A method and apparatus for analyzing the static wind stability of bridges

Abstract

This invention relates to the field of bridge wind resistance design technology, and provides a method and apparatus for analyzing bridge static wind stability. The method includes the following steps: S1, calculating the static wind load; S2, calculating the structural displacement based on the static wind load and extracting the torsional angle; updating the three-component force coefficients and recalculating the static wind load; S3, updating the structural displacement based on the pulsating response; determining whether the deformation of the bridge structure is acceptable; if so, increasing the wind speed by a predetermined step size and repeating steps S1 to S3; if not, repeating steps S2 to S3; S4, when the number of iterations exceeds a predetermined upper limit, reducing the wind speed by one step and decreasing the predetermined step size; repeating steps S1 to S4 until the predetermined step size is less than or equal to the predetermined minimum step size, completing the analysis. This invention overcomes the shortcomings of existing bridge static wind stability analysis methods, which cannot accurately reflect the complex wind environment at the bridge site, leading to significant deviations in the analysis results.

Description

Technical Field

[0001] This invention relates to the field of bridge wind-resistant design technology, and in particular to a method and apparatus for analyzing the static wind stability of bridges. Background Technology

[0002] As the span of a long-span bridge increases, its overall stiffness decreases significantly. In particular, for cable-stayed bridges, the deformation of the structure gradually increases with wind speed. When the deformation exceeds the structure's own resistance capacity, the structure will experience wind instability. Wind instability can seriously threaten the safety of bridge structures. For some very long-span bridges, such as the Akashi Kaikyo Bridge, the critical wind speed for wind stability may be lower than the critical wind speed for flutter, which is extremely detrimental to the wind stability of the bridge.

[0003] However, existing methods for assessing the static wind stability of bridges still lack systematic and in-depth research. They generally only consider the uneven distribution of wind speed along the bridge span, which cannot accurately reflect the complex and ever-changing actual wind environment. The analysis results often differ significantly from the actual situation. In recent years, with the continuous development of transportation demand, many bridges spanning canyons have emerged. The wind environment at the bridge site is complex and ever-changing, and the existing static wind stability analysis methods are no longer applicable. Therefore, there is an urgent need to propose a static wind stability assessment method that can comprehensively reflect the complex wind environment. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing bridge static wind stability analysis methods, which cannot accurately reflect the complex wind environment at the bridge site, resulting in large deviations in the analysis results. This invention provides a bridge static wind stability analysis method and analysis device.

[0005] In a first aspect, the present invention provides a method for analyzing the static wind stability of a bridge, comprising the following steps:

[0006] S1. Set the wind speed and calculate the static wind load on the bridge structure under the three-component force coefficients of the turbulent wind field under the non-uniform wind speed distribution along the bridge span.

[0007] S2. Calculate the structural displacement of the bridge structure based on the static wind load and extract the torsional angle; update the three-component force coefficients based on the torsional angle and recalculate the static wind load on the bridge structure.

[0008] S3. Update the structural displacement based on the pulsating response of the bridge structure; determine whether the deformation of the bridge structure is within an acceptable range based on the structural displacement; if yes, increase the wind speed by a predetermined step size and repeat steps S1 to S3; if no, repeat steps S2 to S3.

[0009] S4. When the number of times the deformation of the bridge structure exceeds the acceptable range is greater than the predetermined iteration upper limit, the wind speed is reduced by one step according to the predetermined step size, and the value of the predetermined step size is decreased; the wind speed is increased according to the predetermined step size, and steps S1 to S4 are repeated until the predetermined step size is less than or equal to the predetermined minimum step size, and the analysis is completed.

[0010] The non-uniform wind speed in step S1 can be obtained through methods such as field measurement, empirical values, and simulation analysis.

[0011] The three force coefficients in steps S1 and S2 can be obtained through methods such as field tests, model tests, and simulation analysis.

[0012] The pulsation response in step S4 can be calculated either before step S4 or when needed (after step S3).

[0013] The inventors of this invention discovered that to accurately reflect the complex wind environment at a bridge site, in addition to considering the uneven distribution of wind speed along the bridge span, the three-component force coefficients and fluctuating load response of the turbulent wind field at the bridge site are also factors that should not be ignored. Furthermore, considering that wind instability is a phenomenon involving the coupling of wind load and bridge structural deformation, this invention proposes a bridge wind stability analysis method that couples multiple factors, including the uneven distribution of wind speed along the bridge span, the three-component force coefficients and their fluctuating response of the turbulent wind field at the bridge site, and the structural displacement of the bridge structure. During the analysis, the wind speed is gradually increased using the deformation of the bridge structure as a criterion, thereby obtaining different... The bridge structure response under wind speed; when the deformation of the bridge structure is not within the acceptable range, the calculation will be repeated to eliminate the calculation error caused by the first calculation; during the calculation process, this scheme will update the three-part force coefficients through the calculation results of the static wind load and recalculate the static wind load, and update the structural displacement through the pulsating response. Compared with the existing technology, it can more accurately reflect the complex wind environment at the bridge site, as well as the coupling between the static wind load and the bridge structure deformation, so as to obtain more accurate analysis results, such as the static wind stability wind speed displacement curve and the static wind stability critical wind speed, which is especially suitable for the refined analysis of the static wind stability of long-span bridges under complex wind conditions.

[0014] Preferably, it further includes the following steps:

[0015] S5. Select the wind speed in the last step as the critical wind speed for calm wind stability.

[0016] The final step, wind speed measurement, specifically refers to the process in steps S1 to S4 where the wind speed is increased multiple times by predetermined step sizes until the predetermined step size is less than the predetermined minimum step size. At this point, the wind speed is no longer increased. For example, let the wind speed be v. i 'i' is the wind speed number. 'i' increments by one each time the wind speed increases by a predetermined step. If the wind speed increases by f-1 times, reaching 'v'... fIf the predetermined step size is less than the predetermined minimum step size, the analysis will stop, and v will be used as the endpoint. f As the critical wind speed for calm and stable conditions.

[0017] Preferably, in step S2, the static wind load of the bridge structure is calculated according to the following formula:

[0018] F H =0.5*ρ*U 2 *C H *D

[0019] F V =0.5*ρ*U 2 *C V *B

[0020] M T =0.5*ρ*U 2 *CM*B 2

[0021] In the formula, F H F represents drag in volume axis coordinates; V M represents lift in body-axis coordinates; T Represents the torque in body-axis coordinates; ρ represents air density; U represents current wind speed; C H C represents the body axis drag coefficient under turbulent wind conditions. V C represents the body axis lift coefficient under turbulent wind conditions. M D represents the body axial moment coefficient under turbulent wind field; B represents the height of the main girder of the bridge; and D represents the width of the main girder of the bridge.

[0022] Preferably, in step S3, the Euclidean norm of the structural displacement is compared to see if it is less than a predetermined threshold; if yes, the deformation of the bridge structure is within an acceptable range; if no, the deformation of the bridge structure exceeds the acceptable range.

[0023] The specific judgment formula for step S3 can be found below:

[0024]

[0025] In the formula, This represents the torsional angle of the j-th main girder node in the i-th load step; represents the torsional angle of the j-th bridge main girder node in the pulsating response; i represents the load step number, and the load step number increases by one each time the wind speed increases by a predetermined step size; j represents the bridge main girder node number; n is the total number of main girder nodes; ε represents the predetermined threshold.

[0026] This solution can ensure the slope of the bridge wind speed displacement curve in each wind speed interval. Only the slope of the last segment Where Δvmin This indicates the minimum step size.

[0027] Preferably, the pulsating response of the bridge structure is calculated according to the following steps:

[0028] A. Generating pulsating wind fields using spectral methods;

[0029] B. Finite element analysis was performed on the bridge structure based on the pulsating wind field to obtain the pulsating response.

[0030] Preferably, the three-component force coefficients under turbulent wind fields are obtained through model wind tunnel tests.

[0031] Preferably, the initial value of the predetermined step size is greater than or equal to 10 m / s and less than or equal to 20 m / s.

[0032] If the predetermined step size is too large, the resolution of the analysis results may be too low; if the predetermined step size is too small, the analysis workload may be too large. Therefore, this scheme recommends a range of values ​​for the predetermined step size. It should be noted that the recommended range here refers to the initial value of the predetermined step size, that is, the predetermined step size value before it is reduced by step S4. After being reduced by step S4, the value of the predetermined step size can be lower than the lower limit of this range, that is, less than 10 m / s.

[0033] Preferably, the value of the predetermined minimum step size is greater than or equal to 2 m / s and less than or equal to 3 m / s.

[0034] If the predetermined minimum step size is too large, it will easily lead to low resolution of the analysis results; if the predetermined minimum step size is too small, it will easily lead to excessive analysis workload. Therefore, this scheme recommends a range of values ​​for the predetermined minimum step size.

[0035] Preferably, when reducing the predetermined step size in step S4, the predetermined step size is reduced by half each time.

[0036] For example, if the initial value of the predetermined step size is Δv, the first time the predetermined step size is reduced, the predetermined step size is reduced to Δv / 2; the second time the predetermined step size is reduced, the predetermined step size is reduced to Δv / 4.

[0037] In a second aspect, the present invention provides a bridge static wind stability analysis device, comprising:

[0038] The memory stores at least one instruction;

[0039] The processor is communicatively connected to the memory and is capable of executing instructions stored in the memory, thereby executing the bridge static wind stability analysis method of the present invention.

[0040] Storage devices, including but not limited to hard disk drives, solid-state drives, and floppy disks.

[0041] Processor, including but not limited to central processing unit and graphics processing unit.

[0042] Compared with existing technologies, the advantages of this invention are as follows:

[0043] 1. This invention provides a method for analyzing the static wind stability of bridges. It couples multiple factors such as the uneven distribution of wind speed along the bridge span, the three-component force coefficients and their pulsating response of the turbulent wind field at the bridge site, and the structural displacement of the bridge structure. Compared with existing technologies, it can more accurately reflect the complex wind environment at the bridge site and the coupling of static wind load and bridge structural deformation, thereby obtaining more accurate analysis results, such as static wind stability wind speed-displacement curves and static wind stability critical wind speeds. It is especially suitable for the refined analysis of the static wind stability of long-span bridges under complex wind environments.

[0044] 2. The present invention provides a bridge static wind stability analysis device, which can perform a bridge static wind stability analysis method of the present invention, thereby obtaining more accurate bridge static wind stability analysis results compared with the prior art. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating a method for analyzing the static wind stability of a bridge according to the present invention.

[0046] Figure 2 This is a schematic diagram of the main beam cross-section under the first load step of the bridge static wind stability analysis method of the present invention;

[0047] Figure 3 This is a schematic diagram of the main beam cross-section under the i-th load step of a bridge static wind stability analysis method according to the present invention.

[0048] Figure 4 This is a schematic diagram of the wind speed displacement during static wind stability analysis of a bridge according to the present invention.

[0049] Figure 5 This is a schematic diagram comparing the wind speed-wind angle of attack curve of the bridge static wind stability analysis method of the present invention with the prior art.

[0050] Icon: 1 - Bridge structure. Detailed Implementation

[0051] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0052] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," and "outer" to indicate orientation or positional relationships in the description of specific embodiments of the present invention is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is typically placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0053] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," and "parallel" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, or parallel, but rather that it can be slightly tilted or have a deviation. For example, "horizontal" merely means that its direction is more horizontal relative to "vertical," not that the structure must be completely horizontal, but that it can be slightly tilted. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," or "parallel" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the present invention.

[0054] Furthermore, the use of terms such as "first," "second," "third," etc. in terminology is merely for distinguishing identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0055] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as 2, 3, 4, 5, 6, 7, 8, or 9, and can even exceed nine.

[0056] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0057] Example 1

[0058] like Figure 1 As shown, a method for analyzing the static wind stability of a bridge includes the following steps:

[0059] S1. Set the wind speed and calculate the static wind load on bridge structure 1 under the three-component force coefficients of turbulent wind field under non-uniform wind speed distribution along the bridge span.

[0060] S2. Calculate the structural displacement of bridge structure 1 based on the static wind load and extract the torsional angle; update the three-component force coefficients based on the torsional angle and recalculate the static wind load on bridge structure 1.

[0061] S3. Update the structural displacement based on the pulsating response of bridge structure 1; determine whether the deformation of bridge structure 1 is within an acceptable range based on the structural displacement; if yes, increase the wind speed by a predetermined step size and repeat steps S1 to S3; if no, repeat steps S2 to S3.

[0062] S4. When the number of times the deformation of bridge structure 1 exceeds the acceptable range is greater than the predetermined iteration upper limit, the wind speed is reduced by one step according to the predetermined step size, and the value of the predetermined step size is decreased; the wind speed is increased according to the predetermined step size, and steps S1 to S4 are repeated until the predetermined step size is less than or equal to the predetermined minimum step size, and the analysis is completed.

[0063] In an optional implementation, the non-uniform wind field and wind speed in step S1 can be obtained by analyzing the wind field characteristics of the bridge site terrain using CFD (Computational Fluid Dynamics) or by conducting on-site measurements.

[0064] In an optional implementation, a segmental model of the bridge structure 1 is established, and the three-component force coefficients, such as those in step S1 or step S2, are obtained through a model wind tunnel test.

[0065] In an optional implementation, parameters such as wind speed, predetermined step size, predetermined minimum step size, and predetermined upper limit of iteration can be determined in advance in step S1; for example, in this embodiment, v is used. i Let i represent the wind speed, where i is the wind speed index. The initial value of i is set to 1, and i is incremented by one each time the wind speed increases by a predetermined step size. The initial value of the wind speed, v1, is set to 20 m / s. Let Δv represent the predetermined step size, and 10 m / s ≤ Δv ≤ 20 m / s. min This indicates the predetermined minimum step size, and 2m / s≤Δv min ≤3m / s, specifically 2.5m / s in this embodiment. Using N max N represents the upper limit of the predetermined iteration, and N max =3; correspondingly, in step S3, the wind speed is increased by a predetermined step size, i.e., v i=v i-1 +Δv; In step S4, NI represents the number of times the deformation of bridge structure 1 exceeds the acceptable range. Then, when NI > N max Then, the wind speed is reduced by one step according to the predetermined step size, that is, the wind speed is reduced from v. i Return to v i-1 .

[0066] In an optional implementation, the static wind load of bridge structure 1 is calculated in step S2 according to the following formula:

[0067] F H =0.5*ρ*U 2 *C H *D

[0068] F V =0.5*ρ*U 2 *C V *B

[0069] M T =0.5*ρ*U 2 *C M *B 2

[0070] In the formula, F H F represents drag in volume axis coordinates; V M represents lift in body-axis coordinates; T Represents the torque in body-axis coordinates; ρ represents air density; U represents current wind speed; C H C represents the body axis drag coefficient under turbulent wind conditions. V C represents the body axis lift coefficient under turbulent wind conditions. M The figure represents the body axial moment coefficient under turbulent wind conditions; D represents the height of the main girder of the bridge; B represents the width of the main girder of the bridge. More detailed steps and information can be found on page 56 of Chen Zhengqing's "Bridge Wind Engineering".

[0071] In an optional implementation, the pulsating response of bridge structure 1 is calculated according to the following steps:

[0072] A. Generating pulsating wind fields using spectral methods;

[0073] B. Finite element analysis was performed on bridge structure 1 based on the pulsating wind field to obtain the pulsating response.

[0074] Step A can be solved using numerical analysis software such as MATLAB and SCILAB, while step B can be analyzed using simulation software such as ANSYS and ABAQUS. Steps A and B can occur either directly in step S4 or before step S4.

[0075] In an optional implementation, the structural displacement is updated in step S3 according to the following formula:

[0076] U′ i =U i +U p

[0077] In the formula, U i U represents the unupdated structural displacement, where i is the wind speed number used to solve for this structural displacement; p Indicates a pulsating response; U′ i This represents the structural displacement updated based on the pulsating response, i.e., based on U′. i Instead of U i Determine whether the deformation of bridge structure 1 is within an acceptable range.

[0078] In an optional implementation, in step S3, it is compared whether the Euclidean norm of the structural displacement is less than a predetermined threshold; if yes, the deformation of bridge structure 1 is within an acceptable range; if no, the deformation of bridge structure 1 exceeds the acceptable range. The specific formula is as follows:

[0079]

[0080] In the formula, This represents the torsional angle of the j-th main girder node in the i-th load step, and Through U i Instead of U′ i Extracted, represents the torsional angle of the j-th bridge main girder node in the pulsating response; i represents the load step number, i.e., the wind speed number; j represents the bridge main girder node number; n represents the total number of main girder nodes; ε represents a predetermined threshold, which is specifically taken as 1 in this embodiment.

[0081] like Figure 4 As shown, this scheme can ensure the slope of the bridge wind speed displacement curve in each wind speed interval. Only the slope of the last segment

[0082] In an optional implementation, when reducing the predetermined step size in step S4, the predetermined step size is reduced by half each time. For example, when reducing the predetermined step size for the first time, the predetermined step size is reduced to Δv / 2; when reducing the predetermined step size for the second time, the predetermined step size is reduced to Δv / 4.

[0083] In an optional implementation, step S4 is followed by the following steps:

[0084] S5. Select the wind speed in the last step as the critical wind speed for calm wind stability.

[0085] For example, Figure 4As shown, in this embodiment, at the 19th wind speed v 19 The analysis ended when the predetermined step size was less than the predetermined minimum step size at a wind speed of 267.5 m / s. Therefore, the 19th wind speed v was selected. 19 =267.5m / s is the critical wind speed for calm and stable conditions.

[0086] In an optional implementation, steps S1 to S4 are all based on finite element analysis using the finite element software ANSYS; correspondingly, a spatial finite element model of the bridge structure 1 needs to be established before step S1.

[0087] like Figure 5 The figure shows a comparison between the wind speed-angle of attack curve obtained in this embodiment and the prior art, wherein the physical meaning of the angle of attack is as follows: Figures 2 to 3 θ0 and θ i As shown, its value changes with the increase of the load step; it can be seen that, based on only considering the non-uniform flow field across the span, considering the three-part force coefficients and pulsating response of the turbulent flow field under the turbulent wind field may greatly improve the critical wind speed for the static wind stability of the bridge. Therefore, this embodiment can more accurately complete the static wind stability analysis of the bridge under complex and variable wind environment.

[0088] Example 2

[0089] A bridge static wind stability analysis device includes a memory and a processor; the memory stores at least one instruction; the processor is communicatively connected to the memory and is able to execute the instructions stored in the memory, thereby executing a bridge static wind stability analysis method as described in Embodiment 1.

[0090] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the static wind stability of bridges, characterized in that, It includes the following steps: S1. Set the wind speed and calculate the static wind load on the bridge structure (1) under the non-uniform wind speed along the bridge span using the three-part force coefficient under turbulent wind field. S2. Calculate the structural displacement of the bridge structure (1) based on the static wind load, and extract the torsional angle; The static wind load on the bridge structure (1) is recalculated based on the updated three-component force coefficients according to the torsion angle. S3. Update the structural displacement based on the pulsating response of the bridge structure (1); determine whether the deformation of the bridge structure (1) is within an acceptable range based on the structural displacement, and compare whether the Euclidean norm of the structural displacement is less than a predetermined threshold using the following formula: In the formula, Representative at the In the first load step, the first... The torsional angle of each main girder node of the bridge. Representing the Torsional angle of a bridge main girder node in pulsating response; The number representing the load step, which is also the wind speed number; The number representing the main beam node of the bridge; The total number of main beam nodes; Represents a predetermined threshold; If yes, the deformation of the bridge structure (1) is within an acceptable range. The wind speed is increased according to the predetermined step size, and steps S1 to S3 are repeated. If no, the deformation of the bridge structure (1) exceeds the acceptable range. Steps S2 to S3 are repeated. S4. When the number of times the deformation of the bridge structure (1) exceeds the acceptable range is greater than the predetermined iteration upper limit, the wind speed is reduced by one step according to the predetermined step size, and the value of the predetermined step size is reduced; the wind speed is increased according to the predetermined step size, and steps S1 to S4 are repeated until the predetermined step size is less than or equal to the predetermined minimum step size, and the analysis is completed.

2. The method for analyzing the static wind stability of a bridge according to claim 1, characterized in that, It also includes the following steps: S5. Select the wind speed in the last step as the critical wind speed for calm wind stability.

3. The method for analyzing the static wind stability of a bridge according to claim 1, characterized in that, In step S2, the static wind load of bridge structure (1) is calculated according to the following formula: In the formula, Represents drag in volume axis coordinates; Represents lift in body-axis coordinates; The torque represents the force in the body axis coordinate system; Represents air density; This represents the current wind speed; The body axis drag coefficient represents the turbulent wind field. Represents the body axis lift coefficient under turbulent wind conditions; The body axis moment coefficient represents the turbulent wind field. Represents the height of the bridge's main girder; This represents the width of the bridge's main beam.

4. A method for analyzing the static wind stability of a bridge according to any one of claims 1 to 3, characterized in that, The pulsating response of the bridge structure (1) is calculated according to the following steps: A. The pulsating wind field is generated by the spectral method; B. Based on the pulsating wind field, the bridge structure (1) is subjected to finite element analysis to obtain the pulsating response.

5. A method for analyzing the static wind stability of a bridge according to any one of claims 1 to 3, characterized in that, The three-component force coefficients under turbulent wind fields were obtained through model wind tunnel tests.

6. A method for analyzing the static wind stability of a bridge according to any one of claims 1 to 3, characterized in that, The initial value of the predetermined step size is greater than or equal to 10 m / s and less than or equal to 20 m / s.

7. A method for analyzing the static wind stability of a bridge according to any one of claims 1 to 3, characterized in that, The predetermined minimum step size is greater than or equal to 2 m / s and less than or equal to 3 m / s.

8. A method for analyzing the static wind stability of a bridge according to any one of claims 1 to 3, characterized in that, In step S4, when reducing the predetermined step size, the predetermined step size is reduced by half each time.

9. A bridge static wind stability analysis device, characterized in that, Include: A memory, wherein the memory stores at least one instruction; A processor, which is communicatively connected to the memory, is capable of executing instructions stored in the memory to perform a bridge static wind stability analysis method as described in any one of claims 1 to 8.

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