Bond and Development of Deformed Square Reinforcing Bars

ACI Structural Journal/May-June 2007 333

ACI Structural Journal, V. 104, No. 3, May-June 2007.MS No. S-2006-182.R1 received May 5, 2006, and reviewed under Institute publication

policies. Copyright © 2007, American Concrete Institute. All rights reserved, includingthe making of copies unless permission is obtained from the copyright proprietors. Pertinentdiscussion including author’s closure, if any, will be published in the March-April2008 ACI Structural Journal if the discussion is received by November 1, 2007.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Square deformed reinforcing bars were widely used prior to andduring the transition to circular deformed reinforcing steel uponadoption of ASTM A 305-50, which standardized geometry, weight,deformation height, and spacing requirements. Bond stress anddevelopment lengths for deformed square bars have traditionallybeen computed as equivalent round bars of equal cross-sectionalarea and weight, although this approach has not been validated.Data is presented from archival research on deformed square andcircular reinforcing bars both prior and subsequent to adoptionand implementation of ASTM A 305-50 that provides informationfor assessment of bond and development of deformed squarereinforcing bars in vintage and historic structures. Pullout testresults show that deformed square bars exhibited average bondstress similar to those of round deformed bars. Based on the archivaltest results and the comparisons presented, treatment of deformedsquare bars as equivalent round bars for calculation of developmentlength appears reasonable and conservative.

Keywords: bond stress; development length; reinforcement.

INTRODUCTIONSquare deformed reinforcing bars were widely used in

concrete building and bridge construction throughout thefirst half of the twentieth century. As these structures age,begin to deteriorate, or undergo use changes, the questions ofremaining capacity and available service life become importantfor making rehabilitation and retrofit decisions. The currentAASHTO’s “Manual for Conditional Evaluation of Bridges”1

and ASCE’s “Guideline for Structural Condition Assessment ofExisting Buildings”2 provide general guidelines for assessmentof concrete bridges and buildings, respectively, in terms ofconcrete compressive strength and reinforcement yieldstrength, but neither guide addresses treatment of differentreinforcing bar geometries, critical for assessment of bothflexural and shear capacity, given the move toward sectionalanalysis methods.

A focus of the archival literature was on service performancedriven by the allowable stress design philosophy used bydesigners of the day. As a result, little of the historic data areavailable to specifically characterize the development lengthnecessary to achieve yielding of the reinforcing. However,sufficient data are available to support recommendations forassessing bond of deformed square reinforcing bars incomparison with deformed round reinforcing bars.

Standardization of deformed reinforcing barsConcrete reinforcing bars evolved during the early part of

the twentieth century to the standardized round bars that areused today. Prior to standardization of geometries anddeformations, however, a wide array of different bar typeswere used. Many were patented systems and employedunique cross-sectional shapes and deformations to enhancebond between the concrete and steel, examples of which canbe seen in Fig. 1 from Abrams’3 early work. Of the manydifferent bar types available, round and square bars were

predominant and square bars were broadly used, particularly fordesigns requiring large bar sizes. While smooth (undeformed)bars were also used, deformed bars were recognized early onto provide superior bond. Due to wide variations in deforma-tion height and geometric patterns used throughout the early1900s, however, consistent bond stresses were not assured.In 1946, Clark4 developed a method of rating many differentpatterns of reinforcing bars based on their average bond stress atseveral predetermined slip values. His investigation led toASTM A 305-47T,5 later adopted as ASTM A 305-49.6 Thespecification provided standard deformation heights andspacing for round bars and also included deformationpatterns for three square bars that corresponded to equivalentround areas (1-1/4 in. square = No. 11; 1-1/8 in. square = No. 10;1 in. square = No. 9). The specification was modified thefollowing year as ASTM A 305-507 and excluded square

Title no. 104-S33

Bond and Development of Deformed Square Reinforcing Barsby Daniel A. Howell and Christopher Higgins

Fig. 1—Reinforcing bars used in Abrams’3 tests.

334 ACI Structural Journal/May-June 2007

bars entirely. Nonetheless, square bars continued to be usedwell into the late 1950s and were still referenced to theASTM A 305 specification on construction documents. It isof interest to note that the current ASTM A 6158 specificationfor deformed reinforcing bars remains identical to the ASTMA 305-507 specification as it pertains to the bar size anddeformation geometry, as seen in Table 1.

Current development length requirementsThe current ACI equation for development length9 is

based on several factors, but the most relevant term for thisinvestigation relates to the bar size and the relevance of thebar cross section on bond efficiency. The simplifieddevelopment length formulas from ACI 318-05 for round

bars with clear spacing not less than 2db and clear cover notless than db are

for No. 6 reinforcing bar and smaller (1a)

for No. 7 reinforcing bar and larger (1b)

If the previous clear spacing and cover requirements arenot met, the simplified development length formulas are

for No. 6 reinforcing bar and smaller (2a)

ldfyψtψeλ

25 fc′-------------------⎝ ⎠⎜ ⎟⎛ ⎞

db=

ldfyψtψeλ

20 fc′-------------------⎝ ⎠⎜ ⎟⎛ ⎞

db=

ld3fyψtψeλ

50 fc′-----------------------⎝ ⎠⎜ ⎟⎛ ⎞

db=

ACI member Daniel A. Howell is a Graduate Research Assistant in the Department ofCivil Engineering at Oregon State University, Corvallis, Oreg.

ACI member Christopher Higgins is an Associate Professor in the Department ofCivil Engineering at Oregon State University. His research interests include evaluationand rehabilitation of aging and deteriorated concrete bridges.

Table 1—ASTM A 3056 and ASTM A 6158 reinforcing bar geometry and deformation requirements

ASTM A 305-496

Nominal size, in. (mm)Diameter, in. (mm)

Cross-sectional area, in.2 (mm2)

Perimeter,in. (mm)

Spacing and height of deformations

Maximum gap (chord of 12-1/2% of nominal perimeter), in. (mm)

Maximum average spacing,

in. (mm)Minimum height,

in. (mm)

Rounds

3/8 (9.525) 0.375 (9.525) 0.11 (70.967) 1.178 (29.921) 0.262 (6.655) 0.015 (0.381) 0.143 (3.632)

1/2 (12.7) 0.500 (12.7) 0.20 (129.032) 1.571 (39.903) 0.350 (8.890) 0.020 (0.508) 0.191 (4.851)

5/8 (15.875) 0.625 (15.875) 0.31 (200.000) 1.963 (49.860) 0.437 (11.100) 0.028 (0.711) 0.239 (6.071)

3/4 (19.05) 0.750 (19.05) 0.44 (283.870) 2.356 (59.842) 0.525 (13.335) 0.038 (0.965) 0.286 (7.264)

7/8 (22.225) 0.875 (22.225) 0.60 (387.096) 2.749 (69.825) 0.612 (15.545) 0.044 (1.118) 0.334 (8.484)

1.00 (25.4) 1.000 (25.4) 0.79 (509.676) 3.142 (79.807) 0.700 (17.780) 0.050 (1.27) 0.383 (9.728)

Squares

1.00 (5.400) 1.000 (25.400) 1.00 (645.160) 4.000 (101.600) 0.700 (17.780) 0.050 (1.270) 0.500 (12.700)

1 1/8 (28.575) 1.125 (28.575) 1.27 (819.353) 4.500 (114.300) 0.787 (20.000) 0.056 (1.422) 0.562 (14.275)

1 1/4 (31.750) 1.250 (31.750) 1.56 (1006.450) 5.000 (127.000) 0.875 (22.225) 0.063 (1.600) 0.625 (15.875)

Rounds having sections equivalent to sections of following squares

1.00 (25.400) 1.128 (28.651) 1.00 (645.160) 3.544 (90.018) 0.790 (20.066) 0.056 (1.422) 0.431 (10.947)

1 1/8 (28.575) 1.270 (32.258) 1.27 (819.353) 3.990 (101.346) 0.889 (22.581) 0.064 (1.626) 0.487 (12.370)

1 1/4 (31.750) 1.410 (35.814) 1.56 (1006.450) 4.430 (112.522) 0.987 (25.070) 0.071 (1.803) 0.540 (13.716)

Note: Certain rounds are rolled to sections equivalent to section of squares. Nominal size shall be taken as diameter of plain rounds having same area as corresponding squares.

ASTM A 6158

Bar no.Nominal weight,

lb/ft (N/m)Diameter, in. (mm)

Cross-sectional area, in.2 (mm2)

Perimeter, in. (mm)

Spacing and height of deformations

Maximum gap (chord of 12-1/2% of nominal perimeter), in. (mm)

Maximum average spacing,

in. (mm)Minimum height,

in. (mm)

3 0.376 (5.487) 0.375 (9.525) 0.11 (70.968) 1.178 (29.921) 0.262 (6.655) 0.015 (0.381) 0.143 (3.632)

4 0.668 (9.749) 0.500 (12.700) 0.20 (129.032) 1.571 (39.903) 0.350 (8.890) 0.020 (0.508) 0.191 (4.851)

5 1.043 (15.221) 0.625 (15.875) 0.31 (200.000) 1.963 (49.860) 0.437 (11.100) 0.028 (0.711) 0.239 (6.071)

6 1.502 (21.920) 0.750 (19.050) 0.44 (283.870) 2.356 (59.842) 0.525 (13.335) 0.038 (0.965) 0.286 (7.264)

7 2.044 (29.830) 0.875 (22.225) 0.60 (387.096) 2.749 (69.825) 0.612 (15.545) 0.044 (1.118) 0.334 (8.484)

8 2.670 (38.966) 1.000 (25.400) 0.79 (509.676) 3.142 (79.807) 0.700 (17.780) 0.050 (1.270) 0.383 (9.728)

9 3.400 (49.619) 1.128 (28.651) 1.00 (645.160) 3.544 (90.018) 0.790 (20.066) 0.056 (1.422) 0.431 (10.947)

10 4.303 (62.798) 1.270 (32.258) 1.27 (819.353) 3.990 (101.346) 0.889 (22.581) 0.064 (1.626) 0.487 (12.370)

11 5.313 (77.537) 1.410 (35.814) 1.56 (1006.450) 4.430 (112.522) 0.987 (25.070) 0.071 (1.803) 0.540 (13.716)

14 7.650 (111.643) 1.693 (43.002) 2.25 (1451.610) 5.320 (135.128) 1.185 (30.099) 0.085 (2.159) 0.648 (16.459)

18 13.600 (198.477) 2.257 (57.328) 4.00 (2580.640) 7.090 (180.086) 1.580 (40.132) 0.102 (2.591) 0.864 (21.946)

Note: 1 in. = 25.4 mm.


for No. 7 reinforcing bar and larger (2b)

where fy equals the yield strength of steel (psi); ψt equals thereinforcement location factor, for bars with more than 12 in.of concrete below them, ψt = 1.3, otherwise ψt = 1.0; ψeequals the coating factor used for epoxy coated bars, foruncoated reinforcement, ψe = 1.0, for epoxy coated bars withcover less than 3db or clear spacing less than 6db, ψe = 1.5,for all other epoxy coated bars, ψe = 1.2; λ equals the light-weight aggregate factor, for lightweight concrete, λ = 1.3,otherwise λ = 1.0; fc′ equals the compressive strength ofconcrete (psi); and db equals the diameter of bar under consider-ation (in.). For uncoated, bottom, round bars in normalweightconcrete, the required development length depends on thebar yield stress, concrete compressive strength, and the bardiameter. The diameter dimension describes the availablebar perimeter by which bond stresses can be developed. Bycomparison, square bars have approximately an 11% largerperimeter than round bars of equivalent area. However, it isnot clear if the square cross-sectional shape can developbond stress as efficiently as round bars.

Experimental methods used forbond stress research

Review of the early literature on bond and anchorage ofreinforcing steel indicated that different researchersemployed a wide array of different specimens, loadingprotocols, material properties, measurement devices, andreference measures. Early investigators such as Abrams3

used pullout tests to analyze bond stress. The specimenconsisted of a bar embedded longitudinally in a concretecylinder or prism with the free or unloaded end of the barprotruding a short distance beyond one end and the loadedend extending a longer fixed distance beyond the concretespecimen. The specimen was placed on a bearing block andtested to failure by either splitting of the concrete or pulloutof the bar. A small number of researchers used lateralrestraints placed along the perimeter of the pullout specimens toprevent splitting of the samples, thus increasing the bondstrength at failure due to the increased constraint.

Alternative test methods were developed because it wasrecognized that the pullout test placed the concretesurrounding the bar in compression and the bar in tension,whereas in practice, both the bar and the concrete are intension. Also, the boundary conditions of the concrete on thebearing plate affected the bond stress. As pointed out byLeonhardt,10 a specimen mounted on a plate or bearing blockinduces friction and produces lateral stresses on the concrete,thereby artificially increasing the measured bond stress.

In spite of the drawbacks, pullout tests remained popularand were used extensively by researchers because the testswere relatively inexpensive and easy to perform, in contrastto alternatives that could produce more realistic stressconditions. Alternative approaches for the pullout testincluded use of a concrete specimen with a bar extendinglongitudinally past the concrete at both ends (double pulloutor tensile specimen), as well as the modified cantileverbeam, beam-end specimen, and full-scale beam tests. Datafrom all of these types of test specimens were used in thesubsequent analyses and the specimen type used in thevarious archival research is reported in Table 2.

ld3fyψtψeλ

40 fc′-----------------------⎝ ⎠⎜ ⎟⎛ ⎞

db=RESEARCH SIGNIFICANCE

The current state of the practice is to treat square bars asequivalent round bars for determining anchorage anddevelopment, although this approach has not been validated.This paper reviews archival technical literature on bond andanchorage of vintage reinforcing bars from the turn of thelast century to the late 1960s to establish recommendationsfor treatment of deformed square reinforcing bars to aid inevaluation of older and historic concrete structures, many ofwhich contain square bars.

ARCHIVAL RESEARCH USED IN STUDYThe specimen details, sorted by researcher, are shown in

Table 2. As seen in this table, many of the tests were on pullouttype specimens without special reinforcing to prevent splittingof the concrete, but several beam tests were also included inthe sample space.

Abrams’3 research in 1913 was the most comprehensivework at the time, involving several hundred pullout tests, butthe concrete strength was low by modern standards (1750 psi[12.07 MPa]). In 1917, Howard11 tested pullout and beamspecimens, but again the concrete strength was relativelylow (1357 psi [9.36 MPa]). Howard’s work included 3/4 in.(19.05 mm) diameter round and 3/4 in. (19.05 mm) squarebars cast vertically and horizontally. His work indicated thatsquare bars developed higher bond stresses than the roundsin both casting positions. Howard also reported that higherbond stress was obtained for bars cast in the vertical position.

In 1920, Slater et al.12 investigated bond stress for barswith anti-corrosive coatings, and used uncoated bars ascontrol specimens. The uncoated bars are used in the currentstudy. In 1936, Gilkey and Ernst13 investigated pullout testsof similar bars in three different strengths of concrete. In1937, Gilkey et al.14 investigated bond strength based on theresults of both traditional pullout tests as well as half beamtests in which specimen strain values were reported using aseries of mirrors projected onto a large grid. In 1937,Wernisch15 investigated both pullout and beam specimens of13 types of round bars with normal- and high-strengthconcrete. Menzel16,28 produced papers in 1939 and 1952 thatincluded round and square pullout specimens. The 1939specimens were cast in prisms with a 1-15/16 in. (49.2 mm)minimum cover based on the contemporary ACI guidelines.The 1952 paper indicated that bars held rigidly in the horizontalposition during casting exhibited reduced bond strengthcompared with horizontal bars permitted to settle a givendistance when cast. The rigidly held bars are included in thecurrent study.

In 1940, Johnston and Cox17 investigated the effect oflocalized surface rust on the bond strength of round andsquare deformed bars using unrusted bars as control specimens.Only the unrusted bars are included in the current study.Watstein18,21 produced papers in 1941 and 1947 thatinvestigated the distribution of bond stress over the embedmentlength in pullout specimens and not simply the maximumaverage bond stress over a given length. In 1945, Watsteinand Seese20 investigated bond efficiency of several bar typesbased on crack width at the outer surface of the concrete,with crack gauges that were mounted at seven locationsalong the length of the specimen. The specimens weremounted into a tensile testing machine that placed both thesteel and concrete in tension. Also in 1945, Kluge and Tuma19

investigated lapped bar splices in beams with two continuousbars placed adjacent to one lapped bar with a clear spacing of


Table 2—Bond and anchorage tests: 1913-1969

Investigator YearTest type

Spiral reinforced

Boundary conditions

Slip at free or loaded

endConcrete

dimensions Specimen type

No. of tests per data

pointfy,ksi

fy,nominal or

actualfc′ ,psi

Embedment length, in.

Reported stress

Casting position

Abrams3 1913 Pullout Yes Spherical bearing block Free end

8 in.diameter cylinder

1/2 in. square

5 40 Nominal 1750 8.0 0.01 in. slip and at failure Vertical

1/2 in. square

9/16 in. diameter round

1 in. square

1 in. square

1-1/8 in. diameter round

Howard11 1917 Pullout No Spherical bearing block Free end

6.75 in.diameter cylinder

12 x 8 x 8 in.

3/4 in. square 1Varied 38.0 to

40.0

Nominal and actual 1357 12.0 or 8.0 0.01 in. slip

and at failure

Vertical and

horizontal

Slater et al.12 1920 Pullout No Spherical bearing block Free end 6 in. diameter

cylinder 1/2 in. square 2 61.3 Nominal and actual 5500 6.0 0.01 in. slip

and at failure Vertical

Gilkey and Ernst13 1936 Pullout No Spherical

bearing block Free end3 in.

diametercylinder


1 65.0 NominalVaried 2360 to

6525

Varied 6.0 to 12.0

0.01 in. slip and at failure Vertical


Gilkey et al.14 1937

Pullout NoPlaster of

paris bearing block

Mirrors and dial

gauges at both ends

4 x 4 x 12 in. in length




1Varied 50.0 to

70.6

Nominal and actual

Varied 3040 to

5438

12.0

At failure only Vertical

Beams NoHalf and full simple span

beams

Mirrors and dial

gauges at both ends

Varied 4 x 6 x 42 to 78 in.

in length

12.0 nominal

Wernisch15 1937

Pullout No Spherical bearing block Free end 6 in. diameter

cylinder3/4 in. diameter

round

4Varied 50.0 to

59.0Nominal

Varied 2830 to

76506.0 At failure

only Vertical

Beams 8 stirrups/ beam

Simple span beam Free end 6 x 12 x 36 in.

in lengthVaried 2 to 3

Varied 3310 to

76506.0 nominal At failure

onlyBottom

horizontal

Menzel16 1939 Pullout No Spherical bearing block Free end 4-7/8 x 6 in.

cube

1 in. diameter round 1 40.0 Nominal

Varied 3600 to

6000

Varied 8.25 to 22.0

At failure only

Vertical and

horizontal1 in. square

Johnston and Cox17 1940 Pullout No Spherical

bearing block Free end6 and 10 in.

diameter cylinder


6

50.0

Nominal and actual

Varied 2320 to

2580

3.0



52.3 4.0


46.0 6.0

1 in. square 44.8 8.0

1-1/4 in. square 40.0 10.0

Watstein18 1941 Pullout No Spherical bearing block Free end

6 in. diameter cylinder


3Varied 43.3 to

50.1

Nominal and actual

4310 18.0 At failure only

Vertical

Kluge and Tuma19 1945 Beams

Stirrups in outer thirds

Simple span lapped bars NA

7 x 7-1/4 x 96 in. and 13 x 14 x 144 in.

1 in. diameter round

1Varied 45.0 to

61.8

Nominal and actual 4700

Varied 7.75 to 43.0

At failure only

Bottom horizontal1/2 in. diameter

round

Watstein and Seese20 1945 Pullout No Concrete in

tension NA6 in.

diameter cylinder

7/8 in. diameter round 3

Varied 47.0 to

57.0

Nominal and actual 3950 12.0 NA Unknown

Watstein21 1947 Pullout No Spherical bearing block

1/4 point from

Tuckerman gauges

6 in.diameter cylinder


Varied 43.0 to

48.0

Nominal and actual 4080 8.0 and 12.0 0.01 in. slip

and at failure Vertical

Collier22 1947 Pullout No Spherical bearing block Loaded end

6 in. square cubes and 6 in. diameter

cylinder

7/8 in. diameter round 5 42.0 Nominal 5350 10.5 0.01 in. slip

and at failureBottom

horizontal

Clark23 1949 Pullout Yes Spherical bearing block Free end 8 x 9 x 10 in.

No. 10 round3 40.0 Nominal 3750 10.0 0.01 in. slip Bottom

horizontal1-1/8 in. square

Walker24 1949 Pullout No Spherical bearing block Free end



Varied 42.4 to

46.8

Nominal and actual

Varied 5730 to

66508.0 0.01 in. slip Vertical

1 in. square

Mains25 1951

Pullout 8 stirrups/ test

Spherical bearing block NA 8 x 12 x

21 in.7/8 in. diameter

round 1 71.5 Nominal

Varied 3460 to

398021.0

At failure only

Bottom horizontal

Beams 10 stirrups/beam Simple span NA 8 x 12.5 x

78 in.

Varied 3760 to

4180

21.0 nominal

Bottom horizontal

Note: 1 in. = 25.4 mm; 1 in.2 = 645 mm2; 1 psi = 6.895 KPa.


Table 2—Bond and anchorage tests: 1913-1969 (cont.)

Investigator YearTest type

Spiral reinforced

Boundary conditions

Slip at free or loaded

endConcrete

dimensions Specimen type

No. of tests per data

pointfy,ksi

fy, nominal or actual

fc′ , psi

Embedment length, in.

Reported stress

Casting position

Walker26 1951 Pullout No Spherical bearing block Free end


3/4 in.diameter round

10

42.4

Nominal and actual

3410

8.00.01 in. slip

and at failure

Vertical3/4 in. diameter round 46.8 3610

1 in. square 46.5 3950

Chamberlin27 1952 Pullout Yes Spherical bearing block Free end

6 in. square and 9 in. square cubes


6 50.0 Nominal 31706.0 0.01 in. slip

and at failure

Vertical3/4 in. diameter

round 9.0

Menzel28 1952 Pullout No Spherical bearing block Loaded end 4-7/8 x 6 in.

cubes

1 in. diameter round 1 45.0 Nominal 3600 22.0 At failure

onlyBottom

horizontal1 in. square

Chinn et al.29 1955 Beams Stirrups in outer third

Simple span lapped bars NA

3.62 to 9 in. x 6 to

7 in. x 87 in.


Varied 57.0 to

79.0Nominal

Varied 3160 to

7480

Varied 5.5 to 24.0

At failure only

Tophorizontal

Chamberlin30 1956 Beams Wire mesh Simple span beam Free end Varied No. 4 round and

No. 6 round 3Varied 46.0 to

50.0Nominal

Varied 3700 to

5870

Varied 3.0 to 16.0

At failure only

Bottom horizontal

Chamberlin31 1958 Beams None Simple span beam Free end 6 x 6 x

36 in. No. 4 round 1 50.0 Nominal 4500 Varied 6.0 to 12.0

At failure only Horizontal

Mathey and Watstein32 1961

Beams Stirrups in outer third

Overhang simple span NA 8 x 18 x

88 in.No. 4 and No. 8

bars

1No. 4 Bar

114.7 and

No. 8 Bar 97.0

Actual

Varied 3495 to

4485

Varied 7.0 to 18.0

At failure only

Bottom horizontal

Pullout Yes Spherical bearing block Free end

10 in. x 10 in. x varied

1Varied 3235 to

4865

Varied 7.0 to 34.0 Bottom

Ferguson and Thompson33 1962 Beams No Simple span

lapped bars NA

12 to 18.34 in. x 9 to 13 in. x varied

No. 7 bar 1 87.5 NominalVaried 2380 to

5950

Varied 15.75 to 28.0

At failure only NA

Ferguson and Breen34 1965 Beams No Simple span

lapped bars NA VariedNo. 8 bar

2 75.0 Nominal 3000 Varied 18.0 to 84.0

At failure only

Bottom horizontalNo. 11 bar

Untrauer and Henry35 1965 Pullout No Spherical

bearing block Loaded end 6 in. cubeNo. 6 bar

1 92.0 NominalVaried 4480 to

69206.0 At failure

only HorizontalNo. 9 bar

Perry and Thompson36 1966 Eccentric

pullout No Bearing block NA Varied No. 7 bar 1 50.0 NominalVaried 2500 to

50009.0 At failure

only On side

Lababidi37 1967 Eccentric pullout No Bearing block NA Varied No. 6 bar 1 75.0 Nominal

Varied 2600 to

51009.0 At failure

only Vertical

Ferguson and Briceno38 1969 Beams No Simple span

lapped bars NA VariedNo. 8 bar Varied 2 to

4 per beam

Varied 65.0 to

70.0Nominal

Varied 2450 to

4350

Varied 32.0 to 85.0

At failure only On side

No. 11 bar

Perry and Jundi39 1969 Eccentric

pullout No Bearing block NA Varied No. 6 bar 1 75.0 NominalVaried 2200 to

50609.0 At failure

only Vertical

Warren40 1969 Beams Stirrups Simple span overhang NA Varied No. 9 bar Varied 2 to

7 per beam

Varied 74.4 to

90.0

Nominal and actual

Varied 3090 to

4360

Varied 35.0 to 76.0


Note: 1 in. = 25.4 mm; 1 in.2 = 645 mm2; 1 psi = 6.895 KPa.

1-1/2 bar diameters. In 1947, Collier22 investigated the bondstrength of reinforcing bars with several deformation patternsusing pullout tests.

In 1949, Clark23 continued the rating technique from his1946 work based on bar stress at given slip values for severaldifferent bar types. His data provides a large sample space,but is limited because the reported bond stress versus slipcurves were determined from an average of two differentembedment lengths. Despite these drawbacks, Clark showedthat, while deformation area per square inch was an importantfactor in bond strength, the spacing of the deformations andthe area between the lugs—the shearing area—was anequally important factor. He suggested a ratio of 5 to 6 forthe shearing area to bearing area. The current inverse ratio,referred to as the relative rib area by ACI 408.3,24 is similarto those recommended in Clark’s report.

In 1949 and in 1951, Walker24,26 investigated spaced andtied reinforcement using pullout specimens. Spacing of thebars varied from 1-1/8 to 1-7/8 in. (28.6 to 47.6 mm) for the

1949 and 1951 tests, respectively. In 1951, Mains25 lookedinto the distribution of bond stress on embedded bars usingstrain gauges mounted longitudinally inside the bars along aprecut channel in both beams and pullout specimens. Helooked at both hooked and straight plain and deformed barsin both series of tests.

Chamberlin27,30,31 undertook several investigations dealingwith bond strength, publishing three journal articles from1952 through 1958. The 1952 article investigated spacing ofspliced bars in pullout specimens. The specimens werespirally reinforced against bursting and lapped bars werespaced at 1-1/2 in. (38.1 mm). In 1956, Chamberlin continuedto look at the spacing of reinforcement in concrete, this timewith a modified concrete beam. While the previous researchinvolved splicing of bars in pullout specimens, the focus ofthe 1956 work dealt with minimum cover for single parallelreinforcing bars placed in concrete beams. Chamberlin useda beam subjected to two-point loads producing a constantmoment region in the center of the beam. Between the point


loads, the reinforcing bar was exposed relative to the adjacentconcrete. To account for varying cover requirements, thewidth of the beam at the location of the reinforcing bar variedwith respect to the fixed width of the aforementioned beam.Chamberlin used the modified beam with cover variationsfrom 1/2 to 5-1/2 in. (12.7 to 139.7 mm) including both plainand deformed reinforcement to investigate average bondstrength. The final series of tests in 1958 investigated thespacing of lapped bars as well as the lap length for beamspecimens. The work involved only one type of deformedbar with no lateral reinforcement against bursting.

In 1955, Chinn et al.29 investigated the bond strength of3/4 in. (19.1 mm) diameter round bars in tension lap splicesin beams. The beams failed due to splitting (no stirrups wereincluded in the specimens) of the side or bottom cover.

In 1961, Mathey and Watstein32 investigated the bondstrength of pullout and beam specimens constructed withhigh yield strength (100 ksi [689.8 MPa]) deformed steelbars based on seven development lengths that varied from7 to 34 in. (177.8 to 863.6 mm). Both types of specimenswere reinforced to prevent lateral bursting with the use ofwelded wire fabric and No. 4 stirrups in the outer third of themember for the pullout and beam specimens, respectively.The beam specimens contained single longitudinal reinforcingbars with eccentric bearings to offset any added compressionat the supports, while the pullout specimens were of thetraditional type.

In 1962, Ferguson and Thompson33 investigated thedevelopment length of high strength reinforcing bars (75 ksi[517.4 MPa]) in beams. The bulk of the work concentratedon No. 7 bars without stirrups. A continuation of the initialinvestigation with larger bars by Ferguson and Breen34 in1965 and Ferguson and Briceno38 in 1969 included No. 8and No. 11 bars in a constant width beam with and withoutstirrups simulating the forces in a retaining wall stem.

In 1965, Untrauer and Henry35 looked into the effect ofnormal pressure on bond strength based on pullout tests of highstrength (92 ksi [634.6 MPa]) round deformed reinforcementbars. Specimens with no applied normal stress were used ascontrol specimens and are included in this study. In 1966,Perry and Thompson36 investigated the maximum bondstress with eccentric pullout specimens with instrumentationsimilar to Mains using strain gauges placed inside thereinforcing bars within a center voided area.

Laboratory tests based on static and dynamic repeatedloadings of pullout specimens were performed by Lababidi37 in1967 as part of a thesis work, which was later published byPerry and Jundi39 in 1969. Both these sources used differentdata for static loading of eccentric pullout specimens based onvarying concrete strength and fixed embedment length.

In 1969, Warren40 reported bond strengths for No. 9 barsin beams with stirrups to guard against splitting. Specimenscontained varying beam width, bar spacing, number of barsper beam, and varying embedment length.

PRESENTATION OF RESULTSThe relevant archival test data were used to assess bond

and development of vintage square bars. Round deformedbar data were used for relative comparisons with the squarebar results. Several investigators reported the concretecompressive strength, reinforcement yield strength, andmaximum average bond stress based on the mean value fromseveral tests with no other accompanying statistical data. Inaddition, some investigators reported actual reinforcement

yield stress while others reported only the nominal yieldstress. Test results were reported at failure or at certain slipvalues (the most common being 0.01 in. [0.25 mm]) and ateither the free or loaded end (for pullout specimens), or forsome cases both ends were reported. Consequently, consideringthe wide ranging variability in the available archival data,some limits were required and not all data could becompared across all of the variables. For consistency, thefollowing conventions were used:• All bars were deformed; no plain bars were included in

the sample space.• Bars that were permitted to settle with the surrounding

concrete were not included in the data.• All of the bars were assumed to be adequately encased

by the surrounding concrete.• Concrete cover was based on the dimensions reported

by the authors and the appropriate simplified ACIdevelopment length equations (Eq. (1) or (2)) were used.

• For square bars, an equivalent diameter (to produce equalround and square steel area) was used in the ACI equations.

• Where the average bond stress was reported, thereinforcing bar stress was determined as the bondstress times the bar embedded surface area divided bythe bar cross-sectional area.

• Where the maximum reinforcing bar tensile stress wasreported, the bond stress was determined as the reinforcingbar stress times the cross-sectional area divided by theembedment surface area, with an upper limit on theembedment length of the ACI development length(Eq. (1) or (2)).

• Reinforcing bar stress or bond stress was evaluated attwo reference points: slip of 0.01 in. (0.25 mm) and/orat maximum applied load where reported.

• Evaluations were made with the nominal yield stress and/or the actual yield stress (where reported) for the reinforcingbar material used in the different research studies.

For each archival test result, and using the constraintsdescribed previously, results were categorized according tothe maximum applied force at failure and the applied force ata measured slip of 0.01 in. (0.25 mm). The reported embedmentlength was normalized by the ACI computed requireddevelopment length (Eq. (1) or (2)) and the reinforcing barstress achieved in the test was normalized by the reportednominal or actual yield stress of reinforcement. Bond stresseswere also computed. None of the square bars in the samplespace were reported to explicitly meet the ASTM A 305-496

requirements. As a result, a direct comparison of equivalentround and square bars meeting the ASTM designation wasnot feasible. However, comparisons between round bars thatdid meet the ASTM A 3057 designation (and thus themodern ASTM A 6158 designation) and square bars undersimilar test conditions were made to identify possibledifferences in bond and development between the differentbar types. The dark solid line in Fig. 2 through 9 representsthe ACI required embedment length.

ANALYSIS AND DISCUSSIONAll of the applicable archival test data are shown in Fig. 2

and 3 with the reported maximum applied force and with theapplied force at a measured end slip of 0.01 in. (0.254 mm).These figures include all specimen types and both deformedround and square bars considering both reported nominaland actual yield stress values. Square bar results are isolatedin Fig. 4 and 5 and consisted of pullout specimens only.


Round bar results are isolated in Fig. 6 and 7 and included alltest specimen types (pullout, eccentric pullouts, and beams).The sample space for bars meeting ASTM A 305-496 isshown in Fig. 8 and 9 according to reinforcing bar size. Thisdata set is representative of reinforcing bar manufacturedfrom the 1950s to the late 1960s. Much of the data in Fig. 8and 9 are from eccentric pullout and beam specimens (defined

herein as alternative specimens) due to changes in the testingmethodology that moved away from direct pullout tests aswell as improvements in metrology. As seen in all thesefigures, there were more test results available with nominalyield stresses for the maximum applied force cases.

Figures 2 and 3 indicate that, regardless of bar type, defor-mation pattern, shape, or spacing, the deformed bars tended

Fig. 2—All test results at maximum force with: (a) reportedactual yield; and (b) reported nominal reinforcing baryield stress (legend at end of paper).

Fig. 3—All test results at slip of 0.01 in. with: (a) reportedactual reinforcing bar yield; and (b) reported nominalreinforcing bar yield stress (legend at end of paper).

Fig. 4—Square bar test results at maximum applied forcewith: (a) reported actual reinforcing bar yield; and (b)reported nominal reinforcing bar yield stress (legend atend of paper).

Fig. 5—Square reinforcing bar test results at slip of 0.01 in.with: (a) reported reinforcing bar yield; and (b) reportednominal reinforcing bar yield stress (legend at end of paper).


to perform at or above the simplified ACI developmentrequirements (and implied ASTM A 6158/ASTM A 3057

deformations), with only a few exceptions. The bars tendedto develop stress in some proportion to the embedded lengthand the ACI requirements provide a reasonable lower bound.Only a few of the tests were conducted with embedments

beyond the specified ACI development length, but even so,many of the bars were able to achieve bar stresses above theyield stress (nominal or actual). For several of the specimenswhere the actual yield strength was reported, the bars wereable to achieve stresses well into the theoretical strain-hardening range. The idealized upper limit on development

Fig. 6—All pullout test results for round reinforcing bar atmaximum applied force with: (a) reported actual bar yield;and (b) reported nominal reinforcing bar yield stress (legend atend of paper).

Fig. 7—Pullout test results for round reinforcing bar meetingASTM A 305 at maximum applied force with: (a) reportedactual reinforcing bar yield; and (b) reported nominalreinforcing bar yield stress (legend at end of paper).

Fig. 8—All alternative test results for round reinforcing barat maximum applied force with: (a) reported actual reinforcingbar yield; and (b) reported nominal reinforcing bar yield stress(legend at end of paper).

Fig. 9—Alternative test results for round reinforcing barmeeting ASTM A 305 at maximum applied force with: (a)reported actual reinforcing bar yield; and (b) reported nominalreinforcing bar yield stress (legend at end of paper).


behavior of the bars, denoted by the dark horizontal line,originally illustrated by Kluge and Tuma,19 demonstratesthat after a reinforcing bar is embedded beyond the lengthrequired to develop the yield strength of the bar, no additionalstrength is possible (until the onset of strain hardening,which is commonly disregarded for design/analysis).

Comparison of average bond stresses for the different bartypes was performed to quantitatively identify differences inbond behavior between round and square bars. Averagebond stresses were calculated for the test results withmaximum applied force, where adequate data were available.The average bond stress was taken as that reported or as theapplied force divided by the embedded surface area (with thelength dimension limited to an upper bound of the ACIdevelopment length). The bond stresses developed in thearchival data for both round and square deformed bars areshown in Fig. 10 as a function of the reported concretestrength. The current ACI implied average bond stress forreinforcing bar No. 6 and smaller and reinforcing bar No. 7and larger, as well as the AASHO allowable bond stressesfrom 1949 and 1953 for unanchored bars are shown in thisfigure for reference. The 1949 AASHO allowable bondstress is the most stringent as these were based onnonstandard deformation requirements prior to adoption ofASTM A 305.5 The bond stresses show scatter with nostrong correlation associated with the compressive strengthfor the pullout specimens. There was also scatter from thealternative specimens. The distribution of average bondstress was normalized with respect to fc′ , and normalizedhistograms for the different reinforcing bar and test types areshown in Fig. 11. The pullout tests for both round and square

bars exhibited a normal distribution while the alternative testtypes exhibited log-normal distributions. The statistics forthese results are reported in Table 3 and the idealizeddistributions are shown in Fig. 12. Cumulative distributionfunctions for the normalized average bond stress of thedifferent reinforcing bar and specimen types are shown inFig. 13. As seen in this figure, the square and round pulloutbars have similar normal distributions with reasonably goodfit over the range of values. The square and round pulloutbars have similar mean and the square pullout bars have aslightly smaller coefficient of variation (COV). As a result,no significant differences were observed for the two rein-forcing bar cross-sectional types in similar test conditions.The alternative specimens do not fit well with the normaldistribution, particularly at the upper and lower tails. Thebetter fit was the log-normal distribution, as this adequatelycaptured both the upper and lower tails. Thus, the more realisticstress conditions produced by the alternative test methodsresulted in lower average bond stresses and different distributionof results. The current ACI approach is based on these moremodern findings for round bars with ASTM A 3055 and A 6158

standardized deformations. Without additional data, it is notpossible to tell precisely how square bars might performunder similar alternative test conditions. Based on thesimilarities between round and square deformed bars in thedirect pullout tests (over a range of concrete strength, reinforcingbar material, and different researchers), however, it is anticipatedthat square bars will also show reduced average bondstresses in the more realistic stress conditions. It is furtherassumed, based on the pullout test similarities, that deformedsquare bar bond stresses in alternative test conditions would

Fig. 12—Statistical distributions of normalized averagebond stress for different reinforcing bar and test types.

Fig. 13—Fit of normalized average bond stress distributionsfor different reinforcing bar and test types.

Fig. 10—Average bond stress versus concrete compressivestrength. (Note: 1 psi = 6.89 KPa.)

Fig. 11—Normalized histograms of average bond stressnormalized with respect to √fc′ .


be of similar magnitude and distribution to those observedfor the deformed round bars.

For the deformed square bars in this study, the normalizedaverage bond stresses were similar to those reported forround bars meeting ASTM A 3055 when using the sidedimension to determine the embedment perimeter. Thus, itappears reasonable to use this value as the reinforcing bargeometry parameter in the ACI development length equations.Using an equivalent round diameter for square bars results indevelopment lengths that are 13% longer then when the sidedimension is used. The difference is relatively small and useof the equivalent diameter is conservative and thusrecommended for analysis purposes.

The round and square bars were also sorted based oncross-sectional area to establish trends associated withreduced bond efficiency for larger bars. Only pullout testresults were used for these comparisons. The normalizedaverage bond stress was shown to decrease as the reinforcingbar cross-sectional area increased, as seen in Fig. 14.Comparison of round and square pullout test results showedthat square bars had slightly higher normalized average bondstress than round bars meeting ASTM A 305,5 except at barssizes above 1.3 in.2 (838.7 mm2), where little data wasavailable. In general, the trends were similar indicating thattransition to longer development lengths for bigger sizedbars is also warranted for square bars, with greater uncertaintyfor square bars above 1 in. (25.4 mm) due to lack of data.

CONCLUSIONSA review of bond and development tests on vintage

deformed square and round reinforcing bars has beenconducted. Experimental results from the available archivalliterature were used to compare the bond performance of

square and round deformed reinforcing bar. The studyincluded bars from the earliest tests of Abrams3 in 1913 tomodern bars up to 1969. The square bars that were reportedin the literature were based on early designs, in which theactual deformation information was not reported, or weremore modern square bars that did not meet the ASTM A 305-496

criteria. Based on review and analysis of the test results, thefollowing conclusions are presented:• Application of the simplified ACI development length

equations to characterize the reinforcing bar stressprovided a reasonable lower bound for both square andround bars across all test types. Similar results werefound for round and square results.

• The ACI approach was similarly conservative for partialreinforcing bar embedments of round and square resultsand indicates that linear interpolation of availablereinforcing bar stress for embedment lengths less thanthe computed development length also appears reasonablefor square reinforcing bar.

• Comparison of average bond stresses for pullout testresults showed that round and square reinforcing bar(computed using the actual perimeter and embedmentlength) have similar normal distributions and squarebars have slightly smaller variability (coefficient ofvariation for square bars was 26.5% compared with32.8 and 34.9% for all round bars and for round barsmeeting ASTM A 305,6 respectively).

• Alternative test types (tensile specimen, modified canti-lever beam, beam-end specimen, and full-scale beamtests) produced lower average bond stresses than pull-out tests for round reinforcing bar and further exhibitedlog-normal distributions. No data from alternative testtypes were available for square reinforcing bar. Giventhe similarities in results between round and squarebars in pullout tests, however, it is anticipated thatsquare reinforcing bar would also exhibit reduced averagebond stress in alternative test conditions.

• Computation of development length using the ACIformula with an equivalent round diameter for squarereinforcing bar results in lengths 13% larger than whenthe side dimension is used. This is conservative andrecommended for practice given the lack of test dataavailable for large square reinforcing bar sizes andalternative test configurations.

FUTURE WORKThe reported investigation was based on bond test results

from previous research conducted in the early 1900s through1969. No square bars meeting ASTM A 305-496 were availablein the archival literature. Therefore, additional tests usingcurrently accepted bond and development evaluation methodsof square bars meeting the deformation requirements of ASTMA 305-507 would be of interest to supplement the database.

ACKNOWLEDGMENTSThe authors wish to thank the Oregon Department of Transportation for

financial support of this research, although the findings and conclusions arethose of the authors and may not represent those acknowledged.

REFERENCES1. AASHTO, Manual for Condition Evaluation of Bridges, American

Association of State Highway and Transportation Officials, Washington,D.C., 2000, pp. 49-72.

2. SEI/ASCE 11-99, “Guideline for Structural Condition Assessment ofExisting Buildings,” American Society of Civil Engineers, 2000, 160 pp.

3. Abrams, D. A., “Tests of Bond between Concrete and Steel,” Bulletin

Table 3—Statistical measures for different reinforcing bar and test types

Reinforcing bar type

Specimen type

Test measure

No. of samples

Mean fb /(f ′c

0.5) COV, %

Square Pullout Maximum force 33 15.4 26.5

All round Pullout Maximum force 115 15.0 32.8

ASTM A 305 round Pullout Maximum

force 29 15.3 34.9

All round Alternative Maximum force 222 8.7 17.1

ASTM A 305 round Alternative Maximum

force 177 8.5 17.3

Fig. 14—Normalized average bond stress for pullout tests ofreinforcing bar with different cross-sectional areas.(Note: 1 in.2 = 645 mm2.)


No. 71, University of Illinois Engineering Experiment Station, 1913, 239 pp.4. Clark, A. P., “Comparative Bond Efficiency of Deformed Concrete

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5. ASTM A 305-47, “Minimum Requirements for the Deformations ofDeformed Steel Bars for Concrete Reinforcement,” ASTM International,West Conshohocken, Pa., 1947.

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8. ASTM A 615/A 615M-05a, “Standard Specification for Deformedand Plain Carbon-Steel Bars for Concrete Reinforcement,” ASTMInternational, West Conshohocken, Pa., 2005, 6 pp.

9. ACI Committee 318, “Building Code Requirements for StructuralConcrete (ACI 318-05) and Commentary (318R-05),” American ConcreteInstitute, Farmington Hills, Mich., 2005, pp. 194-196.

10. Leonhardt, F., “On the Need to Consider the Influence of LateralStresses on Bond,” Proceedings of the Symposium on Bond and CrackFormation in Reinforced Concrete, V. 1, Stockholm, Sweden, 1958, pp. 29-35.

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12. Slater, W. A.; Richart, F. E.; and Scofield, G. G., “Tests of BondResistance Between Concrete and Steel,” Department of Commerce—Technologic Papers of the Bureau of Standards, No. 173, 1920, 68 pp.

13. Gilkey, H. J., and Ernst, G. C., “Pullout Tests for Bond Resistance ofHigh Elastic Limit Steel Bars,” Proceedings of the Highway ResearchBoard, V. 16, 1936, pp. 82-95.

14. Gilkey, H. J.; Chamberlin, S. J.; and Beal, R. W., “Bond Resistanceof High Elastic Steel Bars, Series of 1937,” Proceedings of the HighwayResearch Board, V. 17, 1937, pp. 150-186.

15. Wernisch, G. R., “Bond Studies of Different Types of ReinforcingBars,” ACI JOURNAL, Proceedings V. 34, No. 11, Nov. 1937, pp. 145-164.

16. Menzel, C. A., “Some Factors Influencing Results of Pull-Out BondTests,” ACI JOURNAL, Proceedings V. 35, No. 6, June 1939, pp. 517-542.

17. Johnston, B., and Cox, K. C., “The Bond Strength of Rusted DeformedBars,” ACI JOURNAL, Proceedings V. 37, No. 9, Sept. 1940, pp. 57-72.

18. Watstein, D., “Bond Stress in Concrete Pull-Out Specimens,” ACIJOURNAL, Proceedings V. 38, No. 9, Sept. 1941, pp. 37-52.

19. Kluge, R. W., and Tuma, E. C., “Lapped Bar Splices in ConcreteBeams,” ACI JOURNAL, Proceedings V. 42, No. 9, Sept. 1945, pp. 13-34.

20. Watstein, D., and Seese, N. A., “Effect of Type of Bar on Width ofCracks in Reinforced Concrete Subjected to Tension,” ACI JOURNAL,Proceedings V. 41, No. 2, Feb. 1945, pp. 293-304.

21. Watstein, D., “Distribution of Bond Stress in Concrete Pull-OutSpecimens,” ACI JOURNAL, Proceedings V. 43, No. 5, May 1947, pp. 1041-1052.

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29. Chinn, J.; Ferguson, P. M.; and Thompson, J. N., “Lapped Splices inReinforced Concrete Beams,” ACI JOURNAL, Proceedings V. 52, No. 10,Oct. 1955, pp. 201-213.

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41. ACI Committee 408, “Bond and Development of Straight ReinforcingBars in Tension (ACI 408R-03),” American Concrete Institute, FarmingtonHills, Mich., 2003, 49 pp.

Bond and Development of Deformed Square Reinforcing Bars

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