Suspension bridge main cable finished bridge line shape analytical calculation method considering main cable torsional rigidity, electronic equipment and medium

Abstract

The invention relates to a suspension bridge main cable finished bridge line shape analytical calculation method considering the torsional rigidity of a main cable, electronic equipment and a medium, and the calculation method comprises the following steps: considering the dead weight of the main cable and the load effect of a suspender, simultaneously including the tensile rigidity and the flexural rigidity of the main cable, and constructing a geometric precise equilibrium equation of the main cable under the dead weight and the load of the suspender; the influence of the bending moment in the main cable is ignored, incomplete boundary conditions are considered, and a quadratic approximate solution is solved based on a direct perturbation method; considering the influence of the bending moment of the main cable, combining the complete boundary, solving the influence of the bending moment of the main cable on the static linearity of the suspension bridge based on a direct perturbation method, and obtaining a second-order approximate solution considering the bending moment; through the compatibility condition of the left end point and the right end point, the corrected catenary equation and the second-order approximate solution considering the bending moment are combined. Compared with the prior art, the influence of the bending rigidity of the main cable is considered, the mechanical concept is clear, shape finding under different boundary conditions can be considered, and design and calculation of the main cable can be further guided.

Description

Technical Field

[0001] The invention relates to the field of civil engineering, and in particular to an analytical calculation method for the bridge line shape of a main cable of a suspension bridge taking into account the torsional stiffness of the main cable, electronic equipment and a medium. Background Art

[0002] Due to its beautiful appearance, strong spanning capacity, and clear force mechanism, suspension bridges are recognized as one of the preferred options for crossing rivers and canyons. In recent years, with the breakthrough of key technical issues, suspension bridges are gradually entering the "2000m era".

[0003] In the form-finding calculation of traditional suspension bridges, the main cable is often simplified as a truss unit, and its bending stiffness is ignored. Its numerical and theoretical calculations are relatively simple. This method is suitable for suspension bridges with a span of less than 2000m. As the span of the suspension bridge increases, the diameter of the main cable also increases. Its bending stiffness cannot be ignored, and it is difficult to achieve accurate form-finding using traditional methods. For example, the main span of the Zhangjinggao Yangtze River Bridge is 2300m, the world's largest span suspension bridge. The diameter of the main cable exceeds 1m, and its bending stiffness has a significant impact on the reasonable bridge linearity. Therefore, it is urgent to propose a form-finding calculation method for large-span suspension bridges with spans of 2000m and above that takes into account the bending stiffness of the main cable.

[0004] The calculation process of bridge form-finding considering the stiffness of the main cables is complicated, and the second-order ordinary differential equation is transformed into 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 bridge line shape of the main cables. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method for analyzing the bridge line shape of the main cable of a suspension bridge taking into account the torsional stiffness of the main cable, electronic equipment, and medium, including a main cable static nonlinear equilibrium equation taking into account the tensile stiffness and bending stiffness of the main cable, an explicit calculation method for the line shape 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 shape finding when the boundary of the main cable is consolidated, further guiding the design and calculation of the main cable.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A first aspect of the present invention provides a method for analytically calculating the bridge line shape of the main cable of a suspension bridge taking into account the torsional stiffness of the main cable, comprising the following steps:

[0008] S1: Constructing balanced equations

[0009] Based on the precise Cosserate rod theory, the deadweight of the main cable and the load of the hanger are considered, and the tensile stiffness and bending stiffness of the main cable are incorporated to construct the geometric precise equilibrium equation of the main cable under deadweight and hanger load.

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

[0011] According to the equilibrium equation constructed in S1, the influence of the bending moment in the main cable is ignored and the non-holonomic boundary conditions are considered. The quadratic approximate solution is solved based on the direct perturbation method to obtain the modified catenary equation.

[0012] S3: Approximate solution considering bending moment

[0013] According to the equilibrium equation constructed by S1, the influence of the main cable bending moment is considered and combined with 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 the second-order approximate solution considering the bending moment is obtained;

[0014] S4: Combined solution to find exact solution

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

[0016] Furthermore, in S1, the geometric precise balance equation includes:

[0017]

[0018] M'-Vcosθ+Tsinθ=0 (3)

[0019] x'-sinθ=0 (4)

[0020] y'-cosθ=0 (5)

[0021] Where M is the main cable bending moment;

[0022] ρ is the deadweight of the main cable;

[0023] g is the acceleration due to gravity, which is 9.8 m / s 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 the cable length direction, that is, the stress-free length;

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

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

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

[0030] A is the main cable area;

[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 main cable cross-section rotation angle;

[0034] Fh is the boom force;

[0035] δ(ss i ) is the Dirac equation, s i The position of the boom.

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

[0037] Solve the first approximate solution: Ignore the influence of the bending moment in the main cable and consider the non-holonomic boundary conditions, solve the first approximate solution based on the direct perturbation method, and obtain the rough catenary equation;

[0038] The corrected catenary equation is obtained by further correcting the static configuration of the main cable without considering torsion through quadratic approximation to obtain the corrected catenary equation.

[0039] Furthermore, the rough catenary equation includes:

[0040] V0cosθ+T0sinθ0=0 (6)

[0041] x0'-sinθ0=0 (7)

[0042] y0'-cosθ0=0 (8)

[0043] Among them, x0 is the first-order approximation of x, y0 is the first-order approximation of y, and θ0 is the first-order approximation of θ;

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

[0045]

[0046] Among them, y 0c is the main cable deflection calculated by the catenary method, and 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] Among them, x1 is the first-order approximation of x, y1 is the first-order approximation of y, and θ1 is the first-order approximation of θ. The analytical calculation formula is as follows:

[0052]

[0053] Among them, y 1c is the main cable deflection calculated by the catenary method, L is the cable span, and the analytical solution is shown as follows:

[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, and 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 the complete boundary conditions. By adding the two, the corrected line shape considering the internal bending moment of the main cable but not the complete boundary is obtained.

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

[0059]

[0060] in, for The first-order approximation of for The first-order approximation of for The first-order approximation of the above formula can be solved analytically as follows:

[0061]

[0062]

[0063] Substituting the full boundary conditions yields its explicit second-order equation:

[0064]

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

[0066]

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

[0068] Furthermore, in S5, the compatibility condition finally passing through the left and right endpoints is specifically included, combined with the modified catenary equation and the second-order approximate solution considering the bending moment, and the compatibility condition is shown in the following formula:

[0069]

[0070] y 0c +y 1c =Δ (35)

[0071] Δ is the main cable sag;

[0072] Then, 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 tension 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, comprising a memory and a processor, wherein the processor is used to execute a program in the memory, so as to implement the above-mentioned analytical calculation method for the bridge line shape of the main cable of a suspension bridge taking into account the torsional stiffness of the main cable.

[0074] A third aspect of the present invention is a storage medium containing computer executable instructions, which, when executed by a computer processor, is used to perform the above-mentioned analytical calculation method for the bridge line shape of the main cable of a suspension bridge taking into account the torsional stiffness of the main cable.

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

[0076] 1) By explicitly considering the influence of the bending stiffness of the main cable, the calculation model is made more accurate and complete at the mechanical level. Compared with the traditional calculation method that does not fully consider this factor, the present invention can more realistically reflect the mechanical behavior of the main cable under actual working conditions, and effectively improve the accuracy and reliability of the main cable bridge line shape calculation.

[0077] 2) Its clear mechanical concepts help engineering and technical personnel to deeply understand the stress and deformation mechanism of the main cable, so that in the design process of the main cable of the suspension bridge, they can determine parameters and optimize the scheme based on more scientific and reasonable theoretical basis.

[0078] 3) The unique advantage of the present invention is that it can handle the shape-finding problem when the boundary of the main cable is consolidated, which greatly broadens its scope of application. Whether in the design of the main cable of a conventional suspension bridge or in some suspension bridge projects with special boundary conditions, it can provide accurate and feasible main cable bridge line shape calculation results, thereby providing strong technical support and guarantee for the safe, stable and efficient construction of the entire suspension bridge, and effectively promoting the development and progress of the field of suspension bridge engineering technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of the present invention.

[0080] Figure 2 Calculation results for the main cable hinged at both ends.

[0081] Figure 3 The error bar graph shows the calculation results with and without considering the bending stiffness of the main cable. DETAILED DESCRIPTION

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

[0083] Example 1

[0084] The geometrical precise equilibrium equation of the main cable under deadweight and hanger load in the present invention is based on the Cosserate rod theory and takes into account the tensile stiffness and bending stiffness of the main cable, see Formula 1-5.

[0085] The main cable bridge linear analysis method process in the present invention can be found in Figure 1 , including (1) ignoring the influence of the bending moment in the main cable (M′), considering the incomplete boundary conditions, solving the first-order 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 when torsion is not considered through the quadratic approximation, and obtaining the corrected catenary equation, which contains five unknowns; (3) considering the influence of the main cable bending moment and the complete boundary, solving the influence of the main cable bending moment on the static linearity of the suspension bridge based on the direct perturbation method, and obtaining the first-order approximate solution considering the bending moment; (4) substituting the complete boundary conditions to obtain its explicit second-order equation, the analytical formula obtained by this method also includes five unknowns; (5) finally through the compatibility conditions of the left and right endpoints, combining the corrected catenary equation and the second-order approximate solution considering the bending moment, the final result refers to formulas 18-19.

[0086] In the specific implementation, based on the Cosserate rod theory, the tensile stiffness and bending stiffness of the main cable are considered, and the geometric precise equilibrium equation of the main cable under its own weight and the load of the suspender rod is proposed, as shown in the following formula:

[0087]

[0088] M'-Vcosθ+Tsinθ=0 (3)

[0089] x'-sinθ=0 (4)

[0090] y'-cosθ=0 (5)

[0091] Where M is the main cable bending moment;

[0092] ρ is the deadweight of the main cable;

[0093] g is the acceleration due to gravity, which is 9.8 m / s 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 the cable length direction, that is, the stress-free length;

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

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

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

[0100] A is the main cable area;

[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 main cable cross-section rotation angle;

[0104] F h is the boom force;

[0105] δ(ss i ) is the Dirac equation, s i The position of the boom.

[0106] Where ()′ represents the derivative of s, and the boundary conditions are obtained based on the actual boundaries.

[0107] In the specific implementation, the influence of the bending moment in the main cable (M′) is ignored and the non-holonomic boundary conditions are considered. The first-order approximate solution is solved based on the direct perturbation method to obtain the rough catenary equation.

[0108] V0 cosθ+T0 sinθ0=0 (6)

[0109] x0'-sinθ0=0 (7)

[0110] y0'-cosθ0=0 (8)

[0111] Among them, x0 is the first-order approximation of x, y0 is the first-order approximation of y, and θ0 is the first-order approximation of θ. Substituting the non-holonomic boundary conditions, we can get that its first-order equation is a catenary, and the analytical calculation formula is shown in the following formula.

[0112]

[0113] Among them, y 0c is the main cable deflection calculated by the catenary method, L is the cable span, and all parameters in this formula are functions of the stress-free length s.

[0114] The static configuration of the main cable without considering torsion is further corrected by the quadratic approach to obtain the corrected catenary equation. The corrected catenary equation is calculated as follows:

[0115] V0θ1 cosθ0+T0θ1 sinθ0+T1 sinθ0=0 (12)

[0116] x1'-θ1 sinθ0=0 (13)

[0117] y1'-θ1 cosθ0=0 (14)

[0118] Among them, x1 is the first-order approximation of x, y1 is the first-order approximation of y, and θ1 is the first-order approximation of θ. The analytical calculation formula is as follows:

[0119]

[0120]

[0121] Among them, y 1c is the main cable deflection calculated by the catenary method, and L is the cable span. The analytical solution obtained by the above formula is as follows:

[0122]

[0123] All parameters in this formula are functions of the stress-free length s, where y 0c ,y 1c , s, T0, T1 are unknown variables, and V0 can be calculated based on beam theory.

[0124] In the specific implementation, the influence of the main cable bending moment and the complete boundary are considered, and 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 the first-order approximate solution considering the bending moment is obtained.

[0125]

[0126] in, for The first-order approximation of for The first-order approximation of for The first-order approximation of the above formula can be solved analytically as follows:

[0127]

[0128] Substituting the full boundary conditions yields its explicit second-order equation:

[0129]

[0130]

[0131] The analytical solution can be obtained from the above formula:

[0132]

[0133] By adding the two together, we can get the modified line shape that takes into account the internal bending moment of the main cable but not the complete boundary, and r0 is obtained by substituting into the boundary conditions.

[0134] In the specific implementation, the compatibility conditions of the left and right endpoints are finally combined with the modified catenary equation and the second-order approximate solution considering the bending moment. The compatibility conditions are shown in the following formula:

[0135]

[0136] y 0c +y 1c =Δ (35)

[0137] Δ is the sag of the main cable. Five equations are used to solve five unknowns. Based on the conditions obtained from the two sets of solutions, the geometrically accurate form-finding method considering the tension and torsion stiffness of the main cable is calculated according to equations 18 and 19.

[0138] Example 2

[0139] The present embodiment provides an electronic device, including a memory and a processor, wherein the processor is used to execute a program in the memory, so as to implement the analytical calculation method for the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable as described above. The electronic device provided in the present embodiment plays a key role in the analytical calculation of the bridge line shape of the main cable of a suspension bridge. Its core components include a memory and a processor, which are coupled to each other and work in coordination. As a storage carrier for data and program instructions, the memory may not only include a random access memory (RAM) so as to quickly provide temporary data and instructions required by the processor during the operation of the device, but may also include a non-volatile memory (Non-Volatile Memory), such as at least one disk storage, for persistent storage of important calculation data, program codes, and various parameter information related to the main cable of the suspension bridge. The processor is the computing core of the entire device. It can be a general-purpose processor, such as a central processing unit (CPU), which has powerful comprehensive computing capabilities, can handle complex logical operations and data processing tasks, and is suitable for large-scale data analysis and processing. In the present invention, it can perform precise calculations on massive data in the main cable bridge line shape calculation process; it can also be a network processor (NP), which can efficiently process network data packets in scenarios involving network transmission and interaction of data, and ensure smoothness and stability when communicating data with external devices or systems, such as when transmitting the main cable calculation results to other engineering design software or remote monitoring systems. In addition, the processor may also be a digital signal processor (DSP), which is specially optimized for digital signal processing. When processing the signal data collected by the sensors related to the main cable, it can quickly and accurately perform filtering, transformation and other operations to extract valuable information for calculation; or an application-specific integrated circuit (ASIC). This customized chip can be specially designed and manufactured according to the specific algorithm and logic of the main cable calculation of the suspension bridge in the present invention, so that it has extremely high efficiency and speed when performing related calculation tasks, greatly shortening the calculation time. It can even be a field-programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, which 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 working conditions of different suspension bridge projects.When the processor executes the program stored in the memory, it can accurately implement the analytical calculation method for the bridge line shape of the main cable of the suspension bridge taking into account the torsional stiffness of the main cable as mentioned above.

[0140] Example 3

[0141] The present embodiment provides a storage medium containing computer executable instructions, which, when executed by a computer processor, is used to execute the analytical calculation method for the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable as described above. The storage medium containing computer executable instructions involved in the present embodiment has an indispensable position in the analytical calculation of the bridge line shape of the main cable of a suspension bridge. The storage medium can store computer executable instructions, which, when executed by a computer processor, are specifically used to execute the analytical calculation method for the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable as described above. The types of storage media are rich and varied, and they can be electronic media, such as storage devices based on flash memory technology, which have the characteristics of small size and fast reading and writing speed, and are convenient to use in mobile devices or embedded systems, so that engineering and technical personnel can easily obtain and use the main cable calculation program in different work scenarios; they can also be magnetic media, such as traditional hard disk drives, which have the advantage of large-capacity storage, and can store a large amount of suspension bridge engineering case data, material property data of different types of main cables, and calculation model data under various complex working conditions, etc., to provide sufficient data reserves for comprehensive and in-depth main cable calculation analysis. Optical media is also one of the common types of storage media, such as compact disc-read only memory (CD-ROM), compact disc-read and write (CD-RW) and DVD, which have unique advantages in the long-term preservation and distribution of data and can be used to archive the main cable calculation program and related data or share and communicate between different engineering teams. Electromagnetic media play a role in some specific industrial control or data transmission scenarios to ensure stable and reliable data transmission and storage. In addition, storage media also include semiconductor or solid-state memory, which has fast read and write speed and low energy consumption, and can effectively improve the loading and execution efficiency of calculation programs; magnetic tape still has certain application scenarios in large-scale data backup and long-term storage, and can ensure the security and integrity of main cable calculation data; random access memory (RAM) can be used as a temporary data storage area for the processor during the calculation process, improving the speed of data reading and writing, thereby speeding up the calculation process; read-only memory (ROM) can be used to store some fixed system programs or key data to ensure the stability and reliability of the equipment during startup and operation; hard disk can provide a large storage space to meet the needs of large-scale data storage and frequent reading and writing in the main cable calculation process of suspension bridges. By storing computer instructions in this storage medium, the analytical calculation method for the bridge line shape of the main cable of the suspension bridge can be implemented on different computer devices, which greatly improves the versatility and scalability of the calculation method and lays a solid foundation for its widespread application in the field of suspension bridge engineering.

[0142] Application Example 1

[0143] This application example considers the analytical calculation method of the main cable bridge line shape of a suspension bridge with the torsional stiffness of the main cable. Taking the mid-span of a suspension bridge as an example, its precise linearity under the action of deadweight and uniformly distributed load is calculated respectively.

[0144] (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.

[0145] (2) According to beam theory, the shear force value V along the s direction is obtained 0(s) , where V 0(s) Includes uniformly distributed loads and concentrated loads.

[0146] (3) After obtaining V(s), we can substitute it into Equation 6-8 to obtain 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-terminal catenary. If V(s) only contains uniformly distributed loads, the first-order approximate solution is a catenary. However, the equation contains three unknowns, namely s, y c0 and T0.

[0147] (4) After obtaining the expression for T0, it can be substituted into equations 9-11 to obtain other expressions including s, yc0, yc1, T0 and T1.

[0148] (5) Using the same method, we can obtain Equations 24-26 and 30-32 which take into account the influence of bending moment and the complete boundary.

[0149] (6) According to the compatibility equations 33-35, all unknowns are solved, and finally an analytical calculation method for the bridge line shape 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 hinged at both ends are shown. Figure 3 The calculation results considering the main cable with two ends consolidated are shown.

[0150] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and 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 present invention should be within the scope of protection of the present invention.

Claims

1. An analytical calculation method for the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable, characterized in that: The following steps are included: S1: Constructing balanced equations Based on the precise Cosserate rod theory, the deadweight of the main cable and the load of the hanger are considered, and the tensile stiffness and bending stiffness of the main cable are incorporated to construct the geometric precise equilibrium equation of the main cable under deadweight and hanger load. S2: Ignore the bending moment and find an approximate solution According to the equilibrium equation constructed in S1, the influence of the bending moment in the main cable is ignored and the non-holonomic boundary conditions are considered. The quadratic approximate solution is solved based on the direct perturbation method to obtain the modified catenary equation. S3: Approximate solution considering bending moment According to the equilibrium equation constructed by S1, the influence of the main cable bending moment is considered and combined with 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 the second-order approximate solution considering the bending moment is obtained; S4: Combined solution to find exact solution Finally, through the compatibility conditions of the left and right endpoints, combined with the modified catenary equation and the second-order approximate solution considering the bending moment, the geometrically accurate form-finding method considering the tension and torsional stiffness of the main cable was calculated.

2. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 1 is characterized in that: In S1, the geometric exact balance equation includes: M'-Vcosθ+Tsinθ=0 (3) x'-sinθ=0 (4) y'-cosθ=0 (5) Where M is the main cable bending moment; ρ is the deadweight of the main cable; g is the acceleration due to gravity, which is 9.8 m / s 2 ; T is the horizontal component of the main cable force; V is the shear force of the main cable; s is the length of the main cable along the cable length direction, that is, the stress-free length; x is the horizontal axis coordinate in the inertial coordinate system; y is the vertical axis coordinate in the inertial coordinate system; k0 is the original curvature, which is set to 0; A is the main cable area; E is the elastic modulus of the main cable; I is the moment of inertia of the main cable section; θ is the cross-sectional rotation angle of the main cable; Fh is the boom force; δ(ss i ) is the Dirac equation, s i The position of the boom.

3. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 1 is characterized in that: S2 specifically includes the following steps: Solve the first approximate solution: Ignore the influence of the bending moment in the main cable and consider the non-holonomic boundary conditions, solve the first approximate solution based on the direct perturbation method, and obtain the rough catenary equation; The corrected catenary equation is obtained by further correcting the static configuration of the main cable without considering torsion through quadratic approximation to obtain the corrected catenary equation.

4. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 3 is characterized in that: The rough catenary equation includes: V0 cosθ+T0 sinθ0=0 (6) x0'-sinθ0=0 (7) y0'-cosθ0=0 (8) Among them, x0 is the first-order approximation of x, y0 is the first-order approximation of y, and θ0 is the first-order approximation of θ; The analytical calculation formula of the rough catenary equation includes: Among them, y 0c is the main cable deflection calculated by the catenary method, and L is the cable span.

5. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 3 is characterized in that: The modified catenary equation includes: V0θ1 cosθ0+T0θ1 sinθ0+T1 sinθ0=0 (12) x1'-θ1 sinθ0=0 (13) y1'-θ1 cosθ0=0 (14) Among them, x1 is the first-order approximation of x, y1 is the first-order approximation of y, and θ1 is the first-order approximation of θ. The analytical calculation formula is as follows: Among them, y 1c is the main cable deflection calculated by the catenary method, L is the cable span, and the analytical solution is shown as follows: where y 0c ,y 1c , s, T0, T1 are unknowns, and V0 is calculated based on beam theory.

6. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 1 is characterized in that: 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, and 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 the complete boundary conditions. By adding the two, the corrected line shape considering the internal bending moment of the main cable but not the complete boundary is obtained.

7. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 1 is characterized in that: The process of obtaining the second-order approximate solution considering the bending moment includes: in, for The first-order approximation of for The first-order approximation of for The first-order approximation of the above formula can be solved analytically as follows: Substituting the full boundary conditions yields its explicit second-order equation: The analytical solution obtained from the above formula is: r0 is obtained by substituting into the boundary conditions.

8. The method for calculating the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable according to claim 1 is characterized in that: In S5, the compatibility condition that finally passes through the left and right endpoints is specifically included, combined with the modified catenary equation and the second-order approximate solution considering the bending moment. The compatibility condition is shown in the following formula: and 0c +y 1c =Δ (35) Δ is the main cable sag; Then, 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 tension and torsional stiffness of the main cable is calculated according to equations (18) and (19).

9. An electronic device, comprising a memory and a processor, characterized in that: The processor is used to execute the program in the memory, so as to implement the analytical calculation method for the bridge line shape of the main cable of the suspension bridge considering the torsional stiffness of the main cable as described in any one of claims 1 to 8.

10. A storage medium containing computer executable instructions, characterized in that: The storage medium of the computer executable instructions is used to execute the analytical calculation method for the bridge line shape of the main cable of a suspension bridge considering the torsional stiffness of the main cable as described in any one of claims 1 to 8 when executed by a computer processor.

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