Method and device for shape finding of main cable considering inclined central buckle

Abstract

The application discloses a kind of main cable form finding method and device considering oblique central buckle, it is related to suspension bridge design field, the method includes the component in bridge main cable sling system decomposition;The vertical coordinate and horizontal coordinate of the right end point of the first cable segment of main cable are calculated to obtain, the unstressed length of the first cable segment of main cable, the three-way component force of the right end point of the first cable segment of main cable;The three-way force of sling upper end point and the unstressed length of the cable segment where sling is located are calculated;The three-way force of oblique central buckle upper end point, the three-way force of oblique central buckle lower end point, the unstressed length of the cable segment where oblique central buckle is located are calculated;The three-way component force of main cable left end point, the coordinate of main cable right end point, the three-way force of oblique central buckle lower end point, the three-way force of sling lower end point, the three-way force of sling upper end point and the three-way component force of main cable left end point are sequentially solved;The unstressed length of each cable segment of main cable, each sling and oblique central buckle is obtained.The main cable form finding in the application considers the influence of central buckle, effectively guarantee form finding effect.

Description

Technical Field

[0001] This invention relates to the field of suspension bridge design, specifically to a method and apparatus for finding the shape of the main cable considering an inclined central buckle. Background Technology

[0002] To improve overall stiffness and effectively control the longitudinal displacement of the stiffening girder, suspension bridges are often designed with a diagonally placed central tie near the mid-span. Furthermore, the central tie increases the anti-symmetric torsional frequency of the suspension bridge, delaying the appearance of mode shapes dominated by cable vibrations, thus effectively improving the overall wind resistance stability of the bridge. When installing the central buckle, in order to prevent unloading, the central buckle will be tensioned with a certain initial force. At present, the traditional method is still used for the main cable of the suspension bridge with the central buckle. The central buckle is not considered during the form finding. The central buckle is directly installed on the basis of the line shape. The line shape of the main cable and the line shape of the main beam in the area near the mid-span will change after the central buckle is installed (the size depends on the initial tension of the central buckle). This change is often ignored in the project. The main reasons are: (1) After considering the inclined central buckle in the form finding, the solution becomes extremely complicated (the line shape of the main cable affects the tilt angle of the central buckle. The change of the angle will cause the change of the vertical and horizontal component forces of the central buckle, which in turn affects the magnitude of the force shared by the suspenders. The suspender force directly affects the line shape of the main cable. All factors affect each other and are interlinked). At present, there are no relevant methods and analysis tools; (2) The initial tension of the central buckle only affects the line shape of the main cable and the main beam in the local area of ​​the mid-span. It has little impact on the stress of the components and does not affect the structural safety.

[0003] Therefore, the traditional shape-finding method that does not consider the central buckle has the following problems:

[0004] 1. If the central cable is installed directly on the line shape that is not determined by the central cable, the additional initial tension will change the original main cable line shape, causing the line shape to bend. The additional initial tension will generate a vertical component force, which will also affect the main beam line shape and cause unevenness in local areas of the road surface.

[0005] 2. The installation and tensioning of the central buckle will change the magnitude of the sling force, resulting in force redistribution and deviation from the set value; the sling is vertical before the central buckle is installed, but it will cause the sling to tilt after installation.

[0006] 3. The stress-free length of the central buckle is determined based on the linear shape that ignores its own influence. It has been processed to this length in the factory before installation and is installed after the main cable and slings. During the installation process, both ends of the central buckle (main cable and main beam) will be displaced due to the force, and the length cannot be adjusted, which causes the force to be unloaded. Finally, the initial tension of the central buckle after installation does not reach the set target value. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the present invention aims to provide a main cable alignment method and apparatus that considers the influence of the central buckle, thereby effectively ensuring the alignment effect.

[0008] To achieve the above objectives, the present invention provides a main cable alignment method considering an obliquely placed central buckle, specifically including the following steps:

[0009] The components in the bridge main cable suspension system are decomposed into a main cable segment with a clear stress on the left, a suspension cable with a clear stress at the lower end, an inclined central buckle with a known coordinate of the connection point between the upper end and the main cable, and a coupled ternary group consisting of the main cable segment, the suspension cable and the inclined central buckle.

[0010] Based on the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable and the ordinate of the right end of the first section of the main cable, the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional component of the force at the right end of the first section of the main cable are calculated.

[0011] Based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling, and the vertical force at the lower end of the sling, the triaxial force at the upper end point of the sling and the stress-free length of the sling segment are calculated.

[0012] Based on the coordinates of the upper end point, the lower end point, and the average axial tension of the inclined central buckle, the triaxial force at the upper end point, the triaxial force at the lower end point, and the stress-free length of the cable segment containing the inclined central buckle are calculated.

[0013] A closed-loop iterative method is constructed to sequentially solve the triaxial component force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the sling, the triaxial force at the upper end of the sling, and the triaxial component force at the left end of the main cable, forming a loop. The loop is then iterated until it is closed.

[0014] The main cable suspender system with arbitrary central buckle is decomposed according to the characteristics of the members, and the stress-free length of each cable segment of the main cable, each suspender and the inclined central buckle is obtained through iteration.

[0015] Based on the above technical solution, in the coupling ternary group, the upper end of the sling is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the sling is connected to the lower end of the inclined central buckle. The sum of the vertical force of the sling and the vertical component force of the inclined central buckle is known.

[0016] Based on the above technical solution, the calculation of the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the ordinate of the right end of the first section of the main cable, based on the three-dimensional component force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the ordinate of the right end of the first section of the main cable, specifically includes the following steps:

[0017] Based on the longitudinal component F at the left end of the first section of the main cable xL The vertical component F at the left end of the first section of the main cable yL The lateral component F at the left end of the first section of the main cable zL The coordinates of the left end point (X0, Y0, Z0) and the ordinate of the right end point (X1) of the first cable segment of the main cable are used. The vertical projection length L of the right end point of the first cable segment of the main cable is obtained by iterative calculation using the spatial catenary equation and Newton's method. y Horizontal projection length L z And the stress-free cable length S of the first section of the main cable;

[0018] The three-dimensional force (F) at the right end of the first cable segment of the main cable is calculated based on the force equilibrium condition. xR F yR F zR ), where F xR =-F xL F yR =-F yL +Sω,F zR =-F zL ω represents the weight of the main cable material per meter;

[0019] Based on the vertical projection length L of the right end point of the first section of the main cable. y The vertical coordinate Y1 of the right end point of the first cable segment of the main cable is calculated, and the horizontal projection length L of the right end point of the first cable segment of the main cable is then determined. z The x-coordinate Z1 of the right end of the first cable segment of the main cable is calculated, where Y1 = Y0 + L y Z1 = Z0 + L z .

[0020] Based on the above technical solution, the vertical projection length L of the right end point of the first cable segment of the main cable is obtained by iterative calculation using the spatial catenary equation and Newton's method. y Horizontal projection length L z And the stress-free cable length S of the first section of the main cable, the specific calculation method is as follows:

[0021]

[0022]

[0023]

[0024] Where E represents the elastic modulus of the main cable material, and A represents the cross-sectional area of ​​the main cable.

[0025] Based on the above technical solution, the calculation of the triaxial force at the upper end of the sling and the stress-free length of the sling segment based on the coordinates of the upper end of the sling, the coordinates of the lower end of the sling, and the vertical force at the lower end of the sling includes the following specific steps:

[0026] Find the horizontal projection length L of the sling in local coordinates. 0d and vertical projection length H 0d L 0d =(Z 0d -Z 1d ) / cos(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))), H 0d =Y 0d -Y 1d The coordinates of the upper end point of the sling are (X... 0d Y 0d Z 0d The coordinates of the lower end of the sling are (X). 1d Y 1d Z 1d The vertical force at the lower end of the sling is P. d ;

[0027] Calculate the initial stress-free length S d0 , And let S d1 =S d0 S d2 =1.001*S d0 ;

[0028] Give the stress-free length S of the sling d Assignment, S d =S d1 ;

[0029] Calculate the initial horizontal force F at the upper end of the sling. h0 and the initial vertical force F at the upper end of the sling v0 The calculation method is as follows:

[0030]

[0031]

[0032] Where, ω d Indicates the unit weight of the sling;

[0033] Calculate the horizontal force F at the lower end of the sling. hd and the vertical force F at the lower end of the sling vd The calculation method is as follows:

[0034] F hd=-F h0

[0035] F vd =-F v0 +ω d S d ;

[0036] The new horizontal projected length L of the sling is calculated. 1d And the new vertical projection length H 1d The calculation method is as follows:

[0037]

[0038]

[0039] Among them, E d A represents the elastic modulus of the diagonal rod material. d Represents the cross-sectional area of ​​the diagonal bar;

[0040] The iteration ends based on the difference between the horizontal and vertical projections. For the horizontal projection difference ΔL... d =L 0d -L 1d Vertical projection difference ΔH d =H 0d -H 1d If ΔL d and ΔH d If the absolute value of each value is less than the given limit, the iteration stops; otherwise, the subsequent steps are performed.

[0041] The subsequent steps are as follows:

[0042] Calculate the flexibility coefficients a1 to a3 used for correction, and calculate the initial value correction for iteration. Specifically, first solve for the intermediate coefficients b1 to b3:

[0043]

[0044]

[0045]

[0046] Next, calculate the flexibility coefficients a1 to a3:

[0047]

[0048]

[0049]

[0050] Calculate the initial value correction value ΔF for iteration h0 and ΔF v0 , ΔFh0 =a1ΔL d +a2ΔH d , ΔF v0 =a2ΔL d +a3ΔH d ;

[0051] The initial horizontal force F is obtained by correcting the initial value based on the iterative initial value. h0 and vertical force F v0 F h0 =F h0 +ΔF h0 F v0 =F v0 +ΔF v0 ;

[0052] Calculate the vertical force f1 at the lower end of the sling, f1 = F vd ;

[0053] Re-give the stress-free length S of the sling d Assignment, S d =S d2 The vertical force f2 at the lower end of the new sling is calculated again, f1 = F. vd ;

[0054] Update the stress-free length S of the sling again. d S d =S d2 +(P d -f2)(S d2 -S d1 ) / (f2-f1), and recalculate the new average tension f0 of the sling, f0=F vd P d This represents the target value of the vertical force at the lower end of the sling;

[0055] To determine if convergence, calculate abs((S) d2 -S d1 ) / S d2 If the calculated value is less than a given limit, the iteration stops; otherwise, S is updated. d1 and S d2 S d1 =S d2 S d2 =S d ;

[0056] Calculate the force (F) at the top of the sling in the global coordinate system. xd ,F yd ,F zd ), F xd =F h0 cos(arctan((X0d -X 1d ) / (Z 0d -Z 1d ))), F yd =F v0 F zd =F h0 sin(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))).

[0057] Based on the above technical solution, the closed-loop iterative method sequentially solves for the triaxial force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the sling, the triaxial force at the upper end of the sling, and the triaxial force at the left end of the main cable, forming a loop. This loop is iterated until it is closed. The specific iterative process includes:

[0058] Based on the three-dimensional force (F) at the left end of the first section of the main cable... xR F yR F zR The coordinates of the left end point (X0, Y0, Z0) and the ordinate of the right end point (X1) of the first cable segment of the main cable are calculated to obtain the vertical coordinate (Y1) of the right end point (Y1), the horizontal coordinate (Z1) of the right end point (Z1), and the three-dimensional force (F) at the right end point (F). xR F yR F zR );

[0059] Assign the coordinates (X1, Y1, Z1) of the right end point of the first section of the main cable to the coordinates (X1, Y1, Z1) of the upper end point of the inclined central buckle. 0d Y 0d Z 0d According to the coordinates of the lower endpoint (X) of the obliquely placed center, 1d Y 1d Z 1d ) and average axial tension P k The vertical force at the lower end of the inclined central buckle was calculated.

[0060] Based on the sum of the vertical forces F at the lower end of the sling... z And the vertical force at the lower end of the obliquely placed central buckle. The vertical force P at the lower end of the sling is obtained. d ,

[0061] Based on the coordinates of the left end point (X0, Y0, Z0) of the first section of the main cable and the coordinates of the lower end point (X0, Y0, Z0) of the inclined central buckle... 1d Y 1d Z 1dVertical force P at the lower end of the sling d The triaxial force (F) at the upper end of the sling is calculated. xd F yd F zd );

[0062] Calculate the three-dimensional component of the force at the left end of the first section of the new main cable, i.e., F. xL +F xd F yL +F yd F zL +F zd The triaxial force (F) at the upper end of the sling is calculated based on two adjacent cycles. xd F yd F zd The difference (ΔF) xd ΔF yd ΔF zd ),like If the value is less than the limit, the loop iteration will terminate.

[0063] Based on the above technical solution, the main cable suspender system with arbitrary central buckle is decomposed according to the characteristics of the members, and the stress-free lengths of each cable segment of the main cable, each suspender, and the inclined central buckle are obtained through iteration. Specifically:

[0064] The main cable suspension system with arbitrary central buckle is decomposed according to the characteristics of the members into a main cable segment with clear stress on the left, a suspension cable with clear stress at the lower end, an inclined central buckle with known coordinates of the connection point between the upper end and the main cable, and a coupled ternary group composed of the main cable segment, the suspension cable and the inclined central buckle.

[0065] The stress-free lengths of each cable segment, each suspender, and the inclined central buckle of the main cable are obtained through iteration.

[0066] Based on the above technical solution, the stress-free lengths of each cable segment, each suspender, and the inclined central buckle of the main cable are obtained through iteration. The specific iteration process is as follows:

[0067] Obtain the coordinates of the left end point (X0, Y0, Z0) and the coordinates of the right end point (X0, Y0, Z0) of the main cable. k-1 Y k-1 Z k-1 ), the vertical coordinate Y of the midpoint of the main cable span c The ordinate X of the midpoint of the main cable span c And the sum of the vertical forces P at the lower ends of all the slings. Z In (X0, Y0, Z0), 0 represents the first node of the main cable from left to right. k-1 Y k-1 Z k-1In the diagram, k-1 represents the last node of the main cable from left to right, and k represents the total number of nodes on the main cable.

[0068] Apply the three-dimensional force (F) to the left end of the first cable segment of the main cable. xL F yL F zL ) calculate, where:

[0069] The horizontal projected length L of the entire main cable is calculated as follows:

[0070]

[0071] The calculation method for the vertical projected length H of the entire main cable is as follows:

[0072] H = Y k-1 -Y0,

[0073] The vertical sag-to-span ratio λ is calculated as follows:

[0074] λ=(Z c -(Z k-1 -Z0) / 2) / L,

[0075] Longitudinal component F at the left end of the first cable segment of the main cable xL The calculation method is as follows

[0076] F xL =P Z / λ / 8,

[0077] Vertical component F at the left end of the first cable segment of the main cable yL The calculation method is as follows

[0078] F yL =P z / 2,

[0079] The lateral component F at the left end of the first cable segment of the main cable zL The calculation method is as follows

[0080] F zL =0;

[0081] For the main cable, calculate sequentially from left to right to obtain the vertical coordinate Y of the rightmost endpoint of the main cable. mR and the x-coordinate Z mR and the vertical coordinate Y of the midpoint of the main cable span mc ;

[0082] Based on the calculated vertical coordinate Y of the rightmost end of the main cable mR and the x-coordinate Z mR and the vertical coordinate Y of the midpoint of the main cable span mc The difference between the target value and the target value, i.e., ΔY mR =Y mR-Y k-1 ΔZ mR =Z mR -Z k-1 ΔY mc =Y mc -Y c0 :

[0083] like If the value is less than the given limit, the process ends.

[0084] like If the value is not less than a given limit, then the triaxial force (F) at the left end of the first cable segment of the main cable is... xL F yL F zL ), and the triaxial force at the left end of the first section of the main cable is taken as (F xL +1、F yL F zL ), (F xL F yL +1、F zL ), (F xL F yL F zL +1), and recalculate the vertical and horizontal coordinates of the rightmost endpoint of the main cable, as well as the vertical coordinate of the midpoint of the main cable span, to obtain three new sets of results, namely (Y mR1 Z mR1 Z mc1 ), (Y mR2 Z mR2 Z mc2 ), (Y mR3 Z mR3 Z mc3 This leads to the influence matrix, which is expressed as:

[0085]

[0086] The influence matrix is ​​used to correct the triaxial force at the left end of the first cable segment of the main cable, namely:

[0087]

[0088] Among them, (ΔF xL ΔF yL ΔF zL ) represents the triaxial force at the left end of the first section of the main cable after correction, resulting in F. xL +ΔF xL F yL +ΔF yL F zL +ΔF zLThis is used as the initial value for the new iteration. Then, the vertical and horizontal coordinates of the rightmost endpoint of the main cable, as well as the vertical coordinate of the midpoint of the main cable span, are calculated until... If the value is less than the given limit, the iteration terminates.

[0089] The present invention provides a main cable alignment device considering an obliquely placed central buckle, comprising:

[0090] The decomposition module is used to decompose the components in the bridge main cable suspension system into the main cable segment with clear stress on the left, the suspension cable with clear stress at the lower end, the inclined central buckle with known coordinates of the connection point between the upper end and the main cable, and the coupled ternary group composed of the main cable segment, the suspension cable and the inclined central buckle.

[0091] The first calculation module is used to calculate the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the vertical coordinate of the right end of the first section of the main cable, based on the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the vertical coordinate of the right end of the first section of the main cable.

[0092] The second calculation module is used to calculate the triaxial force at the upper end of the sling and the stress-free length of the sling segment based on the coordinates of the upper end of the sling, the coordinates of the lower end of the sling, and the vertical force at the lower end of the sling.

[0093] The third calculation module is used to calculate the triaxial force at the upper end of the inclined central buckle, the triaxial force at the lower end of the inclined central buckle, and the stress-free length of the cable segment where the inclined central buckle is located, based on the coordinates of the upper end of the inclined central buckle, the coordinates of the lower end of the inclined central buckle, and the average axial tension of the inclined central buckle.

[0094] The fourth calculation module is used to construct a closed-loop iterative method to sequentially solve the triaxial component force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the sling, the triaxial force at the upper end of the sling, and the triaxial component force at the left end of the main cable, forming a loop, and iterating until the loop is closed.

[0095] The execution module is used to decompose the main cable sling system with arbitrary central buckle according to the characteristics of the members, and obtain the stress-free length of each cable segment of the main cable, each sling and the inclined central buckle through iteration.

[0096] Based on the above technical solution, in the coupling ternary group, the upper end of the sling is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the sling is connected to the lower end of the inclined central buckle. The sum of the vertical force of the sling and the vertical component force of the inclined central buckle is known.

[0097] Compared with the prior art, the advantages of the present invention are as follows:

[0098] (1) The main cable alignment takes into account the influence of the central buckle. Therefore, after the central buckle is installed, the main cable alignment can still remain smooth and there will be no bends. The total vertical force at the lower end of the sling can reach the ideal target value. The main beam alignment is smooth and there will be no additional bending moment. The sling remains vertical after the central buckle is installed and will not tilt.

[0099] (2) The processing length of the central buckle is calculated according to the form-finding method that takes into account the influence of the central buckle, so that the initial tension of the central buckle can accurately reach the set target value after installation.

[0100] (3) The present invention can adapt to the main cable shape finding when there are both slings and inclined central buckles at the same time, and is applicable to situations where multiple control methods exist at the same time (such as the slings being controlled by vertical force and the central buckles being controlled by average axial force). Attached Figure Description

[0101] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0102] Figure 1 This is a flowchart of a main cable alignment method considering an obliquely placed central buckle in an embodiment of the present invention;

[0103] Figure 2 A structural diagram of a bridge with a central buckle;

[0104] Figure 3 This is an exploded view of the components. Detailed Implementation

[0105] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments.

[0106] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0107] See Figure 1 As shown, an embodiment of the present invention provides a main cable alignment method considering an obliquely placed central buckle, which specifically includes the following steps:

[0108] S1: Decompose the components in the bridge main cable suspension system into a main cable segment with a clear stress on the left, a suspension cable with a clear stress at the lower end, an inclined central buckle with a known coordinate of the connection point between the upper end and the main cable, and a coupled ternary group consisting of the main cable segment, the suspension cable and the inclined central buckle.

[0109] For the structural diagram of the bridge with a central buckle, please refer to... Figure 2 As shown, the main cable, suspenders, and inclined central buckle are an interconnected unified system. Based on their characteristics, the components in the system are divided into four categories: the main cable segment with clearly defined stress on the left (referred to as cable-1), the suspender with clearly defined stress at the lower end (referred to as cable-2), the inclined central buckle with known coordinates of the connection point between the upper end and the main cable (referred to as cable-3), and the coupled triplet (referred to as cable-group) composed of the main cable segment, suspenders, and inclined central buckle. Meanwhile, the main cable has multiple nodes arranged at intervals. The leftmost end of the main cable is the first node, and the rightmost end is the last node. A cable segment is formed between two connected nodes. For example, from left to right, the first node and the second node of the main cable are the first cable segment of the main cable. The left end of the first cable segment of the main cable is the first node of the main cable, which is the rightmost end of the main cable. The right end of the first cable segment of the main cable is the second node of the main cable. The left end of the second cable segment is the second node of the main cable. The right end of the second cable segment is the third node of the main cable.

[0110] In the coupled triplet, the upper end of the sling is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the sling is connected to the lower end of the inclined central buckle. The sum of the vertical force of the sling and the vertical component of the inclined central buckle is known. However, the distribution between the vertical force of the sling and the sum of the vertical components of the inclined central buckle is unknown; that is, the individual vertical forces are unclear. The nodes form a loop connection, and the unknowns are also interlocked and related.

[0111] The main difference between step S1 and the traditional method is that the main cable sling system with the inclined central buckle is decomposed into four types of components according to the characteristics of the members, and a coupled ternary group is constructed (the upper end of the sling is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the sling is connected to the lower end of the inclined central buckle).

[0112] S2: Based on the three-dimensional force component at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the ordinate of the right end of the first section of the main cable, the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional force component at the right end of the first section of the main cable are calculated; that is, the calculation of the main cable section (cable-1 element) with clear force on the left side is performed.

[0113] In this invention, based on the three-dimensional force components at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the ordinate of the right end of the first section of the main cable, the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional force components at the right end of the first section of the main cable are calculated. Specific steps include:

[0114] S201: Based on the longitudinal component F at the left end of the first section of the main cable xL The vertical component F at the left end of the first section of the main cable yL The lateral component F at the left end of the first section of the main cable zL The coordinates of the left end point (X0, Y0, Z0) and the ordinate of the right end point (X1) of the first cable segment of the main cable are used. The vertical projection length L of the right end point of the first cable segment of the main cable is obtained by iterative calculation using the spatial catenary equation and Newton's method. y Horizontal projection length L z And the stress-free cable length S of the first section of the main cable;

[0115] S202: The three-dimensional component force (F) at the right end of the first cable segment of the main cable is calculated based on the force equilibrium condition. xR F yR F zR ), where F xR =-F xL F yR =-F yL +Sω,F zR =-F zL ω represents the weight of the main cable material per meter;

[0116] S203: Based on the vertical projection length L of the right end point of the first cable segment of the main cable. y The vertical coordinate Y1 of the right end point of the first cable segment of the main cable is calculated, and the horizontal projection length L of the right end point of the first cable segment of the main cable is then determined. z The x-coordinate Z1 of the right end of the first cable segment of the main cable is calculated, where Y1 = Y0 + L y Z1 = Z0 + L z .

[0117] In this invention, the vertical projection length L of the right end point of the first cable segment of the main cable is obtained by using the spatial catenary equation and Newton's method for iterative calculation. y Horizontal projection length L z And the stress-free cable length S of the first section of the main cable, the specific calculation method is as follows:

[0118]

[0119]

[0120]

[0121] Where E represents the elastic modulus of the main cable material, and A represents the cross-sectional area of ​​the main cable.

[0122] S3: Based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling, and the vertical force at the lower end of the sling, calculate the triaxial force at the upper end point of the sling and the stress-free length of the sling segment; that is, perform the calculation of the sling (cable-2 element) with a clear force at the lower end.

[0123] In this invention, based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling, and the vertical force at the lower end of the sling, the triaxial force at the upper end of the sling and the stress-free length of the sling segment are calculated. Specific steps include:

[0124] S301: Calculate the horizontal projection length L of the sling in local coordinates. 0d and vertical projection length H 0d , respectively

[0125] L 0d =(Z 0d -Z 1d ) / cos(arctan((X 0d -X 1d ) / (Z 0d -Z 1d )))

[0126] H 0d =Y 0d -Y 1d ,

[0127] The coordinates of the upper end point of the sling are (X... 0d Y 0d Z 0d The coordinates of the lower end of the sling are (X). 1d Y 1d Z 1d The vertical force at the lower end of the sling is P. d ;

[0128] S302: Calculate the initial stress-free length S d0 , And let S d1 =S d0 S d2 =1.001*S d0 ;

[0129] S303: The stress-free length S of the sling d Assignment, S d =S d1 ;

[0130] S304: Calculate the initial horizontal force F at the upper end of the sling. h0 and the initial vertical force F at the upper end of the sling v0 The calculation method is as follows:

[0131]

[0132]

[0133] Where, ω d Indicates the unit weight of the sling;

[0134] S305: Calculate the horizontal force F at the lower end of the sling. hd and the vertical force F at the lower end of the sling vd The calculation method is as follows:

[0135] F hd =-F h0

[0136] F vd =-F v0 +ω d S d ;

[0137] S306: Calculate the new horizontal projection length L of the sling. 1d And the new vertical projection length H 1d The calculation method is as follows:

[0138]

[0139]

[0140] Among them, E d A represents the elastic modulus of the diagonal rod material. d Represents the cross-sectional area of ​​the diagonal bar;

[0141] Then, the iteration ends based on the difference between the horizontal and vertical projections. For the horizontal projection difference ΔL... d =L 0d -L 1d Vertical projection difference ΔH d =H 0d -H 1d If ΔL d and ΔH d The absolute values ​​are all less than the given limit, such as 10. -3 If the condition is set as needed, the iteration stops; otherwise, proceed to the next step S307.

[0142] S307: Calculate the flexibility coefficients a1 to a3 used for correction, and calculate the initial value correction for iteration. Specifically, first solve for the intermediate coefficients b1 to b3.

[0143]

[0144]

[0145]

[0146] Next, calculate the flexibility coefficients a1 to a3:

[0147]

[0148]

[0149]

[0150] Calculate the initial value correction value ΔF for iteration h0 and ΔF v0 , ΔF h0 =a1ΔL d +a2ΔH d , ΔF v0 =a2ΔL d +a3ΔH d ;

[0151] S308: Based on the iterative initial value correction, the corrected initial horizontal force F is obtained. h0 and vertical force F v0 F h0 =F h0 +ΔF h0 F v0 =F v0 +ΔF v0 Return to S305 and perform steps S305 and S306.

[0152] S309: Calculate the vertical force f1 at the lower end of the sling, f1 = F vd ;

[0153] S310: Re-give the sling stress-free length S d Assignment, S d =S d2 Repeat steps S304 to S309 to calculate the new vertical force f2 at the lower end of the sling, f1 = F. vd ;

[0154] S311: Update the stress-free length S of the sling again. d S d =S d2 +(P d -f2)(S d2 -S d1 ) / (f2-f1), repeat steps S304~S309, and calculate the new average tension f0 of the sling again, f0=F vd ;P d This represents the target value of the vertical force at the lower end of the sling;

[0155] S312: Determine if convergence has occurred, calculate abs((S d2-S d1 ) / S d2 If the calculated value is less than the given limit (e.g., 10), -3 If the setting is not met, the iteration stops; otherwise, S is updated. d1 and S d2 S d1 =S d2 S d2 =S d Return to step S303:;

[0156] S313: Calculate the force (F) at the upper end of the sling in the global coordinate system. xd ,F yd ,F zd ), F xd =F h0 cos(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))), F yd =F v0 F zd =F h0 sin(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))).

[0157] S4: Based on the coordinates of the upper end point, the lower end point, and the average axial tension of the inclined central buckle, calculate the triaxial force at the upper end point, the triaxial force at the lower end point, and the stress-free length of the cable segment where the inclined central buckle is located; that is, solve the inclined central buckle (cable-3 element) whose coordinates of the upper end connection point with the main cable are known.

[0158] The solution for cable-3 is similar to that for cable-2, with the following modifications: (1) Change f1 = F in S309. vd Instead, calculate the average tension. (2) F2 = F in S310 vd Instead, calculate the average tension. (3) S in S311 d =S d2 +(P d -f2)(S d2 -S d1 ) / (f2-f1), change to S d =S d2 +(P k -f2)(S d2 -Sd1 ) / (f2-f1), where P k Let f0 = F be the target value of the average tension of the inclined central buckle. vd Change to calculate average tension

[0159] S5: Construct a closed-loop iterative method to solve the triaxial force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the suspender, the triaxial force at the upper end of the suspender, and the triaxial force at the left end of the main cable in sequence, forming a loop, and iterating until the loop is closed; that is, solving the coupled triplet (cable-group element) composed of the main cable segment, suspender and inclined central buckle.

[0160] In this invention, a closed-loop iterative method is constructed to sequentially solve for the triaxial force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the sling, the triaxial force at the upper end of the sling, and the triaxial force at the left end of the main cable, forming a loop. This loop is iterated until it is closed. The specific iterative process includes:

[0161] a: Based on the three-dimensional force (F) at the left end of the first section of the main cable. xR F yR F zR Using the coordinates (X0, Y0, Z0) of the left end point of the first cable segment and the ordinate (X1) of the right end point of the first cable segment, cable-1 is called to calculate the ordinate (Y1) of the right end point of the first cable segment, the abscissa (Z1) of the right end point of the first cable segment, and the three-dimensional force (F) at the right end point of the first cable segment. xR F yR F zR );

[0162] b: Assign the coordinates (X1, Y1, Z1) of the right end point of the first cable segment of the main cable to the coordinates (X1, Y1, Z1) of the upper end point of the inclined central buckle. 0d Y 0d Z 0d According to the coordinates of the lower endpoint (X) of the obliquely placed center, 1d Y 1d Z 1d ) and average axial tension P k Call cable-3 to calculate the vertical force at the lower end of the inclined center buckle.

[0163] c: Based on the sum of the vertical forces F at the lower end of the sling. z And the vertical force at the lower end of the obliquely placed central buckle. The vertical force P at the lower end of the sling is obtained. d ,

[0164] d: Based on the coordinates of the left end point (X0, Y0, Z0) of the first section of the main cable and the coordinates of the lower end point (X0, Y0, Z0) of the inclined central buckle. 1d Y 1d Z 1d Vertical force P at the lower end of the sling d Call cable-2 to calculate the triaxial force (F) at the upper end of the sling. xd F yd F zd );

[0165] e: Calculate the three-dimensional component of the force at the left end of the first section of the new main cable, i.e., F. xL +F xd F yL +F yd F zL +F zd The triaxial force (F) at the upper end of the sling is calculated based on two adjacent cycles. xd F yd F zd The difference (ΔF) xd ΔF yd ΔF zd ),like Less than the limit (e.g., 10) -3 (This can be set according to accuracy requirements), then the loop iteration will terminate.

[0166] The main difference between step S5 and the traditional method is that the three-dimensional force on the left side of the main cable → the coordinate on the right side of the main cable → the vertical force at the lower end of the inclined central buckle → the vertical force at the lower end of the sling → the three-dimensional force at the upper end of the sling → the three-dimensional force on the left side of the main cable forms a loop, thus constructing a closed-loop iterative method of the triplet.

[0167] S6: Decompose the main cable suspender system with arbitrary central buckle according to the characteristics of the members, and obtain the stress-free length of each cable segment of the main cable, each suspender and the inclined central buckle through iteration.

[0168] In this invention, the main cable suspender system with arbitrary central buckles is decomposed according to the characteristics of the members, and the stress-free lengths of each cable segment of the main cable, each suspender, and the inclined central buckle are obtained through iteration, specifically:

[0169] A: The main cable sling system with arbitrary central buckle is decomposed according to the characteristics of the members into a main cable segment with clear stress on the left, a sling with clear stress at the lower end, an inclined central buckle with known coordinates of the connection point between the upper end and the main cable, and a coupled ternary group consisting of the main cable segment, the sling and the inclined central buckle.

[0170] B: The stress-free lengths of each cable segment, each suspender, and the inclined central buckle of the main cable are obtained through iteration.

[0171] First, identify the cable group (the upper end of the sling is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the sling is connected to the lower end of the inclined central buckle). All other components are single-cable components.

[0172] In this invention, the stress-free lengths of each cable segment of the main cable, each suspender, and the inclined central buckle are obtained through iteration. The specific iteration process is as follows:

[0173] S601: Obtain the coordinates of the left end point (X0, Y0, Z0) and the right end point (X...) of the main cable. k-1 Y k-1 Z k-1 ), the vertical coordinate Y of the midpoint of the main cable span c The ordinate X of the midpoint of the main cable span c And the sum of the vertical forces P at the lower ends of all the slings. Z In (X0, Y0, Z0), 0 represents the first node of the main cable from left to right. k-1 Y k-1 Z k-1 In the diagram, k-1 represents the last node of the main cable from left to right, and k represents the total number of nodes on the main cable.

[0174] Apply the three-dimensional force (F) to the left end of the first cable segment of the main cable. xL F yL F zL ) calculate, where:

[0175] The horizontal projected length L of the entire main cable is calculated as follows:

[0176]

[0177] The calculation method for the vertical projected length H of the entire main cable is as follows:

[0178] H = Y k-1 -Y0,

[0179] The vertical sag-to-span ratio λ is calculated as follows:

[0180] λ=(Z c -(Z k-1 -Z0) / 2) / L,

[0181] Longitudinal component F at the left end of the first cable segment of the main cable xL The calculation method is as follows

[0182] F xL =P Z / λ / 8,

[0183] Vertical component F at the left end of the first cable segment of the main cable yLThe calculation method is as follows

[0184] F yL =P z / 2,

[0185] The lateral component F at the left end of the first cable segment of the main cable zL The calculation method is as follows

[0186] F zL =0;

[0187] S602: For the main cable, calculate sequentially from left to right to obtain the vertical coordinate Y of the rightmost endpoint of the main cable. mR and the x-coordinate Z mR and the vertical coordinate Y of the midpoint of the main cable span mc That is, enter the cell, determine the cell type (4 types), and call different sub-iteration steps (cable-1, cable-2, cable-3 or cable-group) according to the type to perform calculation.

[0188] S603: Based on the calculated vertical coordinate Y of the rightmost end point of the main cable mR and the x-coordinate Z mR and the vertical coordinate Y of the midpoint of the main cable span mc The difference between the target value and the target value, i.e., ΔY mR =Y mR -Y k-1 ΔZ mR =Z mR -Z k-1 ΔY mc =Y mc -Y c0 :

[0189] like Less than a given limit (e.g., 10) -3 (Set as needed), then end;

[0190] like If it is not less than the given limit, then proceed to S604;

[0191] S604: For the triaxial force (F) at the left end of the first cable segment of the main cable. xL F yL F zL ), and the triaxial force at the left end of the first section of the main cable is taken as (F xL +1、F yL F zL ), (F xL F yL +1、F zL ), (F xL F yL F zL+1), repeat S602 and S603, and recalculate the vertical and horizontal coordinates of the rightmost endpoint of the main cable, as well as the vertical coordinate of the midpoint of the main cable span, to obtain 3 new sets of results, namely (Y mR1 Z mR1 Z mc1 ), (Y mR2 Z mR2 Z mc2 ), (Y mR3 Z mR3 Z mc3 This leads to the influence matrix, which is expressed as:

[0192]

[0193] S605: The influence matrix is ​​used to correct the triaxial force at the left end of the first cable segment of the main cable, that is:

[0194]

[0195] Among them, (ΔF xL ΔF yL ΔF zL ) represents the triaxial force at the left end of the first section of the main cable after correction, resulting in F. xL +ΔF xL F yL +ΔF yL F zL +ΔF zL As the new initial value, S602 to S605 are executed repeatedly, and then the vertical and horizontal coordinates of the rightmost endpoint of the main cable and the vertical coordinate of the midpoint of the main cable span are calculated until... If the value is less than the given limit, the iteration terminates.

[0196] In the final step of the iteration, the coordinates (X, Y, Z) of each node of the main cable are... n Y n Z n This determines the spatial alignment of the structure, i.e., its spatial state, and simultaneously obtains the stress-free lengths of each cable segment of the main cable, each suspender, and the inclined central buckle.

[0197] The main difference between step S6 and the traditional method is that it consists of four layers of iteration: the outermost layer is the iteration of the entire system, the second layer is the iteration of triplet, the third layer is the iteration of intra-group suspension cables and central buckles, and the innermost layer is the flexible iteration of the catenary thread unit. Furthermore, each layer uses a different iteration method: the outermost layer uses the influence matrix method, the second layer uses the cyclic method, the third layer uses the bisection method, and the innermost layer uses the flexibility coefficient method.

[0198] The present invention will be specifically described below using the form finding of a cable system with an obliquely placed central buckle as an example.

[0199] Given conditions: The coordinates of the two ends of the main cable are (0, 0, 0) and (60, 0, 0); there are 5 points in the middle of the main cable, with longitudinal coordinates of 10, 20, 30, 40, and 50 respectively; the vertical coordinate of the mid-span point of the main cable is -10; the vertical load-bearing capacity at the lower end of each sling is 500kN; there are 5 slings in total, including 2 inclined central buckles, connected from the mid-span point to the lower ends of slings 2 and 4; the average tension at both ends of the inclined central buckles is 30kN. See [link / details]. Figure 3 .

[0200] The specific steps are as follows:

[0201] (1) Calculate the three-dimensional component force (F) at the leftmost end of the main cable. xL F yL F zL The horizontal projection length of the entire main cable is 60, the vertical sag-to-span ratio is 1 / 6, and the total vertical force at the lower end of the suspender is 2500kN. Therefore, the longitudinal component on the left is 1875kN, the vertical component is 1250kN, and the lateral component is 0.

[0202] (2) The entire structure contains 5 'cable-1', 4 'cable-2', 1 'cable-3', and 1 'cable-group', see Figure 3 From left to right, until all components are calculated, a 5-step overall iteration is performed to meet the convergence limit of 10. -9 The method of this invention achieves stable convergence, high accuracy in iterating the target value, and fast speed, without repeated oscillations during the process.

[0203] Table 1 Final coordinates of main cable nodes (structural alignment)

[0204]

[0205] As shown in Table 1, the final step of the calculation considering the central buckle yields a vertical coordinate of -10.000000 at the mid-span of the main cable, which perfectly matches the target. However, the traditional method, which does not consider the central buckle during shape finding, causes a vertical displacement of 0.427 cm at the mid-span after its installation. The calculation results for points 1 and 2 on the main cable differ by 5.19 cm and 8.29 cm, respectively. The traditional method also results in an angled and no longer smooth main cable profile after the central buckle is installed. (See...) Figure 3 (dashed line), while the method of the present invention takes into account the influence of the central buckle in the shape finding, so the line shape is still smooth.

[0206] Table 2 Internal Forces (kN) of Suspension Cables and Inclined Central Buckle

[0207]

[0208]

[0209] Table 2 shows the longitudinal and vertical forces at the top and bottom of the suspenders and the inclined central buckle. As can be seen from Table 2, considering the form-finding method of the central buckle, the lower end of suspender 2 (the sum of suspender 2 and central buckle 1) and the lower end of suspender 4 (the sum of suspender 4 and central buckle 2) are precisely -500kN. However, the traditional method of calculating the sum of the vertical forces at the lower ends of suspender 2 and suspender 4 after form-finding and then installing the central buckle results in a force of -513.29kN, and the vertical force of the middle suspender 3 is -476.63kN. The forces on both sides are larger, while the forces in the middle are smaller, resulting in an uneven redistribution of the cable forces. The changes in cable forces will further cause changes in the shape of the main beam. The traditional method determines the processing length of the central buckle based on the linear shape without considering the initial tension. During installation, the upper and lower ends deform under stress, causing the initial tension of the central buckle to fail to reach the target value. As shown in Table 2, the initial tension after installation of the central buckle using the traditional method is only 18.59 kN. However, the method of this invention considers the influence of the central buckle during the shape-finding process, enabling the initial tension to accurately reach the target value of 30 kN. Furthermore, the sum of the stress-free lengths of all cable segments in the main cable, calculated using the method of this invention considering the central buckle during shape-finding, is 63.731232 m, while the traditional method yields 63.784482 m, a difference of 5.325 cm.

[0210] In summary, the center buckle affects the main cable alignment and the lower end force of the suspenders. When aligning the main cable, both the suspenders and the center buckle should be considered simultaneously. This invention provides a alignment method that simultaneously considers the angled center buckle, achieving accurate alignment of the main cable system with the angled center buckle.

[0211] This invention decomposes a cable system with an inclined central buckle into four types of components based on the characteristics of the members, and constructs coupled ternary sets (the upper end of the suspender is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the suspender is connected to the lower end of the inclined central buckle). Taking advantage of the interlocking nature of the parameters within the ternary sets, a closed-loop iterative method is created. The overall structural calculation consists of four layers of iteration: the outermost layer is the structural system iteration, the second layer is the ternary set iteration, the third layer is the iteration of the suspenders and central buckle within the group, and the innermost layer is the flexible iteration of the catenary cable unit. Ultimately, it achieves precise shape finding for the cable system with the inclined central buckle. After the central buckle is installed, the main cable alignment remains smooth without any bends, the main beam alignment is smooth, the suspenders do not tilt, and the initial tension of the central buckle accurately reaches the set target value. This invention can be applied to the design of suspension bridges with central buckles.

[0212] In one possible implementation, the present invention also provides a readable storage medium located in a PLC (Programmable Logic Controller) controller, on which a computer program is stored. When executed by a processor, this program implements the steps of the main cable alignment method considering the obliquely positioned central buckle as described below:

[0213] The components in the bridge main cable suspension system are decomposed into a main cable segment with a clear stress on the left, a suspension cable with a clear stress at the lower end, an inclined central buckle with a known coordinate of the connection point between the upper end and the main cable, and a coupled ternary group consisting of the main cable segment, the suspension cable and the inclined central buckle.

[0214] Based on the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable and the ordinate of the right end of the first section of the main cable, the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional component of the force at the right end of the first section of the main cable are calculated.

[0215] Based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling, and the vertical force at the lower end of the sling, the triaxial force at the upper end point of the sling and the stress-free length of the sling segment are calculated.

[0216] Based on the coordinates of the upper end point, the lower end point, and the average axial tension of the inclined central buckle, the triaxial force at the upper end point, the triaxial force at the lower end point, and the stress-free length of the cable segment containing the inclined central buckle are calculated.

[0217] A closed-loop iterative method is constructed to sequentially solve the triaxial component force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the sling, the triaxial force at the upper end of the sling, and the triaxial component force at the left end of the main cable, forming a loop. The loop is then iterated until it is closed.

[0218] The main cable suspender system with arbitrary central buckle is decomposed according to the characteristics of the members, and the stress-free length of each cable segment of the main cable, each suspender and the inclined central buckle is obtained through iteration.

[0219] Storage media may be any combination of one or more computer-readable media. A computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. Computer-readable storage media may be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this document, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0220] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to: wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0221] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0222] The present invention provides a main cable alignment device considering a slanted central buckle, comprising a decomposition module, a first calculation module, a second calculation module, a third calculation module, a fourth calculation module, and an execution module.

[0223] The decomposition module is used to decompose the components in the bridge main cable suspension system into the main cable segment with clear stress on the left, the suspension cable with clear stress at the lower end, the inclined central buckle with known coordinates of the connection point between the upper end and the main cable, and the coupled ternary group consisting of the main cable segment, the suspension cable and the inclined central buckle.

[0224] The first calculation module is used to calculate the vertical and horizontal coordinates of the right end of the first section of the main cable, the stress-free length of the first section of the main cable, and the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the vertical coordinate of the right end of the first section of the main cable, based on the three-dimensional component of the force at the left end of the first section of the main cable, the coordinates of the left end of the first section of the main cable, and the vertical coordinate of the right end of the first section of the main cable.

[0225] The second calculation module is used to calculate the triaxial force at the upper end of the sling and the stress-free length of the sling segment based on the coordinates of the upper end of the sling, the coordinates of the lower end of the sling, and the vertical force at the lower end of the sling.

[0226] The third calculation module is used to calculate the triaxial force at the upper end of the inclined central buckle, the triaxial force at the lower end of the inclined central buckle, and the stress-free length of the cable segment where the inclined central buckle is located, based on the coordinates of the upper end of the inclined central buckle, the coordinates of the lower end of the inclined central buckle, and the average axial tension of the inclined central buckle.

[0227] The fourth calculation module is used to construct a closed-loop iterative method to solve the triaxial component force at the left end of the main cable, the coordinates of the right end of the main cable, the triaxial force at the lower end of the inclined central buckle, the triaxial force at the lower end of the sling, the triaxial force at the upper end of the sling, and the triaxial component force at the left end of the main cable in sequence, forming a loop, and iterating until the loop is closed.

[0228] The execution module is used to decompose the main cable suspender system with arbitrary central buckle according to the characteristics of the members, and obtain the stress-free length of each cable segment of the main cable, each suspender and the inclined central buckle through iteration.

[0229] In this invention, in the coupling triplet, the upper end of the sling is connected to the left side of the main cable segment, the right side of the main cable segment is connected to the upper end of the inclined central buckle, and the lower end of the sling is connected to the lower end of the inclined central buckle. The sum of the vertical force of the sling and the vertical component force of the inclined central buckle is known.

[0230] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

[0231] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

Claims

1. A method for shape finding of a main cable considering a skew central buckle, characterized in that, The method comprises the following steps: The components in the main cable suspension system are decomposed into a left force clear main cable segment, a lower end force clear sling, a slanting central buckle with known coordinates of the upper end connected with the main cable, and a coupled triad composed of the main cable segment, the sling and the slanting central buckle; Based on the three-way force of the left end point of the first segment of the main cable, the coordinates of the left end point of the first segment of the main cable and the longitudinal coordinates of the right end point of the first segment of the main cable, the vertical coordinates and the horizontal coordinates of the right end point of the first segment of the main cable, the unstressed length of the first segment of the main cable and the three-way force of the right end point of the first segment of the main cable are calculated. Based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling and the vertical force of the lower end of the sling, the three-way force of the upper end point of the sling and the unstressed length of the segment where the sling is located are calculated. Based on the coordinates of the upper end point of the slanting central buckle, the coordinates of the lower end point of the slanting central buckle and the average axial tension of the slanting central buckle, the three-way force of the upper end point of the slanting central buckle, the three-way force of the lower end point of the slanting central buckle and the unstressed length of the segment where the slanting central buckle is located are calculated. A closed loop iteration method is constructed to sequentially solve the three-way force of the left end point of the main cable, the coordinates of the right end point of the main cable, the three-way force of the lower end point of the slanting central buckle, the three-way force of the lower end point of the sling, the three-way force of the upper end point of the sling and the three-way force of the left end point of the main cable to form a loop, and the iteration is performed until the loop is closed. The main cable suspension system with central buckles in any form is decomposed according to the characteristics of the members, and the unstressed lengths of the segments of the main cable, the slings and the slanting central buckles are obtained through iteration.

2. A method for form-finding of a main cable considering a skew central buckle as claimed in claim 1, characterized in that: In the coupled triad, the upper end of the sling is connected with the left side of the main cable segment, the right side of the main cable segment is connected with the upper end of the slanting central buckle, the lower end of the sling is connected with the lower end of the slanting central buckle, and the sum of the vertical force of the sling and the vertical component of the slanting central buckle is known.

3. A method for form-finding of a main cable considering a skew central buckle as claimed in claim 2, characterized in that, The specific steps for calculating the vertical coordinates and the horizontal coordinates of the right end point of the first segment of the main cable, the unstressed length of the first segment of the main cable and the three-way force of the right end point of the first segment of the main cable based on the three-way force of the left end point of the first segment of the main cable, the coordinates of the left end point of the first segment of the main cable and the longitudinal coordinates of the right end point of the first segment of the main cable include: According to the longitudinal component force F of the left end point of the first section of the main cable xL , the vertical component force F of the left end point of the first section of the main cable yL , the horizontal component force F of the left end point of the first section of the main cable zL , the left end point coordinate (X0, Y0, Z0) of the first section of the main cable, the longitudinal coordinate X1 of the right end point of the first section of the main cable, the vertical projection length L of the right end point of the first section of the main cable calculated by the spatial catenary equation and using the Newton method iteration y , the horizontal projection length L z , and the unstressed cable length S of the first section of the main cable; According to the force balance condition, the three-way component forces (F xR , F yR , F zR ) of the right end point of the first cable segment of the main cable are calculated, wherein F xR =-F xL , F yR =-F yL +Sω, F zR =-F zL , and ω represents the weight per meter of the main cable material; According to the vertical projection length L of the right end point of the first segment of the main cable y The vertical coordinate Y1 of the right end point of the first segment of the main cable is calculated, and the horizontal projection length L of the right end point of the first segment of the main cable is calculated z The horizontal coordinate Z1 of the right end point of the first segment of the main cable is calculated, wherein Y1=Y0+L y , Z1=Z0+L z .

4. A method for form-finding of a main cable considering a skew central buckle as claimed in claim 3, characterized in that, The vertical projection length L of the right end point of the first cable segment of the main cable is calculated by the spatial catenary equation and using the Newton method iteration y , the horizontal projection length L z , and the unstressed cable length S of the first cable segment of the main cable, and the specific calculation method is: Wherein, E represents the elastic modulus of the main cable material, and A represents the cross-sectional area of the main cable.

5. A method for shape finding of a main cable considering a skew central buckle as claimed in claim 3, characterized in that, The specific steps for calculating the three-way force of the upper end point of the sling and the unstressed length of the segment where the sling is located based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling and the vertical force of the lower end of the sling include: Find the horizontal projection length L of the sling in local coordinates. 0d and vertical projection length H 0d L 0d =(Z 0d -Z 1d ) / cos(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))), H 0d =Y 0d -Y 1d The coordinates of the upper end point of the sling are (X... 0d Y 0d Z 0d The coordinates of the lower end of the sling are (X). 1d Y 1d Z 1d The vertical force at the lower end of the sling is P. d ; Calculate initial unstressed length S d0 , And let S d1 = S d0 , S d2 = 1.001 * S d0 ; Stress-free length of sling S d Assign, S d = S d1 ; calculating the initial horizontal force F at the upper end of the sling h0 and the initial vertical force F at the upper end of the sling v0 in the following manner where ω d represents the sling volume weight; The horizontal force F at the lower end of the sling is calculated hd and the vertical force F at the lower end of the sling is calculated vd in the following manner F hd = -F h0 F vd = -F v0 + ω d S d ; The new horizontal projection length L of the sling is calculated 1d and the new vertical projection length H 1d , calculated as where E d represents the elastic modulus of the diagonal rod material, A d represents the cross-sectional area of the diagonal rod based on the horizontal projection difference ΔL and the vertical projection difference ΔH d = L 0d - L 1d , the vertical projection difference ΔH d = H 0d - H 1d , if the absolute values of ΔL d and ΔH d are both smaller than given limits, the iteration is stopped, otherwise the following steps are performed; The subsequent steps are: The flexible coefficients a1-a3 for correction are calculated, and the iteration initial value correction value is calculated. Specifically, the intermediate coefficients b1-b3 are solved first: Then, the flexible coefficients a1-a3 are calculated: Compute iteration initial value correction value ΔF h0 and ΔF v0 , ΔF h0 = a1ΔL d + a2ΔH d , ΔF v0 = a2ΔL d + a3ΔH d ; Based on the iteration initial value correction value, the initial horizontal force F is corrected to obtain a corrected initial horizontal force F h0 and vertical force F v0 , F h0 = F h0 + ΔF h0 , F v0 = F v0 + ΔF v0 ; Calculate the vertical force f1 at the lower end of the sling, f1 = F vd ; Re-stress length S of the sling d Assign, S d = S d2 Calculate the vertical force f2 of the new lower end point of the sling, f1 = F vd ; The unstressed length S of the sling is updated again d , S d = S d2 + (P d -f2)(S d2 -S d1 ) / (f2-f1), and the new average tension f0 of the sling is calculated again, f0 = F vd , P d is the target value of the vertical force at the lower end of the sling; determining whether or not convergence is achieved, calculating abs((S d2 -S d1 ) / S d2 ), and if the calculated value is less than a given limit, then stopping iteration, otherwise updating S d1 and S d2 , i.e. S d1 =S d2 , S d2 =S d ; Calculate the force (F) at the top of the sling in the global coordinate system. xd ,F yd ,F zd ), F xd =F h0 cos(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))), F yd =F v0 F zd =F h0 sin(arctan((X 0d -X 1d ) / (Z 0d -Z 1d ))).

6. A method for form-finding of a main cable considering a skew central buckle as claimed in claim 5, characterized in that, The closed loop iteration method is constructed to sequentially solve the three-way force of the left end point of the main cable, the coordinates of the right end point of the main cable, the three-way force of the lower end point of the slanting central buckle, the three-way force of the lower end point of the sling, the three-way force of the upper end point of the sling and the three-way force of the left end point of the main cable to form a loop, and the iteration is performed until the loop is closed. The specific iteration process includes: According to the three-directional forces (F xR , F yR , F zR ) of the left end point of the first cable segment of the main cable, the coordinates (X0, Y0, Z0) of the left end point of the first cable segment of the main cable, and the longitudinal coordinate X1 of the right end point of the first cable segment of the main cable, the vertical coordinate Y1, the horizontal coordinate Z1, and the three-directional forces (F xR , F yR , F zR ) of the right end point of the first cable segment of the main cable are calculated. Assign the coordinates (X1, Y1, Z1) of the right end point of the first section of the main cable to the coordinates (X1, Y1, Z1) of the upper end point of the inclined central buckle. 0d Y 0d Z 0d According to the coordinates of the lower endpoint (X) of the obliquely placed center, 1d Y 1d Z 1d ) and average axial tension P k The vertical force at the lower end of the inclined central buckle was calculated. According to the sum of the vertical forces at the lower end of the sling F z and the vertical force at the lower end of the diagonal central shackle the vertical force at the lower end of the sling P d , According to the left end point coordinates (X0, Y0, Z0) of the first section of the main cable, the lower end point coordinates (X 1d , 1d Y , 1d Z ) of the oblique central buckle, and the vertical force P d of the sling lower end point, three-direction forces (F xd , F yd , F zd ) of the sling upper end point are calculated. Calculate the three-directional force of the left end point of the new main cable first segment, i.e. F xL +F xd , F yL +F yd , F zL +F zd , the difference (ΔF xd , ΔF yd , ΔF zd ) of the three-directional force (F xd , F yd , F zd ) of the upper end point of the sling calculated according to the adjacent two times of loop, if is less than the limit value, then terminate the loop iteration.

7. A method for form-finding of a main cable considering a skew central buckle as claimed in claim 6, characterized in that, The main cable suspension system with central buckles in any form is decomposed according to the characteristics of the members, and the unstressed lengths of the segments of the main cable, the slings and the slanting central buckles are obtained through iteration. The main cable suspension system with arbitrary form central buckling is decomposed according to the characteristics of the members, and is decomposed into a left side force clear main cable segment, a lower end force clear sling, a slanting central buckling with the known coordinates of the upper end connected with the main cable, and a coupled three-member group composed of the main cable segment, the sling and the slanting central buckling; The unstressed length of each segment of the main cable, each sling and the slanting central buckling is obtained through iteration.

8. A method for form-finding of a main cable considering a skew central buckle as claimed in claim 7, characterized in that, The unstressed length of each segment of the main cable, each sling and the slanting central buckling is obtained through iteration, and the specific iteration process is as follows: Obtain the coordinates of the left end point (X0, Y0, Z0) and the coordinates of the right end point (X0, Y0, Z0) of the main cable. k-1 Y k-1 Z k-1 ), the vertical coordinate Y of the midpoint of the main cable span c The ordinate X of the midpoint of the main cable span c And the sum of the vertical forces P at the lower ends of all the slings. Z In (X0, Y0, Z0), 0 represents the first node of the main cable from left to right. k-1 Y k-1 Z k-1 In the diagram, k-1 represents the last node of the main cable from left to right, and k represents the total number of nodes on the main cable. Three-directional force (F xL , F yL , F zL ) calculation is performed on the left end point of the first segment of the main cable, wherein: The calculation method of the horizontal projection length L of the whole main cable is The calculation method of the vertical projection length H of the whole main cable is H = Y k-1 - Y0, The calculation method of the vertical vector span ratio λ is λ = (Z c -(Z k-1 -Z0) / 2) / L, the longitudinal component F of the left end point of the first segment of the main cable strand xL is calculated as F xL = P Z / λ / 8, Vertical component of the left end point of the first segment of the main cable stay yL The calculation is as follows F yL = P z / 2, The transverse component force F of the left end point of the first segment of the main cable zL The calculation method is F zL ＝0； For the main cable, the vertical coordinate Y of the rightmost end point of the main cable is obtained by calculation from left to right mR and the horizontal coordinate Z mR , and the vertical coordinate Y of the mid-point of the main cable mc ; Based on the calculated vertical coordinate Y of the rightmost end point of the main cable mR and horizontal coordinate Z mR , and the vertical coordinate Y of the mid-point of the main cable mc , the difference between the target value, i.e. ΔY mR = Y mR - Y k-1 , ΔZ mR = Z mR - Z k-1 , ΔY mc = Y mc - Y c0 : If If the limit is less than the given limit, then end. If not less than a given limit, then the three-way force (F xL , F yL , F zL ) of the left end point of the main cable first segment is taken as (F xL +1, F yL , F zL ), (F xL , F yL +1, F zL ), (F xL , F yL , F zL +1) in turn, and the vertical coordinate and horizontal coordinate of the rightmost end point of the main cable and the vertical coordinate of the mid-point of the main cable are calculated again to obtain three new results, respectively (Y mR1 , Z mR1 , Z mc1 ), (Y mR2 , Z mR2 , Z mc2 ), (Y mR3 , Z mR3 , Z mc3 ), and then an influence matrix is obtained, which is represented as: The three-dimensional force of the left end point of the first segment of the main cable is corrected by using the influence matrix, that is, wherein (ΔF xL , ΔF yL , ΔF zL ) represents the three-directional force at the left end of the first segment of the main cable after correction, and F xL + ΔF xL , F yL + ΔF yL , F zL + ΔF zL are obtained as the new initial values for iteration, and then the vertical coordinate and the horizontal coordinate of the right end of the main cable and the vertical coordinate of the mid-point of the main cable are calculated until is less than the given limit value, the iteration is terminated.

9. A main cable shape-finding device considering a skew central buckle, characterized in that, It comprises: The component in the bridge main cable suspension system is decomposed into a left side force clear main cable segment, a lower end force clear sling, a slanting central buckling with the known coordinates of the upper end connected with the main cable, and a coupled three-member group composed of the main cable segment, the sling and the slanting central buckling by the decomposition module; The first calculation module is used for calculating the vertical coordinate and horizontal coordinate of the right end point of the first segment of the main cable, the unstressed length of the first segment of the main cable, and the three-dimensional force of the right end point of the first segment of the main cable based on the three-dimensional force of the left end point of the first segment of the main cable, the coordinates of the left end point of the first segment of the main cable and the longitudinal coordinate of the right end point of the first segment of the main cable. The second calculation module is used for calculating the three-dimensional force of the upper end point of the sling and the unstressed length of the segment of the sling based on the coordinates of the upper end point of the sling, the coordinates of the lower end point of the sling and the vertical force of the lower end point of the sling. The third calculation module is used for calculating the three-dimensional force of the upper end point of the slanting central buckling, the three-dimensional force of the lower end point of the slanting central buckling and the unstressed length of the segment of the slanting central buckling based on the coordinates of the upper end point of the slanting central buckling, the coordinates of the lower end point of the slanting central buckling and the average axial tension of the slanting central buckling. The fourth calculation module is used for sequentially solving the three-dimensional force of the left end point of the main cable, the coordinates of the right end point of the main cable, the three-dimensional force of the lower end point of the slanting central buckling, the three-dimensional force of the lower end point of the sling, the three-dimensional force of the upper end point of the sling and the three-dimensional force of the left end point of the main cable by the closed loop iteration method, forming a loop, and iterating until the loop is closed. The execution module is used for decomposing the main cable suspension system with arbitrary form central buckling according to the characteristics of the members, and obtaining the unstressed length of each segment of the main cable, each sling and the slanting central buckling through iteration.

10. A main cable formwork device considering a diagonal central buckle according to claim 9, characterized in that: In the coupled three-member group, the upper end of the sling is connected with the left side of the main cable segment, the right side of the main cable segment is connected with the upper end of the slanting central buckling, the lower end of the sling is connected with the lower end of the slanting central buckling, and the sum of the vertical force of the sling and the vertical component of the slanting central buckling is known.

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