Innovative Design Techniques for Sinusoidal-Web Beams: A Reliability-Based Optimization Approach

Round 1

Reviewer 1 Report

The topic addressed in this paper falls within the technical area covered by Buildings Journal and constitutes an interesting problem. The authors presented an elaborated work. However, in its current form, I am of the opinion that this article should not be accepted for publication and needs significant improvements. If they decide to do so, the comments/criticisms listed below should be considered.

1. The 'Introduction' is very short and references [1-6] are not necessarily relevant. There are some more complete works on this area of elements, presenting research on sinusoidal-web beams. The authors are encouraged to restructure the introduction referring to experimental tests / numerical investigation / analytical approaches / codes – see Annex D of EN1993-1-5.

2. The authors present in Chapter 3 “IPE beams with sinusoidal-web configuration”. It is an unhappy identification. IPE/HEA/HEB a.s.o. are element identifications belonging to many other producers. The recommendation is to rename the specimens. Maybe the sections copy the global dimensions of IPE 240 and IPE 100, but they need to have a different name. No information about SIN shape. Is it a standardised shape? There are several producers of such beams in Europe; one is Zeman (https://zebau.com/machines/sin-beam-machine). The profile of SIN shape seems to be too big for the chosen cross-sections.

3. In Table 1 the properties of the materials are presented. It is impossible to have a yield strength corresponding to S275 and an ultimate strength corresponding to more than S460. The interpretation of the tensile testing protocol is not correct.

4. The dimensions of the tested specimens are not clear. Please add a table explaining all dimensions. The steel properties are the same even if the thicknesses are different? Are they representing mean values?

5. In Chapter 3, no information about the failure modes – global or local buckling, interactive buckling? Complete the part with additional information and comments.

5. Details of the numerical analysis presented in Chapter 4 are not sufficiently described and not consistent. “An imperfection value equivalent to 𝐿/1000 has been incorporated” in the numerical analysis. It is very important to understand in which direction (minor/major axes; positive of negative). Moreover, for these cross-sections torsional imperfections could be important. Is there any recommendation for this? There is no information in the experimental part about the measured dimensions and tolerances. Please also check the EN 1993-1-5 and EN 1993-1-14 codes that cover aspects related to numerical modelling. No information about the material used in the numerical modelling. Please add engineering and true stress-strain curves used in simulations. No information about the non-linear analyses.

6. In the probabilistic analysis the initial imperfections (type, size, direction). It is a crucial parameter. Modifying the thicknesses only is not necessarily an optimisation process. In fact, there are no relevant results coming from 5.1 and 5.2.

7. In conclusion, the way of considering the “random nature of variables such as the thickness of the flanges, the thickness of the sinusoidal web plate” is not relevant. It is not sustained by any consistent result. A lot of details are missing, no values, no graphs.

In general, the quality of English language is good.

Author Response

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Reviewer 2 Report

1.The sentence “ The assessment of the minimum collapse value …. probabilistic prob-lems.” seems to be out of context and unrelated to the preceding or following text.

2. The numbers for the beams in Table 2 should be different.

3. The optimization process in Section 5 should provide more intermediate results and explanations to enhance the readability of this article.

Author Response

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Reviewer 3 Report

Well-organized and presented manuscript. no major edits are necessary.

Author Response

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Reviewer 4 Report

The paper studies the impact of the integration of reliability-based optimization design into the numerical modelling of sinusoidal-web steel beams. In order to validate the FE model, a series of geometrically nonlinear analyses have been presented comparing the results with those of four point bending experiments for the two considered case studies. Then, a reliability-based optimization design has been conducted with a Monte-Carlo simulation. The thickness of the flanges, the thickness of the sinusoidal-web plate and the magnitude of the applied loads have been considered as random factors, each characterized by mean value and standard deviation.

The paper is interesting and the subject is appropriate for the journal. Anyway, before proceeding to the publication a minor revision must be performed according to the following comments:

1.  In the introduction the authors should clearly declare that first the comparison of results of numerical analyses and experimental tests is shown to validate FE models, and then the beam parameters obtained with the reliability-based optimization design are discussed.

2.  The authors presented the reliability-based optimization results obtained performing geometrically nonlinear numerical analyses considering linear elastic material behaviour. The authors are encouraged to add a comment on the reliability-based optimization design of the steel beams conducted considering also the nonlinear material behaviour. Is it possible to perform such optimization considering nonlinear material behaviour or does it imply a higher complexity? How the reliability indices could be influenced?

3.  Please show the results reported in Figures 13-14 in terms of sigma/sigma_y as in Figures 8-12.

The paper is generally well written, but please, check some typing errors. For example:

- p. 3, please delete lines 138-139;

- p. 4, line 183, please delete “is the”.

Author Response

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Round 2

Reviewer 1 Report

The authors improved the quality of the manuscript. However, still there are several issues to be solved. They are listed below:

1. Only to my initial comment 3, the authors mentioned the use of stainless steel as material. What kind of stainless steel? Nowhere in the paper is this specified. Clarify this aspect. Moreover, in regard to my initial comment 3, the authors are asked to add the material curves obtained from testing. This aspect is very superficially treated.

2. Seeing now the answers for my initial comment 5 and Figure 8, the failure mode is closer to web crippling and fits with the explanations. Please clarify/confirm.

3. Considering my initial comments 6 and 3, the authors stated, „Rigorous testing procedures have been conducted to characterize the material's mechanical behaviour comprehensively under varying loading conditions”. This comment is too superficial. Please add graphs. It seems that no measurements of initial imperfections were taken. 

„Please add engineering and true stress-strain curves used in simulations. No information about the non-linear analyses.” – not answers to these aspects.

Minor improvements are needed.

Author Response

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Round 3

Reviewer 1 Report

The paper can be accepted for publication.