Out-of-Plane Stability of Circular Steel Tubular Vierendeel Truss Arches Incorporating Torsional Effects of Chords
Round 1
Reviewer 1 Report
The results of “Out-of-plane stability of circular steel tubular Vierendeel truss arches incorporating torsional effects of chords” are of potential interest. The introduction section provides sufficient background of past literatures.. In the result and discussion section, the results are elaborately discussed with figures and tables. The conclusions are supported by the results. All the references are related to this research and also sufficient. However, the following corrections are to be carried out before the acceptance of the Manuscript.
1. Abstract: Mention your recommendation for future research. Also, Include more results in the abstract
2. Key words: It would be good if the key words are arranged in alphabetical order
3. Strengthen the introduction section.
4. Mention the novelty/research gap of your research.
5. Compare your results with existing literatures.
6. Provide a clear images for graphs.
7. What is your recommendation/future scope of your research? Present it in the conclusion section.
8. Mention your research significance/impact in the manuscript.
Author Response
Comment 1
Abstract: Mention your recommendation for future research. Also, Include more results in the abstract.
Response: Thanks for your valuable suggestions. According to your comment, we add the key results of the work to the Abstract in the revised manuscript (page 1, line 21). A paragraph was added to the end of the Conclusions in the revised manuscript (page 17, line 597) to provide recommendation for future research.
Comment 2
Key words: It would be good if the key words are arranged in alphabetical order.
Response: Thanks very much for your kind review. As you suggested, we arranged the key words to be in alphabetical order in the revised manuscript (page 1, line 26).
Comment 3
Strengthen the introduction section.
Response: Thanks very much for your valuable comment. According to your comment, we revised some sentences and paragraphs of the Introduction to strengthen the background and to smooth the logical flow of the context of this study in the revised manuscript (page 1, line 40; page 2, line 74; page 2, line 80; page 2, line 86; page 2, line 90; page 2, line 95).
Comment 4
Mention the novelty/research gap of your research.
Response: Thanks very much for your valuable comment. Some sentences in the 4th and 5th paragraphs of the Introduction were rewritten to state the research gap of this research in the revised manuscript (page 2, line 100; page 3, line 127). Also, a timeline was added in th revised manuscript to highlight the research gap (page 2, Figure 1).
Comment 5
Compare your results with existing literatures.
Response: Thanks for your valuable suggestion. According to your suggestion, we compared the present results (calculated by equations considering the torsional stiffness of chords) with that by equations from existing literatures, and added a table (page 9, Table 1) to show the increment of the present results in the revised manuscript.
Comment 6
Provide clear images for graphs.
Response: Thanks for your careful review. Some figures were modified with higher resolution ( Figure 2, Figure 3, Figure 6) in the revised manuscript.
Comment 7
What is your recommendation/future scope of your research? Present it in the conclusion section.
Response: Thanks for your valuable comment. As you suggested, we added a paragraph in the Conclusions in the revised manuscript to state future outlooks of this work (page 17 line 597).
Comment 8
Mention your research significance/impact in the manuscript.
Response: Thanks for your valuable comment. As you suggested, we have revised the Abstract (page 1, line 9) and the Introduction (page 2, line 100) in the revised manuscript for clear statement of the research significance.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors have done excellent work on the out-of-plane stability of circular steel tubing; however, to improve further, the following points should be considered:
1. Kindly look at the flow chart / process flow of the paper.
2. It is good if you add equations and their assumptions in the annexure.
3. Add a comparative report from other papers by looking at other geographies and other curves.
4. It is preferable to include / compare realist geometrics.
Author Response
Comments and Suggestions for Authors: The authors have done excellent work on the out-of-plane stability of circular steel tubing; however, to improve further, the following points should be considered:
Thank you very much for your kind review. We carefully read through your comments and made revisions accordingly. The corresponding responses are listed in blue under each of your comment.
Comment 1
Kindly look at the flow chart / process flow of the paper.
Response: Thanks for your valuable suggestions. As you suggested, we added a timeline (page 2, Figure 1) to highlight the research gap and a flowchart to illustrate the design procedure of the stability design of the studied Vierendeel truss arches (page 17, Figure 21).
Comment 2
It is good if you add equations and their assumptions in the annexure.
Response: Thanks for your valuable suggestions. As you suggested, we have added equations and their assumptions in the Appendix to the revised manuscript (page 18, line 619).
Comment 3
Add a comparative report from other papers by looking at other geographies and other curves.
Response: Thanks for your valuable suggestions. We added a table to present the comparison between the present results with the previous results available in existing literatures in the revised manuscript (page 9, Table 1). Also, we modified Figure 8 in the revised manuscript (page 8, Figure 8) to show the difference between the proposed sectional torsional stiffnesses with that from existing literatures.
Comment 4
It is preferable to include / compare realist geometrics.
Response: Thank you very much for your kind review. The dimensions of the Vierendeel truss arches studied in this study come from the standard structural members. According to your comment, we added an engineering case (Tianfu Agricultural Expo Main Hall, Award for structural elegance through integrated design and construction for Structural Awards 2022) as the background of this research in the revised manuscript (page 1, line 32).
Author Response File: Author Response.pdf
Reviewer 3 Report
Out-of plane elastic buckling loads for the pin-ended circular steel tubular Vierendeel truss arches have been obtained in conjuction with the sectional torsional stiffness.
The problem is timely and interesting. The topic of this paper is relevant, timely, and of interest to the audience of this journal. However, a revision is needed to address the following concerns before it can be accepted for publication.
There exist some equations which neither are referred to a scientific reference nor are developed in the present study. They certainly require appropriate references.
The current references are appropriate. However, the reference list is brief. Consequently, some recently published papers about the buckling subject should be added in the reference list and cited properly in the text. For instance,
Design Method of Core-Separated Assembled Buckling Restrained Braces Confined by Two Lightweight Concrete-Infilled Tubes. Appl. Sci. 2023, 13(7), 4306; https://doi.org/10.3390/app13074306
Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method. Mathematics 10 (23), 4429. https://doi.org/10.3390/math10234429
In order to demonstrate the accuracy and validity of the present analysis, a benchmark result should be given in a Table by the comparison with the other previously results ( with or without the sectional torsional stiffness) available in the literature.
Author Response
Comments and Suggestions for Authors: Out-of-plane elastic buckling loads for the pin-ended circular steel tubular Vierendeel truss arches have been obtained in conjunction with the sectional torsional stiffness. The problem is timely and interesting. The topic of this paper is relevant, timely, and of interest to the audience of this journal. However, a revision is needed to address the following concerns before it can be accepted for publication.
Thank you very much for your kind review. We carefully read through your comments and made revisions accordingly. The responses are listed in blue under each of your comment.
Comment 1
There exist some equations which neither are referred to a scientific reference nor are developed in the present study. They certainly require appropriate references.
Response: Thanks for your valuable comment. According to your comment, we double checked our manuscript and added two references for Eq. (1) (page 5, line 209) and Eq. (23) (page 14, line 504).
Comment 2
The current references are appropriate. However, the reference list is brief. Consequently, some recently published papers about the buckling subject should be added in the reference list and cited properly in the text. For instance, Design Method of Core-Separated Assembled Buckling Restrained Braces Confined by Two Lightweight Concrete-Infilled Tubes. Appl. Sci. 2023, 13(7), 4306; https://doi.org/10.3390/app13074306
Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method. Mathematics 10 (23), 4429. https://doi.org/10.3390/math10234429
Response: Thanks very much for your kind review. According to your comment, we strengthened the Introduction section and cited the above recently published papers in the revised Introduction (page 2, line 68).
Comment 3
In order to demonstrate the accuracy and validity of the present analysis, a benchmark result should be given in a Table by the comparison with the other previously results ( with or without the sectional torsional stiffness) available in the literature.
Response: Thanks for your valuable suggestion. According to your suggestion, we added the Table 1 in the revised manuscript (page 9) to compare the benchmark results (considering the torsional effect of chords) with the results (ignoring the torsional effect) using existing equations in literatures.
Author Response File: Author Response.pdf
Reviewer 4 Report
Please read the attachment. Thank you.
Comments for author File: Comments.pdf
Author Response
Comments and Suggestions for Authors: Despite their similar sectional stiffness, steel tubular Vierendeel truss arches rarely examine chord torsional effects on out-of-plane buckling. Sectional torsional stiffness and out-of-plane elastic buckling stresses for pin-ended circular steel tubular Vierendeel truss arches are first calculated. Vierendeel truss arches' sectional and out-of-plane elastic buckling stresses are greatly improved by chord torsional stiffness. Numerical fitting and equilibrium theorem calculate pin-ended and fix-ended out-of-plane flexible buckling loads. Sectional torsional stiffness and elastic buckling stresses depend on it/ic. Out-of-plane inelastic buckling is computed in end-fixed Vierendeel truss arches with large it/ic. Chord torsional stiffness boosts ultimate buckling loads. The calculated reduction factors confirm the design curve b from GB50017-2017 or Eurocode 3 and provide a conservative out-of-plane stability design for circular steel tubular Vierendeel truss arches. In short, the reviewer found that the paper has merits and could be acceptable to publish in future forms. Therefore, please revise the manuscript according to the reviewer's comments.
Thank you very much for your kind review. We carefully read through your comments and made revisions accordingly. The revisions and responses are listed in blue under each of your comment.
Comment 1
The article lacks a straightforward research question and objective. It would have been better if the report explicitly stated its research questions to help readers understand the study's purpose.
Response: Thanks for your valuable suggestion. According to your comment, we improved the Abstract (page 1, line 9) and strengthen the Introduction (page 2, line 74; page 2, line 80; page 2, line 86; page 2, line 95) to explicitly state its research question and objective of the article.
Comment 2
The article lacks a comprehensive literature review, and the author could have included more literature to provide context and background information on the topic.
Response: Thanks for your valuable comment. As you suggested, we cited four more references in the Introduction (page 2, line 72; page 2, line 80) and a research timeline to provide more information on the research context and background (Figure 1) in the revised manuscript.
Comment 3
At the end of the introduction part: please add a paragraph to introduce the manuscript outline.
Response: Thanks for your valuable suggestion. As you suggested, we added a paragraph to the end of the Introduction (page 3, line 127) to introduce the manuscript outline.
Comment 4
Figure 2b: Please add a centerline representation - given the axis of symmetry of the circular cross-section according to engineering drawing standards. Usually, it is represented by a bold dotted line.
Response: Thanks for your valuable suggestion. We added the centerline to the Figure 3b (page 4) in the revised manuscript as you suggested.
Comment 5
Please add the raw data for this investigation.
Response: Thanks for your valuable comment. We added the related raw data to a public repository on GitHub and provided the link (https://github.com/yunfeng-a/ABAQUS.git) at the Data Availability Statement (page 18, line 611) in the revised manuscript.
Comment 6
The article is not clear on the methodology used for collecting data. The lack of information on the data collection process limits the ability of other researchers to reference the study.
Response: Thanks very much for your valuable comment. We have added the source files of the two typical FE models and the original data to a public repository on GitHub (https://github.com/yunfeng-a/ABAQUS.git) (page 18, line 611). This could help other researchers to reproduce the results of this work.
Comment 7
References: There is a shortage of references (only 31 papers). Usually, the connections for a scientific article should be between 30 and 50. Please consider adding these appropriate references to introduce your application for the proposed Finite element methods and optimization design:
+An efficient hybrid approach of finite element method, artificial neural network-based multi-objective genetic algorithm for computational optimization of a linear compliant mechanism of nanoindentation tester.
+ Optimizing compliant gripper mechanism design by employing an effective bi-algorithm: fuzzy logic and ANFIS.
Response: Thanks for your valuable suggestion. As you suggested, we cite the above published papers to state the future outlooks about the optimization design of the structural stability based on the present works in the revised manuscript (page 17, line 603).
Comment 8
Citations in the text and references should be followed the journal template. The reviewer suggests that you should search the International Journal of Applied Science or other Journals for more connections that could be used to enrich your literature review. References should be numbered in order of appearance and indicated by a numeral or numerals in square brackets—e.g., [1] or [2,3], or [4–6]. In the text, reference numbers should be in square brackets [ ] and placed before the punctuation; for example, [1], [1–3], or [1,3]. For embedded citations in the text with pagination, use both parentheses and brackets to indicate the reference number and page numbers; for example, [5] (p. 10) or [6] (pp. 101–105).
Response: Thanks for your valuable suggestion. As you suggested, we corrected citation and reference formation according to the journal template of ‘Applied Sciences’.
Comment 9
Please add a flowchart of the design process.
Response: Thanks for your valuable suggestion. As you suggested, we added a flowchart to clearly state the stability design procedure to the revised manuscript (Figure 21, page 17).
Comment 10
For the finite element method: please provide the node and the mesh numbers in this study.
Response: Thanks for your valuable suggestion. As you suggested, we provided more information on the typical models (2834 nodes and 2984 mesh numbers, page 4, line 173). and submitted the source file to a public repository on GitHub (https://github.com/yunfeng-a/ABAQUS.git).
Comment 11
Please provide a mesh independence test for your manuscript.
Response: Thanks for your valuable suggestion. As you suggested, we provided more information on the typical models and their mesh independence validation test (page 4, line 173).
Comment 12
What type of mesh did the authors employ in this study?
Response: Thanks for your valuable comment. We employed the constant-size meshes to model Timoshenko beam element B31 (A 2-node linear beam in space) in this study. This mesh technique has robust numerical precision in capturing the elastic and inelastic buckling behaviors of steel tubular truss arches.
Comment 13
How did the authors validate the results, and what is the main limitation of this study?
Response: Thanks very much for your valuable comment. The numerical buckling loads were firstly validated by the derived theoretical results for a benchmark case: the simple pin-ended Vierendeel truss arches. Then, the results were validated by the fitted equations and previous benchmark researches for the end-fixed truss arches. The limitation of this study is that these results can only provide a conservative prediction on the out-of-plane buckling loads in the Vierendeel truss arches with rectangular cross-sections at some specific dimensions, as described in this work. For extensive application, much more future works should be done to optimize the stability design. According to your comment, we added the limitation and the research outlooks to the last paragraph in the revised manuscript (page 17, line 597).
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Required corrections have been made.
