Bond Characteristics of High-Strength Steel …srizkal/TechPapers2006/bond characteristics...

MS#2003378 1

Bond Characteristics of High-Strength Steel Reinforcement 1 2

Raafat El-Hacha, Hossam El-Agroudy, and Sami H. Rizkalla 3 4

5 Raafat El-Hacha (corresponding author) 6 University of Calgary 7 Department of Civil Engineering 8 2500 University Dr. NW 9 Calgary, AB, T2N 1N4, Canada 10 Email: [email protected] 11 12 Hossam El-Agroudy 13 University of Toronto 14 Department of Civil Engineering 15 35 St. George Street 16 Toronto, ON M5S 1A4, Canada 17 Email: [email protected] 18 19 Sami H. Rizkalla 20 North Carolina State University 21 Constructed Facilities Laboratory 22 2414 Campus Shore Drive 23 Raleigh, NC, 27695-7533, USA 24 E-mail: [email protected] 25 26

AUTHOR’S BIOGRAPHIES 27

ACI Member Raafat El-Hacha is an Assistant Professor in the Department of Civil Engineering 28 at the University of Calgary, Canada. He received his PhD in civil engineering from Queen’s 29 University in 2000. He is a member of the ACI Committee 440, Fiber Reinforced Polymer (FRP) 30 Reinforcement and co-chair of Sub-Committee 440-I, FRP Prestressed Concrete. He is an 31 associate member of ACI-ASCE Committee 423 on Prestressed Concrete, and associate member 32 of ACI 408, Bond and Development of Reinforcement. His research interests include 33 strengthening, reinforcing and prestressing concrete structures with FRP composites. 34 35 Hossam El-Agroudy received his Bachelor degree in 1999 from Ain Shams University, Egypt, 36 and his Master degree in 2003 from North Carolina State University, USA. Currently, he is a 37 PhD student in the Department of Civil Engineering at the University of Toronto, Canada. 38

ACI Fellow Sami H. Rizkalla is a Distinguished Professor of Civil Engineering and 39 Construction, Director of the Constructed Facilities Laboratory (CFL) at the North Carolina State 40 University, and Director of the NSF Industry/University Cooperative Research Center. He is the 41 immediate Past President and the Founder of the Network of Centers of Excellence on Intelligent 42 Sensing for Innovative Structures (ISIS Canada), and Past Chairman of ACI Committee 440 on 43 Fiber-Reinforced-Polymer Reinforcement, and a member of ACI-ASCE Committee 550 on 44 Precast Concrete Structures. 45

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ABSTRACT 1

This paper summarizes an investigation undertaken to study the bond characteristics of high-2

strength steel reinforcement bars commercially known as Micro-composite Multi-structural 3

Formable steel (MMFX). The objective of the investigation is to examine the applicability of the 4

ACI Code 318-02 [15] equation and the current proposed equation by Zuo and Darwin (2000) [12] 5

on bond behavior of steel reinforcement to the concrete member. The experimental program 6

included two phases. The first phase of the experimental program consisted of testing four beam-7

end specimens reinforced with MMFX steel bars, while the second phase included testing of 8

eight beam-splice specimens reinforced with MMFX steel bars. The selected four factors 9

considered in this study were bar size, level of confinement, bonded length and bar cast position. 10

The bond behavior of the MMFX steel bars was found to be similar to that of conventional 11

Grade 420 MPa (60 ksi) steel up to the proportional limit of 550 MPa (80 ksi). The bond strength 12

of the MMFX significantly changes as the tensile stresses developed in the bar exceed the 13

proportional limit. The test results indicated that both, the ACI 318-02 [15] Code equation and the 14

current proposed equation by Zuo and Darwin (2000) [12] on bond are adequate and resulted in 15

conservative prediction at low stress levels p to 550 MPa (80 ksi). However, at high stress levels, 16

the prediction using both equations is unconservative due to the nonlinear behavior of MMFX 17

stress-strain relationship. Based on the limited number of specimens considered in this study, 18

modification to both the ACI 318-02 Code [15] and Zuo and Darwin (2000) [12] equations are 19

proposed to predict the bond forces beyond the proportional limit for MMFX steel bars. 20

21

Keywords: bond; confinement; high strength steel; splice; development; concrete; flexure. 22

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INTRODUCTION 1

Bond behavior of reinforcing steel bars to concrete is one of the most important 2

mechanisms that should be properly designed to ensure satisfactory performance of reinforced 3

concrete structures. In case of deformed steel bars, the bond strength and the process of force 4

transfer from the reinforcing bars to the surrounding concrete significantly relies on the chemical 5

adhesion and the friction (dependent on the bar surface condition), and the mechanical 6

interlocking of the bar ribs on the concrete paste surrounding the bar (dependent on the bar 7

deformation pattern). The latest component contributes more positively to the bond strength of 8

deformed bars and is the major reason for their superior bond effectiveness as explained 9

hereafter. The relative longitudinal movement of the bar with respect to the surrounding concrete 10

is known as the bar slip. When a deformed bar starts to slip, surface adhesion forces are 11

significantly reduced. Such slip activates both the bearing forces on the ribs and the friction 12

forces in between the ribs. As slip increases, the friction forces are also reduced, leaving most of 13

the bond stresses to be transferred through direct bearing on the ribs of the bar. Thus, the bearing 14

stresses on the bar ribs become the principal mechanism of force transfer. Because of the 15

inclination of the rib face, the bearing pressure between the rib and concrete typically act at an 16

angle to the bar longitudinal axis, therefore such force on the concrete can be analyzed into two 17

components; a longitudinal forces parallel to the bar axis which represents the bond force, and a 18

radial forces which causes an outward radial pressure on the surrounding concrete i.e. 19

circumferential tensile stresses in the concrete around the bar which is commonly called wedging 20

action. 21

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Bond Failure 1

The two typical modes of failure used to describe the bond mechanism of reinforcing 2

steel bars and the surrounding concrete are: (a) splitting bond failure which results from splitting 3

of the smallest concrete cover surrounding the bar and is most likely to occur in cases of low 4

levels of confinement around the bonded bar or when the bar spacing is insufficient to resist the 5

lateral concrete tension resulting from the wedging effect of the bar deformations; and (b) direct 6

slip of the bar by pullout failure which results from crushing and shearing off of the concrete 7

keys enclosed between the bar ribs along a cylindrical plan of failure which passes by the bar rib 8

tips. Pullout failure occurs if the radial confinement, caused by the presence of relatively thick 9

concrete covers and/or excessive transverse stirrups, is greater than the transverse bond force that 10

causes splitting of the surrounding concrete. Bond failure resulting from splitting of the concrete 11

is more common in flexural members than direct pullout failure. Current design codes require 12

that both failure modes should be considered in the design of reinforced concrete members. 13

The development length, lb , of a reinforcing steel bar is defined as the minimum required 14

length that the bar must be embedded to develop its yielding strength, controlled by either 15

pullout or splitting. However, if the used length is less than the development length, special 16

anchorage, such as by hooks, must be provided. Because the actual bond stress varies along the 17

length of a bar, design codes provide design equation to specify the development length rather 18

than bond strength. 19

Bond Test Specimens 20

Several bond test specimen configuration have been used to investigate the bond behavior 21

between reinforcing bars and concrete. The major and most commonly used configurations are: 22

pullout specimens, beam-end specimens, beam anchorage specimens, and beam splice 23

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specimens. The nature of both, bond response and bond strength, is affected by the variation in 1

bond specimen configuration. The pullout test does not represent the bond stress development in 2

typical flexural members. The beam-end specimens represent a more realistic type of specimens 3

that can give better and more realistic representation of bond behavior in flexural members since 4

both the reinforcing bars and the surrounding concrete are subjected to tensile stresses. To 5

achieve such state of stresses, the compressive forces must be located away from the reinforcing 6

bar by a distance not less than the bonded length of the tested bar. Also a short length of the 7

tested bar near the concrete free surface has to be unbonded from surrounding concrete to avoid 8

possible conical failure. The beam splice specimens represent full scale specimens designed to 9

directly measure the bond strength of spliced bars. Beam splice specimens replicate a flexural 10

member with a defined bond length and are normally designed and tested under four point 11

loading having the splice length lying within the constant moment region. The ease of their 12

fabrication and the close similarity between the stress profile, in both the concrete and 13

reinforcing bar, and the actual stress profile in real flexural members makes the splice specimens 14

be the main source of the experimental data used by many researchers to establish the current 15

design provisions for development length. 16

Factors Influencing Bond Strength 17

The bond strength and mode of bond failure are affected by many factors. The most 18

important factors are thickness of the clear concrete covers (bottom and/or side), clear spacing 19

between bars, nominal bar diameter, embedment or development and splice length, amount of 20

transverse steel reinforcement, and concrete compressive strength. The individual contributions 21

of these factors are difficult to separate or quantify. Another factor that influences the bond 22

strength of bars is the depth of fresh concrete below the bar during casting. 23

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In general, any increase in confinement of the bar by the surrounding concrete, and/or by 1

transverse reinforcement increases the bond strength and minimizes splitting. Confinement by 2

the concrete is dependent on the clear concrete covers (bottom and/or side) and the bar spacing. 3

Increasing the development/splice length of a reinforcing bar increases its bond strength. The 4

bond strength, for a given length, mobilized by both concrete and transverse reinforcement 5

increases as the bar diameter increases. Bond strength of bars confined by transverse 6

reinforcement increases with the increase in the relative rib area. Top cast bars have lower bond 7

strength than bottom cast bars. Also, bond strength increases with increasing concrete 8

compressive strength for bars not confined by transverse reinforcement approximately with the 9

¼ power of the compressive strength (fc'¼). The additional bond strength; provided by transverse 10

reinforcement, increases approximately with the ¾ power of the compressive strength (fc'¾). Note 11

that the fc'¼ has been shown to provide a better representation of the effect of concrete strength on 12

bon than fc'½. This point is recognized by ACI Committee 408 and within the ACI Code which 13

sets an upper limit on the value of fc'½ for use in design. An increase in the aggregate quantity and 14

strength results also in an increase in bond strength. More details on the factors that affect the 15

bond of reinforcing steel to concrete can be found in the ACI 408R-03 document [1]. 16

Bond characteristics of conventional carbon reinforcement and epoxy-coated 17

reinforcement with concrete has been thoroughly investigated by many researchers 18

[2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] and addressed in terms of bond or development length. Their 19

experimental results contributed to the ACI Committee 408 database on “Bond and Development 20

of Straight Reinforcing Bars in Tension” and were used in formulating the current equation in 21

the ACI 318-02 Code [15] to predict the bond force as well the equation in the ACI 408R-03 22

equation [1]. 23

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The experimental investigation presented in this paper is designed to study the bond 1

behavior of the high-strength steel (commercially known by MMFX steel bar), and included the 2

effect of bar size, level of confinement with transverse reinforcement, bonded length, and bar 3

cast position. The MMFX steel bars exhibit superior mechanical properties when compared with 4

conventional steel reinforcement [13] and conform to the ASTM A 1035-05 Standard [14]. The 5

validity of such innovative reinforcement and their ability to transfer stresses to the surrounding 6

concrete through bond must be considered. To the best knowledge of the authors, very little 7

information is available about the bond strength of high strength steel reinforcement. Therefore, 8

MMFX steel reinforcement was considered to provide database and knowledge of the bond of 9

high strength steel to concrete and to compare the behavior to conventional A615 Grade 420 10

MPa (60 ksi) carbon steel reinforcement. 11

RESEARCH SIGNIFICANCE 12

This research provides significant information on the bond characteristics of the high 13

tensile strength steel bars to concrete. Typical design code equations attempt to predict a required 14

bonded length that will result in yielding of the bar before bond failure. The importance of 15

conducting an experimental investigation to identify the bond characteristic of typical high-16

tensile strength reinforcing steel bars with concrete is to allow for safe, reliable and efficient 17

utilization of this steel. The data collected by two independent experimental programs are 18

compared to the current ACI Code [15] equation as well as the proposed equation by Zuo and 19

Darwin (2000) [12] used to predict the bond force of Grade 420 MPa (60 ksi) steel reinforcing 20

bars. The research provides assessment and limitation of using these equations for available high 21

strength steel bars commercially known as MMFX steel bars. Based on the limited data 22

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presented in this paper, preliminary modifications of the current ACI bond force equations are 1

proposed to extend their use for MMFX steel bars beyond the proportional limit. 2

OBJECTIVES 3

The main objective of this research study is to determine, experimentally, the bond 4

characteristics of straight deformed unhooked high-strength steel bars, commercially known as 5

MMFX steel bars, currently used as flexural reinforcement for concrete members. Results of the 6

experimental program are used to assess the applicability of the current equation proposed by 7

Zuo and Darwin (2000) [12] and the ACI 318-02 [15] code equation for predicting the bond length 8

of high-strength steel bars with concrete. The study provides also an attempt to introduce 9

modifications to the existing equations to predict the bond length of the high-strength MMFX 10

steel bars up to and beyond the proportional limit. 11

EXPERIMENTAL PROGRAM 12

For the MMFX Microcomposite steel bars to be acceptable to the concrete community, a 13

number of design and detailing characteristics must be determined as well as their fundamental 14

mechanical characteristics, including the bond characteristics as reinforcing bars for concrete 15

structures. Two experimental programs were conducted to examine the bond characteristics and 16

the development length of the MMFX bars as tension flexural reinforcement for concrete beams. 17

The objective of the first program was to provide preliminary results for the bond strength of the 18

MMFX to concrete using beam-end specimens reinforced with MMFX steel bars of various 19

sizes. For the beam-end specimens; the parameters considered were bar location during casting 20

and amount of transverse reinforcement confining the bonded length. The second phase of the 21

experimental program represents a more in depth investigation about the bond properties of the 22

MMFX using the large-scale beam-splice specimens. For the beam-splice specimens, the 23

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parameters considered were the bar size and splice length at the maximum constant moment 1

region. 2

Mechanical Properties of MMFX 3

Uniaxial tension tests were conducted to determine the stress-strain characteristics of 4

MMFX steel bars (ASTM E8-01 [16] and ASTM A370-97a [17]). The behavior during testing was 5

monitored using 50 mm (2 in) gage length axial mechanical extensometers and strain gages 6

installed at mid-length of the bars. For comparison purposes, tension tests have been conducted 7

on No.19 (#6) conventional Grade 420 MPa (60 ksi) steel bars with nominal diameter of 19.1 8

mm (0.75 in) as shown in Fig. 1. More details can be found in El-Hacha and Rizkalla [18], [19]. The 9

Young’s Modulus of Elasticity, E, for the MMFX steel determined as the slope of the linear 10

elastic portion of the stress-strain curve [20] was equal to 200×103 MPa (29×106 psi) which is the 11

same value obtained for the Grade 420 MPa (60 ksi) reinforcing steel. As shown in Fig. 1, the 12

MMFX steel does not have a definite yield point and does not exhibit a yielding plateau. For this 13

reason, the 0.2% offset method [20] was used to define the yield strength, fy. The 0.2% offset yield 14

strength was found equal to 827 MPa (120 ksi) for No.19 (#6) and No.25 (#8) bars, and 793 MPa 15

(115 ksi) for No.13 (#4) bar. The strain corresponding to the 0.2% offset yield strength of 16

MMFX was determined as 0.6%. The maximum tensile strength of MMFX, fu, is 1227 MPa (178 17

ksi) for No.19 (#6) and No.25 (#8) and the corresponding strain is 6%, however, for No.13 (#4) 18

the maximum tensile strength is 1138 MPa (165 ksi) at strain of 5%. The behavior of MMFX 19

steel is non-linear beyond yielding up to the maximum tensile strength achieved, after which 20

necking occurred reflected by reduction of the corresponding engineering stress and failure 21

occurred at strain of 13% for No.13 (#4), 20% for No.19 (#6), and 24% for No.25 (#8) steel bars. 22

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Phase I: Beam-End specimens 1

A total of four beam-end specimens with nominal dimension of 356 mm (14 in) wide 508 2

mm (20 in) high and 2032 mm (80 in) long were tested. The beam’s configuration was selected 3

to satisfy the requirements of the ASTM standard 944-99 [21]. Each concrete beam was reinforced 4

with one MMFX steel bar in tension. Three beams were each reinforced with 1No.13 (1#4) 5

MMFX steel bar (beams B1, B2 and B3) and the fourth beam with 1 No.25 (1#8) MMFX steel 6

bar (Beam B4). All the specimens had bottom cast bars except one with top cast (Beam B2). The 7

bonded length used for the No.13 (#4) MMFX steel bar was 356 mm (14 in) (28 db) and a length 8

of 864 mm (34 in) (34db) was used for the No.25 (#8) MMFX steel bar. Four No.25 (#8) Grade 9

420 MPa (60 ksi) deformed steel bars were placed in the tension side of the beam to carry 10

tension force along the debonded length of the specimens. Compression reinforcement was 11

provided by 2No.19 (2#6) Grade 420 MPa (60 ksi) deformed steel bars in each beam. Shear 12

reinforcement consisted of double-legged closed stirrups No.10 (#3) Grade 420 MPa (60 ksi) 13

deformed steel bars at a centre-to-centre spacing of 229 mm (9 in) except for one beam (Beam 14

B3) reinforced with No.13 (#4) MMFX the centre-to-centre spacing of the stirrups was 75 mm (3 15

in) to investigate the effect of confinement on the bond strength. To avoid possible conical 16

failure, the first 102 mm (4 in) of the MMFX steel bar from the concrete surface at the loaded 17

end were debonded using a plastic tube as shown in Fig. 2. The test matrix for the beam-end 18

specimens program is shown in Table 1. Details of the test set-up are shown in Fig. 3. 19

The MMFX steel bar was tensioned using a hydraulic jack and the specimen was held in 20

place using steel beams and Dywidag steel bars anchored to the laboratory floor as shown in Fig. 21

3. The applied tension load was measured using a load cell placed at the jacking side of the 22

beam-end specimen. Three 120 ohms electrical resistance strain gages, installed on the bonded 23

surface of each MMFX steel bar, were used to measure the strain distribution along the bonded 24

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length of the bar, lb, at a distance of lb/6, lb/2 and 5lb/6. A 50 mm (2 in) extensometer was used to 1

measure the strain of the unbonded loaded (jacking) end of the MMFX steel bar. Both the loaded 2

and the unloaded (dead) end slippage were measured using Linear Variable Displacement 3

Transducers (LVDT). 4

The beam-end specimens were cast using normal strength concrete of 41.4 MPa (6000 5

psi) supplied by a local ready-mix plant. Standard concrete cylinder 102 mm × 204 mm (4 in × 8 6

in) were cast according to the ASTM C31-00 Standard [22] for the purpose of determining the 7

compressive strength of the concrete. The concrete cylinders were cured with free water 8

maintained on their surfaces at all times at a temperature 23±2°C (73±3°F) using water storage 9

tank complying with the requirements of ASTM C511-98 Standard Specifications [23]. The 10

average concrete compressive strength for each specimen as measured on the day of testing using 11

three cylinders according to the ASTM C39-01 [24] is given in Table 1. 12

Results of Beam-End Specimens 13

Failure Mode 14

Beams B1, B2, and B3 each reinforced with 1No.13 (1#4) MMFX steel bar failed by 15

rupture of the MMFX bar. As the applied load increased, the number and width of the flexural 16

cracks developed along the bonded length of the MMFX steel bar increased. The spacing 17

between these cracks was approximately equal to the spacing between the stirrups. No signs of 18

bond failure were observed in these beams. It was concluded that the bonded lengths were 19

greater than the development lengths required to develop the ultimate strength of the bar for the 20

levels of confinement provided in the three beams. For the beam reinforced with 1No.25 (1#8) 21

MMFX steel bar, beam B4, a longitudinal crack developed in the concrete cover at the loaded 22

end and propagated towards the unloaded end of the specimen along the steel bar indicating 23

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typical splitting mode of bond failure as shown in Fig. 4. An excessive increase in the width of 1

the first flexural crack near the loaded end was observed. Fig. 5 shows the tensile stress and the 2

average bond stress developed in the MMFX steel bar in beam B4 versus the measured slip at the 3

loaded and unloaded ends of the bar. 4

Bond Distribution 5

Fig. 6 shows the bond stress distribution, ubi, at distance xi from the loaded end along the 6

bonded length of the MMFX steel bar for beam B1 at different stress levels based on the linear 7

behavior of MMFX within the elastic range to determine the stress, fi, corresponding to the 8

measured strain. Figure 6 was developed as follow: at a given bar stress level, the corresponding 9

strain readings along the bonded length as measured by the three strain gages were determined. 10

Using the stress-strain curve obtained from the mechanical properties of the MMFX steel bar, the 11

corresponding stress levels were obtained for each strain gage reading along the bar. These stress 12

values were linearly connected assuming a linear stress distribution along the bonded length. 13

Based on the linear assumption, the bond stress between any two successive strains is assumed to 14

be a constant. Assuming zero values for bond stress at both ends of the bonded length of the bar, 15

the average bond stress between any two successive strains gages were computed. The bond 16

stress distribution was calculated using the following equation: 17

( ))(4 1

1

ii

biibi xx

dffu

−−

=−

− Eq.1 18

By examining all bond stress distribution curves, it is clear that the bond stress 19

distribution is typical to the behavior of conventional steel bars reported by Lutz and Gergely [25] 20

and Azizinamini et al. [7], [26] for stress levels lower than the yield strength. As the induced stresses 21

exceed the yield strength, the shape of the bond stress distribution curve becomes significantly 22

different with the maximum values closer to the loaded end. This could be attributed to the non-23

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linear behavior of the stress-strain relationship of the MMFX which could lead to excessive 1

elongation of the ribs at this high stress zone of the bar near the loaded end. 2

Evaluation of Bonded Length 3

Summary of the predicted and experimental test results is given in Table 2. The actual 4

confinement values, determined using Zuo and Darwin (2000) [12] (Equation 4c or 4d) and ACI 5

318-02 [15] (Equation 11b), shown in Table 2 describe the level of confinement provided by both 6

concrete and transverse reinforcement surrounding the bonded length. The table also shows the 7

confinement limitations 4 and 2.5 specified by both Zuo and Darwin (2000) [12] and ACI 318-8

02 [15], respectively. It can be seen that the level of confinement provided in beams B1, B2, and 9

B3 were higher than the limitations. On the other hand, the level of confinement for beam B4 10

based on Zuo and Darwin (2000) [12] equation was less than the confinement limitation specified 11

by Zuo and Darwin (2000) [12] and greater than the one specified by ACI 318-02 [15]. Using the 12

ACI equation with higher confinement level beyond the limitation of the equation provides, as 13

expected, conservative prediction of the bonded lengths for MMFX in beams B1, B2 and B3. 14

The experimental and the predicted ratio of the bonded length for Zuo and Darwin 15

(2000) [12] and the ACI 318-02 [15] code equations are shown in Fig. 7 and Fig. 8, respectively. 16

Test results indicated that the prediction using both equations is conservative using the 17

confinement limitations imposed by each approach. Using the actual confinement levels which 18

are beyond the specified limitation also provided conservative estimation with one exception for 19

the very high confinement level of 6.4 where stirrups were used every 76 mm (3 in). As the 20

confinement level provided for beam B4 was within the specified limitations for Zuo and Darwin 21

(2000) [12] and ACI 318-02 [15], both equations resulted in more reliable prediction of the bonded 22

length for No.25 (#8) MMFX steel bar. However, since the bonded length provided for No.13 23

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(#4) MMFX steel bar was greater than the required development length, the applicability of both 1

equations cannot be clearly examined. 2

To satisfy the confinement limitations of both Zuo and Darwin (2000) [12] and the ACI 3

code 318-02 [15] equations, the second phase of the experimental program included beam-splice 4

specimens. 5

It should be noted that the test setup used for the beam-end specimens allows only 6

rotation of the section without deflection of the beam at the location of bonded length. Deflection 7

of flexural beams simulated by the beam-splice specimens allows for deflection of the beam 8

which reduces the bond strength of the spliced bars as the deflection forces the spliced bar to 9

exert additional outward pressure on the bottom concrete cover causing a premature failure of the 10

splice. This behavior is supported by Ferguson et al. [27]. 11

Phase II: Beam-Splice Specimens 12

A total of eight large-scale concrete beams reinforced with MMFX steel bars spliced at 13

the midspan were tested. Four specimens were each reinforced with 2No.19 (2#6) MMFX steel 14

bars and the other four with 1No.25 (1#8) MMFX steel bar. The beam-splice specimens were 15

divided into four groups as shown in Table 3. Each group consisted of two specimens with 16

identical concrete dimensions but different in the number (one or two) and the size No.19 (#6) or 17

No.25 (#8) of the reinforcing MMFX steel bars. The specimens in Group I and Group II were 18

rectangular in cross section while in Group III and Group IV, a T-shaped cross section was 19

selected. The spliced lengths varied from one specimen to another and ranged from 305 mm to 20

1829 mm (1.0 ft to 6.0 ft) as shown in Table 3. To minimize the effect of the applied loads on the 21

spliced length, the distance between the end of the splice length and the center of the applied 22

load was always more than 305 mm (1.0 ft). For the specimens reinforced with No25 (#8) 23

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MMFX steel bars, double-legged closed stirrups were evenly distributed along the splice length 1

to provide the required level of confinement around the spliced bars. To prevent possible 2

premature shear failure, shear reinforcement was provided using No.10 (#3) Grade 60 double-3

legged closed stirrups spaced at 127 mm (5 in) along the shear span for all tested beam 4

specimens. Compression reinforcement was provided by 2No.13 (2#4) Grade 420 MPa (60 ksi) 5

steel bars as top reinforcement. The variation in the beam’s dimensions was selected to achieve 6

different stress levels in the MMFX steel bar length at failure. The bottom and side concrete 7

covers and the transverse spacing between the spliced bars were kept constant for all the beams 8

reinforced with 2No.19 (2#6) MMFX steel bars. The selected values were 1.8db, 3db, and 6db 9

where db is the bar diameter. For beams reinforced with 1No.25 (1#8) MMFX steel bar, the 10

bottom and side concrete covers were also kept constant at values of 1.375db and 5db, 11

respectively. The actual measured dimensions of the specimens after casting are given in Table 12

3. 13

The test matrix for the beam-splice test program is shown in Table 3. The first letter of 14

the beam designation “B” stands for Beam; the middle number identifies the bar size No.19 (#6) 15

and No.25 (#8); while the last number represents the spliced length of the bar in inches. Standard 16

concrete cylinder 102 mm × 204 mm (4 in × 8 in) were cast according to the ASTM C31-00 17

Standard [22] for the purpose of determining the compressive strength of the concrete. The 18

concrete cylinders were cured with free water maintained on their surfaces at all times at a 19

temperature 23±2°C (73±3°F) using water storage tank complying with the requirements of 20

ASTM C511-98 Standard Specifications [23]. The average concrete compressive strength 21

determined using three cylinders according to ASTM C39-01 [24] at age of 28 days was 41.8 MPa 22

(6071 psi). The concrete compressive strengths as measured on the day of testing are given in 23

Table 4. 24

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All beams were simply supported loaded in four-point bending. The load was applied 1

using an MTS actuator operated under displacement-control mode at a constant loading rate of 2

1.07 mm/min (0.042 in/min). The constant moment region span was 1829 mm (6 ft) and 2438 3

mm (8 ft) for the 4879 mm (16 ft) and 6096 mm (20 ft) long specimens, respectively, as shown 4

in Fig. 9. The beams were instrumented to measure the deflection at midspan using LVDT. Two 5

120 ohms electrical resistance strain gages were installed on the MMFX steel bars, one on each 6

side of the splice length within the constant moment zone to measure the strain in the bar. 7

Concrete strain at the top surface of the beam specimens was also measured using PI gages. Test 8

set-up and instrumentation of the beam-splice specimens is shown in Fig. 9. The cracks were 9

marked on the beam and crack widths were measured using crack comparator. 10

Results of Beam-Splice Specimens 11

Failure Mode 12

The failure mode of all beam-splice specimens was splitting bond failure. This was 13

associated with formation of an extensive crack pattern along the splice length as shown in Fig. 14

11. As the applied load on the beams increases more flexural cracks developed and diagonal 15

cracks formed within the constant moment region in the rectangular cross-section beam 16

specimens. All beams reinforced with 2No.19 (2#6) MMFX steel bars exhibited an excessive 17

increase in the width of the main flexural cracks, formed at the ends of the splice length, 18

accompanied with bond failure as a result of the bar slippage as shown in Fig. 10. Scattering and 19

spalling of the concrete cover associated with the failure of the specimens reinforced with #6 20

MMFX steel bars due to the absence of the transverse reinforcement as shown in Fig. 10. 21

For the beams reinforced with 1No.25 (1#8) MMFX steel bar with the short splice length 22

showed excessive widening of the main flexural cracks at time of failure as shown in Fig. 11 for 23

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beam B-8-24. Similar behavior was observed in beam B-8-12. However, for the beams with 1

longer splice length no significant increase in the crack width was observed at failure as shown 2

in Fig. 12 for beam B-8-48. Similar behavior was observed in beam B-8-72. The specimens 3

reinforced with No.25 (#8) MMFX steel bars, failure was contained within the splice length as 4

shown in Fig. 11 and Fig. 12. The tensile stresses developed in the MMFX steel bars just before 5

failure calculated using the moment curvature analysis are given in Table 4. 6

Evaluation of Bond Strength and Splice Length 7

The experimental results of the bond force of No.19 (#6) and No.25 (#8) MMFX steel 8

bars were compared with the predictions from the equation proposed by Zuo and Darwin 9

(2000) [12] and the ACI 318-02 [15] code equation. 10

Zuo and Darwin (2000) [12] Equation 11

The bond capacity of the No.19 (#6) and No.25 (#8) MMFX steel bars was evaluated 12

using the equation proposed by Zuo and Darwin (2000) [12] as shown in Fig. 13 and Fig. 14, 13

respectively. Test results indicated that Zuo and Darwin (2000) [12] equation provided 14

conservative prediction of the bond capacity of No.19 (#6) MMFX steel bars at stress levels up 15

to the proportional strength of 579 MPa (84 ksi), and provided very close prediction to the bond 16

capacity of No.25 (#8) MMFX steel bars up to the proportional strength of 607 MPa (88 ksi). 17

However, at higher stress levels, the equation resulted in unconservative prediction for both 18

No.19 (#6) and No.25 (#8) MMFX steel bars. Test results suggested that there is a need to 19

modify Zuo and Darwin (2000) [12] equation to include higher stress level. The stress limitation 20

imposed by the ACI 318-02 [15] code for the maximum allowed design yielding strength of 550 21

MPa (80 ksi) has been selected as an upper boundary for using the equation by Zuo and Darwin 22

MS#2003378 18

(2000) [12]. Therefore, modification of the equation has been proposed beyond the stress level of 1

550 MPa (80 ksi). 2

Bond equations generally relate bar stresses to bond lengths. The equation proposed by 3

Zuo and Darwin (2000) [12] for bond strength of bar not confined with transverse reinforcement 4

(Tb=Tc and Ts=0), in terms of bond force Tb, as is the case for beams B6-12, B6-24, B6-36 and 5

B6-60 is given by: 6

( )[ ]

+++=

′=

′9.01.02.565.043.1

min

maxmin4141 c

cAdcl

fT

fT

bbdc

c

c

b (SI Units) Eq.2 7

( )[ ]

+++=

′=

′9.01.023505.08.59

min

maxmin4141 c

cAdcl

fT

fT

bbdc

c

c

b (Imperial Units) Eq.2a 8

To limit applicability of Equations (2 and 2a) to cases in which a splitting failure 9

governs: 10

( ) 0.49.01.05.01

min

maxmin ≤

++

cc

dcd b

b

(SI or Imperial Units) Eq.2b 11

The above equation (Eq.2) was modified by changing only the numerical constants to 12

ensure conservative predictions at any stress level between 550 MPa (80 ksi) and 831 MPa 13

(120.5 ksi). The proposed modification of Zuo and Darwin (2000) [12] equation for MMFX 14

beyond the stress level of 550 MPa (80 ksi) is: 15

( )

+

++=

′=

′9.01.01205.0

65

min

maxmin4141 c

cAdcl

fT

fT

bbdc

c

c

b (SI Units) Eq.3 16

( )[ ]

+++=

′=

′9.01.050005.034

min

maxmin4141 c

cAdcl

fT

fT

bbdc

c

c

b (Imperial Units) Eq.3a 17

Using the modified equation to predict the bond capacity of the No.19 (#6) MMFX steel 18

bars for stress levels higher than 550 MPa (80 ksi) the maximum test/predict ratio was about 1.22 19

as can be seen in Fig. 13. 20

MS#2003378 19

The Zuo and Darwin (2000) [12] equation for bond strength of bars confined with 1

transverse reinforcement (Tb=Tc +Ts), in terms of bond force Tb, as is the case for beams B8-12, 2

B8-24, B8-48 and B8-72 is given by: 3

( )[ ]

2/1

min

maxmin4/14/1

7449

9.01.02.565.043.1

ctr

dr

bbdc

sc

c

b

fn

NAtt

cc

Adclf

TTfT

′

++

+++=

′+

=′

(SI Units) Eq.4 4

( )[ ]

2/1

min

maxmin4/14/1

414.31

9.01.023505.08.59

ctr

dr

bbdc

sc

c

b

fn

NAtt

cc

Adclf

TTfT

′

++

+++=

′+

=′

(Imperial Units) Eq.4a 5

To limit applicability of Equations (4 and 4a) to cases in which a splitting failure 6

governs: 7

( ) 0.426.6

9.01.05.01 21

min

maxmin ≤

′

+

++ c

trdrb

b

fsn

Attcc

dcd

(SI Units) Eq.4b 8

( ) 0.452.0

9.01.05.01 21

min

maxmin ≤

′

+

++ c

trdrb

b

fsn

Attcc

dcd

(Imperial Units) Eq.4c 9

The first term in Equation (4 or 4a) is the same as for the bar without confinement given 10

by Equation (2 or 2a), and the second term represents the effect of confinement, from the 11

transverse reinforcement provided by the stirrups, on bond strength. The proposed modification 12

of the Zuo and Darwin (2000) [12] equation is: 13

( )

2/1

min

maxmin4/14/1

14806.9

9.01.01205.065

ctr

dr

bbdc

sc

c

b

fn

NAtt

cc

Adclf

TTfT

′

−+

+

++=

′+

=′

(SI Units) Eq.5 14

MS#2003378 20

( )[ ]

2/1

min

maxmin4/14/1

835

9.01.050005.034

ctr

dr

bbdc

sc

c

b

fn

NAtt

cc

Adclf

TTfT

′

−+

+++=

′+

=′


It should be noted, that the first term in proposed Equation (5 or 5a) is Equation (3 or 3a) 2

which represents the case of a bar without confinement. 3

Using Equation (5 or 5a) to predict the bond capacity of No.25 (#8) MMFX steel bars for 4

stress levels higher than 550 MPa (80 ksi), the maximum test/predict ratio is 1.03 as can be seen 5

in Fig. 14. 6

Therefore, based on this limited data, it is recommended to use Zuo and Darwin (2000) [12] 7

equation (Equation 4 or 4a) to predict the splice length of MMFX steel bars for stress levels up to 8

550 MPa (80 ksi) for No.19 (#6) and No.25 (#8), and the modified equations (Equation 5 or 5a) 9

for higher stress levels between 550 MPa (80 ksi) and 831 MPa (120 ksi) for No.19 (#6) bars and 10

between 550 MPa (80 ksi) and 952 MPa (138 ksi) for No.25 (#8) bars. 11

ACI 318-02 [15] Code Equation 12

The bond capacity of the No.19 (#6) and No.25 (#8) MMFX steel bars was evaluated 13

using the current ACI 318-02 [15] code equation as shown in Fig. 15 and Fig. 16, respectively. 14

Test results indicated that the current ACI 318-02 [15] equation provided conservative prediction 15

of the bond capacity of No.19 (#6) and No.25 (#8) MMFX steel bars at stress levels up to the 16

proportional strength of 579 MPa (84 ksi) and 607 MPa (88 ksi), respectively. At higher stress 17

levels, the prediction turned rapidly towards the unconservative side. Therefore, there is a need 18

to modify the current ACI 318-02 [15] equation. As discussed before, 550 MPa (80 ksi) will be 19

also used as the cutoff level for the modified equation. 20

MS#2003378 21

The current ACI 318-02 [15] code equation, for bars not confined with transverse 1

reinforcement (Tb=Tc and Ts=0), as is the case for beams B6-12, B6-24, B6-36 and B6-60, the 2

bond force, Tb, is given by: 3

( )bdc

c

c

b dclfT

fT

5.0185

min2121 +′=′

=′

π (SI Units) Eq.6 4

( )bdc

c

c

b dclfT

fT

5.03

10min2121 +′=

′=

′π (Imperial Units) Eq.6a 5

Equations (6 and 6a) can be rewritten in terms of ld as follows: 6

+′′=

b

bc

y

b

d

ddcf

fdl

5.01

109

min

(SI Units) Eq.7 7

+′′=

b

bc

y

b

d

ddcf

fdl

5.01

403

min


The above Equations (7 and 7a) were written in terms of the yield stress. However, to 9

determine the development length of the bar in the tested beams, this stress should be taken as 10

the actual measured stress in the MMFX steel bars. 11

Based on the tested results, the above equation was modified by changing the numerical 12

constants and addition of a term function of db2. The proposed modification of the ACI 318-02 [15] 13

equation for MMFX beyond stress level of 550 MPa (80 ksi) is: 14

( ) 2min2121 405.0

91

bbdc

c

c

b ddclfT

fT

++′=′

=′

π (SI Units) Eq.8 15

( ) 2min2121 5005.0

1013

bbdc

c

c

b ddclfT

fT

++′=′

=′

π (Imperial Units) Eq.8a 16

Equations (8 and 8a) can be rewritten in terms of ld as follows 17

MS#2003378 22

+′

−′

=

b

b

c

y

b

d

ddc

f

f

dl

5.094

51

min

(SI Units) Eq.9 1

+′

−′

=

b

b

c

y

b

d

ddc

f

f

dl

5.01052

637

min


Using the above modified equation to predict the bond capacity of No.19 (#6) MMFX 3

steel bars for stress levels higher than 550 MPa (80 ksi) the maximum test/predict ratio was 4

about 1.19 as can be seen in Fig. 15. 5

The current ACI 318-02 [15] code equation, for bars confined with transverse 6

reinforcement (Tb=Tc +Ts), in terms of bond force Tb, as is the case for beams B8-12, B8-24, B8-7

48 and B8-72 is given by: 8

( )snfAl

dclf

TTfT yttrd

bdc

sc

c

b

34.101855.0

185

min2121

ππ ++′=

′+

=′

(SI Units) Eq.10 9

( )snfAl

dclf

TTfT yttrd

bdc

sc

c

b

15003105.0

310

min2121

ππ ++′=

′+

=′



++′′=

b

trbc

y

b

d

dkdcf

fdl

5.01

109

min

(SI Units) Eq.11 12

and sn

fAk yttr

tr 34.10= (SI Units) 13

++′′=

b

trbc

y

b

d

dkdcf

fdl

5.01

403

min


MS#2003378 23

and sn

fAk yttr

tr 1500= (Imperial Units) 1

To limit the probability of a pullout failure, ACI 318-02 requires that: 2

5.25.0min ≤

++′

b

trb

dkdc

Eq.11b 3

Based on the tested results, the above equation (Eq.10) was modified by changing the 4

numerical constants only. Therefore, the proposed modification of the ACI 318-02 [15] equation 5

for MMFX beyond stress level of 550 MPa (80 ksi) is: 6

( )snfAl

ddclf

TTfT yttrd

bbdc

sc

c

b

5000405.0

91 2

min2121

ππ +

++′=

′+

=′

(SI Units) Eq.12 7

( )snfAl

ddclf

TTfT yttrd

bbdc

sc

c

b

4105005.0

1013 2

min2121

ππ +

++′=

′+

=′



++′

−′

=

b

trb

c

y

b

d

dkdc

f

f

dl

5.094

51

min

(SI Units) Eq.13 10

and snfA

k yttrtr 556= (SI Units) 11

++′

−′

=

b

trb

c

y

b

d

dkdc

f

f

dl

5.01052

637

min


and snfA

k yttrtr 533= (Imperial Units) 13

Using the above modified equation to predict the bond capacity for No.25 (#8) MMFX 14

bars, for bar stress levels higher than 550 MPa (80 ksi), the maximum test/predict ratio did not 15

MS#2003378 24

exceed 1.0 as can be seen in Fig. 16. The modified ACI 318-02 [15] equation predicted accurately 1

the bond force of the No.25 (#8) MMFX steel bar confined with transverse reinforcement above 2

stress level of 550 MPa. 3

Therefore, based on the limited test data, it is recommended to use of the current ACI 4

318-02 [15] equation (Equation 10) to predict the splice length of MMFX steel bars for stress 5

levels up to 550 MPa (80 ksi) for No.19 (#6) and up to 505 MPa (73ksi) for No.25 (#8) bars, and 6

the modified equation (Equation 12) for stress levels between 550 MPa (80 ksi) and 831 MPa 7

(120.5 ksi) for No.19 (#6) bars and between 505 MPa (73 ksi) and 954 MPa (138.5 ksi) for 8

No.25 (#8) bars. However, for the limited data presented from the current investigation, the 9

modified equations could be considered a tight fit to very few data points shown to illustrate 10

bond behavior at high stress levels and that more data is needed in that range of stress above the 11

proportional limit. Therefore, the existing equations are unconservative at these levels of stress 12

and additional data is needed to derive better expressions for these ranges of stress. The authors 13

recommend that more tests should be conducted to fully develop a more precise equation for 14

higher bond stresses. 15

The experimental and predicted bar stress for No.19 (#6) and No.25 (#8) MMFX steel 16

bars using the current and modified Zuo and Darwin (2000) [12] and ACI 318-02 [15] equations, are 17

shown in Fig. 17 and Fig. 18, respectively. 18

Splice Length/Bar Diameter Ratio 19

The measured bar stresses for No.19 (#6) and No25 (#8) MMFX steel bars versus splice 20

length to the bar diameter are shown in Fig. 19. Tests results indicated that the stress (or bond 21

force) is nearly linearly related, but not proportional, to the splice length to the bar diameter ratio 22

(Ls/db) up to the minimum yield strength for No.19 (#6) and No25 (#8) MMFX steel bars. The 23

MS#2003378 25

relationship suggest also that a splice length of 30db can be safely used to achieve the maximum 1

yield strength of 550 MPa (80 ksi) limited by the current ACI 318-02 Code [15]. As shown in Fig. 2

19, a splice length of 45db can be used to achieve the yield strength of 758 MPa (110 ksi) for 3

MMFX steel bars. The linear, not proportional, relationships extend to a stress of 831 MPa 4

(120.5 ksi) which corresponds to a splice length of 50db. Beyond the yield strength, the 5

relationship becomes highly non-linear and significant splice length is required to achieve higher 6

stress levels which could be impractical to use for typical applications. 7

CONCLUSIONS 8

The following conclusions were made based on the limited number of tested specimens: 9

1. Bond behavior of the MMFX steel bars is similar to that of the conventional Grade 420 10

MPa (60 ksi) carbon steel up to stress level corresponding to the proportional limit imposed 11

by the ACI Code of 550 MPa (80 ksi). At higher stress levels, bond failure changed from 12

the typical sudden and brittle failure, normally observed for conventional steel, to a gradual 13

and ductile failure due to the nonlinear behavior of the MMFX steel bars in this range. 14

2. The nonlinear ductile response of the MMFX bars at high stress levels beyond proportional 15

limit strength, has a strong influence in reducing the bond strength of the MMFX bars 16

compared to Grade 420 MPa (60 ksi) steel. 17

3. The current equations proposed by Zuo and Darwin (2000) [12] and ACI 318-02 Code [15] for 18

bond force, provided conservative prediction of the bond capacity for No.19 (#6) and 19

No.25 (# 8) MMFX steel bars up to 550 MPa (80 ksi). For stress levels exceeding 550 MPa 20

(80 ksi) and up to a stress level of 831 MPa (120.5 ksi) for No.19 (#6) and 955 MPa (138.5 21

ksi) for No.25 (#8) MMFX bars, respectively, both equations were modified to provide 22

better prediction of the bond force capacity. 23

MS#2003378 26

4. Splice length to bar diameter ratio is nearly linearly, but not proportionally, related to the 1

induced stress in the MMFX steel bar up to yield strength. The relationship becomes highly 2

nonlinear beyond a stress level of 758 MPa (110 ksi). 3

ACKNOWLEDGEMENT 4

The authors would like to thank the technical staff and graduate students at the 5

Constructed Facilities Laboratory at NC State University for their help with the laboratory work. 6

The authors are grateful to the support provided by MMFX Technologies Corporation for 7

donating the steel materials. 8

REFERENCES 9

[1] ACI Committee 408R-03, “Bond and Development of Straight Reinforcing Bars in 10 Tension”, American Concrete Institute, September 2003, 49p. 11

[2] Chinn, J., Ferguson, P.M., and Thompson, J.N., 1955, “Lapped Splices in Reinforced 12 Concrete Beams.” ACI Journal, V. 52, No. 2, Oct., pp. 201-214. 13

[3] Chamberlin, S.J., 1958, “Spacing of Spliced Bars in Beams.” ACI Journal, Proceedings V. 14 54, No. 8, Feb., pp. 689-698. 15

[4] Ferguson, P.M., and Breen, J.E., 1965, “Lapped Splices for High strength Reinforcing 16 Bars.” ACI Journal, V. 62, No. 9, Sep., pp. 1063-1078. 17

[5] Hester, C.J., Salamizavaregh, S., Darwin, D., and McCabe, S.L., 1993, “Bond of Epoxy-18 Coated Reinforcement: Splices.” ACI Structural Journal, V. 90, No. 1, Jan.-Feb., pp. 89-19 102. 20

[6] Rezansoff, T., Akanni, A., and Sparling, B., 1993, “Tensile Lap Splice under Static 21 Loading: A Review of the Proposed ACI 318 Code Provisions.” ACI Structural Journal, 22 V. 90, No. 4, Jul.-Aug., pp. 374-384. 23

[7] Azizinamini, A., Stark, M., Roller, J., and Ghosh, S., 1993, “Bond performance of 24 Reinforcing Bars Embedded in High-Strength Concrete.” ACI Structural Journal, V. 90, 25 No. 5, Sep.-Oct., pp. 554-561. 26

[8] Azizinamini, A., Chisala, M., and Ghosh, S., 1995, “Tension Development Length of 27 Reinforcing Bars Embedded in High-Strength Concrete.” Engineering Structures, V. 17, 28 No. 7, pp. 512-522. 29

[9] Darwin, D., Tholen, M.L., Idun, E.K., and Zuo, J., 1996a “Splice Length of High Relative 30 Rib Area Reinforcing Bars.” ACI Structural Journal, V. 93, No. 1, Jan.-Feb., pp. 95-107. 31

MS#2003378 27

[10] Darwin, D., Tholen, M.L., and Idun, E.K., 1996b “Development Length Criteria for 1 Conventional and High Relative Rib Area Reinforcing Bars.” ACI Structural Journal, V. 2 93, No. 3, May-June, pp. 347-359. 3

[11] Zuo, J., and Darwin, D., 1998, “Bond Strength of High Relative Rib Area Reinforcing 4 Bars.” SM Report No.46, University of Kansas, Center for Research, Lawrence, KS, 350 5 pp. 6

[12] Zuo, J., and Darwin, D., 2000, “Splice Length of Conventional and High Relative Rib 7 Area Reinforcing Bars in Normal and High Strength Concrete.” ACI Structural Journal, V. 8 97, No. 4, Jul.-Aug., pp. 630-641. 9

[13] MMFX Steel 2002, Product Bulletin, MMFX Steel Corporation of America, February 10 2002, 13p. (http://www.mmfxsteel.com). 11

[14] ASTM A 1035/A 1035M-05, Standard Specification for Deformed and Plain, Low-carbon, 12 Chromium, Steel Bars for Concrete Reinforcement. 13

[15] ACI 318-02 Code, Building Code requirements for structural Concrete (318-02) and 14 Commentary (318R-02), American Concrete Institute, Farmington Hills, MI. 15

[16] ASTM E8-01, “Standard Test Methods for Tension Testing of Metallic Materials.” 16

[17] ASTM A370-97a, “Standard Test Methods and Definitions for Mechanical Testing of Steel 17 Products.” 18

[18] El-Hacha, R., and Rizkalla, S.H., 2002a, “Fundamental Material Properties of MMFX 19 Steel Bars.” Research Report: RD-02/04, North Carolina State University, Constructed 20 Facilities Laboratory, Raleigh, North Carolina, USA, July 2002, 62pp. 21 (http://www.mmfxsteel.com). 22

[19] El-Hacha, R., Rizkalla, S.H., 2002b, “Behaviour of MMFX-2 Microcomposite Steel and 23 Stainless Steel Bars In Uniaxial Tension.” Technical Report, North Carolina State 24 University, Constructed Facilities Laboratory, Raleigh, North Carolina, USA, November 25 2002, 25pp. Submitted to MMFX Steel Corporation. 26

[20] ASTM E111-97, “Standard Test Methods for Young’s Modulus, Tangent Modulus, and 27 Chord Modulus.” 28

[21] ASTM 944-99, “Standard Test Method for Comparing Bond Strength of Steel Reinforcing 29 Bars to Concrete Using Beam-End Specimens.” 30

[22] ASTM C 31/C 31M-00, “Standard Practice for Making and Curing Concrete Test 31 Specimens in the Field.” 32

[23] ASTM C 511-98, “Standard Specification for Moist Cabinets, Moist Rooms, and Water 33 Storage Tanks Used in the Testing of Hydraulic Cements and Concretes.” 34

[24] ASTM C39-01, “Standard Test Method for Compressive Strength of Cylindrical Concrete 35 Specimens.” 36

[25] Lutz, L.A., and Gergely, P., 1967, “Mechanism of Bond and Slip of Deformed Bars in 37 Concrete.” ACI Journal, V. 64, No. 11, Nov., pp. 711-721. 38

[26] Azizinamini, A., Pavel, R., Hatfield, E., and Ghosh, S.K., 1999, “Behavior of Lap-Spliced 39 Reinforcing Bars Embedded in High-Strength Concrete.” ACI Structural Journal, V. 96, 40 No. 5, Sep.-Oct., pp. 826-835. 41

MS#2003378 28

[27] Ferguson, P.M., and Thompson, J.N., 1962 “Development Length of High Strength 1 Reinforcing Bars.” ACI Journal, V. 58, No. 7, July, pp. 887-921. 2

MS#2003378 29

NOTATION 1

Atr area of each stirrup or tie crossing the potential plane of splitting adjacent to the 2

reinforcement being developed or spliced 3

cb thickness of the clear bottom concrete cover 4

csi half the clear spacing between the spliced bars 5

cso thickness of the clear side concrete cover 6

cmax maximum of cb or cs 7

cmin minimum of cb or cs 8

cs minimum of cso or csi+6.35 mm (csi+0.25 in) 9

c'min minimum of concrete covers surrounding the bar or half the clear spacing between bars, 10

minimum of csi and (cb or cso) 11

bw width of the web of a beam 12

Bf width of the flange of a beam 13

d effective depth of a beam 14

db nominal diameter of the steel bar 15

dst stirrups diameter 16

fc' concrete compressive strength 17

fi bar stress at the location of the strain gage (i) 18

fi-1 bar stress at the location of the next strain gage (i-1) 19

fs tensile stress developed in the MMFX steel bars just before failure as calculated using 20

the moment curvature analysis 21

fy yield strength of tension reinforcement 22

fyt yield strength of transverse reinforcement 23

h beam height 24

MS#2003378 30

ktr transverse reinforcement index 1

lb bonded length of the steel bar 2

ls splice length 3

L beam length 4

n number of MMFX bar, number of spliced MMFX bar 5

N total number of stirrups along the splice length 6

P applied load at failure 7

M calculated bending moment at the time of failure at the splice location including the 8

effect of self-weight of the specimen 9

Rr relative rib area of the reinforcement (ratio of projected rib area normal to bar axis to the 10

product of nominal bar perimeter and the centreline-to-centreline rib spacing 11

S average spacing of the stirrups (transverse reinforcement) 12

td term representing the effect of bar size on Ts. td = 0.03db+0.22 SI units (td = 0.78db+0.22 13

Imperial units) 14

tr term representing the effect of bar size on Ts . tr = 9.6Rr + 0.28 < 1.72 db +0.22 15

Tb total bond force of a developed or spliced bar = Tc + Ts 16

Tc concrete contribution to total bond force, the bond force that would be developed 17

without transverse reinforcement. 18

Ts steel contribution to total bond force, the additional bond strength provided by the 19

transverse steel 20

ubi average bond stress between strain gage (i) and (i-1) 21

xi distance between the loaded end and the strain gage (i) 22

xi-1 distance between the loaded end and the strain gage (i-1) 23

MS#2003378 31

List of Tables 1

Table 1- Test Matrix of Experimental Program 1: Beam-End Specimens 2

Table 2- Summary of Predicted and Experimental Test Results of Experimental Program 1: 3

Beam-End Specimens 4

Table 3- Test Matrix of Experimental Program 2: Beam-Splice Specimens 5

Table 4- Summary of Predicted and Experimental Test Results of Experimental Program 2: 6

Beam-Splice Specimens 7

MS#2003378 32

List of Figures 1

Fig. 1- Stress-Strain Curves of MMFX and Grade 60 Steel Bars 2

Fig. 2- Details of Beam-End Specimens 3

Fig. 3- Test-Set-Up of Beam-End Specimens 4

Fig. 4- Splitting Bond Failure Mode for Beam-End Specimen B4 (Top View) 5

Fig. 5- Average Bond and Tensile Stresses vs. Slip at Loaded and Unloaded End for Beam-End 6 Specimen B4 7

Fig. 6- Bond Stress Distribution along the Bonded Length at Different Stress Levels for Beam-8 End Specimen B1 9

Fig. 7- Experimental/predicted ratio for bonded length for Beam-End Specimens using Zuo and 10 Darwin (2000) Equation 11

Fig. 8- Experimental/predicted ratio for bonded length for Beam-End Specimens using ACI 12 3182-02 Code Equation 13

Fig. 9- Test Set-Up of the Beam-Splice Specimens 14

Fig. 10- Failure of Beam-Splice Specimen B-6-36 15



Fig. 13- Bond Force vs. Splice Length for Beams Reinforced with No.19 (#6) MMFX Steel Bars 18 Using Zuo and Darwin (2000) Equation 19

Fig. 14- Bond Force vs. Splice Length for Beams Reinforced with No.25 (#8) MMFX Steel Bars 20 Using Zuo and Darwin (2000) Equation 21

Fig. 15- Bond Force vs. Splice Length for Beams Reinforced with No.19 (#6) MMFX Steel Bars 22 Using the ACI 3182-02 Code Equation 23

Fig. 16- Bond Force vs. Splice Length for Beams Reinforced with No.25 (#8) MMFX Steel Bars 24 Using the ACI 3182-02 Code Equation 25

Fig. 17- Experimental and Predicted Bar Stress vs. Splice Length for No.19 (#6) and No.25 (#8) 26 MMFX Steel Bars using the Current and Modified Zuo and Darwin (2000) Equation 27

Fig. 18- Experimental and Predicted Bar Stress vs. Splice Length for No.19 (#6) and No.25 (#8) 28 MMFX Steel Bars using the Current and Modified ACI 3182-02 Code Equation 29

Fig. 19- Bars Stress vs. Splice Length/Bar Diameter for Beams Reinforced with No.19 (#6) and 30 No.25 (#8) MMFX Steel Bars 31

32

MS#2003378 34

Table 1-Test Matrix of Experimental Program 1: Beam-End Specimens 33

Concrete Dimensions Concrete Cover Stirrups details

Beam ID n

MMFX bar location

during cast

lb

mm (in)

L mm (in)

b mm (in)

h mm (in)

d mm (in)

db

mm (in)

Cso mm (in)

Cb mm (in)

fc'

MPa (psi)

S mm (in)

dst mm (in)

fyt MPa (ksi)

B1 1No.13 (1#4) Bottom 356

(14)2032 (80)

356 (14)

508 (20)

464 (18.25)

12.7 (0.5)

172 (6.75)

38 (1.5)

36.1 (5240)

229 (9)

9.5 (0.375)

420 (60)

B2 1No.13 (1#4) Top 356

(14)2032 (80)

356 (14)

508 (20)

464 (18.25)

12.7 (0.5)

172 (6.75)

38 (1.5)

36 (5220)

229 (9)

9.5 (0.375)

420 (60)

B3 1No.13 (1#4) Bottom 356

(14)2032 (80)

356 (14)

508 (20)

464 (18.25)

12.7 (0.5)

172 (6.75)

38 (1.5)

36.06 (5230)

76 (3)

9.5 (0.375)

420 (60)

B4 1No.13 (1#8) Bottom 864

(34)2032 (80)

356 (14)

508 (20)

457 (18.0)

25.4 (1.0)

165 (6.50)

38 (1.5)

36.7 (5320)

229 (9)

9.5 (0.375)

420 (60)

34

35

36

37

38

39

40

41

42

43

MS#2003378 35

Table 2- Summary of Predicted and Experimental Test Results of Experimental Program 1: Beam-End Specimens 44 Confinement Beam ID

Results from Bond Force

kN (lb)

Bar Stress MPa (psi)

Bonded Lengthmm (in) Actual Limitation

Zuo and Darwin (2000) [12] Equation 121.84 (27391)

962.1 (139537)

516.6 (20.34) 5.5 4.0

ACI 318-02 [15] Equation 105.8 (23781)

835.3 (121148)

401.6 (15.81) 4.5 2.5 B1

Experimental 152.73 (34334)

1183.4 (171628)

355.6 (14.00)


962.1 (139537)

492 (19.37) 5.5 4.0

ACI 318-02 [15] Equation 105.6 (23736)

835.3 (121148)

385.6 (15.18) 4.5 2.5 B2


1134.2 (164508)

355.6 (14.00)


1149.6 (166742)

386.8 (15.23) 7.0 4.0

ACI 318-02 [15] Equation 151.98 (34168)

1200.1 (174059)

272 (10.71) 6.4 2.5 B3


1139.3 (165236)

355.6 (14.00)


762.0 (110507)

942.6 (37.11) 3.8 4.0

ACI 318-02 [15] Equation 371.19 (83448)

732.6 (106250)

946.7 (37.27) 3.2 2.5 B4


792.9 (115000)

863.6 (34.00)

45

46

47

MS#2003378 36

Table 3 -Test Matrix of Experimental Program 2: Beam-Splice Specimens 48

Concrete dimensions * Cover and spacing Stirrups details along splice length Group

# Specimen

ID

ls

mm (in)

L mm (ft)

bw mm (in)

Bf mm (in)

h mm (in)

d mm (in)

Cso mm (in)

Csi mm (in)

Cb mm (in)

NS

mm (in)

dst mm (in)

fyt MPa (ksi)

I B-6-12 305 (12)

4877 (16.0)

305 (12.0) 311

(12.25) 264

(10.38)60.3

(2.375) 54.0

(2.125) 38

(1.5) 0

II B-6-24 610 (24)

4877 (16.0)

311 (12.25) 362

(14.25) 314

(12.38)54.0

(2.125) 70.0

(2.75) 38

(1.5) 0

III B-6-36 914 (36)

4877 (16.0)

305 (12.0)

613 (24.13)

464 (18.25)

419 (16.5)

54.0 (2.125)

60.3 (2.375)

35 (1.375) 0

IV B-6-60 1524 (60)

6096 (20.0)

305 (12.0)

1219 (48.0)

457 (18.0)

413 (16.25)

57.2 (2.25)

57.2 (2.25)

35 (1.375) 0

I B-8-12 305 (12)

4877 (16.0)

305 (12.0) 305

(12.0) 254

(10.0) 123.8

(4.875) 38 (1.5) 1 305

(12.0) 9.53

(0.375) 420 (60)

II B-8-24 610 (24)

4877 (16.0)

305 (12.0) 356

(14.0) 305

(12.0) 123.8

(4.875) 38 (1.5) 2 305

(12.0) 9.53

(0.375) 420 (60)

III B-8-48 1219 (48)

4877 (16.0)

311 (12.25)

616 (24.25)

470 (18.5)

422 (16.63)

114.3 (4.50) 35

(1.375) 5 245 (9.625)

9.53 (0.375)

420 (60)

IV B-8-72 1829 (72)

6096 (20.0)

305 (12.0)

1219 (48.0)

470 (18.0)

410 (16.13)

120.7 (4.75) 35

(1.375) 7 260.4 (10.25)

9.53 (0.375)

420 (60)

* The dimensions of the specimens were measured after casting 49

50

51

52

53

54

MS#2003378 37

Table 4 - Summary of Predicted and Experimental Test Results of Experimental Program 2: Beam-Splice Specimens 55 fs

MPa (ksi) Prediction using

Zuo and Darwin (2000) Equation

ACI 318-02 Code Equation

Group #

Specimen ID ls

mm (in)

fc'

MPa (psi)

Test

Existing Modified Existing Modified

P

kN (kips)

M

kN.m (kips.in)

I B-6-12 305 (12)

40.0 (5800)

430.82 (62.48)

343.40 (49.8)

432.30 (62.70)

281.05 (40.76)

434.50 (63.02)

77.0 (17.3)

58.4 (517)

II B-6-24 610 (24)

39.4 (5720)

605.09 (87.76)

526.93 (76.42)

534.8 (75.57)

558.20 (80.96)

543.10 (78.74)

135.7 (30.5)

99.88 (884)

III B-6-36 914 (36)

44.0 (6370)

792.708 (114.97)

706.17 (102.42)

648.38 (94.04)

824.72 (119.62)

667.41 (96.79)

246.8 (55.5)

179.98 (1593)

IV B-6-60 1524 (60)

39.4 (5710)

830.62 (120.47)

1055.24 (153.05)

847.4 (122.9)

1301.37 (188.75)

840.10 (121.85)

201.5 (45.3)

189.47 (1677)

I B-8-12 305 (12)

40.0 (5800)

337.77 (48.99)

351.96 (51.05)

423.92 (61.48)

197.29 (28.61)

420.46 (60.98)

49.8 (11.2)

39.88 (353)

II B-8-24 610 (24)

39.4 (5720)

504.60 (73.19)

508.67 (73.78)

526.49 (76.36)

396.6 (57.52)

520.40 (75.48)

88.1 (19.8)

71.29 (631)

III B-8-48 1219 (48)

47.4 (6880)

806.50 (116.98)

863.5 (125.24)

777.98 (112.84)

857.38 (124.35)

808.36 (117.24)

229.1 (51.5)

166.76 (1476)

IV B-8-72 1829 (72)

41.0 (5940)

954.73 (138.47)

1136.96 (164.9)

954.56 (138.45)

1180.65 (171.24)

948.22 (137.53)

206.8 (46.5)

193.88 (1716)

MS#2003378 38

0

200

400

600

800

1000

1200

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

Strain (mm/mm)

Axi

al S

tres

s (M

Pa)

0

20

40

60

80

100

120

140

160

1800 2 4 6 8 10 12 14 16 18 20 22 24

Strain (%)

Axi

al S

tres

s (k

si)

Grade 60 Steel

E = 200GPa (29,000ksi)

MMFX Steel

56

Fig. 1-Stress-Strain Curves of MMFX and Grade 60 Steel Bars 57 58

59

60

61

62

63

64

65

MS#2003378 39

102 mm (4 in) Debonded Length

Lb = 356 mm (14 in) for No.13 (#4) MMFX Lb = 864 mm (34 in) for No.25 (#8) MMFX

356 mm (14 in)

508 mm(20 in)

MMFX bar No.13 or No.25 (#4 or #8)

2No.19 Grade 420 (2 # 6 Grade 60)

4No.25 Grade 420 (4 # 8 Grade 60)

2032 mm (80 in)

MMFX bar

Bonded Length {

66

Fig. 2-Details of Beam-End Specimens 67 68

69

Steel Box Bearing Block Hydraulic Jack

Load Cell

MMFX bar

Strong Concrete Floor

Extensiometer

LVDT at dead end

Bearing Steel Plate

70 Fig. 3-Test-Set-Up of Beam-End Specimens 71

72

73

MS#2003378 40

74

75 Fig. 4-Splitting Bond Failure Mode for Beam-End Specimen B4 (Top View) 76

77

78

79

80

81

82

83

84

85

86

87

88

MS#2003378 41

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Slip (mm)

Ave

rage

Bon

d St

ress

(MPa

)

0

100

200

300

400

500

600

700

800

0 0.1 0.2 0.3 0.4 0.5Slip (in)

Tens

ile S

tres

s (M

Pa)

Loaded End

Unloaded End

Extensiometer LVDT

No.25 (#8) MMFX bar

Strain gages:D3 D2 D1

Loaded End

Unloaded End

Beam-end specimen: B4

89 Fig. 5-Average Bond and Tensile Stresses vs. Slip at Loaded and Unloaded End for Beam-End 90

Specimen B4 91 92 93

MS#2003378 42

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350 400

Distance along the Bonded Length (mm)

Ave

rage

Bon

d St

ress

(MPa

)

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14Distance along the Bonded Length (in)

Ave

rage

Bon

d St

ress

(ksi

)

At Stress Level = 120 ksiAt Stress Level = 100 ksiAt Stress Level =80 ksiAt Stress Level =60 ksiAt Stress Level =40 ksiAt Stress Level =827MPa (120ksi)At Stress Level =690MPa (100ksi)At Stress Level =520MPa (80ksi)At Stress Level =420MPa (60ksi)At Stress Level =276MPa (40ksi)

MMFXbar

Unloaded End

D3 D2 D1 Strain gages

114

102 35

152

Loaded End

fi+1 f i fi-1 fi-2

x ixi-1

u bi

( ))(4 1

1

ii

biibi xx

dffu

−−

=−

−

Extensiometer

Dimension in mm

94 Fig. 6-Bond Stress Distribution along the Bonded Length at Different Stress Levels for Beam-95

End Specimen B1 96 97 98

MS#2003378 43

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

B1, No.13 (#4) MMFX B2, No.13 (#4) MMFX B3, No.13 (#4) MMFX B4, No.25 (#8) MMFX

Zuo and Darwin (2000) Equation

Test

/Pre

dict

ed R

atio

for B

onde

d Le

ngth

Limit confinment level

Actual confinment level

4.04.0 4.0

5.55.5

7.0 3.8

f s = 1186 MPa (172 ksi)

f s = 1138 MPa (165 ksi)

f s = 1138 MPa (165 ksi)

f s = 793 MPa (115 ksi)

99 Fig. 7-Experimental/predicted ratio for bonded length for Beam-End Specimens using Zuo and 100

Darwin (2000) Equation [12] 101 102

MS#2003378 44

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

B1, No.13 (#4) MMFX B2, No.13 (#4) MMFX B3, No.13 (#4) MMFX B4, No.25 (#8) MMFX

ACI 318-02 Code Equation

Test

/Pre

dict

ed R

atio

for B

onde

d Le

ngth

Limit confinment level

Actual confinment level

f s = 1186 MPa (172 ksi)

f s = 1138 MPa (165 ksi)

2.5 2.5 2.5

2.5

4.5 4.5

6.4

3.2

f s = 1138 MPa (165 ksi)

f s = 793 MPa (115 ksi)

103 Fig. 8-Experimental/predicted ratio for bonded length for Beam-End Specimens using ACI 318-104

02 Code Equation [15] 105 106 107

MS#2003378 45

4572 mm or 5791 mm(15 ft or 19 ft)

Strong concrete floor ls

1829 mm of 2438 mm(6 ft or 8 ft)

R or T cross-section

152 mm (0.5 ft)

LVDT

DT Gage

1960 kN (440 kips) MTS Actuator

h

bw

Group I and II specimens (Rectangular cross section)

h

Bf

102 mm (4 in)

bw

Group III and IV specimens (T cross section)

152 mm (0.5 ft)

108 Fig. 9-Test Set-Up of the Beam-Splice Specimens 109

110 111 112 113 114 115 116 117 118 119

MS#2003378 46

120 Fig. 10-Failure of Beam-Splice Specimen B-6-36 121

122 123

124 125

Bottom View

Splice Length

Side View

Splice Length 126

Fig. 11-Failure of Beam-Splice Specimen B-8-24 127 128

Failure Crack

Splice Length 129

Fig. 12-Failure of Beam-Splice Specimen B-8-48 130

MS#2003378 47

0

50000

100000

150000

200000

250000

300000

350000

400000

0 250 500 750 1000 1250 1500 1750

Splice Length (mm)

Bon

d Fo

rce

(N)

0

10000

20000

30000

40000

50000

60000

70000

80000

0 10 20 30 40 50 60 70Splice Length (in)

Bon

d Fo

rce

(lb)

Current Zuo and Darwin (2000) equation

Modified Zuo and Darwin (2000) equation

( ) )(9.01.01205.065

min

maxmin4/1 unitsSI

ccAdcl

fT

bbdc

b

+

++=

′

( )[ ] )(9.01.02.565.043.1min

maxmin4/1 unitsSI

ccAdcl

fT

bbdc

b

+++=

′

Limitation for bar stress =550MPa (80ksi)

(ACI 318-02)

Test Results No. 19 (#6) MMFX Bar

131 Fig. 13-Bond Force vs. Splice Length for Beams Reinforced with No.19 (#6) MMFX Steel Bars 132

Using Zuo and Darwin (2000) Equation [12] 133 134 135 136

MS#2003378 48

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

550000

600000

0 250 500 750 1000 1250 1500 1750

Splice Length (mm)

Bon

d Fo

rce

(N)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

130000

0 10 20 30 40 50 60 70Splice Length (in)

Bon

d Fo

rce

(lb)

Current Zuo and Darwin (2000) equation

Modified Zuo and Darwin (2000) equation


(ACI 318-02)

( )[ ] )(74499.01.02.565.043.1 2/1

min

maxmin4/1

unitsSIfn

NAtt

cc

AdclfT

ctr

drbbdc

b ′

++

+++=

′

( ) )(14806.99.01.01205.065 2/1

min

maxmin4/1

unitsSIfn

NAtt

cc

AdclfT

ctr

drbbdc

b ′

−+

+

++=

′



Using Zuo and Darwin (2000) Equation [12] 139 140

MS#2003378 49

0

50000

100000

150000

200000

250000

300000

350000

400000

0 250 500 750 1000 1250 1500 1750

Splice Length (mm)

Bon

d Fo

rce

(N)

0

10000

20000

30000

40000

50000

60000

70000

80000

0 10 20 30 40 50 60 70Splice Length (in)

Bon

d Fo

rce

(lb)

ACI 318-02 Code equation

Modified ACI 318-02 Code equation


(ACI 318-02)

( ) )(5.0185

min unitsSIdclf

Tbd

c

b +′=′

π

( ) )(405.091 2

min unitsSIddclf

Tbbd

c

b ++′=′

π



Using the ACI 318-02 Code Equation [15] 143 144

MS#2003378 50

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

550000

600000

0 250 500 750 1000 1250 1500 1750

Splice Length (mm)

Bon

d Fo

rce

(N)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

130000

0 10 20 30 40 50 60 70Splice Length (in)

Bon

d Fo

rce

(lb)

ACI 318-02 Code equation

Modified ACI 318-02 Code equation


(ACI 318-02)stress = 505 MPa(73ksi)

( ) )(34.1018

55.0

185

min unitsSIsnfAl

dclf

T yttrdbd

c

b ππ ×++′=

′

( ) )(5000

405.091 2

min unitsSIsnfAl

ddclf

T yttrdbbd

c

b ππ +

++′=

′



Using the ACI 3182-02 Code Equation [15] 147 148 149

MS#2003378 51

0

100

200

300

400

500

600

700

800

900

1000

0 250 500 750 1000 1250 1500 1750

Splice Length (mm)

MM

FX B

ar S

tres

s (M

Pa)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

0 10 20 30 40 50 60 70Splice Length (in)

MM

FX B

ar S

tres

s (k

si)

Experimental Results for No.19 (#6) MMFX BarsExperimental Results for No.25 (#8) MMFX BarsCurrent Zuo and Darwin (2000) Equation for No.19 (#6) MMFX BarsModified Zuo and Darwin (2000) Equation for No.19 (#6) MMFX BarsCurrent Zuo and Darwin (2000) Equation for No.25 (#8) MMFX BarsModified Zuo and Darwin (2000) Equation for No.25 (#8) MMFX BarsSeries3


(ACI 318-02)

150 Fig. 17-Experimental and Predicted Bar Stress vs. Splice Length for No.19 (#6) and No.25 (#8) 151

MMFX Steel Bars using the Current and Modified Zuo and Darwin (2000) Equation [12] 152 153 154

MS#2003378 52

0

100

200

300

400

500

600

700

800

900

1000

0 250 500 750 1000 1250 1500 1750

Splice Length (mm)

MM

FX B

ar S

tres

s (M

Pa)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

0 10 20 30 40 50 60 70Splice Length (in)

MM

FX B

ar S

tres

s (k

si)

Experimental Results for No.19 (#6) MMFX BarsExperimental Results for No.25 (#8) MMFX BarsCurrent ACI 318-02 Code Equation for No.19 (#6) MMFX BarsModified ACI 318-02 Code Equation for No.19 (#6) MMFX BarsCurrent ACI 318-02 Code Equation for No.25 (#8) MMFX BarsModified ACI 318-02 Code Equation for No.25 (#8) MMFX BarsSeries3


(ACI 318-02)

155 Fig. 18-Experimental and Predicted Bar Stress vs. Splice Length for No.19 (#6) and No.25 (#8) 156

MMFX Steel Bars using the Current and Modified the ACI 318-02 Code Equation [15] 157 158

159

MS#2003378 53

0

100

200

300

400

500

600

700

800

900

1000

0 10 20 30 40 50 60 70 80 90

Splice Length/Bar Diameter (L s /d b )

MM

FX B

ar S

tres

s (M

Pa)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

MM

FX B

ar S

tres

s (k

si)

Experimental for No.19 (# 6) MMFX Steel BarsExperimental for No.25 (# 8) MMFX Steel BarsSeries1Series2

CNo.25 (#8) =2.9

CNo.19 (#8) =2.8

CNo.19 (#6) =2.5

CNo.25 (#8) =2.8

CNo.19 (#6) =2.6

CNo.19 (#6) =2.6

CN.19 (#6) =2.6

CNo.25 (#8) =2.9

MMFX Yield Strength = 758MPa (110ksi)

C : Level of Confinment


(ACI 318-02)

160 Fig. 19-Steel Bars Stress vs. Splice Length/Bar Diameter for Beams Reinforced with No.19 (#6) 161

and No.25 (#8) MMFX Steel Bars 162

Bond Characteristics of High-Strength Steel …srizkal/TechPapers2006/bond characteristics...

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Transcript of Bond Characteristics of High-Strength Steel …srizkal/TechPapers2006/bond characteristics...