Influence Law of Axis Deflection on the Mechanical Properties of Steel Stranded Short Slings in Arch Bridges

Round 1

Reviewer 1 Report

The research is very well done and the manuscript contains valuable results. In addition, the manuscript is well structured. However, it is necessary to provide a revision manuscript considering the following points:

1- It is better to extend the literature review part using the recently published papers. 

2- Regarding Figure 1, it is strongly suggested to show different components of the bridge along their names. In addition, it is better to show the dimensions of these parts, separately. 

 3- On page 3 and before Figure 2, it is stated that the weight of each vehicle is set to 330 KN. is it true? please refer to an appropriate reference to valid this value.

4- Related to the finite element simulation, the defined materials, properties such as elastic, plastic, damage parameter, etc. should be reported in the article. 

5- It is strongly suggested to show the vehicle load and the distance between the vehicles and also the loading conditions in a schematic figure. 

6- Regarding Table 1, it is clear that the difference between finite element simulation and theoretically calculation results is about 20%. This value is large and show that the simulation is not accuracy. 

7- Related to the section 3, more details should be described such as mesh processing, mesh convergence, boundary conditions, etc. 

8- Regarding Figure 16, which damage criterion was used ? do you define any damage parameter in the software? 

9- About the fatigue analysis, it is necessary to describe about fatigue criteria, calculation method, properties defined in the material of software and etc. 

10- The biggest mental concern of the reviewer is the validation of the finite element simulation and its comparison with experimental data, which must be done separately for each part. For example fatigue analysis.

Author Response

S1: It is better to extend the literature review part using the recently published papers.

A1: The comments have been accepted. We have extended the literature review by using the recently published papers. Please see the manuscript for detailed revisions.

S2: Regarding Figure 1, it is strongly suggested to show different components of the bridge along their names. In addition, it is better to show the dimensions of these parts, separately.

A2: The comments have been accepted. We have shown different components of the bridge along their names in Figure 1, and shown the dimensions of these parts in the first paragraph of the second part of the paper, separately.

S3: On page 3 and before Figure 2, it is stated that the weight of each vehicle is set to 330 KN. is it true? please refer to an appropriate reference to valid this value.

A3: Yes, it is true. According to the provisions of equivalent load loading method of static load test in “Full Bridge (Static and Dynamic) Load Test Plan” formulated in “Highway Bridge Load Test Regulations (JTG/T J21-01-2015)”, we set the weight of each vehicle to 330kN.

S4: Related to the finite element simulation, the defined materials, properties such as elastic, plastic, damage parameter, etc. should be reported in the article.

A4: The comments have been accepted. We have shown the material, elasticity, plasticity, damage parameters and other properties defined in the finite element simulation through Table 1.

S5: It is strongly suggested to show the vehicle load and the distance between the vehicles and also the loading conditions in a schematic figure.

A5: The comments have been accepted. We have shown the vehicle load and the loading conditions in the first paragraph of part 2.1 of the paper. Please see the manuscript for detailed revisions.

S6: Regarding Table 1, it is clear that the difference between finite element simulation and theoretically calculation results is about 20%. This value is large and show that the simulation is not accuracy.

A6: The maximum error between the finite element simulation results and the theoretical calculation results is 14.3%, indicating that the simulation results are not accurate.

S7: Related to the section 3, more details should be described such as mesh processing, mesh convergence, boundary conditions, etc.

A7: The comments have been accepted. The cells are divided in the following way, the solid cell end face of the center wire is perpendicular to the tension cable cross section, while the solid cell end face within the twisted wire is perpendicular to the helical wire axis. The boundary constraints are such that only axial displacements are applied to the loaded end section nodes in the finite element model, and the degrees of freedom in the vertical axis direction are released to allow for rotation of the lasso. Considering the boundary conditions inside the prestressed cable, an additional "loading section" is proposed in the finite element model. A shared topology is used at both ends of the connection with the body of the cable to ensure the existence of common nodes with each other. A contact unit is established on the wire surface of the cable body, and the wire material is modeled as elastic-plastic. The "loading section" part of the wire surface has no contact unit, and the wire material in the loading section is modeled as pure elasticity and its yield strength is set to a large value so that it is always in an elastic state. The above contents have been added to the first paragraph of the third part of the paper.

S8: Regarding Figure 16, which damage criterion was used? do you define any damage parameter in the software?

A8: We used Von Mises yield criterion and bilinear isotropic reinforcement criterion.

S9: About the fatigue analysis, it is necessary to describe about fatigue criteria, calculation method, properties defined in the material of software and etc.

A9: The comments have been accepted. Specific descriptions of fatigue criteria, calculation methods, properties defined in software materials, etc., have been added to the first paragraph of part four of the paper. Please see the manuscript for detailed revisions.

S10: The biggest mental concern of the reviewer is the validation of the finite element simulation and its comparison with experimental data, which must be done separately for each part. For example fatigue analysis.

A10: The finite element simulation and experiment of a single steel strand have been completed and the details can be seen in the literature published by our team in the reference [9-12] of the paper. Now we have done the fatigue test of 19 slings, and the analysis shows that the finite element simulation agrees with the experiment. Details are shown at the end of parts three and four. Please see the manuscript for detailed revisions.

Author Response File: Author Response.pdf

Reviewer 2 Report

(1)   The significance and necessity of the research should also be further elucidated. The authors merely acknowledged the absence of relevant theoretical or experimental studies on the impact of axis deflection on the mechanical properties of steel-stranded short slings in arch bridges, which lacks specificity.

(2)   The FE model should provide more comprehensive details, including material characteristics, boundary conditions, and other relevant information.

(3)   The accuracy of the simulation cannot be guaranteed as the FE model has not been validated through field testing.

(4)   The temperature can reach up to 45℃. On what grounds?

(5)   Figure 3 is not legible. Please refrain from taking screenshots and instead redraw the figure.

Minor editing of English language required.

Author Response

S1: The significance and necessity of the research should also be further elucidated. The authors merely acknowledged the absence of relevant theoretical or experimental studies on the impact of axis deflection on the mechanical properties of steel-stranded short slings in arch bridges, which lacks specificity.

A1: The comments have been accepted. We have further clarified the significance and necessity of the study in the introduction section of the paper. Please see the manuscript for detailed revisions.

S2: The FE model should provide more comprehensive details, including material characteristics, boundary conditions, and other relevant information.

A2: The comments have been accepted. We have provided the details of material characteristics and boundary conditions, and other relevant information in the third and fourth parts of the article. Please see the manuscript for detailed revisions.

S3: The accuracy of the simulation cannot be guaranteed as the FE model has not been validated through field testing.

A3: The accuracy of the finite element model of the bridge has been verified by field test before the bridge is opened to traffic.

S4: The temperature can reach up to 45℃. On what grounds?

A4: The arch bridge is located in Guangxi, which belongs to the subtropical wind climate zone, and the highest temperature of the bridge floor exceeds 40°C in summer.

S5: Figure 3 is not legible. Please refrain from taking screenshots and instead redraw the figure.

A5: Figure 3 does not contribute much to the discussion and has been deleted.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors investigated the influence law on the mechanical properties of short slings in arch bridges. In the reviewer's opinion, the paper is well-written and well-organized, and the results can help future research on arch bridges. However, there are some minor comments that need to be addressed before the paper can be accepted for publication. Please see my comments below:

1- Please provide more discussion on the necessity and importance of the work in the introduction section of the paper.

2- Please provide the version of the software implemented.

3- Please indicate the applicability of the proposed method to other types of materials.

Author Response

S1: Please provide more discussion on the necessity and importance of the work in the introduction section of the paper.

A1: The comments have been accepted. We have provided more discussion on the necessity and importance of the work. Please see the manuscript for detailed revisions.

S2: Please provide the version of the software implemented

A2: In this paper, we used Midas/Civil (2019) for the arch bridge simulation, ANSYS LS--DYNA (version R19.0) for the static performance finite element analysis of stranded wire suspenders with different axial deflections, and Ansys Workbench 2020R2 for the fatigue performance finite element analysis of stranded wire suspenders with different axial deflections.

S3: Please indicate the applicability of the proposed method to other types of materials.

A3: The method proposed in this paper, including the deflection Angle theory of the cable sling, the S-N curve calculation formula of the cable sling, and the simulated boundary constraint conditions, is only suitable for the analysis of the steel strand.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors tried to provide revised manuscript based on the reviewers' comments and also they answered all comments one by one in logical way. So, I have no more comments and the manuscript can be published in the present form. 

Accept.

Reviewer 2 Report

It has been revised as suggestted.