Method, device and equipment for determining main beam configuration of suspension bridge with side span and medium

Abstract

The invention discloses a method, a device, equipment and a medium for determining the configuration of a main beam of a suspension bridge with a side span, and relates to the field of suspension bridges, the method comprises the following steps: obtaining the dead load cable force of each sling of the suspension bridge, establishing a finite element model only containing a main beam, applying a concentrated load equivalent to the dead load cable force to the lifting point of each sling, and calculating the vertical deformation of the main beam; taking the reverse direction of vertical deformation as a target line shape of the main beam, applying relative break angles between adjacent beam sections of the current main beam, and establishing a mapping matrix between the relative break angles and the influence of the relative break angles on the line shape of the current main beam; constructing and solving a constraint optimization model to obtain an optimal relative break angle between each two adjacent beam sections, and determining a main beam configuration according to the optimal relative break angle between each two adjacent beam sections of the main beam; wherein the constraint optimization model takes an allowable error between a main beam configuration and a main beam target line shape as a constraint condition, and takes a minimum quadratic sum of a relative break angle as a target function. A definite shape finding method is established for the main beam.

Description

Technical Field

[0001] This application relates to the field of suspension bridge design technology, specifically to a method, device, equipment, and medium for determining the main girder configuration of a suspension bridge with side spans. Background Technology

[0002] Suspension bridges are the most common bridge type suitable for bridges with spans of over 1,000 meters. Conventional highway single-span suspension bridges usually do not have small side spans, but instead place expansion joints at the bridge towers, such as the Jiangyin Yangtze River Bridge and the Yangsigang Yangtze River Bridge. However, railway suspension bridges, especially high-speed railway suspension bridges, usually require side spans, or extended spans, to reduce the beam end rotation angle due to the strict control of the beam end rotation angle limit, such as the Wufengshan Yangtze River Bridge.

[0003] For conventional highway suspension bridges, the cable forces can be determined using the rigidly supported continuous beam method. This method involves installing vertical supports at each cable location and using the support reactions under dead load as the cable dead load force for main cable alignment. The advantage of this method is that the vertical displacement of the main girder is zero, and the main girder alignment perfectly matches the design target alignment. However, when used in suspension bridges with side spans, the self-weight of the side spans causes the main girder near the main span to arch upwards. When using the rigidly supported continuous beam method, the cables near the main tower will experience negative cable forces due to unloading, making this method no longer suitable.

[0004] Therefore, for suspension bridges with side spans, the load area method is typically used to determine the cable force, i.e., the cable force is determined based on the dead load within the load area of ​​each cable. However, in this case, the main girder arches upward due to the deflection of the side spans, resulting in a difference between its dead load alignment and the design target alignment. In existing technologies, finite element analysis is often performed on the coordinates and stress-free length of the main cable after the cable alignment is determined. The dead load deformation of the main girder at the time of bridge completion is then reversed and used as the manufacturing alignment of the main girder to offset the deformation at the time of bridge completion. However, in practice, it has been found that there is a difference between the cable force calculated by the finite element method and the cable force calculated by the main cable alignment model. The main girder alignment still deviates to some extent from the design alignment. For high-speed railway suspension bridges with extremely high precision requirements, this deviation can easily cause the track alignment deviation on the bridge to exceed the limit, making it difficult to meet track acceptance requirements. Summary of the Invention

[0005] This application provides a method, apparatus, equipment, and medium for determining the main girder configuration of a suspension bridge with side spans, which can solve the technical problem of large errors between the alignment and design alignment of suspension bridges with side spans in the prior art.

[0006] In a first aspect, embodiments of this application provide a method for determining the main girder configuration of a suspension bridge with side spans, the method comprising:

[0007] Obtain the dead load force of each cable of the suspension bridge, establish a finite element model containing only the main beam, apply a concentrated load of equal value to the dead load force at the suspension point of each cable, and calculate the vertical deformation of the main beam. Using the reverse of vertical deformation as the target alignment of the main beam, relative bends are applied between each adjacent beam segment of the current main beam, and a mapping matrix is ​​established between each relative bend and its influence on the current main beam alignment. Based on the mapping matrix, a constraint optimization model is constructed and solved to obtain the optimal relative bend angle between each adjacent beam segment. The configuration of the main beam is determined according to the optimal relative bend angle between each adjacent beam segment. The constrained optimization model uses the relative bend angles of each beam segment as variables, the allowable error between the main beam configuration and the target alignment of the main beam as constraints, and the minimum sum of squares of the relative bend angles as the objective function.

[0008] In conjunction with the first aspect, in one embodiment, obtaining the constant load force of each suspension cable of the suspension bridge includes: Based on the plan and elevation layout of the suspension bridge, determine the load area range of each cable; Calculate the dead load force borne by each cable based on the dead load and load area range of the main beam; Verify whether the total cable force of the suspenders is balanced with the dead load of the main beam.

[0009] In conjunction with the first aspect, in one implementation, establishing a finite element model including the main beam, applying a concentrated load equal to the dead load cable force at the suspension point of each cable, and calculating the vertical deformation of the main beam includes: Establish a finite element model containing only the main beam, and in the finite element model, simulate the main beam as a continuous beam with vertical supports at the side piers, auxiliary piers and the main tower; Determine the positions of all slings connected to the main beam on the main beam, and apply a concentrated vertical load at each sling point, the magnitude of which is equal to the dead load cable force; Based on the self-weight load and concentrated load of the main beam, the vertical displacement of each suspension point of the main beam is calculated, and the collection of all vertical displacements constitutes the vertical deformation of the main beam.

[0010] In conjunction with the first aspect, in one implementation, the current main beam comprises n beam segments, and there are n-1 connection points between the n beam segments. For the i-th connection point: Apply a unit relative bend at the i-th connection point to simulate the rotational deviation between the i-th beam segment and the (i+1)-th beam segment, where i = 1, 2, ..., n-1; Calculate the vertical displacement of each lifting point of the main beam under the rotational deviation condition at the i-th connection point.

[0011] In conjunction with the first aspect, in one implementation, it further includes: Calculate the vertical displacement of each lifting point of the main beam under the angular deviation condition at all connection points in sequence; The vertical displacements of each lifting point of the main beam under the angular deviation condition at a connection point are arranged as a column vector; Arrange the vertical displacements at all connection points corresponding to a single lifting point of the main beam under the angular deviation condition as a row vector; The column vectors and row vectors are assembled to form a mapping matrix.

[0012] In conjunction with the first aspect, in one implementation method, the constrained optimization model specifically comprises:

[0013] in, Indicates the relative bend angle of each beam segment. Represents the relative angle vector. This represents the transpose of the relative angle vector. Let be the objective function. Indicates the target alignment of the main beam. This indicates the allowable error between the main beam configuration and the target main beam alignment. Indicates the minimum permissible error. Indicates the maximum permissible error. Represents the mapping matrix, +1mm, for 1mm.

[0014] In conjunction with the first aspect, in one implementation, after determining the main beam configuration, the method further includes: Establish a finite element model of the entire bridge, including the main cable, suspenders, main tower, and main girder; Based on the determination of the main beam configuration, the initial coordinates of each segment point of the main cable, the stress-free length of each cable segment of the main cable, and the stress-free length of each suspender are input into the finite element model of the whole bridge. Elastic compression compensation is applied to the main tower components to ensure that the top elevation of the completed tower is the same as the design elevation. Apply the full bridge dead load to the full bridge finite element model to simulate the bridge's initial bridge completion state; Extract the main beam alignment and cable tension from the simulation results and compare them with the design target values.

[0015] Secondly, embodiments of this application provide a device for determining the main girder configuration of the aforementioned side-span suspension bridge, comprising: The first module is used to obtain the dead load force of each cable of the suspension bridge, establish a finite element model containing only the main beam, apply a concentrated load of equal value to the dead load force at the suspension point of each cable, and calculate the vertical deformation of the main beam. The second module is used to apply relative bends to each adjacent beam segment of the current main beam with the reverse of vertical deformation as the target beam shape, and to establish a mapping matrix between each relative bend and the influence of each relative bend on the current main beam shape. The third module is used to construct and solve the constraint optimization model based on the mapping matrix to obtain the optimal relative angle between each adjacent beam segment, and to determine the configuration of the main beam based on the optimal relative angle between each adjacent beam segment of the main beam. The constrained optimization model uses the relative bend angles of each beam segment as variables, the allowable error between the main beam configuration and the target alignment of the main beam as constraints, and the minimum sum of squares of the relative bend angles as the objective function.

[0016] Thirdly, embodiments of this application provide a device for determining the main girder configuration of a suspension bridge with side spans. The device for determining the main girder configuration of a suspension bridge with side spans includes a processor, a memory, and a program for determining the main girder configuration of a suspension bridge with side spans stored in the memory and executable by the processor. When the program for determining the main girder configuration of a suspension bridge with side spans is executed by the processor, it implements the steps of the method for determining the main girder configuration of a suspension bridge with side spans as described in any of the above embodiments.

[0017] Fourthly, embodiments of this application provide a computer-readable storage medium storing a program for determining the main girder configuration of a suspension bridge with side spans. When the program for determining the main girder configuration of a suspension bridge with side spans is executed by a processor, it implements the steps of the method for determining the main girder configuration of a suspension bridge with side spans as described in any of the above embodiments.

[0018] The beneficial effects of the technical solutions provided in this application include: This application embodiment establishes a main girder model and applies cable forces to calculate its deformation, thus establishing a clear form-finding method for the main girder. This solves the problem of deviation between the final bridge alignment and the design alignment caused by only performing form-finding on the main cable, improving the accuracy of the final bridge alignment. This application embodiment applies relative angles to all adjacent girder segments of the entire bridge and establishes a mapping matrix. With the goal of minimizing the sum of squared manufacturing errors, it solves the optimal relative angles for all bridge segments in one go, achieving overall optimal control of the main girder configuration. This solves the technical problem of traditional methods only setting pre-camber in the side spans without proposing a reasonable manufacturing configuration for the main girder on the main span side, leading to large differences in cable forces near the main tower. This application embodiment analyzes the impact of the relative angle of each girder segment on the overall bridge alignment and then optimizes it as a whole. It calculates the adjustment angle for each girder segment of the entire bridge, achieving precise control of the entire main girder alignment. Attached Figure Description

[0019] Figure 1 This is a diagram showing the deviation of the main girder in the completed bridge profile calculated using traditional methods. Figure 2 To set up the residual alignment deviation diagram of the main beam after manufacturing errors using traditional methods; Figure 3 To set up a cable tension error diagram after manufacturing errors using traditional methods; Figure 4 This is a flowchart illustrating the method for determining the main girder configuration of the suspension bridge with side spans in this application; Figure 5 This is a schematic diagram of the elevation layout of a suspension bridge structure provided in an embodiment of this application; Figure 6 A simplified finite element model calculation diagram containing only the main beam is provided for the embodiments of this application; Figure 7 The vertical deformation curve of the main beam under dead load and preset cable force provided in the embodiments of this application; Figure 8 A schematic diagram illustrating the optimization results of the relative bending angles of each beam segment of the main beam provided in the embodiments of this application; Figure 9 This is a diagram showing the bridge alignment error of the main girder calculated according to the embodiments of this application; Figure 10 This is a diagram showing the cable force error calculated according to the embodiments of this application; Figure 11 This is a schematic diagram of the functional modules of the device for determining the main girder configuration of the suspension bridge with side spans in this application; Figure 12 This is a schematic diagram of the hardware structure of the device for determining the main beam configuration of a suspension bridge with side spans involved in the embodiments of this application. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0021] For suspension bridges with side spans, the conventional methods for determining the manufacturing alignment of the main girder in existing technologies have been proven in practice to have significant deviations in alignment and cable force control, making it difficult to meet the engineering requirements of high-speed railways and other projects with extremely high precision requirements for completed bridges.

[0022] Figure 1This is a diagram showing the deviation of the main girder's alignment after the bridge is completed, calculated using traditional methods. First, the main cable alignment is calculated using the same cable forces. Then, the alignment results are substituted into the finite element model of the completed bridge for full-bridge calculation, resulting in the main girder alignment as shown below. Figure 1 As shown, a downward deflection of -286mm is generated on the right side span, corresponding to an upward arch of 216mm on the right side of the main span.

[0023] If this deviation is corrected only through the manufacturing of the main beam, then after the manufacturing error is calculated using the same constraint optimization algorithm, the manufacturing error is set in the finite element model of the completed bridge. Figure 2 The diagram shows the residual alignment deviation of the main girder after setting manufacturing errors using traditional methods. It is evident that although manufacturing errors were set to eliminate the alignment deviation of the completed bridge, approximately 110mm of alignment deviation remains in the main span. This deviation far exceeds the alignment accuracy requirements of high-speed railway tracks and also exceeds the allowable adjustment range for ballast thickness, which will bring significant difficulties to track laying and acceptance. Figure 3 This is a diagram showing the cable force error after setting manufacturing tolerances using traditional methods. The maximum cable force error is approximately 42 kN, exceeding 2%, indicating a significant difference between this cable force and the target cable force, thus failing to achieve the ideal main cable alignment target.

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0025] This application provides a method, apparatus, equipment, and medium for determining the main girder configuration of a suspension bridge with side spans, which can solve the technical problem of large errors between the alignment and design alignment of suspension bridges with side spans in the prior art.

[0026] In one aspect, embodiments of this application provide a method for determining the main girder configuration of a suspension bridge with side spans.

[0027] Figure 4 This is a flowchart illustrating the method for determining the main girder configuration of the suspension bridge with side spans in this application. See also... Figure 4 The method for determining the main girder configuration of a suspension bridge with side spans specifically includes the following steps: Step S1: Obtain the dead load force of each cable of the suspension bridge, establish a finite element model containing only the main beam, apply a concentrated load of equal value to the dead load force at the suspension point of each cable, and calculate the vertical deformation of the main beam.

[0028] In this embodiment of the application, the step S1 of obtaining the dead load force of each cable of the suspension bridge specifically includes the following steps: Step S111: Determine the load area range of each suspension cable based on the plan and elevation layout of the suspension bridge.

[0029] Specifically, based on the plan and elevation layout of the suspension bridge in the specific construction scheme, the load area of ​​each suspension cable is divided along the longitudinal direction of the main beam. For suspension cables arranged at equal intervals, the load area of ​​each cable is the beam segment area corresponding to half the distance between its left and right adjacent suspension cables. The load area of ​​the end suspension cables needs to be determined separately based on the boundary conditions.

[0030] Step S112: Calculate the dead load force borne by each suspender cable based on the dead load and load area range of the main beam.

[0031] Specifically, the load area of ​​each sling is multiplied by the dead load intensity of the main beam, which is the weight per unit length of the main beam, to obtain the dead load force borne by that sling.

[0032] Step S113: Verify whether the total cable force of the suspenders is balanced with the dead load of the main beam.

[0033] Specifically, the dead load forces of all slings are summed and compared with the total dead load of the main beam, which is the total length of the main beam multiplied by the dead load intensity, to ensure that the error between the two is within the allowable range, in order to verify the rationality of the cable force distribution.

[0034] The cable forces determined by the load area method in this application reflect the true distribution of the dead load of the completed bridge, providing a reliable load input for main cable form-finding and main girder deformation analysis. Simultaneously, by verifying the balance between the total cable forces and the total dead load of the main girder, the accuracy of the cable force calculation is ensured, improving the reliability of the overall design process.

[0035] In this embodiment of the application, step S1, which involves establishing a finite element model including the main beam, applying a concentrated load equal to the dead load cable force at the lifting point of each cable, and calculating the vertical deformation of the main beam, includes: Step S121: Establish a finite element model containing only the main beam. In the finite element model, the main beam is simulated as a continuous beam with vertical supports at the side piers, auxiliary piers, and main tower.

[0036] Specifically, the main girder is discretized for simulation. In the model, the main girder is treated as a continuous beam with only vertical displacement constrained at the bottom supports of the side piers, auxiliary piers (if any), and the main tower. This boundary condition simulates the vertical support state of the main girder at these locations when the bridge is completed. By establishing an independent bare beam model, the deformation analysis of the main girder is separated from the overall bridge, making the deformation calculation of the main girder direct and efficient, avoiding the iterative non-convergence problem that may occur when directly performing nonlinear analysis of the entire bridge.

[0037] Step S122: Determine the positions of all slings connected to the main beam on the main beam, and apply a vertically upward concentrated load to each sling, the magnitude of which is equal to the dead load cable force.

[0038] Specifically, based on the dead load force of each suspender cable calculated in step S1, a vertically upward concentrated nodal load is applied to the corresponding suspension point on the main beam model. The magnitude of each load is equal to the dead load force of the corresponding suspender cable. This set of upward forces effectively simulates the lifting effect of the suspenders on the main beam when the bridge is completed. The suspension point is the actual connection point between the suspender cable and the main beam. Simultaneously, the self-weight load of the main beam is applied to the model, typically calculated automatically by the modeling software by inputting the material density, or applied directly as a uniformly distributed load. The self-weight load of the main beam is the weight of the main beam itself.

[0039] Step S123: Based on the self-weight load and concentrated load of the main beam, calculate the vertical displacement of each suspension point of the main beam. The collection of all vertical displacements constitutes the vertical deformation of the main beam.

[0040] Specifically, a linear static analysis was performed on the main beam model after loading. After the calculation was completed, the vertical displacement values ​​of each suspension point on the main beam were extracted. All vertical displacement values ​​constituted the vertical deformation curve of the main beam under the equivalent bridge load. This curve intuitively showed where the main beam would arch and where it would deflect and its specific values.

[0041] Step S2: Using the reverse of vertical deformation as the target alignment of the main beam, apply relative bends to each adjacent beam segment of the current main beam, and establish a mapping matrix between each relative bend and its influence on the current main beam alignment.

[0042] Specifically, the construction of the mapping matrix in step S2 includes the following steps: Step A1: Calculate the vertical displacement of each lifting point of the main beam under the angular deviation condition at all connection points.

[0043] Specifically, the current main beam consists of n beam segments, and there are n-1 connection points between the n beam segments. n-1 angular deviation conditions need to be created. For the i-th connection point: Apply a unit relative bend at the i-th connection point to simulate the rotational deviation between the i-th beam segment and the (i+1)-th beam segment, where i = 1, 2, ..., n-1; calculate the vertical displacement of each lifting point of the main beam under the rotational deviation condition at the i-th connection point.

[0044] For the i-th working condition, the unit relative bend angle is applied only at the corresponding i-th connection point, while the other parameters of the model remain unchanged.

[0045] Step A2: Arrange the vertical displacements of each lifting point of the main beam under the angular deviation condition at a connection point into a column vector.

[0046] Specifically, a linear static analysis was performed, and the vertical displacement changes at each lifting point of the main beam under the rotation deviation condition were recorded. This set of displacement data represents the impact of the rotation deviation condition on the overall alignment of the main beam of the bridge.

[0047] Step A3: Arrange the vertical displacements at all connection points corresponding to a single lifting point of the main beam under the angular deviation condition into a row vector.

[0048] Specifically, the m vertical displacement values ​​calculated under the i-th rotation angle deviation condition are arranged in order of control points to form an m×1 column vector.

[0049] Step A4: Assemble the column vectors and row vectors to form a mapping matrix.

[0050] Specifically, repeating the above calculation for all n-1 working conditions will yield n-1 such column vectors. These column vectors are then arranged from left to right according to their corresponding working condition numbers (from 1 to n-1), forming an m-row, n-1-column matrix, which is the mapping matrix. Each column of the mapping matrix corresponds to a unit error working condition, i.e., a unit rotation angle at a connection point, and each row corresponds to a lifting point position. The physical meaning of the element in the j-th row and i-th column of the mapping matrix is ​​the change in vertical displacement of the i-th lifting point when a unit relative bend is applied at the j-th connection point.

[0051] The constrained optimization model constructed based on this mapping matrix can be solved quickly using existing algorithms. Compared with trial and error adjustments in the full-bridge nonlinear model, the computational efficiency is greatly improved.

[0052] Step S3: Based on the mapping matrix, construct and solve the constraint optimization model to obtain the optimal relative bend angle between each adjacent beam segment. Determine the main beam configuration based on the optimal relative bend angle between each adjacent beam segment. The constraint optimization model uses the relative bend angle of each beam segment as a variable, the allowable error between the main beam configuration and the target line shape of the main beam as a constraint condition, and the minimum sum of squares of the relative bend angles as the objective function.

[0053] In this embodiment of the application, the constrained optimization model is specifically as follows:

[0054] in, Indicates the relative bend angle of each beam segment. Represents the relative angle vector. This represents the transpose of the relative angle vector. Let be the objective function. Indicates the target alignment of the main beam. This indicates the allowable error between the main beam configuration and the target main beam alignment. Indicates the minimum permissible error. Indicates the maximum permissible error. Represents the mapping matrix, +1mm, for 1mm.

[0055] Specifically, using the relative bend angles of each beam segment as variables means determining each value in the relative bend angle vector, i.e., the relative bend angle that needs to be set at each connection point. Using the allowable error between the main beam configuration and the target main beam alignment as a constraint means that the total alignment adjustment calculated using the mapping matrix established in step S2 must infinitely approximate the target main beam alignment vector obtained by reversing the result from step S1, and the deviation must not exceed the preset allowable error. Using the minimum sum of squares of the relative bend angles as the objective function means that among all feasible solutions that satisfy the above alignment allowable error constraints, the solution with the minimum sum of squares of the manufacturing angle deviations is preferentially selected.

[0056] The optimal relative angle vector obtained from the solution is directly used as the preset relative rotation angle between adjacent beam segments during manufacturing. Based on this set of rotation parameters, the beam segments are processed and assembled, and the resulting main beam is the final determined main beam manufacturing configuration. This step, through constraint conditions, further reduces the alignment error of the completed bridge, fundamentally ensuring the ultra-high precision requirements of the high-speed railway track for the beam surface elevation.

[0057] In this embodiment, the method further includes: performing form-finding calculations for the main cable based on the cable forces of each suspender, as well as the preset material, cross-sectional properties, main cable sag-to-span ratio, main cable control point coordinates, and suspender lower end coordinates. The suspender lower end node coordinates should be set as the target value for the designed bridge. After the main cable form-finding calculations, information such as the coordinates of each segment point of the main cable, the stress-free length of each cable segment, and the stress-free length of the suspenders are obtained.

[0058] After determining the main beam configuration and main cable configuration, the following is also included: Step B1: Establish a finite element model of the entire bridge, including the main cable, suspenders, main tower, and main girder.

[0059] Specifically, finite element method (FEM) software is used to establish a spatial model of the entire bridge, including the main cable, suspenders, main tower, and main girder. The geometry of the main girder needs to be constructed based on the optimal relative bend angle determined in step S3, that is, the main girder is manufactured with the optimal relative bend angle.

[0060] Step B2: Based on the determination of the main beam configuration, input the initial coordinates of each segment point of the main cable, the stress-free length of each cable segment of the main cable, and the stress-free length of each suspender in the finite element model of the whole bridge.

[0061] Specifically, the initial coordinates of each segment point of the main cable can represent the initial geometric position of the main cable in the empty cable state. The stress-free length of each cable segment of the main cable can represent the manufacturing length of the main cable in the zero-stress state. The stress-free length of each suspender can represent the manufacturing length of the suspender in the zero-stress state. The purpose of inputting these parameters is to ensure that the bridge alignment achieves the designed alignment under the target load by controlling the stress-free dimensions of each component.

[0062] Step B3: Perform elastic compression compensation on the main tower components to ensure that the top elevation of the completed tower is the same as the design elevation.

[0063] Specifically, in the model, the main tower components are pre-adjusted to compensate for the elastic axial compressive deformation that occurs under the dead load of the completed bridge. This ensures that the tower top elevation in the completed bridge state is consistent with the target elevation on the design drawings when the calculation is completed, thereby guaranteeing the correctness of the main cable alignment.

[0064] Step B4: Apply the full bridge dead load to the full bridge finite element model to simulate the bridge's initial bridge completion state.

[0065] Specifically, since suspension bridges are flexible structures with large displacements, geometric nonlinear effects need to be considered. The simulation examines the process of the bridge reaching equilibrium under its own weight from an initial state of empty cable tension.

[0066] Step B5: Extract the main beam profile and cable tension from the simulation results and compare them with the design target values.

[0067] Specifically, the main girder alignment refers to obtaining the vertical coordinates of each suspension point of the main girder in the completed bridge state. The cable force refers to obtaining the internal force values ​​of each cable in the completed bridge state. The extracted calculation results are then compared item by item with the initially set design target values, namely the designed bridge alignment of the main girder and the expected cable dead load force. Deviations are calculated, and when the absolute error and maximum relative error of the cable force are within the preset range, it indicates that the finite element model and the main cable form-finding model data are consistent, the main girder manufacturing configuration is correct, and the main girder can be manufactured according to this manufacturing error.

[0068] This application embodiment establishes a main girder model and applies cable forces to calculate its deformation, thus establishing a clear form-finding method for the main girder. This solves the problem of deviation between the final bridge alignment and the design alignment caused by only performing form-finding on the main cable, improving the accuracy of the final bridge alignment. This application embodiment applies relative angles to all adjacent girder segments of the entire bridge and establishes a mapping matrix. With the goal of minimizing the sum of squared manufacturing errors, it solves the optimal relative angles for all bridge segments in one go, achieving overall optimal control of the main girder configuration. This solves the technical problem of traditional methods only setting pre-camber in the side spans without proposing a reasonable manufacturing configuration for the main girder on the main span side, leading to large differences in cable forces near the main tower. This application embodiment analyzes the impact of the relative angle of each girder segment on the overall bridge alignment and then optimizes it as a whole. It calculates the adjustment angle for each girder segment of the entire bridge, achieving precise control of the entire main girder alignment.

[0069] In a specific embodiment, taking a railway suspension bridge with a main span of 1060 meters as an example, the implementation process and effect of the method for determining the main beam manufacturing configuration are explained in detail. Figure 5 This is a schematic diagram of the elevation layout of a suspension bridge structure provided in an embodiment of this application. The bridge spans (90m + 1060m + 130m), with the main beams having uniform cross-sections. The dead load intensity is 400kN / m, and beam elements are used for simulation, with each beam segment element being 10m long. Suspension cables are only installed within the main span, with a standard cable spacing of 10m and a distance of 20m between the end cables and the centerline of the main tower.

[0070] Based on the plan and elevation layout of the suspension bridge, the cable force borne by each cable is calculated according to the dead load area. The standard cable force is 2000kN, and the end cable force is 3000kN.

[0071] Based on the cable forces of each suspender, and the pre-determined materials, cross-sectional properties, main cable sag-to-span ratio, coordinates of main cable control points, and coordinates of the lower ends of the suspenders, form-finding calculations are performed for the main cable. The coordinates of the lower ends of the suspenders should be set to the target values ​​for the completed bridge design. After the main cable form-finding calculations, information such as the coordinates of each segment of the main cable, the stress-free length of each cable segment, and the stress-free length of the suspenders are obtained.

[0072] Figure 6 This is a simplified calculation diagram of a finite element model containing only the main beam, provided for embodiments of this application. A finite element model containing only the main beam is established, simulating it as a continuous beam with vertical supports at the side piers, auxiliary piers, and main tower. An upward concentrated load equivalent to the determined dead load cable force is applied at each lifting point of the model, along with the self-weight of the main beam. Through static calculations, the vertical deformation of the main beam under the combined action of the dead load and cable force is obtained.

[0073] Figure 7 The vertical deformation curve of the main beam under dead load and preset cable force is provided for the embodiments of this application. Figure 7As shown, the main beam arches significantly in the middle span, with a maximum arch deformation of 1559 mm.

[0074] The calculated vertical deformation of the main girder is reversed and used as the solution objective for the manufacturing configuration, with a dimension of 129×1 (corresponding to 129 control nodes). In the finite element model of the main girder, unit relative bend angles are applied sequentially to the 127 connection points between the 128 beam segments. The influence of each unit manufacturing error on the vertical displacement of the 129 nodes of the entire bridge is analyzed, forming 127 influence vectors. Combining these vectors constructs a mapping matrix with a dimension of 129×127.

[0075] Subsequently, a constrained optimization model is constructed:

[0076] in, Given 127 relative angle vectors to be determined, solve this quadratic programming problem to obtain a set of optimal relative angles. Figure 8 This is a schematic diagram illustrating the optimized relative bend angles of the main beam segments provided in this embodiment. (See diagram below.) Figure 8 As shown in the embodiments of this application, not only does the side span need to be pre-cambered to counteract downward deflection, but the main span also needs to be pre-cambered to eliminate upward camber.

[0077] A finite element model of the entire bridge, including the main cable, suspenders, main tower, and main girder with manufacturing angles set according to optimization results, is established. All stress-free lengths and initial coordinates obtained from the first step of main cable form finding are input, and elastic compression compensation is applied to the main tower. A first-stage bridge completion calculation considering geometric nonlinearity is then performed.

[0078] Figure 9 This is a diagram showing the alignment error of the main girder of the completed bridge, calculated according to the embodiments of this application. Figure 10 This is a diagram showing the cable tension error calculated according to an embodiment of this application. (Referring to the reference...) Figure 9 and Figure 10 The maximum error between the completed bridge main girder alignment and the design target alignment is less than 3mm, and the error between the cable force of each cable and the target cable force is within 3kN, with a relative error of no more than 0.1%. The extremely small errors in alignment and cable force demonstrate that the main girder manufacturing configuration determined by the method for determining the main girder configuration of the suspension bridge with side spans provided in this application is highly coordinated with the main cable alignment result, enabling a precise match between the completed bridge state and the design target.

[0079] Secondly, embodiments of this application also provide a device for determining the main beam configuration of a suspension bridge with side spans.

[0080] In one embodiment, reference is made to Figure 11 , Figure 11 This is a schematic diagram of the functional modules of the device for determining the main girder configuration of the suspension bridge with side spans in this application.

[0081] like Figure 11 As shown, the device for determining the main girder configuration of a suspension bridge with side spans includes: The first module is used to obtain the dead load force of each cable of the suspension bridge, establish a finite element model containing only the main beam, apply a concentrated load of equal value to the dead load force at the suspension point of each cable, and calculate the vertical deformation of the main beam. The second module is used to apply relative bends to each adjacent beam segment of the current main beam with the reverse of vertical deformation as the target beam shape, and to establish a mapping matrix between each relative bend and the influence of each relative bend on the current main beam shape. The third module is used to construct and solve the constraint optimization model based on the mapping matrix to obtain the optimal relative angle between each adjacent beam segment, and to determine the configuration of the main beam based on the optimal relative angle between each adjacent beam segment. The constrained optimization model uses the relative bend angles of each beam segment as variables, the allowable error between the main beam configuration and the target alignment of the main beam as constraints, and the minimum sum of squares of the relative bend angles as the objective function.

[0082] The functions of each module in the above-mentioned device for determining the main girder configuration of a suspension bridge with side spans correspond to the steps in the above-mentioned method embodiment for determining the main girder configuration of a suspension bridge with side spans. Their functions and implementation processes will not be described in detail here.

[0083] Thirdly, embodiments of this application provide a device for determining the main girder configuration of a suspension bridge with side spans. The device for determining the main girder configuration of a suspension bridge with side spans includes a processor, a memory, and a program for determining the main girder configuration of a suspension bridge with side spans stored in the memory and executable by the processor. When the program for determining the main girder configuration of a suspension bridge with side spans is executed by the processor, it implements the steps of the method for determining the main girder configuration of a suspension bridge with side spans as described in any of the above embodiments.

[0084] The equipment used to determine the main girder configuration of a suspension bridge with side spans can be a personal computer (PC), laptop, server, or other device with data processing capabilities.

[0085] Reference Figure 12 , Figure 12 This is a schematic diagram of the hardware structure of the device for determining the main girder configuration of a suspension bridge with side spans, as described in an embodiment of this application. In this embodiment, the device for determining the main girder configuration of a suspension bridge with side spans may include a processor, a memory, a communication interface, and a communication bus.

[0086] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.

[0087] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces. These interfaces are used for interconnecting devices within the equipment that determines the main girder configuration of the suspension bridge with side spans, as well as for interconnecting the equipment that determines the main girder configuration with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.

[0088] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0089] The processor can be a general-purpose processor, which can call the program for determining the main girder configuration of a suspension bridge with side spans stored in memory and execute the method for determining the main girder configuration of a suspension bridge with side spans provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the program for determining the main girder configuration of a suspension bridge with side spans is called can refer to the various embodiments of the method for determining the main girder configuration of a suspension bridge with side spans in this application, and will not be repeated here.

[0090] Those skilled in the art will understand that Figure 12 The hardware structure shown does not constitute a limitation of this application and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0091] Fourthly, embodiments of this application provide a computer-readable storage medium storing a program for determining the main girder configuration of a suspension bridge with side spans. When the program for determining the main girder configuration of a suspension bridge with side spans is executed by a processor, it implements the steps of the method for determining the main girder configuration of a suspension bridge with side spans as described in any of the above embodiments.

[0092] This application stores a program for determining the main girder configuration of a suspension bridge with side spans on a computer-readable storage medium. When the program for determining the main girder configuration of a suspension bridge with side spans is executed by a processor, it implements the steps of the method for determining the main girder configuration of a suspension bridge with side spans as described above.

[0093] The method implemented when the procedure for determining the main girder configuration of a suspension bridge with side spans is executed can refer to the various embodiments of the method for determining the main girder configuration of a suspension bridge with side spans in this application, and will not be repeated here.

[0094] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0095] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0096] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0097] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0098] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0099] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0100] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for determining the main girder configuration of a suspension bridge with side spans, characterized in that, The method for determining the main girder configuration of the suspension bridge with side spans includes: Obtain the dead load force of each cable of the suspension bridge, establish a finite element model containing only the main beam, apply a concentrated load of equal value to the dead load force at the suspension point of each cable, and calculate the vertical deformation of the main beam. Using the reverse of vertical deformation as the target alignment of the main beam, relative bends are applied between each adjacent beam segment of the current main beam, and a mapping matrix is ​​established between each relative bend and its influence on the current main beam alignment. Based on the mapping matrix, a constraint optimization model is constructed and solved to obtain the optimal relative bend angle between each adjacent beam segment. The configuration of the main beam is determined according to the optimal relative bend angle between each adjacent beam segment. The constrained optimization model uses the relative bend angles of each beam segment as variables, the allowable error between the main beam configuration and the target alignment of the main beam as constraints, and the minimum sum of squares of the relative bend angles as the objective function.

2. The method for determining the main girder configuration of a suspension bridge with side spans according to claim 1, characterized in that, The process of obtaining the dead load force of each cable of the suspension bridge includes: Based on the plan and elevation layout of the suspension bridge, determine the load area range of each cable; Calculate the dead load force borne by each cable based on the dead load and load area range of the main beam; Verify whether the total cable force of the suspenders is balanced with the dead load of the main beam.

3. The method for determining the main girder configuration of a suspension bridge with side spans according to claim 1, characterized in that, The process involves establishing a finite element model of the main beam, applying a concentrated load equal to the dead load cable force at the suspension point of each cable, and calculating the vertical deformation of the main beam, including: Establish a finite element model containing only the main beam, and in the finite element model, simulate the main beam as a continuous beam with vertical supports at the side piers, auxiliary piers and the main tower; Determine the positions of all slings connected to the main beam on the main beam, and apply a concentrated vertical load at each sling point, the magnitude of which is equal to the dead load cable force; Based on the self-weight load and concentrated load of the main beam, the vertical displacement of each suspension point of the main beam is calculated, and the collection of all vertical displacements constitutes the vertical deformation of the main beam.

4. The method for determining the main girder configuration of a suspension bridge with side spans according to claim 1, characterized in that, The current main beam consists of n beam segments, and there are n-1 connection points between the n beam segments. For the i-th connection point: Apply a unit relative bend at the i-th connection point to simulate the rotational deviation between the i-th beam segment and the (i+1)-th beam segment, where i = 1, 2, ..., n-1; Calculate the vertical displacement of each lifting point of the main beam under the rotational deviation condition at the i-th connection point.

5. The method for determining the main girder configuration of a suspension bridge with side spans according to claim 4, characterized in that, Also includes: Calculate the vertical displacement of each lifting point of the main beam under the angular deviation condition at all connection points in sequence; The vertical displacements of each lifting point of the main beam under the angular deviation condition at a connection point are arranged as a column vector; Arrange the vertical displacements at all connection points corresponding to a single lifting point of the main beam under the angular deviation condition as a row vector; The column vectors and row vectors are assembled to form a mapping matrix.

6. The method for determining the main girder configuration of a suspension bridge with side spans according to claim 5, characterized in that, The constrained optimization model is specifically as follows: in, Indicates the relative bend angle of each beam segment. Represents the relative angle vector. This represents the transpose of the relative angle vector. Let be the objective function. Indicates the target alignment of the main beam. This indicates the allowable error between the main beam configuration and the target main beam alignment. Indicates the minimum permissible error. Indicates the maximum permissible error. Represents the mapping matrix, +1mm, for 1mm.

7. The method for determining the main girder configuration of a suspension bridge with side spans according to claim 1, characterized in that, After determining the main beam configuration, the following steps are also included: Establish a finite element model of the entire bridge, including the main cable, suspenders, main tower, and main girder; Based on the determination of the main beam configuration, the initial coordinates of each segment point of the main cable, the stress-free length of each cable segment of the main cable, and the stress-free length of each suspender are input into the finite element model of the whole bridge. Elastic compression compensation is applied to the main tower components to ensure that the top elevation of the completed tower is the same as the design elevation. Apply the full bridge dead load to the full bridge finite element model to simulate the bridge's initial bridge completion state; Extract the main beam alignment and cable tension from the simulation results and compare them with the design target values.

8. A device for determining the main girder configuration of a suspension bridge with side spans, characterized in that, The device for determining the main girder configuration of the suspension bridge with side spans includes: The first module is used to obtain the dead load force of each cable of the suspension bridge, establish a finite element model containing only the main beam, apply a concentrated load of equal value to the dead load force at the suspension point of each cable, and calculate the vertical deformation of the main beam. The second module is used to apply relative bends to each adjacent beam segment of the current main beam with the reverse of vertical deformation as the target beam shape, and to establish a mapping matrix between each relative bend and the influence of each relative bend on the current main beam shape. The third module is used to construct and solve the constraint optimization model based on the mapping matrix to obtain the optimal relative angle between each adjacent beam segment, and to determine the configuration of the main beam based on the optimal relative angle between each adjacent beam segment of the main beam. The constrained optimization model uses the relative bend angles of each beam segment as variables, the allowable error between the main beam configuration and the target alignment of the main beam as constraints, and the minimum sum of squares of the relative bend angles as the objective function.

9. A device for determining the main girder configuration of a suspension bridge with side spans, characterized in that, The device for determining the main girder configuration of the suspension bridge with side spans includes a processor, a memory, and a program for determining the main girder configuration of the suspension bridge with side spans stored in the memory and executable by the processor, wherein when the program for determining the main girder configuration of the suspension bridge with side spans is executed by the processor, the steps of the method for determining the main girder configuration of the suspension bridge with side spans as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program for determining the main girder configuration of a suspension bridge with side spans, wherein when the program for determining the main girder configuration of a suspension bridge with side spans is executed by a processor, it implements the steps of the method for determining the main girder configuration of a suspension bridge with side spans as described in any one of claims 1 to 7.

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