Practical Design of Lattice Cell Towers on Compact Foundations in Mountainous Terrain

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript addresses the practical design of 42 m lattice cell towers for mountainous regions with compact foundations, focusing on the impact of the pyramidal-to-prismatic transition height. The main contribution lies in proposing a simple design rule – placing this transition at around 33 m (roughly 78–80% of the total height) – that is shown to balance stiffness and weight effectively. This is a useful and concrete finding, especially for rapid deployment in constrained environments such as the Carpathians.

The abstract is generally clear and informative, but it reads too promotional. It highlights the novelty and the results without really acknowledging the limitations of the study. For instance, the lack of experimental validation and the rather narrow set of configurations analyzed are weaknesses that should be at least recognized. A more critical tone would increase the credibility of the work.

The introduction does a good job of presenting the context and urgency of the problem, particularly the combination of harsh climatic conditions, limited foundation space, and even the disruption caused by the war in Ukraine. The literature review is updated and includes recent sources, but it feels somewhat uneven: it emphasizes wind and climate-related studies while overlooking earlier or more specific work on tower optimization.

Methodologically, the paper relies entirely on finite element simulations in SCAD Office, using rod elements with articulated joints. While this approach is standard and efficient, it simplifies the real behavior of the structures, especially regarding local buckling or construction imperfections. Only five transition heights were considered, which seems too coarse for a parametric study that aims to draw a general conclusion. Moreover, the applicability of the results beyond the Ukrainian regulatory context remains unclear.

The conclusions are consistent with the results reported: tubular profiles save steel (~14%), while angle profiles give better stiffness and practical advantages in terms of fabrication and maintenance. However, some of the practical recommendations – such as the preference for angle-section towers in mountainous terrain – go beyond the numerical evidence presented. These claims are reasonable but not strongly supported by data within the paper.

As for the references, they are numerous and mostly recent, with articles from well-established journals such as Applied Sciences, Buildings, Structures, and Journal of Wind Engineering and Industrial Aerodynamics. This gives the paper a solid contemporary basis. Still, some references feel rather general and not directly connected to the specific design problem addressed here, and there is little engagement with more classical or international design standards.

Overall, this is a relevant and interesting study with a clear applied contribution. It would benefit from a more critical framing of its limitations, a finer and broader exploration of the parametric space, and a clearer discussion of how the findings can be transferred to contexts outside the immediate Ukrainian case.

Author Response

Reviewer 1

 

Comments 1.

The manuscript addresses the practical design of 42 m lattice cell towers for mountainous regions with compact foundations, focusing on the impact of the pyramidal-to-prismatic transition height. The main contribution lies in proposing a simple design rule – placing this transition at around 33 m (roughly 78–80% of the total height) – that is shown to balance stiffness and weight effectively. This is a useful and concrete finding, especially for rapid deployment in constrained environments such as the Carpathians.

Response 1.

We sincerely thank the reviewer for the time and careful attention given to our work.

 

Comments 2.

The abstract is generally clear and informative, but it reads too promotional. It highlights the novelty and the results without really acknowledging the limitations of the study. For instance, the lack of experimental validation and the rather narrow set of configurations analyzed are weaknesses that should be at least recognized. A more critical tone would increase the credibility of the work.

 

Response 2.

Thank you for the constructive remark.

We agree that the abstract should be both accurate and engaging. Our intent was to communicate the contribution succinctly without overstating claims or implying evidence beyond the presented analysis. We acknowledge that the study is computational and design-oriented (without experimental validation) and that it examines a bounded set of representative configurations. To address your point directly – and in line with the journal’s guidance for authors – we will add a brief “Limitations and scope” note at the end of the Conclusions to explicitly state these boundaries.

For transparency and balance, we will include the following brief note in the Conclusions to delineate scope and limitations.

Limitations and scope.

This study is computational and code-based; experimental verification lies outside its present scope and is planned for future work. The parametric space was intentionally bounded to representative 42 m lattice towers on compact foundations, assessed under regional wind and icing prescriptions and standard load combinations. While such focusing narrows generality, alignment with widely adopted design documents and the use of normalized performance indices are precisely what make the results directly actionable for practitioners and rapid deployments in mountainous terrain.

 

Comments 3.

The introduction does a good job of presenting the context and urgency of the problem, particularly the combination of harsh climatic conditions, limited foundation space, and even the disruption caused by the war in Ukraine. The literature review is updated and includes recent sources, but it feels somewhat uneven: it emphasizes wind and climate-related studies while overlooking earlier or more specific work on tower optimization.

Response 3.

Thank you for the thoughtful observation. We agree the introduction can better reflect the body of research on tower optimization; we have prepared a brief insertion for Section 1 and added the following references (not previously cited) to balance the review.

Text insert

Optimization of lattice telecommunication towers operates on three interlocking levels. First, geometric proportioning – plan form (triangular or square), leg inclinations, panel heights, and the location of the pyramidal-to-prismatic interface – governs global stiffness, steel mass, and natural frequencies; studies on topology and proportioning for towers and related lattice masts consistently show that judicious placement of the transition and rational panelization improve the stiffness–weight balance [1–4]. Second, configuration design covers three choices: the bracing scheme (X, K, or diamond), the grouping of members, and the cross-section family (angles or tubes). It works best when treated as a combined size, shape, and topology problem.
The design must satisfy standard limits on strength, drift, stability, and modal separation.
Modern metaheuristic methods – genetic algorithms and simulated annealing – explore these coupled discrete – continuous spaces effectively. They are often paired with surrogate models and have proven reliable [3–7]. Third, detailing and constructability – joint design, splice locations, tolerances, transport modules, and the interface with compact foundations – should be embedded as hard or penalized constraints so that mathematically optimal solutions remain buildable in constrained mountainous terrain [2, 4–6]. Taken together, this systems view aligns advances in structural optimization with field realities and explains why simple, testable design rules for the transition height can emerge as robust, practitioner-friendly outcomes [1–7].

 Additional literature

1. Tsavdaridis, K.D.; Nicolaou, A.; Mistry, A.D.; Efthymiou, E. Topology Optimisation of Lattice Telecommunication Tower and Performance-Based Design Considering Wind and Ice Loads. Structures 2020, 27, 2379–2399. https://doi.org/10.1016/j.istruc.2020.08.010
2. Ebid, A.M.; El-Aghoury, M.A.; Onyelowe, K.C. Estimating the Optimum Weight for Latticed Power-Transmission Towers Using Different (AI) Techniques. Designs2022, 6, 62. https://doi.org/10.3390/designs6040062
3. Cucuzza, R.; Rosso, M.M.; Aloisio, A.; Melchiorre, J.; Giudice, M.L.; Marano, G.C. Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading.  Sci.2022, 12, 4875. https://doi.org/10.3390/app12104875
4. de Souza, R.R.; Miguel, L.F.F.; Lopez, R.H.; Torii, A.J. A Procedure for the Size, Shape and Topology Optimization of Transmission Line Tower Structures. Engineering Structures 2016, 111, 162–184. https://doi.org/10.1016/j.engstruct.2015.12.005
5. Tort, C.; Şahin, S.; Hasançebi, O. Optimum Design of Steel Lattice Transmission Line Towers Using Simulated Annealing and PLS-TOWER. Computers & Structures 2017, 179, 75–94. https://doi.org/10.1016/j.compstruc.2016.10.017.
6. Khodzhaiev, M.; Reuter, U. Structural Optimization of Transmission Towers Using a Novel Genetic Algorithm Approach with a Variable Length Genome. Engineering Structures 2021, 240, 112306. https://doi.org/10.1016/j.engstruct.2021.112306
7. Kaveh, A.; Gholipour, Y.; Rahami, H. Optimal Design of Transmission Towers Using Genetic Algorithm and Neural Networks. International Journal of Space Structures 2008, 23, 1–19. https://doi.org/10.1260/026635108785342073

 

Comments 4.

Methodologically, the paper relies entirely on finite element simulations in SCAD Office, using rod elements with articulated joints. While this approach is standard and efficient, it simplifies the real behavior of the structures, especially regarding local buckling or construction imperfections. Only five transition heights were considered, which seems too coarse for a parametric study that aims to draw a general conclusion. Moreover, the applicability of the results beyond the Ukrainian regulatory context remains unclear.

Response 4.

 Thank you for the careful methodological critique.

We deliberately adopt a conservative global model with bar elements and pinned (articulated) joints for serviceability and dynamic checks. It's a conscious and balanced choice.

Assuming semi-rigid or rigid joints would over-stiffen the shaft and raise the first frequency – an outcome that might look elegant from a scientific standpoint but is unsafe for practice because it understates drifts and can mask adverse dynamic effects. Local stress concentrations at connections were not modeled in this work, such joint-level behavior lies outside the present scope and will be addressed in a dedicated component-scale study.

 In SCAD Office, member selection and verification were run in pass-through and local modes: tension members were checked for strength; compression members were additionally checked for global and local buckling, with automatic compliance against current building regulations. Geometric imperfections are indirectly accounted for through code-based slenderness, stability, and serviceability checks; detailed imperfection sensitivity is planned for follow-on work.

Regarding the sweep granularity: five transition heights were chosen to bracket the feasible range. The efficiency index shows a smooth, single minimum at 33 m for both tubular and angle towers, clearly visible in the tabular and graphical trends; adding intermediate points would refine the curve without shifting the optimum.

On the regulatory context: the study is intentionally grounded in the Ukrainian framework for loads and steel design (wind region, terrain, elevation, icing) because the authors – although university faculty – are also practicing structural engineers who design a large number of steel structures, including telecommunication towers. Our goal is an applied, immediately usable result that does not conflict with the current national provisions. At the same time, we reference widely used international documents (e.g., EN 1993-3-1, EN 1991-1-4, ANSI/TIA-222, ISO 12494, ISO 4354) to clarify how the workflow and normalized performance indices transfer beyond the Ukrainian context. A brief “Limitations and scope” note in the Conclusions transparently states that the present stage is computational and code-based, with experimental identification (ambient-vibration and drift and strain monitoring) and extensions to additional code frameworks planned next.

Comments 5.

The conclusions are consistent with the results reported: tubular profiles save steel (~14%), while angle profiles give better stiffness and practical advantages in terms of fabrication and maintenance. However, some of the practical recommendations – such as the preference for angle-section towers in mountainous terrain – go beyond the numerical evidence presented. These claims are reasonable but not strongly supported by data within the paper.

Response 5.

In the text, we have clarified why our recommendation favors angle-section towers for mountain sites and we have made the underlying assumptions explicit. Our recommendation is grounded in maintainability under harsh mountainous conditions: angle towers use bolted splices and open joints that are easier to inspect, retighten, or replace; corrosion protection is straightforward. Tubular towers, while aerodynamically smooth, demand dual-side protection (internal and external) and tight to avoid hidden condensation-driven corrosion – tasks that are harder to guarantee with limited access, short weather windows, and high humidity typical of mountainous terrain.

On “rapid deployment” (concise quantitative guidance).

We added a short operational note that summarizes indicative indices (normalized to the angle-tower case =1) based on field practice in mountainous projects. Assembly-time index: angle ≈ 1; tubular ≈ 1.2–1.4 (flanged splices and welded fittings require longer controlled operations). Piece-weight/handling index: angle ≈ 1; tubular ≈ 1.2–1.5 (heavier flange components and tighter tolerances increase lift and alignment effort). These normalized ranges are intended as practical guidance for planners. They do not replace a project-specific bid-level schedule or cost analysis, but they make the deployment rationale transparent and actionable without expanding the paper into a logistics study.

Comments 6.

As for the references, they are numerous and mostly recent, with articles from well-established journals such as Applied Sciences, Buildings, Structures, and Journal of Wind Engineering and Industrial Aerodynamics. This gives the paper a solid contemporary basis. Still, some references feel rather general and not directly connected to the specific design problem addressed here, and there is little engagement with more classical or international design standards.

Response 6.

Thank you sincerely for the careful and constructive remark. You are absolutely right – referencing internationally adopted standards will strengthen the transferability of our findings beyond the Ukrainian context and make our argumentation clearer for a broad engineering audience.

Proposed list of standards (to be added to the references)

1*. CEN. EN 1993-3-1:2006 + A1:2014. Eurocode 3: Design of Steel Structures – Part 3-1: Towers, Masts and Chimneys – Towers and Masts; European Committee for Standardization: Brussels, 2014.

In-text use: We will cite EN 1993-3-1 for the global analysis framework and member verification conventions specific to lattice towers; it supports our modeling assumptions and section pairing logic.

2*. CEN. EN 1991-1-4:2005 + A1:2010. Eurocode 1: Actions on Structures—Part 1-4: General Actions—Wind Actions; European Committee for Standardization: Brussels, 2010.

In-text use: EN 1991-1-4 underpins our wind-action modeling (terrain category, height factors, turbulence intent) and the rationale for keeping the first-mode frequency outside the wind-dominant band discussed in §3.5.

3*. TIA. ANSI/TIA-222-I:2022. Structural Standard for Antenna Supporting Structures, Antennas and Small Wind Turbine Support Structures; Telecommunications Industry Association: Arlington, VA, 2022.

In-text use: We will reference TIA-222-I for telecom-specific load combinations, importance categories, appurtenance effects, and icing/wind provisions relevant to cell towers; readers working under TIA-222-H will find consistent intent and parameters.

4*. ISO. ISO 12494:2017. Atmospheric Icing of Structures; International Organization for Standardization: Geneva, 2017.

In-text use: ISO 12494 provides the atmospheric icing framework (ice thickness/density and exposure), which we use to justify the wind-with-ice load combinations for mountainous sites.

5*. ISO. ISO 4354:2009. Wind Actions on Structures; International Organization for Standardization: Geneva, 2009.

In-text use: ISO 4354 supplies a complementary, internationally neutral basis for wind-action methodology and spectra; we will reference it alongside EN 1991-1-4 when framing the dynamic context for the modal-separation check.

Placement of in-text citations within the manuscript

Materials and Methods: wind and ice modeling, terrain category, and height corrections – EN 1991-1-4, ISO 4354, ISO 12494; global analysis and member checks – EN 1993-3-1; telecom-specific aspects – ANSI/TIA-222-I.

paragraph 3.5: the argument for the wind-dominant frequency range and safe separation of the first mode – EN 1991-1-4 and ISO 4354, with a practice note to ANSI/TIA-222-I.

Final operational note before Conclusions – where we mention maintenance advantages for mountainous sites and wind-with-ice scenarios – ANSI/TIA-222-I, ISO 12494.

Comments 7.

Overall, this is a relevant and interesting study with a clear applied contribution. It would benefit from a more critical framing of its limitations, a finer and broader exploration of the parametric space, and a clearer discussion of how the findings can be transferred to contexts outside the immediate Ukrainian case.

Response 7.

 Thank you for the encouraging assessment and the constructive pointers.

We have addressed your concerns systematically and provided succinct justifications in our responses. The revisions are implemented through concise insertions in Section 1, Section 2 and in the Conclusions, supported by additional references to recent optimization studies and widely used international standards.

Thank you again for helping us strengthen the manuscript’s clarity and practical relevance.

 

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have made certain revisions in response to the previous review comments, mainly reflected in the improvement of expression clarity and argument details. Currently, the abstract more clearly defines the core of the research (the balance between stiffness and weight of 42-meter towers under limited foundations) and key conclusions (33 meters as the optimal transition height, angle-section towers being more suitable for mountainous areas); the introduction strengthens the transformation of engineering problems into research objectives, and further illustrates the research gap in the transition position through literature review; supplementary explanations are provided on the normalization and weighted form of the penalty function to justify its use as an evaluation index. Meanwhile, the argument that the 1.68 Hz natural frequency avoids resonance is supplemented with a comparison of the wind load spectrum range (0.1–1.0 Hz), clarifying the dynamic separation between high-order and low-order frequencies.

However, the core issues remain unresolved. In terms of innovation, the "optimization of transition position" is still a conventional parametric analysis, without proposing new theories or disruptive design concepts, and the difference from existing research on lattice tower geometric optimization is not significant. In terms of research depth, the mechanism why 33 meters is the optimal transition height is not explained from the essence of structural mechanics (such as stiffness distribution and force flow transmission), and there is a lack of quantitative analysis on the fatigue performance and long-term corrosion life of the two cross-sectional forms. In finite element modeling, the mechanical equivalence (e.g., moment of inertia matching) between circular tube and angle steel cross-sections remains unexplained, and the specific calculation processes of wind loads and ice-snow loads are still missing. In terms of the basis for engineering recommendations, quantitative data such as construction cycles and transportation costs required for "rapid deployment" have not been supplemented, and some references with weak relevance to the research topic remain unadjusted.

In summary, although the manuscript has been improved, it still does not fully meet the publication requirements. It is recommended to further deepen the mechanism analysis and supplement quantitative data to enhance innovation and persuasiveness.

Author Response

General comment of the reviewer

The authors have made certain revisions in response to the previous review comments, mainly reflected in the improvement of expression clarity and argument details. Currently, the abstract more clearly defines the core of the research (the balance between stiffness and weight of 42-meter towers under limited foundations) and key conclusions (33 meters as the optimal transition height, angle-section towers being more suitable for mountainous areas); the introduction strengthens the transformation of engineering problems into research objectives, and further illustrates the research gap in the transition position through literature review; supplementary explanations are provided on the normalization and weighted form of the penalty function to justify its use as an evaluation index. Meanwhile, the argument that the 1.68 Hz natural frequency avoids resonance is supplemented with a comparison of the wind load spectrum range (0.1–1.0 Hz), clarifying the dynamic separation between high-order and low-order frequencies.

Response

Thank you sincerely for your constructive critique, thoughtful engagement, and patience throughout the revision process. Your clear guidance helped sharpen the manuscript’s focus, improve clarity of expression, and strengthen the coherence of our arguments. We are grateful for your careful reading and remain fully responsive to any final editorial suggestions.

Comments 1.

In terms of innovation, the "optimization of transition position" is still a conventional parametric analysis, without proposing new theories or disruptive design concepts, and the difference from existing research on lattice tower geometric optimization is not significant.

Response 1.

Parametric analysis is only an instrument to reach a result. The contribution lies in the idea, the approach, the way the task is posed, and the ease of implementation; these are what make the result compelling and elegant. Today truly revolutionary concepts are rare in applied mechanics; progress typically occurs through small cumulative steps, and breakthroughs are preceded by many incremental advances.

Within that understanding, our manuscript does not claim a new structural theory. Its novelty is an implementable design decision framework that reduces a many-parameter tower layout to a single, practice-controllable variable: the height of the transition from a pyramidal lower segment to a prismatic upper segment. The framework couples a code-aligned objective with a transparent constraint-handling penalty and introduces a marginal efficiency index (MEI) to identify where additional steel ceases to deliver proportionate structural benefit. This synthesis yields a concise, verifiable rule for day-to-day design: place the transition at about seventy-eight to eighty percent of the total height (about thirty-three meters in our forty-two-meter reference case). The recommendation improves modal separation, serviceability, and material economy while remaining fully compatible with current detailing practice and standards.

To make this contribution explicit, we revised the abstract, the end of the introduction, and the conclusions to clarify the decision logic, to report the MEI plateau that underpins the recommended band, and to emphasize transferability and code compliance. The result is not a theoretical disruption; it is a disruptively usable method that a design office can adopt without new member types, bespoke joints, or exotic analyses.

Comments 2.

In terms of research depth, the mechanism why 33 meters is the optimal transition height is not explained from the essence of structural mechanics (such as stiffness distribution and force flow transmission), and there is a lack of quantitative analysis on the fatigue performance and long-term corrosion life of the two cross-sectional forms.

Response 2

Our study is APPLIED, not FUNDAMENTAL. It is aimed at a real, practical outcome. The authors are practicing structural engineers, so the results may not look flashy on paper, but they are real, they comply with building codes, and they are ready for implementation. We believe such results merit publication.

We expanded Section 3.4 to articulate the structural mechanism behind the recommended transition band and to quantify it with the MEI calculated between successive candidate transition heights. The central idea is that added stiffness is most valuable where the fundamental mode draws on it the most, which is in the lower portion of the shaft. A pyramidal lower segment increases chord spacing and bracing efficiency near the base, where it has the greatest leverage on the fundamental frequency and drift. Continuing the pyramid too high yields diminishing returns because the modal curvature demand has already decayed, while it adds mass where dynamic amplitudes are larger. A prismatic upper segment avoids that mass penalty and simplifies fabrication. The observed optimum near thirty-three meters in the forty-two-meter tower is precisely where the incremental gain per unit steel flattens, which our MEI makes explicit.

On fatigue and corrosion life, we agree that the cross-sectional form and joint detailing govern stress-range categories, inspection regimes, and coating performance. These durability aspects are intentionally outside the optimization scope of the present paper, which focuses on the transition-height decision under code-level actions and serviceability. We therefore added a Limitations and Scope paragraph in the conclusions stating that high-cycle fatigue verification and life-cycle corrosion assessments will be performed at the execution-design stage using the selected joint details, site wind spectra, and exposure category.

Limitations (insert for Conclusions). This paper does not quantify high-cycle fatigue. Performance depends on joint detailing and the site-specific stress-range spectrum. The transition-height recommendation addresses strength and serviceability only. Fatigue will be verified at the execution-design stage in accordance with the selected detail categories and site spectra.

 

Comments 3.

In finite element modeling, the mechanical equivalence (e.g., moment of inertia matching) between circular tube and angle steel cross-sections remains unexplained, and the specific calculation processes of wind loads and ice-snow loads are still missing.

Response 3

Our comparison does not rely on mechanical “equivalence” in the sense of matching sectional inertias between tubular and angle members. For an civil engineer, the correct yardstick is load-carrying performance under the two code-defined limit-state groups – ultimate and serviceability –within the same global geometry, boundary conditions, and load cases. Accordingly, the finite-element models keep the tower layout identical while sizing representative member families in tubular and in angle configurations to satisfy the relevant strength, stability, and deflection criteria, as well as local sustainability. The Results section already demonstrates this side-by-side performance comparison (Fig.11) and shows how it drives the transition-height recommendation.

To address traceability of actions, we have added a concise loading methodology note that enumerates the steps used to derive wind and ice–snow actions and to feed them into the model.

 

Comments 4.

In terms of the basis for engineering recommendations, quantitative data such as construction cycles and transportation costs required for "rapid deployment" have not been supplemented, and some references with weak relevance to the research topic remain unadjusted.

Response 4

We have clarified why our recommendation favours angle-section towers for mountain sites and we have made the underlying assumptions explicit. The preference is grounded in maintainability under harsh high-elevation conditions: angle towers use bolted splices and open, gusseted joints that are easy to inspect, retighten, or replace, and corrosion protection is straightforward. By contrast, tubular lattice towers rely predominantly on welded nodes and flange assemblies. Any on-site welding demands qualified procedures, preheat control, weather shielding, and non-destructive testing, which are difficult to guarantee with limited access, short weather windows, and high humidity typical of mountainous terrain. Even when tubular segments are shop-welded and connected with bolted flanges, the fittings are heavier and require tighter alignment tolerances, which slows erection and raises handling demands.

To address “rapid deployment” with quantitative yet practical guidance, we added an operational note that reports indicative indices normalised to the angle-tower case = 1. Assembly-time index: angle ≈ 1; tubular ≈ 1.2–1.4 due to flange alignment and weld-related controls. Piece-weight and handling index: angle ≈ 1; tubular ≈ 1.2–1.5 because heavier flange components and tighter tolerances increase lift and fit-up effort. These ranges support early planning and comparison. They do not replace a project-specific schedule or transport costing, but they make the deployment rationale transparent and actionable without expanding the paper into a logistics study.

Finally, we reviewed the bibliography for topical relevance, removed weakly connected items, added recent sources on lattice-tower optimisation, and cited international structural and climatic codes aligned with Ukrainian practice, including EN 1993-3-1, EN 1991-1-4, ANSI/TIA-222, ISO 12494, and ISO 4354.

Text insertion before conclusions.

To consolidate the engineering basis for our recommendations, we synthesize the deployment and maintainability implications of the two section families using the evidence reported above. In our models, tubular towers reduce steel tonnage by about 14 percent, which is attractive at procurement, whereas angle-section towers provide a stiffer global response and lower resonance risk within the examined height and loading regime. In mountainous terrain, field operability becomes decisive: angle towers use bolted splices and open, gusseted joints that are easy to galvanize, inspect, retighten, and repair locally. Tubular systems, though aerodynamically smooth, require both external and internal protection and rely on welded or flanged joints with tighter tolerances and more controlled assembly steps, which are difficult to assure under limited access and short weather windows at altitude. On balance, and assuming the code-based wind-with-icing combinations and the optimized transition height adopted here, this trade-off often shifts the practical choice toward angle-section towers. Transport logistics, crew productivity, and contractor means and methods remain project specific and should be confirmed at bid level. The present paper provides the structural and operational rationale on which those planning checks can build.

Comments 5.

In summary, although the manuscript has been improved, it still does not fully meet the publication requirements. It is recommended to further deepen the mechanism analysis and supplement quantitative data to enhance innovation and persuasiveness.

Response 5

Thank you for the clear summary and constructive guidance. We have carefully considered all comments in aggregate and, accordingly, have substantially revised – and where appropriate, expanded – the manuscript. Amendments and clarifications have been introduced across all sections. We believe the paper has been materially improved through this exchange. The revisions and additions have been highlighted in the updated manuscript in color. Thank you again for your time and thoughtful attention.

Reviewer 3 Report

Comments and Suggestions for Authors

Overall comment:

The manuscript presents a practical, parameter-based study with a usable guide for the transition height in lattice towers. Presentation is clear, and the results align with stated aims, but a few improvements can strengthen clarity, scope alignment, and practical applicability.

Major points:

Title–scope alignment (foundations): The title emphasises "compact foundations," but the model uses an ideal fixed base without foundation design. Please add governing support reactions and a short note on anchorage/compact-foundation implications—or moderate the title.

Mountain wind/topography: Briefly discuss orographic (topographic) wind speed-up and add 1–2 sentences on how the optimal transition height would shift under higher exposure typical of ridges; include a supporting reference.

Joint/eccentricity idealisation: State limitations of hinged/ideal joints and add a short sensitivity or commentary on joint flexibility/eccentricities and potential local stability issues (tubes vs. angles).

Penalty metric: Justify the use of the dimensional product (mass × top displacement) and consider noting an equivalent normalised/weighted metric.

Reproducibility: Add a compact table with member sizes/steel grade and key load cases; if feasible, provide model inputs as Supplementary Material.

 

Minor points:

Move the early mention of the "~33 m optimum" from the Introduction to Results (or clearly mark it as a preview).

Ensure consistent notation, units, and decimal formatting across figures/tables; make figure captions self-contained.

Add a brief note on icing mass assumptions and their influence on modal frequencies/displacements.

Comments on the Quality of English Language

Light language polishing (shorter sentences, consistent terminology) is needed.

Author Response

Overall comment:

The manuscript presents a practical, parameter-based study with a usable guide for the transition height in lattice towers. Presentation is clear, and the results align with stated aims, but a few improvements can strengthen clarity, scope alignment, and practical applicability.

Overall response

Thank you for the thoughtful overview and for the time invested in our manuscript. We have taken your remarks on clarity, scope alignment, and practical applicability on board and prepared concise, targeted revisions accordingly.

Comments 1.

Title–scope alignment (foundations): The title emphasises "compact foundations," but the model uses an ideal fixed base without foundation design. Please add governing support reactions and a short note on anchorage/compact-foundation implications—or moderate the title.

Response 1.

Thank you. We do not design foundations in this paper; foundation engineering for towers is a large, separate topic. Our case concerns a constrained base area that leads to a non-standard base-to-height ratio of about 1:13 for the forty-two-metre tower. In the initial version of the manuscript the theme read “...cell towers in conditions of limited base area for remote mountainous regions,” but the title was adjusted during earlier review. If you prefer, we can revert to that earlier wording. In addition, to address your request without overreaching the scope, we will report the governing support reactions and add a brief note on anchorage implications for compact foundations.

 

Comments 2.

Mountain wind/topography: Briefly discuss orographic (topographic) wind speed-up and add 1–2 sentences on how the optimal transition height would shift under higher exposure typical of ridges; include a supporting reference.

Response 2.

We have expanded the literature and added contextual in-text citations to international standards governing loads and actions. EN 1991-1-4 underpins our wind-action modelling, including terrain categorisation, height and exposure factors, and the rationale for keeping the first-mode frequency outside the wind-dominant band discussed in Section 3.5. ANSI/TIA-222-I is cited for telecom-specific load combinations, importance categories, appurtenance effects, and the provisions for wind with icing; the intent remains consistent for readers working under TIA-222-H. ISO 12494 provides the atmospheric icing framework, including ice thickness, density, and exposure categories for mountainous sites. ISO 4354 supplies a complementary, internationally neutral basis for wind-action methodology and spectra, which we reference alongside EN 1991-1-4 when framing the dynamic context. We also added a concise methodological insert that consolidates wind, icing, and combination rules.

Comments 3.

Joint/eccentricity idealisation: State limitations of hinged/ideal joints and add a short sensitivity or commentary on joint flexibility/eccentricities and potential local stability issues (tubes vs. angles).

Response 3.

Thank you for the careful methodological critique.

We deliberately adopt a conservative global model with bar elements and pinned (articulated) joints for serviceability and dynamic checks. It's a conscious and balanced choice.

Assuming semi-rigid or rigid joints would over-stiffen the shaft and raise the first frequency – an outcome that might look elegant from a scientific standpoint but is unsafe for practice because it understates drifts and can mask adverse dynamic effects. Local stress concentrations at connections were not modeled in this work, such joint-level behavior lies outside the present scope and will be addressed in a dedicated component-scale study.

Regarding this comment, we have added a clear paragraph in the conclusions of the article about the limitations of the model and results.

 

Comments 4.

Penalty metric: Justify the use of the dimensional product (mass × top displacement) and consider noting an equivalent normalised/weighted metric.

Response 4.

We expanded Section 3.4 to clarify why the dimensional product of total mass and top displacement is a suitable, practitioner-facing efficiency measure, and to present its unit-free counterpart. We name and use the marginal efficiency index (MEI) to identify the knee point where additional steel no longer yields commensurate drift reduction. The manuscript now reports this knee near the same transition height that minimizes the base product, reinforcing the recommendation. 

 Comments 5.

Reproducibility: Add a compact table with member sizes/steel grade and key load cases; if feasible, provide model inputs as Supplementary Material.

Response 5.

We added the requested reproducibility details in compact form. A brief insert at the end of Section 2 consolidates load inputs and their distribution, with the wind-application scheme shown in Figures 5–6 and the line wind actions by height linked to member selections in Table 2. Member families and sizes by segment are listed alongside those actions, and the steel grade is identified at the start of Section 2.

Comments 6.

Move the early mention of the "~33 m optimum" from the Introduction to Results (or clearly mark it as a preview).

Response 6.

This is a very good point! We have removed the reference to “33 meters” from the first section of the article.

 

Comments 7.

Ensure consistent notation, units, and decimal formatting across figures/tables; make figure captions self-contained.

Response 7.

We reviewed the notation, units of measurement, and captions of the figures. Several figures are direct scans of software outputs; we do not alter numerical content in such images. In case of emergency, we can duplicate any essential labels or unit notes in the captions to ensure complete clarity.

 

Comments 8.

Add a brief note on icing mass assumptions and their influence on modal frequencies/displacements.

Response 8.

At the end of the paragraph on the modal analysis of the towers, we made the following text insertion.

For winter operation, atmospheric icing increases the distributed mass of chords, bracing, and appurtenances, and this is already reflected in our load cases in accordance with the code-prescribed icing parameters for the selected climatic region. Under abnormal icing that falls outside the code envelope, the same modal check should be repeated with conservative accretion added as lumped or distributed mass to members and appurtenances. The expected effect is a downward shift of the first frequency and a corresponding increase in winter drift. For the recommended geometry the frequency margin remains adequate in typical scenarios, but if a project-specific reassessment shows a reduced margin, it can be restored by a modest upward adjustment of the transition height, by local reinforcement in the lower shaft, or by temporary operating restrictions during extreme icing events.

 

We have revised the manuscript, improved every section, and sincerely hope that the updated version will be well received. Thank you for the careful review and for the time you invested in our work. Your clear, constructive comments helped us sharpen the manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

Reviewer Report for the manuscript:

Practical Design of Lattice Cell Towers on Compact Foundations in Mountainous Terrain

General Comments

The paper addresses the structural design of 42 m-high lattice cell towers for mountainous terrain with compact foundations. The main contribution is a parametric FEM study on the influence of the pyramidal-to-prismatic shaft transition height on stiffness, weight, and modal behavior. Two tower types (tubular vs. angle-section) are analyzed under wind and ice loads, leading to a practical recommendation: the transition should be located at ~78–80% of tower height (≈33 m). Modal analysis confirms natural frequencies above critical resonance ranges. The paper is motivated by industrial failures in the Carpathians and aims to provide design guidance for resilient telecom infrastructure.

Strengths

1. Relevance and topicality: The focus on compact foundations in mountainous terrain is highly relevant, especially under climate change and war-damaged infrastructure contexts.
2. Methodological clarity: The FEM models, boundary conditions, and loading scenarios are described in detail, using SCAD Office software.
3. Novelty: The study isolates a design parameter (transition height) rarely examined in the literature and derives a practical design rule of thumb. Previous studies mainly focus on general tower typologies, load combinations, or material advances. This paper adds a targeted parametric analysis that yields a practical design recommendation (transition at ~33 m for a 42 m tower), which has direct implications for safe and economical tower design.
4. Practicality: Comparison between tubular and angle-section solutions provides engineers with actionable guidance, balancing stiffness, weight, corrosion protection, and maintainability.
5. Structure: The manuscript is logically organized, moving from motivation to methods, results, optimization, and conclusions.

Major Concerns

1. Lack of experimental validation
   The study is entirely numerical. No experimental or field data are provided to validate FEM results. Given the emphasis on real failures in the Carpathians, some reference to actual measured displacements, strains, or monitored tower performance would strengthen confidence in the conclusions. 
2. Simplified connection modelling
   The FEM assumes hinged joints between lattice members, which may not reflect the real semi-rigid behavior of bolted or welded joints. This simplification could underestimate stress concentrations and local instabilities. The limitations of this assumption are not sufficiently discussed.
3. Penalty function formulation
   The optimization uses a displacement × weight penalty function, but this is ad hoc and not justified by reliability-based or cost-based arguments. Alternative criteria (e.g., material cost, reliability index, serviceability limits) should be at least discussed.
4. Wind and ice load treatment
   The load modeling is based on Ukrainian codes but compared to Eurocode EN 1991-1-4 or TIA-222 standards only briefly. A critical comparison with international norms is missing, which reduces the paper’s global applicability.
5. Modal analysis limitations
   The lowest frequencies obtained (1.46–1.68 Hz) are indeed above 1.0 Hz, but still very close. Given uncertainties in load and material properties, a more robust dynamic safety margin analysis would be expected (e.g., sensitivity to top mass changes, damping assumptions).
6. Conclusion: The conclusions are generally consistent with the FEM results presented. The claim that the optimum transition is at 33 m is supported by Table 4 and Figures 12–14. The modal analysis supports the safety margin against resonance. However, since only numerical evidence is provided, the authors should state more clearly that the recommendation is based on numerical modeling only.

Minor Concerns

Literature review: While extensive, it is overly general and does not focus sufficiently on recent works about lattice tower optimization and reliability. Some references are more related to unrelated topics (pipelines, coatings). The paper would benefit from focusing more on recent lattice tower optimization and structural reliability studies.

Figures and tables: Some figures (wind load schemes, displacement diagrams) are of low resolution and should be improved for readability. Table 1 (equipment data) could be simplified since some details (like cable diameters) are not essential. Tables 2–4 are useful and clear. Figures 5 -10 showing wind load application and displacement shapes are too low in resolution and need to be redrawn for clarity. The numerical results (forces, displacements) are consistent but should be discussed with reference to international standards (Eurocode, TIA-222) for wider applicability.

English style: The manuscript is understandable but requires language polishing to improve clarity and remove redundancies.

Clarity in conclusions: The conclusion mixes technical findings with practical comments on corrosion and maintenance. These should be separated into technical conclusions and implementation considerations.

 

Recommendation

Reconsider after major revisions.

The manuscript is potentially valuable, but it currently lacks experimental validation, deeper international code comparison, and a stronger justification of the optimization criterion. Addressing these issues, along with improving figures and language, will significantly enhance the contribution and credibility.

Author Response

General Comments

The paper addresses the structural design of 42 m-high lattice cell towers for mountainous terrain with compact foundations. The main contribution is a parametric FEM study on the influence of the pyramidal-to-prismatic shaft transition height on stiffness, weight, and modal behavior. Two tower types (tubular vs. angle-section) are analyzed under wind and ice loads, leading to a practical recommendation: the transition should be located at ~78–80% of tower height (≈33 m). Modal analysis confirms natural frequencies above critical resonance ranges. The paper is motivated by industrial failures in the Carpathians and aims to provide design guidance for resilient telecom infrastructure.

Strengths

Relevance and topicality: The focus on compact foundations in mountainous terrain is highly relevant, especially under climate change and war-damaged infrastructure contexts.

Methodological clarity: The FEM models, boundary conditions, and loading scenarios are described in detail, using SCAD Office software.

Novelty: The study isolates a design parameter (transition height) rarely examined in the literature and derives a practical design rule of thumb. Previous studies mainly focus on general tower typologies, load combinations, or material advances. This paper adds a targeted parametric analysis that yields a practical design recommendation (transition at ~33 m for a 42 m tower), which has direct implications for safe and economical tower design.

Practicality: Comparison between tubular and angle-section solutions provides engineers with actionable guidance, balancing stiffness, weight, corrosion protection, and maintainability.

Structure: The manuscript is logically organized, moving from motivation to methods, results, optimization, and conclusions.

 

Thank you for your detailed review, the time you devoted, and the constructive guidance you provided. Your precise, actionable comments have meaningfully strengthened the clarity and practical value of our manuscript. We are genuinely grateful for your thoughtful engagement.

Comments 1.

Lack of experimental validation

The study is entirely numerical. No experimental or field data are provided to validate FEM results. Given the emphasis on real failures in the Carpathians, some reference to actual measured displacements, strains, or monitored tower performance would strengthen confidence in the conclusions.

Response 1.

We acknowledge that the present work is theoretical, and we intend to extend it as circumstances allow. Regrettably, the university building that housed our laboratories was destroyed during the war, and our bench program is temporarily suspended. We are continuing the analytical and numerical track in the interim and plan to resume bench and field tests as facilities are restored. We appreciate the emphasis on validation and hope this clarifies what has been verified internally here and how the study fits within our ongoing analytical–experimental agenda. In the meantime, we performed internal consistency checks within the software and cross-checked selected results against hand calculations. The construction of the first five mobile communication towers, accompanied by field observations, is planned; a corresponding publication is anticipated in 2026.

 

Comments 2.

Simplified connection modelling

The FEM assumes hinged joints between lattice members, which may not reflect the real semi-rigid behavior of bolted or welded joints. This simplification could underestimate stress concentrations and local instabilities. The limitations of this assumption are not sufficiently discussed.

Response 2.

Thank you for the careful methodological critique.

We deliberately adopt a conservative global model with bar elements and pinned (articulated) joints for serviceability and dynamic checks. It's a conscious and balanced choice. This yields two-sided estimates that are suitable for practical application.

The thing is that semi-rigid or rigid joints would over-stiffen the shaft and raise the first frequency – an outcome that might look elegant from a scientific standpoint but is unsafe for practice because it understates drifts and can mask adverse dynamic effects. Local stress concentrations at connections were not modeled in this work, such joint-level behavior lies outside the present scope and will be addressed in a dedicated component-scale study.

Regarding this comment, we have added a clear paragraph in the conclusions of the article about the limitations of the model and results.

 

Comments 3.

Penalty function formulation

The optimization uses a displacement × weight penalty function, but this is ad hoc and not justified by reliability-based or cost-based arguments. Alternative criteria (e.g., material cost, reliability index, serviceability limits) should be at least discussed.

Response 3.

We expanded Section 3.4 to articulate the structural mechanism behind the recommended transition band and to quantify it with the Marginal Efficiency Index (MEI) calculated between successive candidate transition heights. We also added a short insert that clarifies why the product of total mass and top displacement is a practical proxy for competing objectives in tower design: it captures the trade-off between serviceability (drift control and modal separation) and logistical economy (tonnage and handling), and it remains transparent to practitioners. In parallel, we note an equivalent normalized and weighted form that places both objectives on a common scale; under any reasonable positive weighting the location of the optimum remains within the same narrow band. The MEI then identifies the knee point beyond which additional steel no longer yields commensurate drift reduction, which is the basis for our recommendation.

Comments 4.

Wind and ice load treatment

The load modeling is based on Ukrainian codes but compared to Eurocode EN 1991-1-4 or TIA-222 standards only briefly. A critical comparison with international norms is missing, which reduces the paper’s global applicability.

Response 4.

Our study is applied, not fundamental. It is aimed at a real, practical outcome. As practicing structural engineers, we focus on results that are code-compliant and ready for implementation. We are, of course, experts in the local regulatory codes – these are native to our practice, and we work with them every day. We agree that global applicability benefits from explicit links to international norms. Accordingly, we reviewed the manuscript and added cross-references to EN 1991-1-4, ANSI/TIA-222, ISO 12494, and ISO 4354 alongside the Ukrainian provisions used for the calculations. A brief methodological bridge now maps the adopted terrain categories, exposure and topographic factors, wind-with-icing combinations, and spectra to their counterparts in these standards, so readers working under Eurocode or TIA can translate the workflow without reinterpretation. We believe this aligns the paper’s practical scope with international practice while keeping the emphasis on a usable design rule.

Comments 5.

Modal analysis limitations

The lowest frequencies obtained (1.46–1.68 Hz) are indeed above 1.0 Hz, but still very close. Given uncertainties in load and material properties, a more robust dynamic safety margin analysis would be expected (e.g., sensitivity to top mass changes, damping assumptions).

Response 5.

Our baseline modal model is intentionally conservative and already represents the heaviest practical configuration for these towers. The structure is analysed fully equipped with high-power appurtenances and with the maximum code-prescribed winter icing for the selected climatic region included as additional mass. The geometry is deliberately demanding, with a base-to-height ratio of about one to thirteen, and the global model uses pinned joints. This combination drives frequencies downward and drifts upward, so any margin demonstrated under these assumptions is conservative with respect to typical field conditions.

The governing mechanism is straightforward. Stiffness provided low in the shaft controls the first mode, whereas icing and equipment increase inertia primarily at elevation. The recommended transition height raises stiffness precisely where it is most effective. As a result, the extra winter mass produces only a modest downward shift of the first frequency and does not erase the dynamic separation achieved by the adopted geometry.

To document robustness, we have added a compact sensitivity note in Section 3.5. It brackets the dynamic margin against reasonable variations in top-mounted mass, including conservative winter accretion already in the load cases, and against customary damping assumptions for lattice towers. Across this envelope the first-mode frequency remains outside the wind-dominant range cited in the standards-based context, and the associated increase in winter drift is predictable and manageable. The pinned-joint idealisation also provides two-sided practical estimates: it yields a lower bound on frequencies and an upper bound on drifts relative to semi-rigid reality, so the reported margin is on the safe side of practice.

Comments 6.

Conclusion: The conclusions are generally consistent with the FEM results presented. The claim that the optimum transition is at 33 m is supported by Table 4 and Figures 12–14. The modal analysis supports the safety margin against resonance. However, since only numerical evidence is provided, the authors should state more clearly that the recommendation is based on numerical modeling only.

Response 6.

We accept this point and make it explicit. The Abstract now states clearly that the transition-height recommendation is derived from numerical modelling. In addition, we added a new insert in the Conclusions that informs the reader of the study’s limits: the findings are based on FE analysis only; project-specific checks are required at execution design; and experimental and field validation will be carried out in subsequent studies. This wording presents the recommendation transparently as numerically grounded and practice-ready within the stated scope.

Comments 7.

Literature review: While extensive, it is overly general and does not focus sufficiently on recent works about lattice tower optimization and reliability. Some references are more related to unrelated topics (pipelines, coatings). The paper would benefit from focusing more on recent lattice tower optimization and structural reliability studies.

Response 7.

We have prepared a brief insertion for Section 1 and added the following references (not previously cited) to balance the review.

Text insert

Optimization of lattice telecommunication towers operates on three interlocking levels. First, geometric proportioning – plan form (triangular or square), leg inclinations, panel heights, and the location of the pyramidal-to-prismatic interface – governs global stiffness, steel mass, and natural frequencies; studies on topology and proportioning for towers and related lattice masts consistently show that judicious placement of the transition and rational panelization improve the stiffness–weight balance [1–4]. Second, configuration design covers three choices: the bracing scheme (X, K, or diamond), the grouping of members, and the cross-section family (angles or tubes). It works best when treated as a combined size, shape, and topology problem.
The design must satisfy standard limits on strength, drift, stability, and modal separation.
Modern metaheuristic methods – genetic algorithms and simulated annealing – explore these coupled discrete – continuous spaces effectively. They are often paired with surrogate models and have proven reliable [3–7]. Third, detailing and constructability – joint design, splice locations, tolerances, transport modules, and the interface with compact foundations – should be embedded as hard or penalized constraints so that mathematically optimal solutions remain buildable in constrained mountainous terrain [2, 4–6]. Taken together, this systems view aligns advances in structural optimization with field realities and explains why simple, testable design rules for the transition height can emerge as robust, practitioner-friendly outcomes [1–7].

 Additional literature

1. Tsavdaridis, K.D.; Nicolaou, A.; Mistry, A.D.; Efthymiou, E. Topology Optimisation of Lattice Telecommunication Tower and Performance-Based Design Considering Wind and Ice Loads. Structures 2020, 27, 2379–2399. https://doi.org/10.1016/j.istruc.2020.08.010
2. Ebid, A.M.; El-Aghoury, M.A.; Onyelowe, K.C. Estimating the Optimum Weight for Latticed Power-Transmission Towers Using Different (AI) Techniques. Designs2022, 6, 62. https://doi.org/10.3390/designs6040062
3. Cucuzza, R.; Rosso, M.M.; Aloisio, A.; Melchiorre, J.; Giudice, M.L.; Marano, G.C. Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading.  Sci.2022, 12, 4875. https://doi.org/10.3390/app12104875
4. de Souza, R.R.; Miguel, L.F.F.; Lopez, R.H.; Torii, A.J. A Procedure for the Size, Shape and Topology Optimization of Transmission Line Tower Structures. Engineering Structures 2016, 111, 162–184. https://doi.org/10.1016/j.engstruct.2015.12.005
5. Tort, C.; Şahin, S.; Hasançebi, O. Optimum Design of Steel Lattice Transmission Line Towers Using Simulated Annealing and PLS-TOWER. Computers & Structures 2017, 179, 75–94. https://doi.org/10.1016/j.compstruc.2016.10.017.
6. Khodzhaiev, M.; Reuter, U. Structural Optimization of Transmission Towers Using a Novel Genetic Algorithm Approach with a Variable Length Genome. Engineering Structures 2021, 240, 112306. https://doi.org/10.1016/j.engstruct.2021.112306
7. Kaveh, A.; Gholipour, Y.; Rahami, H. Optimal Design of Transmission Towers Using Genetic Algorithm and Neural Networks. International Journal of Space Structures 2008, 23, 1–19. https://doi.org/10.1260/026635108785342073

Where non-tower sources remain, they are retained for a clear reason: several papers, though not about towers, exemplify analysis and durability-assessment methods for elongated (slender) steel structures. While not tower-specific, these methods are contextually aligned with our reliability framing and are useful to the argument. In addition, we have added references to international regulatory documents in the field of construction throughout the text.

 

Comments 8.

Figures and tables: Some figures (wind load schemes, displacement diagrams) are of low resolution and should be improved for readability. Table 1 (equipment data) could be simplified since some details (like cable diameters) are not essential. Tables 2–4 are useful and clear. Figures 5 -10 showing wind load application and displacement shapes are too low in resolution and need to be redrawn for clarity. The numerical results (forces, displacements) are consistent but should be discussed with reference to international standards (Eurocode, TIA-222) for wider applicability.

 

Response 8.

The reviewer likely received a PDF in which automatic export down-sampling reduced image quality; the source figures are higher-resolution. We have also added explicit references to EN 1991-1-4 and ANSI/TIA-222 and discuss the numerical results in that standards context for broader applicability.

The reviewer likely received a PDF in which automatic export down-sampling reduced image quality; the source figures are higher-resolution. We have also added explicit references to EN 1991-1-4 and ANSI/TIA-222 and discuss the numerical results in that standards context for broader applicability.

Total added:
1*. CEN. EN 1993-3-1:2006 + A1:2014. Eurocode 3: Design of Steel Structures – Part 3-1: Towers, Masts and Chimneys – Towers and Masts; European Committee for Standardization: Brussels, 2014.

In-text use: We will cite EN 1993-3-1 for the global analysis framework and member verification conventions specific to lattice towers; it supports our modeling assumptions and section pairing logic.

2*. CEN. EN 1991-1-4:2005 + A1:2010. Eurocode 1: Actions on Structures—Part 1-4: General Actions—Wind Actions; European Committee for Standardization: Brussels, 2010.

In-text use: EN 1991-1-4 underpins our wind-action modeling (terrain category, height factors, turbulence intent) and the rationale for keeping the first-mode frequency outside the wind-dominant band discussed in §3.5.

3*. TIA. ANSI/TIA-222-I:2022. Structural Standard for Antenna Supporting Structures, Antennas and Small Wind Turbine Support Structures; Telecommunications Industry Association: Arlington, VA, 2022.

In-text use: We will reference TIA-222-I for telecom-specific load combinations, importance categories, appurtenance effects, and icing/wind provisions relevant to cell towers; readers working under TIA-222-H will find consistent intent and parameters.

4*. ISO. ISO 12494:2017. Atmospheric Icing of Structures; International Organization for Standardization: Geneva, 2017.

In-text use: ISO 12494 provides the atmospheric icing framework (ice thickness/density and exposure), which we use to justify the wind-with-ice load combinations for mountainous sites.

5*. ISO. ISO 4354:2009. Wind Actions on Structures; International Organization for Standardization: Geneva, 2009.

In-text use: ISO 4354 supplies a complementary, internationally neutral basis for wind-action methodology and spectra; we will reference it alongside EN 1991-1-4 when framing the dynamic context for the modal-separation check.

 

Comments 9.

English style: The manuscript is understandable but requires language polishing to improve clarity and remove redundancies.

Clarity in conclusions: The conclusion mixes technical findings with practical comments on corrosion and maintenance. These should be separated into technical conclusions and implementation considerations.

Response 9.

We engaged a professional linguist and native English speaker to polish the manuscript. The Conclusions section has been expanded and revised.

 

The manuscript is potentially valuable, but it currently lacks experimental validation, deeper international code comparison, and a stronger justification of the optimization criterion. Addressing these issues, along with improving figures and language, will significantly enhance the contribution and credibility.

Thank you for a thorough, candid, and constructive review. We have carefully considered every point and substantially revised the manuscript. We truly appreciate the time and care you devoted to our work.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

• Please verify that the photographs are the authors’ own, or otherwise indicate if they originate from another source.

• In Table 2, specify the units corresponding to the contents of the first column.

• The labels of the legends in Figures 7 through 10 are not legible; I recommend enlarging the figures.

• Is it possible to enlarge the strength ratios in Figure 11?

• It is necessary to number the equations in the manuscript.

Author Response

Comment 1.
Please verify that the photographs are the authors’ own, or otherwise indicate if they originate from another source.

Response 1.

We appreciate this careful observation and have undertaken a full audit of all fifteen figures included in the manuscript. We confirm that every visual item is original and author‐generated. Specifically, photographs were taken by the authors in the course of our design and fieldwork activities. The computational visuals (including screen captures of model setup, load cases, and post-processing results) were produced by the authors from within the SCAD Office environment; the problem formulations, boundary conditions, modeling assumptions, and result exports are entirely our own work. Likewise, all schemes, and sketches were created by the authors expressly for this study and have not been reproduced from third-party sources.

 

Comment 2.

In Table 2, specify the units corresponding to the contents of the first column.

Response 2.

Thank you for pointing out this ambiguity. In Table 2 (“Maximum wind loads on the towers and cross-sectional dimensions of the chords”), the first column lists elevation marks along the tower height using the standard civil-engineering convention of millimeters measured from the base reference level (for example, +33,000 … +42,000). We have revised the table to state the units explicitly by changing the first-column header to “Elevation mark, mm” and aligning the numeric entries with that unit.

Comment 3.
The labels of the legends in Figures 7 through 10 are not legible; I recommend enlarging the figures.

Response 3.

We are grateful for this practical suggestion. We carefully verified the figure assets and note that the apparent loss of sharpness occurs primarily at the PDF export stage, where embedded rasters are downsampled, whereas the source images retain higher resolution and legibility in our working files. In the journal’s online layout, readers can open each figure in a larger view (full-screen or zoomed), which restores the crispness of the legend entries and line markers without introducing scaling artifacts that sometimes accompany pre-emptive enlargement at the manuscript stage.

Comment 4.
Is it possible to enlarge the strength ratios in Figure 11?

Response 4.

Figure 11 reports element-wise ratios of the load-bearing capacity utilisation. The numerical overlays (including font size and placement) are produced directly by the SCAD Office post-processor and scale consistently with the finite-element visualization; manual re-editing would risk altering the provenance of the computational output and could be misconstrued as a modification of results. As with the previous comment, the online article viewer allows readers to expand Figure 11 to a full-screen view, at which point the labels are readily legible while preserving the integrity and traceability of the software-generated display. For these reasons, we have not altered the sizing of the labels in the manuscript version.

Comment 5.

It is necessary to number the equations in the manuscript.

Response 5.

Thank you for the recommendation. We have numbered all equations throughout the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The revision has fully addressed the previous review comments. Its content quality and persuasiveness have been significantly improved. No further revisions are required, and it is recommended for publication.

Author Response

Many thanks for your careful review and the time you invested. Your input strengthened the paper. We appreciate the positive assessment, it confirms that the revisions were appropriate. Thank you.

Reviewer 4 Report

Comments and Suggestions for Authors

The paper can be published now.

Author Response

Thank you sincerely for the careful reading of our manuscript and the time you devoted. Working with you has improved the paper. We’re grateful for your positive evaluation - it reassures us that the revisions were well judged. Thank you.