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

Abstract

The invention 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 traffic transportation industry, and the method comprises the following steps: solving an equation of the line position in a plane graph; specifying the actual mileage of the starting point of the line position in the graph; solving the coordinates of the line position in the arbitrary mileage corresponding graph; finding a coordinate point of the central mileage of the abutment of the bridge on the graph; determining the position of the beam according to the offset distance, the beam width, the beam length, the line spacing and the beam seam increment; checking the deflection angle on the graph and checking the deflection angle with the calculated deflection angle; and checking whether the minimum beam seam on the graph meets the requirement or not. The invention provides a lofting method of the simply supported beam on the curve, a curve arrangement calculation result is displayed on a planar graph, so that a designer can intuitively feel an error between a calculation value and a field actual measurement value, and the problem that a system error of a program cannot be found due to only checking input data during curve arrangement calculation re-checking is avoided; and irreparable loss in the construction process can be caused.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering in the transportation industry, and in particular relates to a method for checking the curve arrangement of a railway simply supported beam based on a plane line position. Background Art

[0002] Railway bridges are mainly composed of simply supported beams, which are mostly prefabricated beams. They are uniformly prefabricated as straight beams in the beam yard. In actual projects, the curves of railway lines are often set on bridges, so it is necessary to arrange the simply supported beams in a straight line instead of a curve. This is what we often call curve arrangement. The curve arrangement calculation of the bridge is completed during the design. During construction, the foundation is constructed first, then the bridge piers, and finally the simply supported beams are erected. Therefore, if the curve arrangement calculation is incorrect during the design, it can only be discovered when the simply supported beams are erected during the final construction. At this time, the lower structure of the bridge has been completed, the pier position cannot be changed, the simply supported beam cannot be erected, and the line position cannot be guaranteed. The consequences are disastrous and will cause immeasurable losses to the entire project. Therefore, curve arrangement is an extremely important link in bridge design.

[0003] The process of curve layout calculation is complicated and is related to factors such as beam length, beam width, line spacing, curve position, etc. Although the calculation program for curve layout is already very mature, it is difficult to find internal problems only by reviewing the input data of the program because of the heavy responsibility after making mistakes. There must be a manual verification step. Moreover, when encountering special circumstances, the calculation program cannot fully consider all influencing factors, such as: the layout of long and large bridges will be affected by cumulative errors, the layout calculation of the gradual process section beam when multiple lines become double lines, and the consideration of the influence of limits when arranging existing lines. In order to solve the difficulties of manually reviewing the curve layout, the method of directly lofting the curve layout calculation results on the drawing according to the scale can allow designers to intuitively feel whether the calculated values ​​meet the on-site requirements. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a railway simply supported beam curve arrangement verification method based on plane line position.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for checking the curve arrangement of a railway simply supported beam based on plane line position comprises the following steps:

[0007] A. Solve the equations for the coordinate points on the line in the plane figure;

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

[0009] C. Solve the corresponding coordinates of any mileage on the line position in the plane diagram;

[0010] D. Find the coordinate point of the bridge pier center mileage on the plane map;

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

[0012] F. Check the deflection angle on the plan and compare it with the calculated deflection angle;

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

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

[0015] The plane line of the railway is composed of three basic line types: straight line segment, transition curve segment and arc segment. In the plane diagram, the straight line segment is the starting point C1 (x s ,y s ) and the end point C2(x e ,y e ) is a straight line with a length of L1. If point S1 is on the straight line and the distance from the starting point C1 of the straight line is d1, then the equation of point S1 is:

[0016]

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

[0018]

[0019] Calculate along the vertices of the polyline in turn according to formula (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 consisting of the center O(x0, y0), the starting angle A1 and the end angle A2, with a radius of R and an arc length of L3. If point S3 is on the arc and the arc length from the starting point of the arc is d3, then the equation of point S3 is:

[0022]

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

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

[0025] Then, search along the line starting point and record the length L of the line connecting the starting point i , 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 arc segment; if D>L i , let D = DL i , go to the end of the line, and continue to compare D and Li in the next connected line until D ≤ L i Stop and record the line type at this time;

[0026] Finally, solve the coordinates of the point at a distance D from the starting point of the recording line to obtain the corresponding coordinates of mileage K1 in the figure.

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

[0028] (a) Obtain the mileage K of Pier No. i from the curve layout calculation result table i , offset E i , Line spacing X i 、Long mileage side beam gap increment F i , the mileage K of the i+1th pier i+1 , offset E i+1 , Line spacing X i+1 , Small mileage side beam gap increment F 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 of any point on the line. If the point is on the straight line segment, the starting point C1(x s ,y s ) and the end point C2(x e ,y e ), where left deviation means facing the long mileage and the line turns left, and right deviation means facing the long mileage and the line turns right;

[0030]

[0031] If the point is on a transition curve segment, determine the point 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 After the coordinates are obtained, calculate according to formula (5);

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

[0033]

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

[0035]

[0036] Pt3 (X3, Y3) and Pt4 (X4, Y4) are connected to form line segment AB, and the distance of line segment AB is obtained. The inclination angle θ of line segment AB is calculated as follows:

[0037]

[0038] After subtracting the beam seam from line segment AB, we get 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: double-track railway is the left line, single-track railway is the center line, the single-track line spacing is 0, and the distance B from the line line to the edge of the beam is w According to formula (10), and from Pt5 (X5, Y5) and Pt6 (X6, Y6), the coordinates of the four vertices of the beam 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] Further, the specific process of step F is as follows:

[0044] First, for the i+1th beam between the i-th pier and the i+1th pier, measure its front deflection angle and rear deflection angle on the diagram;

[0045] Then, draw a straight line CD along the tangent angle QJ1 at point Pt3 (X3, Y3), draw a straight line EF along the tangent angle QJ2 at point Pt4 (X4, Y4), 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 foresight deflection angle of the i+1th beam, and the angle between the line segment AB and the straight line EF is the backsight deflection angle of the i+1th beam;

[0046] Finally, compare the front and rear deflection angles measured on the drawing with the calculated values ​​in the curve layout calculation result table. If the error is no more than 2″, it meets the requirements. Otherwise, the calculation result is incorrect.

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

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

[0049] The two selected endpoints are divided into two cases:

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

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

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

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] Aiming at the problem of checking the curved layout of railway bridges, the present invention extracts information such as pier mileage, offset, beam gap, beam width, etc. from the calculated results of the curved layout, and then lays out the simply supported beams in the plan view. It is intuitively felt whether the positions of multiple beams overlap, and the deflection angle is measured and compared with the calculated value, and the minimum beam gap is measured to see whether the requirements are met, so as to check whether the calculated results of the curved layout are correct, thereby realizing the process of reverse verification of the curved layout, forming a double insurance with the forward calculation.

[0055] The present invention solves the problem of single means and easy errors in the forward verification of the curve layout of railway bridges, and the inability to timely discover and correct the on-site beam intrusion limit situation. By laying out the beams on the plan view, the designers can intuitively feel the error between the calculated value and the on-site measured value. The correctness of the curve layout calculation is guaranteed by reverse verification, avoiding irreparable losses in the construction process.

[0056] The present invention is also applicable to the layout review of curved beams in highways and urban rail transit. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0058] Figure 1 is a flow chart of the method of the present invention;

[0059] Figure 2 It is a schematic diagram of the plane line position in the present invention;

[0060] Figure 3 Schematic diagram of the normal angle and tangent angle of the Pt1 coordinate point of the present invention;

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

[0062] Figure 5 It is a schematic diagram of the front view deflection angle and the rear view deflection angle of the present invention;

[0063] Figure 6 Schematic diagram of the coordinates of the four vertices of the beam of the present invention;

[0064] Figure 7 It is a plane display diagram of the beam portion of an embodiment of the present invention;

[0065] Figure 8 This is a plan view of the beam portion after correction according to an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to be able to fully convey the scope of the present invention to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0067] The present invention discloses a method for checking the curve arrangement of railway simply supported beams based on plane line position, such as Figure 1 As shown, the following steps are included:

[0068] A. Solve the equation of the line position in the plane diagram. The specific process is as follows:

[0069] First of all, the plane line of the railway is composed of three basic line types: straight line segment, gentle curve segment and arc segment. Figure 2 As shown, in the plane diagram, the straight line segment is from the starting point C1(x s ,y s ) and the end point C2(x e ,y e ) is a straight line with a length of L1. The transition curve segment is composed of vertices P1(x1,y1), P2(x2,y2),…, P n (x n ,y n ) is a polyline composed of straight lines connected by , with a total length of L2; an arc segment is an arc composed of the center O(x0, y0) and the starting angle A1 and the end angle A2, with a radius of R and an arc length of L3;

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

[0071] Finally, write the equation for point S1 as:

[0072]

[0073] To find the equation of point S2, first determine between which two vertices of the transition curve segment polyline point S2 falls. If S2 falls on vertex P m and P m+1 The following formula needs to be satisfied:

[0074]

[0075] Calculate along the vertices of the polyline in turn according to formula (2) to find the vertex m that meets the requirements, and then the equation of point S2 can be written as:

[0076]

[0077] Write the equation for point S3 as:

[0078]

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

[0080] C. Solve the coordinates corresponding to any mileage on the line position in the plane diagram. The specific process is as follows:

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

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

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

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

[0085] (a) From the curve layout calculation result table, obtain the mileage, offset, beam width, beam length, line spacing, and beam gap increment information of each pier, for example: the mileage K of pier No. i i , offset E i , Line spacing X i 、Long mileage side beam gap increment F i , the mileage K of the i+1th pier i+1 , offset E i+1 , Line spacing X i+1 、Small mileage side beam gap increment F 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 of any point on the line. If the point is on the line, the starting point C1(x s ,y s ) and the end point C2(x e ,y e ), which can be calculated according to formula (5), where left deviation means facing the long mileage and the line turns left, and right deviation means facing the long mileage and the line turns right.

[0087]

[0088] If the point is on a polyline, determine if the point is 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 After obtaining the coordinates, calculate according to formula (5).

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

[0090]

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

[0092]

[0093] Pt3(X3, Y3) and Pt4(X4, Y4) are connected to form a line segment AB, and the distance between the two points AB is obtained. The inclination angle θ of the line segment AB is calculated as follows:

[0094]

[0095] After subtracting the beam seam from line segment AB, we get 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 are generally wired on the left line, and single-track railways are wired on the center line. If the single-track line spacing is 0, then the distance B between the wired line and the edge of the beam is w It can be calculated according to formula (10), and the four vertex coordinates of the beam Pt7 (X7, Y7), Pt8 (X8, Y8), Pt9 (X9, Y9), Pt 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. Find the coordinate point of the center mileage of the bridge pier on the map.

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

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

[0103] First, for the i-th pier and the i+1-th pier, the i+1-th beam between them can measure its forward deflection angle and rearward deflection angle on the diagram.

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

[0105] Finally, compare the front and rear deflection angles measured on the drawing with the calculated values ​​in the curve layout calculation result table. If the error is no more than 2″, it meets the requirements. Otherwise, the calculation result is incorrect.

[0106] G. Check whether the minimum beam gap in the diagram meets the requirements. The specific process is as follows:

[0107] To find the minimum beam gap on the i+1th pier, we need to find the distance between the two nearest endpoints of adjacent beams. The two selected endpoints need to be divided into two cases:

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

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

[0110] Measure the distance between the two points on the diagram. If it is greater than or equal to the minimum beam gap distance of 10 cm, the curve arrangement meets the requirements. Otherwise, it does not meet the requirements. If it does not meet the requirements, it is necessary to increase the initial beam gap and recalculate.

[0111] The present invention will be further described below in conjunction with specific embodiments.

[0112] A 32m simply supported double-track bridge with a beam width of 9.96m and a line spacing of 5m. A curve is set on the bridge. The curve elements are shown in Table 1. The curve is arranged according to the bisection midpoint method. The calculation results are shown in Table 2.

[0113] Table 1 Curve elements

[0114] Intersection Straight point mileage Straight point mileage Circular curve radius (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 layout

[0116]

[0117] According to the method of the present invention, the beam is laid out in the plane view, and the result is shown in FIG. Figure 7 First, compare the calculation results of the deflection angles of piers 4, 5, and 6. See Table 3. It can be seen that the calculation results are basically consistent with the layout measurement results. Then check the minimum beam gap value. Figure 7 It can be seen that the minimum beam gaps on piers 4 and 5 are 9.3 cm and 9 cm respectively, which are less than the specified requirement of 10 cm. Therefore, the calculation results need to be adjusted. Here, the method of increasing the initial beam gap is adopted, that is, the third and fourth columns in Table 2 are modified, and the initial beam gaps of piers 4 and 5 are changed from 5 to 5.5, and then the calculation is performed. The corrected calculation results are shown in Table 4. The calculation results in Table 4 are then set out in the plane according to the method of the present invention, and the results are shown in Table 4. Figure 8 At this time, the minimum beam gap values ​​on Pier 4 and Pier 5 are no less than 10cm, meeting the requirements of curve layout.

[0118] Table 3 Verification of deflection calculation results

[0119]

[0120] Table 4 Calculation results of corrected curve layout

[0121]

[0122] Through examples, it can be seen that the forward calculation method used in the curved layout of railway bridges is relatively simple, and problems are not easy to find. The present invention lays out the simply supported beams in the plan view, and uses the method of graphic reverse verification to allow designers to intuitively feel the error between the calculated value and the actual measured value on site, forming a double insurance with the forward calculation, which can effectively avoid calculation errors.

[0123] The present invention has been described in detail above through embodiments, but the contents described are only exemplary embodiments of the present invention and cannot be considered to limit the scope of implementation of the present invention. The protection scope of the present invention is defined by the claims. Anyone who utilizes the technical solution described in the present invention, or a technician in the field, inspired by the technical solution of the present invention, designs a similar technical solution within the essence and protection scope of the present invention to achieve the above technical effects, or makes equal changes and improvements to the scope of application, shall still belong to the scope of protection covered by the patent of the present invention. It should be noted that in order to make a clear statement, the description of some components and processes that have no direct and obvious connection with the scope of protection of the present invention but are known to those skilled in the art are omitted in the description of the present invention.

Claims

1. A railway simply supported beam curve layout verification method based on plane line position, characterized in that: The following steps are involved: A. Solve the equations for the coordinate points on the line in the plane figure; B. Specify the actual mileage corresponding to the starting point of the line in the plan; C. Solve the corresponding coordinates of any mileage on the line position in the plane diagram; D. Find the coordinate point of the bridge pier center mileage on the plane map; E. Determine the position of the beam based on the offset, beam width, beam length, line spacing, and beam gap increment; F. Check the deflection angle on the plan and compare it with the calculated deflection angle; G. Check whether the minimum beam gap on the plan meets the requirements.

2. The method for checking the curve arrangement of railway simply supported beams based on plane line position according to claim 1 is characterized in that: The specific process of step A is as follows: The plane line of the railway is composed of three basic line types: straight line segment, transition curve segment and arc segment. In the plane diagram, the straight line segment is the starting point C1 (x s ,y s ) and the end point C2(x e ,y e ) is a straight line with a length of L1. If point S1 is on the straight line and the distance from the starting point C1 of the straight line is d1, then the equation of point S1 is: The transition curve segment is composed of vertices P1(x1,y1), P2(x2,y2), ..., P n (x n ,y n ) are connected in sequence, with a total length of L2. If point S2 is on the polyline, the distance from the first vertex P1 along the polyline is d2. First determine the adjacent vertices of point S2 in the polyline. S2 falls on vertex P m and P m+1 When between, the following equation is satisfied: Calculate along the polyline vertices in turn according to formula (2) to find the vertex P that meets the requirements. m , then the equation of point S2 is: The arc segment is an arc consisting of the center O(x0, y0), the starting angle A1 and the end angle A2, with a radius of R and an arc length of L3. If point S3 is on the arc and the arc length from the starting point of the arc is d3, then the equation of point S3 is:

3. The method for checking the curve arrangement of railway simply supported beams based on plane line position according to claim 2 is characterized in that: The specific process of step C is as follows: First, suppose the mileage of the line starting point in the figure is K0, the drawing scale is 1:b, and the distance on the map from any mileage K1 to K0 is D = (K1-K0) / b; Then, search along the line starting point and record the length L of the line connecting the starting point i , 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 arc segment; if D>L i , let D = DL i , go to the end of the line, and continue to compare D and Li in the next connected line until D ≤ L i Stop and record the line type at this time; Finally, solve the coordinates of the point at a distance D from the starting point of the recording line to obtain the corresponding coordinates of mileage K1 in the figure.

4. The method for checking the curve arrangement of railway simply supported beams based on plane line position according to claim 3 is characterized in that: The specific process of step E is as follows: (a) Obtain the mileage K of Pier No. i from the curve layout calculation result table i , offset E i , Line spacing X i 、Long mileage side beam gap increment F i , the mileage K of the i+1th pier i+1 , offset E i+1 , Line spacing X i+1 , Small mileage side beam gap increment F i+1 , the beam width between the two piers is L K , Liang Chang L C ; (b) Find the tangent angle QJ and normal angle TJ of any point on the line. If the point is on the straight line segment, the starting point C1(x s ,y s ) and the end point C2(x e ,y e ), where left deviation means facing the long mileage and the line turns left, and right deviation means facing the long mileage and the line turns right; If the point is on a transition curve segment, determine the point 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 After the coordinates are obtained, calculate according to formula (5); If the point (x d ,y d ) On the arc segment, the coordinates of the center of the arc are O(x0,y0), and the tangent angle and normal angle of this point are calculated according to the following formula: (c) Calculate the mileage K i The corresponding coordinate point Pt1 (X1, Y1), tangent angle QJ1, normal angle TJ1 on the plane map, and then calculate the mileage K i+1 The corresponding coordinate point Pt2 (X2, Y2), tangent angle QJ2, and normal angle TJ2 on the plane; Pt1 and Pt2 are offset along their respective normals by E i / b and E i+1 / b, and get Pt3(X3,Y3) and Pt4(X4,Y4). The coordinate calculation formula is as follows: Pt3 (X3, Y3) and Pt4 (X4, Y4) are connected to form a line segment AB, and the distance of the line segment AB is obtained. The inclination angle θ of the line segment AB is calculated as follows: After subtracting the beam seam from line segment AB, we get points Pt5 (X5, Y5) and Pt6 (X6, Y6). The coordinate calculation formula is as follows: (d) Find the coordinates of the four vertices of the beam: double-track railway is the left line, single-track railway is the center line, the single-track line spacing is 0, and the distance B from the line line to the edge of the beam is w According to formula (10), and from Pt5 (X5, Y5) and Pt6 (X6, Y6), the coordinates of the four vertices of the beam Pt7 (X7, Y7), Pt8 (X8, Y8), Pt9 (X9, Y9), Pt 10 (X 10 ,Y 10 ): B w =[L k -(X i +X i+1 ) / 2] / 2 (10) 5. The method for checking the curve arrangement of railway simply supported beams based on plane line position according to claim 4 is characterized in that: The specific process of step F is as follows: First, for the i+1th beam between the i-th pier and the i+1th pier, measure its front view deflection angle and rear view deflection angle on the diagram; Then, draw a straight line CD along the tangent angle QJ1 at point Pt3 (X3, Y3), draw a straight line EF along the tangent angle QJ2 at point Pt4 (X4, Y4), 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 foresight deflection angle of the i+1th beam, and the angle between the line segment AB and the straight line EF is the backsight deflection angle of the i+1th beam; Finally, compare the front and rear deflection angles measured on the drawing with the calculated values ​​in the curve layout calculation result table. If the error is no more than 2″, it meets the requirements. Otherwise, the calculation result is incorrect.

6. The method for checking the curve arrangement of railway simply supported beams based on plane line position according to claim 5 is characterized in that: The specific process of step G is as follows: Find the minimum beam gap on pier i+1: the distance between the two nearest endpoints of adjacent beams; The two selected endpoints are divided into two cases: (a) If the line deviates to the left, select Pt8(X8,Y8) between the i-th pier and the i+1-th pier, and Pt7(X7,Y7) between the i+1-th pier and the i+2-th pier; (b) If the line deviates to the left, select Pt of Pier i and Pier i+1. 10 (X 10 ,Y 10 ), Pt9(X9,Y9) of the i+1th pier and the i+2th pier; Measure the distance between two selected points on the drawing. If it is not less than 10cm, the curve arrangement meets the requirements, otherwise it does not meet the requirements.

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