Predicting Strand Transfer Length in Pretensioned Concrete:

Eurocode versus North American Practice

José R. Martí-Vargas1 and W. Micah Hale, M.ASCE2

Abstract: Prestressing strands are commonly used in pretensioned prestressed concrete bridge construction. Transfer length is an important
parameter for structural design. This paper presents a comparative study on strand transfer length provisions from Eurocode 2 and North
American practice, and identifies similarities and differences between both models. A database of measured transfer lengths according to sev-
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eral authors has been compiled and compared with predictions according to code provisions. The intervals of predictions are smaller than those
corresponding to the experimental results, and they are smaller when code provisions are more simplified. The interval from Eurocode 2
is greater than that from American Concrete Institute (ACI) code 318, which, in turn, is greater than the interval from AASHTO. The number
of underestimated cases is lower for Eurocode 2 because of the higher predicted values, but situations in which a short transfer length is un-
favorable are neglected by all models because they are not good predictions of shorter measured transfer lengths. When a transfer length estima-
tion criterion is based on an allowable free end slip, more cases are excluded from the ACI code 318 provisions. DOI: 10.1061/(ASCE)
BE.1943-5592.0000456. © 2013 American Society of Civil Engineers.
CE Database subject headings: Bridges; Prestressed concrete; Bonding; Effective stress; Predictions; North America; Europe; Standards
and codes.
Author keywords: Bridge; Prestressed concrete; Bonding; Effective stress.

Introduction length transmission length [European Committee for Standardiza-

tion (CEN) 2004].
The use of prestressing strands is commonplace in the construc- Transfer length is an important parameter for pretensioned con-
tion of pretensioned concrete structures and bridges. There are two crete structural design (Russell and Burns 1996; Barnes et al. 2003).
procedures for prestressing a concrete member through strands: post- In the precast prestressed concrete industry, obtaining a good product
tensioning and pretensioning. The manufacturing process for pre- within a short period of time is essential. Therefore, it is necessary to
tensioned concrete members by pretensioning includes tensioning achieve the required concrete compressive strength as soon as pos-
the prestressing strands between abutments using provisional end sible so that the member can accept the transfer of the prestressing
anchorages, casting concrete around the prestressing strands, and force at detensioning, and the member can be removed from the
releasing the strand tension once the concrete achieves sufficient bed. The accuracy of any attempt to check the actual material stresses
strength, thereby transferring the prestress force to the member. in the end region of pretensioned members depends upon the transfer
The prestressing force in the strands is transferred to the concrete length estimation. In addition, transfer length represents the first
by bond in the end regions of the member. In each end region, the portion of the development length in ACI 318 (anchorage length in
stress in the prestressing strand varies from 0 at the end of the Eurocode 2) over which the prestressing strand should be bonded
member to a constant maximum value (effective stress), which is so that a stress in the prestressing strand at nominal strength of
achieved at a certain distance from the member end. Fig. 1 offers an the member, fps , may develop.
idealization of the prestressing strand stress profile in a pretensioned Consequently, it is necessary to contemplate some implications
prestressed member after prestress transfer. for bridge designs according to strand transfer length:
According to the American Concrete Institute (ACI) code 318 1. A short transfer length increases stresses and the risk of crack-
provisions (ACI 2011), the distance over which the strand should ing by concrete splitting, bursting, or spalling in the end re-
be bonded to the concrete to develop the effective prestress in the gions. This may result in complete bond loss, especially if
prestressing strand is defined as transfer length. Eurocode 2 calls this there is no confining reinforcement (den Uijl 1995). In these
cases, it is possible to redevelop an effective prestressing
force by bond at a distance from the damaged location (Kasan
1
Associate Professor, Institute of Concrete Science and Technology and Harries 2011).
(ICITECH), Universitat Politècnica de València, 4G, Camino de Vera s/n, 2. A long transfer length reduces the available member length to
46022 Valencia, Spain (corresponding author). E-mail: jrmarti@cst.upv.es resist bending moment and shear, and therefore increases
2
Professor, Dept. of Civil Engineering, 4190 Bell Engineering Center, member cost.
Univ. of Arkansas, Fayetteville, AR 72701. E-mail: micah@uark.edu
Moreover, design strength provided by a pretensioned member
Note. This manuscript was submitted on July 21, 2012; approved on
December 11, 2012; published online on May 14, 2013. Discussion period shall be taken as the nominal strength multiplied by the strength
open until May 1, 2014; separate discussions must be submitted for in- reduction factors in sections within the transfer length and also
dividual papers. This paper is part of the Journal of Bridge Engineering, within the development length. If a critical section occurs within
Vol. 18, No. 12, December 1, 2013. ©ASCE, ISSN 1084-0702/2013/12- these regions, where the strand is not fully developed, failure may
1270–1280/$25.00. occur by bond slip (ACI 2011). Thus, web shear cracks, which

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 when a greater slip occurs. As a consequence, the longitudinal
contraction of the prestressing strand results in a radial expansion of
the tendon, which is known as the Hoyer effect (fib 2000; Barnes
et al. 2003).
Janney (1954) was one of the pioneers to research bond char-
acterization and its relation to the transfer length of prestressing
strands. The results obtained by Janney (1954) showed an inelastic
response of the surrounding concrete with radial microcracking
along almost the entire transfer length. On the other hand, according
to Guyon (1953), the hypothesis of uniform bond stress distribu-
tion is an unattainable limit because there will always be a zone
exhibiting elastic behavior along the transfer length. Cousins et al.
(1990) proposed an analytical transfer bond model that considers
both a longer plastic zone and a smaller elastic zone located at the
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Fig. 1. Idealization of the prestressing strand stress profile after pre- end of the transfer length. However, several authors have reported
stress transfer a plastic response along almost the entire strand transfer length
(Janney 1954; Barnes et al. 2003; Martí-Vargas et al. 2007b). Con-
sequently, authors and codes such as Eurocode 2 and ACI 318
generally assume bond models by considering uniform bond stress
extend into the transfer length, can cause a bond-slip failure of the distribution (linear variation of the prestressing stress; see Fig. 1)
prestressing strands (Reed and Peterman 2004). along the transfer length.
Strand transfer length depends on the properties of both the In order for equilibrium to occur, the prestressing strand force
prestressing strand and the surrounding concrete and also on sev- must be equal to the force developed in the prestressing strand over
eral design and manufacture parameters [International Federation the transfer length by assuming the uniform bond stress according
for Structural Concrete (fib) 2000; Precast/Prestressed Concrete to Eq. (1)
Institute (PCI) 2011]. Some of the most important properties and
parameters are concrete strength at the time of detensioning, level fs Ap ¼ Lt Pp Ut (1)
of prestress force at detensioning, concrete cover, strand spacing,
size of the cross section, type of strand, strand diameter, strand
where fs 5 effective stress (strand stress after transfer); Ap 5 cross-
surface condition (clean, oiled, rusted, or epoxy coated), detensioning
sectional area of the prestressing strand; Lt 5 transfer length; Pp
method (sudden or gradual), confining reinforcement around the
5 perimeter of the prestressing strand; and Ut 5 average bond stress
strand, concrete consolidation around strands, time-dependent
along the transfer length.
effects, and vertical strand location in the concrete section.
Based on Eq. (1), researchers have proposed several equations to
There is also no consensus as to the main parameters to be
predict transfer length based on experimental results and theoretical
considered in the models and equations predicting transfer length
studies. Normally, regression analyses and statistical models pro-
(Martí-Vargas et al. 2007b, 2012b). A perfect example of this is
vide descriptions of the effects of the aforementioned properties and
the case of the North American practice (ACI 318) (ACI 2011),
parameters on transfer length (Martí-Vargas et al. 2006a; García-
AASHTO load and resistance factor design bridge design speci-
Taengua et al. 2011). Most of these equations predicting transfer
fications (LRFD BDS) (AASHTO 2012), and Eurocode 2 (CEN
length take a parametric form in accordance with the structure of
2004). Provisions for transfer length are not a function of concrete
Eq. (2) (Martí-Vargas et al. 2007b)
strength in ACI 318 and AASHTO LRFD BDS, while Eurocode 2
provisions include concrete properties.   
fsxn Ap
This paper presents the findings of a research project that ex- Lt ¼ þ k2 × x × l (2)
amined the differences in predicted transfer length when using ðk1 pdÞUt
Eurocode 2 and codes typically used in North America. A carefully
selected database spanning a variety of experimental transfer length where (only an additional notation) fsx 5 prestressing strand stress;
results has been compiled. Based on the data collected, strand n 5 exponent; k1 5 perimeter factor (k1 5 4=3 for a seven-wire
transfer length predictions based on different provisions have been strand; and k1 5 1 for a circular cross section); d 5 nominal diameter
examined. of the prestressing strand; k2 5 adjustment constant; x 5 factor to
account for the type of release; and l 5 factor to obtain bound values
for transfer length.
Background: Transfer Bond Model and Strand Wan et al. (2002b) proposed the application of a top bar effect
Stress Changes factor, and Martí-Vargas et al. (2012a) reported the effects of
concrete composition on bond stress. An additional factor, j, for
For prestressing strands, there are three bond mechanisms (fib transfer length models has been proposed to account for time-
2000): adhesion, friction, and mechanical action. A very small slip dependent increases in transfer length (Caro et al. 2012) based on
destroys adhesion. Then, activation of the friction mechanism and strand stress changes relating to the manufacturing process of
mechanical action takes place, while radial compressive stresses pretensioned prestressed concrete members as follows: (1) strands
around the prestressing strand causes bond stresses due to the are tensioned in a casting bed from zero to the strand stress at jacking,
prestress transfer. These radial compressive stresses are the response fs, jack , which decreases to the strand stress at anchoring, fs,bed , by
of the surrounding concrete to both the strand diameter increase and seating at provisional strands anchoring; (2) the concrete member is
the displacement of the prestressing strand when a slip occurs. The cast around the strands and fs,bed diminishes to the strand stress just
mechanical action in prestressing strands notably differs from that in before prestress transfer, fs0 , because of strand relaxation losses; (3)
wires because their helical shape allows for increased bond stress at release, strands shorten and the surrounding concrete shortens

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 with them; prestress losses due to concrete elastic shortening range ACI 318
from fs0 to the initial effective stress just after prestress transfer,
Current ACI 318 provisions on transfer length first appeared in ACI
fsi , occurs in the central zone of the member (see Fig. 1); and (4)
code 318-63 (ACI 1963) and derive from Eq. (1) using (Tabatabai
several time-dependent prestress losses gradually occur by concrete
and Dickson 1993) fs 5 fse ; Ap 5 0:725pd 2 =4; Pp 5 4pd=3; and
creep and shrinkage and strand relaxation, and, consequently, ef-
Ut 5 2:76 MPa ð400 psi), resulting in (ACI 318, Section 12.9, the
fective stress changes from fsi to a final value of effective stress after
first part of Eq. 12-4)
allowing for all prestress losses, fse .
fse db
Lt ¼ ð fse in psiÞ (7a)
Code Provisions for Transfer Length 3,000

fse db
Eurocode 2 Lt ¼ ð fse in MPaÞ (7b)
20:7
According to Eurocode 2, Section 8.10.2 (CEN 2004), prestress may
be assumed to be transferred to the concrete by a constant bond where fse 5 effective stress in the prestressing strand after allowing
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stress, fbpt , as follows: for all prestress losses; and db 5 nominal diameter of the prestressing
strand.
fbpt ¼ hp1 h1 fctd ðtÞ (3) According to the ACI code 318-63 (ACI 1963) commentary, it is
worth noting that this relationship estimates average transfer length.
where hp1 5 coefficient that takes into account the type of tendon This equation remains to date in ACI code 318-11 (ACI 2011)
and bond situation at release (3.2 for 3- and 7-wire strands); h1 despite a considerable number of proposed modifications (Floyd
accounts for the tendon position during casting (1.0 for good bond et al. 2011). In addition, several authors consider that the use of the
conditions and 0.7 otherwise); and fctd ðtÞ 5 design value of strength term fsi in Eqs. (7a) and (7b) rather than fse for design purposes is
at time of release. more rational because transfer length is established at the release of
The basic transmission (transfer) length (lpt ) value is given by prestress (Shahawy et al. 1992; Deatherage et al. 1994).
As a reasonable limit for the higher transfer length values, Rus-
lpt ¼ a1 a2 fspm0 =fbpt (4) sell and Burns (1996) recommended Eqs. (8a) and (8b) for design
applications
where a1 accounts for the release procedure (1.00 for gradual release fse db
and 1.25 for sudden release); a2 5 tendon area factor (0.25 for Lt ¼ ð fse in psiÞ (8a)
2,000
tendons with circular cross sections and 0.19 for 3- and 7-wire
strands); f 5 nominal tendon diameter; and spm0 5 tendon stress
fse db
just after release. Lt ¼ ð fse in MPaÞ (8b)
The transfer length should be taken as the less favorable of two 13:8
values (lpt1 , lpt2 ), depending on the design situation
Fig. 3 shows the relationship between strand stress and the distance
lpt1 ¼ 0:8lpt (5) over which the strand is bonded to the concrete, as represented by
Eqs. (7a) and (7b). Fig. 3 includes the effects of considering fsi
rather than fse and of predicting transfer length by Eqs. (8a) and
lpt2 ¼ 1:2lpt (6) (8b), which implies Ut 5 1:84 MPa ð267 psiÞ.

Normally, the lower value is used to verify local stresses at pre-

stress transfer, whereas the higher value is used for ultimate limit
states.
The upper design value of transfer length is within the anchorage
length. Fig. 2 illustrates the strand stresses according to the Eurocode 2
transfer length model.
This model coincides with Model Code 2010 (MC-2010) (fib
2010), which also provides two values for the transfer length.
However, both models differ in relation to the obtained bound values
as follows:
• In the Eurocode 2 model, Eq. (4) initially computes a mean
transfer length value, and Eqs. (5) and (6) produce the lower
and upper bound values, respectively; the upper/lower ratio is
1:2=0:8 5 1:5.
• In the MC-2010 transfer length model, the action effect that needs
verifying in the design is considered by a factor ap2 , where
ap2 5 1 to calculate anchorage length when considering moment
and shear capacity, ap2 5 0:5 to verify the transverse stress in
anchorage zone, and the upper/lower ratio is 1=0:5 5 2. With a
nonspecified value of ap2 5 0:75 by averaging the established
values ap2 5 1 and ap2 5 0:5, corresponding to a mean transfer
length value, the calculation of the transfer lengths from MC-
Fig. 2. Strand stresses according to Eurocode 2 transfer length model
2010 and Eurocode 2 coincides.

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 1 fs0
dallowable ¼ fse db ðcustomary unitsÞ (10a)
6,000 Ep

1 fs0
dallowable ¼ fse db ðSI unitsÞ (10b)
41:4 Ep

It is possible to extend Eq. (9) by setting it equal to Eq. (4) by

considering the Eurocode 2 provisions as follows:

1 fs0
dallowable ¼ a1 a2 fspm0 =fbpt ðSI unitsÞ (11)
2 Ep

Eurocode 2 versus North American Practice

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There are similarities between the Eurocode 2 (CEN 2004) and ACI
318 (ACI 2011) provisions for transfer length: (1) both models
consider uniform bond stress; (2) transfer length depends directly on
Fig. 3. Strand stresses according to ACI 318 transfer length model the nominal strand diameter, which is also seen in AASHTO LRFD
BDS (AASHTO 2012); and (3) the effective stress after allowing
for all prestress losses ( fse in ACI 318; sp‘ in Eurocode 2) is the
maximum strand stress considered along the transfer length to
calculate development length. Table 1 summarizes the differences
Table 1. Differences between Eurocode 2 and ACI 318 Provisions for
Transfer Length between both models.

Parameter Eurocode 2 ACI 318

Influence of Concrete Strength
Strand stress Just after release ( fsi ) After all prestress losses ( fse )
Fig. 4 presents the predicted transfer length values of several pre-
Type of value Lower and upper Average value
stressing strand nominal diameters. Eqs. (4), (7a), and (7b) and the
bound values
AASHTO LRFD BDS (AASHTO 2012) provisions provide these
Concrete strength Yes No
lengths. To calculate transfer length, the following relationships
Tendon type Yes No
have been used: fs0 5 0:75fpu , where fpu is nominal strand strength
Tendon position Yes No
and is 1,860 MPa (270 ksi); fsi 5 0:9fs0 ; and fse 5 0:8fs0 . Because
Release procedure Yes No
Eurocode 2 includes the effects of concrete strength, specified
concrete compressive strengths of 50 MPa (7.25 ksi) and 100 MPa
(14.50 ksi) at 28 days of age were used for comparison.
On the other hand, the transfer length requirement mentioned in As seen in Fig. 4, transfer length decreases when concrete
the ACI 318 shear provisions (Section 11.3.4) is 50 strand diameters, strength increases for the lengths predicted from Eurocode 2. The
while the transfer length may be taken as 60 strand diameters simplified model from AASHTO LRFD BDS provides higher
according to AASHTO LRFD BDS (AASHTO 2012) provisions for transfer length values than the ACI 318 provisions. Similar transfer
prestressing strand development (Section 5.11.4.1). length values were obtained from the ACI 318 and Eurocode 2 when
using a specified concrete compressive strength at 28 days equal to
Allowable Free End Strand Slip 100 MPa (14.50 ksi).

Variation in strand stress along the transfer length at prestress

Data Provided from Tests
transfer involves slips between the strand and the surrounding
concrete. It is possible to use these slips as an indirect method to The transfer length may be determined experimentally, and over the
estimate transfer length (Martí-Vargas et al. 2007a). Anderson and years, there have been several experimental research programs ex-
Anderson (1976) used this method as a simple nondestructive as- amining the bond of prestressing strands (by way of example, see
surance procedure to monitor bond quality within precasting plants. references included in Table 2). There are several experimental
Guyon (1953) proposed the following equation for uniform bond methods frequently used to determine transfer length: the longitu-
stress distribution: dinal concrete surface strain profile (Russell and Burns 1997), the
prestressing strand end slip (Guyon 1953), the bond strength de-
dEp termination by push–pullout test (Hegger et al. 2007), and the
Lt ¼ 2 (9)
fs0 prestressing strand force at several cross sections (Martí-Vargas et al.
2006b, 2013).
where d 5 strand end slip; Ep 5 strand modulus of elasticity; and A data set of measured transfer lengths was compiled from an
fs0 5 strand stress immediately before prestress transfer. extensive review of the literature. All transfer lengths were measured
Several authors (Anderson and Anderson 1976; Petrou et al. using one of the three previously mentioned techniques. The data set
2000; Wan et al. 2002a) have established an allowable free end slip includes measured transfer lengths and establishes several require-
(dallowable ), which results in a transfer length equal to that computed ments for materials and manufacture parameters: nominal strand
by the ACI 318 provisions for transfer length. By setting Eq. (9) to be strength of 1,860 MPa (270 ksi), strand diameter of 12.5–13 mm
equal to Eqs. (7a) and (7b), the implied allowable end slip value by (0.49–0.51 in.), and initial strand stress level of 70–80% of the
Eqs. (10a) and (10b) is nominal strand strength.

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Fig. 4. Transfer length for several prestressing strand nominal diameters

Table 2. Transfer Lengths Measured by Several Authors Predicting Strand Transfer Length from
Reported transfer lengths, mm (in.)
Measured Parameters
Number
Reference of tests Minimum Average Maximum
The experimental results previously provided have been compared
with the theoretical predictions obtained from the Eurocode 2 and
Holmberg and Lindgren 4 318 (12.5) 502 (19.8) 673 (26.5) ACI 318 provisions [Eqs. (4), (7a), and (7b)], respectively. Fig. 6
(1970) shows the transfer lengths predicted from the Eurocode 2 provisions,
Dorsten et al. (1984) 8 533 (21.0) 683 (26.9) 864 (34.0) and Fig. 7 provides those from ACI 318 and also offers the AASHTO
Cousins et al. (1990) 20 813 (32.0) 1,262 (49.7) 1,880 (74.0) LRFD BDS prediction [60 × 12:7 5 762 mm ð30 in:Þ] as a reference.
Shahawy et al. (1992) 12 749 (29.5) 765 (30.1) 813 (32.0) As observed, the predicted transfer lengths from Eurocode 2 vary
Mitchell et al. (1993) 14 330 (13.0) 499 (19.6) 710 (28.0) from 650 to 300 mm (25.6–51.2 in.) (Fig. 6), whereas ACI 318 gives
Deatherage et al. (1994) 16 457 (18.0) 602 (23.7) 914 (36.0) predictions within a 600–800 mm (23.6–31.5 in.) interval (Fig. 7).
den Uijl (1995) 8 297 (11.7) 436 (17.2) 608 (23.9) This small interval is because ACI 318 does not consider concrete
Russell and Burns (1996) 34 406 (16.0) 748 (29.5) 1,118 (44.0) properties; indeed, only slight variations based on strand stress and
Rose and Russell (1997) 30 213 (8.4) 392 (15.4) 714 (28.1) diameter affect transfer length predictions for this model. The
Mahmoud et al. (1999) 8 350 (13.8) 469 (18.5) 600 (23.6) AASHTO reference appears as a top value (Fig. 7).
Oh and Kim (2000) 36 434 (17.1) 606 (23.9) 898 (35.4) With the Eurocode 2 predictions (Fig. 6), the higher measured
Martí-Vargas et al. 12 400 (15.7) 533 (21.0) 650 (25.6) values by Cousins et al. (1990) can again be observed. However,
(2007b) Eurocode 2 predicted transfer lengths using Cousins et al. data that
are within a typical range of values.
Figs. 8–10 show the transfer length ratios (calculated/measured)
obtained from Eurocode 2, ACI 318, and AASHTO, respectively,
A total of 12 different sources reporting all the aforemen- versus the measured transfer lengths. These figures also depict the
tioned input variables and spanning a variety of practical transfer average value and the standard deviation of these ratios. For all cases,
length prediction situations were selected for the study, which the ratios decrease as measured transfer lengths increase. The
resulted in 202 transfer length samples. Table 2 summarizes this obtained ratios are grouped closer together when the transfer length
data, and Fig. 5 shows the measured transfer length versus the models are simplified. The results are grouped closest together when
concrete compressive strength at the time of prestress transfer for the AASHTO equation is used, followed by the ACI 318 and then the
this data. Eurocode 2 equations. A total of 80% of the results are within the
In this data set, concrete strength at prestress transfer (fci9 ) covers corresponding average 6 SD range for all three models, although
a wide range, from 20 to 55 MPa (2.9–8 ksi). In general, transfer practically all the measured transfer lengths by Cousins et al. (1990)
length decreases when f9ci increases. Fig. 5 includes trend lines of are excluded from these ranges for being greater, and some results
the test results for some sources showing this relationship. The obtained by den Uijl (1995) and Rose and Russell (1997) are ex-
range of measured transfer lengths for a single concrete compres- cluded because they are smaller.
sive strength is ample. Furthermore, the range of concrete com- The higher ratios correspond to Eurocode 2, followed by
pressive strength values varies considerably for a single transfer AASHTO and ACI 318. Consequently, the number of underestimated
length. The high transfer length results obtained by Cousins et al. transfer lengths (ratio , 1) is smaller for Eurocode 2. Practically the
(1990), which may have been caused by additional unreported only underestimated lengths are the measured transfer lengths by
factors such as strand surface condition, are an anomaly in relation Cousins et al. (1990). However, AASHTO and ACI 318 also un-
to the other test results. derestimate the measured transfer lengths obtained by other authors.

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Fig. 5. Measured transfer length versus concrete compressive strength

Fig. 6. Predicted transfer lengths from Eurocode 2 versus measured transfer lengths

Based on the transfer length predicted from the measured the upper bound value from the North American practice is according
parameters, Fig. 11 depicts the average value 6 SD for the three to Eq. (8), proposed by Russell and Burns (1996). As observed, the
models and also includes the experimental values. The predicted lower and upper bound values from Eurocode 2 range with the
values are greater than the experimental value in all cases. Once interval average value 6 SD of the Eurocode 2 predictions. On the
again, it can be observed that the higher value corresponds to other hand, the lower bound value from Eurocode 2 coincides with
Eurocode 2, followed by AASHTO, which, in turn, comes before the average value from AASHTO.
ACI 318. The intervals’ average value 6 SD are smaller than those Fig. 11 also shows that both the upper values are greater than
corresponding to the experimental results, and they are smaller when those of the greater measured transfer lengths (average value
code provisions are more simplified. The interval from Eurocode 2 is 1 SD). However, no model offers good predictions of the shorter
greater than the interval from ACI 318, which, in turn, is greater than measured transfer lengths (average value 2 SD). The North
that from AASHTO. American practice does not offer this prediction, and the lower
Fig. 11 offers the lower and upper bound values of predicted bound value from Eurocode 2 is much greater than the shorter
transfer lengths, when available. The lower and upper bound values measured transfer lengths. This lower bound value is also greater that
from Eurocode 2 are according to Eqs. (5) and (6), respectively, and the average measured transfer lengths. Therefore, situations in which

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Fig. 7. Predicted transfer lengths from ACI 318 versus measured transfer lengths

Fig. 8. Transfer length ratios calculated/measured from Eurocode 2

a short transfer length is unfavorable are neglected, as are the predicted from measured parameters according to ACI 318 have
verifications of local stresses at prestress transfer. been plotted in Fig. 13.
Both figures show the percentages of the results included in each
sector. As observed in the figures, there is a wide range of end slips
Predicting Allowable Free End Strand Slip
that correspond to the same transfer length. Moreover, there is a wide
Based on the compiled experimental data set, the sources reporting range of transfer length values for a given end slip.
measured values of transfer length and free end strand slip for Figs. 12 and 13 also depict that when the measured transfer length
comparison purposes have been selected. Figs. 12 and 13 depict the is shorter than the predicted transfer length, the allowable free end
measured transfer lengths versus the corresponding free end slip strand slip limit is exceeded in 0.6% of the cases by applying the
recorded in beams by several authors. The allowable free end slip Eurocode 2 provisions and in 2.8% of the cases by applying the ACI
according to Eq. (11) and the average transfer length value predicted 318 provisions. On the other hand, for the measured free end slips
from measured parameters according to Eurocode 2 have been that are less than the allowable free end strand slip, measured transfer
plotted in Fig. 12. Analogously, the allowable free end slip according lengths are longer than the predicted transfer length in 0.6% of the
to Eqs. (10a) and (10b) and the average transfer length value cases by applying the Eurocode 2 provisions and 4.6% of the cases

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Fig. 9. Transfer length ratios calculated/measured from ACI 318

Fig. 10. Transfer length ratios calculated/measured from AASHTO

by applying the ACI 318 provisions. Consequently, the use of an strand stress just after release in Eurocode 2 and after all the prestress
assurance procedure for bond quality based on a limit value for the losses in ACI 318, type of transfer length value (bound values in
allowable free end slip is not completely reliable, and these criteria Eurocode 2 and average values in ACI 318), and concrete strength
exclude more cases when applying the ACI 318 provisions. at release, tendon type, tendon position, and release procedure
(parameters only included in Eurocode 2).
The experimental data used in the study was composed of mea-
Conclusions sured transfer lengths determined by several authors. These results
were compared with the theoretical predictions from Eurocode 2
This research offers a comparative study on transfer length provi- and North American practice. The predicted transfer lengths from
sions from Eurocode 2 and North American practice. Both models ACI 318 were very similar [600–800 mm (23.6–31.5 in.)], which
consider a uniform bond stress, strand diameter, and the effective was expected because this model considers only the strand param-
stress after allowing for all prestress losses for calculating de- eters. The predicted values from Eurocode 2 vary vastly from 650
velopment length. The differences between the models include to 1,300 mm (25.6–51.2) due to the fact that the model considers

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Fig. 11. Typical transfer length values

Fig. 12. Transfer length versus free end slip with Eurocode 2 references

concrete properties. On average, the predicted values are greater value from Eurocode 2 is similar to the average AASHTO value.
than the experimental values in all the transfer length models. However, situations in which a short transfer length is unfavorable
Higher values correspond to Eurocode 2 (it would be a good es- are neglected because no model offers good predictions of shorter
timation of the longer measured transfer lengths), followed by measured transfer lengths. The North American practice does not
AASHTO and then ACI 318 (the best prediction of the average offer this prediction, and the lower bound value from Eurocode 2 is
experimental values). greater than the measured transfer lengths.
Predicted transfer length values result in smaller ranges than The transfer length ratio (calculated/measured) according to
those corresponding to the measured transfer lengths, and these Eurocode 2 and North American practice shows a tendency in which
ranges are smaller when code provisions are more simplified. The these ratios decrease when the measured transfer lengths increase.
range from Eurocode 2 is greater than the range from ACI 318, The number of underestimated cases is smaller for Eurocode 2 be-
which in turn is greater than that from AASHTO. cause of the higher resulting ratios. Finally, the use of a transfer
The Eurocode 2 bound values practically range the interval av- length criterion based on the allowable free end slip excludes more
erage value 6 SD of the Eurocode 2 predictions. The lower bound cases when applying the ACI 318 provisions.

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Fig. 13. Transfer length versus free end slip with ACI 318 references

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