CN113408026A - Railway bridge accurate bend arrangement calculation method - Google Patents

Railway bridge accurate bend arrangement calculation method Download PDF

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CN113408026A
CN113408026A CN202110664027.0A CN202110664027A CN113408026A CN 113408026 A CN113408026 A CN 113408026A CN 202110664027 A CN202110664027 A CN 202110664027A CN 113408026 A CN113408026 A CN 113408026A
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calculating
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CN113408026B (en
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苏伟
王雨权
廖立坚
李艳
刘祥君
刘龙
傅安民
杨智慧
张兴华
白青波
吴迪
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China Railway Design Corp
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Abstract

The invention discloses a method for calculating the arrangement of precise curves of a railway bridge, which comprises the following steps: inputting initial hole span and mileage information; determining a control mileage; inquiring the initial curve elements; calculating the single-line offset; calculating the single-line beam seam increment; calculating a single line deflection angle; calculating the intersection distance 1; updating the pier mileage and curve elements; calculating an amplification factor; calculating the increment of the double-line beam seam; calculating a new intersection distance 2; comparing the intersection point distance 1 with the intersection point distance 2; determining the final offset distance, the offset angle and the beam gap increment; determining the final intersection point distance and bridge pier mileage; and (4) arranging an abutment. Aiming at the problem of arrangement of railway bridges on curves, curve elements of pier calculation points are updated in real time based on iterative operation, offset distance, offset angle and beam joint value increase under the condition of a single line are calculated by utilizing accurate curve elements, then the concept of amplification coefficients is introduced, inner and outer line beam joint value increase during double lines is calculated, and finally the automatic bridge adjustment principle is introduced for bridge abutment arrangement.

Description

Railway bridge accurate bend arrangement calculation method
Technical Field
The invention belongs to the technical field of bridge engineering in the traffic transportation industry, and particularly relates to a method for calculating the accurate curve layout of a railway bridge.
Background
In recent years, high-speed rails have become a beautiful business card in China, and in order to meet the requirements of safety and comfort of high-speed rail operation, railway settlement must be strictly controlled, which results in higher and higher full-line bridge proportion of bridges, for example, 80.7% of the full-line bridge proportion of high-speed rails in Jinghuso.
In the full-line railway bridge, the simply supported beam has a high occupation ratio, and the simply supported beam is connected with the continuous beam in a large number. How to carry out reasonable hole span arrangement in the line curve section to make its beam seam interval reasonable, the simply supported beam atress is even, and the pier offset is accurate, and the construction laying-out is simple and convenient, is an important subject that large-scale railway bridge design faces.
In the prior publications, the offset distance, the offset angle and the added value of the beam gap are calculated based on a specific beam width, such as 3.9m, and a large amount of parameter table lookup work exists. The method cannot adapt to the existing calculation conditions of beam width uncertainty, variable beam width, variable line spacing and the like. The method can not adapt to the situations of curve element loss, automatic adjustment of bridge abutment arrangement, connection of a simply supported beam and a continuous beam and the like, and in the process of calculating the offset distance, the increment of beam seams and the offset angle, the curve element of an initial calculation point is taken as the basis, the problem of movement of the calculation point caused by curve arrangement is ignored, and the algorithms can not accurately process the curve arrangement of the large-scale railway bridge of many kilometers.
Aiming at the problems, a set of railway bridge accurate curve arrangement algorithm is needed to be researched for systematically solving the problem of hole span arrangement of large-scale railway bridges on curves.
Disclosure of Invention
The invention is provided for solving the problems in the prior art, and aims to provide a method for calculating the precise curve layout of a railway bridge.
The technical scheme of the invention is as follows: a railway bridge accurate bend arrangement calculation method comprises the following steps:
A. inputting initial hole span and mileage information
Arranging conventional beam spans according to the requirements of bridges for crossing rivers, roads, pipelines and the like, wherein curve influence is not considered in the arrangement process, and the route mileage corresponds to the position of each pier;
B. determining a controlling range
Determining a controllability mileage of a fixed position at a controllability project of the railway bridge, and arranging the rest holes in a cross-sequence manner;
C. querying initial curve elements
Inquiring and determining curve elements corresponding to the positions of all the abutments;
D. calculating single line offset
Arranging according to a single line curve, and calculating the corresponding offset distance;
E. calculating single line beam seam increment
Arranging according to a single line curve, and calculating the corresponding beam seam increment;
F. calculating single line declination
Arranging according to a single line curve, and calculating the corresponding deflection angle;
G. calculating the intersection distance 1
Adding the added value of the beam joint obtained in the step E to the original beam span length to obtain the intersection point distance 1 of each hole beam;
H. updating mileage and curve elements of pier
G, after the intersection point distance 1 is obtained, the position of each abutment is changed, and the mileage of each abutment and the curve element of the new position are obtained again;
I. calculating the amplification factor
Calculating according to the beam width and the line spacing to obtain an amplification factor;
J. calculating double line beam seam increment
Calculating the beam seam increment of the double lines by using the beam seam increment calculated by the amplification factor and the single line;
K. calculate new intersection distance 2
Calculating a new intersection point distance 2 by using the increment of the beam seam of the double lines obtained in the step J;
l. compare intersection distance 1 with intersection distance 2
Comparing the intersection point distance 1 with the intersection point distance 2, if the two are close, executing the step (M), if not, returning to the step H;
m. determining final offset distance, offset angle and beam gap added value
After iterative convergence, determining the final position of each pier, and then calculating the final offset distance, the offset angle and the beam gap value by using curve elements at the position, wherein the influence of an amplification factor needs to be considered;
n. determining the final intersection point distance and bridge pier mileage
Calculating the final intersection point distance and bridge pier mileage according to the converged beam seam increment;
arrangement of abutment
And determining the arrangement mode according to the curve position of the front platform and the tail platform and the automatic adjustment principle of the bridge platform.
Further, in step a, the hole span is arranged, and the initial input intersection point is the sum of the beam length and the smallest beam seam.
Furthermore, the bridge pier structure in the step B controllability project cannot enter, and the controllability mileage is used as the starting point position of the mileage calculated by other bridge piers.
Further, the curve elements in step C include curve type, radius of circular curve, length of gentle curve, distance from ZH point, distance from HZ point, single and double lines.
Furthermore, in step D, the offset distances are calculated according to the single-line curve, and the calculation formula is as follows:
for calculating the offset of a point on a circular curve:
Figure BDA0003116527340000031
substituting the equivalent radius ρ into the formula (1) instead of R for the offset distance of the calculation point on the relaxation curve, wherein the equivalent radius calculation formula is as follows:
Figure BDA0003116527340000041
for the condition that the continuous beam is connected and the curved beam of the continuous beam is curved, the offset distance is zero;
wherein: e is the offset, f is the rise, L is the intersection point distance, R is the radius of the circular curve, t is the distance from the calculated point to the starting point of the easement curve (the straight or gentle straight point), LSIs the length of the gentle curve.
Furthermore, in the step E, the beam joint increment is calculated according to the arrangement of the single-line curve, and the calculation formula is as follows:
adding value to the beam seam of the calculated point on the circular curve:
Figure BDA0003116527340000042
for the offset distance of the calculation point on the relaxation curve, R is replaced by the equivalent radius rho,
wherein: delta1Added value, Δ, for beam gap caused by string deflection2For added value of beam joint caused by outward shift of deflection anglenAnd delta E is the distance between the intersection points of the n-th hole beam, and the offset distance between the two ends of the calculated beam.
Furthermore, in step F, the single-line curve is arranged, and the corresponding deflection angle is calculated according to the following calculation formula:
for the case of complete curve elements:
(1) the beam part is on a gentle curve on a straight line
Figure BDA0003116527340000043
(2) The beams all being on a gentle curve
Figure BDA0003116527340000044
(3) The beam portion being on the gentle curve and the beam portion being on the circular curve
Figure BDA0003116527340000051
(4) On the whole circular curve of the beam
Figure BDA0003116527340000052
The deflection angle alpha is the sum of the left and right chord tangent angles at the intersection point of the beam crossing center lines,
for the case where the curve elements are incomplete:
Figure BDA0003116527340000053
wherein: f1～F8For chord tangent angle, t, at each calculated point1、t2Respectively, the distance from the calculation point to the starting point (the straight point or the slow straight point) of the easement curve, L is the distance between the calculation points, K is the length of the beam in the range of the circular curve, K is the length of the beam in the range of the easement curve, and t is the distance from the left side of the beam in the range of the starting point (the straight point or the slow straight point) of the easement curve.
Further, the formula for calculating the amplification factor in step I is as follows:
Figure BDA0003116527340000054
wherein:
Figure BDA0003116527340000055
is the double line magnification factor, B is the beam width at the calculation point, and s is the line spacing at the calculation point.
Further, the value-added process of the double-line beam seam calculated in the step J is as follows:
if the actual piling line is the left line, if the left line is on the outer side of the curve, the value of the left line beam seam is increased as follows:
Figure BDA0003116527340000056
after the left line is calculated, calculating the beam joint increment of the right line according to the line spacing:
Figure BDA0003116527340000057
wherein: deltaSheetIncrement of beam seam, delta, calculated for the left line as a single lineLeft side of、ΔRight sideThe actual beam seam increment value of the left and right lines in the double lines is shown, and alpha is the deflection angle at the calculated point.
Furthermore, in step O, the bridge abutment is arranged according to the curve position of the front abutment and the tail abutment and according to the principle of automatic adjustment of the bridge abutment, the arrangement mode is determined as follows:
criterion 1: when the abutment is arranged according to the broken line, the offset distance E of the abutment tail0Calculating the value of the seam delta of the front beam of the platform as 0In front of the table≤ΔMax in front of the tableWhen the abutment is arranged in a straight line, when ΔIn front of the table＞ΔMax in front of the tableShould be arranged according to a broken line, ΔMax in front of the tableThe value, when d is 10cm, corresponds to the table length l0The value of the platform front beam seam is increased, and the calculation formula is as follows:
Figure BDA0003116527340000061
criterion 2: when the abutment is arranged according to a straight line, the distance from the center of the abutment tail to the central line of the line is d, when d is more than 10cm, the abutment is arranged according to a broken line, when d is less than or equal to 10cm, the abutment can be arranged according to a straight line,
for the case of bisecting vectors, d takes the following value:
Figure BDA0003116527340000062
for the tangential arrangement, d takes the following values:
Figure BDA0003116527340000063
note: d is the offset of the tail of the platform, l0Is the abutment length, l is the intersection distance of the beams, R is the radius of the circular curve, ρcTo mitigate the converted radius of the curve at point C, LsTo moderate the curve length.
The invention has the following beneficial effects:
aiming at the problem of arrangement of railway bridges on curves, curve elements of pier calculation points are updated in real time based on iterative operation, offset distance, offset angle and beam joint value increase under the condition of a single line are calculated by utilizing accurate curve elements, then the concept of amplification coefficients is introduced, inner and outer line beam joint value increase during double lines is calculated, and finally the automatic bridge adjustment principle is introduced for bridge abutment arrangement.
The invention can aim at the accurate arrangement of single-line and double-line bridge hole spans of the railway in the field of transportation. The method solves the problems of curved road arrangement of the railway bridge, such as changing the beam width, changing the line spacing, connecting a simply supported beam with a continuous beam, automatically selecting an arrangement mode for the abutment, lacking a transition curve and the like.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of a curve layout of the present invention;
FIG. 3 is a schematic view of a railroad bridge span arrangement of the present invention;
FIG. 4 is a schematic diagram illustrating the calculation of incremental value of beam joints caused by the runout deviation according to the present invention;
FIG. 5 is a schematic diagram illustrating the calculation of the deflection angle for the case of complete curve elements according to the present invention;
FIG. 6 is a schematic diagram illustrating the calculation of the deflection angle in the case of an incomplete curve element according to the present invention;
FIG. 7 is a schematic illustration of a two-wire arrangement of the present invention;
FIG. 8 is a schematic illustration of a calculation of the abutment layout of the present invention;
FIG. 9 is a first graphical representation of a computational interface and results of a curve layout according to the present invention;
FIG. 10 is a second graphical representation of a curve layout calculation interface and results of the present invention;
FIG. 11 is a drawing according to the calculation result of the curve layout according to the present invention.
Detailed Description
The present invention is described in detail below with reference to the accompanying drawings and examples:
as shown in fig. 1 to 11, a method for calculating the arrangement of precise curves of a railroad bridge comprises the following steps:
step A, inputting initial hole span and mileage information
The input hole span information is generally standard beam span, and can be, but is not limited to, 20 m, 24 m and 32m simply supported beams, and the pure beam lengths are 20.6 m, 24.6 m and 32.6 m respectively. When the holes are arranged in a span mode, the minimum beam seam value is generally only 10cm, so that the initial input intersection point distances are 20.7 meters, 24.7 meters and 32.7 meters. And calculating the route mileage of each pier and abutment position.
Step B, determining the control mileage
A fixed position of a railway bridge is required to be determined at a control engineering position, other holes are arranged in a crossing sequence, and the control mileage is unchanged when the railway bridge is arranged at a subsequent curve.
The basis for determining the control mileage is generally a control work point, such as a gas pipeline position needing to be crossed and a main road traffic position needing to be crossed. In these locations, the pier structure cannot enter the controlled area, and therefore, it is necessary to determine the location as a controlled mileage and calculate the starting point location of the mileage using the determined location as a starting point location of each of the other piers.
Step C, inquiring the initial curve element
And determining curve elements corresponding to each abutment position, such as the radius of the curve, the length of a single line and a double line, a gentle curve, the distance of a straight gentle point and the like.
In the step C, railway line curve elements corresponding to the positions of each pier and each abutment need to be searched, and parameters related to later calculation mainly comprise contents such as curve types (circular curves, easement curves and straight lines), circular curve radiuses, easement curve lengths, distances from ZH points (HZ points), single lines and double lines.
Step D, calculating the single-line offset distance, as shown in fig. 2 and 3
Arranging according to a single-line curve, and calculating the corresponding offset distance, wherein the calculation formula is as follows:
for calculating the offset of a point on a circular curve:
Figure BDA0003116527340000081
substituting the equivalent radius ρ into the formula (1) instead of R for the offset distance of the calculation point on the relaxation curve, wherein the equivalent radius calculation formula is as follows:
Figure BDA0003116527340000091
and for the condition that the continuous beam is connected and the curved beam of the continuous beam is bent, the offset distance is zero.
Note: e is the offset distance, f is the rise, l is the intersection point distance, and R is the radius of the circular curve. t is the distance from the calculated point to the starting point of the transition curve (the straight or gentle straight point), LSIs the length of the gentle curve.
Step E, calculating the single-line beam seam increment as shown in figures 3 and 4
Calculating the corresponding beam seam increment value, wherein the calculation formula is as follows:
adding value to the beam seam of the calculated point on the circular curve:
Figure BDA0003116527340000092
for the offset distance of the calculation point on the relaxation curve, R may be replaced by the equivalent radius ρ.
Note: delta1Added value, Δ, for beam gap caused by string deflection2For added value of beam joint caused by outward shift of deflection anglenAnd delta E is the distance between the intersection points of the n-th hole beam, and the offset distance between the two ends of the calculated beam.
Step F, calculating the single-line deflection angle, as shown in FIG. 5 and FIG. 6
Calculating the corresponding deflection angle, wherein the calculation formula is as follows:
for the case of complete curve elements:
(1) the beam part is on a gentle curve on a straight line
Figure BDA0003116527340000093
(2) The beams all being on a gentle curve
Figure BDA0003116527340000094
(3) The beam portion being on the gentle curve and the beam portion being on the circular curve
Figure BDA0003116527340000095
(4) On the whole circular curve of the beam
Figure BDA0003116527340000101
The deflection angle alpha is the sum of the left and right chord tangent angles at the intersection point of the beam crossing center lines.
For the case where the curve elements are incomplete:
Figure BDA0003116527340000102
wherein: f1～F8For chord tangent angle, t, at each calculated point1、t2The distances from the calculated point to the starting point of the relaxation curve (the straight point or the gentle straight point), respectively. L is the calculated intersection point distance, and K is the length of the beam spanning in the range of the circular curve. K is the length of the beam span within the range of the easement curve, and t is the distance from the starting point (straight point or gentle straight point) of the easement curve to the left side of the beam span.
Step G, calculating intersection point distance 1
And E, adding the beam seam increment delta obtained in the step E to the initial input intersection point distance (namely the data of 20.7 meters, 24.7 meters, 32.7 meters and the like).
Step H, updating the mileage and curve elements of the pier
And D, after the intersection point distance 1 is obtained according to the step G, recalculating to obtain the mileage of each abutment and the curve elements of the corresponding positions.
Step I, calculating the amplification factor, as shown in FIG. 7
The amplification factor is calculated as follows:
Figure BDA0003116527340000103
wherein:
Figure BDA0003116527340000104
is the double line magnification factor, B is the beam width at the calculation point, and s is the line spacing at the calculation point.
Step J, calculating the double-line beam seam increment as shown in FIG. 7
The value-added process of the double-line beam seam is calculated as follows:
if the actual piling line is the left line, if the left line is on the outer side of the curve, the value of the left line beam seam is increased as follows:
Figure BDA0003116527340000105
after the left line is calculated, calculating the beam joint increment of the right line according to the line spacing:
Figure BDA0003116527340000111
wherein: deltaSheetIncrement of beam seam, delta, calculated for the left line as a single lineLeft side of、ΔRight sideThe actual beam seam increment value of the left and right lines in the double lines is shown, and alpha is the deflection angle at the calculated point.
Step K, calculating a new intersection distance 2
Calculating the intersection point distance 2 by adding the value delta of the beam joint obtained in the step JLeft side of、ΔRight sidePlus the initial input intersection distance.
Step L, comparing the intersection point distance 1 with the intersection point distance 2
If the difference value is within the allowable range, the next step is carried out, if the difference value is not within the allowable range, the step H is repeated to carry out the circulation.
The allowable range is 1 mm.
Step M, determining final offset distance, offset angle and beam gap added value
And determining the final intersection point distance and the corresponding position when the difference value between the intersection point distance 1 and the intersection point distance 2 in the step L is within the allowable range. And (4) calculating final offset distance, offset angle and beam gap increment by using the curve elements at the corresponding positions, wherein the calculation formulas are the same as (1) to (11).
Step N, determining the final intersection point distance and bridge pier mileage
And D, calculating to obtain the final intersection point distance and the bridge pier mileage by using the final beam seam increment and offset distance obtained in the step M.
Step O, abutment arrangement, as shown in FIG. 8
When the abutment is arranged, according to the curve position of the front abutment and the tail abutment, and according to the principle of automatic adjustment of the abutment, the arrangement mode is determined:
criterion 1: when the abutment is arranged according to the broken line, the offset distance E of the abutment tail0Calculating the value of the seam delta of the front beam of the platform as 0In front of the table≤ΔMax in front of the tableWhen the abutment is arranged in a straight line, when ΔIn front of the table＞ΔMax in front of the tableThe arrangement of the fold lines is needed. DeltaMax in front of the tableThe value, when d is 10cm, corresponds to the table length l0The value of the platform front beam seam is increased, and the calculation formula is as follows:
Figure BDA0003116527340000121
criterion 2: when the bridge abutment is arranged according to a straight line, the distance from the center of the abutment tail to the central line of the line is d, when d is larger than 10cm, the bridge abutment is arranged according to a broken line, and when d is smaller than or equal to 10cm, the bridge abutment can be arranged according to the straight line.
For the case of bisecting vectors, d takes the following value:
Figure BDA0003116527340000122
for the tangential arrangement, d takes the following values:
Figure BDA0003116527340000123
note: d is the offset of the tail of the platform, l0Is the abutment length, l is the intersection point distance of the beams, and R is the radius of the circular curve. RhocTo mitigate the converted radius of the curve at point C, LsTo moderate the curve length.
Example 1
The method for calculating the precise curve layout of the railway bridge is programmed to calculate the curve layout of a '307-crossing national extra large bridge' of a special extra large bridge for stone economy and passenger.
The bridge is located on a curve which faces to the left of a large mileage, the mileage at a ZH point is DK18+890.66, the mileage at an HZ point is DK20+171.29, the radius of a circular curve is 10000, and the radius of a gentle curve is 430. The bridge hole span arrangement form is as follows: 17-32m simple supported beam +1- (60+100+60) m continuous beam +2-32m simple supported beam +1- (48+80+48) m continuous beam +80-32m simple supported beam.
After calculation, a calculation interface and a calculation result of the No. 13-No. 20 bridge pier are selected for display.
Fig. 9-10 are graphical representations of the calculation process and calculation results for pier nos. 13-20 given by the algorithm of the present invention. As can be seen from the figure, the calculation steps are very clear, and the offset distance, the beam seam increment and the offset angle before and after each pier iteration are given. The left and right line mileage and amplification factor of each pier are also calculated.
Fig. 11 is a "curve layout diagram" drawn based on the results of the curve layout calculation for pier nos. 13 to 20.
As can be seen from the table data in fig. 9 to 10 and the drawings shown in fig. 11, the curved arrangement principle of the railroad bridge is satisfied by each pier arranged through the curve.
The bridge given by the present example is constructed and opened to operate, and the algorithm is also subject to the inspection of actual engineering.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A railway bridge accurate bend arrangement calculation method is characterized by comprising the following steps: the method comprises the following steps:
(A) inputting initial hole span and mileage information
Arranging conventional beam spans according to the requirements of bridges for crossing rivers, roads, pipelines and the like, wherein curve influence is not considered in the arrangement process, and the route mileage corresponds to the position of each pier;
(B) determining a controlling range
Determining a controllability mileage of a fixed position at a controllability project of the railway bridge, and arranging the rest holes in a cross-sequence manner;
(C) querying initial curve elements
Inquiring and determining curve elements corresponding to the positions of all the abutments;
(D) calculating single line offset
Arranging according to a single line curve, and calculating the corresponding offset distance;
(E) calculating single line beam seam increment
Arranging according to a single line curve, and calculating the corresponding beam seam increment;
(F) calculating single line declination
Arranging according to a single line curve, and calculating the corresponding deflection angle;
(G) calculating the intersection distance 1
Adding the added value of the beam joint obtained in the step (E) to the original beam span length to obtain the intersection point distance 1 of each hole beam;
(H) updating mileage and curve elements of pier
After the intersection distance 1 is obtained in the step (G), the position of each abutment is changed, and the mileage of each abutment and the curve element of the new position are obtained again;
(I) calculating the amplification factor
Calculating according to the beam width and the line spacing to obtain an amplification factor;
(J) calculating double line beam seam increment
Calculating the beam seam increment of the double lines by using the beam seam increment calculated by the amplification factor and the single line;
(K) calculate new intersection distance 2
Calculating a new intersection point distance 2 by using the increment of the beam seam of the double lines obtained in the step (J);
(L) comparing intersection distance 1 with intersection distance 2
Comparing the sizes of the intersection point distance 1 and the intersection point distance 2, if the two are close, executing the step (M), if not, returning to the step (H);
(M) determining the final offset, angle and beam gap increments
After iterative convergence, determining the final position of each pier, and then calculating the final offset distance, the offset angle and the beam gap value by using curve elements at the position, wherein the influence of an amplification factor needs to be considered;
(N) determining the final intersection point distance and bridge pier mileage
Calculating the final intersection point distance and bridge pier mileage according to the converged beam seam increment;
(O) abutment arrangement
And determining the arrangement mode according to the curve position of the front platform and the tail platform and the automatic adjustment principle of the bridge platform.
2. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: when the holes in the step (A) are arranged in a crossing mode, the initial input intersection point is the sum of the beam length and the smallest beam seam.
3. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: and (B) in the controllability project, the bridge pier structure cannot enter, and the controllability mileage is used as the starting point position of the mileage calculated by other bridge piers.
4. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: the curve elements in the step (C) comprise curve types, circle curve radiuses, relaxation curve lengths, distances from ZH points to HZ points, and single and double lines.
5. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: in the step (D), the single-line curves are arranged, and the corresponding offset distance is calculated, wherein the calculation formula is as follows:
for calculating the offset of a point on a circular curve:
Figure FDA0003116527330000031
substituting the equivalent radius ρ into the formula (1) instead of R for the offset distance of the calculation point on the relaxation curve, wherein the equivalent radius calculation formula is as follows:
Figure FDA0003116527330000032
for the condition that the continuous beam is connected and the curved beam of the continuous beam is curved, the offset distance is zero;
wherein: e is the offset, f is the rise, L is the intersection point distance, R is the radius of the circular curve, t is the distance from the calculated point to the starting point of the easement curve (the straight or gentle straight point), LSIs the length of the gentle curve.
6. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: in the step (E), the beam seam is arranged according to a single-line curve, and the corresponding beam seam increment is calculated according to the following calculation formula:
adding value to the beam seam of the calculated point on the circular curve:
Figure FDA0003116527330000033
for the offset distance of the calculation point on the relaxation curve, R is replaced by the equivalent radius rho,
wherein: delta1Added value, Δ, for beam gap caused by string deflection2For added value of beam joint caused by outward shift of deflection anglenAnd delta E is the distance between the intersection points of the n-th hole beam, and the offset distance between the two ends of the calculated beam.
7. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: in the step (F), the single-line curves are arranged, and the corresponding deflection angle is calculated, wherein the calculation formula is as follows:
for the case of complete curve elements:
(1) the beam part is on a gentle curve on a straight line
Figure FDA0003116527330000041
(2) The beams all being on a gentle curve
Figure FDA0003116527330000042
(3) The beam portion being on the gentle curve and the beam portion being on the circular curve
Figure FDA0003116527330000043
(4) On the whole circular curve of the beam
Figure FDA0003116527330000044
The deflection angle alpha is the sum of the left and right chord tangent angles at the intersection point of the beam crossing center lines,
for the case where the curve elements are incomplete:
Figure FDA0003116527330000045
wherein: f1～F8For chord tangent angle, t, at each calculated point1、t2Respectively, the distance from the calculation point to the starting point (the straight point or the slow straight point) of the easement curve, L is the distance between the calculation points, K is the length of the beam in the range of the circular curve, K is the length of the beam in the range of the easement curve, and t is the distance from the left side of the beam in the range of the starting point (the straight point or the slow straight point) of the easement curve.
8. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: the formula for calculating the amplification factor in step (I) is as follows:
Figure FDA0003116527330000046
wherein:
Figure FDA0003116527330000051
is the double line magnification factor, B is the beam width at the calculation point, and s is the line spacing at the calculation point.
9. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: the value added process of the double beam seam is calculated in the step (J) as follows:
if the actual piling line is the left line, if the left line is on the outer side of the curve, the value of the left line beam seam is increased as follows:
Figure FDA0003116527330000052
after the left line is calculated, calculating the beam joint increment of the right line according to the line spacing:
Figure FDA0003116527330000053
wherein: deltaSheetIncrement of beam seam, delta, calculated for the left line as a single lineLeft side of、ΔRight sideThe actual beam seam increment value of the left and right lines in the double lines is shown, and alpha is the deflection angle at the calculated point.
10. The method for calculating the precise curve layout of the railway bridge according to claim 1, wherein the method comprises the following steps: in the step (O), the arrangement mode is determined according to the curve position of the front platform and the tail platform and the automatic adjustment principle of the bridge platform when the bridge platform is arranged as follows:
criterion 1: when the abutment is arranged according to the broken line, the offset distance E of the abutment tail0Calculating the value of the seam delta of the front beam of the platform as 0In front of the table≤ΔMax in front of the tableWhen the abutment is arranged in a straight line, when ΔIn front of the table＞ΔMax in front of the tableShould be arranged according to a broken line, ΔMax in front of the tableA value of isd is 10cm, corresponds to the table length l0The value of the platform front beam seam is increased, and the calculation formula is as follows:
Figure FDA0003116527330000054
criterion 2: when the abutment is arranged according to a straight line, the distance from the center of the abutment tail to the central line of the line is d, when d is more than 10cm, the abutment is arranged according to a broken line, when d is less than or equal to 10cm, the abutment can be arranged according to a straight line,
for the case of bisecting vectors, d takes the following value:
Figure FDA0003116527330000061
for the tangential arrangement, d takes the following values:
Figure FDA0003116527330000062
note: d is the offset of the tail of the platform, l0Is the abutment length, l is the intersection distance of the beams, R is the radius of the circular curve, ρcTo mitigate the converted radius of the curve at point C, LsTo moderate the curve length.
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