Railway simple supported beam curve arrangement checking method based on plane line position

Abstract

The application discloses a railway simply supported beam curve arrangement checking method based on a plane line position, and belongs to the technical field of bridge engineering in the transportation industry. The method comprises the following steps: solving the equation of the line position in the plane graph; specifying the actual mileage of the starting point of the line position in the graph; solving the coordinates of the line position corresponding to any mileage in the graph; finding the coordinate point of the pier center mileage of the bridge on the graph; determining the position of the beam according to the offset distance, beam width, beam length, line spacing and beam joint increment; checking the offset angle on the graph and comparing it with the calculated offset angle; checking whether the minimum beam joint on the graph meets the requirements. The application provides a lofting method of the simply supported beam on the curve. The calculation result of the curve arrangement is displayed on the plane graph, so that the designer can intuitively feel the error between the calculation value and the field measured value, and the system error of the program cannot be found by only checking the input data during the checking of the curve arrangement calculation, which can cause irreparable losses in the construction process.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology in the transportation industry, and specifically relates to a method for verifying the curve layout of a simply supported railway beam based on the plane alignment. Background Technology

[0002] Railway bridges primarily consist of simply supported beams, which are mostly precast beams. These are uniformly prefabricated as straight beams in the beam yard. However, in actual engineering projects, railway curves are frequently placed on bridges. Therefore, the simply supported beams need to be arranged using a method of substituting straight lines for curves; this is what we commonly refer to as curved arrangement. The curve arrangement calculation for bridges is completed during the design phase. Construction proceeds from bottom to top: first the foundation, then the piers, and finally the simply supported beams. Therefore, if the curve arrangement calculation is incorrect during the design phase, it will only be discovered during the final construction phase when the simply supported beams are being erected. By then, the substructure of the bridge has already been completed, the pier positions cannot be changed, the simply supported beams cannot be erected, and the alignment cannot be guaranteed. The consequences are unimaginable, causing incalculable losses to the entire project. Therefore, curve arrangement is an extremely important aspect of bridge design.

[0003] The calculation process for curve layout is complex, involving factors such as beam length, beam width, line spacing, and curve position. Although the calculation program for curve layout is mature, the responsibility for errors is significant, and it is difficult to detect inherent problems simply by reviewing the program's input data; manual verification is essential. Furthermore, in special cases, the calculation program cannot fully consider all influencing factors. For example, the layout of long bridges is affected by cumulative errors; the layout calculation of beams in the transition process from multi-track to double-track; and the impact of clearance constraints when laying out existing lines. To overcome the difficulties of manual verification of curve layout, a method of directly plotting the curve layout calculation results onto the drawing according to a scale allows designers to intuitively see whether the calculated values ​​meet the site requirements. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for verifying the curve layout of simply supported railway beams based on planar alignment.

[0005] This invention is achieved through the following technical solution:

[0006] A method for verifying the layout of simply supported beam curves in railways based on planar alignment includes the following steps:

[0007] A. Solve for the equations of the coordinate points on the line in the planar diagram;

[0008] B. Specify the actual mileage corresponding to the starting point of the line position on the plan view;

[0009] C. Determine the coordinates of any mileage on the line position in the plan view;

[0010] D. Locate the coordinates of the center mileage of the bridge piers on the plan view;

[0011] E. Determine the beam position based on the offset, beam width, beam length, line spacing, and beam joint increment;

[0012] F. Check the deflection angle on the floor plan and verify it against the calculated deflection angle;

[0013] G. Check whether the minimum beam joint on the floor plan meets the requirements.

[0014] Furthermore, the specific process of step A is as follows:

[0015] The horizontal alignment of a railway is composed of three basic alignment types: straight segments, transition curves, and circular arcs. In the horizontal alignment, the straight segment is formed by the starting point C1(x). s ,y s ) and endpoint C2(x e ,y e If a straight line of length L1 is formed by connecting points C1 and S1, and point S1 lies on this line and is d1 from the starting point C1, then the equation of point S1 is:

[0016]

[0017] The transition curve segment is formed by vertices P1(x1,y1), P2(x2,y2), ..., P n (x n ,y n A series of lines are connected in sequence, with a total length of L2. If point S2 is on this polyline, and the distance from point S2 to the first vertex P1 along the polyline is d2, first determine the vertices adjacent to point S2 in the polyline. S2 falls on vertex P. m and P m+1 The following equation must be satisfied between them:

[0018]

[0019] Calculate sequentially along the vertices of the polyline according to equation (2) to find the vertex P that meets the requirements. m Then the equation of point S2 is:

[0020]

[0021] The arc segment is an arc formed by the center O(x0,y0), the starting angle A1, and the ending angle A2, with radius R and arc length L3. If point S3 lies on the arc and its arc length from the starting point is d3, then the equation of point S3 is:

[0022]

[0023] Furthermore, the specific process of step C is as follows:

[0024] First, let the mileage of the starting point of the line position on the map be K0, the drawing scale be 1:b, and the distance on the map from any mileage K1 to K0 be D = (K1-K0) / b;

[0025] Then, search along the starting point of the line and record the line length L connecting the starting point. i Let i = 1, 2, 3, where L1 represents the length of the straight line segment, L2 represents the length of the transition curve segment, and L3 represents the length of the circular arc segment; if D > L i Let D = DL i Move to the end of the line type and continue the comparison between D and Li in the next connected line type until D≤L. i Stop and record the line type at this point;

[0026] Finally, the coordinates of the point at a distance D from the starting point of the recording line are calculated to obtain the coordinates of mileage K1 in the graph.

[0027] Furthermore, the specific process of step E is as follows:

[0028] (a) Obtain the mileage K of pier i from the curve layout calculation result table. i Offset E i Line spacing X i Incremental F of side beam joints at high mileage i The mileage K of pier i+1 i+1 Offset E i+1 Line spacing X i+1 Increment F of side beam joint at small mileage i+1 The beam width between the two piers is L. K Liang Chang L C ;

[0029] (b) Find the tangent angle QJ and normal angle TJ at any point on the line. If the point is on the line segment, calculate according to formula (5). The starting point of the line is C1(x s ,y s ) and endpoint C2(x e ,y e (The left veil indicates a left turn towards a large mileage, and the right veil indicates a right turn towards a large mileage.)

[0030]

[0031] If the point lies on the transition curve segment, determine that the point is at the vertex P of the polyline. i and P i+1 After that, replace the coordinates of points C1 and C2 with P. i and P i+1 Then calculate according to formula (5) after obtaining the coordinates;

[0032] If the point (x) d ,y d On an arc segment, the center of the arc is O(x0, y0). The tangent angle and normal angle at this point are calculated according to the following formula:

[0033]

[0034] (c) Calculate the mileage K i On the plan view, find the corresponding coordinates Pt1(X1,Y1), tangent angle QJ1, and normal angle TJ1, then calculate the mileage K. i+1 On the planar diagram, the corresponding coordinates are Pt2(X2,Y2), tangent angle QJ2, and normal angle TJ2; Pt1 and Pt2 are offset along their respective normals by E. i / b and E i+1 / b, we get Pt3(X3,Y3) and Pt4(X4,Y4), and the coordinate calculation formula is as follows:

[0035]

[0036] Connect Pt3(X3,Y3) and Pt4(X4,Y4) to form line segment AB. Obtain the distance of line segment AB. The inclination angle θ of line segment AB is calculated using the following formula:

[0037]

[0038] Subtracting the beam joint from line segment AB yields points Pt5(X5,Y5) and Pt6(X6,Y6). The coordinate calculation formula is as follows:

[0039]

[0040] (d) Find the coordinates of the four vertices of the beam: for double-track railways, the left track is used for marking; for single-track railways, the center track is used for marking. Assume the spacing between single-track lines is 0, and the distance B from the marking line to the edge of the beam is... w Calculate according to equation (10), and use Pt5(X5,Y5) and Pt6(X6,Y6) to calculate the coordinates of the four vertices of the beam according to equation (11): Pt7(X7,Y7), Pt8(X8,Y8), Pt9(X9,Y9), Pt 10 (X 10 ,Y 10 ):

[0041] B w =[L k -(X i +X i+1 ) / 2] / 2 (10)

[0042]

[0043] Furthermore, the specific process of step F is as follows:

[0044] First, for the (i+1)th beam between pier i and pier i+1, measure its forward and backward deflection angles on the diagram.

[0045] Then, draw a straight line CD at point Pt3(X3,Y3) along the tangent angle QJ1, and draw a straight line EF at point Pt4(X4,Y4) along the tangent angle QJ2. Connect Pt3(X3,Y3) and Pt4(X4,Y4) to form line segment AB. The angle between the line containing line segment AB and line CD is the front deflection angle of the (i+1)th beam, and the angle between the line containing line segment AB and line EF is the back deflection angle of the (i+1)th beam.

[0046] Finally, compare the forward and backward viewing angles measured on the drawing with the calculated values ​​in the curve layout calculation result table. If the error is no greater than 2″, it meets the requirements; otherwise, the calculation result is incorrect.

[0047] Furthermore, the specific process of step G is as follows:

[0048] Find the minimum beam joint on pier i+1: the distance between the two nearest endpoints of adjacent beams;

[0049] There are two cases when selecting the two endpoints:

[0050] (a) If the line deviates to the left, select Pt8(X8,Y8) for pier i and pier i+1, and Pt7(X7,Y7) for pier i+1 and pier i+2.

[0051] (b) If the line deviates to the left, select Pt for piers i and (i+1)th. 10 (X 10 ,Y 10 Pt9(X9,Y9) for piers i+1 and i+2;

[0052] Measure the distance between the two selected points on the map. If it is not less than 10cm, the curve arrangement meets the requirements; otherwise, it does not.

[0053] Compared with the prior art, the beneficial effects of this invention are as follows:

[0054] This invention addresses the problem of verifying the curve layout of railway bridges. It extracts information such as pier mileage, offset, beam joint, and beam width from the curve layout calculation results. Then, it lays out the simply supported beams on the plan view. By visually assessing whether the positions of multiple beams overlap, measuring the offset angle and comparing it with the calculated value, and measuring the minimum beam joint to check if it meets the requirements, the calculation results of the curve layout are verified to ensure their accuracy. This process of reverse verification of the curve layout is achieved, forming a double guarantee with the forward calculation.

[0055] This invention solves the problems of limited methods and susceptibility to errors in forward verification of railway bridge curve layout, and the inability to promptly detect and correct beam intrusion into the clearance limits. By laying out the beams on a plan view, designers can intuitively perceive the error between the calculated values ​​and the actual measured values ​​on site. Reverse verification ensures the accuracy of the curve layout calculation and avoids irreparable losses during construction.

[0056] This invention is also applicable to the verification of the arrangement of curved beams in highways and urban rail transit. Attached Figure Description

[0057] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0058] Figure 1 This is a flowchart of the method of the present invention;

[0059] Figure 2 This is a schematic diagram of the planar line position in this invention;

[0060] Figure 3 This is a schematic diagram of the normal angle and tangent angle of the Pt1 coordinate point in this invention;

[0061] Figure 4 This is a schematic diagram of the normal angle and tangent angle of the Pt2 coordinate point in this invention;

[0062] Figure 5 This is a schematic diagram of the forward and rearward viewing angles of the present invention;

[0063] Figure 6 This is a schematic diagram showing the coordinates of the four vertices of the beam in this invention;

[0064] Figure 7 This is a plan view of the beam section in an embodiment of the present invention;

[0065] Figure 8 This is a modified plan view of the beam in an embodiment of the present invention. Detailed Implementation

[0066] Exemplary embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the invention to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0067] This invention discloses a method for verifying the layout of simply supported beam curves in railways based on planar alignment, such as... Figure 1 As shown, it includes the following steps:

[0068] A. Solve the equations for the line positions in the planar diagram. The specific process is as follows:

[0069] First, the horizontal alignment of a railway is composed of three basic alignment types: straight sections, transition curve sections, and circular arc sections. For example... Figure 2 As shown in the diagram, in the plan view, the straight line segment starts from the starting point C1(x) s ,y s ) and endpoint C2(x e ,y e The straight line connecting the vertices has a length of L1, and the transition curve segment is formed by vertices P1(x1,y1), P2(x2,y2), ..., P... n (x n ,y n The total length of the polyline segment is L2, which is composed of straight lines connected together. The arc segment is an arc formed by the center O(x0,y0), the starting angle A1, and the ending angle A2. The radius is R and the arc length is L3.

[0070] Then, assume that point S1 is on a straight line and the distance from the starting point C1 of the line is d1; point S2 is on a polyline and the distance from the first vertex P1 along the polyline is d2; and point S3 is on an arc and the arc length from the starting point of the arc is d3.

[0071] Finally, the equation of point S1 is written as:

[0072]

[0073] To find the equation of point S2, first determine which two vertices of the polyline of the transition curve segment S2 lies between. If S2 lies on vertex P... m and P m+1 Between them, the following equation must be satisfied:

[0074]

[0075] Calculate the equation for point S2 sequentially along the vertices of the polyline according to equation (2), find the vertex m that meets the requirements, and then write the equation for point S2 as follows:

[0076]

[0077] Write the equation of point S3 as follows:

[0078]

[0079] B. Specify the actual mileage corresponding to the starting point of the line position on the plan view.

[0080] C. Solve for the coordinates of any mileage on the line position in the plan view. The specific process is as follows:

[0081] First, let the mileage of the starting point of the line position on the map be K0, the drawing scale be 1:b, and the distance on the map from any mileage K1 to K0 be D = (K1-K0) / b;

[0082] Then, search along the starting point of the line and record the line length L connecting the starting point. i Let i = 1, 2, 3, where L1, L2, and L3 represent the lengths of the straight line segment, the transition curve segment, and the circular arc segment, respectively. If D > L i Let D = DL i Go to the end of the line type, and repeat the above steps on the next line type you connect, until D≤L i Stop and record the line type at this point;

[0083] Finally, the coordinates of the point at a distance D from the starting point of the recording line are obtained, which are the coordinates of mileage K1 on the map, calculated according to the method in claim 2.

[0084] Step E determines the beam position based on the offset, beam width, beam length, line spacing, and beam joint increment. The specific process is as follows:

[0085] (a) Obtain the mileage, offset, beam width, beam length, line spacing, and beam joint increment information for each pier from the curve layout calculation result table. For example, the mileage K of pier i. i Offset E i Line spacing X i Incremental F of side beam joints at high mileage i The mileage K of pier i+1 i+1 Offset E i+1 Line spacing X i+1 Increment F of side beam joint at small mileage i+1 The beam width between the two piers is L. K Liang Chang L C .

[0086] (b) Find the tangent angle QJ and normal angle TJ at any point on the line, if the point lies on the line and the starting point of the line is C1(x). s ,y s ) and endpoint C2(x e ,y e The value can be calculated according to formula (5), where left deviation indicates facing a large mileage and the line turns left, and right deviation indicates facing a large mileage and the line turns right.

[0087]

[0088] If the point lies on a polyline, then the point is located at vertex P of the polyline. i and P i+1 After that, replace the coordinates of points C1 and C2 with P. i and P i+1 Then calculate according to formula (5) after obtaining the coordinates.

[0089] If the point (x) d ,y d On an arc, the center of the arc is O(x0, y0). The tangent angle and normal angle at this point are calculated as follows:

[0090]

[0091] (c) Calculate the mileage K i The coordinates of point Pt1(X1,Y1), tangent angle QJ1, and normal angle TJ1 on the graph are as follows: Figure 3 As shown, the mileage K is then calculated. i+1 The coordinates of the point Pt2(X2,Y2), the tangent angle QJ2, and the normal angle TJ2 on the graph are as follows: Figure 4 As shown. Pt1 and Pt2 are offset by E along their respective normals. i / b and E i+1 / b, we get Pt3(X3,Y3) and Pt4(X4,Y4), and the coordinate calculation formula is as follows:

[0092]

[0093] Connect Pt3(X3,Y3) and Pt4(X4,Y4) with line segment AB. The distance between the two points AB is obtained. The angle of inclination θ of line segment AB is calculated using the following formula:

[0094]

[0095] Subtracting the beam joint from line segment AB yields points Pt5(X5,Y5) and Pt6(X6,Y6). The calculation formula is as follows:

[0096]

[0097] (d) Find the coordinates of the four vertices of the beam, such as... Figure 6 As shown, double-track railways generally use the left track for rigging, while single-track railways use the center track. Assuming the single-track spacing is 0, then the distance B from the rigging line to the edge of the beam is... w The coordinates of the four vertices of the beam, Pt7(X7,Y7), Pt8(X8,Y8), Pt9(X9,Y9), and Pt6(X6,Y6), can be calculated using equation (10). 10 (X 10 ,Y 10 The coordinates are calculated according to formula (11).

[0098] B w =[L k -(X i +X i+1 ) / 2] / 2 (10)

[0099]

[0100] D. Locate the coordinates of the center mileage of the bridge piers on the map.

[0101] E. Determine the beam position based on the offset, beam width, beam length, line spacing, and beam joint increment.

[0102] F. Check the deflection angle on the drawing and compare it with the calculated deflection angle in the curve layout calculation result table. The specific process is as follows:

[0103] First, for pier i and pier i+1, the forward and backward tilt angles of the beam between them can be measured on the diagram.

[0104] Then, draw a straight line CD at point Pt3(X3,Y3) along the tangent angle QJ1, and a straight line EF at point Pt4(X4,Y4) along the tangent angle QJ2. Connect Pt3(X3,Y3) and Pt4(X4,Y4) to form line segment AB. The forward deflection angle of the (i+1)th beam is the angle between the line containing AB and line CD, and the backsight deflection angle is the angle between the line containing AB and line EF. Figure 5 As shown.

[0105] Finally, compare the front and back sight angles measured on the drawing with the calculated values ​​in the curve layout calculation result table. If the error is no greater than 2″, it meets the requirements; otherwise, the calculation result is incorrect.

[0106] G. Check whether the minimum beam joint on the drawing meets the requirements. The specific process is as follows:

[0107] Finding the minimum beam joint on pier i+1 is equivalent to finding the distance between the two nearest endpoints of adjacent beams. The selection of these two endpoints needs to be considered in two cases:

[0108] (a) If the line deviates to the left, select Pt8(X8,Y8) for pier i and pier i+1, and Pt7(X7,Y7) for pier i+1 and pier i+2.

[0109] (b) If the line deviates to the left, select Pt for piers i and (i+1)th. 10 (X 10 ,Y 10 Pt9(X9,Y9) for piers i+1 and i+2;

[0110] Measure the distance between these two points on the diagram. If it is greater than or equal to the minimum beam joint distance of 10cm, the curve layout meets the requirements. Otherwise, it does not meet the requirements. If it does not meet the requirements, an initial beam joint needs to be added and the calculation needs to be recalculated.

[0111] The present invention will be further described below with reference to specific embodiments.

[0112] A 32m simply supported double-track bridge with a beam width of 9.96m and a track spacing of 5m is constructed. Curves are installed on the bridge, and the curve elements are shown in Table 1. The curves are arranged according to the mid-span method, and the calculation results are shown in Table 2.

[0113] Table 1 Curve Elements

[0114] intersection Straight and gentle distance mileage at the straight section Radius of the circular curve (m) Length of transition curve (m) Curve direction 1 DK123+376.77 DK127+244.60 6000 270 Left

[0115] Table 2 Calculation results of curve arrangement

[0116]

[0117] The beams were laid out in the plan view according to the method of the present invention, and the results are shown below. Figure 7 First, compare the calculated deflection angles of piers 4, 5, and 6 (see Table 3). It can be seen that the calculated results are basically consistent with the layout measurement results. Next, verify the minimum beam joint value... Figure 7 As can be seen, the minimum beam joints on piers 4 and 5 are 9.3cm and 9cm respectively, which are less than the specified requirement of 10cm. Therefore, the calculation results need to be adjusted. Here, the method of increasing the initial beam joint is adopted, that is, modifying columns 3 and 4 in Table 2, changing the initial beam joint of piers 4 and 5 from 5 to 5.5, and then recalculating. The corrected calculation results are shown in Table 4. Then, the calculation results in Table 4 are laid out on the plan according to the method of this invention. The results are shown in Table 4. Figure 8 At this point, the minimum beam joint value on piers 4 and 5 is no less than 10cm, which meets the requirements for curved layout.

[0118] Table 3 Verification of Deflection Angle Calculation Results

[0119]

[0120] Table 4. Calculation results of the corrected curve arrangement

[0121]

[0122] As can be seen from the examples, the forward calculation method for railway bridge curve layout is relatively simple and problems are not easily detected. This invention lays out the simply supported beam in the plan view and uses the method of reverse verification of the graphic to allow designers to intuitively feel the error between the calculated value and the actual measured value on site. This forms a double insurance with the forward calculation and can effectively avoid calculation errors.

[0123] The present invention has been described in detail above through embodiments, but the content described is only an exemplary embodiment of the present invention and should not be considered as limiting the scope of the present invention. The scope of protection of the present invention is defined by the claims. Any technical solutions designed by those skilled in the art using the technical solutions described in the present invention, or similar technical solutions designed by those skilled in the art under the inspiration of the technical solutions of the present invention, within the substance and scope of protection of the present invention, to achieve the above-mentioned technical effects, or equivalent changes and improvements made to the scope of the application, should still fall within the patent protection scope of the present invention. It should be noted that, for clarity, descriptions of some components and processes that are not directly and obviously related to the scope of protection of the present invention but are known to those skilled in the art have been omitted in the description of the present invention.

Claims

1. A method for checking the curve arrangement of a simply supported railway beam based on the plane line position, characterized in that, The steps include: A. Solve the equation of the coordinate point on the line in the plan; B. Specify the actual mileage corresponding to the starting point of the line in the plan; C. Solve the coordinates corresponding to the mileage in the plan: First, let the mileage of the starting point of the line in the plan be K0, and the drawing scale be 1:b. The distance on the drawing from any mileage K1 to K0 is D=(K1-K0) / b; Then, search along the line type starting point, record the line type length L connected to the starting point i , i = 1, 2, 3, wherein L1 represents the length of the straight line segment, L2 represents the length of the transition curve segment, and L3 represents the length of the circular arc segment; if D > L i , let D = D - L i , go to the end point of the line type, continue to execute the comparison and determination of D and Li in the next connected line type segment until D ≤ L i Stop, record the line type at this time; Finally, solve the coordinates of the point D from the starting point of the distance record line type to get the coordinates corresponding to the mileage K1 in the drawing; D. Find the coordinates of the pier center mileage on the plan; E. Determine the position of the beam according to the offset, beam width, beam length, line spacing, and beam joint increment; F. Check the offset angle on the plan and compare it with the calculated offset angle; G. Check whether the minimum beam joint on the plan meets the requirements.

2. The method for checking the arrangement of simple-supported railway curved beams based on the plane line according to claim 1, characterized in that, The specific process of step A is as follows: The plane line position of railway is combined by three basic line types of straight line segment, easement curve segment and circular arc segment. In the plane view, the straight line segment is a straight line connected by the start point C1(x s ,y s ) and the end point C2(x e ,y e ), the length is L1. If the point S1 is on the straight line segment and the distance from the start point C1 is d1, the equation of the point S1 is: The easement curve segment is a multi-segment line connected by vertexes P1(x1, y1), P2(x2, y2), …, P n (x n ,y n ) in turn, and the total length is L2. If point S2 is on the multi-segment line, the distance from the first vertex P1 along the multi-segment line is d2. The adjacent vertexes of point S2 in the multi-segment line are determined first, and when S2 falls between vertexes P m and P m+1 , the following formula is satisfied: The vertex P satisfying the requirements is found out by sequentially calculating the vertex along the multi-segment line according to formula (2) m The equation of point S2 is: The circular arc segment is composed of a circle center O(x0, y0) and a starting angle A1 and a terminal angle A2, with a radius R and an arc length L3. If point S3 is on the circular arc and the arc length from the starting point of the circular arc is d3, then the equation of point S3 is:

3. The method of claim 2, wherein, The specific process of step E is as follows: (a) From the curve arrangement calculation result table, the mileage K of the ith pier is obtained i , the offset distance E i , the line spacing X i , the large-mileage side beam joint increment F i , the mileage K of the i+1th pier i+1 , the offset distance E i+1 , the line spacing X i+1 , the small-mileage side beam joint increment F i+1 , the beam width between the two piers is L K , the beam length L C ; (b) finding the tangent angle QJ and the normal angle TJ of the line at any point, if the point is on the straight line segment, calculating the tangent angle QJ and the normal angle TJ of the line at any point according to formula (5), the starting point C1(x s ,y s ) and the end point C2(x e ,y e ) of the straight line, wherein left deviation indicates facing the large mileage, the line turns left, and right deviation indicates facing the large mileage, the line turns right; If the point lies on the transition curve segment, determine that the point is at the vertex P of the polyline. i and P i+1 After that, replace the coordinates of points C1 and C2 with P. i and P i+1 Then calculate according to formula (5) after obtaining the coordinates; If the point (x d ,y d ) is on the circular arc segment, the center coordinates of the circular arc are O(x0, y0), and the tangent angle and the normal angle of the point are calculated according to the following formula: (c) calculate the mileage K i corresponding coordinate point Pt1(X1, Y1), tangent angle QJ1, normal angle TJ1 on the plan view, and then calculate the mileage K i+1 corresponding coordinate point Pt2(X2, Y2), tangent angle QJ2, normal angle TJ2 on the plan view, and Pt1 and Pt2 are respectively offset by E along the respective normal i / b and E i+1 / b, get Pt3(X3, Y3) and Pt4(X4, Y4), and the coordinate calculation formula is as follows: Connect Pt3(X3, Y3) and Pt4(X4, Y4) to form a line segment AB, and calculate the distance of line segment AB. The inclination angle θ of line segment AB is calculated as follows: Subtract the beam joint from line segment AB to get points Pt5(X5, Y5) and Pt6(X6, Y6). The coordinate calculation formula is as follows: (d) Calculate the 4 vertex coordinates of the beam: double-track railway is left line, single-track railway is middle line, count single-track line spacing as 0, the distance B between the line and the edge of the beam w (X5, Y5) and Pt6(X6, Y6), the 4 vertex coordinates Pt7(X7, Y7), Pt8(X8, Y8), Pt9(X9, Y9), Pt10(X10, Y10) of the beam are calculated according to formula (11) 10 (X 10 ,Y 10 ): B w = [L k - (X i + X i+1 ) / 2] / 2 (10) 4. The method of claim 3, wherein, The specific process of step F is as follows: First, for the i+1th beam between the ith pier and the i+1th pier, measure the front and rear view angles on the drawing; Then, draw a straight line CD from point Pt3(X3, Y3) along the tangent angle QJ1, and draw a straight line EF from point Pt4(X4, Y4) along the tangent angle QJ2. Connect Pt3(X3, Y3) and Pt4(X4, Y4) to form a line segment AB. The angle between the line segment AB and the straight line CD is the front view angle of the i+1th beam, and the angle between the line segment AB and the straight line EF is the rear view angle of the i+1th beam; Finally, compare the front and rear view angles measured on the drawing with the calculated values in the curve arrangement calculation result table. If the error is not greater than 2, it meets the requirements, otherwise the calculation result is incorrect.

5. The method of claim 4, wherein, The specific process of step G is as follows: Solve the minimum beam joint on the i+1th pier: the distance between the nearest two end points of adjacent beams; The selected two end points have two cases: (a) If the line is left-biased, select Pt8(X8, Y8) of the ith pier and the i+1th pier, and Pt7(X7, Y7) of the i+1th pier and the i+2th pier; (b) if the line is right biased, select the Pt of the ith and i + 1th pylons 10 (X 10 ,Y 10 ), the Pt9 of the i + 1th and i + 2th pylons Measure the distance between the two selected points on the drawing. If it is not less than 10 cm, the curve arrangement meets the requirements, otherwise it does not meet the requirements.

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