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14 PCI JOURNAL
Effect of Allowable CompressiveStress at Release on PrestressLosses and on the Performance
of Precast, Prestressed ConcreteBridge Girders
W. Micah Hale, Ph.D., P.E.Assistant ProfessorThe University of ArkansasFayetteville, Ark.
Bruce W. Russell, Ph.D., P.E.Associate Professor
Oklahoma State UniversityStillwater, Okla.
This paper presents the results of a research program that examinedprestress losses in high-performance concrete bridge girders and theeffects, if any, of compressive stresses at release exceeding the currentallowable stress limit of 0.60 f
ci . Four I-shaped girders were cast
and tested with compressive release stresses ranging from 0.57 fci to0.82 f
ci . Two of the four girders were made with air-entrained concrete;
prestress losses were measured on these as well and compared withlosses in girders made with non-air-entrained concrete. The measuredprestress losses were then compared with prestress losses estimatedusing: (1) the 2004 American Association of Highway TransportationOfficials load-resistant factor design (AASHTO LRFD) Bridge DesignSpecifications (refined method), (2) the PCI Design Handbook methoddescribed by Zia et al., and (3) the method proposed in the NationalCooperative Highway Research Program (NCHRP) Report 496
(detailed method).Of the three methods to estimate losses, the NCHRPReport 496sDetailed Method for Estimating Prestress Losses mostaccurately predicted the measured losses, followed by the Zia et al.equations, and then the 2004 AASHTO LRFD equations. A secondobjective of the research was to provide additional data measuringprestress losses for cases where the actual compressive stresses atrelease exceed the allowable compressive stresses at release. Theresearch results support increasing the allowable compressive stressat release from 0.60 f
ci to 0.70 f
ci .
DURABILITY
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MarchApril 2006 15
Over time, the initial prestressing force that is ap-
plied to a member decreases in magnitude. During
a period of approximately five years, a prestressed
concrete member may lose as much as 25% of the initial pre-
stress force.1,2Elastic shortening, creep, shrinkage, and re-
laxation are the four primary contributors to prestress losses
in pretensioned beams. Of the four, elastic shortening is the
only loss that is not time dependent.
There are many methods used to estimate the effective
prestress force fse (prestress force existing after all losses).The three most widely accepted methods are: (1) the Refined
Estimates of Time Dependent Losses method found in the
2004 American Association of Highway Transportation Of-
ficials load-resistant factor design (AASHTO LRFD)Bridge
Design Specifications, (2) the PCI Design Handbook method,
described by Zia et. al., and (3) lump sum estimates.35
A new method is outlined in the recently published Na-
tional Cooperative Highway Research Program (NCHRP)
Report 496, the Detailed Method for Estimating Prestress
Losses.6The method inNCHRP Report 496was developed
specifically for girders cast with high-strength concrete.
In the research program reported herein, the prestress loss-es of four I-shaped girders were measured and compared with
losses calculated using the following methods: the AASHTO
LRFDBridge Design Specifications, the PCI Design Hand-
book, and the recommendations from the NCHRP Report
496.4
In addition, the beams and their respective prestressing
forces were designed to impose compressive stresses at re-
lease that exceeded the allowable release stresses found
in both AASHTO LRFD Bridge Design Specifications
and the ACI Building Code Requirements for Structural
Concrete (ACI 318-05).7 Currently, AASHTO LRFD and
ACI 318 limit the concrete compressive stresses after releaseto 60% of the concretes release strength (0.60 f
ci ).
This research program examines whether compressive
stresses in excess of 0.60 fci will cause a lasting detrimental
effect to the prestressed concrete member, and whether the
allowable compressive stress can be increased beyond its cur-
rent limit of 0.60 fci .
LITERATURE REVIEW
Prestress Losses
Several ongoing research projects have been conductedrecently to determine the accuracy of design equations used
for estimating prestress losses in high-performance concrete
(HPC) bridge girders. Roller et al. examined the prestress
losses in HPC bridge girders.8Along with prestress losses,
they also measured the creep and shrinkage of the concrete.
Five girders were cast, but prestress losses were reported for
only Girder BT3 and Girder BT5.
The two girders were subjected to two different curing
regimens. Girder BT3 was steam cured for 24 hours at 140 F
(60 C). Curing continued on Girder BT3 for an additional 10
hours until the forms were removed. Girder BT5 was cured
under a waterproof tarpaulin for 10 hours. The forms wereremoved 12 hours after casting.
Prestress losses were measured using internal strain meters.
The research results showed that the AASHTO equations over-
estimated the losses by approximately 50% at 18 months for
Girder BT3. The researchers reported, however, that the steam
curing of Girder BT3 may have affected the prestress losses.
Compared with the early age losses of Girder BT5 (non-steam
cured), those of Girder BT3 were significantly lower.
The results also showed that the AASHTO equations for
estimating creep and shrinkage may be overly conservative
for high strength concrete. The researchers recommended
further study of the creep and shrinkage behavior of HPC todetermine whether the AASHTO equations can be modified.
Roller et al. again examined the prestress losses, but this
research program examined the losses in a bridge built by the
Louisiana Department of Transportation and Development.
Construction of the bridge was completed in October 1999.9
The prestress losses were reported for 12 months. The mea-
sured losses were approximately 35% less than the calculated
losses. These results were consistent with the Roller et al.
research.8
Pessiki et al. examined the effective prestress force in
bridge girders that were 28 years old.10Load tests were per-
formed on the girders to determine the decompression load.Visual observations, strain gauges, and displacement trans-
ducers were used in obtaining the decompression loads. The
average prestress loss for both girders was 18%, compared
with a loss of 33% predicted by the AASHTO equations.
Azizinamini et al.also examined the available prestress in
an existing bridge girder, investigating the effective prestress
force in a 25-year-old girder.11The girder testing showed that
the prestress loss after 25 years of service was 20.7%, which
was less than the 25.7% predicted by the AASHTO equations.
Idriss measured the prestress losses of HPC bridge gird-
ers during construction and during service.12 Deformation
sensors were placed in the girders to measure the prestresslosses. After five months of service, the measured losses
were less than the losses predicted by AASHTO and the
Table 1. Target Release Stresses and Air Content of the Four Girders.
GirderTargeted Allowable Compressive Stresses (fbot/f'ci)
Targeted Total
Air Content (%)
0.60 0.75 2 6
1 - X X -
2 - X - X
3 X - - X
4 X - X -
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16 PCI JOURNAL16 PCI JOURNAL
PCI Design Handbook. The AASHTO and PCI equations
predicted losses of 28% and 22.6%, respectively, which are
both greater than the measured losses of 11%. The reported
losses were measured after only five months of service, how-
ever.
In comparison, the calculated values are final losses for
the entire service life of the beams. Naturally, as the girders
age, they will continue to lose prestress force. The total lossesconsidering the fullness of service life can be expected to dif-
fer from losses measured at only five months of age.
The research demonstrates that the AASHTO equations
consistently overestimate the total prestress losses; instead of
arguing for changes to the prediction methods, however, most
researchers agree that more testing needs to be done before
the prediction equations are modified. The NCHRP Report
496is an outgrowth from efforts of the Transportation Re-
search Board and affiliate members to further document and
support alterations to the loss equations.
Allowable Compressive Stress at Release
The AASHTO LRFD Bridge Design Specifications, the
ACI 318Building Code, and the PCI Design Handbooklimit
the concrete release stress in compression to 60% of the com-
pressive strength at release (0.60 fci ).3,4,7 The reported pur-
pose of the limit is to control creep deformation and damage
due to micro-cracking.13 Practitioners suggest, however, that
the limit for compressive stresses is artificial and the beam
performance is not reduced by exceeding the compressive
stress limit at release.
In many design cases, strict adherence to the rule effec-
tively increases the need for harping strands or, alternatively,
increases the number and length of debonded strands in theend regions of girders. In this manner, the current limit for
compressive release stresses effectively increases production
time and creates additional need for steam curing.14
Unfortunately, little data exist to support increasing the al-
lowable compressive stress at release. Despite the dearth of
published supporting data, many precast, prestressed con-
crete manufacturers, as part of their standard practice, release
strands as long as resulting compressive stresses stay within
75% of the concrete strength. In support of this practice, the
PCI Standard Design Practice reports that no problems have
been reported by allowing compression as high as 0.75 fci.15
Pang investigated the effects of large compressive stresseson the hardened properties of concrete.16 He conducted creep
tests on concrete cylinders loaded at one day of age to 60%,
70%, and 80% of the concretes one-day breaking strengths.
Cylinders loaded to 70% of breaking strength demonstrated no
adverse effects from the sustained loading at early ages.
One of the cylinders that was loaded to 80% of breaking
strength failed under sustained loading, possibly indicating
that 0.80 fci is too large of a compressive stress. Pang fur-
ther reported that the creep at higher stress levels was notexcessive and was similar to creep experienced by concrete
stressed at lower levels. Pang also concluded that the allow-
able compressive limit could be raised to at least 0.70 fci .
Noppakunwijai et al. conducted an experimental research
program that examined the effects of high release stresses
on precast, prestressed concrete girders.17Two girders with
compressive stresses at release of 0.79 fci and 0.84 fci were
cast. The prestress losses of the girders were measured. They
concluded that higher release stresses did not have a negative
impact on the test specimen.
Despite these recent data, the amount of data on the release
stresses of prestressed concrete is very limited, particularlyexperimental data on bridge girders. Therefore, the justifica-
tion for increasing the allowable compressive stress limits at
release primarily has been based on common practices in the
precast/prestressed concrete industry.
EXPERIMENTAL PROGRAM
Scope
Four prestressed concrete girders were cast with targeted
release stresses of 0.60 fci or 0.75 fci . The girder variables
are described in Table 1. Girders 2 and 3 were cast with air-entrained concrete, whereas Girders 1 and 4 used non-air-
entrained concrete. Release stresses for Girders 1 and 2 were
targeted at 0.75 fci . Targeted release stresses for Girders 3
and 4 were 60% of the concrete release strength.
The research results provide data to examine whether the
allowable compressive stress should be increased beyond the
current limit. Prestress losses were measured for each girder
for one year.
Materials
Type III cement was used in all mixtures. The coarse ag-
gregate was a crushed limestone from Davis, Okla., with anominal maximum size of 3/8in. (9.5 mm). The fine aggre-
Table 2. Mixture Proportions for Girders 1 through 4.
Girders 1 and 4 Girders 2 and 3
Cement (lb/yd3) 900 900
Coarse aggregate (lb/yd3) 1790 1790
Fine aggregate (lb/yd3) 1217 1040
Water (lb/yd3) 234 234
Water-cementitions ratio 0.26 0.26
Targeted total air content (%) 2 6
Calculated unit weight (lb/ft3) 153.4 146.8
Note: 1 lb/yd3=0.5933 kg/m3; 1 lb/ft3=16.02 kg/m3.
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MarchApril 2006 17
gate was washed river sand from Dover, Okla., conforming
to ASTM C 33. To provide adequate workability, a water re-
ducing admixture and a high-range water reducing admixture
were used.
An air-entraining admixture was used to attain the required
target total air content. The girders contained 0.60-in.-diameter
(15.2 mm), low-relaxation prestressing strand with a modu-
lus of elasticity of 28,500 ksi (197,000 MPa) and Grade 60
(414 MPa) mild bar reinforcement. All prestressing strands
conformed to ASTM A 416.
Mixtures
The mixtures were designed based on workability and
strength, and are listed in Table 2. Girders 1 and 4 were cast
with the same concrete and did not include air entrainment.
The concrete batched for Girders 2 and 3 included air entrain-
ment, with a sand content adjusted to reflect the increased
volume of air contained in the concrete.
The only differences between the two mixtures were the
air content and quantity of sand used. Girders 1 and 4 had a
targeted total air content of 2%, whereas Girders 2 and 3 had
a targeted total air content of 6%. Girders 2 and 3 used pro-portionately, by volume, less sand than Girders 1 and 4.
Girder Design and Fabrication
The dimensions and cross sections of the girders are shown
in Fig. 1, which was used for all four girders. Each girder
had a depth of 24 in. (0.61 m) and was cast to a length of
24 ft (7.3 m). The gross and transformed section properties are
shown in Table 3.
For Girders 1 and 4, the release strength was targeted
at 8000 psi (55 MPa) with a design strength of 13,000 psi
(90 MPa) at 56 days. For Girders 2 and 3, the release strength
was targeted at 6700 psi (46 MPa) with a 56-day design strengthof 11,000 psi (76 MPa). The strand patterns were varied and were
designed to possess an effective prestress of 185 ksi (1250 MPa)
after elastic shortening but before other time-dependent losses.
Ten fully pretensioned prestressing strands were deployed in
each line for casting; some strands, however, were debonded
through the full length of the girders. The full-length debonding
details are depicted in Fig. 1. For example, Girders 1 and 4 were
cast in the same line using the same mixture for both girders.
Girder 1, however, required ten fully bonded prestressing strands
in order to attain the targeted compressive stresses at release,
whereas Girder 4 required only eight strands.
Because Girders 1 and 4 required the same concrete but
different compressive stresses at release, two strands in
Girder 4 were debonded along the full length to effectively re-
duce the compressive stresses after release. Girders 2 and 3 also
required some debonding to achieve the desired compressive
stresses at release. Split plastic sheathing, taped at each end, was
used to ensure debonding.The girders were cast at Coreslab Structures Inc. of Oklaho-
ma City, Okla. Strands were tensioned individually. The jacking
stresses that are reported in Table 3 were computed from elonga-
tion measurements that were made before and after strand stress-
ing. Elongation measurements were made after the strand chucks
were seated, so the reported jacking stress accounts for seating
losses. For all girders, the jacking stress ranged from approxi-
mately 200 ksi to 204 ksi (1380 MPa to 1410 MPa).
Fig. 1. Shown is the cross section of the girders.Note: 1 in. =25.4 mm.
0.6" dia. P/S strand
Table 3. Gross and Transformed Section Properties.
Section Properties Girder 1 Girder 2 Girder 3 Girder 4Ag(in.
2) 163.25 163.25 163.25 163.25
Atr(in.4) 173.38 175.71 173.40 169.19
Atr(in.4) 13.75 13.75 13.75 13.75
ytr(in.) 13.32 13.20 13.35 13.48
Ig(in.4) 12,399.47 12,399.47 12,399.47 12,399.47
Itr(in.4) 13,223.48 13,488.50 13,215.80 13,007.65
etr(in.) 6.90 7.20 6.40 7.75
Aps(in.2) 2.17 1.953 1.736 1.736
Jacking stress after seating loss (ksi) 204.25 202.20 200.76 204.47
Note: 1 in. =25.4 mm; 1 in.2
= 645 mm2
; 1 in.4
=416,230 mm4
; 1 ksi =6.895 MPa.
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Instrumentation
Prestress losses were calculated from measured concrete
surface strains. Concrete strains were measured using de-tachable mechanical strain (DEMEC) gauges targets. The
DEMEC target points were glued to the concrete surfaces
after the forms were removed but prior to release of the pre-
tensioning force. Strain measurements were initialized prior
to release and were taken again immediately after release.
The difference in readings gives the total concrete strain
within a pair of DEMEC target points.
The DEMEC targets were placed on each side of the bot-
tom bulbs (4.5 in. [113 mm] from the bottom of the gird-
er) and on the top surface of the girders. The targets were
placed 60 in., 68 in., and 76 in. (1.5 m, 1.7 m, and 1.9 m)
from each end and also at 144 in., 152 in., and 160 in. (3.7 m,
3.9 m, and 4.m) from one end.
The distances of 60 in., 68 in., and 76 in. (1.5 m,1.7 m, and 1.9 m) from the girders ends were chosen because
at this distance the prestress forces are fully effective. Also,
strain readings measured at midspan verified that the prestress
forces at 60 in. (1.5 m) were fully effective. The placement of
the targets along the bulb of the girders is shown in Fig. 2.
By knowing the strains at the top of the girder and also the
strains at 4.5 in. (114 mm) from the bottom, the steel strain
at the center of the steels gravity was then calculated. The
DEMEC dial gauges were accurate in estimating stress levels
within 0.20 ksi (1.34 MPa).
Total measured prestress losses were obtained by measur-
ing the concrete strain between the DEMEC targets and thenmultiplying the measured strain by the elastic modulus for
prestressing strands. This method does not account for the
loss in prestress force due to relaxation of the prestressing
strands. The loss due to relaxation is not accompanied by a
corresponding change in strain.
Figures 3and 4show the DEMEC target points that are ad-
hered to the concrete. In Fig. 3, DEMEC target points are lo-
cated on the bottom bulb of the beam, 4.5 in. (114 mm) from
the bottom of the cross section. Figure 4 shows the DEMEC
target points that were glued to the top of the cross section.
Strain readings were taken before cutting the prestressing
strands and immediately (within one or two hours) after cut-ting the strands. Measurements were taken periodically until
the girders were one year old.
RESULTS OF TEST PROGRAM
Fresh and Hardened Concrete Properties
Concrete temperature, slump, fresh air content, unit weight,
and ambient temperature were measured during casting of the
girders. The fresh concrete properties are reported in Table 4.
Girders 1 and 4 were cast with non-air-entrained concrete using
the concrete from the same batch. Girders 2 and 3 were castwith air-entrained concrete using concrete made from the same
batch.
Table 4 indicates that the air content for Girders 1 and 4
was 2.3%, whereas the air content for Girders 2 and 3 was
6.2%. Unit weights and concrete slump are consistent with
measurements made during trial batching when the mixture
proportions were developed.
Hardened concrete properties are shown in Table 5. Each
reported value of compressive strength (ASTM C 39) is the
average of at least three individual tests. Likewise, the report-
ed elastic moduli (ASTM C 469) are the averages of at least
three individual tests. The compressive strength and modu-lus of elasticity were measured from 4 in. 8 in. (100 mm
Fig. 2. Pictured are the detachable mechanical strain gaugetarget locations along the side of the girder.
Fig. 3. The detachable mechanical strain gauge targets areshown on the bulb of the girder.
Fig. 4. The detachable mechanical strain gauge targets areshown on the top of the girder.
DEMEC locations
DEMEC targets
DEMEC targets
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200 mm) cylinders cast from the same concrete as the gird-
ers and cured alongside the girders.
The data show that the concrete compressive strength in-
creased with time for both sets of girders. Likewise, the elas-
tic modulus also increased over time. Compressive strengths
and the modulus of elasticity are reported for a time frame
spanning 360 days, or approximately one year.
Prestress Losses
Prestress losses over time are reported in Table 6. The
data indicate that Girder 2 had the greatest prestress lossesand Girder 4 had the least losses of the four beams. Concrete
strains were measured at irregular intervals after the beams
were cast and prestress release occurred. Time equals zero on
the day of casting.
The data also demonstrate that prestress losses increased
over time, as expected. Table 4 also includes the locations
where the girders were stored and where prestress losses
were measured: the girders were stored outside at Coreslab;
inside at Fears Structural Engineering Laboratory (FSEL);
and outside at FSEL.**
At each location, the girders were simply supported with
cribbing and bracing located 12 in. (305 mm) from each end.Typical support cribbing and bracing can be viewed in Fig. 2,
where the girders are stored outside FSEL.
The reported losses are prestress losses corresponding to
the center of gravity (cg) for the prestressing strands. Strain
readings are taken at DEMEC targets located on the sides of
each girders bottom bulb and at the DEMEC targets located
on the very top of each girder. The strain at the cg is then
determined from the strain readings taken from the DEMEC
target points.
The reported losses are then computed from the cg strains
by multiplying the strain by the strands elastic modulus.
Table 6 lists losses at the ends (average of the two ends) and
at the center of the girder.Table 6 also lists the ratio of maximum compressive stress
at release to compressive strength at release. For Girder 4, the
compressive stress at the extreme bottom fiber is computed to
be 4950 psi (34.1 MPa), or 56.9% of the concretes one-day
strength (that is, 8700 psi [60 MPa]).
Likewise, for Girder 1, the computed compressive stress
at the bottom fiber is 5650 psi (40 MPa), or 64.9% of the
concretes one-day strength. For Girder 3, the computed
compressive stress at the bottom fiber is 4250 psi (29.3 MPa),
or 69.3% of the concretes one-day strength (that is, 6130 psi
[42.3 MPa]). Finally, the highest ratio of stress to strength
occurred on Girder 2, where the maximum compressive stressat release was 82.1% of the concretes compressive strength.
In engineering practice, the concrete is presumed to be lin-
Table 4. Fresh Concrete Properties for Girders 1 Through 4.
Fresh Concrete Properties Girders 1 and 4 Girders 2 and 3
Fresh concrete temperature (F) 68 60
Slump (in.) 10.0 9.75
Air content (%) 2.3 6.2
Unit weight (lb/ft3) 151.1 146.9
Air temperature (F) 36 35
Note: C = (
5
/9)(F -32); 1 in. =25.4 mm; 1 lb/ft
3
=16.02 kg/m
3
.
Table 5. Hardened Concrete Properties of Girders 1 through 4.
Age of Test Girders 1 and 4 Girders 2 and 3
Average Compressive Strength (psi)*
1 day (at release) 8700 6130
14 days 10,190 7110
28 days 11,060 8390
56 days 12,440 9200
180 days 14,460 10,850
360 days 15,610 11,460
Average Modulus of Elasticity (ksi)*
1 day (at release) 5600 4700
14 days 5800 4900
28 days 6000 5500
56 days 6300 5400
180 days 6800 5500
360 days 6900 6000
* Reported values are the average of three tests.Note: 1 psi =0.006895 MPa; 1 ksi =6.895 MPa.
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ear and elastic for stress calculations. In other words, stresses
are proportional to strains and the relationship is defined by
the elastic modulus. Accordingly, the normal engineering
practice to compute the bottom fiber precompression stress is
given by the equation:
fbot =Fsi1
Atr+
etr
Sb( )tr
where Fsiis the prestress force immediately prior to release
and the cross-section properties are all transformed.
If gross properties are used, then the prestress force used
in the equation must be the prestress force immediately after
prestress release to obtain reasonably accurate estimates for
concrete stress. By using the transformed cross-section prop-
erties, the exact computation of concrete stresses (and elas-
tic shortening losses) can be obtained without iteration.
The equation shown, however, assumes Hookes Lawa
linear relationship between stress and strain. In actual gird-
ers, however, with compressive stresses approaching and ex-
ceeding 60% of the compressive strength of the concrete, the
stress versus strain relationships are decidedly nonlinear.
To account for that nonlinearity, an effective modulus of
elasticity (Eeff) was determined and employed in the calcula-
tion of transformed section properties. The effective modulus
was obtained from the parabolic stress versus strain relation-
ship widely known as Hognestads model and given by the
expression18:
fc
fc= 2
c
o
c
o
2
The effective modulus was obtained from the slope of asecant drawn from the origin to a point on the stress versus
strain parabola with the corresponding concrete stress re-
quired to provide equilibrium. The effective moduli range
from 500 ksi to 900 ksi (3.4 GPa to 6.2 GPa) less than the
measured modulus.
It should be noted that a lesser concrete modulus will re-
sult in a proportionately greater elastic shortening loss. The
effective modulus (Eeff) was used to compute stresses in the
concrete after release and the elastic shortening losses.
The losses reported in Table 6 do not include losses due to
steel relaxation. Because relaxation occurs without an accom-panying change in strain, relaxation cannot be measured with
DEMEC points. Relaxation losses were estimated using the
current AASTHO LRFD equations and are incorporated in the
total loss calculations that are discussed later in the paper.
DISCUSSION OF TEST RESULTS
Fresh Concrete Properties
One goal of the research was to develop HPC that could
easily be used in the local precast concrete industry. The
sponsor of the project, the Oklahoma Department of Trans-port, was also interested in our ability to produce air-en-
trained HPC suitable for fabrication of bridge girders.
The slumps of the two mixtures were 9.75 in. and 10 in.
(246 mm and 254 mm), indicating that both mixtures had suf-
ficient workability to produce the girders. As can be seen in Fig.
5and 6, the girders had a smooth finish and there were no hon-
eycombed areas.
Girders 1 and 4 had a targeted air content of 2%, and Girders 2
and 3 had a targeted air content of 6%. One mixture was batched
for Girders 1 and 4, and another mixture was batched for Gird-
ers 2 and 3. The measured total air contents for both mixtures
were within 0.50% of the targeted air contents indicating ourability to produce concrete within specified air content ranges.
Table 6. Measured Prestress Losses.
Average Measured Prestress Losses (ksi)*
Beam
Age
(Days)
Temperature
(F)
Girder 1 Girder 2 Girder 3 Girder 4
fbot/f'c= 64.9% fbot/f'c= 82.1% fbot/f'c= 69.3% fbot/f'c= 56.9%
Ends Center Ends Center Ends Center Ends Center
1 (at
release)36 27.8 27.8 32.8 33.6 24.4 23.4 25.6 24.8
16 40
39.6 40.0 51.2 52.0 41.2 40.2 36.6 35.6129 65 40.2 40.2 53.8 55.4 42.2 41.4 37.2 36.8
43 65 46.0 46.0 61.8 62.4 49.2 48.6 42.8 42.6
60 51 44.6 44.2 59.2 60.2 46.4 46.0 40.6 40.8
84 63 46.2 46.0 63.0 64.2 49.6 48.6 43.2 43.8
120 71 48.0 47.6 64.4 66.0 50.6 50.6 44.6 45.2
180 90 52.4 49.8 69.0 71.6 56.4 55.0 48.4 49.4
360 63 56.8 53.4 72.0 74.0 59.2 58.4 51.6 51.8* Measured losses do not include relaxation losses. Cured outside at Coreslab Structures. Cured inside at Fears Structural Engineering Laboratory.** Cured outside at Fears Structural Engineering Laboratory.
End losses are the average losses from both ends of the girder.Note: C = (5/9)(F -32); 1 ksi =6.895 MPa.
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Note that air content and unit weight were measured in the
plant prior to placing concrete in the forms. During beam
casting, one batch of concrete was discarded due to an exces-
sively high air content of 9%.The unit weights of the mixtures were inversely correlated
to the air contents of the mixtures. The mixture for Girders 1
and 4 had a higher unit weight than the mixture for Girders
2 and 3, as expected. The measured unit weights for all mix-
tures were within 1.5% of the calculated unit weight. The dif-
ferences between the measured and calculated unit weights
were considered acceptable.
Hardened Concrete Properties
The strength gain of the two mixtures cast at Coreslab is
shown in Fig. 7. The difference between the two mixtures is
the total air content within them. The rate of strength gain forthe two mixtures is almost identical, but for each age tested,
the mixture with additional entrained air had a reduced com-
pressive strength by roughly 30%.
Prestress Losses
The measured total losses and the predicted total losses
are shown in Table 7, which also shows the estimated losses
using the three different methods discussed. The AASHTO
method and the PCI Design Handbook method (Zia et al.
equations) both overestimate the total losses, whereas the
recommendations from the NCHRP Report 496 slightly
underestimate total losses. The measured losses in Table 7include the estimates for relaxation losses and for the self-
weight of the girder where necessary. Relaxation losses were
calculated using the AASHTO equation (refined method) and
ranged from 2.0 ksi to 2.8 ksi (13.8 MPa to 19.3 MPa).3Due
to girder size, the compensation for girder self-weight ranged
from 0.05 ksi to 0.09 ksi (0.34 MPa to 0.62 MPa).
Table 8 shows the ratio of predicted losses to measured
losses for each set of prediction equations. Again, the 2004
AASHTO (refined) and Zia et al. equations overestimate
losses.3,5For all the girders (at both midspan and ends), the
AASHTO equations overestimate the prestress losses by
18%. The Zia et al. equations also overestimate the losses byan average of 13%.5
On the other hand, the detailed method from NCHRP Re-
port 496predicted losses that were more accurate than the
other two methods.5The average difference between the mea-
sured losses and predicted losses was 6%.
In comparing the measured total losses with the predicted
losses from the various methods, it should be noted that total
losses are estimated over the whole life of the prestressed
concrete member, which may easily be several decades. On
the other hand, measured losses are reported only for one
year. Equations from the ACI 209 report indicate that shrink-age may increase 10% from one year to fifty years and creep
strains may increase as much as 25% after one year of age.
Therefore, one must conclude that the measured losses are
not the whole loss that will be experienced by the member.
Table 9lists the measured prestress losses at one day versus
the estimated experienced elastic shortening losses from the
three methods. The AASHTO and NCHRP methods employ
transformed cross-section properties and the exact method
to compute elastic shortening so these two methods agree.
The PCI Design Handbookcontains an approximate method
that varies somewhat from the other two methods.
For all four girders, the difference between the prestressloss measured at one day and the predicted elastic shortening
Fig. 6. The girder is photographed with a smooth finish.
0 50 100 150 200 250 300 350 400
2.3 % Air
6.2 % Air
18,000
16,000
14,000
12,000
10,000
8000
6000
4000
2000
0
Age (Days)
Fig. 7. Pictured is the strength gain for the Coreslab mixtures.Note: 1000 psi =6.895 MPa.
Fig. 5. The photograph of the girder shows no honeycombing.
CompressionStrength(psi)
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loss was 4.6 ksi (32 MPa). The differences are accounted for
in that the measured losses include the effects of both shrink-
age and creep, whereas the computed elastic shortening lossis a theoretical calculation based solely on elastic material
properties.
Figure 8 shows the increase in prestress losses over time.
Inspection of the figure reveals two interesting points. One
point is that as time increases, the total prestress loss also in-
creases. The charts, however, clearly show that the losses tend
to level out as time increases beyond 180 days. The second
point, therefore, is that the higher the compressive stress at
release, as expressed as a percentage of the one-day compres-
sive strength, the larger the total amount of prestress losses.
The figure clearly shows the progression where Girder
4, stressed to 56.9% of its one-day strength, has the lowestamount of total loss, whereas Girder 2, stressed to 82.1% of
its one-day compressive strength, experiences much larger
prestress losses.
Release Stresses and Comparison to Allowable Stresses
Table 10shows the transformed cross-sectional properties
for the girders based on the effective elastic modulus for con-
crete, as discussed. For each case, the maximum compressive
stress occurs at the bottom fiber. Maximum stresses, immedi-
ately after release, are reported both in absolute terms and also
as a percentage of each girders one-day compressive strength.In essence, the table shows that the maximum release stress
ranges from a low of 56.9%, which is an allowable stress
within the current code, to 82.1%. The maximum compres-
sive stress in three of the four girders exceeds the allowable
stress given in theAASHTO LRFDand ACI 318.
The targeted maximum release stresses of 0.60 fci and
0.75 fci were not attained because the one-day compressive
strengths for Girders 1 and 4 were higher than targeted and
the one-day compressive strengths for Girders 2 and 3 were
lower than targeted. The release strengths for Girders 1 and
4 were targeted at 8000 psi (55 MPa) based on trial batching
in the laboratory and at Coreslab. The compressive strengthsof Girders 1 and 4, however, were 8700 psi (60 MPa) at one
day.
Girder 1 was designed to have an allowable compressive
stress at release of 0.75 fci , but due to the unexpectedly high
one-day compressive strength, this value was only 0.65 fci .Similarly, Girder 4 was designed to have allowable com-
pressive stress of 0.60 fci , but this value was only 0.57 fci .
The 700 psi (4.8 MPa) increase in strength beyond targeted
Table 7. Total Prestress Losses.
Girders Location
Total Prestress Losses (ksi)
Measured
(1 year)*AASHTO2004 Zia et al. NCHRPReport 496
1Ends 58.9 81.7 72.4 55.3
Center 55.5 81.3 72.1 55.1
2Ends 74.0 80.7 82.9 71.1
Center 76.1 80.3 82.4 70.7
3Ends 61.2 67.1 65.8 58.9
Center 60.6 66.7 65.4 58.6
4Ends 54.6 74.3 65.0 50.5
Center 54.5 73.9 64.7 50.2*Measured losses include relaxation losses and compensation for self-weight.
AASHTO: American Association of Highway Transportation Officials.NCHRP: National Cooperative Highway Research Program.
Note: 1 ksi =6.895 MPa.
Table 8. Ratio of Predicted to Measured Losses.
Girders Location
Ratio of Measured to Predicted Losses
AASHTO*2004 Zia et al. NCHRPReport 496
1Ends 0.72 0.81 1.07
Center 0.68 0.77 1.01
2Ends 0.92 0.89 1.04
Center 0.95 0.92 1.08
3Ends 0.93 0.94 1.05
Center 0.92 0.94 1.05
4Ends 0.73 0.84 1.08
Center 0.74 0.84 1.09
Average 0.82 0.87 1.06*AASHTO: American Association of Highway Transportation Officials.|NCHRP: National Cooperative Highway Research Program.Note: 1 ksi =6.895 MPa.
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MarchApril 2006 23
strength was due to the steam curing used by Coreslab.
Likewise, the one-day compressive strengths of Girders 2
and 3 were lower than targeted. This resulted in higher com-
pressive stresses at release. Girder 2 was designed to have anallowable compressive stress at release of 0.75 fci . Because
the compressive strength of 6130 psi (42.3 MPa) was lower
than targeted, the maximum compressive stress at release was
0.82 fci .
Similarly, Girder 3 was designed to have an allowable com-
pressive stress at release of 0.60 fci , but the stress was 0.69
fci . The low one-day compressive strength resulted from ex-
tremely low ambient temperatures after nightfall, which pre-
vented the steam in the prestressing beds from attaining its
normal temperature.
As noted above, three of the four girders had allowable
compressive stresses at release greater than 0.60 fci
. In allcases, it is worth noting that the prestressing forces were
adequately transferred to the concrete (demonstrated by the
strain measurements that occurred within the end regions of
each girder) and no external signs of distress were visible.
Although the high release stresses did not appear to affect
the girder performance otherwise, higher prestress losses re-
sult from higher compressive stresses at release. This result
is in line with expectations. The total measured losses for the
four girders and the allowable compressive stress at release
are shown in Table 6. As shown in Fig. 8, the girders with the
greatest release stress had the most prestress loss.
The effects of large compressive release stresses are ex-amined in Table 11. In the first column, Table 11 lists the
maximum release stress as a percentage of the one-day com-
pressive strength of the concrete. As noted in Table 11 and
elsewhere, the compressive stresses ranged from 56.9% to
82.1% of release strength. The second column in Table 11
lists the measured prestress losses, which are the average
losses for the ends at each girder. Total losses ranged from a
low of 51.6 ksi (356 MPa) to a high of 72.0 ksi (496 MPa).
The third column of Table 11 lists the jacking stress (ksi) of
the strand immediately prior to release. The reported jacking
stress is based on the elongation measurements made during
stressing of the strands and includes the seating losses. Thejacking stresses listed in the third column, however, do not
include relaxation losses that occur in the 24 hours between
tensioning and release. The fourth column of Table 11 ex-
presses the measured losses as a percentage of the jacking
stresses. In other words, the 27.8% loss reported for Girder 1is obtained by dividing the total measured loss in the second
column by the jacking stress in the third column.
The table clearly shows that increases in the maximum re-
lease stress result in increased prestress losses. The question
becomes, in the cases where the allowable stress provisions of
the specifications were exceededas was the case for Gird-
ers 1, 2, and 3whether the losses indicate that a damaged
condition exists in the concrete due to excessive compressive
stresses at release.
The fifth column addresses that issue by listing the ratio of
prestress losses divided by the release stress. Both losses in
the fourth column and the release stress in the first columnare expressed as a percentage. According to the information
in the fifth column, the ratio of losses to release stresses is
approximately the same for all four beams regardless of the
amount of compressive release stresses. This occurs over a
fairly broad range of values ranging from Girder 4, which
has release stresses within the allowable limits, to Girder 2,
with a release stress that is 82% of the compressive strength
of the concrete.
Table 9. Elastic Shortening Losses.
Girders LocationPrestress Losses Due to Elastic Shortening (ksi)1
Measured AASHTO Predicted Zia et al. NCHRP 496
1Ends2 27.8 23.3 20.9 23.3
Center 27.8 23.2 20.8 23.2
2Ends 32.8 27.4 24.6 27.4
Center 33.6 27.2 24.4 27.2
3 Ends 24.4 20.7 18.7 20.7
Center 23.4 20.6 18.6 20.6
4Ends 25.6 20.4 18.4 20.4
Center 24.8 20.3 18.2 20.3
Average elastic shortening 27.5 22.9 20.6 22.9
Note: 1 ksi =6.895 MPa.
0
10
20
30
40
50
60
70
80
0 50 100 150 200 250 300 350 400
Girde r 2 , fb o t
/fci
= 8 2 . 1 %
Girde r 3 , fbo t
/fc i
= 6 9 . 3 %
G irde r 1 , fbo t
/fci
= 6 4 . 9 %
Girde r4 , fbo t
/fc i
= 5 6 . 9 %
Age (Days)
Fig. 8. Shown are the measured losses for the girders at ends.
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24 PCI JOURNAL24 PCI JOURNAL
It is the authors view that these data provide strong evi-
dence that the allowable release strength of 0.60 fci can be
relaxed to allow higher compressive stresses to be imposed
on the concrete immediately after release.
CONCLUSION
Both the AASHTO LRFD Specifications and the ACI
Building Codescurrently limit the compressive stress at re-
lease stress to 0.60 fci . In this research study, three of four pre-
tensioned concrete girders had release compressive stresses
that exceeded the allowable limit. Maximum release stresses
ranged from 56% to 82% of the concretes one-day compres-
sive strength. In all beams, the high compressive stresses
did not cause any adverse effects to the prestressed concrete
member. Furthermore, the losses that were measured for one
year were in line with expectations and were reasonably pre-dicted by current methods.
Concrete used in this research included both air-entrained
concrete and non-air-entrained concrete. The performance
of the concrete, as measured by prestress losses, was not af-
fected by the inclusion of air entrainment. In other words, the
girders made with air-entrained concrete did not exhibit ex-
traordinary levels of prestress losses. Furthermore, the losses
measured in air-entrained concrete members were predicted
with the same level of accuracy as were the losses measured
in the non-air-entrained concrete.
The 2004 AASHTO (refined method) prediction equations
overestimated the total losses for all girders, predicting lossesthat were approximately 50% greater than the measured loss-
es for Girders 1 and 4. For all girders, the Zia et al. equations
estimated losses that were more accurate than the AASHTO
equations.
TheNCHRP Report 496loss equations (detailed method),
which were developed specifically for high-strength con-crete, predicted losses that were on average within 6% of the
measured losses.
At the release stress of 0.82 fci , all methods (AASHTO,
Zia et al., andNCHRP Report 496) predicted losses that were
within 10% of the measured losses. Increasing the allowable
compressive stress at release resulted in greater prestress
losses. For all girders, the prestress losses increased with
higher release stresses.
RECOMMENDATIONS
Based on the results of this research, it is recommendedthat the allowable stress limit for compression stresses imme-
diately after release be increased from 0.60 fci to 0.70 fci .
ACKNOWLEDGMENT
The authors express their deep gratitude to Coreslab Struc-
tures Inc., Oklahoma City, for donating the materials and
fabricating the four prestressed concrete girders at its plant.
The authors also want to thank Oklahoma State University
in Stillwater for the use of its facilities and in particular to
express their appreciation to the personnel of the Fears Struc-
tural Engineering Laboratory for their care and diligence incarrying out the testing.
Table 10. Girder Properties and Allowable Compressive Stresses.
Parameter Girder 1 Girder 2 Girder 3 Girder 4
fci(psi) 8700 6130 6130 8700
Eeff(ksi) 5022 3862 4159 5122
Atr(in.4) 173.38 175.71 173.40 169.19
ytr(in.) 13.32 13.20 13.35 13.48
Itr(in.4) 13,223.68 13,488.50 13,215.80 13,007.65
etr(in.) 6.90 7.20 6.40 7.75
Jacking stress (ksi) 204.25 202.20 2000.76 204.47
fbot(ksi) 5.646 5.030 4.245 4.949
fbot/ f'c(%) 64.9 82.1 69.3 56.9
Note: 1 in. =25.4 mm; 1 in.2= 645 mm2; 1 in.4=416,230 mm4; 1 psi =0.006895 MPa; 1 ksi =6.895 MPa.
Table 11. Effects of Large Compressive Stresses at Release.
Girders
1 2 3 4 5
Release Stress
(%)
Measured Pre-
stress Loss (ksi)
Jacking Stress
(ksi)(2)/(3) (%) (4)/(1)
1 64.9 56.8 204.25 27.8 0.43
2 82.1 72.0 202.20 35.6 0.43
3 69.3 59.2 200.76 29.5 0.43
4 56.9 51.6 204.47 25.2 0.44Note: 1 ksi =6.895 MPa.
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March April 2006 25
APPENDIX: NOTATION
Ag = gross area of concrete section
Atr = transformed area of concrete section
Ig = moment of inertia of gross concrete section
Itr = moment of inertia of transformed concrete section
yg = distance from bottom fiber to center of gravity of gross
section
ytr = distance from bottom fiber to center of gravity of transformed
section
etr = eccentricity of prestress force of transformed sectionf
ci = concrete compressive strength at release
Aps = area of prestressed reinforcement
Eeff = effective modulus of elasticity at release
fbot = bottom fiber concrete stress at release
Str = bottom fiber section modulus
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