Tower-beam-cable collaborative shape finding method and system of cable-stayed bridge

Abstract

The application relates to a tower-beam-cable collaborative form-finding method of a cable-stayed bridge, which comprises the following steps: establishing a bridge completion finite element model of the cable-stayed bridge, and calculating beam end vertical forces of the cable-stayed bridge; calculating horizontal forces of the cable-stayed bridge, tower end vertical forces and stress-free cable lengths based on the beam end vertical forces of the cable-stayed bridge; determining a main tower manufacturing line shape and vertical displacement of a joint part of the main tower and a main beam based on the tower end vertical forces of the cable-stayed bridge; and determining the main beam manufacturing line shape based on the beam end vertical forces of the cable-stayed bridge. The application directly reversely determines the main beam manufacturing line shape, the main tower manufacturing line shape and the stress-free cable length by taking the beam end vertical force as a target vertical force input. Under the condition of a given target vertical force, the three are uniquely determined by static force balance and deformation coordination conditions, and self-consistent manufacturing line shapes and cable lengths can be obtained, so that the tower straight beam is naturally satisfied after the bridge is completed. The application changes from'multi-target optimization' to 'analytical solution', and the existence of an accurate solution is guaranteed from the mathematical principle, so that systematic deviation is eliminated from the design source.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically to a tower-beam-cable collaborative form-finding method and system for cable-stayed bridges. Background Technology

[0002] With the development of high-speed railway ballastless track cable-stayed bridges, their maximum span can reach 450m. The requirements for the alignment error of the main beam of high-speed railway ballastless track are extremely strict. It is usually required that the alignment deviation of the completed bridge be controlled within the millimeter level (such as within ±5mm). Otherwise, it will directly affect the track smoothness and train operation safety. This puts forward unprecedented high requirements for the design accuracy, manufacturing accuracy and construction control of cable-stayed bridges.

[0003] Among the many factors affecting the accuracy of the completed bridge alignment, the self-consistency and precise attainability of the target completed bridge state given in the design phase are the fundamental prerequisites for determining the final alignment accuracy. If the theoretical completed bridge state given in the design has systematic deviations, then no matter how precise the construction control or how repeatedly the cable adjustments are made, the truly "straight tower and level beam" target state cannot be achieved. However, in the relevant design methods for the completed bridge state of cable-stayed bridges, the given theoretical completed bridge state often has systematic errors at the centimeter level, which cannot meet the accuracy requirements of ballastless track laying.

[0004] The mathematical essence of this problem lies in the fact that in conventional cable-stayed bridges, the cable forces in the mid-span primarily determine the alignment of the main girder, the cable forces in the side-spans primarily determine the alignment of the main girder, and the main tower alignment is jointly determined by the cable forces in the mid-span and side-spans. This problem has three control objectives (level mid-span girder, level side-span girder, and straight tower), but only two sets of independent variables (mid-span cable force set and side-span cable force set), making it mathematically an overdetermined problem. Generally, overdetermined problems do not have exact solutions; therefore, regardless of the cable force optimization algorithm used, it is impossible to simultaneously and precisely satisfy all three objectives, inevitably leaving behind systematic alignment deviations.

[0005] To address the above issues, the relevant technologies mainly adopt the following three strategies: The first type is the overall cable force optimization method for the tower and beam. This method treats the main tower and main beam as a single structure, using the beam alignment and tower misalignment as control targets, and adjusts all cable forces using the influence matrix method. This method can reduce alignment deviation to some extent, but due to the inherent nature of overdetermined problems, it typically only controls the deviation to around 3cm, and the cable force distribution often exhibits local distortion, which is detrimental to the long-term service life of the structure.

[0006] The second type is the side-span and mid-span cable force ratio control method. This method artificially sets a fixed ratio (e.g., 1.05~1.3) between the cable forces in the side span and mid-span to control the stress and displacement of the main tower, while simultaneously adjusting the cable force in the mid-span to level the beam. The side span alignment is approximated by setting a pre-camber in the reverse direction of the completed bridge alignment. However, this method cannot consider the coupling effect between the side span pre-camber and cable force redistribution. Multiple objectives conflict with each other, and the actual side span alignment deviation after bridge completion is usually only reduced by about half (e.g., a theoretical deviation of 10cm, but 4~5cm remains after pre-camber), and cannot be reduced to zero.

[0007] The third type is the construction reverse dismantling iterative method. Starting from the target state of the completed bridge, components are dismantled step by step in reverse construction order to determine the state parameters of each construction stage. This method is theoretically sound, but it is highly dependent on the accurate simulation of the construction plan. Moreover, multiple objectives such as the main beam alignment, main tower offset, cable force distribution, and support reaction force are interdependent. Adjusting any objective will affect other objectives, resulting in repeated iterative corrections during the design process. The computational workload is large, and it is highly dependent on the experience of designers, making it difficult to directly extend to different bridge types. Summary of the Invention

[0008] This application provides a tower-beam-cable collaborative form-finding method and system for cable-stayed bridges, which solves the technical problem in related technologies that the systematic alignment deviation cannot be eliminated when determining the completed state of a cable-stayed bridge, and that repeated iterative cable adjustments are required.

[0009] This application provides a tower-beam-cable collaborative form-finding method for cable-stayed bridges, which includes the following steps: Step S1: Establish a finite element model of the completed cable-stayed bridge and calculate the vertical force at the beam end of the cable stays in the cable-stayed bridge; Step S2: Calculate the horizontal force, tower end vertical force, and stress-free cable length of the stay cable based on the vertical force at the beam end of the stay cable; Step S3: Determine the main tower manufacturing profile and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the cable stay. Step S4: Determine the main beam manufacturing profile based on the vertical force at the beam end of the stay cable.

[0010] In one embodiment, step S1, establishing a finite element model of the completed cable-stayed bridge and calculating the vertical force at the beam end of the cable stays in the cable-stayed bridge, includes: Step S11: Establish the completed finite element model of the cable-stayed bridge and the first bare beam finite element model of the main beam in the cable-stayed bridge; Step S12: Determine the vertical force at the beam end of the stay cable at the mid-span using the rigid support continuous beam method, and use it as the vertical force at the beam end of the stay cable.

[0011] In one embodiment, determining the vertical force of the stay cable at the beam end at the mid-span using the rigid-supported continuous beam method includes: Step S121: Install rigid vertical supports at each cable anchor point of the main beam and perform static analysis on the finite element model of the first bare beam; Step S122: Calculate the reaction force of each rigid vertical support, and use the reaction force as the mid-span vertical force of the cable at the beam end of the mid-span.

[0012] In one embodiment, in step S122, the reaction force is rounded up and used as the mid-span vertical force.

[0013] In one embodiment, determining the vertical force of the stay cable at the beam end at the mid-span using the rigid-supported continuous beam method further includes: Step S123: After determining the reaction force, verify the rationality of the reaction force.

[0014] In one embodiment, step S2, calculating the horizontal force of the stay cable, the vertical force at the tower end, and the stress-free cable length based on the vertical force at the beam end of the stay cable, includes: Step S21: Calculate the horizontal force and tower end vertical force of the cable-stayed cable at the mid-span using the catenary equation based on the vertical force at the beam end of the cable-stayed cable at the mid-span. Step S22: Calculate the horizontal force of the stay cable at the side span according to the horizontal force ratio coefficient of the side span, and calculate the vertical force at the tower end and the vertical force at the beam end of the stay cable at the side span; Step S23: Calculate the stress-free cable length of the stay cable.

[0015] In one embodiment, step S3, determining the main tower manufacturing profile and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable, includes: Step S31: Establish a bare tower finite element model of the main tower of the cable-stayed bridge, and set the initial node coordinates of the main tower according to the target completed bridge state; Step S32: Apply the horizontal force and vertical force at each cable anchor point at the tower end, and apply the support reaction force at the joint node between the main tower and the main beam; Step S33: Perform static analysis on the bare tower finite element model, calculate the vertical and longitudinal displacements of each node of the main tower, and obtain the node coordinates of the main tower manufacturing line. Step S34: Update the initial node coordinates of the main tower to the node coordinates of the main tower manufacturing line; Repeat steps S32-S33 until the longitudinal displacement changes of all main tower nodes calculated in two adjacent iterations are less than the convergence threshold, so as to obtain the manufacturing line of the main tower and the vertical displacement of the joint between the main tower and the main beam.

[0016] In one embodiment, step S4, determining the main beam manufacturing profile based on the vertical force at the beam end of the stay cable, includes: Step S41: Establish the second bare beam finite element model of the main beam, and set the initial node coordinates of the main beam in the target bridge-completed state; Step S42: Apply the horizontal force and vertical force at each stay cable anchor point at the beam end, and apply vertical displacement at the joint node between the main tower and the main beam; Step S43: Perform static analysis on the second bare beam finite element model, calculate the vertical and longitudinal displacements of each node of the main beam, and obtain the node coordinates of the main beam manufacturing line. Step S44: Update the initial node coordinates of the main beam to the node coordinates of the main beam manufacturing line; Repeat steps S42-S43 until the vertical displacement changes of all main beam nodes calculated in two adjacent iterations are less than the convergence threshold, so as to obtain the manufacturing profile of the main beam.

[0017] In one embodiment, the tower-beam-cable collaborative form-finding method for the cable-stayed bridge further includes: Step S5: Establish a finite element model of the entire bridge based on the stress-free cable length of the stay cables, the manufacturing profile of the main tower, and the manufacturing profile of the main beam, and verify the completed bridge status.

[0018] This application also provides a tower-beam-cable collaborative form-finding system for cable-stayed bridges, applying the tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in any of the above claims, comprising: The beam end vertical force calculation module is configured to: establish a completed finite element model of the cable-stayed bridge and calculate the beam end vertical force of the cable stays in the cable-stayed bridge; The cable length calculation module is configured to calculate the horizontal force, tower end vertical force, and stress-free cable length of the cable based on the vertical force at the beam end of the cable. The main tower manufacturing alignment calculation module is configured to: determine the main tower manufacturing alignment and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable; The main beam manufacturing alignment calculation module is configured to determine the main beam manufacturing alignment based on the vertical force at the beam end of the stay cable.

[0019] The beneficial effects of the technical solutions provided in this application include: (1) From a theoretical perspective, using the vertical force at the beam end as the target vertical force input, the manufacturing alignment of the main beam, the manufacturing alignment of the main tower, and the length of the stress-free cable are directly determined in reverse. Given the target vertical force and the coordinates of the anchor points, the above three are uniquely determined by the static equilibrium and deformation coordination conditions, and there is no room for free adjustment due to the conflict of multiple objectives in related technologies. Only one set of target vertical forces is needed to obtain a self-consistent manufacturing alignment and cable length, and the completed bridge will naturally satisfy the requirements of straight towers and flat beams. The transformation from "multi-objective optimization" to "analytical solution" ensures the existence of an accurate solution from a mathematical perspective, thereby eliminating systematic deviations from the design source.

[0020] (2) From a design perspective, the introduction of the main tower manufacturing configuration and the main beam manufacturing configuration as new control methods integrates the tower, beam, and cable into a unified collaborative form-finding framework, thereby decoupling the originally coupled problems. By specifying a target vertical force, the manufacturing alignment of the main beam, the manufacturing alignment of the main tower, and the length of the stress-free cable can be accurately determined simultaneously, and the completed bridge state with a straight tower and flat beam can be automatically obtained. There is no need to repeatedly compromise between alignment and internal force, thus achieving independent control of internal force and alignment.

[0021] (3) In terms of precision, according to the manufacturing alignment and stress-free cable length determined in this embodiment, under the verification of the geometric nonlinearity of the entire bridge, the vertical deviation of the main beam and the horizontal deviation of the main tower can be controlled within the zero error range. This precision breaks through the inherent lower limit of centimeter-level error in related technologies, enabling the self-consistency of the completed bridge state in the design stage to reach the theoretical limit, realizing the precise cutting of manufacturing dimensions and the zero error realization of the completed bridge state, and meeting the increasingly higher requirements of high-speed railway ballastless track cable-stayed bridges for alignment precision.

[0022] (4) In terms of efficiency, independent form finding for the tower and beam requires only a small number of nonlinear iterations (usually 2 to 5 times). Compared with the multiple cycles required by related technologies, which involve repeatedly adjusting cable force, iterating weight, and balancing line shape and tower deflection, the computational efficiency of this embodiment is significantly improved. Attached Figure Description

[0023] 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.

[0024] Figure 1 This is a flowchart illustrating the steps of a tower-beam-cable collaborative form-finding method for a cable-stayed bridge in one embodiment of the present invention.

[0025] Figure 2 This is a bridge elevation layout diagram according to one embodiment of the present invention.

[0026] Figure 3 This is a schematic diagram of the longitudinal manufacturing line of the main tower in one embodiment of the present invention.

[0027] Figure 4 This is a schematic diagram of the main beam manufacturing line in one embodiment of the present invention.

[0028] Figure 5 This is a diagram showing the deviation of the main beam alignment during bridge verification in one embodiment of the present invention.

[0029] Figure 6 This is a diagram showing the deviation of the main tower alignment during bridge construction verification in one embodiment of the present invention. Detailed Implementation

[0030] 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.

[0031] This application provides a tower-beam-cable collaborative form-finding method for cable-stayed bridges, which can solve the technical problems in related technologies where systematic alignment deviations cannot be eliminated when determining the completed state of a cable-stayed bridge, and repeated iterative cable adjustments are required.

[0032] like Figure 1 As shown, Figure 1 This is a flowchart illustrating the steps of a tower-beam-cable collaborative form-finding method for a cable-stayed bridge in one embodiment of the present invention.

[0033] This embodiment provides a tower-beam-cable collaborative form-finding method for cable-stayed bridges, which includes the following steps: Step S1: Establish a finite element model of the completed cable-stayed bridge and calculate the vertical force at the beam end of the cable stays in the cable-stayed bridge; Step S2: Calculate the horizontal force of the stay cable, the vertical force at the tower end, and the length of the stress-free cable based on the vertical force at the beam end of the stay cable; Step S3: Determine the main tower manufacturing profile and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable; Step S4: Determine the main beam manufacturing profile based on the vertical force at the beam end of the stay cable.

[0034] This embodiment provides a high-precision, self-consistent tower-beam-cable collaborative form-finding method for cable-stayed bridges, which has many technical advantages: (1) From a theoretical perspective, using the vertical force at the beam end as the target vertical force input, the manufacturing alignment of the main beam, the manufacturing alignment of the main tower, and the length of the stress-free cable are directly determined in reverse. Given the target vertical force and the coordinates of the anchor points, the above three are uniquely determined by the static equilibrium and deformation coordination conditions, and there is no room for free adjustment due to the conflict of multiple objectives in related technologies. Only one set of target vertical forces is needed to obtain a self-consistent manufacturing alignment and cable length, and the completed bridge will naturally satisfy the requirements of straight towers and flat beams. The transformation from "multi-objective optimization" to "analytical solution" ensures the existence of an accurate solution from a mathematical perspective, thereby eliminating systematic deviations from the design source.

[0035] (2) From a design perspective, the introduction of the main tower manufacturing configuration and the main beam manufacturing configuration as new control methods integrates the tower, beam, and cable into a unified collaborative form-finding framework, thereby decoupling the originally coupled problems. By specifying a target vertical force, the manufacturing alignment of the main beam, the manufacturing alignment of the main tower, and the length of the stress-free cable can be accurately determined simultaneously, and the completed bridge state with a straight tower and flat beam can be automatically obtained. There is no need to repeatedly compromise between alignment and internal force, thus achieving independent control of internal force and alignment.

[0036] (3) In terms of precision, according to the manufacturing alignment and stress-free cable length determined in this embodiment, under the verification of the geometric nonlinearity of the entire bridge, the vertical deviation of the main beam and the horizontal deviation of the main tower can be controlled within the zero error range. This precision breaks through the inherent lower limit of centimeter-level error in related technologies, enabling the self-consistency of the completed bridge state in the design stage to reach the theoretical limit, realizing the precise cutting of manufacturing dimensions and the zero error realization of the completed bridge state, and meeting the increasingly higher requirements of high-speed railway ballastless track cable-stayed bridges for alignment precision.

[0037] (4) In terms of efficiency, independent form finding for the tower and beam requires only a small number of nonlinear iterations (usually 2 to 5 times). Compared with the multiple cycles required by related technologies, which involve repeatedly adjusting cable force, iterating weight, and balancing line shape and tower deflection, the computational efficiency of this embodiment is significantly improved.

[0038] The following provides a detailed explanation of each step.

[0039] In one embodiment, step S1, establishing a finite element model of the completed cable-stayed bridge and calculating the vertical force at the beam end of the stay cables in the cable-stayed bridge, includes: Step S11: Establish the finite element model of the completed cable-stayed bridge and the finite element model of the first bare beam of the main girder in the cable-stayed bridge.

[0040] Specifically, when establishing the completed finite element model of the cable-stayed bridge, the geometric dimensions, material properties (elastic modulus, unit weight), cross-sectional shape, and cross-sectional properties (area, moment of inertia, etc.) of the main girder are determined according to the design drawings. The scope of the main girder model in the completed bridge finite element model covers the entire bridge, including the mid-span, side spans, and auxiliary spans. The basic loads required for the design of the cable-stayed bridge are collected and determined, including the self-weight of the main girder, secondary dead loads such as bridge deck pavement, railings, and tracks, counterweight loads set to control the support reactions or the stress on the main tower, and other long-term loads.

[0041] The target bridge completion state is "straight tower and flat beam", that is, at the time of bridge completion, the theoretical alignment of the main beam is determined according to the design longitudinal section (horizontal straight line, constant longitudinal slope or herringbone slope), the main tower axis is a vertical straight line, and the displacement of the tower and beam joint is coordinated and consistent.

[0042] When establishing the first bare beam finite element model of the main beam, the geometric dimensions, material properties, and cross-sectional properties of the main beam are determined according to the design drawings. The actual constraints (such as vertical constraints) at the side piers, auxiliary piers, and main tower are retained in the model, and the self-weight of the main beam, secondary dead load, and counterweight are applied.

[0043] Step S12: Determine the vertical force at the beam end of the stay cable at the mid-span using the rigid support continuous beam method, and use it as the vertical force at the beam end of the stay cable.

[0044] In one embodiment, determining the vertical force of the stay cable at the beam end at the mid-span using the rigid-supported continuous beam method includes: Step S121: Set rigid vertical supports at each cable anchor point of the main beam and perform static analysis on the finite element model of the first bare beam; Step S122: Calculate the reaction force of each rigid vertical support, and use the reaction force as the vertical force of the stay cable at the beam end at the mid-span. ,in, i This is the search number.

[0045] In one embodiment, in step S122, the reaction force is rounded up and used as the vertical force in the mid-span.

[0046] Specifically, the calculated reaction force is rounded up according to engineering experience (such as multiples of 50kN or 100kN), and the rounded result is used as the vertical force in the mid-span.

[0047] The above method yields the vertical force at the beam end of the stay cable, which is used as the output of this step for subsequent calculations of the stress-free cable length. Of course, other methods can also be used to obtain the vertical force at the beam end of the stay cable.

[0048] In one embodiment, determining the vertical force of the stay cable at the beam end at the mid-span using the rigid-supported continuous beam method further includes: Step S123: After determining the reaction force, verify the rationality of the reaction force.

[0049] Specifically, the verification process includes: Step S1231: Apply the vertical force of the mid-span to the finite element model of the first bare beam, remove the rigid vertical supports at the anchor points of the stay cables, and calculate the support reactions at the side piers, auxiliary piers, and main tower.

[0050] Step S1232: Check whether the reaction force of each support meets the set range according to the design requirements, such as the minimum reaction force safety reserve. This safety reserve should take into account the influence of variable actions such as live load.

[0051] If satisfied, output the vertical force at the beam end of the stay cable; If the conditions are not met, update the counterweight load controlling the support reaction force (e.g., adjust the arrangement or weight), and repeat the above steps until the support reaction force meets the set range.

[0052] In one embodiment, step S2, calculating the horizontal force of the stay cable, the vertical force at the tower end, and the stress-free cable length based on the vertical force at the beam end of the stay cable, includes: Step S21: Calculate the horizontal force and tower end vertical force of the cable-stayed cable at the mid-span using the catenary equation based on the vertical force at the beam end of the cable-stayed cable at the mid-span. Specifically, based on the elastic modulus, mass density, cross-sectional area, coordinates of the anchor points at both ends, and vertical force at the beam ends of each stay cable at the mid-span... The horizontal force of the stay cable at the mid-span was solved using the catenary theory. Then, the vertical force at the tower end can be calculated. The specific analytical formula for the catenary equation can be found in the "Suspension Bridge Handbook" or "Mechanics of Cable Structures" which provides the formula for the catenary arc length; it will not be repeated here.

[0053] Step S22: Calculate the horizontal force of the stay cable at the side span according to the horizontal force ratio coefficient of the side span, and calculate the vertical force at the tower end and the vertical force at the beam end of the stay cable at the side span.

[0054] Specifically, the horizontal force of the stay cables at the side span The calculation formula is: ; in, η The horizontal force ratio coefficient for the side span is taken as 1.05~1.3, determined jointly by the main tower bearing capacity and the reaction force of the auxiliary piers at the side span. Then, the vertical forces at the tower ends and beam ends of the stay cables at the side span are calculated.

[0055] Step S23: Calculate the stress-free cable length of the stay cable. .

[0056] In one embodiment, step S3, determining the main tower manufacturing profile and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable, includes: Step S31: Establish a bare tower finite element model of the main tower in the cable-stayed bridge, and set the initial node coordinates of the main tower according to the target completed bridge state.

[0057] Specifically, when establishing the bare tower finite element model of the main tower, the initial node coordinates of the main tower are set according to the vertical axis of the target bridge state, and the tower bottom is treated as a solidified structure.

[0058] Step S32: Apply horizontal force and vertical force at each stay cable anchor point at the tower end, and apply support reaction force at the joint node between the main tower and the main beam.

[0059] Specifically, the horizontal force and vertical force calculated in step S2 are applied at each cable anchor point at the tower end, and the support reaction force transmitted from the main beam is applied at the joint node between the main tower and the main beam. This support reaction force is taken from the reaction force of the rigid vertical support at the corresponding support of the first main beam finite element model in step S122.

[0060] Step S33: Perform static analysis on the bare tower finite element model, calculate the vertical and longitudinal displacements of each node of the main tower, and obtain the node coordinates of the main tower manufacturing line.

[0061] Specifically, during the static analysis, geometric nonlinearity is considered to calculate the vertical displacement of each node of the main tower. With longitudinal displacement The formula for calculating the node coordinates of the main tower manufacturing line is: Longitudinal direction of the bridge: ; Vertical direction: ; in, The longitudinal bridge node coordinates for the main tower's structural alignment. The design values ​​of the longitudinal bridge node coordinates of the main tower; The vertical node coordinates for the main tower's linear shape. These are the design values ​​for the vertical node coordinates of the main tower.

[0062] Step S34: Update the initial node coordinates of the main tower to the node coordinates of the main tower manufacturing line.

[0063] Repeat steps S32-S33 until the longitudinal displacement changes of all main tower nodes calculated in two adjacent iterations are less than the convergence threshold, in order to obtain the vertical displacement of the main tower manufacturing profile and the joint between the main tower and the main beam. .

[0064] Specifically, due to geometric nonlinearity, the deformation after updating the node coordinates may differ slightly. The initial node coordinates of the main tower are updated to the corrected node coordinates of the main tower manufacturing line, keeping the load constant. The longitudinal displacement change of all main tower nodes calculated in two adjacent iterations is less than the convergence threshold, expressed as: ;in, ε The convergence threshold is set to, for example, 0.1 mm. This refers to the vertical displacement at the junction of the main tower and the main beam. This refers to the final compression of the main tower support, which is used to determine the subsequent main beam manufacturing profile.

[0065] In one embodiment, step S4, determining the main beam manufacturing profile based on the vertical force at the beam end of the stay cable, includes: Step S41: Establish the second bare beam finite element model of the main beam, and set the initial node coordinates of the main beam according to the target completed bridge state.

[0066] Specifically, when establishing the finite element model of the second bare beam of the main girder, the model scope covers the entire bridge, including the middle span, side spans, and auxiliary spans. The initial node coordinates of the main girder are set according to the design longitudinal slope of the target completed bridge state. The model retains the vertical supports at the side piers, auxiliary piers, and main towers, as well as the self-weight of the main girder, the secondary dead load, and the counterweight load.

[0067] Step S42: Apply horizontal force and vertical force at each stay cable anchor point at the beam end, and apply vertical displacement at the joint node between the main tower and the main beam.

[0068] Specifically, the horizontal force calculated in step S2 is applied at each anchor point of the stay cable at the beam end. The vertical force at the beam end calculated in step S1 Forced vertical displacement is applied at the joint between the main tower and the main beam. .

[0069] Step S43: Perform static analysis on the finite element model of the second bare beam, calculate the vertical and longitudinal displacements of each node of the main beam, and obtain the node coordinates of the main beam manufacturing line.

[0070] Specifically, in the static analysis, geometric nonlinearity is considered to calculate the vertical displacement of each node of the main beam. With longitudinal displacement The formula for calculating the node coordinates of the main beam manufacturing line is: Longitudinal direction of the bridge: ; Vertical direction: ; in, The longitudinal bridge node coordinates are used to determine the main girder's structural alignment. The design values ​​of the longitudinal bridge node coordinates of the main girder; The vertical coordinates of the nodes for the main beam manufacturing line. These are the design values ​​for the vertical node coordinates of the main beam.

[0071] Step S44: Update the initial node coordinates of the main beam to the node coordinates of the main beam manufacturing line.

[0072] Repeat steps S42-S43 until the vertical displacement changes of all main beam nodes calculated in two adjacent iterations are less than the convergence threshold, so as to obtain the main beam manufacturing profile.

[0073] Specifically, due to geometric nonlinearity, the deformation after updating the nodal coordinates may differ slightly. The initial nodal coordinates of the main beam are updated to the corrected nodal coordinates of the main beam manufacturing line, keeping the load constant. The vertical displacement change of all main beam nodes calculated in two adjacent iterations is less than the convergence threshold, expressed as: Where ε is the convergence threshold, such as 0.1 mm.

[0074] In one embodiment, the tower-beam-cable collaborative form-finding method for cable-stayed bridges further includes: Step S5: Establish a finite element model of the entire bridge using the stress-free cable length of the stay cables, the manufacturing profile of the main tower, and the manufacturing profile of the main beam, and verify the completed bridge status.

[0075] Specifically, the stress-free length of the stay cable determined in step S2, the manufacturing profile of the main tower determined in step S3, and the manufacturing profile of the main beam determined in step S4 are used as inputs to establish a finite element model of the entire bridge.

[0076] The stay cables are designed as catenary units based on the length of the stress-free cable, with fixed connections at the tower base. The connections of the side piers, auxiliary piers, and tower beams are all designed as vertical supports.

[0077] Finite element analysis was performed on the full bridge model, considering geometric nonlinearity. After the calculation, the vertical displacement of the main girder and the horizontal displacement of the main tower under the completed bridge condition were extracted. The verification results show that the vertical displacement of the main girder and the horizontal displacement of the main tower are close to zero. Within the accuracy of numerical calculation, the ideal completed bridge condition of straight tower, horizontal beam, and self-consistent cable force was accurately achieved, and no iterative cable adjustment was required throughout the process.

[0078] This application also provides a tower-beam-cable collaborative form-finding system for cable-stayed bridges, applying the tower-beam-cable collaborative form-finding method for cable-stayed bridges as described above, which includes: The beam end vertical force calculation module is configured to: establish a completed finite element model of the cable-stayed bridge and calculate the beam end vertical force of the cable stays in the cable-stayed bridge; The cable length calculation module is configured to calculate the horizontal force, tower end vertical force, and stress-free cable length of the cable based on the vertical force at the beam end of the cable. The main tower manufacturing alignment calculation module is configured to: determine the main tower manufacturing alignment and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable; The main beam manufacturing alignment calculation module is configured to determine the main beam manufacturing alignment based on the vertical force at the beam end of the stay cables.

[0079] The functions of each module have been described above, and the same content will not be repeated here.

[0080] The following is a specific example for illustration.

[0081] Taking a double-tower, double-cable-stayed bridge with a main span of 280m as an example, the bridge elevation layout is as follows: Figure 2 As shown (where the unit is meters), the span arrangement of the cable-stayed bridge is: 55m + 92.5m + 280m + 92.5m + 55m. The main tower is a reinforced concrete structure with a height of 110m. The main girder is a steel box girder. The entire bridge has a double cable plane, with 11 pairs of stay cables on each tower. The anchor point spacing at the tower end is 2.5m, and the anchor point spacing at the beam end is 12.5m. The tower-beam connection is a semi-floating system, with vertical supports between the tower and beam, and an auxiliary pier on each side span.

[0082] This embodiment provides a tower-beam-cable collaborative form-finding method for cable-stayed bridges, which includes the following steps: Step S1: Establish a finite element model of the completed cable-stayed bridge and calculate the vertical force at the beam end of the cable stays in the cable-stayed bridge.

[0083] Specifically, when establishing the completed finite element model of the cable-stayed bridge, the geometric dimensions, material properties (elastic modulus, unit weight), cross-sectional shape, and cross-sectional properties (area, moment of inertia, etc.) of the main girder are determined according to the design drawings. The main girder model covers the entire bridge, including the mid-span, side spans, and auxiliary spans. The loads borne by the main girder include the self-weight of the main girder, the 200 kN / m secondary dead load of the entire bridge, and the 150 kN / m counterweight load in the side pier and auxiliary pier areas. The vertical force of the cable stays at the beam ends at the mid-span is determined using the rigid-supported continuous beam method, and is taken as the vertical force at the beam ends of the cable stays. The calculation results are shown in Table 1.

[0084] Step S2: Calculate the horizontal force of the stay cable, the vertical force at the tower end, and the length of the stress-free cable based on the vertical force at the beam end of the stay cable.

[0085] Specifically, taking the 11 pairs of stay cables in the middle span as an example, the cable forces at both ends of the stay cables in the middle span and the length of the stress-free cable are shown in Table 1.

[0086] Table 1 Vertical forces at beam ends, vertical forces at tower ends, and lengths of stress-free cables

[0087] Step S3: Determine the main tower manufacturing profile and the vertical displacement of the connection between the main tower and the main beam based on the vertical force at the tower end of the cable stay.

[0088] Specifically, when the convergence threshold is 0.1 mm, the vertical displacement of the joint between the main tower and the main beam is... This is used to determine the subsequent manufacturing alignment of the main beam. The longitudinal manufacturing alignment of the main tower is as follows: Figure 3As shown in the figure (where the unit is mm), it can be seen that due to the large cable force in the side span at the time of bridge completion, the main tower needs to be pre-offset by 388 mm towards the middle span in order to maintain its verticality at the time of bridge completion.

[0089] Step S4: Determine the main beam manufacturing profile based on the vertical force at the beam end of the stay cable.

[0090] Specifically, when the convergence threshold is 0.1 mm, the manufacturing profile of the main beam is as follows: Figure 4 As shown in the figure (where the unit is mm), the upper arch of the middle span is 26.4 mm, the upper arch of the side span is 14.7 mm, and the lower deflection of the auxiliary span is 11.7 mm.

[0091] Step S5: Establish a finite element model of the entire bridge using the stress-free cable length of the stay cables, the manufacturing profile of the main tower, and the manufacturing profile of the main beam, and verify the completed bridge status.

[0092] Specifically, a finite element analysis was performed on the full bridge model, considering geometric nonlinearity. After the calculation, the vertical and longitudinal displacements of the main beams and main towers in the completed bridge state were extracted, such as... Figure 5 and Figure 6 As shown, in the completed bridge condition, the vertical displacement deviation of the main beam is approximately 0.5 mm, and the longitudinal displacement deviation of the main tower is less than 0.1 mm.

[0093] The above embodiments show that: (1) In this embodiment, the manufacturing alignment and stress-free cable length determined by the collaborative form-finding of the tower, beam, and cable are controlled within the sub-millimeter level in the full-bridge verification that takes into account geometric nonlinear effects. This deviation mainly comes from the allowable error of nonlinear iteration, which can theoretically be further reduced to zero, but is no longer necessary in engineering. Therefore, a precise bridge state with straight towers, flat beams, and self-consistent cable forces is achieved from the design source.

[0094] (2) The above-mentioned precise bridge-forming state is obtained without iterative cable adjustment. Only a set of target vertical forces is required to directly determine the self-consistent manufacturing profile and cable length, avoiding the inefficient process of repeatedly adjusting cable force, iteratively applying weight, and repeatedly balancing profile and tower deflection due to multiple target conflicts in related technologies.

[0095] (3) This embodiment transforms the design of cable-stayed bridges from "multi-objective optimization" to "analytical solution", eliminating systematic deviations from the design source and providing a reliable design tool for cable-stayed bridge projects with extremely high requirements for alignment accuracy, such as ballastless track for high-speed railways.

[0096] It should be noted that the sequence numbers of the embodiments in this application are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. 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 device 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 these processes, methods, products, or devices. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not represent a sequential order, nor do they limit "first," "second," and "third" to different types.

[0097] 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.

[0098] 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.

[0099] 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 the 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.

[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 tower-beam-cable collaborative form-finding method for cable-stayed bridges, characterized in that, It includes the following steps: Step S1: Establish a finite element model of the completed cable-stayed bridge and calculate the vertical force at the beam end of the cable stays in the cable-stayed bridge; Step S2: Calculate the horizontal force, tower end vertical force, and stress-free cable length of the stay cable based on the vertical force at the beam end of the stay cable; Step S3: Determine the main tower manufacturing profile and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the cable stay. Step S4: Determine the main beam manufacturing profile based on the vertical force at the beam end of the stay cable.

2. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 1, characterized in that, Step S1, establishing the completed finite element model of the cable-stayed bridge and calculating the vertical force at the beam ends of the cable stays in the cable-stayed bridge, includes: Step S11: Establish the completed finite element model of the cable-stayed bridge and the first bare beam finite element model of the main beam in the cable-stayed bridge; Step S12: Determine the vertical force at the beam end of the stay cable at the mid-span using the rigid support continuous beam method, and use it as the vertical force at the beam end of the stay cable.

3. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 2, characterized in that, The determination of the vertical force at the mid-span end of the stay cable using the rigidly supported continuous beam method includes: Step S121: Install rigid vertical supports at each cable anchor point of the main beam and perform static analysis on the finite element model of the first bare beam; Step S122: Calculate the reaction force of each rigid vertical support, and use the reaction force as the mid-span vertical force of the cable at the beam end of the mid-span.

4. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 3, characterized in that, In step S122, the reaction force is rounded up and used as the vertical force of the mid-span.

5. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 3, characterized in that, The method for determining the vertical force of the stay cable at the beam end in the mid-span using the rigidly supported continuous beam method also includes: Step S123: After determining the reaction force, verify the rationality of the reaction force.

6. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 2, characterized in that, Step S2, calculating the horizontal force, tower end vertical force, and stress-free cable length of the stay cable based on the beam end vertical force, includes: Step S21: Calculate the horizontal force and tower end vertical force of the cable at the mid-span using the catenary equation based on the vertical force at the beam end of the cable at the mid-span. Step S22: Calculate the horizontal force of the stay cable at the side span according to the horizontal force ratio coefficient of the side span, and calculate the vertical force at the tower end and the vertical force at the beam end of the stay cable at the side span; Step S23: Calculate the stress-free cable length of the stay cable.

7. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 1, characterized in that, Step S3, determining the main tower manufacturing profile and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable, includes: Step S31: Establish a bare tower finite element model of the main tower of the cable-stayed bridge, and set the initial node coordinates of the main tower according to the target completed bridge state; Step S32: Apply the horizontal force and vertical force at each cable anchor point at the tower end, and apply the support reaction force at the joint node between the main tower and the main beam; Step S33: Perform static analysis on the bare tower finite element model, calculate the vertical and longitudinal displacements of each node of the main tower, and obtain the node coordinates of the main tower manufacturing line. Step S34: Update the initial node coordinates of the main tower to the node coordinates of the main tower manufacturing line; Repeat steps S32-S33 until the longitudinal displacement changes of all main tower nodes calculated in two adjacent iterations are less than the convergence threshold, so as to obtain the manufacturing line of the main tower and the vertical displacement of the joint between the main tower and the main beam.

8. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 1, characterized in that, Step S4, determining the main beam manufacturing profile based on the vertical force at the beam end of the stay cable, includes: Step S41: Establish the second bare beam finite element model of the main beam, and set the initial node coordinates of the main beam in the target bridge-completed state; Step S42: Apply the horizontal force and vertical force at each stay cable anchor point at the beam end, and apply vertical displacement at the joint node between the main tower and the main beam; Step S43: Perform static analysis on the second bare beam finite element model, calculate the vertical and longitudinal displacements of each node of the main beam, and obtain the node coordinates of the main beam manufacturing line. Step S44: Update the initial node coordinates of the main beam to the node coordinates of the main beam manufacturing line; Repeat steps S42-S43 until the vertical displacement changes of all main beam nodes calculated in two adjacent iterations are less than the convergence threshold, so as to obtain the manufacturing profile of the main beam.

9. The tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in claim 1, characterized in that, The tower-beam-cable collaborative form-finding method for cable-stayed bridges also includes: Step S5: Establish a finite element model of the entire bridge based on the stress-free cable length of the stay cables, the manufacturing profile of the main tower, and the manufacturing profile of the main beam, and verify the completed bridge status.

10. A tower-beam-cable collaborative form-finding system for a cable-stayed bridge, employing the tower-beam-cable collaborative form-finding method for cable-stayed bridges as described in any one of claims 1 to 9, characterized in that, It includes: The beam end vertical force calculation module is configured to: establish a completed finite element model of the cable-stayed bridge and calculate the beam end vertical force of the cable stays in the cable-stayed bridge; The cable length calculation module is configured to calculate the horizontal force, tower end vertical force, and stress-free cable length of the cable based on the vertical force at the beam end of the cable. The main tower manufacturing alignment calculation module is configured to: determine the main tower manufacturing alignment and the vertical displacement of the joint between the main tower and the main beam based on the vertical force at the tower end of the stay cable; The main beam manufacturing alignment calculation module is configured to determine the main beam manufacturing alignment based on the vertical force at the beam end of the stay cable.

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