A hybrid method and device for determining the completed bridge state of a wind-resistant cable suspension bridge

Abstract

The application relates to a hybrid method and device for determining the completed bridge state of a wind-resistant cable suspension bridge, and belongs to the field of bridge design; the method decomposes the bridge into four substructures of a main beam, a wind-resistant cable, a main cable and a bridge tower, and sequentially solves the substructures according to the stress transmission path; the finite element method is adopted for the main beam and the bridge tower, and the spatial catenary analytical method is adopted for the wind-resistant cable and the main cable; the main beam and the wind-resistant cable system are solved to obtain vertical forces, and the total vertical force at the lower end of the suspension cable is synthesized; the main cable system is solved to obtain the vertical resultant force at the top of the tower; the bridge tower is solved to obtain a temperature compensation value; finally, the results of the substructures are summarized, and control parameters such as the unstressed length are output; the application avoids the convergence difficulty of the overall nonlinear iteration through the substructure decoupling and the rigid-flexible component hybrid algorithm, significantly improves the calculation efficiency and accuracy, fully reflects the nonlinear characteristics of the cable, and provides a reliable basis for the fine design of the wind-resistant cable suspension bridge.

Description

Technical Field

[0001] This application relates to the field of suspension bridge design, and in particular to a hybrid method and apparatus for determining the completed state of a wind-resistant cable suspension bridge. Background Technology

[0002] Wind-resistant cable suspension bridges, as a type of long-span bridge structure, are widely used in complex terrains such as canyons and seas due to their excellent lateral stiffness and wind resistance. Determining the completed bridge condition is a core aspect of bridge control, directly affecting the bridge's aesthetic alignment, structural safety, and operational durability. Accurate calculation of parameters such as cable force, alignment, and tower deflection in the completed bridge condition is the theoretical basis for guiding on-site tensioning, cable segment cutting, and tower top pre-deflection settings, and is crucial for ensuring the final quality of the completed bridge.

[0003] In related technologies, the overall finite element analysis method is typically used to determine the completed state of a suspension bridge. This method establishes the main girder, main cable, wind-resistant cable, and bridge towers in a unified finite element model. By setting a target completed bridge state, a nonlinear iterative algorithm is used to calculate the stress-free length and initial internal forces of each component. In practice, engineers usually rely on general-purpose bridge analysis software to model the entire bridge structure as a whole and approximate the design target by repeatedly adjusting boundary conditions and element parameters, thereby obtaining the required control parameters.

[0004] However, the overall finite element method (FEM) has significant limitations for double-cable-stayed suspension bridges with wind-resistant cable systems. On one hand, the complex geometrical nonlinear coupling between the main cable and the wind-resistant cable results in too many unknowns in the overall model, making iterative calculations difficult to converge or extremely inefficient. On the other hand, when discretizing the cables using the finite element method, it is often difficult to accurately reflect the catenary effect of cables with large sags, leading to insufficient accuracy in the bridge alignment and cable tension, making it difficult to simultaneously meet multi-objective control requirements. Therefore, it is necessary to study and improve this structure, providing a hybrid method and device for determining the completed state of wind-resistant cable suspension bridges, aiming to improve computational accuracy and efficiency. Summary of the Invention

[0005] In view of the shortcomings or deficiencies mentioned in the background technology, the present application provides a hybrid method and apparatus for determining the completed state of a wind-resistant cable suspension bridge, so as to solve the problems of difficulty in iterative convergence, low calculation efficiency, and insufficient accuracy of bridge alignment and cable force when using the overall finite element method to determine the completed state of a wind-resistant cable suspension bridge in related technologies.

[0006] In a first aspect, embodiments of this application provide a hybrid method for determining the completed state of a wind-resistant cable suspension bridge, comprising the following steps: S1. The overall structure of the wind-resistant cable suspension bridge is decomposed into the main beam substructure, the wind-resistant cable system substructure, the main cable system substructure, and the bridge tower structure. S2. Perform independent mechanical solutions on the main beam substructure and the wind-resistant cable system substructure respectively to obtain the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable; S3. Based on the total vertical force at the lower end of each suspender, which is the resultant of the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable, the mechanical solution of the main cable system substructure is performed to obtain the resultant vertical force at the top of the tower of the main cable system. S4. Based on the vertical resultant force at the top of the tower, perform a mechanical solution on the bridge tower substructure to obtain the bridge tower temperature compensation value; S5. Summarize the solution results of each substructure to obtain the control parameters under the bridged state.

[0007] In some embodiments, the main cable system substructure and the wind-resistant cable system substructure are solved using an analytical method based on the spatial catenary theory, while the main beam substructure and the bridge tower substructure are solved using the finite element method.

[0008] Firstly, in some embodiments, the main beam substructure is mechanically solved to obtain the vertical force of the main beam, specifically including: S21. Establish the finite element model of the main beam, take the values ​​according to the design parameters, and apply the self-weight and secondary dead load. S22. Install rigid vertical supports at the anchor points at the lower ends of each sling of the main beam, perform static analysis, and calculate the vertical reaction force at each rigid support point; S23. Remove the rigid vertical support, apply a concentrated force equal in magnitude and vertically upward to the corresponding anchor point, perform static calculations, and obtain the vertical displacement of each concentrated force application point; S24. If the square root of the sum of squares of the vertical displacements does not meet the preset convergence limit, the value of the concentrated force is iteratively updated using the influence matrix method until the convergence limit is met, and the concentrated force obtained after the final iterative convergence is recorded as the vertical force of the main beam.

[0009] Firstly, in some embodiments, the wind-resistant cable system substructure is mechanically solved to obtain the vertical force at the lower end of the wind-resistant cable, specifically including: S25. Set the initial value of the three-dimensional component force at the starting end of the wind-resistant main cable. Starting from the starting end, proceed forward segment by segment, and solve the spatial coordinates of the end node of each cable segment and the stress-free length of the cable segment in turn. Update the three-dimensional component force of the end node according to the self-weight of the cable segment and the force of each connecting cable until the spatial coordinates of the end node of all cable segments and the stress-free length of all wind-resistant cables are obtained. S26. Based on the deviation between the coordinates of the end node obtained by the solution and its target position, correct the initial value of the triaxial component force at the starting end and repeat the above segment-by-segment solution until the deviation meets the preset convergence condition. S27. The vertical force acting on the main beam is obtained by superimposing the forces at the lower ends of each wind-resistant cable under the convergence state, and is denoted as the vertical force at the lower end of the wind-resistant cable.

[0010] Firstly, in some embodiments, the specific implementation of the deviation satisfying the preset convergence condition is as follows: Calculate the differences between the vertical and horizontal coordinates of the rightmost node of the wind-resistant main cable and the horizontal coordinate of the mid-span control point and their respective target values. Take the square root of the sum of the squares of the three differences. If the obtained value is not greater than a preset limit, it is determined that the deviation meets the convergence condition. When solving for the spatial coordinates and stress-free length of the end node of each cable segment by advancing segment by segment, the spatial catenary equation is used. Based on the three-dimensional component forces at the starting end of the current cable segment and the coordinates of the starting end node, the three-dimensional coordinates of the end node of the cable segment and the stress-free length of the cable segment are calculated. The three-dimensional component forces of the end node are updated based on the force equilibrium conditions and the self-weight of the cable segment.

[0011] In some embodiments, the step of performing a mechanical solution on the main cable system substructure based on the total vertical force at the lower end of each suspender, which is the resultant vertical force at the top of the tower of the main cable system, by superimposing the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable, specifically includes: S31. The vertical force of the main beam obtained from the solution of the main beam substructure and the vertical force at the lower end of the wind-resistant cable obtained from the solution of the wind-resistant cable substructure are superimposed to form the total vertical force at the lower end of each cable. S32. Set the initial value of the three-dimensional component force at the starting end of the main cable. Proceed forward segment by segment from the starting end. Based on the combined action of the total vertical force at the lower end of each sling and the self-weight of the main cable segment, solve the spatial coordinates of the end node of each cable segment and the stress-free length of the cable segment in sequence, and update the three-dimensional component force of the end node until the spatial coordinates of the end nodes of all cable segments and the stress-free length of all slings are obtained. S33. Based on the deviation between the coordinates of the end node obtained by the solution and its target position, correct the initial value of the three-dimensional component force at the starting end and repeat the above segment-by-segment solution until the deviation meets the preset convergence condition. S34. Based on the superposition of the vertical forces of the side span and the main cable at the top of the tower, the resultant vertical force at the top of the left and right towers is obtained.

[0012] Firstly, in some embodiments, the step of performing a mechanical solution on the bridge tower substructure based on the vertical resultant force at the top of the tower to obtain the bridge tower temperature compensation value specifically includes: S41. Establish a finite element model of the bridge tower and extract the cross-sectional area, material elastic modulus and linear expansion coefficient of each element of the bridge tower. S42. Apply the vertical resultant force at the top of the left and right towers obtained from solving the main cable substructure as an external load to the top node of the tower, and obtain the axial force of each element of the bridge tower through finite element calculation. S43. Calculate the temperature compensation value required for each unit in each stage based on the axial force, cross-sectional area, elastic modulus and linear expansion coefficient of each unit.

[0013] Firstly, in some embodiments, it further includes: S6. Substitute the structural parameters obtained from solving each substructure into the overall finite element model of the bridge. S7. Perform nonlinear displacement verification. If the displacement deviation between the verification result and the target bridge state is less than a preset threshold, then the structural parameters are confirmed to be valid.

[0014] In some embodiments, the main beam substructure, wind-resistant cable system substructure, main cable system substructure, and bridge tower substructure are solved step by step according to the force transmission law. The main beam substructure and wind-resistant cable system substructure are solved in parallel, and their output results are superimposed as the input of the main cable system substructure. The output of the main cable system substructure is used as the input of the bridge tower substructure.

[0015] Secondly, embodiments of this application provide a hybrid device for determining the completed state of a wind-resistant cable suspension bridge, comprising: The structural decomposition module is used to decompose the overall structure of the wind-resistant cable suspension bridge into the main girder substructure, the wind-resistant cable system substructure, the main cable system substructure, and the bridge tower structure. The main beam solution module is used to perform mechanical solutions on the main beam substructure to obtain the vertical force of the main beam; The wind-resistant cable solution module is used to perform mechanical solutions on the substructure of the wind-resistant cable system to obtain the vertical force at the lower end of the wind-resistant cable. The main cable solution module is used to perform mechanical solutions on the substructure of the main cable system based on the total vertical force at the lower end of each suspender, which is the resultant of the vertical force at the top of the tower of the main cable system, combined with the vertical force at the lower end of the main beam and the vertical force at the lower end of the wind-resistant cable. The bridge tower solution module is used to perform mechanical solutions on the bridge tower substructure based on the vertical resultant force at the top of the tower, and obtain the bridge tower temperature compensation value. The parameter output module is used to summarize the solution results of each substructure and output the control parameters in the bridge state.

[0016] The beneficial effects of the technical solution provided in this application include: The hybrid method for determining the completed state of wind-resistant cable suspension bridges provided in this application decomposes the overall structure of the wind-resistant cable suspension bridge into four independent substructures: the main girder, the wind-resistant cable system, the main cable system, and the bridge towers. Based on the structural force transmission law, a sequential logic of "beam-cable first, then main cable, then bridge tower" is used for mechanical solution, effectively decoupling the complex nonlinear coupling relationship between the main cable and the wind-resistant cable in traditional overall finite element analysis. This method not only avoids the technical difficulty of convergence in the overall iterative calculation of the entire bridge, improving computational efficiency and stability, but also ensures the physical consistency of the stress state of each substructure by progressively transferring boundary conditions. It can accurately obtain key control parameters such as the vertical resultant force at the tower top and temperature compensation values, providing reliable technical support for the refined design of wind-resistant cable suspension bridges. Attached Figure Description

[0017] 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.

[0018] Figure 1 This is a flowchart illustrating the method of an embodiment of this application; Figure 2 This is a schematic diagram of a wind-resistant cable suspension bridge according to an embodiment of this application; Figure 3 This is a schematic diagram of the substructure of the wind-resistant cable system according to an embodiment of this application; Figure 4 This is a schematic diagram of the main cable system substructure according to an embodiment of this application; Figure 5 This is a schematic diagram of the main beam substructure in an embodiment of this application; Figure 6 This is a schematic diagram of a model of a wind-resistant cable according to an embodiment of this application; Figure 7 This is a schematic diagram of the wind-resistant main cable according to an embodiment of this application.

[0019] The attached diagram lists the components represented by each number as follows: 100. Main beam substructure; 200. Wind-resistant cable system substructure; 210. Wind-resistant cable; 220. Wind-resistant main cable; 300. Main cable system substructure; 400. Bridge tower substructure. Detailed Implementation

[0020] 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 only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] This application provides a hybrid method and apparatus for determining the completed state of a wind-resistant cable suspension bridge. It can solve the problems in related technologies where the overall finite element method is used to determine the completed state of a wind-resistant cable suspension bridge, such as the difficulty of iterative convergence due to the complex coupling between the main cable and the wind-resistant cable, the low computational efficiency, and the insufficient accuracy of the completed bridge alignment and cable force.

[0022] See Figures 1 to 4 As shown, the first aspect of this application provides a hybrid method for determining the completed state of a wind-resistant cable suspension bridge, comprising the following steps: S1. The overall structure of the wind-resistant cable suspension bridge is decomposed into the main beam substructure 100, the wind-resistant cable system substructure 200, the main cable system substructure 300, and the bridge tower substructure 400. S2. Solve the mechanical problems independently for the main beam substructure 100 and the wind-resistant cable system substructure 200 to obtain the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable. S3. Based on the total vertical force at the lower end of each suspender, which is the resultant of the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable, the mechanical solution of the main cable system substructure 300 is performed to obtain the resultant vertical force at the top of the tower of the main cable system. S4. Based on the vertical resultant force at the top of the tower, the mechanical solution of the bridge tower substructure 400 is performed to obtain the temperature compensation value of the bridge tower. S5. Summarize the solution results of each substructure to obtain the control parameters under the bridged state.

[0023] The method described in this application simplifies the complex structure of a suspension bridge with wind-resistant cables by decomposing it into individual substructures such as bridge towers, main beams, main cable systems, and wind-resistant cable systems. Following the force transmission law and with a clear sequence, the main beam is solved first to obtain the dead load reaction forces at each support point. Then, the wind-resistant cable system is solved to obtain its own parameters and the vertical force acting on the main beam. Combining the dead load reaction forces and the vertical force, the main cable system is solved to obtain its own parameters and the vertical pressure acting on the top of the main tower. The bridge tower is then solved using the vertical pressure to obtain its temperature compensation value. This completes the solution for each substructure, which is then merged into a whole. The substructures are solved sequentially through the force transmission path, only needing to satisfy their respective linear target values ​​(vertical sag-to-span ratio or lateral sag-to-span ratio), avoiding multi-objective constraints, ensuring the integrity of the whole structure, and avoiding the complex solution of the entire structure.

[0024] Furthermore, different methods were used to solve the problem based on the stress characteristics of each part. Analytical methods were used for the main cable system and wind-resistant cable system, while the finite element method was used for the bridge and main beam. After the parameters of each part were determined, the substructures were combined, and an overall model was established using the finite element method. This approach fully combined the stress characteristics of each part with the advantages and disadvantages of each method, selecting appropriate methods to ensure accurate solutions for each part.

[0025] When solving the main cable system and wind-resistant cable system analytically, the main cable, suspenders, wind-resistant main cables, and wind-resistant tension cables are all solved jointly from plan and elevation perspectives as spatial catenaries. Compared to the finite element method, this method achieves accurate solutions without any simplification. When solving the wind-resistant cable analytically, the set target value is directly used as the tension of the wind-resistant tension cable. The alignment and parameters automatically meet the tension target, avoiding the drawback of the finite element method where the tension of the cable cannot reach the target value.

[0026] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiment of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided. In this method, the main cable system substructure 300 and the wind-resistant cable system substructure 200 are solved using an analytical method based on the spatial catenary theory, while the main beam substructure 100 and the bridge tower substructure 400 are solved using the finite element method. The control parameters include the stress-free length of the cable and the temperature compensation value of the bridge tower.

[0027] In this embodiment, a hybrid solution strategy of "cable analysis - component finite element" is adopted. For the flexible cable system, the analytical method based on the spatial catenary theory is used, which can accurately reflect the large sag nonlinear characteristics of the cable, avoid the errors caused by the discretization simulation of traditional finite element, and significantly improve the calculation accuracy of the bridge alignment and cable force. For rigid components such as main beams and bridge towers, the finite element method is used, which takes into account both calculation efficiency and versatility.

[0028] Meanwhile, this method directly outputs the stress-free length of the cable and the temperature compensation value of the bridge tower as control parameters. The former directly guides the cable processing and cutting, and the latter directly guides the pre-lifting of the bridge tower without the need for secondary conversion. This not only reduces parameter transmission errors, but also provides intuitive and accurate data support for the site, effectively ensuring the completion quality and safety of the wind-resistant cable suspension bridge.

[0029] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiment of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided. In this method, the main girder substructure 100 is mechanically solved to obtain the vertical force of the main girder, specifically including: S21. Establish the finite element model of the main beam, take the values ​​according to the design parameters, and apply the self-weight and secondary dead load. S22. Set rigid vertical supports at the anchor points at the lower ends of each sling of the main beam, perform static analysis, and calculate the vertical reaction force at each rigid support point; S23. Remove the rigid vertical support, apply a concentrated force equal in magnitude and vertically upward at the corresponding anchor point, perform static calculations, and obtain the vertical displacement of each concentrated force application point; S24. If the square root of the sum of squares of vertical displacements does not meet the preset convergence limit, the value of the concentrated force is updated iteratively using the influence matrix method until the convergence limit is met, and the concentrated force obtained after the final iteration convergence is recorded as the vertical force of the main beam.

[0030] In this embodiment, the vertical force of the main beam is determined by an iterative calculation strategy based on the influence matrix method. First, the load distribution is initially estimated in the finite element model using the rigid support reaction force. Then, the displacement convergence criterion is used for iterative correction, which can effectively eliminate the influence of the stiffness deformation of the main beam on the distribution of the cable force and ensure that the calculated vertical force of the main beam accurately meets the requirements of the completed bridge alignment.

[0031] Compared with traditional trial-and-error methods, the introduction of the influence matrix method significantly accelerates the iteration convergence speed and reduces the computational cost. At the same time, it provides high-precision and force-balanced boundary conditions for the subsequent solution of the wind-resistant cable and main cable system, ensuring the reliability and consistency of the calculation results of the entire hybrid method from the source.

[0032] Specifically, a) Establish a finite element model of the main beam: the parameters are taken according to the designed geometric dimensions, material properties and cross-sectional properties of the main beam, the actual constraints at the main tower (such as vertical constraints) are retained, and the self-weight of the main beam and the secondary dead load are applied.

[0033] b) Calculate the vertical force at the lower end of the slings using the rigid support continuous beam method: Set rigid vertical supports at the anchor points at the lower ends of each sling of the main beam, perform static analysis on the main beam model, and calculate the reaction force at the rigid support points.

[0034] c) Iterative vertical force at the lower end of the sling: Remove the rigid vertical support from b), apply a concentrated vertical force at the corresponding position. The magnitude of this force is equal to the reaction force obtained in b). Perform static calculations to determine the vertical displacement of each concentrated force application point. ( , (This refers to the total number of slings, which is also the number of points of concentrated force application). If this condition is not met... Less than a given limit (e.g., 10) -3 (Set as needed), use the influence matrix method to iteratively solve for the new vertical force, and save the vertical force of the last step. ( ).

[0035] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiment of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided. In this method, the wind-resistant cable system substructure 200 is mechanically solved to obtain the vertical force at the lower end of the wind-resistant cable. Specifically, it includes: S25. Set the initial value of the three-dimensional component force at the starting end of the wind-resistant main cable. Starting from the starting end, proceed forward segment by segment, and solve the spatial coordinates of the end node of each cable segment and the stress-free length of the cable segment in turn. Update the three-dimensional component force of the end node according to the self-weight of the cable segment and the force of each connecting cable until the spatial coordinates of the end node of all cable segments and the stress-free length of all wind-resistant cables are obtained. S26. Based on the deviation between the coordinates of the end node obtained by the solution and its target position, correct the initial value of the three-dimensional component force at the starting end and repeat the above segment-by-segment solution until the deviation meets the preset convergence condition. S27. The vertical force acting on the main beam is obtained by superimposing the forces at the lower ends of each wind-resistant cable under the convergence state, and is denoted as the vertical force at the lower end of the wind-resistant cable.

[0036] The specific implementation method of satisfying the preset convergence condition for the deviation in this method is as follows: Calculate the differences between the vertical and horizontal coordinates of the rightmost node of the wind-resistant main cable and the horizontal coordinate of the mid-span control point and their respective target values. Take the square root of the sum of the squares of the three differences. If the obtained value is not greater than the preset limit, the deviation is determined to meet the convergence condition. When solving for the spatial coordinates and stress-free length of the end node of each cable segment by advancing segment by segment, the spatial catenary equation is adopted. Based on the three-dimensional component forces at the starting end of the current cable segment and the coordinates of the starting end node, the three-dimensional coordinates of the end node of the cable segment and the stress-free length of the cable segment are calculated. The three-dimensional component forces of the end node are updated based on the force equilibrium conditions and the self-weight of the cable segment.

[0037] In this embodiment of the application, by adopting a step-by-step forward-progression algorithm based on the spatial catenary equation, the nonlinear deformation characteristics of the cable segment under its own weight are accurately described directly from the mechanical origin, avoiding the cumulative error caused by traditional finite element discretization simulation. Meanwhile, by calculating the coordinate differences of the rightmost node of the wind-resistant main cable and the control point at the mid-span and constructing a convergence criterion, multi-dimensional precise control of the spatial alignment of the wind-resistant cable was achieved, ensuring the mathematical convergence and mechanical balance of the iterative process. This high-precision independent solution method not only significantly improves the calculation reliability of the vertical force at the lower end of the wind-resistant cable and provides accurate and force-balanced boundary conditions for the main cable system substructure 300, but also effectively realizes the decoupling calculation of the wind-resistant cable and the main cable system, reducing the complexity and calculation cost of determining the overall bridge state.

[0038] Specifically, a) Calculation of the wind-resistant main cable segment: The coordinates of the leftmost node of the wind-resistant main cable are... The coordinates of the rightmost node are , The total number of nodes in the main cable is known on both sides, but unknown in the middle. The total horizontal projection length of the entire main cable. Vertical projection length Then the lateral span ratio ( (The design target value for the wind-resistant main cable at mid-span, given the conditions) and the initial longitudinal component force on the left side. ( The total tension of the wind-resistant cables is determined based on the magnitude of the environmental wind load to be resisted (this is a known condition), and the initial lateral component force is... ( Given the coordinates of the wind-resistant main cable at mid-span (and other conditions), and the initial vertical component force. Based on the longitudinal component of the force on the left side of the first cable segment. Vertical component force lateral component force left node coordinates , Right-side node ordinate The vertical projection length of the right-hand sub-point can be obtained iteratively using Newton's method based on the equation of the catenary in space. Horizontal projection length and the length of the stress-free cable segment The force at the right-hand component point can be obtained from the equilibrium condition of forces. , ( (Weight per linear meter of main cable material) , by vertical projection length The vertical coordinates of the right-hand dividing points can be obtained. , by the horizontal projection length The x-coordinates of the right-hand sub-points can be obtained. .

[0039] The equation of a catenary in three-dimensional space is as follows:

[0040] in, The elastic modulus of the main cable material. For cross-sectional area, For density, The stress-free length These represent the projected lengths of the cable segment in three directions. Since the ordinates of all points along the main cable are known, It is also a known quantity.

[0041] b) Based on the connection between the wind-resistant cables and the main wind-resistant cable, determine the number of wind-resistant cables connected to the right-side branch point of the cable segment in step a). Based on the coordinates of the right-side dividing point obtained in step a) and the known coordinates of the lower end of the cable... and average axial force The stress-free length of the cable can be obtained by using a flexible iterative method. Then, the force at the upper end of the cable is obtained from the equilibrium condition of forces. Then calculate the sum of the forces at the upper ends of all cables connected to that point. ,in At the same time, the forces at the lower ends of each cable are calculated. This refers to the nodal forces connected to the main beam.

[0042] c) Apply the force at the right-side component obtained in step a) The force at the upper end of the sling obtained in step b) Overlay and update ,Right now , , And assign the coordinates of the right-hand segment of the newly obtained cable segment to the coordinates of the left-hand segment of the next cable segment, that is... , , Return to step a) and begin the iterative loop for the next cable segment until all cable segments have been calculated, obtaining the vertical coordinate of the rightmost point of the main cable. x-axis and the x-coordinate of the midpoint (control point) .

[0043] d) Determine if the result meets the accuracy requirements. Calculate the vertical coordinate of the rightmost point of the main cable. x-axis and the x-coordinate of the midpoint (control point) The difference from the target value, i.e. , , .if Less than a given limit (e.g., 10) -3 (Set as needed), that is, terminate. If it exceeds the limit, proceed to step e).

[0044] e) Take the three-dimensional component forces on the left side of the cable segment as follows: , , Repeat steps a) through c) to calculate the vertical coordinate of the rightmost point of the main cable. x-axis and the x-coordinate of the midpoint (control point) Three new sets of results were obtained, namely , , Thus, the influence matrix is ​​obtained. .

[0045] f) Correct the initial values ​​of the three-dimensional force components on the left side of the main cable based on the influence matrix from step e), i.e. ,get , , , as the new initial value for iteration, repeat steps a) to f) until the accuracy condition of step d) is met, and then terminate the iteration.

[0046] g) In the result of the last step of the iteration, the coordinates of each node of the main cable This determined the spatial alignment, or spatial configuration, of the wind-resistant cable. At the same time, the stress-free lengths of each section of the wind-resistant main cable and each inclined wind-resistant cable were obtained.

[0047] h) Use b) to obtain the force at the lower end of each cable. Based on the node number connecting the cable to the main beam, the forces at the lower ends of cables with the same node number are superimposed (multiple cables may be connected to the same main beam node), thus obtaining the vertical force exerted by the cable on each node of the main beam. , ( , (Total number of slings).

[0048] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiment of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided. In this method, the total vertical force at the lower end of each cable, synthesized from the superposition of the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cables, is used to perform a mechanical solution on the main cable system substructure 300 to obtain the resultant vertical force at the top of the tower of the main cable system. Specifically, this includes: S31. The vertical force of the main beam obtained from the solution of the main beam substructure 100 and the vertical force of the lower end of the wind-resistant cable obtained from the solution of the wind-resistant cable substructure are superimposed to form the total vertical force of the lower end of each cable. S32. Set the initial value of the three-dimensional component force at the starting end of the main cable. Proceed forward segment by segment from the starting end. Based on the combined action of the total vertical force at the lower end of each sling and the self-weight of the main cable segment, solve the spatial coordinates of the end node of each cable segment and the stress-free length of the cable segment in sequence, and update the three-dimensional component force of the end node until the spatial coordinates of the end nodes of all cable segments and the stress-free length of all slings are obtained. S33. Based on the deviation between the coordinates of the end node obtained by the solution and its target position, correct the initial value of the triaxial force at the starting end and repeat the above segment-by-segment solution until the deviation meets the preset convergence condition. S34. Based on the superposition of the vertical forces of the side span and the main cable at the top of the tower, the resultant vertical force at the top of the left and right towers is obtained.

[0049] In this embodiment, the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable are superimposed to form the total vertical force at the lower end of the suspender cable, which accurately reflects the actual load distribution of the main cable system under the dual-cable cooperative working state, and ensures the accuracy and consistency of the boundary conditions of the mechanical solution. The analytical algorithm that advances step by step is used to solve the spatial shape and stress-free length of the main cable, which can effectively capture the large sag nonlinear characteristics of the main cable and avoid the accuracy loss caused by traditional finite element discretization. In addition, directly calculating the vertical resultant force of the main cables in the side spans and middle spans at the top of the towers provides accurate load input for the independent mechanical solution of the subsequent bridge tower substructure 400, realizing effective decoupling between the main cables and the bridge towers, and significantly improving the calculation efficiency and convergence stability of determining the overall bridge state.

[0050] Specifically, a) the calculations obtained from steps 2) and 3) and Calculate the total vertical force at the lower end of the sling. ( , (This refers to the total number of suspension cables). The ideal alignment of the main girder upon completion of the bridge is: The modeling line of the main beam in step 2) is consistent with that in step 2, and the coordinates of the lower end of the suspender cable are given as known conditions in the design.

[0051] b) The coordinates of the left and right side nodes of the main cable mid-span are respectively , , ( According to the design span-to-span ratio Calculate the vertical height at mid-span of the main cable. This is the target value that the main cable alignment must meet.

[0052] c) Calculate the longitudinal component of the force at the left end and vertical component force initial value, , , This is the sum of the vertical forces at the lower end of the sling, i.e. .

[0053] d) Based on the longitudinal component of the force on the left Vertical component force and the projected length of the cable segment in the horizontal plane The elevation difference between the theoretical vertex and the first bisector of the mid-span can be obtained iteratively from the catenary equation using Newton's method. and stress-free cable length For the first dividing point The force at the first division point of the mid-span can be obtained from the equilibrium condition of forces. , ( The weight of the main cable material per meter (based on the elevation difference) Find the vertical coordinate of the right endpoint of the first cable segment. ,Right now .

[0054] e) Iteration of the sling: The upper end of the sling is the right end of the sling segment, based on the coordinates of the right end of the sling segment in step d). and the known coordinates of the lower end of the sling (Determined by the ideal alignment of the main girder in step a) and the vertical force at the lower end. The stress-free length of the sling can be obtained by using a flexible iterative method. Then, the force at the upper end of the sling is obtained from the equilibrium condition of forces. .

[0055] f) Apply the force at the right end of the cable segment obtained in step d) The force at the upper end of the sling obtained in step e) Overlay and update Return to step d) and begin iterating through the second cable segment until all cable segments have been calculated, obtaining the vertical coordinate of the rightmost point of the main cable. and the vertical coordinates of the midpoint (control point) .

[0056] g) Determine if the result meets the accuracy requirements, and calculate the vertical coordinate of the rightmost point of the main cable. and the vertical coordinates of the midpoint (control point) The difference from the target value, i.e. , .if Less than a given limit (e.g., 10) -3 (Set as needed), that is, terminate; if it exceeds the limit, proceed to step h).

[0057] h) Take the longitudinal and vertical components of the force on the left side of the cable segment as follows: , Repeat steps d) and g) to calculate the vertical coordinate of the rightmost point of the main cable. and the vertical coordinates of the midpoint (control point) Two new sets of results were obtained, respectively , Thus, the influence matrix is ​​obtained. .

[0058] i) Correct the initial iterative value of the left component force of the main cable according to the influence matrix of step h), i.e. ,get , , as the new initial value for iteration, d) to i) are executed repeatedly until the accuracy condition of step g) is met, and the iteration is terminated.

[0059] j) In the final step of the iteration, save the stress-free length of each cable segment in the main span and the spatial coordinates of each node, and save... stress-free length of root sling .

[0060] k) Using the condition that the longitudinal forces at the top of the tower are equal, iteratively calculate the stress-free length of each cable segment in the side span. Using the condition that the resultant forces at the top of the cable saddle are equal, calculate the stress-free length of the cable segment in the anchor span.

[0061] l) Calculate the resultant vertical force at the top of the left and right towers based on the vertical forces of the main cables in the side spans and main spans at the tower tops. , .

[0062] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiment of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided. This method involves performing a mechanical solution on the bridge tower substructure 400 based on the vertical resultant force at the tower top to obtain the bridge tower temperature compensation value. Specifically, it includes: S41. Establish a finite element model of the bridge tower and extract the cross-sectional area, material elastic modulus and linear expansion coefficient of each element of the bridge tower. S42. Apply the vertical resultant force at the top of the left and right towers obtained from solving the main cable substructure as an external load to the top node of the tower, and obtain the axial force of each element of the bridge tower through finite element calculation. S43. Calculate the temperature compensation value required for each unit in each stage based on the axial force, cross-sectional area, elastic modulus and linear expansion coefficient of each unit.

[0063] In this embodiment of the application, the vertical resultant force of the left and right tower tops obtained by solving the main cable substructure is applied as an external load to the bridge tower finite element model, which can accurately reflect the actual axial force distribution borne by the bridge tower in the completed bridge state, and avoid the calculation error caused by inaccurate load estimation in the traditional method. The temperature compensation value is calculated based on the axial force and material physical parameters of each unit, which transforms the complex geometric elevation adjustment into an equivalent temperature load, making it easy to apply directly in control and with clear physical meaning. This method achieves decoupled calculation between the bridge tower and the superstructure cable-stayed beam system, which not only ensures the accuracy of the tower top elevation control and effectively eliminates the adverse effects of bridge tower compression deformation on the bridge alignment, but also improves the overall calculation efficiency and provides a reliable basis for bridge elevation correction.

[0064] Specifically, a) Establish a finite element model of the bridge tower: the parameters are taken according to the designed geometric dimensions, material properties and cross-sectional properties of the bridge tower, the base of the tower is fixed and constrained, and the self-weight of the bridge tower is considered.

[0065] b) Calculate the axial force of each element of the bridge tower: Calculate the resultant vertical force at the top of the left and right towers obtained in step 4). , Finite element analysis was performed on the top node of the bridge tower model to obtain the axial force of each element. .

[0066] c) Calculate the temperature compensation for the compression of the bridge tower: based on the axial force of each element calculated in step b). Unit cross-sectional area (The bridge tower has a variable cross-section structure, with different cross-sectional areas for each unit), material elastic modulus Coefficient of linear expansion of materials The temperature compensation values ​​of each unit are obtained. ,Right now .

[0067] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiments of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided, the method further comprising: S6. Substitute the structural parameters obtained from solving each substructure into the overall finite element model of the bridge. S7. Perform nonlinear displacement verification. If the displacement deviation between the verification result and the target bridge state is less than the preset threshold, the structural parameters are confirmed to be valid.

[0068] In this embodiment of the application, after the substructure is solved independently, a global verification mechanism for the calculation results is constructed by introducing a full-bridge overall finite element model for nonlinear displacement verification. This mechanism can effectively identify and eliminate the cumulative errors or neglected global coupling effects that may be generated by factor structure decomposition. By setting preset thresholds to confirm the validity of structural parameters, it is ensured that the final output control parameters not only meet the local force balance, but also conform to the overall nonlinear mechanical behavior of the bridge. This improves the reliability and safety of determining the completed bridge state while maintaining the efficiency of the decomposition method, providing a double guarantee for the bridge.

[0069] Specifically, based on the separate solutions for the main beam, wind-resistant cable, main cable, and main tower, the structural parameters of each part were obtained, including: stress-free length and node spatial coordinates of the main cable segment, stress-free length of the suspender cable, stress-free length and node spatial coordinates of the wind-resistant main cable segment, stress-free length of the wind-resistant tension cable, and temperature compensation value of the bridge tower unit.

[0070] Based on the above parameters, the main beam, wind-resistant cable, main cable and main tower can be combined to establish a full bridge finite element model. Considering geometric nonlinearity, the displacement response of the structure under self-weight and secondary dead load can be calculated to verify the rationality of the structural parameters.

[0071] The main difference between this step and the traditional method is that this step is a finite element full-bridge solution with all parameters known, rather than a full-bridge iterative solution for unknown parameters.

[0072] This embodiment can use a unified global spatial rectangular coordinate system (X, Y, Z) for the entire bridge. The X-axis is defined along the longitudinal direction of the bridge, pointing downstream (or in the direction of increasing mileage); the Y-axis is vertical, pointing upwards; and the Z-axis is horizontal along the bridge and perpendicular to the bridge axis.

[0073] It is worth noting that, based on the hybrid calculation method of this application, the coordinate dimensions can be differentiated according to the stress characteristics of different substructures; the main cable system mainly bears vertical loads, and the initial iteration uses longitudinal-vertical plane coordinates (X, Y) for simplified calculation; the wind-resistant cable system mainly bears lateral wind loads and is spatially arranged, and uses spatial three-dimensional coordinates (X, Y, Z) for accurate calculation.

[0074] Taking a wind-resistant cable suspension bridge as an example, based on the above coordinate system, the known conditions are as follows: The coordinates of the main cable's main tower IP point are (79.5, 1341.02) and (329.5, 1341.02), and the coordinates of the left and right anchor points are (1.37, 1301.65) and (412.03, 1299.57). The cross-sectional area of ​​the main cable is 0.01493 m². 2 86.738 kN / m³ 3 The cross-sectional area of ​​the sling is 0.000373 m². 2 The longitudinal spacing is 5m; the coordinates of the anchor points at both ends of the wind-resistant main cable are (91, 1307.33, 13) and (329.5, 1305.81, 14.32). The longitudinal spacing of each point on the main cable is 5m, and it consists of 42 cable segments. The transverse coordinate of the mid-span point of the main cable is 4.9m, and the cross-sectional area of ​​the main cable is 0.002641m². 2 The tensile strength of the wind-resistant cables is 7.5 kN, and the cross-sectional area is 0.000278 m². 2 There are 80 in total, arranged in a triangular cross shape.

[0075] The specific steps are as follows: 1) The structure is decomposed into four parts: main beam, wind-resistant cable system, main cable system and bridge tower.

[0076] 2) Calculate the main beam (finite element method). Establish a finite element model of the main beam, set vertical constraints at the lower end of the suspension cable, apply self-weight and secondary dead load, and calculate the vertical reaction force. The results are shown in Table 1. Due to the symmetry of the structure, Table 1 only gives the reaction force values ​​of the symmetrical half of the support points.

[0077] Table 1 Support Reactions of Main Beam

[0078] The point numbers in Table 1 above correspond to... Figure 5The labels are arranged sequentially along the direction of the arrow (longitudinal bridge direction). Point 1 corresponds to label 1, point 2 corresponds to label 2 (label 1 and label 2 are one point apart), point 3 corresponds to label 3 (label 2 and label 3 are one point apart), and so on for subsequent points.

[0079] 3) Calculation of the wind-resistant cable (analytical method). The wind-resistant cable system is fixed at the connection points between the wind-resistant cables and the main beam, with each cable having a force of 7.5 kN. Using the given transverse coordinates of the mid-span of the wind-resistant main cable as the target, the stress-free length of each cable segment, the spatial coordinates of each node, and the stress-free length and vertical force of the cables are obtained through analytical iteration. Then, based on the connection information, the vertical force transmitted from the wind-resistant cables to each connection point of the main beam is calculated, and the results are shown in Table 2. Tables 3 and 4 show the coordinates and stress-free lengths of each node of the wind-resistant main cable (only half of the results are given due to symmetry). These parameters are needed to establish the finite element model of the entire bridge. Figure 3 The planar projection of the spatial alignment of the wind-resistant cable system is shown.

[0080] Table 2 Vertical Force of Wind-Resistant Cables

[0081] The point numbers in Table 2 above correspond to... Figure 6 The positions of the wind-resistant cables 210 are marked sequentially along the direction of the arrows. Point 1 corresponds to label 1, point 2 corresponds to label 2, and so on for subsequent points. The negative sign of the vertical force of the wind-resistant cables indicates that the direction is vertically downward, opposite to the direction of the vertical support reaction force of the main beam.

[0082] Table 3 Coordinates of Wind-Resistant Main Cables

[0083] The point numbers in Table 3 above correspond to... Figure 7 The positions of the 220 medium-strength wind-resistant main cable are marked sequentially along the direction of the arrow. Point 1 corresponds to label 1, point 2 corresponds to label 2, and so on for subsequent points.

[0084] Table 4. Stress-free length of wind-resistant main cable

[0085] The above, in Table 4, the index segment number corresponds to Figure 7 The positions of the 220 medium-strength wind-resistant main cables are marked sequentially along the direction of the arrows. Among them, cable segment number 1' corresponds to label 1', cable segment number 2' (located between points 1 and 2) corresponds to label 2', and so on for subsequent points.

[0086] 4) Calculate the main cable (analytical method). Based on the self-weight vertical force and cable vertical force calculated in Tables 1 and 2, calculate the total vertical force at the lower end of the suspenders. The stress-free lengths of each cable segment and the coordinates of each node in the main span, side spans, and anchor spans, as well as the stress-free lengths of the suspenders, are determined through iteration (see Tables 5 and 6), and used to establish the finite element model of the entire bridge. The resultant vertical force transmitted from the main cable to the top of the bridge tower is 3156.049 kN, the same for both left and right towers; this value is used for the bridge tower calculations. Figure 4 The elevation projection of the main cable system alignment is shown.

[0087] Table 5 Coordinates of various points on the main cable

[0088] The point numbers in Table 5 above correspond to... Figure 4 The labels are arranged sequentially along the direction of the arrows. Point 1 corresponds to label 1, point 2 corresponds to label 2, and so on for subsequent points.

[0089] Table 6. Stress-free length of each cable segment of the main cable

[0090] The above, in Table 6, the index segment number corresponds to Figure 4 The positions of the markers are arranged sequentially along the direction of the arrows. Among them, the line segment number 1' corresponds to the marker 1', the line segment number 2' (located between point numbers 1 and 2) corresponds to the marker 2', and so on for subsequent point numbers.

[0091] 5) Calculation of the bridge tower (finite element method). A finite element model of the bridge tower is established, with fixed constraints at the tower base. A concentrated vertical force from the main cable is applied at the top of the tower, considering the tower's self-weight. The temperature compensation values ​​for each element are obtained as follows: 1.447, 1.827, 2.208, 2.588, 2.969, 3.393, 4.138, and 4.323.

[0092] 6) Calculate the overall structure (finite element method). The previous steps have determined the structural parameters of the decomposed main beam, wind-resistant cable, main cable, and main tower in series. Based on these parameters, a finite element model of the entire bridge is established by merging the components. Considering geometric nonlinearity, the displacement response of the structure under its own weight and secondary dead load is calculated to verify the rationality of the structural parameters. In a specific embodiment of this application, calculations have verified that the maximum deviation between the completed bridge state and the design target state is only 0.007m, which is a millimeter-level error. Therefore, the method proposed in this application decomposes the overall coupled structure, clarifies the order according to the force transmission law, selects an appropriate method to calculate and determine the parameters of each component, and then merges them into a whole. This method avoids the complex iterative calculation of the entire bridge in traditional methods, calculates sequentially, is simple, and achieves high-precision calculation of the ideal state of the completed wind-resistant cable suspension bridge.

[0093] Firstly, in some alternative embodiments: see Figures 1 to 4 As shown in the embodiment of this application, a hybrid method for determining the completed state of a wind-resistant cable suspension bridge is provided. In this method, the main girder substructure 100, the wind-resistant cable system substructure 200, the main cable system substructure 300, and the bridge tower substructure 400 are solved step by step according to the force transmission law. The main girder substructure 100 and the wind-resistant cable system substructure 200 are solved in parallel, and their output results are superimposed as the input of the main cable system substructure 300. The output of the main cable system substructure 300 is used as the input of the bridge tower substructure 400.

[0094] In this embodiment, the orderly decoupling of the complex coupled system is achieved by solving the problem step by step according to the law of force transmission. The parallel solution of the main beam substructure 100 and the wind-resistant cable system substructure 200 can make full use of computing resources and improve the efficiency of parallel processing. The output results of the two are superimposed as the input of the main cable system substructure 300, ensuring the integrity and accuracy of the boundary conditions of the main cable load. The output of the main cable system substructure 300 serves as the input of the bridge tower substructure 400, which truly reflects the physical path of load transmission to the foundation. This combination of serial and parallel calculation logic not only avoids the risk of global iteration non-convergence, but also improves the calculation efficiency and mechanical rationality of determining the completed bridge state, and ensures the reliable source of control parameters.

[0095] See Figures 1 to 4 As shown, a second aspect of this application provides a hybrid device for determining the completed state of a wind-resistant cable suspension bridge, comprising: The structural decomposition module is used to decompose the overall structure of the wind-resistant cable suspension bridge into the main girder substructure 100, the wind-resistant cable system substructure 200, the main cable system substructure 300, and the bridge tower substructure 400. The main beam solution module is used to perform mechanical solutions on the main beam substructure 100 to obtain the vertical force of the main beam; The wind-resistant cable solution module is used to perform mechanical solutions on the wind-resistant cable system substructure 200 to obtain the vertical force at the lower end of the wind-resistant cable. The main cable solution module is used to perform mechanical solutions on the main cable system substructure 300 based on the total vertical force at the lower end of each suspender, which is the resultant of the vertical force at the bottom of the main beam and the vertical force at the bottom of the wind-resistant cable. This results in the vertical resultant force at the top of the tower of the main cable system. The bridge tower solution module is used to perform mechanical solutions on the bridge tower substructure 400 based on the vertical resultant force at the top of the tower, and obtain the bridge tower temperature compensation value. The parameter output module is used to summarize the solution results of each substructure and output the control parameters in the bridge state.

[0096] In this embodiment of the application, the device realizes the automated execution of the above-mentioned hybrid method through a modular architecture. Each functional module corresponds to a method step, ensuring the rigor and traceability of the computational logic. The structural decomposition module realizes digital decoupling of complex bridge systems. Each solution module calculates independently for a specific substructure and automatically transmits boundary conditions, such as the vertical force of the main beam and the resultant force at the top of the tower, through the data interface between modules. This effectively avoids errors in manual data transcription and ensures the consistency of the mechanical model. The parameter output module can directly generate stress-free length and temperature compensation values ​​that can be used for guidance, which improves the standardization of the output results, facilitates integration with the control system, and significantly improves the efficiency and reliability of engineering applications for determining the bridge completion status.

[0097] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0098] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0099] 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.

Claims

1. A hybrid method for determining the completed state of a wind-resistant cable suspension bridge, characterized in that, Includes the following steps: The overall structure of the wind-resistant cable suspension bridge is decomposed into the main girder substructure, the wind-resistant cable system substructure, the main cable system substructure, and the bridge tower structure. Independent mechanical solutions were performed on the main beam substructure and the wind-resistant cable system substructure to obtain the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable. Based on the total vertical force at the lower end of each suspender, which is the resultant of the vertical force of the main beam and the vertical force at the lower end of the wind-resistant cable, the mechanical solution of the main cable system substructure is performed to obtain the resultant vertical force at the top of the tower of the main cable system. The temperature compensation value of the bridge tower is obtained by mechanically solving the structure of the bridge tower based on the vertical resultant force at the top of the tower. By summarizing the solution results of each substructure, the control parameters under the bridged state are obtained.

2. The hybrid method for determining the completed bridge state of a wind-resistant cable suspension bridge as described in claim 1, characterized in that: The main cable system substructure and the wind-resistant cable system substructure are solved using an analytical method based on the spatial catenary theory, while the main girder substructure and the bridge tower substructure are solved using the finite element method.

3. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in claim 1, characterized in that: The main beam substructure is subjected to mechanical analysis, and the vertical forces of the main beam are specifically obtained as follows: Establish a finite element model of the main beam, take the design parameters, and apply the self-weight and secondary dead load; Rigid vertical supports are installed at the anchor points at the lower ends of the suspenders of the main beam. Static analysis is performed to calculate the vertical reaction force at each rigid support point. Remove the rigid vertical support, apply a concentrated force equal in magnitude and vertically upward to the corresponding anchor point, perform static calculations, and obtain the vertical displacement of each concentrated force application point; If the square root of the sum of squared vertical displacements does not meet the preset convergence limit, the value of the concentrated force is iteratively updated using the influence matrix method until the convergence limit is met, and the concentrated force obtained after the final iterative convergence is recorded as the vertical force of the main beam.

4. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in claim 1, characterized in that: The mechanical solution of the substructure of the wind-resistant cable system is performed to obtain the vertical force at the lower end of the wind-resistant cable, specifically including: Set the initial value of the three-dimensional component force at the starting end of the wind-resistant main cable. Starting from the starting end, proceed forward segment by segment, and solve the spatial coordinates of the end node of each cable segment and the stress-free length of the cable segment in turn. Update the three-dimensional component force of the end node according to the self-weight of the cable segment and the force of each connecting cable until the spatial coordinates of the end node of all cable segments and the stress-free length of all wind-resistant cables are obtained. Based on the deviation between the coordinates of the end node obtained by the solution and its target position, the initial values ​​of the three-dimensional component forces at the starting end are corrected and the above segment-by-segment solution is repeated until the deviation meets the preset convergence condition. The vertical force acting on the main beam is obtained by superimposing the forces at the lower ends of each wind-resistant cable under convergent conditions, and is denoted as the vertical force at the lower end of the wind-resistant cable.

5. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in claim 4, characterized in that: The specific implementation method for the deviation to satisfy the preset convergence condition is as follows: Calculate the differences between the vertical and horizontal coordinates of the rightmost node of the wind-resistant main cable and the horizontal coordinate of the mid-span control point and their respective target values. Take the square root of the sum of the squares of the three differences. If the obtained value is not greater than a preset limit, it is determined that the deviation meets the convergence condition. When solving for the spatial coordinates and stress-free length of the end node of each cable segment by advancing segment by segment, the spatial catenary equation is used. Based on the three-dimensional component forces at the starting end of the current cable segment and the coordinates of the starting end node, the three-dimensional coordinates of the end node of the cable segment and the stress-free length of the cable segment are calculated. The three-dimensional component forces of the end node are updated based on the force equilibrium conditions and the self-weight of the cable segment.

6. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in claim 1, characterized in that: The method involves performing a mechanical solution on the main cable system substructure based on the total vertical force at the lower end of each suspender cable, which is the sum of the vertical force at the bottom of the main beam and the vertical force at the bottom of the wind-resistant cables, to obtain the resultant vertical force at the top of the tower of the main cable system. Specifically, this includes: The vertical force of the main beam obtained from the solution of the main beam substructure and the vertical force at the lower end of the wind-resistant cable obtained from the solution of the wind-resistant cable substructure are superimposed to form the total vertical force at the lower end of each cable. Set the initial value of the three-dimensional component force at the starting end of the main cable, and proceed forward segment by segment from the starting end. Based on the combined effect of the total vertical force at the lower end of each sling and the self-weight of the main cable segment, solve the spatial coordinates of the end node of each cable segment and the stress-free length of the cable segment in sequence, and update the three-dimensional component force of the end node until the spatial coordinates of the end nodes of all cable segments and the stress-free length of all slings are obtained. Based on the deviation between the coordinates of the end node obtained by the solution and its target position, the initial values ​​of the three-dimensional component forces at the starting end are corrected and the above segment-by-segment solution is repeated until the deviation meets the preset convergence condition. The resultant vertical force at the top of the left and right towers is obtained by superimposing the vertical forces of the main cables in the side span and middle span at the top of the tower.

7. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in claim 1, characterized in that: The process of performing a mechanical solution on the bridge tower substructure based on the vertical resultant force at the top of the tower to obtain the bridge tower temperature compensation value specifically includes: A finite element model of the bridge tower was established, and the cross-sectional area, material elastic modulus, and coefficient of linear expansion of each element of the bridge tower were extracted. The vertical resultant force at the top of the left and right towers obtained from solving the main cable substructure is applied as an external load to the top node of the tower, and the axial force of each element of the bridge tower is obtained through finite element calculation. Based on the axial force, cross-sectional area, elastic modulus, and linear expansion coefficient of each unit, calculate the temperature compensation value required for each unit at each stage.

8. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in any one of claims 1 to 7, characterized in that, Also includes: Substitute the structural parameters obtained from solving each substructure into the overall finite element model of the bridge. A nonlinear displacement calculation is performed. If the displacement deviation between the calculation result and the target bridge state is less than a preset threshold, the structural parameters are confirmed to be valid.

9. The hybrid method for determining the completed state of a wind-resistant cable suspension bridge as described in claim 1, characterized in that: The main girder substructure, wind-resistant cable system substructure, main cable system substructure, and bridge tower substructure are solved step by step according to the force transmission law. The main girder substructure and wind-resistant cable system substructure are solved in parallel, and their output results are superimposed as the input of the main cable system substructure. The output of the main cable system substructure is used as the input of the bridge tower substructure.

10. A hybrid device for determining the completed state of a wind-resistant cable suspension bridge, characterized in that, include: The structural decomposition module is used to decompose the overall structure of the wind-resistant cable suspension bridge into the main girder substructure, the wind-resistant cable system substructure, the main cable system substructure, and the bridge tower structure. The main beam solution module is used to perform mechanical solutions on the main beam substructure to obtain the vertical force of the main beam; The wind-resistant cable solution module is used to perform mechanical solutions on the substructure of the wind-resistant cable system to obtain the vertical force at the lower end of the wind-resistant cable. The main cable solution module is used to perform mechanical solutions on the substructure of the main cable system based on the total vertical force at the lower end of each suspender, which is the resultant of the vertical force at the top of the tower of the main cable system, combined with the vertical force at the lower end of the main beam and the vertical force at the lower end of the wind-resistant cable. The bridge tower solution module is used to perform mechanical solutions on the bridge tower substructure based on the vertical resultant force at the top of the tower, and obtain the bridge tower temperature compensation value. The parameter output module is used to summarize the solution results of each substructure and output the control parameters in the bridge state.

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