DEVELOPMENT LENGTH OF UNCONFINED … LENGTH OF UNCONFINED CONVENTIONAL AND HIGH-STRENGTH STEEL ......

ACI Structural Journal December 2011

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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

mailto:[email protected]


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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.

24. ASTM A 370-07, “Standard Test Methods and Definitions for Mechanical Testing of Steel

Products,” ASTM International, West Conshohocken, PA, 2007, 47 pp.

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


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


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)


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


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


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


19/25

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


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


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


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


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


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


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

DEVELOPMENT LENGTH OF UNCONFINED … LENGTH OF UNCONFINED CONVENTIONAL AND HIGH-STRENGTH STEEL ......

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