Single-tower ground anchor suspension bridge composite cable saddle side finished bridge anchor cable-span force calculation method

Abstract

The invention discloses a single-tower ground anchor suspension bridge composite cable saddle side finished bridge anchor cable-span force calculation method, which is characterized in that a composite cable saddle is selected, the space trend of a composite cable saddle side anchor cable-span strand is determined, the same cable force of all strands at the tangent point of the composite cable saddle is taken as a calculation principle, and a non-linear equation set is solved to calculate the composite cable saddle side finished bridge anchor cable-span force. And the anchor cable span force of the composite cable saddle side of the single-tower ground anchor type suspension bridge is determined. By means of the calculation method, it can be guaranteed that the composite cable saddle side anchor cable-span force is evenly distributed in the finished bridge state, and the cable strand utilization rate is increased; according to the method, repeated iteration in the calculation process is avoided, convergence is not prone to occurring, the anchor cable-span force is determined in the mode of solving the nonlinear equation set, and the calculation efficiency can be improved while the calculation precision is guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of construction, and in particular to a method for calculating the anchor span cable force of a composite cable saddle side bridge of a single-tower ground-anchor suspension bridge. Background Art

[0002] At present, there is a lack of accurate calculation methods for the anchor span cable strands of the composite saddle of a single-tower ground-anchored suspension bridge. Conventional calculation methods usually simplify the anchor span cable strands and still treat the cable strands together as a main cable. This treatment does not take into account the differences in the spatial positions of the cable strands, making it difficult to accurately calculate the cable force distribution of the anchor span cable strands during the construction stage or in the completed bridge state, which brings blindness to the construction and control and reduces the safety factor of the main cable.

[0003] Therefore, this paper proposes a method for calculating the anchor span cable force of the composite cable saddle side bridge of a single-tower ground-anchored suspension bridge. Summary of the invention

[0004] The present invention designs a method for calculating the cable force of the anchor span of the composite cable saddle side of a single-tower ground-anchored suspension bridge. The method fully considers the spatial orientation of the anchor span cable strands on the composite cable saddle side, takes the same cable force of all cable strands at the tangent point of the composite cable saddle as the calculation principle, and determines the anchor span cable force on the composite cable saddle side of the single-tower ground-anchored suspension bridge by solving a group of nonlinear equations.

[0005] In order to achieve the above technical effects, the present invention is implemented by the following technical solutions: A method for calculating the anchor span cable force of a composite cable saddle side bridge of a single-tower ground-anchored suspension bridge, characterized in that it includes the following steps:

[0006] S1. Select composite saddle: composite saddle is composed of multiple arcs with different radii. Composite saddles with 4 different arc radii are taken as the research objects. From the main span to the anchor span, the radii corresponding to each arc are recorded as R1, R2, R3 and R4, and their central angles are θ1, θ2, θ3 and θ4 respectively. K is the center of the first arc.

[0007] S2. Clarify the direction of the anchor span cable strands on the composite saddle side: After the main cable of the main span passes through the saddle groove of the composite saddle, it is divided into n anchor span cable strands and anchored to the anchor through the turning and dispersion of the composite saddle; the flat bending radius of the main cable strand changes with its lateral arrangement in the saddle groove of the composite saddle; when the main cable enters the composite saddle from the main span, the main cable strand first undergoes vertical bending, and the starting point of the flat bending is closer to the anchor span side than the starting point of the vertical bending; the position of the starting point of the vertical bending relative to the composite saddle will change accordingly with the construction stage, temperature changes and live load, while the starting point of the flat bending remains unchanged relative to the composite saddle. In order to ensure the stability of the main cable strand in the saddle groove of the composite saddle, when designing the composite saddle, it should be ensured that the main cable strand completes the flat bending first and then the vertical bending;

[0008] S3. Determine the cable force distribution mode of the anchor span cable strand on the composite saddle side: Under the premise that the effects of the anchor span cable strand and the main span main cable on the composite saddle meet the equilibrium conditions of the composite saddle, assume that the cable force T of each anchor span cable strand at the tangent point of the composite saddle i are equal;

[0009] S4. Calculate the horizontal bending angle of the anchor span cable strand:

[0010] OK i and r i are the center and radius of the flat bending arc of the i-th cable strand, α i,hb is the horizontal bending angle of the i-th cable strand; N i is the intersection of the angle bisector of the flat bending angle of the i-th cable strand and the horizontal line passing through the starting point of the flat bending. Based on the geometric relationship, the following control equation can be obtained:

[0011]

[0012] Move the right side of formula (1) to the left side to form the error function of the control equation:

[0013]

[0014] In formulas (1) and (2), and The flat bend starting point H i ,s p and anchor point M i The vertical and horizontal distances between

[0015] In order to obtain the flat bending angle of the i-th cable strand, the error function needs to be close to 0; therefore, the objective function is established as follows:

[0016] minf i 2 (·)(3),

[0017] The objective function can be solved by the nonlinear generalized simplified gradient (GRG) method. When the objective function meets the error limit, the flat bending angle of the i-th anchor span cable strand can be determined. Similarly, the flat bending angles of the remaining anchor span cables can be determined by this method.

[0018] S5. Determine 2n+1 basic unknowns: Establish a global coordinate system with K as the origin, with the X-axis pointing horizontally to the right, the Y-axis pointing vertically upward, the Z-axis perpendicular to the XY plane and pointing to the inside of the screen, and V i,ep Establish a local coordinate system for the origin, x i The axis points to the front anchor surface, and the angle between it and the horizontal direction is the bending angle of the cable strand, y iThe axis is vertically downward, and the catenary of the suspended section of the anchor span cable strand is taken as the research object; the number of unknown parameters of the catenary is n, and the unknown length of the projection of the catenary along the xi axis is n. Since "the cable force T of each anchor span cable strand at the tangent point of the composite cable saddle i are equal", so the catenary is along x i The number of unknowns in the axonal force is 1; the total number of unknowns is 2n+1;

[0019] S6. Determine 2n+1 nonlinear equations: 2n+1 nonlinear equations can be constructed based on the elevation closure and horizontal closure of each catenary and the overall force balance at the composite saddle;

[0020] S7. Determine the side anchor span force of the composite saddle.

[0021] Furthermore, in S6, 2n+1 nonlinear equations are determined as follows:

[0022] S6.1, according to the vertical bending tangent point V i,ep The angle between the tangent line and the longitudinal bridge direction is α i,ep Determine the specific position of the vertical bending end point of the cable strand, and then obtain the X and Y coordinates of the vertical bending end point of the anchor span cable strand, which are recorded as and According to the geometric relationship, the following relationship can be obtained:

[0023] When α i,ep <=β,

[0024]

[0025] When β<α i,ep <=β+θ2,

[0026]

[0027] When β+θ2<α i,ep <=β+θ2+θ3,

[0028]

[0029] When β+θ2+θ3<α i,ep <=β+θ2+θ3+θ4,

[0030]

[0031] In formulas (5), (6) and (7), β is the center angle of the first arc anchor span of the composite saddle; θ1, θ2, θ3 and θ4 are the center angles of the four composite saddles; R1, R2, R3 and R4 are the radii of the four composite saddles;

[0032] S6.2, based on the catenary theory, the tangent point Vi,sp The angle between the tangent line and the longitudinal bridge direction is α i,sp It can be expressed as:

[0033] α i,ep =arctan(sinha i,as ) (8),

[0034] According to the closure conditions of the vertical and horizontal directions of the catenary segment of the anchor span cable, the following control equations can be obtained:

[0035]

[0036] In formulas (8), (9) and (10), a i,as is the parameter of the i-th catenary, l i,as is the i-th catenary along x i The projection length of the axis, the unknown number of catenary parameters is n, and the catenary is along the x i The number of unknown axis projection lengths is n;

[0037] S6.3, in formula (9):

[0038] c i,as =-H i,as / q (11),

[0039] The horizontal force of each cable strand can be expressed as:

[0040] H i,ms =H ms / n (12),

[0041] According to the corresponding mechanical equilibrium conditions that the cables on both sides of the composite saddle should meet, it can be obtained that:

[0042]

[0043] In summary, the anchor span cable force can be expressed as:

[0044]

[0045] In equations (11), (12), (13) and (14), q is the self-weight concentration of each cable strand; H ms is the horizontal force of the main cable in the main span, H i,ms is the horizontal force of each cable strand; α i,sp Point V i,sp The angle between the tangent line and the longitudinal bridge direction; T i is the cable force of the ith cable strand at the tangent point of the composite saddle; H i,as is the i-th catenary along x i Cable force on the axis.

[0046] Furthermore, in S7, the side anchor span cable force of the composite cable saddle is determined by combining equations (9), (10), (11), (12), (13) and (14), and using the same method as in S3, the side anchor span cable force of the composite cable saddle can be determined.

[0047] The beneficial effects of the present invention are:

[0048] The present invention fully considers the spatial orientation of the anchor span cable strands on the composite saddle side, takes the same cable force of all cable strands at the tangent point of the composite saddle as the calculation principle, and determines the anchor span cable force on the composite saddle side of the single-tower ground-anchored suspension bridge by solving a group of nonlinear equations; the method can ensure uniform distribution of the anchor span cable force in the bridge state and improve the cable strand utilization rate; and the method avoids repeated iterations in the calculation process, and determines the anchor span cable force by solving a group of nonlinear equations, which can improve the calculation efficiency while ensuring the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0050] Figure 1 This is a schematic plan view of a composite cable saddle according to Example 1 of the present invention;

[0051] Figure 2 This is a schematic elevation diagram of a composite cable saddle according to Example 1 of the present invention;

[0052] Figure 3 This is a schematic diagram of the flat bending of the anchor span cable strands in Example 1 of the present invention;

[0053] Figure 4 This is a schematic diagram of vertical bending of anchor span cable strands in Example 1 of the present invention;

[0054] Figure 5 This is a schematic diagram of the catenary segment of the anchor span cable strand of Example 1 of the present invention;

[0055] Figure 6 This is the elevation view of the Lvzhijiang Bridge in Example 2 of the present invention;

[0056] Figure 7 This is a schematic diagram of the anchoring system of the Lvzhijiang Bridge in Example 2 of the present invention;

[0057] Figure 8 This is a schematic diagram of the cable strand arrangement in the saddle groove of the Lvzhijiang Bridge according to Example 2 of the present invention;

[0058] Fig. 9 Schematic diagram of cable strand arrangement at the front anchor surface of Lvzhijiang Bridge in Example 2 of the present invention;

[0059] Fig.10 This is a schematic diagram of the horizontal bending angle of the anchor span cable strand of the Lvzhijiang Bridge in Example 2 of the present invention;

[0060] Fig.11 This is a schematic diagram of the tangent point coordinates of the anchor span cable strands of the Lvzhijiang Bridge in Example 2 of the present invention;

[0061] Fig.12 This is a schematic diagram of horizontal forces on anchor span cables of Example 2 of the Lvzhijiang Bridge in the completed state of the present invention;

[0062] Fig.13 This is a schematic diagram of the anchor span cable force of Lvzhijiang Bridge in the completed state of Example 2 of the present invention;

[0063] Fig.14 This is the measured anchor span cable force and relative error of Example 2 of the Lvzhijiang Bridge of the present invention. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] Example 1

[0066] See also Figures 1 to 5 As shown, a method for calculating the anchor span cable force of a composite cable saddle side bridge of a single-tower ground-anchor suspension bridge is characterized in that it includes the following steps:

[0067] S1. Selecting composite saddle: composite saddle is composed of multiple arcs with different radii. This paper takes composite saddle with 4 arcs with different radii as the research object. From the main span to the anchor span, the radii corresponding to each arc are denoted as R1, R2, R3 and R4, and their central angles are θ1, θ2, θ3 and θ4 respectively. K is the center of the first arc.

[0068] S2. Clarify the direction of the anchor span cable strands on the composite saddle side: After the main cable of the main span passes through the saddle groove of the composite saddle, it is divided into n anchor span cable strands and anchored to the anchor through the turning and dispersion of the composite saddle; the flat bending radius of the main cable strand changes with its lateral arrangement in the saddle groove of the composite saddle; when the main cable enters the composite saddle from the main span, the main cable strand first undergoes vertical bending, and the starting point of the flat bending is closer to the anchor span side than the starting point of the vertical bending; the position of the starting point of the vertical bending relative to the composite saddle will change accordingly with the construction stage, temperature changes and live load, while the starting point of the flat bending remains unchanged relative to the composite saddle. In order to ensure the stability of the main cable strand in the saddle groove of the composite saddle, when designing the composite saddle, it should be ensured that the main cable strand completes the flat bending first and then the vertical bending. ;

[0069] S3. Determine the cable force distribution mode of the anchor span cable strand on the composite saddle side: Under the premise that the effects of the anchor span cable strand and the main span main cable on the composite saddle meet the equilibrium conditions of the composite saddle, assume that the cable force T of each anchor span cable strand at the tangent point of the composite saddle i are equal;

[0070] S4. Calculate the horizontal bending angle of the anchor span cable strand:

[0071] OK i and r i are the center and radius of the flat bending arc of the i-th cable strand, α i,hb is the horizontal bending angle of the i-th cable strand; N i is the intersection of the angle bisector of the flat bending angle of the i-th cable strand and the horizontal line passing through the starting point of the flat bending. Based on the geometric relationship, the following control equation can be obtained:

[0072]

[0073] Move the right side of formula (1) to the left side to form the error function of the control equation:

[0074]

[0075] In formulas (1) and (2), and The flat bend starting point H i ,s p and anchor point M i The vertical and horizontal distances between

[0076] In order to obtain the flat bending angle of the i-th cable strand, the error function needs to be close to 0; therefore, the objective function is established as follows:

[0077] minf i 2 (·)(3),

[0078] The objective function can be solved by the nonlinear generalized simplified gradient (GRG) method. When the objective function meets the error limit, the flat bending angle of the i-th anchor span cable strand can be determined. Similarly, the flat bending angles of the remaining anchor span cables can be determined by this method.

[0079] S5. Determine 2n+1 basic unknowns: Establish a global coordinate system with K as the origin, with the X-axis pointing horizontally to the right, the Y-axis pointing vertically upward, the Z-axis perpendicular to the XY plane and pointing to the inside of the screen, and V i,ep Establish a local coordinate system for the origin, x i The axis points to the front anchor surface, and the angle between it and the horizontal direction is the bending angle of the cable strand, y i The axis is vertically downward, and the catenary of the suspended section of the anchor span cable strand is taken as the research object; the number of unknown parameters of the catenary is n, and the unknown length of the projection of the catenary along the xi axis is n. Since "the cable force T of each anchor span cable strand at the tangent point of the composite cable saddle i are equal", so the catenary is along x i The number of unknowns in the axonal force is 1. The total number of unknowns is 2n+1;

[0080] S6. Determine 2n+1 nonlinear equations: 2n+1 nonlinear equations can be constructed based on the elevation closure and horizontal closure of each catenary and the overall force balance at the composite saddle;

[0081] S6.1, according to the vertical bending tangent point V i,ep The angle between the tangent line and the longitudinal bridge direction is α i,ep Determine the specific position of the vertical bending end point of the cable strand, and then obtain the X and Y coordinates of the vertical bending end point of the anchor span cable strand, which are recorded as and According to the geometric relationship, the following relationship can be obtained:

[0082] When α i,ep <=β,

[0083]

[0084] When β<α i,ep <=β+θ2,

[0085]

[0086] When β+θ2<α i,ep <=β+θ2+θ3,

[0087]

[0088] When β+θ2+θ3<α i,ep <=β+θ2+θ3+θ4,

[0089]

[0090] In formulas (5), (6) and (7), β is the center angle of the first arc anchor span of the composite saddle; θ1, θ2, θ3 and θ4 are the center angles of the four composite saddles; R1, R2, R3 and R4 are the radii of the four composite saddles;

[0091] S6.2, based on the catenary theory, the tangent point V i,sp The angle between the tangent line and the longitudinal bridge direction is α i,sp It can be expressed as:

[0092] α i,ep =arctan(sinha i,as ) (8),

[0093] According to the closure conditions of the vertical and horizontal directions of the catenary segment of the anchor span cable, the following control equations can be obtained:

[0094]

[0095] In formulas (8), (9) and (10), a i,as is the parameter of the i-th catenary, l i,as is the i-th catenary along x i The projection length of the axis, the unknown number of catenary parameters is n, and the catenary is along the x i The number of unknown axis projection lengths is n;

[0096] S6.3, in formula (9):

[0097] c i,as =-H i,as / q(11),

[0098] The horizontal force of each cable strand can be expressed as:

[0099] H i,ms =H ms / n(12),

[0100] According to the corresponding mechanical equilibrium conditions that the cables on both sides of the composite saddle should meet, it can be obtained that:

[0101]

[0102] In summary, the anchor span cable force can be expressed as:

[0103]

[0104] In equations (11), (12), (13) and (14), q is the self-weight concentration of each cable strand; H ms is the horizontal force of the main cable in the main span, H i,ms is the horizontal force of each cable strand; α i,sp Point Vi,sp The angle between the tangent line and the longitudinal bridge direction; T i is the cable force of the i-th catenary at the tangent point of the composite saddle; H i,as is the i-th catenary along x i Cable force on the axis.

[0105] S7. Determine the span cable force of the side anchor of the composite cable saddle: By combining equations (9), (10), (11), (12), (13) and (14) and using the same method as in S3, the span cable force of the side anchor of the composite cable saddle can be determined.

[0106] Example 2

[0107] This embodiment takes the Lvzhijiang Bridge as an example, and uses the present invention to calculate the anchor span cable force of the composite cable saddle side. The anchor span cable force identification steps are as follows:

[0108] Step 1: Select the composite cable saddle and determine the direction of the composite cable saddle side anchor across the cable strands;

[0109] As a key control project of Yuxi-Chuxiong Expressway, the main bridge structure of Lvzhijiang Bridge is a (140+780)m single-tower single-span ground-anchored steel box girder suspension bridge. Both sides of the bridge are directly connected to the tunnel system. The distance between the two main cables is 28m, and the vertical span ratio of the main cables is 1 / 11; the standard spacing of the suspension cables along the bridge is 11.8m; in order to adapt to the terrain conditions, the bridge only has bridge towers on the Yuxi bank, with a tower height of 156m; the anchoring systems on both sides are tunnel anchors, among which the composite cable saddle is set on the Chuxiong bank, connecting the main span with the anchor span on the Chuxiong bank; the facade layout of the bridge can be seen in Figure 6 .

[0110] The Luzhijiang Bridge is located in a typical "V"-shaped canyon, with very steep terrain on both sides and a mountain as high as 640m. The entrance of the Chuxiong Bank Tunnel is located on a steep wall with a slope of 70-90°. The access roads on both sides of the bridge are long, with sharp bends and steep slopes, and the construction site is narrow, so tunnel anchorage is used on both sides. The angle between the anchor axis of the Chuxiong Bank Tunnel and the horizontal direction is 18.7°, and its cavern structure is an inclined inverted trumpet shape. The front anchor chamber is 30m long, the anchor plug is 37m long, and the rear anchor chamber is 3m long. Figure 7 .

[0111] Step 2, determining the cable force distribution mode of the composite cable saddle side anchor across the cable strands;

[0112] The two main cables of the Lvzhijiang Bridge were erected using the prefabricated parallel wire strand (PPWS) method; each main cable consists of 127 strands, each of which contains 91 Φ5.2 parallel high-strength galvanized steel wires; Figure 8 and Fig. 9 They are respectively the cable strand numbering and arrangement in the saddle groove and on the front anchor surface of the composite cable saddle of Lvzhijiang Bridge; Table 1 is the calculation parameters of the anchor span cable force.

[0113]

[0114]

[0115] Table 1 Anchor span cable force calculation parameters

[0116] Step 3: Calculate the horizontal bending angle of the anchor span cable strand;

[0117] Depend on Fig.10 It can be seen that the cables in the middle row are not affected by horizontal bending, and their horizontal bending angle is 0. From the middle to the two sides, the horizontal bending angle of the cables gradually increases and presents a symmetrical distribution law. As the height of the cables increases, the horizontal bending angle of the cables on both sides gradually decreases.

[0118] Fig.11 is the tangent point coordinate of the anchor span cable strand of Lvzhijiang Bridge on the composite cable saddle; it can be seen that the distribution law of the anchor span cable strand tangent point is similar to that of the cable strand on the front anchor surface, but with the increase of cable strand height, the X coordinate of its tangent point gradually decreases. It shows that: (1) the vertical bending angle of the anchor span cable strand gradually decreases along the cable strand height direction; (2) the top layer of cable strands is first cut off from the composite cable saddle, and then other cables are cut off layer by layer from top to bottom.

[0119] Step 4: Calculate the span force of the composite cable saddle side anchor;

[0120] Substituting the above parameters into the formula described in Example 1, we can obtain Fig.12 The horizontal force in the anchor span of the completed bridge is given by Fig.12 It can be seen that under the premise that all cable strands have equal cable forces, the horizontal component of the cable force is determined by the sum of its horizontal and vertical bending angles; from bottom to top, the horizontal force of the cable strand increases as its vertical bending angle decreases. For the same row of cables, the horizontal bending angle gradually increases from the center of the anchor surface to both sides, so the corresponding horizontal force of the cable strand gradually decreases; similarly, the change of the horizontal bending angle of the cable strand along the height direction has little effect on its horizontal component.

[0121] Fig.13 This is the anchor span cable tension of the completed Lvzhijiang Bridge. The anchor span cable tension of each cable strand is 1010.93kN, and the cable tension is evenly distributed.

[0122] Therefore, in the design of the Lvzhijiang Bridge, the cutting length of each anchor span cable strand was calculated according to the method provided by the present invention, so as to achieve the anchor span cable force reaching the design value in the completed bridge state; Fig.14 The measured anchor span cable force and relative error are shown in Figure 2. It can be seen that the relative errors between the measured anchor span cable forces and the calculated values ​​on the left and right sides are between -2.81% and 2.30%, the anchor span cable forces are evenly distributed, and the errors of all anchor span cable forces are less than 3%, which meets the requirement of Technical Specifications for Highway Bridge and Culvert Construction (JTGT3650-2020) that the anchor span cable tension error is less than 3%.

Claims

1. A method for calculating the anchor span cable force of a composite cable saddle side bridge of a single-tower ground-anchored suspension bridge, comprising the following features: The steps include: S1. Select composite saddle: composite saddle is composed of multiple arcs with different radii. Composite saddles with 4 different arc radii are taken as the research objects. From the main span to the anchor span, the radii corresponding to each arc are recorded as R1, R2, R3 and R4, and their central angles are θ1, θ2, θ3 and θ4 respectively. K is the center of the first arc. S2. Clarify the direction of the anchor span cable strands on the composite saddle side: After the main cable of the main span passes through the saddle groove of the composite saddle, it is divided into n anchor span cable strands and anchored on the anchor through the turning and dispersion of the composite saddle; the flat bending radius of the main cable strands changes with its lateral arrangement in the saddle groove of the composite saddle; when the main cable enters the composite saddle from the main span, the main cable strands are first bent vertically, and the starting point of the flat bending is closer to the anchor span side than the starting point of the vertical bending; The position of the starting point of the vertical bend relative to the composite cable saddle will change with the construction stage, temperature changes and live load, while the starting point of the horizontal bend remains unchanged relative to the composite cable saddle; In order to ensure the stability of the main cable strands in the saddle groove of the composite saddle, when designing the composite saddle, it should be ensured that the main cable strands complete the horizontal bending first and then the vertical bending. S3. Determine the cable force distribution mode of the anchor span cable strand on the composite saddle side: Under the premise that the effects of the anchor span cable strand and the main span main cable on the composite saddle meet the equilibrium conditions of the composite saddle, assume that the cable force T of each anchor span cable strand at the tangent point of the composite saddle i are equal; S4. Calculate the horizontal bending angle of the anchor span cable strand: OK i and r i are the center and radius of the flat bending arc of the i-th cable strand, α i,hb is the horizontal bending angle of the i-th cable strand; N i is the intersection of the angle bisector of the flat bending angle of the i-th cable strand and the horizontal line passing through the starting point of the flat bending. Based on the geometric relationship, the following control equation can be obtained: Move the right side of formula (1) to the left side to form the error function of the control equation: In formulas (1) and (2), and The flat bend starting point H i ,s p and anchor point M i The vertical and horizontal distances between In order to obtain the flat bending angle of the i-th cable strand, the error function needs to be close to 0; therefore, the objective function is established as follows: minf i 2 (·)(3), The objective function can be solved by the nonlinear generalized simplified gradient (GRG) method. When the objective function meets the error limit, the flat bending angle of the i-th anchor span cable strand can be determined. Similarly, the flat bending angles of the remaining anchor span cables can be determined by this method. S5. Determine 2n+1 basic unknowns: Establish a global coordinate system with K as the origin, with the X-axis pointing horizontally to the right, the Y-axis pointing vertically upward, the Z-axis perpendicular to the XY plane and pointing to the inside of the screen, and V i,ep Establish a local coordinate system for the origin, x i The axis points to the front anchor surface, and the angle between it and the horizontal direction is the bending angle of the cable strand, y i The axis is vertically downward, and the catenary of the suspended section of the anchor span cable strand is taken as the research object; the number of unknown parameters of the catenary is n, and the catenary is along x i The unknown length of the axial projection is n. Since the cable force T of each anchor span cable strand at the tangent point of the composite cable saddle is i are equal", so the catenary is along x i The number of unknowns in the axonal force is 1; the total number of unknowns is 2n+1; S6. Determine 2n+1 nonlinear equations: 2n+1 nonlinear equations can be constructed based on the elevation closure and horizontal closure of each catenary and the overall force balance at the composite saddle; S7. Determine the side anchor span force of the composite saddle.

2. The method for calculating the anchor span cable force of a composite cable saddle side bridge of a single-tower ground-anchored suspension bridge according to claim 1 is characterized in that: In S6, 2n+1 nonlinear equations are determined as follows: S6.1, according to the vertical bending tangent point V i,ep The angle between the tangent line and the longitudinal bridge direction is α i,ep Determine the specific position of the vertical bending end point of the cable strand, and then obtain the X and Y coordinates of the vertical bending end point of the anchor span cable strand, which are recorded as and According to the geometric relationship, the following relationship can be obtained: When α i,ep <=β, When β<α i,ep <=β+θ2 when, If β+θ2<α i,ep <=β+θ2+θ3 when, If β+θ2+θ3<α i,ep <=β+θ2+θ3+θ4 when, In formulas (5), (6) and (7), β is the center angle of the first arc anchor span of the composite saddle; θ1, θ2, θ3 and θ4 are the center angles of the four composite saddles; R1, R2, R3 and R4 are the radii of the four composite saddles; S6.2, based on the catenary theory, the tangent point V i,sp The angle between the tangent line and the longitudinal bridge direction is α i,sp It can be expressed as: α i,ep =arctan(sinha i,as ) (8), According to the closure conditions of the vertical and horizontal directions of the catenary segment of the anchor span cable, the following control equations can be obtained: In formulas (8), (9) and (10), a i,as is the parameter of the i-th catenary, l i,as is the i-th catenary along x i The projection length of the axis, the unknown number of catenary parameters is n, and the catenary is along the x i The number of unknown axis projection lengths is n; S6.3, in formula (9): c i,as =-H i,as / q (11), The horizontal force of each cable strand can be expressed as: H i,ms =H ms / n (12), According to the corresponding mechanical equilibrium conditions that the cables on both sides of the composite saddle should meet, it can be obtained that: In summary, the anchor span cable force can be expressed as: In equations (11), (12), (13) and (14), q is the self-weight concentration of each cable strand; H ms is the horizontal force of the main cable in the main span, H i,ms is the horizontal force of each cable strand; α i,sp Point V i,sp The angle between the tangent line and the longitudinal bridge direction; T i is the cable force of the i-th catenary at the tangent point of the composite saddle; H i,as is the i-th catenary along x i Cable force on the axis.

3. The method for calculating the anchor span cable force of a composite cable saddle side bridge of a single-tower ground-anchored suspension bridge according to claim 1 is characterized in that: In S7, the side anchor span cable force of the composite cable saddle is determined by combining equations (9), (10), (11), (12), (13) and (14), and the same method as in S3 is used to determine the side anchor span cable force of the composite cable saddle.

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