Railway bridge prestressed steel strand linear simulation calculation method

Abstract

The application discloses a railway bridge prestressed steel beam line shape simulation calculation method, comprising the following steps: inputting the lead point data of the prestressed steel beam; preprocessing the input lead point data of the prestressed steel beam; calculating the local coordinate system of the plane where each lead point is located; transforming the space coordinates of the lead point to the local coordinate system; calculating the round chamfer of the lead point; trimming the lead line tangent to the round chamfer; and calculating the output result of the line shape of the prestressed steel beam. The application defines a lead point data representation format, constructs a line shape contour input method of the prestressed steel beam, deduces a space coordinate calculation method of the arc curve in the space coordinate system through a three-dimensional space coordinate system conversion and a plane round chamfer calculation method, and thus establishes the railway bridge prestressed steel beam line shape simulation calculation method. The application can accurately represent and simulate the space line shape of the railway bridge prestressed steel beam, and solves the problem of the calculation accuracy of the line shape model of the prestressed steel beam.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology in the transportation industry, and specifically relates to a simulation calculation method for the prestressed steel strand alignment of railway bridges. Background Technology

[0002] To ensure smooth track operation and safe train operation, most high-speed railway lines utilize bridge structures, with bridge structures accounting for over 70% of some lines. The main beams are constructed using prestressed concrete. Ducts are pre-installed within the concrete beams, and after the concrete is poured and cured, prestressed steel strands are inserted and tensioned to form a shared load-bearing structure. Prestressed steel strands significantly improve the load-bearing capacity and crack resistance of the main beams, and can effectively reduce beam height, increase span, and save on overall project costs.

[0003] Prestressed steel strands are crucial components in prestressed concrete structures, requiring careful consideration in modeling calculations, section design, and structural drawing. During structural calculations and section design, the arrangement and spatial location of the prestressed steel strands must be accurately input and continuously adjusted based on the design results until the design limits are met. In the structural drawing stage, since the design drawings are two-dimensional, the spatial shape of the prestressed steel strands must be described by projected lines in both the horizontal and vertical planes. Therefore, accurate calculation and processing of the prestressed steel strand alignment is extremely important for railway bridge design.

[0004] In my country's railway design, the prestressed steel strand alignment generally consists of two types of alignment: straight segments and circular arc segments, which are tangent at their intersection. The prestressed steel strand is input using the traverse method, with the spatial alignment calculated based on the traverse points. A bend in the steel strand alignment in the horizontal plane is called a horizontal bend, and a bend in the vertical plane is called a vertical bend. Sometimes, both horizontal and vertical bends occur simultaneously. In this case, both the straight and circular arc segments appear as spatial straight lines and spatial circular arcs, respectively. While the projection of the straight segment onto the two planes remains a straight line, the projection of the circular arc segment onto the two planes is no longer a circular arc.

[0005] In practice, to simplify the design, the spatial arc is often directly used as the actual line shape of its projection onto the two planes. However, this approach leads to discrepancies between the actual structure and the computational model, reducing the accuracy of railway bridge structural design.

[0006] To address the aforementioned issues, it is essential to develop a simulation calculation method for the prestressed steel strand alignment of railway bridges. This method should accurately simulate and calculate the prestressed steel strand alignment to systematically solve the problem of simulation calculation of prestressed steel strand alignment models for railway bridges. Summary of the Invention

[0007] This invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a simulation calculation method for the prestressed steel strand alignment of railway bridges.

[0008] The technical solution of this invention is: a simulation calculation method for the prestressed steel strand alignment of railway bridges, comprising the following steps:

[0009] A. Input the conductor point data for the prestressed steel strands;

[0010] B. Preprocess the input conductor point data of the prestressed steel strands;

[0011] C. Calculate the local coordinate system of the plane containing each traverse point;

[0012] D. Transform the spatial coordinates of the traverse points to the local coordinate system;

[0013] E. Calculate the chamfer at the traverse points;

[0014] F. Trim the wire so that it is tangent to the rounded chamfer;

[0015] G. Calculate the output results of the prestressed steel strand shape.

[0016] Furthermore, step A involves inputting the conductor point data for the prestressed steel strands. The specific process is as follows:

[0017] The traverse point data input for each traverse point includes the traverse point spatial coordinates, radius, offset direction, offset angle, tilt height, and radius at the offset point; the offset direction, offset angle, tilt height, and radius at the offset point constitute the offset data.

[0018] Furthermore, step B preprocesses the input prestressed steel strand conductor point data, as follows:

[0019] First, calculate the new traverse points based on the offset data for the traverse points that need to be offset in step A;

[0020] Then, the new traverse points are merged with the existing traverse point data, sorted, and renumbered to obtain the preprocessed traverse point data.

[0021] Furthermore, step C calculates the local coordinate system of the plane containing each traverse point, as follows:

[0022] First, obtain the sorted and renumbered traverse point data;

[0023] Then, establish the local coordinate system X-axis for the traverse points;

[0024] The vector from the previous traverse point to the current traverse point is used as the X-axis of the local coordinate system.

[0025] Next, establish the local coordinate system Z-axis for the traverse points;

[0026] The X-axis of the local coordinate system is the vector product of the X-axis and the vector from the previous traverse point to the next traverse point;

[0027] Finally, establish the local coordinate system Y-axis for the traverse points;

[0028] The product of the Z-axis and X-axis of the local coordinate system is used as the Y-axis of the local coordinate system.

[0029] Furthermore, step D transforms the spatial coordinates of the traverse points to the local coordinate system, and the specific process is as follows:

[0030] First, the X-axis, Y-axis, and Z-axis in the local coordinate system are grouped into a transformation matrix;

[0031] Then, the coordinates of the traverse point, the previous traverse point, and the next traverse point in the local coordinate system are calculated using the transformation matrix.

[0032] Furthermore, step E calculates the chamfer of the guide points, the specific process of which is as follows:

[0033] First, connect the previous traverse point to the current traverse point to form a traverse, and establish the parametric equation of the traverse line; then connect the current traverse point to the next traverse point to form a traverse, and establish the parametric equation of the traverse line.

[0034] Then, the coordinates of the center of the chamfered arc are calculated based on the parametric equations of the two lines;

[0035] Next, calculate the feet of the perpendiculars from the center of the circle to the two wires, and take the feet of the perpendiculars as the points of tangency;

[0036] Finally, the arc connecting the two points of tangency is the desired chamfer.

[0037] Furthermore, step F involves trimming the wires tangent to the rounded chamfer, and the specific process is as follows:

[0038] First, break the two wires at the point of tangency;

[0039] Then, use the arc obtained in step E to connect the two tangent points;

[0040] Finally, the result of trimming the line into two straight lines and one arc is taken as the wire trimming result.

[0041] Furthermore, step G calculates the output results of the prestressed steel strand alignment, and the specific process is as follows:

[0042] First, the traverse trimming results are arranged in ascending order according to the traverse point number, forming a linear array that alternates between straight line segments and circular arc segments;

[0043] Then, the linear array is projected onto the XY plane and the XZ plane to obtain the projection points on the XY plane and the XZ plane;

[0044] Finally, all projection points in the two planes are connected to form the prestressed steel strand linear output result.

[0045] Furthermore, for the projection of a line segment, the projection of the line segment into the XY plane and XZ plane is still a line. Calculate the coordinates of the endpoints of the line in the global coordinate system and project them, then connect the projection points with a line.

[0046] Furthermore, for the projection of the arc segment, the arc is discretized into multiple spatial points using the spatial arc discretization method. The overall coordinates of the spatial points are calculated and projected onto the XY plane and XZ plane. Straight lines are then used to connect each projection point in sequence.

[0047] The beneficial effects of this invention are as follows:

[0048] This invention establishes a simulation calculation model for the problem of calculating the prestressed steel strand alignment of railway bridges. By defining a data representation format for traverse points, a method for inputting the prestressed steel strand alignment contour is constructed. Through three-dimensional spatial coordinate system transformation and a planar rounding algorithm, a method for calculating the spatial coordinates of circular arc curves in the spatial coordinate system is derived, thereby establishing a simulation calculation method for the prestressed steel strand alignment of railway bridges and solving the problem of accurate calculation of the spatial alignment of prestressed steel strands in railway bridges.

[0049] This invention can accurately simulate the linearity of prestressed steel strand simulation models in various structures in the transportation field, solving the problem of model calculation accuracy. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the steps of the present invention;

[0051] Figure 2 This is a schematic diagram of the prestressed steel strand conductor point information in this invention;

[0052] Figure 3 This is a schematic diagram of the calculation of the local coordinate system of the guide point in this invention;

[0053] Figure 4 This is a schematic diagram illustrating the chamfer calculation in this invention;

[0054] Figure 5 This is a schematic diagram of the steel strand shape after trimming in this invention;

[0055] Figure 6 This is a schematic diagram illustrating the calculation of the projected coordinates of points using the spatial circular arc discretization method in this invention.

[0056] Figure 7 The spatial shape of the steel strand calculated in this invention is projected onto the XY and XZ planes;

[0057] Figure 8 The spatial alignment of the steel strands calculated for AutoCAD is projected onto the XY and XZ planes. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0059] like Figures 1 to 8 As shown, a simulation calculation method for the prestressed steel strand alignment of railway bridges includes the following steps:

[0060] A. Input the conductor point data for the prestressed steel strands;

[0061] B. Preprocess the input conductor point data of the prestressed steel strands;

[0062] C. Calculate the local coordinate system of the plane containing each traverse point;

[0063] D. Transform the spatial coordinates of the traverse points to the local coordinate system;

[0064] E. Calculate the chamfer at the traverse points;

[0065] F. Trim the wire so that it is tangent to the rounded chamfer;

[0066] G. Calculate the output results of the prestressed steel strand shape.

[0067] Step A involves inputting the conductor point data for the prestressed steel strands. The specific process is as follows:

[0068] The traverse point data input for each traverse point includes the traverse point spatial coordinates, radius, offset direction, offset angle, tilt height, and radius at the offset point; the offset direction, offset angle, tilt height, and radius at the offset point constitute the offset data.

[0069] Step B involves preprocessing the input prestressed steel strand conductor point data. The specific process is as follows:

[0070] First, calculate the new traverse points based on the offset data for the traverse points that need to be offset in step A;

[0071] Then, the new traverse points are merged with the existing traverse point data, sorted, and renumbered to obtain the preprocessed traverse point data.

[0072] Step C calculates the local coordinate system of the plane containing each traverse point. The specific process is as follows:

[0073] First, obtain the sorted and renumbered traverse point data;

[0074] Then, establish the local coordinate system X-axis for the traverse points;

[0075] The vector from the previous traverse point to the current traverse point is used as the X-axis of the local coordinate system.

[0076] Next, establish the local coordinate system Z-axis for the traverse points;

[0077] The X-axis of the local coordinate system is the vector product of the X-axis and the vector from the previous traverse point to the next traverse point;

[0078] Finally, establish the local coordinate system Y-axis for the traverse points;

[0079] The product of the Z-axis and X-axis of the local coordinate system is used as the Y-axis of the local coordinate system.

[0080] Step D involves transforming the spatial coordinates of the traverse points to the local coordinate system. The specific process is as follows:

[0081] First, the X-axis, Y-axis, and Z-axis in the local coordinate system are grouped into a transformation matrix;

[0082] Then, the coordinates of the traverse point, the previous traverse point, and the next traverse point in the local coordinate system are calculated using the transformation matrix.

[0083] Step E calculates the chamfer at the traverse points. The specific process is as follows:

[0084] First, connect the previous traverse point to the current traverse point to form a traverse, and establish the parametric equation of the traverse line; then connect the current traverse point to the next traverse point to form a traverse, and establish the parametric equation of the traverse line.

[0085] Then, the coordinates of the center of the chamfered arc are calculated based on the parametric equations of the two lines;

[0086] Next, calculate the feet of the perpendiculars from the center of the circle to the two wires, and take the feet of the perpendiculars as the points of tangency;

[0087] Finally, the arc connecting the two points of tangency is the desired chamfer.

[0088] Step F involves trimming the wire tangent to the rounded chamfer. The specific process is as follows:

[0089] First, break the two wires at the point of tangency;

[0090] Then, use the arc obtained in step E to connect the two tangent points;

[0091] Finally, the result of trimming the line into two straight lines and one arc is taken as the wire trimming result.

[0092] Step G calculates the output results of the prestressed steel strand alignment. The specific process is as follows:

[0093] First, the traverse trimming results are arranged in ascending order according to the traverse point number, forming a linear array that alternates between straight line segments and circular arc segments;

[0094] Then, the linear array is projected onto the XY plane and the XZ plane to obtain the projection points on the XY plane and the XZ plane;

[0095] Finally, all projection points in the two planes are connected to form the prestressed steel strand linear output result.

[0096] For the projection of a line segment, the projection of the line segment into the XY plane and XZ plane is still a line. Calculate the coordinates of the endpoints of the line in the global coordinate system and project them, then connect the projection points with a line.

[0097] For the projection of the arc segment, the arc is discretized into multiple spatial points using the spatial arc discretization method. The global coordinate system coordinates of the spatial points are calculated and projected onto the XY plane and XZ plane. Straight lines are used to connect each projection point in sequence.

[0098] Specifically, in step A, input the conductor point data for the prestressed steel strands, as follows:

[0099] In step A, input the prestressed steel strand traverse point data. In railway bridge structures, the prestressed steel strands are input using the traverse method. The traverse point refers to the point where the shape of the steel strand changes.

[0100] The input data for a traverse point includes:

[0101] 1. Spatial coordinates of the traverse point (x, y, z);

[0102] 2. The radius r at the traverse point (the radius is 0 when the traverse point is a straight line).

[0103] like Figure 2 As shown, the spatial coordinates of the four traverse points P1 to P4 are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4), respectively. Among them, the traverse point P2 is a circular arc segment with a radius of r2; the remaining three traverse points are all straight line segments with a radius r of 0.

[0104] In addition, to improve input efficiency, new traverse points can be generated by offsetting existing traverse points. Figure 2 Traverse point P5 is derived from traverse point P4 by offset. The traverse point offset input data includes:

[0105] 1. Direction dir (left is -1, right is 1);

[0106] 2. Offset angle α (counterclockwise rotation is positive, clockwise rotation is negative);

[0107] 3. Inclination height h;

[0108] 4. Radius r at the offset point.

[0109] Conductor point offset is generally used for data input at the left and right ends of symmetrical steel strands, such as... Figure 3The prestressed steel strands shown have a total of 4 traverse points, P1 to P4. When inputting the traverse offset method, you only need to input points P2 and P3 first, and then input two sets of offset data to obtain traverses P1 and P4. Taking P1 as an example, the offset data is (dir=-1, α=α2, h=h2, r=0).

[0110] Specifically, step B preprocesses the input prestressed steel strand conductor point data as follows:

[0111] Step B, the preprocessing of traverse point data, involves processing the traverse point offset data from Step A to generate a standard traverse point data format. The specific process is as follows:

[0112] First, calculate the coordinates of the traverse points generated by the offset, so that... Figure 3 Taking point P4 as an example, with offset data (dir=1, α=α3, h=h3, r=0), the formula for calculating the coordinates (x4, y4, z4) of point P4 is:

[0113] x4=x3+dir·h3 / tan|α3| (1)

[0114] y4=y3+dir·sgn(α3)h3 (2)

[0115] z4=z3 ​​(3)

[0116] In the formula, dir is the offset direction; α is the rotation angle; and sgn is the function that returns the positive or negative sign.

[0117] Then, the coordinates of the newly generated traverse points are added to the traverse point data array and sorted in ascending order. Since the prestressed steel strands are arranged along the beam length, and the beam length is generally defined as the x-axis in the design, the traverse points are sorted according to the x-axis coordinate values ​​in ascending order.

[0118] Specifically, step C calculates the local coordinate system of the plane containing each traverse point. The specific process is as follows:

[0119] Step C: Calculate the local coordinate system of the plane containing each traverse point.

[0120] For non-starting and non-ending guide point P i Its preceding traverse point is P. i-1 The next adjacent traverse point is P. i+1 The coordinates of the three traverse points are (x, y, y) i-1 ,y i-1 ,z i-1 ), (x i ,y i ,z i ) and (x i+1 ,y i+1 ,z i+1The global coordinate system is XYZ, and the local coordinate system to be determined is X′Y′Z′, as shown below. Figure 4 As shown.

[0121] The specific calculation process for the local coordinate system is as follows:

[0122] First, take the guide point P i-1 As the origin of the local coordinate system, calculate the distance from this point to the traverse point P. i P i+1 vector v x v2, v x After normalization, it is defined as the X′ axis of the local coordinate system:

[0123] v x =p i -p i-1 =(x i -x i-1 ,y i -y i-1 ,z i -z i-1 (4)

[0124] v2 = p i+1 -p i-1 =(x i+1 -x i-1 ,y i+1 -y i-1 ,z i+1 -z i-1 (5)

[0125] Then, calculate v x v2 cross product v z After normalization, it is defined as the Z′ axis of the local coordinate system:

[0126] v z =v x ×v2 (6)

[0127] Finally, calculate v z v x Cross product v y After normalization, it is defined as the Y′ axis of the local coordinate system:

[0128] v y =v z ×v x (7)

[0129] Using the guide point P i-1 The local coordinate system X′Y′Z′ is obtained by using the origin of the coordinate system.

[0130] Specifically, step D transforms the spatial coordinates of the traverse points to the local coordinate system, and the specific process is as follows:

[0131] First, using the three axes X′Y′Z′ obtained in step C, calculate the direction vectors v of the three axes X′Y′Z′ in the global coordinate system XYZ. x v y v z Let M be the transformation matrix from the global coordinate system to the local coordinate system. Specifically, it is expressed as follows:

[0132]

[0133] Then, for a point P(x,y,z), its coordinates P′(x′,y′,z′) in the local coordinate system X′Y′Z′ are calculated using the following formula:

[0134]

[0135] In the formula, P0 is the coordinate of the origin of the local coordinate system in the global coordinate system, corresponding to P in step C. i-1 Point coordinates.

[0136] Calculate the three traverse points P using formula (9). i-1 P i and P i+1 Coordinate P′ in the local coordinate system i-1 、P′ i and P′ i+1 .

[0137] Specifically, step E calculates the chamfer of the guide points, as follows:

[0138] The three traverse points P′ after the coordinate transformation in step D i-1 、P′ i and P′ i+1 All are located in the local coordinate system X′Y′ plane, and the Z′ coordinate is 0, such as Figure 5 As shown. The in-plane chamfer calculation method can be used. The specific process is as follows:

[0139] First, calculate the line P′ according to the parametric equation format of a line: ax + by + c = 0. i-1 P′ i and line P′ i P′ i+1 The coefficients of the parametric equations:

[0140]

[0141]

[0142] Then, calculate the line P′ i-1 P′ i Midpoint m d1 and line P′i P′ i+1 Midpoint m d2 coordinate:

[0143]

[0144]

[0145] Then, calculate point m. d2 to line P′ i-1 P′ i Distance l1:

[0146]

[0147] In the formula, a1, b1, and c1 are the lines P′ and P′ respectively. i-1 P′ i Coefficients of the parametric equation.

[0148] Then, calculate the coefficient c. 1p c 2p and d:

[0149]

[0150]

[0151] d = a1b2 - a2b1 (17)

[0152] In the formula, r is the radius of the arc, and sgn is the function that returns the positive or negative sign.

[0153] Then, calculate the center C′ of the chamfered arc. i coordinate:

[0154] C′ i =(x rc ,y rc )=((c 2p b1-c 1p b2) / d,(c 1p a2-c 2p a1) / d) (18)

[0155] Arc and two straight lines P′ i-1 P′ i and P′ i P′ i+1 The intersection point can be calculated by the center C′ of the circle. i The foot of the perpendicular between the two lines is obtained, as shown below. Figure 5 As shown, the center of the circle is C′ i The feet of the perpendiculars to the two lines are O′. i-1 O′ i .

[0156] With line P′ i-1 P′ i For example, first calculate the distance from the origin of the local coordinate system to the center C′ of the arc. i and traverse point P′ i-1 vector v rc v i-1 and line P′ i-1 P′ i Direction vector v i Then calculate the foot of the perpendicular O′ i-1 coordinate:

[0157] O′ i-1 =(x Po ,y Po ) = v i-1 -(v i-1 -v rc ) / (v i ·v i )·v i (19)

[0158] Similarly, the center C′ can be calculated. i For line P′ i P′ i+1 foot of the perpendicular O′ i The coordinates of the points will not be elaborated further.

[0159] The chamfer calculation is now complete. The starting and ending points of the chamfer arc are point O′. i-1 and O′ i The center of the circle is C′ i , with radius r.

[0160] Specifically, step F involves trimming the wire tangent to the rounded chamfer, as detailed below:

[0161] First, determine the two perpendicular points O′ obtained in step E. i-1 and O′ i Is it located on line P′? i-1 P′ i and P′ i P′ i+1 Inside.

[0162] When the radius r is too large, the foot of the perpendicular may be outside the line. In this case, the original traverse P′ should be retained. i-1 P′ i and P′ i P′ i+1 No further calculations will be performed.

[0163] When the two feet of the perpendiculars are located on line P′ i-1 P′ i and P′ i P′ i+1When the two lines are perpendicular, they are broken at the point where they meet, which is called trimming the lines.

[0164] The trimmed line becomes P′ i-1 O′ i-1 and O′ i P′ i+1 At the same time, new Arc arc conductors need to be added. i , used to connect O′ i-1 and O′ i Two points. For example... Figure 5 As shown, the center of the arc is C′. i The radius is r, and the starting and ending points are O′ respectively. i-1 and O′ i The rotation direction is rot (clockwise in this case). Circular arc conductors can be described using the following format:

[0165] Arc i =(O′ i-1 ,O′ i ,r,rot) (20)

[0166] Specifically, step G calculates the output results of the prestressed steel strand alignment, as follows:

[0167] The spatial alignment of prestressed steel strands is output data based on their projections in the XY and XZ planes. Therefore, it is necessary to calculate the projected coordinates of the conductors in the XY and XZ planes separately. The specific process is as follows:

[0168] For point P of the circular arc guide i After calculations in steps C to F, the two straight lines P′ i-1 P′ i 、P′ i P′ i+1 It will become three conductor segments: straight line P′ i-1 O′ i-1 Circular arc O′ i-1 O′ i Line O′ i P′ i+1 .

[0169] First, transform the coordinates of the four traverse endpoints to the global coordinate system XYZ, because the traverse point P′ i-1 、P′ i+1 The coordinates in the global coordinate system are the known quantity P. i-1 P i+1 Therefore, only point O′ needs to be calculated. i-1 and O′ i .

[0170] With point O′ i-1For example, the coordinates of this point in the local coordinate system X′Y′Z′ are (x′...). oi ,y′ oi ,z′ oi ), which is also the vector v′ from the origin O′ of the local coordinate system to that point. oi :

[0171] v′ oi =(x′) oi ,y′ oi ,z′ oi ) (twenty one)

[0172] Returns the three coordinate axis vectors v′ of the local coordinate system. x v′ y v′ z In the global coordinate system, the coordinate matrix M′ is:

[0173]

[0174] Transpose matrix M′ and fold it with vector v′ oi Multiply the coordinates and add them to the coordinates O of the local coordinate system origin in the global coordinate system to obtain the coordinates O of the point in the global coordinate system. i-1 :

[0175]

[0176] Similarly, point O′ can be calculated. i Coordinate O in the global coordinate system i I will not go into details.

[0177] For the straight conductor P′ i-1 O′ i-1 and O′ i P′ i+1 Its projection in the XY and XZ planes is still a straight line. The projection coordinates of the endpoint in the XY plane can be obtained by taking the Z coordinate as 0, and the projection coordinates of the endpoint in the XZ plane can be obtained by taking the Y coordinate as 0.

[0178] Therefore, for a straight conductor, its shape in the XY and XZ planes only needs to be calculated at the endpoints, and then connected by a straight line.

[0179] For the circular arc conductor O′ i-1 O′ i The shape of its projection line in the XY and XZ planes is related to the angle between the arc plane and the projection plane: when the two are parallel, the result is still the arc itself; when the two are perpendicular, the result is a straight line; when the two are at a certain angle, the result is an elliptical arc.

[0180] To describe the projected shape of a circular arc on two planes, a spatial circular arc discretization method can be used for calculation. For example... Figure 6 As shown, given 3 traverse points P i-1 P i P i+1 Calculate the spatial arc O i-1 O i The central angle is Select angle step size Discretize the spatial arc into A spatial discrete point (P′) d1 ,P′ d2 ,P′ d3 ,…,P′ dn The coordinates P′ of any discrete point in space in the local coordinate system. di (x′ di ,y′ di )for:

[0181]

[0182]

[0183] In the formula, (x′ ci ,y′ ci ), r and These represent the coordinates of the center of the spatial arc, its radius, and the central angle at the starting point. To calculate the central angle of a discrete point in space, The angle step size.

[0184] Then, calculate the coordinates P of the discrete point in the global coordinate system. di (x di ,y di ,z di ):

[0185]

[0186] In the formula, M′ represents the three coordinate axis vectors v′ of the local coordinate system. x v′ y v′ z In the matrix of the global coordinate system, O represents the coordinates of the origin of the local coordinate system in the global coordinate system (i.e., ...). Figure 6 Point P in i-1 ).

[0187] Spatial discrete point P di The projections of these points onto the XY and XZ planes are respectively point P. di_xy and P di_xz The coordinates are obtained by taking zeros for both the Z and Y coordinates respectively:

[0188] Pdi_xy =(x di_xy ,y di_xy ,0) (27)

[0189] P di_xz =(x di_xz ,0,z di_xz (28)

[0190] Similarly, calculate the coordinates (P) of each discrete point in space in the global coordinate system. d1 ,P d2 ,P d3 ,…,P dn These points are then projected onto the XY and XZ planes respectively to obtain an array of projection points (P). d1_xy ,P d2_xy ,P d3_xy ,…,P dn_xy ) and (P d1_xz ,P d2_xz ,P d3_xz ,…,P dn_xz ).

[0191] These points then intersect with the straight line P. i-1 O i-1 and O i P i+1 Connecting the projection points in the two planes yields the projected shape of the prestressed steel strand's spatial alignment in the XY and XZ planes, which can be used as output data. When the angle step size... When the value is small enough, the calculation results are accurate enough to meet the engineering accuracy requirements.

[0192] Example 1

[0193] The spatial alignment of a prestressed steel strand was calculated using this invention, and the results were compared and verified with those obtained from AutoCAD software.

[0194] The input data for the traverse points is shown in Table 1. In this embodiment, a total of 4 traverse points are input, of which traverse points 1 and 4 need to be offset to the left and right, respectively.

[0195] Table 1 Input data for traverse points

[0196]

[0197]

[0198] First, traverse point preprocessing is performed to generate standard traverse point format from the offset data. For traverse point 1, the coordinates of the traverse point P0 generated to its left are:

[0199]

[0200] Similarly, the coordinates of the newly generated traverse point P5 to the right of traverse point 4 can be calculated as follows:

[0201]

[0202] The preprocessed traverse point coordinate data are shown in Table 2.

[0203] Table 2. Results of Traverse Point Preprocessing

[0204]

[0205] Then calculate the rounded chamfer at the traverse points with a radius not equal to 0. Taking traverse point P1(1,0,0) as an example, its left and right traverse points are P0(0.2,0.8,0) and P2(2,1,3), respectively.

[0206] First, taking the traverse point P0 as the origin of the local coordinate system, calculate the vectors from this point to the traverse points P1 and P2 respectively. v2:

[0207]

[0208] v2 = p2 - p0 = (1.8, 0.2, 3)

[0209] Will normalized v x Defined as the X′ axis of the local coordinate system:

[0210]

[0211] Calculate v x v2 cross product and normalization v z As the Z′ axis of the local coordinate system:

[0212]

[0213] Calculate v z v x Cross product and normalization v y As the Y′ axis of the local coordinate system:

[0214]

[0215] The direction vectors v of the three axes of the local coordinate system X′Y′Z′ in the global coordinate system XYZ x v y v z Assemble the transformation matrix M from the global coordinate system to the local coordinate system:

[0216]

[0217] Then, the coordinates of the traverse points P0, P1, and P2 in the local coordinate system X′Y′Z′ are calculated using the transformation matrix M:

[0218]

[0219]

[0220]

[0221] Then, the rounded chamfer is calculated using the coordinate values ​​P′0, P′1, and P′2 in the local coordinate system. First, the parametric equation coefficients (a1, b1, c1) and (a2, b2, c2) of lines P′0P′1 and P′1P′2 are calculated:

[0222]

[0223]

[0224] Calculate the midpoint m of the line P′0P′1 d1 and the midpoint m of lines P′1P′2 d2 coordinate:

[0225]

[0226]

[0227] Then calculate point m. d2 Distance l1 to line P′0P′1:

[0228]

[0229] Calculate coefficient c 1p c 2p Coordinates of d and the center C′1 of the chamfered arc:

[0230]

[0231]

[0232] d = a1b2 - a2b1 = 3.7523

[0233] C′ i =(x rc ,y rc )=((c 2p b1-c 1p b2) / d,(c 1p a2-c 2p a1) / d)=(0.83137,0.3)

[0234] Calculate the intersection points of the arc with the two lines P′0P′1 and P′1P′2 by calculating the feet of the perpendiculars from the center C′1 of the arc to the two lines. The coordinates of the intersection points O′0 and O′1 in the local coordinate system are (0.83137, 0, 0) and (1.13137, 0.3, 0), respectively. Trim the guide wire tangent to the chamfer, that is, break the lines P0P1 and P1P2 at their feet, and after trimming, they become two lines, P′0P′1 and P′1P′2. i -1O′ i -1、O′ i P′ i+1 And the circular arc O′0O′1. Transform O′0 and O′1 to their coordinates O0 and O1 in the global coordinate system as follows:

[0235] O0 = (0.78787, 0.21213, 0)

[0236] O1 = (1.0905, 0.09045, 0)

[0237] This completes the calculation of the chamfer for traverse point P1. Similarly, the chamfers for traverse points P2, P3, and P4 are calculated respectively. The calculation process will not be repeated here. The calculation results are shown in Table 3.

[0238] Table 3 Calculation results of conductor point chamfer.

[0239]

[0240] To verify the calculation results, AutoCAD was used to calculate the coordinates of the endpoints of the chamfered arcs from traverse points P1 to P4, and the results were compared with those calculated by this method. The results are shown in Table 4.

[0241] Table 4 Comparison of Chamfer Calculation Results

[0242]

[0243] As can be seen from the ratio of the results in Table 4, the simulation calculation method for the prestressed steel strand shape of railway bridges proposed in this invention is very close to the calculation results of AutoCAD, with a maximum error of only 0.15%.

[0244] The spatial shape of the steel strand calculated using the algorithm proposed in this invention is projected onto the XY and XZ planes, and the projection results are as follows: Figure 7 As shown, and as Figure 8 The AutoCAD calculation results shown have consistent projection lines in both the XY and XZ planes.

[0245] Therefore, the simulation calculation method for the prestressed steel strand shape of railway bridges proposed in this invention has a clear theoretical derivation and high calculation accuracy, meeting the requirements of actual engineering simulation calculation.

[0246] This invention establishes a simulation model to address the problem of calculating the prestressed steel strand alignment of railway bridges. By defining a data representation format for traverse points, a method for inputting the prestressed steel strand alignment contour is constructed. Through three-dimensional spatial coordinate system transformation and a planar rounding algorithm, a method for calculating the spatial coordinates of circular arc curves in the spatial coordinate system is derived. Thus, a simulation calculation method for the prestressed steel strand alignment of railway bridges is established, solving the problem of accurate calculation of the spatial alignment of prestressed steel strands in railway bridges.

[0247] This invention can accurately simulate the linearity of prestressed steel strand simulation models in various structures in the transportation field, solving the problem of model calculation accuracy.

Claims

1. A method for simulating and calculating the alignment of prestressed steel strands in railway bridges, characterized in that: Includes the following steps: A. Input the conductor point data for the prestressed steel strands; B. Preprocess the input conductor point data of the prestressed steel strands; C. Calculate the local coordinate system of the plane containing each traverse point; D. Transform the spatial coordinates of the traverse points to the local coordinate system; E. Calculate the chamfer at the traverse points; F. Trim the wire so that it is tangent to the rounded chamfer; G. Calculate the output results of the prestressed steel strand shape.

2. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step A involves inputting the conductor point data for the prestressed steel strands. The specific process is as follows: The traverse point data input for each traverse point includes the traverse point spatial coordinates, radius, offset direction, offset angle, tilt height, and radius at the offset point; the offset direction, offset angle, tilt height, and radius at the offset point constitute the offset data.

3. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step B involves preprocessing the input prestressed steel strand conductor point data. The specific process is as follows: First, calculate the new traverse points based on the offset data for the traverse points that need to be offset in step A; Then, the new traverse points are merged with the existing traverse point data, sorted, and renumbered to obtain the preprocessed traverse point data.

4. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step C calculates the local coordinate system of the plane containing each traverse point. The specific process is as follows: First, obtain the sorted and renumbered traverse point data; Then, establish the local coordinate system X-axis for the traverse points; The vector from the previous traverse point to the current traverse point is used as the X-axis of the local coordinate system. Next, establish the local coordinate system Z-axis for the traverse points; The X-axis of the local coordinate system is the vector product of the X-axis and the vector from the previous traverse point to the next traverse point; Finally, establish the local coordinate system Y-axis for the traverse points; The product of the Z-axis and X-axis of the local coordinate system is used as the Y-axis of the local coordinate system.

5. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step D involves transforming the spatial coordinates of the traverse points to the local coordinate system. The specific process is as follows: First, the X-axis, Y-axis, and Z-axis in the local coordinate system are grouped into a transformation matrix; Then, the coordinates of the traverse point, the previous traverse point, and the next traverse point in the local coordinate system are calculated using the transformation matrix.

6. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step E calculates the chamfer at the traverse points. The specific process is as follows: First, connect the previous traverse point to the current traverse point to form a traverse, and establish the parametric equation of the traverse line; then connect the current traverse point to the next traverse point to form a traverse, and establish the parametric equation of the traverse line. Then, the coordinates of the center of the chamfered arc are calculated based on the parametric equations of the two lines; Next, calculate the feet of the perpendiculars from the center of the circle to the two wires, and take the feet of the perpendiculars as the points of tangency; Finally, the arc connecting the two points of tangency is the desired chamfer.

7. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step F involves trimming the wire tangent to the rounded chamfer. The specific process is as follows: First, break the two wires at the point of tangency; Then, use the arc obtained in step E to connect the two tangent points; Finally, the result of trimming the line into two straight lines and one arc is taken as the wire trimming result.

8. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: Step G calculates the output results of the prestressed steel strand alignment. The specific process is as follows: First, the traverse trimming results are arranged in ascending order according to the traverse point number, forming a linear array that alternates between straight line segments and circular arc segments; Then, the linear array is projected onto the XY plane and the XZ plane to obtain the projection points on the XY plane and the XZ plane; Finally, all projection points in the two planes are connected to form the prestressed steel strand linear output result.

9. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 8, characterized in that: For the projection of a line segment, the projection of the line segment into the XY plane and XZ plane is still a line. Calculate the coordinates of the endpoints of the line in the global coordinate system and project them, then connect the projection points with a line.

10. The method for simulating and calculating the prestressed steel strand alignment of railway bridges according to claim 1, characterized in that: For the projection of the arc segment, the arc is discretized into multiple spatial points using the spatial arc discretization method. The global coordinate system coordinates of the spatial points are calculated and projected onto the XY plane and XZ plane. Straight lines are used to connect each projection point in sequence.

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