Bond Characteristics High-Strength Steel Reinforcement

ACI STRUCTURAL JOURNAL TECHNICAL PAPER Title no, 103-878

Bond Characteristics of High-Strength Steel Reinforcement by Raafat EI-Hacha, Hossam EI-Agroudy, and Sami H, RizkalJa

This paper summarizes an investigation undertaken to study the bond characteristics oj high-strength steel reinforcement bars commercially known as microcomposite, multistructural, fonnable steel (MMFX). The objective a/the investigation is to examine the applicability of the ACI 318-02 equation and a current proposed equation by Zuo and Danvin on bond behavior of steel reinforcement 10 the concrete member. The experimental program included two phases. The jirsfphase of the experimental program consisted oj testing four beam-end specimens reinforced with MMFX steel bars, whereas the second phase included testing eight beam-splice specimens reinforced with MMFX steel bars. The selectedfour factors considered in this study were bar size, level of confinement, bonded length, and bar cast pOSition. The bond behavior of the MMFX steel bars was found to be similar to that of cOIwentional Grade 420 MPa (60 ksi) steel up to the proportional limit of 550 MPa (80 ksi). The bond strength of the MMFX significantly changes as the tensile stresses developed in the bar exceed the proportional limit. The test results indicated that both the ACI 318-02 equation and the current proposed equation by ZliO and Darwin on bond are adequate and resulted in conservative prediction at low stress levels up to 550 MPa (80 ksi). At high stress levels, however, the prediction using both equations is unconservative due to the nonlinear behavior of the MMFX stress-strain relationship. Based on the limited number of specimens considered in this study, modification (0 both the ACI 318-02 equation and the Zuo and Darwin equation is proposed to predict the bond forces beyond the proporlionailimitfor MMFX steel bars.

Keywords: bond; confinement; flexure; splice; steel; strength.

INTRODUCTION Bond behavior of reinforcing steel bars to concrete is one

of the most important mechanisms that should be properly designed to ensure satisfactory performance of reinforced concrete structures, The bond strength and mode of bond failure are affected by many factors, The most important factors are thickness of the clear concrete covers (bottom and/or side), clear spacing between bars, nominal bar diameter, embedment or development and splice length, amount of transverse steel reinforcement, and concrete compressive strength, The individual contributions of these factors are difficult to separate or quantify, Another factor that influences the bond strength of bars is the depth of fresh concrete below the bar during casting.

In general, any increase in confinement of the bar by the surrounding concrete, and/or by transverse reinforcement increases the bond strength and minimizes splitting. Confinement by the concrete is dependent on the clear concrete covers (bottom andlor side) and the bar spacing, Increasing the development/splice length of a reinforcing bar increases its bond strength, The bond strength, for a given length, mobilized by both concrete and transverse reinforcement, increases as the bar diameter increases. Bond strength of bars confined by transverse reinforcement increases with the increase in the relative rib area. Top-cast bars have lower bond strength than bottom-cast bars, Also, bond strength

ACI Structural Journal/November-December 2006

increases with increasing concrete compressive strength for bars not confined by transverse reinforcement approximately with the 1/4 power of the compressive strength (f; 1/4), The additional bond strength, provided by transverse reinforcement, increases approximately with the 3/4 ~ower of the compressive strength (f~ 3/4), Note that the f~ 14 has been shown to provide a better representation of the effect of concrete strength on bond than f~ 112 This point is recognized by ACI Committee 408 and within ACI 318, which sets an upper limit on the value of f~ 1/2 for use in design. An increase in the aggregate quantity and strength results also in an increase in bond strength, More details on the factors that affect the bond of reinforcing steel to concrete can be found in ACI 408R-031

Bond characteristics of cooventional carbon steel reinforcement and epoxy-coated reinforcement with concrete has been thoroughly investigated by many researchers2-12 and addressed in terms of bond or development length, Their experimental results contributed to the ACI Committee 408 database on "Bond and Development of Straight Reinforcing Bars in Tension" and were used in formulating the current equations in both ACI 318-02 13 and ACI 408R-03 1 to predict the bond force,

The experimental investigation presented in this paper is designed to study the bond behavior of the high-strength steel (conunercially known as MMFX steel bar) and included the effect of bar size, level of confinement with transverse reinforcement, bonded length, and bar cast position, The MMFX steel bars exhibit superior mechanical properties when compared with conventional steel reinforcement,14 and the requirements covering deformation dimensions of ribs (length, height, and frequency along bars) are the same as conventional steel bars and confonn to ASTM A 1035-0615

and ASTM A 615-04 ,16 The validity of such innovative reinforcement and its ability to transfer stresses to the surroundi~g concrete through bond must be considered, To the best knowledge of the authors, very little information is available about the bond strength of high-strength steel reinforcement. Therefore, MMFX steel reinforcement was considered to provide a database and kTIowledge of the bond of high-strength steel to concrete and to compare the behavior to conventional A61S Grade 420 MPa (60 ksi) carbon steel reinforcement.

RESEARCH SIGNIFICANCE Typical design code equations attempt to ' predict a

required bonded length that will result in yielding of the bar before bond failure, The importance of conducting an experimental investigation to identify the bond characteristics

ACI Structural Journal, V. 103, No.6, November-December 2006. MS No. 03-378 received July 25. 2005, and reviewed under Institute publication policies.

Copyrighl © 2006, American Concrete Institute. All rights reserved, including the making of copies unless pennission is obtained from the copyright proprietors. Pertinent discussion including author's closure, jf any, will be published in the September-October 2007 ACI Structural Journal if the discussion is received by May I, 2007.

771

Table 1-Test matrix of experimental Program 1: beam-end specimens MMFXbar Concrete dimensions

location Beam ID n during cast lb, m.m L,mm b,mm h.mm

Bl I No. I3 Bottom 356 2032 356 508 B2 I No. I3 Top 356 2032 356 508 B3 I No. 13 Bauam 356 2032 356 508 B4 I No. 2S Bottom 864 2032 356 508

>N""O"'''go' l' ' '' mm ('o'"~) :"'\ ............ (211 6 Gnde 60) sea mm (20 in)

4No.2S Oracle 420 . . (4 N8G'ad~60) MMfXbar~~ ' MM!'X b&r L .1 NOi l orNo 2S ~ {1'1- ) S6mm( 14in)fOrNo.13 (II4) MMI'X (~. 01118) ' (1 4 in) Sanded ungth L. e 864 mm (14 in) for No.2S (_8) MMFX

I 2032 mm -----I (80 in)

Fig. 2-Details of beam-end specimens.

possible conical failure. the flrst 102 mm (4 in.) of the MMFX steel bar from the concrete surface at the loaded end were debonded using a plastic tube. as shown in Fig. 2. The test matrix for the beam-end specimens program is shown in Table 1. Details of the test setup are shown in Fig. 3.

The MMFX steel bar was tensioned using a hydraulic jack. and the specimen was held in place using steel beams and high-strength Dywidag steel bars anchored to the laboralory floor. as shown in Fig. 3. The applied tension load was measured using a load cell placed at the jacking side of the beam-end specimen. Three 6 mm (0.25 in.) 120 ohm electrical resistance strain gauges. installed on the bonded surface of each MMFX steel bar. were used to measure the strain distribution along the bonded length of the bar. lb . at distances of Ib/6. Ib12. and 5Ib/6. A 50 mm (2 in.) extensometer was used to measure the strain of the unbonded loaded Uacking) end of the MMFX steel bar. Both the loaded and the unloaded (dead) end slippage were measured using a linear variable differential transformer (L VDT).

The bearn-end specimens were cast using normal-strength concrete of 41.4 MPa (6000 psi) supplied by a local concrete plant. Standard concrete cylinders 102 x 204 mm (4 x 8 in.) were caSI according to ASTM C 31_0023 for the purpose of determining the compressive strength of the concrete. The concrete cylinders were cured in the same manner as the test specimens. The average concrete compressive strength for each specimen, as measured on the day of testing using three cylinders according to ASTM C 39-01,24 is given in Table 1.

Results of beam-end specimens Failure mode-Beams BI. B2. and B3. each reinforced

with one No. 13 (No.4) MMFX steel bar. failed by rupture of the MMFX bar. As the applied load increased. the number and width of the flexural cracks developed along the bonded length of the MMFX steel bar increased. The spacing between these cracks was approximately equal to the spacing between the stirrups. No signs of bond failure were observed in these beams. It was concluded that the bonded lengths were greater than the development lengths required to develop the ultimate strength of the bar for the levels of confinement provided in the three beams. For the beam reinforced with one No. 25 (No.8) MMFX steel bar (Beam B4). a longitudinal crack developed in the concrele cover at the loaded end and propagated toward the unloaded end of the specimen along the steel bar. indicating a typical


Concrete cover Stirrup details

d. mm db. mm Cso• mm Cb,mm f~, MPa S, mm dst, mm i YI ,mm

464 464 464 457

12.7 172 38 36. 1 229 9.5 420 12.7 172 38 36 229 9.5 420 12.7 172 38 36.06 76 9.5 420 25.4 165 38 36.7 229 9.5 420

"

Fig. 3- Test setup of beam-end specimens.

Fig. 4--Splitting bondfailure mode for beam-end Specimen B4 (top view).

splitting mode of bond failure. as shown in Fig. 4. An excessive increase in the width of the first flexural crack near the loaded end was observed. Figure 5 shows the Iensile stress and the average bond stress developed in the MMFX steel bar in Beam B4 versus the measured slip at the loaded and unloaded ends of the bar.

Bond distribution- Figure 6 shows the bond stress distribution Ub; at distance x; from the loaded end along the bonded length of the MMFX steel bar for Beam B I at different stress levels based on the linear behavior of MMFX within the elastic range to determine the stress /;. corresponding to the measured strain. Figure 6 was developed as follows: at a given bar stress level, the .corresponding strain readings along the bonded length. as measured by the three strain gauges, were determined. Using the stress-strain curve oblained from the mechanical properties of the MMFX steel bar. the corresponding stress levels were obtained for each strain gauge reading along the bar. These stress values were

773

Table 3-Test matrix of Experimental Program 2: beam-splice specimens

Concrete dimensions • Group Specimen

no. lD (,. mm L. mrn bw• mm Bf , mm h. mrn I B-6-12 305 4877 305 - 311

11 B-6-24 610 4877 311 - 362

III B-6-36 9 14 4877 305 61 3 464

IV B-6-60 1524 6096 305 121 9 457

I B-8-12 305 4877 305 - 305

11 B-8-24 610 4877 305 356

III B-8-48 1219 4877 311 6 16 470

IV B-8-n 1829 6096 305 1219 470 . DimenSIOns of specimens were measured after castmg.

specimens allows only rotation of the section without deflection of the beam at the location of bonded length. Deflection of flexural beams simulated by the beam-splice specimens allows for deflection of the beam, which reduces the bond strength of the spliced bars as the deflection forces the spliced bar to exert additional outward pressure on the bottom concrete cover, causing a premature failure of the splice. TIris behavior is supported by Ferguson and Thompson.27

Phase II: beam-splice specimens A total of eight large-scale concrete beams reinforced with

MMFX steel bars splicea at the midspan were tested. Four specimens were each reinforced with two No. 19 (No.6) MMFX steel bars and the other four with one No. 25 (No.8) MMFX steel bar. The beam-splice specimens were divided into four groups, as shown in Table 3. Each group consisted of two specimens with identical concrete dimensions but had different amounts (one or two) and sizes (No. 19 or No. 25 [No.6 or No.8]) of the reinforcing MMFX steel bars. The specimens in Groups I and II were rectangular in cross section, whereas those in Groups III and IV had T-shaped cross sections. The spliced lengths varied from one specimen to another and ranged from 305 to 1829 mm (1.0 to 6.0 tt), as shown in Table 3. To minimize the effect of the applied loads on the spliced length, the distance between the end of the splice length and the center of the applied load was always more than 305 rum (1.0 tt) . For the specimens reinforced with No. 25 (No.8) MMFX steel bars. double-legged closed stirrups were evenly distributed along the splice length to provide the required level of confinement around the spliced bars . To prevent possible premature shear failure , shear reinforcement was provided using No. 10 (No.3) Grade 60 double-legged closed stirrups spaced at 127 rum (5 in.) along the shear span for all tested beam specimens. Compression reinforcement was provided by two No. 13 (two No.4) Grade 420 MPa (60 ksi) steel bars as top reinforcement. The variation in tbe beam's dimensions was selected to achieve different stress levels in the MMFX steel bar length at failure. The bottom and side concrete covers and the transverse spacing between the spliced bars were kept constant for all the beams reinforced with two No. 19 (two No.6) MMFX steel bars. The selected values were 1. 8db, 3db, and 6db• where db is the bar diameter. For beams reinforced with one No. 25 (No.8) MMFX steel bar, the bottom and side concrete covers were also kept constant at values of 1.375db and 5db, respectively. Table 3 shows the actual measured dimensions of the specimens after casting.

The test matrix for the beam-splice test program is shown in Table 3. The first letter of the beam designation "B" stands for Beam; the middle number identifies the bar size- No. 19


Cover and spacing Stirrup details along splice length

d. mrn Csa.mm Csi, mm Cb,mm N S. mrn ds" mm fyl' MPa 264

314

419

143

254

305

422

410

~ • • J

~ • 0 m ~ 0

~ ~

~ ~

E ~

~

60.3 54.0 38 0 - - -54.0 70.0 38 0 - - -54.0 60.3 35 0 - -57.2 57.2 35 0 - - -

123.8 - 38 I 305 9.53 420

123.8 38 2 305 9.53 420

114.3 - 35 5 245 9.53 420

120.7 - 35 7 260.4 9.53 420

0.9 m LImit confinment level I

IiiI Actual conflnrnent level 0.'

0.'

0.8

0.5

0.'

0.3

81, No.13 (/II4) MMFX B2, No.13(/II4) MMFX 8 3, NQ.13 (II4) MMFX B<I .No.25(II8) w.t=X

Zuo and Darwin (2000) Equation

Fig. 7- Experimentallpredicted ratio for bonded length for beam-end specimens using Zuo and Dmwin12 equation.

£ c • ~ ~

~ • 0 m ~ 0 ~ • ~ j ~ f ~ ~ • ~

0.'

0. '

0.'

0.5

0.'

0.3

0.2

0.'

0

III Urnlt confinrnent level :

iii Actual confinment level

81 , No.13(#4)MMFX 82, No.13 (AI4)MMFX 83. No.13 (#4) MMF"X 84, No.25 (/l8)MMFX

ACI318-02 Code Equation

Fig. 8-Experimentallpredicted ratio for bonded length f or beam-end specimens using ACI 318-0213 equatioll.

and No. 25 (No.6 and No. 8); whereas the last number represents the spliced length of the bar, in inches. Standard concrete cylinders, 102 x 204 rum (4 x 8 in.), were cast according to ASTM C 31_0023 for the purpose of determining the compressive strength of the concrete. The concrete cylinders were cured in the same manner as the test specimens. The average concrete compressive strength, determined using three cylinders according to ASTM C 39-01 ,24 at the age of 28 days was 41.8 MPa (6071 psi). Table 4 shows the concrete compressive strengths as measured on the day of testing.

All beams were simply supported loaded in four-point bending. The load was applied using an MTS actuator operated

775

Fig. 12-Failure of beam-splice Specimen B-8-48.

just before failure, calculated using the moment curvature analysis, are given in Table 4.

Evaluation of bond strength and splice length The experimental results of the bond force of No. 19 and

No. 25 (No.6 and No. 8) MMFX steel bars were compared with the rredictions from the e~uation proposed by Zuo and Darwin 1 and the ACI 318-02 3 equation. The bond force was calculated from the bar stress detennined using the experimental stress-strain curve of the MMFX bar (Fig. I) for the corresponding measured strain reading in the bar, as measured by the strain gauges attached to the MMFX steel bars.

Zuo and Darwinl2 equarion-The bond capacity of the No. 19 and No. 25 (No.6 and No.8) MMFX steel bars was evaluated using the equation proposed by Zuo and Darwin,I2 as shown in Fig. 13 and 14, re';j'ectively. Test results indicated that the Zuo and Darwin 1 equation provided conservative prediction of the bond capacity of No. 19 (No.6) MMFX steel bars at stress levels up to the proportional strength of 579 MPa (84 ksi), and provided a very close prediction to the bond capacity of No. 25 (No.8) MMFX steel bars up to the proportional strength of 607 MPa (88 ksi). At higher stress levels; however, the equation resulted in unconservative prediction for both No. 19 and No. 25 (No.6 and No.8) MMFX steel bars. Test results suggested that there is a need to modify the Zuo and Darwinl2 equation to include a higher stress level. The stress limitation imposed by ACI 318-02 13 for the maximum allowed design yielding strength of 550 MPa (80 ksi) has been selected as an upper boundary for using the equation by Zuo and Darwin12 Therefore, modification of the equation has been proposed beyond the stress level of 550 MPa (80 ksi).

Bond equations generally relate bar stresses to bond lengths. The equation proposed by Zuo and Darwinl2 for bond strength of bars not confined with transverse reinforcement (Tb = Tc and Ts = 0), in terms of bond force Tb, as is the case for Beams B6-12, B6-24, B6-36, and B6-60, is given by

SI units

Imperial units


Splice Length (In)

" 20 30 40 50 60 70

::, ,,[1.43/,k_ +O.Sd.l+S6.ZA.(O.JC- +0.9) (Sf uMirs) 80000 J. c ...

"'0000

60000

L'wTent Luo and OllWln (WUU) cqva\1OII

TCSlRaults No. 19 (N6) MMFXBar

_ . ~l!ml~(,!",!-.bo.!!~~;7i:)~i)

Modified ZUG . nd Dlrwin (2000) equl lion

;'" -[! I.(c_ .. O.ScI,)+ 120A, I 0.1:: +0.9) (Sf tlMIIJ )

o~--~--~--~--~~~~--~--~~ o 250 51)0 750 1000 1250 1500 1750

Splice Length (mm)

""00 60000 g ~ j ' 0000 ~

< o

"""0 · 20000

"x,oo

Fig. 13-Bond force versus splice length for beams reillforced with No. 19 (No.6) MMFX steel bars using Zuo and DarwinJ2 equation.

_ '00000 Z

. """"" " & """"'" 21 250000 o • 200000

"'''00 ,-"""'"

o 10

Splice length (In) 20 30 ., 50 70

o~--~~~~~~~~~--~--~ o 200 500 150 1000 1250 1500 1150

Splice length (mm)

10000

Fig. 14-Bolldforce versus splice length for beams reinforced with No. 25 (No.8) MMFX steel bars using Zuo and Darwin12 equation.

To limit the applicability of Eq. (2a) and (2b) to cases in which a splitting failure governs

SI orimperial units

Equations (2a) or (2b) were modified by changing only the numerical constants to ensure conservative predictions at any stress level between 550 and 831 MPa (80 and 120.5 ksi). The proposed modification of the Zuo and Darwin 12 equation for MMFX beyond the stress level of 550 MPa (80 ksi) is

SI units

(3a)

777

Imperial units

Equations (6a) and (6b) can be rewritten in terms of Id as follows

SI units

Id !ilL I = db 10 J1[ (" ;";n + 0.5db)

db

(7a)

Imperial units

Id llL I = db 40 J1[ (C ;";n + O.5db)

db

(7b)

Equations (7a) and (7b) were written in terms of the yield stress. To determine the development length of the bar in the tested beams. however. this stress should be taken as the actual measured stress in the MMFX steel bars.

Based on the tested results. Eg. (6a) or (6b) was modified by changing the numerical constants and addition of a term function of d/. The proposed modification of the ACI 318_0213

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

SI units

Tb T, 1. 2 - = -= - ldn(e . + O.5db) + 40db f~1 /2 f~I / 2 9 min

Imperial units

(8a)

(8b)

Equations (8a) and (8b) can be rewritten in terms of Id• as follows

SI units

lL - sl Id

= Jj;

db ~(c ;";n + O.5db) (9a)

9 db

Imperial units

lL - 637 Id

= Jj;

(9b) db 52 (C ;";n + O.Sdb)

10 db


Splice Length (in) 0 " " 30 " " 60 " 600000

T. 5 ( . ) , wJ. A~f~ "0000 550000

,; • IS '," '- +O.Sd, .. IS"' IOJ.4, .. (SI ~"i1s) " 0000

500000 ACI JI8-02 Codecq\ll.Uon 1'0000

"0000 700000

_ 400000 Test Results No. 25 90000 ~ ~ (*8) MMFX Bar 80000 GI 350000 .

" "'000 " & 300000 Limiw"", IOttwSInM "'~PI(ao"'i} & ~ 2SOOOO

- . - . - - - (AClJis-:ii2i - . 60000 ~ <

0 60000 0

= """ = "'" "0000

r, e' (' OSd) 4OJ'J - .A..I" 30000 ($II1"~) 700000 .1:- 9,trc ... + .• + ," SOOOm

'DODO

50000 70000

0 0 250 500 750 7000 1250 1500 1150

Splice Length (mm)

Fig. 16-Bondforce versus splice length for beams reinforced with No. 25 (No.8) MMFX steel bars using ACI 318-0213

equation.

Using Eq. (8a) or (8b) to predict the bond capacity of No. 19 (No.6) MMFX steel bars for stress levels higher than 550 MPa (80 ksi). the maximum test/predict ratio was approximately 1.19. as can be seen in Fig. 15.

The current ACI 318-0213 equation. for bars confmed with transverse reinforcement (Tb = T, + T,). in terms of bond force Tb• as is the case for Beams B8-l2. B8-24. B8-48. and B8-72. is given by

SI units

Tb = T, + T,= 2. ldn(c'. + 0 5db) + 5 nldA"/,, (lOa)

/~1 12 /;112 18 ,",". 181O.34sn

Imperial units

(lOb)

Equations (lOa) and (lOb) can be rewritten in terms of Id as follows

SI units

Imperial units

and k = A,,!,, " ISOOsn

(lla)

779

, ."

900 .. l 100

!. • "" • g

"" ~

~ m . 00 ~ ~

~ 300 ~

'" '00

0 0

CIlo.2> .... '*2.9

~~~~~~~~1~ __ N,.t!,~:~6 __ ____ _

lim;la1ioft fur bu strtu -~50MI'a l8Oksi) -_._ . _._- -_._._- --- ---_ . _ -----

\0

(ACI 3I B_0l)

C"'-2SIHl aZ.8

20

_ Experlmantal for No.19 (116) MMFX Steel Bin _Experimentill for No.25 (118) MMFX Steel Bars

C : Level of Confinment

30 50 60 10 00

SptJce Length/Bar Diameter (L .ld b)

'" 130

120

'" 100 ';i

"-90

j 00

10 ~ 60

m ~ ~

" ~ ~

" 30

20

" 90

Fig. 19-5teel bar stress versus splice length/bar diameter for beams reinforced with No. 19 (No.6) and No. 25 (No. 8) MMFX steel bars.

Midspan Deflection (in)

0 0.' ,., 2 225 50

200 ' 6-&60 (p =0.45%) 45

'" B-{J·72 (p -0.40%)

40

~150 35 'i: "-~ 125

30 ~ •

" 25 .9 1 100 ~

'ii 20 ~ ~ 75 'ii < ~

" < 50 ,. 25 ,

0 0 0 ,. 20 30 40 50 60

Midspan Deflection (mm)

Fig. 20-Load-midspan deflection for beams reinforced with No. 19 (No.6) and No. 25 (No.8) MMFX steel bars.

is nearly linearly related, but not proportional, to the splice length to the bar diameter ratio (L,ldb) up to the minimum yield strength for No. 19 and No. 25 (No.6 and No.8) MMFX steel bars. The relationship also suggests that a splice length of 30db can be safely used to achieve the maximum yield strength of 550 MPa (80 ksi) limited by ACI 318-02. 13 As shown in Fig. 19, a splice length of 45db can be used to achieve the yield strength of758 MPa (110 ksi) for MMFX steel bars. The linear, not proportional, relationships extend to a stress of 831 MPa (120.5 ksi), which corresponds to a splice length of 50db. Beyond the yield strength, the relationship becomes highly nonlinear and significant splice length is required to achieve higher stress levels, which could be impractical to use for typical applications.

Load-midspan deflection-The load-midspan deflection behavior for the beam-splice specimens reinforced with two No. 19 (No.6) MMFX bars and specimens reinforced with one No. 25 (No.8) MMFX bar with different splice lengths ranging from 305 to 1829 mm (12 to 72 in.) are shown in Fig. 20. Two important points are worth noting. As can be seen, for the beams reinforced with two No. 19 (No.6) MMFX bars or with one No. 25 (No.8) MMFX bar, the behavior is affected by the splice length in which increasing the splice length increased the deflection at ultimate. By comparing the beams with tbe same splice length (such as


B-6-12 and B-8-12) throughout the post-cracked portion of the load-midspan deflection, and at any given load level, the deflection for the beams with a higher reinforcement ratio is always less than that for beams with a lower reinforcement ratio. This behavior is due to the higher stiffness as a result of the higher reinforcement ratio. Throughout the postcracking behavior, the stiffnesses presented by the slopes of the curves were also different. For beams with a lower reinforcement ratio, the slope was less than for beams with a higher reinforcement ratio. The difference was found to be closely matching the difference in the reinforcement ratio between the beams with higher reinforcement ratios and the beams with lower reinforcement ratios. The ultimate load-carrying capacity is bigher for beams with higher reinforcement ratios than beams with lower reinforcement ratios. Note that the results of Beams B-6-36 and B-8-48 are not shown in Fig. 20 due to problems that occurred during the test in measuring the deflection at midspan.

CONCLUSIONS The following conclusions were made based on the limited

number of tested specimens: 1. Bond behavior of the MMFX steel bars is similar to that

of the conventional Grade 420 MPa (60 ksi) carbon steel up to the stress level corresronding to the proportional limit, imposed by ACI 318-02, 3 of 550 MPa (80 ksi). At higher stress levels, bond failure changed from the typical sudden and brittle failure, normally observed for conventional steel, to a gradual and ductile failure due to the nonlinear behavior of the MMFX steel bars in this range;

2. The nonlinear ductile response of the MMFX bars at high stress levels beyond proportional limit strength bas a strong influence in reducing the bond strength of the MMFX bars compared with Grade 420 MPa (60 ksi) steel;

3. The current eguations proposed by Zuo and Darwin l 2

and ACI 318_02 13 for bond force provided conservative prediction of the bond capacity for No. 19 and No. 25 (No.6 and No.8) MMFX steel bars up to 550 MPa (80 ksi) . For stress levels exceeding 550 MPa (80 ksi) and up to a stress level of 831 MPa (120.5 ksi) for No. 19 (No.6) MMFX bars, and 955 MPa (138.5 ksi) for No. 25 (No. 8) MMFX bars, respectively, both equations were modified to provide better prediction of the bond force capacity; and

4. The splice length to bar diameter ratio is nearly linearly, but not proportionally, related to the induced stress in the MMFX steel bar up to yield strength. The relationship becomes highly nonlinear beyond a stress level of758 MPa (llO ksi).

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

at the Constructed Facilities Laboratory at N.C. State University for their help with the laboratory work. The authors are grateful to the support provided by MMFX Tcchnologies Corp. for donating the steel materials.

NOTATION Aty area of each stirrup or tie crossing potential plane of splitting

adjacent to reinforcemenl being developed or spliced Bf width of flange of beam bw width of web of beam Cb thickness of clear bottom concrete cover Cm/U = maximum of cb or Cs c'~il1 minimum of concrete covers surrounding bar or half clear spacing

between bars, minimum of c si and (cb or cso)

cmill minimum of cb or Cs Cs minimum of eso or csi + 6.35 mm (Csi + 0.25 in.) esi half clear spacing between spliced bars C so thickness of clear side concrete cover

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Bond Characteristics High-Strength Steel Reinforcement

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