Method for determining key parameters of a cable structure

Abstract

The application discloses a method for determining key parameters of a cable structure and relates to the technical field of bridge construction. The method comprises the following steps: obtaining the position information of two end points and a lowest point of a catenary of the cable structure, the cross-sectional area of the cable structure, the gravity per unit length and the elastic modulus; establishing a functional relationship about the position information of the cable structure and the cross-sectional area of the cable structure, the gravity per unit length and the elastic modulus based on the balance of cable element force and Hooke's law; and determining the key parameters of the cable structure according to the functional relationship about the position information of the two end points and the lowest point of the catenary of the cable structure and the cross-sectional area of the cable structure, the gravity per unit length and the elastic modulus. The method solves the problems that the calculation of a suspension cable in the prior art usually adopts a finite element program simulation analysis, the model is complex to establish, the calculation amount is large, and the correctness of the calculation result cannot be determined.

Description

Technical Field

[0001] This invention relates to the field of bridge construction technology, and specifically to a method for determining key parameters of cable structures. Background Technology

[0002] Suspension cables are the main load-bearing components of suspension bridges. The alignment and stress of the suspension cables undergo a series of changes from erection to the final opening of the bridge to traffic, ultimately achieving the designed bridge alignment and cable forces. Therefore, determining the initial erection state of the suspension cables is particularly important. If the cable cutting length and initial alignment are incorrect, it will be difficult to achieve the ideal bridge state, affecting the structural stress and posing potential safety hazards for bridge operation.

[0003] In existing technologies, suspension bridge calculations typically employ finite element method (FEM) simulations. This method requires building the entire bridge structure, which is a complex process. Furthermore, the way boundary and load settings are configured in the FEM simulation significantly impacts nonlinear calculations. This approach suffers from problems such as complex model building, high computational load, and difficulty in verifying the accuracy of the calculation results. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a method for determining the key parameters of cable structures, which can solve the problems that the calculation of suspension cables usually adopts finite element program simulation analysis, which has the problems of complex model building, large amount of calculation, and inability to judge the correctness of calculation results.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This solution provides a method for determining key parameters of cable structures, including the following steps:

[0007] Obtain the location information of the two endpoints and the lowest point of the catenary of the cable structure, as well as the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure.

[0008] Based on the equilibrium of forces in cable elements and Hooke's law, a functional relationship is established between the positional information of the cable structure and the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure.

[0009] Based on the position information of the two endpoints and the lowest point of the catenary of the cable structure, and the functional relationship between the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure, the key parameters of the cable structure are determined.

[0010] In some alternative schemes, the functional relationship includes:

[0011]

[0012] Where X is the x-coordinate of the cable structure, Z is the y-coordinate of the cable structure, and a is the first constant. F H Let q0 be the horizontal force of the cable structure element, q0 be the gravity per unit length of the cable structure, and u be the first variable. m is the second constant. E is the elastic modulus of the cable structure, A0 is the cross-sectional area of ​​the cable structure, C1 is the first integration constant, and C2 is the second integration constant.

[0013] In some alternative solutions, the determination of key parameters of the cable structure based on the positional information of the two endpoints and the lowest point of the catenary of the cable structure, and the functional relationship between the cross-sectional area of ​​the cable structure, the gravity per unit length, and the elastic modulus, includes:

[0014] The coordinates of these three points are determined based on the position information of the two endpoints and the lowest point of the catenary of the cable structure.

[0015] By combining the coordinates of the two endpoints and the lowest point of the catenary of the cable structure with the aforementioned functional relationship, a system of transcendental equations is determined.

[0016] Solve the system of transcendental equations to determine the first constant, the second constant, the first integration constant, and the second integration constant;

[0017] Based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, obtain the coordinates of any point in the cable structure, the cable force at any point, the stress-free length, and the stress-bearing length.

[0018] In some alternative solutions, determining the coordinates of the three points based on the position information of the two endpoints and the lowest point of the catenary of the cable structure includes:

[0019] Establish a coordinate system with the first endpoint of the catenary of the cable structure as the origin, with the horizontal direction as the abscissa axis and the vertical direction as the ordinate axis;

[0020] Determine the coordinates of the second endpoint based on the horizontal distance from the first endpoint to the second endpoint and the vertical distance from the second endpoint to the horizontal axis.

[0021] Determine the ordinate of the lowest point based on the vertical distance from the lowest point to the horizontal axis.

[0022] In some alternative solutions, the method of combining the coordinates of the two endpoints and the lowest point of the catenary of the cable structure with the functional relationship to determine the transcendental equations includes:

[0023] By combining the coordinates of the first endpoint, the second endpoint, and the ordinate of the lowest point with the aforementioned functional relationship, the transcendental equation system is determined:

[0024] First endpoint:

[0025] Second endpoint:

[0026] Lowest point:

[0027] Among them, u A Let u be the value of the first variable at its first endpoint. B u is the value of the first variable at the second endpoint. D sinhu is the value of the first variable at its lowest point. D =0,coshu D =1, l is the horizontal distance from the first endpoint to the second endpoint, H is the vertical distance from the second endpoint to the horizontal axis, and f is the vertical distance from the lowest point to the horizontal axis.

[0028] In some alternative solutions, solving the transcendental equations to determine the first constant, the second constant, the first integration constant, and the second integration constant includes:

[0029] Express the complex unknowns in the transcendental equation system as simple unknowns and construct an iterative function;

[0030] Solve the iterative function and, in conjunction with the aforementioned functional relationship, determine the first constant, the second constant, the first integration constant, and the second integration constant.

[0031] In some alternative solutions, the process of solving the iterative function and determining the first constant, the second constant, the first integration constant, and the second integration constant, in conjunction with the functional relationship, includes:

[0032] By using the bisection method for iteration, and by conditional judgment and setting the stop condition for the bisection method, a solution that meets the required accuracy can be obtained.

[0033] Based on the solution of the iterative equation and the functional relationship, determine the first constant, the second constant, the first integration constant, and the second integration constant.

[0034] In some optional schemes, the coordinates and cable forces at any point in the cable structure are obtained based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, including:

[0035] Based on the horizontal distance between any point in the cable structure and the first endpoint, obtain the first variable at any point in the cable structure;

[0036] Based on the first variable at any point in the cable structure and the aforementioned functional relationship, obtain the coordinates of any point in the cable structure;

[0037] According to the formula: Determine the cable force at any point in the cable structure;

[0038] Among them, T E Let u be the cable force at any point in the cable structure. ELet be the first variable at any point in the cable structure.

[0039] In some alternative solutions, the stress-free length of the cable structure is obtained based on a first constant, a second constant, a first integration constant, a second integration constant, and the aforementioned functional relationship, including:

[0040] According to the formula: S0=a×(sinhu) B -sinhu A ), to obtain the stress-free length of the cable structure;

[0041] Where S0 is the stress-free length of the cable structure.

[0042] In some alternative solutions, the stress-bearing length of the cable structure is obtained based on a first constant, a second constant, a first integration constant, a second integration constant, and the aforementioned functional relationship, including:

[0043] According to the formula:

[0044]

[0045] Obtain the stress length of the cable structure, where S is the stress length of the cable structure.

[0046] Compared with existing technologies, the advantages of this invention are as follows: This solution obtains the position information of the two endpoints and the lowest point of the catenary of the cable structure, as well as the cross-sectional area, unit length gravity, and elastic modulus of the cable structure; based on the equilibrium of cable element forces and Hooke's law, it establishes a functional relationship between the position information of the cable structure and its cross-sectional area, unit length gravity, and elastic modulus; and based on this functional relationship, it determines the key parameters of the cable structure. This solves the problem that existing technologies typically use finite element analysis programs for cable calculations, which result in complex model establishment, large computational load, and the inability to determine the correctness of the calculation results. Attached Figure Description

[0047] 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.

[0048] Figure 1 This is a schematic diagram illustrating the steps of the method for determining key parameters of the cable structure in an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram showing the positional relationship between the two endpoints and the lowest point of the cable structure in an embodiment of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0051] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0052] like Figure 1 and Figure 2 As shown, the present invention provides a method for determining key parameters of a cable structure, comprising the following steps:

[0053] S1: Obtain the position information of the two endpoints and the lowest point of the catenary of the cable structure, as well as the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure.

[0054] S2: Based on the equilibrium of forces in the cable element and Hooke's law, establish a functional relationship between the positional information of the cable structure and the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure.

[0055] S3: Determine the key parameters of the cable structure based on the position information of the two endpoints and the lowest point of the catenary of the cable structure and the functional relationship between the cross-sectional area of ​​the cable structure, the gravity per unit length, and the elastic modulus.

[0056] In this embodiment, the present invention obtains the position information of the two endpoints and the lowest point of the catenary of the cable structure, as well as the cross-sectional area, unit weight, and elastic modulus of the cable structure. Based on the equilibrium of the cable element forces and Hooke's law, a functional relationship is established between the position information of the cable structure and its cross-sectional area, unit weight, and elastic modulus. Based on this functional relationship, the key parameters of the cable structure are determined. This solves the problem that in the prior art, the calculation of suspension cables typically uses finite element simulation analysis, which results in complex model establishment, large computational load, and the inability to determine the correctness of the calculation results.

[0057] In some optional embodiments, the functional relationship includes:

[0058]

[0059] Where X is the x-coordinate of the cable structure, Z is the y-coordinate of the cable structure, and a is the first constant. F HLet q0 be the horizontal force of the cable structure element, q0 be the gravity per unit length of the cable structure, and u be the first variable. m is the second constant. E is the elastic modulus of the cable structure, A0 is the cross-sectional area of ​​the cable structure, C1 is the first integration constant, and C2 is the second integration constant.

[0060] In some optional embodiments, determining the key parameters of the cable structure based on the position information of the two endpoints and the lowest point of the catenary of the cable structure and the functional relationship between the cross-sectional area of ​​the cable structure, the gravity per unit length, and the elastic modulus includes:

[0061] The coordinates of these three points are determined based on the position information of the two endpoints and the lowest point of the catenary of the cable structure.

[0062] By combining the coordinates of the two endpoints and the lowest point of the catenary of the cable structure with the aforementioned functional relationship, a system of transcendental equations is determined.

[0063] Solve the system of transcendental equations to determine the first constant, the second constant, the first integration constant, and the second integration constant;

[0064] Based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, obtain the coordinates of any point in the cable structure, the cable force at any point, the stress-free length, and the stress-bearing length.

[0065] In some optional embodiments, determining the coordinates of the three points based on the position information of the two endpoints and the lowest point of the catenary of the cable structure includes:

[0066] Establish a coordinate system with the first endpoint of the catenary of the cable structure as the origin, with the horizontal direction as the abscissa axis and the vertical direction as the ordinate axis;

[0067] Determine the coordinates of the second endpoint based on the horizontal distance from the first endpoint to the second endpoint and the vertical distance from the second endpoint to the horizontal axis.

[0068] Determine the ordinate of the lowest point based on the vertical distance from the lowest point to the horizontal axis.

[0069] In some optional embodiments, the step of combining the coordinates of the two endpoints and the lowest point of the catenary of the cable structure with the functional relationship to determine the transcendental equations includes:

[0070] By combining the coordinates of the first endpoint, the second endpoint, and the ordinate of the lowest point with the aforementioned functional relationship, the transcendental equation system is determined:

[0071] First endpoint:

[0072] Second endpoint:

[0073] Lowest point:

[0074] Among them, u A Let u be the value of the first variable at its first endpoint. B u is the value of the first variable at the second endpoint. D sinhu is the value of the first variable at its lowest point. D =0,coshu D =1, l is the horizontal distance from the first endpoint to the second endpoint, H is the vertical distance from the second endpoint to the horizontal axis, and f is the vertical distance from the lowest point to the horizontal axis.

[0075] In some optional embodiments, solving the transcendental equations to determine the first constant, the second constant, the first integration constant, and the second integration constant includes:

[0076] Express the complex unknowns in the transcendental equation system as simple unknowns and construct an iterative function;

[0077] Solve the iterative function and, in conjunction with the aforementioned functional relationship, determine the first constant, the second constant, the first integration constant, and the second integration constant.

[0078] In this embodiment, let coshu A =x,coshu B =y, substitute it, and get the function for x:

[0079]

[0080] in

[0081] In some optional embodiments, solving the iterative function and determining the first constant, the second constant, the first integration constant, and the second integration constant in conjunction with the functional relationship includes:

[0082] By using the bisection method for iteration, and by conditional judgment and setting the stop condition for the bisection method, a solution that meets the required accuracy can be obtained.

[0083] Based on the solution of the iterative equation and the functional relationship, determine the first constant, the second constant, the first integration constant, and the second integration constant.

[0084] In this embodiment, a solution with satisfactory accuracy is obtained by using a loop statement, setting an initial value, iterating using the binary search method, and judging conditions and setting conditions to terminate the loop.

[0085] Loop statements include:

[0086]

[0087] In this embodiment, the initial values ​​for iteration are: x(1) = 1.000001, x'(1) = 1.85.

[0088] In some optional embodiments, obtaining the coordinates and cable force at any point in the cable structure based on the first constant, the second constant, the first integration constant, the second integration constant, and the functional relationship includes:

[0089] Based on the horizontal distance between any point in the cable structure and the first endpoint, obtain the first variable at any point in the cable structure;

[0090] Based on the first variable at any point in the cable structure and the aforementioned functional relationship, obtain the coordinates of any point in the cable structure;

[0091] According to the formula: Determine the cable force at any point in the cable structure;

[0092] Among them, T E Let u be the cable force at any point in the cable structure. E Let be the first variable at any point in the cable structure.

[0093] In some optional embodiments, the stress-free length of the cable structure is obtained based on a first constant, a second constant, a first integration constant, a second integration constant, and the functional relationship, including:

[0094] According to the formula: S0=a×(sinhu) B -sinhu A ), to obtain the stress-free length of the cable structure;

[0095] Where S0 is the stress-free length of the cable structure.

[0096] In some optional embodiments, the stress length of the cable structure is obtained based on a first constant, a second constant, a first integration constant, a second integration constant, and the functional relationship, including:

[0097] According to the formula:

[0098]

[0099] Obtain the stress length of the cable structure, where S is the stress length of the cable structure.

[0100] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0101] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0102] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for determining key parameters of a cable structure, characterized in that, Includes the following steps: Obtain the location information of the two endpoints and the lowest point of the catenary of the cable structure, as well as the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure. Based on the equilibrium of forces in cable elements and Hooke's law, a functional relationship is established between the positional information of the cable structure and the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure. Based on the position information of the two endpoints and the lowest point of the catenary of the cable structure, the key parameters of the cable structure are determined according to the functional relationship between the cross-sectional area, the gravity per unit length and the elastic modulus of the cable structure. The functional relationship includes: in, The x-axis represents the cable structure. The vertical axis represents the cable structure. As the first constant, , For horizontal forces in cable-stayed structural elements, The weight per unit length of the cable structure. As the first variable, , As the second constant, , The elastic modulus of the cable structure, For the cross-sectional area of ​​the cable structure, The first integral constant is... It is the second integral constant; The method for determining key parameters of a cable structure based on the positional information of the two endpoints and the lowest point of the catenary, and the functional relationship between the cross-sectional area, gravity per unit length, and elastic modulus of the cable structure, includes: The coordinates of these three points are determined based on the position information of the two endpoints and the lowest point of the catenary of the cable structure. By combining the coordinates of the two endpoints and the lowest point of the catenary of the cable structure with the aforementioned functional relationship, a system of transcendental equations is determined. Solve the system of transcendental equations to determine the first constant, the second constant, the first integration constant, and the second integration constant; Based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, obtain the coordinates of any point in the cable structure, the cable force at any point, the stress-free length, and the stress-bearing length.

2. The method for determining key parameters of a cable structure as described in claim 1, characterized in that, The determination of the coordinates of these three points based on the position information of the two endpoints and the lowest point of the catenary of the cable structure includes: Establish a coordinate system with the first endpoint of the catenary of the cable structure as the origin, with the horizontal direction as the abscissa axis and the vertical direction as the ordinate axis; Determine the coordinates of the second endpoint based on the horizontal distance from the first endpoint to the second endpoint and the vertical distance from the second endpoint to the horizontal axis. Determine the ordinate of the lowest point based on the vertical distance from the lowest point to the horizontal axis.

3. The method for determining key parameters of a cable structure as described in claim 2, characterized in that, The method of combining the coordinates of the two endpoints and the lowest point of the catenary of the cable structure with the functional relationship to determine the transcendental equation system includes: By combining the coordinates of the first endpoint, the second endpoint, and the ordinate of the lowest point with the aforementioned functional relationship, the transcendental equation system is determined: First endpoint: Second endpoint: Lowest point: in, The value of the first variable at its first endpoint. The value of the first variable at the second endpoint. The value of the first variable at the lowest point. , , The horizontal distance from the first endpoint to the second endpoint. This represents the vertical distance from the second endpoint to the horizontal axis. This is the vertical distance from the lowest point to the horizontal axis.

4. The method for determining key parameters of a cable structure as described in claim 3, characterized in that, Solving the transcendental equations and determining the first constant, the second constant, the first integration constant, and the second integration constant includes: Express the complex unknowns in the transcendental equation system as simple unknowns and construct an iterative function; Solve the iterative function and, in conjunction with the aforementioned functional relationship, determine the first constant, the second constant, the first integration constant, and the second integration constant.

5. The method for determining key parameters of a cable structure as described in claim 4, characterized in that, The solution to the iterative function, and the determination of the first constant, the second constant, the first integration constant, and the second integration constant based on the functional relationship, include: By using the bisection method for iteration, and by conditional judgment and setting the stop condition for the bisection method, a solution that meets the required accuracy can be obtained. Based on the solution of the iterative equation and the functional relationship, determine the first constant, the second constant, the first integration constant, and the second integration constant.

6. The method for determining key parameters of a cable structure as described in claim 1, characterized in that, Based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, obtain the coordinates and cable force at any point in the cable structure, including: Based on the horizontal distance between any point in the cable structure and the first endpoint, obtain the first variable at any point in the cable structure; Based on the first variable at any point in the cable structure and the aforementioned functional relationship, obtain the coordinates of any point in the cable structure; According to the formula: Determine the cable force at any point in the cable structure; in, For any point in the cable structure, the cable force is... Let be the first variable at any point in the cable structure.

7. The method for determining key parameters of a cable structure as described in claim 1, characterized in that, Based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, the stress-free length of the cable structure is obtained, including: According to the formula: Obtain the stress-free length of the cable structure; in, The stress-free length of the cable structure.

8. The method for determining key parameters of a cable structure as described in claim 1, characterized in that, Based on the first constant, the second constant, the first integration constant, the second integration constant, and the aforementioned functional relationship, the stress-bearing length of the cable structure is obtained, including: According to the formula: Obtain the stress length of the cable structure, where, The stress length of the cable structure.

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