DEVELOPMENT LENGTH OF UNCONFINED … LENGTH OF UNCONFINED CONVENTIONAL AND HIGH-STRENGTH STEEL ......
Transcript of DEVELOPMENT LENGTH OF UNCONFINED … LENGTH OF UNCONFINED CONVENTIONAL AND HIGH-STRENGTH STEEL ......
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DEVELOPMENT LENGTH OF UNCONFINED CONVENTIONAL
AND HIGH-STRENGTH STEEL REINFORCING BARS
Hosny, A.; Seliem, H. M.; Rizkalla, S. and Zia, P.
Corresponding Author Sami Rizkalla
North Carolina State University
Constructed Facilities Laboratory (CFL)
2414 Campus Shore Dr.
Raleigh, NC 27695-7533
Email: [email protected]
Phone: 919-513-4336
Authors’ Biographies
ACI Member Amr Hosny is formerly a Post-Doctoral Research Associate at the Civil,
Construction and Environmental Engineering Department, North Carolina State University
where he received his Ph.D. in 2010. He is currently a Structural Engineer at BergerABAM Inc.,
in Houston, TX.
ACI Member Hatem M. Seliem is an Assistant Professor, Helwan University, Egypt. He
received Ph.D. from North Carolina State University in 2007, and obtained his B.Sc. and M.Sc.
from Cairo University, Egypt with honors in 2000 and 2002, respectively.
ACI Fellow Sami H. Rizkalla is Distinguished Professor of Civil and Construction Engineering
in the Department of Civil, Construction, and Environmental Engineering, North Carolina State
University, where he also serves as the Director of the Constructed Facilities Laboratory and
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NSF I/UCRC in Repair of Structures and Bridges. He is also a fellow of ASCE, CSCE, EIC,
IIFC and PCI.
ACI honorary member Paul Zia is a Distinguished University Professor Emeritus at North
Carolina State University. He served as ACI President in 1989, and is a member of several ACI
committees including ACI 363, High-Strength Concrete; joint ACI ASCE 423, Prestressed
Concrete; ACI 445, Shear and Torsion; the Concrete Research Council; and Technology
Transfer Advisory Group.
Abstract
The development length equation specified by ACI 318-08 and the similar equation
recommended by ACI Committee 408 are based on extensive test results using conventional
reinforcement conforming to ASTM A615 and ASTM A706. With the development of new
ASTM A1035 high-strength steel reinforcement, several studies have been conducted to examine
whether the current equations are applicable for the new high-strength reinforcing steel. These
studies have shown that the current equations could, in some cases, overestimate in some cases
the bond strength of high-strength steel bars. This paper proposes a new equation for the bond
strength of unconfined reinforcing bars of all three types of steel. The proposed equation is
compared to extensive test data reported in the literature, and is found to be more accurate than
the current ACI 318-08 and ACI 408R-03 equations.
Keywords
Bond, high-strength steel, splice length, development length, reinforcement.
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INTRODUCTION
Adequate bond strength between concrete and reinforcing bars is necessary for the design
of reinforced concrete structures. In addition, reinforcing bars are often spliced in order to
transfer the force from one bar to another through the surrounding concrete. Therefore, accurate
predictions of the development length and the bond strength of spliced bars are essential for safe
design.
The current equations for development length specified by ACI 318-081 are based on the
recommendations of ACI 408R-032. The equations were developed based on extensive test data
using conventional reinforcing bars conforming to ASTM A6153 and ASTM A706
4. Whether
these equations are applicable to the new ASTM A10355 high-strength reinforcing bars is a
critical issue for design. An extensive experimental program6,7,8,9,10,11
was conducted at three
universities; each was responsible to independently test independently a total of 22 large-scale
splice specimens providing a total of 66 tested specimens. Test results of theThe experimental
program provided extensive data demonstrating the effects of the bar diameter, concrete cover,
concrete compressive strength, splice length and the confining transverse reinforcement in the
splice zone on the splice strength. Details of the experimental program and the test results have
been published in a previous paper by the authors in 20096. The experimental program revealed
that the development length equation given by ACI 318-081 is applicable only for confined
spliced bars. For unconfined spliced bars, the equation recommended by ACI 408R-032 should
be used.
This paper focuses only on the test results of the specimens without confining transverse
reinforcement, and presents a detailed analysis of the factors that affect the strength of
unconfined splices. Based on the test results of the experimental program, as well as extensive
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test data reported in the literature12-22
, a new and simple equation is developed for the prediction
of development length of unconfined reinforcing bars conforming to ASTM A6153 and ASTM
A7064, as well as ASTM A1035
5.
RESEARCH SIGNIFICANCE
Current ACI 318-081 and ACI 408R-03
2 equations for development length of reinforcing
steel bars are primarily empirical and were derived based on research conducted mostly using
steels with yield strength limited to 80 ksi (552 MPa) and conforming to ASTM A6153 and
ASTM A7064. Recent studies
6,7,8,9,10,11,12 have shown that ACI 318-08 and ACI 408R-03
equations could overestimate in some cases the bond strength of high-strength steel bars without
confinement. Based on the results of an extensive experimental program conducted at three
universities6 and other published results, this paper presents a simple equation, which can be
used to evaluate the development length for unconfined conventional as well as high-strength
steel reinforcing bars. The equation incorporates the critical parameters normally recognized to
control influence the bond behavior.
EXPERIMENTAL PROGRAM
The experimental program6,7,8,9,10,11
conducted by the three universities consisted of 66
large-scale splice specimens. The three different bar sizes considered were No 5. (No 16) bars
for slab specimens and No. 8 (No. 25) and No. 11 (No. 36) bars for beam specimens. The test
specimens used ASTM A1035 Grade 100 bars. The concrete covers on the side and the bottom
of the specimens was ere made equal, and ranged from 3/4 in. to 3.0 in. (19 mm to 76 mm). The
splice lengths of the specimens were designed using Equation (4-11a) of ACI 408R-032. The
specimens were tested in a four point bending setup to provide a constant moment region within
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the splice zone as shown in Figure 1. For complete details of the experimental program, see
Reference 6.
This paper makes use of only the results of 32 splice specimens without confining
transverse reinforcement within the splice zone. These specimens include 10 slab type specimens
reinforced with No. 5 (No. 16) bars, 14 beam type specimens reinforced with No. 8 (No. 25) bars
and 8 beam type specimens reinforced with No. 11 (No. 36) reinforcing bars as listed in Table 1.
The table also shows the concrete compressive strength, splice length, concrete cover, and the
maximum stresses in the spliced bars which were calculated using cracked section analysis based
on the maximum measured loads. The specimens were identified using a four-part identification
system as follows: The first part, “5, 8 or 11”, designates the size of the spliced bar. The second
part, “5 or 8”, designates the targeted concrete compressive strength in ksi. The third part, “O or
X”, designates the selected splice length to achieve a specified stress level of 80 or 100 ksi (555
or 690 MPa), respectively. The fourth part designates the concrete cover in inches.
TEST RESULTS
The results of the experimental program6 showed that failure of beams without confining
transverse reinforcement within the splice zone was explosive with spalling of the concrete cover
from the entire length of the splice as shown in Figure 2. When transverse confinement
reinforcement was used in the splice zone, the beams were capable of carrying more loads,
splitting cracks were allowed to propagate along the splice zone and the cover spalling was
gradual. The experimental program also showed that without confining transverse reinforcement,
the maximum stresses that were developed in the spliced bars were 120, 110 and 96 ksi (830,
760 and 665 MPa) for No. 5, No. 8 and No. 11 (No. 16, No. 25 and No. 36) bars, respectively.
However, when confining transverse reinforcement was used along the splice lengths of No. 8
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and No. 11 (No. 25 and No. 36) bars, stress levels up to 150 ksi (1035 MPa) were developed in
the bars. These stresses were calculated using cracked section analysis based on the
maximum measured loads. Based on the Hognestad model for concrete, strain
compatibility was used to determine the strains at the location of the reinforcing bars at
failure. Using the stress-strain relationship of the ASTM A1035 steel, the maximum
developed stresses in the reinforcing bars were determined. In addition, these values
were compared to the readings of the strain gages placed at the ends of the splices
where the maximum stresses should occur.
FORMULATION OF EQUATION FOR DEVELOPMENT LENGTH
The equation for the development length was formulated by considering only the results
of the specimens without confining transverse reinforcement along the splice length. The
maximum measured loads were used to determine the maximum stresses developed in the
spliced bars before failure. These stresses were used to examine the effect of the different
parameters that control the bond characteristics of the reinforcing steel bars. Test results confirm
the established knowledge that increasing the concrete compressive strength increases the load-
carrying capacity of the members. To eliminate the effect of variation of the concrete
compressive strength (fc’) within the tested beams, the measured steel stresses (fs) were
normalized by the quadratic root of the concrete strength ('4
cf ) as recommended by ACI
Committee 408. The normalized values are given in the Column (6) of Table 1.
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Effect of Splice Length
To study the effect of the splice length (ld), the stresses based on the maximum measured
loads carried by the unconfined spliced bars of the specimens having the same concrete cover
and similar concrete compressive strength were compared with each other as given in Table 1.
The analysis indicates that the percentage increase in the splice length, given in Column (8), is
not proportional to the percentage increase in the normalized stresses induced in the spliced bars
given in Column (7). For example, for No. 8 (No. 25) bars, increasing the splice length by 32
percent, as for beams 8-5-O-1.5 vs. 8-5-X-1.5, increased the splice strength only by 13 percent.
Similarly, for No. 11 (No. 36) bars, increasing the splice length by 34 percent as for beams
11-5-O-3.0 vs. 11-5-X-3.0, increased the splice strength by only 10 percent. For beams 11-5-O-
2.0 and 11-5-X-2.0 reinforced with No. 11 (No. 36) bars, the test results indicate that by
increasing the splice length from 69 to 91 in. (1753 to 2311 mm), or in terms of the bar diameter
from 49 db to 65 db, the increase in the stresses in the spliced bars was only 4 percent. This
behavior clearly indicates that as the splice lengths increase, they become less effective in
increasing the splice strength and the use of very long splice lengths does not increase the bond
capacity. This behavior, also observed by El-Hacha et al.12
, is attributed to the well-known fact
that the distribution of bond stresses is nonlinear over long splice length. While the assumption
of uniform bond stress distribution may be reasonably accurate for short splice lengths, it is
unconservative for long splice lengths23
. Examining the increase in the stresses developed in the
spliced bars relative to the length of the splice, it was found that the splice strength is
proportional to the square root of the ratio of splice length to bar diameter ( d
b
l
d) as given in
Table 1, which is similar to what was reported by Canbay and Frosh23
for conventional steel bars.
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Effect of Concrete Cover
To investigate the effect of the concrete cover (c), the normalized stresses in the previous
step were further normalized to the square root of the ratio of the splice length to the bar
diameter to eliminate the effect of the splice length as given in Column (6) of Table 2. The
results show that increasing the concrete cover by 67 percent, as for beams 8-8-O-1.5 vs. 8-5-O-
2.5, caused the normalized splice strength to increase by 30 percent. Similarly, increasing the
concrete cover of beams 11-5-O-2.0 vs. 11-8-O-3.0 by 50 percent increased the normalized
stresses by only 29 percent only. This behavior can be expected since the distribution of tensile
stresses across the concrete cover is not uniform23
. Similar to conventional steel bars23
, it was
found that the splice strength is proportional to the square root of the ratio of the thickness of the
concrete cover to the diameter of the reinforcing bar (b
c
d) as given in Column (9) of Table 2.
For beams 8-8-O-1.5 vs. 8-5-O-2.5, the increase in the splice length is 30% and the square root
of the ratio of the concrete cover to the bar diameter is increased by a similar value of 29%.
Proposed Development Length Equation for Unconfined Bars
Based on the evaluation of the effects of the various parameters, the stresses in the
unconfined spliced bars were normalized with respect to the concrete strength, splice length, and
concrete cover by using the proposed relationships discussed above as given in Table 3.
It can be seen from this table that the average value of the normalized stresses for the test
specimens with spliced bars without confinement reinforcement is 1144 with a coefficient of
variation of 0.126. This indicates that the proposed relationships between the splice strength and
the concrete strength, splice length, concrete cover, and bar diameter can reasonably represent
the effect of these parameters on the bond strength of ASTM A1035 Grade 100 steel bars.
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This finding highlights the potential for developing a simple expression to predict the
stresses in unconfined spliced bars. Figure 3 shows a plot of the values of Ω in the last column of
Table 3 against the corresponding values of ld/db. Based on this plot, it can be seen that the
average value of Ω is 1144 (or 27.4 using SI units) for all values of ld/db. Accordingly, one can
obtain the following simple and general expression:
b
dc
sd
clff
min4 ' ...1144
Units: psi and in. Eq. 1
b
dc
sd
clff
min4 ' ...4.27
Units: MPa and mm Eq. 2
where, fs = stresses in spliced bars; db = nominal diameter of spliced bars; fc’ = concrete
compressive strength; ld = splice length or development length; cmin= minimum of cb or cs; cb =
clear bottom cover; cs = minimum of cso or csi + 0.25 in. (6.4 mm); cso = clear side cover; csi=
half of clear spacing between spliced bars. The constant 1144 (or 27.4) is the average of the
normalized stresses to the concrete compressive strength, concrete cover, splice length and bar
diameter. To ensure a higher safety factor, the constant is reduced by one standard deviation,
resulting in the proposed equation for predicting the stresses in unconfined spliced steel bars as
follows:
b
dc
sd
clff
min4 ' ...1000
Units: psi and in. Eq. 3
b
dc
sd
clff
min4 ' ...24
Units: MPa and mm Eq. 4
Equations 3 and 4 can be rearranged to determine the splice length for ASTM A1035 Grade 100
reinforcing bars as follows:
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2 2
6 ' '
min min
(0.001 )
10 .
s b s bd
c c
f d f dl
c f c f Units: psi and in. Eq.5
2 2
' '
min min
(0.042 )
576.
s b s bd
c c
f d f dl
c f c f Units: MPa and mm Eq.6
Validation of the proposed equation
Equation 5 was used to predict the stresses in the ASTM A1035 spliced bars of the beams
without confining transverse reinforcement tested in the experimental program. These results are
compared to the predicted stresses using the ACI 318-08 equation and the equation
recommended by ACI Committee 408 as shown in Table 4. The table shows the ratios of the
measured to the predicted stresses, in addition to the average, standard deviation and coefficient
of variation of these ratios. The results are also graphically presented in Figure 4 showing the
distribution of the ratios of the measured to predicted stresses of the tested beams.
Both Table 4 and Figure 4 demonstrate that the ACI 318-08 equation provides the highest
scatter of the results with an average of 1.14, and a coefficient of variation of 0.20 and a Rroot
Mmean Ssquare Eerror (RMSE) of 16.2, when compared to both Equation 5 and the ACI 408
equation. Of the three equations, Equation 5 shows the best prediction of the stresses in the
spliced bars with the ratio of the measured to predicted stress ranging between 1.0 and 1.1, and
an average of 1.14 with a coefficient of variation of 0.12 and the least lowest RMSE of 14.4.
To further examine the validity of Equation 5, it was used to predict the results of other
experimental programs reported in the literature. These experimental programs included the
work done by El-Hacha, 200612
; Zuo and Darwin, 200013
; Azizinamini et al., 199914
; Hamad and
Itani, 199815
; Darwin et al., 199616
; Azizinamini et al., 199317
; Tepfers, 197318
; Ferguson and
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Breen, 196519
; Chamberlin, 195820
; Camberlin, 195621
and Chinn et al., 195522
. Table A in the
appendix summarizes these test programs. The collected database included only tests using
beam-splice specimens with unconfined, uncoated, bottom-cast, and bar sizes of No. 4, 5, 6, 8
and 11 (No. 13, 16, 19, 25 and 36). The range of the ratio of the splice length to bar diameter
considered was 12 to 80. Tests with splice length to bar diameter less than 12 were excluded
because these short splices are not used in practice. The concrete cover included in the collected
data ranged from 0.5 in. (13 mm) to 3.0 in. (76 mm). The database also included conventional
steel and high strength steel bars as well as high strength concrete. The total number of tests
considered in this evaluation was 213 including the data presented in this paper.
The comparisons of the results using the three equations are presented in Figure 5. The
results show the conservatism of the ACI 318-08 equation with 80 specimens having a ratio of
measured to predicted stress more than 1.6. The figure also shows that the proposed Equation 5
produces the least scatter of the results with an average of 1.10 and a coefficient of variation of
0.13 as given in Table 5.
Furthermore, for comparison purposes, the proposed equation (Eq. 5 or 6), ACI 318 and
ACI 408 equations were used to predict the splice lengths required to achieve different stress
levels as shown in Figure 6. It should be noted that Figure 6 was developed using concrete
strength of 5000 psi (34.5 MPa) and concrete cover of 2.0 in. (51 mm), which are commonly
used in practice. It is evident from Figure 6 that ACI 318 equation represents a linear relationship
between development length and bar stress (thus bond stress) with no limitation on the
development length. Increasing ld will result in increase of bar stress (or bond strength). For the
ACI 408R-03 equation, it is also almost linear but with less reduced slope, meaning that
increasing ld will result in increase of bond strength but with less amountless so compared to the
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ACI 318 equation. However, it has been demonstrated that the longer the splice length, the less
effective it becomes, which is clearly reflected by the proposed Equation 5. It is worth noting
that predictions by Equation 5 and the ACI 408 equation match closely up to stress level of
approximately 60 ksi (414 MPa). At higher stress levels, Equation 5 would require increasingly
longer splice length. The ACI 318 and ACI 408 equations were both calibrated for conventional
reinforcing bars and are not applicable to stress levels above 80 ksi (552 MPa) as shown by the
dotted lines in Figure 6. The significance of the proposed equation is that for longer development
lengths (i.e. higher ld/db ratios), the non-linearity of the equation clearly indicates that increasing
the splice length will not efficiently increase the splice strength. In such cases, the use of
couplers to splice high strength steel bars would be a more economical alternative, especially
when high stress levels are to be developed without the use of transverse confining reinforcement.
CONCLUSIONS
Based on the test results of 213 beams and slabs reinforced with unconfined spliced bars
using ASTM A1035 Grade 100 high-strength steel bars as well as conventional steel reinforcing
bars conforming to ASTM A615 and ASTM A706, the following simple and general equation
can be used to determine the development length of unconfined reinforcing bars:
2
'
min
(0.001 )s bd
c
f dl
c f Units: psi and in.
2
'
min
(0.042 )s bd
c
f dl
c f Units: MPa and mm
The equation accounts for the specified stresses in the spliced bars, fs; the nominal bar diameter,
db; concrete strength, fc’; and the minimum concrete cover, cmin.
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The proposed equation compares well with extensive test results developed by the
authors and other researchers reported in the literature. In addition, the proposed equation
provides better prediction of the development strength in comparison to the equations given by
ACI 318-08 and ACI Committee 408.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of MMFX Technologies Corporation for
sponsoring this study and supplying the steel materials. The authors would also like to thank
Jerry Atkinson at the Constructed Facilities Laboratory for his untiring help with the laboratory
work. In addition, the help provided by Charles DeVoto III, Matthew Sumpter, and Jarod
Wheeler, graduate students at the Constructed Facilities Laboratory is greatly appreciated.
REFERENCES
1. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05)
and Commentary (ACI 318R-05),” American Concrete Institute, Farmington Hills, MI, 2005,
430 pp.
2. ACI Committee 408, “Bond and Development of Straight Reinforcing in Tension (ACI
408R-03),” American Concrete Institute, Farmington Hills, MI, 2003, 49 pp.
3. ASTM A615/A615M REV B, “Standard Specification for Deformed and Plain Carbon-Steel
Bars for Concrete Reinforcement”, ASTM International, West Conshohocken, PA, 2009, 6
pp.
4. ASTM A706/A706M REV B, “Standard Specification for Low-Alloy Deformed and Plain
Bars for Concrete Reinforcement”, ASTM International, West Conshohocken, PA, 2009, 6
pp.
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5. ASTM A1035/A1035M, “Standard Specification for Deformed and Plain, Low-Carbon,
Chromium, Steel Bars for Concrete Reinforcement, ASTM International, West
Conshohocken, PA, 2009, 5 pp.
6. Seliem, H. M.; Hosny, A.; Rizkalla, S.; Zia, P.; Briggs, M.; Miller, S.; Darwin, D.; Browning,
J.; Glass, G. M.; Hoyt, K,; Donnelly, K. and Jirsa, J. O., 2009, “Bond Characteristics of
ASTM A1025 Steel Reinforcing Bars”, ACI Structural Journal, V. 106, No. 4, July-August
2009, pp. 530-539.
7. Briggs, M.; Miller, S.; Darwin, D.; and Browning, J., “Bond Behavior of Grade 100 ASTM
A1035 Reinforcing Steel in Beam-Splice Specimens”, SL Report 07-01, The University of
Kansas Center for Research Inc., Lawrence, KS, August 2007 (revised October 2007), 83 pp.
8. Glass, G. M., “Performance of Tension Lap Splices with MMFX High Strength Reinforcing
Bars”, M.Sc. thesis, University of Texas at Austin, Austin, TX, 2007, 141 pp.
9. Hosny, A., “Bond Behavior of High Performance Reinforcing Bars for Concrete Structures,”
M.Sc. Thesis, North Carolina State University, Raleigh, NC, 2007, 150 pp.
10. Seliem, H. M., “Behavior of Concrete Bridges Reinforced with High-Performance Steel
Reinforcing Bars,” Ph.D. Dissertation, North Carolina State University, Raleigh, NC, 2007,
259 pp.
11. Seliem, H. M.; Hosny, A.; Rizkalla, S., “Evaluation of Bond Characteristics of MMFX Steel”,
Technical Report No. RD-07-02, Constructed Facilities Laboratory (CFL), North Carolina
State University, Raleigh, NC, 2007, 71 pp.
12. El-Hacha, R., El-Agroudy, H., and Rizkalla, S. H., “Bond Characteristics of High-Strength
Steel Reinforcement,” ACI Structural Journal, Nov.-Dec. 2006, V. 103, No. 6, pp. 771-782.
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13. Zuo, J. and Darwin, D, “Splice Strength of Conventional and High Relative Rib Area Bars in
Normal and High-Strength Concrete”, ACI Structural Journal, Jul-Aug 2000, V. 97, No. 4,
pp. 630-641.
14. Azizinamini, A.; Pavel, R.; Hatfield, E. and Gosh, S., “Behavior of Lap-Spliced Bars
Embedded in High-Strength Concrete”, ACI Structural Journal, Sept-Oct 1999, V. 96, No. 5,
pp. 826-835.
15. Hamad, B. and Itani, M., “Bond Strength of Reinforcement in High-Performance Concrete:
The Role of Silica Fume, Casting Position, and Superplasticizer Dosage”, ACI Materials
Journal, Sept-Oct 1998, V. 95, No. 5, pp. 499-511.
16. Darwin, D.; Tholen, M.; Idun, E. and Zuo, J., “Splice Strength of High Relative Rib Area
Reinforcing Bars”, ACI Structural Journal, Jan-Feb 1996, V. 93, No. 1, pp. 95-107.
17. Azizinamini, A.; Stark, M.; Roller. J. and Gosh, S., “Bond performance of Reinforcing Bars
Embedded in High-Strength Concrete”, ACI Structural Journal, Sept-Oct 1993, V. 90, No. 5,
pp. 554-561.
18. Tepfers, R., 1973, “A Theory of Bond Applied to Overlapped Tensile Reinforcement Splices
for Deformed Bars”, Division of Concrete Structures, Chalmers University of Technology,
Göteberg, Publication No. 73:2, 328 pp.
19. Ferguson, P. and Breen, J., “Lapped Splices for High Strength Reinforcing Bars”, Journal of
the American Concrete Institute, September 1965, V. 62, No. 9, pp. 1063-1078.
20. Chamberlin, S., “Spacing of Spliced Bars in Beams”, Journal of the American Concrete
Institute, February 1958, V. 54, No. 2, pp. 689-697.
21. Chamberlin, S., “Spacing of Reinforcement in Beams”, Journal of the American Concrete
Institute, February 1956, V. 53, No. 7, pp. 113-134.
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22. Chinn, J.; Ferguson, P. and Thompson, J., “Lapped Splices in Reinforced Concrete Beams”,
Journal of the American Concrete Institute (ACI), October 1955, V. 52, No. 10, pp. 201-213.
23. Canbay, E. and Frosh, R. J., “Bond Strength of Lap-Spliced Bars,” ACI Structural Journal, V.
102, No. 4, Jul.-Aug. 2005, pp. 605-614.
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LIST OF TABLES
Table 1 - Effect of splice length on bond strength of high-strength steel bars
Table 2 - Effect of concrete cover on bond strength of high-strength steel bars
Table 3 - Normalized stresses in unconfined spliced bars from test results
Table 4 - Comparison of the measured to predicted stresses
Table 5 - Statistical data for the measured to predicted stress ratios using the three equations for
all the specimens
LIST OF FIGURES
Figure 1 - Test setup for the splice beams tested at NCSU
Figure 2 - Splitting failure of an unconfined splice beam
Figure 3 - Distribution of the constant versus ld/db for the tested specimens
Figure 4 - Distribution of the measured / predicted stress ratios for the tested specimens
Figure 5 - Distribution of the measured / predicted stress ratios for all the specimens
Figure 6 - Prediction of splice lengths according to Equation 5, ACI 318-08, and ACI
Committee 408 equations
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TABLES
Table 1: Effect of splice length on bond strength of high-strength steel bars
Specimen
ID
f'c
psi
ld
in.
c
in.
fs
ksi 4 '
c
s
f
f
Increase in
4 '
c
s
f
f(in %)
Increase in
ld
(in %)
Increase
inb
d
d
l
(in %)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Specimens with No. 5 (No. 16) bars
5-5-O-3/4 5200 33 0.75 80 9421 14 33 15
5-5-X-3/4 5200 44 0.75 91 10716
5-5-O-1¼ 5200 18 1.25 88 10363 25 39 18
5-5-X-1¼ 5200 25 1.25 110 12954
5-5-O-2.0 5700 15 2.00 97 11164 24 33 15
5-5-X-2.0 5700 20 2.00 120 13811
5-5-O-3/4 5490 32 0.80 77 8945 12 34 16
5-5-X-3/4 4670 43 0.70 83 10040
5-5-O-1¼ 5490 18 1.09 87 10142 9 39 18
5-5-X-1¼ 4670 25 0.98 91 11032
Specimens with No. 8 (No. 25) bars
8-5-O-1.5 5000 47 1.50 74 8800 13 32 15
8-5-X-1.5 4700 62 1.50 82 9904
8-5-O-1.5* 5200 40 1.50 72 8479
17 55 24 8-5-O-1.5 4700 62 1.50 82 9904
8-8-O-1.5 8300 40 1.50 80 8381 9 35 16
8-8-X-1.5 7800 54 1.50 86 9151
8-5-O-1.5 5260 47 1.40 78 9182 12 34 16
8-5-X-1.5 5940 63 1.41 90 10274
8-8-O-2.5 8660 27 2.30 80 8262 17 33 15
8-8-X-2.5 7990 36 2.38 91 9667
8-5-O-2.5 6020 31 2.50 96 10901 16 32 15
8-5-X-2.5 5820 41 2.50 110 12596
8-8-O-1.5 8400 40 1.50 91 9505 14 35 16
8-8-X-1.5 10200 54 1.50 109 10846
Specimens with No. 11 (No. 36) bars
11-5-O-3.0 5000 50 2.75 75 8919 10 34 16
11-5-X-3.0 5400 67 2.75 84 9799
11-8-O-2.0 9370 58 1.89 68 6912 15 36 17
11-8-X-2.0 9910 79 1.85 79 7918
11-5-O-2.0 5340 69 2.00 74 8655 4 32 15
11-5-X-2.0 4060 91 2.00 72 9021
11-8-O-3.0 6070 43 3.00 78 8837 14 33 15
11-8-X-3.0 8380 57 3.00 96 10033
1 in. = 25.4 mm; 1000 psi = 6.895 MPa * Duplicate specimen
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Table 2: Effect of concrete cover on bond strength of high-strength steel bars
Specimens
ID
f'c
psi
ld
in.
c
in.
fs
ksi
'4
s
dc
b
f
lf
d
Increase in
'4
s
dc
b
f
lf
d
(in %)
Increase
in
c
(in %)
Increase
in
bd
c
(in %)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Specimens with No. 5 (No. 16) bars
5-5-O-3/4 5200 33 0.75 80 1296 49 67 29
5-5-O-1¼ 5200 18 1.25 88 1931
5-5-X-3/4 5200 44 0.75 91 1277 60 67 29
5-5-X-1¼ 5200 25 1.25 110 2048
5-5-O-1¼ 5200 18 1.25 88 1931 18 60 26
5-5-O-2.0 5700 15 2.00 97 2279
5-5-X-1¼ 5200 25 1.25 110 2048 19 60 26
5-5-X-2.0 5700 20 2.00 120 2441
5-5-O-3/4 5490 32 0.80 77 1255 51 36 17
5-5-O-1¼ 5490 18 1.09 87 1890
5-5-X-3/4 4670 43 0.70 83 1205 45 40 18
5-5-X-1¼ 4670 25 0.98 91 1744
Specimens with No. 8 (No. 25) bars
8-5-O-1.5 5260 47 1.40 78 1339 19 64 28
8-8-O-2.5 8660 27 2.30 80 1590
8-5-X-1.5 5940 63 1.41 90 1294 24 69 30
8-8-X-2.5 7990 36 2.38 91 1611
8-8-O-1.5 8400 40 1.50 91 1503 30 67 29
8-5-O-2.5 6020 31 2.50 96 1958
8-8-X-1.5 10200 54 1.50 109 1476 33 67 29
8-5-X-2.5 5820 41 2.50 110 1967
Specimens with No. 11 (No. 36) bars
11-8-O-2.0 9370 58 1.89 68 1078 39 46 21
11-5-O-3.0 5000 50 2.75 75 1498
11-8-X-2.0 9910 79 1.85 79 1058 34 49 22
11-5-X-3.0 5400 67 2.75 84 1422
11-5-O-2.0 5340 69 2.00 74 1237 29 50 22
11-8-O-3.0 6070 43 3.00 78 1600
11-5-X-2.0 4060 91 2.00 72 1123 41 50 22
11-8-X-3.0 8380 57 3.00 96 1578
1 in. = 25.4 mm; 1000 psi = 6.895 MPa
ACI Structural Journal December 2011
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Table 3: Normalized stresses in unconfined spliced bars from test results
Specimen ID f'c psi
ld
in.
c
in.
fs
ksi '4
s
dc
b b
f
l cf
d d
Specimens with No. 5 (No. 16) bars
5-5-O-3/4 5200 33 0.75 80 1184
5-5-X-3/4 5200 44 0.75 91 1166
5-5-O-1¼ 5200 18 1.25 88 1365
5-5-X-1¼ 5200 25 1.25 110 1448
5-5-O-2.0 5700 15 2.00 97 1274
5-5-X-2.0 5700 20 2.00 120 1365
5-5-O-3/4 5490 32 0.80 77 1109
5-5-X-3/4 4670 43 0.70 83 1138
5-5-O-1¼ 5490 18 1.09 87 1431
5-5-X-1¼ 4670 25 0.98 91 1393
Specimens with No. 8 (No. 25) bars
8-5-O-1.5 5000 47 1.50 74 1048
8-5-X-1.5 4700 62 1.50 82 1027
8-5-O-1.5* 5200 40 1.50 72 1095
8-8-O-1.5 8300 40 1.50 80 1082
8-8-X-1.5 7800 54 1.50 86 1017
8-5-O-1.5 5260 47 1.40 78 1132
8-5-X-1.5 5940 63 1.41 90 1090
8-8-O-2.5 8660 27 2.30 80 1048
8-8-X-2.5 7990 36 2.38 91 1044
8-5-O-2.5 6020 31 2.50 96 1238
8-5-X-2.5 5820 41 2.50 110 1244
8-8-O-1.5 8400 40 1.50 91 1227
8-8-X-1.5 10200 54 1.50 109 1205
Specimens with No. 11 (No. 36) bars
11-5-O-3.0 5000 50 2.75 75 1072
11-5-X-3.0 5400 67 2.75 84 1018
11-8-O-2.0 9370 58 1.89 68 931
11-8-X-2.0 9910 79 1.85 79 923
11-5-O-2.0 5340 69 2.00 74 1039
11-5-X-2.0 4060 91 2.00 72 943
11-8-O-3.0 6070 43 3.00 78 1097
11-8-X-3.0 8380 57 3.00 96 1082
AVERAGE 1144
144 1 in. = 25.4 mm; 1000 psi = 6.895 MPa
ST. DEV. 144
* Duplicate specimen
COV 0.126
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Table 4: Comparison of the measured to predicted bar stresses
Beam
Measured
Bar
Stresses
ksi
Predicted Bar Stress
ACI 318 ACI 408 Proposed Eq. 5
Stress ratio Stress ratio Stress ratio
Specimens with No. 5 (No. 16) bars
5-5-O-3/4 80 61 1.31 61 1.30 68 1.18
5-5-X-3/4 91 81 1.12 75 1.21 78 1.17
5-5-O-1¼ 88 55 1.59 58 1.53 64 1.37
5-5-X-1¼ 110 77 1.43 72 1.52 76 1.45
5-5-O-2.0 97 77 1.25 72 1.35 76 1.27
5-5-X-2.0 120 129 0.93 106 1.14 98 1.22
5-5-O-3/4 77 65 1.19 64 1.21 70 1.10
5-5-X-3/4 83 70 1.18 68 1.21 73 1.14
5-5-O-1¼ 87 50 1.75 54 1.62 61 1.43
5-5-X-1¼ 91 57 1.59 59 1.53 65 1.39
Specimens with No. 8 (No. 25) bars
8-5-O-1.5 74 66 1.11 65 1.13 71 1.05
8-5-X-1.5 82 85 0.96 79 1.04 80 1.03
8-5-O-1.5* 72 58 1.25 59 1.22 66 1.09
8-8-O-1.5 80 73 1.10 67 1.20 74 1.08
8-8-X-1.5 86 95 0.90 81 1.07 85 1.02
8-5-O-1.5 78 64 1.23 63 1.23 69 1.13
8-5-X-1.5 90 91 0.99 81 1.12 83 1.09
8-8-O-2.5 80 77 1.04 69 1.16 76 1.05
8-8-X-2.5 91 102 0.89 84 1.08 88 1.04
8-5-O-2.5 96 80 1.20 73 1.31 78 1.24
8-5-X-2.5 110 104 1.06 89 1.23 88 1.24
8-8-O-1.5 91 73 1.24 67 1.36 74 1.23
8-8-X-1.5 109 109 1.00 86 1.26 90 1.21
Specimens with No. 11 (No. 36) bars
11-5-O-3.0 75 65 1.15 65 1.16 70 1.07
11-5-X-3.0 84 91 0.93 81 1.03 83 1.02
11-8-O-2.0 68 71 0.96 65 1.05 73 0.93
11-8-X-2.0 79 98 0.81 80 0.99 86 0.92
11-5-O-2.0 74 68 1.09 66 1.12 71 1.04
11-5-X-2.0 72 78 0.93 75 0.96 76 0.94
11-8-O-3.0 78 67 1.16 65 1.20 71 1.10
11-8-X-3.0 96 105 0.91 86 1.12 89 1.08
AVERAGE 1.14
1.22
1.14
ST. DEV. 0.22 0.16 0.14
COV 0.20 0.14 0.12
Min. 0.81 0.96 0.92
Max. 1.75 1.62 1.45
RMSE 16.2 17.7 14.4
1 in. = 25.4 mm; 1000 psi = 6.895 MPa RMSE = Root Mean Square Errors * Duplicate specimen
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Table 5: Statistical data for the measured to predicted stress ratios using the three equations for
all the specimens
ACI 318-08 ACI 408 Proposed Eq. 5
AVERAGE 1.56 1.23 1.10
ST. DEV. 0.50 0.16 0.14
COV 0.32 0.13 0.13
Min. 0.65 0.86 0.80
Max. 3.23 1.64 1.46
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FIGURES 1
2 3
Fig. 1: Test setup for the splice beams tested at NCSU 4
5
6
7 8
Fig. 2: Splitting failure of an unconfined splice beam 9
8-5-O-1.5
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1 Fig. 3: Distribution of the constant versus ld/db for the tested specimens 2
3
4 Fig. 4: Distribution of the measured / predicted stress ratios for the tested specimens 5
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1 Fig. 5: Distribution of the measured / predicted stress ratios for all the specimens 2
3
4
(a) No. 8 (No. 25) spliced bars (b) No. 11 (No. 36) spliced bars
5
Fig. 6: Prediction of development lengths according to Equation 5, ACI 318-08, and ACI 6
Committee 408 equations 7
8
9
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APPENDIX 1
2
Table A: Summary of the collected data 3
Reference Number
of tests
Bar Size
# (No.)
Range of Splice Length
in. (mm)
Range of Cover
in. (mm)
Seliem et al. 6
10 5 (16) 15-44 (381-1118) 0.75-2.00 (19-51)
14 8 (25) 31-63 (787-1600) 1.29-2.50 (33-64)
8 11 (36) 43-91 (1092-2311) 2.00-3.00 (51-76)
El-Hacha, 2006 12
4 6 (19) 12-60 (305-1524) 1.50 (38)
Zuo and Darwin, 2000 13
1 5 (16) 17 (432) 1.273 (32)
14 8 (25) 17-40 (432-1016) 0.902-3.032 (23-77)
6 11 (36) 28-30 (711-762) 1.313-1.977 (33-50)
Azizinamini et al., 1999 14
13 8 (25) 10-41 (254-1041) 1.00-2.00 (25-51)
21 11 (36) 13-80 (330-2032) 1.41-2.82 (36-72)
Hamad and Itani, 1998 15
14 8 (25) 12 (305) 1.5 (38)
Darwin et al., 1996 16
2 5 (16) 16-17 (406-432) 1.266-1.281 (32-33)
9 8 (25) 16-26 (406-660) 1.313-2.938 (33-75)
2 11 (36) 40 (1016) 1.895-1.908 (48-48)
Azizinamini et al., 1993 17
16 11 (36) 13-80 (330-2032) 1.41 (36)
Tepfers, 1973 18
12 6 (16) 10-52 (254-1321) 0.787-1.614 (10-41)
Ferguson and Breen,
1965 19
13 8 (25) 18-80 (457-2032) 1.38-1.75 (35-44)
13 11 (36) 34-83 (864-2096) 1.31-2.06 (33-52)
Chamberlin, 1958 20
6 4 (13) 6 (152) 0.50-1.00 (13-25)
Chamberlin, 1958 21
10 4 (13) 6-16 (152-406) 0.50-1.00 (13-25)
Chinn et al., 1955 22
25 6 (19) 11-24 (152-406) 0.75-1.62 (19-41)
4
5
6
7