Design method for static wind stability control structure of catwalk of space cable suspension bridge

Abstract

The invention discloses a design method for a static wind stability control structure of a catwalk of a space cable suspension bridge, and belongs to the technical field of bridge engineering construction. The method comprises the steps that on the basis of catwalk parameters and engineering constraints, all wind-resistant cable candidate position and angle sets meeting the symmetry requirement are generated; aiming at each candidate combination, by establishing a contribution efficiency model and a mechanical equilibrium equation, solving optimal tension meeting catwalk linear constraint and primarily selecting cable specifications; calculating a system comprehensive efficiency index or a multi-objective optimization value of each combination; the optimal position, angle, tension and specification parameters are screened out; finally, checking calculation is carried out through a finite element model, a final scheme is determined if specifications are met, and otherwise, feedback adjustment is carried out. According to the method, systematization and quantitative optimization of wind-resistant cable design are achieved, and design efficiency and economical efficiency can be improved on the premise that catwalk construction precision and static wind stability are guaranteed.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically to a structural design method for controlling the static wind stability of a catwalk in a spatial cable suspension bridge. Background Technology

[0002] Spatial cable suspension bridges are an emerging bridge type. Compared to traditional suspension bridges, spatial cable suspension bridges offer superior aerodynamic stability, greater lateral stiffness, and better aesthetics, and are increasingly demonstrating broad application potential under the constraints of planar cable systems. However, the catwalk structure of a three-span spatial cable suspension bridge differs significantly from typical catwalks. During the main cable erection phase, because the main cable strands are very close together, the catwalk is not two independent sections but a single, integrated structure. When the bridge deck is erected, the integrated catwalk is divided into two independent catwalks.

[0003] Clearly, this new type of split, openable catwalk has lower stiffness than traditional typical catwalk structures, making it more prone to wind-induced vibration. Horizontal vibration damping cables are a common measure to control catwalk vibration and improve wind resistance, connecting two catwalk sections with horizontal steel wire ropes. However, this is obviously unsuitable for catwalks in the main cable erection phase of a spatial cable suspension bridge. On the other hand, using a wind-resistant cable system is also a common method, involving installing wind-resistant cables beneath the catwalk and wind-resistant hangers connecting them to the catwalk surface to enhance wind resistance. However, the anchorage of the wind-resistant cables is far from the anchorage systems of the main cable and the catwalk load-bearing ropes, which means it cannot share the same survey and design scheme as the main cable and must be surveyed and designed separately. The spatially curved shape of the wind-resistant cables presents challenges in both the erection and hanger installation phases, making construction difficult. Furthermore, considering the large-span flexibility of the catwalk structure, the self-weight of traditional wind-resistant cables can affect the catwalk alignment, making it difficult to meet on-site construction requirements.

[0004] The wind-induced static vibration structure of conventional space cable suspension bridges, as described above, is typically designed and installed based on engineering experience. However, there is no universally applicable and effective design method for the design and construction of wind-resistant cables. In actual construction, space cable suspension bridges require the installation of several wind-resistant cables, and the placement of each cable relies heavily on manual experience. The vibration-damping structure formed by these cables may not achieve the desired effect, and even if it does, it may result in material waste.

[0005] Therefore, there is an urgent need to develop a design method for wind-induced static vibration suppression structures for catwalks of space cable suspension bridges, so that designers can design suitable vibration suppression structures that can meet the vibration suppression requirements while avoiding the problems of material waste and increased costs. Summary of the Invention

[0006] The purpose of this application is to address the shortcomings of the aforementioned background technology and provide a structural design method for controlling the static wind stability of a catwalk on a spatial cable suspension bridge.

[0007] The technical solution of this application is: a design method for a static wind stability control structure of a catwalk for a space cable suspension bridge, comprising: Based on the catwalk parameters, design wind speed, allowable deviation of catwalk alignment, and available gantry locations on the catwalk, list all candidate locations and angles for wind-resistant cables that satisfy the symmetry constraint. For each candidate position and angle combination of the wind-resistant cable in the set, the optimal tension of the wind-resistant cable that satisfies the linear constraint and the corresponding preliminary wind-resistant cable specification are calculated. For each combination, based on its optimal tension and initially selected cable specifications, calculate the overall system performance index or target optimization value for that combination. Based on the system's comprehensive performance index or target optimization value, the optimal wind-resistant cable position, angle, tension, and cable specification parameters are selected from the set. The optimal parameters are substituted into the finite element model for verification and analysis to determine whether they meet the design specifications. If they do, the wind-resistant cable arrangement position and angle corresponding to the optimal parameters are taken as the final design scheme.

[0008] According to the design method for static wind stability control of the catwalk of a spatial cable suspension bridge provided in this application, the constraint conditions are constructed according to the following formula. in: ΔZ catwalk —The change in the alignment of the catwalk after the installation of wind-resistant cables; ΔZ —The catwalk line describes the value; T min —Minimum tension of the wind-resistant cable in working condition; T i ——No. i The tension of the wind-resistant cable in operation; T break —Critical value for tensile fracture of wind-resistant cable; β i ——No. i The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; V cr —Critical wind speed at which the catwalk-wind-resistant cable system becomes unstable in still wind; V d —Design test wind speed; x —Wind speed coefficient; Based on the above constraints, a set of all candidate locations for wind-resistant cables that satisfy the symmetry constraints is listed.

[0009] According to the design method for the static wind stability control structure of the catwalk of a spatial cable suspension bridge provided in this application, the method for calculating each candidate position and angle set of wind-resistant cables includes: calculating within a set angle range between the wind-resistant cable and the longitudinal vertical plane of the bridge according to a set angle step, and calculating the optimal tension that satisfies the linear constraints according to the following formula. in: C i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; H ij ——No. j The vertical force of the wind-resistant cable on the first i Influence coefficient of vertical displacement of the catwalk at the anchor point of the wind-resistant cable; β j ——No. j The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; T 0，j ——No. j The optimal tension of the wind-resistant cable, where i, j = 1, 2, 3…m, and m is the total number of wind-resistant cables; λ — a constant.

[0010] According to the design method for static wind stability control structure of a catwalk for a spatial cable suspension bridge provided in this application, the following formula is used to calculate the first [value] per unit length and per unit tension. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catenary under specific positions and angles. in: C i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; β i ——No. i The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; l i (p i ) ——No. i The horizontal lever arm from the anchor point of the wind-resistant cable to the mid-span or maximum displacement point of the catwalk. L i (p i ) ——No. i The length of the wind-resistant cable.

[0011] According to the design method for the static wind stability control structure of the catwalk of a spatial cable suspension bridge provided in this application, the method for solving the preliminary cable specifications that satisfy the linear constraints includes: calculating the preliminary cable specifications that satisfy the linear constraints according to the following formula. in: A i —The first selection that satisfies the linear constraints i Cross-sectional area of ​​the wind-resistant cable; T 0，i ——No. i The optimal tension of the wind-resistant cable; f safe —Safety factor; s u —Ultimate tensile strength of wind-resistant cable material; Δ T i (q w ,P,β) —At the design wind speed, the first [factor] caused by wind load i The additional tension of the wind-resistant cable is determined by the position of the wind-resistant cable. P i ,angle β i and wind load q w The function.

[0012] According to the design method for the static wind stability control structure of the catwalk of a spatial cable suspension bridge provided in this application, the method for calculating the comprehensive system performance index includes: calculating the comprehensive system performance index according to the following formula. in: S total ——No. i The overall system performance index of wind-resistant cables; m — Total number of wind-resistant cables; C i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; T 0,i ——No. i The optimal tension of the wind-resistant cable.

[0013] According to the design method for the static wind stability control structure of the catwalk of a spatial cable suspension bridge provided in this application, the method for calculating the target optimization value includes: Where: minJ — the target optimization value; d h,max —Maximum lateral displacement of the catwalk; d h,allow — Allowable lateral displacement design value for catwalk; d v,max —Maximum vertical displacement of the catwalk; d v,allow — Allowable vertical displacement of the catwalk; i max —Maximum torsion angle of the catwalk; i allow — Allowable design value for catwalk torsion angle; w 1 — Lateral displacement weighting coefficient; w 2 —Vertical displacement weighting coefficient; w 3 —Twist angle weighting coefficient.

[0014] According to the design method of the static wind stability control structure of the catwalk of the spatial cable suspension bridge provided in this application, the method of selecting the optimal parameters based on the system comprehensive performance index or the target optimization value includes: when using the system comprehensive performance index, selecting the candidate position and angle combination of the wind-resistant cable with the largest index as the optimal parameters; When using the target optimization value, the candidate position and angle combination of the wind-resistant cable with the smallest value is selected as the optimal parameter.

[0015] According to the design method for the static wind stability control structure of the catwalk of a spatial cable suspension bridge provided in this application, if the design specifications are not met, the candidate parameter set can be adjusted or the constraints can be relaxed and then recalculated.

[0016] According to the design method for the static wind stability control structure of a catwalk for a spatial cable suspension bridge provided in this application, the method for determining whether the design specifications are met includes: The critical wind speed for static wind instability of the catwalk-wind-resistant cable system shall not be less than the product of the design test wind speed and the wind speed coefficient, and the wind speed coefficient shall be a safety factor of not less than 1.2. The maximum lateral displacement, maximum vertical displacement, and maximum torsional angle of the catwalk shall not exceed their respective design allowable values; If the above conditions are met, then the design specifications are deemed to be met; otherwise, they are not.

[0017] The advantages of this application are as follows: 1. The design method of this application is a complete, systematic and logically rigorous design process, which is the general outline of the whole method. By generating all candidate sets that satisfy the symmetry constraints, the completeness of the search space is ensured, avoiding engineers from comparing only a few schemes based on experience, which may lead to missing the global optimal solution; the entire design process organically integrates four key design variables: position, angle, tension, and specifications, and ultimately points to the comprehensive system performance or multi-objective optimization value, changing the shortcomings of traditional design, which often considers these parameters step by step and in isolation, and realizing the linkage optimization between parameters; the last step of the design process requires the optimized parameters to be substituted into the finite element model for verification; this forms a complete design closed loop of parameterized screening, theoretical optimization, and numerical simulation verification, which greatly improves the reliability and credibility of the design results and meets the requirements of the high safety standards of modern bridge engineering; this design method provides designers with a standardized and repeatable decision-making framework, reduces the excessive reliance on the experience of individual experts in the design process, and is conducive to the inheritance of technology and the stability of project quality; 2. The design method in this application quantifies and formalizes key design constraints, clarifying that the wind-resistant system cannot be achieved at the expense of excessively altering the catwalk alignment; the catwalk is the benchmark for main cable erection, and its alignment accuracy directly affects the final bridge alignment; this constraint ensures that the core objective of construction accuracy is not compromised; tension safety domain control defines a clear safety range for the working tension of the wind-resistant cable; the lower limit ensures that the wind-resistant cable maintains a certain tension under any working condition, avoiding slack failure; the upper limit adopts a high safety factor, typically not exceeding 40% of the breaking tensile force, leaving sufficient margin for wind load fluctuations and construction errors, reflecting a conservative design principle; angled engineering is feasible. The scope of this domain improves engineering feasibility. If the included angle is too small (<15°), the horizontal component of the wind-resistant cable will be insufficient, resulting in poor lateral displacement resistance, and the vertical component will be too large, causing the catwalk to be excessively lifted. If the included angle is too large (>75°), the wind-resistant cable will tend to be vertical, providing almost no lateral constraint, and may hinder construction below. This constraint eliminates a large number of theoretically existing but engineeringally ineffective or even harmful solutions. The fundamental requirement of system stability is the ultimate goal of wind-resistant design—ensuring that the entire catwalk-wind-resistant cable system does not experience instability in calm winds. Using this as a hard constraint for screening candidate solutions eliminates unsafe solutions from entering the subsequent optimization process from the source, improving overall efficiency. 3. The optimal tension distribution model of this application constructs a coupled system equation. The contribution efficiency of each wind-resistant cable and its vertical constraint effect at the catwalk anchorage point (determined by tension, angle, and influence coefficient) should reach a balance. The optimal tension obtained by solving this equation is a set of optimal tensions that maximizes the lateral suppression effectiveness of each wind-resistant cable under the premise of satisfying the vertical alignment constraint of the catwalk (i.e., without generating excessive vertical deformation). This resolves the contradiction between applying force to suppress lateral displacement and avoiding harmful vertical deformation. 4. The calculation of optimal tension in this application involves how to scientifically distribute the tension of each wind-resistant cable. This calculation method reflects the contribution of angle to lateral constraint effectiveness (the closer the included angle is to 90°, the greater the lateral component force) and the amplification effect of lever arm length (the longer the lever arm, the more significant the effect of suppressing mid-span displacement). Shorter wind-resistant cables (usually with greater stiffness) can transmit force more efficiently. The contribution efficiency is a dimensionless performance index that precisely quantifies the "cost-effectiveness" of wind-resistant cables of unit length and unit tension in suppressing lateral displacement at the mid-span of the catwalk at a specific location and angle. This provides a scientific basis for optimizing tension distribution. 5. The calculation method for the initial cable specifications in this application achieves a seamless connection from mechanical requirements to component selection, reflecting refined design and comprehensive consideration of load combinations. In the calculation formula, the cable area is not only determined by the optimal working tension, but also superimposed with the additional tension directly caused by wind load. This accurately reflects the true stress state of the wind-resistant cable under actual wind load, namely static tension and dynamic wind load increment. The safety factor is introduced independently and clearly, which clearly distinguishes the ultimate strength of the material from the allowable stress, conforms to the design concept of the specification, and facilitates the adjustment of the safety level according to the importance of the project. The minimum cross-sectional area that meets the strength requirements is quickly estimated in the optimization cycle, providing reasonable "specification" parameters for subsequent comprehensive performance evaluation or target optimization, avoiding the blind selection of excessively heavy or light cables. 6. The system comprehensive performance index of this application is essentially the sum of the unit performance of each wind-resistant cable multiplied by its actual output. This index directly quantifies the total ability of the entire wind-resistant cable system to suppress the lateral displacement of the catwalk. Maximizing the system comprehensive performance index means distributing tension in the most efficient way to achieve the strongest overall lateral constraint effect. It has a single objective and is computationally efficient, making it suitable for situations where lateral displacement control is the primary concern. 7. The multi-objective optimization value of this application is a more comprehensive and advanced evaluation system; the system's comprehensive performance index considers the three key responses of lateral displacement, vertical displacement, and torsional angle simultaneously, more realistically reflecting the complex deformation state of the catwalk under wind load; normalization by dividing by their respective allowable values ​​eliminates the influence of dimensions; and the weighting coefficients allow designers to flexibly adjust the priority of different control objectives according to the specific bridge characteristics, construction stage, and wind field characteristics. 8. This application provides a clear and unique mathematical criterion for the final decision, eliminating the ambiguity of human decision-making; whether it is the maximum efficiency or the overall optimal, it transforms a complex engineering decision problem into a clear numerical comparison problem; this makes the design process objective, transparent and traceable, greatly enhances the persuasiveness of the design results, and facilitates communication in team collaboration and scheme review. 9. This application explicitly uses the critical wind speed for calm wind instability and the displacement / torsion angle limit as the final evaluation criteria; this is the ultimate test of all previous optimization results, ensuring that the solution is not only appropriate but also safe, and fully meets or exceeds the requirements of industry standards. 10. The design method of this application is an iterative process, which gives the method flexibility and robustness. When the initial optimization result fails the final verification due to overly strict constraints, this mechanism allows the designer to provide feedback and adjustments (such as adding candidate positions, fine-tuning allowable displacements, etc.) to restart the optimization process until a feasible solution that satisfies all hard safety specifications and is as good as possible under the current conditions is found. This simulates the complete thought process of design, verification and adjustment.

[0018] This application provides a catwalk wind-resistant design method that evolves from experience-driven to model and optimization algorithm-driven approaches. This method covers the entire process from parameter generation, theoretical optimization, component selection to simulation verification. It introduces concepts such as contribution efficiency, coupled equilibrium equations, and multi-objective optimization to ensure that the design is based on sound principles. Through quantitative constraints and optimization objectives, it achieves precise control over the catwalk's static wind response (displacement, torsion, and stability). Through programmed screening and calculation, it can quickly locate high-performance solutions within a vast design space, significantly improving design efficiency and quality. Strict constraints, safety factors, and closed-loop verification ensure the fundamental safety of the solution. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the design method for wind-resistant cables of a catwalk for a spatial cable suspension bridge, as provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the planar arrangement of the catwalk and wind-resistant cable in one embodiment of the present invention. Detailed Implementation

[0020] The embodiments of this application are described in detail below, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0021] In the description of this application, it should be understood that the terms "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They 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. Therefore, they should not be construed as limitations on this application.

[0022] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0023] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0024] This application relates to a design method for the static wind stability control structure of a catwalk in a spatial cable suspension bridge. The design method is used to design the installation position and angle of the wind-resistant cable that effectively suppresses wind-induced static vibrations of the catwalk. This design method has the following advantages: It shifts from experience-driven to model-driven, transforming the designer's experience into calculable rules and algorithms, making the design process clearer; from local trial and error to global optimization, automatically searching for the best-performing combination in a vast feasible solution space, resulting in higher design quality; from single-objective to multi-objective collaboration, it can coordinate and balance multiple often conflicting design objectives such as lateral stiffness, vertical alignment, and torsional control; from qualitative judgment to quantitative evaluation, each scheme has a clear quantitative score, providing a clear and objective basis for decision-making; and it offers high robustness and engineering practicality, with a built-in iterative adjustment mechanism that can flexibly respond to complex engineering constraints and unexpected situations, ensuring that a safe, economical, and feasible design scheme is always delivered.

[0025] Specifically, this application provides a complete method for designing a structure to suppress wind-induced static vibrations in the catwalk of a space cable suspension bridge. For example... Figure 1 As shown, firstly, based on the catwalk design parameters, design wind speed at the bridge site, allowable deviations in the catwalk alignment, and the pre-set positions of the construction gantry, an exhaustive set of candidate combinations of spatial positions and angles for wind-resistant cables that meet the symmetrical arrangement requirements is generated. Next, for each candidate combination in the set, a mechanical equilibrium equation is established to solve for the optimal initial tension of each wind-resistant cable under the premise of meeting the catwalk alignment control requirements, and the cable specifications that meet the strength requirements are initially selected accordingly. Then, a quantified system comprehensive performance index or a multi-objective optimization value is calculated for each combination of position, angle, tension, and specification. Based on this index or optimization value, all candidate combinations are sorted and filtered to determine an optimal set of parameter combinations. Finally, this optimal set of parameters is input into a refined spatial finite element model for static wind response and stability verification. If the verification results meet all design specifications, the scheme is adopted as the final design; if not, feedback is provided to adjust the design parameters, and the optimization calculation is performed again.

[0026] The location in this application refers to the installation position of the upper end of the wind-resistant cable on the catwalk. The wind-resistant cable is installed at both ends of the gantry on the catwalk, forming a set of symmetrical constraint structures; the angle refers to the angle between the wind-resistant cable and the longitudinal vertical plane of the bridge.

[0027] This method transforms wind-resistant cable design from an experience-based trial-and-error process into a systematic search and decision-making process based on explicit rules and optimization objectives. By constructing a design space encompassing all feasible solutions, and within this space, optimization is performed using mechanical criteria and multi-objective evaluation functions. Finally, safety verification is conducted through high-fidelity numerical simulation, thereby ensuring the global excellence, scientific rigor, and reliability of the design results.

[0028] The design methodology presented in this application constructs an automated and standardized design process from parameter input to solution output. Its greatest advantage lies in achieving global optimization and avoiding local optima; forming a closed loop between design and verification to ensure the reliability of the solution; and transforming personal design experience into executable algorithmic rules, thereby improving design efficiency and the repeatability of quality.

[0029] In some embodiments of this application, the method for setting the above-mentioned design constraints has been optimized. Specifically, this embodiment clarifies and mathematically quantifies the four core constraints that the wind-resistant cable design must meet. These constraints include: Catwalk Linear Variation Constraints ( |∆Z catwalk |≤∆Z） ; Wind-resistant cable working tension safety range constraints ( T min ≤T i ≤0.4T break ); Reasonable range constraints of the included angle of the wind-resistant cable ( β i ∈[15°, 75°]); and overall system stability constraints ( V cr ≥ξV d , where ξ≥1.2).

[0030] in: ΔZ catwalk —The change in the alignment of the catwalk after the installation of wind-resistant cables; ΔZ —The catwalk line describes the value; T min —Minimum tension of the wind-resistant cable in working condition; T i ——No. i The tension of the wind-resistant cable in operation; T break —Critical value for tensile fracture of wind-resistant cable; β i ——No. i The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; V cr —Critical wind speed at which the catwalk-wind-resistant cable system becomes unstable in still wind; Vd —Design test wind speed; x —Wind speed coefficient.

[0031] When generating the set of candidate locations and angles for wind-resistant cables, it is essential to ensure that all candidate solutions potentially satisfy these symmetries and fundamental engineering constraints.

[0032] These constraints correspond to different core requirements in bridge construction: alignment constraints ensure the accuracy of main cable erection; tension constraints ensure the strength and operational safety of the wind-resistant cable; angle constraints ensure the effectiveness and feasibility of wind-resistant measures; and stability constraints are the fundamental safety baseline for wind-resistant design. By pre-selecting these constraints as conditions for generating candidate solutions, a large number of invalid solutions that do not meet basic engineering logic and safety requirements can be eliminated in advance, greatly improving the efficiency of subsequent optimization calculations.

[0033] When actually constructing the catenary, the maximum allowable adjustment value of the catenary alignment is determined based on the accuracy requirements of the main cable erection. D Z Determine the breaking strength based on the initially selected cable material (such as steel wire rope). T break ;set up T min To maintain the minimum tension required for a certain stiffness of the wind-resistant cable (e.g., 50kN), the upper limit of tension is set at 0.4. T break Set the included angle β The search range is 15° to 75°; the design verification wind speed is set. V d (e.g., 40m / s) and calm wind stability safety factor x (Take 1.2).

[0034] When selecting anchor points on the catwalk structure, the gantry position is automatically selected, and symmetrical anchor point pairs are generated. For each anchor point, only candidate angle values ​​within the range of [15°, 75°] for the wind-resistant cable are generated. The resulting initial set implicitly satisfies the constraints of symmetry, angle range, and feasibility.

[0035] This embodiment transforms fuzzy engineering experience—such as the prohibition of excessive linear changes, the requirement that cables be neither too loose nor too tight, the need for appropriate angles, and the requirement for sufficient stability—into precise mathematical inequalities. This provides clear boundary conditions for computer-aided design, making the scheme generation and selection process objective, quantifiable, and programmable, ensuring from the outset that all subsequent analyses are conducted within a safe and reasonable framework.

[0036] In other embodiments of this application, this embodiment provides a specific calculation method for solving the optimal tension of wind-resistant cables that satisfy linear constraints. First, for a specific wind-resistant cable location and wind-resistant cable combination, in [β min ，β max Within a set step size (e.g.) β 0 To construct computational combinations, such as combinations of position and angle ( P i ,β i ) The contribution efficiency is calculated according to the following formula: in: C i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; β i ——No. i The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; l i (p i ) ——No. i The horizontal lever arm from the anchor point of the wind-resistant cable to the mid-span or maximum displacement point of the catwalk. L i (p i ) ——No. i The length of the wind-resistant cable.

[0037] Calculate the contribution efficiency of each wind-resistant cable to suppressing the lateral displacement at the mid-span of the catwalk. C i .

[0038] Then, establish a system of equations: in: C i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; H ij ——No. j The vertical force of the wind-resistant cable on the first i Influence coefficient of vertical displacement of the catwalk at the anchor point of the wind-resistant cable; β j ——No. j The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; T0，j ——No. j The optimal tension of the wind-resistant cable, where i, j = 1, 2, 3…m, and m is the total number of wind-resistant cables; λ — a constant.

[0039] Solving this system of linear equations will yield a set of optimal tensions. T 0，i This tension allows the lateral damping effect of each wind-resistant cable to achieve the best balance with the vertical displacement effect it causes.

[0040] Contribution efficiency in the above formula C i The physical meaning is: under unit tension, a certain wind-resistant cable, due to its spatial position ( P i ) and angle ( β i The effect of limiting lateral displacement at mid-span of the catwalk, as determined by [the factor]. Contribution efficiency. C i The larger the value, the more efficient the cable arrangement. The core principle of the equations is collaborative work and deformation coordination: to minimize the vertical change in the catwalk's alignment after applying wind-resistant cable tension (satisfying...). ∆Z (Constraints) The vertical displacements of the catwalk caused by the vertical components of the wind-resistant cables must be coordinated and canceled out. The equations solved yield... T 0,i It is precisely this that makes it highly efficient (contributing to efficiency) C i The optimal distribution scheme is to ensure that the larger wind-resistant cable bears more tension, while the net vertical deformation under the combined tension of all wind-resistant cables is strictly controlled.

[0041] In actual calculations, for a wind-resistant cable at a specific location (i.e. P i (It is certain), so the angle of the wind-resistant cable needs to be set when selecting it. The angle of the wind-resistant cable starts from [ β min ，β max The process is carried out according to a set step size, assuming a set of candidate ( P i ,β i A simplified mechanical model of the catwalk was established. Based on this model, the vertical displacement of each point on the catwalk under a unit vertical force at each wind-resistant cable anchorage point was calculated, thus obtaining the influence coefficient matrix. According to (… P i ,β i Based on the geometric relationship, calculate the strength of each wind-resistant cable. l i andL i Then, their respective contribution efficiencies are calculated according to the formula. C i ;Will C i 、β i 、H ij Substitute into the above system of equations. This is a system of equations... T 0,i and l A system of linear equations with unknowns, the number of equations equals the number of wind-resistant cables plus 1 (introduction). l The solution can be obtained directly using linear algebra methods (such as matrix inversion).

[0042] Solution T 0,i This refers to the optimal working tension that satisfies the vertical alignment constraint of the catwalk (usually set to minimize change) under this candidate combination.

[0043] This embodiment provides a scientific calculation path from layout scheme to optimal tension determination. Its greatest advantage lies in solving a core problem in wind-resistant design: increasing tension can better suppress lateral sway, but excessive or unbalanced tension can cause the catwalk to become skewed. This is addressed by introducing contribution efficiency. C i By establishing deformation compatibility equations, this method can automatically find a set of tensions that maximize the lateral stiffness of the entire wind-resistant cable system while minimizing interference with the construction baseline. This is something that traditional empirical or trial-and-error methods cannot achieve precisely.

[0044] In a further embodiment of this application, the method for determining the initial cable specifications described above has been optimized. Specifically, this embodiment provides a method for initially selecting the specifications of a wind-resistant cable based on optimal tension and wind load. After obtaining the optimal tension... T 0,i Then, it is necessary to estimate the wind load at the design wind speed. q w Under the action, the first i Additional tension generated by the wind on the root wind-resistant cable ΔT i The additional tension is at the location of the wind-resistant cable. P i ,angle β i And the function of wind load. Then, calculate according to the following formula: in: A i —The first selection that satisfies the linear constraints i Cross-sectional area of ​​the wind-resistant cable; T 0，i ——No. i The optimal tension of the wind-resistant cable; f safe —The safety factor is usually set at 2.0 to 2.5; s u —Ultimate tensile strength of wind-resistant cable material; Δ T i (q w ,P,β) —At the design wind speed, the first [factor] caused by wind load i The additional tension of the wind-resistant cable is determined by the position of the wind-resistant cable. P i ,angle β i and wind load q w The function.

[0045] The wind-resistant cable bears two main loads during operation: one is the initial tension preset to provide system stiffness. T 0,i Secondly, under the action of wind, the additional wind-induced tension experienced by the cable structure itself. ΔT i Cable specifications (cross-sectional area) A i The cable must be able to withstand the combined effect of these two loads. The above formula reflects the most basic strength design principle: the maximum possible tensile force of the cable ( T 0,i +ΔT i After dividing by the safety factor, it cannot exceed the allowable stress of the material. s u / f safe ).in ΔT i The calculation needs to take into account the projected area and dynamic response of the wind-resistant cable to the wind load based on its spatial attitude.

[0046] In actual calculations, for the first i The wind-resistant cable, based on its spatial angle β i Given the diameter (which can be initially estimated), calculate its projected area under crosswind conditions, and then calculate the static wind load it bears. Apply this wind load to the cable structure calculation model of the wind-resistant cable itself (the wind-resistant cable can be simplified to a cable fixed at both ends), and solve for its tension increment. ΔT iThis process can be accomplished through simplified formulas or rapid iterative calculations; a safety factor is selected. f safe (e.g., 2.5 according to the specification) and cable material strength s u (e.g., 1770 MPa); will T 0,i 、ΔT i 、f safe ,s u Substituting into the above formula, the required minimum cross-sectional area can be calculated. A imin ;according to A imin From the wire rope product catalog, select one with a nominal cross-sectional area slightly larger than [the specified value]. A imin The standard specifications were used as the initial cable specifications for this candidate solution.

[0047] This embodiment directly links mechanical requirements with component selection. Its advantages are: 1) The load combination is comprehensive, including working tension and wind load increment, which is more in line with the actual stress. 2) A clear safety factor was introduced, and the design process was standardized and rigorous; 3) The selection process is completed quickly in the optimization cycle, providing key parameters for evaluating the economy (material usage) and effectiveness of different schemes (because the cable's own weight affects the system behavior), making the optimization no longer a pure mechanical optimization, but an optimization related to the actual cost of the project.

[0048] In a preferred embodiment of this application, this embodiment provides an index for evaluating the effectiveness of a wind-resistant cable deployment scheme: the overall system effectiveness index is calculated according to the following formula. in: S total ——No. i The overall system performance index of wind-resistant cables; m — Total number of wind-resistant cables; C i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; T 0,i ——No. i The optimal tension of the wind-resistant cable.

[0049] The overall system performance index characterizes the total effective resistance that the entire wind-resistant cable system can provide to suppress lateral displacement at the mid-span of the catwalk under optimal tension distribution.

[0050] Contribution efficiency C i This is an efficiency coefficient that measures the lateral restraint capability of a single wind-resistant cable under unit tension. It is then compared with the optimal tension actually allocated to that wind-resistant cable. T 0,i Multiplying these values ​​gives the actual contribution of that wind-resistant cable to the overall lateral stiffness of the system. Summing the contributions of all wind-resistant cables yields... S total This naturally represents the overall ability of the entire wind-resistant cable system to suppress lateral displacement of the catwalk. S total The larger the value, the better the potential effect of the arrangement in controlling the lateral static displacement of the catwalk.

[0051] The advantages of the system comprehensive performance index lie in its clear physical meaning and extremely simple calculation. It condenses the performance of a complex spatial structure system into a single scalar value. In preliminary design or when lateral displacement control is the primary objective, this index can be used to quickly and intuitively sort and initially select from a large number of candidate schemes, identifying the schemes with the strongest lateral reinforcement capabilities. This significantly narrows down the scope of subsequent detailed comparisons and improves overall design efficiency.

[0052] In some embodiments of this application, the above-described evaluation method based on multi-objective optimization values ​​has been optimized. This embodiment provides a more comprehensive scheme evaluation method by constructing an objective optimization function J. This function simultaneously considers the maximum lateral displacement of the catwalk. d h,max Maximum vertical displacement d v,max and maximum twist angle i max They were then normalized to their respective design allowable values. d h,allow 、d v,allow 、the allow The objective function is defined as: Where: minJ — the target optimization value; d h,max —Maximum lateral displacement of the catwalk; d h,allow — Allowable lateral displacement design value for catwalk; dv,max —Maximum vertical displacement of the catwalk; d v,allow — Allowable vertical displacement of the catwalk; i max —Maximum torsion angle of the catwalk; i allow — Allowable design value for catwalk torsion angle; w 1 — Lateral displacement weighting coefficient; w 2 —Vertical displacement weighting coefficient; w 3 —Twist angle weighting coefficient.

[0053] in w 1 , w 2 , w 3 These are the weighting coefficients, and w 1 +w 2 +w 3 =1 By establishing a simplified analysis model of the catwalk including wind-resistant cables, and applying the design wind load, the maximum lateral displacement of the catwalk was calculated. d h,max Maximum vertical displacement of the catwalk d v,max Maximum torsion angle of the cat path i max The J value can then be obtained.

[0054] The response of a catwalk under wind load is a complex spatially coupled deformation; simply controlling lateral displacement may induce unfavorable vertical deformation or torsion. This embodiment employs multi-objective optimization and weighted comprehensive evaluation. First, the three control objectives (displacement and torsion) with different dimensions and importance are normalized by dividing by the allowable value, transforming them into dimensionless values ​​representing utilization or safety. Then, the weighting coefficients set by the designer are used... w i The J value reflects the preference or priority of different control objectives in a specific engineering context. The smaller the J value, the better the scheme performs in terms of weighted overall performance, meaning that all responses are far from the critical state and the overall safety margin is more balanced.

[0055] In actual calculations, the design allowable values ​​for the three control objectives are determined (according to specifications or construction requirements); the weights are determined based on the actual engineering conditions, for example, for bridges where wind resistance stability is of particular concern. w 1 (Lateral displacement weight) can be taken as 0.6; for stages where the accuracy of main cable strand erection is extremely high, w 3 (Twist angle weight) can be taken as 0.5; in general, it can be taken as... w 1 =0.5, w 2 =0.3, w 3 =0.2; For a candidate solution (known) P,β,T 0 ,A The maximum lateral displacement of the catwalk under design wind load is calculated using a simplified, fast analysis model (such as a linear procedure based on the stiffness matrix). d h,max Maximum vertical displacement of the catwalk d v,max Maximum torsion angle of the cat path i max Substitute the calculation results and weights into the formula to calculate the J value of the scheme.

[0056] The calculation method in this embodiment overcomes the limitations of a single indicator (such as focusing only on lateral displacement) and more realistically reflects the working status of the catwalk. By adjusting the weighting coefficients, the same method can flexibly adapt to different bridges, different construction stages, and different risk concerns, achieving true performance-based and customized design. This is more practically valuable in engineering than fixed-weight evaluation methods.

[0057] In other embodiments of this application, the selection criteria for the optimal solution described above have been optimized. Specifically, this embodiment specifies how to select the optimal solution from all candidate solutions based on the calculated evaluation indicators. When the above-mentioned system comprehensive performance indicators are used... S total When used as an evaluation basis, select S total The candidate solution with the largest value is selected as the optimal solution. When using the above target optimization value... J When used as an evaluation basis, select J The candidate solution with the smallest value is selected as the optimal solution.

[0058] The screening method in this embodiment essentially defines a specific decision function. In optimization theory, all candidate solutions constitute a solution set. The role of the decision function is to score each solution in the solution set and rank them in total order based on the scores. System overall performance index S total It's a benefit-oriented indicator; the higher the better; target optimization value. J It is a cost-related indicator, and the smaller the better. Selecting based on this criterion transforms engineering design decisions into a mathematical optimization problem, ensuring that the final choice is an objective and unambiguous optimal solution within the given evaluation system.

[0059] In actual calculations, after calculating all N One candidate solution S total(i) or J (i) (i=1,2,...,N) After: If used S total For metrics, find the index. k , making S total(k) =max{S total(1) ,S total(2) ,...,S total(N) } The k-th solution is the optimal one; If using J For metrics, find the index. k , making J (k) =min{J (1) ,J (2) ,...,J (N) } No. k Scheme number 1 is the optimal one.

[0060] The screening method in this embodiment completely eliminates subjective preferences and controversies that may arise in the selection of alternatives, making the design conclusions highly persuasive. Furthermore, this screening method is well-suited for computer program execution, requiring only a single sorting or extreme value search operation to complete the decision, making it a crucial link between optimization calculations and the final output.

[0061] In some embodiments of this application, this embodiment optimizes the iterative adjustment when the above scheme does not meet the specifications. Specifically, this embodiment specifies the feedback and adjustment strategy to be adopted when the finite element verification based on the optimal parameters does not meet the design specifications. The adjustment direction includes two aspects: first, adjusting the candidate parameter set, such as increasing the number of wind-resistant cables, increasing the position of candidate anchor points, and reducing the search step size of the wind-resistant cable angle to perform a more refined search; second, relaxing the constraints, such as appropriately increasing the allowable deviation of the catenary profile within an acceptable range. ΔZ Alternatively, consult with structural engineers to determine if it is possible to appropriately increase the local stiffness of the catwalk itself.

[0062] The optimal solution obtained in the initial optimization fails under higher-precision model verification, indicating that a perfect solution that fully satisfies all high criteria may not exist within the current design space (defined by initial constraints and parameter set). In this case, it is necessary to expand the design space (adjust / add candidate parameters) or lower the requirements (relax constraints) to find new feasible solutions. This is an important feedback mechanism that simulates the problem-solving logic of engineers.

[0063] In practice, if the finite element analysis fails, first analyze the main reasons for the failure (such as excessive lateral displacement, excessive torsional angle, or insufficient stability); if the failure is due to excessive control parameters, try relaxing the corresponding allowable values ​​(e.g., adjusting the tolerances). ΔZ (Adjust from 10cm to 15cm), and then re-execute the optimization process; if the potential of the solution itself is insufficient, modify the candidate set: add anchor point candidate positions in key areas (such as near the middle of the span); or on the basis of the original solution, try to add a pair (two) wind-resistant cables to form a larger set of wind-resistant cable solutions, and re-optimize; substitute the adjusted new parameters or new constraints, re-run the complete process, obtain the new optimal parameters, and then verify the calculation.

[0064] This embodiment is not a rigid process, but a system with feedback and adaptive capabilities. This ensures that the method can always find an acceptable solution to the actual engineering problem, avoiding infinite loops caused by a single calculation failure, and greatly improving the practicality and robustness of the method.

[0065] In a further embodiment of this application, the method for determining compliance with the final design specifications has been optimized. Specifically, this embodiment details the specification clauses used to determine whether the final design scheme is qualified. The determination must meet all of the following conditions: 1) Critical wind speed for static instability of catwalk-wind-resistant cable system V cr ≥ξ*V d ,in xA safety factor of not less than 1.2; 2) Maximum lateral displacement of the catwalk d h,max ≤δ h,allow ; 3) Maximum vertical displacement of the catwalk d v,max ≤δ v,allow ; 4) Maximum twist angle of the catwalk i max ≤θ allow ; If all conditions are met, the design specification is deemed to be met; if any condition is not met, the design specification is deemed not met.

[0066] The first requirement is overall stability, which is the bottom line to prevent catastrophic damage and ensures a high safety factor. x Ensure sufficient safety reserves. The second, third, and fourth points concern functional and construction precision requirements, ensuring that the catwalk remains a stable and level working platform under wind loads, guaranteeing the precision of subsequent procedures such as main cable erection. These four points constitute a complete, multi-layered safety and performance evaluation system.

[0067] In practice, after obtaining the optimal parameters and establishing a high-precision finite element model, a nonlinear static wind stability analysis is performed. By gradually increasing the wind speed until the system diverges, the critical wind speed is obtained. V cr In design wind speed V d Under wind load conditions, a static analysis was performed to extract the displacement and torsional angular response contour maps of the entire catwalk structure and identify the maximum values. d h,max ,d v,max , i max ;Will V cr Compared with 1.2 V d The comparison involves comparing the maximum value of the three responses with their respective allowable values; a logical AND operation is then performed: if: (V cr ≥1.2V d )&&(d h,max ≤δ h,allow )&&(d v,max ≤δ v,allow )&&(θmax ≤θ allow ) If the verification is successful, output "Verification passed"; otherwise, output "Verification failed" and proceed to the above example.

[0068] This embodiment integrates the specific requirements of industry standards into the endpoint of the methodology, ensuring that the output of the entire design method directly aligns with national or industry mandatory standards, thus guaranteeing the legality and compliance of the design results. Simultaneously, it places the most crucial and time-consuming detailed numerical simulation in the final verification stage, rather than performing it in every optimization step, forming a highly efficient model that combines rapid screening and optimization with precise simulation verification.

[0069] When implementing the design method for the static wind stability control structure of the catwalk of the spatial cable suspension bridge in this application, such as... Figure 2 As shown, the wind-resistant design of the construction catwalk for a 520-meter main span spatial cable suspension bridge is used as an example to illustrate the complete design process by comprehensively applying all the above embodiments.

[0070] Step 1: Initialization and Candidate Solution Generation Input: The catwalk span is 520m; the catwalk gantry numbers are defined from south to north bank as 1 to 9; the wind-resistant cables are 6×36WS+IWR galvanized steel wire ropes with a strength of 1960MPa; in the model, six positions of the wind-resistant cables on the gantry and five angles between the wind-resistant cables and the longitudinal vertical plane of the bridge were selected. β There are a total of 60 layout schemes, as shown in Table 1. Table 1 Wind-resistant cable layout scheme Design reference wind speed V d =45m / s, catwalk alignment control requirements ΔZ =0.15m.

[0071] Procedure: On both sides of the catwalk, design anchor points for the wind-resistant cables and the catwalk according to the gantry positions in Table 1, and set anchor points on the lower side of the catwalk. For each anchor point, consider five angles β=15°, 30°, 45°, 60°, and 75° to generate left-right symmetrical combinations, and initially obtain the candidate layout scheme set in Table 1.

[0072] Step 2: Single-Solution Optimization Analysis Loop operate: Calculate contribution efficiency C i For scheme A (for example, installing wind-resistant cables at points 1, 3, 7, and 9 of the gantry, with β = 40°, such as...) Figure 2 As shown), the wind-resistant cable is calculated based on its geometric relationship.l i and L i Substitute into the formula to find their respective C i .

[0073] Solving for optimal tension T 0,i Establish a simplified catwalk support system model and calculate the influence matrix. H ;Will C i 、β i 、H Substituting into the equilibrium equations and solving the linear equations, the optimal tension of the eight wind-resistant cables under this scheme is obtained. T (0,1) ~T (0,8) .

[0074] Preliminary selection of cable specifications A i Estimate the additional tension of each wind-resistant cable under a wind speed of 45 m / s. ΔT i Take a safety factor f safe =2.5, calculate the required cross-sectional area. A imin Select standard specifications (e.g., Φ48mm) from the product library. A =803mm 2 ).

[0075] Step 3: Evaluation and Comparison of Options operate: Calculate evaluation metrics: After completing step two, you can choose any of the following methods to evaluate all candidate solutions: Method 1: Calculate the overall system performance index for each scheme. S total ; Method 2: Establish a rapid analysis model of the catwalk including wind-resistant cables, and calculate the wind load of each scheme. d h,max , d v,max ,i max Set weights w 1 =0.5, w 2 =0.2, w 3 Given 0.3 and the corresponding allowable value, calculate the objective function J; Selecting the optimal solution: Based on the indicators used, select...S total The scheme with the largest or smallest J is denoted as the "initial optimal scheme". Suppose that scheme B (wind-resistant cables are installed at positions 1, 2, 8, and 9, with a β=50° combination) wins.

[0076] Step 4: Detailed Verification and Iteration operate: Establish a high-precision finite element model: Using the precise parameters (position, angle, tension, specifications) of Scheme B, establish a three-dimensional nonlinear finite element model to accurately simulate the catwalk cable net, wind-resistant cable, connectors, etc. Perform compliance verification of the specifications: A calm wind stability analysis was performed, and the results were obtained. V cr =58m / s; Inspection: 1.2 V d =54m / s, V cr (58)>54, passed.

[0077] Static analysis was performed with a wind load of 45 m / s, and the results were: d h,max =1.8m, d v,max =0.12m, i max =0.8°; Set tolerance values: d h,allow =2.0m, d v,allow =0.15m, i allow =1.0°; Check: All response values ​​are less than the allowable value, pass.

[0078] Output results: All calculations passed, and Scheme B is deemed to meet the design specifications. All design parameters of Scheme B (wind-resistant cable anchorage coordinates, spatial angle, installation tension, and wire rope specifications) are output as the basis for the final construction drawing design.

[0079] (Assumption: If the verification finds...) i max If 1.2° > 1.0°, then it fails. The process then proceeds to adjustment: for example, by adjusting the weights. w 3 Increase the value from 0.3 to 0.4 and re-compare the options; or, based on option B, add a pair of small-angle wind-resistant cables near the mid-span to suppress torsion, generate a new set of options, and re-optimize until a solution that passes the verification is found. The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of this application as claimed. The scope of protection of this application is defined by the appended claims and their equivalents.

Claims

1. A structural design method for controlling the static wind stability of a catwalk on a spatial cable suspension bridge, characterized in that, include: Based on the catwalk parameters, design wind speed, allowable deviation of catwalk alignment, and available gantry locations on the catwalk, list all candidate locations and angles for wind-resistant cables that satisfy the symmetry constraint. For each candidate position and angle combination of the wind-resistant cable in the set, the optimal tension of the wind-resistant cable that satisfies the linear constraint and the corresponding preliminary wind-resistant cable specification are calculated. For each combination, based on its optimal tension and initially selected cable specifications, calculate the overall system performance index or target optimization value for that combination. Based on the system's comprehensive performance index or target optimization value, the optimal wind-resistant cable position, angle, tension, and cable specification parameters are selected from the set. The optimal parameters are substituted into the finite element model for verification and analysis to determine whether they meet the design specifications. If they do, the wind-resistant cable arrangement position and angle corresponding to the optimal parameters are taken as the final design scheme.

2. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, Construct constraints according to the following formula. in: ΔZ catwalk —The change in the alignment of the catwalk after the installation of wind-resistant cables; ΔZ —The catwalk line describes the value; T min —Minimum tension of the wind-resistant cable in working condition; T i ——No. i The tension of the wind-resistant cable in operation; T break —Critical value for tensile fracture of wind-resistant cable; β i ——No. i The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; V cr —Critical wind speed at which the catwalk-wind-resistant cable system becomes unstable in still wind; V d —Design test wind speed; ξ —Wind speed coefficient; Based on the above constraints, a set of all candidate locations for wind-resistant cables that satisfy the symmetry constraints is listed.

3. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, The method for calculating each candidate position and angle set of the wind-resistant cable includes: calculating within a set angle range between the wind-resistant cable and the longitudinal vertical plane of the bridge according to a set angle step, and calculating the optimal tension that satisfies the alignment constraints according to the following formula. in: Γ i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; H ij ——No. j The vertical force of the wind-resistant cable on the first i Influence coefficient of vertical displacement of the catwalk at the anchor point of the wind-resistant cable; β j ——No. j The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; T 0，j ——No. j The optimal tension of the wind-resistant cable, where i, j = 1, 2, 3…m, and m is the total number of wind-resistant cables; λ — constant.

4. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 3, characterized in that, Calculate the first unit length and unit tension using the following formula. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catenary under specific positions and angles. in: Γ i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; β i ——No. i The angle between the wind-resistant cable and the longitudinal vertical plane of the bridge; l i (p i ) ——No. i The horizontal lever arm from the anchor point of the wind-resistant cable to the mid-span or maximum displacement point of the catwalk. L i (p i ) ——No. i The length of the wind-resistant cable.

5. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 3, characterized in that, The method for determining the initial cable specifications that satisfy the linear constraints includes: calculating the initial cable specifications that satisfy the linear constraints according to the following formula. in: A i —The first selection that satisfies the linear constraints i Cross-sectional area of ​​the wind-resistant cable; T 0，i ——No. i The optimal tension of the wind-resistant cable; f safe —Safety factor; σ u —Ultimate tensile strength of wind-resistant cable material; Δ T i (q w ,P,β) —At the design wind speed, the first [factor] caused by wind load i The additional tension of the wind-resistant cable is determined by the position of the wind-resistant cable. P i ,angle β i and wind load q w The function.

6. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, The methods for calculating the overall system performance index include: calculating the overall system performance index according to the following formula, in: S total ——No. i The overall system performance index of wind-resistant cables; m — Total number of wind-resistant cables; Γ i ——No. i The contribution efficiency of the wind-resistant cable in suppressing the lateral displacement at the mid-span of the catwalk; T 0,i ——No. i The optimal tension of the wind-resistant cable.

7. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, Methods for calculating the target optimization value include: in: minJ —Target optimization value; δ h,max —Maximum lateral displacement of the catwalk; δ h,allow — Allowable lateral displacement design value for catwalk; δ v,max —Maximum vertical displacement of the catwalk; δ v,allow — Allowable vertical displacement of the catwalk; θ max —Maximum torsion angle of the catwalk; θ allow — Allowable design value for catwalk torsion angle; w 1 — Lateral displacement weighting coefficient; w 2 —Vertical displacement weighting coefficient; w 3 —Twist angle weighting coefficient.

8. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, The method for selecting the optimal parameters based on the system comprehensive performance index or the target optimization value includes: when using the system comprehensive performance index, selecting the candidate position and angle combination of the wind-resistant cable with the largest index as the optimal parameters; When using the target optimization value, the candidate position and angle combination of the wind-resistant cable with the smallest value is selected as the optimal parameter.

9. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, If the design specifications are not met, adjust the set of candidate parameters or relax the constraints and recalculate.

10. The design method for a static wind stability control structure of a catwalk for a spatial cable suspension bridge according to claim 1, characterized in that, The methods for determining whether the design specifications are met include: The critical wind speed for static wind instability of the catwalk-wind-resistant cable system shall not be less than the product of the design test wind speed and the wind speed coefficient, and the wind speed coefficient shall be a safety factor of not less than 1.

2. The maximum lateral displacement, maximum vertical displacement, and maximum torsional angle of the catwalk shall not exceed their respective design allowable values; If the above conditions are met, then the design specifications are deemed to be met; otherwise, they are not.

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