PRESTRESS LOSS AND CREEP CAMBER IN A HIGHWAY BRIDGE WITH REINFORCED CONCRETE SLAB ON PRETENSIONED PRESTRESSED CONCRETE BEAMS

by

Howard L. Furr, Research Engineer

Raouf Sinno, Former Assistant Research Engineer

Leonard L. Ingram, Research Associate

Research Report Number 69-3 (Final)

Creep in Prestressed Concrete

Research Project Number 2-5-63-69

Sponsored by

The Texas Highway Department In Cooperation with the

U. S. Department of Transportation, Federal Highway Administration Bureau of Public Roads

October 1968

TEXAS TRANSPORTATION INSTITUTE Texas A&M University

College Station, Texas

ACKNOWLEDGEMENTS

The valuable assistance of Mr. H. D. Butler, Designing

Engineer, Texas Highway Departmen~ in carrying out the work

reported here is gratefully acknowledged.

The opLnLons, findings and conclusions expressed in this repcrt are those of the authors and not necessarily those of the Bureau of Public Roads.

ii

TABLE OF CONTENTS

Chapter

1 INTRODUCTION . . . . . . .

2 CAMBER AND PRESTRESS LOSSES IN BEAMS WITH DRAPED STRANDS AND WITH STRAIGHT

3

4

APPENDIX

STRANDS

CREEP, CAMBER, AND PRESTRESS LOSSES HOUSTON BRIDGE . . . .

SUMMARY AND CONCLUSIONS

COMPUTER PROGRAM . . .

iii

Page

1

3

24

92

97

LIST OF FIGURES

Figure Page

2-1 Prestressed Beam Details, Lufkin Beams . 7

2-2 Measured Strains at Release of Prestress.

2-3

2-4

2-5

2-6

2-7

2-8

3-1

3-2

3-3

3-4

3-5

Predicted Strains under Full Dead Load after Prestress Loss .

Computed Strains under Full Dead Load after Prestress Loss Anticipated at One Year Age . . . . . • •

Stress Variations in Beams

Strains at Bottom Gage Points

Beam Camber

Camber Profiles

Prestress Loss .

General Plan of Bridge .

Bridge Plans and Section Details

Slab Gages and Shrinkage Specimen

Total Creep and Shrinkage of Slab Concrete ....

. . • . . . 11

11

12

14

15

18

21

29

30

31

39

Unit Creep Curve of Slab Concrete (Lightweight). 39

3-6 Total Creep and Shrinkage of Slab Concrete -Normal Weight Prisms . • . . • . . . . . . .40

3-7 Unit Creep Curve of Slab Concrete (Normal Weight) .. 40

3-8 Total Creep and Shrinkage of Beam Concrete (Lightweight Prisms) . . • • . . . . . 42

3-9 Unit Creep Curve of Beam Concrete (Light..,ight). 42

3-10 Total Creep and Shrinkage of Beam Control (Normal Weight Prisms) . . • . . . . . • . • . . . . . . . • 43

iv

Figure Page

3-11 Unit Creep Curve of Beam Concrete (Nonnal Weight). . . . . . . . . . . . . . 43

3-12 Shrinkage in NW Concrete Slab 3 ft. X 3 ft. X 7 1/4 in. . . . . . . . . . . . 44

3-13 Shrinkage in LW Concrete Slab 3 ft. X 3 ft. X 7 1/4 in. . . . . . . . . 44

3-14 Shrinkage Curve of Beam Concr~te, Normal Weight . . . . . . . . . . . . . . 45

3-15 Shrinkage Curve of Beam Concrete, Lightweight . . . . . . 45

3-16 Strain in Bridge Beam Ll-5, LW 50

3-17 Strain in Bridge Beam L3-5, NW 51

3-18 Strain in Bridge Beam L4-5, LW 52

3-19 Strain in Bridge Beam L4-5 (Cont'd.) 53

3-20 Strain in Bridge Beam Rl -:5, LW 54

3-21 Strain in Bridge Beam R4 -5, LW 55

3-22 Average Temperature and Relative Humidity at Houston, Texas 59

3-23 Strain in Slab LS -1, LW 60

3-24 Strain in Slab LS -3, LW 61

3-25 Strain in Slab LS-4, LW 62

3-26 Strain in Slab RS -1, LW 63

3-27 Strain in Slab RS -4, NW 64

3-28 Deflection of Bridge Beam Ll-5, UJ 66

3-29 Deflection of Bridge Beams Ll-1, 3, 6, 8, LW 67

3-30 Deflection of Bridge Beam L3-5, NW 68

3-31 Deflection of Bridge Beam L3-l, 3, 6, 8, NW. 69

3-32 Deflection of Bridge Beam L4-5, Ul 70

3-33 Deflection of Bridge Beams L4 -1, 3, 6, 8, LW 71

v

Figure Page

3-34 Deflection of Bridge Beam Rl-5, LVI 72

3-35 Deflection of Bridge Beam RZ-5, LW 73

3-36 Deflection of Bridge Beam R3-5, NW 74

3-37 Deflection of Bridge Beam R4-5, LW 75

3-38 Prestress Loss in Bridge Beam Ll-5, LW 81

3-39 Prestress Loss in Bridge Beam L3-5, NH 82

3-40 Prestress Loss in Bridge Beam L4-5, LW 83

3-41 Prestress Loss in Bridge Beam Rl-5, LW 84

3-41 Prestress Loss in Bridge Beam R4 -5, L\1 85

:3-43 Influence of Changes in Sets of Modulus, Shrinkage, and Creep on Mid--sptn Deflections. . . . . . . . . . . . . . . 86

3-44 Influence of Changes in Sets of Modulus, Shrinkage, and Creep on Prestress Loss at Mid -span . . . . . . . . . . . . . 90

vi

LIST OF TABLES

Table Page

2.1 Pres tressed Test Beam 6

2. 2 Strains at Release 9

2.3 Beam Camber Due to Prestress and Self Weight 16

2. 4 Pres tress Losses in Steel 20

3.1 Beam and Slab Designation 27

3. 2 Properties of Slab Concrete 34

3. 3 Mid-span Deflections of Beams 57

3.4 Prestress Losses at Mid-span 77

3. 5 Changes in Final Mid -span Camber and Prestress Loss with Changes in Modulus of Beam Concrete . . • . . . . . . 79

vii

ABSTRACT

A numerical procedure using a step-by-step method is used for

computing both elastic and time dependent strains, deflections, and

prestress losses in full size pretensioned prestressed concrete

highway bridge beams. Both lightweight and normal weight structural

concretes are used. The method uses creep and shrinkage functions,

derived from control specimens, for making predictions.

The computed strains, deflections, and prestress losses agreed

well, for the most part, with measured values during the time interval

from d&te of casting of the slabs to end of tests. The beams were

about 320 days old when the slab was cast, and tests terminated at

660-day beam age.

Measured elastic beam deflections under the weight of the plastic

slab were a little over 50% of the deflections computed by theory,

Prestress losses were about 15% in 40 ft. long lightweight concrete

beams at 660 days. The 56 ft. LW beam loss at the same age was about

21% and the NW beam 14 1/2%.

The changes in camber and prestress losses after the slab waz,

cast were minoro

viii

CHAPTER 1

INTRODUCTION

A study of strains, camber, and prestress loss in pretensioned,

prestressed beams began in 1964 is concluded with this report. The

purpose of the study was to provide information that could be used

by the highway bridge designer in prestressed concrete construction.

It was concerned almost altogether with lightweight concrete because

of certain advantages promised in that material and because little

information on full size field structures made of that material was

available.

A mathematical method for computing creep in prestressed beams

was applied in predicting creep strains in laboratory beams early in

the program. That application indicated that the approach would be

feasible in predicting camber and prestress losses in full size

prestressed highway bridge beams, and the program was extended for

that purpose. Creep of concrete only, not steel, was treated.

After a study and field tests of instrumentation requirements,

a full size bridge, then in the design stages, was designated as a

test bridge for proving the prediction method.

An earlier report (1) gave details of the early work in the

development of the prediction method. It also reported strains, camber,

and prestress losses over a 300-day period for the beams of the test

bridge.

In the study of the beams for the test bridge, questions con­

cerning camber of beams with straight strands as compared with beams

with draped strands arose. In order to develop some information

1

that would bear on those questions, four full size test beams were

built, Two o:ti those were straight strand beams with bond broken

over end portions of some of the tendons, The other two beams had

draped strands,

This report discusses the four test beams in Chapter 2, and

the longer discussion of the continuation of the full size bridge

study is given in Chapter 3o

2

CHAPTER 2

CAMBER AND PRESTRESS LOSSES IN BEAMS WITH DRAPED STRANDS

AND WITH STRAIGHT STRANDS - LUFKIN BEAMS

2.1 Introduction

Camber in beams occurs only when strains at the top and bottom

differ, and if such differences are minimized, camber will be

minimized. Prestress loss, on the other hand, develops as the

concrete strains at the centroid of the steel, whether or not the

strains in the section vary from top to bottom.

Arrangement of prestressing steel in different patterns

within a beam makes it possible to balance, approximately, the

shear and moment capacities with the requirements o£ external

loads. Post tensioned members have been more adaptable to such

arrange~ents than pretensioned members.

The draped strand pattern used widely in highway bridge beams

lowers the centroid of prestressing steel near mid-span. That

arrangement provides a moment resistance which gradually increases

from the end to the mid-span region where imposed moments are highest.

The total pretensioning force is carried through the full length of

the beam, but its eccentricity from the beam centroid decreases from

near mid-span, the hold down points, to the ends.·of; the beam.

Since the full prestress is carried the full length of the beam,

concrete strains, and consequently prestress loss, will have a

corresponding development along the beam. The great difference

between stresses at top and bottom of the beam near mid-span will

3

cause deflections consistent with those differences.

The same general moment.resistant characteristics realized in

the draped strand beam can be built into a beam with properly

treated straight strands. In the latter, moment resisting capacity

may be controlled by breaking bond between the strands and concrete

in well defined, carefully controlled patterns. A beam with a

gradual reduction of the number of effective strands between mid-span

and its ends, accomplished by breaking bond over successive partial

lengths of strands, will accomplish that control. The bond may be

broken by placing an impervious rigid sleeve, such as plastic tubing,

over the desired length. Such a beam would carry increasing amounts

of prestressing force between the end and mid-span, and would possibly

suffer less prestress loss than the draped strand beam.

A study was made of draped strand beams and blanketed strand

beams for purposes of comparing deflections and prestress losses.

The beams were made in two pairs, one pair was of normal weight con­

crete; the other, lightweight. Each pair consisted of one beam with

draped strands and one with. straight blanketed strands. The beams

were fabricated at Lufkin, Texas, and are referred to here as Lufkin

beams.

Details of the study follow.

2. 2 Objectives

1. To determine the effect on camber and prestress loss when

bond of prestressing strands is broken over a portion of length of

full size highway bridge beams.

2. To compare the behavior of full size normal weight and

lightweight highway bridge beams with partial blanketing of prestressing

4

strands.

2.3 Test Specimens --Lufkin Beams

Four full size 50 ft. prestressed concrete beams, Texas Highway

Department Type B served as the test specimens. Two of those beams

were made of normal weight concrete, and two were of lightweight

concrete. One normal weight and one lightweight beam were prestressed

with draped strands. The prestressing strands in the other two were

straight. Part of those straight strands were encased in impervious

plastic tubes over a portion of each end for purposes of breaking

bond of those blanketed strands. Full bond was assumed to be effec­

tive 2 ft. from the end of the tubes. Fig. 2-1 gives details of

those beams.

Strain gage points and elevation points were installed in these

beams in the same way as those described in an earlier report (1).

All beams were cured under wet mat until cylinder breaks

indicated that release strength had been reached. After removal

from the prestressing line they were cured an additional three days

under impervious matting. The beams were wetted frequently by rain

during their first three weeks of open yard storage.

2.4 Materials

Prestressing steel was specified as 250 K, stress relieved,

9/16 inch diameter, 7-wire strand meeting ASTM Specification A-416

with 27,000 lb. minimum ultimate strength. No tests were made on

this material.

Normal weight concrete was made with Type III cement, natural

sand, and crushed limestone proportioned by weight at 1:1 .. 82:3.10,

respectively. The ·water-'cement ratio was 0. 51.

5

Mark

LWB

NWB

LW

NW

TABLE 2 .1 PRESTRESSED TEST BEAMS

Note: All beams 50 ft long; transported 130 miles by truck on April 22/68

Condrete Strands D te Type Cast Release

LW Straight, blanketed 3/13/68 3/15/68

NW Straight, blanketed 3/13/68 3/15/68

LW Draped 3/20/68 3/22/68

NW Draped 3/20/68 3/22/68

6

2' 4~'

I ,. ,.

I

, __ _ ', __ _ , __ _ (., E

' ~ ~ . '

0 0

olo

0 0

®

3' o' 3' o" 3' o' 3' 0'

0 0 0 0 0 0 0 0 0 0

olo olo olo ala- olo Gl~~PT;:~t1o~ 17"

0 0 0 0 0 0

® © ©

GAGE POINT LOCATIONS DRAPED STRAND BEAMS

OMIT STATIONS B, D, F

a I o--, 3 .. 0 0

© ©

LENGTH OF BLANKETED PORTION OF STRANO

BLANKETED STRANO

MEASURED FROM END OF BEAM (FT)

STRANO ACTUAL

0

C2,0,C4,C5 ' 62, 63, 64, B5 '

A3, A4 , A2, A5 " AI, A6 "

123456

SECTION THO TYPE B

FIGURE 2-1

7' 4~" 13' 4~" 11' o"

ELEVATION POINT""' (TVPICAU

0 0 0 0

olo cgc ala --· 1--- ::::,__- ---!----~ ~ MIDSPAN--........... ----------~==--==---

--r== -- !:=.:=- = __:=:: =-~ ~ ~-~---== -- ~===== •:::e=~~--~ = of.-~ --

© 5'0" HOLOOOWN POINT

"'

' ~'" TYPE DESIGNATION

EFFECTIVE (in)

0 '' DRAPED ,.

' ' '" DRAPED cw

' ' 6.13

BLANKETED ,. " 6.75 " " 7.26 BLANKETED cw

" " 7.70

®

DRAPED STRAND DETAILS END OF BEAM e = 7.84 in MIDSPAN e=ll.llin

BLANKETED STRANO ARE STRAIGHT' DETAILS ARE SHOWN BELOW

NUMBER fc' (PSI)

" STRANDS 2 DAYS 70AYS 150 DAYS 2 DAYS

" 5a20 6740 6690 ·~

" 6620 ,;oo "~ 3120

" "~ "" o;oo 5360

" 5060 5970 7080 ""

PRESTRESSED BEAM DETAILS LUFKIN BEAMS

Eel KSI I UNIT WEIGHT

70AYS 150 oms lb/11°

5150 ·= "" "00 "' 0000 0000

MO "00 '"

, .. ,,

Lightweight concrete was made with Type III cement, natural sand,

and expanded shale (Featherlite Ranger) coarse aggregate.

The weight ratios were 1:1.36:1.52,·and the added water-cement

ratio was 0.49. It contained 6% air (by pressure meter) and had

a plastic weight of 119 lb./cf. The expanded shale was wet down

overnight by sprinkler before mixing.

Slumps varied from 2 to 3 3/4 in.

2.5 Tests

Compression tests made on the standard 6 in. diameter cylinders

yielded strength and stress-strain data for each concrete. Cylinders

were preloaded to 30 kips three times before data collection began

in these tests. Dial gages, mounted in each quadrant, measured

strains over a six in. gage length. Strength and strains were

averaged for three cylinders for each test.

• were determined at 1/2 f .

c

The secant moduli

Elevations and strains were taken from each beam just before

release, just after release, daily for the first five days, weekly

for one month, and at two to three week intervals thereafter.

Strains were averaged for the corresponding

on opposite sides of the beam. Elevations were reduced to give

camber at each elevation point.

Curves of strains and of elevations versus time were developed

from the test data.

2.6 Test Results and Discussion

A. Strains

Beam strains for both sets of beams are listed in Table 2.2 and

are displayed graphically in Fig. 2-2.

8

Beam

NWB

LWB

NW

LW

Ratio:

TABLE 2.2 STRAINS AT RELEASE

Position End

Computed

Top ---Bottom ---

Top ---Bottom ---

Top -5 Bottom 442

Top -12 Bottom 602

Computed bottom {:~ Measured bottom tLw

Measured

80 195

90 240

-25 415

-35 545

End

1.065 1.105

STRAIN (MICRO-INS)

Quarter Span

Computed ·Measured

--- ll5 --- 375

--- llO --- 470

6 -5 433 400

-12 -20 599 545

Quarter Span

1.083 1.099

Mid-span

Computed Measured

------

------

-6 440

-36 612

Mid-span

1.1431 1.166J

140 435

120 555

-5 385

-40 525

Avg.=l.ll

The purpose of breaking bond was to reduce the difference in

stress between the top of the beam and the bottom in order to reduce

corresponding strain differences and thereby reduce camber of the

beam. It is shown in Fig. 2-2 that the change in strains between

top and bottom of the blanketed strand beams is much less than the

change in draped strand beams. The reduction would not only cut

down on elastic strains, but it would reduce time dependent camber

as well.

Fig. 2-3 shows the strain gradient for the four beams under

full dead load having undergone all anticipated elastic and time­

dependent prestress losses at one year age. Prestress losses of

15% for normal weight concrete and 20% for lightweight concrete,

determined in previous tests of similar beams (1), were used in

computing strains•

Beams with draped strands undergo considerable changes in

stress and strain between ends and mid-span, and further change

is brought about with the addition of dead loads. See Figs. 2-2,

2-3, and -2-4. Camber, depending on the strain gradient from top

to bottom of beam, would be expected to be greater in the draped

beams than in their companion straight blanketed strand beams.

Fig. 2-7 confirms that expectation. Under design live load plus

impact, mid-span stresses in the bottom of the beam become essen­

tially zero and the top stresses increase some 200 to 350 psi,

well within limits of practice.

The fact that the addition of full dead load to prestressed

beams reduces the stress gradient from top to bottom suggests that

10

--------------------------------------------------

TOP SURFACE OF BEAM

0

' 0

LIGHTWEIGHT NORMAL WEIGHT

BOTTOM

TENSION

-200 0 200

STRAIN (MICROINCHESl

-200 0

---- BLANKETED STRAND --- -- DRAPED STRAND

200

STRAIN (MJCROINCHES)

600

FIGURE 2-2 MEASURED STRAINS AT RELEASE OF PRESTRESS

BOTTOM TENSION

-200 0 200

STRAIN

(MICROJNCHES)

LIGHTWEIGHT

400

TENSION

600 -200

BLANKETED STRAND

----- DRAPED STRANO

0

0

I

' 1., NORMAL WEIG

' lg "' "' I~ ~ ~~ ~ ,I "' \ z

" I I 1\

\ \

200

STRAIN

(MICROINCHES)

\ COMPRESSION

400 600

FIGURE 2-3 COMPUTED STRAINS UNDER FULL DEAD LOAD AFTER

PRESTRESS LOSS ANTICIPATED AT ONE YEAR AGE

HT

"'" 2000

ill w ~ ~ ~ '"" ·-

1000

z Q

~ 500

BOTTOM AT RELEASE

BOTTOM

WITH FULL DL AFTER ALL ESTIMATED LOSSES

--f--,1:---~~---t~--~--~--~~---" " " " < TOP AT RELEASE

DISTANCE FROM END OF BEAM (ft)

(a) BEAM NW

"" BOTTOM AT RELEASE

>000 1:---------------~"---------"

""" 1000

~ ~ -500

DISTANCE FROM (ft}

(c) BEAM

BOTTOM

"

END OF BEAM

LW

" <

WITH FULL OL AFTER ALL ESTIMATED LOSSES

TOP AT RELEASE

FIGURE 2-4 STRESS

2500

00 <WOO 00 w ~ ~ 00

"'" 1000

~

" ~

BOTTOM AT RELEASE

WITH FULL Dl AFTER ALL ESTIMATED LOSSES

-+-8 oef----c-----o----co---~o-'-'_'_'c'c-''_'_'_'_'' 10 IS 2.0 25

2500

:woo

z

~ -500

"

DISTANCE FROM END OF BEAM

( fl)

(b) BEAM NWB

<

BOTTOM AT RELEASE

DISTANCE FROM END OF BEAM

(ft)

(d) BEAM LWB

VAR lATIONS IN BEAMS

the beams should be loaded as soon after casting as the situation

permits. The early loading would reduce camber growth due to sus­

tained prestress and possibly permit a deck slab of more uniform

thickness.

The influence of broken bond on strains in some of the prestress­

ing strands can be seen in Fig. 2-5. The narrow range of strains in

the draped strand beams is reflected in the curves of Fig. 2-4(a) and

(c) where little change in stress at release is seen along the length

of the beam. In the same way, the spread of strain curves for

blanketed strand beams is reflected in the stress changes displayed

in Fig. 2-4(b) and (d).

No attempt was made to smooth out the strain plots because the

display is intended to show only the trend of strains along the beam

length.

The blanketed strand beams, both normal weight and lightweight,

deflected considerably less than the corresponding draped strand

beams, Fig. 2-6 and Table 2.3. At mid-span the ratio of upward

deflection of the blanketed strand normal weight beam to that of

its companion draped strand beam was 0.57. The corresponding ratio

for lightweight beams was 0.62. Corresponding values at quarter

span were 0.50 and 0.58, respectively.

Fig. 2-6 indicates that creep camber in the blanketed strand

beams had reached near stability at about six weeks to two months

age, whereas the draped strand beams continued to creep noticeably

at the end of the test period.

13

z ..... z

<i) I 0

z <[ c::: 1--en

1200

1000

800

600

400

200

f ~:,.····)'

v 0

0

NO~MA~ WE1

1GH-f BEhM ,· I

STATION G I {MIDSP~Nl~ ~ ~

i""- ........ STRAIND BEJM

i:,.,, f'''''fRAN~E OF STRAINS IN BLANKETED ----.... , ... - ---~--

f--- ----/' ... r-..-- -- 'STATION A (END)

- BLANKETED STRANO BEAM (NWB) --- DRAPED STRAND BEAM (NW) STATION A

-~ RANGi OF STtAINS liN DRAlED STRiND BEiM STATiONS BIG

20 40 60 80 100 120 140

AGE DAYS AFTER RELEASE

1200r=+++=+=~~~ Ll T 1

WE T BEAM y 0 ~dv" G I ..

~ IOOO~;t;;l~;;~~~~~;~.~~,~~-~==r::t::l::l::~~,·~···•• z 800~ 'f

0 II'·•> RAowE oF!nRAIN' IN BLANKETED STRANo lE.IM

1

600[llJIJ~EE~~ Z ~ oo.llvNA(ENrn

c:::<C 4 0 0 I ,.J

If" BLANKETED STRAND BEAM (LWB)

1-- --.-,_, ___ -,- RANGE OF STRAINS IN DRAPED STRAND BEAM en 200~--~--~--+-~""+---,---,---,---,----r---r---+---+---+--~

20 40 60 80 100 120 140

AGE DAYS AFTER RELEASE

FIG. 2-5 STRAINS AT BOTTOM GAGE POINTS IN BEAM

1.5

1.0

..,...,~

0.5 .....

z 0

z ~ 1.0 f-u w ....J0.5 "-w 0

0

.. --20

-- ~----

20

-- I~M~~-:_N_J_j __ ---- --- --- -- / _lt4 ~':AN _ 1 ---- -· ·- --- i

TOTAL CAMBER --NW,E --NW

40 60 80 100 120 140

-- -- --1-- --- ----f---1----CREEP CAMBER AT MIDSPAN -~' -NW

40 60 80 100 120 140

0.

5k 1--t-t-4-:t:tER %-:;;:N-§;t-1--~--r-j 0 w ~ 00 00 00 ~ ~

I. 5 I. 0 -·

r:.... 0. 5v

z 0

z 0 I. 0

f­u ~0. "­w 0

5

0 /'

AGE-DAYS

(a) CAMBER OF NORMAL WEIGHT CONCRETE BEAMS

_____ t"'" _________

>--- -- - k _l __ ~----- - --- SPAN-! ~MIDSPAN - - lt4

TOTAL I __!___LWB

CA~BER -~-LW

20 40 60 80 100 120 140

1---1--- --+--- 1--· 1--- -- --~--1---......,

CREEP CAMBER AT MIDSPAN cw• ---LW

20 40 60 80 100 120 140

~5

U__j,l ~f-=-+f-:==f.£=e ;-=FA~=,.=rA~=~~09s=PAN=f5=:~-f~. -i[-]--1---i]-----1] 0 20 40 60 80 100 120 140

AGE-DAYS

(b) CAMBER OF LIGHTWEIGHT CONCRETE BEAMS

FIG. 2-6 BEAM CAMBER

---·-···--

Beam

NW

NWB

LW

LWB

Note:

TABLE 2.3 BEAM CAMBER DUE TO PRESTRESS AND SELF WEIGHT

Mid-span Camber Qtr-span Camber Ratio of Cambers for Blanketed Strand

140 Day Re 140 Day Bm to T.hat for P.ra

Release Total Creep lease Total Creep Elastic Creep

Com- Meas- Cmptd Meas- Mid- Qtr- Mid- Qtr-puted ured • ured span span span span

Msrd

0.67 0.62 1.07 1.22 • 60 0.40 0.70 .31 .68 .50 .47 • 84

0.47 0.42 1.12 • 70 .28 0.20 0.45 .26

0.97 0.85 1.14 1.68 • 83 0.57 1.14 .57 .72 .40 .52 • 75

. 74 0.61 1.21 1.04 .43 0.23 .77 .43

4 d b "d 5 wL + Compute cam er at m1 -span = 384 EI (Defl due to prestress).

Prestress deflections were computed by moment/areas. Camber is expressed in inches.

ed Strand Beam.

Total

Mid- Qtr- Total span span

Elastic

.57 .50 1.97

1.67

.62 .58 1.97

1.71

Elastic camber accounted for 51% of the total camber for

draped strand beams, and 59% for blanketed strand beams. Both

beam types showed less measured elastic camber than computed.

The drag of the bottom form on the ends of beams at release could

possibly account for a small portion of the difference. The second

elevation readings were taken on the day after release, and by

that time creep had progressed noticeably. The influence of the size

of beam (2), modulus of elasticity, and of the stress gradient

in the beam possibly account for a further portion of the 10% to

20% between those computed and measured cambers.

Camber profiles shown in Fig. 2-7 give a good indication of the

effect of blanketed strands on elastic and time dependent deflections.

The ends, quarter span, and mid-span points are represented, and

those points are connected by straight lines to aid in visualization

of the profile. The draped strand beam profile is clearly the fam­

iliar parabolic type. The blanketed strand beam profile, however,

is not so simple.

By referring to Fig. 2-4, it can be seen that the stress gradient

at various sections of the blanketed strand beams, carrying only

their own weights, varies from a relativley low value at ends to

higher values at mid-span. Between the ends and quarter span sec­

tions, the gradient diverges, and one would expect the deflection·

profile to be concave upward along that region. Over the central

region, the gradient gradually increases to a uniform value at 8 ft.

from mid-span. Such a stress variation between top and bottom of

1.5 NORMAL WEIGHT BEAMS

z 1.0

TOTAL (140 DAY)"--.,....,... ..,. ......... ..,. .

....-"" a:: .......... ~ ,....- TOTAL (140 DAY)

:!!: / ~............ -----~.5 - --~

l~~~~~/~~~~~~~-~--~-~E~LA~S~T~IC:!~~~~~ / ....- ...- ELASTIC ........ ~::;;;.--

, ..-~ - BLANKETED STRAND ..<:""' -- DRAPED STRAND

END QTR. SPAN MID SPAN

POSITION ALONG BEAM

1.5

LIGHT WEIGHT BEAMS

~ 1.0

a:: w CD :!!: <( (.) .5

END

TOTAL (140 DAY)

-- BLANKED STRAND -- DRAPED STRAND

QTR.SPAN MID SPAN

POSITION ALONG BEAM

FIGURE 2.7 CAMBER PROFILES

--·--·~·~~~~~~~- ~~~~~~~~--~~~~-

beam would produce a concave downward type of curve. By that reasoning

the blanketed strand beam profile reverses curvature between the end

and mid-span. Such a curve would fit the points shown in Fig. 2-7.

It is very likely that the difference in strains at top and bottom

of the beam in the central region of the span accounted for most of

the blanketed strand beam camber.

C. Prestress Loss

The losses in pre-release steel stresses are tabulated in Table

2.4. They were computed by dividing the product of strain and

modulus of elasticity by pre-release stresses. Strains at the level

of the centroid of prestressing steel were used for the computations.

The variations of prestress losses with time at Stations A, C,

and G corresponding approximately to the end, quarter span, and mid­

span stations, are shown in Fig. 2-8.

The loss of prestress that is of primary interest to the designer

of simply supported beams is that at mid-span. However, if prestress just

sufficient to resist imposed loads is designed into the beam, the loss

at every section becomes of equal importance. That is the condition

approached, but not entirely realized, in the blanketed strand beams

of this series. Ideally, stresses would be low at beam ends and would

increase toward mid-span to meet the demands of anticipated loads.

Prestress losses in such a situation would vary somewhat like the

stresses.

The trend of losses shown in Table 2.4 follows the above reasoning.

Draped strand beam losses are lower at ends than at mid-span, of course,

but the difference is not so great, percentage wise, as for blanketed

strand beams. 19

TABLE 2.4 PRESTRESS LOSSES IN STEEL

AGE

Release

140 day

* Estimated.

BEAM

NW NWB LW LWB

NW NWB LW LWB

(End) Sta A

* 3.5 2.5 7.5 3.0

9.5 6.5

14.0 7.5

20

PRESTRESS LOSS (%)

Sta C Sta E

5.6 6.8 4.8 5.3 8.2 8.7 6.2 7.4

13 14 10 12 15.5 16 13 15

(Midspan) Sta G

6.5 6.5 8.5 8.5

14 13.5 16.5 16.5

,.~

• f

w 20

§ 1-z 15

en ~

:f ~ ..... 10 ~ :e i 5

0 0

vr

t"'

If"" •

l2 20 0 ..J i=' 15

GAG~ POINT A-END

NW 6RAPED

0 -;:-- ~-~·· 1-· 0

NW 8LANK1ETEO

20 40 60 60 100 120

LW bRAPEID GAGE POINT A-END 0

i 0 0 0 0

0 0 . . ·- . . i LW BLANKETED

20 40 60 80 100 120

I I lfN~ DRAP~D 0

,.,.., " :v/ ~LA~KETE9/ _GAGE POINT C-1/4 SPAN

I I 20 40 60 80 100 120

)Lw D~APED - -0

.-- 0 . . LW I BLANIETEf

1 GAGE POI~i-- C

11!4 s;AN

I

20 40 60 80 100 120

/N~ DR1PED

. ' . NW BLANKETED

1GAGE POINT G-MIDSPAN

I

I 20 40 60 60 100 120

J J J.o- • ' z

~ ~ 10

~-·-' ...

1'-LW I DRAP1D AND BLANKETED .A? • 0

1- <L w-

~ 5

0 0

GAGE POINT G-MIDSPAN

I I 20 40 60 80 100 120

AGE DAYS AFTER RELEASE

FIGURE 2-8 PRESTRESS LOSS

0

140

.I

140

140

140

140

Mid-span losses at the end of the tests were about the same for

the two beams of a given concrete. Normal weight concrete losses

were about 14% and lightweight 16 1/2%. There is not as much

difference in losses for these two concretes as was found in tests

of Houston beams (1). At 140-day age the Houston beams had almost

stabilized, and the 56 ft. normal weight and lightweight beams had

lost 15% and 22% respectively of the initial prestress at 140-day

age. Normal weight concrete losses were about the same for the

two sets, but the Houston lightweight series lost considerably

more prestress than the present series. Differences in curing

methods and slight differences in mixes could account for at least

some of the differences in behavior.

2.7 Conclusions

Results of the tests on four full size pretensioned prestressed

highway bridge beams show that:

A. Blanketed strand beams can be designed to have less

elastic and time dependent camber than draped strand

beams.

B. Mid-span prestress losses for a given concrete were

about the same for the designs studied.

2.8 Remarks:

Blanketed strand beams require a little more design time than

do draped strand beams, but the additional effort is not excessive.

There appears to be some advantage in the former type in that hold­

downs are not required in the fabrication process thereby somewhat

22

I -

simplifying construction. Camber is reduced by blanketing, and in

larger spans.with deeper beams a comparison of blanketed strand

design with the normal draped strand type possibly should be made

by the designer.

Disadvantages in blanketed strand beams are: (1) blanketing

operations during fabrication must be carefully supervised, (2)

there is a question of location of the section of full bond of

blanketed strands near the end of broken bond, and (3) the effects

on ultimate load capacity and repeated load capacity of blanketed

strands are not known.

The designer can determine the layout of prestressing strands

necessary for producing a desired camber in his beams by means of

computer program in the Appendix. A plot of deflection versus.

eccentricity of strand can be produced from deflections found

from different input eccentricities. Such a plot is almost linear.

Desiring a given camber at time of construction, one might enter

the chart with desired camber and read eccentricity of pre.stressing

steel necessary for that camber. He must, however, realize that

concrete stresses change with eccentricity, and he should always

check for overstress.

23

CHAPTER 3

CREEP, CAMBER, AND PRESTRESS LOSSES - HOUSTON BRIDGE

3.1 Introduction

The bridge studied in this chapter was introduced in a previous

report (1) in which details of a study of the prestressed beams

fabricated for the Houston, Texas Urban Expressway test bridge were

given. Details of the study which continued approximately one

year subsequent to that report, are given in this chapter. The

period of primary concern here begins at about 320-day age of the beams

when the deck slabs were cast. The bridge, although not open to the

public, was opened to construction traffic about one month after the

deck was cast. ·

In order to prove a method proposed for predicting time dependent

strains, camber, and prestress loss, measurements of strains and

elevations were collected :from the structure. At the beginning, the

prestressed beams were instrumented in the casting yard and measurements

were made for strains and elevations before the prestress was

applied, after it was applied, and periodically thereafter until the

end of the test. Those strains and elevations were compared with

corresponding values computed from a step-by-step method discussed in

detail in Ref. 1. Prestress losses computed from strain measurements

were also compared with values predicted by the step-by-step method.

After the slab was cast the problem of predictions became consid­

erably more complicated because of restrained differential shrinkage

24

and creep between the cast-in-place slab and the precast prestressed

beams, and the different properties of beam and slab concretes.

Branson (3) summarized the work of Bartlett and Birkland, among

others, in outlining the composite section method of analysis used

here for accounting for differences in free strain of slab and

beam. Hasnat (4) concluded, from laboratory beam tests, that

stresses predicted by that method were in good agreement with his

test results.

Briefly, the composite section method permits the slab and the

beam to strain freely. Equal and opposite forces are then applied to

the,slab and beam, at their interface, sufficient to bring those

elements back together. The forces so applied are then used to find

the axial and bending components of stresses in slab and beam due to

that action. Those stresses are then added to stresses computed

earlier to produce total stresses for that instant of time.

Short time increments of five days were used for determining

strain increments from test curves, and the beams were divided into

150 incremental lengths for purposes of computing cambers. A study

by Sinno (6) showed that increments of this duration and length

are entirely satisfactory for good precision.

The flow diagram for the computations is given in considerable

detail in the appendix.

3.2 Description of the Test Bridge

Details of the bridge, the prestressed beams, and beam instru­

mentation are given in Ref. 1.

25

The dual bridges, separated by an open joint were designed for

four 12 ft. traffic lanes over one 40 ft. span and three 56 ft. spans.

The Texas Highway Department Type B prestressed concrete beams, spaced

on 7' - 10 1/2" centers, supported the 7 1/4 in. deck slab during

casting.

Information on beams and slabs is given in Table 3.1.

3.3 Objectives of the Study

The objectives of the study were:

A. Development of a method for predicting camber and

prestress losses in the bridge.

B. Determine camber history of the deck.

C. Determine prestress loss in the beams.

3.4 Test Specimens I

I

A. A number of 6 in. diameter x 12 in. long cylinders were cast

on location from slab batches. Those specimens were used for

'strength and modulus tests of the concretes used in the slab.

B. Two shrinkage prisms and two creep prisms, 3 in. x 3 in. x

16 in., were cast with each instrumented slab in the bridge.

Those prisms were instrumented with mechanical gage points set

10 in. apart on two opposite long sides of each of the prisms.

They were prepared and treated in the same way as those de-

scribed in Ref. 1, and dimensional details, too, were the same.

The creep prisms were mounted individually in frames and

loaded to 1500 psi compression in a universal testing machine.

26

TABLE 3.1 BEAM AND SLAB DESIGNATIONS

Span Type of Beam Span Concrete Type Date Cast Bridge Number Instru- Designation (ft) Beam Slab Beam Slab

mentati0n

Left 1 El~l) Ll-1 40 LW LW 8/24/66 6/28/67

El. Ll-3 40 LW LW 8/24/66

s(2)& El. Ll-5 40 LW LW 8/24/66

El. Ll-6 40 . LW LW 8/24/66

El. Ll-8 40 LW LW 8/24/66

2 None None 56 LW NW

3 El. L3-1 56 NW LW 9/10/66 . 8/7/67

El. L3-3 56 . NW LW . 9/10/66

El. & s L3-5 56 NW LW 9/10/66

El. L3-6 56 . NW UJ 9/10/66

El. L3-8 56 . NW LW 9/10/66

4 El. L4-1 56 LW LW 9/10/66 7/12/67

El. L4-3 56 LW LW 9/10/66

El. & s L4-5 56 LW LW 9/10/66

El. L4-6 56 LW LW 9/10/66

El. L4-8 56 LW LW 9/10/66

Right 1 El. & s R1-5 40 LW LW 8/27/66 7/27/67

2 El. R2-5 56 LW LW 9/16/66

3 El. R3-5 56 NW LW 9/10/66

4 El. & s R4-5 56 LW NW 9/1/66 7/26/67

1. Elevation.

2. St:Fain,

27

That stress was maintained by heavy helical springs confined

between the prism and the frame. Details of the arrangement

are shown in Fig. 5-3 of Ref. 1.

The shrinkage prisms were never loaded, and they served

to provide control measurements of strain (shrinkage) to be

used in determining creep per psi in the creep prisms.

C. The prestressed beams and their companion 4 ft. long non­

loaded shrinkage specimens, described in Ref. 1, continued

under test throughout the period. The beams were hauled on

pole trailers to the bridge site and were erected by mobile

crane; They ware approximately 10 months old when erected.

D. The deck slab, 7 1/4 in. thick, was made of lightweight

concrete in all except spans L-2 and R4. Fig. 3-1 and 3-2

and Table 3.1 give details of the slab.

Two sets of mechanical gage points were installed on the

top and bottom of the slab at each beam gage station. The

bottom gages were set directly below those on the top surface.

One set was located midway be·tween beams 5 and 4, and the

other was set 3 in. out from the top vertical face of beam

5 on the side toward beam 4. See Fig. 3~3.

A bottom-of-slab gage, then, was located 3 in. from the

top gage on a beam, as close as possible for required clearance

in gaging. The other one was set as far away from the beam

gage as possible to still be at the same station.

28

TRAFFIC ~

~ ',',~~,~~:.~ .• ---1-r~·<t_ SOUTH PARK BLVD. " ., "' #h N 20"41'25"W

/I\

_cT---~U ___ ~u:''~--~i+i~i! ____ _Q~L_~~--------~~~L-~+'----~--YI , m 1 1 I J!! 1 1: 1 11 r 1 !I 11 1 :; :: II I'll,, .• , II I 'II II II N I II II~ CLEAR.· ~ II rt;>t6'F-F---.. II I "f II

I ,, -' : r it f-""'"' -' Ill J -' .,., "h~~~ II -' II

~ ~;~N7:;~o;:3;'\ II II II ~ iII 11 !11 II! 11 r~No ~;~GE II;. I 610--....,.

-c~"%,~cf. ¥."~\'""C"'-\-il \11-, -----i-i-!-ilr*--------r lllf-i------,-,-i--ili--l [li--11---11-i-~----ill-'t7;';,,~c;;~7'i:s~ ;;;·3"-

\ t" OPEN JT._!

II II

MEDIAN

1.75•1::SLOPE RIPRAP

ll II "'.'"-n--I II 11 1

I i II I 111 I "'"" "" ,_, - 111 ''""'11 1

I II 100' ,_, II ~~ I: I '"" I

I \\ t_ 44' F-F ! U· 44' F-F lr1 :II ¢ IIi wsLOPE

I II llr-----~----l~il-~c_c_'-----1111 I '" Ill """ II II II

i I :I II ~ II ~~~ :, II "? ,, . .,JI! ill li I i I II - "' """ 1 t!11 Ill I

-2'--_

11 1 1 ~ I 11'-"'---J,"_' 1'1

11 11 I ! j 1 RAILING TYPE E-7-.. 11- F-F -II

SPAN I

RAILIN;_A TYPE E 7

~l 9f-I\\~IX 1.75 ~~ ~ !!1~1~

-~ ' 2~1B"¢0.S X 24----; 1 u

" " : : SIDEWALK I I (FUTURE) :: : .}-I0~30''¢D.S. X 42'

JE:5'-6"8ELL

. ~ ~

" " !! "

PLAN VIEW

OVERALL LENGTH 208.00'

4 SIMPLE PRESTRESSED CONCRETE BEAM SPANS@ (40'-56'-56-56')

SPAN 2 SPAN 3

tt-610 PROFILE) I /RAILING TYPE E-3

I +3.7% -3.7%

/ I

it ~ ~~· ~ ~

" ' dt- 4;_ SOUTH PARK BLVD

'

" " " " " " "

SPAN 4

/~AILING TYPE E 7

2~ ~mr=~ ~j ~ " i' '' . .,~ I I r+-2~18"¢0.5. X 24' I I U

" " 'I: [ i---aN30"¢o.s. x 32' :J.._a-30"¢0S.X 32' " I .j..--I0-3d'¢D.S.X42' it-a-30'¢0.S.X 32'

-~ 't_ 7'- 0" BELL

" k

~7'-0"BELL " ~5'-6"BELL H

~~'-O"BELL

ELEVATION VIEW

FIGURE 3-1 GENERAL PLAN OF BRIDGE

CROSS SECTION-WESTBOUND SHOWING INTERIOR- OIAFRAMS

LOOKING IN DIRECTION OF DECREASING STATIONS

r--Jo'-o" 24'-o" ·''"''' 4'-o" 9'-s"-"11.1=::._ ' 02FT T 1 -FACE OF E-7 RAILING F~~~.,·-=o" ~~~'"

8' "\.._CROWN DIAGRAM~: :g • .04F~ ,0' ~· ILl 610 8. !!.j ~ I' OPEN JT. gg; ~:31 -...... I"R~

TY.E<~RAILI~, , 3...--EN'D _oF A~RMOR JT. ""e . "'j ~EN~ OF •-A~MOR ~T-~ .:·

) ( ) (t----;1) ( ) ( ~ -tt ,._,. a sPA. III 7'-lor· s3'-o"------------l~'-ai--

CROSS SECTION- EASTBOUND SHOWING EXTERIOR OIAFRAMS

LOOKING IN DIRECTION OF INCREASING STATIONS

--+---20'-0"

~-"_·-·-·---~-----'-''_·_·------~~+_~_-_-_-_-~,·--·-·----~ ~'t---1;;== = = == -,-== = = = ~ II

~

-~ : :..::... 0 0

~~

_____ _lL ____ _ ,-------,-----, II O~PHRAM----.1 I

_____ _lL ____ _ -----,-----

11 _____ _lL ____ _ -----,-----

11 _____ _LL ____ _

-----,-----11

_____ _lL ____ _ -----,-----11 _____ _lL ____ _ -----,-----11 TYPE 8 BMS (MOD)

_____ _lL ____ _ -----,-----11

_____ _lL ____ _ ------------

TYPICAL 40'- 0 11 SPAN PLAN

1L JOINT

TYPICAL 56'- 0 11 SPAN PLAN

FIGURE 3-2 BRIDGE PLAN AND SECTION DETAILS

' -~ ST , C

=~ ::J t. OF BEAM

SLAB PLAN

3' -II 1/4" GAGE POINT~ •

L,o_j 36"

GAGE POINT

1--------- 36'''-----~

0 (b) SLAB SHRINKAGE SPECIMEN ' --

q_ OF BEAM

SECTION A-A

(a) GAGE SLAB POINTS

FIG. 3-3 SLAB GAGES AND SHRINKAGE SPECIMEN

The slabs were cured under wet mat six days from the time

of finishing. The wood bottom forms remained in place at least

until the wet mat cure was complete.

E. One 3' ft. square shrinkage slab 7 1/4 in. thick was made for

each instrumented deck slab. It was cast from the slab batch,

and was instrumented by a set of mechanical gage points centered

on one principal axis on each 3 ft. square surface. These

specimens were never loaded, their purpose being to serve as

shrinkage control specimens for the reinforced slab.

In order to begin collection of strain data as soon as

possible, the slab shrinkage specimens were stood on one edge

after hardening, and the wood forms were then removed. They

were then blanketed with a heavy quilted cotton mat which was

kept wet throughout the curing period of the companion slab.

3.5 Materials

The THD Class A,5 sack,normal weight concrete had a water to cement

ratio of 0.50, and a weight ratio of sand to gravel of 1.00 to 1.75.

Slumps varied from 2 in. to 3 1/4 in.

The THD Class X,5 1/2 sack,lightweight concrete used natural sand

fines and the same expanded shale coarse aggregate as used in the beams.

A slump averaging about 3 1/2 in. was obtained from the mix with a

weight ratio of sand to C.A. of 1.22 to 1.00.

Air entraining and dispersing agents were used in both mixes. Air,

by pressure meter, was nominally 5% for NW and 8% for LW.

32

Table 3.2 provides data on strength, secant modulus, and weight

of the concrete. Different methods of curing were used by Texas

Highway Department and Texas Transportation Instllitute, and cylinder

strengths in that table reflect those different methods. Values of

secant moduli were developed from tests on cylinders cured under the

same conditions as the slab.

3.6 Tests

A. Concrete compressive strength tests were performed by the

Texas Highway Department on cylinders handled according to its

specifications.

Stress-strain tests were made on 6 in. diameter x 12 in.

long cylinders cast in cardboard molds. Those cylinders were

cured at the bridge site under a wet mat, the same as used in

slab cure. After curing, they were stored in open air until

tested. Strains were averaged from 6 in. gage length readings

from 4 dial gages spaced at 90 degrees on the cylinders. The

secant modulus at 1/2 f' was determined from averaging strains c

from three cylinders for each test.

Strength and stress-strain tests were made on the creep

prisms incidental to their restrained load tests. Those

strength tests were not planned in the formal program, and

only limited data were collected.

B. Shrinkage and creep tests on specimens cast in 1967 from beam

concrete continued throughout the period. Those specimens and

tests are described in Chapter 5 of Ref. 1.

33

TABLE 3,2, SLAB CONCRETE PROPERTIES

THD Test* TTI Test **·

Slab lrype Age f' Unit Speciman f' EZf~ Specimer c c (psi) ~~~i~ . (psi (ksi) y

LS-1 LW 1 da 10 hr - - 2222 2273 prism 2 da 5 hr - - . 2611 '2653 prism 7 day - - 3277 3080 p1;ism 7 day 4710 cyl 3893 3100 cyl 8 - - - 3100 prism

28 5677 112.0 cyl 4144 3234 cyl

LS-2 NW 7 4207 . · .

LS-3 LW 5 2220 3160 prism 7 4470 cyl 2890 3211 prism

10 3260 3684 cyl 28 5090 110.4 cyl 4200 3281 only 1

cyl

LS-4 LW 3 - 3111 2936 prism 7 cyl 3556 3175 prism 7 3837 3397 3192 cyl

28 4823 111.1 cyl 5055 3010 prism

RS-1 LW 5 3944 3130 prism 7 4000 3000 prism 7 (3092) 2920 cyl

28 4720 112.4 cyl 32 4233 cyl 89 4529 cyl

RS-2 LW 7 4603 cyl 28 5433 110.4 cyl

RS-3 LW 7 4197 28 5217 110.3

.

RS-4 NW 5 2667 4677 prism 7 3333 4630 prism 7 3990 . 2950 5017 cyl

33 3778 4500 prism 90 3816 5021 cvl

* Std. test of and by THD personnel; cyls from water bath cure. ** Specimens field cured under same condition as slab; air dry at test;

1 -Prisms loaded to 3 kips· three· times before.recording; 3 - Cyls loaded to 30 kips three. time!! before recording.

34

Shrinkage and creep tests were carried out on the prisms

cast with each instrumented slab, and shrinkage tests were

made on the 3 ft. square slab specimens. Test procedures and

methods were the same as reported for similar specimens in

Chapter 5, Ref. 1.

c. Strain measurements on five prestressed beams were continued

throughout the test. Those measurements are discussed in

Ref. 1, and details on gage point locations and beams are

given in Tables 5.1 and 2 of that report. Briefly, the beams

were 40 ft. artd 56 ft. THD Type B pretensioned prestressed

beams gaged with mechanical gage points on both sides at one

end, one quarter span point, and at mid-span near the top and

bottom and mid-depth of the beams. Strain readings read from

a demountable gage over a 10 in. gage length were taken before

and after release, before and after slab casting and periodically

throughout the test period.

D. Strain measurements were made on each of the two top-of-slab

gages and the two bottom-of-slab gages. The first readings

were made on the day after casting, and they continued period­

ically until the close of tests almost one year later. Daily

readings were taken for 5 days, weekly readings for one month,

then from two to four week intervals elapsed between readings.

E. Elevation readings were taken from elevation points on beams

throughout the test period. Those points, cast in the beams

when they were fabricated, were covered with slab concrete from

a fraction of an inch to 1 1/2 in. when the slab was cast. The

35

tops were uncovered while slab concrete was still plastic so

that uninterrupted continuity in elevatio'n readings could be

realized.

Readings were made before and after forms were placed;

before and after steel was placed, and before and after slabs

were cast. Those readings were made on the same time schedule

as strain readings.

All readings of bridge elevation and strains were made

early during the day beginning at or before sunrise. The

direct rays from the sun had little time to act on the struc­

ture before readings were taken.

3.7 Test Results and Discussion

A. Strength and Secant Modulus of Slab Concrete

Some cylinder tests were made by THD, and others were

made by TTl. Conditions of treatment of specimens were

different in the two sets of tests, and it is only for that

reason that both sets of values are given. The secant moduli

were determined from TTl tests and it is deemed advisable to

give TTl breaking strengths, too, to answer questions that

might arise about correlation of values.

THD Test results: Tests made by THD included measurement

of air content by pressure meter, unit weight, and breaking

strength. The results of those tests are shown in Table 3.2.

The cylinders were cast in steel molds and cured in water, and

values shown for THD strength represent the average of 3 breaks

on cylinders removed from the bath shortly before the test.

36

TTI Tests: Breaking strength and secant modulus for

both cylinders and 3 in. x 3 in. x 16 in. prisms are given

in Table 3.2 for tests made by TTI. Cylinders were cast in

cardboard molds and field cured in the same way as the bridge

slab and for the same period. Upon completion of the 6-day

cure, specimens were stored in air in a small construction

hut at the bridge site. Specimens tested before termination

of the 6 day curing period were wrapped in wet mats then

transported to the testing laboratory. They were removed

from the wet mats about 2 hours prior to testing in a

universal testing machin.e.

Strains from cylinders were taken over a 6 in. gage

length from 4 dial gages equally spaced around the cylinder.

The gage length on the 16 in. long prisms was 10 in., and

strains were read from two opposite faces by a demountable

gage from gage points set in the concrete. Except as noted

in the table, the values shown for cylinders represent the

average from three specimens. Values for prisms represent

values from one specimen.

Although it is not a point to be studied at length here,

it should be noted that the THD standard treatment of cylinders

produced considerably greater strengths than was developed in

the TTI cylinders cast in cardboard molds and field cured with

the slab. Under TTI tests there is good agreement between

37

prism and cylinder secant moduli but strength values are not

in"good agreement, the cylinder strengths tending to be some­

what higher than the prism strengths. The greater length

to thickness ratio for prisms; the greater influence of possible

defects in the 9 sq. in. section of prism than the 28.3 sq. in.

section of the cylinder; and the effect of shape might account

for the differences. The secant moduli found in the tests are

considerably higher than would be found from the current American

Concrete Standard Building Code Requirements for Reinforced

Concrete (ACl 318-63) (5) using test values for unit weight

and breaking strength.

B. Shrinkage

Shrinkage in small prisms used as companion specimens to

creep specimens is displayed in Fig. 3-4 for lightweight slab

concrete; Fig"'" 3-6 for normal weight slab concrete; and in Fig.

3-10 for normal weight beam concrete. Shrinkages from those

non-loaded specimens were deducted from strains read from

spring loaded prisms to give creep in the stressed prisms.

They are used in no other way in this work, but it is of some

interest to compare values of the 4 different concretes, the

beam concretes being about 660 days old at termination and

slab "Concrete about 320.

Fig, 3-t4, 6, 8,;:and 10 show that the LW priSIR· shr"inkage

was more than that .. for the NW pr:Lsms in bo,t!i J>.eam and slab

conare.tes. rTermirtab,values at 660 daysr for• beam rconc:rfete were 260

38

z ' z

"' b z <[ a:: 1-en

~ ' z

'

1200

1000

BOO

600

400 I ! 200 v

0 0

/ /

/

/

40

. \rEEP + SHRINKAGE STRESS 1500 PSI)

/ v SPECIMENS 3 X 3 X 16

LIGHT WEIGHT CONCRETE

I I ,..... SHRINKAGE -

80 120 160 200 240 280

AGE- DAYS AFTER LOADING

FIGURE 3-4 TOTAL CREEP AND SHRINKAGE OF SLAB CONCRETE (LIGHT WEIGHT}

1000

800

I SPJCIM~NS 1 3 X~ X I~

LIGHT WEIGHT CONCRETE

z 600

"' b z <[ a:: l­en

400 \€= 545T -20+T

~ ........__MEASURED _, 200

( 0

0 40 80 120 160 200 240 280

AGE- DAYS AFTER LOADING

FIGURE 3-5 UNIT CREEP CURVE OF SLAB

CONCRETE (LIGHT WEIGHT}

1600

1400

z 1200

' ~ 1000

"' ' Q 800

z <i' 600 a:: t;

400

) v

1/ I

200

/ 0

0

FIGURE 3-6

1000

_ BOO

ZCfl -~ <! ....... 600 a:: f-Z

" /

I I I I CREEP + SHRINKAGE

I/ (STRESS 1500 PSI)

/ I

0

Vo ~

SPECIMENS 3 X 3 X 16

40

....

NORMAL WEIGHT CONCRETE

T I SHRINKAGE

7 0

v -0 -80 120 160 200 240 280 320

AGE-DAYS AFTER LOADING

TOTAL CREEP AND SHRINKAGE OF SLAB CONCRETE (NORMAL WEIGHT}

SPECIMENS 3 X 3 X 16

NORMAL WEIGHT CONCRETE .

I I MEASURED-..

(/) ::::: 400

t::z z~­=>'o 200 (f'--____ € • 550 T

II+T 0

0 40 80 120 160 200

AGE -DAYS AFTER LOADING

240 280 320

FIGURE 3-7 UNIT CREEP CURVE OF SLAB CONCRETE (NORMAL WEIGHT}

microinches for LW and 215 for NW, a ratio of 1.22. Corres­

ponding values at 300 days for slab concrete were 370 and 285

microinches, giving a ra~io of 1.30.

Both NW and LW slab prisms showed more shrinkage, 130%

to 150%, than the beam prisms over the same age period, This

was not over the same calendar period, however, the beams

having been cast about 10 months before the slabs.

Shrinkages of the large specimens, 4 ft. long full section

beams and 3 ft. square by 7 1/2 in. thick slabs, are of consid­

erable interest because they were used in predicting strains

in the bridge. Those specimens, being of the same section as

the bridge elements and being relatively large, should have

about the same shrinkage as the bridge members tf all were

free to shrink.

Shrinkage versus age plots for the non-loaded slab

shrtnkage specimens are shown in Fig. 3-12, NW concrete, and

Fig. 3-13, LW concrete. The average of two gages, one on each

3 ft. square face, for one specimen is shown for NW concrete.

The average of two opposite side gages on four specimens is

shown for the LW concrete. The plots of shrinkage read from

the latter specimens were so nearly identical that it would be

difficult to discern differences on plots to the scale used here.

The non-loaded 4 ft. shrinkage beam shrinkages are shown

in Fig. 3-14 for normal weight concrete and Fig. 3-15 for

lightweight.

41

1800

1600

1400

(/) 1200

"' ' z 1000

' "" t

BOO

z 600

~ 400 ,_

(})

200

50

~ 40

0

0 z ' ~ 30 0

CREEP +SHRINKAGE ;-::-_?L-3 a Cl-4

ISTRES\.~

~

t itt'· •

11

v ~ .. 40 80

E• 4001

"'"

0

0

• • . dREEP +SHRINKAGE

CL-1 a CL-2 (STRESS 2000 pr

. 0 .

\SHRINKAGE SL2 a

1SL3

120 160

"' -- f-

0

v 0 0

r-0 .. .

SPECIMENS 3X3XI6 LIGHTWEIGHT CONCRETE

. . . . 200 240 280 320 360 400 440

AGE-DAYS AFTER LOADING

FIGURE 3-8 CREEP AND SHRINKAGE IN 3X3X16 SPECIMENS

FOR BEAM CONCRETE (LIGHTWEIGHT)

. -- 0 r-- r-- r--

~ 20 v .t v"' MEASURE~---

SPECIMENS 3X3XI6 z ~ 10

01£/ 0

tii 0 0 40 120 80

:IIGHTfEIG~T C'l"CRYE

160 200 240 280 320 360 400 440

AGE-DAYS AFTER LOADING

FIGURE 3-9 UNIT CREEP CURVE OF BEAM CONCRETE (LIGHTWEIGHT)

0 0

0

• .

. . . 480 520 560 600 640

-- r- -- r-

480 520 560 600 640

1200

1000

;;;; '

800 f--;;;; w 600 Q z 400 <i "' 200 f-

/ v

<f)

400

300

200

.,;)

b" 100

SPECIMEN 3X3X16 NORMAL WEIGHT CONCRETE

0 REEP + SHRINKAGE

!'-- 0 0

CH-3 a CH-4 STRESS 3000 pol l 0 0 0

0 0 0 0 0 0 0 0 0

0

1""0 0 0 0

Vo fSREEP + SHRINKAGE CH-I 8. CH•2

(STRESS 20

100 ~1IJ 0

0 0 0

'-.._5SHRINKAGE 0 0

0 0 SH-2 8. SH-3

40 80 120 160 200 240 280 320 360 400 440 480 520

AGE- DAYS AFTER LOADING

FIGURE 3-10 TOTAL CREEP AND SHRINKAGE OF BEAM CONCRETE ( NORMAL WEIGHT )

I SPECIMEN 3X3XI6 NORMAL WEIGHT CONCRETE

€ • 225t I". 0 lS+r

,....r "-MEASUREO .

I

40 80 120 160 200 240 280 320 360 400 440 480 520

AGE-DAYS AFTER LOADING

'

0

560

560

FIGURE 3-11 UNIT CREEP CURVE OF BEAM CONCRETE (NORMAL WEIGHT)

0 0

0 0

600 640

.

600 6 40

z 800

' z 600

'b 400

z <( 200 0::: ~,r1" I- 0 (/) 0 40 80

SPECIMEN 3ft X 3ft X7t in

0

120 160 200 240 280 320

AGE-DAYS AFTER CASTING

FIGURE 3-12 SHRINKAGE OF NORMAL WEIGHT SLAB

800

z-_(/) <(:>::: 600 o::' 1-z

400 (J)...,_

I I I I I I SPECIMEN 3ft X 3ft X 7! in AVERAGE OF 4 SPECIMENS

1-z Z'f'o 200 :J_

v 40 80 120 160 200 240 280 320

AGE- DAYS AFTER CASTING

FIGURE 3-13 SHRINKAGE OF LIGHTWEIGHT SLABS

z '

800

;;: 600

"' Q 400 z <i' 200

~

;;: 800

' ;;: 600

"' Q 400 ;;: <{ 200

~

v

I>""

0 0 0

40 80 120

40 80 120

SHRINKAGE BEAM SH-1 4FT. LONG

NORMAL WEIGHT CONCRETE l/e~~ --:.r::.EASURED IO+T

-· -- ·- r-- .,.., I ·-

0 0

160 200 240 280 320 360 400 440 480

AGE- DAYS AFTER CASTING

FIGURE 3-14 SHRINKAGE CURVE OF BEAM CONCRETE , ( NORMAL WEIGHT)

SHRINKAGE BEAM SL-1 4 FT. LONG

LIGHT WEIGHT CONCRETE

/MEASURED (£ c gQQ.I_ IO+T

0 0 0 0 0

160 200 240 280 320 360 400 440 480

AGE- DAYS AFTER CASTING

FIGURE 3-15 SHRINKAGE CURVE OF BEAM CONCRETE , ( LIGHTWEIGHT )

520 560 600

520 560 600

Shrinkage at the LW slab specimen, Fig. 3-13, bears a close

resemblance to the LW beam specimen, Fig. 3-15, in both

magnitude and shape of curve. About 200 microinches of strain

appears to be the value about which they fluctuate slightly.

Shrinkage of the NW beam specimen, on the other hand, Fig.

3-14, is somewhat higher than that for the slab specimen,

Fig. 3-12. The former attains about 300 microinches of strain

against some 200 for the latter. The difference appears to

have occurred at very early age of the beam specimen when a

rapid rate of shrinkage occurred. Comparisons of shrinkage

from different size specimens of the same concrete show that

NW beam prism shrinkage terminated at 210 microinches against

300 for the NW 4 ft. long full size section at the same

terminal age. It would be expected that the former would

have shrunk much more than the latter. No explanation can

be given to explain the behavior.

The LW beam prisms terminal shrinkage was 240 microinches

against about 200 for the LW 4 ft. long full size beam specimens.

This is in the direction that one would expect, and size and

shape factors would probably account for difference in magnitudes.

Deck slab NW concrete prism shrinkage, Fig. 3-6, was about

150% as much as that from the 3 ft. square specimen of NW slab

concrete at termination, Fig. 3-12. The corresponding LW

specimens, Figs. 3-4 and 3-13 showed about 200% as much shrink­

age for the prism as for the slab.

46

The hyperbolic functional representations of shrinkage

strains, see Ref. 1, Ch. 5, were changed for the beam specimens

from those given in Figs. 5-13 and 5-14 of Ref. 1 to those

shown in Figs. 3-14 and 3-15. The increased data collected

over a larger period of time showed that the ordinates should

be raised a little and that the shapes at early age would be

changed only slightly. Those curves were used in predictions

of beam strains, camber, and prestress losses which are to be

discussed in sections that follow.

C. Creep in Small Specimens

Creep in specimens under sustained load is important here

because it was used in predicting creep strains, camber, and

prestress loss in full size prestressed beams, and in the

composite beam-slab.

All sustained load prisms of slab concrete were loaded

to 1500 psi and that stress was maintained by means of heavy

helical springs as explained in Ref. 1. The total strain read

from those specimens was reduced by the amount of shrinkage

from the non-loaded prisms to give creep. Unit creep per ksi

was obtained by dividing creep by the product of gage length

and 1500 psi sustained stress.

Chapter 1 of Ref. 1 gives details of applying the unit

creep in making predictions of creep in prestressed beams.

Unit creep in beam concrete was shown in Chapter 5, Ref. 1

for the first 300 days of the test. Those creeps are carried

47

--------------·~----- ---------··------·,- --------·- ·----

to 660 days, termination of the test, in this report, Figs.

3-9 and 3-11. The extended portions covering 360 days to the

end of testing show increases for both NW and LW specimens,

but the increase is greater for LW.

Similar information for slab concrete is given in Fig.

3-5 for LW, and Fig. 3-7 for NW.

The unit creep of LW beam concrete is considerably

greater than that of the NW beam throughout the history to

termination at 660 days. Slab unit creep is, however, almost

the same for both concretes.

D. Strains in Beams

Measurements of strain in five prestressed beams for a

period of 660 days are represented in Figs. 3-16 to 3-21.

Readings of strain were taken just before and just after

prestress. release, at beam erection, and at slab casting.

The event of slab casting is clearly reflected in the plots

at about 300-day age.

When the slab was cast the fibers elongated at the bottom

gage and compressed at the top gage. Little change was noted

in the gages at mid-depth, near the centroid of the beam. The

mid-span gages showed the greatest strains at .!!hat event because

of the higher bending moment at mid-span caused by the weight

of the plastic slab. The strain curves for the first few days

after casting of the slab have the characteristic shape of

early creep curves.

48

Points on the curves are scattered somewhat, although care

in measuring technique and time scheduling was followed. Some

fluctuations due to seasonal changes may be noted in these

plots as well as in the shrinkage curves of Figs. 3-4, 6, and 8.

Weather information, temperature and relative humidity, Fig.

3-22, has been included to help explain those seasonal changes.

Each point on the plot of temperature represents the average

of 3 hour readings over a period of 10 days, and each R.H.

point represnets the average over those same 10 days.

Strain predictions, made by the method outlined in

detail in Ref. 1, and shown in the Appendix in the form of a

computer flow diagram, are shown in Figs. 3-16 to 3-21 by

dashed lines.

Predictions for Ll-5 strains, Fig. 3-16, are good up to

the time of casting of the slab. After that time there is

considerable disagreement, especially at the end of the beam,

station A. Terminal predictions,660 day, are good for all of

the other beams. Agreement of predictions with measured values

at intermediate ages is generally fair tc>~good.

These tests showed that strain measurements were very

sensitive to changes, showing more scatter than the elevation

measurements which did not appear to be so sensitive. Good

agreement can be seen in camber in beam Ll-5, for instance,

over the entire test period whereas strains, as indicated

above, are not always in agreement. Strain comparisons are

49

140 0

120 0 son6M--..

0 ~100

,;-eo \2 zso

v 011 0 .

~40 0 ~ j1"' -W'

20 0 TOP

0 ~

40

120 0

ZIOOO

' I-- BOTTL

k<:r-t' ~ 80 w

Q 60

z <t 40 0: t; 20

120

OIP 0

olf. 0

ol#'

0

100 0

z ::::::80 ;;;

I?

40

k' -

. -MIDDLE', .

c-MIDDLE

., -LTD?

80 120

-

I ./TOP

80 120

01;/

0 ~I~LE

'/ w 80 Q _...

0

11'1 0

z40

" 0:20

~ 0

In 0

. MTDLE

40 80 120

I . . I

. . . . BOTTOM

STATION A . . .

. . j<~' . . .

. l . 1-- • -- --_j . 'I'- I . .

' : : 160 200 240 280 320 360 400 440 480 520 560 600 640

I . I . I . .

' I I c1.....:+- - f-- - +--l- !-- -- -- - 1--'- - 1-- --I--BOTTOM . MIDDLE I

STATION B L-. _,_ f-- 1-· +- -- ,..: 1--

MIDDLE/ • I ' . . .

MEASURED ..I.-

----PREDICTED 1¥ . . . i !

! TOP

• , I I I 160 200 240 280 320 360 400 440 480 520 560 600 640

scinorv . .

" i ~ .f.: + ~+ ! ' -- -+- 1--1-· 1-- 1--1--sonoM I ' .STATION c I .

+- ~---~-17-- f-- ~ I . . I 1..- -~ 1-- 1-- I· 1- ·- 1-- -+ --TOP--. •J .

!'-raP I--s LAB CAST

160 200 240 280 320 360 400 440 480 520 560 600 0 64

AGE -DAYS AFTER RELEASE

FIGURE 3-16 STRAINS IN BRIDGE BEAM Ll-5 (LW)

1200

~ 1000

' ~ 800

• Q 600

z 400 :;:;

0: 1- 200 U)

1200

~ 1000

' ~ 800

~Q 600

z ~ 40 0

~ 200

r--ft

'L -

/

/ 1/ I

BOTTO~~ - I ~OLE p,

TOP-----...

'

I 40 eo

BOTTOM 1:::::,. -:I~LE 1::..

,,L ~

0 0 40 80

1200 BOTTO~~

z 1000

' / ~ BOO • Q 600

z 400 :;:;

0: 1- 20 U)

I MIDDLE :;o-...

tf"" I I I '"'~ V...+~.,- 0

0

l 0 I

40 eo

A _J-_ r-- .__, r,. I r:··· -'-- r-- f-· I ·-t 1- ~-

' I'-- s~:mo~ STATtON A , I r ,

- f.,- -- --1 ~-, ! I . --·

..__MIDDLE r··· .

1--.-' - r- . I . -I

I .

-·· Tr I

120 160 200 240 280 320 360 400 440 480 520 560 600 640

--l-~- : STATION B I - f--.__,- f.- ·-.

" 0

0 io 0

, 0 I BOTTOM ' '

0

" ~ ' - , 1 I ~ . j ' -...._ MIDDLE L I -"

! ' I. I I i

' I MEASURED 1'--- TOP PREDICTED

I I I I ! I '

120 160 200 240 280 320 360 400 440 480 520 560 600 640

--+----1-- I i ' I --,--- - --, STATION c ! 0

' ~

0 0 ~ BOTTOM 0 0 .

-- ..L F . ' ' ' I 0

' MIDDLE

I I - --f - i . I I ! - f--H-sL~B CAST I '"'

120 160 200 240 280 320 360 400 440 480 520 560 600 640

AGE· DAYS AFTER RELEASE

FIGURE 3-17 STRAIN IN BRIDGE BEAM L 3-5 (NW)

2000

1800

1600

z 1400

' ~ 1200

w Q 1000

2 BOO

~ 1- 600 <f)

400

200

v /

1/ v /

'I/ / b'

L

lt7

I

BOTTOM-

f-<--... - BOTTOM

MIDDLE -.._MIDDLE

TOP

0 0 40 so 120

1800

1600

1400

~ 1200 '

0

f /' ~ w 1000

Q BOO

I 0

"' J-z <1

600 0:: {/

f-<f)

400

200 • f,'

40 so 120

160

160

0 - - I I

I l ~

I

STATION A

' 0

0 I

I

. .

~ ~ . . TOP

200 240 280 320 360 400 440 480 520 560 600 640

/sbnoJ 0 0

0

sbTroML b.? STATION B 0

0

MIDDLE

" f-- 1--

[7 ·-MI~Dlt:. .

""' . -- -- 1-- '--... TOP

MEASURED r-

!--I-SLAB CAST - PREDICTED

T~P/ i I I 200 240 280 320 360 400 440 480 520 560 600 640

AGE·DAYS AFTER RELEASE

FIGURE 3-18 STRAINS IN BRIDGE BEAM L4-5 (LW)

180 0

160 0

140 0 ~ ;', ~ 1200

olf( «< 100 ' Q

80 z oi;Y ~ 600 1-Cf) 400

200 )'

-- 1--1--

t""o 0

f-

40 80 120

BOTT t---

STATION c "-- BOTTOM

t--- ·--:

MID+L I=_

1---

"--.MIDDLE - --.... -'oe_

0 j I

" TOP . -~-SLAB CAST

l I J. 160 200 240 280 320 360 400 440 480 520

AGE DAYS AFTER RELEASE

FIGURE 3-19 STRAINS IN BRIDGE BEAM L4-5 (CONT.) (LW)

0

0

!::-':::

560 600 640

120 0

~1000

' ~800 w Q60 z

,( or <C 40 a: ~ 20

0

0 v7 ali"'

1200

ziOOO

' ~BOO f

1-- - r---- - ---f-- --,_,.-

-40 80 120

-I- ·-.~ -

BO~TOM STATION A 0

0

0 0

BOTTOM v MIDDLE 0

1-_:! ,~ ·- - 0

0 ,..... _/

~IDOL . £!OP TOP_---, .6

~ .

160 200 240 280 320 360 400 440 400 520

+~M STATION 8

- -- ,._ ·- --, 0 - 0

0

' 0 ~O;TOM/ < 0 ... )'

~ ~DOLE~_ 00

vo . Q 600

z <i 400 a: t;; 200

0

1200

21000

~ 800

~ 600

/ yt'·

v /_

'/" z <{40 a: 1-(f) 20 0~

~

0

~ ....

40

40

+oP--.

80 120

--- - - 1--

MIDDLE -MIDDLE . 80 120

MIDDLE • - ~ . . r"' MEASURED

TOP_/ '

- PREDICTED

160 200 240 280 320 360 400 440 480 520

I STATION c - 1-- r-- ~r~ ~ ·- r-,

0 -BOTTO~/ ,..._

0 0

0 ~ f-- ~ . TO

"'-.. . '---reP SLAB CAST

160 200 240 280 320 360 400 440 480 520

AGE- DAYS AFTER RELEASE

FIGURE 3-20 STRAIN IN BRIDGE BEAM Rl-5 (LW)

0

0

560 600 640

0

560 600 640

1--_--

560 600 6 40

•oo

'""' BOTTOM

z'<OO

II ~1200 ~1000 zsoo

" 1"60 ,c ~

0-

,00

0 0

'" 0

v-

c_

---

,,. TO~,

I so ' 20

!<0 0 BOTTOM-.... 1:_:

/ ~120

' z 0

// ... -,ooo b -so z

0

~60 ,_ ~.,

,/

0

20 ,I? -

--MIDDL;_ -

"' - -· t-·

.

so !20

•o '"

r--f---- . t-:_

,,. . " ,,.

'" 200

TTOM

MIDDLE-.., --=- --MI~OLE .

-- . -- f-· -. - ~ATION 1--

A

" 0 "' "' "' "' '"" "'

f---j r- r-- -,

BOTTOM l . --"-~ ... -

~ !-"" . ~- f-· r--- -·

' . MEASURED rr- i'"I"T ··~ r I ..

i STATION sl '" '" 320 '" '" 5:!0

---· '"' '"

0 r-:::::::1 BOTTOM - --- -- r-- J ·-C:., 1 0

0

0-j. ~120 z ;;; 100 b -so z 0

~600 ,_

',r;. ~.,

200

0 0

-/

,..... MIDDLE --

1-"" MIDDlE

..:=c· ~ -" 80 !20

--··

.. w• . w•

'" '"

BOTTOM -r ..

I -. ---. ~SLAB CAST

STATION c 240 280 320 360 400

AGE-DAYS AFTER RELEASE

-"-..

"' ''" 5

FIGURE 3-21 STRAINS IN BRIDGE BEAM R4-5 (LW)

''

f-· --

.

'"' ""' 6<0

. ' r-~ --

500 600 6<0

.

560 600 6<0

used as a validity test of the program in Ref. 1, but deflec­

tions show better agree~ent. The primary use of strain

measurements was made in computing prestress losses.

E. Strains in Slabs

Slab strains were due to shrinkage of slab and of beams,

and to creep of beams and slabs. Because of low stresses in

the slabs, little creep strain would be expected. And, as a

matter of fact, if shrinkage strains from the 3 ft. square

specimens are compared with their slab mate it is seen that

there is little difference between the shrinkage at the bottom

of the slab and that in the specimen.

The averages of the two bottom-of-slab strains are in

general agreement with the readings from the top gage points

in the beams. The beam gages are about 3 in. below the slab

gages and the two slab gages are offset 3 in. and about 40 in.

from the center line of the beam, and some small differe.nces

in strain would be evident between the beam and slab gages.

Figures 3-23 to 3-27 show that predictions of slab strains

agree well with measured values, which further strengthens the

validity of the overall method.

F. Deflections

Both theoretical and measured mid-span deflections of the

beams are tabulated in Table 3.3. Values of release camber,

taken from Ref. 1, are also shown. Values of deflection under

slab load in spans L4 and R2 are subject to some question

56'

TABLE 3.3 MID-SPAN DEFLECTIONS OF BEAMS

Ratio 11 release Release Elastic Defl(~easured) minus Final Ratio

.

Camber Due to Slab Theory 11 slab Camber Concrete Measured Theory Measured Ratio (Net elastic it Final camber )

Item Span BM Slab (in.) (in) (in) defl. (in.)) (in.) [\Net elastic de fl.

Ll-1 40 LW LW 0.38 0.208 0.102 0.49 0.278 0.50 1.80 3 40 LW LW 0.40 0.208 0.114 0.55 0.286 0.43 1.51 5 40 U'l LW 0.43 0.208 0.065 0.31 0.365 0.50 1.37 6 40 LW LW 0.18 0.208 0.102 0.49 0.278 0.41 1.47 8 40 11'1 LW 0.40 0.208 0.102 0.49 0.298 0.46 1.54

Average = (0.398) (. 208) (0.097) (0. 42) (0.301) (0.46) (1.5)

L3-l 56 NW LW 0.65 0.453 0.276 0.61 .374 0.70 1.87 3 56 NW LW 0.58 0.453 0.325 0. 72 .255 0.58 2.28 5 56 NW LW 0.62 0.453 0.264 0.58 .356 0.58 1.63 6 56 NW LW 0.62 0.453 0.186 0.41 .434 0.53 1.22 8 56 NW LW 0.65 0.453 0.234 0.52 .416 0.53 1.27

Average = (0. 62) (0. 453) (0.257) (0.57) (0.367) (0.582) (1. 6)

IL4-l 56 LW LW 1.31 0.828 0.359 0.43 .951 1.49 1.57 3 56 LW LW 1. 32 0.828 0.814 0.98 .506 1.46 2.88 5 56 LW LW 1.37 0.828 0.570 )* 0.69 .800 1.62 2.03 6 56 LW LW 1.26 0. 828 o. 456t 0.56 • 804 1.45 1.80 8 56 Ul LW 1.36 0.828 0.500 0.60 .860 1.26 1.47

Average = (1.32) (0.828) (0.540) (0. 65) (0. 784) (1. 46) (1. 9)

*. See pg. 58. {Continued)

U1 (X)

TABLE 3. 3 (Con 1 t)

Rl-5 40 LW LW 0.33 0.208 0.154 0.74 .176 0.38 2.16 R2-5 56 LW LW 1.30 0.828 0.557* 0.67 .734 1.20 1.64 R3-5 56 NW NW 0.64 0.453 0.234 0.52 .406 0.60 1.48 R4-5 56 LW NW 1.12 1.035 0.666 0.64 .454 o. 72 1.59

Note: Effective spans are 38'-9" and 54'-9"; wgts are 150 pcf and 120 pcf for the reinforced concretes; moduli of elasticity are 5900 ksi and 3220 ksi for NW and LW in the calculations.

* Questionable values because elevation points were cut off by construction crew during placement of the slab.

'"" ~ ::32 60

0 0 . ' •

~~ • • • !5§ 00

!,;;;~

~"' " ~

• • 0 ~ • • • . • 0 • • : • • • ' • 0 0 • • • • ' : t • • • • • . . • • • • • • • ' • • 0 • • • • 0 0

0 AVERAGE TEMPERATURE

~ " .A. AVERAGE RELATIVE HUMIDITY

I EACH POINT REPRE:Smrn IODI<Y AVERAGE)

~ ., ,, '" ,, '" ,, .o "'

,.,

i ' • ' 0 i ' ! ~ > ' ' 1 TIME- DAYS

FIGURE 3-22 AVERAGE TEMPERATURE AND RELATIVE HUMIDITY AT HOUSTON, TEXAS

z ' ;?; 200

<D / ' Q 0

z <t 200 0:: f-- 0 (f)

0-

z ' ;?; 200

<D ,.....-(· Q 0

z <i' 200 0:: J f-- 0 (f)

z ' ;?;

<D 200 b /"

z 0

<t 0:: 200 f--(f) --

TOP I SURFlcE \ 0

0 0 ... - ' ' 0

BOTTOM SURFACE' STATION A '

--k~ +- ' ' ' '

TOP ~URFAlE ...... ~ -- -· 0 0 '

STATION B /BOTTOM SURFACE. __ f.,..

-I- 0 - ·-' ' ' I 0

---MEASURED ---- PREDICTED

I I / TOP SURFACE

-r- ' '

STATION C BOTT~;_ ~URFACE

-1-- +:: -I- "- t-0

' 40 80 120 160 200 240 280

AGE-DAYS AFTER CASTING

FIGURE 3-23 STRAIN IN SLAB LS-I (LW)

~-·---~-·~·---------

'

'

'

' 0

·- ·-320 360

I

! f ' I " I t I I ~ '

;;;; ' z 200 cl)

Q z 0 <( 0:: 200 f-{f)

z ~ 200

"' Q 0 z <( 200 0:: f­{f) 0

;;;; ' ;;;; 200

<D

Q 0 z <( 200 0:: f­{f) 0

TO~ SUJFACE~ ,_...., f-

0 - 0

0

STATION A BOTTOM SURFACE ~ I 0

J I 0

r--r-- "I' ..._

0 I 40 80 120 160 200 240 280

1

ToP kuRFJcE'\

-----1-- -· 0

STATION B BOTTOM SURFACE-~ 0

I 0

-r ·- --~ --1-· r-· p 0 10 I

0 40 80 120 160 200 240 280

~OP ~URFA~E ~ -- o_ - - f--- 1-- --- 0 0

STATION c _BOTTOM SURFACE

_L J J. I 0

1-o- 1- -0

0

0

0 40 80 120 160 200 240 280

AGE-DAYS AFTER CASTING

FIGURE 3-24 STRAIN IN SLAB LS- 3 (LW)

-~20 360

-320 360

-320 360

z ' z 200 <D

' 0 0

z 200 <(

a:: f- 0 (f)

~ ' 200 ~ <D ' 0 0

z 200 <( a:: f- 0 (f)

z

' 200 ~

<D

Q 0

z 200 <(

a:: f- 0 (f)

TOP 1uRFAbE.____

,.- - ,..- 0 DISCONTINUED ibESTROYED BY TRAFFIC)

0

STA1TION A

BOT;~ SU1RFAC -::-+- 0

"'~ f

TOP LRFAhE..._ 0 0 -- - 0 ,.. 0

STATION 8 0

~ljlM ~RFACE 0

·- -rT-·-0 , I

-MEASURED

--PREDICTED

TOP ~URFAbE.____ 0 0

8 -- 0

0

'

BOTTOM SURFACE---. STATION c - --1 ..... 0 -=- 0 o I I

40 80 120 160 200 240

AGE-DAYS AFTER CASTING

FIGURE 3-25 STRAIN (LW)

IN SLAB

-- -0

0

0

0

0

0

---1--0

280 320 360

LS-4

z ' ;;;;;; 200

0 z

. <( 200 0:::

tn 0

~ ;;;;;; 200

tOQ 0

z <( 200 0:::

tn

z '

0

;;;;;; 200 tO

Q 0 z <{ 200 0:::

tn 0

~

-""' ~

~

il'""

1TOP kuRF~CE ~ 0 - 0 0

BOT~ OM SURFACE- 0 STATION- A 0

--f---- 0 f-- r-· 0 ·---r--0 0

/,TOP SURFACE

1-r-· 0 0

/~OTT OM SURFACE STATION-S

' 0

,{ ...,... r- --1-· ---- --r -MEASURED --PREDICTED

/~OP SURFACE 0 -

0 0

I_ 0 0

STATION- C /BOTTOM SURFACE 0

-'-1- 0 1--- --I 0 I 0 0

40 80 120 160 200 240 280 320 360

AGE- DAYS AFTER CASTING

FIGURE 3-26 STRAIN IN SLAB RS-1 (LW)

z ' z 200 <D

b 0 z ~ 200 1-U) 0

z

' z 200

b 0 z <1: 200 0:: 1-U) 0

z ' z 200

0 z <( 200 0:: 1-U) 0

~

'?

'""" 'r

,..

~

~ 0

~OP ~URFAbE" - ·-f--·-- r-----0 0

0 0

STATION A BOTTOM SURFACE-.. -- 0

I'

TOP I SUR~ACE- 1 0

0

STATION B BOTTOM SURFACE--. -0 0

0

--- MEASURED

---PREDICTED

TOP 1

SURFlCE '.

0 0

STATION c BOTTOM SURFACE_"

0

40 80 120 160 200 240

AGE-DAYS AFTER CASTING

FIGURE3-27 STRAIN IN SLAB (NW)

0

0

·---1-0

0

··--0

0

280 320

RS-4

-

r---

--

360

because the bolts that had been used as elevation points in

the beams were cut off by construction workers before elevation

readings could be taken just before the slab was cast. The

values shown are based on the assumption that elevations read

about one week prior to casting were the same as those just

before casting.

Plots of deflection versus age appear in Figs. 3-28 to

3-37 where both measured deflection and predicted deflection

are shown. Predictions are based on the method explained in

Ref. 1, where changes in slope of the deflected beams are

computed over short lengths of beam from strains at top and

bottom. The strains are taken from the function defining the

curve of measured strains.

The slab forms were suspended from the beams by hangers,

which is common practice in this type of construction. The

beams rested on rubber pads at their end seats and they were

not shored during slab casting. Deflections under the weight

of plastic slab were computed on the basis of a uniformly

loaded simple beam.

Agreement between predicted and measured deflections are

good except for the period before casting of the slab in spans

L-4 and R-2, Figs. 3-33 and 3-35, and for the complete period

for span R-4, Fig. 3-37. Ref. 1 shows poor agreement, too, in

spans R-2 and R-4. Beams in span R-4 r.emained seven days on

the prestressing line before release of prestress, against one

65

~5

;;;:: 2.0

' z 0 1.5 F u w 1.0 _j

"-w 0.5 Cl

0

2. 5

~ 2. 0 ' z

Q I. 1-u ~ I.

5

0

~ 0. 5

0 0

2.5

~ 2.0 z 0 f= 1.5 u ~ 1.0 "-~ 0. 511""'

40

40

40.

I ' I I

-~' ~~

i

80 120 160

I I

80 1~0 160

80 120 160

' BEAM Ll-5 STATION B -+-+-

DAY CAST 8/24/66 MEASURED DAY RE'LEASED 8/26/66 PREDICTED

I I I

I 1--SrA8 AST

1 0 I 200 ~40 280 320 360 400 440 480

I

BEAM Ll-5 STATION c DAY CAST 8/24/66 MEASURED

DAY RELEASED 8/26/66 PREDICTED

I I

I~ 10 I 1 I-1LA8

1c•s

200 240 280 320 360 400 440 480

BEAM Ll-5 STATION D

DAY CAST 8/24/66 MEASURED DAY RELEASED 8/26/66 PREDICTED

ISL~8 C~ST

I T 200 240 280 3~0 360 400 440 480

AGE-DAYS AFTER RELEASE

FIGURE 3-28 DEFLECTION OF BRIDGE BEAMS LW BEAMS. LW SLAB

I

5~0 560 600 640

~

520 560 600 640

5~0 560 600 640

;;; ' z

0

~ -' ~ w 0

;;;

' z Q

g ~ w 0

;;; ' z

0

~ rC w 0

2 .5

2 .0

I. 5

I. 0

0 . 5

0 0

2. 5

2. 0

5

0

0. 5

2

2

0 0

5

0

5

0

0 .5

0 0

2.5

20

1.5

1.0

0.5

0 0

BE~M Ll_,l STA~IO~ C

DAY CAST 8/24/66 MEASURED

D~YL Rs~EA~D 812~.f.66_L -:tPRE.£.1CTED . I ~SLAB CAST

40 80 120 160 200 240 280 320 360 400 440 480

I I BEL L-3 1 srJTIO~ c

I I DAY CAST 'e/24/66 MEASURED DAY RELEASED B/26/66 4.-PREDICTEO

I I F-~LAB CAST

40 80 120 160 200 240 280 320 360 400 440 480

I I I I I I I I BE~M L-61

sr1TIOJ c I I I I I I I I

DAY CAST 6/24/66 MEASURED OAr REILEA_iED -~2::.66 _L =-c :::1 .PREDlCTED

I I I I I I I I F-sLAB c'Asr 40 80 120 160 200 240 280 320 360 400 440 480

I BElM ~l-8l ST1TIO~ C I

DAY CAST 8/24/66 MEASURED

~~ R!l::4~0. ~12~66 - .-:REOICTED

J I 40 80 120

I ~--~LAB CAST

160 200 240 280 320 360 400 440 480

AGE-DAYS AFTER RELEASE

FIGURE 3-29 DEFLECTION OF BRIDGE BEAMS LW BEAMS, LW SLAB

5 20 560 600 640

-520 560 600 640

520 560 600 640

520 560 600 640

2.5

z 2.0

2: 0 1.5 >= (.)

1.0 w -' "-w 0.5 0

v

40 80 120

2.5

z 2.0

' z 0 1.5 >= ·fil 1.0 -' "-

0

v w 0.5 0

40 80 120

2.5

~ 2.0 ' z

0 1.5 f-(.) w 1.0 -' "-w 0.5 0

/ 0

0 0 40 80 120

BEAM ~3-5 STATI10 N I B

1 I

DAY CAST 9/10/66 MEASURED DAY RELEASED 9/12/66 ~--- PREDICTED

1-~ 0

I-SLAB CAST

160 200 240 280 320 360 400 440

I I

BEAM L3-5 STATION C

DAY CAST 9/10/66 MEASURED DAY RELEASED 9/12/66 ----PREDICTED - - -

0

0

~SLA CAT

160 200 240 280 320 360 400 440

BEAM L3-51

S;ATION D

DAY CAST 9/10/66 MEASURED DAY RELEASED 9/12/66-----PREDICTEO

SLAB CA,ST

160 200 240 280 300 340 400 440

AGE-DAYS AFTER RELEASE

FIGURE 3-30 DEFLECTION OF BRIDGE BEAMS NW BEAMS, LW SLAB

'

480 520 560 600 640

~ ·-0

480 520 560 600 640

0

480 520 560 600 640

"" ' z 0 f: lil ~ w 0

"" ' z 0 f: " w ~ ~

"" ' z 0

t w ~

"­w 0

"" ' z Q

g "­w 0

2. 5

2. 0

15

10 v 0. of-

00

2.5

2.0

5

1.0 V"

0. 5

00

2. 5

2. 0

I. 5

o,r 0. 5

0 0

2.5

2.0

1.5

I.D If''

0. 5

BEAM L3 I STATION c ~

DAY CAST 9/10/66 MEASURED f- DA1 RE1EASfD r!2166 -

1 PREI'CT~D I I

80 120 160 200 240 280 320 400 440 480 520

I I BEAM L3 3 STATION c

-- - -- - -- -,-::--sLA CAST I I

I I I - .l ' DAY CAST 9/10/66 - MEASURED r-. '

40

..

40

40

D~Y R~LEA~ED 19/12(66 I I PR~DICT~D I I ! 80 120 160 200 240 280 320 360 400 44 0 460

I 1 BEAM L3-6 STATION c

-I- -- -- - r-- - -- -oT- - _ _, SLAB CAST J

' r-- I DAY CAST 9/10/66 --- MEASURED

o•r "rL •• 1.D rl2r 1

- -

1

- 1 '"·rDICT1D I I 80 120 160 200 240 280 400 440 480

I I I I I I BEAM L3-B, STATION c

-- - - --~-+---,- - _-+ 1

1'--SLAf CAST I ' ' I :-:-4 l. -· DAY CAST 9/10/66 MEASURED

OAT REILEA~ED i/12f66 I 1 1

PRE1DLcr;o I I I

80 120 160 200 240 280 400 440 460

AGE- DAYS AFTER RELEASE

FIGURE 3-31 DEFLECTION OF BRIDGE BEAMS NW BEAMS, LW SLAB

I 520

--

520

L-

520

560 600 640

--560 GOO 640

-- !::_- r--

560 600 640

f-· -560 600 640

2.5

~ 2.0 ' z

Q 1.5

l:i w 1.0

-0 0

~r

...J "-w 0.5 0

40 80 120 160

2.5

~ 2.0 ' z

-- - --0

If/ 0 ;:: 1.5

u 1.0 w

...J "-w 0.5 0

40 80 120 160

2.5

~ 2.0 ' z - r·

Q 1.5 f-u

1.0 w v

...J "-w 0.5 0

40 80 120 160

BEAM L4-5 STATION B'

0

SLAB CAST--! 0 0 r--- r-·0' ~-

DAY CAST 9/16/66 MEASURED

DAJ R~LEASED 19/17/66 -~~ PRE~ICTED

200 240 280 320 340 400 440 480

BEAM L4 5 STATION c SL 8 c ST I

,-,- ..... -1· -- -DAY CAST 9/16/66 MEASURED

.

DAY RELEASED 9/17/66 --- PREDICTED

J I l J I J I I J I 200 240 280 320 360 400 440 480

BEAM L4-5 STATION D SLAB CAST

F- .! 1--- f--- 1---DAY CAST 9/16/66 MEASURED

DAY R~LEASED 9/17/66 --- PREDICTED

200 240 280 320 360 400 440 480

AGE- DAYS AFTER RELEASE

FIGURE 3-32 DEFLECTION OF BRIDGE BEAMS LW BEAMS, LW SLAB

520 560 600 640

--r----- r---·

520 560 600 640

1--- - 1--· ·- I-'- --

520 560 600 640

" ~ 2.0 !, ~I.

,If' ...J 1.0 "-~ 0. 5

5

z T 2. z

g :: ov 5

0 "-~ o. 5

00

5 2

~ 2. 0 ' z Q!. ,ki'"

0 t; ~I. ~ 0.

"' 2 '

5

0 0

5

:~ i5 I.

~ ~ 0.

0

5

00

----

SLAB C ST

' ' I DAY CAST 9/16/66 --- MEASURED

D~J REfEASIED flj~6 ~-l"YRE~ICTED ' ' BEAM L4-l STATION c ! 40 80 120 160 200 240 280 320 360 400 440 480

-~- ' -

- 0 -SLAB CAST

' ' ' ' i DAY CAST 9/16/66 --- MEASURED

O,Y R1LEArEO_l9'1J/6s,--c 1 PR1DICT1

Eo BEAM L4-3 STATION C

40 80 120 16 0 200 240 280 3 20 360 4 00 440 480

-- - I I - I fsL,8 c.jST

. DAY CAST 9/16/66 I --- MEASURED I 01 "j'EAIEO l'T6 ~-~-~ PR'i"'T BEAM L4-6 STATION C

40 80 120 160 200 240 280 320 360 400 440 480

-- ----

LAB !:;AST

' DAY CAST 9/16/66 --- MEASURED

DAI "'i"AjED 1smf" 1--1-\ PRE1o"r;o BEAM L4-8 STATION C

40 80 12 0 160 200 240 280 320 360 400 440 480

AGE-DAYS AFTER RELEASE

FIGURE 3-33 DEFLECTION OF BRIDGE BEAMS LW BEAMS, LW SLAB

520 560 800 640

- - .

520 560 600 640

520 560 600 640

520 560 6 00 640

2.5

i':: '

2.0 z Q 1.5 1-u

1.0 w ...1 "-w 0.5 Cl

2.5

i':: I

2.0

z Q 1.5 1-u 1.0 w ...1 "-w Cl

0.5 .-

2.5

i':: I

2.0 z Q 1.5 1-u

1.0 w ...1 "-w 0.5 Cl

BEAM Rl-5 'sTATION B

DAY CAST 8/27/66 I I 1

MEASURED DAY RELEASED 8/30/66 ---- PREDICTED

c- t-- - - - I-_- - 1-- ,__ _j--SLA8 CAST

"f 40 80 120 160 200 240 280 320 360 400 440 480

BEAM R 1-5 STATION C

' DAY CAST 8/27/66 MEASURED

DAY RELEASED 8/30/66 ---- PREDICTED

1-- ---- -- - -- - r-- - -- - 1-----r-fl S~A8 CtST

40

OAY DAY

40

-l 80 120 160 200 240 280 320 360 400 440 480

BEdM Rl-5 ~TATION D CAST 8/2; /66

1 I I 1 ME~SURED

RELEASED 8/30/66 ----PREDICTED

80 120 160

f--sLAB CAST

200 240 280 320 360 400 440 480

AGE -DAYS AFTER RELEASE

FIGURE 3-34 DEFLECTION OF BRIDGE BEAMS LW BEAMS, LW SLAB

'

520 560 600 640

520 560 600 640

520 560 600 640

2.5

z 2.0 ' z

Q 1.5 1-u 1.0 w

~ ..J "-w 0.5 0

2.5

z 2.0 ' z

0 1.5 l(/

>= u 1.0 w

..J "-w 0.5 Cl

2.5

~ I

2.0

z Q 1.5 1-u

1.0 w ,.

..J "-w 0.5 Cl

BEAM R2-5 STATION B

-- - ,..-- - r- f-- -+ f-- ]1 - --0 t-

0 0

DAY CAST 9/16/66 MEASURED !--sLAB CAST

Dy .RILEA,ED 19117166 1-l-1 PRrCTIED

40 80 120 160 200 240 280 320 360 400 440 480

- I-- - I 1-.- 0

'-' 0 0

DAY CAST 9/16/66 MEASURED DAY RELEASED

19/17/66 ----PREDICTED --SLAB CAST

BEAM R2-5 STATION C

40 80 120 160 200 240 280 320 360 400 440 480

.

BEAM R2-5 STATION D

-- - -- - -- -· ·- -- - -, I -- 1--

1-- I ·- - -DAY CAST 9/16/66 MEASURED I

DT RILEA,ED t/17(661 I

I PR,DICTIED I-SLAB CAST

40 80 120 160 200 240 280 320 360 400 440 480

AGE -DAYS AFTER RELEASE

FIGURE 3-35 DEFLECTION OF BRIDGE BEAMS LW BEAMS, LW SLAB

-520 560 600 640

·-

520 560 600 640

1- -~- - - _ _,.

520 560 600 640

2.5

"' :1.0

' z Q 1.5 1-0

1.0 w -' LL w 0.5

/. 0

Cl

2.5

"' 2.0 ' z

Q 1.5 1-0 1.0 w -' LL iK w 0.5 Cl

2.5

"' 2.0

' z 0 1.5 i= &l 1.0 Ii w 0.5 Cl

..,

BEAM R3-5 STATION B

DAY C~ST 0

9110;66 1

' ' ME~SUR0

EO DAY RELEASED 9/12/66 ----PREDICTED

- ,_. 0 j.

b.-sLAB CAST

40 80 120 160 200 240 280 320 360 440 440 480

BEAM R3-5 STATION C

DAY CAST 9/10~66 1 I 1 ME~SU~ED DAY RELEASED 9/12/66 ~ = -: =;. ~RE,£!C.!E!2_ t--1--- r·r--- r· - -, -0

40

0 0

40

0 0

~ 0

!-SLAB CAST

80 120 160 200 240 280 320 360 400 440 480

BEAM R3-5 STATION D

DA~ C~ST ~110;66 I I I 0

MEASUR~D DAY RELEASED 9/12/66 -- - - PREDICTED

-- -- t-0

80 120 160

!-,SLAB CAST

200 240 280 320 360 400 440 480

AGE-DAYS AFTER RELEASE

FIGURE 3-36 DEFLECTION OF BRIDGE BEAMS NW BEAMS, NW SLAB

520 560 600 640

·- --520 560 600 640

520 560 600 640

2.5

;!; 2.0 ' z

0 1.5 i= u

1.0 w 1/'. ~-

-' "-w 0.5 Cl

40

2.5

z 2.0 ' ....

/ z 0 1.5 ;= ,Yo u w 1.0 -' "-w 0.5 Cl

0 0 40

2.5

z 2.0

' z Q 1.5 1-- _....!--' u 1.0 w -' "-w 0.5 Cl

40

BEAM R4-5, STATION B

--- -- -- -- - ---- - !---- -- - .

,

DAY CAST 9/1/66 MEASURED - ·-DT R1LEArD rs,

1

66 1-1

- 1 PRE

1

DIC1ED ~SLAB CAST

80 120 160 200 240 280 320 360 400 440 480

-f---- -- - f---1-- - !-- -- - t-------:

BEAM 1R4-5. STATION C

r-- r--

~SLAB CAST

80 120 160 200 240 280 320 360 400 440 480

BE~M ~4 -~. ~TATI~N ~ --1--1-- -- -- - --I---- -- -- --: - C--

, I I ~

DAY CAST 9/1/-66 MEASURED J DAr R~LEA~ED l9/8~66 ;- -;--

1

PREIDICTIED !'-SLAB CAST

80 120 160 200 240 280 320 360 400 440 480

AGE- DAYS AFTER RELEASE

FIGURE 3-37 DEFLECTION OF BRIDGE BEAMS LW BEAMS, NW SLAB

-- r-· --

520 560 600 640

r-- -- r--· 1--

520 560 600 640

-· -- r-· --, ,

520 560 600 640

to three days for the other beams, and agreement between

measured and predicted values for R-4 beams has been poor

throughout.

If the curves of predicted deflections given in Ref. 1

are compared with those in this report, differences will be

noted for the period from release of prestress to casting of

slab. Those di~ferences come about because the extension of

data curves for creep and shrinkage extended over a much larger

period in the latter report, and the function defining those

strains was changed by the greater coverage of time.

The information developed in Table 3.4 is of such interest

to the designer in estimating deflections to obtain the desired

deck profile after the slab is cast. The measured elastic

deflection at the time the slab was cast is in all cases,

except for questionable reading in L4-3, much less than the

value calculated from a uniformly loaded beam. The measured

values come from elevation readings just before and just after

casting of the slab; a period of some 4 to 6 hours elapsed

between those readings. The ratio of measured to theoretical

deflection at mid-span averages 0.47 in the 40 ft. LW beam Ll.

The corresponding value from one beam in span Rl, identical to

Ll, was 0.75; both sets of beams carried LW slabs. The only

known difference in the beams is that Ll beams were steamed

and prestress was released at 2~ay age whereas Rl beams were

TABLE.3.4 PRESTRESS LOSSES AT MIDSPAN

Midspan (Sta. C) Beam Span Concrete Prestress Loss (% of Pre-release) Ratio of Losses

(Determined from strain measurements) (Time deEendent) (ft) Bm Slab Release Slab Cast Net Final Time Elastic ·

(elastic) (elastic) elastic Dependent*

Ll-5 40 LW LW 7.44 -1.57 5.87 15.93 10.06 1. 71

Rl-5 40 LW LW 6.01 -1.43 4.58 14.92 10.34 2.26

L4-5 56 LW LW 11.75 -2.97 8.78 21.83 13.05 1.49

R4-5 56 LW NW 10.45 -2.16 8.29 20.84 12.55 1.51

L3-5 56 NW LW 7.46 -1.46 6.00 14.57 8.57 1.43

* Final minus total elastic .

cured under wet mat and prestress was released at 3 day age.

The corresponding deflection ratio for 56 ft. LW beams carrying

LW slabs are 0.65 average for L4 and 0.67 for R2-5.

Normal weight beams of span L2 carrying a LW slab deflected

0.57 as much as was computed when the slab was added, and NW

beam R3-5 carrying NW slab deflected 0.52 as much.

The 56 ft. LW beam carrying NW slab, R4-5, deflected (),64

of the computed value under the weight of the plastic slab.

Summarizing the information on elastic deflection under

the weight 6f the plastic slab, the following approximate

percentages of measured to computed deflections were found:

40 ft. LW beam, LW slab 47%

56 ft. LW beam, LW slab 66%

56 ft. LW beam, NW slab 64%

56 ft. NW beam, NW slab 52%

56 ft. NW beam, LW slab 57%

The time lapse from beginning to finish of the slab pour

was about 2 1/2 to 3 hours and the pour progressed smoothly

from the outside of the bridge, beam #9, to the inside, beam

#1. From all that is known of the history of the beams, slabs,

and construction procedures nothing is known that would explain

the great difference between theoretical and measured deflections.

The variation of concrete secant modulus produces some

changes in deflection, but the changes are small. In Table 3.5

78

TABLE 3.5 CHANGES IN FINAL MIDSPAN CAMBER AND PRESTRESS LOSS WITH CHANGES IN MODULUS OF BEAM CONCRETE. (Values were computed by the step-by-step procedure given in the Appendix)

.

BEAM E/E measured Midspan Midspan % Camber Prestress

(in) Loss (%)

L3-5 80 0.699 16.05

90 o. 716 15.70

(56 I NW) 100 0.732 15.42

110 0.745 15.19

120 0.757 15.00

L4-5 80 1. 381 22.22

90 1.405 21.80

(56 I LW) 100 1.424 21.43

110 1.439 21.12

120 1.435 20.84

79

final deflections at mid-span are given for a NW and LW beam

where the moduli were varied from 80% to 120% of the measured

value. Determinations were made by the step-by-step method of

computations outlined in the Appendix. That table shows a very

small change in deflection brought about by the change in

modulus. The 56 ft. NW beam changed only 0.058 in. over the

40% change in modulus, and the 56 ft. LW beam changed 0.054 in.

These results indicate that the relatively small changes in

concrete modulus would not produce appreciable changes in

deflections.

A range of deflections, from low to high, that would

result from certain incorrect values of secant modulus, shrink­

age, and unit creep is shown in Fig. 3-43 for NW and LW beams.

Overestimation of deflection will result from a modulus

lower than the true value and from creep and shrinkage estimates

too high. Too high modulus with too low creep and shrinkage

will result in underestimates of deflection. For the values

used in Fig. 3-43, the modulus variation was 20% lower to 20%

higher than measured modulus. Corresponding creep and shrinkage

were 40% higher and 40% lower than measured. Such variations

produce elastic deflections that are 20% too high or low due to

modulus. Changes primarily due to creep and shrinkage occur

early after release of prestress with some change noted, too,

after slab placement. Most of the time dependent changes in

so

(f) (f) 2 5

s- 20 1-

~ffi 15 wu ~ffi I 0 (f) a. ~- 5 a.

25 (f) (f) gj:" 20

(f)Z 15 (f)w

wu o::O::

10 ,_w Cfl"-w-

5 0:: a.

25 (f) (f) gi= 20

(f)Z 15 Cflw wu o::O:: 10 ,_w (f)~ w 5 0:: a.

.

/ ---

40 80 120

/ I--

40 80 120

/ .....

40 80 120

STATION A

. -t . -+ -- r- ·-~-~LAB CAST

160 200 240 280 320 360 400 440 480 520

STATION 8

I I I

- -I-SLAB CAST

MEASURED ----PREDICTED

I I I 160 200 240 280 320 360 400 440 480 520

STATION C

!

j:-'Suit cAS'T - - --I

160 200 240 280 320 360 400 440 480 520

AGE· DAYS AFTER RELEASE

FIGURE 3-38 PRESTRESS LOSS IN BRIDGE BEAM Ll-5 LW BEAM, LW SLAB

r- r- ·-

560 600 640

- -

560 600 640

I -

560 600 640

(J) (J)

'3-,_ rnZ rnw wu

"'"' ,_u rn"-w-

"' "-

(J) (J) o_ _,,_ rnZ rnW wu

"'"' ,_w rn"-w-"' "-

rn rn '3-,_ rnZ rnW wU

"'"' ,_w rn!!:: w

"' "-

25

20

15

10 L 1/

5

25

20

15

10 v 5

0 0

25

20

15

10 /

5

40 80 120

-,

40 80 120

....-:

40 80 120

STATION A

i"=S~A8 C~ST

160 200 240 280 320 360 400 440 480 520

I VATION B

f-SLAB C~ST

t"""T I

MEASURED --- PREDICTED

I I _I 160 200 240 280 320 360 400 440 480 520

STATION C

-- -- r-- -· 1---

1-sLAB CAST

i

160 200 240 280 320 360 400 440 480 520

AGE- DAYS AFTER RELEASE

FIGURE 3-39 PRESTRESS LOSS IN BRIDGE BEAM L3-5 NW BEAM, LW SLAB

560 600 640

560 600 640

560 600 640

<n <n

30

25

gi= 20

~ri} 15 wu g:ffi 10 <n!:.

5 w 0: 0..

30

5

0-

1~/ 'I

0 0

30

25 <n <n 20 3->-<nz 15 <nw wu o:"' 10 r-W <no.. w- 5 0:

II

0..

- - - I

40 80 120

- ----

40 80 120

-c-- ,_. -· -

40 80 120

I

·~:::st.,; "'c.sl' -- - r- ·-

STATION A '

160 200 240 280 320 360 400 440 480 520

I I STATION B

I--~A8 CAs~ -- -- -· ·1 I I

I I I MEASURED

-----PREDICTED

I I I 160 200 240 280 320 360 400 440 480 520

STATION C

-+- ~-~-SLA8 CAST

I 160 200 240 280 320 360 400 440 480 520

AGE- DAYS AFTER RELEASE

FIGURE 3-40 PRESTRESS LOSS IN BRIDGE BEAM L4-5 LW BEAM, LW SLAB

I

I i I

560 600 640

-

560 600 640

-

560 600 640

25 en en g~ 20

enZ 15 "'w w'-' o:"' 10 1-w en"-w-

5 0:

.... r:- -~ I

a_

40 80 120

25 en U) o_ -'I-

20

enZ 15 enw w'-' o:<r 1-w 10 en"-w-

5 0:

·- -{/'

a_

40 80 120

25 en en 20 3-1-"'z 15 enW w'-' o:<r 10 1-w ~~ 5 0:

-- - -~-

/" a_

40 80 120

STATION A

I SLAB CAST

160 200 240 280 320 360 400 440 480 520

STATION B I f-sLls clsr

' t--1·

MEASURED ----PREDICTED

I I I 160 200 240 280 320 360 400 440 480 520

STATION C

I--SLAB CAST

'1 I I

160 200 240 280 320 360 400 440 480 520

AGE· DAYS AFTER RELEASE

FIGURE 3-41 PRESTRESS LOSS IN BRIDGE BEAM R 1- 5 LW BEAM, LW SLAB

560 600 640

I

560 600 640

'

560 600 640

3 0

5 1--· ~--- +-

It~ v

40 80

30

25 en en I-- ---20 gi= enZ ! ....

15 enW w<.> a:"' 10 ,_w en"-w-

5 0:

r;

a. 0

0

30

25 en en 3- 20

1-(IJ z 15 enW w<.> 0::: 0::: 10 ,_w en!!, i.i! 5 a.

-~

1/,...

40

--1-

..--

40

80

t-

80

+--

120

120

120

STATION A

+-- 1--t -- :i. ~SLA~ CAST

160 200 240 280 320 360 400 440 480 520

STATION 8

- +-- r--- +-- :+ +-- l- -~-I

~SLAB CAST

I I MEASURED

---- PREDICTED

I I 160 200 240 280 320 360 400 440 480 520

STATION C

4-f..- I-- 1--- --r:=-sLAB CAST

160 200 240 280 320 360 400 440 480 520

AGE- DAYS AFTER RELEASE

FIGURE 3-42 PRESTRESS LOSS IN BRIDGE BEAM R4-5 LW BEAM, NW SLAB

+-, I

560 600 640

560 600 640

I--

560 600 640

4.0

~ 3.5

z 3.0 0 f= 2.5

&l ~ 2.0

~ 1.5 z i't (f) 1.0 Cl

::E 0.5

4.0

~3.5

z 3.0 0 t; 2.s w i 2.0 w

/

~

I '/

I I

"' 0 '0 •o '00 '00 0<0

1-"

40 80 120 160

./

,......-.....

I I I I I I I I I I liTO? t:.BOTTOM ~ tiMii)D[E

1,20 0.80 1.25 0.76 TOP CURVE 1.27 0.74 1.25 0.86 MIDDLE CURVE 1.25 0.71 1.25 0.65 BOTTOM CURVE

I

I BEAM L3-5 56FT NW

200 240 280 320 360

AGE-DAYS

I I I

TOP CURVE

MIDDLE CURVE

BOTTOM CURVE

I I I I I I I I I l

E SHRINKAGE UNIT CREEP MEASURED E MEASURED SHRINKAGE MEASURED UNIT CREEP

0,80 1.40 1.40

1.00 r.oo 1.00

1.20 0.60 OBO

I '

I _j_

400 440 480 520 560 600 640

I I I I I I I I I I E SHRINKAGE UNIT CREEP

MEASURED E MEASURED SHRINKAGE MEASURED UNIT CREEP

0.80 1.40 1.40

1.00 1.00 1.00

1,20 0.60 0.60

Cl I. z 5/ b. TOP /lBOTTOM

~ it 1.0 gs ::E 0. 5

0

"' t.MIODLE -0 1.20 0.80 20 '20 0.79

•o 1.20 0.77 >00 1.[8 0.77 BEAM L 4-5 >00 _\:~ 0.75 56FT LW . .., 0 0.70

0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 6 0 0 64 0 AGE-DAYS

FIG. 3-43 INFLUENCE OF CHANGES IN SETS OF MODULUS, SHRINKAGE AND CREEP ON MIDSPAN DEFLECTION

Fig. 3-43 occurred within the period from release of prestress

to about two months thereafter. High and low predictions vary

from 126% to 65% of datum losses respectively for the NW beam,

and from 121% to 69%, respectively, for the LW beam.

Sinno's studies (Ref. 6, Table 6.12) showed that changes

in unit creep and shrinkage produce little change in deflections

when the modulus remains unchanged. This indicates that elastic

strains account for much of the change, and that can be seen in

Fig. 3-43.

Modulus of elasticity predictions within 20% of actual

val~es appear to be reasonable. Test records of creep and

shrinkage for various concretes under various conditions should

permit the designer to predict those values within 40% of

actualvalues. If predictions can be made within those limits,

deflections at mid-span should be within the range of 70% to

130% of theoretically exact values.

'G. Prestress Loss

Prestress losses determined from measured strains in the

beams extrapolated to the centroid of the prestressing steel

are represented by the "MEASURED" curves in Figs. 3-38 through

3-42. Losses determined from predicted strains at cgs of the

steel are represented by the "PREDICTED" curves in those figures.

The greatest variance of predictions from measured curves

in the final year appear in Fig. 3-38 for beam Ll-5, and Fig.

87

3-40 for beam L4-5. There is generally good agreement at the

end of the test period, although differences occur in some

cases over periods between the beginning and the end.

The loss at mid-span, station C, was about the same value

at the end of tests as it was before the slab was cast. There

was generally a little increase in losses, after slab casting,

at beam end, station A, and quarter span, station B.

Mid-span prestress losses are tabulated in Table 3.4.

Elastic losses occurred at release of prestress and elastic

increases occurred when the slabs were cast. The algebraic

sum of those two values has been designated as net elastic loss.

Terminal date losses in the 40 ft. LW beams at mid-span

were approximately 15%, and in the 56 ft. LW beams, approximately

21%. The 56 ft. NW beam showed 14 1/2% loss at mid-span. Table

3.5 shows very mmnor changes in losses with changes in concrete

modulus.

Time dependent losses, final minus net elastic loss, were

10% for 40 ft. LW beams, 13% for 56 ft. LW beams, ::and 8 1/2% for

56 ft. NW beams. The ratios of time dependent to net elastic

losses averaged about 2.0 for 40 ft. LW beams, 1.5 for 56 ft.

LW beams, and 1.4 for 56 ft. NW beams. Corresponding ratios

of final to release losses can be found from values in Table

3.4 to be 2.3, 1.9, and 1.9, respectively.

Final losses may be closely approximated as 2 times the

elastic losses at release for both concretes in the longer beams,

and at about 2.3 for the shorter span LW beams.

88

A range of prestress losses based on prediction of secant

modulus, shrinkage, and creep values from too high to too low

are shown for a NW and a LW beam in Fig. 3-44. Data for the

curves in that figure were developed in a way similar to that

used for the deflection study. The datum values, the middle

curves in the figure, were based on measured values of secant

modulus, shrinkage, and unit creep. A low modulus, 80% of

measured, and high shrinkage and creep, 140% of measured, pro­

duced the high loss curves. The low loss curve came from

modulus of 120% of measured, and shrinkage and creep at 60%

of measured. Losses ranged between the limits of 68% to 131%

of theoretically correct values for the NW beam, and from 73%

to 126% for the LW beam.

It is tempting to compare span ratios with prestress loss

ratios, although there is little data on which to make the

comparisons. The ratio of long to short span, 56/40, is 1.4

whereas the ratio of final losses in corresponding spans for

LW beams is 21.33/15.42, or 1.38 -- almost the same.

The practice that some designers follow in estimating

total losses to be about 15% and 20%, respectively for NW and

LW, appears, from these results, to be a good one.

3.8 Conclusions

Results of tests made on the full size highway bridge made of

pretensioned prestressed beams and cast in place slabs show that:

40

;::: 35 z w ~ 30 w ~ 25 <f)

<f) 20 g <f) 15 <f)

~ 10 1-rz 5 0:: "-

1-z w &! w "-(f)

g (f) (f) w 0::

t; w 0:: "-

35

I

!/ v

/ (/ /"

I I I I I

' MEASURED E

TOP CURVE 0.80

MIDDLE CURVE 1.00

BOTTOM CURVE 1.20

/ ,.-

40 so 120

..... !--"'" ,...-

' MEASURED E

TOP CURVE 0.80

MIDDLE CURVE 1.00

BOTTOM CURVE 1.20

_l_ I I I _L

40 80 120

FIGURE 3-44

I I I I I I I I I I I I I I I I SHRINKAGE UNIT CREEP LOSS TOP LOSS BOTTOM

MEASURED SHRINKAGE MEASURED UNIT CREEP ., LOSS MIDDLE I.DSS MIDDLE

1.40 1.40 0 1.20 0.80

" 1.29 0.71 1.00 1.00 60 1.29 0.70 0.60 I 0.60 '" 1.31 0.70

'" 1.30 0.68

'" 1.30 0.68

I I

BEAM L3-5 56Ft NW

160 200 240 280 320 360 400 440 480 520 560 600

AGE-DAYS

·;:~TL~;5'

~~ I ~~~ MEASOR<O UNIT CREEP "' 0 1.40 1.40 20 1.24 0.78 1.00 1.00

I

60 1.24 0.75

0.60 0.60 _i~ ':~~~- Jlii I I _j_ _j I I I

160 200 240 280 320 360 400 440 480 520 560 600

AGE- DAYS

INFLUENCE OF CHANGES IN SETS OF MODULUS, SHRINKAGE, AND CREEP ON PRESTRESS LOSS AT MIDSPAN

640

6 40

A. Time dependent camber and prestress lossed in prestressed

beams can be closely predicted provided that accurate shrink­

age and creep data are available.

B. The gains in time dependent camber and prestress loss in beams

10 months old at slab casting were very small for the period

between slab casting and termination of tests, a period of

about one year.

C. The measured elastic deflection of prestressed beams under the

weight of the plastic slab was just a little over one-half the

deflection computed by theory.

D. The total final beam camber at mid-span was about 1.6 and 1.9

times the net elastic camber (due to release of prestress and

casting of the deck slab) for 56 ft. NW and LW beams, respectively.

E. The time dependent prestress loss was approximately 1.5 times

the net elastic loss (due to prestress release and casting of

the deck slab) in 56 ft. NW and LW beams. It was higher for

the 40 ft. beams.

F. The theoretical effect of over and under estimates of elastic

modulus, shrinkage, and creep may be computed by the step-by­

step procedure outlined in the report. The most severe

combination of 20% error in modulus and 40% error in creep and

in shrinkage resulted in approximately 30% error in mid-span

deflection and prestress loss.

91

CHAPTER 4

SUMMARY AND CONCLUSIONS

4,1 The Objectives of the Overall program

The development of a method that would enable one to predict

creep, camber, and prestress loss in pretensioned prestressed light­

weight concrete bridge beams was the primary objective of the study.

A secondary objective was the comparison of deflections and

prestress losses in draped strand prestressed beams with those of

straight strand beams,

In addition to those objectives, it was desirable to gather

information on the behavior of full size prestressed co~crete beams.

That information would include values of camber prestress loss,

creep, and shrinkage of ):>earns of .a lightweight concret!" and a normal

weight concrete,

A final objective was to study the creep behavior of the composite

prestressed concrete beam - cast in place reinforced concrete slab

full size highway bridge.

4.3 The Program

Laboratory tests in the early stages proved the method of.prediction

to be a valid one and pilot tests on instrumentation on a full size

bridge proved the instrumentation plan to be workable,

The main test program called for instrumentation of five full

size pretensioned prestressed beams from which strains and elevations

were read from the day of casting until they reached an age of 660 days.

At approximately 300-day age the beams were erected in the bridge, and

92

the deck slab was cast. Strain and elevation readings from the slab

and beams continued from that age to termination of the program.

Creep and shrinkage data collected from control specimens were

used in a program for predicting strain, camber, and pres tress loss

in the beams and slabs, No relaxation of steel was included.

Four full size pretensioned prestressed concrete bridge beams

were cast and instrumented to compare the behavior of draped strand

beams with that of straight strand beams, Two normal weight beams

were used, one with draped strand and the other with straight strands,

Two similar beams of lightweight concrete were used.

4.3 The Conclusions

A. The step-by-step method produces reliable predictions of

camber and prestress losses in pretensioned prestressed concrete beams,

Control creep, shrinkage, and modulus of elasticity representative of

the prototype specimen should be used in the program.

B. At release of prestress there was good agreement between

computed and measured camber. The 40 ft. LW beams cambered approxi­

mately 0,40 in, at mid-span when prestress was released. The 56 ft.

LW beams averaged approximately 1,32 in. mid-span camber at release,

and the NW beams 0,62 in. There was excellent agreement between

computed and measured camber at release.

C. When the slab was placed, beam age approximately 300 days,

computed elastic deflections, due to the plastic slab, were much

greater in all beams than measured values. The ratios of measured

93

to computed mid-span deflections due to that cause were 0.47 for 40 ft.

LW, 0.65 for 56 ft. LW, and 0.57 for 56 ft. NW. Modulus of elasticity

measurements up to 90 day age indicated no great change in early

modulus values. Size effects and possibly the wetting of the top of

the beams worked toward holding these deflections to low values.

D. The ratio of 660 day camber, in the beam-slab bridge, to the

net measured. elastic deflection under prestress release and slab

casting, was 1.5 for the 40 ft. LW beams, 1.9 for the 56 ft. LW beams,

and 1.6 for the 56 ft. HW beams.

E. Ratios of time dependent prestress losses to elastic prestress

losses varied with the type of concrete, curing of beams, and combina­

tions of beam and slab concretes. The ratios for the 56 ft. beams

varied from 1.43 to 1.51.

F. Pre.stress losses, or percentages .of the pre-release stress

in strands, were approximately 15% for 40 ft. LW beams; 21% for 56 ft.

LW beams;·and 14 1/2% for 56 ft. NW beams, all at mid-span at 66Q-day

age.

G. Changes in elastic modulus of plus or minus 20%, with no

changes in creep or shrinkage, caused less than plus or minus 1%

change in prestress loss in theoretical calculations. Those changes

do, however, cause changes in elastic deflections in amounts propor­

tional to the change in the modulus.

H. Severe divergences in creep and shrinkage from actual (datum)

values in combination with 20% change in modulus of elasticity, from

its actual value, cause variations from datum values of deflections

and prestress losses.

94

Based on datum values computed from actual moduli, cree~ and

shrinkage, errors in estimations of those parameters would cause

deflections and prestress losses at mid-span shown below:

Decrease E to 80% of datum and increase creep and

shrinkage to 140% of datum:

Beam

56 ft, NW

56 ft. LW

Deflection (% datum)

126

119

Prestress Loss (% datum)

131

124

Increase E to 120% of datum and decrease creep and

shrinkage to 60% of datum:

Beam

56 ft. NW

56 ft. LW

Deflection (% datum)

65

70

Prestress Loss (% datum)

68

73

I. There was little difference in prestress loss in draped

strand and blanketed strand 50 ft. beams at 140 day age, Camber ratios

of the blanketed strand beams to those of the draped strand beams

were 0 • .57 for NW beams and 0.62 for LW beams, respectively.

95

REFERENCES

1. Furr, Howard L. and Raouf Sinno. "Creep in Prestressed Light­weight Concrete," Research Report 69-2, Study 2-5-63-69, Texas Transportation Institute, Texas A&M University, College Station, Texas. October 1967.

2. Torben C. Hansen and Alan H. Matlock, "Influence of Size and Shape of Member on the Shrinkage and Creep of Concrete," Journal of the American Concrete Institute, February 1946, Proceeding v. 63, page 267.

3. Dan E. Branson, "Time-Dependent Effects in Composite Concrete Beams," Journal of the American Concrete Institute, February 1964, Proc. v. 61, No. 2, pp 213-230.

4. Abul Hasnat, Behavior of Prestressed Composite T-Beams of Light­weight Aggregate Concrete, Ph.D. Dissertation, Texas A&M University, College Station, Texas, January 1965 (101 pages).

5. ACI Standard Building Code Requirements for Reinforced Concrete (ACI 318-63), American Concrete Institute, Detroit, Michigan, 1963.

6. Raouf Sinno, The Time Dependent Deflections of Prestressed Concrete Bridge Beams, Ph.D. Dissertation, Texas A&M University, College Station, Texas, January 1968 (178 pages).

96

APPENDIX

DETAILED FLOW DIAGRAM FOR PREDICTING PRESTRESSED

BEAM CAMBER, PRESTRESS LOSS, AND STRAINS

97

Symbols for Computer Program

ID

IDB

ENER

CGC

D

uw

AC

XL

H

STNO

AST

ED

EM

Project identification

Beam identification

Moment of inertia of beam gross section (in,4)

Distance from bottom of beam to the centroid of the

gross section (in,)

overall depth of beam (in,)

Weight per lineal ft, of beam (lb./ft.)

Gross area of beam cross section (in,2)

Beam span C-L of supports (ft.)

Distance from mid-span to hold-down point (ft.)

Number of prestressing tendons

Area of one prestressing tendon (in,2)

Eccentricity of effective prestressing strands at

end support (dist, from CGC to CGS) (in,)

Eccentricity of effective prestressing strands at

mid-span (in.)

PS Anchorage force per tendon (lb.)

EC Modulus of elasticity of beam concrete (ksi)

ES Modulus of elasticity of prestressing steel (ksi)

EA, EB, EX Distance from mid-span to station A, B, X (ft.)

ASH Shrinkage strain for beam concrete at infinite

time (microinches per in.)

BSH Age at which 50% of ASH develops (days)

ACR Creep strain in beam concrete at infinite time

(microinches per in.)

98

BCR Age at which 50% of ACR develops (days)

XN Length of time increment (days)

XNT Length of prediction period (days)

XLX Number of strain increments

XA, XB, XC Distance from center of support to. stations A, B, C (ft.)

GT Distance from top of beam to top gage point (in.)

GB, GM Distance from bottom of beam to bottom gage point and

middle gage point, respectively (in,)

XINC Time duration from day of casting of beam to day of

prestress release (days)

w Width of slab for one beam (flange width) (ft.)

T Thickness of slab (in,)

uws weight per lineal ft. at slab width W (lb,/ft,)

ECSL Modulus of elasticity for slab concrete (ksi)

..• ASHSL '-;,

Shrinkage strain in slab concrete at infinite

time (micro inches per in.)

BSHSL Age at which 50% of ASHSL develops (days)

ACRSL Creep strain in slab concrete at infinite time

(micro inches per in,)

BCRSL Age at which 50% of ACRSL develops (days)

XCAST Age of beams when slabs were cast (days)

INCSL Time duration of free shrinkage of slab between

casting date and date when it is assumed to be

effective in transmitting shrinkage induced stress

to beam (days)

99

KIF Integer control which directs the program to include

or not to include camber and/or strain

KIF = 1

KIF 2

KIF = 3

program predicts camber

program predicts strains

program predicts camber and strains

100

PROGRAM FOR PREDICTING STRESSES, STRAINS, AND CAMBER IN PRESTRESSED CONCRETE BEAM AND IN COMPOSITE REINFORCED CONCRETE SLAB WITH PRESTRESSED CONCRETE BEAM

BEAM DATA

SLAB DATA

ID[ ], !DB[ ], ENER, CGC, D, UW, AC, XL, H, STNO, AST, ED, EM, PS, EC, ES, ·EA, EB, EX, ASH, BSH, ACR, BCR, XN, XNT, XLX, XA, XB, XC, GT, GB, GM, XINC

W, T, UWS, ECSL, ASHSL, BSHSL, ACRSL, BCRSL, XCAST, INCSL, KIF

IN = XN + .01

INT = XNT+.Ol±XN

INC = XINC + .01

!CAST = XCAST+.Ol

KIF 0

101

COMPOSITE BEAM PROPERTIES

WRITE HDGS, BEAM AND SLAB PROPS.

ASL = W x 12. x T x ECSL/EC

ENERSL = ASL x T x T/12.

CGCCM = (ASL X (T/2. +D) + AC x CGC)/(ASL + AC)

E~ERCM = ASLx(T/2.+D) 2+ACxCGC2

+ENERSL+ENER-(ASL+AC)xCGCCM2

CTCM = D - CGCCM

ZTCM = ENERCM/CTCM

ZBCM = ENERCM/CGCCM

CTSLCM = D + T - CGCCM

ZTSLCM = ENERCM/CTSLCM

CBSLCM = D - CGCCM

ZBSLCM = ENERCM/CBSLCM

ACM = AC + ASL

ID[ ] , IDE'[ ] , XL, STNO, D, AST, AC, ES, ENER, PS, CCC, E,D, UW, EM, EC, ASH, BSH, ACR, BCR, W, CGCCM, T, ENERCM, UWS, ZTSLCM, ECSL,ZBSLCM, ZTCM, ZBCM, ASHSL, BSHSL, ACRSL, BCRSL'

10;?.

COMPUTE BEAM PROPS

CT = D - CGC

Z.T = ENER/CT

:ilB = ENER/CGC

DE = (EM-ED~,(,(XL:X:• 5-H)

M = 1

X = 0.0

17 E=ED+DExX

COMPUTE STRESSES AND STRAINS IN BEAM IMMEDIATELY AFTER RELEASE:

E > EM

No

103

Yes E=EM

DLM = (UWxXLx.5xX-UWxX2x.5)xl2.

ZC ENER/E

DLMS = (UWSxXLx.5xX-UWSxXxXx.5)x12.

ZCCM = ENERCM/(E+CGCCM-CGC)

AS = STNO x AST

p = PS x STNO

RP = AS/AC

RN = ES/EC

PSS 2 = Px(l./(l.+RPxRN+E xASx RN/ENER))/AS+(Diilll!:EAASx RN/(ENERx(l.+RPxRN+EAxASx RN/ENER)))/AS

FCT = PSSxRP-PSSxASxE/ZT+DLM/ZT

FCB = PSSxRP+PSSxASxE/tB-DLM/ZB

FCS = PSSxRP+PSSxASxE/ZC-DLM/ZC

ELT = FCT/EC

ELB = FCB/EC

1il!G4

-----------------

SHRT=CREEPT#CREEPB=p.O

L = 1

I J-1

INCREMENTAL CREEP AND SHRINKAGE STRAINS IN BEAM

SHR=O.O

CRT = CR(FCT,I)-CR(FCT,I-IN)

CRB CR(FCB,I)-CR(FCB,I-IN)

CRS CR(FCS,I)-CR(FCS,I-IN)

SHR = SHRK(I+INC)-SHRK(I+INC-IN)

No I > INC

L-----------------~~Yes

lOS

DSTS "'''SHR + .. CRS

DP = DSTS x ES

DF = DP x AS

DFCT = DF/AC-DFxE/ZT

DFCB = DF/AC+DFxE/ZB

DFCS = DF/AC+DFxE/ZC

FCT = FCT - DFCT

FCB = FCB - DFCB

FCS = FCS - DFCS

DSTT DFCT/EC

DSTB = DFCB/EC

DSTS = DFCS/EC

CREEPT = CREEP'l1+CRT-DS TT

CREEPB = OREEPB+CRB-DSTB

SHRT SHRT + SHR

<lST CREEPT + SHRT

CSB = CREEPB + SHRT

106

TOTAL STRAINS Al~D ROTATION OF INCREMENTAL LENGTH OF BEAM

DP

FCT

FCS

FCB

ELT

ELB

TST(L)

TSB(L)

DIF(L,M)

TST(L) =CST +ELT

TSB(L) CSB + ELB

DIF(L,M) = {(TSB(L)-TST6 (L))/D)xlo.-

L = L+l

Yes

No

;=, DLMSy; (ZCltEC)xESxAS

CONTINUE

= FCT+DLMS/ZT+DP/AC-DPxE/ZT

FCS-DLMS/ZC+DP/AC+DPxE/ZC

= FCB-DLMS/ZB+DP/AC+DPxE/ZB

= ELT+DLMS/(ZTxEC)+(DP/AC-DPx E/ZT)/EC ELB-DLMS/(ZBxEC)+(DP/AC+DPx E/ZB)/EC CST + ELT

= CSB + ELB

~ ((TSB(L)-TST(L))/D)xl0.-6

DIFFERENTIAL SHRINKAGE

No

SHSL = 0.0

FSLB(L-1)=0.0

E=E+CGCCM-CGC

I = I + IN

II=J-I+IN

108

·~--- ·--------------

Yes

SHSL = SLABSH(II+INCSL)­SLABSH(II-IN+ INCSL)

SHR

DSH

S FORCE

SMl

SM2

FSLBl

FCTl

FCBl

FCSl

~· SHRK(J+INC)-SHRK(J-IN+INC)

"' SHSL - SHR

= DSH/ ((D+Th 4. x (ECSLxENERSL+ ECxENER))+l./(ASLxECSL) +1. I (ACxEC))

= S FORCEx.5x(D+T)/(l.+ECxENER/ (ECSLxENERSL))

= SMlxECxENER/(ECSL*ENERSL)

=~~ FORCE/ASL-SMlxTx.5/ENERSL

s FORCE/AC + SM2/ZT

= s FORCE/AC ~ SM2/ZB

= s FORCE/AC - SM2/ZC

ADJUST CONCR STRESSES DUE TO STRESS r----------------L--------------~ CHANGE AT CGS

DFl

FCTl

FCBl

"FCSl xES x AS/EC

= FCTl-(DFl/ACM-DFlxE/ZTCM)

= FCBl-(DFl/ACM+DFlxE/ZBCM)

FCSl = FCSl-(DFl/ACM+DFlxE/ZCCM)

FSLBl FSLBl-(DFl/ACM-DFlxE/ZBSLC~ .

1U9

NET SHRINKAGE STRAINS

SHRT=SHR+FCTl /EC

SHRB=SHR+FCBl/EC

DIFFERENTIAL CREEP

CRSLB = SLABCR(FSLB(L-l),II)-SLABCR(FSLB(L-D,II-IN)

CRT = CR(FCT ,J) - CR(FCT ,J-IN)

CRB = CR(FCB,J) - CR(FCB,J-IN)

CRS = CR(FCS,J) - CR(FCS,J-IN)

DCR = CRSLB - CRT

CFORCE = DCR/((D+T) 2/(4.xECSLxENERSL+ECxENER))+ 1./(ASLxECSL)+l./(ACxEC)

CMl = CFORCEx.Sx(D+T)/(l.+ECxENER/(ECSLxENERSL))

CMZ = CMl X' EC x EjjjER/ (ECSL x: ENERSL)

FSLBZ = -CFORCE/ ASL -::(!;MI> x T x • 5/ENERSL

FCTZ = CFORCE/AC + CMZ/ZT

FCBZ = CFORCE/AC - CMZ/ZB

FCSZ = CFORCE/AC - CMZ/ZC

110

ADJUST CONCRETE DUE TO STRESS CHANGE AT CGS

STRESSES

DF2 = FCS2 x ES x AS/EC

FCT2 = FCT2-(DF2/ACM-DF2xE/ZTCM)

FCB2 FCB2-(DF2/ACM+DF2xE/ZBCM)

FCS2 FCS2-(DF2/ACM+DF2xE/ZCCM)

FSLB2 = FSLB2-(DF2/ACM-DF2xE/ZBSLCM)

NET CREEP STRAINS

CRT = CRT+FCT2/Ec·

CRB = CRB+FCB2/EC

CREEPT = CREEPT+CRT

CREEPB = CREEPB+CRB

l'H

NET TOTAL STRAINS, STRESS LOSSES, ~------------~--------------~ AND STRESSES FSLB(L)

FCT

FCS

FCB

L

TSB(L)

TST(L)

DIF(L,M)

= FSLB(L-1)+FSLB1+FSLB2

= FCT +' ,FCTL+ FCTZ

= FCS + FCS1 + FCSZ

= FCB + FCB1 + FCBZ

= L + 1

= TSB(L-1)+SHRB+CRB

TST(L-1)+SHRT+CRT

= (TSB(L)-TST(L))/Dx10-6

CALL ANOTHER DIFFERENTIAL LENGTH OF BEAM

r-------1 X = X+XL/XLX

MLX = (XLX+.01)/2.

M = M + 1

56 No Yes

112

M = M-1

L = L-1

MAX. CAMBER

DL = XL/XLX

MA = EA/DL

MB = EB/DL

MC = EX/DL

YMAX = 0.0

I = 1,M

CI I

YMAX = YMAX + DIF(J,I) x (CI- .5) X DL2 X 144.

113

56

CAMBER AT THREE OTHER POINTS ,

YA = 0.0

JJ = M+1-I

CA = I

YA = YA + DIF(J,JJ) x (EA- CA x DL +.5 X DL) X DL X 144.

CAMA = YMAX-YA

YB = 0.0

JJ = M+l-I

CB = I

YB = YB + DIF(J,JJ) x (EB- CB x DL + .5 X DL) x DL x 144.

114

CAMB = YMAX-YB

58 YC = 0.0

I = 1,11C

JJ = M+l-I

CC = I

'---'-i YC = YC + DIF(J ,JJ) x (EX - CC x DL + .5 x DL) X DL X 144.

CAMC = YMAX-YC

N = JxiN-IN

Yes

N = N-IN

115

N, CAMA, CAME , CAMC, YMAX

IF STRAINS AND STRESSES ARE DESIRED, CALL SUBR. STRAIN

(2,3)

CALL SUBROUTINE

STRAIN

STOP

CONTINUE

No

116

CHEK

Yes

RETURl" 1

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

SUBROUTINE STRAIN (AC, XL, XA, XB, XC, GT, GB, GM, ENER, CGC, D, UW, EC, STNO, AST, ED, EM, PS, ES, IN, INT, INC, H, W, T, UWS, ECSL, ICAST, INCSL, ID, IDB)

DIMENSION ID( TSLT(

) , IDB ( ),TSLB(

), TST( ), FSLT(

), TSM( ), TSB( ) , FSLB ( )

), TSS(

COMMON ASH, BSH, ACR, BCR, ASHSL, BSHSL, ACRSL, BCRSL

ID(I) I=1,18 '.

IDB(I)I=1,18

BEAM PROPE RTIES AT GAGE PT s.

CT = D - CGC - GT

ZT = ENER/CT

CB = CGC - GB

ZB = ENER/CB

CM = D - CGC - GM

ZM = ENER/CM

CTB = D - CGC

ZTB = ENER/CTB

DE = (EM-ED)/(XLx.S-H)

117

), STLOSS( ) ,

COMPOSITE BEAM PROPERTIES AT GAGE POINTS

ASL = W x 12. x T x ECSL/EC

ENERSL = ASL x T x T/12.

CGCCM = (ASLx(T/2.+D)+ACxCGC)/(ASL+AC)

ENERCM = ASLx(T(2.+D) 2+ACxCGC2

+ENERSL + ENER-(ASL+AC)x CGCCM2

CTBCM , = D - CGCCM

ZTBCM ENERCM/CTBCM

CTCM = CTBCM - GT

ZTCM = ENERCM/CTCM

CBCM = CGCCM - GB

ZBCM - ENERCM/CBCM

CMCM = GM - CGCCM

ZMCM . = ENERCM/CMCM

CTSLCM = D + T - CGCCM

ZTSLCM = ENERCM/CTSLCM

CBSLCM = D - CGCCM

ZBSLCM = ENERCM/CBSLCM

ACM = AC + ASL

118

WRITE HDG AND GIVEN DATA

XL, STNO, D, AST, AC, ES, ENER .. , PS, CGC, ED, UW, EM, EC, ASH, BSH, ACR, BCR, W, CGCCM, T, ENERCM, UWS, ZTSLCM, ECSL, ZBSLCM, ZTCM, ZBCM, ASHSL, BSHSL, ACRSL, BCRSL

Zero

E ED+DExXB

DLM = (UWxXLx.5 xXB-UWxXB2 x.5x12.

DLM =

DLMS

zc

ZCCM =

K = 1

Pos

E ED+DExXA

UWxXLx .5 x XA -UW X XA2 X .5 X 12.

(UWS x XL 2x .5 x XA

-UWS X XA X .$X 12.

ENER/E

ENERCM/(E+CGCCM-CGC)

119

DLM = (UWxXLx. 5 xxc-uwxxc2 x.5)x12.

y y DLMS = (UWSxXLx.S DLMS = (UWSxXLx.52

x XB-UWSx xXC-UWSxXG XB2x.S)xl"2. x.S)xl2.

~ ZC = ENER/E ZC = ENER/E

~ \6;) ~ ZCCM = ENERCM/(E+ ZCCM = ENERCM/(E+

CGCCM-CGC) CGCCM-CGC)

!

.. AS = SI'NOxAST

p = PS X STNO

PIN = P/AS

~

1!20

FCT = -PxE/ZT+P/AC+DLM/ZT

FCB = PxE/ZB+P/AC-DLM/ZB

FCM = -PxE/ZM+P/AC+DLM/ZM

FCS = P/AC - DLM/ZC

K, FCT, FCM, FCB, PIN

CREEP AND STRESSES BEFORE CASTING SLAB

PSS

RP = AS/AC

RN = ES/EC

. 2 = P X (1./ (1.. + RP x. RN + E x ASK

RN/ENER))J<I.~Lt; fPM1 x ]): x2. AS x RNI

(ENER X (1. + RP X RN + E X AS X

RN/ENER)))/AS

1:21

FCTB = PSSxRP-PSSxASxE/ZTB+DLM/ZTB

FCT = PSSxRP-PSSxASxE/ZT+DLM/ZT

FCM = PSSxRP-PSSxASxE/ZM+DLM/ZM

FCB = PSSxRP+PSSxASxE/ZB-DLM/ZB

FCS = PSSxRP+PSSxASxE/ZC-DLM/ZC

ELT = FCT/EC

ELM = FCM/EC

ELB = FCB/EC

ELS = FCS/EC

ELT, ELM, ELB, ELS

]J22

SHRT "' 0.0

CREEPT = 0.0

CREEPM = 0.0

CREEPB = 0.0

CREEPS = 0.0

L = 1

I = J-1

CRT = CR(FCT,I)-CR(FCT,I-IN)

CRM = CR(FCM,I)-CR(FCM,I-IN)

CRB = CR(FCB,I)-CR(FCB,I-IN)

CRS = CR(FCS,I)-CR(FCS,I-IN)

123

'>----.,~ SHR = 0. 0 No

. SHR = SHRK(I+INC):.;.SHRK(!ILHN+INC)

DSTS = SHR+CRS

DP = DSTSxES

PSS = PSS-DP

DF = DP x AS

DFCTB = DF/AC-DFxE/ZTB

DFCT = DF/AC-DFxE/ZT

DFCM = DF/AC-DFxE/ZM

DFCB DF/AC-DFxE/ZB

DFCS = DF/AC-DFxE/ZC

FCTB = FCTB-DFCTB

FCT = FCT - DFCT

FCM = FCM - DFCM

FCB FCB DFCB

FCS FCS DFCS

DSTT = DFCT /EC

DSTM = DFCM/EC

DSTB = DFCB/EC

DSTS = DFCS/EC

PSS = PSS + DSTS x ES

CREEPT = CREEPT+CRT~DSTT

CREEPM = CREEPM+CRM-DSTM

CREEPB CREEPB+CRB-DSTB

CREEPS ·- CREEPS+CRS-DSTS

125

SHRT = SHRT + SHR

CST = CREEPT+SHRT

CSM = CREEPH+SHRT

CSB = CREEPB+SHRT

CSS = CREEPS+SHRT

P = PSS

TST(L) = CST+ELT

TSM(L) CSM+ELM

TSB(L) CSB+ELB

TSS(L) = CSS+ELS

STLOSS(L) = (PIN~PSS) x 100./PIN

L = L+l

1;26

,.

I, P, FCT, FCM, FCB, FCS, CREEPT, CREEPM, CREEPB, CREEPS, CST, CSM, CSB, CSS

(I-ICAST) <0"-----w.l

STRESSES AND STRAINS AFTER CASTING SLAB (IF SLAB IS CAST) No

Yes CONTINUE

DP = DLMS/(ZCxEC)xESxAS

PSS = PSS+DP/AS

FCTB = FCTB+DLMS /ZTB.+DP / AC-DPxE/ZTB

FCT FCT+llLMS/ZT+ElP/AC-'llPxE/ZT

FCM = FCM+DLMS/ZM+DP/AC-DPxE/ZM

FCS = FCS-DLMS/ZC+DP/AC+DPxE/ZC

FCB = FCB-DLMS/ZB+DP/AC+DPxE/ZB

127

ELT ~ ELT+DLMS/(ZTxEC)+(DP/AC-DPxE/ZT)/EC

ELM~ ELM+DLMS/(ZMxEC)+(DP/AC-DPxE/ZM)/EC

ELS = ELS-DLMS/(ZCxEC)+(DP/AC+DPxE/ZC)/EC

ELB = ELB-DLMS/(ZBxEC)+(DP/AC+DPxE/ZB)/EC

TST(L) CST+ELT

TSS(L) = CSS+ELS

TSB(L) CSB+ELB

TSM(L) = CSM+ELM

STLOSS(L) (PIN-PSS).xlOO·. }PIN

P = PSS

148

'

I, P, FCT, FCM, FCB, FCS, CREEPT, CREEPM, CREEPB, CREEPS, CST, CSM, CSB, CSS

DIFFERENTIAL SHRINKAGE BTWN TOP OF BEAM AND BOTTOM OF SLAB KK = 1,199

TSLT(KK) = 0.0

TSLB(KK) = 0.0

FSLT(KK) 0.0

FSLB(KK) = 0.0

E = E+CGCCM-CGC

I I + IN

I,INT,IN

129

II = J-I+IN

No

SHSL SLABSH(II + INCSL) -SLABSH(II-IN+INCSL)

SHR = SHRK(J+INC)-SHRK(J-IN+INC)

DSH = SHSL-SHR

SHSL 0.0

SFORCE = DSH/((D+T) 2/4.'x (ECSL x ENERSL + EC x ENER)) + 1./(ASL x ECSL)+ 1./(AC x EC))

SM1 = SFORCEx.Sx(D+T)/(1.+ECxENER/(ECSLxENERSL))

SM2 = SM1 x EC x ENER/(ECSL x ENERSL)

l30

75

FSLTl = -SFORCE/ASL+SM1xTx.5/ENERSL

FSLB1 = -SFORCE/ASL-SM1xTx.5/ENERSL

FCTB1 = SFORCE/AC + SM2/ZTB

FCTl = SFORCE/AC + SM2/ZT

FCB1 = SFORCE/AC - SM2/ZB

FCS1 = SFORCE/AC - SM2/ZC

FCM1 = SFORCE/AC + SM2/ZM

ADJUST CONCRETE STRESSES DUE TO STRESS CHANGE AT CGS OF BEAM

DF1 = FCS1 x ES x AS/EC

FCTB1 = FCTB1 - (DF1/ACM-DF1xE/ZTBCM)

FCT1 = FCTl - (DF1/ACM-DF1xE/ZTCM)

FCM1 = FCM1 - (DF1/ACM-DF1xE/ZMCM)

FCB1 = FCB1 - (DF1/ACM+DF1xE/ZBCM)

FCS1 = FCS1 - (DF1/ACM+DF1xE/ZCCM)

FSLT1 = FSLT1 -(DF1/ACM-DF1xE/ZTSLCM)

FSLB1 = FSLB1-(DF1/ACM-DF1xE/ZBSLCM)

131

D 0

76

NET SHRINKAGE STRAINS IN BEAM AND SLAB

SHSLT = SHSL+FSLTl/ECSL

SHSLB = SHSL+FSLBl/ECSL

SHRTB = SHR: +' FCTBI,(EC

SHRT = SHR + FCTl/EC

SHRB = SHR + FCBl/EC

SHRM = SHR + FCMl/EC

SHRS = SHR + FCSl/EC

IFFERENTIAL CREEP BTWN fOP F BEAM AND BOTTOI>l OF SLAB

.

CRSLT = SLABCR(FSLT(L-l),II)-SLABCR(FSLT(L-l),II-IN)

CRSLB = SLABCR(FSLB(L-l),II)-SLABCR(FSLB(L-l),II-IN)

CRTB = CR(FCTB, J) - CR(F€'];:6., J ~ !N)

CRT = CR(FCT, J) - CR(FCT, J - IN)

CRB = CR(FCT, J) - CR(FCB, J - IN)

CRM = CR(FCM, J) - CR(FCM, J - IN)

CRS = CR(FCS, J) - CR(FCS, J - IN)

132

DCR = CRSLB-CRTB

J CFORCE = DCR/((D+T) 2/(4. x (ECSL xENERSL + EC x

ENER)) + 1./(ASL x ECSL) + 1./(AC x EC))

CM1 = CFORCEx. 5x (D+T) / ( 1. +ECxENER/ (ECSLxENERSL) )

CM2 = CMl x EC x ENER/(ECSL x ENERSL)

FSLT2 = -CFORCE/ASL + CM1 x T X .5/ENERSL

FSLB2 = -CFORCE/ASL - CM1 x T X .5/ENERSL

FCTB2 = CFORCE/AC + CM2/ZTB

FCT2 = CFORCE/AC + CM2/ZT

FCB2 = CFORCE/AC - CM2/ZB

FCM2 = CFORCE/AC + CM2/ZM

FCS2 = CFORCE/AC - CM2/ZC

133

ADJUST CONCRETE STRESSES DUE TO STRESS CHANGE AT CGS

DF2 = FCS2 x ES x AS/EC

FCTB2 = FCTB2 -(DF2/ACM-DF2xE/ZTBCM)

FCT2 = FCT2 -(DF2/ACM-DF2xE/ZTCM)

FCM2 = FCM2 -(DF2/ACM-DF2xE/ZMCM)

FCB2 = FCB2 -(DF2/ACM+DF2xE/ZBCM)

FCS2 = FCS2 -(DF2/ACM+DF2xE/ZCCM)

FSLT2 = FSLT2 -(DF2/ACM-pF2xE/ZTSLCM)

FSLB.2 = FSLB2 -(DF2/ACM-DF2xE/ZBSLCM)

H4

r.

----------------·~--

NET CREEP STRAINS IN BEAM AND SLAB

CRSLT

CRSLB

CRT

CRB

CRS

CRM

=

=

CREEPT =

CREEPB =

CREEPM =

CREEPS =

.

CRSLT+FSLT2/ECSL

CRSLB+FSLB2/ECSL

CRT + FCT2/EC

CRB + FCB2/EC

CRS + FCS2/EC

CRM + FCM2/EC

CREEPT + CRT

CREEPB + CRB

CREEPM + CRM

CREEPS + CRS

~· NET T STRES STRES

OTAL STRAINS, S LOSSES, AND SES

·.

FSLT(L)

FSLB(L)

L

CST

CSM

CSB

css

TST(L)

TSM(L)

TSS(L)

TSB(L)

TSLT(L)

TSLB(L)

DP

PSS

STLOSS(L)

FCTB

FCT

FCM

FCS

FCB

p

• = FSLT(L-l)+FSLT1+FSLT2

= FSLB(L-l)+FSLB1+FSLB2

= L + 1

= CST+ SHRT + CRT

= CSM + SHRM + CRM

= CSB + SHRB + CRB

= CSS + SHRS + CRS

= TST(L-l)+SHRT+CRT

= TSM(L-l)+SHRM+CRM

= TSS(L~l)+SHRS+CRS

= TSB(L~l)+SHRB+CRB

= TSLT(L-l)+SHSLT+CRSLT

= TSLB(L~l)+SHSLB+CRSLB

= (SHRS + CRS) x ES

= PSS - DP

= (PIN-PSS)xlOO./PIN

= FCTB + FCTBl + FCn2'

= FCT + FCTl + FCT2

= FCM + FCMl + FCM2

= FCS + FCSl + FCS2

= FCB + FCBl + FCB2

• = PSS l0J I

J, P, FCT, FCM, FCB, FCS, CREEPT, CREEPM, CREEPB, CREEPS, CST, CSM, CSB, CSS

CONTINUE

FREESH = SLABSH(INCSL)

I = JxiN-IN

NO YES

137

TSLT(J) = TSLT(J)+FREESH

TSLB(J) = TSLB(J)+FREESH

NO

>--::=:::--~ I = I-IN YES

I, TST(J), TSM(J), TSB(J), TSS(J), STLOSS(J), FSLT(J), FSLB(J), TSLT(J), TSLB(J)

1------1 CONTINUE

K = K + 1

(NO) >----:YE=s---.1 RETURN

138

FUNCTION CR(FC, I) COMMON ASH, BSH, ACR, BCR, ASHSL, BSHSL,ACRSL, BCRSL, (CREEP AT ANY TU1E)

~------Y~e~s--------~T = I

No CREEP = (ACRxT)/(BCR+T)

CR = 0.0 CR FC x CREEP/1000.

, RETURN

139

FUNCTION SHR(I) .COMMON ASH, BSH, ACR, BCR, ASHSL, BSHSL, ACRSL, BCRSL

SHRINKAGE AT ANY TIME

Yes '>---__;;.:::::. ___ --ilioo-IT = I

No

SHRK = (ASKxT)/(BSH+T)

SHRK = 0.0

RETURN

140

,_,

{r

FUNCTION SLABGR (FC, II) COMMON ASH, BS!!, ACR, BCR, ASHSL, BSHSL, ACRSL, BCRSL

c OMPUTE REEP IN SLAB AT ANY TIME

II > 0 . Yes T II =

No SCREEP = ACRSLxT/(BCRSL+T)

SLABCR = 0.0 ~ SLABCR = FCxSCREEP/1000.

~ I

RETURN

141

FUNCTION SLABSH (II) COMMON ASH, BSH, ACR, BCR, ASHSL, BSHSL, ACRSL, BCRSL

COMPUTE SHRINKAGE IN SLAB AT ANY TIME

II > 0 Yes T = II

No SLABSH = ASHSLxT/(BSHSL+T)

SLABSH = 0.0

RETURN

142

..

ARRANGEMENT OF DATA CARDS

1 11 21 31 41 51 61 71 80

1 I ID H+ER CARD IDINTIFYING THI PROJECT I I I I I 2 !DB HElDER CARD ID~TIFYING THI BEAM I I l I I 3 I ENER CGC I D uw I AC I XL I H I l 4 I STNO AST I ED EM I PS I EC I ES I I

f-' 5 I EA EB I EX I l I I I ..,. "'

6 I ASH BSH I ACR BCR I XN I XNT I XLX I I 7 I XA XB I XC GT I GB I GM I XINC l I

8 [ w T I uws ECSL I I I I I 9 ASHSL BSHSL ACRSL BCRSL XCAST INCSL KIF

See notes on next sheet.

Notes:

l. Cards number l and 2 may contain any information, alphabetic or numeric.

2. Each variable in cards 3 through 8 may occupy any position within the

ten columns, and all values must be expressed in decimal form.

3. The first 5 variables on card 9 may occupy and position with the ten

columns and must be in decimal form.

INCSL must occupy columns 51 and 52, must be right adjusted, and

must not be in decimal form.

KIF must occupy columns 53 and 54, must be right adjusted, and must

not be in decimal form.

4. The last card in the data deck, card nuinber 10, whould carry the

number of beams to be run at the same time in columns 1-10 (any

pesition) in decimal form.

144