Reinforced Concrete Corbels-Shear Strength Model and Design Formula. Paper by Gaetano Russo, Raffaele Venir, Margherita Pauletta, and Giuliana Somma/AUTHORS’ CLOSURE

Reinforced Concrete Corbels-Shear Strength Model and Design Formula. Paper by Gaetano Russo, Raffaele Venir, Margherita Pauletta, and Giuliana Somma/AUTHORS’ CLOSURE

Muñez, Pedro R

Discussion by Pedro R. Muñez

PhD, Principal of PRM Engineering, Structural Consulting Engineers, Newburyport, Mass.

The behavior of corbels or brackets to support the vertical shear forces Vu and the horizontal forces Nu can be greatly enhanced by providing a steel rod in the middle of the strut section of the corbel that resists the crushing forces (flexural compression).

Similar to what is done with concrete columns that are reinforced vertically with steel bars, the same could be done with this strut portion of the corbel, providing a much more higher axial load capacity, with this portion becoming a reinforced strut where both the concrete section of the strut and the steel bar embedded in the middle of the strut both contribute to the axial load in proportion to their corresponding cross-sectional properties of concrete and steel.

Similar to what is done with steel brackets supporting loads in cantilever, this reinforced strut into the corbel will provide a more reliable strength to support the external loads.

The authors mention in the second paragraph that “all the failure modes tend to converge into a single topology of failure mode called beam-shear failure.” They also indicate that one of the failure modes is the diagonal splitting, which is characterized by the opening of one or more diagonal cracks followed by shear failure in the compressed zone of the strut.

The discusser believes the authors should take into account that, by introducing a steel rod in the middle of the strut section, this part of the strut-and-tie model will provide added strength to the strut, which will minimize the effects of softening of the concrete in the strut, which will in turn minimize the cracked conditions and premature shear failures in the strut.

A suggestion to the authors and future researches would be to look into incorporating some type of steel reinforcement in the strut section as shown in the following edited version of Fig. A. Ast is the steel bar in the concrete strut, making it a reinforced concrete strut.

The diagonal steel reinforcement in the strut Ast becomes a principal diagonal reinforcement of the corbel. This is not a current practice right now, but it is very effective and costeffective way to reinforce the corbel and to enhance the loadcarrying capacity of the corbel.

The authors indicated that “The stirrups contribute to the corbel shear strength by increasing the compressive strength of the concrete strut, the resistance due to the aggregate interlock, and the dowel action at the cracked interface.” Why not eliminate too many of the unknowns; and by including the steel bar in the strut section, it is possible to get a better prediction of the strength provided by the reinforced strut section.

The compressive force in the strut Cc, noted in Eq. (16), will have another component that will be due to the stress in the steel bar in the strut times the cross-sectional area of the steel in the strut. This additional component will provide a more direct way to support the compressive force in the strut by the added steel bar, and will avoid a premature failure mode in the strut section due to shear failure.

It would be interesting to hear from the authors what they think about the possibility of extending their research work by incorporating a reinforced strut section and study the failure modes to see what enhancements could be achieved by reinforcing the compressive strut in the corbel.

AUTHORS CLOSURE

Reply to discussion of Lu and Lin

The discussion of Lu and Lin suggests that extending the application of the proposed formula to corbels with shear span-to-depth ratios (a/d) > 1 is relevant and will be taken into account by the authors. It will be possible to extend the formula by taking into account further investigations on experimental results about the shear strength of corbels with a/d > 1. Reference 25 cited by the discussers will also be considered. However, the paper of Hwang and Lee25 was not taken under consideration because the first submission of the paper goes back to a period immediately after the publication of Hwang and Lee,25 and the authors did not see this publication.

Regarding the comparison between the SST model by Hwang and Lee25 and the proposed formula (Eq. (46)), it has to be stressed that Eq. (46) is proposed to calculate the nominal value of the corbel shear strength. Hence, in some cases, the formula can be unconservative in the prediction because the numerical coefficient c1 = 0.8 that appears in it has been calibrated to obtain an average of experimental-tocalculated shear strength ratios equal to 1. Consequently, Eq. (46) cannot be used for design. Therefore, Eq. (53) is proposed in the paper. According to Eurocode rules, Eq. (53) provides that no more than 5% of the specimens are unsafe. This has been obtained by multiplying Eq. (46) by the coefficient 0.69. Consequently, Eq. (53) is the one to be compared with the discussers’ model.

The experimental-to-calculated shear strength ratios provided by Eq. (53) are shown in the last column of Table B, which is otherwise the same as Table A presented by the discussers. The conservativeness of the proposed design formula (Eq. (53)) is assessed by the average of experimentalto- calculated shear strength ratios, which is equal to 1.17.

In conclusion, the design formula (Eq. (53)) proposed in the paper is conservative as is the SST model,25 the average of the former being equal to 1.17, while the average of the latter is 1.13.

Reply to discussion of Muñoz

The discusser’s suggestion to introduce a steel rod in the middle of the strut section to provide a much greater axial load capacity of the strut is very interesting and has to be evaluated.

The authors agree with the idea that the contribution of the steel may be taken into account in the compression force in the strut Cc. The presence of only the steel rod in the middle of the strut section, however, does not appear sufficient to greatly increase the strength of the strut, essentially for two reasons.

First, if high forces are applied to the corbel, relative slip may occur between the rod and the surrounding concrete (because the rod is stiffer), giving rise to bond forces. The radial components of the bond forces are balanced against rings of tensile stress in the concrete.26 These tensile stresses have to be added to the other tensile stresses, perpendicular to the strut, caused by the compression parallel to the strut. The combination of both tensile stresses may lead to an earlier splitting of concrete parallel to the axis of the strut.

Moreover, as the steel rod is under compression and not tied by stirrups, instability may arise, further aggravating the condition of the concrete.

In a recent work,27 specimens with reinforcing bars positioned in the direction of the concrete strut have been tested. Even with the bars yielding in compression, the nodal efficiency factor Βs (ACI 318-0528), appearing in the equation of the effective compressive strength fcu of the concrete in a strut ( fcu = 0.85Βs fc?), was not increased by the steel reinforcement.27 Brown et al.27 also highlighted that in Eq. (A-4) of ACI 318-05,28 Appendix A, bars that are parallel to the anticipated cracking direction are not included for the purposes of reinforcing the strut. For these compression bars, the sine term is zero, and thus the compression bars do not affect the efficiency factor.

Higher efficiency factors are obtained, in general, by introducing reinforcing bars crossing the concrete strut (typical shear reinforcement) with the aim of resisting to the tensile stresses and limiting concrete cracking.

In light of the previous considerations, it appears more convenient to place not only longitudinal steel rods in the concrete strut, but also transversal reinforcement. A dual contribution may be obtained in the following ways: the contribution to the strut compression strength due to the longitudinal compression reinforcement, and the increase of concrete strength due to confinement exerted by the transversal reinforcement, which can also limit concrete cracking.

To extend the research work by incorporating the reinforced strut section would be possible if a sufficient number of experimental results will be obtained or found in the literature. The 243 test data used to build up the proposed formula are relevant to specimens without a steel rod in the middle of the strut section of the corbel. The only specimens of this type known to the authors at the time the paper was written had been tested by Kriz and Raths1 under combined vertical and horizontal loading. These researchers placed steel rods in the middle of the strut between the loading plate and the supporting plates to eliminate frictional restraint to lateral deformations during the test.

REFERENCES

26. Tepfers, R., “Cracking of Concrete Cover Along Anchored Deformed Reinforcing Bars,” Magazine of Concrete Research, V. 31, No. 106, 1979, pp. 3-12.

27. Brown, M. D.; Sankovich, C. L.; Bayrak, O.; and Jirsa, J., “Behavior and Efficiency of Bottle-Shaped Struts,” ACI Structural Journal, V. 103, No. 3, May-June 2006, pp. 348-355.

28. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05),” American Concrete Institute, Farmington Hills, Mich., 2005, 430 pp.

Copyright American Concrete Institute Nov/Dec 2006

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