Method and system for determining initial equilibrium state of spatial cable-stayed bridge

Abstract

This invention discloses a method and system for determining the initial equilibrium state of a spatial cable-stayed bridge, relating to the field of bridge construction technology. The method includes dividing the main cable into multiple segments using the main tower and suspenders as segment nodes, and defining the main cable segments between adjacent segment nodes as straight lines. Based on the main cable segmentation results, the spatial parameters of the main cable segments between adjacent segment nodes are calculated, and the stress condition of each main cable segment is determined. Based on the stress condition and length of the main cable segments, the stress-free length of each main cable segment is calculated. This invention does not rely on finite element analysis programs; it allows for direct modeling and analysis of suspension bridges, effectively improving work efficiency.

Description

Technical Field

[0001] This invention relates to the field of bridge construction technology, and specifically to a method and system for determining the initial equilibrium state of a spatial cable bridge. Background Technology

[0002] Suspension bridges are a relatively old type of bridge, favored for their rational stress distribution and aesthetically pleasing design. Traditional suspension bridges consist of a flexible structural system comprised of main cables, stiffening girders, main towers, anchorages, and suspenders. Due to the significant nonlinearity of the stress distribution in suspension bridge structures, specialized functions within finite element analysis software are required for analysis. The analysis and calculation of suspension bridges aims to determine the bridge's equilibrium state, and real-time equilibrium status is the most crucial step.

[0003] Currently, the functions provided by commonly used finite element analysis software are quite limited. They can only analyze double-tower suspension bridges, and the model needs to be modified according to the actual bridge structure during the analysis process, which greatly affects the efficiency of suspension bridge analysis. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a method and system for determining the initial equilibrium state of a spatial cable bridge. This method can analyze suspension bridges directly by modeling without relying on finite element programs, thus effectively improving work efficiency.

[0005] To achieve the above objectives, the present invention provides a method for determining the initial equilibrium state of a spatial cable bridge, specifically including the following steps:

[0006] Using the main tower and suspenders as segmentation nodes, the main cable is divided into multiple small segments, and the main cable segments between adjacent segmentation nodes are set as straight lines;

[0007] Based on the main cable segmentation results, the spatial parameters of the main cable segments between adjacent segment nodes are calculated, and the stress conditions of each main cable segment are determined.

[0008] Based on the stress conditions and lengths of the main cable segments, the stress-free lengths of each main cable segment are calculated.

[0009] Based on the above technical solution, the specific steps for calculating the spatial parameters of the main cable segments between adjacent segment nodes include:

[0010] A three-dimensional coordinate system is established with the center point of the bridge as the origin, and the coordinates of the two ends of the main cable segment are obtained.

[0011] Based on the coordinates of the two ends of the main cable segment, the angle between the main cable segment and the horizontal plane, as well as the angle between the horizontal projection line of the main cable segment and the X-axis of the three-dimensional coordinate system, are obtained.

[0012] Based on the above technical solution, determining the stress condition of each main cable segment specifically includes:

[0013] Based on the mechanical equilibrium algorithm, the tension of one main cable segment at the common endpoint of the two main cable segments and the tension of the other main cable segment at the common endpoint of the two main cable segments are calculated.

[0014] Based on the mechanical equilibrium algorithm, the tension at one end of one of the two adjacent main cable segments, where the end is not a common end of the two main cable segments, and the tension at one end of the other main cable segment, where the end is not a common end of the two main cable segments, are calculated.

[0015] Based on the above technical solution, the calculation of the tension in one of the two adjacent main cable segments at the common endpoint of the two main cable segments is specifically as follows:

[0016]

[0017] in, θ1 represents the angle between one of the two adjacent main cable segments and the horizontal plane, θ2 represents the angle between the horizontal projection line of one of the two adjacent main cable segments and the X-axis of the three-dimensional coordinate system, θ1′ represents the angle between the other two adjacent main cable segments and the horizontal plane, θ2′ represents the angle between the horizontal projection line of one of the two adjacent main cable segments and the X-axis of the three-dimensional coordinate system, θ1′ represents the angle between the other two adjacent main cable segments and the horizontal plane, and θ2′ represents the angle between the horizontal projection line of the other two adjacent main cable segments and the X-axis of the three-dimensional coordinate system.

[0018] Based on the above technical solution, the calculation of the tension of one main cable segment at the common endpoint of the two adjacent main cable segments is as follows:

[0019]

[0020] in, This indicates the tension in one of two adjacent main cable segments at the common endpoint of the two main cable segments.

[0021] Based on the above technical solution, after calculating the stress-free length of each main cable segment, the method further includes: calculating the stress-free length of each segment within the main cable segment.

[0022] Based on the above technical solution, the stress-free length of each segment within the main cable is calculated using the following method:

[0023] Ln =α n ×L

[0024]

[0025] Among them, L n α represents the stress-free length of the nth segment within the main cable segment. n L represents the length distribution coefficient of the nth segment within the main cable segment, and L represents the stress-free length of the main cable segment. n Let l represent the length of the nth segment within the main cable segment, and l represent the length of the main cable segment.

[0026] The present invention provides a system for determining the initial equilibrium state of a spatial cable bridge, comprising:

[0027] The segmentation module is used to divide the main cable into multiple segments using the main tower and suspenders as segmentation nodes, and to set the main cable segments between adjacent segmentation nodes as straight lines;

[0028] The determination module is used to calculate the spatial parameters of the main cable segments between adjacent segment nodes based on the main cable division results, and to determine the stress situation of each main cable segment.

[0029] The calculation module is used to calculate the stress-free length of each main cable segment based on the stress condition and length of the main cable segment.

[0030] Based on the above technical solution, the calculation of the spatial parameters of the main cable segments between adjacent segment nodes includes the following specific process:

[0031] A three-dimensional coordinate system is established with the center point of the bridge as the origin, and the coordinates of the two ends of the main cable segment are obtained.

[0032] Based on the coordinates of the two ends of the main cable segment, the angle between the main cable segment and the horizontal plane, as well as the angle between the horizontal projection line of the main cable segment and the X-axis of the three-dimensional coordinate system, are obtained.

[0033] Based on the above technical solution, determining the stress condition of each main cable segment specifically includes:

[0034] Based on the mechanical equilibrium algorithm, the tension of one main cable segment at the common endpoint of the two main cable segments and the tension of the other main cable segment at the common endpoint of the two main cable segments are calculated.

[0035] Based on the mechanical equilibrium algorithm, the tension at one end of one of the two adjacent main cable segments, where the end is not a common end of the two main cable segments, and the tension at one end of the other main cable segment, where the end is not a common end of the two main cable segments, are calculated.

[0036] Compared with the prior art, the advantages of the present invention are as follows: by dividing the main cable into multiple segments with the main tower and suspenders as segment nodes, and assuming that the main cable segments between adjacent segment nodes are straight lines, the stress-free length of each main cable segment can be obtained by using an approximation method. Therefore, the analysis of the suspension bridge can be realized by direct modeling without relying on the finite element program, which effectively improves the work efficiency. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart illustrating a method for determining the initial equilibrium state of a spatial cable bridge according to an embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of the bridge's elevation.

[0040] Figure 3 A spatial diagram of a small section of the main cable;

[0041] Figure 4 This is a schematic diagram of a small segment within the main cable. Detailed Implementation

[0042] This invention provides a method for determining the initial equilibrium state of a spatial cable-stayed bridge. By dividing the main cable into multiple segments using the main tower and suspenders as segment nodes, and assuming that the main cable segments between adjacent segment nodes are straight lines, the stress-free length of each main cable segment can be obtained using an approximation method. This eliminates the need for finite element analysis programs, allowing direct modeling of the suspension bridge and significantly improving work efficiency. Correspondingly, this invention also provides a system for determining the initial equilibrium state of a spatial cable-stayed bridge.

[0043] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments.

[0044] To address the limitations of finite element software in analyzing suspension bridges, see [reference needed]. Figure 1 As shown, this embodiment of the invention provides a method for determining the initial equilibrium state of a spatial cable bridge, which can effectively overcome software limitations and improve work efficiency. The method specifically includes the following steps:

[0045] S1: Using the main tower and suspenders as segmentation nodes, the main cable is divided into multiple small segments, and the main cable segments between adjacent segmentation nodes are set as straight lines;

[0046] For example, see Figure 2 As shown, the main cable is divided into multiple segments by the main tower and suspenders. Figure 2 In the diagram, AB represents a main cable segment, and BC represents a main cable segment. Figure 2 The numbers in the diagram represent the serial numbers of the main tower and the gantry.

[0047] S2: Based on the main cable segmentation results, calculate the spatial parameters of the main cable segments between adjacent segment nodes and determine the stress conditions of each main cable segment.

[0048] In this embodiment of the invention, the spatial parameters of the main cable segments between adjacent segment nodes are calculated, and the specific steps include:

[0049] S201: Establish a three-dimensional coordinate system with the center origin of the bridge to obtain the coordinates of the two ends of the main cable segment;

[0050] S202: Based on the coordinates of the two ends of the main cable segment, obtain the angle between the main cable segment and the horizontal plane, as well as the angle between the horizontal projection line of the main cable segment and the X-axis of the three-dimensional coordinate system.

[0051] See Figure 3 As shown, for a certain main cable segment AB, with endpoints A and B, a three-dimensional coordinate system is established with the bridge's center origin to obtain the coordinates of endpoints A and B. Then, based on the coordinates of endpoints A and B, the angle θ1 between the main cable segment AB and the horizontal plane, and the angle θ2 between the horizontal projection line of the main cable segment AB and the X-axis of the three-dimensional coordinate system are calculated. The stressed length of the main cable between main cable segments AB is approximately calculated as a straight line.

[0052] In this embodiment of the invention, determining the stress state of each main cable segment specifically includes:

[0053] S211: Based on the mechanical equilibrium algorithm, the tension of one main cable segment at the common endpoint of the two main cable segments and the tension of the other main cable segment at the common endpoint of the two main cable segments are calculated.

[0054] S212: Based on the mechanical equilibrium algorithm, calculate the tension at one end of one of the two adjacent main cable segments, where the end is not the common end of the two main cable segments, and the tension at one end of the other main cable segment, where the end is not the common end of the two main cable segments.

[0055] In this invention, the tension of one of two adjacent main cable segments at the common endpoint of the two main cable segments is calculated. The specific calculation method is as follows:

[0056]

[0057] in, θ1 represents the angle between one of the two adjacent main cable segments and the horizontal plane, θ2 represents the angle between the horizontal projection line of one of the two adjacent main cable segments and the X-axis of the three-dimensional coordinate system, θ1′ represents the angle between the other two adjacent main cable segments and the horizontal plane, θ2′ represents the angle between the horizontal projection line of one of the two adjacent main cable segments and the X-axis of the three-dimensional coordinate system, θ1′ represents the angle between the other two adjacent main cable segments and the horizontal plane, and θ2′ represents the angle between the horizontal projection line of the other two adjacent main cable segments and the X-axis of the three-dimensional coordinate system.

[0058] In this invention, the tension of one main cable segment at the common endpoint of two adjacent main cable segments is calculated. The specific calculation method is as follows:

[0059]

[0060] in, This indicates the tension in one of two adjacent main cable segments at the common endpoint of the two main cable segments.

[0061] The following example illustrates the tension calculation process described above.

[0062] Taking main cable segments AB and BC as examples, main cable segments AB and BC are two adjacent main cable segments, and their endpoint B is a common endpoint. Using the mechanical equilibrium formula, the tension of main cable segment AB at endpoint B can be derived as follows:

[0063]

[0064] at this time, Let θ1 represent the tension of the main cable segment AB at endpoint B, D represent the tension of the suspender at endpoint B, β represent the angle between the suspender at endpoint B and the horizontal plane, θ1 represent the angle between the main cable segment AB and the horizontal plane, θ2 represent the angle between the horizontal projection line of the main cable segment AB and the X-axis of the three-dimensional coordinate system, θ1′ represent the angle between the main cable segment BC and the horizontal plane, and θ2′ represent the angle between the horizontal projection line of the main cable segment BC and the X-axis of the three-dimensional coordinate system.

[0065] The tension at end point B of the main cable segment BC can be derived as follows:

[0066]

[0067] at this time, This indicates the tension of the main cable segment BC at endpoint B.

[0068] Similarly, the tension of the main cable segment AB at end point A and the tension of the main cable segment BC at end point C can be derived. Then, the main cable tension of each main cable segment is averaged to obtain the main cable tension of each main cable segment.

[0069] S3: Calculate the stress-free length of each main cable segment based on its stress condition and length.

[0070] In actual bridge calculations, there may be several nodes within a main cable segment. Therefore, after calculating the stress-free length of each main cable segment, the calculation also includes calculating the stress-free length of each segment within the main cable segment.

[0071] In this invention, the stress-free length of each segment within the main cable is calculated, and the specific calculation method is as follows:

[0072] L n =α n ×L

[0073]

[0074] Among them, L n α represents the stress-free length of the nth segment within the main cable segment. n Let L represent the length distribution coefficient of the nth segment within the main cable segment, L represent the stress-free length of the main cable segment, l represent the length of the nth segment within the main cable segment, and l represent the length of the main cable segment.

[0075] n

[0076] The following example illustrates the calculation of the stress-free length of each segment within the main cable.

[0077] See Figure 4 As shown, there are nodes M1 and M2 within the main cable segment AB, thus dividing the main cable segment AB into segments AM1, M1M2, and M2B. The stress-free length of each segment within the main cable segment AB is calculated as follows:

[0078]

[0079]

[0080]

[0081] in, This represents the stress-free length of segment A M1. Indicates the stress-free length of the small segments M1 and M2. L represents the stress-free length of the short segment M2B. ABThis represents the stress-free length of the main cable segment AB. This represents the length allocation coefficient of segment AM1. This represents the length distribution coefficient of the small segments M1 and M2. This represents the length allocation coefficient for the small segment M2B;

[0082]

[0083]

[0084]

[0085] in, Indicates the length of segment AM1. Indicates the length of the smaller segments M1 and M2. Indicates the length of the small segment M2B, l AB This indicates the length of the main cable segment AB.

[0086] This invention, by assuming that the main cables of adjacent nodes are straight, uses an approximation method to obtain the stress-free force of each main cable segment, which is easy to operate. The calculation function provided by the finite element program requires repeated model building, which is time-consuming and labor-intensive. However, this invention does not need to rely on the finite element program and can directly build the model. It overcomes the limitation of the finite element program only being applicable to two towers. This invention can be applied to solving the initial equilibrium state of multi-tower suspension bridges.

[0087] The present invention provides a system for determining the initial equilibrium state of a spatial cable bridge, comprising a partitioning module, a determination module, and a calculation module.

[0088] The segmentation module is used to divide the main cable into multiple segments using the main tower and suspenders as segmentation nodes, and to define the main cable segments between adjacent segmentation nodes as straight lines; the determination module is used to calculate the spatial parameters of the main cable segments between adjacent segmentation nodes based on the main cable segmentation results, and to determine the stress condition of each main cable segment; the calculation module is used to calculate the stress-free length of each main cable segment based on the stress condition and length of the main cable segment.

[0089] In this invention, the spatial parameters of the main cable segments between adjacent segment nodes are calculated, and the specific process includes:

[0090] A three-dimensional coordinate system is established with the center point of the bridge as the origin, and the coordinates of the two ends of the main cable segment are obtained.

[0091] Based on the coordinates of the two ends of the main cable segment, the angle between the main cable segment and the horizontal plane, as well as the angle between the horizontal projection line of the main cable segment and the X-axis of the three-dimensional coordinate system, are obtained.

[0092] In this invention, determining the stress state of each main cable segment specifically includes:

[0093] Based on the mechanical equilibrium algorithm, the tension of one main cable segment at the common endpoint of the two main cable segments and the tension of the other main cable segment at the common endpoint of the two main cable segments are calculated.

[0094] Based on the mechanical equilibrium algorithm, the tension at one end of one of the two adjacent main cable segments, where the end is not a common end of the two main cable segments, and the tension at one end of the other main cable segment, where the end is not a common end of the two main cable segments, are calculated.

[0095] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

[0096] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

Claims

1. A method for determining the initial equilibrium state of a spatial cable-stayed bridge, characterized in that, Specifically, the following steps are included: Using the main tower and suspenders as segmentation nodes, the main cable is divided into multiple small segments, and the main cable segments between adjacent segmentation nodes are set as straight lines; Based on the main cable segmentation results, the spatial parameters of the main cable segments between adjacent segment nodes are calculated, and the stress conditions of each main cable segment are determined. Based on the stress conditions and lengths of the main cable segments, the stress-free lengths of each main cable segment are calculated. The specific steps for calculating the spatial parameters of the main cable segments between adjacent segment nodes include: A three-dimensional coordinate system is established with the center point of the bridge as the origin, and the coordinates of the two ends of the main cable segment are obtained. Based on the coordinates of the two ends of the main cable segment, the angle between the main cable segment and the horizontal plane, and the angle between the horizontal projection line of the main cable segment and the X-axis of the three-dimensional coordinate system are obtained. Specifically, determining the stress state of each main cable segment includes: Based on the mechanical equilibrium algorithm, the tension of one main cable segment at the common endpoint of the two main cable segments and the tension of the other main cable segment at the common endpoint of the two main cable segments are calculated. Based on the mechanical equilibrium algorithm, the tension at one end of one of the two adjacent main cable segments, where the end is not the common end of the two main cable segments, and the tension at one end of the other main cable segment, where the end is not the common end of the two main cable segments, are calculated. After calculating the stress-free length of each main cable segment, the process also includes: calculating the stress-free length of each segment within the main cable segment.

2. The method for determining the initial equilibrium state of a spatial cable bridge as described in claim 1, characterized in that, The calculation obtains the tension of one of the two adjacent main cable segments at the common endpoint of the two main cable segments. The specific calculation method is as follows: in, This indicates the tension in one of two adjacent main cable segments at the common endpoint of the two main cable segments. This indicates the tension in the suspender at the common endpoint of two adjacent main cable segments. This indicates the angle between the suspender at the common endpoint of two adjacent main cable segments and the horizontal plane. This indicates the angle between one of the main cable segments and the horizontal plane in two adjacent main cable segments. This represents the angle between the horizontal projection line of one of the main cable segments and the X-axis of the three-dimensional coordinate system, within two adjacent main cable segments. This indicates the angle between one of two adjacent main cable segments and the horizontal plane. This represents the angle between the horizontal projection line of one of the two adjacent main cable segments and the X-axis of the three-dimensional coordinate system.

3. The method for determining the initial equilibrium state of a spatial cable bridge as described in claim 2, characterized in that, The calculation yields the tension in one of two adjacent main cable segments at the common endpoint of the two main cable segments. The specific calculation method is as follows: in, This indicates the tension in one of two adjacent main cable segments at the common endpoint of the two main cable segments.

4. The method for determining the initial equilibrium state of a spatial cable bridge as described in claim 1, characterized in that, The calculation of the stress-free length of each segment within the main cable is performed as follows: in, Indicates the first segment within the main cable A short segment of stress-free length, Indicates the first segment within the main cable The length distribution coefficient of each segment This indicates the stress-free length of a short section of the main cable. Indicates the first segment within the main cable The length of a small segment This indicates the length of a small section of the main cable.

5. A system for determining the initial equilibrium state of a spatial cable bridge, characterized in that, include: The segmentation module is used to divide the main cable into multiple segments using the main tower and suspenders as segmentation nodes, and to set the main cable segments between adjacent segmentation nodes as straight lines; The determination module is used to calculate the spatial parameters of the main cable segments between adjacent segment nodes based on the main cable division results, and to determine the stress situation of each main cable segment. The calculation module is used to calculate the stress-free length of each main cable segment based on the stress condition and length of the main cable segment. The specific steps for calculating the spatial parameters of the main cable segments between adjacent segment nodes include: A three-dimensional coordinate system is established with the center point of the bridge as the origin, and the coordinates of the two ends of the main cable segment are obtained. Based on the coordinates of the two ends of the main cable segment, the angle between the main cable segment and the horizontal plane, and the angle between the horizontal projection line of the main cable segment and the X-axis of the three-dimensional coordinate system are obtained. Specifically, determining the stress state of each main cable segment includes: Based on the mechanical equilibrium algorithm, the tension of one main cable segment at the common endpoint of the two main cable segments and the tension of the other main cable segment at the common endpoint of the two main cable segments are calculated. Based on the mechanical equilibrium algorithm, the tension at one end of one of the two adjacent main cable segments, where the end is not the common end of the two main cable segments, and the tension at one end of the other main cable segment, where the end is not the common end of the two main cable segments, are calculated. After calculating the stress-free length of each main cable segment, the process also includes: calculating the stress-free length of each segment within the main cable segment.

Images