Table 9. Research studies with rectangular specimens included
in the correlation with FHWA equations.

Organization Strand Dia. | Transfer |. Development
(in) Length Length
Data Points | Data Points
Used Used
FHWA Phase I 3/8 32 8
_ 05 32 8
0.6 32 8
Preston and Janney 0.5 2 0
Louisiana State Univ./ 3/8 4 0
Univ. of New Orleans :
McGill University. 0.5 28 0
0.62 24 0
North Carolina State 3/8 . 24 7
University 0.5 48 10
0.6 28 5
Univ. of Oklahoma 0.5 36 18
Univ. of South Florida/ 0.5 Special 5 0
Univ. of Illinois at
Chicago
Univ. of Texas at Austin 0.5 18 0
for TxDOT 0.6 16 oO”
Totals 329 64

53

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FOREWORD

This report, 4 New Development Length Equation for Pretensioned Strands in Bridge Beams and
Piles, presents the results of research conducted by the Federal Highway Administration
(FHWA) at the Turner-Fairbank Highway Research Center in McLean, Virginia, with assistance
from personnel representing Construction Technology Laboratories, Inc.

This research was conducted to investigate the accuracy of the current American Association of
State Highway and Transportation Officials (AASHTO) equations for the transfer and
development of pretensioned strands. Research results indicated that the AASHTO equation was
unconservative for members constructed with normal-strength concrete. FHWA researchers
formulated new transfer and development length equations based on FHWA’s research results,
and then correlated these equations with results from 16 other research studies to make sure that
the equations would be representative of the total applicable data to-date. Guidelines for the use
of these equations for beams and piles are also provided.

; Au b VIMY

Charles J. Nemmers, P.E.

Director

Office of Engineering
Research and Development

PROTECTED UNDER INTERNATIONAL COPYRIGHT
ALL RIGHTS RESERVED.

NATIONAL TECHNICAL INFORMATION SERVICE
U.S. DEPARTMENT OF COMMERCE

R iced trom
best available copy.

NOTICE

This document is disseminated under the sponsorship of the Department of Transportation in the
interest of information exchange. The United States Government assumes no liability for its
contents or use thereof. This report does not constitute a standard, specification, or regulation.

The United States Government does not endorse products or manufacturers. Trade and
manufacturers’ names appear in this report only because they are considered essential to the
object of the document.


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f, value was assumed to equal the one that was provided. The parameters f,, and f*,, were
seldom provided, and these parameters were calculated using structural analyses.

FHWA researchers performed the same structural analyses that they performed for the FHWA
Phase III (full-size beams) study, using the two computer programs developed by Dr. Beshah and
Dr. Gagarin.

For the first program, inputs were required for concrete strength, modulus of elasticity, and
modulus of rupture; properties of the strand; and loading and cross-section information for a
given development length test. The load and deflection data from the test was then used in
combination with the aforementioned input items in an iterative approach that yielded the
effective prestress force, f,..

The second program was used to determine f*,,. For the second program, all of the inputs and
values determined by the first program were used, as well as the rneasured value of the external
concrete strain of the top fiber (compression fiber) at the load point, if it was available. As long
as the measured value of the external concrete strain of the top fiber was available, then it was
used with the other inputs in an iterative approach to determine the stress and strain of the bottom
strands at failure of the member (f*,, and €,,, respectively).

If FHWA researchers did not receive data on the external concrete strain of the top fiber, then the
second computer program would not work. Therefore, Dr. Beshah and Dr. Gagarin created a
third computer program, which used the load and deflection data in a complex iterative approach
that yielded f*,, and €,,. (Note that running the computer programs to determine the f,, and f*,,
values was a lengthy process that took approximately 3 hours per computer run.)

STATISTICAL COMPARISONS

In chapter 3, Equation (7) was presented as a best-fit equation for transfer length, and Equation
(8) was presented as a best-fit equation for flexural bond length. When these two equations were
combined, resulting'in Equation (9), it was a best-fit line for overall development length. These
equations were considered best fit with respect to the FHWA full-size girder data. Once the data
were assembled from all of the other studies, including the FHWA rectangular specimen data,
then FHWA researchers began determining whether these equations were representative of all of
the data. :

During this process of correlating Equations (7) through (9) with all of the data from other
studies, a few other re-examinations and re-evaluations were conducted. The issue of unit weight
as a possible parameter in Equations (7) through (9) was re-examined; the idea of using the area
of strand rather than the diameter of strand as a parameter in the equations was re-evaluated; and
the possibility of using log, natural log, semi-log, and natural semi-log as equation types was also
evaluated.

FHWA researchers re-examined the unit weight as a potential parameter. They reviewed all of

the other studies used in the correlation to find any measured values of unit weight. These values
were scarce. The concrete mixes for each of the studies were then examined to see whether the

62


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73


results from other studies as well. This equation has been correlated with research results from
other studies.

Chapters 2 and 3 will describe the FHWA Phase II research results in detail and show how those
results were used to develop the new equation. Chapters 4 and 5 will discuss the correlation of
the new equation with research results from other studies and will draw final conclusions based
on those correlations.


39.

40.

41.

42.

43,

44.

45.

46.

47.

48.

Engineering of Purdue University and the Indiana Department of Transportation, June
1993.

O.A. Abdalla, J.A. Ramirez, and R.H. Lee. Strand Debonding in Pretensioned
Beams—Precast Prestressed Concrete Bridge Girders With Debonded Strands, Part 2
Final Report: Simply Supported Tests, Publication No. FHWA/INDOT/JHRP-92-25,
School of Civil Engineering of Purdue University and the Indiana Department of
Transportation, June 1993

M.A. Issa, R. Sen, and A. Amer. “Comparative Study of Transfer Length in Fiberglass
and Steel Pretensioned Concrete Members,” PC/ Journal, Vol. 38, No. 6,
November/December 1993, pp. 52-63.

1.0. Unay, B. Russell, N. Burns, and M. Kreger. Measurement of Transfer Length on
Prestressing Strands in Prestressed Concrete Specimens, Publication No. FHWA/TX-
91+1210-1, Center for Transportation Research at the University of Texas at Austin,
Austin, Texas, March 1991.

B.A. Lutz, B.W. Russell, and N.H. Burns. Measurement of Development Length of 0.5-
inch and 0.6-inch Diameter Prestressing Strand in Fully-Bonded Concrete Beams,
Publication No. FHWA/TX-92+1210-3, Center for Transportation Research at the
University of Texas at Austin, Austin, Texas, February 1992.

L.G. ZumBrunnen, B.W. Russell, and N.H. Burns. Behavior of Statically Loaded
Pretensioned Concrete Beams With 0.5-inch Diameter Debonded Strands, Publication
No. FHWA/TX-92+1210-4, Center for Transportation Research at the University of
Texas at Austin, Austin, Texas, January 1992.

B.W. Russell and N.H. Burns. Design Guidelines for Transfer, Development and.
Debonding of Large Diameter Seven Wire Strands in Pretensioned Concrete Girders,
Publication No. FHWA/TX-93+1210-5F, Center for Transportation Research at the
University of Texas at Austin, Austin, Texas, January 1993.

B.W, Russell, N.H. Burns, and L.G. ZumBrunnen. “Predicting the Bond Behavior of
Prestressed Concrete Beams Containing Debonded Strands,” PCI Journal, Vol. 39, No. 5,
September/October 1994, pp. 60-77.

B.W. Russell and N.H. Burns. “Fatigue Tests on Prestressed Concrete Beams Made With
Debonded Strands,” PC/ Journal, Vol. 39, No. 6, November/December 1994, pp. 70-88.

B.W. Russell and N.H. Burns.-““Measured Transfer Lengths of 0.5 and 0.6 in Strands in
Pretensioned Concrete,” PCI Journal, Vol. 41, No. 5, September/October 1996, pp. 44-
65.

S.P. Gross and N.H. Burns. Transfer and Development Length of 15.2 mm (0.6 in)
Diameter Prestressing Strand in High Performance Concrete: Results of the Hoblitzell-

122


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97


CHAPTER 3: FORMULATION OF A NEW DEVELOPMENT LENGTH EQUATION
FROM FHWA RESULTS

As was described in the previous chapter, results from the FHWA development length
experimentation on full-size girders indicated that the existing AASHTO equation was
unconservative and that the Buckner equation was inconsistent. Therefore, a new development
length equation was needed. FHWA decided to formulate the equation based on the FHWA full-
size girder research results, and.then correlate this equation with other research results to make ~
sure that the equation would be representative of the total applicable data to date. This chapter
will describe the formulation of the new equation based on the FHWA full-size girder research
results.

NEW TRANSFER LENGTH EXPRESSION

As was previously described in chapter 1, the transfer length is a component of the development
length. However; it is also a stand-alone parameter because of its use in the shear provisions of.
the AASHTO Specifications and the ACI Building Code. In these provisions, the transfer length
of the strand is used to determine the component of prestressing force in a draped (inclined)
strand that can be used to resist shear. Therefore, it was important to have.an expression for
transfer'length that could be used independent of the total development length expression.

A number of parameters were investigated for possible use in the new transfer length equation.
These included:

Concrete compressive strength-at 28 days, (f”,). -
Square root of concrete compressive strength at 28 days, (Vf’,).
Concrete compressive strength at transfer of prestress, (f’,,).
Square root of concrete compressive strength at transfer of prestress, (Vf’,,).
Concrete modulus of elasticity at 28 days, (E,).
Concrete modulus of elasticity at transfer of Prestress, (E,)-
Concrete unit weight, (w,). :
Prestressing strand diameter, (D).

- Area of prestressing steel strand, (A,*). >
Stress in prestressing strand prior to transfer of prestress, (he
Effective prestress, (f,,).

rr  ?

These parameters were investigated initially by inspecting the data and then evaluating the most
promising parameters, which were evaluated along with the measured 28-day values of transfer
length using regression analyses. It should be noted that the unit weight of the concrete was
examined, but it was determined that there was not enough variation of the unit weight within the
FHWA girder study to include it as a ‘variable.

Regression analyses are fe statistical studies of relationships between variables.°” Before doing
regression analyses, researchers plotted different combinations of the variables’ measured values.
As the FHWA researchers plotted data, it was apparent that the relationship between some of the
variables was approximately linear. They performed straight-line regression analyses to test the
assumption that the relationship was of the following form:

CF
33 | Preceding page blank


objective of the study was to develop design guidelines for transfer length, development length,
and debonding for uncoated steel strands in pretensioned concrete beams.

The sizes of the rectangular specimens varied from 127 mm (5 in) high x 102 mm (4 in) wide to
330 mm (13 in) high x 127 mm (5 in) wide, and contained either 12.7-mm- (0.5-in-) or 15.2-mm-
(0.6-in-) diameter strands spaced primarily at 50.8 mm (2 in). Transfer length was determined for
these rectangular specimens.

The full-size, AASHTO-type I-girders ranged in size from 559 mm (22 in) high to 1016 mm (40
in) high, both with and without composite decks. The debonding length, pattern, and cut-off
(abrupt versus gradual) were varied, and beams with fully-bonded strands were included for
comparison. The beams contained multiple 12.7-mm- (0.5-in-) or 15.2-mm- (0.6-in-) diameter
strands, spaced at 50.8 mm (2 in). All of the beams underwent static loading to failure, but some
of the beams experienced fatigue loading prior to the static loading to failure. Transfer and
development lengths were determined for all of the girders.

Only data from members with fully-bonded strands were used for the correlation with the new
FHWA equations. Transfer length results from 17 rectangular specimens, and transfer and
development length results from 10 full-size, AASHTO-type I-girders were used in the
correlation. (See references 41 through 47.)

University of “Texas at Austin—Louetta Road Overpass Project

In July 1993, FHWA and the Texas Department of Transportation, in conjunction with the
University of Texas at Austin, signed a cooperative agreement for the Louetta Road Overpass
High Performance Concrete (HPC) Bridge Project. This agreement included, among other items,
two designs of the two parallel bridges that made up the Louetta Road Overpass: one design with
normal concrete and the other design with HPC. The design for the HPC option involved the use
of 15.2-mm- (0.6-in-) diameter pretensioned strands at a spacing of 50 mm (1.97 in) in a new
beam shape—the U-beam.

At the time of the design, the FHWA 1988 memorandum was in effect, and this placed a
moratorium on the use of 15.2-mm- (0.6-in-) diameter strands and restricted the center-to-center
strand spacing to four times the diameter of the strand. For 15.2-mm- (0.6-in-) diameter strands,
this spacing restriction would have resulted in a spacing of 61.0 mm (2.4 in). Therefore, research
was needed to demonstrate that the 15.2-mm- (0.6-in-) diameter strands could be used
successfully at 50-mm (1.97-in) spacing in a beam constructed with the same concrete that would
be in the actual bridge beams.

Researchers first contemplated testing a U-beam containing the full complement of 15.2-mm-
(0.6-in-) diameter strands. However, because of the capacity limitations of conventional
structural laboratories (such as the Ferguson Laboratory at the University of Texas at Austin), a
U-beam with the full complement of strands (more than 50 strands) could not be tested to failure.
Therefore, a deep beam was designed that would simulate the flexural and bond behaviors of the
U-beams. The deep beam chosen was a solid rectangular section and was called the Hoblitzell-
Buckner beam, named after its designers, Jim Hoblitzell of FHWA and Dale Buckner of Virginia

58


were also results obtained from this program. The results from these two computer programs are
provided in tables 1, 6, and 7. Table 1 provides f,, values determined from the structural analyses
(listed as “actual f,,”), while tables 6 and 7 provide f*,, and €,, values determined from the
structural analyses and are termed “actual f*,,” and “actual €,,.” Table 6 provides the values for
members constructed with normal-strength concrete (compressive strength between 34.4 MPa
and 44.8 MPa [5 ksi and 6.5 ksi}), while table 7 provides the values for members constructed
with high-strength concrete (compressive strength between 68.9 MPa and 89.6 MPa [10 ksi and
13 ksi]). .

In general, the strains in the strands at flexural failure for the non-composite girders (girders
alone) were very close to the yield point of the strand, 0.010 mm/mm (0.010 in/in). This
contrasted with the strains in the strands at flexural failure for the composite girders (girders with
decks), where the strains were greater than or equal to 0.030 mm/mm (0.030 in/in). This
difference in strain values was first noted by Buckner” and is significant for two reasons. First,
the strand that meets ASTM A 416” is guaranteed to be able to sustain an elongation of 3.5
percent, which is equivalent to a strain of 0.035 mm/mm (0.035 in/in). Therefore, as the strain in
the strand approaches 0.035, the development length test is approaching the capacity of the
strand. Second, engineers are familiar with the property of all materials whereby as a material
elongates in one direction, that elongation is accompanied by contraction in the transverse
direction of the material. This is the basis for the familiar Poisson’s ratio. This property applies
to strand. As the strand elongates to a strain of 0.030 or greater, then it contracts in diameter.
This contraction is in a direction that pulls the strand away from the concrete/strand interface, so
the more the strand elongates, the more the cross-sectional dimension contracts, and the potential
for bond worsens. Therefore, the strains in the strands indicated that the worst-case scenario for
bond of strands had been tested.

29


method. FHWA researchers had to recalculate the transfer lengths (from the other studies) that
did not use the 95-percent plateau method so that they could accurately compare data from all the
studies. This included the FHWA Phase I (rectangular specimens) study, which had been
determined. using the 100-percent plateau method.

FHWA researchers, to determine the transfer lengths by the 95-percent plateau method, used the
following process. First, FHWA researchers gleaned concrete strain data from all of the reports
and articles for the studies. (Frequently, the strain plots were available in an appendix of a
report.) Next, the principal investigators for the research studies in question were contacted and
were asked to provide electronic-files of the concrete strain data. If the concrete strain plots or
electronic files of the concrete strain data were available, then FHWA researchers calculated the
100-percent and 95-percent plateau values.

The 95-percent plateau values were physically plotted on the concrete strain graphs and the
transfer lengths were then determined from the graphs. (In one instance, a within-study
correlation was established between the 100-percent plateau transfer lengths and the 95-percent
plateau transfer lengths. This correlation was used to calculate the remaining 95-percent transfer
lengths for that study.) Although this process was time-consuming, it resulted in uniformly
determined values of transfer length that could be correlated with one another:

Development Length Analysis

To correlate the development length results from other studies with the new FHWA development
length equation, the parameters used directly in the new equation had to be obtained from the
other studies’ results. Specifically, the parameters fell into two categories: parameters that were
provided in the study’s associated literature, and parameters that had to be determined.

The parameters that were directly in the new equation were f,,, f., f,., f.. and D. If these five
parameters were provided in the study’s associated literature, then the FHWA researchers
performed the correlation. However, if these five parameters were-not directly provided in the
study’s associated literature, then those parameters had to be either obtained from the principal

investigator, assumed, or calculated using structural analysis.

In general, if any of the five parameters were missing, FHWA researchers then contacted the
principal investigator, if at all possible, and requested the information. For a variety of reasons,
sometimes that information was available, sometimes it was not. If the information was not
available, then FHWA researchers were required to assume reasonable values for the missing
parameters or perform structural analysis, or both. _

The. strand diameter, D, was always provided in the literature, and the parameter f,, was usually
provided in the literature. If £, was not provided, then that parameter was assumed to equal 0.75
f,, (where f”, is the ultimate stress of the prestressing steel), which is the maximum stress
allowed prior to transfer for low-relaxation strands in pretensioned members, as stated in Article
9.15.1 of the AASHTO Specifications.”

FHWA researchers wanted both the design and actual values of f”, to be able to correlate the
data. Usually both of these fc values were provided, but if only one was provided, then the other

61


. The flexural failures are shown by the circular symbols. Flexural failures are acceptable
(good) failure types because there is warning (excessive deflection and cracking) before
the failure.

. The combination failures are shown by the diamond symbols. This is when flexural
failure occurred at the same time as slip/shear failure. These combination failures
indicated that the embedment length being tested was the exact development length.

Each figure includes all data (data from rectangular specimens as well as full-size beams). Along
the y-axis, the actual measured embedment lengths are plotted. Along the x-axis, the
development lengths calculated by a given development length equation are plotted. In the
figures, the lines represent the cases in which the measured embedment length equaled the
calculated development length using the given equation.

As seen in these figures, if a slip/shear failure fell above an equation line, the equation was
unconservative. It was unconservative because a slip/shear failure indicated that the development
length being tested was too short. Therefore, if the development length being tested was too
short, yet the equation predicted a value for development length even shorter than the one being
tested, then the equation predicted a development length that was too short. Therefore, the
development length predicted from the equation was unconservative.

Figure 35 represents two equations: the AASHTO equation and the line representing 1.6 times
the AASHTO equation line (as prescribed by the 1988 FHWA Memorandum“). Many
slip/shear failures fell above the AASHTO equation, illustrating that this equation is
unconservative.

In chapter 1, the AASHTO equation was presented as a reasonable mean. It is evident from
figure 35 that the AASHTO development length equation represents an average equation for the
data points and not a conservative equation.

A portion of the development length data is shown again with the AASHTO equation and the
line representing 1.6 times the AASHTO equation in figures 36 and 37, with the data grouped by
concrete compressive strength. The data with concrete strengths between 34.4 and 48.2 MPa
(5000 and 7000 psi) are seen in figure 36, while figure 37 illustrates the data with concrete
strengths between 55.1 and 68.9 MPa (8000 and 10,000 psi).

For the normal-strength concrete data shown in figure 36, the AASHTO equation is
unconservative, with many slip/shear failures falling above the equation line. As can be seen in
this same figure, the line representing the AASHTO equation multiplied by 1.6 is reasonably
conservative, with only one slip/shear failure falling on this line.

For the high-strength concrete data shown in figure 37, both equations are conservative.
However, the line representing 1.6 times the AASHTO equation is overly conservative. It
requires a much longer development length than is needed. It provides no benefit (credit) to the
designer for using high-strength concrete because it is simply a multiplier of an equation that
provides no benefit (credit) for using high-strength concrete.

98


15.

16.

17.

18.

19.

20.

21.

22.

23.

24,

25.

26.

S.N. Lane. “Development Length of Uncoated Prestressing Strand,” Proceedings of the
12th Structures Congress, Vol. 1, American Society of Civil Engineers, Atlanta, Georgia,
April 1994, pp. 624-629. .-

S.N. Lane. “Development Length of Epoxy-Coated Prestressing Strand,” Proceedings of
the 12th FIP Congress, Vol. 2, Federation Internationale De La Precontrainte,
Washington, DC, May/June 1994, pp. J12-J15.

C.D. Buckner. An Analysis of Transfer and Development Lengths for Pretensioned
Concrete Structures, Publication No. FHWA-RD-94-049, Federal Highway
Administration, Washington, DC, December 1994.

U.S. Department of Transportation, Federal Highway Administration Memorandum,
“Prestressing Strand for Pretension Applications Revisited,” May 8, 1996.

“Standard Specification for Steel Strand, Uncoated Seven-Wire for Prestressed
Concrete,” ASTM A 416-90a, /990 Annual Book of ASTM Standards, Vol. 01.04,
ASTM, Conshohocken, Pennsylvania. .

B.W. Russell and G.A. Paulsgrove. “Fundamental Mechanisms for the Development of
Pretensioned Strands,” School of Civil Engineering and Environmental Science at the
University of Oklahoma, Norman, Oklahoma, July 1996.

R. Johnson and G. Bhattacharyya. Statistics: Principles and Methods, John Wiley &
Sons, New York, Revised Printing, 1985.

TableCurve 2D for Windows Automated Curve Fitting Software User's Manual, Jandel
Scientific, San Rafael, California, 1994.

T.E. Cousins, J.M. Stallings, and M.B. Simmons. “Effect of Strand Spacing on
Development of Prestressing Strand,” Project No. 65308, Auburm University, Auburn,
Alabama, August 1993. .

M.B. Simmons. “Transfer and Development in Pretensioned, Prestressed Concrete
Girders Using % inch Diameter Strand,” Dissertation for Auburn University, Auburn,
Alabama, December 1995. .

P.B. Shing, D. Cooke, D.M. Frangopol, M.A. Leonard, M.L. McMullen, and W. Hutter.
“Colorado Showcase on HPC Box-Girder Bridge: Development and Transfer Length
Tests,” Proceedings of the PCI/FHWA International Symposium on High Performance
Concrete, Precast/Prestressed Concrete Institute, Chicago, IL, October 1997, pp. 705-716.

D.E. Cooke, P.B, Shing, and D.M. Frangopol. Colorado Study on Transfer and
Development Length of Prestressing Strand in High Performance Concrete Box Girders,
Colorado. Report No. CDOT-DTD-R-98-7, Department of Civil, Environmental, and
Architectural Engineering of the University of Colorado at Boulder and the Colorado
Department of Transportation, Denver, Colorado, July 1998.

120


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TABLE OF CONTENTS

Chapter Page
1. INTRODUCTION AND BACKGROUND ...........0 0000s c cence eee eens 1
WHAT IS DEVELOPMENT LENGTH? . -1
CURRENT AASHTO EQUATION ...... 23
FHWA 1988 MEMORANDUM ........... 24
HISTORY OF THE AASHTO EQUATION .. 5
RESEARCH STUDIES .................. -.6
FHWA 1996 MEMORANDUM ........... 0600 ccc ccc cence een eee 8
FORMULATION OF NEW DEVELOPMENT LENGTH EQUATION
AND CONTENTS OF THIS REPORT .......... 60.2... c cece eee aee 8
2. FHWA PHASE II RESEARCH STUDY RESULTS ..................20.005. 11
DESCRIPTION OF MEMBERS
Beams
Prestressing Strand ..
Concrete ........... ee
INSTRUMENTATION ...... 0.02. c cece tet eee ee
Mechanical Gauge Points
End Slip................
Jacking Force .. ee
Loads .. 1... eee eee tenet t ene
Electrical Resistance Strain Gauges .............0.0 0c eee eee 15
Deflection ............... 000000 ... 16
Other Measurements ... 16
TRANSFER LENGTH RESULTS. ....... 2.0000 e ccc een ene ee 16
DEVELOPMENT LENGTH RESULTS ............6.. 000 c eee eee 22
STRUCTURAL ANALYSIS ... 0.0.0.0 cee eee ee 24
3. FORMULATION OF A NEW DEVELOPMENT LENGTH EQUATION
FROM FHWA RESULTS .... 2.2.60. occ nnn ence ene 33
NEW TRANSFER LENGTH EXPRESSION ...... ».33
NEW FLEXURAL BOND LENGTH EXPRESSION .. 36
NEW DEVELOPMENT LENGTH EXPRESSION .................-4- 40
4. CORRELATION OF NEW DEVELOPMENT LENGTH EQUATION WITH

OTHER RESEARCH RESULTS
BREADTH OF ALL STUDIES ..
DATA REQUIREMENTS FOR CORRELATION OF OTHER
RESEARCH RESULTS WITH NEW EQUATION ............-...5-5- 45

Concrete . 46
Prestressing Strand .......... 6.00 c cee cence nent ene ents 46
Structural Member Types ............... 000 e eee eee ee eeee 46

Measurements .......... 0.000 cece eee ence nett een nee 47

iii


FHWA researchers decided to modify Equation (6) slightly by rounding-off the values of the
constants to obtain:

-21 (1)

and then to adopt Equation (7) as the proposed transfer length expression pending correlation
with data from other studies. It should be noted that Equation (7) was presented as a potential
transfer length equation in a progress report to the AASHTO Technical Committee on Concrete
(AASHTO Committee No. T-10) on May 13, 1996 in Philadelphia, PA.

NEW FLEXURAL BOND LENGTH EXPRESSION

The flexural bond length represents the additional bond length needed beyond the transfer length
to support the ultimate strength of the member. It is not a stand-alone expression, but rather a
major portion of the development length. The following parameters were investigated for
possible use in the flexural bond length expression:

Concrete compressive strength at 28 days, (f°).

Square root of concrete compressive strength at 28 days, (v’ P,).
Concrete modulus of elasticity at 28 days, (E,).

Concrete unit weight, (w,).

Depth of concrete rectangular stress block, (a).

Prestressing strand diameter, (D).

Area of prestressing steel strand, (A,*).

Effective prestress, (f,,).

Stress in prestressing strand at ultimate strength of the member, (f*.,).
Strain in prestressing strand at ultimate strength of the member, (€,,).

It should be noted that the unit weight of the concrete was examined, but it was determined that
there was not enough variation of the unit weight within the FHWA girder study to include it as a
variable. The rest of the parameters were investigated initially by inspection of data and then the
most promising parameters were numerically evaluated along with the “measured” values of
flexural bond length. There is no way to exactly measure the flexural bond length. The term
“measured flexural bond length” means that for a given end of a beam, the measured transfer
length was subtracted from the embedment length used in that end’s development length test to
obtain the “measured” flexural bond length.

36


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76


Mn

: , PB99-146664
A New Development Length Equation
for Pretensioned Strands in Bridge

Beams and Piles

PUBLICATION NO. FHWA-RD-98-116 DECEMBER 1998

a

US.Department of Transportation
Federal Highway Administration

Research and Development
Turner-Fairbank Highway Research Center
6300 Georgetown Pike

McLean, VA 22101-2296





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ii


CHAPTER 5: SUMMARY, FINAL RECOMMENDATIONS, AND CONCLUSIONS

In 1988, FHWA issued a memorandum that outlawed the use of 15.2-mm- (0.6-in-) diameter
strands, restricted the spacing of strands, and applied a multiplier to AASHTO’s development
length equation (Equation (1))."” This memorandum initiated considerable research on the
subject of bond of pretensioned strands in concrete.

Forty-one research studies have been undertaken since 1988 to clarify the issues in the
memorandum. If these studies are added to the bulk of research undertaken prior to the FHWA
memorandum, a total of more than 60 studies have been conducted on the topic of transfer and
development lengths of pretensioned strands in prestressed concrete.

Construction Technology Laboratories, Inc. (CTL) conducted a study for FHWA on the history
of the AASHTO equation. This study documented that the AASHTO transfer and flexural bond
length expressions, which make up the development length equation (see Equations (1) and (2)),
were actually average expressions, reflecting reasonable means for the data, rather than
conservative expressions. Because both components of the AASHTO development length
equation reflected reasonable means and not conservative values, the AASHTO equation itself
can be expected to be only an average equation and not a conservative equation.

Another important study was conducted for FHWA by Dr. Dale Buckner.” In an effort to
resolve conflicting recommendations from various researchers, Buckner reviewed the research
results available up to 1993 on the topic of transfer and development lengths of pretensioned
strands in prestressed concrete. He then proposed a new development length equation for
pretensioned strands in concrete (Equation (3)).

Other researchers conducted studies on the same topic after the Buckner equation was proposed,
including FHWA researchers. Because of this research, FHWA issued a memorandum in 1996
that lifted two of the provisions from the 1988 FHWA memorandum."

The 1996 FHWA memorandum allowed the use of 15.2-mm- (0.6-in-) diameter strands and
allowed reduced strand spacings for 12.7-mm- and 15.2-mm- (0.5-in- and 0.6-in-) diameter
strands. However, the multiplier for the AASHTO development length equation was retained
until a new development length equation proposed by FHWA was reviewed and commented
upon by the AASHTO Bridge Subcommittee on Bridges and Structures.

This new FHWA development length equation emanated from a large research study conducted
at FHWA’s Structures Laboratory at the Turner-Fairbank Highway Research Center in McLean,
VA. Phase I of the study involved 50 rectangular prestressed concrete specimens, while Phase II
involved 64 members: 32 AASHTO Type II prestressed concrete I-beams and 32 prestressed
concrete sub-deck panels. Half of these members for both phases contained uncoated strands,
while the other half contained epoxy-coated strands. Only research results from the members
containing uncoated strands were discussed in this report.

Results from the FHWA rectangular specimens (Phase I) indicated that the AASHTO transfer

and development length equations were unconservative for members constructed with normal-
strength concrete."

103



compression zone was actually weaker than the tension zone. Thus, the compression zone failed
first. A flexural failure signified adequate embedment length.

In a few instances, a flexural failure occurred at the same time as a bond failure of some strands.
In those instances, the failure was labeled a slip/flexural failure. Because slip and flexural
failures were occurring at the same time, that type of failure signified that the embedment length
being tested equaled the actual development length.

The reason for girder failure at one end of the girder dictated what the embedment length would
be for the opposite end of that girder. If a flexural failure occurred, then the embedment length
was decreased for the test on the opposite end. If a bond failure occurred, then the embedment
length was increased for the test on the opposite end. This iterative approach was employed until
both ends of both girders were tested and the development length was determined. The results
from all of the FHWA Phase II girder development length tests are shown in tables 3, 4, and 5.
Table 3 includes data for the normal-strength, non-composite girders (girders alone); table 4
includes data for the high-strength, non-composite girders; and table 5 provides data for the
normal-strength concrete girders made composite with a deck.

The values in tables 3, 4, and 5 are compared with predicted values of development length from
the AASHTO and Buckner equations. For every girder fabricated with normal-strength concrete,
the measured development length was longer than the AASHTO-predicted development length.
The Buckner equation was inconsistent when compared to the measured values of development
length in normal-strength concrete; sometimes the Buckner value was shorter than the measured
value and sometimes it was longer than the measured value. When compared to measured values
for high-strength concrete, the development length values predicted by AASHTO and Buckner
were consistently longer than the measured values. It is also evident from tables 3 and 4 that the
measured values of development length for a given strand size were shorter for high-strength
concrete than for normal-strength concrete.

Because of the unconservative AASHTO equation and the inconsistent Buckner equation for
normal-strength concrete, it was determined that a new development length equation was
needed—a new equation that could provide conservative predictions of development length for
all concrete strengths, yet not be overly conservative for high-strength concretes.

STRUCTURAL ANALYSIS
Because the FHWA girder results indicated the need for a new development length equation, the
FHWA researchers decided to examine a host of variables for possible inclusion in a new

equation. These variables were:

° Concrete compressive strength at 28 days, (f”,).
° Square root of concrete compressive strength at 28 days, (Vf’,).

24


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Because both components of the AASHTO development length equation reflect reasonable
means and not conservative values, then the AASHTO equation itself can only be expected to be
an average equation and not a conservative equation.

RESEARCH STUDIES

As a result of the FHWA memorandum, 41 research studies have been undertaken since 1988 to
clarify the issues in the memorandum on prestressing strand transfer and development lengths.
Some of these studies have been completed and some are still underway. If these studies are
added to the bulk of research undertaken prior to the FHWA memorandum, then a total of more
than 60 studies have been undertaken on this topic. For some of these studies, the transfer and
development length experimentation was the sole objective of the study; for others, it was an
important constituent of a broader study objective.

FHWA has undertaken its own study on bond of prestressing strand. Entitled “Investigation of
Development Length of Uncoated and Epoxy-Coated Prestressing Strand,” the study began in the
spring of 1990 and consisted of two phases. Phase I involved rectangular prestressed concrete
specimens ranging in size from 102 x 102 x 3658 mm (4 in x 4 in x 12 ft) to 356 x 356 x 8534
mm (14 in x 14 in x 28 ft). Three strand sizes were used in the following diameters: 9.5 mm, 12.7
mm, and 15.2 mm (3/8 in, 0.5 in, and 0.6 in), and the specimens contained either one or four
strands. Some specimens contained only uncoated strands, while others included only epoxy-
coated strands. The rectangular specimens were fabricated and tested at FHWA’s Structures
Laboratory, part of the Turner-Fairbank Highway Research Center in McLean, Virginia.

The results for the specimens containing uncoated strands indicated that the AASHTO
expressions for transfer and development length were not conservative for specimens containing
multiple uncoated strands of all diameters. The details of this phase of the research are provided
in other publications. (See references 3, 15, and 16.)

Prior to 1993, research results from many of the other studies were being issued and these
contained numerous conflicting recommendations. In an effort to resolve these conflicting
recommendations, FHWA initiated in January 1993 an impartial review of the research results
available up to that time. Dr. C. Dale Buckner, on sabbatical from the Virginia Military Institute,
performed this review during 1993, and issued a summary report."” Included within this
summary report was the proposed new development length equation shown below:

D
L,= fe + AP Se (DY 3)

where:
L,= Development length, (in)


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69


Table 6. Development length test results from structural analysis of FHWA research beams
constructed with normal-strength concrete.

Girder No. End Design f*,,, | Actual f*,,, | Designe,,, | Actual e,,,
ksi) ksi) in/in) in/in)

5US5-1 A 264.8 180 0.0147 0.00631
5US5-1 B 264.8 266 0.0147 0.01621
5U5-2 A 264.8 208 0.0147 0.00729
5U5-2 B 264.8 267 0.0147 0.01608
5U5-3 A 268.2 261 0.0292 0.01127
5U5-3. B 268.2 264 0.0292 0.01337
5U5-4 A 268.2 268 0.0292 0.03136
5U5-5 A 263.9 264 0.0135 0.01427
5U5-5 B 263.9 * 0.0135 *

5U5-6 A 263.9 265 0.0135 0.01437
5U5-6 B 263.9 264 0.0135 0.01384
5US-7 A 268.5 268 0.0337 0.02854
5US5-7 B 268.5 246 0.0337 0.00868
5US5-8 A 268.5 t 0.0337 t

5US5-8 B 268.5 269 0.0337 0.04008
6U5-1 A 260.6 262 0.0112 0.01222
6U5-2 A 260.6 210 0.0112 0.00735
6U5-2 B 260.6 263 0.0112 0.01315
6U5-3 A 268.3 268 0.0305 0.02431
6U5-3 B 268.3 268 0.0305 0.02431
6U5-4 B 268.3 268 0.0305 0.03144

* Not able to be determined because all strain and deflection data were lost due to power failure

in laboratory.

t Not able to be determined because there was an error in recorded strains during testing.

30

1 in/in = 1 mm/mn, 1 ksi = 6.89 MPa


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° T-Beams.
. Solid Rectangular Beams.

These full-size beams were considered both with and without composite decks. The cross-
sections of the full-size beam types considered are shown in figures 12 and 13. Rectangular
specimens of all dimensions were also considered. Pretensioned concrete decks and sub-deck
panels were not considered as they were beyond the scope of the current study.

Because there was limited data available on transfer and development lengths of pretensioned
piles, Dr. Beshah and Dr. Gagarin (of Starodoub, working for Construction Technology .
Laboratories, Inc. under a contract with FHWA) conducted a theoretical analysis of two different
pile sections. The pile sections considered in the theoretical study are shown in figure 13. One of
the sections was a 610-mm- (24-in-) square solid-section pile, and the other was a 762-mm- (30-
in-) square pile with a centralized 483-mm (19-in) void.

Measurements

Because some of the studies only measured transfer length, while others measured transfer and
development length (and a few only measured development length), separate criteria were set up
for transfer length and for development length.

The criteria for transfer length data required that actual concrete strains be measured and that the
transfer length be determined from those strain measurements. Transfer lengths that were
calculated from other measurements (such as end slips), and were not determined from strain
plots, were not considered.

The preferred method of determining the transfer lengths from the strain plots was the 95-percent
plateau method. Other methods of determining transfer length, such as the 100-percent plateau
method or the slope-intercept method, were allowed. However, if a method other than the 95-
percent method was used, then the actual strain data had to be recorded and available for use so
that the FHWA researchers could re-plot the actual strain data and determine the 95-percent
plateau transfer lengths from it. Although this was a time-consuming process for the FHWA
researchers, it ensured that correct transfer length values were being compared.

47


Figure 11 shows similar data to figure 10, except that in figure 11, the design values for the
parameters are used. Similar conclusions can be drawn for figure 11 as were drawn for figure 10.

The FHWA researchers decided to adopt Equation (9) as the proposed development length

expression pending correlation with data from other studies. The correlation of this expression
with data from other studies will be discussed in chapter 4.

43


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49.

50.

S51.

52.

53.

54,

55.

56.

Buckner Beam Tests, Draft Research Report No. 9-580-2, Center for Transportation
Research at the University of Texas at Austin, Austin, Texas, Publication Pending.

MLL. Ralls, R.L. Carrasquillo, and N.H. Bums. “Texas High Performance Concrete
Bridges,” Proceedings of the Fourth International Symposium in Utilization of High-
Strength/High-Performance Concrete, Volume 3, Paris, France, May 1996, pp. 1475-
1482.

A.N. Shah, N.H. Burns, R.L. Carrasquillo, and D.W. Fowler. Bond Behavior of 0.6-inch
Diameter Prestressing Strand at Two-inch Grid Spacing in Fully-Bonded High Strength
and Normal Strength Composite Texas Type C Beams, Draft Research Report No. 9-589-
2, Center for Transportation Research at the University of Texas at Austin, Austin, Texas,
Publication Pending.

RN. Bruce, B.T. Martin, H.G. Russell, and J.J. Roller. Feasibility Evaluation of Utilizing
High-Strength Concrete in Design and Construction of Highway Bridge Structures,
Publication No. FHWA/LA-94-282, Louisiana Transportation Research Center, Baton
Rouge, Louisiana, January 1994.

C. Ozyildirim and J. Gomez. High-Performance Concrete in a Bridge Structure in
Richlands, Virginia, Draft Interim Report, Virginia Transportation Research Council,
Charlottesville, Virginia, Publication Pending.

C. Ozyildirim, J. Gomez, and M. Elnahal. “High Performance Concrete Applications in
Bridge Structures in Virginia,” ASCE Proceedings: Worldwide Advances in Structural
Concrete and Masonry, American Society of Civil Engineers, New York, 1996, pp. 153-
163.

C. Ozyildirim and J. Gomez. “Virginia’s Bridge Structures With High Performance
Concrete,” Proceedings of the PCI/FHWA International Symposium on High
Performance Concrete, Precast/Prestressed Concrete Institute, Chicago, IL, October
1997, pp. 681-690,

M.F. Stocker and M.A. Sozen. “Investigation of Prestressed Concrete for Highway
Bridges, Part VI: Bond Characteristics of Prestressing Strand,” Bulletin 503, University
of Illinois at Urbana, 1970.

MF. Petrou and W.S. Joiner. Continuing Investigation of Strand Slippage in 24 inch

Octagonal Prestressed Concrete Piles, Publication No. FHWA-SC-96-04, University of
South Carolina, Columbia, South Carolina, May 1996.

123


of strand rather than the diameter of strand as a parameter in the equations was re-evaluated; and
the possibility of using log, natural log, semi-log, and natural semi-log as equation types was also
evaluated. Statistical analyses were performed that determined coefficients of correlation for each
of the cases described-above. The coefficients of correlation were compared, and it was
concluded that Equations (7), (8), and (9) were the best overall choices for the transfer length,
flexural bond length, and development length equations, respectively.

Even though it was determined that these equations were the best overall equations, they still
only represented the mean of the data (best fit), They were not conservative equations. Therefore,
the constants for these equations were adjusted so that the equations were conservative; no longer
were they best-fit equations, but they now exceeded the requirements for a 95-percent confidence
interval for the data.

The recommended transfer length equation is as follows:

=n?
f

t

-5 (14)

The recommended flexural bond length equation is as follows:

640", - ;
p BL at as)

Equations (14) and (15) were added together to provide the recommended development length
equation, which is as follows:

4f, 6-4 (Fy “Se )(P)
tee - 5): uu Se +. 415 (16)
oe i a ]

It was noted during the review of these equations that there were relatively few data points for
members with a concrete compressive strength, f’,, over 10,000 psi. Therefore, until more data
becomes available, FHWA researchers determined that values of f, greater than 10,000 psi
shall be taken as 10,000 psi for use in Equations (14), (15), and (16). Equations (14), (15),
and (16) are English-unit equations. The values of the constants in Equations (14), (15), and
(16) will change when the equations are converted for metric use.

107


OIL

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popuog Ajjny ut Suroedg pu yout-z ye pueng | uoneyodsuery jo uounredag sexoy ‘o[|inbseued ‘suing
Su10suQ, BuIssonsalg JaJOUIBIG-YOu!-9'0 JO JOLAeYag puog pur unjsny Je sexo] Jo Ajisiaaluy) “BAOpsoc ‘ssoly “yes
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aed aplLL uonEzZUesIO si0qyny



27.
28.

29.

30.
31.
32.
33.

34.

35.
36.
37.

38.

M.A. Shahawy, M. Issa, and B. Batchelor. “Strand Transfer Lengths in Full Scale
AASHTO Prestressed Concrete Girders,” PCI Journal, Vol. 37, No. 3, May/June 1992,
pp. 84-96.

M. Shahawy. An Investigation of Shear Strength of Prestressed Concrete AASHTO Type
I Girders, Research Report, Structural Research Center, Florida Department of
Transportation, May 1993.

H.K. Preston. “Characteristics of 15% Stronger 7-Wire Strand, ” PCI Journal, Vol. 8, No.
1, February 1963, pp. 39-45.

T.E. Cousins, M.H. Badeaux, and S. Moustafa. “Proposed Test for Determining Bond
Characteristics of Prestressing Strand,” PC/ Journal, Vol. 37, No. 1, January/February
1992, pp. 66-73. -

D. Mitchell, W.D. Cook, A.A. Khan, and T. Tham. “Influence of High Strength Concrete
on Transfer and Development Length of Pretensioning Strand,” PC/ Journal, Vol. 38,
No. 3, May/June 1993, pp. 52-66.

T.M. Ahlborn, C.E. French, and R.T. Leon. “Applications of High-Strength Concrete to
Long-Span Prestressed Bridge Girders,” Transportation Research Record, No. 1476, pp.
22-30.

C. French and T. Ahlborn. “Tests of Two High Performance Concrete Prestressed Bridge
Girders,” Proceedings of the PCI/FHWA International Symposium on High Performance

‘Concrete, Precast/Prestressed Concrete Institute, Chicago, IL, October 1997, pp. 394-405.

D. Dorgan. “Implementation of High Strength Concrete Research for Prestressed
Girders—A DOT’s Perspective,” Proceedings of the PCI/FHWA International
Symposium on High Performance Concrete, Precast/Prestressed Concrete Institute,
Chicago, IL, October: 1997, Pp. 467-474.

T. Cousins, D. Johnston, and P. Zia. “Transfer and Development Length of Epoxy Coated
and Uncoated Prestressing Strand,” PCI Journal, Vol. 35, No. 4, July/August 1990, pp.

-92-103.

B.W. Russell and D.R. Rose. “Investigation of Standardized Tests to Measure the Bond
Performance of Prestressing Strand,” School of Civil Engineering’and Environmental
Science at the University of Oklahoma, Norman, Oklahoma, July 1996.

D.R. Rose and B.W. Russell. “Investigation of Standardized Tests to Measure the Bond
Performance of Prestressing Strand,” PCJ Journal, Vol. 42, No. 4, July/August 1997, pp.
56-80.

O.A. Abdalla, J.A. Ramirez,-and R.H. Lee. Strand Debonding in Pretensioned Beams -

Precast Prestressed Concrete Bridge Girders With Debonded Strands. Part I Final
Report: Continuity Issues, Publication No. FHWA/INDOT/JHRP-92-24, School of Civil

121


Technical Report Documentation Page

1, Report No. 2. Goverment Accession No.

FHWA-RD-98-116

3. Recipient's Catalog No.

4. Title and Subtitle

A NEW DEVELOPMENT LENGTH EQUATION FOR PRETENSIONED STRANDS
IN BRIDGE BEAMS AND PILES

5. Report Date
December 1998

6. Performing Organization Code

7. Author(s)
Susan N. Lane

8. Performing Organization Report No.

9. Performing Organization Name and Address
Structures Division

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

10, Work Unit No. (TRAIS)
3Dia

11. Contract or Grant No.

12. Sponsoring Agency Name and Address
Office of Engineering R & D

Federal Highway Administration

6300 Georgetown Pike

13. Type of Report and Period Covered

Final Report
Spring 1990 - September 1998

14. Sponsoring Agency Code

McLean, VA 22101-2296

15. Supplementary Notes

16. Abstract

In 1988, the Federal Highway Administration (FHWA) issued a memorandum that outlawed the use of 15.2-mm- (0.6-in-)
diameter strands, restricted the spacing of strands, and applied a multiplier to the American Association of State Highway and
Transportation Officials' (AASHTO) development length equation. This memorandum initiated considerable research on the
subject of bond of pretensioned strands in concrete. Forty-one research studies have been undertaken since 1988 to clarify the
issues in the memorandum.

One of the studies initiated was a large research study conducted at FHWA's Structures Laboratory at the Turner-Fairbank
Highway Research Center. Phase | of the study involved 50 rectangular prestressed concrete specimens, while Phase II
involved 64 members: 32 AASHTO Type I! prestressed concrete |-beams and 32 prestressed concrete sub-deck panels. Half of
these members for both phases contained uncoated strands, while the other half contained epoxy-coated strands. Only the
results from the members containing uncoated strands in rectangular specimens and beams were discussed in this report.

Results from the FHWA research were used to evaluate the current AASHTO equation for development length as well as a
development length equation proposed by Dr. C. Dale Buckner of the Virginia Military Institute. Research results indicated that
the AASHTO equation was unconservative for members constructed with normal-strength concrete and the Buckner equation
was inconsistent for members constructed with normal-strength concrete. Both equations were conservative for members.
constructed with high-strength concrete.

Because of these results, it was determined that a new development length equation was needed -~ an equation that could
provide conservative predictions of transfer and development lengths for all concrete strengths, yet not be overly conservative
for high-strength concretes. FHWA researchers formulated new transfer and development length equations based on FHWA's
full-size beam research results, and then correlated these equations with results from other research studies to make sure that
the equations would be representative of the total applicable data to date. Data from 16 studies were used in the correlation
process. The transfer and development length equations based only on the FHWA beam results were refined based on the
correlation process, and new transfer and development length equations were proposed. Guidelines for the use of these
equations for beams and piles were provided.

18. Distribution Statement

No restrictions. This document is available to the public through
the National Technical Information Service, Springfield, Virginia
22161.

17. Key Words

Bridges, bridge design, prestressed concrete, pretensioning,
bond, transfer length, development length, prestressing
strand.

419. Security Classif. (of this report) 20. Security Classif. (of this page) 21.No. of Pages | 22. Price

Unclassified Unclassified 134

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
This form was electronically produced by Elite Federal Forms, Inc.

(


load could:be applied to the sections (piles), as well as the flexural load, to cover the situation of
a ship impacting a pile. It was determined from this theoretical parametric study that the axial
load had no detrimental effect on the development length, and that the FHWA development
length equation (Equation (16)) was conservative for piles.

The effect of strand position during casting is an issue that was raised by Dr. Buckner is his study
for FHWA."” The ACI code and the AASHTO Specifications” acknowledge and account for
the “top bar effect” for reinforcing bars (hereafter known as “rebars”) in regular reinforced
concrete. The top bar effect is the condition where rebars at the tops of members do not bond as
well to the surrounding concrete as rebars at the bottom of members. Rebars that are placed with
305,mm (12 in) or more of concrete cast below (beneath) them are “top bars.” As the bleed water
(excess water) from the concrete beneath the rebars rises, some of it can be trapped directly
beneath each rebar. The bond between the rebar arid the concrete below the rebar is, therefore,
weakened due to the presence of the bleed water: The ACI code and AASHTO Specifications
prescribe that a multiplier of 1.3 must be applied to the rebar development length equation for
these “top” rebars, so that additional development length.is provided. Dr. Buckner concluded that
the same “top bar effect” applies to top strands as well as to top rebars. He cites evidence from a
University of Illinois study where the bond strength of strands was reduced by about 25 percent
when strands had 254 mm (10 in) of concrete beneath them compared to 50.8 (2 in) of concrete
beneath them.®*

A conclusion from Dr. Buckner’s study was that the development length should be multiplied by
a factor of 1.3 for any strands (straight or draped) that end in the upper one-third of the member
depth and have 305 mm (12 in) or more of concrete cast beneath them."'”*)

Strand position during casting is an important issue for piles. Piles are cast horizontally and
strands are placed around the perimeter of the piles. The top and bottom of the pile is not marked
(noted) during casting. Once a pile is cast and removed from the prestressing bed, then its
orientation (position) during casting is lost. Therefore, piles installed in a bridge have an
anonymous casting position, and it is impossible to tell which strands were “top strands” or
“bottom strands” during ‘casting of the pile. Assuming there is 50.8 mm (2 in)-of concrete cover
for each layer of strands, any pile that has a cross-sectional dimension of 356 mm (14 in) or
greater will have strands that have 305 mm (12 in) or more of concrete cast beneath them and fit
the “top bar” criteria. Therefore, some of the strands in piles with a cross-sectional dimension of
356 mm (14 in) or greater will be subject to the “top bar effect,” and these strands will have
worse bond to the concrete. A ship could impact any side of the pile; it could impact the “top”,
“bottom”, or “sides” of the pile (with “top”, “bottom”, and.“‘sides” referring to the initial casting
position). Therefore, a multiplier should be applied to the development length equation for
strands in piles to ensure that all sides of a pile could successfully withstand a ship impact.

Recent research by the University of South Carolina indicated that top strands do exhibit greater
end slip at detensioning than bottom strands—sometimes two to three times the amount of end
slip for top strands as compared to bottom strands.” :

While there is no ACI nor AASHTO equation linking end slip at detensioning to transfer and

development lengths, end slip at détensioning is widely held as an indicator of bond. If there is a
long end slip at detensioning, this results in long transfer and development lengths. Therefore,

100


members they used were full-size Bulb-Tee girders and piles. The objective of the study was to
evaluate and demonstrate the feasibility of using high-strength concrete in bridge members.
Some of the girders were used in static tests to failure, while some underwent fatigue testing.
Transfer lengths were determined for the girders used for the static tests, based on strains
measured at release of prestress force, at 28 days, before and after the deck cast, and prior to the
static test to failure. These transfer lengths were used in the correlation with the new FHWA
equations.©" : :

Virginia Department of Transportation

Virginia DOT and FHWA collaborated on an’ HPC bridge project-called the Richlands Bridge.
After designing the bridge using HPC, it was determined that it was most economical to use
15.2-mm- (0.6-in-) diameter strands at 50.8-mm (2-in) spacing in the high-strength HPC beams.
However, similar to the two Texas projects, the FHWA 1988 memorandum was still in place;
therefore, research was required to demonstrate that the 15.2-mm- (0.6-in-) diameter strands
could be used successfully at the 50.8-mm (2-in) spacing in an I-beam made of concrete, which
had the same mix design as the actual Richlands Bridge beams.

Two 9.4-m- (31-ft-) long AASHTO Type II pretensioned concrete J-beams with composite decks
were fabricated and structural testing occurred at FHWA’s Structures Laboratory at the Tumer-
Fairbank Highway Research Center in McLean, VA. The girders contained six straight 15.2-mm-
(0.6-in-) diameter bottom strands, and two 15.2-mm- (0.6-in-) diameter draped strands, all
spaced at 50.8 mm (2 in). The compressive strength of the concrete at release ranged from 55.0
MPa to 58.7 MPa (7980 psi to 8520 psi), and the concrete compressive strength at 28 days varied
between 70.1 and 73.2 MPa (10,170 and 10,620 psi). The concrete compressive strength of the
cast-in-place deck at 28 days was 81.2 MPa (11,790 psi). Transfer lengths were determined from
strain measurements at release of the prestress force and immediately prior to the development
length tests. Development length tests were conducted for all four ends of the beams. Both the
transfer length and development length results were used in the correlation with the new FHWA
equations.©**”

TRANSFER LENGTH AND. DEVELOPMENT LENGTH ANALYSES

For all of the aforementioned studies, the data and results for a given study were recorded and
determined according to the goals and procedures specific to that study. Those goals and
procedures may have been different from the goals and procedures of FHWA’s study. Therefore,
to compare and correlate results among the studies, all of the data, including transfer length and
development length results, had to be in similar forms.

Transfer Length Analysis

As was described in chapter 2, Buckner’s study concluded that the recommended method for
determining transfer lengths from measured strains was the 95-percent plateau method. This
method was used to determine all of the transfer lengths for the FHWA Phase II (full-size
members) study. However, not all the researchers who performed the other studies used this
method to determine transfer lengths. Some studies determined transfer lengths using methods
such as the slope-intercept method, the 100-percent plateau method, or the 95-percent plateau

60


correlation process; if a study did not meet these requirements, then its data were not used in the
correlation process. Note that some of the studies listed in table 8 were theoretical studies,
meaning that no new data were introduced, but a new equation or theory of bond was presented.
These theoretical studies were examined and their theory considered where appropriate.

Data requirements or criteria were established in the following categories:

° Concrete.
. Prestressing Strand.
. Structural Member Types.
° Measurements:
— Transfer Length Measurements.

— Development Length Measurements.
The specifics of the criteria established for these items are described in the following sections:
Concrete

There was no restriction placed on the concrete compressive strength; concrete of all
compressive strengths were considered. The only restriction on the concrete was that it had to be
normal-weight concrete—lightweight concrete was not included in this comparison/correlation.

Prestressing Strand
The criteria for the prestressing strand follow:

° The prestressing strand used in the members needed to be uncoated strand; no epoxy-
coated strand was considered.

. The strands could be either Grade 250 or Grade 270 strands—their guaranteed ultimate
tensile strengths were either 1722 MPa or 1860 MPa (250 ksi or 270 ksi).

. Only low-relaxation strand was considered because that is what is commonly available

. Now; stress-relieved strands were not considered for the correlation.

. The strands needed to be fully-bonded for the full length of the member; debonded
strands were beyond the scope of this study.

. The sizes of strands that were included were diameters of 9.5 mm, 12.7 mm; 12.7 mm
Special, and 15.2 mm (3/8 in, 0.5 in, 0.5 in Special, and 0.6 in).

. The strands could be arranged in any strand pattern, including draped strands.

Structural Member Types

Both full-size beams and rectangular specimens were considered. The full-size beam types
considered were:

AASHTO Standard I-Beams.
State-Specific I-Beams.
Bulb-Tees.

Box Beams.


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Hence, the transfer lengths determined from these strains were more easily and reliably
determined.

The FHWA Phase II transfer length values for beams with uncoated strands grew an average of

~ 30 percent from the time of transfer to 28 days. After 28 days, the transfer length only grew an
additional 7 percent (average) until the time of the development length test, which occurred at an
age of 185 days, or approximately 6 months (on average).

It should be noted that Russell and Paulsgrove, in their report based on the strand bond research
done at the University of Oklahoma, cited that transfer length increased 30 percent between
transfer and the development length test.°” For the FHWA data, most of the growth took place
between transfer and 28 days. Because of this and because of the larger magnitude of the
Whittemore readings, which resulted in better plots of the strain data, the 28-day values of
transfer length were chosen as the cited data.

The values shown in table 2 are compared with predicted transfer length values computed using
the AASHTO equation (f,,D/3) and the Buckner equation (f,D/3). It is evident (as shown in table
2) that measured values of transfer length were greater than the values predicted by AASHTO
and Buckner for all of the strands in normal-strength concrete. It is also evident that measured
values of transfer length were less than the values predicted by AASHTO and Buckner for all of
the strands in high-strength concrete. A third observation from this table is that measured transfer
length values for a given size of strand were consistently lower in high-strength concrete than in
normal-strength concrete. However, neither the values predicted by the AASHTO equation nor
the values predicted by the Buckner equation indicate this trend.

Based on this FHWA data, it was concluded that a more conservative equation was needed for
transfer lengths in normal-strength concrete and that a revised equation was needed that would
give lower transfer length values when high-strength concrete was used. This would provide a
substantiated benefit for designers to use high-strength concrete.

20


hooked up to a data acquisition system and were recorded continuously as the load changed
during the development length test.

Deflection

Deflections were measured at mid-span and at the single-load point using linear potentiometers.
These devices were also connected to the data acquisition system and were read and recorded
continuously as the load changed during the development length test.

Other Measurements

Many other measurements were taken during this large research study. Other components of the
study that were measured included:

Internal concrete temperatures during curing.

Cambers.

Concrete shrinkage.

Unit weights of the concrete.

Moduli of elasticity of the concrete at release and at 28 days.
Split-cylinder concrete strengths.

Compressive strengths of the concrete (taken at the same time as the mechanical gauge
readings and end slip readings). :

. Coefficient of thermal expansion of the concrete.

. Pull-out strengths of untensioned strands in concrete blocks.

° Amounts of any phosphate residue on the surface of the strands.

oe eee ee

However, the results and analyses from these measurements are beyond the scope of this paper.
TRANSFER LENGTH RESULTS

The transfer length is the distance required from the end of the member to fully transfer the
effective prestressing force from the prestressing strand to the concrete by bond (see figure 3).
There are three different methods for determining the transfer length using a graph: the 100-
percent plateau method, the 95-percent plateau method, and the slope-intercept method. In all
three methods, the strains calculated from the mechanical gauge point (Whittemore point)
readings are plotted. These plots typically show a region of linearly varying strain leading to a
tegion of constant strain, called the strain plateau. This is shown in figure 4.

For the 100-percent plateau method, the points defining the plateau are identified. The strain
values of these points are then averaged together to produce a single constant strain value for the
plateau. A horizontal line is drawn on the graph to represent the constant strain plateau (see
figure 4). At the point where the linearly varying portion of the plot intersects the constant strain
plateau, a vertical line is drawn to the x-axis. The value on the x-axis that corresponds to its
intersection with the vertical line is the 100-percent plateau transfer length.

16


In figure 38, all of the development length data are plotted along with the Buckner equation
predictions. Many slip/shear failures fell above the line, indicating that predicted development
lengths were shorter than actual development lengths. This situation is unconservative.

The data are grouped by concrete strength in figures 39 and 40, with figure 39 graphing normal-
strength concrete data and figure 40 plotting high-strength concrete data. These figures show that
the Buckner equation is not conservative for members constructed with normal-strength concrete,
but is conservative for members constructed with high-strength concrete.

The new FHWA development length equation is plotted along with all of the. development length
data in figure 41. No slip/shear failures fell above the line, indicating that it is a conservative
equation. It is replotted in figures 42 and 43 with the normal-strength concrete data and high-
strength concrete data, respectively. No slip/shear failures fell above the line; therefore, the
FHWA equation is a conservative equation. Figure 43 shows that the FHWA equation is
conservative for high-strength concrete data, without being overly conservative.

As seen in figures 23 through 43, the best choice for a development length equation is the FHWA
development length equation (Equation (16)). It is conservative for all data, and provides a
benefit to the designer for using high-strength concrete.

Although the current stop-gap measure of multiplying the AASHTO equation by 1.6 is
reasonably conservative for the development length data, it is overly conservative and requires a
much longer development length than is needed for members constructed with high-strength
concrete. Since the AASHTO equation provides no benefit (credit) to the designer for using
high-strength concrete, that same equation multiplied by 1.6 does not provide any benefit (credit)
to the designer when using high-strength concrete. The new FHWA equation provides a better
fit.

There were relatively few data points available for members with a concrete compressive
strength, f”,, over 10,000 psi. Therefore, until more data becomes available, it was determined
that values of f, greater than 10,000 psi shall be taken as 10,000 psi for use in Equation
(16).

THEORETICAL ANALYSIS FOR PILES

FHWA researchers wanted Equations (14) through (16) to apply not only to beams, but also to
piles, because piles, under certain loading conditions, must resist flexural loads. However, there
were limited data available on transfer and development lengths of pretensioned concrete piles.
Therefore, it was decided that a theoretical parametric study would be performed using two
different pile sections to see whether Equation (16) would be conservative for pretensioned piles.

Two sections were selected for this parametric study, a solid 610-mm- (24-in-) square section
and a 760-mm- (30-in-) square section containing a 483-mm (19-in) concentric void (see figure
13).

The structural analysis computer programs that were used with the beam data were written to
handle only flexural loads. Dr. Beshah and Dr. Gagarin modified the programs so that an axial

99


Concrete compressive strength at transfer of prestress, (f°,;).

Square root of concrete compressive strength at transfer of prestress, (vf’,;).
Concrete modulus of elasticity at 28 days, (E,).

Concrete modulus of elasticity at transfer of prestress, (E,;).

Concrete unit weight, (w,).

Depth of concrete rectangular stress block, (a).

Prestressing strand diameter, (D).

Area of prestressing steel strand, (A,*).

Stress in prestressing strand prior to transfer of prestress, (f,,).
Effective prestress, (f,,).

Stress in prestressing strand at ultimate strength of the member, (f*,,).
Strain in prestressing strand at ultimate strength of the member, (€,,).

Cr rr

Many of these parameters were measured during experimentation or were easily determined from
measured values. Parameters that fit into this category were the concrete strengths at various ages
(and the square roots of these concrete strengths), the strand diameter and area, the modulus of
elasticity of the concrete at various ages, the concrete unit weight, and the stress in the strand
prior to transfer. However, certain parameters were not measured nor were easily determined
from measured values. Parameters that fit into this category were the depth of the rectangular
stress block, the effective prestress, and the stress and strain of the strands at ultimate strength of
the member. The AASHTO Specification does provide equations for calculating the amount of
prestress losses and thereby determining the effective prestress, f,,. These equations have been
routinely used for normal-strength concrete, but insufficient data existed to determine whether or
not they were accurate for high-strength concrete. The AASHTO Specification also provides an
equation (Equation 9-17) for calculating the stress in the strand.at ultimate strength of the
member, f*,,. This AASHTO equation was based on the ACI Building Code equation to
determine the same parameter. Section R18.7.2 of the Commentary for the ACI Building Code
on the ACI equation indicates that use of that equation is appropriate when all of the prestressing
strand is in the tension zone, and that a strain compatibility and equilibrium method of analysis
should be used in lieu of the equation when any of the prestressing strand is in the compression
zone. For the FHWA girders, two of the prestressing strands were located in the compression
zone (top flange), thereby eliminating use of the ACI and AASHTO equations and necessitating
the use of a strain compatibility method of analysis.

In order to determine these hard-to-obtain parameters, two computer programs were developed
by Dr. Fassil Beshah and Dr. Nicolas Gagarin that were based on the strain compatibility method
of analysis. For the first program, inputs were required for concrete strength, modulus of
elasticity, and modulus of rupture; properties of the strand; and loading and cross-section
information for a given development length test. The load and deflection data from the test was
then used in combination with the aforementioned input items in an iterative approach that
yielded the effective prestress force, f,,. For the second program, all of the inputs and values
determined by the first program were used as well as the measured external concrete strain of the
top fiber (compression fiber) at the load point. This concrete top fiber strain was measured
continuously during each FHWA girder development length test. By using the value of this strain
at failure, then the stress and strain of the bottom strands at failure of the member, f*,, and €,,,
respectively, were determined by an iterative approach contained within the second computer

program. The distance to the neutral axis, “a”, and the depth of the rectangular stress block, “c”,

28


APPENDIX A: NOTATION

ACI and AASHTO oe oot
AASHTO Standard

Report LRFD Specification
Symbol Notation Notation Description
a a a Depth of concrete rectangular stress block
AS* A As Area of prestressed reinforcement in the
. tension zone :
b y-intercept
D d, D Nominal diameter of prestressing strand
E, E, E, Modulus of elasticity of concrete at 28
days
E, E, E, Modulus of elasticity of concrete at
detensioning
E, E,. E, Modulus of elasticity of prestressed
reinforcement
¢ f, f, Concrete compressive strength at 28 days
fy ei Py Concrete compressive strength at
detensioning
fre Stress in prestressing strand prior to
transfer of prestress
f, f, f, Modulus of rupture of concrete
f,, fi, f, Effective stress in prestressed
reinforcement after all losses
f,, Stress in prestressed reinforcement at time
of initial prestress (immediately after
release in a pretensioned member)—from
Buckner report
f*., f, fy Average stress in prestressed
reinforcement at ultimate load
Ly ty Development length
'e Embedment length for development
length test
Ly Flexural bond length

109


Table 8. Research studies with full-size beams included in the correlation with FHWA

equations.
Organization Beam Type Strand Dia. | Transfer Development
(in) Length Length
Data Points | Data Points
Used | Used
Aubum University T-Beam 0.5 26 22
Univ. of Colorado Box Beam 0.6 : 8 4
at Boulder .
FHWA Phase II* AASHTO II 0.5 36 : 15
0.6 24 10
Florida DOT : AASHTO II 0.5 - 10 -0
. 7 0.5 Special 0 16
0.6 5 5
Univ. of Minnesota. | MN-45M I-Beam 0.6 4 4
Purdue University AASHTO I 0.5 0 3
Box Beam 0.5 0 1
| Univ. of Texas at Texas 22" I-Beam . 05 6
Austin for TxDOT 0.6 . . 12 9
Univ. of Texas at Solid Rectangular - 0.6 3 3
Austin—Louetta
Road (Hoblitzell/
Buckner Beams)
Univ. of Texas at Texas “C” I-Beam 0.6 16 8
Austin—San
Angelo
Tulane Univ./CTL Bulb-Tee 0.5 30 0
Virginia DOT AASHTO II 0.6 8 4
Totals 188 110
*Used in original formulation of equations. lin=25.4mm

52


were not included in the correlation. This did not imply that those studies were invalid. It simply
meant that those studies had objectives that were beyond the scope of this report, that
measurements were made or materials used that were other than those described in the criteria
above, or that the study data could not be supplied by the cut-off date.

The data from the following studies were used in the correlation:

Auburn University.

University of Colorado at Boulder.

FHWA Phase I (rectangular specimens).

Florida Department of Transportation.

Preston and Janney.

Louisiana State University and the University of New Orleans.
McGill University.

University of Minnesota.

North Carolina State University.

University of Oklahoma.

Purdue University.

University of South Florida and the University of Illinois at Chicago.
University of Texas at Austin for Texas DOT.

University of Texas at Austin—Louetta Road Overpass Project.
University of Texas at Austin—San Angelo Bridge Project.
Tulane University and Construction Technology Laboratories, Inc.
Virginia DOT.

ry

The data from the other studies often required FHWA researchers to conduct additional structural
analyses. For the transfer length data, many researchers in other studies determined transfer
length using methods such as the slope-intercept method, the 100-percent plateau method, or the
95-percent plateau method. Because the 95-percent plateau method was established as the
recommended method for determining transfer length, FHWA researchers had to take the data
from the other studies that had not used the 95-percent plateau method and determine the transfer
lengths using the 95-percent plateau method.

If the parameters used in the development length equation (Equation (9)) were not provided in
the study, then FHWA researchers had to perform a structural analysis for every member in that
study to determine the missing parameters. This resulted in the creation of a third computer
program for structural analysis (created by Dr. Beshah and Dr. Gagarin) to assist in structural
analyses for members that had load and deflection data available, but not data on the external
concrete strain of the top fiber, from their development length tests.

Statistical comparisons or correlations were then performed using the data from other studies and
the proposed transfer, flexural bond, and development length equations (Equations (7) through

(9)).
During this process of correlating Equations (7) through (9) with all of the data from other

studies, a few other re-examinations and re-evaluations were conducted. The issue of unit weight
as a possible parameter in Equations (7) through (9) was re-examined; the idea of using the area

106


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70


DEVELOPMENT LENGTH RESULTS

Development length experimentation was performed on each end of each girder, provided that
there was sufficient length to perform a second test on a girder. The girders were fabricated in
identical pairs in order to represent a specific girder type, such as “15.2-mm- (0.6-in-) diameter
strands at 50-mm (2-in) spacing in high-strength concrete.” In that way, a total of four
development length tests could be performed for each girder type (pair of girders).

Each end of each girder was instrumented with linear variable displacement transducers (LVDT)
on each strand. These LVDTs measured the distance that a strand would slip into the girder end
during loading of the girder. Electrical resistance strain gauges were placed along the top fiber of
the concrete. For a non-composite girder, the top fiber of the concrete was the surface of the top
flange; for the composite girder, the top fiber of the concrete was the surface of the deck.

Deflection was measured using linear potentiometers at the load point and at mid-span for each
of the tests. Loads applied to the girders were measured using a load cell. All of these measuring
devices were connected to a data acquisition system and were read continuously during a
development length test.

Testing for development length was a trial-and-error (or iterative) approach. For the first test, the
development length was calculated from a known equation, such as the AASHTO or Buckner
equation. This length was called the embedment length. A single-point load was applied to the
girder at a distance from the end of the girder equal to the embedment length (see figure 5). This
load was incrementally increased until either a bond failure or a flexural failure occurred.

A bond failure was marked by the strands slipping inward. The FHWA researchers set a
measurement of 0.25 mm (0.01 in) of slip as the threshold value for determining whether a strand
had failed in bond slip. It was determined that if the strand slipped by that value, then the stress
state in the beam had been significantly altered. Each of the girders had two top strands, and
either eight or nine bottom strands. If a majority of the bottom strands slipped, or if the girder
could not support the increased load as the strands were slipping, then the test was deemed a
bond failure. In general, the slip failures were accompanied by shear cracking in the end regions.
Of the 13 girder tests that resulted in bond failures, 12 of these were accompanied by shear
cracking. A bond failure signified inadequate embedment length.

A flexural failure was marked by flexural cracking at or near the load point, flexure-shear
cracking as the cracks got farther away from the load point, and crushing of the compression
zone concrete. If the compression zone concrete was crushed, or if the girder would not support
increased load, then the test was deemed a flexural failure. In general, when a flexural failure
occurred, no strands slipped—even though some shear cracks may have been present in the end
regions at the time of flexural failure. Typically, one would think that a flexural failure would be
marked by the breaking of strands rather than the crushing of concrete. However, because of the
full row of strands in the bottom row of the girder and because of the relatively small
compression zone at the top of the girder (alone) or at the top of the composite girder, the

22


As seen in these figures, if a slip/shear failure fell above an equation line, the equation was
unconservative. It was unconservative because a slip/shear failure indicated that the development
length being tested was too short. Therefore, if the development length being tested was too
short, yet the equation predicted a value for development length even shorter than the one being
tested, then the equation predicted a development length that was too short. Therefore, the
development length predicted from the equation was unconservative.

Figures 23 through 26 and 28 through 32 illustrate cases where normal-strength concrete was
used (f', between 34.4 and 48.2 MPa [5000 and 7000 psi]). It is evident from many of these
figures that the AASHTO and Buckner equations were unconservative because slip/shear failures
fell above those lines. In one instance, the case of 12.7-mm- (0.5-in-) diameter strands in 34.4-
MPa (5000-psi) concrete members (figure 24), the line representing 1.6 times the AASHTO
equation was unconservative. However, the new FHWA equation was consistently conservative
when using normal-strength concrete (f’, between 34.4 and 48.2 MPa [5000 and 7000 psi]).

In figure 25, there were some combination failures that fell above all four of the equations. These
represented the extreme worst case in terms of long development lengths, but did provide some
waming signs due to the flexural failure component of the combination failure.

Figures 27, 33, and 34 illustrate cases in which high-strength concrete was used (f, between 55.1
and 68.9 MPa [8000 and 10,000 psi]). Development lengths determined in the research studies
were consistently shorter in high-strength concrete. The AASHTO equation was sometimes
unconservative (figures 27 and 34) and sometimes conservative (figure 33) for the high-strength
concrete members. The Buckner equation was consistently conservative, but it over-predicted
development length by a large margin (figures 27 and 34). The FHWA equation was crafted such
that designers were given credit for using high-strength concrete and therefore obtained shorter
development lengths. Therefore, the FHWA equation is conservative for these cases, but not
overly conservative (see figures 27, 33, and 34).

Figures 28 and 29 were included to illustrate the case of using 12.7-mm (0.5-in) Special diameter
strand. Figure 28 was drawn using a diameter of 0.50 inches in the equations, whilé figure 29
was drawn using a diameter of 0.52 inches in the equations. Although there appears to be only
one data point on this graph, the one point is actually 15 different development length tests
conducted by Florida DOT at the same embedment length.°” **) Therefore, when plotted, they all
appear at the same point. There was virtually no difference between figures 28 and 29,
illustrating that none of the development length equations were very sensitive to the slight
variation in the diameter of the 12.7-mm (0.5-in) Special diameter strands.

Additional graphs of the development length data are provided in figures 35 through 43. In each
of these figures, the different failure modes are again represented by different symbols:

. The slip/shear failures are shown by the square symbols. Slip/shear failures are the worst
types of failure—they occur with no warning and should be avoided.

88


CURRENT AASHTO EQUATION

Currently, the equation for development length is the same in both the American Association of
State Highway and Transportation Officials (AASHTO) Bridge Specifications (AASHTO:
Specifications) and in the American Concrete Institute's (ACI) Building Code Requirements for
Structural Concrete (ACI building code). These organizations use different notations in their
equations; however, for this paper, the current AASHTO notations will be used. See appendix A
for a list of notations.

In Article 9.28.1 of the AASHTO Specifications,” the development teneth of a pretensioned
concrete member is given by Equation 9-32 as:

cam ~ Ff) (D) a

where f*,, and f,, are as previously defined, and D is the nominal diameter of the strand in inches.
This article in the AASHTO Specifications is similar to Article 12.9.1 in the ACI building
code. Henceforth in this paper, Equation (1) will be referred to as the “AASHTO equation.”
This equation is sometimes confusing to designers because it does not separate the development
length into its constituent parts, but rather merges the two parts together. The equation can be
rewritten in terms of its constituent parts as:

D
L,= fn. + Pu Se (DY Q)

where

q = development length

D
12 = transfer length, and


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77


LIST OF TABLES

Table No.
1. AASHTO Type II beams with uncoated strands used in FHWA research study
2. Measured and predicted transfer lengths at 28 days for FHWA research beams ..
3. Development length test results for normal-strength, non-composite FHWA
research beams ........ 20.6. cece cece eee e teen ee eee ence eben ees 25
4. Development length test results for high-strength, non-composite FHWA
research beams
5. Development length test results for normal-strength, composite FHWA research beams 27
6. Additional development length test results from structural analysis of FHWA research
beams constructed with normal-strength concrete 0.0.0.0... ccc cece eee eee eee 30
7. Additional development length test results from structural analysis of FHWA research
beams constructed with high-strength concrete ...... 0.00. c cece cece e eee eee eee 31
8. Research studies with full-size beams included in the correlation with FHWA
equations oc e ene ent eee teen tees 52
9. Research studies with rectangular specimens included in the correlation with FHWA
EQUATIONS 2... ee ee eee n ene eet e tenn eee t ene ee 53

vii


A similar approach was used to determine a new flexural bond length expression. A host of
variables were investigated. Researchers initially inspected the data and then numerically
evaluated the most promising parameters, along with the “measured” values of the flexural bond
length. Because there is no way to directly measure the flexural bond length, the measured
transfer length was subtracted from the embedment length being tested to obtain the “measured”
flexural bond length. More than 3400 equation types were initially evaluated, including linear,
non-linear, log (Base 10 and natural log), and semi-log (Base 10 and natural log) equations, using
a computer program called TableCurve 2D. A simple equation filter was also used to ensure that
the equation selected was not only an accurate equation, but also:an understandable and usable
equation. .

TableCurve 2D used a DOF-adjusted coefficient of determination as an evaluation criterion
between possible equations. FHWA researchers then chose the combination of variables and the
equation that had the highest coefficient of determination, and was understandable and usable as
the best obtainable flexural bond length equation. That best obtainable flexural bond length
equation is given in Equation (8). :

The new development length equation (Equation (9)) was the sum of the new transfer length
equation (Equation (7)) and the new flexural bond length equation (Equation (8)). The FHWA
researchers adopted Equation (9) as the proposed development length equation pending
correlation with data from other studies.

FHWA undertook an extensive literature search on the topic of the bond of pretensioned strands
in concrete and identified more than 60 studies on this topic. As was previously noted, these
studies were on a variety of topics related to the bond of pretensioned strands. For some of the
studies, the transfer and development length experimentation was the sole objective of the study;
for others, transfer and development length experimentation was an important constituent of a
broader study objective. FHWA researchers established data requirements or criteria that a study
had to meet for it to be included in the correlation of the new transfer. and development length
equations. Criteria were established in the following areas:

. Concrete.

. Prestressing strand.

. Structural member types.

. Transfer and/or development length measurements.

All 62 of the bond-related studies were examined in detail to see whether their study focus,
instrumentation, and data met the criteria described in the previous section. If their study focus;
instrumentation, and data met the criteria described previously, then that study was included in
the correlation. If their study focus, instrumentation, and data did not meet the criteria, then the
study results were not included in the correlation. Also, if the study focus, instrumentation, and
data met the criteria, but some data were not readily available, that data had to be given to
FHWA researchers by a certain date to be included in the correlation process. If the data were not
received by the cut-off date, then the study results were not included in the correlation.

Sixteen studies, in addition to FHWA’s Phase I (rectangular specimens) data, met the criteria,
had the data available by the cut-off date, and were used in the correlation. Many fine studies

105


Similar to the other two equations, the FHWA transfer length equation was conservative for
members constructed with high-strength concrete (see figure 22). This was significant because
the FHWA equation has the parameter “concrete strength, (f”,)” in the denominator of the
equation. Because the concrete-strength parameter is in the denominator, a designer obtains a
shorter transfer length as the concrete strength increases. This shows that the FHWA transfer
length equation is not only conservative, but it also benefits the designer who uses high-strength
concrete. :

These figures indicate that the best choice for a transfer length equation is the FHWA transfer
length equation (Equation (14)).

There were relatively few data points for members with a concrete compressive strength, f ,, over
10,000 psi. Therefore, until more data becomes available, it was determined that values of P,
greater than 10,000 psi shall be taken as 10,000 psi for use in Equation (14).

Figures 23 through 34 compare four development length equations:

. The new FHWA equation—Equation (16).

. The AASHTO equation—Equation (1).

° The current stop-gap measure of 1.6 times the AASHTO equation (as per the 1988
FHWA memorandum).

. The Buckner equation—Equation (3).

Each figure includes all data (data from rectangular specimens as well as full-size beams) for a
given strand diameter and concrete strength, such as 12.7-mm.- (0.5-in-) diameter strands in
members where the concrete compressive strength at 28 days is 34.4 MPa (5000 psi). Along the
y-axis, the actual measured development lengths are plotted. Along the x-axis, the quantity (f*,, -
f,,) is plotted because it is a quantity that is contained within all of the equations.

For each graph, it was assumed that the stress in the strands prior to transfer (f,,) was 1395 MPa
(202,500 psi). To generate the line showing the Buckner equation, a value for the constant Ahad
to be assumed. The value for 4 was calculated for each data point using Equation (4), and then
the values of A for all of the data points on a given graph were averaged together to provide the
value for A used to generate the Buckner equation line for a particular graph.

In these figures, the different failure modes are represented by different symbols:

. The slip/shear failures are shown by the square symbols. Slip/shear failures are the worst
types of failure—they occur with no warning and should be avoided.

. The flexural failures are shown by the circular symbols. Flexural failures are acceptable
(good) failure types because there is warning (excessive deflection and cracking) before
the failure.

. The combination failures are shown by the diamond symbols. This is when flexural

failure occurs at the same time as slip/shear failure. These combination failures indicated
that the embedment length being tested was the exact development length.

75


the trends noted by the University of South Carolina researchers are important indicators of
longer transfer and development lengths for “top” strands in piles.

Based on all of the above, the FHWA researchers recommend that the FHWA transfer and
development length equations (Equations (14) and (16), respectively) be used for piles, and
that a 1.3 multiplier be applied to Equations (14) and (16) for any strands (straight or
draped) in any member (beam or pile) that has 305 mm (12 in) or more of concrete cast
beneath them. However, the 1.3 multiplier should not be applied to strands in beams that do not

fit this criterion.
There should be more physical research conducted on pretensioned piles, either by the University

of South Carolina and/or by other researchers in the future, to experimentally verify the findings
of the theoretical analysis for piles and the top strand/top bar effect.

101


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86


FHWA Phase I

Because the new equations were developed based on the data on full-size beams from the FHWA
Phase II study, the data from the FHWA Phase I rectangular specimens were not included.
Therefore, the data from the rectangular specimens containing uncoated strands were
incorporated into the correlation. These rectangular specimens ranged in size from 102 mm x 102
mm x 3658 mm (4 in x 4 in x 12 ft) to 356 mm x 356 mm x 8534 mm (14 in x 14 in x 28 ft).

Three strand sizes were used in the following diameters: 9.5 mm, 12.7 mm, and 15.2 mm (% in,
0.5 in, and 0.6 in), and the specimens contained one or four strands. The concrete compressive
strength of the rectangular specimens at 28 days was between 34.4 MPa and 44.8 MPa (5000 psi
and 6500 psi). The FHWA researchers determined transfer length at many ages and development
lengths for these members.°'*"'®

Florida Department of Transportation

Researchers at the Florida Department of Transportation’s Structural Laboratory in Tallahassee,
FL, conducted experimentation on pretensioned strands in full-size AASHTO Type I girders.

The girders were 914 mm (36 in) high and were 12.5 m (41 ft) long. Each one had a composite
deck that was 203 mm (8 in) thick and 1067 mm (42 in) wide. Thirty-three girders were
fabricated for this study, and they contained either 12.7-mm-, 12.7-mm Special, or 15.2-mm-
(0.5-in-, 0.5-in Special, or 0.6-in-) diameter strands. The study examined the effects of the
amount (percentage) of debonded strands and the amount of shear reinforcement on the transfer
and development lengths of the strands. The design concrete compressive strength at 28 days was
41.3 MPa (6000 psi) for the girders and the deck.

The transfer and development lengths were determined for all of the members. Sixteen of the
girders, all fully-bonded, were used in the correlation with the FHWA equations, but not all of
the data were available for all of the girders by the cut-off date. Therefore, the transfer lengths”
were used for the ““A1-00” girders, the development lengths were used for the “BO-00” and “B1-
00” girders, and the transfer and development lengths were used for the “C1-00” girders.”

Preston and Janney .
This was the first study to report on the bond of Grade 270 strands. The members consisted of six
rectangular specimens, each containing one 12.7-mm- (0.5-in-) diameter strand. Two of the
specimens contained Grade 270 stress-relieved strands that had a clean and bright surface
condition. These two specimens were included in the correlation before it was discovered that the
strands were stress-relieved. Despite the fact that they were stress-relieved, they were kept in the
study to allow researchers to see their effect on the data.

The rectangular specimens measured 88.9 mm x 108 mm x 2.44 m (3.5 in x 4.25 in x 8 ft). The
design compressive strength of the concrete at 28 days was 34.4 MPa (5000 psi). Only transfer
lengths were determined for these specimens (specimens #2 and #6), and these transfer lengths
were used in the correlation.°”

54


In one instance, other researchers had determined transfer lengths by the 100-percent plateau
method, and FHWA researchers established a correlation between the transfer length determined
by the 100-percent method and the transfer lengths determined by the 95-percent method, so that
all of the data did not have to be re-plotted for that study.

The criteria for the development length tests focused on certain measurements that had to be
made during the test. The end slip of the strands had to be measured during the test so that the
researchers could numerically determine if any of the strands had slipped. Tests that included
only visual estimations of strand end slips and not physical end slip measurements were not
considered. End slips during development length testing were typically very small numbers (on
the order of 0.025 to 0.25 mm [0.001 to 0.01 in]) and were hard to determine visually. Therefore,
they needed to be measured.

Additional requirements for development length testing included the measurement of deflection
and/or concrete surface strain during the test. If either deflection or concrete surface strain (or
both) were measured, then a strain-compatibility analysis could be conducted that would provide
the needed parameters for use in the correlation of the new equations.

The development length testing could be conducted with either one-point or two-point loading;
either one was acceptable for use in the correlation.

OTHER STUDIES USED IN THE CORRELATION WITH THE NEW EQUATIONS

All 62 of the bond-related studies were examined in detail to see whether their study focus,
instrumentation, and data met the criteria described in the previous section. As was previously
noted, these studies were on a variety of topics related to the bond of pretensioned strands. For
some of the studies, the transfer and development length experimentation was the sole objective
of the study; for others, transfer and development length experimentation was an important
constituent of a broader study objective.

If their study focus, instrumentation, and data met the criteria described previously, then that
study was included in the correlation. If their study focus, instrumentation, and data did not meet
the criteria, then the study results were not included in the correlation. Also, if the study focus,
instrumentation, and data met the criteria, but some data were not readily available, that data had
to be given to FHWA researchers by a certain date to be included in the correlation process. If
the data were not received by the cut-off date, then the study results were not included in the
correlation.

FHWA researchers determined that 16 of the other studies, in addition to the FHWA Phase I
(rectangular specimen) data, met the criteria and their data were provided to FHWA researchers
by the cut-off date. Those studies were included in the correlation. Many fine studies were not
included in the correlation. This does not imply that those studies were invalid. It simply means
that those studies had objectives that were beyond the scope of this report, that measurements
were made or materials used which were other than those described in the criteria above, or that
the study data could not be supplied by the cut-off date.

50


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CHAPTER 4: CORRELATION OF NEW DEVELOPMENT LENGTH EQUATION
WITH OTHER RESEARCH RESULTS -

The new expressions $ for transfer length, flexural bond length, and development length
(Equations (7), (8), and (9) from chapter 3) correlated well with the FHWA Phase II beam data.
The correlation of the new equations with the FHWA beam data was a necessary, but not
sufficient, criterion for acceptance of the new equations. The results of other research studies also
had to correlate well with the new equations. Therefore, the FHWA researchers needed to find all
of the research results on the topic of bond of pretensioned strands in concrete and ascertain
which of those research studies could be correlated with the equations.

For the new equations to correlate with the other studies, the other studies had to use similar
materials and had to have key measurements taken. If the appropriate components were missing,
the data were not correlated with the new equations for transfer length, flexural bond length, and
development length. Once researchers determined which studies had the appropriate components
and were eligible to correlate with the new equations, they began the actual correlation process.
This chapter will describe that process. -

BREADTH OF ALL STUDIES:

FHWA undertook a worldwide literature search to find all of the research that had been
conducted on the topic of bond of pretensioned members. A total of 62 studies were discovered
on this topic. For some of the studies, the transfer and development length experimentation was
the sole objective of the study; for others, transfer and development length experimentation v was
an important constituent of a broader study objective.

A list of all of the studies to date on the topic of bond of pretensioned members is provided in
Appendix B. The dates listed in that table are the dates when the main publication (report or
article) that emanated from the study was published.

Prior to the FHWA memorandum in 1988, which included the years 1949 to 1988, there had only
been 20 research studies undertaken on this.topic. Once the FHWA memorandum was issued, a
flood of studies ensued. From.the period of 1988-1994, there were 21 studies undertaken. The
Buckner study was completed and his new equation was proposed in 1994. From 1994 to the
present, there have been 21 additional studies undertaken or ongoing. These numbers indicated
that an incredible amount of research had occurred on this topic in the last decade—42 studies to
date. The review and correlation of these studies presented a formidable challenge to the FHWA
researchers.

DATA REQUIREMENTS FOR CORRELATION OF OTHER RESEARCH RESULTS
WITH NEW EQUATION

To ensure that correct comparisons were being made (i.e., comparing apples to apples and not
apples to oranges), the FHWA researchers set up data requirements for the studies, Each study
had to meet (conform to) these requirements to be eligible to participate in the correlation.
process. These requirements focused on the materials used in the study, as well as the type of
measurements made in the study. If a study met these requirements, then its data were used in the

45


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74


f,,= Stress in prestressed reinforcement at time of initial
prestress (immediately after release in a pretensioned
member), (psi)

D= Diameter of strand, (in)
A= Multiplying factor applied to flexural bond length
f*,,= Average stress in prestressing steel at ultimate load, (psi)

f£,= Effective steel prestress after losses, (psi)

Dr. Buckner theorized that the flexural bond length (the second term in Equation (3) above) was
dependent upon the strain in the strand at maximum load—if more strain was present, then more
flexural bond length would be required. Dr. Buckner’s constant A reflects that. For general
applications, the expression for A is:

A = (0.6 +40 &) (4)

where: €,,= Strain in prestressing steel at ultimate load, (microstrain)
Henceforth in this paper, Equation (3) will be referred to as the “Buckner equation.” It should be
noted that many of the studies that used high-strength concrete (high-strength concrete being
concrete with an f, greater than 55 MPa [8 ksi]) had not been completed at the time of the
Buckner study, so Buckner was not able to use their results.

Phase II of the FHWA study began after the Buckner report had been drafted, and it was planned
to use the FHWA Phase II members to evaluate the proposed Buckner equation. Phase II
involved full-size prestressed concrete girders and deck panels that were fabricated at a precast
concrete plant. A total of 32 AASHTO Type II prestressed concrete I-girders and 32 prestressed
concrete deck panels were fabricated in February through April of 1994. The girders used 12.7-
and 15.2-mm- (0.5- and 0.6-in-) diameter strands, while the deck panels contained 9.5-mm- (3/8-
in-) diameter strands. Some specimens contained only uncoated strands, while others included
only epoxy-coated strands. Composite decks were added at the FHWA Structures Laboratory to
some of the girders and deck panels. Testing was completed in summer 1995, and the results of
these tests showed that the AASHTO equation was not conservative for girders with uncoated
strands. It also showed that the Buckner equation was inconsistent for girders with uncoated
strands—sometimes it was conservative and sometimes it was not conservative. See chapter 2 for
detailed results from the FHWA Phase II study.


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49


TABLE OF CONTENTS (continued)

Chapter Page
OTHER STUDIES USED IN THE CORRELATION WITH THE
NEW EQUATIONS ....0 0.200 e eee ee 50
Auburn University .......0.... 00. e cece eee eee teens 51
University of Colorado at Boulder . .. 51
FHWA Phase! ...............--.05. 154
Florida Department of Transportation ........................ 34
Preston and Janney ............ 0.6. e cece cece ene eens 54
Louisiana State University and the University of New Orleans ....55
McGill University ...... 2.0.0... 55
University of Minnesota .. 55
North Carolina State University . 56
University of Oklahoma ...... -.. 56
Purdue University .......... 00. c cece cee cece eee 57
University of South Florida and the University of Illinois
at Chicago 2.0.0... ccc cence teen ees 57
University of Texas at Austin for Texas DOT ................... 57
University of Texas at Austin—Louetta Road Overpass Project ...58
University of Texas at Austin—San Angelo Bridge Project ....... 59
Tulane University and Construction Technology
Laboratories, Inc. (CTL) ..........0. 00.00 c eee e cece ee 59
Virginia Department of Transportation .....................05 60
TRANSFER LENGTH AND DEVELOPMENT LENGTH ANALYSES .. 60
Transfer Length Analysis ............... 00. ccc ee eevee eee eee 60
Development Length Analysis . +. 61
STATISTICAL COMPARISONS ......... +62
THEORETICAL ANALYSIS FOR PILES ..............0. 0000000005 99
5. SUMMARY, FINAL RECOMMENDATIONS, AND CONCLUSIONS ........ 103
APPENDIX A: NOTATION

APPENDIX B: RESEARCH STUDIES ON THE BOND OF PRETENSIONED
STRANDS IN CONCRETE ...... 00... c ccc nn tne eens 111

REFERENCES ... 2.0.10 nee nn nee nnn eens 119

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66


Table 2. Measured and predicted transfer lengths at 28 days for FHWA research beams.

FHWA Predicted Predicted

Girder Strand Measured Measured AASHTO Buckner
No. Pattern P. Transfer Length | Transfer Transfer
(psi) End A | er vent Length
(in) i

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6,440 63.0 40.6 32.1 40.5

* No plateau was reached by the end of instrumentation (at 56 in), so no transfer length could be
determined.
1 in = 25.4 mm, 1 psi = 6.89 kPa

21


Even though it was determined that Equations (7) through (9) were the overall best-fit equations,
these equations still only represented the mean of the data. They were not conservative equations.
Therefore, the constants for these equations were adjusted so that the equations were
conservative. They were no longer best-fit equations—they exceeded the requirement of a 95-
percent confidence interval for the data. The revised transfer length equation is as follows:

(14)

The revised flexural bond length equation is as follows:

= SAP hI). (1s)

“pp tf,

Equations (14) and (15) were then added together to provide the revised development length
equation:

4H, 2 6.4 (f', ~f,, )(D)
L,=(-—@ - 5)+(~—8# en ss 16
aI rf 7 ] (16)

During the review of these equations, there were relatively few data points encountered for
members with a concrete compressive strength, f”,, over 10,000 psi. Therefore, until more data
becomes available, it was determined that values of f, greater than 10,000 psi shall be taken
as 10,000 psi for use in Equations (14), (15), and (16). Equations (14), (15), and (16) are
English-unit equations. The values of the constants in Equations (14), (15), and (16) will
change when the equations are converted for metric use.

Figures 14-through 16 show all of the transfer length data, for all full-size beams and rectangular
specimens. Along the y-axis, the actual measured-transfer lengths from the various studies are
plotted. Along the x-axis, the transfer lengths calculated by the AASHTO transfer length
equation (see Equation (2)) for those members are plotted. The line drawn in the figures
represents the cases in which the measured transfer lengths exactly equal the calculated transfer
lengths using the AASHTO equation. Any points falling above this line are unconservative
because the value that was measured was greater than the value that was predicted.

As discussed in chapter 1, the AASHTO transfer length equation was only meant to be an
average expression, not a conservative one (see figure 14). In figure 14, the points are

64


Purdue University

A total of 10 precast, prestressed beams (8 I-beams and 2 box beams) were constructed and
tested as part of the Purdue study for the Indiana Department of Transportation and the FHWA.
Eight of these beams (six I-beams and two box beams) were made into four sets of two
continuous beams, complete with a composite deck cast on top of them. The I-beams were’
standard AASHTO Type I pretensioned concrete I-beams, while the box beams were standard
Indiana State Type CB-27 box beams (686 mm [27 in] high with a 470-mm- [18.5-in-] high
void). The other two I-beams were stand-alone beams (i.¢., not made continuous). For each of the
five pairs of beams, one of the beams contained fully-bonded 12.7-mm- (0.5-in-) diameter
strands, while the other contained some debonded 12.7-mm- (0.5-in-) diameter strands. The
design concrete compressive strength at 28 days was 41.3 MPa (6000 psi) for the beams.

The main objective of the study was to evaluate the effects of strand debonding on the flexural
and shear behavior of precast, pretensioned bridge beams made continuous with a cast-in-place
slab and diaphragm. The four sets of beams were first tested compositely, and then broken apart.
The outer ends of the beams were then tested individually for shear and bond. The two stand-
alone beams were tested only for shear and bond. The shear and bond tests functioned as
development length tests. No transfer lengths were determined. One of the sets of I-beams
contained stress-relieved strands, while the other three sets of I-beams and the box beams
contained low-relaxation strands. Only the test results from the three I-beams and one box beam
containing fully-bonded, low-relaxation strands were used in the correlation with the new FHWA
equations.°*

University of South Florida and the University of Illinois at Chicago

The main objective of the study by the University of South Florida and the University of Illinois
at Chicago for the Florida Department of Transportation was to compare the transfer lengths of
fiberglass strands and steel strands in prestressed-concrete members.

A total of 12 rectangular specimens were constructed, and 5 of these contained a single 12.7-mm
(0.5-in) Special diameter concentric strand that was uncoated. The 12.7-mm (0.5-in) Special
diameter strand has a slightly larger cross-sectional area than the normal 12.7-mm- (0.5-in-)
diameter strand—namely, 107.7 mm? (0.167 in’) for the 12.7-mm (0.5-in) Special diameter-
strand compared to 98.7 mm? (0.153 in’) for the 12.7-mm- (0.5-in-) diameter strand. The other
seven rectangular specimens contained fiberglass strands. The rectangular specimens measured
152 mm x 102 mm x 2590 mm (6 in x 4 in x 102 in). The compressive strength of the concrete at
28 days ranged from 6500 psi to 7300 psi. Only transfer lengths were determined for the-
rectangular specimens; no development length testing was performed. The transfer length results
for the five rectangular specimens containing the steel strands were used in the correlation.“

University of Texas at Austin for Texas DOT

This huge study, which was conducted by the University of Texas at Austin for Texas DOT and”
FHWA, consisted of constructing and testing 74 prestressed concrete members. Fifty of the
members were rectangular specimens (containing 1, 3, or 5 strands), while 24 of the members
were full-size AASHTO-type I-beams (containing anywhere from 4 to 24 strands). The main

57


Prestressing Strand

All of the prestressing strands used in the beams were uncoated seven-wire, Grade 270 (1860
MPa [270 ksi] guaranteed ultimate tensile strength), low-relaxation strand, conforming to ASTM
Standard A 416-90." The strand was used in the “as-received” condition, having occasional
surface rust visible, but no pitting.

Concrete

Two different concrete mixes were used for the beams: one normal-strength mix and one high-
strength mix. This was done to investigate the effect of concrete strength on development length.
Twelve of the beams were fabricated with the normal-strength concrete mix. This normal-
strength mix was designed to yield a 28-day compressive strength between 34.4 MPa and 44.8
MPa (5 ksi and 6.5 ksi). The limits of concrete strength, or “windows” of strength, were used so
that differentiation could be made between the normal-strength and high-strength concretes. This
mix was also designed to have a compressive strength at release of the prestress force equal to
27.6 MPa (4 ksi). Actual average compressive strengths for the normal-strength concretes were
31.5 MPa (4.6 ksi) at release, 44.2 MPa (6.4 ksi) for air-cured cylinders at 28 days, and 49.2 MPa
(7.2 ksi) for moist-cured cylinders at 28 days.

Four of the beams were fabricated with the high-strength concrete mix. This mix was designed to
yield a 28-day compressive strength between 68.9 MPa and 89.6 MPa (10 ksi and 13 ksi). Again,
a window of strength was specified so that differentiation could be made between the normal-
strength and high-strength concrete. The mix was also designed to have a compressive strength at
release equal to 48.2 MPa (7 ksi). Actual average compressive strengths for the high-strength
concretes were 54.3 MPa (7.9 ksi) at release, 71.3 MPa (10.4 ksi) for air-cured cylinders at 28
days, and 74.2 MPa (10.8 ksi) for moist-cured cylinders at 28 days.

INSTRUMENTATION
Mechanical Gauge Points

Mechanical gauge points (called Whittemore points) were attached to each beam on the exterior
concrete surface to measure concrete surface strains. For most of the beams, these Whittemore
points were placed at regularly spaced intervals along the top and bottom flanges at the level of
the strands; some of the beams only had Whittemore points along the bottom flange. Spacings
for the Whittemore points were 100 mm (3.94 in) for the top and bottom flanges at the ends of
the beams, and 200 mm (7.87 in) for the top flanges along the mid-span regions of the beams.
The distances between the Whittemore points were read both prior to and after detensioning. The
differences in values between the two sets of readings were used to determine the strains in the
concrete after detensioning. A full set of readings were also taken when the concrete was 7, 14,
and 28 days old; prior to and after a composite deck was cast; and immediately before the
development length experimentation. :

14


Table 7. Development length test results from structural analysis of FHWA research beams

constructed with high-strength concrete.

0.0218

in/in in/in)

0.01271

0.0218

0.02067

0.0218

0.01139

0.0218

0.02076

0.0161

0.01416

0.0161

0.01538

0.0161

0.01336

0.0161

31

0.01190

1 in/in = 1 mm/mm, 1 ksi = 6.89 MPa


Each of the studies included in the correlation are briefly described below. Tables 8 and 9 list the
studies, the types of members used in the studies, and the number of data points from each study
that were used in the correlation.

Auburn University

Auburn University researchers conducted a study for the Alaska Department of Transportation
and Public Facilities that focused on the effect of strand spacing on the development length of
pretensioned strands. Experimentation was conducted on 559-mm- (22-in-) high T-beams that
contained nine 12.7-mm- (0.5-in-) diameter strands. The spacing of the strands was either 44.4
mm or 50.8 mm (1.75 in or 2.0 in). The concrete compressive strength varied between normal-
strength concrete (41.3 to 55.1 MPa [6 to 8 ksi]) and high-strength concrete (68.9 to 82.7 MPa
[10 to 12 ksi]). Both transfer and development length were determined for the 14 T-beams.®*TM”

University of Colorado at Boulder

Researchers at the University of Colorado at Boulder tested 15.2-mm- (0.6-in-) diameter strands
contained in box beams to determine their transfer and development lengths for the Colorado
Department of Transportation and FHWA. The objective of the study was to verify the adequacy
of the members containing the 15.2-mm- (0.6-in-) diameter strands. If adequate, that size of
strand would then be used in box girders in a high-performance concrete bridge ’project in
Colorado. .

Although three box beams were fabricated and made composite with a concrete deck, only two
of the members (beam numbers 1 and 2) were used in the correlation with the new FHWA
equation because of time constraints. The box beams were 381 mm (15 in) wide and 483 mm.(19
in) high, with a 229-mm- (9-in-) wide void and a 70-mm- (2.75-in-) thick composite deck.

The concrete compressive strength of the beams at 28 days was 71.0 MPa (10,300 psi), and the

concrete compressive strength of the deck at 7 days was 48.2 MPa (7000 psi). Both transfer
length and development length were determined for these members.°*??

51


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84


The parameters listed previously were numerically evaluated using a computer program called
TableCurve 2D. This program numerically scans data for a given set of parameters and evaluates
the relationship between the parameters against a set of equation types to provide the best-fit
equations for the parameters. Using this program, the parameters were evaluated with
TableCurve 2D and more than 3400 equation types were initially examined. These included the
following:

Linear equations.

Non-linear equations.

Log (Base 10) equations.

Natural log (Base e) equations.
Semi-log (Base 10) equations.
Semi-natural log (Base e) equations.

TableCurve 2D uses the method of least squares to determine the best-fit equations.” The
FHWA researchers also used an option on the TableCurve 2D program that applies a simple
equation filter, which weeds out the more complex of the equation types. This was done to
ensure that the equation selected was not only an accurate equation, but an understandable and
usable equation as well.

The TableCurve 2D program produced a list of possible equations that were ranked by their
degree-of-freedom (DOF)-adjusted coefficient of determination. This DOF-adjusted coefficient
of determination is a measurement of the goodness of fit of the data with a given equation.” The
FHWA researchers could then compare the best-fit line equations using the DOF-adjusted
coefficient of determination and select the best equation. The combination of variables and best-
fit equation that had the highest DOF-adjusted coefficient of determination and was also
understandable and usable was then chosen as the best obtainable flexural bond length equation.

The measured (or actual) values of the variables listed above were used in the analysis process
just described. The best-fit equation that was chosen as the flexural bond length equation is
shown below: .

6.4 (f",, -f,, )(D)
i 26 (8)

where L,, is the flexural bond length.

Figure 8 shows a graph of the measured values of flexural bond length versus the expression
(f., - f,.)D/f,. The expression (f*,, - f,,)D/f’, also contains the measured (actual) values of the
parameters in it. Equation (8) is also plotted in this figure. It should be noted that Equation (8) is
a best-fit curve; it is not a conservative equation nor does it contain any factor of safety. It is
simply a reasonable mean for the measured data from the FHWA Phase II beams.

38


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strands, spaced at 50.8 mm (2 in). The concrete compressive strengths of these girders at 28 days
varied between 77 and 83 MPa (11,100 and 12,100 psi). Transfer lengths, cambers, and prestress
losses were determined for these girders, and then fatigue testing ensued. After fatigue testing,
the girders were tested to failure to determine their ultimate and shear capacities. The transfer
and development lengths for both girders were used in the correlation.°??

North Carolina State University

A total of 60 rectangular specimens were constructed as part of the North Carolina State
University study for the North Carolina Department of Transportation and the FHWA. The
principal objective of the study was to evaluate the bond of various diameters and surface
conditions of epoxy-coated prestressing strands. To provide a comparison, many members were
also constructed with uncoated strands. Thirty-two of the 60 specimens contained epoxy-coated ~
strands, while 28 of them contained uncoated strands. The strand diameters varied between 9.5
mm, 12.7 mm, and 15.2 mm (% in, 0.5 in, and 0.6 in), while the compressive strength of the
concrete at 28 days ranged from 31.9 to 59.2 MPa (4630 to 8590 psi). Transfer lengths were

) determined at six different time intervals, and development length tests were conducted both with
and without fatigue testing. Elevated temperature tests were also performed on some of the
specimens. Transfer and development lengths for 27 of the specimens with uncoated strands
were used in the correlation.“*?

University of Oklahoma

Researchers at the University of Oklahoma conducted research for the Precast/Prestressed
Concrete Institute to investigate a standardized method for measuring bond performance of
prestressing strands. Their research consisted of using strands from three different anonymous
strand manufacturers in tensioned and untensioned pull-out tests and comparing these results to
transfer lengths measured in rectangular specimens to see if a correlation existed.

The strand-surface condition from one of the manufacturers’ strands was varied to demonstrate
its effect on transfer and development lengths. The four different strand-surface conditions were:

‘ As-Received—Just as it was received from the strand manufacturer.

. Cleaned—Cleaned with a solvent.

. Weathered—Exposed to the environment for a given time period before being used.
. Lubricated—Lubnicated with silane.

Seventeen rectangular specimens were constructed as part of this study. University of Oklahoma
researchers performed transfer and development length experimentation with these specimens.
The specimens were 152 mm (6 in) wide by 305 mm (12 in) high, and either 5.2 m (17 ft) or 7.3
m (24 ft) long. Each specimen contained two 12.7-mm- (0.5-in-) diameter strands.

The concrete compressive strength at 28 days ranged from 33.0 to 43.1 MPa (4790 to 6260 psi).
The transfer and development lengths for 17 of the rectangular specimens (specified as AA, BA,
CA, CC, CS, and CW specimens in that study) were used in the correlation with the new FHWA
equation.°°°*”)

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CHAPTER 1: INTRODUCTION AND BACKGROUND

Prestressed concrete bridges are a main staple of America’s bridges. Almost half of the new
bridges constructed throughout America have prestressed concrete superstructures, indicating
that prestressed concrete has become the material of choice for new bridges. This represents a
major development over the last half century, since the use of prestressed concrete for bridges
began in the United States in 1949 with the initiation of construction of Philadelphia’s Walnut
Lane Bridge.” There are two types of prestressed concrete: pretensioned and post-tensioned.
Pretensioned members are first constructed by tensioning the prestessing strands in a stressing
bed. The concrete is then cast and cured, and once the concrete reaches a certain specified
strength, the strands are released (or detensioned). The prestressing force in a prestressing strand
is then transferred from the strand to the concrete by bond. This occurs in the end regions of
pretensioned members.

Post-tensioned members are constructed by first placing and aligning empty ducts in a form. The
concrete is then cast and cured, and the strands are placed inside the ducts. Once the concrete
reaches a certain specified strength, the strands are tensioned and permanently anchored in place.
The strands transfer their initial prestress force to the concrete through use of the permanent end
anchorages.

WHAT IS DEVELOPMENT LENGTH?

Because the prestressing strands in pretensioned members transfer their force all the way up to
the ultimate load of the member to the concrete by bond, a certain distance is needed to
effectively allow bond to develop between the concrete and the strands. This distance, which is
measured from the end of the member, is called the development length. Because the prestressing
force is transferred from the strands to the concrete through the permanent end anchorages in a
post-tensioned member—rather than through bond—there is no development length for a post-
tensioned member.®*)

The development length is made up of two components: transfer length and flexural bond length.
(See figure 1.) The transfer length is the distance from the end of the member needed to fully
transfer the effective prestressing force by bond from the prestressing strand to the concrete. The
effective prestressing force corresponds to the effective prestressing stress in the strand, f,,. As
seen in figure 1, the transfer length corresponds to the distance needed from the end of the
member to develop the effective prestressing stress, f,,, in the strand. The flexural bond length is
the length needed beyond the transfer length to achieve bonding between the prestressing strand
and the concrete to attain the stress in the strand at the ultimate load of the member, f*,,. (See
references 3 through 6.)


Because designers would only have design values of parameters and not have the actual values of
the parameters while they were doing their design, the FHWA researchers plotted Equation (8)
on a graph of measured values of transfer length versus the expression (f*,, - f,,)D/f’,, which
contained design values of those parameters. This is shown in figure 9. Figure 9 illustrates that
Equation (8) is not necessarily the best-fit curve for this set of data. However, it is a conservative
curve for the design values. FHWA researchers decided to adopt Equation (8) as the proposed
flexural bond length expression pending correlation with data from other studies.

NEW DEVELOPMENT LENGTH EXPRESSION
The development length is the sum of the transfer length and the flexural bond length. Therefore,

the new development length expression is the sum of Equation (7) and Equation (8), and is
shown below:

4h 6.4 (fy “Se )(D) :
a - 21 + [206 (9)
‘ f, t. }

The first term of this equation represents the transfer length, while the second term represents the
flexural bond length. Equation (9) is shown graphically with the FHWA beam data in figure 10.
Note that the measured values for the parameters are used in figure 10.

In this figure, flexural, slip/shear, and combination flexural/slip failures are shown. Although no
failure of an actual bridge beam is desirable, if a beam failure is unavoidable, the engineer prefers
a warning so that loss of life can be prevented. The flexural failures are the failures that provide
warning signs (such as vertical cracks and excessive deflection); these are the “good” failures.
The slip/shear failures occur without warning and are the failures that should be prevented. The
combination flexural/slip failures are failures in which flexure and slip occur at exactly the same
time and indicate that the embedment length being tested is the actual development length for
that beam. .

In figure 10, all slip failures should fall below-the curve. This would indicate that the embedment
length (or development length) calculated (or provided) is greater than that which would cause a
slip failure. Flexural failures can fall above or below the curve because they are the “good”
failure types. Figure 10 shows that the curve is adequate for ensuring against a slip failure, but it
does not provide a safety margin.

40




y=mx+b (5)

where: y= dependent variable
m= __ slope of the line
= independent variable
= y-intercept

The method of least squares was used to determine the best-fit line. This method minimizes the y
distances between the measured y-values and the y-values calculated using the equation y=mx+b.
This method was used to determine best-fit lines for different combinations of variables. The
FHWA researchers could then compare the best-fit lines between different combinations of
variables using a parameter called the “coefficient of determination.” The coefficient of
determination is a measure of the strength of a linear relation.” The coefficient of determination
can vary between zero and one. A coefficient of determination of zero indicates that there is no
relationship and a coefficient of determination of one indicates a perfect relationship. The
combination of variables and best-fit line that had the highest coefficient of determination was
then chosen as the best obtainable transfer length equation.

The measured (or actual) values of the variables listed above were used in the regression analysis
process just described. The best-fit line that obtained the highest coefficient of determination was
chosen as the transfer length equation and is shown below:

3.927, D
= 39? Sy P - 20.67 (6)

t ra

where L, is the transfer length.

Figure 6 shows a graph of the measured values of transfer length versus the expression f, D/P,
for data from the FHWA Phase II beams. The expression f,,D/f’, also contains the measured
(actual) values of the parameters in it. Equation (6) is also plotted in this figure. It should be
noted that Equation (6) is a best-fit line; it is not a conservative equation nor does it contain any
factor of safety. It simply predicts mean values for transfer length based on the measured data
from the FHWA Phase II girders.

Because designers would not be privy to actual values of parameters while they were doing their
design, the FHWA researchers plotted Equation (6) on a graph of measured values of transfer
length versus the expression f,,D/f’., which contained design values of those parameters. This is
shown in figure 7. It can be seen from this figure that Equation (6) is not necessarily the best-fit
line for this set of data. However, it is a more conservative line for the design values.

34


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FHWA 1996 MEMORANDUM

By the early part of 1996, considerable research had been completed on the transfer and
development length of uncoated prestressing strands, especially 15.2-mm- (0.6-in-) diameter
strands spaced at 50.8 mm (2 in). Also at this time, FHWA was encouraging the use of high-
performance concrete (HPC) in bridges and some States formed partnerships with FHWA to
design and construct HPC bridges. In order to effectively use the higher strengths found in some
HPC, the use of larger diameter prestressing strands was needed. This resulted in a need to use
15.2-mm- (0.6-in-) diameter strands, and a need to use these strands at the current spacing for
12.7-mm- (0.5-in-) diameter strands, namely 50.8 mm (2 in). A number of research studies had
not only demonstrated successful use of the 15.2-mm- (0.6-in-) diameter strands at 50.8-mm (2-
in) spacings, but had also demonstrated successful use of 12.7-mm- (0.5-in-) diameter strands at
44-mm (1.75-in) spacings.

Therefore, FHWA evaluated the data available at that time on 12.7- and 15.2-mm- (0.5- and 0.6-
in-) diameter strands at reduced spacings of 44.4 mm and 50.8 mm (1.75 in and 2 in),
respectively, and issued a revised memorandum in May 1996. This memorandum:

. Allowed the use of 15.2-mm- (0.6-in-) diameter strands in pretensioned applications.

. Allowed the following center-to-center strand spacings:
—15.2-mm- (0.6-in-) diameter strands at 50.8-mm (2-in) spacing
—12.7-mm- (0.5-in-) diameter strands at 44.4-mm (1.75-in) spacing

. Retained the multipliers for fully-bonded and debonded strands for use with the
AASHTO development length equation.

The memorandum stated that the multipliers were to be retained “... until such time as a currently
proposed development length equation by FHWA is reviewed and commented upon by the
AASHTO Bridge Subcommittee on Bridges and Structures ...”"'®?

The AASHTO Subcommittee on Bridges and Structures’ Technical Committee #T-10 on
Concrete, commonly known as AASHTO T-10, followed up the FHWA 1996 memorandum with
a proposed revision to Article 9.26.2.1 of the AASHTO bridge specifications.” This revised
article specified the minimum spacing for certain diameters of prestressing strands, and
effectively allowed the spacings cited in the FHWA memorandum. This revised article was
passed by the AASHTO Subcommittee on Bridges and Structures by letter ballot in fall 1997.

FORMULATION OF NEW DEVELOPMENT LENGTH EQUATION AND CONTENTS
OF THIS REPORT

Because the FHWA transfer and development length experimentation on the Phase II members
showed that the AASHTO and Buckner equations were “unconservative” in many instances, a
new development length equation was needed. A new development length equation has been
developed by FHWA based on the FHWA Phase II research results for beams. This new
development length equation is representative of the FHWA research results and of research


LIST OF FIGURES

Figure No. Page
1. Development length of prestressing strand ......... 0... cece cece cece e eens 2
2. Cross-sectional views of FHWA research beams ............. 60.0000 eee ee evens 12
3. Strain profile for typical pretensioned concrete rectangular specimen at 28 days...... 17
4. Strain profile illustrating methods for determining transfer length for one end of a
rectangular SpeciMeN ©... 6... ec eee cece een een teen nee e ene nee
5. Development length test set-up . 6.0... cece cette ene eee
6. Relationship between measured values of £,D/f, and measured transfer length ......
7. Relationship between design values of f,,D/f, and measured transfer length .........
8. Relationship between measured values of D(f*,,-f,,)/P, and flexural bond length for
FHWA Phase II beams only ...... 0... cece cee cece eee n een ee eee eee 39
9. Relationship between design values of D(f*.,-f,.)/P, and flexural bond length for
FHWA Phase II beams only ...... 0... cc ccc eee cece eee ete eee anes 41
10. Relationship between measured values of f, D/P, + D(f*,,-f./P, and
embedment length for FHWA Phase II beams only ................00000eeeueee 42
11. Relationship between design values of f,D/f, + D(f*,,-f,,)/P, and embedment
length for FHWA Phase II beams only ........... 00 cece eee e eee cece ee ene
12. Cross-sections of full-size beams and piles ...................
13. Additional cross-sections of full-size beams and piles
14. Comparison of measured transfer length values for all members with the AASHTO
CTLs Ce) RR 66
15, Comparison of measured transfer length values for members having concrete strengths
between 34.4 and 48.2 MPa (5000 and 7000 psi) with the AASHTO equation ....... 67
16. | Comparison of measured transfer length values for members having concrete strengths
between 55.1 and 68.9 MPa (8000 and 10,000 psi) with the AASHTO equation ...... 68
17. Comparison of measured transfer length values for all members with the Buckner
CTe LO C0) 6 69
18. | Comparison of measured transfer length values for members having concrete strengths
between 34.4 and 48.2 MPa (5000 and 7000 psi) with the Buckner equation......... 70
19. Comparison of measured transfer length values for members having concrete strengths
between 55.1 and 68.9 MPa (8000 and 10,000 psi) with the Buckner equation ....... 71
20. | Comparison of measured transfer length values for all members with the FHWA
[Te 080) 5 72
21. | Comparison of measured transfer length values for members having concrete strengths
between 34.4 and 48.2 MPa (5000 and 7000 psi) with the FHWA equation ......... 73
22. Comparison of measured transfer length values for members having concrete strengths
between 55.1 and 68.9 MPa (8000 and 10,000 psi) with the FHWA equation ........ 74
23. Comparison of development length equations for data with a strand diameter of 9.5 mm
(3/8 in) and a concrete strength of 34.4 MPa (5000 psi) ........... 0.020. 0e ec eee 76
24. Comparison of development length equations for data with a strand diameter of 12.7 mm
(0.5 in) and a concrete strength of 34.4 MPa (5000 psi) ............ cece eee eee 77
25. Comparison of development length equations for data with a strand diameter of 12.7 mm
(0.5 in) and a concrete strength of 41.3 MPa (6000 psi) ..................0000 008 78


Phase II was then undertaken by FHWA to evaluate the AASHTO and Buckner equations for
full-size members. Results from the full-size beams showed that the AASHTO transfer and
development length equations were unconservative for members constructed with normal-
strength concrete. The AASHTO transfer and development length equations were conservative
for full-size beams that were constructed with high-strength concrete.

Results from the FHWA I-beam research also demonstrated that the Buckner transfer length
equation was unconservative for beams constructed with normal-strength concrete, but was
conservative for members constructed with high-strength concrete.

The Buckner development length equation was inconsistent when compared to the measured
values of development length in normal-strength concrete—sometimes the Buckner equation was
unconservative (the predicted value was shorter than the measured value) and sometimes it was
conservative (the predicted value was longer than the measured value), When compared to
measured values for high-strength concrete, the Buckner development length equation values
were consistently conservative (the predicted values were longer than the measured values).

It was also evident from the FHWA I-beam research that measured values of transfer and
development lengths for a given strand size were shorter for high-strength concrete than for
normal-strength concrete. :

Because the AASHTO equation was unconservative for normal-strength concrete and the
Buckner equation was inconsistent for normal-strength concrete, it was determined that a new
development length equation was needed—an equation that could provide conservative
predictions of transfer and development lengths for all concrete strengths, yet not be overly
conservative for high-strength concretes.

FHWA researchers decided to formulate the new equation based on FHWA’s full-size beam
research results, and then correlate the equation with other research results to make sure that the
equation would be representative of the total applicable data to date.

A list of possible parameters for use in new transfer and development length equations was
compiled. Many of the parameters had been measured during FHWA’s full-size beam
experimentation; however, other parameters had to be determined from structural analyses of that
measured data. Two computer programs for structural analyses were developed by Dr. Fassil
Beshah and Dr. Nicolas Gagarin, based on the strain-compatibility method of analysis. These
programs were used to determine the remaining parameters.

For the new transfer length equation, all of the parameters were investigated initially by
inspecting the data and then evaluating the most promising parameters. The promising
parameters were evaluated along with the measured 28-day values of transfer length from
FHWA’s full-size beams using regression analyses. FHWA researchers employed a statistical
approach, using the coefficient of determination as an evaluation criterion, to choose a best-fit
line. FHWA researchers slightly modified that best-fit line by rounding-off the constants and
obtained a new transfer length equation (Equation (7)).

104


researchers could determine the unit weight from the quantity and quality information on
-constituent mix materials.

Jon Mullarky, formerly of the National Ready Mix Concrete Association, examined the data and
determined that accurate unit weight calculations could not be determined from the concrete-mix
constituent information unless the specific gravity of the aggregates and the air content of the
final mixture were provided. This information was not available for most of the studies, and
values for these parameters varied too much for confident assumptions to be made. Researchers
concluded that the information on unit weight was insufficient and, therefore, it could not be
evaluated as a parameter for the equations.

FHWA researchers re-evaluated the idea of using the area of strand rather than the diameter of
strand as a parameter in the equations using data from the other studies. They chose to re-
evaluate the parameter because some states used 12.7-mm (0.5-in) Special diameter strand in
their bridges. This size of strand has the same nominal diameter, but each of the seven wires
comprising the Special strand is slightly larger than the wires in normal 12.7-mm- (0.5-in-)
diameter strand. Therefore, the area of steel for the 12.7-mm (0.5-in) Special diameter strand is
larger than it is for the normal 12.7-mm- (0.5-in-) diameter strand. The area of steel for the 12.7-
mm (0.5-in) Special diameter strand is 107.7 mm’ (0.167 in’), while the area of steel for the
normal 12.7-mm- (0.5-in-) diameter strand is 98.7 mm? (0.153 in”).

While re-evaluating the idea of using the area of steel rather than the diameter of strand as a
parameter in the equation, FHWA researchers also re-evaluated equation types that had
logarithmic functions associated with them. The following equation types were re-examined with
all of the data:

y=mx +b 6)
log, {y) = m log,,(x) +b (10)
In (y)=m In(x)+b (11)
y =m log,, (x) +b (12)
y=mIn(x)+b . (13) . : .

where log,, is the Base 10 logarithm and In is the natural logarithm (logarithm to the Base-e). For
each.of the above equations, researchers performed regression analyses on all the’ data to -
determine the constants m and b for two instances: (1) when diameter D was used as a parameter
and (2) when the area of steel strand A*, was used as a parameter. Researchers then statistically
analyzed the data to determine coefficients of correlation for each of these cases.

Coefficients of correlation are “... a measure of the strength of the linear relationship between the
x and y variables.”*” The coefficients of correlation were compared, and FHWA researchers
concluded that Equations (7), (8), and (9), using the-diameter of the strand as a parameter, were
the best overall choices for the transfer length, flexural bond length, and development length
equations, respectively.

63


The 95-percent plateau method is similar to the 100-percent plateau method, and it is also shown
in figure 4. The steps are initially the same, including determining and drawing the horizontal
line representing the constant strain plateau; however, once the constant strain plateau has been
determined, it is multiplied by 0.95 to obtain a 95-percent constant strain value. Then a second
horizontal line, representing the 95-percent constant strain plateau, is drawn on the graph. At the
point where the linearly varying portion of the plot intersects this 95-percent constant strain
plateau, a vertical line is drawn to the x-axis. The value on the x-axis that corresponds to its
intersection with the vertical line is the 95-percent plateau transfer length.

The slope-intercept method consists of plotting two lines on the graph: a horizontal line
representing the 100-percent strain plateau and a second straight line that represents the points in
the linearly varying strain region (see figure 4). The intersection of these two straight lines is the
key point, and the location of this point is highly dependent upon how the second line is drawn.
At the intersection point, a vertical line is drawn to the x-axis. The value on the x-axis that
corresponds to its intersection with the vertical line is the slope-intercept transfer length.

The approximately 60 research studies on development length to date have used all three
methods to determine transfer length. To be able to compare transfer lengths of one study to
transfer lengths of another study, some consistent method of determining transfer lengths needs
to be employed. Buckner examined this issue in his work for FHWA, and in the process, he
identified several possible sources of error that influence the various methods of determining
transfer lengths. He identified errors caused by overlapping gauge lengths, shear lag, and beam
weight in eccentrically prestressed members."” His study concluded that:

“The 95 percent constant strain method ... provides a simple, objective, upper-
bound estimate of transfer length and is recommended as the basis for reporting
transfer lengths in future studies.”'”

Because of Buckner’s recommendation, the FHWA Phase II transfer lengths were determined by
the 95-percent plateau method, even though the FHWA Phase I transfer lengths had been
determined by the 100-percent plateau method. The transfer lengths for the Phase II beams are
provided in table 2.

The Phase II transfer lengths are those determined at 28 days of concrete age. The 28-day values
of transfer length were used for two reasons:

. Magnitude of the Whittemore readings at 28 days.
° Growth of transfer length with time.

The Whittemore readings taken at transfer were small measurements, and their magnitudes were
close to the accuracy of the instrument. However, after 28 days had elapsed, the magnitudes of
the Whittemore readings increased because of creep and shrinkage. The plots of the strains
determined from the Whittemore readings were more defined at 28 days than at the time of
transfer.

18


Sw "Sg )(D) = flexural bond length.

There is one other provision in the AASHTO Specifications related to development length, and
that is found in Article 9.20.2.4. This article states that the transfer length component of the
development length for strand may be assumed to be equal to 50 times the nominal diameter of
the strand. This AASHTO article is similar to the ACI building code Article 11.4.3. Both
expressions are used to help determine the component of a draped prestressing strand that can be
used to resist shear.

FHWA 1988 MEMORANDUM

On October 26, 1988, the Federal Highway Administration (FHWA) issued a memorandum
concerning the use of prestressing strands in pretensioned applications for prestressed concrete
bridges. The memorandum:

. Disallowed the use of 15.2-mm- (0.6-in-) diameter strands in pretensioned applications.

. Restricted the minimum center-to-center strand spacing to four times the nominal
diameter of the strand.

° Increased the required development length for fully-bonded and debonded strands by 1.6
and 2.0 times AASHTO Equation 9-32, respectively.

The FHWA memorandum indicated that its restrictions were adopted only as an interim measure,
until research results indicated otherwise and AASHTO adopted the results.

FHWA issued this memorandum to address two technical incompatibilities. The first
incompatibility was between the strands used in the research studies leading to the AASHTO
equation and the strands now in use. The second incompatibility was that the development length
values resulting from the AASHTO equation did not agree with research results published at that
time.

The first incompatibility was between the strands used to create the AASHTO equation and the
strands now in use. The research data on which the AASHTO equation was based was for stress-
relieved strands with ultimate strengths of 1720 MPa (250 ksi). The stress in these strands
immediately after prestress transfer could not exceed 70 percent of the ultimate stress of the
strands. In contrast, the current practice is to use low-relaxation strands with ultimate strengths of
1860 MPa (270 ksi). Since 1986, the stress in these strands can go up to (but cannot exceed) 75
percent of the ultimate stress of the strands. Thus, current strands are stronger and can
accommodate a higher overall stressing force than the strands used to create the AASHTO
equation. Also, the prestressing force is now allowed to attain a higher percentage of the ultimate
strength of the strands than was allowed for the data used to create the AASHTO equation.


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85


The second incompatibility involved research results. The research was conducted in the 1980’s
by North Carolina State University. It indicated that the development lengths of uncoated
strands with ultimate strengths of 1860 MPa (270 ksi) were greater than that predicted by the
AASHTO equation.

HISTORY OF THE AASHTO EQUATION

Due to the questions concerning the validity of the AASHTO equation, it was decided by FHWA
to sponsor a study that would determine how the AASHTO equation came to be. Construction
Technology Laboratories, Inc. (CTL) conducted this study for FHWA. By consulting past
versions of AASHTO and ACI documents, as well as published and unpublished ACI Committee
423 documents and individuals from this committee, they found that the AASHTO equation
reflected average values rather than conservative ones.

Their study found that the AASHTO equation was first used in the 1963 ACI Building Code”
and was adopted for use in the AASHTO Specifications in 1973." The equation was based on
two research studies. These studies, conducted during the 1950’s and 1960’s by Hanson and -
Kaar"» and by Kaar, Lafraugh, and Mass,” used stress-relieved strands with an ultimate
strength of 1720 MPa (250 ksi) and included little work on 15.2-mm- (0.6-in-) diameter strands.
In both of these studies, the stress in the strands immediately after prestress transfer could not
exceed 70 percent of the ultimate stress in the steel strand. Even though the AASHTO equation
was based on these research studies, it does not reflect the values for development length that
Kaar and Hanson propose. CTL researchers Tabatabai and Dickson further explain:

“The ACI 318R-63 Commentary also states that the transfer and flexural bond
equations are based on published papers by Kaar et al. and Hanson and Kaar ...
However, those two papers do not specifically propose the equations represented
in the code. In fact, Hanson and Kaar recommended embedment lengths far more
conservative than AASHTO Equation 9-32 to prevent general bond slip.”

The portion of the AASHTO equation relating to transfer length, f,,D/3, is based on an assumed
average value of bond stress. Because of this, the above expression for transfer length represents
an average value for transfer length, and not a conservative value. The commentary for the 1963
ACI building code confirms this by stating that “the value of f,,.D/3 for transfer length is an
average value based on data reported by Kaar et al. ...’""

Similarly, the expression for flexural bond length contained within the AASHTO equation, (f*,, -
f,,)D, also represents average values for flexural bond lengths and not conservative values.
Tabatabai and Dickson state:

“The flexural bond length relationship ((f*,, - f,,.)D) is the equation of a line drawn
through data points on a graph of (f*,, - f,,) versus ((L - L,)/D). In the view of the
ACI Committee 423 [joint ASCE-ACI Committee 423 on Prestressed Concrete],
the proposed line represented a reasonable mean for the data points without being
unreasonable for long bonded lengths.”


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Military Institute. Two of the Hoblitzell-Buckner beams were constructed at Texas Concrete in
Houston, TX, and shipped to and tested at the University of Texas at Austin.

The beams measured 1067 mm (42 in) in height and were 356 mm (14 in) wide, and contained
six 15.2-mm- (0.6-in-) diameter strands spaced at 50:8 mm (2 in) in one row at the bottoms of the
sections. Three No. 9 steel reinforcing bars were also placed in the tops of the beams. The
concrete’s design compressive strengths were 41.1 MPa (6000 psi) at detensioning and 55.2 MPa
(8000 psi) at 28 days. Actual concrete compressive strengths were 48.5 MPa (7040 psi) at
detensioning, and ranged between 81.4 and 81.9 MPa (11,810 and 11,890 psi) at 28 days.

The concrete compressive strength of the beams had increased to just more than 90 MPa (13,000
psi) by the time that the beams underwent development length testing. Both transfer and
development length tests were performed for each end of each beam. The-results from these tests
were included in the correlation with the new FHWA equations.“*4”

University of Texas at Austin—San Angelo Bridge Project

Similar to the Louetta Road Overpass project, a second HPC bridge project was initiated in
Texas for the San Angelo-Bridge. The partners in this project were again FHWA and Texas
DOT, in conjunction with the University of Texas at Austin. For this bridge, it was desired to use
15.2-mm- (0.6-in-) diameter strands at 50-mm (2-in) spacings in I-beams. The bridge consisted
of two parallel structures, one that would primarily be designed and constructed with normal
concrete and one that would primarily be designed and constructed with HPC.

Since this project took place while the 1988 FHWA memorandum was still in effect, the
researchers were required to demonstrate that the 15.2-mm- (0.6-in-) diameter strands would
work successfully at the reduced spacing in an I-beam constructed with concrete similar to that to
be used in the actual bridge beams.

Two sets of two I-beams were fabricated for the research. One set of beams represented the
normal concrete and one set represented the higher-strength HPC. All beams were Texas Type
“C” beams, which were 1016 mm (40 in) high, with a 559-mm- (22-in-) wide bottom flange and
a 356-mm- (14-in-) wide top flange. Each beam contained sixteen 15.2-mm- (0.6-in-) diameter
strands in the bottom flange and four 15.2-mm- (0.6-in-) diameter strands in the top flange; all
strands were spaced at 50.8 mm (2 in).

The normal concrete set of beams had an actual concrete compressive strength of 46.4 MPa
(6740 psi) at 28 days, while the higher strength HPC set of beams had an actual concrete
compressive strength of 88.0 MPa (12,770 psi) at 28 days. Each beam had a composite deck cast
at the Ferguson Laboratory at the University of Texas at Austin. Transfer and development
length tests were performed for each end of each beam. These results were used in the correlation
with the new FHWA equations.“

Tulane University and Construction Technology Laboratories, Inc. (CTL)

Tulane University and Construction Technology Laboratories, Inc. (CTL) performed this study
for the Louisiana Department of Transportation and Development. The prestressed concrete

59


approximately divided, with approximately half of the points above the line and half below the
line.

In-figure 15, only the data for members with normal-strength concrete (f, between 34.4 and 48.2
MPa [5000 and 7000 psi]) were shown. This figure indicates that the current AASHTO equation
is unconservative for predicting transfer lengths in this range of concrete strengths.

Data for members with high-strength concrete (fc between 55.1 and 68.9 MPa [8000 and 10,000
psi]) were plotted in figure 16. The transfer lengths determined in the research studies involving
the high-strength concrete were consistently shorter than transfer lengths in normal-strength
concrete. Because those transfer lengths are consistently shorter, the AASHTO transfer length
equation is conservative for members constructed with high-strength concrete.

Figures 17 through 19 compare all of the transfer length data to transfer length predictions by
Buckner’s transfer length equation, f,,D/3 (see Equation (3)). It is apparent from figure 17 that
Buckner’s transfer length equation is more an average expression than a conservative expression
because a considerable number of points fall above the line.

The same trend is seen in figure 18, which illustrates the data and the Buckner-predicted transfer
lengths for all members constructed with normal-strength concrete. However, when only data
and predicted values for transfer lengths in high-strength concrete members were plotted, the
Buckner transfer length equation was conservative (see figure 19).

Figures 20 through 22 show the transfer length data and transfer length predictions using the
FHWA transfer length equation (Equation (14)). Figure 20 shows only a few data points falling
above the line, which indicates that the FHWA equation is conservative. The same conclusion
was drawn from the data shown in figure 21, which is the graph of data and FHWA-predicted
transfer lengths for members constructed with normal-strength concrete.

65




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End Slip

The end slip of each strand at both ends of each beam was measured. Before detensioning, a
small channel-shaped fixture was attached to a strand adjacent to the end of a beam. Holes were
bored in the legs of the fixture so it could accommodate a digital depth gauge that was used to
measure the distance from the outer leg of the fixture to the concrete surface. This distance was
measured before detensioning.

After detensioning, each strand was cut so that a minimum of 50.8 mm (2 in) still projected from
the end of the member and the channel-shaped fixture was still attached to the projecting ends of
strands. The distances were measured again after detensioning. The difference between these two
distance values was the end slip of the strand at detensioning. A full set of end slip readings were
taken at the same time that the mechanical gauge points were read for all of the time intervals
described previously.

The end slip of the strand was also measured during the development length experimentation.
Before a beam’s development length testing, the last set of end slip readings were taken and then
the channel-shaped fixtures were removed. Linear voltage displacement transducers (LVDTs)
were attached to the projecting ends of all strands at the end of the member to be tested. As
loading on that end of the member progressed, the LVDTs measured any changes in distances
between where the LVDTs were attached to the strands and the concrete surface. Any changes in
these distances, known as end slips, were caused by the strands losing their bond during the
development length test loading and slipping inward.

Jacking Force

Each strand for each beam was tensioned individually using a single-strand prestressing jack.
The jack was connected to a pressure gauge to measure force from the pressure applied to the
jack. The actual elongation of each strand was also measured. This elongation was used, along
with the physical properties of the strands, to calculate the stress in the strand prior to release.

Loads

Single-point loads during the development length experimentation were applied using a
hydraulic jack and were measured using load cells placed at the hydraulic jack. The load cells
were attached to a data acquisition system, which allowed the load values to be read and
displayed on a computer screen every 2 seconds.

Electrical Resistance Strain Gauges

One or two electrical resistance strain gauges (hereafter simply called “strain gauges”) were
attached to the top of the member prior to the development length test for a given end of the
beam. If the beam was non-composite, then one strain gauge was used and it was affixed to the
top flange of the beam approximately 152 mm (6 in) away from the load. If the beam was
composite with a deck, then two strain gauges were affixed to the top of the deck, one on either
side of the load (approximately 152 mm [6 in] away from the load). These strain gauges were

15


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CHAPTER 2: FHWA PHASE II RESEARCH STUDY RESULTS

As discussed in the previous chapter, the FHWA study entitled “Investigation of Development
Length of Uncoated and Epoxy-Coated Prestressing Strand” began in the spring of 1990 and
consisted of two phases. Phase I involved 50 rectangular prestressed concrete members, while
Phase II involved 64 members: 32 AASHTO Type II prestressed concrete I-beams and 32
prestressed concrete sub-deck panels. For Phase II, half of the beams and half of the deck panels
contained uncoated strands, while the other halves contained epoxy-coated strands. This report
discusses only the 16 beams that contained uncoated strands in Phase II.

DESCRIPTION OF MEMBERS
Beams

Three different strand patterns were used in the beams—-strand patterns A, B, and C (see figure
2). These strand patterns were chosen to investigate how various strand diameters and spacings
affected development length, and to see if any of these patterns resulted in cracking of the
member at detensioning. Strand pattern A contained eight strands, 12.7 mm (0.5 in) in diameter,
spaced at 50.8 mm (2 in) in one row in the bottom flange and two strands of the same diameter in
the top flange. Strand pattern B contained nine strands, 12.7 mm (0.5 in) in diameter, spaced at
44.4 mm (1.75 in) in one row in the bottom flange and two strands of the same diameter in the
top flange. Strand pattern C had eight strands, 15.2 mm (0.6 in) in diameter, spaced at 50.8 mm
(2 in) in one row in the bottom flange and two strands of the same diameter in the top flange. All
of the strands were fully stressed.

All of the beams were 9.46 m (31 ft) long, and all contained single-leg stirrups that were placed
on alternate sides of the cross-section every 76.2 mm (3 in). For the first 0.92 m (3 ft) of each
end of the beam, confinement reinforcement was placed in the top and bottom flanges.
Accelerated curing was used for all members. Detensioning was accomplished through flame-
cutting.

Six of the beams were made composite with a cast-in-place concrete deck that was cast at the
FHWA Structures Laboratory. The other 10 beams did not have a deck cast on them. This was
done to see how a higher maximum strain in the strand at failure would affect development
length. When a deck is made composite with the beam and this composite member is then tested
to failure, a high strain in the strand at failure can be achieved for flexural failures. These strains
are typically near 0.03 or 3 percent. If the non-composite beam is tested to failure, typically the
strain in the strand at a flexural failure is near the yield point of the strand, which is 0.01 or 1
percent. Table 1 lists the beams used in the study that had uncoated strands.

ee

: 1a
WW Preceding Page blank


Louisiana State University and the University of New Orleans

Researchers from Louisiana State University and-the University of New Orleans conducted this
research study for the Precast/Prestressed Concrete Institute to find a standard test for
determining bond characteristics of prestressing strand. As part of this research, four rectangular
pretensioned concrete specimens were constructed using a single 9.5-mm- (%-in-) diameter,
Grade 270, low-relaxation strand in each specimen; for two of the specimens, the strand was
uncoated, and for two of the specimens, the strand was epoxy-coated. The rectangular specimens
measured 89 mm x 89 mm (3.5 in x 3.5 in) in cross-section, and 2.44 m (8 ft) in length.

Only transfer lengths were determined for the specimens; there was no development length
testing. The transfer lengths for the rectangular specimens containing uncoated strands were used
in the correlation.

McGill University

This research study was conducted by McGill University with funding by the Natural Sciences
and Engineering Research Council of Canada and was completed under the Networks of Centres
of Excellence program.

The main objective of the study was to examine the impact that the high compressive strength of
the concrete has on transfer and development lengths. The main variables were the size
(diameter) of the strands (9.5 mm, 12.7 mm, and 15.7 mm [3/8 in, 0.5 in, and 0.62 in]), and the
28-day compressive strength of the concrete (31 to 89 MPa [4500 to 12,900 psi]).

Canadian-manufactured strand was used in the study and not U.S.-manufactured strand. Note
that the largest size of strand had a diameter of 15.7 mm (0.62 in), and was not the more common
American size of 15.2 mm (0.60 in).

The smallest-size strands were stress-relieved strands; members containing this strand were not
used in the correlation. The other two larger-size strands were low-relaxation strands, and
members containing these strands were used in the correlation.

Twenty-two rectangular specimens were fabricated as part of the study; their sizes ranged from
100 mm x 200 mm (3.9 in x 7.9 in) to 200 mm x 250 mm (7.9 in x 9.8 in). Transfer lengths at
transfer and at 21 days, as well as development lengths, were determined for the specimens.
FHWA researchers did not receive the development length data by the cut-off date, but did have
access to the transfer length data. Therefore, only the transfer lengths for the 14 specimens
containing the low-relaxation strands were used in the correlation with the new FHWA
equations.°”

University of Minnesota
A study on the applicability of using high-strength concrete to build full-size bridge girders took
place at the University of Minnesota. This research consisted of fabricating and testing two full-

size Minnesota 45M I-girders with composite decks. These girders were 1.14 m (45 in) high and
40.5 m (132 ft-9 in) long. Each girder contained 46 uncoated 15.2-mm- (0.6-in-) diameter

55




It was desired that the above equations (Equations (14) through (16)) apply not only to beams but
also to piles, because piles, under certain loading conditions, must resist flexural loads. However,
there were limited data available on piles. Therefore, a theoretical parametric study was
performed using two different pile sections to see if the recommended development length
equation (Equation (16)) was conservative for pretensioned piles.

The theoretical parametric study results concluded that the axial load existing in piles had no
detrimental effect on the development length and that the FHWA development length equation
(Equation (16)) was conservative for piles.

Another factor to consider when examining the topic of transfer and development lengths of
pretensioned strands in prestressed concrete piles is the effect of strand position during the
casting of the piles. Because piles are cast horizontally and strands are placed around the
perimeter of the pile, evidence shows that strands at the top of pile sections during casting exhibit
significantly more end slip at detensioning than do the bottom strands. Because end slip is widely
held as an indicator of bond, the longer end slips at detensioning result in longer transfer and
development lengths.

AASHTO and ACI have recognized and addressed the phenomenon of worse bond (longer
development lengths) for top reinforcing bars (rebars) by their application of a 1.3 multiplier to
the general development length equation for rebars. Therefore, FHWA researchers recommend
that the FHWA transfer and development length equations (Equations (14) and (16),
respectively) be used for piles, and that a 1.3 multiplier be applied to Equations (14) and
(16) for any strands (straight or draped) in any member (beam or pile) that has 305 mm (12
in) or more of concrete cast beneath them. However, the 1.3 multiplier should not be applied
to strands in beams that do not fit this criterion.

FHWA researchers hope that ongoing and/or future physical research on pretensioned piles can
experimentally verify the findings of the theoretical analysis for piles, and further define the top
strand effect.

The new FHWA transfer and development length equations, Equations (14) and (16),
respectively, have been established on the basis of the FHWA full-size beam data and correlated
conservatively with research results from other studies with the guidelines outlined above. They
are recommended for immediate use in the design of pretensioned beams and piles.

108


ACI and AASHTO
AASHTO Standard

Report LRFD Specification
Symbol Notation Notation Description
L, Transfer length
m Slope of line
Ww, Ww. ww, Unit weight of concrete
x Independent variable
y Dependent variable
Es Strain in prestressed reinforcement at
nominal strength—from Buckner report
€, Strain in prestressing strand at ultimate
strength of the member
a Multiplying factor applied to flexural

bond length term in Buckner
equation—from Buckner report

110


LIST OF FIGURES (continued) ,

Figure No. Page
26. | Comparison of development length equations for data with a strand diameter of

12.7 mm (0.5 in) and a concrete strength of 48.2 MPa (7000 psi) ..............008 79
27. Comparison of development length equations for data with a strand diameter of

12.7 mm (0.5 in) and a concrete strength of 68.9 MPa (10,000 psi) ...............- 80
28. | Comparison of development length equations for data with a strand diameter of

12.7 mm (0.50 in) Special and a concrete strength of 41.3 MPa (6000 psi) .......... 81
29. Comparison of development length equations for data with a strand diameter of

12.7 mm (0.52 in) Special and a concrete strength of 41.3 MPa (6000 psi) .......... 82
30. | Comparison of development length equations for data with a strand diameter of

15.2 mm (0.6 in) and a concrete strength of 34.4 MPa (5000 psi) .............0005 83
31. | Comparison of development length equations for data with a strand diameter of

15.2 mm (0.6 in) and a concrete strength of 41.3 MPa (6000 psi) .............000. 84
32. Comparison of development length equations for data with a strand diameter of

15.2 mm (0.6 in) and a concrete strength of 48.2 MPa (7000 psi) ...............05 85
33. Comparison of development length equations for data with a strand diameter of

15.2 mm (0.6 in) and a concrete strength of 55.1 MPa (8000 psi) ................. 86
34. | Comparison of development length equations for data with a strand diameter of

15.2 mm (0.6 in) and a concrete strength of 68.9 MPa (10,000 psi) ................ 87
35. | Comparison of measured development length values for all members with

the AASHTO and 1.6 AASHTO equations ........... 0.0. e cece eee eee eens 89
36. | Comparison of measured development length values for members having concrete

strengths between 34.4 and 48.2 MPa (5000 and 7000 psi) with the AASHTO and 1.6

AASHTO equations .... 00... ieee tee nent ett nent eee 90
37. | Comparison of measured development length values for members having concrete

strengths between 55.1 and 68.9 MPa (8000 and 10,000 psi) with the AASHTO and

1.6 AASHTO equations ...... 0.6... c ccc ec ee en nee ee rt nee enee 91
38. | Comparison of measured development length values for all members with the

Buckner equation ..... 2... 6c eee eee enn n eet teen eens 92
39. - Comparison of measured development length values for members having concrete

strengths between 34.4 and 48.2 MPa (5000 and 7000 psi) with the Buckner equation . 93
40. | Comparison of measured development length values for members having concrete

strengths between 55.1 and 68.9 MPa (8000 and 10,000 psi) with the Buckner

Equation one eee e ne eens 94
41. | Comparison of measured development length values for all members with the FHWA

EQUatION 6. ee ee ee eee n eben eee 95
42. Comparison of measured development length values for members having concrete

strengths between 34.4 and 48.2 MPa (5000 and 7000 psi) with the FHWA equation . . 96
43. | Comparison of measured development length values for members having concrete

strengths between 55.1 and 68.9 MPa (8000 and 10,000 psi) with the FHWA
equation 2.6... cece eee ene Leen eee eect ene nee 97


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10.

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14.

REFERENCES

E.P. Small and J. Cooper. “Condition of the Nation’s Highway Bridges: A Look at the
Past, Present, and Future,” 7R News, Number 194, January-February 1998, pp. 3-8.

T.Y. Lin. Design of Prestressed Concrete Structures, John Wiley & Sons, New York,
1955.

*§.N. Lane. “Development Length of Prestressing Strand,” ” Public Roads, Vol, 54; No. 2,

September 1990, pp. 200-205.

T.E. Cousins, D.W. Johnston, and P. Zia. “Bond of Epoxy: Coated Prestressing Strand,”
Publication No. FHWA/NC/87-005, Federal Highway Administration, Washington, DC,
December 1986.

A.H. Nilson. Design of Prestressed Concrete, John Wiley & Sons, New York, 1978.

Building Code Requirements for Structural Concrete (ACI 318-95) and Commentary
(ACI 318R-95), ACI 318-95 and ACI 318R-95, American Concrete Institute, Farmington

- Hills, Michigan, 1995.

Standard Specifications for Highway Bridges, Sixteenth Edition, American Association
of State Highway and Transportation Officials, Washington, DC, 1996.

H. Tabatabai and T.J. Dickson. The History of the Prestressing Strand Development
Length Equation, Publication No. FHWA-RD-93-076, Federal Highway Administration,
Washington, DC, February 1995.

Building Code Requirements for Reinforced Concrete, ACI 318-63, American Concrete
Institute, Detroit, Michigan, 1963.

Standard Specifications for Highway Bridges, Eleventh Edition, American Association of
State Highway and Transportation Officials, Washington, DC, 1973.

N.W. Hanson and P.H. Kaar. “Flexural Bond Tests of Pretensioned Prestressed Beams,”
ACI Journal, Proceedings, Vol. 55, No. 7, January 1959, pp. 783-802.-

P.H. Kaar, R.W, LaFraugh, and M.A. Mass. “Influence of Concrete Strength on Strand
Transfer Length,” PCJ Journal, Vol. 8, No. 5, October 1963, pp. 47-67.

Commentary on Building Code Requirements for Reinforced Concrete, ACI 318R-63,
American Concrete Institute, Detroit, Michigan, 1963.

U.S. Department of Transportation, Federal Highway Administration Memorandum,
“Prestressing Strand for Pretension Applications—Development Length Revisited,”
October 26, 1988.

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119 | Preceding page blank
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