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flexural tests demonstrate that the anchorage ability of the following relationship between NASP values in concrete and
strands is improved as concrete strength increases. NASP values in mortar (standard NASP values):
( NASPconcrete )
3.6 Discussion of Design = 0.49139 f ci0.51702 (3.3)
NASP
Recommendations
The equation was further modified to fit the NASP values
The current AASHTO code provisions do not include as a function of square root of concrete strengths. Figure 3.13
the effects of concrete strength when calculating the is a plot of normalized NASP values against the square roots
required development length of prestressing strands. As a of corresponding concrete strengths. Following is the rela-
result, the development length for strands is the same tionship shown in Figure 3.13:
regardless of concrete strength. However, the results of this
research clearly demonstrate that the required transfer ( NASPconcrete )
= 0.51 fci (3.4)
and development lengths are shortened as concrete NASP
strength increases.
With the help of this relationship, it was possible to use the
The approach develops from the findings of the research:
Standardized NASP Bond Test, conducted in mortar, to
estimate the bond strength as if the test were conducted in con-
1. The current AASHTO transfer length of 60db is adequate
crete with various strengths. The graphs in Figures 3.9 through
to predict the transfer length of prestressing strands in
3.13 demonstrate that the NASP Bond Test pull-out value in
"normal strength concrete" (4-ksi release strength).
concrete is inversely proportional to the square root of the con-
2. The data support modification of the AASHTO transfer
crete strength. From these data, one can further assert that the
length to account for variations in concrete release strength
average bond stress, taken as the pull-out force divided by the
and in recognition of the finding that bond strength
bonded length, is also inversely proportional to the concrete
improves in proportion to the square root of the concrete
strength at release. Further evidence for this same relationship
strength.
between bond strength and pull-out force is found in Figures
3. The current AASHTO development length equation can
3.24 through 3.32, which chart measured transfer lengths ver-
be used to adequately predict required development
sus concrete strengths. The transfer length data demonstrate
lengths for "normal strength concrete" with a release
that transfer lengths change inversely with concrete release
strength in the range of 4 ksi and a design strength of 6 ksi.
strength. Figure 3.32, which charts transfer length measured on
4. The data demonstrate that shorter development lengths
three different strand samples, shows that transfer lengths are
are required as concrete strength increases.
approximately inversely proportionate to the square root of the
concrete strength. The best fit power regression indicates an ex-
3.6.1 Discussion of Transfer Length ponent of -0.46 for measured concrete strengths at release.
Recommendations This is approximately equal to the inverse of the square root. It
can therefore be concluded that transfer length is inversely pro-
The standard NASP Bond Test is a test where a prestress-
portional to the square root of concrete strength. Therefore, a
ing strand is pulled from sand-cement mortar. The mortar is
transfer length expression is recommended that is equivalent
made from sand, cement, and water and possesses a 1-day
to the current design expression of 60 strand diameters at a
compressive strength of 4,500 to 5,000 psi. The NASP Bond
release strength of 4 ksi, but that shortens in proportion to the
Test can be modified to perform the test in concretes with
square root of the concrete strength at release. The recom-
varying concrete strengths. However, the NASP Bond Test
mended code provision also provides a minimum transfer
values used in the discussions regarding minimum Bond Val-
length of 40 db. The 40 db value corresponds to 10-ksi concrete,
ues are pull-out strengths obtained from the standardized
which was the highest 1-day strength tested.
NASP Bond Test performed in mortar.
The transfer length equation is modified by the square root
The results from NASP pull-out tests in concrete are pre-
of the concrete release strength, as follows:
sented and compared in this section. Figure 3.12 presents
normalized NASP values (obtained by dividing the NASP 120db
lt = (3.5)
pull-out values in concrete by the NASP standardized test val- fci
ues [from tests conducted in mortar]) versus the concrete
strengths for the NASP tests in concrete. The tests demon- where
strate remarkable correlation between the bond-ability of lt = transfer length (in.),
prestressing strand and the concrete strength. Compared f ci = release concrete strength (ksi), and
with a power regression, the chart in Figure 3.12 shows the db = diameter or prestressing strand (in.).
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Using concrete release strength of 4 ksi, this equation re- where
sults in a transfer length equal to 60 db. The recommendation ld = development length,
for transfer length is only modified so that a minimum length lt = transfer length,
for transfer length is used, regardless of concrete strength. db = diameter of the prestressing strand, and
The recommendation effectively limits improvements in f c = design concrete strength.
transfer length based on a concrete release strength of 9 ksi,
Using concrete design strength of 6 ksi, which roughly cor-
which is less than the maximum release strength obtained in
responds to a "normal" concrete strength within the industry
the beams cast for this research (9.7 ksi on rectangular
and forms the base case from the experimental results, the co-
beams). Therefore, the final recommended expression for
efficient of 225 corresponds to flexural bond length of 90
transfer length is the following:
strand diameters.
120 Like the transfer length expression, the development
lt = db 40db (3.6)
fci length expression is limited by a minimum value. The rec-
ommended expression for development length, therefore, is
based on a limiting concrete strength of approximately 14
3.6.2 Development Length ksi, which is slightly less than the maximum concrete
Recommendations strength attained in beams tested in the research program
(14.9 ksi). Thus, the recommended development length
Since the inception of the pretensioned, prestressed concrete equation is as follows:
industry in the United States, the development length equation
has been made from the sum of two components: (1) transfer 120 225
ld = + db 100db (3.8)
length and (2) "flexural bond length," which is the additional f ci f c
length of bond beyond the transfer length required for devel-
opment. This approach has been utilized in the industry for
decades. Research continues to demonstrate that the approach 3.6.3 Distribution of Failure Types in Beams
is adequate to explain observed behavior and predict results. Tested
Thus, the same approach is followed, but with modifications
to include the effects of varying concrete strengths: This section presents the development length test results in
graphical fashion. The result of each beam test, whether flex-
· The results demonstrate that for all types of 0.5 in. ural failure or bond failure, is plotted on a chart showing con-
strands--Strands A/B and Strand D--flexural failures oc- crete strength versus embedment length. The recommended
curred at embedment lengths of 73 in. The embedment design equation for development length is also shown on
length of 73 in. corresponds to 100 percent of the current each of the charts. Note that the development length varies
code provision for development length for these speci- with concrete strength. For the purpose of plotting the values
mens. The results included tests on beams made with while using the equation, release strength is taken as 66.7 per-
concrete strength of approximately 4 ksi at release and cent of the design strength. This is a reasonable ratio of release
approximately 6 ksi at the time of the beam test. strength to design strength, borne out by years of experience
· The results uniformly indicate that the development length in prestressed concrete.
requirements diminish with increasing concrete strength. Figure 3.49 shows the results of development length tests
· The required development length calculated from the cur- on Strand D. Strand D demonstrated below average to poor
rent code provisions is approximately 150 db, although bond performance with a relatively low NASP Bond Test
some variations will exist due to variations in strand stress- result (6,890 lb), longer transfer lengths, and longer devel-
ing, beam geometry and subsequent variations in com- opment length requirements than Strands A/B. Figure 3.49
puted prestress losses. shows that bond failures occurred in rectangular beams
· If the transfer length is approximately 60 db, and the devel- with embedment lengths of 58 in. at the lower concrete
opment length is approximately 150 db, then the flexural strengths. More importantly, the figure shows improve-
bond length must be approximately 90 db. ment in strand bond behavior as concrete strengths in-
creased.
The development length expression can then be written as Note, however, that bond failures occurred in I-shaped
follows: beams cast with Strand D. Results of the tests demonstrate that
the Strand D, with an NASP Bond Test value of only 6,890 lb,
225db does not provide adequate bond-ability with concrete. Figure
ld = lt + (3.7)
fc 3.50 shows the results of development length tests on Strands
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16000
14000
12000 Proposed Design Equation
c (psi)
Concrete Strength, f'
10000
8000
6000
4000
2000
0
0 20 40 60 80 100
Embedment length (in.)
Flexural Failures - R-Beams Bond Failures - R-Beams Flexural Failures - I-Beams Bond Failures - I-Beams
Figure 3.49. Distribution of bond and flexural failures for Strand D (0.5 in.).
A and B. Both of these strands can be considered "high bond- Figure 3.51 shows the distribution of bond and flexural
ing," since the NASP Bond Test value was so high. Strand B failures for 0.6 in. strand, Strand A6, with respect to concrete
was cast in the 4 ksi rectangular beams and I-shaped beams, strength and embedment lengths. As in Figure 3.50, the pro-
and Strand A was used in the higher strength rectangular posed design equation is shown in Figure 3.51 along with the
beams. The chart shows that the high-bonding strand was de- beam test results. There are no bond failures occurring in the
veloped in all concrete strengths, even in embedment lengths region where embedment length exceeds the calculated
as short as 46 in. The proposed design equation is shown on development length using the proposed equation. The tests
the chart along with the beam test results. support the proposed equation for development length.
16000
14000
c (psi)
12000
Concrete Strength, f'
10000
8000
6000
Proposed Design Equation
4000
2000
0
0 20 40 60 80 100
Embedment length (in.)
Flexural Failures = R-beams Flexural Failures = I-beams
Proposed Equation Curve Shear Failures = I-beams
Figure 3.50. Distribution of bond and flexural failures for Strands A/B (0.5 in.).
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16000
14000
12000 Proposed Design
Equation
10000
c (psi)
8000
f'
6000
4000
2000
0
0 20 40 60 80 100 120
Embedment length (in.)
Bond Failures = R-beams Flexural Failures = R-beams
Flexural Failures = I-beams Proposed Equation Curve
Figure 3.51. Distribution of bond and flexural failures for
Strand A6 (0.6 in.).
3.6.4 NASP Value and Bond Performance worst performer of the four strands in both single strand
and double strand beams, with bond failures at the AASHTO
Along with the recommendation for the development development length of 73 in.
length design expression, it is important to recommend a Strand FF from Russell and Brown's research (2004) is the
minimum value from the NASP Bond Test. First of all, how- same strand labeled Strand D in the NCHRP research. As seen
ever, it was important to establish a correlation between the in Tables 3.31 and 3.32, Russell and Brown reported a NASP
NASP pull-out test values and the bond performance of the Bond Test value of 7,300 lb for Strand FF. This compares with
same strands in transfer and in development length tests. a NASP Bond Test value of 6,890 lb in the NCHRP testing.
Russell and Brown (2004) measured transfer lengths and per- Strand FF demonstrated the ability to develop adequate ten-
formed flexural tests on rectangular-shaped beams. Table 3.31 sion in an embedment length of 73 in. in the rectangular
and Table 3.32 summarize the test results and the failure beams. However, if one looks at the results of the I-shaped
modes obtained from flexural tests performed by Russell and beams in Table 3.27, one can see that Strand D or Strand FF
Brown (2004).The NASP pull-out test values are also given. was unable to develop adequate strand tension at the devel-
Strand II had the lowest NASP Bond Test value, only 4,140 opment length of 73 in.
lb. Strand II is the same strand as that labeled Strand E in the
NCHRP research. One can see also that Strand II was the
Table 3.32. Failure mode on beams made with two
strands (Russell and Brown 2004).
Table 3.31. Failure modes on single-strand beams
(Russell and Brown 2004).
fc Average NASP Embedment Length
Beam No.
56 Days Pull-Out Value (in)
fc Average NASP Embedment Length (psi) (lb)
Beam No.
56 Days Pull-Out Value (in) 58 73
(psi) (lb) II21 6,290 4,140 B F
58 73
II22 6,280 4,140 B B
II11 6,290 4,140 B F
FF21 6,260 7,300 F F
II12 6,280 4,140 B B
FF22 6,070 7,300 F F
FF11 6,260 7,300 V F
HH21 6,330 10,700 F F
FF12 6,070 7,300 B F
HH22 6,300 10,700 F F
HH11 6,330 10,700 F F
AA21 6,220 14,950 F F
HH12 6,300 10,700 B F
AA22 6,160 14,950 F F
AA11 6,220 14,950 F F
AA12 6,160 14,950 F F F = Flexural Failure
F = Flexural Failure V = Shear Failure
V = Shear Failure
B = Bond Failure B = Bond Failure
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Also, in Russell and Brown's research (2004), NASP Round Table 3.33. Bond failures at 58 in. and 73 in.
IV testing, Strand HH demonstrated the ability to develop ad- for all 0.5 in. strands--I-shaped beams and
equate strand tension at the development length of 73 in. The rectangular beams.
NASP Bond Test value was 10,700 lb. One bond failure oc-
curred at an embedment length of 58 in. This occurred in a Number of Bond Failures
Strand NASP Value
single strand beam. The results from NASP Round IV testing (lb)
Name 58-in 73-in
reported by Russell and Brown (2004) indicate that the bond Embedment Embedment
performance of Strand HH was adequate. Length Length
Figure 3.52 shows the distribution of bond and flexural II 4,140 4 2
failures for Strand HH (0.5 in.) with respect to the concrete D 6,590 3 2*
strength and the provided embedment lengths. There are no
FF 7,300 1 0
bond failures occurring in the region where provided em-
bedment length exceeds the calculated development length HH 10,700 1 0
using the proposed equation. The tests support the proposed AA 14,950 0 0
equation for development length and also indicate that bond
B 20,210 0 0
performance of strand HH was adequate.
No bond failure was recorded on the beams with Strand A 20,950 0 0
AA. Comparing the NASP values of these strands, the follow- * Embedment lengths were 72 in. instead of 73 in.
ing observation can be made: as the NASP value increases,
chances of bond failure at provided embedment length de-
crease. In other words, Strand II had the lowest NASP value The number of bond failures is lower for strands with
and the highest number of bond failures, Strand FF and higher NASP pull-out values. Strand HH, with NASP pull-
Strand HH had NASP values lying between those of Strand II out value of 10,700 lb, lies at a critical position (boldfaced in
and Strand AA, and bond failures were noted on fewer occa- Table 3.33): strands with NASP pull-out values lower than
sions for Stand FF and Strand HH than for Strand II. Strand Strand HH's pull-out value sustained bond failures, but no
AA had the highest NASP value and no bond failures, sug- strands with NASP pull-out values higher than Strand HH's
gesting that it was capable of developing enough anchorage pull-out value suffered bond failure. Embedment lengths of
to achieve flexural failures. A higher NASP value seems to in- 58 in. and 73 in. correspond to 80 percent and 100 percent,
dicate better bonding qualities for the strand. respectively, of the code provision for development length.
Table 3.33 presents the number of failures obtained for all Strand HH suffered a bond failure at an embedment length
types of strands (0.5 in.) including NASP Round III Strands. of 58 in., but none at 73 in. These data show that a NASP
In Table 3.33, strands are arranged in the order of increasing pull-out value of 10,700 lb is adequate to develop enough an-
NASP pull-out values. The number of bond failures obtained chorage for achieving flexural failures at the code-specified
at 58-in. and 73-in. embedment lengths is shown. development length.
16000
14000
Proposed Design
c (psi)
12000 Equation
Concrete Strength, f'
10000
8000
6000
4000
Flexural Failures - Round III Single Strand Beams
2000 Bond Failures - Round III Single Strand Beams
Flexural Failures - Round III Double Strand Beams
0
0 20 40 60 80 100
Embedment length (in.)
Figure 3.52. Distribution of bond and flexural failures for Strand
HH (Russell and Brown 2004).
