Spatial self-anchored suspension bridge main cable shape finding calculation method

Abstract

The invention discloses a spatial self-anchored suspension bridge main cable shape finding calculation method, and belongs to the field of bridge structure design, and the method comprises the following steps: S1, initializing an iteration initial value; s2, respectively carrying out iterative calculation on node relations of the slings and single main cable sections between the slings, and completing iterative calculation of each cable section of the main cable; s3, carrying out deformation compatibility condition judgment on the main cable; s4, if the error precision is not met, calculating the correction amount of the iteration initial value, updating the initial force iteration value, and executing S2; s5, if the error precision is met, other main cable crossing calculation is carried out, and S1 to S4 are repeated; s6, performing finite element calculation; s7, checking whether the error between the coordinate value of the control point of the main beam model and the design value meets the precision requirement or not; if not, correcting the initial strain of the main beam and returning to S6; and if yes, executing S8: taking the counter force at the vertical constraint position of the model obtained in the step S7 as the vertical force borne by the corresponding sling at the anchoring point of the stiffening beam until the main cable line shape at the moment is determined to be the final line shape in the bridge forming state.

Description

Technical Field

[0001] This invention relates to the field of bridge structure design, specifically to a method for calculating the form of the main cable of a spatial self-anchored suspension bridge. Background Technology

[0002] Spatial self-anchored suspension bridges are a unique bridge structure. Their main cables and suspenders form a stable three-dimensional cable system, giving them numerous advantages. For example, in terms of mechanical performance, the spatial self-anchored suspension bridge uses a spatial main cable system, which significantly improves lateral and torsional stiffness compared to planar cable suspension bridges, resulting in stronger wind resistance and better dynamic stability. Furthermore, unlike traditional ground-anchored suspension bridges, the self-anchored main cable is anchored to the main girder, eliminating the need for anchorage facilities, thus saving construction costs and providing greater adaptability to different terrains. Moreover, in terms of aesthetics, spatial self-anchored suspension bridges are visually appealing and often become urban landmarks, such as the San Francisco-Oakland Bay Bridge and the Jinan Phoenix Road Yellow River Bridge, and are widely used in urban, municipal, and scenic bridge construction. Due to these advantages, spatial self-anchored suspension bridges play a vital role in modern bridge construction, especially in urban bridge construction.

[0003] However, the anchorage of the main cable and main girder in a spatial self-anchored suspension bridge exhibits a coupling effect, and the mechanical behavior of the cable structure typically displays strong geometric nonlinearity. Furthermore, the complexity of the spatial main cable suspension bridge system, with its multi-directional coupled forces, undoubtedly increases the difficulty of calculating the main cable alignment. Simultaneously, spatial self-anchored suspension bridges belong to a tower-beam-cable self-balancing system, where the main cable alignment and the tension in the suspenders affect the bridge's final state. Therefore, main cable alignment calculations based on a reasonable final bridge state are crucial for improving the structure's safety and economy.

[0004] Currently, the main cable alignment calculation for spatial self-anchored suspension bridges is mostly accomplished by establishing a detailed finite element model of the entire bridge. Although this method can achieve the main cable alignment calculation to a certain extent, the entire calculation process is cumbersome, inefficient, and prone to non-convergence, exhibiting significant limitations. How to quickly and effectively calculate the main cable alignment of spatial self-anchored suspension bridges under reasonable bridge completion conditions has become an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] To address one or more of the aforementioned deficiencies or improvement needs in existing technologies, this invention provides a method for calculating the form-finding of the main cable of a spatial self-anchored suspension bridge. This method can accurately calculate the form-finding of the main cable of a spatial self-anchored suspension bridge, and has advantages such as high computational efficiency and accuracy meeting design requirements. It is fully adaptable to the design and calculation needs of spatial self-anchored suspension bridges. To achieve the above objectives, the present invention provides a method for calculating the form of the main cable of a spatial self-anchored suspension bridge, which includes the following steps: S1: Obtain the basic design parameters of the spatial self-anchored suspension bridge and use them to initialize the initial values ​​of the iteration; among which, the initial values ​​of the iteration include the initial value of the vertical force of the suspenders at the anchorage point of the stiffening girder and the initial force iteration value of the main cable at the end anchorage point; S2: Using the spatial force system equilibrium relationship and the spatial segmented catenary theory, the node relationships of the suspenders and individual main cable segments between suspenders are iteratively calculated based on the initial iterative values, and the iterative calculation of each cable segment of the main cable is completed accordingly. S3: Determine the deformation compatibility condition of the main cable; if the relative error value... Not greater than the allowable error If the error accuracy is met, the calculation for this main cable span is completed, and step S5 is executed; if the error accuracy is not met, step S4 is executed. S4: Calculate the correction amount of the initial iteration value and update the initial force iteration value, then return to execute step S2; S5: Proceed to the calculation of other main cables, repeat steps S1~S4, and complete the full bridge main cable form-finding calculation of the spatial self-anchored suspension bridge. S6. Based on the internal force values ​​of the main cable obtained in S5 and the initial alignment of the stiffening girder of the spatial self-anchored suspension bridge, establish a finite element model of a rigidly supported continuous beam containing only the main girder, and complete the finite element calculation. S7. Check whether the error between the calculated coordinate values ​​of the control points of the main beam model and the design values ​​meets the accuracy requirements; if yes, extract the reaction force at the vertical constraint of the model and execute step S8; if no, correct the initial strain of the main beam of the rigid support continuous beam finite element model through the error value of the main beam control points, and return to step S6 for calculation. S8. The reaction force at the vertical constraint point of the model obtained in step S7 is taken as the vertical force borne by the suspender at the anchor point of the stiffening beam. ,calculate The initial value of the vertical force of the suspender at the anchorage point of the stiffening beam during the form-finding of the main cable in this round of space. relative error ;like If so, then the main cable alignment at this point is considered to be the alignment of the final bridge-completed state, where, The initial value is the allowable relative error of the vertical force at the anchor point of the sling; otherwise, the initial value of the vertical force at the anchor point of the stiffening beam is corrected. Repeat steps S2 to S5.

[0006] As a further improvement to the present invention, the basic design parameters preferably include the following design contents: (1) Foundation design parameters for the main cable and slings, including elastic modulus, cross-sectional area and material density; (2) The main cable at the anchor point at the top of the tower and the cable release point at the side span , , Coordinate values; vertical sag of the main cable in the mid-span and design lateral verticality ; (3) Spacing of plane suspension cables along the longitudinal direction of the bridge and the anchorage points of the slings and stiffening beams , , Coordinate values; (4) Design alignment and structural parameters of the stiffening girder and the average unit weight of the stiffening girder when the dead load is uniformly distributed. .

[0007] As a further improvement of the present invention, the initial values ​​for initialization iteration include calculating the initial value of the vertical force of the suspender at the anchorage point of the stiffening beam using the uniformly distributed mass method, and calculating the initial force iteration value of the main cable at the end anchorage point based on the parabolic theory of the cable shape; the relevant calculation formulas are as follows:

[0008]

[0009] In the formula, For the first The vertical force borne by the suspender cable at the anchorage point of the stiffening beam; The dead load of the stiffening beam is changed to a uniformly distributed average unit weight; For slings The length of the stiffening girder bearing the average weight; , , The anchor points at the main cable ends are respectively , , The force of three parts towards; Main cable sag; The length of the stiffening girder corresponding to the main cable; To widen the stiffening beam; It is the ratio of lateral sag to half beam width.

[0010] As a further improvement to the present invention, the iterative calculation of each cable segment of the main cable includes:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] In the formula, , and These are the elastic modulus, effective cross-sectional area, and weight of the main cable, respectively. Main cable The stress-free length of the segment; , , The first Main cable end node exist , and The main cable component force; , , The first Main cable end node exist , and The main cable component force; For the first Main cable end node The horizontal resultant force; , and The first The main cable section is in , and Length of direction; The weight of the sling; and respectively slings At the rope clamp and Component force; and respectively slings At the stiffening girder anchorage point and Component forces, satisfying the relationship ; , These are the connection points between the slings and the main cable. place and To coordinates; , These are the main cable at the end anchor point. and To coordinates.

[0022] As a further improvement of the present invention, the relative error value The calculations include:

[0023]

[0024] In the formula, Main cable end design anchor points The difference in direction; when calculating the side span, The main cable between the anchorage points of the main tower and the stiffening girder When calculating the distance difference between the two spans, The lateral sag of the main cable in the middle span is designed; Design sag for the main cable in the mid-span; calculate the sag for the side spans. and All are the number of main cable segments. When calculating the mid-span, if there are suspension cables in the span, Number of main cable segments This is half the number of main cable segments. If there are no suspenders in the middle of the span, it is equivalent to having suspenders in the middle of the span, and the corresponding suspender force is zero. , and These represent the error between the calculated value and the corresponding design value; This represents the allowable deviation value for the coordinates.

[0025] As a further improvement of the present invention, in S4, the correction amount of the initial force iteration value of the main cable at the end anchor point is calculated according to the influence matrix method, and the initial force iteration value of the main cable at the end anchor point is updated. This process is preferably as follows: (4.1) Solve separately , and The corresponding changes in error are obtained, and the influence matrix is ​​constructed:

[0026] Among them, the influence matrix The elements in the first, second, and third columns are respectively , and Caused error , and The amount of change; (4.2) Solving for the initial value correction vector : ; (4.3) Anchor the main cable end at , , The force is corrected to three parts as follows: , and ;in, This is the reduction factor.

[0027] As a further improvement to the present invention, let the first... In the next iteration, the iteration variable is: , , The first result calculated according to the influence matrix The increment of the variable in the next iteration is , , Introducing a reduction factor The subsequent calculations are as follows:

[0028] when ,or ,or hour:

[0029] when ,or ,or hour: .

[0030] As a further improvement of the present invention, in S5, the calculation order is to calculate the middle span first and then the side spans.

[0031] As a further improvement of the present invention, when performing finite element calculation in S6, the effect of the sling on the main beam is replaced by vertical constraint, the effect of the main cable on the main beam is ignored, and the horizontal and vertical components of the spatial main cable calculated in steps S1 to S5 are applied at the main cable detachment point of the main beam to complete the geometric nonlinear model finite element calculation considering large displacement effect and beam-column effect.

[0032] The aforementioned improved technical features can be combined with each other as long as they do not conflict with each other.

[0033] In summary, the beneficial effects of the above-described technical solutions conceived by this invention compared with the prior art include: This invention discloses a method for calculating the form-finding of the main cable of a spatial self-anchored suspension bridge, comprising the following steps: S1: Initialize the initial values ​​for iteration; S2: Based on the initial values ​​for iteration, perform iterative calculations on the nodes of the suspenders and individual main cable segments between suspenders, and complete the iterative calculations for each cable segment of the main cable accordingly; S3: Deformation compatibility condition determination for the main cable; S4: If the error accuracy is not met, calculate the correction amount of the initial values ​​for iteration and update the initial force iteration value, and return to execute S2; S5: If the error accuracy is met, proceed to the calculation of other main cables, and repeat S1~S4; S6: Perform finite element calculation; S7: Check whether the error between the calculated coordinate values ​​of the control points of the main beam model and the design values ​​meets the accuracy requirements; if not, correct the initial strain of the main beam and return to S6; if yes, execute S8: Use the reaction force at the vertical constraint point of the model obtained in step S7 as the vertical force borne by the corresponding suspender at the anchorage point of the stiffening beam. This continues until the main cable alignment at this point is determined to be the final alignment of the completed bridge.

[0034] The method for calculating the form-finding of the main cable of a spatial self-anchored suspension bridge in this invention is based on a reasonable completed bridge state. It uses a combination of numerical calculation and finite element simulation to repeatedly correct the completed bridge alignment while continuously adjusting the cable tension, ultimately ensuring it meets design requirements. The entire method is simple, convenient to operate, fully meets the needs of engineering design, and has advantages such as high computational efficiency and clear concepts, showing broad application prospects. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of the spatial self-anchored suspension bridge main cable form-finding calculation method in an embodiment of the present invention; Figure 2 This is a structural schematic diagram of a spatial self-anchored suspension bridge in an embodiment of the present invention; including (a) a partial schematic diagram; and (b) a schematic diagram of the rigid support continuous beam method. Figure 3 This is a simplified calculation diagram of the main cable in the embodiment of the present invention; it includes (a) a simplified calculation diagram of the overall main cable; and (b) a simplified calculation diagram of a part of the main cable. Figure 4 This is a diagram illustrating the geometric relationship of the slings and their stress relationship with the main cable in an embodiment of the present invention; Figure 5 , Figure 6 This is a diagram showing the bridge layout and standard cross-section of a spatial self-anchored suspension bridge in an embodiment of the present invention. Figure 7 This is a partial schematic diagram of the spatial main cable alignment of a spatial self-anchored suspension bridge calculated using the algorithm described in this embodiment of the invention. Figures 8-11 It is the result of the completed bridge state after the spatial self-anchored suspension bridge is calculated using an algorithm to determine the spatial main cable alignment. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0038] In the description of this invention, it should be understood that, unless otherwise expressly specified and limited, the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," etc., indicating the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and are not intended to 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 invention.

[0039] Furthermore, unless otherwise expressly defined, 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 indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise expressly and specifically defined.

[0040] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; 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 of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0041] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0042] Below, for reference Figures 1-11 This invention describes a method for calculating the form of the main cable of a spatial self-anchored suspension bridge according to a preferred embodiment of the present invention.

[0043] Specifically, the preferred embodiment of the spatial self-anchored suspension bridge main cable form-finding calculation method includes the following process: S1: Obtain the basic design parameters of the spatial self-anchored suspension bridge and use them to initialize the initial values ​​of the iteration; among which, the initial values ​​of the iteration include the initial value of the vertical force of the suspenders at the anchorage point of the stiffening girder and the initial force iteration value of the main cable at the end anchorage point; Specifically, the basic design parameters in the preferred embodiment preferably include the following design contents: (1) Foundation design parameters for the main cable and slings, including elastic modulus, cross-sectional area and material density; (2) The main cable at the anchor point at the top of the tower and the cable release point at the side span , , Coordinate values; vertical sag of the main cable in the mid-span and design lateral verticality ; (3) Spacing of plane suspension cables along the longitudinal direction of the bridge and the anchorage points of the slings and stiffening beams , , Coordinate values; (4) Design alignment and structural parameters of the stiffening girder and the average unit weight of the stiffening girder when the dead load is uniformly distributed. .

[0044] Simultaneously, the initial values ​​for the initial iteration are optimized by calculating the initial vertical force of the suspender cable at the stiffening girder anchorage point using the uniformly distributed mass method, and by calculating the initial force iteration value of the main cable at the end anchorage point based on the parabolic theory of the cable shape. The relevant calculation formulas are as follows:

[0045]

[0046] In the formula, For the first The vertical force borne by the suspender cable at the anchorage point of the stiffening beam; The dead load of the stiffening beam is changed to a uniformly distributed average unit weight; For slings The length of the stiffening girder bearing the average unit weight is, in actual calculations, equal to the length of the first stiffening girder. The main cable section is in Length of direction ; , , The anchor points at the main cable ends are respectively , , The force of three parts towards; Main cable sag; The length of the stiffening girder corresponding to the main cable; To widen the stiffening beam; It is the ratio of lateral sag to half beam width.

[0047] S2: Using the spatial force system equilibrium relationship and the spatial segmented catenary theory, the node relationships of the suspenders and individual main cable segments between suspenders are iteratively calculated based on the initial iterative values, and the iterative calculation of each cable segment of the main cable is completed accordingly. Specifically, the iterative calculations for each cable segment of the main cable include:

[0048]

[0049]

[0050]

[0051] In the formula, , and These are the elastic modulus, effective cross-sectional area, and weight of the main cable, respectively. Main cable The stress-free length of the segment; , , The first Main cable end node exist , and The main cable component force; For the first Main cable end node The horizontal resultant force; , and The first The main cable section is in , and Length of direction; like Figure 4 As shown, the planar sling Force balance calculations include:

[0052]

[0053]

[0054]

[0055] In the formula, The weight of the sling; and respectively slings At the rope clamp and Component force; and respectively slings At the stiffening girder anchorage point and Component forces, satisfying the relationship ; , These are the connection points between the slings and the main cable. place and To coordinates; , These are the main cable at the end anchor point. and To coordinates.

[0056] like Figure 3 As shown, the first The force balance calculation for the main cable segment includes:

[0057]

[0058]

[0059] In the formula, , , The first Main cable end node exist , and The force of the main cable is directed towards the main cable.

[0060] S3: Determine the deformation compatibility condition of the main cable; if the error accuracy is met, i.e., the relative error value is not greater than the allowable error ( If the error accuracy is not met, then the calculation for this main cable span is completed, and step S5 is executed; if the error accuracy is not met, then step S4 is executed. Specifically, relative error value The calculations include:

[0061]

[0062] In the formula, Main cable end design anchor points The difference in direction; when calculating the side span, The main cable between the anchorage points of the main tower and the stiffening girder When calculating the distance difference between the two spans, The lateral sag of the main cable in the middle span is designed; Design sag for the main cable in the mid-span; calculate the sag for the side spans. and All are the number of main cable segments. When calculating the mid-span, if there are suspension cables in the span, Number of main cable segments This is half the number of main cable segments. If there are no suspenders in the middle of the span, it is equivalent to having suspenders in the middle of the span, and the corresponding suspender force is zero. , and These represent the error between the calculated value and the corresponding design value; This represents the allowable deviation value for the coordinates.

[0063] S4: Calculate the correction amount of the initial iteration value and update the initial force iteration value, then return to execute step S2; In actual calculations, the correction amount of the initial force iteration value of the main cable at the end anchor point is calculated based on the influence matrix method, and the initial force iteration value of the main cable at the end anchor point is updated. This process is preferably as follows: (4.1) Solve separately , and The corresponding changes in error are obtained, and the influence matrix is ​​constructed:

[0064] Among them, the influence matrix The elements in the first, second, and third columns are respectively , and Caused error , and The amount of change.

[0065] (4.2) Solving for the initial value correction vector :

[0066] (4.3) Anchor the main cable end at , , The force is corrected to three parts as follows: , and ;in, This is the reduction factor.

[0067] Specifically, to ensure that the correction amount does not jump too much and to avoid the iterative variable changing sign, a reduction coefficient is introduced. To ensure the convergence of the computation. At this point, let the... In the next iteration, the iteration variable is: , , The first result calculated according to the influence matrix The increment of the variable in the next iteration is , , Introducing a reduction factor After appropriate adjustments, calculate using the following formula:

[0068] when ,or ,or hour:

[0069] when ,or ,or hour: .

[0070] S5: Proceed to the calculation of other main cables, repeat steps S1~S4, and complete the main cable form-finding calculation of the entire spatial self-anchored suspension bridge.

[0071] In actual calculations, the preferred order is to calculate the middle span first, followed by the side spans. That is, the longitudinal horizontal component of the main cable force along the bridge direction is calculated first from the middle span. Then, based on the principle that the longitudinal horizontal components of the main cable force along the bridge direction are equal on both sides of the tower top, the side spans are calculated. The longitudinal horizontal force of the main cable in the middle span is used as the basis for calculating the main cable force in the side spans. Given the parameters, the vertical load on the main cable of the side span. and transverse horizontal force Iterative calculations are performed, using the vertical height difference and lateral offset between the side span cable scattering point and the tower apex as boundary conditions. Steps S1 to S4 are used to iteratively solve the alignment of the side span main cable to complete the alignment calculation of the main cable.

[0072] S6. Based on the internal force values ​​of the main cable obtained in S5 and the initial alignment of the stiffening girder of the spatial self-anchored suspension bridge, establish a finite element model of a rigidly supported continuous beam containing only the main girder, and complete the finite element calculation. In actual calculations, the effect of the suspenders on the main beam is preferably replaced by vertical constraints, and the effect of the main cable on the main beam is ignored. The horizontal and vertical components of the spatial main cable calculated in steps S1 to S5 are applied at the main cable release point of the main beam to complete the geometric nonlinear model finite element calculation considering large displacement effects and beam-column effects.

[0073] S7. Check whether the error between the calculated coordinates of the control points of the main beam model and the design values ​​meets the accuracy requirements (e.g., ±1cm). If yes, extract the reaction force at the vertical constraint of the model and execute step S8. If no, correct the initial strain of the main beam of the rigidly supported continuous beam finite element model by using the error value of the main beam control points, and return to step S6 for calculation.

[0074] S8. The reaction force at the vertical constraint point of the model obtained in step S7 is taken as the vertical force borne by the suspender at the anchor point of the stiffening beam. ,calculate The initial value of the vertical force of the suspender at the anchorage point of the stiffening beam during the form-finding of the main cable in this round of space. relative error ;like If so, then the main cable alignment at this point is considered to be the alignment of the final bridge-completed state, where, The initial value is the allowable relative error of the vertical force at the anchor point of the sling; otherwise, the initial value of the vertical force at the anchor point of the stiffening beam is corrected. Repeat steps S2 to S5.

[0075] In a specific preferred embodiment, the bridge type and bridge end face selection of the spatial self-anchored suspension bridge are as follows: Figure 5 , Figure 6 As shown in the image.

[0076] Following the aforementioned steps S1~S8, the main cable alignment of the spatial self-anchored suspension bridge is calculated, and the resulting spatial main cable alignment is as follows: Figure 7 As shown in the figure, using this main cable alignment, a finite element model of the entire bridge was established for bridge completion calculations, and the calculation results are as follows. Figures 8-11 As shown in the image.

[0077] The calculation results show that, after the main cable shape-finding calculation, the stiffening girder has a very small vertical deflection and uniform stress at the upper and lower edges, and the bridge alignment meets the engineering design requirements.

[0078] The method for calculating the form-finding of the main cable of a spatial self-anchored suspension bridge in this invention is based on a reasonable completed bridge state. It uses a combination of numerical calculation and finite element simulation to repeatedly correct the completed bridge alignment while continuously adjusting the cable tension, ultimately ensuring it meets design requirements. The entire method is simple, convenient to operate, fully meets the needs of engineering design, and has advantages such as high computational efficiency and clear concepts, showing broad application prospects.

[0079] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for shape finding of a main cable of a spatial self-anchored suspension bridge, characterized in that, The method comprises the following steps: S1: obtaining basic design parameters of the spatial self-anchored suspension bridge and initializing iteration initial values based on the basic design parameters; wherein the iteration initial values comprise vertical force initial values of the hangers at the stiffening beam anchorage points and initial force iteration values of the main cables at the end anchorage points; S2: based on the iteration initial values, performing iteration calculation on the node relationship of the hangers and single main cable segment between the hangers by using spatial force system balance relationship and spatial segmented catenary theory, and completing iteration calculation on each cable segment of the main cables; S3: deformation compatibility condition of the main cable is determined; if the relative error value is not greater than the allowable error , the error precision is met, the calculation of the main cable of the current span is completed, and step S5 is executed; if the error precision is not met, step S4 is executed. S4: calculating a correction amount of the iteration initial values and updating the initial force iteration values, and returning to step S2 for execution; S5: switching to calculation of other spans of the main cables, repeating steps S1-S4, and completing the main cable form finding calculation of the spatial self-anchored suspension bridge; S6: establishing a rigid support continuous beam finite element model containing only the main beam according to the main cable internal force values obtained in S5 and the initial shape of the stiffening beam of the spatial self-anchored suspension bridge, and completing finite element calculation; S7: checking whether the error between the control point coordinate values of the calculated main beam model and the design values meets the accuracy requirement; if yes, extracting the reaction force at the vertical restraint of the model and executing step S8; if not, correcting the initial strain of the main beam of the rigid support continuous beam finite element model through the error values of the main beam control points, and returning to step S6 for calculation; S8: take the vertical force of the model obtained in step S7 at the vertical constraint as the vertical force of the corresponding sling at the stiffening girder anchorage point , calculate the relative error of the initial value of the vertical force of the sling at the stiffening girder anchorage point when finding the shape of the main cable of the wheel space ; if , it is considered that the main cable shape at this time is the final bridge state shape, wherein is the allowable value of the vertical force relative error of the sling lower anchorage point; otherwise, the initial value of the vertical force of the sling at the stiffening girder anchorage point is corrected to , and steps S2-S5 are re-executed.​ 2. The method for form finding of the main cable of a spatial self-anchored suspension bridge according to claim 1, characterized in that, The basic design parameters preferably comprise the following design contents: (1) basic design parameters of the main cables and the hangers, including elastic modulus, cross-sectional area and material density; (2) the vertical sag of the main cable at the tower top anchorage and the side span splay anchorage , , coordinate value; vertical sag of the main cable in the midspan and design lateral sag ; (3) Spacing of planar hangers in the bridge longitudinal direction and the hanger to stiffening girder anchorage point , , Coordinate value; (4) the design alignment and the construction parameters of the stiffening beam and the average specific weight of the uniform load of the stiffening beam .

3. The method for form finding of the main cable of a spatial self-anchored suspension bridge according to claim 2, characterized in that, The initialization of the iteration initial values comprises calculating the vertical force initial values of the hangers at the stiffening beam anchorage points by using the uniform mass method, and calculating the initial force iteration values of the main cables at the end anchorage points according to the parabolic theory of cable shape; the related calculation formulas are as follows: wherein, is the average dead weight of the stiffening girder; is the vertical force taken by the root sling at the stiffening girder anchorage point; is the average dead weight of the stiffening girder where the stiffening girder dead load becomes uniform; is the average dead weight taken by the sling is the length of the stiffening girder for the average dead weight taken by the sling , , are the three components of the main cable end anchorage point in the directions of the stiffening girder , , are the three components of the main cable end anchorage point in the directions of the stiffening girder is the sag of the main cable; is the corresponding stiffening girder length of the main cable; is the stiffening girder width; is the ratio of the transverse sag to the half girder width.

4. The method for form finding of the main cable of a spatial self-anchored suspension bridge according to claim 3, characterized in that, The iteration calculation of each cable segment of the main cables comprises: wherein, , , are the elastic modulus, the effective cross-sectional area and the specific weight of the main cable, respectively; is the unstressed length of the main cable in the first segment; , , , are the end node coordinates of the main cable in the first segment in the directions , are the main cable component forces in the directions , , , , , are the end node coordinates of the main cable in the second segment in the directions , are the main cable component forces in the directions , , , is the horizontal resultant force of the main cable at the end node of the second segment; , , , , are the lengths of the main cable in the first segment in the directions , , , , is the specific weight of the sling; and are the sling component forces in the directions at the cable clamp, and , and are the sling component forces in the directions at the stiffening girder anchorage point, and , ; , are the coordinates of the sling and main cable connection point in the directions , , , , are the coordinates of the main cable at the end anchor point in the directions , .

5. The method of claim 4, wherein, Relative error values The calculation of the relative error values comprises: In the formula, The distance between the anchorage points for the main cable end design The difference in the distance; calculate the side span, The distance between the anchorage points for the main cable between the main tower and the stiffening beam The difference in the distance; calculate the side span, Design the lateral sag for the main cable of the middle span; Design the sag for the main cable of the middle span; calculate the side span, And Both are the number of main cable segments, calculated for the middle span, if there is a sling in the span, The number of main cable segments, Half the number of main cable segments, if there is no sling in the span, equivalent to having a sling in the span, with a sling force of zero; , And The error between the calculated value and the corresponding design value, respectively; The allowed deviation of the coordinates.

6. The method for form finding of the main cable of a spatial self-anchored suspension bridge according to claim 5, characterized in that, In S4, the correction amount of the initial force iteration values of the main cables at the end anchorage points is calculated according to the influence matrix method, and the initial force iteration values of the main cables at the end anchorage points are updated; this process is preferably as follows: (4.1) solving , and respectively, to obtain the corresponding error amount changes, and construct an influence matrix: wherein the first, second and third column elements of the influence matrix are , and respectively the amount of change in error , and caused by the first, second and third column elements of the influence matrix (4.2) Solving the initial value correction vector : ； (4.3) Anchoring the main cable end at , , The three-component force is corrected to: , and ; wherein, is a reduction factor.

7. The method of form finding of a main cable of a spatial self-anchored suspension bridge according to claim 6, characterized in that, Let the iteration variable be , , the increment of the iteration variable calculated according to the influence matrix be , , and the calculation after introducing the reduction coefficient be as follows: When , or , or : When , or , or : .

8. The method of claim 7, wherein, In S5, the calculation sequence of the middle span first and then the side span is adopted.

9. The method of claim 8, wherein, In the finite element calculation in S6, the action of the hangers on the main beam is replaced by vertical restraint, the action of the main cables on the main beam is ignored, and the horizontal component force and the vertical component force of the spatial main cables at the main cable spreader points of the main beam calculated in steps S1-S5 are applied at the main cable spreader points, so as to complete the model finite element calculation considering geometric nonlinearity and beam-column effect.

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