Reviewer:

The Authors only partially revised the manuscript according to the Reviewers’ comments. Indeed, some points that I’ve asked to clarify in the paper have been, at least, only explained in the reply to my comments (it appears to me that this is true also for the comments by the other Reviewers). Therefore, I pointed out what I think the Authors should still clarify in the text of the manuscript in order to make the paper clearer for the readers.

Authors’ reply:

The authors would like to sincerely thank Reviewer 2 for the comments and for the time spent reviewing the paper. As the reviewer points out, the authors have clarified the text of the manuscript.

Comment No.1:

The Authors should clarify the motivations for considering horizontal forces in designing horizontal braces, since this is the key concept of the paper. Moreover, since horizontal forces may arise from different causes (wind, earthquake, instability of vertical members, etc.), the Authors should specify if the considered horizontal forces intensity is ascribable to only some effects, or to all of them. This, also to be consistent with the answer to comment 5 (see below).

Authors’ reply:

The authors sincerely thank Reviewer 2 for pointing it out. In practical engineering, structure will bear vertical and horizontal loads, in which horizontal load includes wind load, earthquake loads and crane loads besides providing support for the structure stability. In previous literature, extensive studies on column-braced systems subjected to vertical loads were carried out by Tong, G.S.,Zhang, Y.C. and Zhao, J.Y. et al. [3-6]. But no important definitive research has been conducted on the design intermediate height horizontal brace forces of column-braced systems under horizontal and vertical loads.

To clarify this, the following texts were added to the revised manuscript (page 1, line 39-line 41):

In practical engineering, the structure will bear vertical and horizontal loads, in which horizontal load includes wind loads, earthquake loads and crane loads besides providing support for the structural stability.

References

[3] Tong, G.S.; Chen, S.P. Design requirement for bracing between columns. Industrial Construction 2003, 33, 9-12 (in Chinese).

[4] Li, D. Stability analysis and bracing requirements of longitudinal braced frames. Zhejiang University: Hangzhou, China, 2005.

[5] Zhang, Y.C.; Zhao, J.Y.; Zhang, W.Y. Parametric Studies on Inter-column Brace Forces. Advances in Structural Engineering 2008, 11, 305-315.

[6] Zhao, J.Y.; Zhang, Y.C.; Lin, Y.Y. Study on mid-height horizontal bracing forces considering random initial geometric imperfections. Journal of Constructional Steel Research 2014, 92, 55-66.

Comment No.2:

The choice of planar schemes instead of full 3D frames must be discussed in the paper (the Authors gave explanations only in their reply to my comments).

Authors’ reply:

The authors are grateful to the Reviewer 2 for this comment.

To clarify this, the following texts were added to the revised manuscript (page 2, line 63-line 67):

The purpose of this paper is to only study the longitudinal brace force of horizontal brace, because longitudinal direction is about the weak axis of column and will cause overall instability. The transverse frame was not considered, because it is about the strong axis of column and will not cause overall instability. So the planar schemes was chosen.

Comment No.3:

I point out again that it is desirable for the understanding of a broader audience to relate the dimensions of columns and braces to normalized profiles; if this is not possible, please specify why in the paper.

Authors’ reply:

The authors are grateful to the Reviewer 2 for this comment. The size of the column was limited to the horizontal brace length (b=6 m) and the ratio of horizontal brace length to column height (b/L) in order to ensure the half slenderness ratio (λ_c = 100) of column about the weak axis in the design, so the dimensions of columns and braces could not adopt normalized profiles.

To clarify this, the following texts were added to the revised manuscript (page 3, line 93-line 94):

According to the limitation of the above conditions, the dimensions of columns and braces could not adopt the normalized profiles.

Comment No.4:

Please broader explain in the paper choice of values in line 108; the only reference to [17] and [18] is for me not enough.

Authors’ reply:

The authors sincerely thank Reviewer 2 for this comment. The authors have consulted a large number of literatures and the statistical results of mean value and the mean square deviation are only given in Ref. [21]. Ref. [21] is the only relevant literature that we can refer to at present.

References

[21] Tong, G.S.; Chen, S.F. Design forces of horizontal inter-column braces. Journal of Constructional Steel Research 1987, 75, 363-370.

Comment No.5:

In connection with what it is said in comment 1 (see above), please, explain in the paper why possible values of horizontal forces are limited to 1/10 of the single vertical force P since, for example, in the case of seismic loads, horizontal forces can be much larger.

Authors’ reply:

The authors are grateful to the Reviewer 2 for this comment. In some cases, such as earthquake load, the horizontal load will be more than 0.1 P, which is not the research scope of this paper. The authors would like to mention that the authors are planning to conduct an extensive parametric study and proposed new equations based on extensive tests and FE analysis data in a separate paper, but this will be done in the future.

To clarify this, the following texts were added to the revised manuscript (page 11, line 270-line 274):

and the application range of equations for design intermediate height horizontal brace forces is that the value of γ is not more than 0.1.

In some cases, such as earthquake load, the horizontal load will be more than 0.1 P, which is beyond the research scope of this paper. An extensive parametric study would be conducted and new equations would be proposed based on the extensive parametric study data in a separate paper, but this will be done in the future.

Comment No.6:

Section 6.2: please, explain in the paper how (11)-(13) have been obtained.

Authors’ reply:

The authors would like to thank Reviewer 2 for this comment. Equations (11)-(14) were obtained by curve fitting method from the FE analysis results summarized in Table 5.

To clarify this, the following texts were added to the revised manuscript (page 11, line 265-line 267):

The equations for design intermediate height horizontal brace forces were obtained by curve fitting method from the FE analysis results summarized in Table 5, which are shown as follows.

Comment No.7:

There is still the issue that the reported items are mostly ascribable to China-area scholars: the Author added 2 international references and 2 Chinese references; moreover, the references are quite limited. Please, enlarge the literature review also considering not-Chinese Authors.

Authors’ reply:

The authors would like to thank Reviewer 2 for this comment. To enlarge the literature review, the following references were added to the revised manuscript.

References

[13] Dou C.; Pi Y.L. Effects of Geometric Imperfections on Flexural Buckling Resistance of Laterally Braced Columns. Journal of Structural Engineering 2016 142 04016048.

[14] Czepiżak D.; Biegus A. Refined calculation of lateral bracing systems due to global geometrical imperfections. Journal of Constructional Steel Research 2016 119 30-38.

[15] Klasson A.; Crocetti R.; Björnsson I.; Hansson E.F. Design for lateral stability of slender timber beams considering slip in the lateral bracing system. Structures 2018 16 157-163.

[25] Piątkowski M. Experimental research on load of transversal roof bracing due to geometrical imperfections of truss. Engineering Structures 2021 242 112558.

[26] Wang L.; Helwig T.A. Critical Imperfections for Beam Bracing Systems. Journal of Structural Engineering 2005 131 933-940.