CN112035929B - Method for calculating linear shape of suspension cable pipeline bridge-forming wind cable - Google Patents

Method for calculating linear shape of suspension cable pipeline bridge-forming wind cable Download PDF

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CN112035929B
CN112035929B CN202010899712.7A CN202010899712A CN112035929B CN 112035929 B CN112035929 B CN 112035929B CN 202010899712 A CN202010899712 A CN 202010899712A CN 112035929 B CN112035929 B CN 112035929B
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wind cable
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左雷彬
胡川川
杨威
詹胜文
刘思萌
陈晓晖
李国辉
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China National Petroleum Corp
China Petroleum Pipeline Engineering Corp
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China Petroleum Pipeline Engineering Corp
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Abstract

The invention relates to a method for calculating the linear shape of an air cable of a suspension cable pipeline bridge, belonging to the field of oil and gas pipeline crossing design and comprising the following steps of: estimating three-directional component force of the initial end of the wind cable according to the space parabola theory; calculating linear coordinates of the wind cable and the unstressed length of each cable section by taking the three-dimensional component force at the starting end of the wind cable as an iteration initial value; and correcting the three-dimensional component force at the starting end of the wind cable by using an influence matrix method, and recalculating to obtain the linear coordinate of the wind cable and the unstressed length of each cable section. The invention solves the problems of inaccurate design, excessive assumption and large calculation error in the prior art, and the design and calculation are carried out by adopting the method, so that the calculation accuracy of the line shape and the stress-free length of the wind cable for the bridge formation of the suspension cable pipeline bridge can be greatly improved.

Description

Method for calculating linear shape of suspension cable pipeline bridge-forming wind cable
Technical Field
The invention relates to a method for calculating the linear shape of an air cable of a suspension cable pipeline bridge forming bridge, and belongs to the field of oil and gas pipeline crossing design.
Background
The pipeline suspension bridge generally comprises a main cable, a sling cable, a wind stay cable, a stabilizing cable (a conjugate cable), a stiffening beam, a cable tower, an anchor and the like. Because its main use is to carry oil, natural gas or water, will set up the support on the bridge floor usually and be used for erectting the pipeline to set up simple and easy access way and make things convenient for the construction and the later stage maintenance of pipeline. The pipeline suspension bridge has small span ratio, small structural rigidity and sensitive wind resistance problem, and a wind cable system is generally required to be arranged. The stress characteristics of the pipeline suspension bridge are as follows: the load acting on the bridge deck and the vertical load generated by the wind cable are transmitted to the main cable through the sling, and then transmitted to the cable tower and the anchorage; the horizontal load acting on the bridge deck is transmitted to the main wind cable through the wind cable and then to the anchor; the force transmission path is clear.
The pipeline suspension bridge is a cable system with a flexible cable structure as a main bearing structure. After the cable structure is stressed, the stress characteristics of small strain and large deformation are reflected, especially for the spatial wind cable structure. Under the action of load, the load and the deformation present an obvious nonlinear relation, and the classical structural mechanics is not applicable any more, because the classical structural mechanics neglects the micro deformation of the structure, and the equilibrium equation is established on the geometric position before the deformation. Calculating a large deformed structure, an equilibrium equation should be established at the deformed position, and iterative calculation is needed.
At present, engineering designers mainly use a plane parabola theory to design a wind cable system: the wind cable and the wind cable are assumed to be in the same inclined plane, and the linear and unstressed lengths of the wind cable and the wind cable are analyzed and calculated only in the plane. However, the actual line shape of the wind cable section between the inhaul cables is a spatial catenary line, so that the line shape of the whole wind cable is greatly different from that of a parabola, and the wind cable and the wind inhaul cables are not in the same plane. The linear shape and the unstressed length of the wind cable are calculated only by utilizing the space parabola theory, so that the difference between the real linear shape and the designed linear shape is large, and the problems that the wind cable system is difficult to install and even cannot be installed are caused.
Disclosure of Invention
In order to solve the problems and accurately calculate the linear shape of the suspension cable crossing into the bridge-forming wind cable, the invention aims to provide a linear shape calculating method of the suspension cable pipeline bridge-forming wind cable. The bridge wind cable line shape is calculated by introducing a segmented catenary theory and an influence matrix method, and is finally converged to a design target line shape after repeated iterative calculation.
A method for calculating the linear shape of a suspension cable pipeline bridge forming wind cable comprises the following steps:
step 1, estimating three-directional component force H at the starting end of the wind cable according to a space parabola theoryFX0、HFY0And VF0；
Step 2, three-way component force H is given to the initial end of the wind cableFX0、HFY0And VF0For iterative initial values, calculating each cable segment of the wind cable from the beginning to the end comprises the following steps:
step 2.1, according to the three-directional component force of the starting end of the ith cable section and the longitudinal bridge length x of the ith cable sectioniCalculating the stress-free length S of the ith cable section of the air outlet cable by using a wind cable balance equationFiAnd the length y of the transverse bridge and the vertical bridgei、zi；
Step 2.2, for the ith wind cable, calculating the coordinate of the lower hanging point of the wind cable according to the wind cable balance equation in the step 2.1, and simultaneously calculating the vertical component force P of the upper hanging point of the air outlet cable according to the known coordinate of the upper hanging point of the wind cable and the design transverse component force of the upper hanging pointEDZJiUnstressed length S of wind cableFDi；
Step 2.3, calculating by the balance equation of the end node of the ith cable section to obtain the three-dimensional component of the start end of the (i + 1) th cable section, repeating the step 2.1-2.2, and calculating to obtain the unstressed length S of the (i + 1) th cable section of the wind cableFi+1And the transverse and vertical bridge length y of the i +1 th cable sectioni+1、zi+1And the vertical component force P of the lifting point of the (i + 1) th wind cableFDZJi+1And the unstressed length S of the (i + 1) th wind guy cableFDi+1Until the nth cable section and the nth wind cable are reached;
and 3, correcting three-way component force H at the starting end of the wind cable by using an influence matrix method by taking the horizontal and vertical coordinates of the tail end of the wind cable and the horizontal coordinate of the designated point in the span as target valuesFX0、HFY0、VF0And repeating iteration until the target variable error is smaller than an allowable value, and calculating to obtain the line shape of the bridge forming wind cable and the stress-free length of each cable section.
Further, estimating three-directional component force H at the starting end of the wind cable according to the space parabola theory in the step 1FX0、 HFY0And VF0The following were used:
Figure BDA0002659502160000031
Figure BDA0002659502160000032
Figure BDA0002659502160000033
wherein the content of the first and second substances,
Figure BDA0002659502160000034
in the formula, HFX0、HFY0And VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable, wherein l is the span of the wind cable, and w is the equivalent uniform load of the wind cable along the span length in the plane of the wind cable; f is the sag of the wind cable in the plane of the wind cable; y isFDJi，zFDJi，yFDIi，zFDIiRespectively are the horizontal and vertical coordinates of the upper and lower hanging points of the wind guy cable; pyi，PziThe vertical component force and the horizontal component force of the upper end of the wind cable are respectively, i is a positive integer from 1 to n, and n is the number of cable sections from the starting end to the tail end of the wind cable.
Further, the transverse bridge length y of the ith cable section of the wind cable is calculated in the step 2.1iAnd vertical bridge length ziAnd a stress-free length SFiThe method comprises the following steps:
Figure BDA0002659502160000035
Figure BDA0002659502160000036
Figure BDA0002659502160000037
Figure BDA0002659502160000038
in the formula, xi，yi，ziThe lengths of the ith cable section of the wind cable in the longitudinal bridge direction, the transverse bridge direction and the vertical bridge direction are respectively; sFiE and AFRespectively is the unstressed length, the elastic modulus and the section area of the ith cable section of the wind cable; q. q.sFThe dead weight concentration of the wind cable section is obtained; hFXi-1，HFYi-1And VFi-1Respectively the longitudinal, transverse and vertical component forces of the starting end of the ith cable section of the wind cable; hi-1The resultant force of the horizontal plane of the starting end of the ith cable section of the wind cable is obtained;
wherein the known quantity comprises the longitudinal bridge length x of the ith cable section of the wind cableiElastic modulus E of wind cable and cross-sectional area A of wind cableFDead weight concentration q of wind cable sectionFLongitudinal component force H of the starting end of the ith cable section of the wind cableFXi-1Transverse component force HFYi-1And a vertical component force VFi-1。
Further, calculating the vertical component force P of the wind cable lifting point in step 2.2FDZJiUnstressed length S of wind cableFDiThe method comprises the following steps:
the recursion relation of three-way component force at the beginning of each cable section of the wind cable is as follows:
Figure BDA0002659502160000041
HFX0、HFY0and VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable; hFXi，HFYiAnd VFiRespectively the longitudinal direction, the transverse direction and the vertical direction of the starting end of the ith cable section of the wind cableComponent force;
for each wind cable, known quantities include: transverse distance y between upper and lower hanging points of wind stay cableFDJi-yFDIiVertical distance z between upper and lower suspension points of wind guy cableFDJi-zFDIiDead weight concentration q of wind guy cableFDWind cable lifting point transverse component force PFDYJi。
Further, in the step 3, obtaining the unstressed length of each cable section of the wind cable, the horizontal and vertical coordinates and the vertical component force and the unstressed length of each wind cable hoisting point by using an influence matrix method through iterative calculation comprises the following steps:
step 3.1, an objective function f (X) is established, where X ═ H (H)FX0，HFY0，VF0)；
Figure BDA0002659502160000042
In the formula, HFX0、HFY0And VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable; n is the number of cable sections from the starting end to the tail end of the wind cable, and m is the number of cable sections from the starting end to the designated point inside the span; y isi，ziThe horizontal length and the vertical length of the ith cable section of the wind cable are respectively; Δ y and Δ z are the coordinate difference between the beginning and the end of the wind cable, respectively, fzThe difference value of the vertical coordinates of the designated point in the span and the wind cable starting end is obtained; the ey is the transverse coordinate error of the tail end of the wind cable, the ex is the vertical coordinate error of the tail end of the wind cable, and the ef is the vertical coordinate error of the designated point inside the span;
h is to beFX0＝HFX0+1，HFY0＝HFY0，VF0＝VF0，HFX0＝HFX0，HFY0＝HFY0+1，VF0＝VF0And HFX0＝HFX0，HFY0＝HFY0，VF0＝VF0+1 is substituted into equation (11), and the corresponding error change amount is calculated, thereby obtaining an influence matrix:
Figure BDA0002659502160000051
wherein the first isThe two and three columns of elements are respectively HFX0，HFY0，VF0The amount of change in the induced errors ey, ez and ef;
step 3.2, solving the initial value correction vector (delta H)FX0，ΔHFY0，ΔVF0)T；
Figure BDA0002659502160000052
Step 3.3, correcting the longitudinal, transverse and vertical component forces of the wind cable starting end
Figure BDA0002659502160000053
VF0＝VF0+ΔVF0And iterating the calculation again until the errors ey, ez and ef are smaller than the allowable values to obtain the corrected three-way component force H at the initial end of the wind cableFX0、HFY0、VF0And repeating the steps 2.1-2.3, and recalculating to obtain the unstressed length of each cable section of the wind cable, the transverse and vertical bridge axial length, the vertical component force of each wind cable lifting point and the unstressed length so as to obtain the wind cable line shape.
The invention has the beneficial effects that:
the invention relates to a calculation method for the linear shape and the stress-free length of a bridge-forming wind cable of a suspension cable pipeline bridge, which is a breakthrough of the design of a suspension cable crossing wind cable system under the condition that the current oil and gas pipeline crossing industry has no specific specification and a system is not formed, provides a set of complete design theory and calculation method for the calculation of the linear shape and the stress-free length of the bridge-forming wind cable of the suspension cable pipeline bridge, and can finally design a calculation method for the linear shape of the bridge-forming wind cable meeting the requirements by combining the design of control point coordinates and the design of wind cable pulling force. The calculation method adopts the segmented catenary and uses numerical iteration to calculate the spatial wind cable shape, so that the calculation method is an accurate calculation method. The segmental catenary method has no assumed error when a finite element method is used for calculation, determines the cable force and curve shape of each part according to the mechanical balance condition and the deformation compatibility condition, automatically counts all nonlinearity of the cable curve, and greatly improves the calculation precision compared with a finite element. Therefore, the problems of inaccurate design, excessive assumption and large calculation error in the prior art can be solved by the calculation method, and the design and calculation are carried out by adopting the method, so that the calculation accuracy of the line shape and the stress-free length of the bridge-forming wind cable of the large-span suspended cable pipeline bridge can be greatly improved, the design rationality of the suspended cable pipeline bridge wind cable is further improved, and the construction difficulty is reduced.
Drawings
FIG. 1 is a flow chart of a method for calculating the linear shape of a suspension cable pipeline bridge formation wind cable according to the invention;
FIG. 2 is a graphical representation of a spatial cable wind calculation;
fig. 3 is a spatial cable wind bracing calculation diagram.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention makes the following assumptions on the space cable-shaped suspension bridge wind cable system:
(1) the wind cable and the wind cable are ideal flexible cables with small strain, the materials of the wind cable and the wind cable meet Hooke's law, and the Poisson effect is ignored.
(2) The wind guy cable only inclines along the transverse bridge direction in the bridge forming state, and the inclination error of the wind guy cable in the longitudinal bridge direction in the construction process is ignored.
A method for calculating the linear shape of a suspension cable pipeline bridge forming wind cable comprises the following steps:
step 1, estimating three-directional component force H at the starting end of the wind cable according to a space parabola theoryFX0、HFY0And VF0；
Step 2, three-way component force H is given to the initial end of the wind cableFX0、HFY0And VF0For iterative initial values, calculating each cable segment of the wind cable from the beginning to the end comprises the following steps:
step 2.1, according to the three-directional component force of the starting end of the ith cable section and the longitudinal bridge length x of the ith cable sectioniCalculating the stress-free length S of the ith cable section of the air outlet cable by using a wind cable balance equationFiAnd the length y of the transverse bridge and the vertical bridgei、zi；
Step 2.2, for the ith wind cable, calculating the coordinate of the lower hanging point of the wind cable according to the wind cable balance equation in the step 2.1, and simultaneously calculating the vertical component force P of the upper hanging point of the air outlet cable according to the known coordinate of the upper hanging point of the wind cable and the design transverse component force of the upper hanging pointFDZJiUnstressed length S of wind cableFDi；
Step 2.3, calculating by the balance equation of the end node of the ith cable section to obtain the three-dimensional component of the start end of the (i + 1) th cable section, repeating the step 2.1-2.2, and calculating to obtain the unstressed length S of the (i + 1) th cable section of the wind cableFi+1And the transverse and vertical bridge length y of the i +1 th cable sectioni+1、zi+1And the vertical component force P of the lifting point of the (i + 1) th wind cableFDZJi+1And the unstressed length S of the (i + 1) th wind guy cableEDi+1Until the nth cable section and the nth wind cable are reached;
and 3, correcting three-way component force H at the starting end of the wind cable by using an influence matrix method by taking the horizontal and vertical coordinates of the tail end of the wind cable and the horizontal coordinate of the designated point in the span as target valuesFX0、HFY0、VF0And repeating iteration until the target variable error is smaller than an allowable value, and calculating to obtain the line shape of the bridge forming wind cable and the stress-free length of each cable section.
Estimating three-directional component force H at the starting end of the wind cable according to the space parabola theory in the step 1FX0、HFY0And VF0The following were used:
Figure BDA0002659502160000071
Figure BDA0002659502160000072
Figure BDA0002659502160000073
wherein the content of the first and second substances,
Figure BDA0002659502160000074
in the formula, HFX0、HFY0And VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable, wherein l is the span of the wind cable, and w is the equivalent uniform load of the wind cable along the span length in the plane of the wind cable; f is the sag of the wind cable in the plane of the wind cable; y isFDJi，zFDJi，yFDIi，zFDIiRespectively are the horizontal and vertical coordinates of the upper and lower hanging points of the wind guy cable; pyi，PziThe vertical component force and the horizontal component force of the upper end of the wind cable are respectively, i is a positive integer from 1 to n, and n is the number of cable sections from the starting end to the tail end of the wind cable.
Step 2.1, the transverse bridge length y of the ith cable section of the wind cable is calculatediAnd vertical bridge length ziAnd a stress-free length SFiThe method is as follows, as shown in figure 2, for the space cable, because the internode only has the dead weight effect, the cable segments are always on a vertical plane, and only the projection of each cable segment on the horizontal plane has different included angles with the axis of the bridge. Therefore, each cable segment satisfies, in the respective vertical plane:
Figure BDA0002659502160000081
Figure BDA0002659502160000082
Figure BDA0002659502160000083
Figure BDA0002659502160000084
in the formula, xi，yi，ziThe lengths of the ith cable section of the wind cable in the longitudinal bridge direction, the transverse bridge direction and the vertical bridge direction are respectively; sFiE and AFRespectively is the unstressed length, the elastic modulus and the section area of the ith cable section of the wind cable; q. q.sFThe dead weight concentration of the wind cable section is obtained; hFXi-1，HFYi-1And VFi-1Respectively the longitudinal, transverse and vertical component forces of the starting end of the ith cable section of the wind cable; hi-1The resultant force of the horizontal plane of the starting end of the ith cable section of the wind cable is obtained;
wherein the known quantity comprises the longitudinal bridge length x of the ith cable section of the wind cableiElastic modulus E of wind cable and cross-sectional area A of wind cableFDead weight concentration q of wind cable sectionFLongitudinal component force H of the starting end of the ith cable section of the wind cableFXi-1Transverse component force HFYi-1And a vertical component force VFi-1。
Step 2.2, vertical component force P of wind cable lifting point is calculatedFDZJiUnstressed length S of wind cableFDiThe method comprises the following steps:
the spatial cable-shaped wind guy cable inclines along the transverse bridge direction, and the calculation precision can be ensured only by regarding the wind guy cable as an elastic catenary. As shown in fig. 3, the recursion relationship of the three-directional component at the beginning of each cable segment of the wind cable is as follows:
Figure BDA0002659502160000091
HFX0、HFY0and VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable; hFXi，HFYiAnd VFiRespectively the longitudinal, transverse and vertical component forces of the starting end of the ith cable section of the wind cable;
for each wind cable, known quantities include: transverse distance y between upper and lower hanging points of wind stay cableFDJi-yFDIiVertical distance z between upper and lower suspension points of wind guy cableFDJi-zFDIiDead weight concentration q of wind guy cableFDWind cable lifting point transverse component force PFDYJi。
The formula (5) to the formula (9) form a balance equation of the spatial cable-shaped wind cable.
In the step 3, the unstressed length, the horizontal and vertical coordinates and the vertical component force and the unstressed length of each wind cable lifting point of each wind cable are obtained by iterative calculation by using an influence matrix method, and the method comprises the following steps:
step 3.1, an objective function f (X) is established, where X ═ H (H)FX0，HFY0，VF0)；
Figure BDA0002659502160000092
In the formula, HFX0、HFY0And VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable; n is the number of cable sections from the starting end to the tail end of the wind cable, and m is the number of cable sections from the starting end to the designated point inside the span; y isi，ziThe horizontal length and the vertical length of the ith cable section of the wind cable are respectively; Δ y and Δ z are the coordinate difference between the beginning and the end of the wind cable, respectively, fzThe difference value of the vertical coordinates of the designated point in the span and the wind cable starting end is obtained; the ey is the transverse coordinate error of the tail end of the wind cable, ez is the vertical coordinate error of the tail end of the wind cable, and ef is the vertical coordinate error of the designated point in the span;
h is to beFX0＝HFX0+1，HFY0＝HFY0，VF0＝VF0，HFX0＝HFX0，HFY0＝HFY0+1，VF0＝VF0And HFX0＝HFX0，HFY0＝HFY0，VF0＝VF0+1 is substituted into equation (11), and the corresponding error change amount is calculated, thereby obtaining an influence matrix:
Figure BDA0002659502160000101
wherein the first, second and third column elements are each HFX0，HFY0，VF0The amount of change in the induced errors ey, ez and ef;
step 3.2, solving the initial value correction vector (delta H)FX0，ΔHFY0，ΔVF0)T；
Figure BDA0002659502160000102
Step 3.3, correcting the longitudinal, transverse and vertical component forces of the wind cable starting end
Figure BDA0002659502160000103
VF0＝VF0+ΔVF0And iterating the calculation again until the errors ey, ez and ef are smaller than the allowable values to obtain the corrected three-way component force H at the initial end of the wind cableFX0、HFY0、VF0And repeating the steps 2.1-2.3, and recalculating to obtain the unstressed length of each cable section of the wind cable, the transverse and vertical bridge axial length, the vertical component force of each wind cable lifting point and the unstressed length so as to obtain the wind cable line shape.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A method for calculating the linear shape of a suspension cable pipeline bridge forming wind cable is characterized by comprising the following steps:
step 1, estimating three-directional component force H at the starting end of the wind cable according to a space parabola theoryFX0、HFY0And VF0；
Step 2, three-way component force H is given to the initial end of the wind cableFX0、HFY0And VF0For iterative initial values, calculating each cable segment of the wind cable from the beginning to the end comprises the following steps:
step 2.1, according to the three-directional component force of the starting end of the ith cable section and the longitudinal bridge length x of the ith cable sectioniCalculating the stress-free length S of the ith cable section of the air outlet cable by using a wind cable balance equationFiAnd the length y of the transverse bridge and the vertical bridgei、zi；
Step 2.2, for the ith wind cable, calculating the coordinate of the lower hanging point of the wind cable according to the wind cable balance equation in the step 2.1, and simultaneously calculating the vertical component force P of the upper hanging point of the air outlet cable according to the known coordinate of the upper hanging point of the wind cable and the design transverse component force of the upper hanging pointFDZJiUnstressed length S of wind cableFDi；
And 2.3, calculating by using an ith cable section end node balance equation to obtain an i +1 th cable section start end three-way component force, and repeating the step 2.1-2.2, calculating to obtain the unstressed length S of the i +1 th cable section of the wind cableFi+1And the transverse and vertical bridge length y of the i +1 th cable sectioni+1、zi+1And the vertical component force P of the lifting point of the (i + 1) th wind cableFDZJi+1And the unstressed length S of the (i + 1) th wind guy cableFDi+1Until the nth cable section and the nth wind cable are reached;
and 3, correcting three-way component force H at the starting end of the wind cable by using an influence matrix method by taking the horizontal and vertical coordinates of the tail end of the wind cable and the horizontal coordinate of the designated point in the span as target valuesFX0、HFY0、VF0And repeating iteration until the target variable error is smaller than an allowable value, and calculating to obtain the line shape of the bridge forming wind cable and the stress-free length of each cable section.
2. The method for calculating the wind cable linear shape of the bridge-forming of the suspended pipeline bridge according to claim 1, wherein in the step 1, the three-directional component H at the starting end of the wind cable is estimated according to the space parabola theoryFX0、HFY0And VF0The following were used:
Figure FDA0002659502150000021
Figure FDA0002659502150000022
Figure FDA0002659502150000023
wherein the content of the first and second substances,
Figure FDA0002659502150000024
in the formula, HFX0、HFY0And VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable, wherein l is the span of the wind cable, and w is the equivalent uniform load of the wind cable along the span length in the plane of the wind cable; f is the sag of the wind cable in the plane of the wind cable; y isFDJi，zFDJi，yFDIi，zFDIiRespectively are the horizontal and vertical coordinates of the upper and lower hanging points of the wind guy cable; pyi，PziThe vertical component force and the horizontal component force of the upper end of the wind cable are respectively, i is a positive integer from 1 to n, and n is the number of cable sections from the starting end to the tail end of the wind cable.
3. The method for calculating the linear shape of the suspension cable pipeline bridge-forming wind cable according to claim 1, wherein the transverse bridge length y of the ith cable section of the wind cable is calculated in step 2.1iAnd vertical bridge length ziAnd a stress-free length SFiThe method comprises the following steps:
Figure FDA0002659502150000025
Figure FDA0002659502150000026
Figure FDA0002659502150000031
Figure FDA0002659502150000032
in the formula, xi,yi,ziThe lengths of the ith cable section of the wind cable in the longitudinal bridge direction, the transverse bridge direction and the vertical bridge direction are respectively; sFiE and AFRespectively is the unstressed length, the elastic modulus and the section area of the ith cable section of the wind cable; q. q.sFThe dead weight concentration of the wind cable section is obtained; hFXi-1,HFYi-1And VFi-1Respectively the longitudinal, transverse and vertical component forces of the starting end of the ith cable section of the wind cable; hi-1The resultant force of the horizontal plane of the starting end of the ith cable section of the wind cable is obtained;
wherein the known quantity comprises the longitudinal bridge length x of the ith cable section of the wind cableiElastic modulus E of wind cable and cross-sectional area A of wind cableFDead weight concentration q of wind cable sectionFLongitudinal component force H of the starting end of the ith cable section of the wind cableFXi-1Transverse component force HFYi-1And a vertical component force VFi-1。
4. The method for calculating the linear shape of the wind cable of the suspension cable pipeline bridge forming bridge according to the claim 3, wherein the vertical component force P of the wind cable lifting point is calculated in the step 2.2FDZJiUnstressed length S of wind cableFDiThe method comprises the following steps:
the recursion relation of three-way component force at the beginning of each cable section of the wind cable is as follows:
Figure FDA0002659502150000033
HFX0、HFY0and VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable; hFXi,HFYiAnd VFiRespectively the longitudinal, transverse and vertical component forces of the starting end of the ith cable section of the wind cable;
for each wind cable, known quantities include: transverse distance y between upper and lower hanging points of wind stay cableFDJi-yFDIiVertical distance z between upper and lower suspension points of wind guy cableFDJi-zFDIiDead weight concentration q of wind guy cableFDWind cable lifting point transverse component force PFDYJi。
5. The method for calculating the linear shape of the wind cable of the suspension cable pipeline bridge forming bridge according to the claim 1, wherein the step 3 of obtaining the unstressed length, the horizontal and vertical coordinates of each cable section of the wind cable and the vertical component force and the unstressed length of the hoisting point of each wind cable by using an influence matrix method through iterative calculation comprises the following steps:
step 3.1, an objective function f (X) is established, where X ═ H (H)FX0,HFY0,VF0)；
Figure FDA0002659502150000041
In the formula, HFX0、HFY0And VF0Respectively longitudinal, transverse and vertical component forces at the starting end of the wind cable; n is the number of cable sections from the starting end to the tail end of the wind cable, and m is the number of cable sections from the starting end to the designated point inside the span; y isi,ziThe horizontal length and the vertical length of the ith cable section of the wind cable are respectively; Δ y and Δ z are the coordinate difference between the beginning and the end of the wind cable, respectively, fzThe difference value of the vertical coordinates of the designated point in the span and the wind cable starting end is obtained; the ey is the transverse coordinate error of the tail end of the wind cable, ez is the vertical coordinate error of the tail end of the wind cable, and ef is the vertical coordinate error of the designated point in the span;
h is to beFX0＝HFX0+1,HFY0＝HFY0,VF0＝VF0,HFX0＝HFX0,HFY0＝HFY0+1,VF0＝VF0And HFX0＝HFX0,HFY0＝HFY0,VF0＝VF0+1 is substituted into equation (11), and the corresponding error change amount is calculated, thereby obtaining an influence matrix:
Figure FDA0002659502150000042
wherein the first, second and third column elements are each HFX0,HFY0,VF0The amount of change in the induced errors ey, ez and ef;
step 3.2, solving the initial value correction vector (delta H)FX0,ΔHFY0,ΔVF0)T；
Figure FDA0002659502150000051
Step 3.3, correcting the longitudinal, transverse and vertical component forces H of the wind cable starting endFX0＝HFX0+ΔHFX0,
Figure FDA0002659502150000052
VF0＝VF0+ΔVF0Re-iterating the calculation untilThe errors ey, ez and ef are smaller than the allowable value, and the corrected three-way component force H at the starting end of the wind cable is obtainedFX0、HFY0、VF0And repeating the steps 2.1-2.3, and recalculating to obtain the unstressed length of each cable section of the wind cable, the transverse and vertical bridge axial length, the vertical component force of each wind cable lifting point and the unstressed length so as to obtain the wind cable line shape.
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