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Determining Slipping Stress of Prestressing
Strands in Confined Sections
ARTICLE in ACI STRUCTURAL JOURNAL · NOVEMBER 2012
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Mohamed K. ElBatanouny
Wiss Janney Elstner Associates Inc.
31 PUBLICATIONS 52 CITATIONS
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Paul Ziehl
University of South Carolina
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Available from: Mohamed K. ElBatanouny
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Title no. 109S66
ACI STRUCTURAL JOURNAL TECHNICAL PAPER
ACI Structural Journal, V. 109, No. 6, NovemberDecember 2012.
MS No. S2010340.R1 received November 18, 2011, and reviewed under Institute
publication policies. Copyright © 2012, American Concrete Institute. All rights
reserved, including the making of copies unless permission is obtained from the
copyright proprietors. Pertinent discussion including author’s closure, if any, will be
published in the SeptemberOctober 2013 ACI Structural Journal if the discussion is
received by May 1, 2013.
ACI Structural Journal/NovemberDecember 2012 767
Determining Slipping Stress of Prestressing Strands in
Confined Sections
by Mohamed K. ElBatanouny and Paul H. Ziehl
Development length and slipping stress of prestressing strands
subjected to confining stress is not wellquantified and the appro
priateness of the ACI 31811 equation under such conditions can
be questioned. In 1992, a test was performed on nineteen 14 in.
(356 mm) square prestressed concrete piles with a clamping force
applied during testing under lateral load. The findings indicated
that the ACI 31811 equation for development length of prestressing
strands may not be suitable when used for sections subjected to
confining stress. In this study, a modified equation that accounts for
the effect of concrete confinement is discussed and compared to the
published 1992 results and the ACI 31811 equation. The moment
strength of the sections is also compared using momentcurvature
analysis by comparing three different slipping values: 1) those
obtained from experimental results; 2) the ACI 31811 equation;
and 3) the modified equation.
Keywords: confining stress; development length; moment capacity; slipping.
INTRODUCTION
The use of precast, prestressed concrete piles in bridge
construction is common in the United States; however,
the performance of such units under seismic loading is
not entirely clear. The behavior of the connection between
prestressed piles and castinplace (CIP) reinforced concrete
caps is particularly not wellunderstood. Current South
Carolina Department of Transportation (SCDOT) connec
tion details1,2 require the plain embedment of the pile into
the bent cap one pile diameter with a construction tolerance
of ±6 in. (±152 mm). Plain embedment requires no special
detailing to the pile end or the embedment region and no
special treatment of the pile surface, such as roughening
or grooving. The ductility and moment capacity of such
connections is of interest because this short embedment
length is often much less than the length required for devel
opment of the full tensile strength of the prestressing strands
within the embedded region.
Generally, the development length of prestressing strands
is calculated from ACI 31811, Eq. (124).3 In the case of
piles embedded in CIP caps, the embedment length is usually
far less than the development length. Therefore, the strands
are predicted to slip at a level of stress less than their nominal
capacity. This stress is referred to as the “slipping stress.”
The ACI 31811 equation was developed for the case of
superstructure elements not subjected to confining stress.
Therefore, the application of this equation to substructure
elements having significant confining stress may not be
appropriate. A pile embedded in a CIP cap is subjected to
the shrinkage of the confining concrete in the cap, which
creates confining stress (also known as “clamping force”)
on the pile, which serves to enhance the bond between
the prestressing strand and the surrounding concrete. This
leads to a decrease in the development length and an asso
ciated increase in the slipping stress of the prestressing
strand.4,5 This effect became very apparent during the testing
of a series of precast concrete piles embedded in CIP bent
caps at the University of South Carolina Structures Labora
tory.5 Because the embedment length of the piles was much
less than the development length of prestressing strands, the
strands were expected to slip prior to achieving the nominal
capacity. Significant differences were found between the
experimental results and those predicted by ACI 31811,
Eq. (124).5
Shahawy and Issa4 discussed the findings of a significant
experimental investigation related to the effect of confine
ment from CIP caps to prestressed concrete piles with
emphasis on the resulting behavior under lateral load. The
results showed that the development length of prestressing
strands was enhanced due to confining stress. They concluded
that using the ACI 31811 equation without consideration of
confinement will lead to very conservative values.
This study makes use of the experimental results reported
by Shahawy and Issa4 to investigate the appropriateness of
a potential modification to the ACI 31811 equation.5 The
theoretical slipping stress calculated from the modified
equation and ACI 31811, Eq. (124), are compared.
The calculation of the moment strength of piles in seismic
regions is a critical issue. A momentcurvature analysis6 was
performed to calculate the moment strength of the sections
using the modified equation and the ACI 31811 equation.
These were then compared to calculated moments using
measured slipping stress values from the Shahawy and
Issa4 study. Furthermore, finite element models were created
to investigate the value and distribution of the confining
stress due to shrinkage for use in the modified equation.
RESEARCH SIGNIFICANCE
Several important investigations have addressed the suit
ability of ACI 31811, Eq. (124), for development length7,8;
however, only a few have considered the effect of confine
ment.4,5 The ACI 31811 equation for calculating the devel
opment length of prestressing strands was derived for
unconfined sections and does not account for the effect of
confinement. To account for the effect of confinement, a
potential modification to the ACI 31811 equation is devel
oped and described. The results from the modified equation
are compared to published experimental results that directly
addressed the effect of confinement for the development
length of prestressing strands.
Page 5
770 ACI Structural Journal/NovemberDecember 2012
3. An equation proposed by Zia and Mostafa,8 as shown
in Eq. (4a). Their approach used the same parameters
used in calculating the development length of prestressing
strands, with the exception of two terms: fsi, which is the
stress in prestressing steel at transfer (ksi), and fc′, which
is the compressive stress of concrete at the time of initial
prestressing (ksi). The effective stress of the prestressing
strand, fse, and the nominal flexural strength of the
prestressing strand, fps, should be used (ksi).
( )1.5 4.6 1.25sid b ps se b
c
f
L d f f d
f
=  + 
′
(4a)
3.68
0.8 1.2d siss se ps
b c b
L f
f f f
d f d
=  + + ≤
′
(4b)
Comparisons between these three approaches are
summarized in Table 2. The comparisons indicate that
the ACI 31811 equation is conservative when confining
stress is applied to the concrete section. The Zia and
Mostafa8 proposed equation (Eq. (4b)) was more conser
vative than the ACI 31811 equation. The Shahawy and
Issa4 proposed equation (Eq. (2b)) has a good match with the
experimental data. However, this equation uses the slipping
stress of the strand as an input. More detailed discussion is
provided in the following sections.
HISTORY OF ACI 31811 EQUATION
The expression for the development length of prestressing
strands found in ACI 31811 was proposed by Mattock9 and
members of ACI Committee 423.10 The expression divides
the development length into two parts: transfer length and
flexural bond length. To develop the expression for transfer
length,11 results of a study by Hanson and Kaar12 and Kaar et
al.13 were used. They stated a value for average transfer bond
stress ut = 400 psi (2.76 MPa). For flexural bond length,
another approach was used based on the definition of general
bond slip introduced by Janney.14 Janney14 stated that when
the peak of the high bond stress wave reaches the transfer
length, general bond slip occurs and leads to a reduction in
the frictional resistance resulting from the Hoyer effect.15
Hanson and Kaar12 agreed with Janney’s14 explanation, but
they did not state a value for the average flexural bond stress.
Due to the difficulty of codifying this concept, Mattock9 and
the members of ACI Committee 42310 used the data of
Hanson and Kaar’s12 beam tests to formulate an approach
based on an average flexural bond stress. They constructed
a straightline relationship by subtracting the estimated
transfer length from the embedment length of the strand. The
increase in strand stress due to flexure was determined to be
the difference between the strand stress at the load causing
slip and the effective stress due to prestressing. The use of
a constant slope for the flexural bond length implies a value
of average flexural bond stress ufb = 140 psi (0.96 MPa).5 It
is worth noting that the assumption of average flexural bond
stress was made to simplify the approach and makes it easier
to codify. The expressions for transfer length and flexural
bond length are shown in Eq. (5) and (6), respectively.
Table 2—Shahawy and Issa4 test results and calculated slipping stresses
Specimen number Embedment length, in.
Theoretical ultimate
moment, kipin.
Measured ultimate
moment, kipin.
Measured steel stress
at failure, ksi
Slipping stress, ksi
Eq. (1b) Eq. (2b) Eq. (4b)
A1E 36 1560 1840 256 180 256 167
A2E 36 1460 1800 263 190 263 177
A3I 36 1530 1550 254 180 254 166
A4I 36 1440 1550 253 181 253 167
B1E 42 1530 1620 262 199 262 182
B2E 42 1520 1870 261 199 261 183
B3E 42 1480 1760 257 197 257 180
B4E 42 1600 1560 260 196 260 179
B5E 42 1520 1840 263 200 263 185
B6I 42 1520 1600 259 197 259 181
C1E 48 1550 1510 260 208 260 190
C2E 48 1520 1690 258 206 258 188
C3I 48 1600 1760 262 209 262 190
C4I 48 1520 1660 258 206 258 188
C5I 48 1520 1690 260 210 260 192
C6E 48 1520 1700 258 207 258 189
D1E 60 1570 1730 262 233 261 210
D2I 60 1520 1730 261 235 261 212
D3E 60 1520 1620 260 233 260 210
Notes: 1 in. = 25.4 mm; 1 kipin. = 0.11298 kNm; 1 ksi = 6.895 MPa.
Page 6
ACI Structural Journal/NovemberDecember 2012 771
7.36 3000
ps se se se
t b b
t t
A f f f
L d d
o u u
∗
= = ∗ = ∗
S ∗ ∗
(5)
( ) ( )
7.36 1000
ps se ps se
fb b b
fb
f f f f
L d d
u
 
= =
∗
(6)
where Lt is transfer length (in.); Lfb is flexural bond length
(in.); So is the strand perimeter (So = 4/3 * p * db [in.]);
and Aps is the strand crosssectional area (Aps = 0.725 * p *
db
2/4 [in.2]).
EFFECT OF CONFINEMENT ON EFFECTIVE
TRANSFER LENGTH
Transfer length in the absence of confinement is a function
of diameter, effective prestress, and average transfer bond
stress. Mechanisms contributing to the value of average
transfer bond stress can be categorized into three groups:
adhesion, friction, and mechanical interlock.11 Adhesion
is destroyed by the relative slip between the strand and the
surrounding concrete and the contribution of mechanical
interlock in the average transfer bond stress can be neglected
due to “unwinding.”16
Frictional bond stress is developed as a result of the radial
compressive stresses, which are attributed to the Hoyer
effect,15 where longitudinal contraction results in radial
expansion of the tendon. This Poisson’s expansion induces
compression perpendicular to the steelconcrete interface. In
the absence of confinement, the value of the average transfer
bond stress is assumed to be ut = 400 psi (2.76 MPa). When
confinement occurs, it is convenient to represent the effect
as an increase in the apparent bond stress. It should be noted
that confinement does not change the transfer length itself.
Rather, confinement decreases the potential for slipping of
the strands within the transfer zone.
To account for this behavior, a new term referred to as the
“effective transfer length” (Lte) is proposed. This term takes
into account both the unconfined average transfer bond and
the increase in bond stress due to confinement. The value of
the resulting apparent bond stress is determined by adding
the average transfer bond stress (400 psi [2.76 MPa]) to the
average bond stress that is due to confinement. The average
bond stress due to confinement is calculated by multiplying
the confining stress by the coefficient of friction between the
steel and concrete (m). The resulting average bond stress is
shown in Eq. (7).
400tc cavu = + m ∗s (7)
where utc is the average confined bond stress within the
transfer zone (psi); scav is the average confining stress
applied to the prestressed concrete section; and m is the coef
ficient of friction between the steel and concrete (generally
taken as m = 0.417).
EFFECT OF CONFINEMENT ON
FLEXURAL BOND LENGTH
For the confined flexural bond stress ufbc (psi), the same
approach was used, assuming that the confining stress would
only affect the friction stress. Due to the reduction in strand
diameter resulting from the increase in strand stress in the
average flexural bond stress zone, the Hoyer effect15 is
reduced and ufb is implied in the ACI 31811 equation to be
equal to 140 psi (0.96 MPa).5 The reduction of the Hoyer
effect15 leads to a decrease in the frictional forces resulting
from the confining stress. A ratio between the average transfer
bond stress and the average flexural bond stress was used
to decrease the effect of the confining stress, where ut /ufb =
2.86. Therefore, Eq. (8a) is introduced to assess the average
flexural bond stress, including the effect of confining stress.
Another reason to use this factor is the fact that microcracks
will form in the pile/bentcap system at higher levels of load
(average flexural bond stress only appears after cracking14),
causing the confining stress from the shrinkage of the bent
cap to decrease. In the test program considered, however, the
confining stress is not expected to decrease, as it was applied
to the specimens permanently via a clamping force.4 There
fore, for the test program considered, the reduction factor of
2.86 was neglected, as presented in Eq. (8b).
140
2.86
cav
fbcu
m ∗s
= + (8a)
140fbc cavu = + m ∗s (8b)
POTENTIAL MODIFICATION TO ACI 31811
EQUATION (ACCOUNTING FOR CONFINEMENT)
Replacing the average flexural bond stress term in the
expression of flexural bond stress given in Eq. (6) by the
confined flexural bond stress will modify the equation to
account for confining stress. In the cases where confining
stress is present, the values of both confined transfer bond
stress (Eq. (7)) and confined flexural bond stress (Eq. (8a))
are greater than those of the average transfer bond stress and
average flexural bond stress, respectively, thereby decreasing
the development length (Eq. (9a)) and increasing the slipping
stress of prestressing strands (Eq. (9b)). It is noted that the
effect of confinement does not change the transfer length.
Rather, it reduces the potential for slipping of the strands
due to an increase in the apparent bond stress. The first part
of the equation represents the effective transfer length, while
the second part represents the flexural bond length, where
Ldc is the confined development length (in.). Equations (7)
and (8a) are used to define the values for confined transfer
bond stress and confined flexural bond stress, respectively.
7.36 7.36
ps sese
dc b b
tc fbc
f ff
L d d
u u

= ∗ + ∗
∗ ∗
(9a)
7.36 tc fbcdss fbc se ps
b tc
u uL
f u f f
d u

= ∗ ∗ + ≤ (9b)
MOMENTCURVATURE ANALYSIS
A detailed momentcurvature analysis was conducted
using a numerical program.6 Using the compressive strength
data in Table 1, each of the 19 piles was modeled according
to its material properties. Two concrete material models were
Page 10
ACI Structural Journal/NovemberDecember 2012 775
as a benchmark, the results obtained from the modified equa
tion (Eq. (9a)) provide a better match than those obtained
with the ACI 31811 equation (Eq. (1a)).
Design recommendation and limitations
The confining stress is a function of shrinkage; therefore,
it is predicted that the value of confining stress will continue
to increase with time. At higher levels of confining stress,
microcracks may form to relieve the high stress, which leads
to a drop in the magnitude of the confining stress. Therefore,
an upper limit of 750 psi (5.2 MPa) is proposed to take into
account the effect of microcracking at high levels of confine
ment. This value is partially based on an ongoing laboratory
investigation, where piles are plainly embedded in CIP bent
caps and tested under reverse lateral cyclic loading to check
the moment capacity and ductility of the connection.24,25 This
upperlimit value is assumed to be the maximum confining
stress acting on the embedded end of the pile. A simplified
equation (Eq. (12)) is proposed by substituting this upper
limit value in Eq. (9a).5
5000 1800
ps sese
dc b b
f ff
L d d

= ∗ + ∗ (12)
The results from the actual piletoCIPbentcap connec
tions show that Eq. (12) has a better comparison with the
experimental results than the ACI 31811 equation5; however,
the use of Eq. (12) with the data described in this paper is not
appropriate, as the confining stress was artificially simulated
with steel plates for the Shahawy and Issa4 study.
The ACI 31811 equation is more conservative than the
modified equation. Therefore, it is not recommended that
the modified equation approach be used in practice in the
absence of further investigation and verification. The results
presented in this study are limited to the use of 0.5 in.
(13 mm) lowrelaxation sevenwire prestressing strands.
The appropriateness of using Eq. (12) with a different strand
diameter requires further investigation.
SUMMARY AND CONCLUSIONS
The appropriateness of ACI 31811, Eq. (124), for the
calculation of development length for prestressing strands
in confined sections was studied. A modified equation
was developed and introduced in this paper to account for
confinement. The experimental results of Shahawy and
Issa4 were used to develop a momentcurvature analysis.
The results were compared to calculated results from the
ACI 31811 equation and the modified equation. The conclu
sions of this study can be drawn as follows:
1. Confining stress affects the bond between prestressing
strands and concrete by increasing the effective average
bond stress within the transfer zone and the average flexural
bond stress. This enhances (increases) the stress required to
cause slipping.
2. Equation (9a) was developed for calculating develop
ment length in cases where confining stress takes place. One
such case occurs when precast piles are embedded in CIP
bent caps.
3. A better fit to the published experimental data was
obtained for confined sections with Eq. (9b) than with the
ACI 31811 equation (Eq. (1b)). The results of both equations
are conservative when compared to the experimental results.
4. The difference between the modified equation and the
ACI 31811 equation becomes more significant as shorter
embedment lengths are used in the pile/bentcap system.
5. The embedment length of prestressed piles in CIP bent
caps has a notable effect on the slipping stress of prestressing
strands and the moment capacity of the section.
6. The modified equation (Eq. (9a) and (9b)) provided
a reasonable fit to the experimental data described in this
paper. Further consideration is recommended prior to imple
mentation of these equations for purposes of design. Among
other items, it is recommended that confining stresses be
monitored in field applications.
ACKNOWLEDGMENTS
The authors wish to express their gratitude and sincere appreciation to
the South Carolina Department of Transportation (SCDOT) and the Federal
Highway Administration (FHWA) for financial support. The opinions, find
ings, and conclusions expressed in this paper are those of the authors and
not necessarily those of SCDOT or FHWA.
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Determining Slipping Stress of Prestressing
Strands in Confined Sections
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Mohamed K. ElBatanouny
Wiss Janney Elstner Associates Inc.
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Paul Ziehl
University of South Carolina
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Available from: Mohamed K. ElBatanouny
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Title no. 109S66
ACI STRUCTURAL JOURNAL TECHNICAL PAPER
ACI Structural Journal, V. 109, No. 6, NovemberDecember 2012.
MS No. S2010340.R1 received November 18, 2011, and reviewed under Institute
publication policies. Copyright © 2012, American Concrete Institute. All rights
reserved, including the making of copies unless permission is obtained from the
copyright proprietors. Pertinent discussion including author’s closure, if any, will be
published in the SeptemberOctober 2013 ACI Structural Journal if the discussion is
received by May 1, 2013.
ACI Structural Journal/NovemberDecember 2012 767
Determining Slipping Stress of Prestressing Strands in
Confined Sections
by Mohamed K. ElBatanouny and Paul H. Ziehl
Development length and slipping stress of prestressing strands
subjected to confining stress is not wellquantified and the appro
priateness of the ACI 31811 equation under such conditions can
be questioned. In 1992, a test was performed on nineteen 14 in.
(356 mm) square prestressed concrete piles with a clamping force
applied during testing under lateral load. The findings indicated
that the ACI 31811 equation for development length of prestressing
strands may not be suitable when used for sections subjected to
confining stress. In this study, a modified equation that accounts for
the effect of concrete confinement is discussed and compared to the
published 1992 results and the ACI 31811 equation. The moment
strength of the sections is also compared using momentcurvature
analysis by comparing three different slipping values: 1) those
obtained from experimental results; 2) the ACI 31811 equation;
and 3) the modified equation.
Keywords: confining stress; development length; moment capacity; slipping.
INTRODUCTION
The use of precast, prestressed concrete piles in bridge
construction is common in the United States; however,
the performance of such units under seismic loading is
not entirely clear. The behavior of the connection between
prestressed piles and castinplace (CIP) reinforced concrete
caps is particularly not wellunderstood. Current South
Carolina Department of Transportation (SCDOT) connec
tion details1,2 require the plain embedment of the pile into
the bent cap one pile diameter with a construction tolerance
of ±6 in. (±152 mm). Plain embedment requires no special
detailing to the pile end or the embedment region and no
special treatment of the pile surface, such as roughening
or grooving. The ductility and moment capacity of such
connections is of interest because this short embedment
length is often much less than the length required for devel
opment of the full tensile strength of the prestressing strands
within the embedded region.
Generally, the development length of prestressing strands
is calculated from ACI 31811, Eq. (124).3 In the case of
piles embedded in CIP caps, the embedment length is usually
far less than the development length. Therefore, the strands
are predicted to slip at a level of stress less than their nominal
capacity. This stress is referred to as the “slipping stress.”
The ACI 31811 equation was developed for the case of
superstructure elements not subjected to confining stress.
Therefore, the application of this equation to substructure
elements having significant confining stress may not be
appropriate. A pile embedded in a CIP cap is subjected to
the shrinkage of the confining concrete in the cap, which
creates confining stress (also known as “clamping force”)
on the pile, which serves to enhance the bond between
the prestressing strand and the surrounding concrete. This
leads to a decrease in the development length and an asso
ciated increase in the slipping stress of the prestressing
strand.4,5 This effect became very apparent during the testing
of a series of precast concrete piles embedded in CIP bent
caps at the University of South Carolina Structures Labora
tory.5 Because the embedment length of the piles was much
less than the development length of prestressing strands, the
strands were expected to slip prior to achieving the nominal
capacity. Significant differences were found between the
experimental results and those predicted by ACI 31811,
Eq. (124).5
Shahawy and Issa4 discussed the findings of a significant
experimental investigation related to the effect of confine
ment from CIP caps to prestressed concrete piles with
emphasis on the resulting behavior under lateral load. The
results showed that the development length of prestressing
strands was enhanced due to confining stress. They concluded
that using the ACI 31811 equation without consideration of
confinement will lead to very conservative values.
This study makes use of the experimental results reported
by Shahawy and Issa4 to investigate the appropriateness of
a potential modification to the ACI 31811 equation.5 The
theoretical slipping stress calculated from the modified
equation and ACI 31811, Eq. (124), are compared.
The calculation of the moment strength of piles in seismic
regions is a critical issue. A momentcurvature analysis6 was
performed to calculate the moment strength of the sections
using the modified equation and the ACI 31811 equation.
These were then compared to calculated moments using
measured slipping stress values from the Shahawy and
Issa4 study. Furthermore, finite element models were created
to investigate the value and distribution of the confining
stress due to shrinkage for use in the modified equation.
RESEARCH SIGNIFICANCE
Several important investigations have addressed the suit
ability of ACI 31811, Eq. (124), for development length7,8;
however, only a few have considered the effect of confine
ment.4,5 The ACI 31811 equation for calculating the devel
opment length of prestressing strands was derived for
unconfined sections and does not account for the effect of
confinement. To account for the effect of confinement, a
potential modification to the ACI 31811 equation is devel
oped and described. The results from the modified equation
are compared to published experimental results that directly
addressed the effect of confinement for the development
length of prestressing strands.
Page 5
770 ACI Structural Journal/NovemberDecember 2012
3. An equation proposed by Zia and Mostafa,8 as shown
in Eq. (4a). Their approach used the same parameters
used in calculating the development length of prestressing
strands, with the exception of two terms: fsi, which is the
stress in prestressing steel at transfer (ksi), and fc′, which
is the compressive stress of concrete at the time of initial
prestressing (ksi). The effective stress of the prestressing
strand, fse, and the nominal flexural strength of the
prestressing strand, fps, should be used (ksi).
( )1.5 4.6 1.25sid b ps se b
c
f
L d f f d
f
=  + 
′
(4a)
3.68
0.8 1.2d siss se ps
b c b
L f
f f f
d f d
=  + + ≤
′
(4b)
Comparisons between these three approaches are
summarized in Table 2. The comparisons indicate that
the ACI 31811 equation is conservative when confining
stress is applied to the concrete section. The Zia and
Mostafa8 proposed equation (Eq. (4b)) was more conser
vative than the ACI 31811 equation. The Shahawy and
Issa4 proposed equation (Eq. (2b)) has a good match with the
experimental data. However, this equation uses the slipping
stress of the strand as an input. More detailed discussion is
provided in the following sections.
HISTORY OF ACI 31811 EQUATION
The expression for the development length of prestressing
strands found in ACI 31811 was proposed by Mattock9 and
members of ACI Committee 423.10 The expression divides
the development length into two parts: transfer length and
flexural bond length. To develop the expression for transfer
length,11 results of a study by Hanson and Kaar12 and Kaar et
al.13 were used. They stated a value for average transfer bond
stress ut = 400 psi (2.76 MPa). For flexural bond length,
another approach was used based on the definition of general
bond slip introduced by Janney.14 Janney14 stated that when
the peak of the high bond stress wave reaches the transfer
length, general bond slip occurs and leads to a reduction in
the frictional resistance resulting from the Hoyer effect.15
Hanson and Kaar12 agreed with Janney’s14 explanation, but
they did not state a value for the average flexural bond stress.
Due to the difficulty of codifying this concept, Mattock9 and
the members of ACI Committee 42310 used the data of
Hanson and Kaar’s12 beam tests to formulate an approach
based on an average flexural bond stress. They constructed
a straightline relationship by subtracting the estimated
transfer length from the embedment length of the strand. The
increase in strand stress due to flexure was determined to be
the difference between the strand stress at the load causing
slip and the effective stress due to prestressing. The use of
a constant slope for the flexural bond length implies a value
of average flexural bond stress ufb = 140 psi (0.96 MPa).5 It
is worth noting that the assumption of average flexural bond
stress was made to simplify the approach and makes it easier
to codify. The expressions for transfer length and flexural
bond length are shown in Eq. (5) and (6), respectively.
Table 2—Shahawy and Issa4 test results and calculated slipping stresses
Specimen number Embedment length, in.
Theoretical ultimate
moment, kipin.
Measured ultimate
moment, kipin.
Measured steel stress
at failure, ksi
Slipping stress, ksi
Eq. (1b) Eq. (2b) Eq. (4b)
A1E 36 1560 1840 256 180 256 167
A2E 36 1460 1800 263 190 263 177
A3I 36 1530 1550 254 180 254 166
A4I 36 1440 1550 253 181 253 167
B1E 42 1530 1620 262 199 262 182
B2E 42 1520 1870 261 199 261 183
B3E 42 1480 1760 257 197 257 180
B4E 42 1600 1560 260 196 260 179
B5E 42 1520 1840 263 200 263 185
B6I 42 1520 1600 259 197 259 181
C1E 48 1550 1510 260 208 260 190
C2E 48 1520 1690 258 206 258 188
C3I 48 1600 1760 262 209 262 190
C4I 48 1520 1660 258 206 258 188
C5I 48 1520 1690 260 210 260 192
C6E 48 1520 1700 258 207 258 189
D1E 60 1570 1730 262 233 261 210
D2I 60 1520 1730 261 235 261 212
D3E 60 1520 1620 260 233 260 210
Notes: 1 in. = 25.4 mm; 1 kipin. = 0.11298 kNm; 1 ksi = 6.895 MPa.
Page 6
ACI Structural Journal/NovemberDecember 2012 771
7.36 3000
ps se se se
t b b
t t
A f f f
L d d
o u u
∗
= = ∗ = ∗
S ∗ ∗
(5)
( ) ( )
7.36 1000
ps se ps se
fb b b
fb
f f f f
L d d
u
 
= =
∗
(6)
where Lt is transfer length (in.); Lfb is flexural bond length
(in.); So is the strand perimeter (So = 4/3 * p * db [in.]);
and Aps is the strand crosssectional area (Aps = 0.725 * p *
db
2/4 [in.2]).
EFFECT OF CONFINEMENT ON EFFECTIVE
TRANSFER LENGTH
Transfer length in the absence of confinement is a function
of diameter, effective prestress, and average transfer bond
stress. Mechanisms contributing to the value of average
transfer bond stress can be categorized into three groups:
adhesion, friction, and mechanical interlock.11 Adhesion
is destroyed by the relative slip between the strand and the
surrounding concrete and the contribution of mechanical
interlock in the average transfer bond stress can be neglected
due to “unwinding.”16
Frictional bond stress is developed as a result of the radial
compressive stresses, which are attributed to the Hoyer
effect,15 where longitudinal contraction results in radial
expansion of the tendon. This Poisson’s expansion induces
compression perpendicular to the steelconcrete interface. In
the absence of confinement, the value of the average transfer
bond stress is assumed to be ut = 400 psi (2.76 MPa). When
confinement occurs, it is convenient to represent the effect
as an increase in the apparent bond stress. It should be noted
that confinement does not change the transfer length itself.
Rather, confinement decreases the potential for slipping of
the strands within the transfer zone.
To account for this behavior, a new term referred to as the
“effective transfer length” (Lte) is proposed. This term takes
into account both the unconfined average transfer bond and
the increase in bond stress due to confinement. The value of
the resulting apparent bond stress is determined by adding
the average transfer bond stress (400 psi [2.76 MPa]) to the
average bond stress that is due to confinement. The average
bond stress due to confinement is calculated by multiplying
the confining stress by the coefficient of friction between the
steel and concrete (m). The resulting average bond stress is
shown in Eq. (7).
400tc cavu = + m ∗s (7)
where utc is the average confined bond stress within the
transfer zone (psi); scav is the average confining stress
applied to the prestressed concrete section; and m is the coef
ficient of friction between the steel and concrete (generally
taken as m = 0.417).
EFFECT OF CONFINEMENT ON
FLEXURAL BOND LENGTH
For the confined flexural bond stress ufbc (psi), the same
approach was used, assuming that the confining stress would
only affect the friction stress. Due to the reduction in strand
diameter resulting from the increase in strand stress in the
average flexural bond stress zone, the Hoyer effect15 is
reduced and ufb is implied in the ACI 31811 equation to be
equal to 140 psi (0.96 MPa).5 The reduction of the Hoyer
effect15 leads to a decrease in the frictional forces resulting
from the confining stress. A ratio between the average transfer
bond stress and the average flexural bond stress was used
to decrease the effect of the confining stress, where ut /ufb =
2.86. Therefore, Eq. (8a) is introduced to assess the average
flexural bond stress, including the effect of confining stress.
Another reason to use this factor is the fact that microcracks
will form in the pile/bentcap system at higher levels of load
(average flexural bond stress only appears after cracking14),
causing the confining stress from the shrinkage of the bent
cap to decrease. In the test program considered, however, the
confining stress is not expected to decrease, as it was applied
to the specimens permanently via a clamping force.4 There
fore, for the test program considered, the reduction factor of
2.86 was neglected, as presented in Eq. (8b).
140
2.86
cav
fbcu
m ∗s
= + (8a)
140fbc cavu = + m ∗s (8b)
POTENTIAL MODIFICATION TO ACI 31811
EQUATION (ACCOUNTING FOR CONFINEMENT)
Replacing the average flexural bond stress term in the
expression of flexural bond stress given in Eq. (6) by the
confined flexural bond stress will modify the equation to
account for confining stress. In the cases where confining
stress is present, the values of both confined transfer bond
stress (Eq. (7)) and confined flexural bond stress (Eq. (8a))
are greater than those of the average transfer bond stress and
average flexural bond stress, respectively, thereby decreasing
the development length (Eq. (9a)) and increasing the slipping
stress of prestressing strands (Eq. (9b)). It is noted that the
effect of confinement does not change the transfer length.
Rather, it reduces the potential for slipping of the strands
due to an increase in the apparent bond stress. The first part
of the equation represents the effective transfer length, while
the second part represents the flexural bond length, where
Ldc is the confined development length (in.). Equations (7)
and (8a) are used to define the values for confined transfer
bond stress and confined flexural bond stress, respectively.
7.36 7.36
ps sese
dc b b
tc fbc
f ff
L d d
u u

= ∗ + ∗
∗ ∗
(9a)
7.36 tc fbcdss fbc se ps
b tc
u uL
f u f f
d u

= ∗ ∗ + ≤ (9b)
MOMENTCURVATURE ANALYSIS
A detailed momentcurvature analysis was conducted
using a numerical program.6 Using the compressive strength
data in Table 1, each of the 19 piles was modeled according
to its material properties. Two concrete material models were
Page 10
ACI Structural Journal/NovemberDecember 2012 775
as a benchmark, the results obtained from the modified equa
tion (Eq. (9a)) provide a better match than those obtained
with the ACI 31811 equation (Eq. (1a)).
Design recommendation and limitations
The confining stress is a function of shrinkage; therefore,
it is predicted that the value of confining stress will continue
to increase with time. At higher levels of confining stress,
microcracks may form to relieve the high stress, which leads
to a drop in the magnitude of the confining stress. Therefore,
an upper limit of 750 psi (5.2 MPa) is proposed to take into
account the effect of microcracking at high levels of confine
ment. This value is partially based on an ongoing laboratory
investigation, where piles are plainly embedded in CIP bent
caps and tested under reverse lateral cyclic loading to check
the moment capacity and ductility of the connection.24,25 This
upperlimit value is assumed to be the maximum confining
stress acting on the embedded end of the pile. A simplified
equation (Eq. (12)) is proposed by substituting this upper
limit value in Eq. (9a).5
5000 1800
ps sese
dc b b
f ff
L d d

= ∗ + ∗ (12)
The results from the actual piletoCIPbentcap connec
tions show that Eq. (12) has a better comparison with the
experimental results than the ACI 31811 equation5; however,
the use of Eq. (12) with the data described in this paper is not
appropriate, as the confining stress was artificially simulated
with steel plates for the Shahawy and Issa4 study.
The ACI 31811 equation is more conservative than the
modified equation. Therefore, it is not recommended that
the modified equation approach be used in practice in the
absence of further investigation and verification. The results
presented in this study are limited to the use of 0.5 in.
(13 mm) lowrelaxation sevenwire prestressing strands.
The appropriateness of using Eq. (12) with a different strand
diameter requires further investigation.
SUMMARY AND CONCLUSIONS
The appropriateness of ACI 31811, Eq. (124), for the
calculation of development length for prestressing strands
in confined sections was studied. A modified equation
was developed and introduced in this paper to account for
confinement. The experimental results of Shahawy and
Issa4 were used to develop a momentcurvature analysis.
The results were compared to calculated results from the
ACI 31811 equation and the modified equation. The conclu
sions of this study can be drawn as follows:
1. Confining stress affects the bond between prestressing
strands and concrete by increasing the effective average
bond stress within the transfer zone and the average flexural
bond stress. This enhances (increases) the stress required to
cause slipping.
2. Equation (9a) was developed for calculating develop
ment length in cases where confining stress takes place. One
such case occurs when precast piles are embedded in CIP
bent caps.
3. A better fit to the published experimental data was
obtained for confined sections with Eq. (9b) than with the
ACI 31811 equation (Eq. (1b)). The results of both equations
are conservative when compared to the experimental results.
4. The difference between the modified equation and the
ACI 31811 equation becomes more significant as shorter
embedment lengths are used in the pile/bentcap system.
5. The embedment length of prestressed piles in CIP bent
caps has a notable effect on the slipping stress of prestressing
strands and the moment capacity of the section.
6. The modified equation (Eq. (9a) and (9b)) provided
a reasonable fit to the experimental data described in this
paper. Further consideration is recommended prior to imple
mentation of these equations for purposes of design. Among
other items, it is recommended that confining stresses be
monitored in field applications.
ACKNOWLEDGMENTS
The authors wish to express their gratitude and sincere appreciation to
the South Carolina Department of Transportation (SCDOT) and the Federal
Highway Administration (FHWA) for financial support. The opinions, find
ings, and conclusions expressed in this paper are those of the authors and
not necessarily those of SCDOT or FHWA.
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