Fine calculation method of suspension bridge cable system

Abstract

The invention belongs to the technical field of bridge design and construction monitoring, and provides a refined calculation method for a suspension bridge cable system. A plurality of parameters such as cable saddle pre-deviation, splay cable saddle pre-deviation, cable tower compression deformation, variation of a cable strand at a tangency point of the cable saddle, elongation of the cable strand in the cable saddle and the like are put in the same calculation model; the bridge forming state and the empty cable state of the main cable and the construction state under any construction load are determined through a gradual point-by-point balance iteration main cable shape finding calculation method, the calculation precision is gradually improved, the calculation speed is high, and convergence is easy. According to the invention, the influence of the horizontal displacement of the cable saddle and the change of the tangent point of the main cable on the line shape of the main cable can be simulated, the friction influence of the cable strand and the cable saddle groove can be calculated, the elongation of the main cable in the saddle groove can be corrected, and the more accurate bridging line shape of the main cable, the cable saddle pre-bias and the splay cable saddle pre-bias can be obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge design and construction monitoring, and relates to a refined calculation method for a suspension bridge cable system. Background Art

[0002] There are significant differences in the line shape and cable force of the main cable of a suspension bridge in the two states of empty cable and completed bridge. As the construction progresses, the weight of the stiffening beam is gradually applied to the main cable, resulting in a significantly greater increase in the cable force of the main cable of the main span than that of the main cable of the side span. This unbalanced growth makes the horizontal component of the main cable of the main span significantly greater than that of the side span, which in turn generates a large bending moment on the cable tower, posing a threat to its safety. Generally, the relative span of the main cable of the main span and the side span is adjusted by pushing the cable saddle, thereby balancing the horizontal component of the main cable on both sides of the cable tower. Therefore, accurately setting the pre-bias of the cable saddle is not only related to the structural safety, but also directly affects the final line shape of the main cable. The saddle groove design of the cable saddle is usually arc-shaped, and the main cable and the cable saddle form two asymmetric tangent points on both sides. During the pushing process, the cable saddle translates relative to the cable tower, causing the two tangent points to change, which greatly increases the complexity of the main cable line shape calculation. At present, the main methods for calculating this complex process are: Fan Lichu et al. used bar units or beam units to simulate the cable saddle structure and its jacking process in "Research on the Fine Algorithm of Erection Parameters of Large-span Suspension Bridge Structures"; Li Chuanxi used multi-segment arc composite curve cable saddles to solve the offset in "Nonlinear Fine Calculation Theory and Application of Hybrid Beam Suspension Bridges". These methods do not take into account the various factors affecting the main cable line shape, such as the pre-bias of the cable saddle, the pre-bias of the loose cable saddle, the compression deformation of the cable tower, the change of the cable strand at the tangent point at the cable saddle, and the elongation of the cable strand in the cable saddle. Therefore, the error of the main cable bridge line shape obtained is large; some methods use catenary for iterative calculation, and the calculation process is relatively complicated, which is difficult to implement when considering multiple influencing factors.

[0003] Therefore, the refined calculation method of the present invention puts multiple parameters such as saddle pre-deviation, loose cable saddle pre-deviation, tower compression deformation, change of cable strand tangent point at saddle, elongation of cable strand in saddle into the same calculation model, and determines the bridge-built state and empty cable state of the main cable and the construction state under any construction load through a progressive point-by-point equilibrium iterative main cable form-finding calculation method. Summary of the invention

[0004] The purpose of the present invention is to provide a refined calculation method for the cable system of a suspension bridge, which can simulate the influence of the horizontal displacement of the saddle and the change of the main cable tangent point on the main cable line shape, calculate the friction influence between the cable strand and the saddle groove, correct the elongation of the main cable in the saddle groove, and obtain more accurate main cable bridge line shape and saddle offset.

[0005] In the design process of a suspension bridge, designers will first determine key parameters such as the structural alignment, component size, and material type in the completed state, and use the finite element method to perform preliminary analysis and calculation to ensure that the structure meets the requirements of relevant specifications, and determine the internal forces and preliminary alignment of the completed state. On this basis, the present invention performs more refined calculations on the cable system, aiming to accurately obtain critical construction control parameters such as the empty cable alignment and saddle offset, providing more detailed and accurate guidance for the construction of suspension bridges.

[0006] The technical solution of the present invention:

[0007] A refined calculation method for a suspension bridge cable system, the steps are as follows:

[0008] The main span, side span, anchor span, tower height, anchor span height, main cable sag, suspender horizontal coordinate and suspender force (including cable clamp weight), main cable area, elastic modulus, and unit length weight are known. The bridge status of the main cable is determined by the progressive point-by-point equilibrium iterative main cable form-finding calculation method, which includes the following three steps:

[0009] (1) The main cable calculation model is established based on the IP points of the cable saddle and loose cable saddle. The main cable is only subjected to the hanger force (including the weight of the cable clamp). The point-by-point equilibrium iteration method is used to iterate each node of the main span, then each node of the side span, and then each node of the anchor span. The main cable horizontal force component is equal as the control principle. The main span rise reaches the design value as the convergence condition. The form-finding calculation of the main cable is performed to obtain the bridge state C1.

[0010] (2) Calculate the deadweight of the main cable based on the length of each main cable section obtained in the completed bridge state C1, and add it to the suspender force as the new node load. Repeat the calculation in step (1) to obtain the completed bridge state C2;

[0011] (3) Calculate the coordinates of the tangent points of the main cables at the cable saddle and the loose cable saddle respectively, and use this as a reference to redetermine the span of each span, the main cable's sagittal height and other parameters, establish a new main cable calculation model, use the load in step (2), perform point-by-point equilibrium iterative calculation again, and obtain the bridge state C3.

[0012] The form-finding calculation of the main cable in the construction state (including the empty cable state and any construction load) is completed through the following steps:

[0013] (1) Estimate the initial value of the cable saddle pre-deviation d0, calculate the length of each section of the main cable in the main span in the empty cable state according to the main cable strain obtained in the C1 bridge state, calculate the deadweight of the empty cable according to the node concentrated force, and change the cable saddle pre-deviation d0 through multiple cycles until the two ends of the main cable reach the design elevation;

[0014] (2) The length of each main cable section in the anchor span in the empty cable state is calculated based on the main cable strain obtained in the C1 bridge state. The deadweight of the empty cable is calculated as the node concentrated force. The pre-bias θ of the loose cable saddle is changed through multiple cycles until the end point of the main cable in the anchor span reaches the design elevation.

[0015] (3) The length of each main cable section in the side span in the empty cable state is calculated based on the main cable strain obtained in the C1 bridge state. The deadweight of the empty cable is calculated as the node concentrated force. The saddle pre-bias d0 is changed through multiple cycles until the end point of the main cable in the side span reaches the design elevation (considering the compression deformation of the cable tower);

[0016] (4) Considering the friction between the main cable and the saddle groove in the saddle and loose cable saddle, calculate the coordinates of the main cable tangent point after the elastic elongation of the arc part of the main cable in the saddle groove causes the main cable to change. After correcting the tangent point coordinates, repeat steps (1) to (3) to obtain the line shape of the main cable in the empty cable state;

[0017] (5) During a certain construction process, the load of the stiffening beam is applied to the corresponding main cable node in the form of a node force through the hanger. The construction load is recorded as: F i , (i=1,2,…,n), F of the nodes without construction loads i Take the value as 0, and calculate according to steps (1)-(3) to obtain the preliminary construction state main cable line shape and the horizontal component H2 of the main cable. This state is called S1 construction state;

[0018] (6) Using the formula ε i =(H0-H2) / EA / cosθ i-1 Calculate the main cable strain using the formula α i =α i-1 +P i / H2 main cable angle coefficient, and then recalculate the main cable line shape and saddle offset and loose saddle offset under the premise of balanced horizontal force of each span according to steps (1)-(3).

[0019] Beneficial effects of the present invention:

[0020] (1) The main cable form-finding calculation method of progressive point-by-point equilibrium iteration is used to determine the main cable linear shape, cable force, cable saddle pre-bias and loose cable saddle pre-bias parameters, which gradually improves the calculation accuracy, has fast calculation speed and is easy to converge.

[0021] (2) By placing multiple parameters such as the saddle pre-bias, loose cable saddle pre-bias, tower compression deformation, change in the cable strand tangent point at the saddle, and cable strand elongation in the saddle in the same calculation model, it is possible to simulate the horizontal displacement of the saddle and the influence of the change in the main cable tangent point on the main cable line shape, calculate the friction between the cable strand and the saddle groove, correct the elongation of the main cable in the saddle groove, and obtain a more accurate main cable bridge line shape and saddle offset.

[0022] (3) It can not only calculate the linear shape of the main cable in the completed and empty cable states, but also calculate the construction state under any construction load, providing a new algorithm for the construction control of suspension bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a structural diagram of the cable system of a suspension bridge.

[0024] Figure 2 It is a detailed drawing of the key points of cable saddles and loose cable saddles.

[0025] Figure 3 It is a calculation flow chart.

[0026] In the figure: 1 main cable; 2 saddle. DETAILED DESCRIPTION

[0027] The specific implementation of the present invention is described in detail below in conjunction with the technical scheme and the accompanying drawings.

[0028] A refined calculation method for a suspension bridge cable system, the steps are as follows:

[0029] Main design parameters: Main span S m , side span S s , Anchor span S a , divide nodes on the main cable at each cable clamp position, and divide an appropriate number of nodes on the main cable without cable clamps. The horizontal coordinate of each span node is represented by x i (i=0,1,…,n), where n represents the maximum node number in the span, the tower height is c, the anchor span height is h, the main cable height is f, and the force at each node in the completed bridge state is P i , (i=1,2,…,n), mainly the suspender force (including the weight of the cable clamp, the suspender force below includes the weight of the cable clamp), the node force is 0 where there is no suspender, the main cable area, elastic modulus, and unit length weight are: A, E, q. For the cable system structure diagram and the key point details of the saddle and loose saddle, see Figure 1 , Figure 2 , perform progressive point-by-point equilibrium iteration calculations of the bridge alignment, empty cable alignment, and construction alignment under arbitrary construction loads according to the following steps.

[0030] S1. Calculate the main span: Substitute the main span hanger force and the horizontal coordinates of the locations of the span nodes into formula (1) to calculate the vertical force R at the IP point of the main cable of the main span y ;

[0031]

[0032] Where P i is the force at each node in the bridge state; S mis the main span; x i is the horizontal coordinate of each span node, i = 0, 1, ..., n, n is the maximum number of nodes in the span; P i is the force at each node in the bridge state, i = 1, 2, ..., n;

[0033] S2. Estimate the horizontal component H0 of the main cable force in the main span and substitute it into formula (2) to obtain the angle coefficient α0 of the main cable at the IP point of the main span:

[0034] α0=-R y / H0 (2)

[0035] S3. Using formulas (3) and (4), calculate the y coordinates and corresponding angle coefficients of each node of the main cable of the main span;

[0036] y i =y i-1 +α i-1 (x i -x i-1 ) (3)

[0037] α i =α i-1 +P i / H0 (4)

[0038] Where, i = 1, 2, ..., n;

[0039] S4. Calculate the deviation dy between the main cable mid-span alignment and the mid-span sag f in the completed bridge state:

[0040] dy=f-|y middle |

[0041] Where, f is the main cable height; y middle is the y coordinate of the main cable span. If the absolute value of dy is greater than 0.5 mm, change the size of H0 and return to S2 to recalculate until |dy|<0.5 mm is satisfied and then exit the main span linear iterative calculation;

[0042] S5. Calculate the side span: Substitute the side span hanger force and the horizontal coordinates of the positions of the nodes in each span into formula (1), and replace the main span S in formula (1) with m Replaced by side span S s , calculate the vertical force Rs of the main cable at the IP point of the loose cable saddle y ;

[0043] S6, using the horizontal component H0 of the main cable force in the main span obtained by iterative calculation of S1-S4 as the equilibrium condition, substitute it into formula (5) to obtain the angle coefficient α of the main cable at the IP point of the side span main cable s0 :

[0044] α s0 =Rsy / H s0 (5)

[0045] S7. Similarly, using formulas (3) and (4), calculate the y coordinates of each node of the side span main cable and the corresponding angle coefficient;

[0046] S8. Calculate the deviation dys between the end point coordinates of the side span main cable and the completed bridge state:

[0047] dys=c-|y s |

[0048] Where c is the height of the tower; y s is the y coordinate of the end point of the side span main cable. If the absolute value of dys is greater than 0.5 mm, change α s0 The size of the side span cable is calculated, and the calculation is returned to S7 for recalculation until |dys|<0.5mm is satisfied, and the side span main cable shape calculation is exited;

[0049] S9, perform anchor span calculation: perform iterative calculation on the anchor span according to the calculation steps of S5-S7, and obtain the y coordinates and corresponding angle coefficients of each node of the anchor span main cable;

[0050] S10. Calculate the deviation dya between the anchor span main cable end point coordinates and the bridge state:

[0051] dya=h-|y a |

[0052] Where h is the height between the theoretical anchor point of the main cable and the IP point of the loose cable saddle; y a is the y coordinate of the end point of the anchor span main cable. If the absolute value of dya is greater than 0.5 mm, change α a0 The size of the anchor span is calculated, and the calculation is returned to S9 to be recalculated until |dya|<0.5mm is satisfied. Then the anchor span main cable linear shape calculation is exited, and the C1 bridge state is obtained.

[0053] S11. Calculate the length l of each main cable section i and the dependent variable ε i : Calculate the deadweight of each main cable section according to the calculated length of each main cable section, and superimpose it with the suspender force according to formula (6) to obtain a new suspender force. Repeat the calculation process of S1-S10 to obtain the C2 bridge state;

[0054] P i =P i +0.5q(l i +l i+1 ) (6)

[0055] Where q is the weight of the main cable per unit length;

[0056] S12, respectively calculate the coordinates (x a ,y a )、(x b ,y b ) into formulas (7)-(12), the coordinates of the saddle center are calculated as (x c ,y c ), the coordinates of the tangent points of the saddle arc are (xt1, yt1), (xt2, yt2), and the length of the outer chord of the arc is L a , L b ;

[0057]

[0058] Where r is the theoretical radius of the saddle;

[0059] S13, assuming that the friction coefficient between the main cable and the saddle groove is μ, calculate the coordinates of the first pair of nodes on both sides of the saddle and the saddle tangent point after the elastic elongation of the main cable in the arc part of the saddle causes the change according to formulas (13)-(15);

[0060]

[0061]

[0062] Where A is the main cable area and E is the elastic modulus;

[0063] S14, respectively calculate the coordinates (x a1 ,y a1 )、(x b1 ,y b1 ) is substituted into formulas (7)-(12), and the coordinates of the center of the scattered cable saddle are calculated as (x c1 ,y c1 ), the coordinates of the tangent points of the scattered saddle arc are (xt3, yt3) and (xt4, yt4), and the length of the outer chord of the arc is L a1 , L b1 ;

[0064] S15, using the method of S13, calculate the change of the tangent points on both sides of the loose cable saddle under the influence of friction;

[0065] S16. Correct the coordinates of the two end nodes of the main span and the main span of the main cable according to formula (16);

[0066]

[0067] S17. In the coordinate system with the IP point of the loose cable saddle as the origin, the coordinates of the two end nodes of the side span main cable, the side span span, and the tower height are corrected according to formula (17);

[0068]

[0069] S18. Correct the coordinates of the end node of the anchor span main cable at the loose cable saddle, the anchor span diameter, and the anchor span height according to formula (18);

[0070]

[0071] S19, using the revised design parameters, recalculate the steps of S1-S11 to obtain the C3 bridge state considering the cable saddle and loose cable saddle;

[0072] S20, main span empty cable state calculation, assuming a saddle pre-bias d0, the main span becomes S m =S m +2d0; the empty cable deadweight is calculated based on the node concentrated force, Pc i =0.5q(l i +l i+1 ), estimate the initial value of the horizontal force H1 of the empty cable, and calculate the vertical force R at the IP point of the main cable according to formula (1): y1 ;

[0073] S21: H1 replaces H0 and is substituted into formula (2) to obtain the angle coefficient α of the main cable at the IP point of the main span. 01 ;

[0074] S22: Calculate the main cable strain and main cable angle coefficient using formulas (19) and (20):

[0075] ε i =H0 / EA / cosθ i-1 (19)

[0076] α i =α i-1 +Pc i / H1 (20)

[0077] S23: Assume α c0 The initial value of is used, and the main cable coordinates are calculated using formulas (21) and (22):

[0078] x i+j =x i+j-1 +dx i (twenty one)

[0079] y i+j =y i+j-1 +dy i (twenty two)

[0080] Among them, dx i ,dy i They represent the main cable node displacements respectively and are calculated using the following formula;

[0081] dx i =(1-ε i+j ) i+j cos(atan(α i+j-1 ))

[0082] dy i =(1-ε i+j ) i+j sin(atan(α i+j-1 ))

[0083] Where, i = 1, 2, ..., n; j = 0, 1, ..., k + 1-i, the length and strain of each section of the main cable are the results obtained in the last round of step S11;

[0084] S24, if not satisfied |y n -yt1|<0.5mm, modify α0, return to S23 and recalculate until |yt1|<0.5mm n -yt1|<0.5mm, end the iteration;

[0085] S25, compare the difference d=x between the assumed saddle pre-bias d0 and the calculated actual displacement of the main cable end point n -S m -xt1, if d<0.5mm is satisfied, the loop ends; otherwise, the size of d0 is changed and the loop returns to S20 for re-iteration calculation until d<0.5mm is satisfied and the two ends of the main cable reach the design elevation;

[0086] S26, calculation of the empty cable state of the anchor span. According to the length of each section of the main cable obtained in the last round of S11, the line shape of the main cable is calculated using the method of S23. Since the horizontal force components of the main cables of the main span, side span and anchor span are equal, H1 is the same when calculating each span;

[0087] S27, the cable saddle rotates by θ, causing the coordinates of the tangent points of the cable saddle arc (xt3, yt3) and (xt4, yt4) to change, and the displacements are dx3, dy3, dx4, dy4 respectively;

[0088]

[0089]

[0090] Where w is the vertical height from the IP point of the loose cable saddle to the rotation center of the loose cable saddle support;

[0091] If it does not satisfy |y n-yt4+dy4|<0.5mm, use formula (25) to update the coordinates of the tangent point of the scattered cable saddle arc, modify α0, and return to S23 to recalculate until |y n -yt4+dy4|<0.5mm, the iteration ends; the displacement d1 of the IP point of the loose cable saddle in the anchor span equilibrium state is obtained;

[0092] S28, side span empty cable state calculation, side span span is: S s =S s -d0+d1: Based on the length of each section of the main cable obtained in the last round of S11, the line shape of the main cable is calculated using the method of S23. At this time, the horizontal component of the main cable used is H1;

[0093] S29, if not satisfied |y n -yt2+dy3|<0.5mm, use formula (25) to update the coordinates of the tangent point of the scattered saddle arc, and modify α s0 , return to S23 and recalculate until |y is satisfied n -yt2+dy3|<0.5mm, the iteration ends, and the displacement d of the saddle IP point in the side span equilibrium state is obtained;

[0094] S30, compare the difference between the assumed saddle pre-bias d0 and the calculated actual displacement of the main cable end point: d = x n -S m -xt1, if |d|<0.5mm is not satisfied, change the size of d0, return to S20 and iterate again until |d|<0.5mm is satisfied; end the loop, and obtain the line shape of the empty cable state and the saddle pre-bias and loose saddle pre-bias;

[0095] S31. Construction status calculation: During the construction process, the load of the stiffening beam is applied to the corresponding main cable node in the form of node force through the hanger, so the construction load is F i , (i=1,2,…,n), F of the nodes without construction loads i Take the value as 0; calculate S20 to S30, and obtain the preliminary construction state linear shape and the horizontal component force H2 of the main cable;

[0096] S32. Calculate the main cable strain and main cable angle coefficient using formulas (26) and (27):

[0097] ε i =(H0-H2) / EA / cosθ i-1 (26)

[0098] α i =α i-1 +F i / H2 (27)

[0099] Then, the process returns to S23 to S30 to recalculate the main cable line shape, saddle offset, and loose saddle offset under the premise that the horizontal component forces of each span are balanced.

[0100] Example

[0101] The main span of a suspension bridge is 300m, the side span is 100m, the anchor span is 15m, the hanger spacing is 10m, the hanger force of the completed bridge is 1000kN, the tower height is 42m, the anchor span height is 10m, the main cable rise is 40m, and the main cable cross-sectional area is 0.137564m 2 , elastic modulus 200GPa, weight per unit length 11.55kN / m.

[0102] S1: First calculate the main span, substitute the hanger force and the horizontal coordinate of the hanger position into formula (1) to calculate the vertical force R at the IP point of the main cable y =14500kN.

[0103] S2: Estimate the horizontal component of the main cable force H0 = 25000 kN, and substitute it into formula (2) to obtain the angle coefficient of the main cable at the IP point of the main span α0 = -0.58

[0104] S3: Using formulas (3) and (4), calculate the y coordinates of each node of the main cable and the corresponding angle coefficient (dimensionless) (see Table 1)

[0105] Table 1 y coordinates of each node of the main cable and the corresponding angle coefficient (unit: m)

[0106] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[y i ]]> -5.33 -10.30 -14.90 -19.13 -22.99 -26.48 -29.61 -32.37 -34.76 -36.78 αi -0.39 -0.50 -0.46 -0.42 -0.39 -0.35 -0.31 -0.28 -0.24 -0.20 <![CDATA[x i ]]> 110 120 130 140 150 160 170 180 190 200 <![CDATA[y i ]]> -38.44 -39.72 -40.64 -41.20 -41.38 -41.20 -40.64 -39.72 -38.44 -36.78 αi -0.13 -0.09 -0.06 -0.02 0.02 0.06 0.09 0.13 0.17 0.20 <![CDATA[x i ]]> 210 220 230 240 250 260 270 280 290 300 <![CDATA[y i ]]> -34.76 -32.37 -29.61 -26.48 -22.99 -19.13 -14.90 -10.30 -5.33 0.00 αi 0.24 0.28 0.31 0.35 0.39 0.42 0.46 0.50 0.53 0.57

[0107] S4: Calculate the deviation dy between the main cable mid-span alignment and the mid-span sag f in the completed bridge state:

[0108] dy=40-|-41.38|=1.38m

[0109] Obviously, the absolute value of dy is greater than 0.5mm, so change the size of H0 and return to S2 to recalculate. After 23 iterative calculations, when |dy|<0.5mm is satisfied, exit the main span linear iterative calculation.

[0110] S5: Then perform the side span calculation, substitute the side span hanger force and the horizontal coordinate of the hanger position into formula (1), the side span span is 100m, and calculate the vertical force Rs of the main cable at the IP point of the loose cable saddle y =4500kN.

[0111] S6: Take the horizontal component of the main cable force H0 = 28125 kN obtained by iterative calculation of S1-S4 as the equilibrium condition and substitute it into formula (5) to obtain the angle coefficient α of the main cable at the IP point of the side span main cable: s0 =0.16

[0112] S7: Using formulas (3) and (4), calculate the y coordinate of the side span main cable and the angle coefficient of each node (see Table 2).

[0113] Table 2 Y coordinates of each node of the main cable and the corresponding angle coefficient (unit: m)

[0114] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[y i ]]> 1.60 3.56 5.87 8.53 11.56 14.93 18.67 22.76 27.20 32.00 αsi 0.20 0.23 0.27 0.30 0.34 0.37 0.41 0.44 0.48 0.52

[0115] S8: Calculate the deviation dsy between the end point coordinates of the side span main cable and the completed bridge state:

[0116] dsy=42-|32|=10m

[0117] If the absolute value of dsy is greater than 0.5 mm, change α s0 The size of the side span cable is returned to S7 for recalculation until |dsy|<0.5mm is satisfied. Exit the side span main cable shape calculation.

[0118] S9: perform anchor span calculation again, and iteratively calculate the anchor span according to the calculation steps of S5-S7 to obtain the y coordinate of the anchor span main cable node and the corresponding angle coefficient.

[0119] Table 3 y coordinates of each node of the main cable and the corresponding angle coefficient (unit: m)

[0120] <![CDATA[x i ]]> 0 5 10 15 <![CDATA[y i ]]> 0 3.333 6.667 10.000 <![CDATA[α ai ]]> 0.67 0.67 0.67 0.67

[0121] S10: Calculate the deviation between the anchor span main cable end point coordinates and the completed bridge state day:

[0122] day=10-|10|=0

[0123] If |day|<0.5mm is satisfied, the anchor span main cable linearity calculation is exited and the C1 bridge state is obtained.

[0124] Table 4 Coordinates of main cables in the main span of C1 bridge completion state (origin at the IP point of the cable saddle)

[0125]

[0126]

[0127] Table 5 Coordinates of main cables of side spans in C1 completed bridge state (origin at IP point of scattered cable saddle)

[0128] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[y i ]]> 2.600 5.556 8.867 12.533 16.556 20.933 25.667 30.756 36.200 42.000

[0129] Table 6 Coordinates of main cables of anchor span C1 in completed bridge state (origin at anchor point)

[0130] <![CDATA[x i ]]> 5 10 15 <![CDATA[y i ]]> 3.333 6.667 10.000

[0131] S11: Calculate the length and strain of each main cable segment: l i ,ε i , calculate the deadweight of each main cable section according to the calculated length of each main cable section, and superimpose it with the suspender force according to formula (6) to obtain the new suspender force (Table 7), and then repeat the calculation process of S1-S10 to obtain the C2 bridge state.

[0132] Table 7 Main span updated hanger force (unit: kN)

[0133] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[P i ]]> 1129 1127 1126 1124 1123 1121 1120 1119 1118 1117 <![CDATA[x i ]]> 110 120 130 140 150 160 170 180 190 200 <![CDATA[P i ]]> 1117 1116 1116 1116 1116 1116 1116 1116 1117 1117 <![CDATA[x i ]]> 210 220 230 240 250 260 270 280 290 <![CDATA[P i ]]> 1118 1119 1120 1121 1123 1124 1126 1127 1129

[0134] Table 8 Hanger force after side span update (unit: kN)

[0135] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 <![CDATA[P i ]]> 1120 1121 1122 1124 1125 1127 1129 1131 1133

[0136] Table 9 Coordinates of main cables in the main span of C2 completed bridge (unit: m)

[0137] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[y i ]]> -5.169 -9.978 -14.427 -18.518 -22.252 -25.627 -28.647 -31.309 -33.616 -35.567 <![CDATA[x i ]]> 110 120 130 140 150 160 170 180 190 200 <![CDATA[y i ]]> -37.164 -38.405 -39.291 -39.823 -40.000 -39.823 -39.291 -38.405 -37.164 -35.567 <![CDATA[x i ]]> 210 220 230 240 250 260 270 280 290 300 <![CDATA[y i ]]> -33.616 -31.309 -28.647 -25.627 -22.252 -18.518 -14.427 -9.978 -5.169 0.000

[0138] Table 10 Coordinates of main cables of side spans in C2 completed bridge state (unit: m)

[0139] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[y i ]]> 2.590 5.537 8.840 12.500 16.519 20.895 25.631 30.727 36.183 42.000

[0140] Table 11 Coordinates of main cables of anchor span C2 in completed bridge state (origin at anchor point, unit: m)

[0141] <![CDATA[x i ]]> 5 10 15 <![CDATA[y i ]]> 3.265 6.598 10.000

[0142] S12: Substitute the coordinates of the first node of the main span and side span of the C2 bridge in the completed state (10, -5.164) and (-10, -5.817) obtained in step S11 into formulas (7)-(12) respectively, and calculate the coordinates of the center of the saddle circle as (0.142, -5.702), and the coordinates of the tangent points of the saddle arc as (2.438, -1.260) and (-2.372, -1.380).

[0143] S13: The friction coefficient between the main cable and the saddle groove is μ=0.25. The coordinates of the tangent point of the saddle after the elastic elongation of the main cable in the arc part of the saddle causes the change are calculated according to formulas (13)-(15): (2.436, -1.258) and (-2.371, -1.378).

[0144] S14: Substitute the coordinates of the first node of the side span and anchor span near the IP point of the loose cable saddle obtained in step S11 (10.000, 2.596) and (-5.000, -3.402) into formulas (7)-(12) respectively, and calculate the coordinates of the center of the loose cable saddle as (2.0722, -4.6278), and the coordinates of the tangent point of the loose cable saddle arc as: (0.816, 0.212) and (-0.701, -0.468).

[0145] S15: Using the method of step S13, calculate the coordinates of the tangent points on both sides of the loose cable saddle after the influence of friction is changed: (0.810, 0.210), (-0.695, -0.463).

[0146] S16: According to formula (16), the coordinates of the two end nodes of the main span and the main span are corrected to 295.128m.

[0147] S17: In the coordinate system with the IP point of the loose cable saddle as the origin, the coordinates of the two end nodes of the side span main cable are corrected according to formula (17): (-0.695, -0.463) and (89.299, 41.532), the side span span is 97.629m, and the tower height is 40.622m.

[0148] S18: According to formula (18), the coordinates of the end node of the anchor span main cable at the loose cable saddle are corrected, the anchor span span is 14.305m, and the anchor span height is 9.537m.

[0149] S19: Use the revised design parameters to recalculate the steps of S1-S11 to obtain the C3 bridge state considering the cable saddle and loose cable saddle.

[0150] Table 12 Coordinates of main cables in the main span of C3 completed bridge (unit: m)

[0151] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 100 <![CDATA[y i ]]> -5.164 -9.974 -14.424 -18.516 -22.249 -25.626 -28.645 -31.308 -33.615 -35.567 <![CDATA[x i ]]> 110 120 130 140 150 160 170 180 190 200 <![CDATA[y i ]]> -37.163 -38.404 -39.291 -39.823 -40.000 -39.823 -39.291 -38.404 -37.163 -35.567 <![CDATA[x i ]]> 210 220 230 240 250 260 270 280 290 300 <![CDATA[y i ]]> -33.615 -31.308 -28.645 -25.626 -22.249 -18.516 -14.424 -9.974 -5.164 0.000

[0152] Table 13 Coordinates of main cables of side spans in C3 completed bridge state (unit: m)

[0153] <![CDATA[x i ]]> 10 20 30 40 50 60 70 80 90 97.628 <![CDATA[y i ]]> 2.591 5.538 8.841 12.502 16.521 20.898 25.634 30.730 36.187 40.620

[0154] Table 14 Coordinates of main cables of anchor span in C3 completed bridge state (origin at anchor point, unit: m)

[0155] <![CDATA[x i ]]> 5 10 14.274 <![CDATA[y i ]]> 3.268 6.602 9.506

[0156] S20: Calculation of the main span empty cable state, assuming a saddle pre-bias of 0.15m, the main span becomes: S m =300.3m. The deadweight of the empty cable is calculated according to the node concentrated force, and the initial value of the empty cable horizontal force is estimated to be 4591.6kN. The vertical force R at the IP point of the main cable is calculated according to formula (1): y=2507kN.

[0157] S21: H1 = 4591.6 kN Substitute H0 into formula (2) to obtain the angle coefficient of the main cable at the IP point of the main span main cable α0 = -0.55.

[0158] S22: Calculate the main cable strain and main cable angle coefficient using formulas (19) and (20):

[0159] Table 15 Main cable coordinate strain

[0160] Segment 1 2 3 4 5 6 7 8 9 10 Unit: με 1150.1 1133.9 1118.7 1104.4 1091.2 1079 1067.9 1058 1049.2 1041.6 Segment 11 12 13 14 15 16 17 18 19 20 Unit: με 1035.3 1030.2 1026.3 1023.7 1022.4 1022.4 1023.7 1026.3 1030.2 1035.3 Segment 21 22 23 24 25 26 27 28 29 30 Unit: με 1041.6 1049.2 1058 1067.9 1079 1091.2 1104.4 1118.7 1133.9 1150.1

[0161] Table 16 Main cable angle coefficient

[0162] Segment 1 2 3 4 5 6 7 8 9 10 <![CDATA[α i ]]> -0.514 -0.478 -0.442 -0.407 -0.372 -0.269 -0.235 -0.202 -0.168 -0.135 Segment 11 12 13 14 15 16 17 18 19 20 <![CDATA[α i ]]> -0.102 -0.069 -0.036 -0.003 0.029 0.062 0.095 0.128 0.161 0.194 Segment 21 22 23 24 25 26 27 28 29 30 <![CDATA[α i ]]> 0.227 0.261 0.295 0.330 0.364 0.399 0.435 0.471 0.503 0.516

[0163] S23: Assuming the initial value of α0, use formulas (21) and (22) to calculate the main cable coordinates:

[0164] Table 17 Main cable coordinates (unit: m)

[0165] <![CDATA[x i ]]> 9.899 19.757 29.622 39.492 49.367 59.248 69.323 79.386 89.435 99.472 <![CDATA[y i ]]> -1.260 -5.334 -10.400 -15.114 -19.480 -23.501 -27.181 -29.896 -32.264 -34.291 <![CDATA[x i ]]> 109.49 119.51 129.51 139.51 149.50 159.49 169.47 179.46 189.44 199.43 <![CDATA[y i ]]> -35.979 -37.332 -38.353 -39.043 -39.405 -39.440 -39.148 -38.529 -37.583 -36.307 <![CDATA[x i ]]> 209.42 219.42 229.42 239.43 249.44 259.46 269.48 279.51 289.54 297.13 <![CDATA[y i ]]> -34.702 -32.764 -30.490 -27.878 -24.924 -21.624 -17.975 -13.972 -9.611 -4.888

[0166] S24: The above results obviously do not satisfy |y n -yt1|<0.5mm, modify α0, return to S23 and recalculate until |yt1|<0.5mm n -yt1|<0.5mm, end the iteration.

[0167] S25: Compare the difference between the assumed saddle pre-bias d0 and the calculated actual displacement of the main cable endpoints: d = 0.193, which does not satisfy d < 0.5 mm. Change the size of d0 and return to S20 to iterate again until d < 0.5 mm is satisfied, and the two endpoints of the main cable reach the design elevation.

[0168] S26: Calculation of the empty cable state of the anchor span. Based on the length of each section of the main cable obtained in the last round of step S11, the linear shape of the main cable is calculated using the method of step S23. Since the horizontal force components of the main cables of the main span, side span and anchor span are equal, H1=4591.6kN is the same when calculating each span.

[0169] S27: The cable saddle rotates by θ, causing the coordinates of the tangent points of the cable saddle arc to become: (0.768, 0.199), (-0.701, -0.468), and the displacements dx3, dy3, dx4, dy4 are: -0.042, 0.011, -0.006, 0.005 (m) respectively. n -yt4+dy4|<0.5mm, use formula (25) to update the coordinates of the tangent point of the scattered saddle arc, and modify α a0, return to S23 and recalculate until |y is satisfied n -yt4+dy4|<0.5mm, the iteration ends. The displacement of the loose cable saddle IP point in the anchor span equilibrium state is obtained as d1=0.054m.

[0170] S28: Calculation of empty cable status of side span, the side span is: S s =99.904m Based on the length of each section of the main cable obtained in the last round of step S11, the linear shape of the main cable is calculated using the method in step S23.

[0171] S29: Does not satisfy |y n -yt2+dy3|<0.5mm, use formula (25) to update the coordinates of the tangent point of the scattered saddle arc, and modify α s0 , return to S23 and recalculate until |y is satisfied n -yt2+dy3|<0.5mm, the iteration ends. The displacement of the IP point of the scattered cable saddle under the side span equilibrium state is obtained as d0=0.179m.

[0172] S30: Compare the difference between the assumed saddle pre-bias d0 and the calculated actual displacement of the main cable end point: d = x n -S m -xt1, does not satisfy |d|<0.5mm, change the size of d0, return to S20 and iterate again until |d|<0.5mm is satisfied. End the loop, and get the line shape of the empty cable state and the pre-bias of the cable saddle 0.126m and the pre-bias of the loose cable saddle 0.046m.

[0173] Table 18 Main span main cable aerial cable coordinates (unit: m)

[0174] <![CDATA[x i ]]> 10.019 20.035 30.055 40.076 50.097 60.116 70.132 80.145 90.153 100.16 <![CDATA[y i ]]> -5.105 -9.853 -14.228 -18.236 -21.879 -25.161 -28.087 -30.659 -32.880 -34.755 <![CDATA[x i ]]> 110.15 120.15 130.14 140.13 150.12 160.11 170.10 180.10 190.09 200.09 <![CDATA[y i ]]> -36.285 -37.472 -38.319 -38.826 -38.995 -38.826 -38.319 -37.472 -36.285 -34.755 <![CDATA[x i ]]> 210.10 220.10 230.12 240.13 250.15 260.17 270.19 280.21 290.23 297.81 <![CDATA[y i ]]> -32.880 -30.659 -28.087 -25.161 -21.879 -18.236 -14.228 -9.853 -5.105 -1.260

[0175] Table 19 Side span main cable aerial cable coordinates (unit: m)

[0176] <![CDATA[x i ]]> 9.987 19.980 29.969 39.954 49.937 59.919 69.902 79.888 89.878 97.501 <![CDATA[y i ]]> 2.597 5.527 8.829 12.496 16.526 20.914 25.657 30.753 36.200 40.620

[0177] Table 20 Anchor span main cable air cable coordinates (unit: m)

[0178] <![CDATA[x i ]]> 5 10 14.274 <![CDATA[y i ]]> 3.268 6.602 9.506

[0179] S31: Construction status calculation. During a certain construction process, the load of the stiffening beam is applied to the corresponding main cable node through the hanger in the form of node force. The load applied to the sixth hanger of the main span and the side span is 3000kN. Calculate the steps from S20 to S30, and get the preliminary construction status line shape and the horizontal component force H2 = 4773.86kN of the main cable.

[0180] S32: Calculate the main cable strain and main cable angle coefficient using formulas (26) and (27)

[0181] Then return to steps from S23 to S30, and recalculate the main cable line shape (see Table 21-23) and the saddle offset of 0.306m and the loose cable saddle offset of 0.027m under the premise of balanced horizontal component forces in each span.

[0182] Table 21 Main span main cable aerial cable coordinates (unit: m)

[0183] <![CDATA[x i ]]> 9.974 19.922 29.866 39.806 49.742 59.674 69.778 79.863 89.929 99.977 <![CDATA[y i ]]> -5.194 -10.082 -14.626 -18.830 -22.699 -26.237 -28.842 -31.115 -33.059 -34.678 <![CDATA[x i ]]> 110.01 120.02 130.03 140.03 150.02 160.01 169.99 179.98 189.98 199.98 <![CDATA[y i ]]> -35.977 -36.958 -37.623 -37.974 -38.012 -37.739 -37.153 -36.254 -35.041 -33.511 <![CDATA[x i ]]> 209.98 220.00 230.03 240.08 250.14 260.21 270.30 280.40 290.51 298.17 <![CDATA[y i ]]> -31.663 -29.492 -26.996 -24.169 -21.009 -17.511 -13.670 -9.480 -4.938 -1.260

[0184] Table 22 Side span main cable aerial cable coordinates (unit: m)

[0185] <![CDATA[x i ]]> 9.988 20.018 30.056 40.104 50.164 60.237 70.073 79.916 89.770 97.295 <![CDATA[y i ]]> 2.479 5.279 8.427 11.919 15.753 19.926 24.969 30.335 36.025 40.610

[0186] Table 23 Anchor span main cable air cable coordinates (unit: m)

[0187] <![CDATA[x i ]]> 5 10 14.286 <![CDATA[y i ]]> 3.286 6.632 9.517

Claims

1. A refined calculation method for a suspension bridge cable system, given the main span, side span, anchor span, tower height, anchor span height, main cable sag, suspender rod horizontal coordinate, suspender rod force, main cable area, elastic modulus, and unit length weight; characterized in that: The bridge-forming state of the main cable is determined by a progressive point-by-point equilibrium iterative main cable form-finding calculation method, including the following steps: (1) The main cable calculation model is established based on the IP points of the cable saddle and loose cable saddle. The main cable is only subjected to the hanger force. The point-by-point equilibrium iteration method is used to iterate each node of the main span, each node of the side span, and each node of the anchor span. The main cable horizontal force component is equal as the control principle. The main span rise reaches the design value as the convergence condition. The form-finding calculation of the main cable is performed to obtain the C1 bridge state. (2) Calculate the deadweight of the main cable based on the length of each main cable section obtained in the completed bridge state C1, and add it to the suspender force as the new node load. Repeat the calculation in step (1) to obtain the completed bridge state C2; (3) Calculate the coordinates of the tangent points of the main cables at the cable saddle and the loose cable saddle respectively, and use this as a reference to redetermine the spans of each span and the main cable sagitta, establish a new main cable calculation model, use the new node loads in step (2), perform point-by-point equilibrium iterative calculations again, and obtain the C3 bridge state.

2. The refined calculation method for the suspension bridge cable system according to claim 1 is characterized in that: The form-finding calculation of the main cable in the construction state is completed through the following steps: (1) Estimate the initial value of the cable saddle pre-deviation d0, calculate the length of each section of the main cable in the main span in the empty cable state according to the main cable strain obtained in the completed bridge state C1, and calculate the deadweight of the empty cable as the node concentrated force. Change the cable saddle pre-deviation d0 through multiple cycles until the two ends of the main cable reach the design elevation; (2) The length of each main cable section of the anchor span in the empty cable state is calculated based on the main cable strain obtained in the completed bridge state C1. The deadweight of the empty cable is calculated as the node concentrated force. The size of the pre-bias θ of the loose cable saddle is changed through multiple cycles until the end point of the main cable in the anchor span section reaches the design elevation. (3) The length of each main cable section in the side span in the empty cable state is calculated based on the main cable strain obtained in the completed bridge state C1. The deadweight of the empty cable is calculated as the node concentrated force. The saddle pre-bias d0 is changed through multiple cycles until the end point of the main cable in the side span reaches the design elevation. (4) Considering the friction between the main cable and the saddle groove in the saddle and loose cable saddle, calculate the coordinates of the main cable tangent point after the elastic elongation of the arc part of the main cable in the saddle groove causes the main cable to change. After correcting the tangent point coordinates, repeat steps (1) to (3) to obtain the line shape of the main cable in the empty cable state; (5) During a certain construction process, the load of the stiffening beam is applied to the corresponding main cable node in the form of a node force through the hanger. The construction load is recorded as: F i , (i=1,2,…,n), F of the nodes without construction loads i Take the value as 0, and calculate according to steps (1)-(3) to obtain the preliminary main cable line shape and the horizontal component H2 of the main cable in the construction state. This state is called construction state S1; (6) Using the formula ε i =(H0-H2) / EA / cosθ i-1 Calculate the main cable strain using the formula α i =α i-1 +P i / H2 main cable angle coefficient, and then recalculate the main cable line shape and saddle offset and loose saddle offset under the premise of balanced horizontal force of each span according to steps (1)-(3).

3. The refined calculation method for the suspension bridge cable system according to claim 2 is characterized in that: Here are the steps: S1. Calculate the main span: Substitute the main span hanger force and the horizontal coordinates of the locations of the nodes in each span into formula (1) to calculate the vertical force Ry at the IP point of the main cable in the main span; Where P i is the force at each node in the bridge state; S m is the main span; x i is the horizontal coordinate of each span node, i = 0, 1, ..., n, n is the maximum number of nodes in the span; P i is the force at each node in the bridge state, i = 1, 2, ..., n; S2. Estimate the horizontal component H0 of the main cable force in the main span and substitute it into formula (2) to obtain the angle coefficient α0 of the main cable at the IP point of the main span: α0=-R y / H0 (2) S3. Using formulas (3) and (4), calculate the y coordinates and corresponding angle coefficients of each node of the main cable of the main span; and i =and i-1 +α i-1 (x i -x i-1 ) (3) a i =a i-1 +P i / H0 (4) Where, i = 1, 2, ..., n; S4. Calculate the deviation dy between the main cable mid-span alignment and the mid-span sag f in the completed bridge state: dy=f-|y middle | Where, f is the main cable height; y middle is the y coordinate of the main cable span; if the absolute value of dy is greater than 0.5mm, change the size of H0 and return to S2 to recalculate until |dy|<0.5mm is satisfied and then exit the main span linear iterative calculation; S5. Calculate the side span: Substitute the side span hanger force and the horizontal coordinates of the positions of the nodes in each span into formula (1), and replace the main span S in formula (1) with m Replaced by side span S s , calculate the vertical force Rs of the main cable at the IP point of the loose cable saddle y ; S6, using the horizontal component H0 of the main cable force of the main span obtained by iterative calculation of S1-S4 as the equilibrium condition, substitute it into formula (5) to obtain the angle coefficient α of the main cable at the IP point of the side span main cable s0 : α s0 =Rs y / H s0 (5) S7. Similarly, using formulas (3) and (4), calculate the y coordinates of each node of the side span main cable and the corresponding angle coefficient; S8. Calculate the deviation dys between the end point coordinates of the side span main cable and the completed bridge state: dys=c-|y s | Where c is the height of the tower; y s is the y coordinate of the end point of the side span main cable; if the absolute value of dys is greater than 0.5 mm, change α s0 The size of the side span cable is calculated, and the calculation is returned to S7 for recalculation until |dys|<0.5mm is satisfied, and the side span main cable shape calculation is exited; S9, perform anchor span calculation: perform iterative calculation on the anchor span according to the calculation steps of S5-S7, and obtain the y coordinates and corresponding angle coefficients of each node of the anchor span main cable; S10. Calculate the deviation dya between the anchor span main cable end point coordinates and the bridge state: dya=h-|y a | Where h is the height between the theoretical anchor point of the main cable and the IP point of the loose cable saddle; y a is the y coordinate of the end point of the anchor span main cable; if the absolute value of dya is greater than 0.5mm, change α a0 The size of the anchor span is calculated, and the calculation is returned to S9 to be recalculated until |dya|<0.5mm is satisfied. Then the anchor span main cable linear shape calculation is exited, and the C1 bridge state is obtained. S11. Calculate the length l of each main cable section i and the dependent variable ε i : Calculate the deadweight of each main cable section according to the calculated length of each main cable section, and superimpose it with the suspender force according to formula (6) to obtain a new suspender force. Repeat the calculation process of S1-S10 to obtain the C2 bridge state; P i =P i +0.5q(l i +l i+1 ) (6) Where q is the weight of the main cable per unit length; S12, according to the coordinates of the first node (x a ,y a )、(x b ,y b ) calculates the coordinates of the saddle center as (x c ,y c ), the coordinates of the tangent points of the saddle arc are (xt1, yt1), (xt2, yt2), and the length of the outer chord of the arc is L a , L b ; Where r is the theoretical radius of the saddle. S13, assuming that the friction coefficient between the main cable and the saddle groove is μ, calculate the coordinates of the first pair of nodes on both sides of the saddle and the saddle tangent point after the elastic elongation of the main cable in the arc part of the saddle causes the change; Where A is the main cable area and E is the elastic modulus; S14, respectively calculate the coordinates (x a1 ,y a1 )、(x b1 ,y b1 ) is substituted into formulas (7)-(12), and the coordinates of the center of the scattered cable saddle are calculated as (x c1 ,y c1 ), the coordinates of the tangent points of the scattered saddle arc are (xt3, yt3) and (xt4, yt4), and the length of the outer chord of the arc is L a1 , L b1 ; S15, using the method of S13, calculate the change of the tangent points on both sides of the loose cable saddle under the influence of friction; S16. Correct the coordinates of the two end nodes of the main span and the main span of the main cable according to formula (16); S17. In the coordinate system with the IP point of the loose cable saddle as the origin, the coordinates of the two end nodes of the side span main cable, the side span span, and the tower height are corrected according to formula (17); S18. Correct the coordinates of the end node of the anchor span main cable at the loose cable saddle, the anchor span diameter, and the anchor span height according to formula (18); S19, using the revised design parameters, recalculate the steps of S1-S11 to obtain the C3 bridge state considering the cable saddle and loose cable saddle; S20, main span empty cable state calculation, assuming a saddle pre-bias d0, the main span becomes S m =S m +2d0; the empty cable deadweight is calculated based on the node concentrated force, Pc i =0.5q(l i +l i+1 ), estimate the initial value of the horizontal force H1 of the empty cable, and calculate the vertical force Ry1 of the IP point of the main cable according to formula (1); S21: H1 replaces H0 and is substituted into formula (2) to obtain the angle coefficient α of the main cable at the IP point of the main span. 01 ; S22: Calculate the main cable strain and main cable angle coefficient using formulas (19) and (20): e i =H0 / EA / cosθ i-1 (19) a i =a i-1 +Pc i / H1 (20) S23: Assume α c0 The initial value of , calculate the main cable coordinates: x i+j =x i+j-1 +dx i (21) the i+j =y i+j-1 +to i (22) Among them, dx i ,dy i They represent the main cable node displacements respectively and are calculated using the following formula; dx i =(1-e i+j )l i+j cos(atan(a i+j-1 )) day i =(1-e i+j )l i+j sin(atan(a i+j-1 )) Wherein, i = 1, 2, ..., n; j = 0, 1, ..., k+1-i, and the length and strain of each section of the main cable are the results obtained from the last round of step S11; S24, if not satisfied |y n -yt1|<0.5mm, modify α0, return to S23 and recalculate until |yt1|<0.5mm n -yt1|<0.5mm, end the iteration; S25, compare the difference d=x between the assumed saddle pre-bias d0 and the calculated actual displacement of the main cable end point n -S m -xt1, if d < 0.5 mm is satisfied, the loop ends; otherwise, the size of d0 is changed and the loop returns to S20 for re-iteration calculation until d < 0.5 mm is satisfied and the two end points of the main cable reach the design elevation; S26, calculation of the empty cable state of the anchor span. According to the length of each section of the main cable obtained in the last round of S11, the line shape of the main cable is calculated using the method of S23. Since the horizontal force components of the main cables of the main span, side span and anchor span are equal, H1 is the same when calculating each span; S27, the cable saddle rotates by θ, causing the coordinates of the tangent points of the cable saddle arc (xt3, yt3) and (xt4, yt4) to change, and the displacements are dx3, dy3, dx4, dy4 respectively; Where w is the vertical height from the IP point of the loose cable saddle to the rotation center of the loose cable saddle support; If it does not satisfy |y n -yt4+dy4|<0.5mm, use formula (25) to update the coordinates of the tangent point of the scattered cable saddle arc, and modify α s0 , return to S23 and recalculate until |y is satisfied n -yt4+dy4|<0.5mm, the iteration ends; the displacement d1 of the IP point of the loose cable saddle in the anchor span equilibrium state is obtained; S28, side span empty cable state calculation, side span span is: S s =S s -d0+d1: Based on the length of each section of the main cable obtained in the last round of S11, the line shape of the main cable is calculated using the method of S23. At this time, the horizontal component of the main cable used is H1; S29, if not satisfied |y n -yt2+dy3|<0.5mm, use formula (25) to update the coordinates of the tangent point of the scattered cable saddle arc, and modify α s0 , return to S23 and recalculate until |y is satisfied n -yt2+dy3|<0.5mm, the iteration ends, and the displacement d of the saddle IP point in the side span equilibrium state is obtained; S30, compare the difference between the assumed saddle pre-bias d0 and the calculated actual displacement of the main cable end point: d = x n -S m -xt1, if |d|<0.5mm is not satisfied, change the size of d0, return to S20 and iterate again until |d|<0.5mm is satisfied; end the loop, and obtain the linear shape of the empty cable state and the saddle pre-bias and loose saddle pre-bias; S31. Construction status calculation: During the construction process, the load of the stiffening beam is applied to the corresponding main cable node in the form of node force through the hanger, so the construction load is F i , (i=1,2,…,n), F of the nodes without construction loads i Take the value as 0; calculate S20 to S30, and obtain the preliminary construction state linear shape and the horizontal component force H2 of the main cable; S32. Calculate the main cable strain and main cable angle coefficient using formulas (26) and (27): e i =(H0-H2) / EA / cosθ i-1 (26) a i =a i-1 +F i / H2 (27) Then, the process returns to S23 to S30 to recalculate the main cable line shape, saddle offset, and loose saddle offset under the premise that the horizontal component forces of each span are balanced.

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