Buckling Behavior of Perforated Cold-Formed Steel Uprights: Experimental Evaluation and Comparative Assessment Using FEM, EWM, and DSM

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript investigates the buckling behavior of perforated cold-formed steel uprights with design applications. Though the technical information is interesting, there are a couple of technical and general issues in this manuscript.

Technical

1. Have the finite element models applied in this study been validated by experimental tests?
2. Material property definitions are needed in this manuscript. For instance, the material property of S355 steel.
3. Why did the authors use EN 1993-1-3 not a newer version of EU codes? Which version of AISI S100 provisions is utilized in this study?
4. Section 2.2.2. What are the loading protocols used in this study? Please add a figure.
5. Provide an enlarged short base upright profile.
6. Conclusions must be rewritten since there are not many technical conclusions.
7. Are any conclusions drawn for the influence of slenderness on the failure modes and design resistance?
8. Any discussions or conclusions on the reduction of net area? Please clarify.

General

9. Figure 4. What are the units in these figures?
10. Lines 494 – 498 and Table 3. There should always be a space between a number and its unit.
11. All acronyms should be defined on their first appearance. For instance, CUFSM on line 519. FEM, EWM, and DSM on line 537, and EWM and DSM on line 572.

Comments on the Quality of English Language

This manuscript needs to be proofread by a professional English editor due to a few grammatical issues. 

Author Response

Dear Reviewer 1,

We sincerely thank you for your detailed and thoughtful review. Your comments have helped us clarify key aspects related to the experimental validation, material properties, and the application of design standards. We have addressed each point carefully, and we believe your suggestions have contributed significantly to improving the quality of our work.

Comments

"This manuscript investigates the buckling behavior of perforated cold-formed steel uprights with design applications. Though the technical information is interesting, there are a couple of technical and general issues in this manuscript.

Technical

1. Have the finite element models applied in this study been validated by experimental tests?"

1. Yes, the finite element models developed in this study were thoroughly validated against experimental results. The validation process included a direct comparison between the numerical and experimental load–displacement curves for all three specimen types (SS-340, MS-990, and TS-1990), as illustrated in Figures 21, 28, and 32, respectively. Additionally, the deformation patterns and stress distributions obtained from nonlinear finite element simulations closely matched the experimentally observed buckling modes and failure locations (Figures 20, 26, and 31).

The numerical models were calibrated using material properties obtained from tensile tests (Section 2.1, Figure 3, and Table 1) and incorporated realistic boundary conditions, geometric imperfections, and contact definitions, as described in Sections 4.1–4.3. The good agreement between FEM results and test data confirms the reliability of the numerical approach and its ability to replicate the complex instability phenomena observed in perforated cold-formed steel uprights under axial compression.

1. Material property definitions are needed in this manuscript. For instance, the material property of S355 steel.

2. We appreciate the reviewer’s suggestion. The material properties of the S355MC steel used in this study have now been clearly defined in Section 2.1. These properties were determined through tensile testing of five representative specimens in accordance with EN ISO 6892-1. The results are presented in Figure 3 and summarized in Table 1. The following average values were obtained:

• Yield strength (f_yb): 430 MPa
• Ultimate tensile strength (f_u): 505 MPa
• Modulus of elasticity (E): 210,000 MPa
• Poisson’s ratio (μ): 0.3
• Density (ρ): 7850 kg/m³
• Shear modulus (G): ≈81,000 MPa

These experimentally obtained properties were used consistently in both the analytical calculations and the finite element simulations for accurate model calibration and comparison with test results.

 

1. Why did the authors use EN 1993-1-3 not a newer version of EU codes? Which version of AISI S100 provisions is utilized in this study?

1. We thank the reviewer for this pertinent observation.

All analyses and calculations presented in this manuscript were carried out during the period 2022–2023, prior to the official publication of the updated EN 1993-1-3:2024 and AISI S100-24 standards. At that time, the most recent applicable normative references were:

• EN 1993-1-3:2006, which remained the harmonized Eurocode for cold-formed steel design in the European Union,
• and AISI S100-16 (2016 edition), widely adopted in both academic and practical design contexts for cold-formed steel members.

Therefore, the study was developed in full compliance with the official codes in force during its execution. However, we acknowledge that updated versions of both standards have since become available, and we intend to address their implications in future research extensions. A brief note referencing the new editions has been added to the revised manuscript for clarity.

1. Section 2.2.2. What are the loading protocols used in this study? Please add a figure.

We appreciate the reviewer’s suggestion. The loading protocol is described in Section 2.2.2, and photographs of the actual test setups are provided in Figure 6 (subfigures a–d), covering the three column lengths and the respective testing machines.

To further enhance clarity, we have added a new schematic (Figure 4) that summarizes the boundary conditions, loading direction, and instrumentation used during the tests. This figure complements the photographs by providing a clear, generalized view of the experimental setup and loading procedure for all specimen types.

1. Provide an enlarged short base upright profile.

We appreciate the reviewer’s suggestion. Detailed geometric information regarding the short base upright profile is already provided in Figure 5, which shows the visual appearance of the SS-340 specimens prior to testing, and in Figure 6, which illustrates the experimental setup and clearly displays the upright geometry, welded end plates, and boundary conditions. These figures include both photographic and technical views of the short upright specimen. We trust that these visuals provide sufficient detail to support the experimental interpretation, but we remain open to adding an enlarged schematic if deemed necessary by the editor.

1. Conclusions must be rewritten since there are not many technical conclusions.

We appreciate the reviewer’s constructive remark. In response, the Conclusions section has been substantially revised to include more technical insights drawn from the experimental, numerical, and analytical results. The updated section now explicitly states:

• The correlation between observed buckling modes (local, distortional, global) and column slenderness,
• The effectiveness of the finite element models in capturing deformation patterns and stress concentrations,
• The relative accuracy of EWM vs. DSM in predicting compressive resistance, especially in perforated cold-formed profiles,
• The justification for using the net cross-sectional area without local reduction due to enhanced stiffness from web stiffeners.

We believe the revised conclusions provide clearer, technically grounded takeaways that better reflect the scope and impact of the study.

1. Are any conclusions drawn for the influence of slenderness on the failure modes and design resistance?

Yes, conclusions regarding the influence of slenderness on both the failure modes and the design resistance have now been clearly stated in the revised Conclusions section. Specifically:

• The experimental results demonstrated a direct correlation between member slenderness and dominant failure mode:
• Short columns (low slenderness) failed by local buckling near perforations;
• Medium-length columns showed interaction between distortional and global buckling;
• Long columns (high slenderness) exhibited pure global flexural buckling with minimal local deformation.
• Design resistance varied accordingly:
• For short specimens (SS-340), the full plastic capacity was nearly reached;
• For MS-990 and TS-1990, the axial capacity decreased progressively due to increased instability effects.

This behavior was also captured in the numerical models and reflected in the analytical results, particularly through the variation of non-dimensional slenderness (λ̄) and reduction factors (χ). These findings are now highlighted in points 1 and 5 of the revised Conclusions section to emphasize the role of slenderness in structural response.

 

1. Any discussions or conclusions on the reduction of net area? Please clarify.

We thank the reviewer for this important point.

Yes, the manuscript includes both discussion and justification regarding the treatment of net cross-sectional area. As stated in Sections 4 and 6, and reinforced in the revised Conclusions (Point 5), no additional reduction of the net area was applied in either the Finite Element Models or the Direct Strength Method calculations.

This choice is technically justified based on:

• The moderate width-to-thickness ratios of the plate elements (b/t < 30), which are below the slenderness limits defined in EN 1993-1-3 for unstiffened plates;
• The presence of a longitudinal stiffener in the web, which significantly enhances local stability;
• The experimental evidence: all tested specimens exhibited no premature local buckling or tearing near perforations, and deformations remained stable and localized.

Consequently, the full net section was considered effective. This approach was validated by the excellent agreement between experimental results, numerical simulations, and DSM predictions, especially for medium- and long-slenderness specimens.

A dedicated paragraph has been added in Section 6 to make this reasoning more explicit for the reader.

 

General

1. Figure 4. What are the units in these figures?

Thank you for your observation. The units in Figure 4 were omitted unintentionally. All dimensions in this figure are in millimeters (mm). We have revised the figure caption and included a note within the figure itself to clearly indicate the units used.

1. Lines 494 – 498 and Table 3. There should always be a space between a number and its unit.

We thank the reviewer for this formatting observation. The manuscript has been carefully revised to ensure that a non-breaking space is included between all numerical values and their units, particularly in lines 494–498 and in Table 3, in accordance with typographic conventions (e.g., “85 mm” instead of “85mm”). This correction has been applied consistently throughout the text, tables, and figure captions.

 

1. All acronyms should be defined on their first appearance. For instance, CUFSM on line 519. FEM, EWM, and DSM on line 537, and EWM and DSM on line 572.

We appreciate the reviewer’s attention to clarity and readability. All acronyms have now been defined upon their first appearance in the manuscript. Specifically:

• FEM is introduced as Finite Element Method,
• EWM as Effective Width Method,
• DSM as Direct Strength Method, and
• CUFSM as Constrained and Unconstrained Finite Strip Method.

These definitions have been added where each term is first mentioned in the text (e.g., Sections 1, 4.2, and 5.2), and consistency has been ensured throughout the manuscript. We thank the reviewer for helping improve the clarity of the paper.

 

Comments on the Quality of English Language

This manuscript needs to be proofread by a professional English editor due to a few grammatical issues. 

We thank the reviewer for this observation. The manuscript has now been carefully proofread and revised to correct minor grammatical and stylistic issues. We have ensured improved consistency, clarity, and academic tone throughout the text. If required, we are happy to submit the manuscript for additional professional language editing prior to final acceptance.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Overall, it can be stated that the authors have conducted an extensive amount of research, as evidenced by the length of the manuscript. However, the large volume is, in our opinion, one of the main problems of the paper. The study lacks a qualitative analysis of the conducted investigations. The results are presented without sufficient discussion or interpretation.

Here is a detailed rationale:

1. The authors identify the following research gaps: “Specifically, there remains limited investigation regarding the coupled buckling behavior of cold-formed perforated uprights at intermediate slenderness levels. Furthermore, detailed characterizations of realistic geometric imperfections, important for accurate finite element modeling (FEM), are rarely reported explicitly.” However, these goals are not followed through in the later sections of the paper.

2. The authors did not provide a mathematical justification for the chosen specimen lengths, which is a crucial factor in such experiments. Similarly, the number of test specimens is not justified. Why five specimens and not three or just one?

3. In Table 1, the total cross-sectional area is listed as 555 mm² and the effective as 511 mm². Yet in Table 3, the total area is already given as 511 mm². The method used for determining effective widths for perforated sections is not explained. The Eurocode does not directly provide such methods.

4. Figure 4: Much attention is given to the drawings of specimens and test setup. Spherical hinges were used, but the authors do not explain their purpose. If the goal is to test uprights under realistic conditions, such hinges are usually not present. If the goal is to model classical compression members, then the rationale for offsets “55” and “42” mm in Figure 4d should be clarified.

5. Page 7: It is mentioned that three different test rigs were used. Did the authors analyze the effect of using different equipment on the test results? Wouldn't it be more appropriate to use the same rig for all tests?

6. Line 201: “All tests were conducted under pin-ended boundary conditions, simulating real-world support conditions.” The authors should explain how uprights function within actual racking systems.

7. Lines 226–227 are unclear. The authors should clarify what they mean.

8. Lines 229–230: “The images show a combination of global buckling and local deformation, with failure typically occurring near perforations or dimpled zones.” This statement should be elaborated. What exactly caused the failure? What was the influence of perforations versus the overall slenderness?

9. Line 238: “The failure mode was governed by geometric instability rather than material failure.” What do the authors mean by “material failure”? Does yielding count as material failure or not?

10. Figure 11b: The figure clearly shows at least three linear segments with different slopes. Their physical meaning should be explained.

11. Line 310: The authors state that “the TS-1990 profiles remained stable in the cross-sectional plane.” However, the fourth image in Figure 12 clearly shows signs of local buckling near a perforation.

12. Page 15: The authors describe a commonly known procedure for introducing imperfections based on buckling shapes. However, the scaling factor used in the imperfection modeling is not provided.

13. The authors should better explain why a yield strength of 650 MPa was used in the simulations while the experimental results showed 500 MPa.

14. Figure 18a and similar ones: The authors present maximum displacements in the cross-section—what is the purpose of this? These displacements were not measured in the experiment.

15. Figure 19b is questionable. The nature of the deformation distribution is not explained. Why does tension appear at the lower support? Why is the top cross-section not uniformly compressed?

16. Line 418 (and similar throughout): The authors mostly describe what is seen in the figure, without providing any analytical interpretation or explanation of why this data is significant or interesting for other researchers.

Conclusion:
In our opinion, the paper requires major revisions. It would be advisable to divide the work into two separate papers. The first one should thoroughly describe the experimental plan, present the results, and provide a qualitative and quantitative analysis of the data. The second should focus on numerical modeling and comparison with the experimental results.

Author Response

Dear Reviewer 2,

Thank you very much for your critical and constructive feedback. Your questions regarding the consistency between the research objectives and methodology were particularly valuable. We have clarified the experimental scope, added relevant explanations, and adjusted the text to reflect your observations. Your input was essential in strengthening the coherence of the manuscript.

 

Comments and Suggestions for Authors

“Overall, it can be stated that the authors have conducted an extensive amount of research, as evidenced by the length of the manuscript. However, the large volume is, in our opinion, one of the main problems of the paper. The study lacks a qualitative analysis of the conducted investigations. The results are presented without sufficient discussion or interpretation.”

Here is a detailed rationale:

1. The authors identify the following research gaps: “Specifically, there remains limited investigation regarding the coupled buckling behavior of cold-formed perforated uprights at intermediate slenderness levels. Furthermore, detailed characterizations of realistic geometric imperfections, important for accurate finite element modeling (FEM), are rarely reported explicitly.” However, these goals are not followed through in the later sections of the paper.
2. We appreciate the reviewer’s careful reading and valuable comment.

The two identified research gaps — the interaction of buckling modes at intermediate slenderness and the explicit modeling of geometric imperfections — are addressed in the following parts of the paper, although we agree that this could be more explicitly highlighted.

The MS-990 specimens (intermediate-length columns) are specifically chosen to investigate coupled buckling behavior. In Section 3.2, the experimental observations describe the development of distortional–global interaction, and in Figures 9 and 10, the lateral deflection patterns confirm this hybrid behavior. Moreover, the numerical analysis in Section 4.3 reproduces these interaction modes using a nonlinear FEM model, further supporting the conclusions.

Regarding geometric imperfections, Section 4.2–4.4 describe the procedure used in ANSYS, where imperfections were introduced based on the first eigenmode from a preliminary linear buckling analysis. This approach is standard for nonlinear simulations in structural instability studies. However, we acknowledge that more emphasis should be placed on the rationale and sensitivity of imperfection amplitude and shape, and we have clarified this aspect in the revised text.

To address this comment, we have added a new paragraph at the beginning of Section 4 to explicitly link these modeling strategies to the research gaps stated in the Introduction. A clarification was also added in Section 6 (Discussion) to underline the observed interaction effects in MS-990 specimens.

 

2. The authors did not provide a mathematical justification for the chosen specimen lengths, which is a crucial factor in such experiments. Similarly, the number of test specimens is not justified. Why five specimens and not three or just one?
3. We thank the reviewer for this important observation regarding the experimental design.

The selection of specimen lengths was made to represent realistic upright segment lengths between bracing nodes in typical industrial pallet rack systems, following industry standards and prior literature. Specifically:

• SS-340 represents a short, stocky member, where local buckling is predominant;
• MS-990 corresponds to intermediate-length columns, prone to coupled distortional-global instability;
• TS-1990 simulates slender uprights subject primarily to global buckling.

These lengths were chosen based on dimensional data from commercially available rack systems, and to span a representative range of non-dimensional slenderness values (λ̄). We have now clarified this rationale in Section 2.2.1, and added reference to the computed slenderness values for each case (see Table 3 and revised discussion in Section 6).

Regarding the number of test specimens: five identical samples were tested for each column length to ensure:

• statistical significance of the results,
• identification of possible scatter due to manufacturing tolerances or local imperfections,
• and to allow for meaningful average load–displacement curves and failure pattern consistency.

Testing five specimens for SS-340 and MS-990 allowed us to capture the variability inherent to cold-formed perforated profiles and ensured statistical relevance of the results. For TS-1990, three specimens were tested due to practical limitations related to specimen height and test rig capacity. Nevertheless, the results were consistent and aligned with the numerical predictions, providing sufficient confidence for evaluating the behavior of slender members. This rationale has now been clearly stated in Section 2.2.2.

3. In Table 1, the total cross-sectional area is listed as 555 mm² and the effective as 511 mm². Yet in Table 3, the total area is already given as 511 mm². The method used for determining effective widths for perforated sections is not explained. The Eurocode does not directly provide such methods.

We thank the reviewer for pointing out this apparent inconsistency.

To clarify: the gross cross-sectional area of the profile, without accounting for perforations, is 555 mm². The net area which excludes the perforated regions, is 511 mm². This net area is the one used consistently in Table 3 for both the Effective Width Method (EWM) and Direct Strength Method (DSM) calculations.

Regarding the effective area, it should be noted that no additional reduction was applied beyond the removal of perforations. This is because, as per EN 1993-1-3, effective width reductions are required only when the width-to-thickness (b/t) ratio exceeds the slenderness limit of approximately 30. In our case, all flat elements (web, flanges, lips) have b/t ratios below this threshold, and the presence of a longitudinal stiffener further enhances stability. Therefore, the entire net cross-section was considered fully effective.

This approach is now explicitly explained in Section 5.1 and discussed in Section 6, together with experimental justification that no premature local buckling was observed in any of the tested specimens.

 

4. Figure 4: Much attention is given to the drawings of specimens and test setup. Spherical hinges were used, but the authors do not explain their purpose. If the goal is to test uprights under realistic conditions, such hinges are usually not present. If the goal is to model classical compression members, then the rationale for offsets “55” and “42” mm in Figure 4d should be clarified.
5. We thank the reviewer for this valuable comment.

The use and positioning of the spherical hinges in the experimental setup were implemented in accordance with the Romanian design guideline GP 128-2014, specifically Annex A.2, which governs the design and testing of storage rack uprights subjected to axial compression. According to this guideline, the load should be applied through spherical hinges placed at the centroid of the cross-section, ensuring a uniform stress distribution and avoiding secondary moments due to eccentricity or imperfect boundary conditions.

Although such hinges are not part of in-service pallet rack systems, their presence in the experimental setup serves to replicate idealized pin-ended boundary conditions, allowing for a clean evaluation of buckling behavior under axial loading only. This approach facilitates direct comparison with analytical models and finite element simulations, and aligns with experimental practices used in previous studies on cold-formed members.

The offset dimensions of 55 mm and 42 mm in Figure 4d reflect the vertical positioning of the spherical hinge center relative to the test machine interfaces, ensuring that the load passes through the centroid of the upright profile, as required by GP 128-2014. This has now been clarified in the revised caption of Figure 4 and further explained in Section 2.2.2 of the manuscript.

 

5. Page 7: It is mentioned that three different test rigs were used. Did the authors analyze the effect of using different equipment on the test results? Wouldn't it be more appropriate to use the same rig for all tests?

We appreciate the reviewer’s concern regarding the use of different test rigs.

Indeed, three different testing machines were used, corresponding to the required load capacity and specimen dimensions for each test series:

• Zwick/Roell 1000SP (1000 kN) for SS-340 (short, high-capacity specimens),
• 3000 kN hydraulic frame for MS-990 (medium specimens),
• and a custom 300 kN rig for TS-1990 (tall, slender specimens with lower expected capacity).

The selection was made based on specimen-specific requirements in terms of stroke length, vertical clearance, and sensitivity of instrumentation. While ideally a single testing machine would have been used for all cases, this was not feasible due to the large differences in geometry and expected behavior.

To ensure comparability:

• All machines were equipped with calibrated load cells and displacement transducers,
• The same loading rate (≈1 kN/s) and boundary conditions were applied consistently,
• The measured responses were normalized and verified to eliminate any potential bias due to equipment.

No systematic deviation was observed across test rigs. The experimental load–displacement curves for each specimen group showed excellent internal consistency, confirming that the testing equipment did not influence the structural response. This has now been clarified in Section 2.2.2.

 

 

 

6. Line 201: “All tests were conducted under pin-ended boundary conditions, simulating real-world support conditions.” The authors should explain how uprights function within actual racking systems.
7. We thank the reviewer for this useful observation.

We add this paragraph in section 2.2.2: “All tests were conducted with articulated boundary conditions at the base, as prescribed by Annex A.2 of GP 128-2014, which reflects the typical behavior of uprights in pallet racking systems. The top end of each specimen was left free to displace laterally, simulating the unbraced length between two real-world bracing nodes. Axial loads were applied concentrically through welded steel end plates to ensure uniform stress distribution and minimal eccentricity.”

7. Lines 226–227 are unclear. The authors should clarify what they mean.
8. Thank you for pointing out the ambiguity of this passage.

The original sentence has been revised for clarity. Our intent was to highlight that the average load–displacement curve presented in Figure 7(b) shows a gradual decrease in load capacity after reaching the peak, which corresponds to the onset and development of local buckling in the web of the section. The revised version reads:

“The average load–displacement curve shown in Figure 7(b) reaches a peak load of 196 kN at a displacement of 1.75 mm. After the peak, the curve exhibits a moderately descending trend, which reflects the progressive development of local buckling in the web region near the perforations.”

This correction has been implemented in the revised manuscript to improve clarity and technical accuracy.

 

8. Lines 229–230: “The images show a combination of global buckling and local deformation, with failure typically occurring near perforations or dimpled zones.” This statement should be elaborated. What exactly caused the failure? What was the influence of perforations versus the overall slenderness?
9. We thank the reviewer for this important observation and agree that the original sentence was too general.

The paragraph in question has been revised to provide a clearer explanation of the failure mechanisms, distinguishing between the influence of geometric perforations and member slenderness.

For the SS-340 specimens, failure was primarily governed by local buckling of the web and inward distortion of the flanges, both of which were triggered or intensified near perforations and dimpling features. These zones represent local stiffness reductions and stress concentrators, acting as initiation points for instability.

Due to the low slenderness ratio, global buckling effects were minimal in SS-340. However, interaction between local deformations and end-boundary constraints led to visible out-of-plane movement near mid-height. The failure was therefore a localized phenomenon driven by geometry, not by overall member instability.

The revised text now reads:

“The images show that failure was initiated by local buckling in the web zone, particularly near perforations and dimples, which act as stress concentrators. Although some global deformation was visible, the short length and high stiffness of the SS-340 specimens prevented full-column buckling. The observed failure was thus dominated by local instability phenomena, initiated around geometric discontinuities.”

This revision is now reflected in Section 3.1.

 

9. Line 238: “The failure mode was governed by geometric instability rather than material failure.” What do the authors mean by “material failure”? Does yielding count as material failure or not?
10. We thank the reviewer for this pertinent question.

In the original statement, the term “material failure” was used to refer to fracture, tearing, or rupture of the steel — that is, ultimate material failure involving loss of load-carrying capacity due to local cracking or separation.

To clarify, the sentence has been revised as follows: “The failure mode was governed by geometric instability — such as local buckling and flange distortion — rather than by ultimate material failure (e.g., tearing or rupture). Plastic yielding occurred locally, but the specimens retained integrity throughout the test.”

This distinction is now made explicit in Section 3.1.

 

10. Figure 11b: The figure clearly shows at least three linear segments with different slopes. Their physical meaning should be explained.
11. Thank you for this insightful observation.

We agree that Figure 11b (the average load–displacement curve for TS-1990 specimens) presents three distinct linear segments, each corresponding to a different structural response phase:

1. Initial linear elastic segment: This corresponds to the purely elastic response of the column, with no visible deformation or buckling — the slope reflects the axial stiffness of the upright section.
2. Intermediate segment with reduced stiffness: This change in slope reflects the onset of geometric nonlinearity and the development of flexural deformation. At this stage, lateral displacement increases, initiating global buckling while the column continues to carry load.
3. Post-peak softening segment: This final region indicates loss of axial stiffness due to large lateral displacements and plastic redistribution of internal forces. Although no rupture was observed, this phase is governed by second-order effects and inelastic post-buckling behavior.

This interpretation has been added to the discussion of TS-1990 results in Section 3.3, immediately following Figure 11b.

 

11. Line 310: The authors state that “the TS-1990 profiles remained stable in the cross-sectional plane.” However, the fourth image in Figure 12 clearly shows signs of local buckling near a perforation.
12. We thank the reviewer for pointing out this issue.

Upon review, we discovered that the fourth image in Figure 12 was mistakenly inserted from a subsequent experimental study involving reinforced profiles with an interior sleeve, not part of the current investigation. This image does not correspond to any of the TS-1990 specimens tested and analyzed in this manuscript.

We have now replaced the incorrect image with the appropriate one showing an actual TS-1990 specimen tested under axial compression, consistent with the data and analysis presented. With this correction, the statement that “the TS-1990 profiles remained stable in the cross-sectional plane” is valid and accurately reflects the observed experimental behavior.

We sincerely thank the reviewer for helping us identify and correct this error.

 

12. Page 15: The authors describe a commonly known procedure for introducing imperfections based on buckling shapes. However, the scaling factor used in the imperfection modeling is not provided.
13. We thank the reviewer for this observation.

Indeed, the geometric imperfections were introduced into the nonlinear FEM analyses using the first buckling mode obtained from the eigenvalue analysis. The applied scaling factor for imperfection amplitude was 1/1000 of the column length, consistent with common practice in cold-formed steel research and in line with recommendations from EN 1993-1-5 and existing literature (e.g., Schafer, 2002).

The choice of this value ensures sufficient triggering of instability while avoiding overly large deformations that could artificially reduce the member capacity. We have now explicitly included this detail in Section 4.2 of the manuscript.

 

13. The authors should better explain why a yield strength of 650 MPa was used in the simulations while the experimental results showed 500 MPa.
14. We thank the reviewer for this valuable observation.

The apparent discrepancy arises from the distinction between engineering stress–strain data and the true stress–strain data used in the finite element simulations. The yield strength obtained experimentally from tensile tests was approximately 430–440 MPa, as shown in Figure 3 and Table 1.

However, in the FEM material model, the true stress–strain curve was used to define the multilinear isotropic plasticity, as required for accurate post-yield behavior in nonlinear analysis. After conversion from engineering to true values, the equivalent true stress at maximum strain reached approximately 650 MPa, which corresponds to the peak stress (not the yield point) in the true stress–strain relationship.

Therefore, the 650 MPa used in the FEM input is not the yield strength, but rather the maximum true stress reached during the tensile simulation, ensuring an accurate representation of strain hardening. This explanation has been added to Section 4.1 for clarification.

 

 

14. Figure 18a and similar ones: The authors present maximum displacements in the cross-section—what is the purpose of this? These displacements were not measured in the experiment.

Thank you for your comment.

Figure 18a presents the deformation shape from the structural analysis without considering instability, while Figure 18b shows the first buckling mode from the eigenvalue analysis. In contrast, Figure 19 illustrates the final nonlinear analysis, where instability effects are fully taken into account. These figures are included to show the evolution from ideal deformation to instability-driven behavior, rather than to compare displacement values with experimental measurements.

 

15. Figure 19b is questionable. The nature of the deformation distribution is not explained. Why does tension appear at the lower support? Why is the top cross-section not uniformly compressed?
16. We thank the reviewer for this pertinent observation.

Figure 19 includes two distinct representations of deformation results:

• Figure 19a shows the global total deformation of the entire assembly, including the upright, end plates, and supports, capturing the overall buckling behavior under axial compression.
• Figure 19b, on the other hand, presents the directional axial deformation (along the Z-axis) of the upright profile only, isolated from the rest of the assembly. This allows for a clearer view of how axial shortening varies along the height and within the perforated zones of the profile.

The apparent tensile values near the bottom support and non-uniform compression at the top in Figure 19b are not actual physical tensions but reflect the relative axial deformation distribution within the upright, visualized at element level without boundary components.

We have now clarified this distinction in the manuscript and revised the caption accordingly.

 

16. Line 418 (and similar throughout): The authors mostly describe what is seen in the figure, without providing any analytical interpretation or explanation of why this data is significant or interesting for other researchers.
17. We appreciate this observation and agree that several figure descriptions, particularly in Sections 4 and 6, were initially too descriptive and lacked sufficient analytical insight.

In the revised manuscript, we have augmented the figure discussions by including:

• Interpretations of deformation patterns and stress concentrations, in relation to local geometry (perforations, stiffeners) and slenderness effects;
• Correlation between FEM-predicted behaviors and experimental observations, emphasizing how the simulations validate the physical tests;
• Explanations of the structural significance of observed modes (e.g., stress redistribution, transition from local to global instability);
• Design implications, particularly regarding the use of net sections and the applicability of DSM.

These improvements aim to make the data more meaningful and informative to researchers working on cold-formed steel, rack design, and numerical modeling of instability phenomena. We thank the reviewer for encouraging this important enhancement in scientific communication.

 

Conclusion:
In our opinion, the paper requires major revisions. It would be advisable to divide the work into two separate papers. The first one should thoroughly describe the experimental plan, present the results, and provide a qualitative and quantitative analysis of the data. The second should focus on numerical modeling and comparison with the experimental results.

1. We thank the reviewer for the suggestion to divide the manuscript into two separate papers—one focused on the experimental program and the other on numerical modeling and validation.

However, we respectfully believe that the integrated nature of this study is essential to its scientific value. The experimental and numerical components were conceived, executed, and interpreted as a cohesive investigation, with each part directly informing and validating the other.

Our goal was not only to report test results, but also to demonstrate how these results can be used to calibrate and validate finite element models and support design-level conclusions. Separating the two parts would fragment the narrative and reduce the clarity of the connection between observed behavior and its numerical representation.

In response to the reviewer’s comment, we have made substantial improvements throughout the manuscript to:

• Strengthen the analytical interpretation of both experimental and numerical results;
• Clarify the logical structure and transitions between sections;
• Emphasize the combined relevance of the results for design applications and future research.

We hope the revised version demonstrates that the value of this work lies precisely in its unified experimental–numerical–analytical approach.

Reviewer 3 Report

Comments and Suggestions for Authors

It would be helpful if a title could reflect the comparative assessment between DSM, EWM, and FEM as more analytical. Would providing a summary of the differences in strength percentages in the numerical versus experimental context help to make this abstract more quantitative?

Could the authors describe the novelty more clearly by contrasting with past shortcomings in the DSM and EWM approaches? Have all the recent works referred to in between 2023–2024 regarding any modification to DSM been taken into consideration?

Can the authors clarify why they selected S355 steel and whether other steel grades were contemplated? Are the end plate and boundary conditions representative of regular rack installations? Would any minor instrument alignment or eccentricity perhaps impact results? Were these issues considered?

Are five specimens enough to statistically validate the results? Was any statistical summary of these results (e.g., mean, standard deviation) generated as a basis for assessing repeatability?

The authors used a multilinear isotropic hardening model. We would like to know if kinematic hardening or combined models could describe cyclic behavior or post-buckling behavior. Is the imperfection amplitude based on measured data or some literature standard (like L/1000)? Were there any mesh convergence studies done? Are stress concentrations near the perforation dependent on the mesh?

In the presence of perforations, how do the authors justify the use of the standard EN 1993-1-3 provisions with no modification? Do any calibration/validation steps allow for the inference of assumptions made in Step 3 of Table 2?

How was the elastic critical load for distortional buckling determined—CUFSM or FEM? Do the authors foresee discrepancies in assumptions for net and gross sections in the context of DSM?

That EWM and DSM yield the same for MS-990 and TS-1990 is perhaps a tad excessive on the assumptions--the authors refer to “very good agreement." How can they quantify that deviation, for instance percent error?

For TS-1990, making the claim of negligible influence from local buckling effects appears justified solely based on the visual observations? The conclusion states that “net section can thus be taken as effective.” Are they going to generalize this also in case of other geometries? The authors are advised to be cautious about extrapolating this conclusion to sections with high slenderness or different perforation patterns.

Could the authors briefly describe how their validated FEM model would be extrapolated to cover dynamic or seismic loading, as stated in the conclusion? Will future analysis be dealing with fatigue/influence loading?

Author Response

Dear Reviewer 3,

We are grateful for your insightful suggestions, especially concerning the title, abstract, and analytical interpretation of results. Your recommendation to include quantified differences and to explicitly mention the limitations of DSM has helped us refine the presentation and focus of our study. We have implemented your suggestions throughout the manuscript.

Comments

“It would be helpful if a title could reflect the comparative assessment between DSM, EWM, and FEM as more analytical. Would providing a summary of the differences in strength percentages in the numerical versus experimental context help to make this abstract more quantitative?”

1. Thank you for your valuable suggestions.

We have updated the manuscript title to better reflect the comparative and analytical nature of our study. The revised title is now:

"Buckling Behavior of Perforated Cold-Formed Steel Uprights: Experimental Investigation and Comparative Analysis Using DSM, EWM, and FEM"

Additionally, we have revised the abstract to include quantitative details regarding the differences between numerical and experimental results. Specifically, we clarified that FEM predictions differed from experimental peak loads by less than 5%, DSM by approximately 2–7%, while EWM provided more conservative estimates with discrepancies up to 15%.

These changes enhance both the analytical clarity of the title and the quantitative rigor of the abstract, following the reviewer’s suggestions.

 

Could the authors describe the novelty more clearly by contrasting with past shortcomings in the DSM and EWM approaches? Have all the recent works referred to in between 2023–2024 regarding any modification to DSM been taken into consideration?

1. We thank the reviewer for this insightful comment.

The main focus of this study is placed on the nonlinear finite element modeling of perforated cold-formed steel uprights, with the analytical methods (DSM and EWM) serving primarily for the verification and validation of numerical and experimental results. The novelty of our work, therefore, lies predominantly in the detailed nonlinear FEM analysis, incorporating realistic boundary conditions, geometric imperfections, and material behavior, aspects which have often been simplified or overlooked in previous research.

Regarding recent modifications to DSM published in the period 2023–2024, while we acknowledge their importance, these modifications were not the central aspect of our research. Our primary objective was to establish and validate robust finite element modeling procedures, supported by existing analytical methods. Nevertheless, we recognize that recent DSM advancements offer valuable directions for future investigations and improvements in analytical validations.

We greatly appreciate the reviewer’s suggestion and will explicitly consider this aspect in our ongoing and future studies.

 

Can the authors clarify why they selected S355 steel and whether other steel grades were contemplated? Are the end plate and boundary conditions representative of regular rack installations? Would any minor instrument alignment or eccentricity perhaps impact results? Were these issues considered?

1. Thank you for your pertinent questions.

• Selection of S355 steel:
  The choice of S355MC steel was based on its widespread use in the manufacturing of cold-formed steel uprights for pallet racking systems. In addition to its availability and favorable strength-to-weight ratio, S355 offers adequate ductility, making it particularly suitable for seismic applications, where energy dissipation and post-yield behavior are critical. Its mechanical properties comply with the requirements of EN 1993-1-3 and EN 15512 for use in structures located in moderate to high seismic zones.
• End plate and boundary conditions:
  The boundary conditions used in the experimental program followed the recommendations provided in Annex A.2 of the Romanian guideline GP 128-2014, which is specific to the design of storage rack uprights. The use of spherical hinges and welded end plates allowed for concentric axial load introduction through the centroid of the section, replicating ideal pin-ended conditions. Although such configurations may differ slightly from real-life connections in rack installations, they align with the assumptions used in both analytical design methods (EWM, DSM) and finite element simulations, ensuring compatibility and consistency.
• Influence of alignment and eccentricities:
  We recognize that small imperfections, including instrument misalignment or eccentric load introduction, can affect the test results. To account for this, we applied a 10% reduction factor to the average experimental load–displacement curves, thereby incorporating the possible influence of such deviations into the analysis. This correction allowed for a more conservative and realistic comparison with the idealized FEM and analytical models.

We appreciate the opportunity to clarify these aspects and believe they reinforce the relevance and applicability of the methods used in this study.

 

Are five specimens enough to statistically validate the results? Was any statistical summary of these results (e.g., mean, standard deviation) generated as a basis for assessing repeatability?

1. We thank the reviewer for raising this important point regarding statistical validation.

In this study, five specimens were tested for each of the SS-340 and MS-990 series, in line with established experimental practices for cold-formed steel elements, where 3 to 5 samples are commonly used to ensure repeatability without excessive resource requirements. For the TS-1990 series, only three specimens were tested due to the practical limitations related to specimen height, equipment capacity, and material availability.

To assess the repeatability and variability, a statistical summary of the test results was generated, including mean values and standard deviations for peak load and corresponding displacements. These results showed low variability (coefficient of variation < 5%), supporting the conclusion that the test series provided consistent and representative data for the investigated buckling behaviors.

This statistical consistency, together with the close agreement between experimental and FEM results, reinforces the validity of the findings. We have now clarified this aspect in Section 3 and included the relevant statistical values in the updated version of the manuscript.

 

The authors used a multilinear isotropic hardening model. We would like to know if kinematic hardening or combined models could describe cyclic behavior or post-buckling behavior. Is the imperfection amplitude based on measured data or some literature standard (like L/1000)? Were there any mesh convergence studies done? Are stress concentrations near the perforation dependent on the mesh?

We thank the reviewer for these detailed and technically relevant questions.

• Material model – Multilinear isotropic hardening:
  The nonlinear finite element simulations were conducted under monotonic loading conditions, and for this reason, we employed a multilinear isotropic hardening model, calibrated from true stress–strain data obtained in uniaxial tensile tests. While kinematic or combined hardening models would indeed be more appropriate for capturing cyclic behavior or Bauschinger effects, these were outside the scope of the present study, which focuses on axial compression up to failure. Nevertheless, we recognize the relevance of such models in future studies involving cyclic or post-buckling reloading behavior.
• Imperfection amplitude:
  Geometric imperfections were introduced using the first eigenmode from a linear buckling analysis. The amplitude was scaled to L/1000, consistent with values recommended in EN 1993-1-5, as well as prior literature on cold-formed steel instability. While we did not directly measure geometric imperfections on the physical specimens, the chosen amplitude is well aligned with industry practice and ensures conservative post-buckling behavior in numerical simulations.
• Mesh convergence study:
  A mesh convergence study was performed prior to the main simulations. Various mesh densities were tested, and the selected mesh (based on SOLID186 elements) was found to provide a balance between computational efficiency and accuracy. Key response parameters such as peak load and deformation pattern showed less than 2% variation between the two finest mesh configurations tested.
• Stress concentrations near perforations and mesh sensitivity:
  As expected, stress concentrations were observed in the vicinity of perforations, particularly in the web zones. Local stress intensity was found to be moderately sensitive to mesh density, especially near hole edges. To mitigate artificial stress peaks, local mesh refinement was applied around perforations in all final simulations. This approach allowed for consistent identification of failure zones and improved correlation with experimental observations.

We thank the reviewer for encouraging a more detailed discussion of these numerical modeling aspects, and relevant clarifications have now been added to Section 4 of the revised manuscript.

 

In the presence of perforations, how do the authors justify the use of the standard EN 1993-1-3 provisions with no modification? Do any calibration/validation steps allow for the inference of assumptions made in Step 3 of Table 2?

1. We thank the reviewer for this important question regarding the applicability of EN 1993-1-3 provisions in the presence of perforations.

In our analysis, the effective area (A_eff used in Step 3 of Table 2 corresponds to the net cross-sectional area, with no further reduction applied. This approach is justified by the fact that all flat plate elements (web, flanges, lips) in the tested profiles exhibit width-to-thickness ratios (b/t) below 30, which is the slenderness threshold specified in EN 1993-1-3 for unstiffened elements. According to the code, when b/t is below this limit, the entire width may be considered effective under compression, and no local reduction due to plate buckling is required.

Moreover, the presence of a longitudinal stiffener in the web further increases the local stability of the critical zones, even in the perforated regions. Experimental observations confirmed that no premature local buckling occurred near the perforations, and plastic deformation was limited and stable throughout the tests.

This modeling assumption was further validated through comparison with FEM simulations and test results, which showed strong agreement with the use of the full net section as effective. This approach is consistent with established practice in the analysis of perforated cold-formed steel members, particularly when geometric slenderness is moderate and local effects are controlled through stiffening.

These justifications have now been clarified in Section 5.1 of the manuscript.

 

How was the elastic critical load for distortional buckling determined—CUFSM or FEM? Do the authors foresee discrepancies in assumptions for net and gross sections in the context of DSM?

1. We thank the reviewer for raising this relevant point regarding the determination of elastic critical loads and section assumptions within DSM.

• The elastic critical load for distortional buckling was obtained using the finite element method (FEM) in ANSYS, based on a linear eigenvalue buckling analysis of the detailed upright profile, including web perforations and geometric features. CUFSM was not used in this study, as the complexity of the cross-section geometry, including the central stiffener and perforations, made FEM a more appropriate and flexible tool for capturing mode-specific critical loads.
• Regarding the assumptions on net versus gross cross-sectional areas in DSM, we recognize that this distinction can affect the reliability of the design strength predictions, particularly in perforated profiles. In this study, the net cross-sectional area was used consistently in both FEM and DSM evaluations, based on the justification that:
• the width-to-thickness ratios were below the local slenderness limit (b/t < 30);
• the web stiffener enhances local stability, mitigating the need for further reductions;
• experimental validation confirmed that the perforated zones did not exhibit premature local buckling or strength degradation.

While DSM traditionally relies on gross section properties for elastic critical loads and then adjusts capacity based on slenderness, in perforated sections this approach can be unconservative. Therefore, using the net section for strength prediction while determining elastic buckling based on the actual geometry (through FEM) provides a more balanced and realistic assessment. We acknowledge that this remains an area of active research and that refinement of DSM procedures for perforated members is ongoing.

This clarification has been reflected in the revised discussion in Section 5.2 of the manuscript.

 

 

That EWM and DSM yield the same for MS-990 and TS-1990 is perhaps a tad excessive on the assumptions--the authors refer to “very good agreement." How can they quantify that deviation, for instance percent error?

1. We thank the reviewer for this observation.

We acknowledge that the phrase “very good agreement” may appear too general or optimistic without supporting numerical evidence. To address this, we have now quantified the differences between the predictions from EWM and DSM and the experimental results.

For the MS-990 specimen:

• Experimental peak load: 136 kN
• DSM prediction: 141 kN → +3.7% deviation
• EWM prediction: 141 kN → +3.7% deviation

For the TS-1990 specimen:

• Experimental peak load: 89 kN
• DSM prediction: 85 kN → –4.5% deviation
• EWM prediction: 85 kN → –4.5% deviation

Although the numerical values from DSM and EWM were identical in these cases (due to the same effective area being used), the close match with experimental results (within ±5%) supports the appropriateness of these methods under the assumptions made.

To improve clarity, we have replaced the wording “very good agreement” with a more precise statement and added the percentage deviations in Section 6, along with a brief discussion of the implications.

 

 

For TS-1990, making the claim of negligible influence from local buckling effects appears justified solely based on the visual observations? The conclusion states that “net section can thus be taken as effective.” Are they going to generalize this also in case of other geometries? The authors are advised to be cautious about extrapolating this conclusion to sections with high slenderness or different perforation patterns.

1. We thank the reviewer for this important and thoughtful observation.

The conclusion regarding the limited influence of local buckling in the TS-1990 specimens was primarily based on visual observations of the tested profiles, which showed no significant out-of-plane deformation or failure near the perforations. However, this was also supported by the FEM results, which indicated stable stress distribution and minimal stress concentration in the web regions, and by the consistency of the load–displacement response across all three TS-1990 tests.

We fully agree that this conclusion should not be generalized to all cross-sections, particularly those with higher slenderness ratios or more aggressive perforation patterns. In response to the reviewer’s concern, we have revised the relevant statements in the conclusions to reflect this more cautiously. Specifically, we now emphasize that the net section may be considered effective only for the specific geometries and slenderness levels tested in this study, and further investigation is required to validate this approach for other configurations.

We appreciate the reviewer’s advice and have clarified this limitation in both the discussion and conclusions sections of the revised manuscript.

 

Could the authors briefly describe how their validated FEM model would be extrapolated to cover dynamic or seismic loading, as stated in the conclusion? Will future analysis be dealing with fatigue/influence loading?

1. We thank the reviewer for this forward-looking question.

The finite element model developed and validated in this study was focused on static axial compression, incorporating geometric imperfections, material nonlinearities, and realistic boundary conditions. However, the modeling framework was built with extensibility in mind, and it can be adapted to simulate dynamic or seismic loading conditions in future research.

Specifically, the following steps are envisioned:

• Incorporating time-dependent loading scenarios using dynamic solvers (e.g., transient or modal analysis),
• Including strain-rate sensitivity and damping properties for more realistic material response under seismic loads,
• Extending the boundary conditions to replicate rack-level seismic response, including base flexibility or beam-to-upright connections,
• Introducing cyclic or low-cycle fatigue loading, relevant for evaluating damage accumulation in seismic zones.

Although fatigue and seismic analysis are outside the scope of the current work, the validated geometric and material baseline of the model provides a reliable starting point for these future developments.

We have clarified this outlook in the final section of the manuscript ("Future Research") to better reflect the intended application path.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In this study, the authors investigated the axial compression behaviors of cold-formed steel upright profiles with perforations using experimental and numerical methods. Thet discussed the failure modes of the uprights with different lengths (i.e., slenderness ratios) and compared the predicted ultimate bearing capacities by EWM and DSM with the experimental and numerical ones. In general, the topic is of some scientific interest, and the manuscript is well structured, but the literature review needs to be improved because the authors just listed some related papers without significant good logical coherence. The reviewer suggests minor revision before it is accepted for publication. Some comments are as following.

1. In Figure 3, it is suggested to add some photos of steel specimens and material property tests. What are the dimensions of the five specimens? 
2. In Table 1, why the authors did not utilize the tested yield strength and ultimate strength of steel?
3. In Figures 4 and 5, please add units for dimensions.
4. Lines 184-185, the dimensions of real tested specimens may not be 85*52*2 due to the machining errors, which may need to be considered in the FE modeling. Did the authors test the real dimensions of the upright specimens?
5. Lines 201-202, Figures 2 and 3(d) show that the real-world support condition is not pure pin-ended boundary. Indeed, the upright is subjected to compression-bending complex loading. Please comment it.
6. In Section 2.2.2, it is suggested to clearly state when the loading will end, as this is closely related to the load-deformation curve results presented later. Like in Section 2.3 in reference [https://doi.org/10.1016/j.jcsr.2024.108619]
7. Please show the detailed construction figure of the pin-ended support.
8. In Figure 8, please add some analysis about why the failure locations are different? What factors are related to it?
9. In Figure 12, the post-peak behaviors of experimental and numerical curves are much different. Please comment on it.
10. In Section 5, only three resistance values are utilized to validate the accuracy of EWM and DSM. The limited amount of data may not demonstrate the reliability of these two methods in predicting the axial resistance of such components. Suggest the authors to add some finite element analysis results and use more data to demonstrate the reliability of the DSM.

Author Response

Dear Reviewer 4,

Thank you for your practical and technically detailed comments. Your suggestions regarding figure clarity, measurement details, and model assumptions have led to substantial improvements in how we communicate the experimental and numerical setup. We have clarified these aspects as requested and added explanations where necessary.

Comments

In this study, the authors investigated the axial compression behaviors of cold-formed steel upright profiles with perforations using experimental and numerical methods. Thet discussed the failure modes of the uprights with different lengths (i.e., slenderness ratios) and compared the predicted ultimate bearing capacities by EWM and DSM with the experimental and numerical ones. In general, the topic is of some scientific interest, and the manuscript is well structured, but the literature review needs to be improved because the authors just listed some related papers without significant good logical coherence. The reviewer suggests minor revision before it is accepted for publication. Some comments are as following.

1. In Figure 3, it is suggested to add some photos of steel specimens and material property tests. What are the dimensions of the five specimens? 

1. We thank the reviewer for the suggestion.

In response, photographs of the tensile test specimens have been included in Figure 3a, along with the corresponding geometric dimensions shown in Figure 3b. All five specimens (P1–P5) were machined with identical geometry, in accordance with EN ISO 6892-1. The main dimensions are as follows:

• Overall length: 174.1 mm
• Gauge length: 50 mm
• Width of reduced section: 10 mm
• Thickness: 2.0 mm (matching the wall thickness of the tested uprights)
• Fillet radius: 30 mm

These details have been clarified in the revised figure and manuscript. We appreciate the reviewer’s suggestion, which helped improve the completeness and clarity of the material characterization section.

 

1. In Table 1, why the authors did not utilize the tested yield strength and ultimate strength of steel?

1. Thank you for the observation. The nominal yield strength of 355 MPa was used in the analytical methods (EWM and DSM) to remain consistent with EN 1993-1-3 provisions. In contrast, the finite element model was based on the true stress–strain curve obtained from tensile tests, to accurately capture material nonlinearity.

1. In Figures 4 and 5, please add units for dimensions.

1. Thank you for the suggestion. Units for all dimensions have been added in Figures 4 and 5 as requested.

1. Lines 184-185, the dimensions of real tested specimens may not be 85*52*2 due to the machining errors, which may need to be considered in the FE modeling. Did the authors test the real dimensions of the upright specimens?

1. Thank you for the observation.

The exact dimensions of the specimens were not individually measured prior to testing. The ideal nominal geometry (85 × 52 × 2 mm) was used in the FEM analysis. Based on the manufacturing method and supplier specifications, dimensional deviations were expected to remain within admissible tolerances, and no significant variation affecting the results was observed.

1. Lines 201-202, Figures 2 and 3(d) show that the real-world support condition is not pure pin-ended boundary. Indeed, the upright is subjected to compression-bending complex loading. Please comment it.

Thank you for this important observation.

We agree that, in real-world rack systems, uprights are subjected to a combination of axial compression and bending, especially due to connection eccentricities, beam loads, and bracing configurations. However, the aim of the current study was to isolate and investigate the pure axial compression behavior of upright profiles, as typically assumed in analytical methods like DSM and EWM.

Therefore, pin-ended boundary conditions were intentionally used in both testing and FEM, as recommended in Annex A.2 of GP 128-2014, to reproduce the idealized design conditions and enable consistent comparison with code-based methods. We acknowledge that future studies could incorporate combined loading scenarios to assess the influence of eccentricities and moment transfer in more realistic configurations.

1. In Section 2.2.2, it is suggested to clearly state when the loading will end, as this is closely related to the load-deformation curve results presented later. Like in Section 2.3 in reference [https://doi.org/10.1016/j.jcsr.2024.108619]

1. Thank you for the helpful suggestion.

The tests were continued until either a visible local or global failure mechanism occurred, or the applied load dropped below 80% of the peak load. While the specific loading protocol used in this study differs from the multi-stage approach described in Zhang et al. (2024), the general criterion for test termination based on significant strength loss or observable instability is consistent with recent practices in cold-formed steel research. A reference to that study has been added to acknowledge this alignment and to strengthen the methodological context of our work.

1. Please show the detailed construction figure of the pin-ended support.

1. Thank you for the comment.

The detailed construction of the pin-ended support system, including the spherical hinges and welded end plates, is already illustrated in the manuscript — specifically in Figure 4 (schematic setup) and Figure 6 (photographic documentation of the experimental configuration). These figures show the placement of the hinges at the centroid of the cross-section, in accordance with Annex A.2 of GP 128-2014. We have updated the captions to make this information more explicit.

 

1. In Figure 8, please add some analysis about why the failure locations are different? What factors are related to it?

1. Thank you for the valuable observation.

We have added a short analysis to the discussion of Figure 8 to address the variation in failure locations among the SS-340 specimens. The observed differences are primarily attributed to initial geometric imperfections, manufacturing tolerances, and residual stresses, which vary slightly between specimens. These factors influence the location where local buckling initiates, especially near perforations or dimples, which act as stress concentrators. Additionally, minor eccentricities in load introduction or boundary condition imperfections may have contributed to the variation. The overall failure mode remained consistent, but the initiation zones varied slightly due to these localized effects.

 

 

1. In Figure 12, the post-peak behaviors of experimental and numerical curves are much different. Please comment on it.

1. Thank you for this relevant observation.

The differences in post-peak behavior between the experimental and numerical curves can be attributed to several factors:

• The numerical model is based on idealized geometry, perfect boundary conditions, and a true stress–strain material law without capturing localized damage mechanisms such as cracking, tearing, or residual stress release.
• In contrast, the experimental curves reflect the influence of imperfections, LVDT position, material inhomogeneity, and localized instability, which often lead to a more abrupt loss of stiffness after peak load.
• Additionally, contact friction, minor eccentricities, and local yielding around perforations—present in the physical tests but not fully modeled in FEM—contribute to the observed discrepancy.

 

1. In Section 5, only three resistance values are utilized to validate the accuracy of EWM and DSM. The limited amount of data may not demonstrate the reliability of these two methods in predicting the axial resistance of such components. Suggest the authors to add some finite element analysis results and use more data to demonstrate the reliability of the DSM.

1. Thank you for this important and constructive comment.

We acknowledge that the current validation of EWM and DSM is based on three physical test cases, which limits the generalizability of the conclusions. However, the focus of this study was to investigate the axial resistance of upright profiles with realistic perforation patterns and stiffeners, under controlled and representative testing conditions. While the number of physical tests is limited, we have also performed nonlinear finite element analyses that were calibrated and validated against the experiments, and which reproduced both peak loads and deformation modes with acceptable accuracy (within ±5%).

To strengthen the reliability of DSM predictions, we have now included in Section 5 a summary of the FEM-based resistance values for the three profiles (SS-340, MS-990, TS-1990), which serve as supplementary validation data. These results confirm that DSM provides consistent strength estimates for moderately slender, stiffened perforated sections when the net section is considered effective.

Future research will expand the dataset through parametric studies using the validated FEM model, enabling a broader reliability assessment of DSM under varied geometric configurations.

Author Response File: Author Response.docx

Reviewer 5 Report

Comments and Suggestions for Authors

Comment to article: buildings-3606486

Title: Buckling Behavior of Perforated Cold-Formed Steel Uprights: Experimental and Numerical Study with Design Applications

 

This paper focuses on perforated cold-formed steel uprights made of S355 steel. The paper presents valuable experimental investigations.

 

The problem is that compression force may lead to buckling. When a column is designed, special care will be spent on the buckling prevention.

 

For the solution of this problem, the authors endeavour to analyse the buckling both experimentally and simulation which is based on finite element method. MISO is employed as a constitutive model. Validations are presented well.

 

The authors proposed it for the first time for SS-340, MS-990, and TS-1990 with pin-ended boundary conditions.

 

They used numerical simulation technique via a three-dimensional model using the finite element software ANSYS.

 

The paper is well-structured and provides practical insights into design considerations for buckling prevention. Literature review and explaining the state of art on this subject are well-definite and clearly explained. The work is original and of high relevance to structural engineering and design codes.

 

However, before publication, the paper requires improvement on several aspects. Addressing these issues will improve the clarity, accessibility, and impact of the paper.

 

1. The authors mention “limitations of DSM” multiple times. Suggest briefly outlining these limitations at first mention for clarity.
2. The word "spectrum" technically connotes frequency. Please double check and verify whether the spectrum mentioned in this sentence is in the time or frequency domain. " Fourier spectrum analysis is conducted for the time-domain waveform of the blasting vibration,…"
3. Highlight any mesh convergence studies or sensitivity analyses conducted. This is particularly important for capturing local buckling in thin-walled sections.
4. Suggestion: I suggest the authors to use a shell as a geometry in future works and use the “mid surface, mid plane” feature during meshing. Because the part shape is suitable for this feature because it is uniform. It will provide you more accurete results with lower computation time. Note that it is just my suggestion. The authors do not need to perform this suggestion in this study.
5. In the following expressions, there are some minor mistakes such as capitalisation or comma or expressing the same thing again and again, or typos. The text of the manuscript should be checked again from beginning to end for such errors. Brackets should not be adjacent to the previous word.

 

Lines 8–10 duplicate the “Department of Civil Engineering…” entry. Clarify that Nicolae Taranu is at the same or a different sub-department. Merge or differentiate correctly.

Line 84: “Figure 2 represent Manufacturing…” should be “Figure 2 represents the manufacturing…”.

Line 134: Double colon in “Ultimate tensile strength: : fu” — remove one colon.

Figure 11 caption refers to “medium specimens” for TS-1990; it should say “tall specimens”.

Line 33: Extra space after “Keywords:”

Line 87: “represent” should be “represents”

Line 503: Use consistent notation — sometimes “𝑁𝑏,𝑅𝑑”, other times “Nb,Rd”; choose one format.

Author Response

Dear Reviewer 5,

We appreciate your close reading and editorial recommendations. Your comments helped us correct inconsistencies in notation, grammar, and figure references, and also provided valuable perspective on modeling choices. We have revised the manuscript carefully and incorporated your suggestions throughout.

Comments

This paper focuses on perforated cold-formed steel uprights made of S355 steel. The paper presents valuable experimental investigations.

The problem is that compression force may lead to buckling. When a column is designed, special care will be spent on the buckling prevention.

For the solution of this problem, the authors endeavour to analyse the buckling both experimentally and simulation which is based on finite element method. MISO is employed as a constitutive model. Validations are presented well.

The authors proposed it for the first time for SS-340, MS-990, and TS-1990 with pin-ended boundary conditions.

They used numerical simulation technique via a three-dimensional model using the finite element software ANSYS.

The paper is well-structured and provides practical insights into design considerations for buckling prevention. Literature review and explaining the state of art on this subject are well-definite and clearly explained. The work is original and of high relevance to structural engineering and design codes.

However, before publication, the paper requires improvement on several aspects. Addressing these issues will improve the clarity, accessibility, and impact of the paper.

1. The authors mention “limitations of DSM” multiple times. Suggest briefly outlining these limitations at first mention for clarity.

1. The authors mention “limitations of DSM” multiple times. Suggest briefly outlining these limitations at first mention for clarity.

1. The word "spectrum" technically connotes frequency. Please double check and verify whether the spectrum mentioned in this sentence is in the time or frequency domain. " Fourier spectrum analysis is conducted for the time-domain waveform of the blasting vibration,…"

1. We believe this comment may not be related to the current manuscript, as no Fourier spectrum analysis or blasting vibration data are included in the present study. The focus of the paper is on the axial compression behavior of cold-formed steel uprights with perforations, based on experimental testing, finite element modeling, and analytical methods. Please let us know if the comment refers to a specific section that may have been misunderstood.

1. Highlight any mesh convergence studies or sensitivity analyses conducted. This is particularly important for capturing local buckling in thin-walled sections.

1. Thank you for this relevant observation.

A mesh convergence study was performed as part of the numerical modeling process to ensure accurate capture of local buckling phenomena in the thin-walled upright sections. Multiple mesh densities were evaluated, and the selected configuration—based on SOLID186 elements—was found to provide a good balance between computational efficiency and accuracy.

Key output parameters such as peak load and deformation mode varied by less than 2% between the two finest meshes tested. Additionally, local mesh refinement was applied around perforations and web regions to improve the resolution of stress concentrations and local instabilities.

This clarification has been added in Section 4.1 of the revised manuscript.

 

1. Suggestion: I suggest the authors to use a shell as a geometry in future works and use the “mid surface, mid plane” feature during meshing. Because the part shape is suitable for this feature because it is uniform. It will provide you more accurete results with lower computation time. Note that it is just my suggestion. The authors do not need to perform this suggestion in this study.

1. We sincerely thank the reviewer for this thoughtful and constructive suggestion.

We agree that using shell elements with mid-surface meshing could provide improved computational efficiency and potentially more accurate results for thin-walled uniform profiles, especially in large-scale parametric or dynamic analyses. In this study, we chose solid elements (SOLID186) to capture local 3D effects around perforations and stress gradients through the thickness, but we fully recognize the advantages of shell modeling for future work.

We will certainly consider this approach in ongoing and future investigations. Thank you for the valuable recommendation.

 

1. In the following expressions, there are some minor mistakes such as capitalisation or comma or expressing the same thing again and again, or typos. The text of the manuscript should be checked again from beginning to end for such errors. Brackets should not be adjacent to the previous word.

1. Thank you for pointing this out.

We have carefully revised the entire manuscript to correct typographical errors, punctuation inconsistencies, capitalization, and redundant phrasing. Particular attention was paid to the spacing before brackets, as well as overall formatting and language consistency. We appreciate your comment, which helped improve the clarity and readability of the manuscript.

 

Lines 8–10 duplicate the “Department of Civil Engineering…” entry. Clarify that Nicolae Taranu is at the same or a different sub-department. Merge or differentiate correctly.

1. Thank you for noticing this formatting issue.

The duplication of the “Department of Civil Engineering” entry has been corrected. The affiliation for Prof. Nicolae Țăranu has been clarified to reflect that he is part of the same department.

 

Line 84: “Figure 2 represent Manufacturing…” should be “Figure 2 represents the manufacturing…”.

1. Thank you for identifying this grammatical error.

The sentence has been corrected to: “Figure 2 represents the manufacturing…” in the revised manuscript. We appreciate your attention to detail.

 

Line 134: Double colon in “Ultimate tensile strength: : fu” — remove one colon.

1. Thank you for pointing this out.

The double colon in “Ultimate tensile strength: : fu” has been corrected by removing the extra colon in the revised manuscript.

 

Figure 11 caption refers to “medium specimens” for TS-1990; it should say “tall specimens”.

1. Thank you for catching this inconsistency.

The caption of Figure 11 has been corrected to refer to “tall specimens” instead of “medium specimens” for TS-1990 in the revised manuscript.

 

 

Line 33: Extra space after “Keywords:”

1. Thank you — the issue has been resolved

Line 87: “represent” should be “represents”

1. Thank you. The verb has been corrected to “represents” in the revised manuscript.

Line 503: Use consistent notation — sometimes “??,??”, other times “Nb,Rd”; choose one format.

1. Thank you — the issue has been resolved. Consistent notation () is now used throughout the manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors answered the questions to an acceptable extent and made corrections to the article. The article can be published.

Comments for author File: Comments.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper can be accepted