Two-way curved arch bridge main arch ring bottom surface disease distribution diagram drawing method

Abstract

The invention discloses a method for drawing a bottom surface disease distribution diagram of a main arch ring of a two-way curved arch bridge. According to the method, arch rib and arch wave numbers, an arch rib local coordinate system, an arch wave local coordinate system, a disease position recording standard, an overall coordinate system, an arch rib disease position description standard, an arch wave disease position description standard and a disease pattern drawing standard are included. On one hand, a set of independent local coordinate system based on a horizontal projection plane is established for each arch rib and arch wave of the main arch ring of the two-way curved arch bridge, on the other hand, a three-dimensional curved surface is expanded into a two-dimensional curved surface along the bridge direction and the transverse bridge direction, and an overall coordinate system reflecting the actual size of the main arch ring is established; local disease coordinates are reflected in the actual position of the main arch ring of the two-way curved arch bridge through coordinate conversion, and accurate disease drawing of the complex three-dimensional curved surface of the main arch ring of the two-way curved arch bridge is achieved.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically, it relates to a method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge. Background Technology

[0002] In bridge inspection, it is frequently necessary to map the distribution of defects on the surface of the bridge's main girder and calculate their dimensions and quantities. When creating this map, the location of the defects on the bridge's main girder surface needs to be known. Bridge inspection reports often require the spatial location information of the defects to be presented in the form of two-dimensional images.

[0003] The main beam of a bridge is a three-dimensional spatial structure. The usual practice is to divide the outer surface of the main beam into independent two-dimensional surfaces and record the location of defects on each surface to obtain the distribution of defects on the surface of the main beam. Traditional methods can only be applied to main beams with planar and regular surfaces. When facing three-dimensional curved surfaces such as arch bridges, especially complex spatial curved surfaces such as hyperbolic arch bridges, traditional methods have the following disadvantages: (1) A coordinate system cannot be directly established on the curved surface, and the size of the main arch ring cannot be described; (2) Defects on the main arch ring are mostly three-dimensional, that is, they extend in the transverse, longitudinal, and vertical directions. Traditional methods cannot describe the specific location and size of defects; (3) It is impossible to convert the three-dimensional spatial position into a two-dimensional planar position and unfold it into a two-dimensional distribution map, etc. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a method for drawing the distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge. On the one hand, it establishes an independent local coordinate system based on a horizontal projection plane for each arch rib and arch wave of the main arch ring of the hyperbolic arch bridge, which is convenient for recording the location of defects. On the other hand, it unfolds the three-dimensional curved surface into a two-dimensional curved surface along the longitudinal and transverse directions of the bridge, and establishes an overall coordinate system that reflects the actual size of the main arch ring. Through coordinate transformation, the coordinates of local defects are reflected in the actual position of the main arch ring of the hyperbolic arch bridge, thus realizing the accurate drawing of defects on the complex three-dimensional curved surface of the main arch ring of the hyperbolic arch bridge.

[0005] The method for drawing the distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge includes the arch rib and arch wave numbering, the local coordinate system of the arch rib, the local coordinate system of the arch wave, the standard for recording the location of defects, the overall coordinate system, the standard for describing the location of defects in the arch rib, the standard for describing the location of defects in the arch wave, and the standard for drawing defect patterns.

[0006] The arch ribs and arch waves are numbered, and each arch rib and arch wave is separated and its number, as well as its longitudinal dimension and transverse dimension on the horizontal projection plane, are recorded.

[0007] The local coordinate system of the arch rib and the local coordinate system of the arch wave are established with the horizontal projection plane of the bottom surface of the main arch ring as the location recording plane of the components and defects. Independent local coordinate systems of each arch rib and arch wave on the bottom surface of the main arch ring are established on this horizontal projection plane.

[0008] The disease location recording standard is used to describe the location of the disease in the local coordinate system of the arch rib and the local coordinate system of the arch wave, and to preliminarily determine the spatial location of the disease.

[0009] The overall coordinate system is established by stretching each arch rib and arch wave on the bottom surface of the main arch ring, which is actually a three-dimensional curved surface, into independent two-dimensional planes along the longitudinal and transverse directions of the bridge. These independent two-dimensional planes are then spliced ​​together to form an overall two-dimensional plane. An overall coordinate system for the bottom surface of the main arch ring is then established on this overall two-dimensional plane. Based on this, the actual spatial location of the defects is determined.

[0010] The arch rib defect location description standard is used to convert the defect coordinates recorded in the local coordinate system of the arch rib through the defect location recording standard into coordinates in the global coordinate system.

[0011] The arch wave defect location description standard is used to convert the defect coordinates recorded in the local coordinate system of the arch wave by the defect location recording standard into coordinates in the global coordinate system.

[0012] The disease pattern drawing standard is used to draw diseases on the overall coordinate system according to the transformed coordinates.

[0013] Establish independent local coordinate systems for each arch rib and arch wave on the bottom surface of the main arch ring. The longitudinal direction of the bridge is taken as the X direction, and the transverse direction of the bridge is taken as the Y direction. The left and right directions are determined based on the direction of increasing X. The right end point of the small station side of each arch rib and arch wave is taken as the origin. The longitudinal dimension Lxi of the horizontal projection plane in the arch rib and arch wave number is the boundary of the X direction, and the transverse dimension Lyi of the horizontal projection plane is the boundary of the Y direction.

[0014] Establish a standard for recording the location of the defects. Define the two endpoints and intermediate points of a linear defect, and the turning points along the perimeter of a surface defect as nodes. Project each node onto a horizontal plane. Within the local coordinate system of the arch rib and the local coordinate system of the arch wave, define the distance from the projection point of each node to the side boundary of the small station number on the horizontal projection plane as the abscissa x, and the distance from the projection point of each node to the right boundary of the horizontal projection plane as the ordinate y, forming the coordinates (x, y) of the node. For linear defects, define the node with the smallest abscissa x as the starting point X1, and assign serial numbers to the nodes sequentially along the direction of the linear defect towards the large station number or left, resulting in Xi. For surface defects, define the node with the smallest abscissa x as the starting point X1, and assign serial numbers to the nodes sequentially along the perimeter in a clockwise direction, resulting in Xi. If there are multiple nodes with the smallest abscissa, define the node with the smallest ordinate as the starting point X1. The coordinates of each node are (x, y).i ,y i In special cases, when the surface defect is a rectangle parallel to the bridge direction, only the coordinates of any two pairs of vertex nodes need to be recorded.

[0015] Record the component number, dimensions, node coordinates, and node sequence number according to the method described in the arch rib and arch wave numbering, the local coordinate system of the arch rib, the local coordinate system of the arch wave, and the standard for recording the location of defects.

[0016] Establish the overall coordinate system for the bottom surface of the main arch ring. The bottom surface of the main arch ring, which is actually a three-dimensional curved surface, is stretched into a two-dimensional plane along the longitudinal and transverse directions of the bridge, with the longitudinal direction as the X direction and the transverse direction as the Y direction. The left and right sides are determined based on the direction of increasing X, with the right endpoint of the side with the small station number as the origin. Calculate the arc length integral of the longitudinal arch axis equation for each arch rib and arch wave between 0 and Lxi, as Lxi`, representing the boundary of each component in the X direction. Calculate the arc length integral of the transverse arch axis equation for each arch wave between 0 and Lyi, as Lyi``. Add each Lyi`` to the transverse dimension Lyi of the horizontal projection plane of each arch rib, resulting in Ly`, representing the boundary in the Y direction.

[0017] Establish a standard for describing the location of arch rib defects. The defects are extended into two-dimensional defects along with the establishment of the overall coordinate system. The coordinates (x, y, y) of a certain node are recorded in the local coordinate system of the arch rib. i ,y i Find the equation of the arch axis from 0 to x. i The integral of the arc length between them is x i `, plus the transverse dimensions Lyi`` of all arch waves on the right side of the component where the node is located and the transverse dimensions Lyi of all horizontal projection planes of the arch ribs, is yi`, where the coordinates (x, y) of the node are recorded in the local coordinate system of the arch rib. i ,y i That is, converting to coordinates (x, y) in the global coordinate system. i `,y i Transform the coordinates of all nodes on all arch ribs in the global coordinate system.

[0018] Establish the standard for describing the location of the arch wave defects. The defects are extended into two-dimensional defects along with the establishment of the overall coordinate system. The coordinates (x, y, y) of a certain node are recorded in the local coordinate system of the arch wave. i ,y i Find the equation of the arch wave along the arch axis in the direction of 0 to x. i The integral of the arc length between them is x i Find the equation of the transverse arch axis of the arch bridge in the range from 0 to y. iThe arc length integral between them is yi``, and yi`` plus the transverse dimensions Lyi` of all the arch waves on the right side of the member where the node is located and the transverse dimensions Lyi of all the horizontal projection planes of the arch ribs is yi`. The coordinates (x, y) of the node recorded in the local coordinate system of the arch waves are yi`. i ,y i That is, converting to coordinates (x, y) in the global coordinate system. i `,y i Transform the coordinates of all nodes on all arches in the global coordinate system.

[0019] Establish a standard for drawing the aforementioned disease patterns. Use the overall two-dimensional plane formed by the overall coordinate system as the base map for drawing the disease distribution map, where Lxi` represents the length of each component along the bridge direction, and Ly` represents the width along the bridge direction. Preferably, the base map is white with black text and black lines. Different types of diseases are distinguished by different symbols (including color and style).

[0020] The standards for recording the location of defects, describing the location of defects in the arch ribs, and describing the location of defects in the arch waves can record and draw irregular line and surface defects, and can be used to calculate engineering quantities (length, width, and area).

[0021] The method for drawing the distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge provided by this invention has the following advantages: (1) By projecting the three-dimensional curved surface onto the horizontal plane, a horizontal two-dimensional projection surface is obtained. Local coordinates are established on this two-dimensional plane and the location of the disease is recorded on this basis, providing a convenient and quick way to record the disease.

[0022] (2) By unfolding the three-dimensional surface along the longitudinal and transverse directions of the bridge in the horizontal plane to establish an overall coordinate system, the true dimensions of the three-dimensional surface were obtained. By using the arc length integration method of the arch axis along the longitudinal and transverse directions, the coordinates in the local coordinate system were transformed into the coordinates in the overall coordinate system, and the precise location and dimensions of the defect in space were obtained.

[0023] (3) By recording the position and coordinate transformation of each key node, the irregular disease on the regular three-dimensional surface can be quickly recorded and accurately described. Attached Figure Description

[0024] Figure 1 : Schematic diagram of local coordinate system defects in arch ribs converted to global coordinate system defects.

[0025] Figure 2 : Schematic diagram of the transformation of local coordinate system defects of the arch wave into global coordinate system defects. Detailed Implementation

[0026] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer, the invention will be further described in detail below. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Example

[0027] This example provides a method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge, which includes 9 steps: S1: Disassemble each arch rib and arch wave, and record their respective numbers and the horizontal projection plane dimensions along the bridge direction Lxi and the horizontal projection plane dimensions along the bridge direction Lyi.

[0028] S2: Establish independent local coordinate systems for each arch rib and arch wave on the bottom surface of the main arch ring. Project the main arch ring onto the horizontal plane to obtain a two-dimensional horizontal projection plane, where the longitudinal direction of the bridge is the X direction and the transverse direction of the bridge is the Y direction. The left and right sides are determined based on the direction of increasing X. The right endpoint of the small station side of each arch rib and arch wave is the origin. The longitudinal dimension Lxi of the horizontal projection plane is the boundary of the X direction, and the transverse dimension Lyi of the horizontal projection plane is the boundary of the Y direction.

[0029] S3: Establish standards for recording disease location. Define the two endpoints and intermediate points of a linear disease, and the turning points along the perimeter of a surface disease as nodes. Project each node onto a horizontal plane. Within the local coordinate system of the arch rib and the local coordinate system of the arch wave, define the distance from the projection point of each node to the side boundary of the small station number on the horizontal projection plane as the abscissa (x), and the distance from the projection point of each node to the right boundary of the horizontal projection plane as the ordinate (y), forming the coordinates (x, y) of that node. For linear diseases, define the node with the smallest abscissa (x) as the starting point X1, and assign serial numbers to nodes sequentially along the linear disease towards the large station number side or left, resulting in Xi. For surface diseases, define the node with the smallest abscissa as the starting point X1, and assign serial numbers to nodes sequentially along the perimeter in a clockwise direction, resulting in Xi. If there are multiple nodes with the smallest abscissa, define the node with the smallest ordinate as the starting point X1. The coordinates of each node are (x, y). i ,y i In special cases, when the surface defect is a rectangle parallel to the bridge direction, only the coordinates of any two pairs of vertex nodes need to be recorded.

[0030] S4: Based on the above arch rib and arch wave numbering, arch rib local coordinate system, arch wave local coordinate system and the standard description method for recording the location of defects, record the component number, dimensions, coordinates and serial numbers of each node.

[0031] S5: Establish the overall coordinate system of the main arch ring bottom surface. Stretch each arch rib and arch wave of the main arch ring bottom surface (actually a three-dimensional curved surface) along the longitudinal and transverse directions into a two-dimensional plane. These independent two-dimensional planes are then spliced ​​together to form an overall two-dimensional plane. Establish the overall coordinate system of the main arch ring bottom surface on this overall two-dimensional plane. The longitudinal direction is taken as the X direction, and the transverse direction as the Y direction. Left and right are determined based on the direction of increasing X, with the right endpoint of the side with the small station number as the origin. Calculate the arc length integral of the longitudinal arch axis equation of each arch rib and arch wave between 0 and Lxi, which is Lxi`, representing the boundary of each component in the X direction. Calculate the arc length integral of the transverse arch axis equation of each arch wave between 0 and Lyi, which is Lyi``. Add each Lyi`` to the transverse dimension Lyi of the horizontal projection plane of each arch rib, which is Ly`, representing the boundary in the Y direction. The specific steps for calculating the arc length integral are as follows: S5-1: Determine the explicit equation of the arch axis.

[0032] S5-2: Establish the differential expression for arc length.

[0033] S5-3: Establish the integral expression for arc length.

[0034] S5-4: Find the integral.

[0035] S6: Establish a standard for describing the location of arch rib defects. Defects are extended into two-dimensional defects along with the establishment of the overall coordinate system. Following the method in S5, the coordinates (x, y, y) of a certain node are recorded in the local coordinate system of the arch rib. i ,y i Find the equation of the arch axis from 0 to x. i The integral of the arc length between them is x i `, plus the transverse dimensions Lyi`` of all arch waves on the right side of the component where the node is located and the transverse dimensions Lyi of all horizontal projection planes of the arch ribs, is yi`, where the coordinates (x, y) of this node are recorded in the local coordinate system of the arch rib. i ,y i That is, converting to coordinates in the global coordinate system (x) i `,y i `).

[0036] S7: Establish a standard for describing the location of arch wave defects. Defects are extended into two-dimensional defects along with the establishment of the overall coordinate system. This refers to the coordinates (x, y, y) recorded for a specific node in the local coordinate system of the arch wave. i ,y i Find the equation of the arch wave along the arch axis in the direction of 0 to x. i The integral of the arc length between them is x i Find the equation of the transverse arch axis of the arch bridge in the range from 0 to y. i The arc length integral between the points is yi``. Adding yi`` to the transverse dimensions Lyi`` of all the arch waves to the right of the member where the node is located, and the transverse dimensions Lyi of all the horizontal projection planes of the arch ribs, gives yi`. The coordinates (x, y) of this node recorded in the local coordinate system of the arch wave are...i ,y i That is, converting to coordinates in the global coordinate system (x) i `,y i `).

[0037] S8: Convert the coordinates of all nodes in the local coordinate system of the arch rib and arch wave to the coordinates in the global coordinate system according to S6 and S7.

[0038] S9: Establish standards for drawing disease patterns and draw disease distribution maps. The steps are as follows: S9-1: Draw the base map layer. Use the overall 2D plane from S5 as the base map layer, with Lxi` as the length (horizontal) and Ly` as the width (horizontal). The image has a white background, and the base map border is drawn with black lines.

[0039] S9-2: Draw the nodes. For each node, draw its coordinates in the global coordinate system obtained through S6 and S7 (x...). i `,y i `) is drawn on the disease layer.

[0040] S9-3: Draw the defects. For line defects, connect the nodes sequentially according to the recorded node numbers to obtain the final location and shape of the line defect. For area defects, connect the nodes sequentially according to the recorded node numbers, and finally connect the end point to the start point to obtain the final location and shape of the area defect.

[0041] S9-4: Define disease styles. Set different legends for different diseases according to their types, including different colors, styles, etc.

[0042] S9-5: Fill in defects. Fill each defect according to the defect style defined in S9-4. Line defects only need color and do not need to be filled.

Claims

1. A method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge, characterized in that: Including the arch rib and arch wave number (1), the local coordinate system of the arch rib (2), the local coordinate system of the arch wave (3), the standard for recording the location of the disease (4), the overall coordinate system (5), the standard for describing the location of the arch rib disease (6), the standard for describing the location of the arch wave disease (7), and the standard for drawing the disease pattern (8). The arch ribs and arch waves are numbered (1), each arch rib and arch wave is split, and their respective numbers and the horizontal projection plane dimensions along the bridge direction and the horizontal projection plane dimensions along the bridge direction are recorded. The local coordinate system (2) for the arch rib and the local coordinate system (3) for the arch wave are established on the horizontal projection plane of the bottom surface of the main arch ring as the location recording plane of the components and defects. Independent local coordinate systems for each arch rib and arch wave on the bottom surface of the main arch ring are established on this horizontal projection plane. The disease location recording standard (4) is used to describe the location of the disease in the local coordinate system (2) of the arch rib and the local coordinate system (3) of the arch wave, and to preliminarily determine the spatial location of the disease; The overall coordinate system (5) stretches each arch rib and arch wave of the main arch ring bottom surface, which is actually a three-dimensional spatial curved surface, into an independent two-dimensional plane along the longitudinal and transverse directions of the bridge. The independent two-dimensional planes are spliced ​​together to form an overall two-dimensional plane, and an overall coordinate system of the main arch ring bottom surface is established on the overall two-dimensional plane. Based on this, the actual spatial location of the defect is determined; The arch rib defect location description standard (6) converts the defect coordinates recorded in the local coordinate system (2) of the arch rib through the defect location recording standard (4) into coordinates in the global coordinate system (5); The description standard for the location of the arch wave defect (7) converts the defect coordinates recorded in the local coordinate system (3) of the arch wave by the defect location recording standard (4) into coordinates in the global coordinate system (5); The disease pattern drawing standard (8) is used to draw diseases on the overall coordinate system (5) according to the transformed coordinates.

2. The method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge according to claim 1, characterized in that: Establish independent local coordinate systems (2) and (3) for each arch rib and arch wave on the bottom surface of the main arch ring. The X direction is the longitudinal direction of the bridge and the Y direction is the transverse direction of the bridge. The left and right directions are determined based on the direction of increasing X. The right end point of the small pile number side of each arch rib and arch wave is the origin. The longitudinal dimension Lxi of the horizontal projection plane in the arch rib and arch wave number (1) is the boundary of the X direction, and the transverse dimension Lyi of the horizontal projection plane is the boundary of the Y direction.

3. The method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge according to claim 1, characterized in that: Establish the standard for recording the location of the defects (4); define the two endpoints and the middle points of the line defects, and the turning points along the perimeter of the surface defects as nodes. Project each node onto the horizontal plane. Within the local coordinate system (2) of the arch rib and the local coordinate system (3) of the arch wave, define the distance of each node's projection point from the small station side boundary of the horizontal projection plane as the horizontal coordinate x, and define the distance of each node's projection point from the right side boundary of the horizontal projection plane as the vertical coordinate y, thus forming the coordinates (x, y) of the node. For line defects, define the node with the smallest horizontal coordinate x as the starting point X1, and assign serial numbers to the nodes along the line defects toward the large station side or left side, which are then Xi; for surface defects, define the node with the smallest horizontal coordinate x as the starting point X1, and assign serial numbers to the nodes along the perimeter clockwise, which are then Xi. If there are multiple nodes with the smallest horizontal coordinate, define the node with the smallest vertical coordinate as the starting point X1, and assign the coordinates of each node as (x, y). i ,y i (Special case: When the surface defect is a rectangle parallel to the bridge direction, only the coordinates of any two pairs of vertex nodes need to be recorded.) 4. The method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge according to claim 1, characterized in that: Establish the overall coordinate system of the bottom surface of the main arch ring (5); stretch the bottom surface of the main arch ring, which is actually a three-dimensional spatial curved surface, into a two-dimensional plane along the longitudinal and transverse directions of the bridge, with the longitudinal direction of the bridge as the X direction and the transverse direction of the bridge as the Y direction. Determine the left and right sides based on the direction of increasing X, and take the right end point of the small station side as the origin; calculate the arc length integral of the longitudinal arch axis equation of each arch rib and arch wave between 0 and Lxi as Lxi`, which is the boundary of each component in the X direction; calculate the arc length integral of the transverse arch axis equation of each arch wave between 0 and Lyi as Lyi``, and add the transverse dimension Lyi of the horizontal projection surface of each arch rib to each Lyi`` to get Ly`, which is the boundary in the Y direction.

5. The method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge according to claim 1, characterized in that: Establish a standard for describing the location of arch rib defects (6); the defects are extended into two-dimensional defects in tandem with the establishment of the overall coordinate system (5), and the coordinates (x, y, y) of a certain node are recorded in the local coordinate system (2) of the arch rib. i ,y i Find the equation of the arch axis from 0 to x. i The integral of the arc length between them is x i `, plus the transverse dimensions Lyi`` of all the arch waves on the right side of the component where the node is located and the transverse dimensions Lyi of all the horizontal projection planes of the arch ribs, is yi`, and the coordinates (x) of the node recorded in the local coordinate system (2) of the arch rib are yi`. i ,y i That is, converting to coordinates (x) in the global coordinate system (5). i `,y i `), transform the coordinates of all nodes on all arch ribs in the global coordinate system (5).

6. The method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge according to claim 1, characterized in that: Establish the arch wave defect location description standard (7); the defect extends into a two-dimensional defect along with the establishment of the overall coordinate system (5), and the coordinates (x, y, y) of a certain node are recorded in the local coordinate system (3) of the arch wave. i ,y i Find the equation of the arch wave along the arch axis in the direction of 0 to x. i The integral of the arc length between them is x i Find the equation of the transverse arch axis of the arch bridge in the range from 0 to y. i The integral of the arc length between them is yi``, and yi`` plus the transverse dimensions Lyi`` of all the arch waves on the right side of the component where the node is located and the transverse dimensions Lyi of all the horizontal projection planes of the arch ribs is yi`. The coordinates (x) of the node recorded in the local coordinate system (3) of the arch waves are yi`. i ,y i That is, converting to coordinates (x) in the global coordinate system (5). i `,y i `), transform the coordinates of all nodes on all arches in the global coordinate system (5).

7. The method for drawing a distribution map of defects on the bottom surface of the main arch ring of a hyperbolic arch bridge according to claim 1, characterized in that: Establish the standard for drawing the disease pattern (8); use the overall two-dimensional plane formed by the overall coordinate system (5) as the base map for drawing the disease distribution map, where Lxi` is the length of each component in the longitudinal direction of the bridge, and Ly` is the width in the transverse direction of the bridge.

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