

til

§ .06 .r! +l CJ Q) r-I ct-J

~ ~ a .09 ell

rc:J

i!

.12

\~ '~~

~

~ ~ ~ ~ ~

~omputed for Assumed stress~ ~-. ~ r r- Measured

. +5% ~ 0

o

t'- __ ......

. ............ P5 ~ r---.: ----""'--r-----1- __ t- __

Computed for Assumed stress - r------r---. ~ r--------r-.-. ~

Computed for Assumed stress -5~ J....I -----r------500 1000 1500

Time in Hours

Fig. 36. Measured Deflections and Computed "Exact" Deflections for Beam ML-l

~--1"'"--

i

2000

'"

Page 108: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

0

l Ul Q)

..c:

~ .02

I~

'X ....... -r---... '<II

"--.. ---. ~ 0 ·rl +' t) Q)

r-f Cf.-I

~ .04

a Ul rd

i!

.06

Computed for Assumed stress +5~

I r~ Computed for Assumed stress I I ........... .......... I ............... ~ ........... r---- -.....

p....- --. ~-- -- .. "'--~ • \ - ...... - .... 1\ ---------

~Computed for Assumed Stress -5%

\ Measured

500 1000 1500

Time in Hours

Fig. 37. ~asured Deflections and Computed "Exact It Deflections for Beam ML-2

"'--

2000

'-0 "->

Page 109: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

o

~

.03

Ul OJ

~ \'S ~

..c:

~ . 06

Q 0 'rl +' t) (!)

r-I ct-f

8 .09 § P-4 Ul rd

~

.12

.15 o

~ ""' ~ ~ -......

r~ ~

"-"- .............

~ -~

~ -.............. / - Method A ~ ......

~ ~ r

~ "- ,. -LA --- .. ~

j~asured. --~ .... r- M:!thod B - Vary ing

~ -- --..... r -. ............ Load ....... l/ ~

" V ~thod. B - Constant - ~asured _ Load ,

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

500 1000 1500

Time in Hours

Fig. 38. Measured Deflections and Computed "Approximate" Ikf1ections for Beam ML-1

-

-2000

'-0 W

Page 110: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

1! til ~ Q) ~ ~.

~ r:l 0

oM +> () Q)

....-I CH

~

[ tfl rd

it

1 8

.02

0

.02

.04

.06

M=thcxl A

~asured

500 1000 1500

Time in Hours

Fig. 39. ~asured Versus Computed "Approximate 11 Midspan Deflections for Beam ML-2

2000

-.0 ~

Page 111: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

.12

U) .09 (l)

..c: CJ q ·rl

q 0 ·rl -fJ .06 CJ (l)

" ft--l Q) Q

~~ ~~

q

a U)

rc:J .03 ·rl ~ II

~

, o

o

MU-l - Measured \

\

MU-l - Based on _

~ ~- .. - ~-Beam stra~s .... .-fIIIIIII""'- ,-- \ ~~

----- la---~

,. ......... ,-.- -.-._1 ~-1-- 1

~ ~ ,......

1---.~ I'""'"

;'" ~ ~ ~-- \ ~ ~ MU-2 - Measurea .... " ~ ..-~ ~

~ ~ ---- \. - MU-2 - Based on Beam Strains

500 1000 1500

Time in Hours

Fig. 40. Measured Deflections and Deflections Based on Beam Strains for Unloaded Beams MU-l and MU .... 2

,.--p.....-

----

2000

j

I

I

-.0 01

Page 112: BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG … · BEHAVIOR OF PRESTRESSED CONCRETE BEAMS UNDER LONG-TIME LOADING A Thesis by P. E. Murphy Issued as a Part of the 5i xth Progress·

50

40

c.a en (J)

H -P CI)

rl cd 30 oM -P oM ~ H

~ 0

-P ~ 4) 20 C) H 4) ~

~ oM

~

~ ~

~ V

rt-~ c.a C1l 0 H 10

I-----~

o o

,."",---~ ~

....."..~

--------:::::::: ~

III"""

~ ~ ~ ...."

V """, ~

........ ~

~

computed Curves For

ML-l fsi =- 137.4 ksi

MU-2 fSi = 149.4 ksi

ML-2 fSi :: 149.4 ksi

MU-1 fsi = 149.4 ksi

500 1000 1500

Time in Hours

Fio - 41. Plot of Prestress Losses for all Beams

ft MU-l rML-2

'I

r MU-2 :J,;.MU-l ML-2

L t'MU-2i ML-l

~ML-l

2000

-.0 ~