CN113957790A - Method for calculating transverse deflection angle during installation of space main cable clamp - Google Patents

Method for calculating transverse deflection angle during installation of space main cable clamp Download PDF

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CN113957790A
CN113957790A CN202111313872.XA CN202111313872A CN113957790A CN 113957790 A CN113957790 A CN 113957790A CN 202111313872 A CN202111313872 A CN 202111313872A CN 113957790 A CN113957790 A CN 113957790A
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cable
bridge
state
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CN113957790B (en
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肖海珠
何东升
潘韬
高宗余
刘俊峰
李帅帅
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China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
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China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
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    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E01D19/16—Suspension cables; Cable clamps for suspension cables ; Pre- or post-stressed cables
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D11/00—Suspension or cable-stayed bridges
    • E01D11/02—Suspension bridges
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D21/00—Methods or apparatus specially adapted for erecting or assembling bridges
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The application relates to the technical field of bridge engineering, in particular to a method for calculating a transverse deflection angle during installation of a space main cable clamp, which comprises the following steps: calculating a first transverse angle of the cable clamp in the bridge state on a finite element model of the space cable bridge in the bridge state; calculating a second transverse angle of the cable clamp in the empty cable state on a finite element model of the space cable bridge in the empty cable state; and calculating the transverse deflection angle of the cable clamp through the first transverse angle and the second transverse angle. The invention provides a reasonable calculation method for the transverse deflection angle when the space main cable clamp is installed, so that the cable clamp is positioned more accurately. According to the invention, the transverse position of the cable clamp is respectively obtained through the selection of the starting point and the two states of the bridge, namely the empty cable and the bridge forming, so that the calculation process is optimized, and the calculation amount is reduced.

Description

Method for calculating transverse deflection angle during installation of space main cable clamp
Technical Field
The application relates to the technical field of bridge engineering, in particular to a method for calculating a transverse deflection angle during installation of a space main cable clamp.
Background
The spanning capability of the cable bridge is exclusively the head of the bridge in the common bridge type. With the continuous improvement of bridge design and construction level. The suspension bridge is composed of a main cable, a suspender, a bridge tower, an anchorage, a main cable saddle, a scattered cable saddle, a cable clamp and the like. Wherein the cable clamp is mounted on the main cable for connecting the main cable and the suspension rod.
In the conventional construction process, the installation of the cable clamp is carried out in an empty cable state. At the moment, the main cable saddle is not positioned at the designed position of the bridge at the tower top, but has a certain pre-deviation amount towards the side span, so that the installation position of the cable clamp is different from the position of the cable clamp in the bridge state. When the suspension bridge is designed, the suspension bridge comprises a plane main cable and a space main cable, wherein the plane main cable means that each hoisting point on the main cable is in the same vertical plane, and when X represents a longitudinal bridge direction, Y represents a transverse bridge direction and Z represents a vertical bridge direction, Y coordinates of all points on the main cable are the same. At present, most of large-span suspension bridges adopt a plane main cable, the installation and the positioning of a cable clamp only need to calculate the value of a vertical coordinate X at the hanging point of the cable clamp, and the calculation theory of the installation position of the cable clamp is mature.
The spatial main cable suspension bridge means that due to the action of horizontal force at the hoisting point, different coordinate values exist in the horizontal direction of each hoisting point on the main cable. The installation and positioning of the cable clamp need to calculate the vertical coordinate X value at the hanging point of the cable clamp, and also need to calculate the deflection angle of the cable clamp rotating around the axis of the main cable. When the transverse deflection angle of the cable clamp installation deviates from the actual one, the following two problems arise: firstly, the sling and the ear plates at the two ends of the sling are not coplanar, so that the sling is bent transversely, the sling and the ear plates generate secondary bending stress, and the sling is easy to damage; secondly, the sling force deviates from the center of the main cable, and the steel wire of the main cable generates under the action of additional torqueAnd (5) secondary stress. The main cable is typically modeled in finite elements with catenary elements, with each element having a node of only (x)i，yi，zi) Three degrees of freedom of displacement, no degree of freedom of rotation (Rx)i，Ryi，Rzi). After the x coordinate of the hanging point of the cable clamp is calculated by the existing calculation method, the longitudinal installation position of the cable clamp is determined, but the transverse deflection angle during the installation of the cable clamp cannot be calculated. The spatial main cable suspension bridge is only applied to a small-span self-anchored suspension bridge at present, the deflection angle during the installation of a cable clamp is determined through a test or a rough estimation formula, and on the published literature, no method for reasonably calculating the transverse deflection angle during the installation of the spatial main cable clamp is found at present.
Disclosure of Invention
The embodiment of the application provides a method for calculating a transverse deflection angle during installation of a space main cable clamp, which aims to solve the problem that the deflection angle is difficult to calculate accurately during installation of the space main cable clamp in the related technology.
In a first aspect, a method for calculating a lateral deflection angle when a space main cable clamp is installed is provided, and is characterized by comprising the following steps:
calculating a first transverse angle of the cable clamp in the bridge state on a finite element model of the space cable bridge in the bridge state; calculating a second transverse angle of the cable clamp in the empty cable state on a finite element model of the space cable bridge in the empty cable state; and calculating the transverse deflection angle of the cable clamp through the first transverse angle and the second transverse angle.
In some embodiments, the calculating a first transverse angle of the cable clamp in the bridge state on the finite element model of the spatial cable bridge in the bridge state comprises:
establishing a first calculation point of the transverse angle of the cable clamp in the bridge state on a finite element model of the space cable bridge in the bridge state, and calculating a first unit vector at a node of the cable clamp in the bridge state and the unit vector of the calculation point;
calculating a first transverse angle of the cable clamp in the bridge state according to the unit vector at the node of the cable clamp in the bridge state and the unit vector of the starting point;
in some embodiments, the establishing a first starting point of the lateral angle of the cable clamp in the bridge state on the finite element model of the spatial cable bridge in the bridge state, and calculating a first unit vector at the node of the cable clamp in the bridge state and the starting point unit vector, comprises:
outputting coordinates of the cable clamp node in the bridge state, internal force components of two sections of catenary units adjacent to the cable clamp node and direction vectors of suspension ropes, wherein the suspension ropes are connected with the cable clamp node and calculated into a first average tangent vector of a main cable at the cable clamp node in the bridge state;
calculating a first unit vector of the cable clamp node in a bridge state according to the first average tangent vector and the sling direction vector;
establishing a first starting point of the transverse angle of the cable clamp according to the first average tangent vector and the sling direction vector, and calculating a unit vector of the first starting point.
In some embodiments, said establishing a first starting point of a transverse angle of said cable clamp from said first mean tangent vector and said sling direction vector and calculating a unit vector of said first starting point comprises:
setting the longitudinal bridge direction of the finite element model of the space cable bridge in the bridge state as an X axis, setting the transverse bridge direction as a Y axis and setting the vertical bridge direction as a Z axis;
establishing an intersection line between a first plane formed by the average tangent vector and the Z axis and a vertical plane of the first average tangent vector as a first calculation point of a transverse deflection angle of the cable clamp in a bridge state;
and calculating a unit vector of the first starting point according to the normal vector of the first plane and the first average tangent vector.
In some embodiments, said calculating a first unit vector of said cable clamp node in a bridge state from said first mean tangent vector and said sling direction vector comprises:
calculating a vertical vector that is perpendicular to both the first average tangent vector and the sling direction vector;
and calculating a first unit vector of the cable clamp in the bridge state according to the vertical vector and the first average tangent vector.
In some embodiments, calculating the second transverse angle of the cable clamp in the empty cable state on the finite element model of the empty cable bridge in the empty cable state includes:
adding a rigid arm perpendicular to the axis of the main cable at a cable clamp node on a finite element model of the space cable bridge in an empty cable state, and calculating a second starting point of the transverse angle of the cable clamp and a unit vector of the steel arm in the empty cable state;
and calculating a second transverse angle of the cable clamp in the cable-empty state according to the unit vector of the steel arm and the unit vector of the cable clamp in the cable-empty state, and calculating a transverse deflection angle of the cable clamp according to the first transverse angle and the second transverse angle.
In some embodiments, adding a rigid arm perpendicular to the main cable axis at the cable clamp node point on the finite element model of the space cable bridge in the empty cable state, and calculating a second starting point of the transverse angle of the cable clamp in the empty cable state and a unit vector of the steel arm includes:
outputting coordinates of the cable clamp node in an empty cable state;
and calculating the unit vector of the steel arm according to the coordinates of the cable clamp node and the first unit vector of the cable clamp.
In some embodiments, adding a rigid arm perpendicular to the main cable axis at the cable clamp node point on the finite element model of the space cable bridge in the empty cable state, and calculating a second starting point of the transverse angle of the cable clamp in the empty cable state and a unit vector of the steel arm includes:
setting the longitudinal bridge direction of the finite element model of the space cable bridge in the empty cable state as an X axis, setting the transverse bridge direction as a Y axis and setting the vertical bridge direction as a Z axis, outputting the coordinates of the cable clamp node in the empty cable state and force components in two sections of catenary units adjacent to the cable clamp node, and calculating a second average tangent vector of a main cable at the cable clamp node in the empty cable state;
and establishing a second starting point according to the second average tangent vector and the Z axis, and calculating a unit vector of the second starting point.
In some embodiments, said establishing a second starting point from said second mean tangent vector and said Z-axis and calculating a unit vector for said second starting point comprises:
calculating a normal vector of a third plane where the second average tangent vector and the Z axis are located, and taking an intersection line of the third plane and a vertical plane of the second average tangent vector as a second calculation point; and calculating a unit vector of the second starting point according to the normal vector of the third plane and the second average tangent vector.
In some embodiments, calculating the second transverse angle of the cable clamp in the empty cable state on the finite element model of the empty cable bridge in the empty cable state includes:
and connecting the space beam units to form nodes at two ends of the main cable catenary unit of the space cable finite element model in a bridge state to establish the space cable finite element model in the empty cable state, so that the space beam units and the catenary unit share the nodes in some embodiments.
The beneficial effect that technical scheme that this application provided brought includes:
(1) the invention provides a reasonable calculation method for the transverse deflection angle when the space main cable clamp is installed, so that the cable clamp is positioned more accurately.
(2) According to the invention, the transverse position of the cable clamp is respectively obtained through the selection of the starting point and the two states of the bridge, namely the empty cable and the bridge forming, so that the calculation process is optimized, and the calculation amount is reduced.
(3) The calculation method of the transverse deflection angle provides convenience for subsequent calculation through the selection of the starting point.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, 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 flowchart of a method for calculating a lateral deflection angle when a space main cable clamp is installed according to an embodiment of the present application;
fig. 2 is a schematic structural diagram of a spatial main cable suspension bridge provided in an embodiment of the present application;
fig. 3 is a schematic diagram illustrating a cell composition at a node according to an embodiment of the present application;
FIG. 4 is a schematic view of a vector at a node of a cable clamp according to an embodiment of the present application;
FIG. 5 is a schematic view of the positioning of the cable clamp lateral deflection angle provided by the embodiment of the present application;
fig. 6 is a schematic three-dimensional model diagram of a full bridge of a spatial cable bridge according to an embodiment of the present application.
In the figure, 1-main cable, 2-sling, 3-stiffening beam, 4-bridge tower and 5-stayed cable.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The invention provides a method for calculating a transverse deflection angle during installation of a space main cable clamp, which comprises the following steps:
s1, calculating a first transverse angle of the cable clamp in the bridge forming state on a finite element model of the space cable bridge in the bridge forming state.
Specifically, a first calculation point of the transverse angle of the cable clamp in the bridge state is established on a finite element model of the space cable bridge in the bridge state, and a first unit vector at the node of the cable clamp in the bridge state and the unit vector of the calculation point are calculated; and calculating a first transverse angle of the cable clamp in the bridge state according to the unit vector at the node of the cable clamp in the bridge state and the unit vector of the starting point.
It is understood that the step S1 includes: outputting coordinates of the cable clamp node in the bridge state, internal force components of two sections of catenary units adjacent to the cable clamp node and direction vectors of suspension ropes, wherein the suspension ropes are connected with the cable clamp node and calculated into a first average tangent vector of a main cable at the cable clamp node in the bridge state; calculating a first unit vector of the cable clamp node in a bridge state according to the first average tangent vector and the direction vector of the sling; establishing a first starting point of the transverse angle of the cable clamp according to the first average tangent vector and the direction vector of the sling, and calculating a unit vector of the first starting point.
Preferably, in the calculation method for establishing the calculation point and the calculation point unit vector: setting the longitudinal bridge direction of the finite element model of the space cable bridge in the bridge state as an X axis, setting the transverse bridge direction as a Y axis and setting the vertical bridge direction as a Z axis; establishing an intersection line between a first plane formed by the average tangent vector and the Z axis and a vertical plane of the first average tangent vector as a first calculation point of a transverse deflection angle of the cable clamp in a bridge state; and calculating a unit vector of the first starting point according to the normal vector of the first plane and the first average tangent vector.
In some embodiments, the calculating the first unit vector of the cable clamp node in the bridge state comprises: calculating a vertical vector perpendicular to both the first average tangent vector and the direction vector of the sling; and calculating a first unit vector of the cable clamp in the bridge state according to the vertical vector and the first average tangent vector.
Specifically, referring to fig. 4, 5 and 6, step S1 includes the following 5 steps:
step 1: establishing a bridge finite element model of space cable linear iterative computation, setting a main cable of the space cable in a bridge forming state as a catenary unit, wherein X represents a longitudinal bridge direction, Y represents a transverse bridge direction, and Z represents a vertical bridge direction. Specifically, as shown in fig. 2, X represents a longitudinal direction, Y represents a transverse direction, and Z represents a vertical direction. Establishing a space main cable finite element model with a main cable 1 and a sling 2 as a catenary unit and a stiffening beam 3 and a bridge tower 4 as beam units, applying constant load on the model, and obtaining the bridge forming line shape of the space main cable through iterative calculation.
Step 2: outputting coordinates of a cable clamp node i and a unit internal force component of two sections of catenary units adjacent to the cable clamp node i at the cable clamp node
Figure BDA0003342902930000081
And
Figure BDA0003342902930000082
and the direction vector of each sling connected with the node of the cable clamp
Figure BDA0003342902930000083
Specifically, coordinates (x) of each node on the main cable at the position of the output cable clampi，yi，zi) Section (i-1) catenaries cell internal force component at node i
Figure BDA0003342902930000084
Intra-cell force component of ith segment catenary cell at i-node
Figure BDA0003342902930000085
Direction vector of sling
Figure BDA0003342902930000086
And step 3: by force component in the unit
Figure BDA0003342902930000087
And force component in unit
Figure BDA0003342902930000088
Calculating a first average tangent line of the main cable at the i-nodeMeasurement of
Figure BDA0003342902930000089
In some embodiments, step 3 above includes:
according to the formula:
Figure BDA00033429029300000810
Figure BDA00033429029300000811
respectively obtaining tangent unit vectors (l) of two sections of catenary units adjacent to the cable clamp node i at the node ii，mi，ni)i-1And (l)i，mi，ni)i；
Then according to the formula:
Figure BDA00033429029300000812
obtaining a first average tangent vector of the main cable at the i node under the bridge forming state
Figure BDA00033429029300000813
And 4, step 4: by a first mean tangent vector
Figure BDA0003342902930000091
Z-axis and direction vector of sling
Figure BDA0003342902930000092
Calculating a unit vector of a first starting point of a cable clamp about a main cable transverse deflection angle
Figure BDA0003342902930000093
First unit vector when forming bridge with cable clamp
Figure BDA0003342902930000094
Specifically, as shown in fig. 3 and 4, the first average tangent vector
Figure BDA0003342902930000095
And the Z axis form a first plane (i.e., PZ plane shown in FIG. 4), and the normal vector of the first plane is calculated
Figure BDA0003342902930000096
With the first plane and the average tangent vector
Figure BDA0003342902930000097
Is the first starting point of the transverse deflection angle of the cable clamp.
According to the formula:
Figure BDA0003342902930000098
obtaining the unit vector of the intersecting line
Figure BDA0003342902930000099
(i.e. the unit vector of the first starting point), i.e. in unit vectors
Figure BDA00033429029300000910
Is the first starting point. The reason for taking the vertical line as the starting point is that the plumb line can be easily determined in nature (the plumb line is determined by hanging a cone below a common line when a house is built, namely the Z axis in the text), and the calculation is convenient. In addition to the intersecting lines mentioned in the present invention, other intersecting lines are also possible as starting points.
Further, the first average tangent vector
Figure BDA00033429029300000911
And the direction vector of the sling
Figure BDA00033429029300000912
Forming a second plane (i.e. a plane in which the two vectors exist simultaneously), and calculating a normal vector of the second plane
Figure BDA0003342902930000101
According to the formula:
Figure BDA0003342902930000102
obtaining a first unit vector when the cable clip forms a bridge
Figure BDA0003342902930000103
From the calculation formula, the vector
Figure BDA0003342902930000104
Are all located in a first plane.
And 5: a first unit vector through the cable clamp
Figure BDA0003342902930000105
Unit vector of the first calculation point
Figure BDA0003342902930000106
Determining the transverse angle theta of the cable clamp during bridgingi(ii) a Transverse angle of the cable clamp when forming a bridge:
Figure BDA0003342902930000107
and S2, calculating a second transverse angle of the cable clamp in the empty cable state on the finite element model of the space cable bridge in the empty cable state.
Specifically, a rigid arm perpendicular to the axis of the main cable is added at a cable clamp node on a finite element model of the space cable bridge in an empty cable state, and a second starting point of the transverse angle of the cable clamp in the empty cable state and a unit vector of the steel arm are calculated; and calculating a second transverse angle of the cable clamp in the cable-empty state according to the unit vector of the steel arm and the unit vector of the cable clamp in the cable-empty state, and calculating a transverse deflection angle of the cable clamp according to the first transverse angle and the second transverse angle.
In some embodiments, coordinates of the cable clamp node in an empty cable state are output; and calculating the unit vector of the steel arm according to the coordinates of the cable clamp node and the first unit vector of the cable clamp.
Preferably, step S2 includes: setting the longitudinal bridge direction of the finite element model of the space cable bridge in the empty cable state as an X axis, setting the transverse bridge direction as a Y axis and setting the vertical bridge direction as a Z axis, outputting the coordinates of the cable clamp node in the empty cable state and force components in two sections of catenary units adjacent to the cable clamp node, and calculating a second average tangent vector of a main cable at the cable clamp node in the empty cable state; and establishing a second starting point according to the second average tangent vector and the Z axis, and calculating a unit vector of the second starting point.
It should be noted that the establishment of the second starting point and the calculation of the unit vector thereof are similar to the establishment and calculation of the first calculation point in step S1.
Specifically, the calculation of the unit vector of the second starting point includes: calculating a normal vector of a third plane where the second average tangent vector and the Z axis are located, and taking an intersection line of the third plane and a vertical plane of the second average tangent vector as a second calculation point; and calculating a unit vector of the second starting point according to the normal vector of the third plane and the second average tangent vector. The third plane is the plane containing both the second mean tangent vector and the Z-axis.
Specifically, step S2 includes the following 5 steps:
step 1: and connecting nodes at two ends of the main cable catenary unit by using a space beam unit to establish a finite element model of the empty cable, wherein the space beam unit and the catenary unit share a node. Specifically, in the bridged finite element model generated in step S1, the space beam elements are used to connect the nodes at the two ends of the catenary element on the main cable, the space beam elements and the catenary element share a node, the cross-sectional characteristics of the beam elements include the torsional rigidity of the equivalent cross section of the input main cable and a slight flexural rigidity, and the capacity weight is 0.
Step 2: at each cable clamp nodeA rigid arm perpendicular to the axis of the main cable is added at the position i, and the unit vector of the rigid arm is calculated after the construction stage analysis is carried out on the empty cable finite element model
Figure BDA0003342902930000111
It is worth mentioning that a rigid arm perpendicular to the axis of the main cable is added at each cable clamp node, one end of the rigid arm is an i node (namely the cable clamp node) on the main cable, and the coordinate is (x)i，yi，zi) The other end is an i' node with coordinates of
Figure BDA0003342902930000112
Wherein
Figure BDA0003342902930000121
Is the unit vector when the cable clamp is bridged. The steel arm does not exist in the actual bridge, and the torsion angle is calculated by adding the steel arm to the finite element model.
And step 3: respectively outputting the unit internal force components of two sections of catenary units adjacent to the cable clamp node i at the node i
Figure BDA0003342902930000122
And
Figure BDA0003342902930000123
calculating a second average tangent vector of the main cable at the i-node
Figure BDA0003342902930000124
Specifically, as shown in fig. 5, after the construction stage analysis is performed on the air cable finite element model, the coordinate of the node i is obtained as (x)i0，yi0，zi0) And the coordinate of the node i' at the other end of the corresponding steel arm is (x)i′0，yi′0，zi′0)；
According to the formula:
Figure BDA0003342902930000125
obtaining the unit vector of the rigid arm
Figure BDA0003342902930000126
According to the formula:
Figure BDA0003342902930000127
Figure BDA0003342902930000128
obtaining a tangent unit vector (l) of the catenary unit of the (i-1) th segment at the node ii0，mi0，ni0)i-1And the tangent unit vector (l) of the ith segment catenary element at the i-nodei0，mi0，ni0)iWherein
Figure BDA0003342902930000131
Is the intra-cell force term of the catenary cell at node i for the (i-1) th segment,
Figure BDA0003342902930000132
the force component in the unit of the ith section of the catenary unit at the node i is defined;
according to the tangent unit vector (l) of the ith segment catenary unit at the i nodei0，mi0，ni0)iAnd the tangent unit vector (l) of the segment (i-1) catenary element at node ii0，mi0，ni0)i-1Calculating the second average tangent vector of the main cable at the i node
Figure BDA0003342902930000133
Wherein:
Figure BDA0003342902930000134
and 4, step 4: according to the second average tangent vector
Figure BDA0003342902930000135
Determining the unit vector of the second starting point of the cable clamp transverse angle in the empty cable with the Z axis
Figure BDA0003342902930000136
It will be appreciated that the establishment of the second starting point is similar to step 4 above, said second mean tangent vector
Figure BDA0003342902930000137
And a Z-axis vector forming a third plane normal to
Figure BDA0003342902930000138
According to the formula:
Figure BDA0003342902930000139
obtaining the unit vector of the second starting point of the horizontal angle of the cable clamp when the cable clamp is empty
Figure BDA00033429029300001310
And 5: unit vector passing through the second starting point
Figure BDA0003342902930000141
And a unit vector of the rigid arm
Figure BDA0003342902930000142
Calculating the transverse angle theta of the cable clamp during cable emptyingi0
According to the formula:
Figure BDA0003342902930000143
obtaining the transverse angle theta of the cable clamp in the empty cablei0。
And S3, calculating a transverse deflection angle of the cable clamp through the first transverse angle and the second transverse angle.
Specifically, the difference between the first transverse angle and the second transverse angle is the transverse deflection angle of the cable clamp.
The transverse angle theta of the cable clamp during bridgingiTransverse angle theta of cable clamp in the empty cablei0For the transverse deflection angle when the cable clamp is installed: thetai-θi0。
It will be appreciated that the lateral deflection angle can be used to calculate the increase in stress in the wire in the main cable caused by twisting of the main cable.
Furthermore, when the empty cable clamp is positioned, if the distance between the cable clamp mark point and the center of the main cable is D, the transverse deviation of the cable clamp mark point from the center of the main cable is delta Yd＝D·sinθi0. Give (x)i0，ΔYd) Two parameters can determine the theoretical position of the spatial main cable clamp during installation.
The invention further provides a specific embodiment, which takes the space main cable of the cable-stayed suspension cable cooperation system bridge shown in fig. 6 as an embodiment, and selects node D22 marked in fig. 6 to explain a specific calculation method of the transverse deflection angle during installation of the cable clamp.
The coordinates of the D22 node on the main cable are:
(xi，yi，zi)＝(-343.1，-9.884，143.163),
the coordinates of the lower lifting point of the sling are as follows:
(xd，i，yd，i，zd，i)＝(-343.1，-13.7，65.238)，
the direction vector of the sling is as follows:
Figure BDA0003342902930000151
the force component in the catenary cell at the node D22 of the section before the node D22 is as follows:
Figure BDA0003342902930000152
the tangent unit vector of the catenary unit at the node D22 before the node D22 is as follows:
Figure BDA0003342902930000153
the force component in the catenary cell at the D22 node after the D22 node is as follows:
Figure BDA0003342902930000154
the tangent unit vector of the catenary unit at the node D22 after the node D22 is as follows:
Figure BDA0003342902930000155
calculating a first average tangent vector of the main cable at the node D22 as:
Figure BDA0003342902930000161
the unit vector of the intersection line between the vertical plane of the first mean tangent vector p → the plane of the vector p → and the Z-axis (i.e. the unit vector of the first point of addition) is calculated:
Figure BDA0003342902930000162
computing
Figure BDA0003342902930000163
And
Figure BDA0003342902930000164
form a normal vector of a plane
Figure BDA0003342902930000165
Figure BDA0003342902930000166
The direction vector of the sling is in the first average tangent vector
Figure BDA0003342902930000167
The unit vector of the normal in-plane projection of (1), i.e. the unit vector of the sling
Figure BDA0003342902930000168
Transverse angle of the cable clamp when forming a bridge:
Figure BDA0003342902930000169
establishing a finite element model when the bridge is empty, adding a virtual rigid arm at an i node where a cable clamp is positioned at the moment, wherein the coordinates of an i' node at the other end of the rigid arm are as follows:
Figure BDA00033429029300001610
calculating the second average tangent vector of the main cable at the i node when the main cable is empty according to the similar steps in the bridge forming state
Figure BDA00033429029300001611
Second mean tangent vector
Figure BDA00033429029300001612
Unit vector of the intersection line of the vertical plane and the plane
Figure BDA0003342902930000171
Transverse angle of cable clamp in case of empty cable
Figure BDA0003342902930000172
The angle of rotation of the cable clamp about the main cable axis (i.e. the transverse deflection angle) during the process from empty to bridging is θi-θi0＝0.440°。
In summary, the transverse angles of the cable clamps of the bridge are respectively calculated through the finite element models of the bridge when the bridge is formed and the bridge is empty, and then the transverse deflection angles of the space main cable when the cable clamps are installed are obtained. A method for calculating the transverse deflection angle of a cable clamp is provided for a space main cable bridge. And can be used for avoiding because the hoist cable is not coplanar with the otic placode at hoist cable both ends and leading to hoist cable horizontal bending through the accurate positioning cable clip, the condition that hoist cable and otic placode produced crooked secondary stress and damaged the hoist cable takes place, has meanwhile also solved hoist cable power and has deviated main cable center, and the main cable produces the problem of secondary stress at additional moment of torsion effect steel wire down. The calculation method of the cable clamp transverse deflection angle in the invention brings convenience to the whole calculation process by establishing a vertical starting point in the finite element model.
In the description of the present application, it should be noted that the terms "upper", "lower", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are only for convenience in describing the present application and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and operate, and thus, should not be construed as limiting the present application. Unless expressly stated or limited otherwise, the terms "mounted," "connected," and "connected" are intended to be inclusive and mean, for example, that they may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art as appropriate.
It is noted that, in the present application, relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above description is merely exemplary of the present application and is presented to enable those skilled in the art to understand and practice the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A method for calculating a transverse deflection angle during installation of a space main cable clamp is characterized by comprising the following steps:
calculating a first transverse angle of the cable clamp in the bridge state on a finite element model of the space cable bridge in the bridge state;
calculating a second transverse angle of the cable clamp in the empty cable state on a finite element model of the space cable bridge in the empty cable state;
and calculating the transverse deflection angle of the cable clamp through the first transverse angle and the second transverse angle.
2. The method of claim 1, wherein calculating the first transverse angle of the clamp in the bridge state on the finite element model of the spatial cable bridge in the bridge state comprises:
establishing a first calculation point of the transverse angle of the cable clamp in the bridge state on a finite element model of the space cable bridge in the bridge state, and calculating a first unit vector at a node of the cable clamp in the bridge state and the unit vector of the calculation point;
and calculating a first transverse angle of the cable clamp in the bridge state according to the unit vector at the node of the cable clamp in the bridge state and the unit vector of the starting point.
3. The calculation method according to claim 2, wherein the establishing a first starting point of the lateral angle of the cable clamp in the bridge state on the finite element model of the space cable bridge in the bridge state, and calculating a first unit vector at a node of the cable clamp in the bridge state and the starting point unit vector, comprises:
outputting coordinates of the cable clamp node in the bridge state, force components in two sections of catenary units adjacent to the cable clamp node and direction vectors of slings connected with the cable clamp node, and calculating a first average tangent vector of a main cable at the cable clamp node in the bridge state;
calculating a first unit vector of the cable clamp node in a bridge state according to the first average tangent vector and the direction vector of the sling;
establishing a first starting point of the transverse angle of the cable clamp according to the first average tangent vector and the direction vector of the sling, and calculating a unit vector of the first starting point.
4. The method of claim 3, wherein said establishing a first starting point of a transverse angle of the rope clamp based on the first average tangent vector and the directional vector of the suspension rope, and calculating a unit vector of the first starting point comprises:
setting the longitudinal bridge direction of the finite element model of the space cable bridge in the bridge state as an X axis, setting the transverse bridge direction as a Y axis and setting the vertical bridge direction as a Z axis;
establishing an intersection line between a first plane formed by the first average tangent vector and the Z axis and a vertical plane of the first average tangent vector as a first starting point of a transverse deflection angle of the cable clamp in a bridge state;
and calculating a unit vector of the first starting point according to the normal vector of the first plane and the first average tangent vector.
5. The method of claim 3, wherein said calculating a first unit vector for said cable clamp node in a bridge state from said first average tangent vector and a direction vector of said suspension cable comprises:
calculating a vertical vector perpendicular to both the first average tangent vector and the direction vector of the sling;
and calculating a first unit vector of the cable clamp in the bridge state according to the vertical vector and the first average tangent vector.
6. The method of claim 1, wherein calculating the second transverse angle of the clamp in the empty cable state on a finite element model of the space cable bridge in the empty cable state comprises:
adding a rigid arm perpendicular to the axis of the main cable at a cable clamp node on a finite element model of the space cable bridge in an empty cable state, and calculating a second starting point of the transverse angle of the cable clamp and a unit vector of the steel arm in the empty cable state;
and calculating a second transverse angle of the cable clamp in the cable-empty state according to the unit vector of the steel arm and the unit vector of the cable clamp in the cable-empty state, and calculating a transverse deflection angle of the cable clamp according to the first transverse angle and the second transverse angle.
7. The calculation method as claimed in claim 6, wherein the step of adding a rigid arm perpendicular to the main cable axis at the cable clamp node on the finite element model of the space cable bridge in the empty cable state and calculating a second starting point of the transverse angle of the cable clamp in the empty cable state and a unit vector of the steel arm comprises:
outputting coordinates of the cable clamp node in an empty cable state;
and calculating the unit vector of the steel arm according to the coordinates of the cable clamp node and the first unit vector of the cable clamp.
8. The calculation method as claimed in claim 6, wherein the step of adding a rigid arm perpendicular to the main cable axis at the cable clamp node on the finite element model of the space cable bridge in the empty cable state and calculating a second starting point of the transverse angle of the cable clamp in the empty cable state and a unit vector of the steel arm comprises:
setting the longitudinal bridge direction of the finite element model of the space cable bridge in the empty cable state as an X axis, setting the transverse bridge direction as a Y axis and setting the vertical bridge direction as a Z axis, outputting the coordinates of the cable clamp node in the empty cable state and force components in two sections of catenary units adjacent to the cable clamp node, and calculating a second average tangent vector of a main cable at the cable clamp node in the empty cable state;
and establishing a second starting point according to the second average tangent vector and the Z axis, and calculating a unit vector of the second starting point.
9. The computing method of claim 8, wherein said establishing a second starting point based on said second mean tangent vector and said Z-axis and computing a unit vector for said second starting point comprises:
calculating a normal vector of a third plane where the second average tangent vector and the Z axis are located, and taking an intersection line of the third plane and a vertical plane of the second average tangent vector as a second calculation point;
and calculating a unit vector of the second starting point according to the normal vector of the third plane and the second average tangent vector.
10. The method of claim 1, wherein calculating the second transverse angle of the clamp in the empty cable state on a finite element model of the space cable bridge in the empty cable state comprises:
and connecting the space beam units to form nodes at two ends of a main cable catenary unit of the space cable finite element model in a bridge state to establish the space cable finite element model in the empty cable state, so that the space beam units and the catenary unit share the nodes.
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Publication number Priority date Publication date Assignee Title
CN116598953A (en) * 2023-03-23 2023-08-15 深中通道管理中心 Large-diameter main cable riding type cable clamping empty cable state torsion control method and system

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CN107587429A (en) * 2017-08-04 2018-01-16 东南大学 Cord clip of suspension bridge installation site modification method
CN111523172A (en) * 2020-05-11 2020-08-11 重庆交通大学 Bridge forming linear analysis method for main cable of spatial special-shaped cable surface suspension bridge

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Publication number Priority date Publication date Assignee Title
WO2017129937A1 (en) * 2016-01-28 2017-08-03 John Michael Corney Long span suspension bridges - cable geometry
CN107587429A (en) * 2017-08-04 2018-01-16 东南大学 Cord clip of suspension bridge installation site modification method
CN111523172A (en) * 2020-05-11 2020-08-11 重庆交通大学 Bridge forming linear analysis method for main cable of spatial special-shaped cable surface suspension bridge

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Publication number Priority date Publication date Assignee Title
CN116598953A (en) * 2023-03-23 2023-08-15 深中通道管理中心 Large-diameter main cable riding type cable clamping empty cable state torsion control method and system
CN116598953B (en) * 2023-03-23 2024-03-29 深中通道管理中心 Large-diameter main cable riding type cable clamping empty cable state torsion control method and system

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