Shear Strength Models for Reinforced Concrete Slender Beams: Comparative Analysis and Parametric Evaluation

Round 1

Reviewer 1 Report

The topic is in the journal's scope, and it is fairly well-written which is expected from papers submitted to the Buildings Journal. Researchers have collected a good-size database of experimental data on RC slender beams, analyzed them, and drawn conclusions. However, the current manuscript can use improvements in some areas, as follows:

1.      Overall, this is a well-written manuscript, but some grammatical and formatting issues are visible and a moderate editorial change could be helpful. Here are some examples of these issues:

·         Line 12: ‘has’ needs to change to ‘have’ (grammar error)

·         Line 14: Numbers less than 10 should be shown in letter form.

·         Lines 180-188: Please rewrite and make a coherent paragraph.

2.      Lines 113-114: After mentioning all previous studies, the authors try to build a case for WHY their research was necessary by saying “In summary, the key parameters influencing shear strength of RC slender beams should be further discussed for the existing models”. This is a good start but needs expansion. Thinking about these questions might help: “Overall, what other researchers covered well?”, “what they lacked to address?”, “which models became well-accepted and why?”, etc.

3.      Lines 203, 206, 212, … : In the test, the vertical axis in the following figures is introduced as “V_exp/V_cal” but in Figures 1-4 the vertical axis is “V_test/V_cal”. Please use either and be consistent everywhere.

4.      Lines 20, 236, … : In some occasions in the text, a comparison between models is done by simply saying “better”. Maybe a more scientific way of comparing models would be more effective and informative for the readers. For example: more accurate in this area, more conservative, etc.

5.      Figures 1 & 2: experimental results are compared with code results, and it is shown that in the majority of cases, code predicts higher numbers. Can the authors clarify if they have included the ‘safety factors’ (that codes usually include in calculating the capacity) or not? Table 1 of the appendix shows that in the case of one design code (CSA A23.3) factored strengths are used but not the others.

6.      The authors did a good job analyzing and summarizing the data for each model and provided good statistical insight. However, what seems to be lacking is the structural insight into why a model is doing better in one area versus another. For example, lines 481-484 read “When predicting the RC slender beams with stirrup, the 481 model of Bazant-Kim [40] is more accurate than the rest models because its average strength ratio is closer to 1.0 and the standard deviation and quartile range are smaller than other models”. What characteristic of the Bazant-Kim model makes it to have a good average strength ratio (close to 1) and small standard deviation? In the end, the Buildings Journal is a civil engineering journal, so this type of information may be useful/interesting to the journal audience.

Author Response

The authors wish to thank the editor and two reviewers for their very thorough, insightful,and constructive reviews. All comments have been addressed in the revised version of the manuscript. Original comments of each reviewer have been placed in boxes in this document and specific responses have been placed in italics for ease of reference. In the responses, all the numbers of figures, tables, and lines refer to the revised manuscript, unless otherwise specified. Please see the attachment.

1. The topic is in the journal's scope, and it is fairly well-written which is expected from papers submitted to the Buildings Journal. Researchers have collected a good-size database of experimental data on RC slender beams, analyzed them, and drawn conclusions. However, the current manuscript can use improvements in some areas, as follows:

The authors thank the reviewer for the valuable and careful comments. All of the following comments have been addressed in the revised manuscript.

In order to make the meaning of the full text more clear, the full test has been checked and corrected in the revised manuscript (e.g. Lines 12, 115-116, 183-189 et al.).

1. Overall, this is a well-written manuscript, but some grammatical and formatting issues are visible and a moderate editorial change could be helpful. Here are some examples of these issues:

• Line 12: ‘has’ needs to change to ‘have’ (grammar error)
• Line 14: Numbers less than 10 should be shown in letter form.
• Lines 180-188: Please rewrite and make a coherent paragraph.

The authors thank the reviewer for the valuable and careful comments. The revisions on line 12, 14, 178-185 have been highlighted in red. And the full test has been checked and corrected in the revised manuscript the same formatting issues have been revised, eg. lines 120, 121, 129, 212, 534, 535, et al.

2. Lines 113-114: After mentioning all previous studies, the authors try to build a case for WHY their research was necessary by saying “In summary, the key parameters influencing shear strength of RC slender beams should be further discussed for the existing models”. This is a good start but needs expansion. Thinking about these questions might help: “Overall, what other researchers covered well?”, “what they lacked to address?”, “which models became well-accepted and why?”, etc.

Thanks. The summary of the lack of issues addressed by various researchers have been further added in lines 112-115 of the revised manuscript. “In summary, the key parameters influencing shear strength of RC slender beams are not completely considered evaluated in these models and the parameter classification interval is unclear, so which should be further discussed for the existing models.”

3. Lines 203, 206, 212, … : In the test, the vertical axis in the following figures is introduced as “V_exp/V_cal” but in Figures 1-4 the vertical axis is “V_test/V_cal”. Please use either and be consistent everywhere.

The revision has been made. To keep the text consistent with the figures, V_exp/V_cal has been revised to V_test/V_cal in line 199, 202,209, 214, 218, 229, 309, 319, 323, 332, 386, 446, 473, 496, 538

4. Lines 20, 236, … : In some occasions in the text, a comparison between models is done by simply saying “better”. Maybe a more scientific way of comparing models would be more effective and informative for the readers. For example: more accurate in this area, more conservative, etc.

Thanks. The revision has been made. The word 'better' has been changed to a more informative and effective phrase in line 20, 21, 73, 80, 100-101, 110, 232, 246, 345, 370, 458-459, 547, 553, 555.

5. Figures 1 & 2: experimental results are compared with code results, and it is shown that in the majority of cases, code predicts higher numbers. Can the authors clarify if they have included the ‘safety factors’ (that codes usually include in calculating the capacity) or not? Table 1 of the appendix shows that in the case of one design code (CSA A23.3) factored strengths are used but not the others.

The authors thank the editor for the careful review. In this paper, the safety factor is not included in the calculation of the formula of  codes. For the evaluation of existing formulas, the average value of the measured strength of the material is adopted and the  ‘safety factors’ is ignored. There is some existing literature supporting this viewpoint. For example: (1) Alqarni, A.S.; Albidah, A.S.; Alaskar, A.M.; Abadel, A.A. The effect of coarse aggregate characteristics on the shear behavior of reinforced concrete slender beams. Constr. Build. Mater. 2020, 264, 120189; (2) Hassan, A. a. A.; Hossain, K.M.A.; Lacherni, M. Behavior of full-scale self-consolidating concrete beams in shear. Cem. Concr. Compos. 2008, 30, 588–596.; (3) Angelakos, D.; Bentz, E.C.; Collins, M.P. Effect of concrete strength and minimum stirrups on shear strength of large members. ACI Struct. J. 2001, 98, 290–300., etc. The ‘safety factors’ has been removed.  Please see Appendix Table 1 of the revised manuscript.

6. The authors did a good job analyzing and summarizing the data for each model and provided good statistical insight. However, what seems to be lacking is the structural insight into why a model is doing better in one area versus another. For example, lines 481-484 read “When predicting the RC slender beams with stirrup, the 481 model of Bazant-Kim [40] is more accurate than the rest models because its average strength ratio is closer to 1.0 and the standard deviation and quartile range are smaller than other models”. What characteristic of the Bazant-Kim model makes it to have a good average strength ratio (close to 1) and small standard deviation? In the end, the Buildings Journal is a civil engineering journal, so this type of information may be useful/interesting to the journal audience.

The authors thank the editor for the careful review. The structural insight have been further added in lines 370-374 and lines 478-480 of the revised manuscript.

Lines 370-374: It may be that Zsutty and Gunawan proposed models based on separate analyses of beam action and arch action to minimize extensive dispersion of shear stress values under arch action. As a result of regression analysis of the data, Gunawan and Zsutty considered the effects of shear span-to-depth ratio in the form of (a/d)^-1 and (a/d)^-1/3 respectively.

Lines 478-480: This may be due to the fact that Bazant-Kim [40] applies fracture mechanics to the extension of mortar cracks in the contact area between large aggregate pieces, correlating the concrete strength with the maximum aggregate size. 

Author Response File: Author Response.pdf

Reviewer 2 Report

The subject is very interesting.

Analytical work has been performed methodically.

All major Codes have been covered quite efficiently, except Eurocodes. EC2 is referred in line 85 and elsewhere, but not in subchapter 2.1. EC8-Part3 (concerns existing structures and uses different formulas from EC2) is totally ignored. Inclusion of the relevant formulas would cover the subject more effectively.

As for the models presented, the criteria for their choice seem to be quite arbitrary. Paying a look at Scopus, one can easily verify the following Table.

A very known researcher on the subject (Kotsovos M.) who has formulated the CFP theory, has 126 published 124 documents (more than 100 on the subject) and owns an h-index factor of 24. In his published book by Springer “Compressive Force-Path Method”, a large number of experiments on slender beams are presented and commented. 

By the way, the publication of M. Kotsovos referred at [15] is very old and needs updating and supplementing.

Addition of comparison to Kotsovos’ model would cover the subject more effectively.

Appendix Table 2, 1^st column should be titled “Researcher”, instead of “Design Codes”

Conclusions are rather limited, for the amount of work performed and need supplementation

Comments for author File: Comments.pdf

Author Response

The authors wish to thank the editor and two reviewers for their very thorough, insightful,and constructive reviews. All comments have been addressed in the revised version of the manuscript. The revisions have been highlighted in red. Original comments of each reviewer have been placed in boxes in this document and specific responses have been placed in italics for ease of reference. In the responses, all the numbers of figures, tables, and lines refer to the revised manuscript, unless otherwise specified.

Reviewer #2:

The subject is very interesting.

Analytical work has been performed methodically.

The authors thank the reviewer for the valuable and careful comments. All of the following comments have been addressed in the revised version of the manuscript.

1. All major Codes have been covered quite efficiently, except Eurocodes. EC2 is referred in line 85 and elsewhere, but not in subchapter 2.1.

Agree. A brief introduction about the EC2 has been added in lines 143-144 of the revised manuscript.

2. EC8-Part3 (concerns existing structures and uses different formulas from EC2) is totally ignored. Inclusion of the relevant formulas would cover the subject more effectively.

The authors thank the reviewer for the valuable and careful comments. This paper focuses on the shear strength under concentrated loading. EC8 is a code for the design of structures for earthquake resistance. In EC8-Part3, the relevant formula is used to calculate the shear strength of members under cyclic loading (as defined in defined in EC8-Part3, A.3.3). As a result, the shear strength formula in EC8-Part3 is not discussed.

3. As for the models presented, the criteria for their choice seem to be quite arbitrary. Paying a look at Scopus, one can easily verify the following Table.

The authors thank the editor for the careful review. Formulas are chosen based on different mechanistic models and considering both classical formulas and those proposed in recent years. Please see lines149-168 of the revised manuscript.

4. A very known researcher on the subject (Kotsovos M.) who has formulated the CFP theory, has 126 published 124 documents (more than 100 on the subject) and owns an h-index factor of 24. In his published book by Springer “Compressive Force-Path Method”, a large number of experiments on slender beams are presented and commented. By the way, the publication of M. Kotsovos referred at [15] is very old and needs updating and supplementing.

Thanks. The publication of M. Kotsovos referred at [15] has been updated and supplemented. Please see lines 626-627 of the revised manuscript.

5. Addition of comparison to Kotsovos’ model would cover the subject more effectively.

The authors thank the editor for the careful review. The predictions of the Kotsovos' model has been added and discussed in the revised manuscript, eg. Figure 3, Lines 273, Figure 4, Lines 275 et al. In addition, the prediction results of Fujita model is relatively worst, so the correspongting results have been removed.  

6. Appendix Table 2, 1^stcolumn should be titled “Researcher”, instead of “Design Codes”

Agree. The revision has been made in the Appendix Table 2, 1^stcolumn of the revised manuscript.

7. Conclusions are rather limited, for the amount of work performed and need supplementation.

Agree. The authors thank the editor for the careful review. Conclusions have been supplemented. Please see lines 541-567 of the revised manuscript.

The main factors influencing the shear strength of slender beams mainly include the shear span-to-depth ratio, the effective depth, the concrete strength, and the stirrup ratio. Some factors are considered by these sixteen models are different. According to overall prediction results, the prediction accuracy of the shear strength models from five researchers and seven codes is greatly affected by the presence or absence of stirrups. For researchers’ models, the prediction results of Zsutty’s, Gunawan’s, and Bazant-Kim’s models are more reliable than others for both beams with stirrups and without stirrups, and their average values are between 1.05 and 1.14. For codes, except GB50010 and TS500, the results of other code models for beams with stirrups are less than that for beams without stirrups. For both beams with stirrups and without stirrups, the models of ACI and JSCE exhibit superior prediction accuracy and safety margins with mean values ranging between 1.19 and 1.28.

According to evaluation and discussion of key parameters, the effects of shear span-to-depth ratio, concrete strength and stirrup ratio on shear strength are reasonably considered by Bazant-Kim, Zsutty, and Gunawan’s models. Bazant-Kim and Zsutty exhibit the most reasonable prediction for beams with a/d＜3.5 and Gunawan and Zsutty’s models provide more accurate prediction than Bazant-Kim for beams with a/d≥3.5. For codes, the BS8110 code gives the most safety estimation for RC slender beams with a/d≥3.5. The prediction of JSCE exhibits superiority over those of others for beams with a/d＜3.5 and stirrup ratios (ρsw ≥0). 

There exists a significant size effect in the models in national codes and some research, which has not been well considered. Bazant-Kim give accurate results for the case of d≤450 mm. While Zsutty accurately predict the case of beams with stirrup under d＞450 mm. The prediction of Gunawan is not sensitive to the effective depth, but slightly underestimates the experimental results. For codes, JSCE remain high safety levels for beams under d≤225 mm and d＞450 mm, and BS8110 gives high safety margin for beams under 225mm＜d≤450mm. 

Author Response File: Author Response.pdf