Analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge considering the torsional stiffness of the main cable; electronic equipment; and dielectric materials.

Abstract

This invention relates to an analytical calculation method, electronic equipment, and medium for the final bridge alignment of a suspension bridge main cable considering the torsional stiffness of the main cable. The calculation method includes: considering the self-weight of the main cable and the loads from the suspenders, while incorporating the tensile and bending stiffness of the main cable to construct a geometrically accurate equilibrium equation for the main cable under its own weight and suspender loads; neglecting the influence of the bending moment within the main cable and considering incomplete boundary conditions, solving for a second-order approximate solution based on the direct perturbation method; considering the influence of the bending moment of the main cable and combining it with complete boundary conditions, solving for the influence of the bending moment on the static linearity of the suspension bridge based on the direct perturbation method to obtain a second-order approximate solution considering the bending moment; and combining the modified catenary equation and the second-order approximate solution considering the bending moment with the compatibility conditions of the left and right endpoints. Compared with existing technologies, this invention considers the influence of the bending stiffness of the main cable, has a clear mechanical concept, and can consider form finding under different boundary conditions, which can further guide the design and calculation of the main cable.

Description

Technical Field

[0001] This invention relates to the field of civil engineering, and in particular to an analytical calculation method, electronic equipment, and medium for the bridge alignment of the main cable of a suspension bridge considering the torsional stiffness of the main cable. Background Technology

[0002] Due to their aesthetic appeal, strong spanning capacity, and well-defined stress mechanisms, suspension bridges are widely recognized as one of the preferred solutions for crossing rivers and canyons. In recent years, with breakthroughs in key technologies, suspension bridges are gradually entering the "2000m era."

[0003] Traditional form-finding calculations for suspension bridges often simplify the main cable into truss elements, neglecting its bending stiffness. This method is relatively simple in both numerical and theoretical calculations and is suitable for suspension bridges with spans less than 2000m. However, as the span of a suspension bridge increases, the diameter of the main cable also increases, and its bending stiffness becomes significant, making accurate form-finding difficult with traditional methods. For example, the Zhangjinggao Yangtze River Bridge, with a main span of 2300m, is the world's largest suspension bridge, and its main cable diameter exceeds 1m. Its bending stiffness has a significant impact on the rational linearity of the completed bridge. Therefore, there is an urgent need to propose a form-finding calculation method for large-span suspension bridges with spans of 2000m and larger that considers the bending stiffness of the main cable.

[0004] The form-finding analysis of the bridge after considering the stiffness of the main cable is complicated. The calculation process is changed from a second-order ordinary differential equation to a fourth-order ordinary differential equation. It is difficult to obtain an accurate solution using traditional methods, and it is also difficult to obtain the final bridge alignment of the main cable. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide an analytical calculation method, electronic equipment, and medium for the bridge alignment of the main cable of a suspension bridge that considers the torsional stiffness of the main cable. This includes the static nonlinear equilibrium equation of the main cable considering the tensile and bending stiffness of the main cable, the explicit calculation method of the alignment and internal forces, which can take into account the influence of the bending stiffness of the main cable, has a clear mechanical concept, and can consider the form finding when the boundary of the main cable is fixed, further guiding the design and calculation of the main cable.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] The first aspect of this invention provides an analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge, considering the torsional stiffness of the main cable, comprising the following steps:

[0008] S1: Constructing the equilibrium equation

[0009] Based on the precise Cosserate rod theory, considering the self-weight of the main cable and the load of the suspenders, and incorporating the tensile stiffness and bending stiffness of the main cable, a geometrically precise equilibrium equation for the main cable under its self-weight and suspender load is constructed.

[0010] S2: Ignore bending moment and find an approximate solution

[0011] Based on the equilibrium equations constructed in S1, the influence of the bending moment in the main cable is ignored and the non-holonomic boundary conditions are considered. The second approximate solution is obtained by solving the direct perturbation method, and the modified catenary equation is obtained.

[0012] S3: Considering bending moment to find an approximate solution

[0013] Based on the equilibrium equations constructed in S1, considering the influence of the main cable bending moment and combining the complete boundary, the influence of the main cable bending moment on the static linearity of the suspension bridge is solved using the direct perturbation method, resulting in a second-order approximate solution considering the bending moment.

[0014] S4: Combining the solution with exact solution

[0015] Finally, by using the compatibility conditions of the left and right endpoints, combined with the modified catenary equation and the second-order approximate solution considering bending moment, a geometrically accurate form-finding method considering the tensile and torsional stiffness of the main cable is calculated.

[0016] Furthermore, in S1, the geometrically precise equilibrium equations include:

[0017]

[0018] M'-Vcosθ+Tsinθ=0 (3)

[0019] x'-sinθ=0 (4)

[0020] y'-cosθ=0 (5)

[0021] Among them, M is the bending moment of the main cable;

[0022] ρ is the self-weight of the main cable;

[0023] g is the acceleration due to gravity, taken as 9.8 m / s². 2 ;

[0024] T is the horizontal component of the main cable force;

[0025] V is the shear force of the main cable;

[0026] s is the length of the main cable along its length, i.e., the stress-free length;

[0027] x is the x-axis coordinate in the inertial coordinate system;

[0028] y is the vertical coordinate in the inertial coordinate system;

[0029] k0 is the original curvature, which is set to 0;

[0030] A is the area of ​​the main cable;

[0031] E is the elastic modulus of the main cable;

[0032] I is the moment of inertia of the main cable section;

[0033] θ is the rotation angle of the main cable section;

[0034] Fh is the force of the lifting rod;

[0035] δ(ss i ) is the Dirac equation, s i This indicates the location of the boom.

[0036] Furthermore, S2 specifically includes the following steps:

[0037] Solving for a first-order approximate solution: Ignoring the influence of the internal bending moment of the main cable and considering the non-holonomic boundary conditions, a first-order approximate solution is obtained based on the direct perturbation method, resulting in a rough catenary equation;

[0038] The corrected catenary equation is obtained by further modifying the static configuration of the main cable without considering torsion through a second approximation.

[0039] Furthermore, the rough catenary equation includes:

[0040] V0 cosθ+T0 sinθ0=0 (6)

[0041] x0'-sinθ0=0 (7)

[0042] y0'-cosθ0=0 (8)

[0043] Where x0 is a first-order approximation of x, y0 is a first-order approximation of y, and θ0 is a first-order approximation of θ;

[0044] The analytical calculation formula for the rough catenary equation includes:

[0045]

[0046] Among them, y 0c L represents the main cable deflection calculated using the catenary method, where L is the cable span.

[0047] Furthermore, the modified catenary equation includes:

[0048] V0θ1 cosθ0+T0θ1 sinθ0+T1 sinθ0=0 (12)

[0049] x1'-θ1 sinθ0=0 (13)

[0050] y1'-θ1 cosθ0=0 (14)

[0051] Where x1 is a first-order approximation of x, y1 is a first-order approximation of y, and θ1 is a first-order approximation of θ. The analytical calculation formula is as follows:

[0052]

[0053] Among them, y 1c The main cable deflection is calculated using the catenary method, where L is the cable span. The analytical solution is shown in the following equation:

[0054]

[0055] Where y 0c y 1c , s, T0, T1 are unknowns, and V0 is calculated based on beam theory.

[0056] Furthermore, S3 specifically includes the following steps:

[0057] Considering the influence of the main cable bending moment and the complete boundary, the influence of the main cable bending moment on the static linearity of the suspension bridge is solved based on the direct perturbation method. The first-order approximate solution considering the bending moment is obtained, the corresponding analytical solution is determined, and the explicit second-order equation and analytical solution are obtained by substituting them into the complete boundary conditions. By adding the two, the corrected line shape considering the bending moment inside the main cable but the non-complete boundary is obtained.

[0058] Furthermore, the process of obtaining the second-order approximate solution for the bending moment includes:

[0059]

[0060] in, for The first-order approximation, for The first-order approximation, for The first-order approximation, from the above equation, yields the analytical solution as follows:

[0061]

[0062]

[0063] Substituting the complete boundary conditions, we obtain its explicit second-order equation:

[0064]

[0065] The analytical solution obtained from the above equation is:

[0066]

[0067] r0 is obtained by substituting the boundary conditions.

[0068] Furthermore, S5 specifically includes the compatibility condition for the final passage through the left and right endpoints. Combining the modified catenary equation and the second-order approximate solution considering bending moment, the compatibility condition is shown in the following equation:

[0069]

[0070] y 0c +y 1c =Δ (35)

[0071] Δ is the main cable sag.

[0072] Then, the five unknowns are solved by five equations. Based on the conditions obtained from the two sets of solutions, the geometrically accurate form-finding method considering the tensile and torsional stiffness of the main cable is calculated according to equations (18) and (19).

[0073] A second aspect of the present invention provides an electronic device, including a memory and a processor, wherein the processor is configured to execute a program in the memory to implement the analytical calculation method for the main cable alignment of a suspension bridge considering the torsional stiffness of the main cable as described above.

[0074] A third aspect of the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the analytical calculation method for the main cable alignment of a suspension bridge considering the torsional stiffness of the main cable as described above.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] 1) By explicitly considering the influence of the main cable's bending stiffness, the calculation model becomes more accurate and complete at the mechanical level. Compared with traditional calculation methods that do not fully consider this factor, this invention can more realistically reflect the mechanical behavior of the main cable under actual working conditions, effectively improving the accuracy and reliability of the main cable's bridge alignment calculation.

[0077] 2) Its clear mechanical concepts help engineers to understand the stress and deformation mechanism of the main cable, so that parameters can be determined and schemes optimized based on more scientific and reasonable theoretical basis in the design process of suspension bridge main cables.

[0078] 3) The unique advantage of this invention lies in its ability to handle the shape-finding problem when the main cable boundary is fixed, which greatly broadens its application scope. Whether in the design of conventional suspension bridge main cables or in some suspension bridge projects with special boundary conditions, it can provide accurate and feasible calculation results of the main cable bridge alignment, thereby providing strong technical support and guarantee for the safe, stable and efficient construction of the entire suspension bridge, and powerfully promoting the development and progress of the suspension bridge engineering technology field. Attached Figure Description

[0079] Figure 1 This is a flowchart of the present invention.

[0080] Figure 2 The calculation results are for the main cable with hinged ends.

[0081] Figure 3 Error bar charts showing the calculation results considering the bending stiffness of the main cable and those not considering the bending stiffness of the main cable. Detailed Implementation

[0082] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0083] Example 1

[0084] The geometrically accurate equilibrium equation of the main cable under its own weight and suspender load in this invention is based on the Cosserate rod theory and takes into account the tensile stiffness and bending stiffness of the main cable, as shown in Equations 1-5.

[0085] The flowchart of the main cable bridging linear analytical method in this invention is as follows: Figure 1 The process includes: (1) Ignoring the influence of the bending moment (M′) in the main cable, considering the non-holonomic boundary conditions, solving the first approximate solution based on the direct perturbation method, and solving the differential equation to obtain the catenary equation; (2) Further correcting the static configuration of the main cable without considering torsion through the second approximation, and obtaining the corrected catenary equation, which contains five unknowns; (3) Considering the influence of the bending moment of the main cable and the holonomic boundary, solving the influence of the bending moment of the main cable on the static linearity of the suspension bridge based on the direct perturbation method, and obtaining the first approximate solution considering the bending moment; (4) Substituting the holonomic boundary conditions to obtain its explicit second-order equation, the analytical formula obtained by this method also contains five unknowns; (5) Finally, through the compatibility conditions of the left and right endpoints, combining the corrected catenary equation and the second approximate solution considering the bending moment, the final result is shown in Equations 18-19.

[0086] In practical implementation, based on the Cosserate rod theory, considering the tensile and bending stiffness of the main cable, a geometrically accurate equilibrium equation for the main cable under its own weight and suspender load is proposed, as shown in the following equation:

[0087]

[0088] M'-Vcosθ+Tsinθ=0 (3)

[0089] x'-sinθ=0 (4)

[0090] y'-cosθ=0 (5)

[0091] Among them, M is the bending moment of the main cable;

[0092] ρ is the self-weight of the main cable;

[0093] g is the acceleration due to gravity, taken as 9.8 m / s². 2 ;

[0094] T is the horizontal component of the main cable force;

[0095] V is the shear force of the main cable;

[0096] s is the length of the main cable along its length, i.e., the stress-free length;

[0097] x is the x-axis coordinate in the inertial coordinate system;

[0098] y is the vertical coordinate in the inertial coordinate system;

[0099] k0 is the original curvature, which is set to 0;

[0100] A is the area of ​​the main cable;

[0101] E is the elastic modulus of the main cable;

[0102] I is the moment of inertia of the main cable section;

[0103] θ is the rotation angle of the main cable section;

[0104] F h For the lifting rod force;

[0105] δ(ss i ) is the Dirac equation, s i This indicates the location of the boom.

[0106] In practice, the influence of the bending moment inside the main cable (M′) is ignored, and non-holonomic boundary conditions are considered. The first approximate solution is obtained based on the direct perturbation method, resulting in a rough catenary equation.

[0107] V0 cosθ+T0 sinθ0=0 (6)

[0108] x0'-sinθ0=0 (7)

[0109] y0'-cosθ0=0 (8)

[0110] Where x0 is a first-order approximation of x, y0 is a first-order approximation of y, and θ0 is a first-order approximation of θ. Substituting the nonholonomic boundary conditions, we obtain that its first-order equation is a catenary, and the analytical calculation formula is shown below.

[0111]

[0112] Among them, y 0cThe main cable deflection is calculated using the catenary method, where L is the cable span. All parameters in this formula are functions of the stress-free length s.

[0113] By further modifying the static configuration of the main cable without considering torsion using a second approximation, the modified catenary equation is obtained. The modified catenary equation is calculated as follows:

[0114] V0θ1 cosθ0+T0θ1 sinθ0+T1 sinθ0=0 (12)

[0115] x1'-θ1 sinθ0=0 (13)

[0116] y1'-θ1 cosθ0=0 (14)

[0117] Where x1 is a first-order approximation of x, y1 is a first-order approximation of y, and θ1 is a first-order approximation of θ. The analytical calculation formula is as follows:

[0118]

[0119]

[0120] Among them, y 1c Let L be the main cable deflection calculated using the catenary method, and L be the cable span. The analytical solution obtained from the above formula is shown below:

[0121]

[0122] In this formula, all parameters are functions of the stress-free length s, where y 0c y 1c , s, T0, T1 are unknowns, and V0 can be calculated according to beam theory.

[0123] In practice, considering the influence of the main cable bending moment and the complete boundary, the influence of the main cable bending moment on the static linearity of the suspension bridge is solved based on the direct perturbation method, and a first-order approximate solution considering the bending moment is obtained.

[0124]

[0125] in, for The first-order approximation, for The first-order approximation, for The first-order approximation, from the above equation, yields the analytical solution as follows:

[0126]

[0127] Substituting the complete boundary conditions, we obtain its explicit second-order equation:

[0128]

[0129] The analytical solution can be obtained from the above equation:

[0130]

[0131] Adding the two together yields a corrected alignment that takes into account the bending moment within the main cable but is not a complete boundary condition; r0 is obtained by substituting the boundary conditions.

[0132] In practical implementation, the final solution is determined by the compatibility conditions at both ends, combined with the modified catenary equation and the second-order approximate solution considering bending moment. The compatibility conditions are shown in the following equation:

[0133]

[0134] y 0c +y 1c =Δ (35)

[0135] Δ is the main cable sag. Five equations are used to solve for five unknowns. Based on the conditions obtained from the two sets of solutions, a geometrically accurate form-finding method considering the tensile and torsional stiffness of the main cable is calculated according to Equations 18 and 19.

[0136] Example 2

[0137] This embodiment provides an electronic device, including a memory and a processor. The processor executes a program stored in the memory to implement the analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge, considering the torsional stiffness of the main cable, as described above. The electronic device provided in this embodiment plays a crucial role in the analytical calculation of the completed bridge alignment of the main cable of a suspension bridge. Its core components include a memory and a processor, which are coupled and work collaboratively. The memory, as a storage medium for data and program instructions, may include not only random access memory (RAM) to quickly provide the processor with temporary data and instructions during device operation, but also non-volatile memory, such as at least one disk storage device, for persistently storing important calculation data, program code, and various parameter information related to the main cable of the suspension bridge. The processor is the core of the entire device's computation. It can be a general-purpose processor, such as a central processing unit (CPU), which has powerful comprehensive computing capabilities and can handle complex logical operations and data processing tasks. It is suitable for the analysis and processing of large-scale data and can perform accurate calculations on massive amounts of data during the main cable bridging alignment calculation process in this invention. Alternatively, it can be a network processor (NP), which can efficiently process network data packets in scenarios involving network transmission and interaction of data, ensuring the smoothness and stability of data communication with external devices or systems. For example, it plays a role in transmitting the main cable calculation results to other engineering design software or remote monitoring systems. Furthermore, the processor could also be a Digital Signal Processor (DSP), specifically optimized for digital signal processing. When processing signal data collected by sensors related to the main cable, it can quickly and accurately perform filtering, transformation, and other operations to extract valuable information for calculation. Alternatively, it could be an Application Specific Integrated Circuit (ASIC). This customized chip can be specially designed and manufactured according to the specific algorithms and logic for calculating the main cable of the suspension bridge in this invention, thus achieving extremely high efficiency and speed in performing related calculation tasks and significantly shortening the calculation time. It could even be a Field-Programmable Gate Array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. These have flexible programmability and can dynamically adjust and optimize the hardware logic according to actual needs to adapt to the special calculation requirements and complex operating conditions of different suspension bridge projects.When the processor executes the program stored in memory, it can accurately implement the analytical calculation method for the main cable alignment of a suspension bridge, taking into account the torsional stiffness of the main cable, as described above.

[0138] Example 3

[0139] This embodiment provides a storage medium containing computer-executable instructions. When executed by a computer processor, the storage medium contains computer-executable instructions to perform the analytical calculation method for the main cable alignment of a suspension bridge, considering the torsional stiffness of the main cable, as described above. The storage medium containing computer-executable instructions involved in this embodiment plays an indispensable role in the analytical calculation of the main cable alignment of a suspension bridge. This storage medium can store computer-executable instructions, which, when executed by a computer processor, are specifically used to perform the analytical calculation method for the main cable alignment of a suspension bridge, considering the torsional stiffness of the main cable, as described above. Storage media can be of various types, including electronic media such as flash memory-based storage devices, which are small in size and have high read / write speeds, making them convenient for use in mobile devices or embedded systems, allowing engineers to easily access and use the main cable calculation program in different work scenarios; or magnetic media, such as traditional hard disk drives, which have the advantage of large-capacity storage, capable of storing large amounts of suspension bridge engineering case data, material property data of different types of main cables, and calculation model data under various complex working conditions, providing sufficient data reserves for comprehensive and in-depth main cable calculation and analysis. Optical media, such as CD-ROM, CD-RW, and DVD, are also common storage media types. They have unique advantages in long-term data preservation and distribution, and can be used to archive and preserve the main cable calculation program and related data or to share and exchange them between different engineering teams. Electromagnetic media play a role in certain industrial control or data transmission scenarios, ensuring stable and reliable data transmission and storage. In addition, storage media also include semiconductor or solid-state memory, which has fast read and write speeds and low power consumption, effectively improving the loading and execution efficiency of calculation programs; magnetic tape still has certain applications in large-scale data backup and long-term storage, ensuring the security and integrity of the main cable calculation data; random access memory (RAM) can serve as a temporary data storage area for the processor during calculation, improving the speed of data reading and writing, thereby accelerating the calculation process; read-only memory (ROM) can be used to store some fixed system programs or critical data, ensuring the stability and reliability of the equipment during startup and operation; hard disks can provide large storage space to meet the needs of large-scale data storage and frequent read and write operations in the main cable calculation process of suspension bridges. By storing computer instructions through this storage medium, the analytical calculation method for the main cable alignment of a suspension bridge can be implemented on different computer devices, greatly improving the versatility and scalability of the calculation method and laying a solid foundation for its widespread application in the field of suspension bridge engineering.

[0140] Application Example 1

[0141] This application example considers the analytical calculation method of the main cable's completed bridge alignment for suspension bridges, taking the mid-span of a suspension bridge as an example, to calculate its accurate linearity under self-weight and uniformly distributed loads.

[0142] (1) Input the parameters of the suspension bridge, including E, I, A, ρ, A, g, main beam span L, rise-to-span ratio and other related parameters.

[0143] (2) According to beam theory, the shear force V along the s direction is obtained. 0(s) V 0(s) This includes uniformly distributed loads and concentrated loads.

[0144] (3) After obtaining V(s), substituting it into Equation 6-8, we can calculate the first-order approximate solution without considering the influence of bending moment. Since the influence of bending moment is not considered, V(s) is a multi-ended catenary. If V(s) only contains uniformly distributed load, the first-order approximate solution is a catenary, but in this case, the equation contains three unknowns, namely s, y c0 And T0.

[0145] (4) After obtaining the expression for T0, it can be substituted into equation 9-11 to obtain another expression including s, yc0, yc1, T0 and T1.

[0146] (5) Using the same method, we can obtain Equations 24-26 and 30-32 that take into account the effects of bending moment and the complete boundary.

[0147] (6) Based on the compatibility equations 33-35, all unknowns are solved, and finally the analytical calculation method of the main cable of the suspension bridge considering the torsional stiffness of the main cable is obtained. Figure 2 The calculation results considering the main cable with hinged ends are presented. Figure 3 The calculation results are shown, taking into account the main cable fixed at both ends.

[0148] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. An analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge, considering the torsional stiffness of the main cable, characterized in that, Package the following steps: S1: Constructing the equilibrium equation Based on the precise Cosserate rod theory, considering the self-weight of the main cable and the load of the suspenders, and incorporating the tensile stiffness and bending stiffness of the main cable, a geometrically precise equilibrium equation for the main cable under its self-weight and suspender load is constructed. S2: Ignore bending moment and find an approximate solution Based on the equilibrium equations constructed in S1, the influence of the bending moment in the main cable is ignored and the non-holonomic boundary conditions are considered. The second approximate solution is obtained by solving the direct perturbation method, and the modified catenary equation is obtained. S3: Considering bending moment to find an approximate solution Based on the equilibrium equations constructed in S1, considering the influence of the main cable bending moment and combining the complete boundary, the influence of the main cable bending moment on the static linearity of the suspension bridge is solved using the direct perturbation method, resulting in a second-order approximate solution considering the bending moment. S4: Combining the solution with exact solution Finally, by using the compatibility conditions of the left and right endpoints, combined with the modified catenary equation and the second-order approximate solution considering bending moment, a geometrically accurate form-finding method considering the tensile and torsional stiffness of the main cable is calculated. In S1, the geometrically exact equilibrium equations include: (1) (2) (3) (4) (5) Among them, M is the bending moment of the main cable; The weight of the main cable itself; g is the acceleration due to gravity, taken as 9.8 m / s². 2 ; T The horizontal component of the main cable force; V The shear force of the main cable; s The length of the main cable along its length, i.e., the stress-free length; x is the x-axis coordinate in the inertial coordinate system; y is the vertical coordinate in the inertial coordinate system; κ0 is the original curvature, which is set to 0; A is the area of ​​the main cable; E is the elastic modulus of the main cable; I is the moment of inertia of the main cable section; θ is the rotation angle of the main cable section; Fh is the force of the lifting rod; For the Dirac equation, s i This indicates the location of the boom; S2 specifically includes the following steps: Solving for a first-order approximate solution: Ignoring the influence of the bending moment inside the main cable and considering the non-holonomic boundary conditions, a first-order approximate solution is obtained based on the direct perturbation method, resulting in a rough catenary equation; The corrected catenary equation is obtained by further correcting the static configuration of the main cable without considering torsion through a second approximation. S3 specifically includes the following steps: Considering the influence of the main cable bending moment and the complete boundary, the influence of the main cable bending moment on the static linearity of the suspension bridge is solved based on the direct perturbation method. The first-order approximate solution considering the bending moment is obtained, the corresponding analytical solution is determined, and the explicit second-order equation and analytical solution are obtained by substituting them into the complete boundary conditions. By adding the two, the corrected line shape considering the bending moment inside the main cable but the non-complete boundary is obtained.

2. The analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge considering the torsional stiffness of the main cable, as described in claim 1, is characterized in that... The rough catenary equation includes: (6) (7) (8) in, x 0 for x The first-order approximation, y 0 for y The first-order approximation, θ 0 for θ The first-order approximation; The analytical calculation formula for the rough catenary equation includes: (9) (10) (11) Among them, y 0c The main cable deflection is calculated using the catenary method. L This refers to the cable span.

3. The analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge considering the torsional stiffness of the main cable, as described in claim 2, is characterized in that... The corrected catenary equation includes: (12) (13) (14) Where x1 is a first-order approximation of x, y1 is a first-order approximation of y, and θ1 is a first-order approximation of θ. The analytical calculation formula is as follows: (15) (16) (17) Among them, y 1c The main cable deflection is calculated using the catenary method, where L is the cable span. The analytical solution is shown in the following equation: (18) (19) (20) Where y 0c y 1c , s, T0, T1 are unknowns, and V0 is calculated based on beam theory.

4. The analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge considering the torsional stiffness of the main cable, as described in claim 3, is characterized in that... The process of obtaining the second-order approximate solution considering bending moment includes: (21) (22) (23) in, for The first-order approximation, for The first-order approximation, for The first-order approximation, from the above equation, yields the analytical solution as follows: (24) (25) (26) Substituting the complete boundary conditions, we obtain its explicit second-order equation: (27) (28) (29) The analytical solution obtained from the above equation is: (30) (31) (32) r0 is obtained by substituting the boundary conditions.

5. The analytical calculation method for the completed bridge alignment of the main cable of a suspension bridge considering the torsional stiffness of the main cable, as described in claim 4, is characterized in that... S4 specifically includes the compatibility condition for the final passage through the left and right endpoints. Combining the modified catenary equation and the second-order approximate solution considering bending moment, the compatibility condition is shown in the following equation: (33) (34) (33) (34) (35) Main cable sag; Then, the five unknowns are solved by solving five equations. Based on the conditions obtained from the two sets of solutions, the geometrically accurate form-finding method considering the tensile and torsional stiffness of the main cable is calculated according to equations (18) and (19).

6. An electronic device, comprising a memory and a processor, characterized in that, The processor is used to execute the program in the memory to implement the analytical calculation method for the main cable alignment of a suspension bridge considering the torsional stiffness of the main cable as described in any one of claims 1 to 5.

7. A storage medium containing computer-executable instructions, characterized in that, When executed by a computer processor, the storage medium containing the computer-executable instructions is used to perform the analytical calculation method for the main cable alignment of a suspension bridge considering the torsional stiffness of the main cable as described in any one of claims 1 to 5.

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