Strand Transfer Lengths
in Full Scale AASHTO
Prestressed Concrete Girders
Mohsen A. Shahawy,
Ph.D., P.E.
Chief Structural Analyst
Structural Research Center
Florida Department of Transportation
Tallahassee , Florida
Moussa lssa, Ph.D., P.E.
Structural Analyst
Structural Research Center
Florida Department of Transportation
Tallahassee , Florida
Barrington deV Batchelor,
Ph.D., P.Eng., D.I.C.
Professo r of Civil Engineering
Queen 's University
Kingston , Ontario
Canada
84
The results of an experimental and analytical
investigation of the transfer length of 0.5 and
0.6 in. (13 and 15 mm) diameter prestressing
strands in full scale AASHTO girders are
presented. Based on the results, it is concluded that the current provisions of the ACt
Code and AASHTO Specifications for
transfer length appear to be inadequate.
Recommendations for changes to the code
provisions and specifications are presented.
n the des ign of prestressed concrete beams , it is usual to
aim fo r maximum eccentricity of the prestressing force
where the bending moment is the largest. In a si mply
supported beam, this point is located at or near the midspan
and the required eccentricity at the supports is considerably
smaller. It has been customary to drape or harp the strands
in order to avoid the occurrence of unduly high tensile
stresses near the supports.
Recently , the debonding of strands near the supports has
been used to achieve the same results. Such "shielded" or
"b lanketed " strands al low the use of straight st rands
throughout the beam and this arrangement has been found
to be convenient, economical and safe. Conseq uently, the
prestress ing industry has wide ly adopted the concept of
shielding instead of draping or harping of strands.
In prestressed concrete construction, it is necessary to
transfer the tendon force to the concrete. This is achieved in
pretensioned members by bond at the ends of the members
when the tendons are released. The length over .which the
initia l prestressing force is effectively transferred to concrete is known as the "transfer length."
Another type of bond mechanism , termed "flex ura l
bond," is mobilized when a member is subjected to bending
I
PCI JOURNAL
due to externally applied loads. As
these loads are increased, the stress in
the strand also increases. The additional length over which this increase
in strand force is transmitted is known
as the "flexural bond length." The sum
of the transfer length and the flexural
bond length at ultimate load conditions
is termed the "development length."
The adequacy of the current provisions in the ACI Code' and AASHTO
Specifications 2 with respect to transfer
and development lengths has been the
source of much controversy. Several
comprehensive research studies are
now in progress in North America in
order to investigate these controversial
code provisions.
The Structural Research Center of
the Florida Department of Transportation (FDOT) is involved in this
study and plans to test 33 full-scale
AASHTO Type II girders to determine
transfer and development lengths with
and without shielding. This paper
addresses the findings relative to transfer lengths of the specimens tested.
with steel diameter and level of prestress. Strands develop some mechanical bond with concrete in addition to
friction; thus, the transfer length of
strand is shorter than that of smooth
wire of comparable diameter.
CURRENT ACI/AASHTO
PROVISIONS
The provisions of the ACI Code' and
the AASHTO Specifications2 are essentially the same. Therefore, for discussion purposes, the transfer and development length provisions of both codes
can be considered interchangeable.
The current ACI provisions for
development length of prestressing
strand, contained in Section 12.9 of the
1989 ACI Building Code and Commentary, are summarized as follows:
Section 12.9.1: Three or seven-wire
pretensioning strand shall be bonded
beyond the critical section for a development length, in inches, not less than:
where
PREVIOUS
INVESTIGATIONS
Since the early studies by Hoyer and
Friedrich3 on bond between steel and
concrete, several investigations have
been conducted to determine the transfer length of strand in prestressed concrete members. A summary of these
investigations was presented earlier by
Zia and Mostafa• and Shahawy et al., 5
and will not be repeated here except as
considered necessary. Recent work
dealing with transfer length of uncoated strand includes papers by
Brooks et al., 6 Cousins, Johnston and
Zia, 7•8 and Deatherage and Burdette!
It is generally accepted that a large
number of parameters may affect the
transfer length of strand. This includes:
• Size and type of steel
• Stress and surface condition of steel
• Strength, consistency and degree of
consolidation of concrete around
steel
• Concrete cover and degree of confinement of steel
• Type of release (gradual, or sudden
by flame cutting or sawing)
• Time-dependent effects
In general, transfer length increases
May-June 1992
dv
:ips
he
= strand diameter, in.
=stress in prestressed steel at
nominal strength, ksi
=effective prestress, ksi
Section 12.9.2: Investigation may be
limited to cross sections nearest each
end of the member that are required to
develop full design strength under
specified factored loads.
Section 12.9.3: Where bonding of a
strand does not extend to end of member, and design includes tension at service load in precompressed tensile
zone as permitted by Section 18.4.2,
development length specified in Section 12.9 .1 shall be doubled.
Eq. (1) can be rewritten' in the form:
In Eq. (2), the value of he depends on
the initial prestress, hi• at transfer and
the loss in prestress. Zia and Mostafa•
have pointed out that the denominator
"3" in the expression for It in Eq. (2)
represents a conservative average concrete strength in ksi. Similarly, in the
expression for lb in Eq. (2), a denominator of 1 ksi is implied, which represents a factored value of an average
bond stress of 250 psi (1.7 MPa).
According to the ACI Code requirement, the transfer length would be
approximately equal to 50.4 times the
nominal strand diameter, assuming
that the specified tensile strength of
the prestressing strand, fpu = 270 ksi
(1860 MPa), the initial stress in strand
before losses, hi = 0.74fpu• and a prestress loss of 20 percent. Note that a
value of 50 strand diameters is
assumed as the strand transfer length
in Section 11.4.3 of the 1989 ACI
Building Code.
From a comprehensive study of past
research, Zia and Mostafa• proposed
the following equation for transfer
length It:
where !/; is the compressive strength
of concrete at transfer (ksi).
Eq. (3) is applicable to concrete
strengths ranging from 2000 to 8000 psi
(14 to 55 MPa) and accounts for effects
of strand size, initial prestress and concrete strength at transfer. This equation
gives transfer lengths comparable to
those specified in the ACI Building
Code, particularly for cases where the
concrete strength at transfer is low.
Cousins, Johnston and Zia 8 have
proposed a more explicit expression
for It as follows:
where
ut
The first term represents the transfer
length, /~' which is the distance over
which the strand must be bonded to
the concrete to develop the effective
prestress, he• in the strand. The second
term represents the additional length
termed the flexural bond length, lb,
over which the strand must be bonded
to develop a stress, J,s, at the nominal
strength of the member.
=plastic transfer bond stress,
which is proportional to slope of
linear portion of curve for steel
stress vs. distance from end of
beam
B =bond modulus, or slope of bond
stress curve in elastic zone
Aps = cross-sectional area of prestressing steel
In order to reflect the known effect
of concrete compressive strength, f/,
85
Predictions from Eqs. (3) and (6)
will be compared with the experimental results obtained in the study described in this paper.
Table 1. AASHTO Type II girder test specimens.
Girder
No.
Size
of
strands
in.
Nymber
of
strands
Number of
shielded
strands
Web
reinforcement
Percent of
shielding
North
South
DESCRIPTION
OF TEST GIRDERS
Group AI
Al-00-R
Al-00-R/2
Al -00-3R/2
Al-00-M
Al-25-3R
AI -50-3R
0.5
0.5
0.5
0.5
0.5
0.5
16
16
16
16
16
16
0
0
0
0
4
0.6
0.6
0.6
0.6
II
11
8
00
00
00
00
25
50
R
R/2
3R/2
M
3R
3R
R
R/2
3RJ2
M
3R
3R
0
0
3
5
00
00
27.3
45 .5
R
3R/2
R
R
R
3R/2
R
R
.
The test specimens consisted of full scale AASHTO Type II, 41 ft (12.5 m)
long prestressed concrete girders. All
girders were designed for the same
flexural strength, and were fabricated
by Dura-Stress Inc. of Leesburg ,
Florida.
The main variables in the test program were the size of prestress ing
strands [0.5 and 0.6 in. (13 and 15
mm) diameter], percentage of shielded
strands and web shear reinforcement
ratio. Details of the test program are
shown in Table 1.
The beams were divided into two
groups, designated A and C. The letters A and C define the strand size in
each group [i.e., A and C represent 0.5
and 0.6 in. (13 and 15 mm) diameter,
respectively]. The beams were generally labeled according to the strand
Group Cl
CI -00-R
Cl-00-3R/2
Cl -25-R
CI-50-R
11
11
R: Required web shear reinforcement based on AASHTO Specifications.
M: Minimum web shear reinforcement specified by AASHTO.
Note: I in. = 25.4 mm.
Eq. (5) wa s modified by Cou sins,
Johnston and Zia to the form :
{![; )! B] +
fse Apsl (1tdb u; {![; )
U; = 6. 7 and B = 300 psi/in. (82
kPa/mm) for uncoated strand, which
upon substitution reduces Eq. (5 ) to
the form :
It= 0.5 [(U;
(5 )
{![; +
It = 0.0112
In the above express ion U; = U t I
They further proposed values of
m.
0.048 (Ap,ldb) (f se/ {![; ) (6)
20'-6 "
I
2 -6"
• 4 DOUBlE STIRRUP~ 3 in.
4'-Q'
DOUBLE
STIRRUPS
4'-0'
a·-o·
SINGLE
SINGLE
STIRRUPS
36 "
a·-o·
SINGLE
STIRRUPS
AASHT O TYPE II
4'-o·
• ·-o·
SINGLE
STIRRUPS
DOUBLE
STIRRUPS
I
4 . 2"
18 "
A - Series
C-bar
36.5'
2•0.60" 2 TOK Lo- Lax Slranda
Pulled to 5,000 Lba. n ch
l
7"
~-
7 ! Q D-bar
3 .5
18"
14"
Note: 1 ln.=25.4 mm
1 b = 4.45 N
C - Seri es
Fig. 1. Details of test girders.
86
PCI JOURNAL
SHIELDING PATTERN FOR 1/2" DIAM. STRANDS
•
UNSHIELDED STRAND
0
•
•• •
•••••
• •• • • • •
STRAND SHIELDED
FOR 5 '·6" FROM
END OF BEAM
•
•• •
••o ••
•
NO SHIELDED STRANDS
•
o•
0
• 0 0 0.
•
• 0 0 0 ••
• 0 0 0 ••
4 SHIELDED STRANDS
B SttELDED STRANDS
(25!1 SttELDING)
(50!1 SHIELDING)
(0 !I SHIELDING)
SHIELDING PATTERN FOR 0.6" DIAM. STRANDS
•
UNSHIELDED STRAND
0
•
•••••
•••••
STRAND SHIELDED
FOR 4'·6" FROM
END OF BEAM
•
•
• • 0 ••
• 0 0 0 •
• 0. 0.
• 0. 0.
3 SHIELDED STRANDS
NO SHIELDED STRANDS
(27!1 SHIELDING)
( 0 !I SHIELDING)
5 SHIELDED STRANDS
(45!1 SHIELDING)
Fig. 2. Details of shielding.
41'-0"
~
20'-6 "
BEAM
20'-6"
l
IAASHTO
~o~
8 . 5'
l
3 • 10'
"I
1
I.
1
21
2o·j_.-o· I eo·J. acr
1
1
1
( a )
d
TYPE lj
I_co·l
21
2o·l_
Strain Gages
(2.5'
l
3 . 10'
gllgll
len;th)
a 1 s·
~0~
NO SHIELDING
Note : 1 ln. a 25.4 mm
41'-0"
<f_ BEAM
20'-6'
20'-6'
1
IAASHTO
~{
20 •
TYPE I~
~.
l3 ...{
a·
1
l
( b )
/
,.,
Strain Gages
(UI'gag•*'~Jfh)
20 1
a·
~-
1
25% AND 50%
SHIELDING
CONCRETE SURF ACE STRAIN GAGES AT THE C.G. OF STEEL
Fig. 3. Locations of strain gauges.
size, degree of shielding (0, 25 and 50
percent) and the amount of shear reinforcement (R, R/2 and M); for example, A 1-00-R is interpreted as:
A denotes strand diameter of 0.5 in.
(1 3 mm).
May-June 1992
AASHTO Specifications.
Details of the test girders are shown
in Fig. 1. "Shielding patterns of strands
are shown in Fig. 2, with 0.5 in. (13 mm)
diameter strands shielded up to 5.5 ft
(1680 mm) from each end of the beam,
and 0.6 in. (15 mm) diameter strands
shielded up to 4.5 ft (1370 mm).
The strand spacing for both groups
was kept constant at 2 in. (50 mm),
which is less than that specified by
AASHTO for the 0.6 in. (15 mm) diameter strands. This was intended to provide some information on the effect of
the smaller strand spacing at transfer.
00 denotes zero shielding.
R denotes required shear reinforcement
based on AASHTO Specifications.
Table 1 shows that replacement of R
by M indicates the minimum shear
reinforcement as required in the
TEST PROCEDURE AND
INSTRUMENTATION
A pilot test was conducted to determine the best type of instrumentation
for transfer length evaluation. In the
pilot test, an attempt was made to
determine the transfer length by the
use of electrical resistance strain
gauges (ERSGs) placed on the strands
before casting of concrete and at set
distances on the concrete surface
before release.
In addition, demountable mechanical gauge (DEMEC ) points were
87
Fig. 4a. Overall view of prestressed concrete girder showing flame cutting operation .
Fig. 4b. Close-up view of flame cutting operation at end of girder.
placed along lines in the bottom flange
of a girder. The two types of gauges
were intended to provide independent
checks of the results.
The ERSGs tended to perform more
consistently than the DEMEC gauges,
the results from which showed large
scatter, indicating the need for a large
database to establish reliable trends.
The mechanical gauges and ERSGs
placed on the strands were eliminated
after the pilot test.
The use of 2.5 in. (64 mm) ERSGs
placed on the concrete surface at set dis88
tances along the length of the beam at
the level of the centroid of the prestressing steel gave consistent results and was
used in all subsequent te sts . Fig . 3
shows the instrumentation details.
Since the surface condition of the
strands is known to affect bond
strength , every attempt was made to
adhere to the construction procedure
of pre s tressed concrete girders in
terms of the time steps between stages
and the total time of construction. The
prestress ing strands were received
encased in moisture -proof wrapping
and were kept in the same condition
until the time of installation in the prestressing bed.
The strands were exposed to weathering in the casting bed until concrete
casting, which took place approximately 36 to 48 hours after the strands
were installed. In general , the strands
were shiny with minor rust spots at the
time of concrete casting.
All girders in each group were cast
simultaneously end to end, in a 300 ft
(91.5 m) long prestressing bed. Two
of the prestressing strands in each
group were instrumented with five
ERSGs after applying an initial pretensioning force of 3 kips (13.34 kN).
After the instrumentation was completed, an the strands were later fully
stressed to the specified pretension of
0.75 fpu [202.5 ksi (1396 MPa)].
This process took approximate ly 2
hours, after which shear and confinement reinforcement for each beam
was placed and tied. The girder forms
were then put back in place in preparation for concrete placement on the
following day.
During concrete placement in the
forms , six concrete cy linders were
made for each beam. These concrete
cy linders were used to monitor the
concrete com press i ve strength at
transfer. After placement of concrete,
the top surfaces of the girders were
sprayed with a curing compound and
left to harden for 6 hours.
The forms were then removed, followed imm ediately by spraying all
exposed surfaces of the girders with
the curing compound. The girders
were allowed to cure for another 18
hours before the ERSGs were placed
at predetermined locations along the
length of the girders at the level of the
centroid of the prestressing steel.
The tran sfer of the prestre ss ing
force to the girders took place approximately 48 hours after concrete casting . The pre s tressing force wa s
released by flame cutting one strand at
a time simultaneously at six different
locations as shown in Figs. 4a and 4b.
The strain gauge readings were monitored continuously during the release
process. Upon the complete release of
the prestressi ng force to the girders,
the strain gauge readings were recorded every 2 hours for 2 days.
PCI JOURNAL
•
STRAIN X 10-
100%
7 5%
50%
25%
•
•
....
6
North End
800
Transfer
Transfer
Transfer
Transfer
South End
BOO
700
700
It= 30 in.
600
600
500
500
400
• •
300
....
....
....
....
200
•
•
• •
300
•
200
....
100
•
24
Note : 1 in.
48
96
72
120
144
400
•
•
168
300
324
348
372
100
0
396
420
444
468 492
DISTANCE ALONG GIRDER (ln.)
= 25.4mm
Fig. 5a. Transfer length results (Girder A 1·00-R).
STRAIN X 10
BOO
700
•
100%
75%
.... 50%
25 %
-6
._
I
t
600
North End
•
= 30 in.
•
Transfer
Transfer
Transfer
Transfer
South End
BOO
I
t
= 30 in.
700
600
500
•
•
• •
300
200
....
....
....
200
100
•
• •
100
400
300
0
0
24
72
48
96
120
Note: 1 in. = 25 .4 mm
144
168
192
300
324
500
348
372
400
0
396
420
444
468
492
DISTANCE ALONG GIRDER (in.)
Fig . 5b . Transfer length results (Girder A 1-00-R/2).
•
STRAIN X 10
•
-6
...
North End
•
700
100% Transfer
75% Transfer
50% Transfer
25% Transfer
South End
700
in.
600
It= 30
•
500
400
300
•
200
... ...
100
•
...
•
•
0
0
24
Note : 1 in.
48
= 25 .4
mm
72
96
120
168
324
400
• • •••
... ... ... ... ...
• • •••
•
...
•
144
500
•
•
•
600
348
372
396
420
300
200
100
444
468
492
0
DISTANCE ALONG GIRDER (in.)
Fig. 5c. Transfer length results (Girder A 1-00-M).
May-June 1992
89
-6
•
•
North End
STRAIN X 10
...
•
~It = 30 in.
700
600
... oo
•
300
Transfer
Transfer
Transfer
Transfer
South End
•
• •
•
•
•
....
....
....
....
•
...
100
• •
•
•
0
24
72
48
96
120
144
168
192
300
324
BOO
•
•
200
0
700
It= 30 in .
•
500
100%
75 %
50 %
25 %
500
400
• •
•
... ...
• • •••
348
372
396
420
300
200
100
0
444
468
492
DISTANCE ALONG GIRDER (in.)
Note : 1 in. = 25.4 mm
Fig. 5d. Transfer length resu lts (Girder A 1-00-3R/2).
-6
STRAIN X 10
600
North End
South End
It= 34 in.
It = 34 in.
500
•
•
400
600
500
400
300
300
200
200
100
100
0
24
12
36
48
60
72
84
96
108
120
408
396
420
432
4 44
456
468
480
492
DISTANCE ALONG GIRDER (in.}
Note: 1 in.= 25.4 mm
Fig. 6a. Transfer length results (Girder C1 -00-R) .
-6
STRAIN x 10
South End
North End
It= 36 in.
600
in.
•
500
6oo
500
400
400
300
300
200
200
100
100
0 ~~~~~~~~~~~~~+4~+4~~~M+~~~+W~~~~~~~~~~~~~~~~~~~ 0
0
12
No te: 1 in.
24
= 25.5
36
mm
48
60
72
84
96
108
120
360
372
384
396
408
420
432
444
456
468
480
492
DISTANCE ALONG GIRDER (in.)
Fig. 6b. Transfer length results (Girder C1-00-3R/2) .
90
PCI JOURNAL
-6
STRAIN x 10
600
600
in.
500
500
End of Shieldin
400
400
300
300
200
200
100
100
0
0
0
12
Note : 1 ln.
24
= 25.4 .mm
36
48
60
72
84
96
108 120
132 144
DISTANCE ALONG GIRDER (in.)
Fig. ?a. Transfer length results [Girder A 1-25-3R (north end)].
PRESENTATION AND
DISCUSSION OF RESULTS
Transfer Length
In measuring the transfer length, the
lines of constant slope and constant
strain in the plot of measured strain vs.
distance from the end of a beam are
joined by a smooth curve. The transfer
length is taken as the distance from the
end of the girder to the point of tangent with the line of constant strain.
This method was considered to be
the best representation of the test
resuHs since the ERSGs provided
smooth and well defined curves as can
be seen in Figs. 5 through l 0. These
figures present the transfer length
results for all girders.
It can be seen that, generally, strain
STRAIN x 10 -S
600
= 30 in.
500
500
. _ End of Shielding
400
400
300
300
200
200
100
100
0
348 360
Note : 1 in.
a
372
25.4 mm
384 396
408
420
432
444
456
468
480
492
DISTANCE ALONG GIRDER (in.)
Fig. ?b. Transfer length results [Girder A1-25-3R (south end)].
May-June 1992
91
STRAIN
-6
x 10
700
700
600
600
500
500
400
400
300
300
200
200
100
1 00
0
0
0
24
12
Note : 1 in.
= 25.4
36
48
60
72
84
96
108
120
132
1 44
DISTANCE ALONG GIRDER (in.)
mm
Fig. 8a. Transfer length results [G irder A 1-50-3R (north end)].
-6
STRAIN x 10
600
600
32 in.
500
500
End of Shielding
400
400
0
0
348
360
Note : 1 in.
= 25.4
372
mm
384
396
408
420
432
444
456
468
480
492
DISTANCE ALONG GIRDER (in.)
Fig . 8b. Transfer length results [G irder A 1-50-3R (south end)].
values increased from zero at the end
of the beam up to a point where they
became approximately constant and at
wh ich the f ull prestress had been
transferred to the concrete. It is also
apparent th at there ex ists an initia l
92
zone in which the strain development
is approximately linear, indicating linear variation of strand stress and constant (plastic) bond stress.
Beyond this zo ne , th ere exists a
short nonlinear porti on of the strain
curve over which the slip is relatively
small and the bond stress is approximately proportional to the slip. This
behavior conforms to the model used
by Cousins, John ston and Z ia,' who
adapted it from Guyon. '0
PC I JOURNAL
Table 2. Transfer length results for Groups A1 and C1.
Girder
No.
Measured transfer
length, in.
Steel stress
at transfer
fs;, ksi
Efft;ctive steel
stressfse•
ksi
Compressive
concrete strength
at transfer f ;;, ksi
North
South
Avg.
AI-00-R
AI-00-R/2
AI-00-3R/2
AI-00-M
AI-25-3R
30
30
30
30
29
30*
30
30
30
30
30
30*
30
30
30
30
29.5
30*
183.4
183.5
183.4
184.5
184.0
161.4
161.5
162.4
162.4
162.2
5.11
5.11
5.11
5.11
5.11
AI-50-3R
30
29*
32
32*
31
30.5*
184.4
162.1
5. 11
CI-00-R
CI-00-3R/2
34
36
34
35
34
35.5
184.5
184.4
162.4
163.5
5.64
5.64
Cl-25-R
36
32*
NA
NA
36
32*
184.5
164.0
5.64
CI-50-R
36
34*
32
32*
34
33*
184.5
163.5
5.64
Group AI
Transfer Length of
Shielded Strands
Group Cl
* Results from the second region of transfer for the beams with shielded strands.
N01e: I in . = 25.4 mm; I ksi = 6.895 MPa.
Table 3. Comparison between measured and calculated transfer length results.
Predicted transfer length
Girder
No.
Average measured
transfer length
in.
(fs,IJ)db
in.
(fs;l3)db
in.
Eq. (3)
in.
Eq. (6)
in.
Measured
(fs;l3)db
Group AI
Al-00-R
Al-00-R/2
Al-00-3R/2
Al-00-M
AI-25 -3 R
30
30
30
30
29.5
30*
26.90
26.90
26.90
27. 10
27. 1
27.1
30.57
30.58
30.57
30.75
30.67
30.67
22.40
22.90
22.90
23. 10
22.40
22.40
34.52
34.52
34.52
34.52
34.52
34.52
0.98
0.98
0.98
0.98
0.96
0.98
AI-50-3R
31
30.5*
27.1
27.1
30.73
30.73
22.46
22.46
34.52
34.52
1.00
0.99
Cl-00-R
CI-00-3R/2
CI-25-R
34
35.5
36
32*
32.48
32.70
32.80
32.80
36.90
36.88
36.90
36.90
24.50
24.80
24.80
24.80
37.98
37.98
37.98
37.98
0.92
0.96
0.98
0.88
CI-50-R
34
33*
32.70
32.70
36.90
36.90
24.80
24.80
37.98
37.98
0.92
0.89
Group Cl
* Results from the second region of transfer for the beams with shielded strands.
Note: I in . = 25.4 mm.
Transfer Length of
Unshielded Strands
Figs. Sa through 5d show the transfer length measurements for the girders with unshielded strands in Group
A l at different stages of transfer. The
data were recorded at 25, 50, 75 and
May-June 1992
recorded for 48 hours after transfer,
revealed no significant changes in the
measured transfer length.
Figs. 6a and 6b show the results for
Girders Cl-00-R and Cl-00-3R/2. It can
be seen that the average transfer length
of 0.6 in. ( 15 mm) diameter strand is
approximately 34 in. (864 mm).
I 00 percent of force release. It can be
seen from these figures that the transfer length for 0.5 in. (13 mm) diameter
strand at all stages of transfer is
approximately 30 in . (762 mm). It
should be noted, also, that the analysis
of the strain gauge data, which were
Figs. 7 through 10 show the measured concrete strains for Beams A l25-3R, A l-50-3R , C 1-25-R and C 150-R. In all the figures, there exist
two distinct transfer regions. For the
beams with 25 percent shielding, the
first region indicates the transfer of 75
percent of the prestressing force . The
second region starts from the termination point of shielding [66 and 54 in.
(1680 and 1370 mm) from the beam
ends for Groups A I and C I, respectively] and indicates the transfer of the
balance of the prestressing force .
A close examination of the values of
measured strains at the end of each
region indicates a ratio which corresponds to the force transferred. Similar observations can be made for girders with 50 percent shielding (see
Figs. 8 and 10).
The transfer length data for the
north end of Beam C1-25-R were not
mea sured due to a malfunction of
some channels of the data acquisition
system. A summary of all test results
is presented in Table 2.
From Figs. 7 through 10, it can be
concluded that the transfer length for
beams with shielded strands should be
defined as the sum of the shielded distance and the appropriate transfer length
for a certain strand diameter. Based on
this definition, the transfer length for
shielded beams with 0.5 and 0.6 in. ( 13
and 15 mm) diameter strands would be
66 + 30 in. = 96 in. (2440 mm) and 54 +
34 in. = 88 in. (2235 mm) from the end
of the member, respectively.
Comparison of
Analytical and Test Results
The transfer length results were
compared with analytical predictions
from Eq. (3) , Eq. (6), ACI/AASHTO
Cfsel3)db [Eq. (2)] and with (f5 ;/3)db.
The comparison between the average
93
-6
STRAIN x 10
700
600
600
500
500
400
300
300
200
200
100
100
0
0
0
12
Note : 1 in.
24
36
48
60
72
84
96
108
120
132
144
DISTANCE ALONG GIRDER (in.)
= 25.4mm
Fig. 9. Transfer length results [Girder C1-25-R (north end)).
measured transfer length and the analytical predictions is presented in
Table 3.
By comparing the results of Table 3,
it can be seen that Eq. (3) underesti-
STRAIN
x 10
mate s transfer length s by approxi mately 35 percent while Eq. (6) results
in an overestimation of 11 to 15 percent. The ACI/AASHTO prediction
for transfer length, Cfsel3 )db, appears
to be inadequate for both shielded and
unshielded systems. However, if the
values of fsi are used instead of fse in
the ACI/AASHTO e quation s , an
excellent comparison results.
-6
7 00
It =
600
34 in.
600
of Shielding
5 00
500
•
4 00
300
300
200
2 00
•
100
0
0
12
24
No te : 1 in. ;:: 25 .4 mm
36
48
60
72
84
96
10 8
12 0
13 2
14 4
156
DISTANCE ALONG GIRDER (in.)
Fig. 1Oa. Transfer length results [Girder C1-50-R (north end)) .
94
PCI JOURNAL
STRAIN
-6
X
10
700
700
= 32
600
in
600
. _ End
500
•
400
500
400
It=
32 in.
300
300
•
200
200
100
100
0
0
336
348
Note : 1 in.
= 25 .4
360
mm
372
384
396
408
420
432
444
456
4 68
480
492
DISTANCE ALONG GIRDER (in.)
Fig. 1Ob. Transfer length results [Girder C1-50-R (south end)].
Effect of Spacing of 0.6 in.
(15 mm) Diameter Strands
At transfer, the behavior of the girders in Group C 1 was similar to that of
Group Al. No cracking or spalling
was observed at the time of detensioning. It appears that a minimum spacing
of 2 in. (50 mm) for the 0.6 in. (15 mm)
diameter strands is sufficient to guard
against cracking at transfer. The code
requirement of a minimum spacing of
four strand diameters for the 0.6 in.
( 15 mm) strands appears to be very
conservative and is not supported by
any published research.
mm) diameter strands in girders with
unshielded strands are 30 in. (762 mm)
(60db) and 34 in. (864 mm) (57db) ,
respectively.
4. The transfer length for beams
with shielded strands should be
defined as the sum of the shielded distance and the appropriate transfer
length for a particular strand diameter.
5. The code requirement of a minimum spacing of four strand diameters
for 0.6 in. (15 mm) diameter strands
appears to be very conservative. A
spacing of 2 in. (50 mm) in Group Cl
did not result in any signs of cracking
or deterioration in the girders.
CONCLUSIONS
RECOMMENDATIONS
The following conclusions are based
on the results of the investigation
reported in this paper:
1. The current ACI/AASHTO provisions for transfer length appear to be
inadequate.
2. The use of fsi instead of fse in the
ACI/AASHTO equation provides
close comparison with test results .
3. The average measured transfer
lengths for 0.5 and 0.6 in . (13 and 15
1. It is recommended that the following equation be used to calculate
the transfer length, l~' of prestressing
strands:
(a) Unshielded strands:
l, = (fs;/3) db
(b) Shielded strands:
l, =length of shielding from end
plus (f5;/3) db
2. A change of the ACI/AASHTO
provision for minimum spacing of 0.6
May-June 1992
in. (15 mm) diameter strands from
four strand diameters to 2 in. (51 mm)
should be considered.
ACKNOWLEDGMENTS
The cooperation and contributions
of the prestressed concrete industry of
Florida to this extensive study are
highly appreciated. These contributions include the manufacture and
transportation of the girders to the laboratory by Dura-Stress Inc., Leesburg,
Florida. The extent of the contribution
to the research project is a model for
other industries to follow.
The help provided by G. Kent
Fuller, vice president of Dura-Stress
Inc., throughout the project is fully
appreciated. The cooperation and
encouragement of Daniel P. Jenny,
former vice president and research
director of PCI, and Fred McGee,
executive director of the Florida Prestressed Concrete Association, are
appreciated.
Sincere thanks are expressed to the
entire staff of the Structural Research
Center, Florida Department of Transportation.
95
REFERENCES
I. ACI Committee 318, " Building Code
Requirements for Reinforced Concrete (ACI 318-89)," American Concrete Institute, Detroit, MI, 1989.
2. AASHTO , Standard Spe cifications
for Highway Bridges, American Association of State Highway and Transportation Officials, Washington, D.C. ,
1977.
3. Hoyer, E., and Friedrich, E., " Beitrag
ziir Frage der Hafspannung in Eisenbetonbauteilen ," Beton und Eisen ,
Berlin, 1939, V. 30, No 6. See also K.
Billig , Prestressed Concrete , Van
Nostrand Co., New York, NY, 1953.
4. Zia, P. , and Mostafa, T. , "Development Length of Prestressing Strands,"
96
PCI JOURNAL, V. 22, No. 5, September-October 1977, pp. 54-65.
5. Shahawy, M. , Issa, M. , and Polodna,
M. , "Development Length of Prestressed Concrete Piles," Structural
Research Center, Florida Department
of Transportation, Report No. SSR01-90, March 1990, I 02 pp.
6. Brooks, M. D. , Gerstle, K. H., and
Logan, D. R. , "Effect of Initial Strand
Slip on the Strength of Hollow-Core
Slabs," PCI JOURNAL, V. 33, No. 1,
January-February 1988, pp. 90-111.
7. Cousins, T., Johnston, D., and Zia, P .,
" Transfer Length of Epoxy Coated
Prestressing Strand," Department of
Civil Engineering , Nort h Carolina
State University at Raleigh, December
1986.
8. Cousins, T., Johnston, D., and Zia, P.,
"Transfer and Development Length of
Epoxy Coated and Uncoated Prestressing Strand," PCI JOURNAL, V. 35,
No.4, July-August 1990, pp. 92-103.
9. Deatherage, J. H., and Burdette , G. ,
" Development Length and Lateral
Spacing Requirements of Prestressing
Strand for Prestressed Concrete Bridge
Products ," Report , Transportation
Center, The University of Tennessee,
Knoxville, TN, September 1991.
10. Guyon, Y., Prestr essed Concrete,
Volume 1, John Wiley & Sons , Inc. ,
New York, NY, 1960.
PCI JOURNAL