Sectional Model Wind Tunnel Test and Research on the Wind-Induced Vibration Response of a Curved Beam Unilateral Stayed Bridge

Round 1

Reviewer 1 Report

The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers.

 

Author Response

Response to Reviewers’ Comments

We appreciate the careful reading and valuable comments given by the reviewers. We have made changes in the manuscript (indicated there by yellow highlighter) by taking into account the reviewers’ comments and suggestions. The following summarizes the detailed responses to reviewer 1 and reviewer 2.

Point 1(from Reviewer 1 and Reviewer 2): I The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers.The abstract should be improved. The abstract should contain the motivation and most important information of the study.

 Response 1: The linear curve distribution of the beam and the asymmetrical layout of the stay cables make CBUSBs different from traditional cable-stayed bridges. The motivation of this paper is to study the wind-induced vibration characteristics of a new type of cable-stayed bridge and the interaction between its stay cables and curved beams. The first sentence of Abstract in the original manuscript has been revised to indicate the motivation for this paper, as follows: (see page 1 and lines 14-18 in the revised paper)

"The linear curve distribution of the beam and the asymmetrical layout of the stay cables may have beneficial or adverse influence on cable-stayed bridges. Sectional model wind tunnel tests and numerical simulations were used to analyze the influence of these two factors on the wind-induced vibration characteristics of a curved beam unilateral stayed bridges (CBUSB) and the interaction between its stay cables and curved beams"

Some important informations are added in Section of Abstract. These added informations involves the model design, aerodynamic force tests, band-pass filter technology, the direction of wind loads in numerical simulation, fast Fourier transform technology, wind speed range to verify aerodynamic stability, and the influence of curvature change, as follows: (see page 1, lines 18-28 in the revised paper)

"According to the basic similarity law, the sectional models of a CBUSB example were designed and manufactured. The aerodynamic force and wind-induced vibration of the models were measured in an atmospheric boundary wind tunnel laboratory to obtain the aerodynamic coefficient and displacement respectively."

"Based on the wind tunnel test results, the verified finite element model was used to determine the displacement, acceleration, and cable tension of the CBUSB excited by buffeting force under 5 curvature cases and 4 cable layout cases."

"Then, band-pass filter technology and fast Fourier transform technology were used to analyze the influence of these two parameters on the wind-induced vibration characteristics of the CBUSB."

"Results show that the CBUSB has good aerodynamic stability in the wind tunnel at low and high wind speeds."

"With increasing curvature, the high-order modal vibration and modal coupling vibration of the CBUSB may be generated."

To make Abstract concise, we delete the detailed scheme of cable layout cases but retained the number of such cases. In addition, we delete some unnecessary expressions of "From the perspective of improving pedestrian comfort" and "From the point of view of reducing wind-induced vibration". These revisions are as follows: (see page 1 and lines 28-32 in the revised paper)

"The frequency, the proportion of wind-induced vibration response components and the distribution characteristics of spectrum energy of the CBUSB will be affected by 4 cable layout schemes."

"Cables are arranged on both sides of the bridge and near the center of curvature which can improve pedestrian comfort and reduce wind-induced vibration respectively."

 

Point 2(from Reviewer 2): It is stated several times that the wind-induced displacement is obtained using the sectional model test. However, only the vortex-induced vibration is measured in the sectional model test. Indeed, the sectional model test cannot accurately obtain the wind-induced response due to several assumptions involved in the test, e.g., the three-dimensional effect is not considered. How is the self-excited force considered in the finite element analysis? It is suggested to enrich the introduction with some recent efforts on wind-induced vibration of bridges, e.g., Tuned mass damper for self-excited vibration control: Optimization involving nonlinear aeroelastic effect.

Response 2: In this paper, the sectional model vibration testing is aimed at verifying the accuracy of the established finite element model under static wind loads and the aerodynamic stability of the CBUSB, rather than predicting the wind effect of the CBUSB. Because the sectional model vibration test shows that no aerodynamic instability occurs at low and high wind speeds, the wind-induced vibration of the CBUSB is mainly buffeting excited by the boundary layer turbulent winds. Based on the verified finite element model, the drag coefficient determined by the sectional model aerodynamic force testing, and the accurate numerical turbulent wind field, we analyze the buffeting characteristics of the CBUSB in the along-wind direction rather than in the 3D direction. Thus, we add the limitation of the research scope in the "Introduction" Section. Additionally, we add two latest research results on the buffeting control of stay-cable bridges in the "Introduction" Section. These revisions are as follows (see page 2, lines 92-97 and page 3, lines 118-121 in the revised paper):

"Two important variables of the ventilation rate of guardrails and the roughness on the beam surface can be used for aerodynamic optimization design to control the buffeting of suspension bridges[23]. A new numerical framework for bridge buffeting optimization design was proposed, which can reduce the buffeting response by changing the shape of bridge decks[24]."

"Based on the test data, the full bridge finite element model of the CBUSB is established, and the influence of curvature parameters and different cable layout schemes on buffeting responses of the CBUSB is studied through the established model."

References

23. Wu B.; Zhang, L.L.; Yang Y.; Liu, L.J.; Ni Z.J. Refined timedomain buffeting analysis of a long-span suspension bridge in mountainous urban terrain. Adv. Civ. Eng. 2020, 2020, 4703169．(CrossRef)
24. Montoya M.C.; Hernández S.; Nieto F.; Kareem A. Aerostructural design of bridges focusing on the buffeting response: Formulation, parametric studies and deck shape tailoring. J. Wind Eng. Ind. Aerodyn. 2020, 204, 104243．(CrossRef)

 

Point 3(from Reviewer 2): In Fig. 1(b), it is helpful to provide the location of the stay cable.

Response 3: The location of the stay cable has been added in Figure 1 (b). (see page 4 and lines 140-142 in the revised paper)

 

Point 4(from Reviewer 2): It is suggested to provide the Reynolds number.

Response 4: The Reynolds numbers have been added in section 2.4, as follows (see page 7 and lines 228-229 in the revised paper):

"The Reynolds numbers scope of the model is 0.97×10⁵ and 5.66×10⁵ in wind speed cases."

 

Point 5(from Reviewer 2): In Fig. 9, it is suggested to provide the mean torsional displacement since it is often more important.

Response 5: We have added the mean torsional displacement of the CBUSB, as follows: (see page 10, lines 281-284 and lines 290-292 in the revised paper)

"Based on the quasi-steady assumption and the results of aerodynamic force tests, the mean lift force and the mean torque are applied to the finite element model (Figure.1 (a)), and then the mean vertical displacement, , and the mean torsional displacement, , at the midspan of the finite element model are calculated."

 

Point 6(from Reviewer 2): Careful proofreading is suggested.

Response 6: Three inaccurate expressions are revised, as follows:

1. The expression "has a negligible effect" is replaced by "has not a negligible effect"; (see page 2 and lines 80-81 in the revised paper)

"Similarly, the change in curvature has not a negligible effect on the wind-induced vibration of the curved beam bridges."

2. To clearly explain the cause of fatigue damage, the sentence of "Therefore, this ratio may cause long-term dynamic response fatigue damage and lead to cable fracture; thus, further study on cable fracture for CBUSB is required." is rephrased; (see page 14 and lines 377-378 in the revised paper)

"Due to the long-term dynamic response, the potential for fatigue damage and fracture damage of the cables need to be further studied."

3. The 2.4 Section title "Design and fabrication of section model and vibration test system " is replaced by "Sectional model vibration tests of CBUSB"; (see page 7 and line 225 in the revised paper)

4. The Figure 6 title "The distribution of aerodynamic coefficients with a wind attack angle " is replaced by "Measuring points of sectional model vibration testing "; (see page 8 and line 233 in the revised paper)

5. The expression "(bridge example in this Section 2.1)" is replaced by "(as same as the CBUSB example.)".(see page 15 and lines 390-391 in the revised paper)

"Cables are arranged near the center of the curvature (as same as the CBUSB example) in Figure. 14(b)"

 

Point 7(from Reviewer 1 and Reviewer 2): English language and style: Moderate English changes required

Response 7: A native English-speaker has reviewed and edited the original text to polish the language. Some revisions are as follows:

1.The expression "is used to", "connect" and "to" are replaced by "is used for", " connection of " and " and ", respectively; (see page 5 and lines 165-167 in the revised paper)

"The sectional model is shown in Figure 2, and a blue steel sheet is used for the connection of the three-component force/torque sensor and the sectional model in the aerodynamic force testing."

2.The words "was" and "vibration" are replaced by "is" and "sectional model vibration tests", respectively; (see page 5 and lines 168-169 in the revised paper)

"The same sectional model is used for sectional model vibration tests and aerodynamic force tests."

3.The word "was" is replaced by "is";(see page 5 and lines 184-185 in the revised paper)

"The fast Fourier transform method[29] is used to determine the vertical and torsion frequencies."

4.The sentence " M_z is independent of θ." is rephrased; (see page 6 and line 206 in the revised paper)

"There is no trigonometric relationship between M_z and θ."

5. The expression "0.130" is replaced by "0.130 m";(see page 7 and line 217 in the revised paper)

"the values of B and Hm are 0.130 m and 0.702 m"

6. The word "was" is replaced by "is";(see page 11 and lines 299-301 in the revised paper)

"The height range of the simulated turbulent wind fields is 90.00–100.66 m and the CBUSB is 90.00 m above the ground."

7.We introduce adverbials and attributes into the sentences of "The above verification of wind field characteristics and comparisons between the finite element and sectional models vibration test results show that the physical parameters, static wind load characteristics, and dynamic wind load application of the finite element model meet the expected requirements, indicating that the next parametric analysis is accurate and reasonable" to make the expression of the revised paper clearer, as follows (see pages 11 and 12, lines 319-323 in the revised paper):

"According to the verification of wind field characteristics and the comparison between the finite element calculation result and the sectional model vibration test result, physical parameters, static wind load characteristics, and dynamic wind load applications of the finite element model have accurate simulation reliability, which shows that the next parametric analysis is accurate and reasonable."

8. The expression "After that" is replaced by "Then"; (see page 12 and lines 338-339 in the revised paper)

"Then, the definitions of curvature cases 1–4 are shown in Figure 11."

9.By summarizing the sectional model wind tunnel test and the finite element analysis as research methods, we revise the first paragraph in Sections of Conclusion, as follows (see page 16 and lines 436-439 in the revised paper):

"In this study, the curved beam unilateral stayed bridge (CBUSB) in China is taken as an example. Sectional model wind tunnel tests are used as a reference, and a finite element model is established to analyze the influence of CUBSB curvature and stay cable arrangement on wind-induced vibration response."

 

Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents an interesting study on the wind-induced response of a curved beam unilateral stayed bridge. The topic is within the scope of this journal. The paper contains novel information that is worthy to be published as a journal paper. The following issues are suggested as possible improvements to the paper.

1. The abstract should be improved. The abstract should contain the motivation and most important information of the study.

2. It is stated several times that the wind-induced displacement is obtained using the sectional model test. However, only the vortex-induced vibration is measured in the sectional model test. Indeed, the sectional model test cannot accurately obtain the wind-induced response due to several assumptions involved in the test, e.g., the three-dimensional effect is not considered.

3. In Fig. 1(b), it is helpful to provide the location of the stay cable.

4. It is suggested to provide the Reynolds number.

5. In Fig. 9, it is suggested to provide the mean torsional displacement since it is often more important.

6. How is the self-excited force considered in the finite element analysis?

7. It is suggested to enrich the introduction with some recent efforts on wind-induced vibration of bridges, e.g., Tuned mass damper for self-excited vibration control: Optimization involving nonlinear aeroelastic effect.

8. Careful proofreading is suggested.

Author Response

Response to Reviewers’ Comments

We appreciate the careful reading and valuable comments given by the reviewers. We have made changes in the manuscript (indicated there by yellow highlighter) by taking into account the reviewers’ comments and suggestions. The following summarizes the detailed responses to reviewer 1 and reviewer 2.

Point 1(from Reviewer 1 and Reviewer 2): The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers.The abstract should be improved. The abstract should contain the motivation and most important information of the study.

 Response 1: The linear curve distribution of the beam and the asymmetrical layout of the stay cables make CBUSBs different from traditional cable-stayed bridges. The motivation of this paper is to study the wind-induced vibration characteristics of a new type of cable-stayed bridge and the interaction between its stay cables and curved beams. The first sentence of Abstract in the original manuscript has been revised to indicate the motivation for this paper, as follows: (see page 1 and lines 14-18 in the revised paper)

"The linear curve distribution of the beam and the asymmetrical layout of the stay cables may have beneficial or adverse influence on cable-stayed bridges. Sectional model wind tunnel tests and numerical simulations were used to analyze the influence of these two factors on the wind-induced vibration characteristics of a curved beam unilateral stayed bridges (CBUSB) and the interaction between its stay cables and curved beams"

Some important informations are added in Section of Abstract. These added informations involves the model design, aerodynamic force tests, band-pass filter technology, the direction of wind loads in numerical simulation, fast Fourier transform technology, wind speed range to verify aerodynamic stability, and the influence of curvature change, as follows: (see page 1, lines 18-28 in the revised paper)

"According to the basic similarity law, the sectional models of a CBUSB example were designed and manufactured. The aerodynamic force and wind-induced vibration of the models were measured in an atmospheric boundary wind tunnel laboratory to obtain the aerodynamic coefficient and displacement respectively."

"Based on the wind tunnel test results, the verified finite element model was used to determine the displacement, acceleration, and cable tension of the CBUSB excited by buffeting force under 5 curvature cases and 4 cable layout cases."

"Then, band-pass filter technology and fast Fourier transform technology were used to analyze the influence of these two parameters on the wind-induced vibration characteristics of the CBUSB."

"Results show that the CBUSB has good aerodynamic stability in the wind tunnel at low and high wind speeds."

"With increasing curvature, the high-order modal vibration and modal coupling vibration of the CBUSB may be generated."

To make Abstract concise, we delete the detailed scheme of cable layout cases but retained the number of such cases. In addition, we delete some unnecessary expressions of "From the perspective of improving pedestrian comfort" and "From the point of view of reducing wind-induced vibration". These revisions are as follows: (see page 1 and lines 28-32 in the revised paper)

"The frequency, the proportion of wind-induced vibration response components and the distribution characteristics of spectrum energy of the CBUSB will be affected by 4 cable layout schemes."

"Cables are arranged on both sides of the bridge and near the center of curvature which can improve pedestrian comfort and reduce wind-induced vibration respectively."

 

Point 2(from Reviewer 2): It is stated several times that the wind-induced displacement is obtained using the sectional model test. However, only the vortex-induced vibration is measured in the sectional model test. Indeed, the sectional model test cannot accurately obtain the wind-induced response due to several assumptions involved in the test, e.g., the three-dimensional effect is not considered. How is the self-excited force considered in the finite element analysis? It is suggested to enrich the introduction with some recent efforts on wind-induced vibration of bridges, e.g., Tuned mass damper for self-excited vibration control: Optimization involving nonlinear aeroelastic effect.

Response 2: In this paper, the sectional model vibration testing is aimed at verifying the accuracy of the established finite element model under static wind loads and the aerodynamic stability of the CBUSB, rather than predicting the wind effect of the CBUSB. Because the sectional model vibration test shows that no aerodynamic instability occurs at low and high wind speeds, the wind-induced vibration of the CBUSB is mainly buffeting excited by the boundary layer turbulent winds. Based on the verified finite element model, the drag coefficient determined by the sectional model aerodynamic force testing, and the accurate numerical turbulent wind field, we analyze the buffeting characteristics of the CBUSB in the along-wind direction rather than in the 3D direction. Thus, we add the limitation of the research scope in the "Introduction" Section. Additionally, we add two latest research results on the buffeting control of stay-cable bridges in the "Introduction" Section. These revisions are as follows (see page 2, lines 92-97 and page 3, lines 118-121 in the revised paper):

"Two important variables of the ventilation rate of guardrails and the roughness on the beam surface can be used for aerodynamic optimization design to control the buffeting of suspension bridges[23]. A new numerical framework for bridge buffeting optimization design was proposed, which can reduce the buffeting response by changing the shape of bridge decks[24]."

"Based on the test data, the full bridge finite element model of the CBUSB is established, and the influence of curvature parameters and different cable layout schemes on buffeting responses of the CBUSB is studied through the established model."

References

23. Wu B.; Zhang, L.L.; Yang Y.; Liu, L.J.; Ni Z.J. Refined timedomain buffeting analysis of a long-span suspension bridge in mountainous urban terrain. Adv. Civ. Eng. 2020, 2020, 4703169．(CrossRef)
24. Montoya M.C.; Hernández S.; Nieto F.; Kareem A. Aerostructural design of bridges focusing on the buffeting response: Formulation, parametric studies and deck shape tailoring. J. Wind Eng. Ind. Aerodyn. 2020, 204, 104243．(CrossRef)

 

Point 3(from Reviewer 2): In Fig. 1(b), it is helpful to provide the location of the stay cable.

Response 3: The location of the stay cable has been added in Figure 1 (b). (see page 4 and lines 140-142 in the revised paper)

 

Point 4(from Reviewer 2): It is suggested to provide the Reynolds number.

Response 4: The Reynolds numbers have been added in section 2.4, as follows (see page 7 and lines 228-229 in the revised paper):

"The Reynolds numbers scope of the model is 0.97×10⁵ and 5.66×10⁵ in wind speed cases."

 

Point 5(from Reviewer 2): In Fig. 9, it is suggested to provide the mean torsional displacement since it is often more important.

Response 5: We have added the mean torsional displacement of the CBUSB, as follows: (see page 10, lines 281-284 and lines 290-292 in the revised paper)

"Based on the quasi-steady assumption and the results of aerodynamic force tests, the mean lift force and the mean torque are applied to the finite element model (Figure.1 (a)), and then the mean vertical displacement, , and the mean torsional displacement, , at the midspan of the finite element model are calculated."

 

Point 6(from Reviewer 2): Careful proofreading is suggested.

Response 6: Three inaccurate expressions are revised, as follows:

1. The expression "has a negligible effect" is replaced by "has not a negligible effect"; (see page 2 and lines 80-81 in the revised paper)

"Similarly, the change in curvature has not a negligible effect on the wind-induced vibration of the curved beam bridges."

2. To clearly explain the cause of fatigue damage, the sentence of "Therefore, this ratio may cause long-term dynamic response fatigue damage and lead to cable fracture; thus, further study on cable fracture for CBUSB is required." is rephrased; (see page 14 and lines 377-378 in the revised paper)

"Due to the long-term dynamic response, the potential for fatigue damage and fracture damage of the cables need to be further studied."

3. The 2.4 Section title "Design and fabrication of section model and vibration test system " is replaced by "Sectional model vibration tests of CBUSB"; (see page 7 and line 225 in the revised paper)

4. The Figure 6 title "The distribution of aerodynamic coefficients with a wind attack angle " is replaced by "Measuring points of sectional model vibration testing "; (see page 8 and line 233 in the revised paper)

5. The expression "(bridge example in this Section 2.1)" is replaced by "(as same as the CBUSB example.)".(see page 15 and lines 390-391 in the revised paper)

"Cables are arranged near the center of the curvature (as same as the CBUSB example) in Figure. 14(b)"

 

Point 7(from Reviewer 1 and Reviewer 2): English language and style: Moderate English changes required

Response 7: A native English-speaker has reviewed and edited the original text to polish the language. Some revisions are as follows:

1.The expression "is used to", "connect" and "to" are replaced by "is used for", " connection of " and " and ", respectively; (see page 5 and lines 165-167 in the revised paper)

"The sectional model is shown in Figure 2, and a blue steel sheet is used for the connection of the three-component force/torque sensor and the sectional model in the aerodynamic force testing."

2.The words "was" and "vibration" are replaced by "is" and "sectional model vibration tests", respectively; (see page 5 and lines 168-169 in the revised paper)

"The same sectional model is used for sectional model vibration tests and aerodynamic force tests."

3.The word "was" is replaced by "is";(see page 5 and lines 184-185 in the revised paper)

"The fast Fourier transform method[29] is used to determine the vertical and torsion frequencies."

4.The sentence " M_z is independent of θ." is rephrased; (see page 6 and line 206 in the revised paper)

"There is no trigonometric relationship between M_z and θ."

5. The expression "0.130" is replaced by "0.130 m";(see page 7 and line 217 in the revised paper)

"the values of B and Hm are 0.130 m and 0.702 m"

6. The word "was" is replaced by "is";(see page 11 and lines 299-301 in the revised paper)

"The height range of the simulated turbulent wind fields is 90.00–100.66 m and the CBUSB is 90.00 m above the ground."

7.We introduce adverbials and attributes into the sentences of "The above verification of wind field characteristics and comparisons between the finite element and sectional models vibration test results show that the physical parameters, static wind load characteristics, and dynamic wind load application of the finite element model meet the expected requirements, indicating that the next parametric analysis is accurate and reasonable" to make the expression of the revised paper clearer, as follows (see pages 11 and 12, lines 319-323 in the revised paper):

"According to the verification of wind field characteristics and the comparison between the finite element calculation result and the sectional model vibration test result, physical parameters, static wind load characteristics, and dynamic wind load applications of the finite element model have accurate simulation reliability, which shows that the next parametric analysis is accurate and reasonable."

8. The expression "After that" is replaced by "Then"; (see page 12 and lines 338-339 in the revised paper)

"Then, the definitions of curvature cases 1–4 are shown in Figure 11."

9.By summarizing the sectional model wind tunnel test and the finite element analysis as research methods, we revise the first paragraph in Sections of Conclusion, as follows (see page 16 and lines 436-439 in the revised paper):

"In this study, the curved beam unilateral stayed bridge (CBUSB) in China is taken as an example. Sectional model wind tunnel tests are used as a reference, and a finite element model is established to analyze the influence of CUBSB curvature and stay cable arrangement on wind-induced vibration response."

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments to the previous version are properly addressed.