Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review of the manuscript „Optimization of Geometric Parameters of a Cross-Beam Glued Laminated Timber Floor System” submitted to Construction Materials journal by Gilodo et al.

I consider the topic of the study to be well-justified and scientifically interesting. The article contains a few unfortunate formulations, so it would be worthwhile to review it once more for language accuracy. My comments are provided below:

I find that the introduction is written somewhat too generally, which diminishes its scientific character and makes it resemble more a technical report introduction. In my opinion, it lacks references to the results of other studies on similar optimizations and does not clearly highlight the novelty of the present work in that context. Furthermore, as a reader, I feel that each paragraph reads as an isolated statement of fact, and there is little sense of logical continuity throughout the text.

What do the authors mean by stating 'Despite their advantages, the efficient design of glulam floor systems—particularly those with cross-beam configurations—remains a challenge'? Why is this considered a particular challenge in the case of cross-beam configurations? I believe that the mentioned geometric parameters and structural material properties should be taken into account in every case and will always affect structural performance and material consumption.

The statement 'Suboptimal configurations can lead to excessive deflection, increased cost, and reduced reliability' would benefit from being supported by specific references. It is unclear which studies or experimental results confirm these issues.

The mention of Design of Experiments (DOE) and Response Surface Methodology (RSM) is appropriate, however, the introduction could briefly explain why these methods are particularly suitable for optimizing glulam cross-beam systems.

The methodology section would benefit from a more detailed description of the numerical modeling. In particular, the magnitude and type of applied loads (e.g., uniform, point, or combination loads) should be specified to improve reproducibility. Additionally, the finite element modeling assumptions, including element types, mesh density, and joint behavior (rigid or pinned), should be clarified to ensure transparency and allow the results to be properly evaluated.

The interpretation of Y-values (Y > 1, Y < 1) appears inconsistent and should be clarified.

While the Excel Analysis ToolPak is acceptable, the authors could discuss potential limitations of this software for regression modeling and consider more robust statistical packages for future work.

It would be helpful to mention limitations of the predictive model, especially regarding extrapolation beyond the studied parameter ranges, to avoid overinterpretation of the results.

The discussion could clarify the validation of the predictive regression model against the finite element simulations to confirm its reliability across the studied parameter space.

The discussion clearly compares selected structural configurations, however, the choice of δ = 0.05 as the threshold for technical and economic acceptability should be justified or referenced.

It would be beneficial to discuss the limitations of the study, including variability in wood properties, environmental factors, and the assumptions of the FEM model.

While the reported material savings (25-30%) are significant, it would strengthen the conclusions to explain how these values are derived from the optimization process rather than assumed.

Overall, the study addresses a relevant and scientifically interesting topic, providing a rather clear methodology and insightful analysis of cross-beam glulam floor optimization. However, the manuscript would benefit from minor corrections and improvement in scientific character of the text. Looking at the references and the introduction, the text gives the impression of reading a technical report rather than a scientific article. This should be revised to enhance the scientific level of the work.

Comments on the Quality of English Language

It should be improved. 

Author Response

Dear Reviewer,

We sincerely thank you for your thorough review and insightful comments on our manuscript, "Optimization of Geometric Parameters of a Cross-Beam Glued Laminated Timber Floor System." We agree with your observations regarding the need for a more scientific character, enhanced methodological detail, and clearer justification of the study's limitations and outcomes.

We have undertaken a major revision of the manuscript to address all the points you raised. The new version is titled "Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology" (стаття_Scopus_R4_eng.docx).

Below is a point-by-point response to your comments.

General Comments

Comment 1, 2, 3, 15 (General character, scientific style, language, and logical flow): The reviewer noted that the introduction was "too general" and the manuscript resembled a "technical report", lacking logical continuity and clear highlighting of novelty. The quality of the English language was also marked for improvement.

Response: Addressed. We have fundamentally rewritten the entire manuscript to improve its scientific style, language, and logical flow.

The Introduction has been revised to eliminate the "technical report" feel. We removed the bullet-pointed lists for "Relevance" and "Tasks" (from the original document) and replaced them with a cohesive, narrative-driven section that clearly defines the state-of-the-art, the research gap, and the study's objectives.

We have added several new, detailed sections to enhance the scientific rigor, including Section 2.2 (FEM Assumptions), Section 4.3 (Model Validation), Section 4.4 (Material Efficiency), and Section 5 (Limitations and Future Work).

The entire document has undergone a thorough professional language review.

Specific Comments

Comment 4 (Clarification of "challenge"): The reviewer asked why the design of cross-beam configurations is a "particular challenge".

Response: Addressed. We have clarified this in the Introduction. The challenge arises because "the structural behavior is governed by a complex, three-dimensional interaction between primary and secondary beams, often involving biaxial bending and compressive forces that simple one-dimensional beam theory cannot adequately capture".

Comment 5 (References for "Suboptimal configurations"): The reviewer requested references to support the statement that suboptimal configurations lead to issues.

Response: Done. We have added references [7, 9] to support this statement in the Introduction.

Comment 6 (Justification for DOE and RSM): The reviewer asked why DOE and RSM methods are particularly suitable for this problem.

Response: Done. We have added a specific justification in the Introduction, stating that these methods "are particularly well-suited for this problem as they can efficiently model the complex, non-linear relationships and quadratic interactions between multiple geometric variables, which simpler one-factor-at-a-time analyses would miss".

Comment 7 (Methodology details): The reviewer requested a more detailed description of the numerical modeling, including applied loads, element types, mesh density, and joint behavior.

Response: Done. We have added a new, comprehensive section, "2.2. Finite Element Model (FEM) Assumptions". This section now explicitly details:

Loads: "a uniformly distributed service load of 2.5 kN/m²".

Element Type: "one-dimensional ('member') elements".

Joints/Supports: "pinned (hinged)" corner supports and "rigid connections" at beam intersections.

Mesh: "a mesh-refinement strategy ensuring at least ten finite elements per member".

We also added material properties for GL24h and a worked example of the Eurocode 5 check.

Comment 8 (Inconsistent Y-value interpretation): The reviewer noted that the interpretation of Y-values (Y > 1) was inconsistent.

Response: Corrected. Thank you for identifying this typo. We have corrected this error and added a new dedicated section "3.2 Predictive model and interpretation" to clearly define the Y-value meanings: Y > 1.0 (unsafe), Y = 1.0 (optimal), and Y < 1.0 (safe but inefficient).

Comment 9 (Limitations of Excel): The reviewer suggested discussing the limitations of using the Excel Analysis ToolPak.

Response: Addressed. We have added a comment in Section 3.2 acknowledging this: "...it is acknowledged that more advanced statistical software could provide more comprehensive diagnostic capabilities, which may be explored in future work".

Comment 10 (Model extrapolation limits): The reviewer suggested mentioning the limitations of the model regarding extrapolation.

Response: Done. We have added a specific warning at the end of Section 3.2: "It is important to note that this predictive model (Equation 8) is validated only within the tested parameter ranges (Table 1). Extrapolating beyond these limits... is not recommended".

Comment 11 (Model validation): The reviewer asked for clarification on the validation of the predictive regression model against the FEM simulations.

Response: Done. We have added a new section "4.3. Model Validation". This section explicitly states that the high R² value (0.982) "demonstrates that the second-order regression model (Equation 8) provides an excellent fit to the data generated by the FEM simulations within the investigated parameter space".

Comment 12 (Justification of δ = 0.05 threshold): The reviewer asked for a justification for the δ = 0.05 threshold.

Response: Revised. We have clarified our optimization constraints in Section 4.2 (Pareto analysis). The formal constraint is now (0.9 < Y ≤1.0) . We justify this choice not as an arbitrary 5% rule, but as a "practical engineering target" and a "rational engineering compromise" to balance material efficiency with structural safety.

Comment 13 (Discussion of study limitations): The reviewer suggested discussing limitations such as wood property variability and FEM assumptions.

Response: Done. We have added a new, comprehensive "Section 5. Limitations and Future Work". This section specifically addresses the limitations of "FEM Assumptions" (rigid connections), "Material Properties" (using deterministic values instead of accounting for variability), and the "Scope of Parameters" (specific span and load).

Comment 14 (Derivation of material savings): The reviewer asked for an explanation of how the 25-30% material savings were derived, not just assumed.

Response: Done. We have added a new section "4.4. Material Efficiency" to provide a clear, quantitative explanation. The saving is "derived by comparing the optimized solution (Point 10, V = 1.127 m³) with other structural 'safe' (Y < 1.0) yet non-optimal designs". We provide a specific example (Point 18) which has a volume of 2.252 m³ and "requiring almost twice the material".

We believe that these revisions have substantially improved the manuscript and directly addressed all of your valuable concerns. We thank you once again for your constructive feedback.

 

Sincerely,

Oleksandr Gilodo,

Andrii Arsirii,

Sergii Kroviakov,

and Oleksandr Gimanov

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript entitled “Optimization of Geometric Parameters of a Cross-Beam Glued Laminated Timber Floor System” has been carefully reviewed. The evaluation focused on the scientific soundness, methodological consistency, clarity of presentation, and adequacy of data interpretation according to the journal’s standards. The following detailed comments are provided section by section to assist the authors in improving the technical quality, structure, and readability of the paper before publication.

 

1. Title and Abstract

The title correctly represents the scope but should be more concise and specific. Consider including the key method used (e.g., Response Surface Methodology) or emphasizing “parametric optimization.”

The abstract is too descriptive and verbose. It should clearly outline: (1) the research gap; (2) the methodology; (3) key quantitative results; and (4) implications.

Statistical results (R² > 0.98) and the mention of Pareto optimization are good, but no numerical result for material savings is explicitly stated—this should be quantified.

The abstract mixes background information with results. Move contextual phrases like “addressing the critical need for…” to the introduction.

Sentences such as “makes significant contributions to timber engineering…” sound self-promotional; rephrase to objective, evidence-based conclusions.

 

2. Introduction

The introduction lacks a clear structure separating: (a) state-of-the-art, (b) research gap, and (c) study objectives.

References are numerous but not critically discussed; many are generic reviews without specific linkage to the research gap.

The paragraph “Relevance of the study” repeats earlier justifications. Combine and streamline to avoid redundancy.

There is an abrupt transition from discussing sustainability to detailing experimental variables; insert a bridging statement that connects environmental motivation to geometric optimization.

The “aim” and “main tasks” section should be reformulated in concise academic English (e.g., avoid list formatting within the introduction; merge into one paragraph).

Citations [1–7], [12–15] are referred to collectively; clarify which studies support which statements (avoid large grouped references).

 

3. Methodology

The methodology section describes software (Dlubal RFEM) and parameters but lacks sufficient detail for reproducibility. Specify:

Material properties used (GLT grade, modulus of elasticity, density, etc.).

Boundary conditions and load cases beyond “pinned supports.”

Mesh type and refinement strategy in RFEM.

Equation formatting is inconsistent—use consistent variable notation (x₁, x₂, etc.) throughout and define all symbols once.

Figures should be labeled clearly and described; Figure 1 lacks captions explaining each subfigure.

There is no validation or comparison with analytical or experimental data. A finite element model requires at least a brief validation step or literature-based verification.

Explain why three factors were chosen and whether the chosen ranges are representative of real construction practice.

Include a rationale for using Excel for regression modeling; for scientific rigor, specialized software or statistical validation (e.g., ANOVA, residual analysis) should be presented.

The methodology reads partly like a manual. Simplify step-by-step lists and emphasize methodological reasoning (why these steps were taken, not how).

 

4. Results and Analysis

 

The regression model (Equation 8) is presented but without coefficient significance tables or ANOVA summaries. Include statistical validation tables (p-values, standard errors, F-test).

Units should be clarified for all parameters and results.

Figures 2–3: improve graphical quality (axis labels, units, legends). Avoid duplication of interpretations (“as shown in Fig. 6,” “in Fig. 7”) since there are only three subfigures; these references appear inconsistent.

The text mentions “sub-beam type (x₄)” and “slab thickness (x₃ = 0.167)”—these variables are not defined elsewhere, suggesting an editing inconsistency.

The regression equation (Eq. 8) includes many coefficients with large magnitudes; discuss multicollinearity and model robustness.

There is excessive descriptive narrative; emphasize main trends, sensitivity ranking, and physical interpretation of results instead.

The statement “p < 0.05” is made but no table supports it. Include the statistical test output.

 

5. Optimization and Discussion

The optimization section correctly applies Pareto frontier analysis but lacks methodological transparency. Explain how the Pareto front was constructed (manual plotting or optimization algorithm?).

The criterion (0.9 < Y ≤ 1) is arbitrary; justify this constraint from standards or engineering practice.

Figures 3 and Table 3 require better captioning, including what “δ = 1 − Y” represents.

Discussion should connect results to previous literature—how do these optimized configurations compare to existing design rules in Eurocode 5 or other studies?

The paragraph “Thus, we have developed an analytical model…” repeats information from earlier sections. Focus the discussion on interpretation, not summary.

There is no uncertainty or limitation analysis. Discuss the model’s applicability limits (e.g., beam spacing range, span length).

 

6. Conclusions

The conclusions are mostly descriptive. Reformulate to highlight key findings quantitatively (e.g., “Optimization reduced timber volume by X% with <Y% change in load utilization”).

Remove phrases such as “demonstrates potential” and “shows high significance,” which are evaluative.

Explicitly state practical implications (e.g., potential for use in mid-rise timber floors, need for experimental validation).

Limit the conclusions to 3–5 concise statements; move detailed advantages (technological flexibility, transparency, etc.) to the Discussion section.

 

7. References

References are recent and relevant but poorly integrated. The text cites multiple statistical textbooks ([10]–[15], [29], [30])—these should be consolidated and used more purposefully.

Verify consistency in reference formatting (e.g., “Compos Struct.” vs. “Composite Structures”).

Check that all cited works are actually referenced in the text (some are repeated).

Replace outdated or non-peer-reviewed sources (e.g., Microsoft Support web page) with appropriate methodological references for regression implementation.

Comments on the Quality of English Language

The manuscript is understandable but requires professional English editing. Common issues include:

Overuse of passive voice and long compound sentences.

Redundant phrases (“simultaneously considering,” “in light of increasing demands,” “based on the accepted assumptions”).

Inconsistent use of tenses between sections.

Equation formatting and figure numbering should follow MDPI style guidelines.

Ensure that all symbols (η, σ, fc, fm, etc.) are properly italicized and defined where first introduced.

Author Response

Dear Reviewer,

We thank you for your exceptionally thorough and highly constructive review of our manuscript. Your detailed section-by-section analysis identified significant weaknesses in the original paper's structure, methodological transparency, and statistical validation. We have undertaken a major revision to address every point you raised, which has substantially improved the quality and scientific rigor of the work.

The revised manuscript is now titled "Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology" (стаття_Scopus_R4_eng.docx).

Below, we provide a point-by-point response to your comprehensive comments.

General Comments

Comment on English Language: The reviewer noted that the English could be improved.

Response: Addressed. The entire manuscript has undergone a comprehensive professional language review to correct issues with passive voice, tense consistency, and redundant phrasing, as you rightly pointed out.

Comment on Section Ratings: The reviewer indicated that the Introduction, Methods, Results, Conclusions, and Figures/Tables all required improvement.

Response: Addressed. As detailed below, we have fundamentally restructured or rewritten all of these sections to meet the high standards you suggested.

Title and Abstract

Comment 1 (Title): The title should be more concise and specific (e.g., mention RSM or parametric optimization).

Response: Done. We have changed the title to: "Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology".

Comment 2-6 (Abstract): The abstract was too descriptive, mixed background with results, lacked quantitative savings, and used self-promotional language.

Response: Addressed. The Abstract has been completely rewritten.

• It is now structured to clearly present the research gap (lack of systematic optimization guidelines), methodology (DOE, FEM, RSM), key quantitative results (R² > 0.98; optimal solution Y = 0.974), and implications (a validated tool for designers).
• We have added a specific quantitative result for material savings ("reduces the required timber volume by approximately 10% compared with other efficient designs and by over 60% compared with inefficient... designs").
• All subjective or self-promotional phrases ("makes significant contributions...") have been removed and replaced with objective statements.

Introduction

Comment 7, 9, 11 (Structure): The introduction lacked a clear structure (state-of-the-art, gap, objectives), was repetitive ("Relevance of the study"), and used list formatting for aims/tasks.

Response: Addressed. The Introduction has been completely rewritten. The original subsections ("Relevance," "Aim," "Tasks") have been removed and integrated into a single, cohesive narrative that now logically flows from the state-of-the-art to the specific research gap (the need for a systematic methodology for this specific 3D problem) and concludes with the study's clear objectives.

Comment 8 (References): References were not critically discussed and were grouped in large clusters.

Response: Addressed. We have critically integrated the references into the new Introduction, using them to build the argument for the research gap (e.g., citing specific optimization reviews to show what is missing). We have also broken up the large reference clusters.

Comment 10 (Abrupt transition): The text transitioned abruptly from sustainability to experimental variables.

Response: Corrected. This transition has been smoothed in the rewritten Introduction by logically connecting the need for material efficiency (sustainability) to the method of achieving it (parametric optimization).

Methodology

Comment 12-15 (Lack of detail): The section lacked sufficient detail for reproducibility (material properties, boundary conditions, loads, mesh).

Response: Done. This was a critical omission. We have added a new, detailed Section 2.2 "Finite Element Model (FEM) Assumptions". This section now explicitly specifies:

• Material Properties: GL24h glulam, including modulus of elasticity (E), shear modulus (G), and characteristic compressive strength.
• Boundary Conditions & Loads: Pinned corner supports and a uniformly distributed service load of 2.5 kN/m², plus self-weight.
• Mesh Strategy: A refinement strategy ensuring at least ten finite elements per member.
• We also added details on rigid internal connections and the analysis type.

Comment 16, 17 (Formatting): Equation formatting was inconsistent and Figure 1 lacked subfigure captions.

Response: Corrected. All equations and variables have been standardized. Figure 1 now includes clear (a), (b), (c), and (d) labels with corresponding descriptions in the caption.

Comment 18 (Validation): The FEM model lacked validation.

Response: Addressed. We have added a new subsection "2.2. Finite Element Model (FEM) Assumptions" which includes a paragraph on "FEM validation". We clarify that while full-scale experiments were not in scope, the model was verified against analytical solutions for simple beam configurations, showing strong agreement.

Comment 19 (Factor Rationale): The rationale for choosing the three factors and their ranges was missing.

Response: Addressed. We have added a new paragraph in Section 2.1 explaining this: "These three factors were chosen because they are the primary drivers..." and that the ranges "are dimensionless, making the methodology scalable and representative of typical... ratios used in practical construction."

Comment 20 (Excel & Statistical Validation): The use of Excel was not justified and lacked rigorous statistical validation (ANOVA, residuals).

Response: Addressed. This is a key improvement.

• In Section 3.1, we now acknowledge the use of the Analysis ToolPak.
• More importantly, in Section 3.2, we have added Table 3: "Statistical validation of the regression model coefficient (Equation 8)". This new table provides the full ANOVA summary, including Coefficients, Standard Error, t-Stat, and P-values for every term in the model, as well as the F-statistic. This directly addresses the need for statistical validation.
• We also added a paragraph discussing the statistical significance (P-values < 0.05).

Comment 21 (Manual style): The methodology read like a step-by-step list.

Response: Addressed. The "step-by-step" list for the regression procedure in Section 3.1 has been streamlined into a concise paragraph to improve the academic tone.

 

Results and Analysis

Comment 22, 28 (Statistical validation): The regression model was presented without significance tables (ANOVA) and was overly descriptive.

Response: Done. As noted above, we have added Table 3 in Section 3.2, which provides the full statistical validation (P-values, t-Stats, F-statistic) that was missing. The narrative now focuses on interpreting these statistics rather than just describing the surfaces.

Comment 23 (Units): Units should be clarified.

Response: Done. We have reviewed the manuscript to ensure all parameters and results are clearly defined with their units (e.g., in Section 2.2, Table 2, and the new worked example).

Comment 24 (Figure Quality): Figure 2-3 quality needed improvement (labels, units).

Response: Addressed. The figures themselves are the same, but their captions and the accompanying text have been significantly improved. The axes (x₁, x₂, Y) are now clearly defined in the text, and the new Figure 2 caption explicitly states what each plot represents (e.g., "(a) x₃ = 0.25 (thin beams)").

Comment 25, 26 (Inconsistent references): The text referred to non-existent figures (Fig. 6, 7) and undefined variables...

Response: Corrected. These were errors from a previous draft. All such incorrect references have been removed from the manuscript. The text now correctly refers only to Figures 1, 2, and 3, and all variables are defined.

Comment 27 (Multicollinearity): The reviewer suggested discussing multicollinearity due to large coefficients.

Response: Addressed. We added a discussion for this in Section 3.2: "The relatively large magnitudes of some coefficients... are an expected mathematical outcome of model fitting to small input variables... Given the high R² and consistently strong P-values, this does not indicate a multicollinearity issue; rather, it confirms the model's sensitivity..."

Optimization and Discussion

Comment 29 (Pareto Front Construction): The method for constructing the Pareto front was not transparent.

Response: Addressed. We have clarified this in Section 4.2: "...which was generated by manually plotting the 27 discrete experimental outcomes from Table 2 against the two objectives...".

Comment 30 (Arbitrary Criterion): The criterion (0.9 < Y ≤ 1) was noted as arbitrary.

Response: Addressed. We have added a detailed justification in Section 4.2 (Pareto analysis). We explicitly state that this is "not an explicit requirement of Eurocode 5 but represents a practical engineering target" and a "rational engineering compromise... representing designs that achieve at least 90% utilization".

Comment 31 (Figure/Table Captions): Figure 3 and Table 3 (now Table 4) needed better captioning (what is δ = 1 − Y?).

Response: Done. The caption for Figure 3 and the header in Table 4 (formerly Table 3) now explicitly define δ=1-Y

Comment 32 (Literature Connection): The discussion did not connect results to previous literature.

Response: Addressed. The rewritten Discussion and new Section 5 (Limitations) now provide this context by comparing our findings to the need for practical design tools and contrasting our ULS (Ultimate Limit State) focus with SLS (Serviceability Limit State) studies, which are now cited as future work.

Comment 33 (Repetitive paragraph): The paragraph "Thus, we have developed an analytical model..." was repetitive.

Response: Removed. This repetitive summary paragraph has been removed from the start of Section 3.3.

Comment 34 (Limitations): No limitation analysis was included.

Response: Done. We have added a new, comprehensive Section 5: "Limitations and Future Work". This section directly addresses the model’s limitations, including: (1) FEM Assumptions (rigid joints), (2) Material Properties (deterministic vs. variable), (3) Scope of Parameters (specific span/load), (4) System Scope (excluding the slab), and (5) Optimization Objectives (ULS vs. SLS).

Conclusions

Comment 35-38 (Conclusions): The conclusions were descriptive, evaluative ("demonstrates potential"), and not concise.

Response: Addressed. The Conclusions section has been completely rewritten.

• It now leads with quantitative findings: "identified a technically optimal configuration (x₁=0.250, x₂=0.042, x₃=0.5) that achieves near-complete load utilization (Y = 0.974)..."
• All evaluative, subjective phrases ("demonstrates potential") have been removed.
• The practical implications are now clearly stated: "material savings of to 25-30% compared with conventional... designs".
• The section is now concise and focused only on the key findings.

 

References

Comment 39-42 (References): References were poorly integrated, inconsistently formatted, and included non-peer-reviewed sources (Microsoft Support).

Response: Addressed.

We have reviewed and consolidated the references, removing the generic Microsoft Support link.

We have carefully reformatted all references to ensure consistency (e.g., journal abbreviations).

We have checked to ensure all cited works are present in the list and duplicates are removed.

 

We believe these extensive revisions, guided by your detailed feedback, have transformed the manuscript into a much stronger, more transparent, and statistically sound scientific article. We thank you again for your invaluable contribution.

Sincerely,

Oleksandr Gilodo, Andrii Arsirii, Sergii Kroviakov, and Oleksandr Gimanov

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for this interesting and insightful study on the optimization of timber volume in cross-beam GLT floor systems.  The work is an important possible contribution to the improving material efficiency in the design of these floor systems.

While the manuscript is interesting as presented, the work could be improved by addressing a set of major and minor considerations:

Major - 

1. It is not clear what the assumptions are at the point where the cross beams reach contact each other.  These members can not be fabricated to be continuous in both directions, and if that is the assumption, there is an unrealistic behavior that can not be reproduced in the field.  It is important to clarify this and ensure that reader is aware of how this work might be relevant for actual construction.
2. The thickness of the supported slab is a variable that is mentioned, but not modeled, in this work.  The total timber volume will be impacted by the slab thickness (if it is timber), and the optimal solution will be impacted by the supported spans and floor slab strength and stiffness. It is necessary to explore this in the explanation of the work (Introduction and Methodology) and ensure that the reader can effectively apply the results from this work.

Minor points 

110-122 – Repetitive explanation of use of RFEM, combine and shorten

134 – Please state clearly if this is a Eurocode equation (and where it is found).  If this is not from the Eurocode, please provide a reference.

185 – 186  The authors describe two opposite effects for Y>1.  Please clarify

192 – Refers to Figure 2 with x3=0.167.  Based on the label for Figure 2, no image of x3=0.167 is included.

195 – Refers to Figure 7.  No Figure 7 found in the manuscript. 

227 – Refers to Figure 8.  No Figure 8 found in the manuscript

234 – Is the value 0.1 positive, or is this an absolute value?

238 – This sentence needs to be completed.

257 – Refers to Figure 8.  No Figure 8 in the manuscript

Author Response

Dear Reviewer,

Thank you for your review and for your insightful comments on our study. We appreciate your positive feedback on the importance of the work. You have raised two major, practical considerations regarding the model's assumptions which we agree are critical for the application of this work. We have addressed these, along with all minor points, in the revised manuscript.

The revised manuscript is titled "Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology" (стаття_Scopus_R4_eng.docx).

Below is our detailed response to your comments.

 

Major Comments

Comment 1 (Beam connections): The reviewer rightly pointed out that the assumption of continuous beams in both directions is unrealistic for field fabrication and that the assumptions at beam intersections were unclear.

Response: Addressed. This is a crucial point. We have added a new section, "2.2. Finite Element Model (FEM) Assumptions", to explicitly clarify this.

• We now state that "All beam-to-beam intersections within the grid were modeled as rigid connections, ensuring full moment and shear transfer."
• We acknowledge this simplification: "This assumption – while a simplification of practical semi-rigid joinery – is a common... approach... in parametric studies."
• Most importantly, we have added a new "Section 5. Limitations and Future Work", which includes a specific point on "FEM Assumptions". This limitation section now clearly states that "In practice, glulam joints exhibit semi-rigid behavior" and that future work should model this.

Comment 2 (Slab thickness): The reviewer noted that the slab thickness, while mentioned, was not modeled and that it would impact the total timber volume and the optimal solution.

Response: Addressed. We agree completely. The mention of slab thickness in the original draft was an error and has been removed to avoid confusion.

• We have added a new limitation in "Section 5. Limitations and Future Work" called "Slab and System Scope".
• This new section explicitly states: "The study focused exclusively on the timber volume of the cross-beam grid. It did not include the volume or structural contribution of the floor slab... A holistic optimization including the slab volume and stiffness as variables would represent a valuable extension of this work."

 

Minor Points

• Comment (Lines 110-122): Repetitive explanation of RFEM.
• Response: Corrected. We have consolidated the Methodology section and removed this redundancy to improve readability.
• Comment (Line 134 - Equation): The reviewer asked if the equation (presumably Eq. 4-5) is from Eurocode and where it is found.
• Response: Done. We have clarified in Section 2.1 that the "Verification was carried out in accordance with Clause 6.2.4 of Eurocode 5 [9] for combined biaxial bending and compression." We also added a "worked example" to clearly demonstrate the application of these equations.
• Comment (Lines 185–186): The authors describe two opposite effects for Y > 1.
• Response: Corrected. This was a typo in the original draft. We have corrected this and added a new, clear Section 3.2 "Predictive model and interpretation". This section now unambiguously defines Y > 1.0 as the region where "the element fails to satisfy the strength requirements... This design region is structurally unsafe and therefore unacceptable."
• Comment (Line 192 - Fig 2): Refers to x₃ = 0.167, which is not included.
• Response: Corrected. This was an error from a previous draft. This incorrect reference has been removed. The new Figure 2 caption and text correctly refer only to the plotted values: (a) x₃ = 0.25, (b) x₃ = 0.33, and (c) x₃ = 0.50.
• Comment (Lines 195, 227, 257): References to non-existent Figures 7 and 8.
• Response: Corrected. These were numbering errors. All figure references in the manuscript have been corrected. The paper now correctly refers only to Figures 1, 2, and 3.
• Comment (Line 234 - value 0.1): Is the value 0.1 positive, or is this an absolute value?
• Response: Clarified. This refers to the deviation, δ. We have clarified this in Section 4.2 (Pareto analysis). The optimization constraint is now clearly defined as (0.9 < Y ≤1.0) which corresponds to δ. The Pareto plot (Figure 3) now also clearly labels the x-axis as "Deviation from optimum δ = 1 - Y, confirming it is a positive deviation value.
• Comment (Line 238): The sentence needs to be completed.
• Response: Corrected. This incomplete sentence was part of a paragraph that has been removed or rewritten during the extensive revisions.

 

We thank you again for your practical and constructive feedback, which has helped us to clarify the assumptions and scope of our model significantly.

Sincerely,

Oleksandr Gilodo,

Andrii Arsirii,

Sergii Kroviakov,

and Oleksandr Gimanov

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The paper couples finite-element modeling in RFEM with a three-factor DOE/response-surface workflow to explore cross-beam glulam floor systems and screen configurations that use less timber while maintaining code-compliant strength. The dataset (27 design points) and the fitted quadratic model are presented clearly enough to support pre-design screening, and a Pareto view highlights “balanced” options with strength utilization close to unity at comparatively low volume. Overall, the topic is timely, the framing is practical for engineers, and the optimization path is well motivated for resource-efficient timber design.

My main recommendations to the esteemed authors are as follows:

1) Specify wood grade(s) and material constants (including shear modulus), how connections between primary/secondary members are modeled, support conditions, mesh density, and convergence checks. Document load cases/combination rules, service class, modification, and partial factors, and show at least one worked example of the bi-axial bending plus compression check referenced to Eurocode 5.

2) Add constraints and reporting for deflection limits, vibration/comfort (and—if relevant—acoustics and fire), since focusing only on ultimate strength can push the “optimum” toward solutions that are not buildable in practice.

3) Accompany the headline with regression diagnostics—ANOVA table, coefficient confidence intervals, residual plots (normality and homoscedasticity), multicollinearity metrics (e.g., VIF), and an external validation at additional design points off the 3×3×3 grid. Clarify the exact Analysis ToolPak settings used.

4) Resolve conflicting references to undeclared factors and the mis-numbered figures (the text refers to figures that don’t exist in the list). Ensure consistent definitions of variables, axis labels, units, and decimal punctuation across tables/plots; verify that all highlighted “optimal” designs are truly Pareto-efficient relative to the complete set of 27 cases.

5) Justify the volume equation and the factor accounting for two orthogonal beam sets, and state explicitly whether the tally includes only secondary members or also primaries and decking; if only a subset is counted, explain the design intent and limitations.

6) Soften superlatives in the Abstract/Conclusions and align claims with statistical evidence rather than qualitative phrasing.

7) Unify reference numbering and remove duplicates; ensure accurate standards and book citations; normalize the author-contribution formatting and initials to MDPI style.

Overall, the manuscript offers a useful, engineer-friendly optimization pathway with practical promise. Still, it needs stronger methodological transparency, fuller statistical validation, consistent figures/notation, and explicit serviceability-driven constraints to meet journal standards and real-world design needs.

Author Response

Dear Reviewer 4,

We thank you for your highly practical and detailed review. We appreciate your positive assessment of the topic as "timely" and the engineering approach as "practical" and "well-motivated".

Your seven main recommendations were exceptionally clear and have been instrumental in significantly enhancing the methodological transparency and statistical validation of our paper. We have addressed all of them in the revised manuscript, now titled "Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology" (стаття_Scopus_R4_eng.docx).

Below is a point-by-point response to your recommendations.

 

1) Specify FEM Details (Material, Connections, Loads, Example): You recommended specifying all FEM constants, modeling assumptions, and providing a worked example of the Eurocode 5 check.

Response: Done. This was a critical omission. We have added extensive details in the Methodology section:

• Material Properties: Section 2.1 now specifies the grade (GL24h), Modulus of Elasticity (E = 11,500 MPa), Shear Modulus (G = 690 N/mm²), and other constants.
• Modeling Assumptions: A new Section 2.2 (FEM Assumptions) has been added. It explicitly details the support conditions ("pinned (hinged)" at corners), connection modeling ("rigid connections" at intersections), and mesh strategy ("at least ten finite elements per member").
• Loads & Factors: We clarified the "Service Class 1" (Section 2.1) and the applied load ("uniformly distributed service load of 2.5 kN/m²" in Section 2.2).
• Worked Example: A detailed worked example for a critical element is now included in Section 2.1, demonstrating the full biaxial bending and compression check from Eurocode 5 (Clause 6.2.4), including the k_mod

2) Add Constraints (Deflection, Vibration): You correctly noted that focusing only on ULS (strength) can lead to impractical solutions and suggested adding SLS (deflection, vibration) constraints.

Response: Addressed. We agree that this is a key practical limitation of the current study's scope. We have added a new Section 5 (Limitations and Future Work). This section includes a specific point, "Optimization Objectives", which explicitly states that the study focused only on ULS and that "Future research could expand the optimization to include serviceability limit states (SLS), such as deflection and vibration performance, as additional or primary objectives."

3) Add Regression Diagnostics (ANOVA, Multicollinearity): You requested full statistical validation for the regression model, including an ANOVA table, confidence intervals, and discussion of multicollinearity.

Response: Done. We have significantly expanded Section 3.2.

• We added Table 3: "Statistical validation of the regression model coefficient (Equation 8)". This new table provides the full statistical diagnostics you requested, including Coefficients, Standard Error, t-Stat, P-values, R-Square, and the F-statistic.
• We added a new paragraph in Section 3.2 to discuss potential multicollinearity. We explain that the large coefficients are an expected mathematical result of small input variables and that the high R² and strong P-values confirm the model's sensitivity rather than indicating a multicollinearity problem.

4) Resolve Conflicting References: You identified conflicting references to undeclared factors (like x₄) and misnumbered figures.

Response: Corrected. These were errors from a previous draft and have been completely removed. The manuscript now correctly and consistently refers only to the three defined variables (x₁, x₂, x₃) and the correct figures (Figure 1, 2, and 3).

5) Justify Volume Equation: You asked for a justification of the volume equation (Eq. 6) and clarity on what it includes.

Response: Clarified. In Section 3.1, we now explicitly define all components of Equation 6. The "2" accounts for the two orthogonal beam sets. We also clarified that this volume represents the "timber volume of the secondary beams within the cross-beam glulam system." This scope is further reinforced in the new Section 5 (Limitations), which states the study "focused exclusively on the timber volume of the cross-beam grid."

6) Soften Superlatives: You recommended softening superlatives in the Abstract and Conclusions to align claims with statistical evidence.

Response: Done. We have rewritten the Abstract and Conclusions to be strictly objective and data-driven. All subjective phrases ("exceptional capability," "significant contributions") have been removed and replaced with quantitative evidence (e.g., "R² > 0.98", "Y = 0.974", and specific material saving percentages).

7) Unify References and Formatting: You requested unification of reference numbering, removal of duplicates, and normalization of author contributions.

Response: Done. We have thoroughly reviewed and reformatted the entire reference list to ensure consistency and remove duplicates. The Author Contributions section has also been standardized into the required paragraph format.

 

We believe these changes, based directly on your expert recommendations, have made the manuscript far more robust, transparent, and useful for practical application. We thank you again for your constructive and valuable feedback.

Sincerely,

Oleksandr Gilodo,

Andrii Arsirii,

Sergii Kroviakov,

and Oleksandr Gimanov

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Sir/Madam, the authors have made the necessary revisions. The paper can be accepted for publication in its present form.

Author Response

Dear Reviewer 2,

We are delighted to hear that you find the revised manuscript suitable for publication.

We would like to express our sincere gratitude for your exceptionally thorough and constructive critique during the first round of review. Your detailed suggestions regarding the statistical validation, structural organization, and methodological transparency were invaluable. They played a vital role in elevating the scientific rigor and overall quality of our work.

Thank you for your time and your contribution to this research.

Sincerely,

Oleksandr Gilodo,

Andrii Arsirii,

Sergii Kroviakov,

and Oleksandr Gimanov

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for your responses to the comments

Author Response

Dear Reviewer,

We sincerely thank you for reviewing our responses and for your continued time and effort in evaluating our manuscript, "Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology". We are glad to hear that you have received our responses to your comments.

We noticed, however, that the evaluation grid in the latest report still reflects the ratings from the initial round of review (e.g., marking "Must be improved" for Methods and Figures). Since we have endeavored to address all your major and minor points in the revised manuscript—including clarifying the FEM assumptions and correcting the figure references—we wanted to respectfully clarify if these ratings were intended to remain unchanged.

If you are satisfied with our revisions, would it be possible to kindly update the evaluation form to reflect the current state of the manuscript? This would be greatly appreciated and would help facilitate the final decision process.

Thank you once again for your valuable guidance which has significantly improved our work.

Sincerely,

Oleksandr Gilodo, Andrii Arsirii, Sergii Kroviakov, and Oleksandr Gimanov

Reviewer 4 Report

Comments and Suggestions for Authors

Тhe authors have addressed the majority of my previous comments to a satisfactory degree. The finite element modelling assumptions, material properties, boundary conditions, and Eurocode 5 verification are now clearly presented. The statistical validation of the regression model has been substantially improved, and the definition of the optimization scope and timber volume is now much more precise. The revisions to the abstract, conclusions, and references have also strengthened the manuscript.

I therefore recommend minor revision, with the following remaining substantive points:

1) While the new Limitations section explicitly states that the current study focuses only on ULS and that future work should include SLS criteria, it would be useful for practitioners if the authors could slightly expand this discussion. In particular, please comment more explicitly on the potential risk that the ULS-optimal configurations may be governed by deflection or vibration limits in typical spans, and clarify under what conditions the presented optimization results are most applicable in practice.

2) I suggest adding one or two sentences (in the Conclusions) explaining how a practicing engineer could use the proposed regression model/response surfaces in preliminary design (for example, as a rapid tool for estimating timber volume for given spans and spacings, within the stated limitations).

With these minor additions, I believe the manuscript will be fully ready for publication.

Author Response

Dear Reviewer,

We are sincerely grateful for your positive evaluation of our revised manuscript and for recognizing the improvements made to the FEM assumptions, statistical validation, and scope definitions. We appreciate your recommendation for minor revisions, as your final two suggestions add significant practical value to the paper.

We have incorporated your suggestions into the manuscript as follows:

1) Expanded Discussion on ULS vs. SLS Risks: Reviewer Comment: Comment more explicitly on the potential risk that ULS-optimal configurations may be governed by deflection/vibration and clarify applicability. Response: We have expanded the "Optimization Objectives" paragraph in Section 5 (Limitations and Future Work). We now explicitly state that SLS criteria (deflection and vibration) often govern design in typical spans and that the ULS-optimal configurations may carry a risk of insufficient stiffness. We clarified that the current results are most applicable as a baseline for efficiency or for high-load scenarios where strength is dominant.

2) Practical Application in Conclusions: Reviewer Comment: Add sentences explaining how a practicing engineer could use the regression model in preliminary design. Response: We have added a closing statement to Section 6 (General Conclusions) explaining that engineers can use the proposed regression model as a "rapid pre-design tool" for estimating timber volume and screening geometric configurations prior to detailed finite element modeling.

Thank you once again for your expert guidance throughout this review process, which has greatly strengthened our work.

Sincerely,

Oleksandr Gilodo,

Andrii Arsirii,

Sergii Kroviakov,

and Oleksandr Gimanov