Bearing Capacity and Failure Mode of a Light-Steel Tubular K-joint Connected by a Novel U-shape Connector

Round 1

Reviewer 1 Report

Dear Authors

The manuscript is very interesting, very close to my field of research, which is damage and fracture mechanics. I do believe that the results of this work would assist other researchers and students.

The language is quite fine. The topic was properly addressed through experiments and numerical analyses.  Conclusions are supportive.

However, in order to enhance the manuscript quality and to the best attention, please address the following comments in the revised version.

1. There are too many figures! I do recommend the authors to reduce the number of figures by merging them together and simplify as much as possible. Figures were presented in good quality.
2. Introduction is mainly focused on the literature review, and the last paragraph is focusing on the introductory section. It is recommended to split them or change the title of the section to have a better overview.
3. Although some innovative points stated along the paper, it is not straightforward to realize that. I do recommend the authors to stress the novelty of the work in the introduction ending section.
4. Have you thought about thickness variation in the specimens?
5. The paper seriously lacks a table of nomenclature.
6. Regarding the coupon test, it was used to characterise the material properties, correct? If so, please specify the loading conditions? Do you have the stress/strain curves?
7. How did you define the clip gauge? Referring to Figure 8-right?
8. Regarding the force application stated in subsection 3.1., why did you use different load intervals? I meant, 4 kN and then 2kN?
9. In subsection 3.2., it was stated that “A prior FEA shows that failure mode of the K-joint is sever deformation of the U-138 shape connector and chord local plastification” never talked before! Please clarify this matter.
10. Subsection 4.1, why the failure mode of three K-joint specimens in each group is almost the same? Based on what?
11. The force displacement curves presented in figure 16 – 17 -18 -19, at which point did you extract these data?
12. Concerning the Fem analyses, what is the total number of elements and nodes allocated to the FE mesh?
13. Have you made any convergence studies on the mesh density and element types?
14. About the screws modelling in the FEM, have you considered the pre-load on the bolts?
15. Have you run your simulations through static or dynamic step? Please give some explanation on this matter?
16. Have you considered the mass scaling in your FEM model?
17. What is the computational cost for this analysis? Please discuss it. So, other researchers could estimate the effort if they want to carry out such examples.
18. Subsection 5.2, it was stated that “It can be seen that the loading-displacement curve obtained from FEA generally terminates much earlier compared to experimental results due to sever connector deformation in FE modelling.” Why did you conclude this? Does not make any sense, if there is a difference between the FEM and experimental solutions, it must be related to the model definition and essential and natural boundary conditions. Therefore, I do recommend the authors to clarify this matter.
19. How did you define the plastic behaviour in your numerical model?
20. Did you consider the nonlinear geometrical effect in your analyses?
21. Why did not you present some graphical representation of the stress, strain or displacement fields? Specifically, to see if the plasticification happened in the experiments is also observed in the numerical simulations or not. Please discuss this.
22. Please unify all decimals when presenting the numbers.

Very Best

The Reviewer

Author Response

Reply to reviewers’ comments

Reviewer 1:

The manuscript is very interesting, very close to my field of research, which is damage and fracture mechanics. I do believe that the results of this work would assist other researchers and students. The language is quite fine. The topic was properly addressed through experiments and numerical analyses.  Conclusions are supportive. However, in order to enhance the manuscript quality and to the best attention, please address the following comments in the revised version.

1. There are too many figures! I do recommend the authors to reduce the number of figures by merging them together and simplify as much as possible. Figures were presented in good quality.

Reply:

Yes, the authors agree on that there are too many figures in the manuscript. Figures 12(c), 13(c), 14(c) and 15(c) have been removed in the revised manuscript. Other figures have been kept in order to provide all the details of the present study so that other researchers may repeat the experimental and numerical results.

2. Introduction is mainly focused on the literature review, and the last paragraph is focusing on the introductory section. It is recommended to split them or change the title of the section to have a better overview.

Reply:

  After literature review, the authors briefly introduce the proposed joint. Logic of writing is reasonable. In addition, the last paragraph is very short. Therefore, the authors wish to keep the current last paragraph in the introduction section. 

3. Although some innovative points stated along the paper, it is not straightforward to realize that. I do recommend the authors to stress the novelty of the work in the introduction ending section.

Reply:

Novelty of the present study is focused on the proposed connection method for connecting thin-walled SHS members. The proposed connection has several advantages compared to traditional gusset plate and welding connection methods. Advantages of the proposed connection have been elaborated in the last paragraph of the introduction section. Please refer to lines 83 – 91 in the revised manuscript.

4. Have you thought about thickness variation in the specimens?

Reply:

Thickness variation of the U-shape connector and the SHS members have not been considered in the experimental tests. In the FE analyses, thickness variation of the SHS members has been investigated. For instance, effect of the brace-to-chord wall thickness ratio on the ultimate bearing capacity of the investigated K-joints has been investigated. Please refer to section 5.3.

5. The paper seriously lacks a table of nomenclature.

Reply:

Nomenclature has been added in the revised manuscript.

6. Regarding the coupon test, it was used to characterize the material properties, correct? If so, please specify the loading conditions? Do you have the stress/strain curves?

Reply:

Yes, coupon test is for measuring the material properties of each steel, including the yield stress, ultimate stress and elongation rate. Axial loading is applied to each coupon specimen at a speed of 10N/s. The authors have tried to measure the full stress-strain curve using strain gauges. However, after steel yielded, the strain gauges separated quickly with the corresponding coupon specimen. Therefore, the authors have not obtained the full stress-strain curves. It is proved that it may not be feasible to measure the full stress-strain curves of steel coupon specimens using strain gauges. Therefore, in order to avoid confusing readers, strain gauges in Figure 8 have been removed in the revised manuscript.

Sentence ‘Axial tensile loading is applied to each coupon specimen at a speed of 10N/s’ has been added to the revised manuscript. Please refer to lines 126 and 127.

7. How did you define the clip gauge? Referring to Figure 8-right?

Reply:

The authors have not used clip gauge in this study. In the right part of Figure 8, strain gauges instead of clip gauge were drawn. In the revised manuscript, the strain gauges have been removed from the right part of Figure 8. Please refer to the reply above.

8. Regarding the force application stated in subsection 3.1., why did you use different load intervals? I meant, 4 kN and then 2kN?

Reply:

A small loading can result in a very large displacement (or deformation) after steel yielded. Therefore, normally researchers will reduce the loading interval in order to capture the loading-displacement (or deformation) curve more accurately after steel yielded.

9. In subsection 3.2., it was stated that “A prior FEA shows that failure mode of the K-joint is sever deformation of the U-shape connector and chord local plastification” never talked before! Please clarify this matter.

Reply:

Before testing each K-joint specimen, a trial FEA was carried out to estimate the ultimate bearing capacity and the failure mode. In the revised manuscript, word ‘prior’ has been changed to ‘trial’. Please refer to line 141 in the revised manuscript.

10. Subsection 4.1, why the failure mode of three K-joint specimens in each group is almost the same? Based on what?

Reply:

The actual dimensions of three K-joint specimens in each group are almost identical. Please refer to Table 1, Table 2 and Figure 4. Also, the material properties of the U-shape connector and SHS members are very close for the three K-joint specimens in each group. Please refer to Table 2. That’s why the failure mode of three K-joint specimens in each group is almost the same.

11. The force displacement curves presented in Figures 16 -19, at which point did you extract these data?

Reply:

In Figures 16 – 19, values of each data point are obtained from the records of the loading and displacement transducers, respectively. For each K-joint specimen, there are eight loading-displacement curves because eight displacement transducers have been used to monitor the deformation of the U-shape connector in testing.

12. Concerning the FEM analyses, what is the total number of elements and nodes allocated to the FE mesh?

Reply:

Number of elements and nodes of the FE mesh model of a K-joint is about 13 and 8 thousand, respectively.

13. Have you made any convergence studies on the mesh density and element types?

Reply:

Yes, the authors have carried out a mesh convergence study on the FE model of the K-joint. Because experimental results can also be used to validate the FE model, the authors have not introduced the mesh convergence study results in the manuscript.

14. About the screws modelling in the FEM, have you considered the pre-load on the bolts?

Reply:

The authors thought that the pre-load in the self-drilling screws has a negligible effect on the ultimate bearing capacity of the investigated K-joints. Therefore, in the FEA, the authors have not considered the pre-load in the self-drilling screws.

15. Have you run your simulations through static or dynamic step? Please give some explanation on this matter.

Reply:

A general static analysis using ‘Risk’ method has been run for each FE model in this study. Sentence ‘A general static analysis has been run for each FE model in this study’ has been added in the revised manuscript. Please refer to lines 253 and 254 in the revised manuscript.

16. Have you considered the mass scaling in your FEM model?

Reply:

The authors have not considered the mass scaling in FEA.

17. What is the computational cost for this analysis? Please discuss it. So, other researchers could estimate the effort if they want to carry out such examples.

Reply:

FE model of each investigated K-joint has about 13 thousand elements and 8 thousand nodes. The FEA for calculating the ultimate bearing capacity takes about 1 hour to complete using a normal PC with an 8GB memory and 4 CPUs. The authors are not able to estimate the computational cost when other PCs are used for running the FE models investigated in this study.

18. Subsection 5.2, it was stated that “It can be seen that the loading-displacement curve obtained from FEA generally terminates much earlier compared to experimental results due to sever connector deformation in FE modelling.” Why did you conclude this? Does not make any sense, if there is a difference between the FEM and experimental solutions, it must be related to the model definition and essential and natural boundary conditions. Therefore, I do recommend the authors to clarify this matter.

Reply:

Yes, the authors agree with the reviewer’s comment. This conclusion has been removed in the revised manuscript.

19. How did you define the plastic behaviour in your numerical model?

Reply:

Plastic behavior is deemed to happen where the Mises stress exceeds the steel yield stress.

20. Did you consider the nonlinear geometrical effect in your analyses?

Reply:

Yes, the authors have considered the nonlinear geometry effect in the FEA.

21. Why did not you present some graphical representation of the stress, strain or displacement fields? Specifically, to see if the plasticification happened in the experiments is also observed in the numerical simulations or not. Please discuss this.

Reply:

The authors actually have done such a comparison. However, as mentioned before, there are already too many figures in this manuscript. In addition, this study concerns more on the ultimate bearing capacity and failure mode of the proposed K-joint. Therefore, the authors have not introduced the comparison of the stress and strain between the experimental and FEA results.

22. Please unify all decimals when presenting the numbers.

Reply:

Yes! The authors have unified the decimal of numbers in each table in the revised manuscript.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper shows an idea of connection method for K-shaped SHS steel member using tapping screws. And several experiments and analytical investigations were carried out. This reviewer think several improvement are required to publish this article, especially lack of scientific new finding.

The positions of self-drilling screw shown in Figure 4 differ from 6 and 12.

The authors should show position of displacement transducer in detail in figure Figure 11.

Stability (variation coefficient and/or standard deviation) of ultimate bearing capacity should be investigated from the results shown in Table 3.

Experimental result corresponds to FEA in Figure 23 (c)? This author don't think so.

The authors compared the response of displacement at 7B to validate of FE model. Why only 7B? Several displacement transducers and strain gauges were installed, and they are useful for validation.

The authors adopt solid element C3D8R, but this element can simulate with accuracy for out-of-plane bending behavior? How many divisions?

Analytical parameters, "gamma", "tau_1" and "n" in Table 4, should be explained by using figure. Cannot be catch clearly.

This reviewer think the proposed connecting method will be loosen by vibration and cyclic loading condition. The authors should add the long-term behavior using several literatures.

Author Response

Reply to reviewers’ comments

Reviewer 2:

This paper shows an idea of connection method for K-shaped SHS steel member using tapping screws. And several experiments and analytical investigations were carried out. This reviewer thinks several improvements are required to publish this article, especially lack of scientific new finding.

1. The positions of self-drilling screw shown in Figure 4 differ from 6 and 12.

Reply:

The authors apologize for the mistakes made in the original manuscript. Firstly, for the K-joints assembled using ULW connector, arrangement patten of the self-drilling screws in the braces is different to other K-joints. This has been corrected in Figure 4(d) in the revised manuscript. Secondly, specimen in Figure 12(c) in the original manuscript is from another patch of tests for investigating the arrangement pattens of self-drilling screws in the braces. Figure 12(c) has been removed in the revised manuscript. Effect of the arrangement pattens of self-drilling screws in the braces on the ultimate bearing capacity of the K-joint will be introduced in a separate study.

2. The authors should show position of displacement transducer in detail in Figure 11.

Reply:

Figure 11 has been improved in the revised manuscript. Sentence ‘The displacement transducers were located either in the center of four screw-holes or the middle of two screw-holes’ has been added in the revised manuscript. Please refer to lines 143 – 145 in the revised manuscript.

3. Stability (variation coefficient and/or standard deviation) of ultimate bearing capacity should be investigated from the results shown in Table 3.

Reply:

Variation of the ultimate bearing capacities of three specimens in each group is not large. The authors think it may not be necessary to calculate the variation coefficient and standard deviation as readers can directly observe the variation of the ultimate bearing capacities of different specimens from Table 3.

4. Experimental result corresponds to FEA in Figure 23 (c)? This reviewer doesn't think so.

Reply:

The authors have double checked two curves shown in Figure 23(c) and they are correct. Large difference between two curves may be due to the initial imperfection of the U-shape connector of the K-joint specimen.

5. The authors compared the response of displacement at 7B to validate of FE model. Why only 7B? Several displacement transducers and strain gauges were installed, and they are useful for validation.

Reply:

It is because of that displacement obtained from displacement-transducer 7B is the maximum and displacements measured from other transducers are smaller. When the measured displacement is small, a slight slide of the displacement-transducer can lead to a large error. Therefore, only displacement obtained from displacement-transducer 7B (the maximum) is adopted to validate the FE model.

6. The authors adopt solid element C3D8R, but this element can simulate with accuracy for out-of-plane bending behavior? How many divisions?

Reply:

The authors cannot fully understand this comment. The authors guess the reviewer thinks that solid element C3D8R is not a good choice for modelling the proposed K-joints in this study. From the comparison shown in Figures 23(a) – 23(c), it can be seen that FE modelling in this study is acceptable.

7. Analytical parameters, "γ", "τ₁" and "n" in Table 4, should be explained by using figure. Cannot be caught clearly.

Reply:

   Another reviewer gives the same comment (comment 5 from reviewer 1). Therefore, the authors add the nomenclature at the end of the revised manuscript.

8. This reviewer thinks the proposed connecting method will be loosen by vibration and cyclic loading condition. The authors should add the long-term behavior using several literatures.

Reply:

The proposed connection is for low-rise residential and farm buildings. Normally there is no large vibration or cyclic loading. Therefore, the authors have not investigated the performance of the proposed connection under vibration and cyclic loadings. However, the authors think that the reviewer proposes a very good question. The authors will conduct research on the performance of the proposed connection under vibration and cyclic loadings in future.

In addition to the corrections made above, the authors have also made other necessary corrections. Please refer to the revised manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Dear Authors

The Reviewer truly appreciates the corrections. At this stage, an acceptance is recommended.

Good luck

Very best

The Reviewer 

Author Response

Dear Reviewer:

Thanks a lot for giving us valuable comments.

  Best regards,

Dr. Tao Li

Reviewer 2 Report

4. Experimental result corresponds to FEA in Figure 23 (c)? This reviewer doesn't think so.

Reply:

The authors have double checked two curves shown in Figure 23(c) and they are correct. Large difference between two curves may be due to the initial imperfection of the U-shape connector of the K-joint specimen.

Comment to Reply:

Revised position was not found.

If so, this reviewer thinks the authors should show all specimen results (UTW-2, -3).

5. The authors compared the response of displacement at 7B to validate of FE model. Why only 7B? Several displacement transducers and strain gauges were installed, and they are useful for validation.

Reply:

It is because of that displacement obtained from displacement-transducer 7B is the maximum and displacements measured from other transducers are smaller. When the measured displacement is small, a slight slide of the displacement-transducer can lead to a large error. Therefore, only displacement obtained from displacement-transducer 7B (the maximum) is adopted to validate the FE model.

Comment to Reply:

Strain gauges were not attached? And similar residual deformation (plastification in Figure 12-15) could be successfully observed by FEA? This reviewer think validation data should be improved.

Author Response

Dear Reviewer,

  Thanks a lot for giving us valuable comments. Please find our reponse to your valuable comments in the attached file.

  Best regards,

Dr. Tao Li

Author Response File: Author Response.pdf