Steel Failure of Anchor Channels Under Fire Conditions—Proposal for a Temperature-Based Design Method

Round 1

Reviewer 1 Report

The steel failure of anchor channels under fire conditions is being addressed in this paper. The aim of the study is to examine the resistance behaviour of anchor channels under fire while presenting a  design model for steel-related failure models. The authors have used 3D FEA model incorporating the ISO 834-1 fire conditions to model the fire behaviour of anchor channels in uncracked concrete. The study is innovative and relevant to the design sector as it provides a more efficient, cost-effective, and scalable method for fire resistance evaluation. This provides a rational design approach, reducing reliance on expensive fire tests. The approach of the study is interesting and original, and the paper is well written with very minor sense remarks. The conclusions made on this study align with the presented evidence, demonstrating that the proposed model  conservatively predicts fire resistance, and it can be applied to more generalized conditions.

The following lines will need to be improved to provide clarity.

Lines 192- 193: “A 3D model was developed. The geometrical aspects of anchor channels that do not  allow 2D or 1D simplification.”

Author Response

Dear Reviewer 1,

Thank you for the valuable comments. Please find below our proposed resolution:

Comment: Lines 192- 193: “A 3D model was developed. The geometrical aspects of anchor channels that do not  allow 2D or 1D simplification.”

Proposed resolution: The sentence was modified to reflect the author's intention: "A 3D model was developed. The geometrical aspects of anchor channels that do not allow 2D or 1D simplification because the channel and bolt are not axisymmetric and because the problem includes two materials (steel and concrete)."

Reviewer 2 Report

Details of the article are included in the earlier sections of the review and are further described in the attached file.

Details of the article are included in the earlier sections of the review and are further described in the attached file.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 2,

Thank you for your valuable comments. Please find our proposed responses below:

 

Comment: The suggestions in the paragraph between lines 143 and 148 are not entirely clear to me! What manipulations are being referred to here?

Response: The following text (underlined) has been added to better reflect the authors' opinion: "

 

The assessment of the fire test results is based on a minimum of 5 tests of which 4 tests shall show a failure time of more than 60 minutes in order to presumably cover the whole fire resistance duration. This method allows for manipulation of the assessment via selective testing where the obtained test results would favor the obtention of a relatively higher trend curve (or line) based on the potentially better statistical distribution of the results (Figure 2). Densifying the test effort on one side of the curve (beyond the minimum test effort of 5 fire tests) would put a higher statistical weight on that part contributing to a pseudo-enhancement of the performance. The opposite also stands true where if the manufacturer wants to add more fire tests in the intent of enhancing the statistical distribution and hence obtaining a more representative behavior, if the tests yield relatively long failure times, the evaluation method leads to shifting the curve further down giving a pseudo-reduction of the performance."

 

Comment: Figure 2 is also not entirely clear! After analysing the first two chapters, I get the impression that they are only intended for people already familiar with the topic presented. 

Response: Correct. This figure is extracted from EAD 330008. The application of European Assessment Documents is only of interest to Technical Assessment Bodies (TABs) applying their guidelines to Manufacturer applications to access the European Market via CE marking for their construction products. Some of test and evaluation methods in these EADs have been developed a long time ago where little knowledge was available and "leaps of faith" were made. The goal of our paper here is to modernize the fire design part of this construction product (anchor channels).

 

Comment: The graphs presented in Figures 3 and 4 comply with the referenced standard [20]. In Figures 3 and 4, the temperature axis is incorrectly described (it is temeprature and should be temperature).

Response: Thank you for catching this. The axis titles for Figures 3 to 7 have been corrected.

 

Comment: The graph shown in Figure 5 is referenced in the referenced standard [19], but relates to the selected moisture content of the concrete mass - u = 1.5% to be exact. Why was this moisture content chosen when three levels of 0, 1.5 and 3% are given in the standard [19]?

Response: The moisture content of 1,5% was adopted because it has been established a few years ago that this moisture content (along with the French assumption for the conductivity curve) give the most accurate predictions of calculations compared to fire test measurements. These assumptions have been reflected in the practice of the anchor industry in EOTA TR 082, and in the practice of reinforced concrete in the second generation Eurocode 2 (EN 1992-1-2:2023).

 

Comment: The diagrams shown in Figures 6 and 7 are referenced in the referenced standard [19]. In Figures 5, 6 and 7, the temperature axis is incorrectly described (it is temeprature and should be temperature).

Response: Thank you for catching this. The axis titles for Figures 3 to 7 have been corrected.

 

Comment: What does section 3.3.5 of the article refer to (there is only a title!)?

Response: The authors looked for this section and couldn't find it in the manuscript. Please provide more information on the wherabouts of this error (page, line or position in relation to a Figure or Table).

 

Comment: In figure 11 there needs to be a distinction between graphs e.g. a, b and c.

Response: The three sub-graphs were named (a), (b) and (c). The text below the figure was updated to reflect this as well: 

The method described in the previous equations and figures is summarized in Figure 11 for all steel-related failure modes. "First, the temperature of the different parts of the anchor channel are obtained through finite element modelling (Figure 11 (a)). It should be noted that the temperature of the anchor was taken at the hottest part (closest to the fire exposed surface), i.e., the temperature at the channel/anchor connection. Then, using the previously determined strength reduction factors for each failure mode (Figure 11 (b)), it is possible to associate the temperature at a given time under fire conditions with the temperature-dependent reduction factor giving the fire resistance vs. exposure time relationship (Figure 11 (c))."

 

Comment: In figure 11a you cannot see the temperature distribution in the anchor marked in grey (maybe we need to
introduce markers?)

Response: It should be noted that the temperature of the anchor was taken at the hottest part (closest to the fire exposed surface), i.e., the temperature at the channel/anchor connection. This makes the green and grey curves superimpose. This has been reflected in the text before the Figure.

 

Comment: In figure 11b most of the graphs overlap and the graph becomes unreadable - need to change!

Response: Changinf this graph means that we will need to introduce 4 new graphs just for the reduction factors. The authors believe that the tables giving the values of the reduction factors above are sufficient. The intent of this graph is purely informative. Therefore, we propose to keep it as it is.

 

Comment: The horizontal axis in figure 11b does not represent time, but temperature!

Response: Thanks for this catch! This has been corrected.

 

Comment: I am surprised by the results shown in figure 12. Rather this temperature distribution is appropriate for concrete heated from below, but I have doubts about the steel of the rail and the fixing anchor in the concrete. Why does the temperature not propagate along the anchor fixed in the concrete? 

Response: The boundary conditions presented in Figure 8 demonstrate the studied problem. Fire coming from below in Figure 12 is the design case the authors are trying to address. The exposed surfaces of concrete and steel are not protected from the ISO 834-1 fire conditions. The isotherms show a curved tendency demonstrating the steel's capacity to create a thermal bridge towards the inner parts of the concrete element. This has been also shown in other studies on different anchor technologies (i.e., bonded anchors under fire conditions, see Al-Mansouri, 2020). We would like to invite the reviewer to consider the association between the colors in the legend on the left hand side and the isotherms (clear blue to dark bue show a gradient varying from 425°C to 84°C). This shows that the temperature indeed propagates through the anchors. The temperature however cannot propagate through the bolt attached to the lips of the channel because this is a steel to steel connection between the bolt and the lips. Nothing connects the bolt to the back of the channel (gap), therefore, temperature cannot diffuse higher in this point compared to the channel/anchor situation presented above.

 

Comment: The proposed method fundamentally overestimates the fire resistance results of the fixings (even more than twice - this does not harmonise with Figure 19 - please explain!) compared to the fire tests (Figures 13, 14 and 17). This is not exactly a positive result!

Response: Correct. The method is conservative and its lvel of conservatism is assessed and presented in Figure 19. Conservatism in fire design may come from different factors presented above Figure 19. If the goal was to show correct predictions, then the entry data should be based on mean ultimate properties of concrete and steel (on the thermophysical properties and the strength properties). The authors believe this is not a negative point and propose to accept the arguments presented above Figure 19. The ratio of 1/3 (lowest calculated/tested value) may be considered relatively good because in the anchor industry, significantly lower values (much higher conservatism) have been accepted for fire design (i.e., fire design of bonded anchors).

 

Comment: In Figure 15, on the other hand, we observe the opposite situation (it is a safe situation)! In contrast, a very
good agreement between the results of the proposed method and the fire tests is obtained in Figure 16. Table 8 is not very clear. Please indicate clearly what is the result of the test (measured value) and what is the result of the model (calculated value)! The conclusions are very general. In my opinion they poorly summarise the work done. Indeed, I agree with the
authors that the model needs further validation. 

Response: Figures 13 to 17 aim to isolate the calculation for each failure mode in comparison to the fire test results. This come in handy when the evaluators and manufacturers wonder for example about the choice of not conducting tests in mid-span to assess the flexural strength of the channel through fire tests (some failure modes would never show up in a fire test). This is also beneficial because it shows that, for the case of anchor channlels directly exposed to fire conditions, the failure of the bolt and lips always govern and may alternate from one to the other for different fire exposure times. The level of reduction of some failure modes (i.e., bolt) compared to others (i.e., lips) shows that an error may be made when mising all steel-related failure modes in a single evaluation (the EAD method). This is explained to some extent between Figures 17 and 18.

 

Comment: The literature is modest. It comprises 26 items (including only 12 articles!). Of the 12 articles, as many as 6 are articles by the authors of this work themselves. Surprisingly for a journal article, as many as 5 doctoral theses are cited here (items 5, 9, 10, 14 and 23, including one by the authors at number 5)! I believe that these are not published materials! Eight items in the literature list are standards and legislation. The literature item under number 17 was not recognised! 

Response: This issue was raised by the editor and other reviewers. We acknowledge the concern regarding the proportion of self-citations in the original manuscript. The field of post-installed anchors under fire exposure is indeed highly specialized, and much of the most recent and detailed experimental and analytical work has been carried out by our institution (CSTB). As a result, several of our past publications constitute key references for the current state of the art. That said, we have revised the manuscript to expand the literature review and now include 5 references authored outside our group (up from 3 previously), alongside 14 internal references (totaling 19). We have carefully selected external sources based on relevance and recency, although the number of publications directly related to this specific topic remains limited internationally. We trust that the revised balance reflects both the importance of CSTB's contribution to the field and our efforts to integrate broader context where available.

Reviewer 3 Report

In general, the work is of good value. Meanwhile, I have the following comments

• The calibration process of the numerical model wasn't described.
• Important definitions and abbreviations haven't been stated.
• The conclusions aren't sufficient enough.

In general, the work is of good value. Meanwhile, I have the following comments

• There are some spelling and grammatical mistakes that need to be corrected e.g. "Thy" in line 28.
• The calibration process of the numerical model wasn't described. The results shown in figures 13, 14, 15 and 17 show significant differences between the experimental results and the numerical model results which points out that the model isn't calibrated.
• The results shown in figures 13, 14, 15 and 17 show that the experimental results don't include any tests done at fire durations less than about 45 minutes. Please provide reason(s) for that.
• Important definitions and abbreviations haven't been stated including terms such as "NRk,s,a,fi", "NRk,s,c,fi", "NRk,s,l,fi", "NRk,s,fi"and "NRk,s,flex,fi". Please rectify that.
• The conclusions aren't sufficient enough whether in terms of not including any numerical values and/or percentages or in terms of relating the conclusions to the results.

Author Response

Response to Reviewer 3:

Thank you for the helpful comments. Please find our responses below:

1. Spelling and grammar:
   We have corrected the typo mentioned ("Thy") along with other spelling and grammatical issues throughout the manuscript.

2. Calibration of the numerical model:
   Each of the figures (13, 14, 15, and 17) shows the capacity related to a specific failure mode. The goal was not to calibrate a global model but to compare each failure mode individually with the fire test results. This approach helps explain, for example, why flexural failure does not occur in fire tests, while lip and bolt failures are more likely. This is clarified in the text.

3. Lack of tests under 45 minutes:
   According to EAD 330008, at least one test point is required between 30 and 60 minutes, with four more above 60 minutes. The tests were planned accordingly. The goal of this paper is to show the inadequacy of the old rules adopted in the EAD and to modernize fire design through a temperature-based approach.

4. Missing definitions:
   The terms “NRk,s,a,fi”, “NRk,s,c,fi”, “NRk,s,l,fi”, etc., are defined in Section 3.5. We’ve made their presence more visible for clarity.

5. Conclusions:
   We believe the conclusions are in line with the objectives of the paper. They summarize the key findings, particularly regarding which failure modes govern under fire. A more detailed discussion with numerical proposals is planned for future work within standardization groups such as EOTA, CAMA, and EN 1992-4.

Reviewer 4 Report

The paper presents a novel and well-structured approach to the fire resistance design of anchor channels, leveraging numerical simulations and temperature-based reduction factors. This work is a significant contribution to the field of fire engineering for anchor channels and offers a promising alternative to traditional testing methods. The following major comments need to be addressed before publication:

1. The abstract should be improved by adding some quantitative results.
2. A more detailed discussion of the limitations of current prescriptive or test-based methods is needed in the introduction section.
3. The paper assumes specific boundary conditions (e.g., adiabatic lateral surfaces and convective and radiative heat transfer coefficients). A sensitivity analysis of these assumptions could enhance the robustness of the model and provide insights into how variations in these parameters might affect the results.
4. The paper focuses on individual steel-related failure modes but does not adequately discuss how these modes might interact under fire conditions. For example, the combined effect of lip failure and bolt failure could be explored to better understand the overall system behaviour.
5. The paper mentions that the model is conservative compared to experimental results; it does not fully explain the sources of conservatism.
6. A more detailed analysis of why the model yields conservative results (e.g., Eurocode material properties and boundary conditions) would improve transparency and credibility.
7. The conclusion focuses on the validation of the proposed method but does not fully address its broader implications for the industry. For example, the paper could discuss how this method might streamline the qualification process for anchor channels or reduce reliance on expensive fire tests.
8. Highlight the limitations of the study and future research directions in the paper.

The paper presents a novel and well-structured approach to the fire resistance design of anchor channels, leveraging numerical simulations and temperature-based reduction factors. This work is a significant contribution to the field of fire engineering for anchor channels and offers a promising alternative to traditional testing methods. The following major comments need to be addressed before publication:

1. The abstract should be improved by adding some quantitative results.
2. A more detailed discussion of the limitations of current prescriptive or test-based methods is needed in the introduction section.
3. The paper assumes specific boundary conditions (e.g., adiabatic lateral surfaces and convective and radiative heat transfer coefficients). A sensitivity analysis of these assumptions could enhance the robustness of the model and provide insights into how variations in these parameters might affect the results.
4. The paper focuses on individual steel-related failure modes but does not adequately discuss how these modes might interact under fire conditions. For example, the combined effect of lip failure and bolt failure could be explored to better understand the overall system behaviour.
5. The paper mentions that the model is conservative compared to experimental results; it does not fully explain the sources of conservatism.
6. A more detailed analysis of why the model yields conservative results (e.g., Eurocode material properties and boundary conditions) would improve transparency and credibility.
7. The conclusion focuses on the validation of the proposed method but does not fully address its broader implications for the industry. For example, the paper could discuss how this method might streamline the qualification process for anchor channels or reduce reliance on expensive fire tests.
8. Highlight the limitations of the study and future research directions in the paper.

Author Response

We thank the reviewer for the encouraging feedback and helpful suggestions. Please find our responses below:

• Abstract:
  The abstract has been updated to include a few quantitative results to better reflect the outcomes of the study.

• Limitations of current methods:
  The limitations of current prescriptive and test-based methods are already discussed in the literature review. We also added a few sentences in the conclusion to reflect on the limitations of the proposed temperature-based method.

• Boundary conditions and sensitivity:
  The boundary conditions used in the model were chosen to be representative of the experimental configurations. A detailed sensitivity analysis on these parameters has been conducted as part of Omar Al-Mansouri’s PhD thesis (2020) on bonded anchors under fire conditions (more sensitive products). Repeating that work here would go beyond the scope of this paper.

• Interaction of failure modes:
  The method follows the current design approach, which treats steel-related failure modes separately and uses the most critical (lowest) strength for design. While combined behavior may exist, designing for the most critical individual mode is in line with practice and ensures safety.

• Sources of conservatism:
  The conservative nature of the model is discussed in the section between Table 8 and Figure 19. The reasons mainly relate to material properties and boundary condition assumptions, consistent with Eurocode provisions.

• Model conservatism (clarification):
  As noted above, the sources of conservatism have been explained, and similar concerns raised by other reviewers have been addressed.

• Broader industry implications:
  We agree that broader implications for the industry are important. However, we believe these are best addressed through ongoing discussions in standardization groups such as EOTA, CAMA, and CEN/EN 1992-4, rather than within the scope of this paper.

• Limitations and future work:
  Additional comments were added in the conclusion section to highlight limitations of the current work and identify directions for future research.

Round 2

Reviewer 2 Report

The article has undergone minor changes from the original version. Some editorial comments have been corrected. The authors have removed sections 3.3.1 (line 277), 3.3.2 (line 285), 3.3.3 (line 292), 3.3.4 (line 299), the unhelpful section 3.3.5 (line 306) and 3.3.6 (line 307). They have replaced them with emphasis. They were surprised to see my comment on section 3.3.5. However, in the applmech-3517864-peer-review-v1.pdf version these elements exist! Many additional information and comments have been included in the responses to my comments. I regret a little that these clarifications were not included in the text of the article.

No comments

Author Response

Dear Reviewer 2,

Thank you for your valuable comments. Please find our proposed responses to round 2 in bold below:

 

Comment: The suggestions in the paragraph between lines 143 and 148 are not entirely clear to me! What manipulations are being referred to here?

Response: The following text (underlined) has been added to better reflect the authors' opinion: "

 

The assessment of the fire test results is based on a minimum of 5 tests of which 4 tests shall show a failure time of more than 60 minutes in order to presumably cover the whole fire resistance duration. This method allows for manipulation of the assessment via selective testing where the obtained test results would favor the obtention of a relatively higher trend curve (or line) based on the potentially better statistical distribution of the results (Figure 2). Densifying the test effort on one side of the curve (beyond the minimum test effort of 5 fire tests) would put a higher statistical weight on that part contributing to a pseudo-enhancement of the performance. The opposite also stands true where if the manufacturer wants to add more fire tests in the intent of enhancing the statistical distribution and hence obtaining a more representative behavior, if the tests yield relatively long failure times, the evaluation method leads to shifting the curve further down giving a pseudo-reduction of the performance."

No round 2 update needed. This is already reflected in the manuscript.

 

Comment: Figure 2 is also not entirely clear! After analysing the first two chapters, I get the impression that they are only intended for people already familiar with the topic presented. 

Response: Correct. This figure is extracted from EAD 330008. The application of European Assessment Documents is only of interest to Technical Assessment Bodies (TABs) applying their guidelines to Manufacturer applications to access the European Market via CE marking for their construction products. Some of test and evaluation methods in these EADs have been developed a long time ago where little knowledge was available and "leaps of faith" were made. The goal of our paper here is to modernize the fire design part of this construction product (anchor channels).

Round 2 update: The following text has been added to the end of Section 2: This paper is of interest to European Technical Assessment Bodies to demonstrate that the testing, evaluation, and design guidelines developed initially in EAD 330008 based on the existing knowledge at that time are obsolete, and to propose a modernization (rationalization) of fire design for the specific case of anchor channels.

 

Comment: The graphs presented in Figures 3 and 4 comply with the referenced standard [20]. In Figures 3 and 4, the temperature axis is incorrectly described (it is temeprature and should be temperature).

Response: Thank you for catching this. The axis titles for Figures 3 to 7 have been corrected.

No round 2 update needed. This is already reflected in the manuscript.

 

Comment: The graph shown in Figure 5 is referenced in the referenced standard [19], but relates to the selected moisture content of the concrete mass - u = 1.5% to be exact. Why was this moisture content chosen when three levels of 0, 1.5 and 3% are given in the standard [19]?

Response: The moisture content of 1,5% was adopted because it has been established a few years ago that this moisture content (along with the French assumption for the conductivity curve) give the most accurate predictions of calculations compared to fire test measurements. These assumptions have been reflected in the practice of the anchor industry in EOTA TR 082, and in the practice of reinforced concrete in the second generation Eurocode 2 (EN 1992-1-2:2023).

Round 2 update: The following text has been added to the text between Figures 4 and 5: A moisture content of 1,5% was adopted for concrete based on the French practice (French National Annex) of the first generation EN 1992-1-2 which will become the harmonized approach in the second generation EN 1992-1-2.

 

Comment: The diagrams shown in Figures 6 and 7 are referenced in the referenced standard [19]. In Figures 5, 6 and 7, the temperature axis is incorrectly described (it is temeprature and should be temperature).

Response: Thank you for catching this. The axis titles for Figures 3 to 7 have been corrected.

No round 2 update needed. This is already reflected in the manuscript.

 

Comment: What does section 3.3.5 of the article refer to (there is only a title!)?

Response: The authors looked for this section and couldn't find it in the manuscript. Please provide more information on the wherabouts of this error (page, line or position in relation to a Figure or Table).

No round 2 update needed.

 

Comment: In figure 11 there needs to be a distinction between graphs e.g. a, b and c.

Response: The three sub-graphs were named (a), (b) and (c). The text below the figure was updated to reflect this as well: 

The method described in the previous equations and figures is summarized in Figure 11 for all steel-related failure modes. "First, the temperature of the different parts of the anchor channel are obtained through finite element modelling (Figure 11 (a)). It should be noted that the temperature of the anchor was taken at the hottest part (closest to the fire exposed surface), i.e., the temperature at the channel/anchor connection. Then, using the previously determined strength reduction factors for each failure mode (Figure 11 (b)), it is possible to associate the temperature at a given time under fire conditions with the temperature-dependent reduction factor giving the fire resistance vs. exposure time relationship (Figure 11 (c))."

No round 2 update needed. This is already reflected in the manuscript.

 

Comment: In figure 11a you cannot see the temperature distribution in the anchor marked in grey (maybe we need to
introduce markers?)

Response: It should be noted that the temperature of the anchor was taken at the hottest part (closest to the fire exposed surface), i.e., the temperature at the channel/anchor connection. This makes the green and grey curves superimpose. This has been reflected in the text before the Figure.

No round 2 update needed. This is already reflected in the manuscript.

 

Comment: In figure 11b most of the graphs overlap and the graph becomes unreadable - need to change!

Response: Changing this graph means that we will need to introduce 4 new graphs just for the reduction factors. The authors believe that the tables giving the values of the reduction factors above are sufficient. The intent of this graph is purely informative. Therefore, we propose to keep it as it is.

No round 2 update needed. The authors deem their initial response appropriate.

 

Comment: The horizontal axis in figure 11b does not represent time, but temperature!

Response: Thanks for this catch! This has been corrected.

No round 2 update needed. This is already reflected in the manuscript.

 

Comment: I am surprised by the results shown in figure 12. Rather this temperature distribution is appropriate for concrete heated from below, but I have doubts about the steel of the rail and the fixing anchor in the concrete. Why does the temperature not propagate along the anchor fixed in the concrete? 

Response: The boundary conditions presented in Figure 8 demonstrate the studied problem. Fire coming from below in Figure 12 is the design case the authors are trying to address. The exposed surfaces of concrete and steel are not protected from the ISO 834-1 fire conditions. The isotherms show a curved tendency demonstrating the steel's capacity to create a thermal bridge towards the inner parts of the concrete element. This has been also shown in other studies on different anchor technologies (i.e., bonded anchors under fire conditions, see Al-Mansouri, 2020). We would like to invite the reviewer to consider the association between the colors in the legend on the left hand side and the isotherms (clear blue to dark blue show a gradient varying from 425°C to 84°C). This shows that the temperature indeed propagates through the anchors. The temperature however cannot propagate through the bolt attached to the lips of the channel because this is a steel to steel connection between the bolt and the lips. Nothing connects the bolt to the back of the channel (gap), therefore, temperature cannot diffuse higher in this point compared to the channel/anchor situation presented above.

Round 2 update: The following text has been added to the paragraph before Figure 12: The boundary conditions presented in Figure 8 demonstrate the studied problem. Fire coming from below in Figure 12 is the design case the paper addresses. The exposed surfaces of concrete and steel are not protected from the ISO 834-1 ‎[21] fire conditions. The isotherms show a curved tendency demonstrating the steel's capacity to create a thermal bridge towards the inner parts of the concrete element.

 

 

Comment: The proposed method fundamentally overestimates the fire resistance results of the fixings (even more than twice - this does not harmonise with Figure 19 - please explain!) compared to the fire tests (Figures 13, 14 and 17). This is not exactly a positive result!

Response: Correct. The method is conservative and its level of conservatism is assessed and presented in Figure 19. Conservatism in fire design may come from different factors presented above Figure 19. If the goal was to show correct predictions, then the entry data should be based on mean ultimate properties of concrete and steel (on the thermophysical properties and the strength properties). The authors believe this is not a negative point and propose to accept the arguments presented above Figure 19. The ratio of 1/3 (lowest calculated/tested value) may be considered relatively good because in the anchor industry, significantly lower values (much higher conservatism) have been accepted for fire design (i.e., fire design of bonded anchors).

No round 2 update needed. The authors deem their initial response appropriate.

 

Comment: In Figure 15, on the other hand, we observe the opposite situation (it is a safe situation)! In contrast, a very
good agreement between the results of the proposed method and the fire tests is obtained in Figure 16. Table 8 is not very clear. Please indicate clearly what is the result of the test (measured value) and what is the result of the model (calculated value)! The conclusions are very general. In my opinion they poorly summarise the work done. Indeed, I agree with the
authors that the model needs further validation. 

Response: Figures 13 to 17 aim to isolate the calculation for each failure mode in comparison to the fire test results. This comes in handy when the evaluators and manufacturers wonder for example about the choice of not conducting tests in mid-span to assess the flexural strength of the channel through fire tests (some failure modes would never show up in a fire test). This is also beneficial because it shows that, for the case of anchor channels directly exposed to fire conditions, the failure of the bolt and lips always govern and may alternate from one to the other for different fire exposure times. The level of reduction of some failure modes (i.e., bolt) compared to others (i.e., lips) shows that an error may be made when mixing all steel-related failure modes in a single evaluation (the EAD method). This is explained to some extent between Figures 17 and 18.

Round 2 update: The following text was added after Figure 17: Figure 13 to Figure 17 aim to isolate the calculation for each failure mode in comparison to the fire test results. This comes in handy when the evaluators and manufacturers wonder about the choice of not conducting tests in mid-span to assess the flexural strength of the channel through fire tests (some failure modes may never show up in a fire test). This is also beneficial because it shows that, for the case of anchor channels directly exposed to fire conditions, the failure of the bolt and lips always govern and may alternate from one to the other for different fire exposure times. The level of reduction of some failure modes (i.e., bolt) compared to others (i.e., lips) shows that an error may be made when mixing all steel-related failure modes in a single evaluation (the EAD method).

 

 

Comment: The literature is modest. It comprises 26 items (including only 12 articles!). Of the 12 articles, as many as 6 are articles by the authors of this work themselves. Surprisingly for a journal article, as many as 5 doctoral theses are cited here (items 5, 9, 10, 14 and 23, including one by the authors at number 5)! I believe that these are not published materials! Eight items in the literature list are standards and legislation. The literature item under number 17 was not recognised! 

Response: This issue was raised by the editor and other reviewers. We acknowledge the concern regarding the proportion of self-citations in the original manuscript. The field of post-installed anchors under fire exposure is indeed highly specialized, and much of the most recent and detailed experimental and analytical work has been carried out by our institution (CSTB). As a result, several of our past publications constitute key references for the current state of the art. That said, we have revised the manuscript to expand the literature review and now include 5 references authored outside our group (up from 3 previously), alongside 14 internal references (totaling 19). We have carefully selected external sources based on relevance and recency, although the number of publications directly related to this specific topic remains limited internationally. We trust that the revised balance reflects both the importance of CSTB's contribution to the field and our efforts to integrate broader context where available.

No round 2 update needed. The authors deem their initial response appropriate.

Reviewer 3 Report

The authors have satisfactorily addressed all the comments from the previous round. The reviewer has no further comments.

The authors have satisfactorily addressed all the comments from the previous round. The reviewer has no further comments.

Author Response

The authors would like to thank the reviewer for his/her contribution.

Reviewer 4 Report

The author put some effort into enhancing the manuscript. Now it's ready for publications. 

The author put some effort into enhancing the manuscript. Now it's ready for publications. 

Author Response

Th eauthors would like to thank the reviewer for his/her contribution.