Masonry Dome Behavior under Gravity Loads Based on the Support Condition by Considering Variable Curves and Thicknesses
Round 1
Reviewer 1 Report
The submitted article deal with domes construction. Different idealized case studies, varying the geometry and the boundary conditions have been studied and reported.
The aim of the article seems to investigate the role of the geometry and the boundary conditions in the dome’s behavior, the location and the number of neutral hoops. This approach is addressed by a parametric design of the geometry and an automated finite element analysis procedure, considering shell elements. Such issue is widely investigated by the literature and different approaches for closed form solutions are developed. In addition, more advanced numerical models are present in the literature dealing with more complex problems.
It is difficult to find a novelty in regard to the research point of view. From the practical point of view the provided information is limited.
Author Response
Point 1: It is not easy to find a novelty regarding the research point of view.
Response 1: In previous researches, a double-masonry dome behavior with a single neutral hoop is mentioned. On the other hand, there is no attention to the support condition to determine masonry dome behavior. In this research, a comprehensive definition of masonry dome behavior consists of single, double, and treble masonry dome behavior is presented by determining neutral hoop(s) based on support conditions besides various thicknesses and curves.
By classifying masonry dome based on various support conditions and considering the various thicknesses and curves, the results are:
1- Single masonry behavior; No neutral hoop,
2- Double masonry behavior, all hoops are compressive; Single neutral hoop
3- Double masonry behavior, hoops are compressive and tensile; Single neutral hoop
4- Treble -masonry dome; Double neutral hoops. (No one even mentions this kind of masonry dome behavior)
The using method in this article is so novel, and it is related to the parametric engineering that led anybody to change the parameters and reach the aim.
Point 2: From the practical point of view, the provided information is limited.
Response 2: In this article, an attempt has been made to enable researchers to analyze all types of domes against gravity used for low-risk earthquake regions and the initial process of the other analysis. This method presents a parametric analysis that its variables are changeable and it is extendable to all forms and curves of the dome and various thicknesses. According to their dome’s variable, researchers can analyze domes in terms of gravity load. We will write a code in various standards to analyze models based on lateral loads in future attempts. This article is the beginning of extensive research that enables engineers to analyze their domes in the shortest time against different loads by changing their data.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript has a new form after the revision. I suggest to omit section 4.2 and add units to axes of diagrams of Fig. 8
Comments for author File: Comments.pdf
Author Response
Point 1: The manuscript has a new form after the revision. I suggest omitting section 4.2.
Response 1.1: Section 4.2 is omitted, and some explanation is added end of the method section.
Point 2: add units to axes of diagrams of Fig. 8
Response 2: The units are added to Fig. 5 in the new version.
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper investigates the influence on the dome stress state of the support conditions. To this scope several FEM analyzes have been conducted. In particular, the results of some case studies are graphically and numerically illustrated and comment.
It is opinion of the Reviewer that the paper may be considered for possible publication on the Journal, since its contents are interesting and aligned with the Journal topic. However, before its publication a major revision is need, in order to improve manuscript quality in accordance to the following comments/indications.
Point 1. Introduction. It is not clear the novelty of the paper. Please specify this in the introduction. In addition, Reviewer believes that it should be at least mentioned that the paper is mainly addressed to the dome behavior under vertical (gravity loads). Currently, there are many works in order also to investigate also the seismic behavior of domes, starting also by observing damages suffered in recent earthquakes. Among the others, Authors may refer to:
Lagomarsino, Sergio, and Stefano Podestà. 2004. “Seismic Vulnerability of Ancient Churches: I. Damage Assessment and Emergency Planning.” Earthquake Spectra 20 (2): 377–94. https://doi.org/10.1193/1.1737735.
Fuentes, D. D., Baquedano Julià, P. A., D’Amato, M., Laterza, M., 2019. Preliminary seismic damage assessment of Mexican churches after September 2017 earthquakes. International Journal of Architectural Heritage: 1–21. Published on line
In addition, Reviewer does not understand what is the ‘Springer line’. Please, clarify this in the text. Authors refers to some ‘chosen curves’ that, at this point of the manuscript, are not yet introduced. Please add comment on this.
Point 2. Section ‘Method’. Reviewer believes that this section should be moved after the Section 3, that is the state of art reported in the manuscript. In addition, referring to what is reported in the section method, likely a figure would help in understanding what is explained within.
Point 3. Section ‘Numerical Analysis of Masonry Dome without considering Neutral Hoop’. It is not clear where the assumption of not considering the neutral hoop is reported within this section, and how the studies here invoked are linked to the aim declared within the section title. Please clarify these aspects.
Point 4. Section ‘Karamba Analysis Process’. Reviewer suggests of condensing this part. A question that would be useful to clarify is how the neutral hoop is found.
Point 5. Section ‘Case Studies’. Since support condition is a key aspect of the study Reviewer invites Authors in better specifying the following conditions assumed: Fixed, Free in X and Y, Free in all axes (Domes place on the drum), and Free in all axes (Domes place on the drum with the pendentive). Probably a Figure would help in better understanding this issue.
Point 6. Section ‘Case Studies’. This section is very interesting. However, an explanation of what is reported in the section and on what is the aim of all comparisons will help the Reader in understanding the work. Please, also describe what is reported in Figure 8a-L.
Point 7. It is stated that ‘According to Eddy and Lévy method, developed by Stefano Galassi, Giulia Misseri, Luisa Rovero, and Giacomo Tempesta, cracks are caused by tensile stress’. Please introduce this method and also refer it. Figure 9 should be better commented.
Point 8. Conclusion should be revised according to main findings of the manuscript.
Author Response
Point 1: Introduction
Point 1.1: It is not clear the novelty of the paper. Please specify this in the introduction.
Response 1.1: It is added to the introduction.
Point 1.2: Reviewer believes that it should be at least mentioned that the paper is mainly addressed to the dome behavior under vertical (gravity loads).
Response 1.2: “under gravity Load” is added to the title and abstract. In the introduction section, this issue is explained.
Point 1.3: Currently, there are many works to investigate the seismic behavior of domes, also starting by observing damages suffered in recent earthquakes. Among the others, Authors may refer to:
Response 1.3: Its explanation is added to the introduction, and mentioned articles are referred to as researchers’ attempts.
Point 1.4: The reviewer does not understand what the ‘Springer line’ is. Please, clarify this in the text.
Response 1.4: Springer line is changed to a boundary line.
Point 2: Section ‘Method’ Reviewer believes that this section should be moved after Section 3.
Response 2: The method section is moved after the “Evolution of Masonry Dome Analysis “Section.
Point 3: Section ‘Numerical Analysis of Masonry Dome without considering Neutral Hoop’. It is not clear where the assumption of not considering the neutral hoop is reported within this section and how the studies here invoked are linked to the aim declared within the section title. Please clarify these aspects.
Response 3: As mentioned in Table 1, some architects design masonry domes based on geometry, and the others analyzed them by reversing the catenary shape of the rope. Therefore, their analysis method was based on geometry and shape, such as thrust lines. This section shows the history of the masonry domes analysis evolution without using the neutral hoop in their design and analysis. In the continuation of the previous part, the next part of this section presented the numerical analysis of the dome based on the thrust line with the neutral hoop in the following previous part.
Point 4: Section ‘Karamba Analysis Process.’ The reviewer suggests condensing this part. A question that would be useful to clarify is how the neutral hoop is found.
Response 4: This section has been deleted in the revised version. The condensing part is added to the end of the method section.
Point 5. Section ‘Case Studies’. Since support condition is a key aspect of the study Reviewer invites Authors to better specifying the following conditions assumed: Fixed, Free in X and Y, Free in all axes (Domes place on the drum), and Free in all axes (Domes place on the drum with the pendentive). Probably a Figure would help in better understanding this issue.
Response 5: In the revised version, the assumed support conditions are illustrated in Figure 4.
Point 6.1. Section ‘Case Studies’. This section is very interesting. An explanation of what is reported in the section and all comparisons will help the Reader understand the work.
Response 6.1: This section's primary aim is to represent the masonry dome behavior by determining the number of the neutral hoop(s). This aim is shown in Table 12.
Point 6.2. Please, also describe what is reported in Figure 8a-L.
Response 6.2: Figure 5a-L (in the edited version) shows the effect of support condition on p.s σ1 (hoop stress) classified based on the dome’s curves. This Figure shows the difference between various dome curves. Also, it shows the neutral hoops and the compression and tension area on domes.
Point 7. It is stated that ‘According to Eddy and Lévy method, developed by Stefano Galassi, Giulia Misseri, Luisa Rovero, and Giacomo Tempesta, cracks are caused by tensile stress. Please introduce this method and also refer to it. Figure 9 should be better commented.
Response 7: Eddy’s method is explained comprehensively in section 3.2, but the Eddy and Lévy method is added to section 4.4.
Point 8. The conclusion should be revised according to the main findings of the manuscript.
Response 8: The conclusion has been revised according to the main findings of the manuscript. The first paragraph is about the importance of support conditions. The results of four types of support conditions are mentioned in the next four paragraphs. The fifth paragraph is relative to the results of the dome’s thickness and curves, and all types of masonry dome behavior are described in the last paragraphs.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The present article does not provide any significant modification in respect to the previous submitted versions. I do not find an essential improvement of the manuscript, generally speaking or in respect to the previous comments I have raised. The text has only some slight modification in order to avoid some "conflicts" with the previous comments, however the essence of the work is the same.
I still highlight that masonry domes are well studied in literature and very advanced concepts of their investigation are available. Still the following points, in my point of view are not properly addressed.
- objectives of the research work.
- the numerical strategy refers only to parametric design however a vast issue of numerical approaches is not even mentioned or treated.
- what is the novelty of the article and the practical value of the approach.
In this regard I suggest to decline the article for further consideration.
Author Response
Points:
objectives of the research work.
the numerical strategy refers only to parametric design; however, a vast issue of numerical approaches is not even mentioned or treated.
what is the novelty of the article and the practical value of the approach?
Response:
Thank you so much for taking the time to review this article. You made general comments that are very valuable, and the authors have tried to apply the points in the revised article. The correction, based on the opinions of all authors, from the beginning until now, is as follows:
1- Changing the general form of the article based on its main variable:
The initial article was based on the number of neutral loops; some case studies with different curves and thicknesses were added to the article after the reviewer's request—this subject increased pages from 18 to 26 pages. Therefore, the article form is arranged based on the support condition. Two reviewers have prepared this form of the article, and they have announced that they have accepted this article based on this form.
2- English Language: The authors have used the powerful Grammarly software after the corrections made on the original article by English language experts. This software is used professionally for editing scientific articles. I sent reviewers its document in the previous step.
3- As mentioned before, the design objectives are based on the analysis of masonry domes based on gravity loads to obtain tensile and compressive zones in the dome. This analysis is used as a preliminary study in specialized analysis on a special building. On the other hand, this research is the ultimate goal for domes in low-risk earthquakes. This research can help architects in the initial design step and help engineers strengthen, restore, and conserve them.
4- In this research, a new computational method has been used to allow engineers to analyze wide forms of domes with various parameters. This article introduces parametric design in dome calculations, and with its development, various earthquake calculation methods such as pushover can be added to it.
5 - Different strategies have been done on numerical calculations, each of which is about a specific issue and not general—for example, calculating the dome's failure point under the loads. Nevertheless, in this article, the dome's behavior has been considered generally, and calculations have been made to find the dome's behavior. As you know, specialized topics such as the dome's failure point under the loads are related to various parameters, including the arrangement of bricks and mortar, and also should pay special attention to the specific materials used for each building and cracks on the dome and the construction weaknesses of the dome should also be considered. On the other hand, in earthquake calculations, the dome alone can not be used as a criterion and should be studied in the building complex. Also, earthquake calculations have lots of parameters that greatly increase the variables of the article. In addition, it must be calculated a few special case studies that could not give general instructions in design to architects and restorers. In addition to the mentioned numerical analysis in section 3.4, the computational strategy in this article is only to achieve the general behavior of the dome based on gravity loads, which will surely be developed in the future based on the programming in the current plugin. At this step, first, attention is paid to the general behavior of the dome, which is very useful for designs made by architects and restorers.
6. The diversity of numerical approaches is not comprehensively mentioned because earthquake analysis has been mentioned in most of them. In this paper, since the discussion of earthquakes is not mentioned, these approaches are not discussed in general, and only numerical calculations related to gravity loads are mentioned.
7- In this research, unlike the achievements of previous researchers, the second neutral hoop has been obtained, which shows the new behavior of masonry domes behavior under gravity load. Therefore, the innovation of this research is based on achieving a new behavior of the dome under gravity loads. Another new behavior in the masonry dome is a neutral hoop with a quite compressive behavior. Therefore, four types of masonry dome behavior have been identified, two of which are completely new and innovative.
Generally, the authors attempt to catch the satisfaction of all reviewers, although their opinions are not aligned. All article's forms and variables and the arrangement of the contents have been made based on the reviewers' opinions and comments in detail. Therefore, it is the authors' honor to revise the article according to your valuable comments in detail to improve the article's quality better than before.
Reviewer 3 Report
The paper has been revised in detail according to the comments provided. Reviewer suggests of accepting the revised paper in the current form.
Author Response
Point1: The paper has been revised in detail according to the comments provided. The reviewer suggests accepting the revised paper in the current form.
Response 1: Thanks for your accurate review and valuable comments. The authors have made all efforts to implement all your comments and have revised the article according to your opinion. It is our tremendous honor to caught your satisfaction.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
The paper is dealing with masonry domes. The authors make a wide literature review and then they study the number and the position of neutral hoop of domes with various support conditions and crown. The part of the manuscript that presents the research is poor and of not a good quality and must be enriched with more data from the study.
Specific comments are on the attached pdf file
Comments for author File: Comments.pdf
Reviewer 2 Report
The presented paper treats a wide and well studied structural typology, masonry domes. Domes are one of the most classical construction typologies, being sustainable, long-lasting constructions, architecturally elegant, and moreover part of architectural heritage in most cases. Many approaches of their analysis and conservation strategies are available in the literature. Some of these are referred to in the text, however a vast and important works are not referred.
The structure of the text is quite confusing and very poorly constructed in terms of readability, consistency and presenting sound results. The following aspects have been challenging to be found in the present article:
- objectives of the research work!
- the numerical strategy is not very clear!
- what is the novelty of the article?
- what is the meaning of novel behavior of masonry domes? (“novel behavior” is quite a strange term!)
- it is not clear why was paid so much attention to Newton-Raphson method!
Generally speaking, the research has many flaws, and in the present form it is difficult to distinguish the aim and how it was achieved. It resembles that the main conclusion was to observe and report where were located the zero-stress zones in a dome. Being very confusing, both the followed strategy and methodology, everything becomes questionable for a research article.
My consideration is to decline the present article. The authors are encouraged to widen their study and research and compare with more similar papers and consider rewriting their work according to an acceptable form.
Reviewer 3 Report
This research presents a computational study on the hoop stresses and “neutral hoops” in masonry domes. In general, the literature review and general flow of the submitted manuscript are ok. However, the research does not seem to be complete. The variation of the hoop stresses in a masonry dome is a well-studied subject in the literature, and the reviewer could not find novel or new information about this issue in the article. The support condition certainly influences the hoop forces, as expected. However, the outcomes of this study can not be generalized. Authors should provide more comprehensive results considering different dome geometries with varying curvatures.
