CN114491760A

CN114491760A - Method and device for calculating installation angle of anchor pull rod

Info

Publication number: CN114491760A
Application number: CN202210111126.0A
Authority: CN
Inventors: 霍学晋; 王东绪; 杨明芳; 汪珍; 陈佳; 苗润池; 刘芸欣
Original assignee: China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
Current assignee: China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
Priority date: 2022-01-24
Filing date: 2022-01-24
Publication date: 2022-05-13

Abstract

The invention relates to a method and a device for calculating an installation angle of an anchor pull rod, which comprises the steps of obtaining theoretical vertex coordinates of a scattered cable saddle and coordinates of a wire strand anchoring point, and calculating a tangent angle of a flat bending end point of the wire strand and a tangent angle of an initial vertical bending end point of the wire strand according to the theoretical vertex coordinates of the scattered cable saddle and the coordinates of the wire strand anchoring point; acquiring the total balance force of the main side-span cable, and calculating the tension of each strand according to the strand flat-bent end point chamfer, the strand initial vertical-bent end point chamfer and the total balance force of the main side-span cable; traversing each strand, and iteratively calculating the unstressed length of the suspended section of the strand and the coordinates of the upper end part of the anchor pull rod of the strand according to the coordinates of the anchor point of the strand, the tangent angle of the flat bent end point of the strand, the tangent angle of the initial vertical bent end point of the strand, the tension of each strand and the vertical position of the strand in the saddle groove; and calculating the installation angle of the anchor rod according to the iteratively calculated coordinates of the upper end part of the strand anchor rod. Meanwhile, the problem that the stress-free length of the suspension section strand in the related technology is inaccurate to calculate can be solved.

Description

Method and device for calculating installation angle of anchor pull rod

Technical Field

The invention relates to the technical field of suspension bridge design, in particular to a method and a device for calculating an installation angle of an anchor pull rod.

Background

At present, when a suspension bridge is designed, the installation angle of each anchor pull rod needs to be calculated and is reflected on a design drawing. The construction of the suspension bridge anchor span is very complex, and is reflected in the following 3 aspects: 1) due to the anchoring requirement, the cable strand is in a space scattering state in the anchoring span; 2) the cable saddle is a complex space body consisting of a plurality of vertical curved circular arcs and flat curved circular arcs with different radiuses, so that each strand has different vertical curved end points and flat curved end points; 3) the end part of the cable strand is anchored by a steel anchor pull rod, the anchor pull rod is in an inclined state, and the inclined installation angles are different. Due to the complex structure, the accurate analysis of the suspension bridge anchor span is extremely complex, the installation angle of the anchor pull rod, the stress-free length of the suspension section of the wire strand, the positions of the vertical bending end point and the horizontal bending end point of the cable saddle, the tension force of the wire strand and the like are mutually associated and coupled, and any change can cause other changes along with the change.

In the related art, a simplified method is adopted for calculation of the installation angle of the anchor rod, and no accurate analysis method and related research exist. The simplified method is to take the straight line angle of the anchor point (the lower end point of the anchor rod, given by design) of the anchor surface after connecting the IP point of the cable saddle and the strand as the installation angle of the anchor rod, and the simplified method has the following problems:

(1) the state of the suspension section of the wire strand in the anchor span under the action of self weight is a catenary instead of a straight line, so that the tangential direction of the end force of the wire strand is deviated from the installation angle of the anchor pull rod, the steel anchor pull rod generates additional bending moment, the stress is not good, and the catenary is replaced by the straight line, so that the calculation of the stress-free length of the wire strand in the suspension section is inaccurate;

(2) the accurate coordinates of the vertical bending end point and the horizontal bending end point of each strand cannot be obtained, and the stress-free length of the closely-attached section of the strand and the saddle groove in the scattered cable saddle groove cannot be accurately calculated, so that the blanking length of the full-bridge strand has errors;

(3) the sum of the component force of the tension of each wire strand of the anchor span obtained by calculation on the inclined surface of the cable saddle is unequal to the component force of the main cable of the side span, so that the cable saddle still can slide on the inclined surface, the tension of each wire strand of the anchor span can be redistributed after sliding, the tension of each wire strand is finally unequal, and the overall safety coefficient of the anchor span is reduced.

Disclosure of Invention

The embodiment of the invention provides a method and a device for calculating an anchor rod installation angle, which are used for calculating the anchor rod installation angle and solving the problem of inaccurate calculation of the stress-free length of a suspension section strand in the related technology.

The embodiment of the invention provides a method for calculating an installation angle of an anchor pull rod, which is characterized by comprising the following steps:

acquiring theoretical vertex coordinates of the scattered cable saddle and coordinates of a strand anchoring point, and calculating a strand flat bending end point chamfer and a strand initial vertical bending end point chamfer according to the theoretical vertex coordinates of the scattered cable saddle and the coordinates of the strand anchoring point;

acquiring the total balance force of the main side-span cable, and calculating the tension of each strand according to the strand flat-bent end point chamfer, the strand initial vertical-bent end point chamfer and the total balance force of the main side-span cable;

traversing each strand, and iteratively calculating the unstressed length of the suspended section of the strand and the coordinates of the upper end part of the anchor pull rod of the strand according to the coordinates of the anchor point of the strand, the tangent angle of the flat bent end point of the strand, the tangent angle of the initial vertical bent end point of the strand, the tension of each strand and the vertical position of the strand in the saddle groove;

and calculating the installation angle of the anchor rod according to the iteratively calculated coordinates of the upper end part of the strand anchor rod.

In some embodiments, before acquiring the theoretical vertex coordinates of the saddle and the coordinates of the anchor points of the strands, the method further comprises the following steps:

defining a global coordinate system OXYZ, wherein the Y axis of the global coordinate system is vertically upward;

defining a local coordinate system oxyz, wherein the origin of the local coordinate system is an intersection point o of a vertical line and a slip plane when the theoretical vertex of the cable saddle makes the vertical line towards the slip plane, and the y-axis direction of the local coordinate system is the self-weight direction of a catenary cable;

definition of saddle seatMarker system

The saddle local coordinate system is obtained by rotating the local coordinate system around the horizontal z-axis of the saddle counterclockwise by an angle beta, and

said local coordinate system oxyz is directed to saddle local coordinate system

Is a conversion matrix of

Defining a local coordinate system of the anchor surface of the strand, and enabling a conversion matrix of the local coordinate system of the anchor surface of the strand and the overall coordinate system OXYZ to be

Local coordinate system of saddle

The theoretical vertex coordinates of the cable saddle are

And is

Wherein beta is the angle of inclination of the slip plane, (X)_ip、 Y_ip、Z_ip) The coordinates of the theoretical vertex of the cable saddle are (X) under the overall coordinate system OXYZ_o、 Y_o、Z_o) The coordinate of the o point under the overall coordinate system OXYZ is shown;

saddle local coordinate system

The coordinates of the anchoring point of the silk strand are

And is

Wherein (X)_0i、Y_0i、Z_0i) The coordinates of the strand anchoring points under the overall coordinate system OXYZ are adopted, and

wherein

Is T_mTranspose matrix of (x'_0i、y′_0i、z′_0i) For a predetermined strand anchoring point in said strand anchoring surface local coordinate system W_mThe lower coordinate, i is 1 to N, N is the total number of strands, (X)_m、Y_m、Z_m) The coordinates of the center of the anchor surface under the overall coordinate system OXYZ are shown.

In some embodiments, the calculating the strand flat bend end point chamfer and the strand initial vertical bend end point chamfer according to the scattered cable saddle theoretical vertex coordinates and the strand anchoring point coordinates comprises the following steps:

establish the equation Ax²+ Bx + C is 0, and

A＝1+a²，B＝2×(a×b-a×x_pc-z_pc)，

solving an equation to obtain the flat bent end of each strand at the anchor span sideTransverse coordinate z of point_piAccording to

Solving strand flat-bending end point tangent angle theta of No. i strand_iWherein

R_hIs the flat bending radius of the cable saddle groove, x_pcAnd z_pcRespectively the ordinate and abscissa of the circle center of the flat curved arc, z_0siThe transverse position of the strand in the saddle groove;

the method for calculating the initial vertical bending end point chamfer angle of the strand according to the theoretical vertex coordinate of the scattered cable saddle and the anchor point coordinate of the strand comprises the following steps:

according to

Calculating the initial vertical bending end point cutting angle gamma of the No. i strand_i。

In some embodiments, obtaining the total balance force of the side span main cable and calculating the tension of each strand according to the tangent angle of the flat bending end point of each strand and the tangent angle of the initial vertical bending end point of each strand comprises the following steps:

step 01, according to F_R＝F_XRcosβ+F_YRsinβ、F_L＝F_RAnd

calculating the component force F of the main cable force along the sliding surface_RThe total balance force F of the side span main cable_LAnd the tension f of each strand_iWherein F is_XRLongitudinal component of tension force of main cable across side span, F_YRIs the vertical component of the tension force of the side span main cable.

In some embodiments, traversing each strand, and iteratively calculating the unstressed length of the strand suspended section and the coordinates of the upper end of the strand anchor rod according to the coordinates of the strand anchor point, the strand horizontal bend end point cut angle, the strand initial vertical bend end point cut angle, the tension of each strand and the vertical position of the strand in the saddle groove comprises the following steps:

step 02: selecting No. i silk strand, setting the first middleVariables of

And an iteration variable γ; cutting the vertical bent end point of the No. i silk strand into an angle gamma_iTo the intermediate variable

And combining the first intermediate variable

To the iteration variable γ;

step 03: according to

And

and

f_h＝f_xl/cos(atan(f_zl/f_xl) And f) and_v＝f_ylcalculating the resultant force f of the selected strand on the horizontal plane_hAnd resultant force f in the vertical direction_vWherein

Is T_ZThe transposed matrix of (2);

step 04: calculating the coordinates of the tail points of the vertical bends of the wire strands according to the vertical bend radius of the cable scattering saddle groove, the central angle corresponding to the circular arc section of the vertical bend line of the saddle groove and the vertical position of the wire strands in the saddle groove;

step 05: iteratively calculating the initial unstressed length S of the suspended section of the strand according to the coordinates of the anchoring point of the strand, the coordinates of the vertical bending end point of the strand, the resultant force of the selected strand on the horizontal plane and the resultant force of the selected strand in the vertical direction₀And the current unstressed length S of the strand suspended section;

step 06: judgment of | (S-S)₀)/S₀If the | meets the preset precision, if so, determining whether the | meets the preset precisionAccording to

Calculating a first vertical position difference delta h of the wire strand at the upper end part of the anchor rod₁Otherwise, assigning the value of the current unstressed length S to the initial unstressed length S₀Then returns to step 02ExecuteStep 02 to step 05;

step 07: setting a second intermediate variable

And make

And is

Then returning to step 02 to execute step 02 to step 06 according to the method

Calculating the second vertical position difference delta h of the wire strand at the upper end part of the anchor rod₂；

And step 08: setting a third intermediate variable

And make

And is

Then returning to step 02 and executing steps 02 to 06, according to

Calculating the third vertical position difference delta h of the wire strand at the upper end part of the anchor rod₀Wherein y is_siIs the vertical coordinate, L, of the end point of the selected vertical bend of the strand in the local coordinate system oxyz_mgiIs the anchor rod length;

step 09: judgment of

If the preset precision is met, terminating the iteration if the preset precision is met, otherwise, enabling the iteration to be ended

Δh₁＝Δh₂And Δ h₂＝Δh₀Then, the step 02 is returned to and the steps 02 to 08 are executed:

step 10: according to x_mi＝x_si-Lcos(atan((z_si-z_0i)/(x_si-x_0i)))、y_mi＝y_si+ H and z_mi＝z_si+Lsin(atan((z_si-z_0i)/(x_si-x_0i) )) calculating coordinates (x) of the upper end of the strand anchor rod_mi、 y_mi、z_mi) And taking the current value of the iteration variable gamma as the final vertical bending end point cutting angle of the No. i strand, and taking the current unstressed length S calculated by iteration as the unstressed length of the final strand suspended section of the No. i strand.

updating the final strand vertical bending end point tangent angle value calculated by the current iteration to gamma_iAnd will update gamma_iSubstitution into

Obtaining an iteratively calculated side span main cable total balance force F'_L；

In | (F'_L-F_L)/F_LIf the | does not meet the preset precision, the updated gamma is used_iGo back to step 01 to calculate updated F_LAnd f_iAnd with said updated gamma_i、F_LAnd f_iThe loop from step 02 to step 10 is entered.

In some embodiments, the step 04 comprises the steps of:

supposing that the saddle groove vertical bending line consists of n sections of circular arcs, and enabling the vertical bending radius R of the cable scattering saddle groove corresponding to each section of circular arc_vIs represented by R_vkWherein k is an integer from 1 to n;

making the R to_vkThe corresponding central angle is denoted by phi_kAnd according to R_ki＝R_vk+D_iCalculating the vertical bending radius R of the No. i strand in the saddle groove_kiWherein D is_iThe vertical height of the No. i silk strand on the section of the main cable is defined;

when gamma is less than or equal to phi₁According to

Calculating the ordinate of the end point of the vertical bend of the selected strand

And vertical coordinate

When phi is₁＜γ≤φ₁+φ₂According to

And vertical coordinate

When phi is₁+φ₂＜γ≤φ₁+φ₂+φ₃According to

Calculating the end point of the vertical bend of the selected strandOrdinate of the curve

And vertical coordinate

When phi is₁+φ₂+φ₃When < gamma, according to

And vertical coordinate

According to

Calculating the abscissa of the end point of the vertical bend of the selected strand

According to

Will be in the saddle local coordinate system

Coordinates of vertical bending end point of lower selected strand

Converting the position of the filament to a local coordinate system oxyz to obtain the coordinates (x) of the end point of the vertical bend of the selected filament under the local coordinate system oxyz_si、y_si、z_si)。

In some embodiments, said step 05 comprises the steps of:

according to

Calculating the initial unstressed length S of the suspended section of the strand₀Wherein L is_mgiFor the anchor rod length, (x)_0i、y_0i、z_0i) Is the coordinate of the lower strand anchoring point of the local coordinate system oxyz, (x)_si、y_si、z_si) The coordinates of the vertical bent end points of the lower strands of the local coordinate system oxyz are obtained;

according to f'_v＝f_v-ωS₀And f'_h＝f_hCalculating the vertical force f 'of the wire strand at the upper end of the anchor rod'_vAnd resultant force in the horizontal plane f'_hAccording to

Calculating the inclination angle of the upper end of the anchor rod

According to

Calculating the horizontal projection length L of the silk strands;

according to

And calculating the current unstressed length S and the vertical projection length H of the strands, wherein EA is the tensile rigidity of the strands, and omega is the bulk density of the main cable.

In some embodiments, the calculating the anchor rod installation angle from the iteratively calculated upper end coordinates of the strand anchor rod includes the steps of:

according to

Converting the coordinates of the upper end part of the strand anchor rod into an integral coordinate system OXYZ, and performing transformation according to lambda on the integral coordinate system OXYZ₁＝atan((Y_mi-Y_0i)/X_mi)、λ₂＝atan((Z_mi-Z_0i)/X_mi) And λ₃＝atan(tan(λ₁)/cos(λ₂) Calculating the anchor rod installation angle, where λ₁Is the included angle between the projection of the anchor pull rod on the XY plane and the X axis, lambda₂Is the included angle between the projection of the anchor rod on the XZ plane and the X axis, lambda₃Is the angle between the anchor rod and the XZ plane.

In a second aspect, an embodiment of the present invention provides an apparatus for calculating an installation angle of an anchor rod, where the apparatus includes: the iteration initial value acquisition module is used for acquiring theoretical vertex coordinates of the scattered cable saddle and coordinates of the anchoring points of the strands and calculating tangent angles of the flat bending end points of the strands and the initial vertical bending end points of the strands according to the theoretical vertex coordinates of the scattered cable saddle and the coordinates of the anchoring points of the strands;

an iterative computation module to:

the mounting angle calculation module is used for calculating the mounting angle of the anchor rod according to the iteratively calculated coordinates of the upper end part of the strand anchor rod;

the iteration initial value obtaining module is further configured to:

defining a saddle local coordinate system

the local coordinate system oxyz is towards saddle local coordinate system

Is a conversion matrix of

Local coordinate system of saddle

The theoretical vertex coordinates of the scattered cable saddle are

And is provided with

saddle local coordinate system

The coordinates of the anchoring point of the strand are

And is

Wherein (X)_0i、Y_0i、Z_0i) The coordinates of the strand anchoring point under the global coordinate system OXYZ, and

wherein

Is T_mTranspose matrix of (x'_0i、y′_0i、z′_0i) For a predetermined strand anchoring point in said strand anchoring surface local coordinate system W_mThe lower coordinate, i is 1 to N, N is the total number of strands, (X)_m、Y_m、 Z_m) The coordinates of the center of the anchor surface under the overall coordinate system OXYZ are taken as the coordinates;

establish the equation Ax²+ Bx + C is 0, and

A＝1+a²，B＝2×(a×b-a×x_pc-z_pc)，

solving an equation to obtain the transverse coordinate z of each strand flat-bending end point on the anchor span side_piAnd according to

according to

Calculating the initial vertical bending end point cutting angle gamma of the No. i strand_i；

The iterative computation module is further configured to: performing the following steps 01 to 10;

the step 01 comprises the following steps: according to F_R＝F_XRcosβ+F_YRsinβ、F_L＝F_RAnd

calculating the component force F of the main cable force along the sliding surface_RThe total balance force F of the side span main cable_LAnd the tension f of each strand_iWherein F is_XRLongitudinal component of tension force of main cable across side span, F_YRVertical component force of the tension force of the side span main cable;

step 02 includes: selecting No. i silk strand, setting the first intermediate variable

And an iteration variable γ; cutting the vertical bent end point of the No. i silk strand into an angle gamma_iIs assigned to the intermediate variable

And combining the first intermediate variable

To the iteration variable γ;

step 03 comprises: according to

And

and

Is T_ZThe transposed matrix of (2);

step 04 comprises: calculating the coordinates of the tail points of the vertical bends of the strands according to the vertical bend radius of the cable scattering saddle groove, the central angle corresponding to the arc section of the vertical bend line of the saddle groove and the vertical position of the strands in the saddle groove;

step 05 comprises: iteratively calculating the initial unstressed length S of the suspended section of the strand according to the coordinates of the anchoring point of the strand, the coordinates of the vertical bent end point of the strand, the resultant force of the selected strand on the horizontal plane and the resultant force of the selected strand in the vertical direction₀And the current unstressed length S of the strand suspended section;

step 06 comprises: judgment of | (S-S)₀)/S₀If | satisfies the preset precision, if yes, according to

step 07 includes: setting a second intermediate variable

And make

And is

Then returning to step 02 to execute step 02 to step 06 according to the method

Step 08 comprises: setting a third intermediate variable

And make it possible to

And is

Then returning to step 02 and executing steps 02 to 06, according to

step 09 includes: judgment of

Δh₁＝Δh₂And Δ h₂＝Δh₀Then returning to the step 02 and executing the step 02 to the step 08;

the step 10 comprises: according to x_mi＝x_si-Lcos(atan((z_si-z_0i)/(x_si-x_0i)))、y_mi＝y_si+ H and z_mi＝z_si+Lsin(atan((z_si-z_0i)/(x_si-x_0i) )) calculating coordinates (x) of the upper end of the strand anchor rod_mi、y_mi、z_mi) Taking the current value of the iteration variable gamma as the final vertical bending end point cutting angle of the No. i strand, and taking the current unstressed length S calculated by iteration as the unstressed length of the final strand suspended section of the No. i strand;

the step 04 comprises the steps of:

when gamma is less than or equal to phi₁According to

And vertical coordinate

When phi is₁＜γ≤φ₁+φ₂According to

And vertical coordinate

When phi is₁+φ₂＜γ≤φ₁+φ₂+φ₃According to

And vertical coordinate

When phi is₁+φ₂+φ₃When < gamma, according to

And vertical coordinate

According to

According to

Will be in the saddle local coordinate system

Coordinates of vertical bending end point of lower selected strand

Converting to local coordinate system oxyz to obtain local partCoordinate (x) of selected end point of vertical bending of filament strand under coordinate system oxyz_si、y_si、z_si)；

Said step 05 comprises the steps of:

according to

Calculating the inclination angle of the upper end of the anchor rod

According to

Calculating the horizontal projection length L of the silk strands;

according to

Calculating the current unstressed length S and the vertical projection length H of the strand, wherein EA is the tensile rigidity of the strand, and omega is the bulk density of the main cable;

the iterative computation module is further configured to:

updating the final strand vertical bending end point tangent angle value calculated by the current iteration to gamma_iAnd will updated gamma_iSubstitution into

In | (F'_L-F_L)/F_LIf the | does not meet the preset precision, the updated gamma is used_iGo back to step 01 to calculate updated F_LAnd f_iAnd with said updated gamma_i、F_LAnd f_iEntering a loop from step 02 to step 10;

the installation angle calculation module is further configured to:

according to

The technical scheme provided by the invention has the beneficial effects that:

the embodiment of the invention provides a method for accurately calculating the stress-free length of a closely-attached section of a strand in a scattered cable saddle groove and the saddle groove. Through the coordinates of the vertical bending end point and the horizontal bending end point of the wire strand, the unstressed length of the closely-attached section of the wire strand and the saddle groove in the scattered cable saddle groove can be accurately calculated, so that the full-bridge blanking total length of the wire strand is more accurate, and the factory processing and field erection can be accurately controlled; in addition, through the coordinates of the end points of the vertical bending and the end points of the horizontal bending, a designer can easily judge whether the horizontal bending of the strand occurs before the vertical bending, and further determine whether the design parameters of the saddle groove and the design coordinates of the rear anchor point of the strand need to be adjusted.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a schematic flowchart of a method for calculating an anchor rod installation angle according to an embodiment of the present invention;

FIG. 2 is a schematic view of the strand alignment within the saddle slot provided by an embodiment of the present invention;

FIG. 3 is a schematic view of the spreading and anchoring of the anchor cross-filament strands according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of a local coordinate system according to an embodiment of the present invention;

fig. 5 is a schematic vertical and plane view of a cable saddle according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.

In one specific embodiment, the anchor rod installation angle is calculated according to the following method steps:

step (1): define 3 coordinate systems (global coordinate system OXYZ, local coordinate system OXYZ and saddle local coordinate system)

) And drawing a vertical line from the theoretical top of the cable saddle to the slip plane, and taking the intersection point of the vertical line and the slip plane as a point o.

Wherein, the Y axis of the overall coordinate system OXYZ is vertical upwards; the local coordinate system OXYZ is translated to the origin O of the global coordinate system OXYZObtaining an intersection point o; saddle local coordinate system

The local coordinate system oxyz is rotated counterclockwise around the horizontal z-axis by an angle β, which is the inclination angle of the slip plane (given the known conditions of the design).

It follows that the local coordinate system oxyz is directed to the saddle local coordinate system

Is converted into a matrix

The coordinate of the theoretical vertex of the cable saddle is known as (X) under the overall coordinate system OXYZ_ip、Y_ip、 Z_ip) The vertical height from the theoretical vertex to the slip plane is H₀(given the known conditions of the design), the coordinate of the o point in the global coordinate system OXYZ is (X)_o、Y_o、Z_o) Wherein X is_o＝X_ip+H₀sinβcosβ、Y_o＝Y_ip+H₀sinβsinβ、Z_o＝Z_ip。

By setting a local coordinate system oxyz and a saddle local coordinate system

The two coordinate systems assist in calculation, and can facilitate solution of a strand catenary equation and saddle related parameters.

Step (2), converting the theoretical vertex coordinates of the cable saddle into a local coordinate system of the cable saddle

Then, the theoretical vertex coordinates of the cable saddle are obtained as

Step (3), setting a local coordinate system W of the anchor surface of the strand_m(the inclination angle alpha is designed by the anchor surface to ensureGiven that α is given by design), then W_mThe transformation matrix of the coordinate system and the global coordinate system OXYZ is

The coordinate of the center of the anchor surface under the overall coordinate system OXYZ is (X)_m、Y_m、Z_m) (known conditions) in the local coordinate system W of the anchor surface of the strand_mNext, the given strand anchor point coordinates are designed to be (x'_0i、y′_0i、z′_0i) (i is 1 to N, N is the total number of strands), and the coordinates are converted to an overall coordinate system oyx, i.e. the system is a system of three dimensional coordinates

Then converted into saddle local coordinate system

Under the condition that

And (4) calculating coordinates of the flat bending end points of all the strands at the anchor span side. Can be in the saddle local coordinate system

Calculating the transverse coordinate z of the flat bending end point of each strand_piAnd a flat bend tangent angle theta_i(i is 1-N, N is the total number of strands), and establishing an equation according to the geometrical relationship: ax²+ Bx + C ═ 0, where a ═ 1+ a²， B＝2×(a×b-a×x_pc-z_pc)，

The transverse coordinate z can be obtained by solving the equation_piAnd flat bend corner cuts

Wherein R is_hIs the flat bending radius of the cable saddle groove, x_pcAnd z_pcRespectively the ordinate and abscissa of the circle center of the flat curved arc, z_0siThe transverse position of the strands in the saddle slots, determined by the strand alignment, is given by design and is a known condition.

And (5) calculating an iterative initial value of the tangent angle of the end point of the vertical bend of the strand (the tangent angle of the end point of the initial vertical bend of the strand). According to a local coordinate system of the saddle

Lower strand anchor point coordinates

And cable saddle IP point

Calculating iterative initial value of vertical bending end point cutting angle of silk strand

(i is 1 to N, N is the total number of strands).

And (6) calculating the total balance force (namely the component force along the slip plane) of the side-span main cable. Let F_RIs a side span main cable force along a slip plane (a cable saddle local coordinate system)

Shaft) component, from a longitudinal component F of the main cable tension_XRAnd a vertical component force F_YRTo obtain i.e. F_R＝F_XRcosβ+F_YRsin beta; according to the mechanical equilibrium condition in the direction of the slip plane, i.e. F_L＝F_R (F_LFor anchoring across each strand in the local coordinate system of the cable saddle

Axial divisionThe sum of the forces).

Step (7) according to the tangent angle theta of the flat bending end point_iAnd initial vertical bend end point tangent angle gamma_iAnd formulas

The tension of the strand can be obtained

This step ensures that each strand has the same safety factor, and that the tensions of the strands are equal.

And (8) entering a strand loop (i is 1-N), and executing the steps from 8-01 to 8-10 until all strands are traversed.

Step 8-01, setting a first intermediate variable aiming at No. i silk strands

(i.e. the

) And combining the first intermediate variable

Is given to the iteration variable gamma (i.e. the value of

)。

8-02, in a saddle local coordinate system

Then the three-dimensional component force of the strand is obtained,

and

converting the three-dimensional component force to be under a local coordinate system oxyz (the self-weight direction of the catenary cable is the vertical y direction) to obtain

(

Is T_ZTransposed matrix of) and calculates the resultant force f on the horizontal plane_h＝f_xl/cos(atan(f_zl/f_xl) Resultant force f) in the vertical direction_v＝f_yl。

Step 8-03, a saddle local coordinate system is adopted

Lower strand anchor point coordinates

Conversion to local coordinate system oxyz, i.e.

Step 8-04, calculating the coordinate (x) of the end point of the vertical bending of the silk strand under the local coordinate system oxyz_si、 y_si、z_si). The vertical radius of curvature of the cable saddle groove is R_vk(assuming that the saddle-groove vertical bending line is composed of n segments of circular arcs, k is an integer from 1 to n), and the corresponding central angle is phi_k，D_iCalculating the vertical bending radius R of the No. i wire strand in the saddle groove for the vertical height of the No. i wire strand on the section of the main cable (taking the saddle groove top as the reference)_kiIs R_ki＝R_vk+D_i。

In the saddle local coordinate system

Next, the coordinates of the end point of the vertical bend of the strand are calculated according to the area where the end point of the vertical bend of the strand is located and the vertical position of the end point in the saddle groove:

when gamma is less than or equal to phi₁Sometimes:

phi when₁＜γ≤φ₁+φ₂Sometimes:

③ when phi₁+φ₂＜γ≤φ₁+φ₂+φ₃Sometimes:

phi when₁+φ₂+φ₃When < gamma:

when k is more than or equal to 4, the longitudinal coordinate of the vertical bending end point of the strand can be obtained by analogy

And vertical coordinate

And pass through

Further calculating the horizontal coordinate of the vertical bending end point of the strand

Then coordinate transformation is carried out to obtain a saddle local coordinate system

Vertical bending end point coordinate of lower strand

Converting the position of the filament into a local coordinate system oxyz to obtain the coordinates (x) of the vertical bending end point of the filament under the local coordinate system oxyz_si、y_si、z_si) Namely that

8-05, under a local coordinate system oxyz, according to a basic equation of a catenary cable unit, anchoring point coordinates (x) by the strands_0i、y_0i、z_0i) Strand vertical bend end point coordinate (x)_si、y_si、z_si) Length L of anchor rod_mgiThe stress-free length of the strand free section and the coordinates of the lower end point of the strand (i.e. the coordinates of the upper end of the anchor rod) are iteratively calculated. The vertical planes defining the strand anchor points and the end points of the vertical bends are strand planes, each strand having a different strand plane.

The iterative process is 8-05-a to 8-05-f.

8-05-a, according to

Calculating the initial unstressed length, the vertical force f 'of the wire strand at the upper end of the anchor rod'_v＝f_v-ωS₀Resultant force in the horizontal plane f'_h＝f_h；

8-05-b, the end of the strand suspension section in the strand plane is tangent to the anchor rod, so that the angle of inclination of the upper end of the anchor rod

Should be equal to the tangent angle of the strand ends, i.e.

The anchor rod can be ensured not to generate additional bending moment.

8-05-c, according to

Calculating the horizontal projection length L of the silk strands;

8-05-d, iteratively calculating the current unstressed length S and the vertical projection length H of the strand according to a basic equation of a catenary unit, wherein the basic equation of the catenary unit is as follows:

wherein EA is the tensile stiffness of the strands and omega is the bulk density of the main cable.

8-05-e, performing precision judgment on the unstressed length calculated by current iteration: if (S-S)₀)/S₀| is less than the preset precision (the preset precision can be set to 10)^-6And | (S-S)₀)/S₀The smaller the value of | can make the precision of the calculation result higher), then enter 8-05-f, otherwise make S₀Return 8-05-a, and execute 8-05-a through 8-05-e.

8-05-f, according to

Calculating a first vertical position difference delta h of the wire strand at the upper end part of the anchor rod₁。

Step 8-06, let

Returning to the step 8-01, and substituting the updated parameter values into the parameter values after the step 8-01 to the step 8-05

Calculate Δ h₂。

Step 8-07, order

Calculate Δ h₀。

Step 8-08, judgment

Whether or not it is less than a preset accuracy (the preset accuracy may be set to 10)^-6And is and

smaller values may result in higher accuracy of the calculated results); if so, terminating the iteration, otherwise, order

Δh₁＝Δh₂，Δh₂＝Δh₀. And 8-01, and executing the steps 8-01 to 8-08 until the preset precision is met, and then terminating the iteration.

Step 8-09, according to the formula x_mi＝x_si-Lcos(atan((z_si-z_0i)/(x_si-x_0i)))、 y_mi＝y_si+ H and z_mi＝z_si+Lsin(atan((z_si-z_0i)/(x_si-x_0i) )) calculates the upper end coordinates (x) of the strand anchor rod in the local coordinate system oxyz_mi、y_mi、z_mi)。

Step 8-10, taking the iteration final value gamma as the final vertical bending cutting angle of the No. i silk strand, namely gamma_iTaking the updated unstressed length S as the final unstressed length S of the strand_iI.e. S_i＝S。

And 8-11, returning to the step 8-01, and recycling the step 8-01 to the step 8-10 until all the strands are calculated. To this end, the end points of the vertical bends of all strands are obtainedVertical bending cutting angle gamma_iAnd the unstressed length S of the suspended section (the part between the end point of the vertical bend and the upper end part of the anchor rod) of the anchor cross inner wire strand_i。

Step (9), the tangent angle theta of the flat bending end point obtained by current iterative computation is used_iAnd vertical bend end point tangent angle gamma_iSubstitution into

Calculating a new local coordinate system of each strand of the anchor span side on the scattered cable saddle

Sum of axial component forces F'_LAnd judging | (F'_L-F_L)/F_LWhether | is smaller than a preset precision (the preset precision can be set to 10)^-6And | (F'_L-F_L)/F_LThe smaller the | value is, the higher the precision of the calculation result is, if yes, the calculation is terminated, otherwise, the vertical bending end point tangent angle gamma is updated_iAnd returning to the step (7).

Step (10), transforming the coordinates of the upper end part of each strand anchor rod under the local coordinate system OXYZ to the coordinates under the integral coordinate system OXYZ,

calculating the installation angle of each anchor rod under an overall coordinate system OXYZ, wherein the included angle between the projection of the anchor rod on the XY plane and the X axis is lambda₁＝atan((Y_mi-Y_0i)/X_mi) The included angle between the projection of the anchor pull rod on the XZ plane and the X axis is lambda₂＝atan((Z_mi-Z_0i)/X_mi) Angle lambda between anchor rod and XZ plane₃＝atan(tan(λ₁)/cos(λ₂))。

Therefore, the accurate anchor rod installation angle of each strand and the accurate stress-free length of each strand suspension section can be obtained, and the vertical bending tangent point and the horizontal bending tangent point coordinates of each strand in the scattered cable saddle groove are determined.

Compared with the related art, the design and installation angle of the anchor rod is calculated by obtaining the coordinates of the upper end part of the strand anchor rod through iteration and then calculating the design and installation angle of the anchor rod according to the coordinates of the upper end part and the lower end part. The beneficial effects include: the method is a completely accurate method without any simplification, the installation angle of the anchor rod, the unstressed length of the suspension section of the wire strand, the positions of the vertical bending end point and the horizontal bending end point of the cable saddle and the tension of the wire strand are simultaneously obtained through coupling iteration, so that the result simultaneously meets a plurality of conditions, including: the tension of the wire strand does not generate additional bending moment at the end part of the anchor pull rod; the sum of the inclined plane component forces of the strand pulling force at the end point of the vertical bend is completely equal to the side span main cable component force; the upper end of the suspension section wire strand is accurately tangent to the cable saddle groove at the end point of the vertical bend; the stress-free length of the strand and the tension of the strand satisfy the catenary equation. Meanwhile, the stress-free length of the closely-attached section of the strand and the saddle groove in the scattered cable saddle groove can be accurately calculated according to the coordinates of the vertical bending end point and the horizontal bending end point of the strand, so that the full-bridge blanking total length of the strand is more accurate, and the factory processing and field erection can be accurately controlled; in addition, through the coordinates of the end points of the vertical bending and the end points of the horizontal bending, a designer can easily judge whether the horizontal bending of the strand occurs before the vertical bending, and further determine whether the design parameters of the saddle groove and the design coordinates of the rear anchor point of the strand need to be adjusted. In addition, the tension of each strand is completely equal, the saddle does not slide any more, the internal force is not redistributed any more, the safety factors of the strands are ensured to be the same, and the durability of the strands can be improved; the end part of the anchor rod does not generate additional bending moment, and only receives the axial tension, so that the durability of the anchor rod can be improved.

In a specific process of calculating the installation angle of the anchor rod, known conditions are as follows: the elastic modulus E of the main cable strand is 1.973E8kPa, the bulk weight omega is 76.917kN/m3, the cross section area A of the strand is 0.003017m2 (the product EA of the elastic modulus E and the cross section area A of the strand is the tensile rigidity of the strand), as shown in figure 5, the IP point coordinate of the cable saddle is (-895.994, 49.876, 0), the inclination angle beta of the sliding surface of the cable saddle is 28.77 degrees, and the component force F of the side-span main cable on the sliding surface_R699212.27kN, height D of strand in saddle groove_i0.063m, the included angle between the normal line of the anchor surface and the horizontal line (the designed inclination angle alpha of the anchor surface) is 36 degrees, and the radius R of the flat bending of the saddle groove of the cable saddle_hIs 18m, the vertical bend consists of 4 sections of circular arcs, and the radius R of the vertical bend_kiAre respectively 12.5m, 9.5m, 6m and 3.5m, and the included angle phi_kRespectively 8 degrees, 7 degrees and 7 degrees.

As shown in FIG. 2, the main cable is composed of 352 strands, and for example, the calculation is performed by taking No. 1 strand at the lowest end of the middle and No. 56 strand with a larger installation angle of the anchor rod as an example, the vertical distances from the centers of the two strands to the top of the saddle groove are respectively 0.0315 and 0.3465m, the transverse distances from the center line of the saddle groove are respectively 0m and 0.66m, the anchoring center coordinates of the anchoring surface are (-921.887, 31.073 and 0), the coordinates of the No. 1 strand are (-7.875 and 0), the coordinates of the No. 56 strand are (-4.5 and-6.15) in the local coordinate system of the anchoring surface, and the length L of the anchor rod is L_mgiAre all 1.78 m.

The method comprises the following specific steps:

1) as shown in fig. 3 and 4, a local coordinate system oxyz and a saddle local coordinate system are established

And coordinate transformation is carried out on the basic parameters, and the method comprises the following steps: theoretical vertex coordinates of the cable saddle, coordinates of anchoring points of the strands and the like;

2) calculating the coordinates of the flat bending end points of the strands to obtain the coordinates of the flat bending end points of No. 1 strand of (0,0.231, 0) and the flat bending cutting angle theta_i0 DEG, the coordinates of the flat bending end point of the No. 56 silk strand are (-1.545, 0.429, -0.933), and the flat bending cutting angle theta_i9.984 degrees;

3) calculating iterative initial values of the vertical bending end point cutting angles to obtain No. 1 and No. 56 strand vertical bending end point cutting angles gamma₁And gamma₅₆Corresponding to 19.784 ° and 14.950 °.

4) And (5) performing iterative calculation from the step (8) to the step (10) to obtain the results of the installation angle of each wire strand anchor rod, the unstressed length of the suspended section, the coordinates of the end point of the vertical bend, the tension force and the like.

According to the traditional method, the angle of a straight line connected between the IP point of the strand saddle and the anchor point of the strand is used as the installation angle of the anchor pull rod of the corresponding strand, so that the spatial distribution of the strand around the curved surface of the strand saddle cannot be considered, and the condition that the anchor span strand is in a catenary state rather than a straight line under the action of self weight is ignored. Because the traditional method simplifies the processing excessively, certain errors exist in the calculation of the installation angle. Table 1 shows the results of comparing the installation angles of the No. 1 and No. 56 strand anchor rods calculated by the present invention and the conventional method.

TABLE 1 Anchor brace installation Angle results

As can be seen from Table 1, for the No. 1 strand located at the center line, the error is relatively small, and the included angle lambda between the projection of the anchor rod on the XY plane and the X axis₁The error of (2.84%) is larger for No. 56 strands far from the central line, and the included angle lambda between the projection of the anchor rod on the XY plane and the X axis₁The error of the anchor rod in the X-axis.

In addition, the method can accurately calculate the unstressed length of the suspension section of the wire strand, the coordinates of the flat bending end point and the vertical bending end point of the wire strand and the cable saddle and the tension of each wire strand, and accurately ensure that the installation angle of the anchor rod is equal to the tangent angle at the lower end of the wire strand, so that the anchor rod cannot generate additional bending moment, and other results such as the unstressed length of the suspension section are shown in a table 2.

TABLE 2 other results

An embodiment of the present invention further provides a computer storage medium, where a computer program is stored on the computer storage medium, where the computer program, when executed by a processor, implements the steps of the method for calculating the installation angle of the anchor rod according to any one of claims 1 to 9.

It will be understood by those of ordinary skill in the art that functional modules/units in all or some of the steps of the methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. In a hardware implementation, the division between functional modules/units mentioned in the above description does not necessarily correspond to the division of physical components; for example, one physical component may have multiple functions, or one function or step may be performed by several physical components in cooperation. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable storage media, which may include computer readable storage media (or non-transitory media) and communication media (or transitory media).

The above embodiments are only specific embodiments of the present invention, but the scope of the embodiments of the present invention is not limited thereto, and any person skilled in the art can easily think of various equivalent modifications or substitutions within the technical scope of the embodiments of the present invention, and these modifications or substitutions should be covered by the scope of the embodiments of the present invention. Therefore, the protection scope of the embodiments of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for calculating the installation angle of an anchor rod is characterized by comprising the following steps:

2. The method of calculating an anchor rod installation angle of claim 1,

before acquiring the theoretical vertex coordinates of the cable saddle and the coordinates of the anchor points of the strands, the method further comprises the following steps:

defining a saddle local coordinate system

the local coordinate system oxyz is towards saddle local coordinate system

Is a conversion matrix of

Local coordinate system of saddle

The theoretical vertex coordinates of the cable saddle are

And is

Wherein beta is the angle of inclination of the slip plane, (X)_ip、Y_ip、Z_ip) The coordinates of the theoretical vertex of the cable saddle are (X) under the overall coordinate system OXYZ_o、Y_o、Z_o) The coordinate of the o point under the overall coordinate system OXYZ is shown;

saddle local coordinate system

The coordinates of the anchoring point of the silk strand are

And is

wherein

3. The method of calculating an anchor rod installation angle of claim 2,

the method for calculating the tangent angle of the flat bent end point of the strand and the tangent angle of the initial vertical bent end point of the strand according to the theoretical vertex coordinate of the scattered cable saddle and the anchoring point coordinate of the strand comprises the following steps:

establish the equation Ax²+ Bx + C is 0, and

A＝1+a²，B＝2×(a×b-a×x_pc-z_pc)，

solving an equation to obtain the transverse coordinate z of each strand flat-bending end point on the anchor span side_piAccording to

according to

4. The method of calculating an anchor rod installation angle of claim 3,

acquiring the total balance force of the side span main cable and calculating the tension of each strand according to the strand flat bending end point chamfer and the strand initial vertical bending end point chamfer, wherein the method comprises the following steps:

step 01, according to F_R＝F_XRcosβ+F_YRsinβ、F_L＝F_RAnd

calculating the component force F of the main cable force along the sliding surface_RThe total balance force F of the side span main cable_LAnd the tension f of each strand_iWherein F is_XRLongitudinal component of tension force of main cable across side span, F_YRIs a vertical component of the side span main cable tension force.

5. The method of calculating an anchor rod installation angle of claim 4,

traversing each strand, and iteratively calculating the unstressed length of the suspended section of the strand and the coordinates of the upper end part of the anchor pull rod of the strand according to the coordinates of the anchor point of the strand, the tangent angle of the flat bent end point of the strand, the tangent angle of the initial vertical bent end point of the strand, the tension of each strand and the vertical position of the strand in the saddle groove, wherein the method comprises the following steps:

step 02: selecting No. i silk strand, setting the first intermediate variable

And combining the first intermediate variable

To the iteration variable γ;

step 03: according to

And

and

Is T_ZThe transposed matrix of (2);

step 04: calculating the coordinates of the tail points of the vertical bends of the strands according to the vertical bend radius of the cable scattering saddle groove, the central angle corresponding to the arc section of the vertical bend line of the saddle groove and the vertical position of the strands in the saddle groove;

step 06: judgment of | (S-S)₀)/S₀If | satisfies the preset precision, if yes, according to

step 07: setting a second intermediate variable

And make

And is

Then returning to step 02 to execute step 02 to step 06 according to the method

Step 08: setting a third intermediate variable

And make

And is

Then returning to step 02 and executing steps 02 to 06, according to

step 09: judgment of

step 10: according to x_mi＝x_si-Lcos(atan((z_si-z_0i)/(x_si-x_0i)))、y_mi＝y_si+ H and z_mi＝z_si+Lsin(atan((z_si-z_0i)/(x_si-x_0i) )) calculating coordinates (x) of the upper end of the strand anchor rod_mi、y_mi、z_mi) And taking the current value of the iteration variable gamma as the final vertical bending end point cutting angle of the No. i silk strand, and taking the current stress-free length S calculated by iteration as the stress-free length of the final silk strand suspension section of the No. i silk strand.

6. The method of calculating an anchor rod installation angle of claim 5,

7. The method of calculating an anchor rod installation angle of claim 5, wherein said step 04 comprises the steps of:

making the R to_vkCorrespond toThe central angle of (a) is expressed as phi_kAnd according to R_ki＝R_vk+D_iCalculating the vertical bending radius R of the No. i strand in the saddle groove_kiWherein D is_iThe vertical height of the No. i silk strand on the section of the main cable is defined;

when gamma is less than or equal to phi₁According to

And vertical coordinate

When phi is₁＜γ≤φ₁+φ₂According to

And vertical coordinate

When phi is₁+φ₂＜γ≤φ₁+φ₂+φ₃According to

And vertical coordinate

When phi is₁+φ₂+φ₃When < gamma, according to

And vertical coordinate

According to

According to

Will be in the saddle local coordinate system

Vertical bending end point coordinate of lower selected strand

Converting the position of the filament into a local coordinate system oxyz to obtain the coordinates (x) of the end point of the vertical bend of the selected filament under the local coordinate system oxyz_si、y_si、z_si)。

8. The method of calculating an anchor rod installation angle of claim 5,

the step 05 comprises the steps of:

according to

Calculating the initial unstressed length S of the suspended section of the strand₀Wherein, L_mgiFor the anchor rod length, (x)_0i、y_0i、z_0i) Is the coordinate of the lower strand anchoring point of the local coordinate system oxyz, (x)_si、y_si、z_si) The coordinates of the vertical bent end points of the lower strands of the local coordinate system oxyz are obtained;

Calculating the inclination angle of the upper end of the anchor rod

According to

Calculating the horizontal projection length L of the silk strands;

according to

And calculating the current unstressed length S and the vertical projection length H of the strand, wherein EA is the tensile rigidity of the strand, and omega is the bulk density of the main cable.

9. The method of calculating an anchor rod installation angle of claim 5,

the anchor rod installation angle is calculated according to the iteratively calculated upper end coordinates of the strand anchor rod, and the method comprises the following steps:

according to

Converting the coordinates of the upper end part of the strand anchor rod into an integral coordinate system OXYZ, and performing transformation according to lambda on the integral coordinate system OXYZ₁＝atan((Y_mi-Y_0i)/X_mi)、λ₂＝atan((Z_mi-Z_0i)/X_mi) And λ₃＝atan(tan(λ₁)/cos(λ₂) Calculating the anchor rod installation angle, where λ₁Is the included angle between the projection of the anchor pull rod on the XY plane and the X axis, lambda₂Is the included angle between the projection of the anchor pull rod on the XZ plane and the X axis, lambda₃Is the angle between the anchor rod and the XZ plane.

10. An apparatus for calculating an installation angle of an anchor rod, comprising: the iteration initial value acquisition module is used for acquiring theoretical vertex coordinates of the scattered cable saddle and coordinates of the anchoring points of the strands and calculating tangent angles of the flat bending end points of the strands and the initial vertical bending end points of the strands according to the theoretical vertex coordinates of the scattered cable saddle and the coordinates of the anchoring points of the strands;

an iterative computation module to:

the iteration initial value obtaining module is further configured to:

defining a saddle local coordinate system

the local coordinate system oxyz is towards saddle local coordinate system

Is a conversion matrix of

Local coordinate system of saddle

The theoretical vertex coordinates of the cable saddle are

And is

saddle local coordinate system

The coordinates of the anchoring point of the silk strand are

And is provided with

wherein

Is T_mTranspose matrix of (x'_0i、y′_0i、z′_0i) For a predetermined strand anchoring point in said strand anchoring surface local coordinate system W_mThe lower coordinate, i is 1 to N, N is the total number of strands, (X)_m、Y_m、Z_m) The coordinates of the center of the anchor surface under the overall coordinate system OXYZ are taken as the coordinates;

establish the equation Ax²+ Bx + C is 0, and

A＝1+a²，B＝2×(a×b-a×x_pc-z_pc)，

according to

And combining the first intermediate variable

To the iteration variable γ;

step 03 comprises: according to

And

and

Is T_ZThe transposed matrix of (2);

the step 04 comprises the following steps: calculating the coordinates of the tail points of the vertical bends of the strands according to the vertical bend radius of the cable scattering saddle groove, the central angle corresponding to the arc section of the vertical bend line of the saddle groove and the vertical position of the strands in the saddle groove;

step 05 comprises: iteratively calculating the initial unstressed length S of the suspended section of the strand according to the coordinates of the anchoring point of the strand, the coordinates of the vertical bending end point of the strand, the resultant force of the selected strand on the horizontal plane and the resultant force of the selected strand in the vertical direction₀And the current unstressed length S of the strand suspended section;

step 07 includes: setting a second intermediate variable

And make it possible to

And is

Then returning to step 02 to execute step 02 to step 06 according to the method

Step 08 comprises: setting a third intermediate variable

And make

And is

Then returning to step 02 and executing steps 02 to 06, according to

step 09 includes: judgment of

the step 04 comprises the steps of:

when gamma is less than or equal to phi₁According to

And vertical coordinate

When phi is₁＜γ≤φ₁+φ₂According to

And vertical coordinate

When phi is₁+φ₂＜γ≤φ₁+φ₂+φ₃According to

And vertical coordinate

When phi is₁+φ₂+φ₃When < gamma, according to

And vertical coordinate

According to

According to

Will be in the saddle local coordinate system

Coordinates of vertical bending end point of lower selected strand

Converting the position of the filament to a local coordinate system oxyz to obtain the coordinates (x) of the end point of the vertical bend of the selected filament under the local coordinate system oxyz_si、y_si、z_si)；

The step 05 comprises the steps of:

according to

Calculating the initial unstressed length S of the suspended section of the strand₀Wherein L is_mgiAnchor pull rod length, (x)_0i、y_0i、z_0i) Is the coordinate of the lower strand anchoring point of the local coordinate system oxyz, (x)_si、y_si、z_si) The coordinates of the vertical bent end points of the lower strands of the local coordinate system oxyz are obtained;

Calculating the inclination angle of the upper end of the anchor rod

According to

Calculating the horizontal projection length L of the silk strands;

according to

the iterative computation module is further configured to:

the installation angle calculation module is further configured to:

according to

Converting the coordinates of the upper end part of the strand anchor rod into an integral coordinate system OXYZ, and performing transformation according to lambda on the integral coordinate system OXYZ₁＝atan((Y_mi-Y_0i)/X_mi)、λ₂＝atan((Z_mi-Z_0i)/X_mi) And λ₃＝atan(tan(λ₁)/cos(λ₂) Calculating the anchor rod installation angle, where λ₁Is the included angle between the projection of the anchor pull rod on the XY plane and the X axis, lambda₂For anchoringThe angle between the projection of the rod in the XZ plane and the X axis, λ₃Is the angle between the anchor rod and the XZ plane.