Flexural Design of Concrete Beams Reinforced with High Strength ...

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The simplified elastic-plastic relationship with a yield strength of 100 ksi (690 MPa) was selected to be consistent with the yield strength requirements of ASTM  ...
Closure on Flexural Strength Design of Concrete Beams Reinforced with High- Strength Steel Bars.

The authors would like to thank Dr. Windisch for his insightful and constructive discussion. The following response addresses the questions raised by Dr. Windisch.

• The simplified elastic-plastic relationship with a yield strength of 100 ksi (690 MPa) was selected to be consistent with the yield strength requirements of ASTM Standard A 10351 for certain high- strength steel reinforcements. The authors recognize that the proposed elastic-plastic stress-strain relationship would provide quite conservative predictions of the strength capacity compared to the actual non-linear stress-strain relationship. However, it is their purpose to present a simple and conservative method for practical design without having to perform non-linear analysis by practicing engineers.

• The proposed tension-controlled strain limit of 0.009 was selected to ensure that a concrete beam reinforced with high-strength steel and designed using the proposed simplified method would exhibit desirable behavior according to the deformability criteria outlined in the paper. For a given cross-section with a given concrete strength the high-strength steel reinforcement was designed, using the material behavior of the steel defined by Eq. (1) in the paper, to satisfy the tension controlled strain limit of 0.0066. For the same cross- section, concrete strength and reinforcing details the nominal flexural strength of the section was calculated using the simplified 100 ksi (690 MPa) model. The corresponding strain in the steel, using the simplified model, was found to be equal to 0.009. The same analysis was conducted for sections with various concrete strengths ranging from 4 ksi (28 MPa) to 10 ksi (69 MPa). The strain limit of 0.009 was found to be consistent in all cases. The difference between the tension-controlled strain limits for the two models is primarily due to the difference between the calculated stress in the tension steel at the 0.0066 strain limit and the difference of the neutral axis depth calculated using both models as summarized in Table 3 of the paper.

• According to section 10.3.3 of the ACI 318-08 building code2 the compression controlled strain limit is defined as the net strain in the tensile reinforcement at balanced strain conditions. For Grade 60 reinforcing steel this corresponds to a compression-controlled strain limit of 0.002. Using the proposed simplified 100 ksi (690 MPa) model, the tensile strain in the reinforcement at balanced strain conditions is 0.0034. To simplify the expression for the capacity reduction factor, φ, in the transition region a compression controlled strain limit of 0.004 was selected. While this is not strictly consistent with the definition provided by ACI 318-08, the authors feel that it represents a reasonable simplification for design purposes, particularly in light of the analyses that were conducted, and described in the paper, to verify the elastic behavior of beams designed using the proposed strain limit.

Similar to the ACI provisions, the proposed compression-controlled strain limit of 0.004 is independent of the concrete strength. While high-strength reinforcing steel can be used in conjunction with normal- strength concrete, the use of high-strength concrete together with high-strength reinforcing steel would result in a more efficient design.

• The proposed design guidelines were formulated to be consistent with the requirements of the ACI 318 building code2. The current ACI code does not include limitations on allowable crack widths. Rather, cracking is controlled by placing a limitation on the maximum spacing between longitudinal reinforcing bars to ensure a uniform distribution of flexural cracks along the length of the beam. The discussion of crack width presented in the paper was intended as a representative example to indicate that, in one example, using the proposed guidelines did not results in excessive cracking of the beam. The crack width of 0.02 in (0.5 mm) is used to illustrate the approximate magnitude of the crack width which can be expected using the proposed design guidelines. The reported crack width is not intended to be a precise, definitive measure of the expected crack width. Nevertheless the reported crack width of 0.02 in (0.5 mm) is on the same order of magnitude as the allowable crack width of 0.016 in (0.4 mm) allowed by the Eurocode 2 for aesthetic purposes.

• The authors agree that the proposed guidelines are conservative and therefore do not represent the most efficient use of the high-strength characteristics of the steel. However, the proposed guidelines represent an incremental increase the allowable yield strength of steel that may be used in design. This could possibly result in a gradual, safe integration of high-strength reinforcing steel into the ACI 318 code.


1. American Society for Testing of Materials. (2007). Standard specification for deformed and plain, low-carbon, chromium, steel bars for concrete reinforcement. ASTM A 1035-07. West Conshohocken, PA: ASTM International. 2. ACI Committee 318. “Building code requirements for structural concrete (ACI 318-08)”. American Concrete Institute: Farmington Hills, 2008.