Bond and Development of Deformed Square Reinforcing Bars

Bond and Development of Deformed Square Reinforcing Bars

Howell, Daniel A

Square deformed reinforcing bars were widely used prior to and during the transition to circular deformed reinforcing steel upon adoption of ASTM A 305-50, which standardized geometry, weight, deformation height, and spacing requirements. Bond stress and development lengths for deformed square bars have traditionally been computed as equivalent round bars of equal cross-sectional area and weight, although this approach has not been validated. Data is presented from archival research on deformed square and circular reinforcing bars both prior and subsequent to adoption and implementation of ASTM A 305-50 that provides information for assessment of bond and development of deformed square reinforcing bars in vintage and historic structures. Pullout test results show that deformed square bars exhibited average bond stress similar to those of round deformed bars. Based on the archival test results and the comparisons presented, treatment of deformed square bars as equivalent round bars for calculation of development length appears reasonable and conservative.

Keywords: bond stress; development length; reinforcement.

(ProQuest-CSA LLC: … denotes formulae omitted.)


Square deformed reinforcing bars were widely used in concrete building and bridge construction throughout the first half of the twentieth century. As these structures age, begin to deteriorate, or undergo use changes, the questions of remaining capacity and available service life become important for making rehabilitation and retrofit decisions. The current AASHTO’s “Manual for Conditional Evaluation of Bridges”1 and ASCE’s “Guideline for Structural Condition Assessment of Existing Buildings”2 provide general guidelines for assessment of concrete bridges and buildings, respectively, in terms of concrete compressive strength and reinforcement yield strength, but neither guide addresses treatment of different reinforcing bar geometries, critical for assessment of both flexural and shear capacity, given the move toward sectional analysis methods.

A focus of the archival literature was on service performance driven by the allowable stress design philosophy used by designers of the day. As a result, little of the historic data are available to specifically characterize the development length necessary to achieve yielding of the reinforcing. However, sufficient data are available to support recommendations for assessing bond of deformed square reinforcing bars in comparison with deformed round reinforcing bars.

Standardization of deformed reinforcing bars

Concrete reinforcing bars evolved during the early part of the twentieth century to the standardized round bars that are used today. Prior to standardization of geometries and deformations, however, a wide array of different bar types were used. Many were patented systems and employed unique cross-sectional shapes and deformations to enhance bond between the concrete and steel, examples of which can be seen in Fig. 1 from Abrams’3 early work. Of the many different bar types available, round and square bars were predominant and square bars were broadly used, particularly for designs requiring large bar sizes. While smooth (undeformed) bars were also used, deformed bars were recognized early on to provide superior bond. Due to wide variations in deformation height and geometric patterns used throughout the early 1900s, however, consistent bond stresses were not assured. In 1946, Clark4 developed a method of rating many different patterns of reinforcing bars based on their average bond stress at several predetermined slip values. His investigation led to ASTM A 305-47T,5 later adopted as ASTM A 305-49.6 The specification provided standard deformation heights and spacing for round bars and also included deformation patterns for three square bars that corresponded to equivalent round areas (1-1/4 in. square = No. 11; 1-1/8 in. square = No. 10; 1 in. square = No. 9). The specification was modified the following year as ASTM A 305-507 and excluded square bars entirely. Nonetheless, square bars continued to be used well into the late 1950s and were still referenced to the ASTM A 305 specification on construction documents. It is of interest to note that the current ASTM A 6158 specification for deformed reinforcing bars remains identical to the ASTM A 305-507 specification as it pertains to the bar size and deformation geometry, as seen in Table 1.

Current development length requirements

The current ACI equation for development length9 is based on several factors, but the most relevant term for this investigation relates to the bar size and the relevance of the bar cross section on bond efficiency. The simplified development length formulas from ACI 318-05 for round bars with clear spacing not less than 2^sub db^ and clear cover not less than d^sub b^ 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 are not met, the simplified development length formulas are

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

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

where f^sub y^ equals the yield strength of steel (psi); ψ^sub t^ equals the reinforcement location factor, for bars with more than 12 in. of concrete below them, ψ^sub t^ = 1.3, otherwise ψ^sub t^ = 1.0; ψ^sub e^ equals the coating factor used for epoxy coated bars, for uncoated reinforcement, ψ^sub e^ = 1.0, for epoxy coated bars with cover less than 3d^sub b^ or clear spacing less than 6d^sub b^, ψ^sub e^ = 1.5, for all other epoxy coated bars, ψ^sub e^ = 1.2; λ equals the lightweight aggregate factor, for lightweight concrete, λ = 1.3, otherwise λ = 1.0; f^sub c^’ equals the compressive strength of concrete (psi); and d^sub b^ equals the diameter of bar under consideration (in.). For uncoated, bottom, round bars in normalweight concrete, the required development length depends on the bar yield stress, concrete compressive strength, and the bar diameter. The diameter dimension describes the available bar perimeter by which bond stresses can be developed. By comparison, square bars have approximately an 11% larger perimeter than round bars of equivalent area. However, it is not clear if the square cross-sectional shape can develop bond stress as efficiently as round bars.

Experimental methods used for bond stress research

Review of the early literature on bond and anchorage of reinforcing steel indicated that different researchers employed a wide array of different specimens, loading protocols, material properties, measurement devices, and reference measures. Early investigators such as Abrams3 used pullout tests to analyze bond stress. The specimen consisted of a bar embedded longitudinally in a concrete cylinder or prism with the free or unloaded end of the bar protruding a short distance beyond one end and the loaded end extending a longer fixed distance beyond the concrete specimen. The specimen was placed on a bearing block and tested to failure by either splitting of the concrete or pullout of the bar. A small number of researchers used lateral restraints placed along the perimeter of the pullout specimens to prevent splitting of the samples, thus increasing the bond strength at failure due to the increased constraint.

Alternative test methods were developed because it was recognized that the pullout test placed the concrete surrounding the bar in compression and the bar in tension, whereas in practice, both the bar and the concrete are in tension. Also, the boundary conditions of the concrete on the bearing plate affected the bond stress. As pointed out by Leonhardt,10 a specimen mounted on a plate or bearing block induces friction and produces lateral stresses on the concrete, thereby artificially increasing the measured bond stress.

In spite of the drawbacks, pullout tests remained popular and were used extensively by researchers because the tests were relatively inexpensive and easy to perform, in contrast to alternatives that could produce more realistic stress conditions. Alternative approaches for the pullout test included use of a concrete specimen with a bar extending longitudinally past the concrete at both ends (double pullout or tensile specimen), as well as the modified cantilever beam, beam-end specimen, and full-scale beam tests. Data from all of these types of test specimens were used in the subsequent analyses and the specimen type used in the various archival research is reported in Table 2.


The current state of the practice is to treat square bars as equivalent round bars for determining anchorage and development, although this approach has not been validated. This paper reviews archival technical literature on bond and anchorage of vintage reinforcing bars from the turn of the last century to the late 1960s to establish recommendations for treatment of deformed square reinforcing bars to aid in evaluation of older and historic concrete structures, many of which contain square bars.


The specimen details, sorted by researcher, are shown in Table 2. As seen in this table, many of the tests were on pullout type specimens without special reinforcing to prevent splitting of the concrete, but several beam tests were also included in the sample space.

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

In 1920, Slater et al.12 investigated bond stress for bars with anti-corrosive coatings, and used uncoated bars as control specimens. The uncoated bars are used in the current study. In 1936, Gilkey and Ernst13 investigated pullout tests of similar bars in three different strengths of concrete. In 1937, Gilkey et al.14 investigated bond strength based on the results of both traditional pullout tests as well as half beam tests in which specimen strain values were reported using a series of mirrors projected onto a large grid. In 1937, Wernisch15 investigated both pullout and beam specimens of 13 types of round bars with normal- and high-strength concrete. Menzel16,28 produced papers in 1939 and 1952 that included round and square pullout specimens. The 1939 specimens 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 horizontal position during casting exhibited reduced bond strength compared with horizontal bars permitted to settle a given distance when cast. The rigidly held bars are included in the current study.

In 1940, Johnston and Cox17 investigated the effect of localized surface rust on the bond strength of round and square 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 that investigated the distribution of bond stress over the embedment length in pullout specimens and not simply the maximum average bond stress over a given length. In 1945, Watstein and Seese20 investigated bond efficiency of several bar types based on crack width at the outer surface of the concrete, with crack gauges that were mounted at seven locations along the length of the specimen. The specimens were mounted into a tensile testing machine that placed both the steel and concrete in tension. Also in 1945, Kluge and Tuma19 investigated lapped bar splices in beams with two continuous bars placed adjacent to one lapped bar with a clear spacing of 1-1/2 bar diameters. In 1947, Collier22 investigated the bond strength of reinforcing bars with several deformation patterns using pullout tests.

In 1949, Clark23 continued the rating technique from his 1946 work based on bar stress at given slip values for several different bar types. His data provides a large sample space, but is limited because the reported bond stress versus slip curves were determined from an average of two different embedment lengths. Despite these drawbacks, Clark showed that, while deformation area per square inch was an important factor in bond strength, the spacing of the deformations and the area between the lugs-the shearing area-was an equally important factor. He suggested a ratio of 5 to 6 for the shearing area to bearing area. The current inverse ratio, referred to as the relative rib area by ACI 408.3,24 is similar to those recommended in Clark’s report.

In 1949 and in 1951, Walker24,26 investigated spaced and tied reinforcement using pullout specimens. Spacing of the bars 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 looked into the distribution of bond stress on embedded bars using strain gauges mounted longitudinally inside the bars along a precut channel in both beams and pullout specimens. He looked at both hooked and straight plain and deformed bars in both series of tests.

Chamberlin27,30,31 undertook several investigations dealing with bond strength, publishing three journal articles from 1952 through 1958. The 1952 article investigated spacing of spliced bars in pullout specimens. The specimens were spirally reinforced against bursting and lapped bars were spaced at 1-1/2 in. (38.1 mm). In 1956, Chamberlin continued to look at the spacing of reinforcement in concrete, this time with a modified concrete beam. While the previous research involved splicing of bars in pullout specimens, the focus of the 1956 work dealt with minimum cover for single parallel reinforcing bars placed in concrete beams. Chamberlin used a beam subjected to two-point loads producing a constant moment region in the center of the beam. Between the point loads, the reinforcing bar was exposed relative to the adjacent concrete. To account for varying cover requirements, the width of the beam at the location of the reinforcing bar varied with respect to the fixed width of the aforementioned beam. Chamberlin used the modified beam with cover variations from 1/2 to 5-1/2 in. (12.7 to 139.7 mm) including both plain and deformed reinforcement to investigate average bond strength. The final series of tests in 1958 investigated the spacing of lapped bars as well as the lap length for beam specimens. The work involved only one type of deformed bar with no lateral reinforcement against bursting.

In 1955, Chinn et al.29 investigated the bond strength of 3/4 in. (19.1 mm) diameter round bars in tension lap splices in beams. The beams failed due to splitting (no stirrups were included in the specimens) of the side or bottom cover.

In 1961, Mathey and Watstein32 investigated the bond strength of pullout and beam specimens constructed with high yield strength (100 ksi [689.8 MPa]) deformed steel bars based on seven development lengths that varied from 7 to 34 in. (177.8 to 863.6 mm). Both types of specimens were reinforced to prevent lateral bursting with the use of welded wire fabric and No. 4 stirrups in the outer third of the member for the pullout and beam specimens, respectively. The beam specimens contained single longitudinal reinforcing bars with eccentric bearings to offset any added compression at the supports, while the pullout specimens were of the traditional type.

In 1962, Ferguson and Thompson33 investigated the development length of high strength reinforcing bars (75 ksi [517.4 MPa]) in beams. The bulk of the work concentrated on No. 7 bars without stirrups. A continuation of the initial investigation with larger bars by Ferguson and Breen34 in 1965 and Ferguson and Briceno38 in 1969 included No. 8 and No. 11 bars in a constant width beam with and without stirrups simulating the forces in a retaining wall stem.

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

Laboratory tests based on static and dynamic repeated loadings of pullout specimens were performed by Lababidi37 in 1967 as part of a thesis work, which was later published by Perry and Jundi39 in 1969. Both these sources used different data for static loading of eccentric pullout specimens based on varying concrete strength and fixed embedment length.

In 1969, Warren40 reported bond strengths for No. 9 bars in beams with stirrups to guard against splitting. Specimens contained varying beam width, bar spacing, number of bars per beam, and varying embedment length.


The relevant archival test data were used to assess bond and development of vintage square bars. Round deformed bar data were used for relative comparisons with the square bar results. Several investigators reported the concrete compressive strength, reinforcement yield strength, and maximum average bond stress based on the mean value from several tests with no other accompanying statistical data. In addition, some investigators reported actual reinforcement yield stress while others reported only the nominal yield stress. Test results were reported at failure or at certain slip values (the most common being 0.01 in. [0.25 mm]) and at either the free or loaded end (for pullout specimens), or for some cases both ends were reported. Consequently, considering the wide ranging variability in the available archival data, some limits were required and not all data could be compared across all of the variables. For consistency, the following 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 ACI development length equations (Eq. (1) or (2)) were used.

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

* Where the average bond stress was reported, the reinforcing bar stress was determined as the bond stress times the bar embedded surface area divided by the bar cross-sectional area.

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

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

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

For each archival test result, and using the constraints described previously, results were categorized according to the maximum applied force at failure and the applied force at a measured slip of 0.01 in. (0.25 mm). The reported embedment length was normalized by the ACI computed required development length (Eq. (1) or (2)) and the reinforcing bar stress achieved in the test was normalized by the reported nominal or actual yield stress of reinforcement. Bond stresses were also computed. None of the square bars in the sample space were reported to explicitly meet the ASTM A 305-496 requirements. As a result, a direct comparison of equivalent round and square bars meeting the ASTM designation was not feasible. However, comparisons between round bars that did meet the ASTM A 3057 designation (and thus the modern ASTM A 6158 designation) and square bars under similar test conditions were made to identify possible differences in bond and development between the different bar types. The dark solid line in Fig. 2 through 9 represents the ACI required embedment length.


All of the applicable archival test data are shown in Fig. 2 and 3 with the reported maximum applied force and with the applied force at a measured end slip of 0.01 in. (0.254 mm). These figures include all specimen types and both deformed round and square bars considering both reported nominal and actual yield stress values. Square bar results are isolated in Fig. 4 and 5 and consisted of pullout specimens only. Round bar results are isolated in Fig. 6 and 7 and included all test specimen types (pullout, eccentric pullouts, and beams). The sample space for bars meeting ASTM A 305-496 is shown in Fig. 8 and 9 according to reinforcing bar size. This data set is representative of reinforcing bar manufactured from the 1950s to the late 1960s. Much of the data in Fig. 8 and 9 are from eccentric pullout and beam specimens (defined herein as alternative specimens) due to changes in the testing methodology that moved away from direct pullout tests as well as improvements in metrology. As seen in all these figures, there were more test results available with nominal yield stresses for the maximum applied force cases.

Figures 2 and 3 indicate that, regardless of bar type, deformation pattern, shape, or spacing, the deformed bars tended to perform at or above the simplified ACI development requirements (and implied ASTM A 6158/ASTM A 3057 deformations), with only a few exceptions. The bars tended to develop stress in some proportion to the embedded length and 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 the yield stress (nominal or actual). For several of the specimens where the actual yield strength was reported, the bars were able to achieve stresses well into the theoretical strainhardening range. The idealized upper limit on development behavior of the bars, denoted by the dark horizontal line, originally illustrated by Kluge and Tuma,19 demonstrates that after a reinforcing bar is embedded beyond the length required to develop the yield strength of the bar, no additional strength is possible (until the onset of strain hardening, which is commonly disregarded for design/analysis).

Comparison of average bond stresses for the different bar types was performed to quantitatively identify differences in bond behavior between round and square bars. Average bond stresses were calculated for the test results with maximum applied force, where adequate data were available. The average bond stress was taken as that reported or as the applied force divided by the embedded surface area (with the length dimension limited to an upper bound of the ACI development length). The bond stresses developed in the archival data for both round and square deformed bars are shown in Fig. 10 as a function of the reported concrete strength. The current ACI implied average bond stress for reinforcing bar No. 6 and smaller and reinforcing bar No. 7 and larger, as well as the AASHO allowable bond stresses from 1949 and 1953 for unanchored bars are shown in this figure for reference. The 1949 AASHO allowable bond stress is the most stringent as these were based on nonstandard deformation requirements prior to adoption of ASTM A 305.5 The bond stresses show scatter with no strong correlation associated with the compressive strength for the pullout specimens. There was also scatter from the alternative specimens. The distribution of average bond stress was normalized with respect to f^sub c^’, and normalized histograms for the different reinforcing bar and test types are shown in Fig. 11. The pullout tests for both round and square bars exhibited a normal distribution while the alternative test types exhibited log-normal distributions. The statistics for these results are reported in Table 3 and the idealized distributions are shown in Fig. 12. Cumulative distribution functions for the normalized average bond stress of the different reinforcing bar and specimen types are shown in Fig. 13. As seen in this figure, the square and round pullout bars have similar normal distributions with reasonably good fit over the range of values. The square and round pullout bars have similar mean and the square pullout bars have a slightly smaller coefficient of variation (COV). As a result, no significant differences were observed for the two reinforcing bar cross-sectional types in similar test conditions. The alternative specimens do not fit well with the normal distribution, particularly at the upper and lower tails. The better fit was the log-normal distribution, as this adequately captured both the upper and lower tails. Thus, the more realistic stress conditions produced by the alternative test methods resulted in lower average bond stresses and different distribution of results. The current ACI approach is based on these more modern findings for round bars with ASTM A 3055 and A 6158 standardized deformations. Without additional data, it is not possible to tell precisely how square bars might perform under similar alternative test conditions. Based on the similarities between round and square deformed bars in the direct pullout tests (over a range of concrete strength, reinforcing bar material, and different researchers), however, it is anticipated that square bars will also show reduced average bond stresses in the more realistic stress conditions. It is further assumed, based on the pullout test similarities, that deformed square bar bond stresses in alternative test conditions would be of similar magnitude and distribution to those observed for the deformed round bars.

For the deformed square bars in this study, the normalized average bond stresses were similar to those reported for round bars meeting ASTM A 3055 when using the side dimension to determine the embedment perimeter. Thus, it appears reasonable to use this value as the reinforcing bar geometry parameter in the ACI development length equations. Using an equivalent round diameter for square bars results in development lengths that are 13% longer then when the side dimension is used. The difference is relatively small and use of the equivalent diameter is conservative and thus recommended for analysis purposes.

The round and square bars were also sorted based on cross-sectional area to establish trends associated with reduced bond efficiency for larger bars. Only pullout test results were used for these comparisons. The normalized average bond stress was shown to decrease as the reinforcing bar cross-sectional area increased, as seen in Fig. 14. Comparison of round and square pullout test results showed that square bars had slightly higher normalized average bond stress than round bars meeting ASTM A 305,5 except at bars sizes above 1.3 in.2 (838.7 mm2), where little data was available. In general, the trends were similar indicating that transition to longer development lengths for bigger sized bars is also warranted for square bars, with greater uncertainty for square bars above 1 in. (25.4 mm) due to lack of data.


A review of bond and development tests on vintage deformed square and round reinforcing bars has been conducted. Experimental results from the available archival literature were used to compare the bond performance of square and round deformed reinforcing bar. The study included bars from the earliest tests of Abrams3 in 1913 to modern bars up to 1969. The square bars that were reported in the literature were based on early designs, in which the actual deformation information was not reported, or were more modern square bars that did not meet the ASTM A 305-496 criteria. Based on review and analysis of the test results, the following conclusions are presented:

* Application of the simplified ACI development length equations to characterize the reinforcing bar stress provided a reasonable lower bound for both square and round bars across all test types. Similar results were found for round and square results.

* The ACI approach was similarly conservative for partial reinforcing bar embedments of round and square results and indicates that linear interpolation of available reinforcing bar stress for embedment lengths less than the computed development length also appears reasonable for square reinforcing bar.

* Comparison of average bond stresses for pullout test results showed that round and square reinforcing bar (computed using the actual perimeter and embedment length) have similar normal distributions and square bars have slightly smaller variability (coefficient of variation for square bars was 26.5% compared with 32.8 and 34.9% for all round bars and for round bars meeting ASTM A 305,6 respectively).

* Alternative test types (tensile specimen, modified cantilever beam, beam-end specimen, and full-scale beam tests) produced lower average bond stresses than pullout tests for round reinforcing bar and further exhibited log-normal distributions. No data from alternative test types were available for square reinforcing bar. Given the similarities in results between round and square bars in pullout tests, however, it is anticipated that square reinforcing bar would also exhibit reduced average bond stress in alternative test conditions.

* Computation of development length using the ACI formula with an equivalent round diameter for square reinforcing bar results in lengths 13% larger than when the side dimension is used. This is conservative and recommended for practice given the lack of test data available for large square reinforcing bar sizes and alternative test configurations.


The reported investigation was based on bond test results from previous research conducted in the early 1900s through 1969. No square bars meeting ASTM A 305-496 were available in the archival literature. Therefore, additional tests using currently accepted bond and development evaluation methods of square bars meeting the deformation requirements of ASTM A 305-507 would be of interest to supplement the database.


The authors wish to thank the Oregon Department of Transportation for financial support of this research, although the findings and conclusions are those of the authors and may not represent those acknowledged.


1. 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 of Existing Buildings,” American Society of Civil Engineers, 2000, 160 pp.

3. Abrams, D. A., “Tests of Bond between Concrete and Steel,” Bulletin No. 71, University of Illinois Engineering Experiment Station, 1913, 239 pp.

4. Clark, A. P., “Comparative Bond Efficiency of Deformed Concrete Reinforcing Bars,” ACI JOURNAL, Proceedings V. 43, No. 11, Nov. 1946, pp. 381-400.

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

6. ASTM A 305-49, “Minimum Requirements for the Deformations of Deformed Steel Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, Pa., 1949, 3 pp.

7. ASTM A 305-50, “Minimum Requirements for the Deformations of Deformed Steel Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, Pa., 1950, 3 pp.

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

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

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

11. Howard, G. C., “Tests of Bond Between Concrete and Steel,” PhD thesis, Lehigh University, South Bethlehem, Pa., 1917, 70 pp.

12. Slater, W. A.; Richart, F. E.; and Scofield, G. G., “Tests of Bond Resistance 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 of High Elastic Limit Steel Bars,” Proceedings of the Highway Research Board, V. 16, 1936, pp. 82-95.

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

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

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

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

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

19. Kluge, R. W., and Tuma, E. C., “Lapped Bar Splices in Concrete Beams,” 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 of Cracks 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-Out Specimens,” ACI JOURNAL, Proceedings V. 43, No. 5, May 1947, pp. 1041-1052.

22. Collier, S. T., “Bond Characteristics of Commercial and Prepared Reinforcing Bars,” ACI JOURNAL, Proceedings V. 43, No. 6, June 1947, pp. 1125-1134.

23. Clark, A. P., “Bond of Concrete Reinforcing Bars,” ACI JOURNAL, Proceedings V. 46, No. 11, Nov. 1949, pp. 161-184.

24. Walker, W. T., “Spaced and Tied Reinforcing Bar Splices,” Laboratory Report No. SP-20, Research and Geology Division, U.S. Bureau of Reclamation, 1949, pp. 1-11.

25. Mains, R. M., “Measurement of the Distribution of Tensile and Bond Stresses Along Reinforcing Bars,” ACI JOURNAL, Proceedings V. 48, No. 11, Nov. 1951, pp. 225-252.

26. Walker, W. T., “Laboratory Tests of Spaced and Tied Reinforcing Bars,” ACI JOURNAL, Proceedings V. 47, No. 1, Jan. 1951, pp. 365-372.

27. Chamberlin, S. J., “Spacing of Spliced Bars in Tension Pull-Out Specimens,” ACI JOURNAL, Proceedings V. 49, No. 12, Dec. 1952, pp. 261-274.

28. Menzel, C. A., “An Investigation of Bond, Anchorage and Related Factors in Reinforced Concrete Beams,” Research Department Bulletin 42, Portland Cement Association, Nov. 1952, 114 pp.

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

30. Chamberlin, S. J., “Spacing of Reinforcement in Beams,” ACI JOURNAL, Proceedings V. 53, No. 7, July 1956, pp. 113-134.

31. Chamberlin, S. J., “Spacing of Spliced Bars in Beams,” ACI JOURNAL, Proceedings V. 54, No. 2, Feb. 1958, pp. 689-697.

32. Mathey, R. G., and Watstein, D., “Investigation of Bond in Beam and Pull-Out Specimens with High-Yield-Strength Deformed Bars,” ACI JOURNAL, Proceedings V. 57, No. 3, Mar. 1961, pp. 1071-1090.

33. Ferguson, P. M., and Thompson, J. N., “Development Length of High Strength Reinforcing Bars in Bond,” ACI JOURNAL, Proceedings V. 59, No. 7, July 1962, pp. 887-922.

34. Ferguson, P. M., and Breen, J. E., “Lapped Splices for High Strength Reinforcing Bars,” ACI JOURNAL, Proceedings V. 62, No. 9, Sept. 1965, pp. 1063-1078.

35. Untrauer, R. E., and Henry, R. L., “Influence of Normal Pressure on Bond Strength,” ACI JOURNAL, Proceedings V. 62, No. 5, May 1965, pp. 577-586.

36. Perry, E. S., and Thompson, J. N., “Bond Stress Distribution on Reinforcing Steel in Beams and Pullout Specimens,” ACI JOURNAL, Proceedings V. 63, No. 8, Aug. 1966, pp. 865-876.

37. Lababidi, M. F., “Bond Stress Distribution Along Reinforcing Bars Subjected to Repeated Dynamic Loadings,” MS Thesis, the University of Texas at Austin, Austin, Tex., 1967, 68 pp.

38. Ferguson, P. M., and Briceno, E. A., “Tensile Lap Splices-Part 1: Retaining Wall Type, Varying Moment Zone,” Research Report No. 113-2, Center for Highway Research, the University of Texas at Austin, Austin, Tex. 1969, 31 pp.

39. Perry, E. S., and Jundi, N., “Pullout Bond Stress Distribution Under Static and Dynamic Repeated Loadings,” ACI JOURNAL, Proceedings V. 66, No. 5, May 1969, pp. 377-380.

40. Warren, G. E., “Anchorage Strength of Tensile Steel in Reinforced Concrete Beams,” PhD thesis, Iowa State University, Ames, Iowa, 1969, 104 pp.

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

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

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

Copyright American Concrete Institute May/Jun 2007

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