A method and device for fixed-length loading of live load of a long-span railway bridge

Abstract

The present application relates to the technical field of railway bridge design, and particularly relates to a method and device for fixed-length loading of live load of a large-span railway bridge, which comprises the following steps: loading a moving load track on the bridge by using a moving unit concentrated force method to obtain an influence line of a set parameter; dividing the fixed-length live load into loads of left-end uniform force, middle concentrated force and right-end uniform force; adjusting the setting position of the middle concentrated force end and the length of the left-end uniform force region at each setting position; obtaining the response value of the fixed-length live load corresponding to the setting position of the middle concentrated force end and the length of the left-end uniform force according to the influence line; and taking the most unfavorable loading form corresponding to the response value as a static load working condition to perform a most unfavorable effect nonlinear analysis on the bridge. The method can solve the problem in the prior art that the loading lengths of the left-end and right-end uniform forces are directly assumed to be equal, only an approximate solution can be obtained, and the most unfavorable effect value of the fixed-length live load obtained is inaccurate.

Description

Technical Field

[0001] This invention relates to the field of railway bridge design technology, specifically to a method and apparatus for fixed-length loading of live loads on long-span railway bridges. Background Technology

[0002] The railway bridge and culvert design code specifies an infinitely long live load mode. However, with the increasing span of bridges, which have reached the kilometer level, the bridge span exceeds the actual train length. Trains cannot cover the entire span while running on the bridge, and applying an infinitely long load would result in an overestimation of the load. The railway ZK live load consists of four concentrated forces plus uniformly distributed forces on both sides. If a fixed-length load is adopted, the total length is fixed, but how will the length of the uniformly distributed forces on both sides be distributed? One equation cannot solve for two unknowns. Furthermore, the code stipulates that when the length of the influence line section with opposite signs is greater than 15m, it should be loaded with an empty car live load of 10kN / m. The most unfavorable loading position, the distribution of the loading length of the uniformly distributed forces on both sides, and the loading in the opposite-sign zone must be considered simultaneously to obtain the most unfavorable effect value. However, these factors influence each other, making accurate analysis extremely difficult. Fixed-length loading is a new problem arising from the increasing span of railway bridges, which exceeds the length of trains. Currently, there is no fixed-length live load technology specifically for large-span railway bridges; only simplified methods exist.

[0003] The simplified method avoids the issue of how to distribute the uniformly distributed force lengths on both sides, directly assuming that the loading lengths of the uniformly distributed forces on both sides are equal, thus the loading lengths of the uniformly distributed forces on both sides can be directly determined. Regarding the judgment of loading in areas with different sign indices, the simplified method does not consider the relationship with the loading range of the uniformly distributed force, directly judging the loading area of ​​areas with different sign indices based on the characteristics of the entire influence line. This method has the following problems: the maximum or minimum value does not necessarily occur when the loading lengths of the uniformly distributed forces on both sides are equal; assuming that the lengths of the uniformly distributed forces on both sides are equal cannot accurately find the most unfavorable extreme value, only an approximate solution; in reality, whether to load in areas with different sign indices is related to the loading range of the uniformly distributed force; relying solely on the characteristics of the influence line can lead to misjudgments, causing empty-load loading even when the length of the influence line segment of the area with different sign indices within the loading range is less than 15m, resulting in deviations in the results; the load loading position, the distribution length of the uniformly distributed forces on both sides, and the judgment of loading in areas with different sign indices are not considered simultaneously, thus failing to obtain the most unfavorable extreme value. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this application is to provide a fixed-length loading method and device for live loads on long-span railway bridges. This method solves the problem that existing technologies directly assume that the loading lengths of uniformly distributed forces on both sides are equal, which can only obtain approximate solutions and lead to inaccurate values ​​of the most unfavorable effects of fixed-length live loads.

[0005] To achieve the above objectives, the technical solution adopted in this application is as follows:

[0006] On one hand, the present invention provides a method for fixed-length loading of live load on long-span railway bridges, comprising the following steps:

[0007] The moving load track on the bridge is loaded using a moving unit concentrated force method, and the influence line of the set parameters is obtained;

[0008] The fixed-length live load is divided into a uniformly distributed force region at the left end, a concentrated force region in the middle, and a uniformly distributed force region at the right end.

[0009] Adjust the setting position of the end of the intermediate concentrated force area, and adjust the length of the uniformly distributed force area on the left end at each setting position. Based on the influence line, obtain the response value of a fixed-length live load corresponding to the setting position of the end of the intermediate concentrated force area and the length of the uniformly distributed force area on the left end for different setting positions.

[0010] The loading form corresponding to the most unfavorable response value is used as the static load condition for nonlinear analysis of the most unfavorable effect on the bridge.

[0011] In some optional solutions, the adjustment of the setting position of the end of the intermediate concentrated force region, and the adjustment of the length of the uniformly distributed force region at each setting position, and the obtaining of the response values ​​of a fixed-length live load corresponding to different setting positions of the ends of the intermediate concentrated force region and different lengths of the uniformly distributed force region at the left end according to the influence line, include:

[0012] The end of the central concentrated force region is located at the peak of the influence line;

[0013] The initial value of the length of the uniformly distributed force region at the left end is set to zero. The length of the uniformly distributed force region at the left end is adjusted by a first set length difference to obtain the maximum value among all fixed-length live load response values ​​corresponding to the length of the uniformly distributed force region at the left end obtained by adjusting by the first set length difference. Taking the length of the uniformly distributed force region at the left end corresponding to the maximum value among the fixed-length live load response values ​​obtained by adjusting by the first set length difference as the center, and using the first set length difference as the search range, the length of the uniformly distributed force region at the left end is adjusted by a second set length difference to obtain the maximum value among all fixed-length live load response values ​​corresponding to the length of the uniformly distributed force region at the left end obtained by adjusting by the second set length difference, wherein the second set length difference is less than the first length difference. The position of the end of the intermediate concentrated force region is adjusted, and this step is repeated to obtain the maximum response value of the length of the uniformly distributed force region at the left end corresponding to different positions of the end of the intermediate concentrated force region.

[0014] In some alternative solutions, when adjusting the position of the ends of the intermediate concentrated force region,

[0015] Adjust the position of the end of the intermediate concentrated force area in the positive direction with the first spacing difference until the maximum response value of the fixed-length live load corresponding to the end of the intermediate concentrated force area becomes smaller. Then, adjust the position of the end of the intermediate concentrated force area in the reverse direction with half of the first spacing difference. Continue to adjust the position of the end of the intermediate concentrated force area according to the change of the maximum response value of the fixed-length live load until the maximum response value of the left end of the fixed-length live load uniformly distributed force area corresponding to the position of the end of the intermediate concentrated force area is obtained.

[0016] Adjust the position of the end of the intermediate concentrated force region in the reverse direction by the first spacing difference until the maximum response value of the fixed-length live load corresponding to the end position of the intermediate concentrated force region becomes smaller. Then, adjust the position of the end of the intermediate concentrated force region in the forward direction by half of the first spacing difference. Continue to adjust the position of the end of the intermediate concentrated force region according to the change of the maximum response value of the fixed-length live load until the maximum response value of the uniformly distributed force region on the left end of the fixed-length live load corresponding to the position of the end of the intermediate concentrated force region is obtained.

[0017] In some alternative schemes, when adjusting the length of the uniformly distributed force region at the left end by a first predetermined length difference, and obtaining the maximum value among all the fixed-length live load response values ​​corresponding to the lengths of the uniformly distributed force regions at the left end obtained by adjusting by the first predetermined length difference:

[0018] The length of the uniformly distributed force region at the left end is adjusted by the first set length difference. Each adjustment of the length of the uniformly distributed force region at the left end yields a corresponding fixed-length live load response value. If the current fixed-length live load response value is greater than the previous fixed-length live load response value, the fixed-length live load response value is updated until the length of the uniformly distributed force region at the left end increases to the maximum limit.

[0019] Centered on the length of the left-end uniformly distributed force region corresponding to the maximum value among the fixed-length live load response values ​​obtained by adjusting with the first set length difference, and with the first set length difference as the search range, the length of the left-end uniformly distributed force region is adjusted with the second set length difference to obtain the maximum value among all the fixed-length live load response values ​​corresponding to the length of the left-end uniformly distributed force region obtained by adjusting with the second set length difference:

[0020] The length of the uniformly distributed force region at the left end is adjusted by the second set length difference. Each adjustment of the length of the uniformly distributed force region at the left end yields a corresponding fixed-length live load response value. If the current fixed-length live load response value is greater than the previous fixed-length live load response value, the fixed-length live load response value is updated until the entire search range is searched.

[0021] In some alternative schemes, when the position is set at the end of any intermediate concentrated force region and the length of the uniformly distributed force region at the left end, the response value of the corresponding fixed-length live load is obtained according to the influence line:

[0022] Based on the location of the intermediate concentrated force region and the influence line value at the corresponding location, the response value corresponding to the intermediate concentrated force is obtained;

[0023] Based on the location of the uniform force region on the left end and the influence line, determine the opposite loading region within the uniform force region on the left end, and load the uniform force region on the left end and the opposite loading region according to the influence line to obtain the response value corresponding to the uniform force on the left end.

[0024] Based on the location of the uniformly distributed force region on the right, and in conjunction with the influence line, determine the loading regions with opposite signs within the uniformly distributed force region on the right, and load the uniformly distributed force region on the right and the loading regions with opposite signs according to the influence line, to obtain the response value corresponding to the uniformly distributed force on the right.

[0025] The response values ​​corresponding to the concentrated force in the middle, the uniformly distributed force at the left end, and the uniformly distributed force at the right end are superimposed to obtain the response value of the live load of constant length.

[0026] In some alternative schemes, when the position is set at the end of any intermediate concentrated force region and the length of the uniformly distributed force region at the left end, the response value of the corresponding fixed-length live load is obtained according to the influence line:

[0027] The preset uniformly distributed forces at the left and right ends are both w, and the four concentrated forces in the middle are Q1=Q2=Q3=Q4=Q. The distance between adjacent concentrated forces in the middle is L1, and the distance between the concentrated forces in the middle and the uniformly distributed forces at the left and right ends is L2. The preset loading position of the first concentrated force at the left end is x, and the length of the uniformly distributed force region at the left end is L. x ;

[0028] Determine whether x - L2 - Lx and x - L2 are less than 0.

[0029] If x-L2-Lx is less than 0 and x-L2 is greater than 0, then the loading range of the uniformly distributed force on the left end is updated to 0 to x-L2; if x-L2 is less than 0, then the loading range of the uniformly distributed force on the left end is set to 0.

[0030] Determine whether x+3*L1+L2 and x+L-Lx-L2 are greater than Z. If x+L-Lx-L2 is greater than Z and x+3*L1+L2 is less than Z, then update the loading range of the uniformly distributed force on the right end to x+3*L1+L2~Z. If x+3*L1+L2 is greater than Z, then set the loading range of the uniformly distributed force on the right end to 0.

[0031] If x+L1 is greater than Z, then the concentrated force Q2 is 0; if x+2*L1 is greater than Z, then the concentrated force Q3 is 0; if x+3*L1 is greater than Z, then the concentrated force Q4 is 0. Z is the length of the moving load track, and L is the length of the fixed-length live load.

[0032] In some optional solutions, obtaining the response value corresponding to the intermediate concentrated force based on the location of the intermediate concentrated force region and the influence line value at the corresponding location includes:

[0033] Determine the segments where the four concentrated force positions x, x+L1, x+2*L1, and x+3*L1 are located, and obtain y1, y2, y3, and y4 based on the influence line values ​​of the corresponding positions. Then, calculate the response value of the intermediate concentrated force by superimposing the values.

[0034] In some optional solutions, the determination of the opposite-sign loading area within the left-end uniformly distributed force area based on the setting position of the left-end uniformly distributed force area and the influence line, and the determination of the opposite-sign loading area within the right-end uniformly distributed force area based on the setting position of the right-end uniformly distributed force area and the influence line, both include:

[0035] Calculate the ordinates of all points with a vertical coordinate of 0 within the uniformly distributed force region on the left or right end;

[0036] Calculate the distance l between any two adjacent points based on the ordinates of all points with a vertical coordinate of 0. dj And calculate the influence line value y at the midpoint of each pair of adjacent points. dj ;

[0037] For each pair of adjacent point segments, determine whether it is an area requiring loading of the opposite number zone. If l dj >=l0 and y dj If the value is less than 0, then the segment is a loading area for areas with different numbers, and l0 is the length of the area with different numbers that needs to be loaded.

[0038] In some alternative solutions, the loading of the uniformly distributed force region at the left end based on the influence line, and the loading of the uniformly distributed force region at the right end based on the influence line, include:

[0039] The moving load track is divided into multiple track units;

[0040] The loading range within the uniformly distributed force region is determined based on the relative relationship between each track unit and the uniformly distributed force region.

[0041] Based on the loading range within the uniformly distributed force region and in conjunction with the influence line, the response value of the uniformly distributed force region is obtained.

[0042] In some alternative solutions, when loading regions with different symbols,

[0043] Based on the sign of the influence lines at the ends of the track unit and the uniform force distribution area, determine whether to apply load. If loading is required, determine the response value of the loading area with the opposite sign by combining the influence lines.

[0044] On the other hand, the present invention provides a fixed-length loading device for live loads on long-span railway bridges, comprising the following steps:

[0045] The influence line acquisition module is used to load the moving load track on the bridge using a moving unit concentrated force to acquire the influence line with set parameters.

[0046] The parameter setting module is used to divide a fixed-length live load into a uniformly distributed force region at the left end, a concentrated force region in the middle, and a uniformly distributed force region at the right end.

[0047] The response value solving module is used to adjust the setting position of the end of the intermediate concentrated force region and adjust the length of the uniformly distributed force region on the left end at each setting position. Based on the influence line, the response value of the fixed-length live load corresponding to the setting position of the end of the intermediate concentrated force region and the length of the uniformly distributed force region on the left end is obtained.

[0048] The analysis module is used to perform nonlinear analysis of the most unfavorable effects on the bridge by taking the loading form corresponding to the most unfavorable response value as a static load condition.

[0049] The beneficial effects of the technical solution provided in this application include: it can determine the distribution length of the uniformly distributed force at both ends of the fixed-length live load. Compared with the traditional method of directly specifying the distribution length of the uniformly distributed force at both ends, it can find a more unfavorable length distribution method and calculate the true extreme value of the effect. By taking the loading form corresponding to the most unfavorable response value as the static load condition, the bridge can be subjected to the most unfavorable effect nonlinear analysis, and the final true value of the most unfavorable effect of the fixed-length live load can be obtained. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of a fixed-length loading method for live load on long-span railway bridges, as described in this application.

[0052] Figure 2 This is a schematic diagram of the vertical displacement influence line in an embodiment of this application;

[0053] Figure 3 This is a schematic diagram illustrating the division of the concentrated force in the middle and the distributed forces at both ends in the embodiments of this application;

[0054] Figure 4 This is a schematic diagram of fixed-length live load loading in an embodiment of this application. Detailed Implementation

[0055] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0056] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0057] like Figure 1 As shown in the figure, this application provides a method for fixed-length live load application on a long-span railway bridge, including the following steps:

[0058] like Figure 2 As shown, S1: The moving load track on the bridge is loaded using a moving unit concentrated force to obtain the influence line of the set parameters.

[0059] In this example, parameters are set such as vertical displacement at mid-span, cable force, and bending moment at the base of the tower.

[0060] The left endpoint of the moving load track has a ordinate of 0, and the right endpoint has a ordinate of Z (representing the total span of the bridge), both known based on the structural scale. The moving load track is divided into multiple track units (3 units are sufficient for accuracy; more units can be used). The ordinate of each unit and its corresponding unit number are recorded. The influence line value calculated in step 1 is used to calculate the numerical value y at each unit point using linear interpolation. i (i = 1 to n, where n is the total number of segment points), and determine the segment point number and ordinate corresponding to the maximum value of the influence line. Let the segment point number be k, and the ordinate of that point be x. k .

[0061] S2: The fixed-length live load is divided into a uniformly distributed force region on the left, a concentrated force region in the middle, and a uniformly distributed force region on the right.

[0062] Step S2 specifically includes:

[0063] like Figure 3 and 4 As shown, the fixed-length live load is divided into three parts: a uniformly distributed force at the left end, a concentrated force in the middle, and a uniformly distributed force at the right end. The position of the fixed-length live load is marked by the position of the first concentrated force at the left end. Let the position of the first concentrated force at the left end on the loading track be x. Let the value of the uniformly distributed force be w, and the value of the concentrated force be Q. Let the four concentrated forces Q1 = Q2 = Q3 = Q4 = Q, and the values ​​can be determined according to the specifications or by user customization. Let the loading length of the area with opposite signs be greater than l0, and the load be w0.

[0064] Let the load length be L (determined by the user as needed, and is a constant), and let the length of the uniformly distributed force at the left end be L. x (Unknown quantity), then the length of the uniformly distributed force on the right end is LL. x -4*L1, thus determining the loading range of the uniformly distributed forces at both ends on the beam and the loading positions of the four concentrated forces in the middle on the beam, that is, the loading range of the uniformly distributed force at the left end is x-L2-L. x ~x-L2, the range of the uniformly distributed force on the right end is x+3*L1+L2~x+LL x -L2, the positions of the four concentrated forces in the middle are x, x+L1, x+2*L1, and x+3*L1, respectively. L1 = 1.6 and L2 = 0.8 are the distances between concentrated forces and between a concentrated force and a uniformly distributed force, as specified in the "Railway Bridge and Culvert Design Code". (The remaining text appears to be incomplete and requires further context.) x The load application location and fixed-length distribution method can be determined, x and L x Both are unknowns; the ultimate goal of the search process is to determine x and L, which produce the most unfavorable load effect. x The values ​​of and are coupled and cannot be solved sequentially; they must be determined simultaneously.

[0065] S3: Adjust the setting position of the end of the intermediate concentrated force area, and adjust the length of the uniformly distributed force area on the left end at each setting position. Based on the influence line, obtain the response value of the fixed-length live load corresponding to the setting position of the end of the intermediate concentrated force area and the length of the uniformly distributed force area on the left end.

[0066] Step S3 specifically includes:

[0067] S31: Position the end of the intermediate concentrated force region at the peak of the influence line.

[0068] S32: Set the initial value of the length of the left-end uniformly distributed force region to zero. Adjust the length of the left-end uniformly distributed force region by a first set length difference to obtain the maximum value among all fixed-length live load response values ​​corresponding to the length of the left-end uniformly distributed force region obtained by adjusting the first set length difference. Using the length of the left-end uniformly distributed force region corresponding to the maximum value among the fixed-length live load response values ​​obtained by adjusting the first set length difference as the center, and the first set length difference as the search range, adjust the length of the left-end uniformly distributed force region by a second set length difference to obtain the maximum value among all fixed-length live load response values ​​corresponding to the length of the left-end uniformly distributed force region obtained by adjusting the second set length difference, wherein the second set length difference is less than the first length difference. Adjust the position of the end of the intermediate concentrated force region and repeat this step to obtain the maximum response value of the fixed-length live load left-end uniformly distributed force region length adjustment corresponding to different intermediate concentrated force region end setting positions.

[0069] In some alternative embodiments, when adjusting the position of the end of the intermediate concentrated force region:

[0070] Adjust the position of the end of the intermediate concentrated force region in the positive direction with the first spacing difference until the maximum response value of the fixed-length live load corresponding to the end position of the intermediate concentrated force region becomes smaller. Then, adjust the position of the end of the intermediate concentrated force region in the reverse direction with half of the first spacing difference. Continue to adjust the position of the end of the intermediate concentrated force region according to the change of the maximum response value of the fixed-length live load until the maximum response value of the uniformly distributed force region on the left end of the fixed-length live load corresponding to the position of the end of the intermediate concentrated force region is obtained.

[0071] Specifically, increase the value of x at the end of the concentrated force region by 0.5 each step, and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load until M becomes small. Then stop increasing the x value, decrease it by 0.25, and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load. If the new M value is greater than the result of the previous two steps, increase the x value by 0.125 and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load. If the new M value is only greater than the result of the previous step, decrease the x value by 0.125 and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load. Stop the forward calculation.

[0072] Adjust the position of the end of the intermediate concentrated force region in the reverse direction by the first spacing difference until the maximum response value of the fixed-length live load corresponding to the end position of the intermediate concentrated force region becomes smaller. Then, adjust the position of the end of the intermediate concentrated force region in the forward direction by half of the first spacing difference. Continue to adjust the position of the end of the intermediate concentrated force region according to the change of the maximum response value of the fixed-length live load until the maximum response value of the uniformly distributed force region on the left end of the fixed-length live load corresponding to the position of the end of the intermediate concentrated force region is obtained.

[0073] Specifically, decrease the value of x at the end of the concentrated force region by 0.5 in each step, and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load until the value of M becomes small. Then stop decreasing the value of x and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load. If the new value of M is greater than the result of the previous two steps, decrease the value of x by 0.125 and calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load. If the new value of M is only greater than the result of the previous step, calculate the response value M of all left-end uniformly distributed force regions corresponding to a fixed-length live load. Stop the reverse calculation.

[0074] In some optional embodiments, when adjusting the length of the uniformly distributed force region at the left end by a first predetermined length difference to obtain the maximum value among all the fixed-length live load response values ​​corresponding to the lengths of the uniformly distributed force regions at the left end obtained by adjusting by the first predetermined length difference:

[0075] The length of the uniformly distributed force region at the left end is adjusted by the first set length difference. Each adjustment of the length of the uniformly distributed force region at the left end yields a corresponding fixed-length live load response value. If the current fixed-length live load response value is greater than the previous fixed-length live load response value, the fixed-length live load response value is updated until the length of the uniformly distributed force region at the left end increases to the maximum limit.

[0076] Specifically, the length Lx of the uniformly distributed force region at the left end is searched in large steps. Let the length Lx of the uniformly distributed force region at the left end be 2.0, 4.0, 6.0, ..., L-4*L1, respectively. Each iteration will yield a fixed-length live load response value. After all iterations are completed, the maximum value among all fixed-length live load response values ​​is determined and denoted as M. Alternatively, if the current fixed-length live load response value M is greater than the previous fixed-length live load response value M, the fixed-length live load response value M is updated until the length of the uniformly distributed force region at the left end increases to the maximum limit M. In this example, the maximum limit is L-4*L1.

[0077] Centered on the length of the left-end uniformly distributed force region corresponding to the maximum value among the fixed-length live load response values ​​obtained by adjusting with the first set length difference, and with the first set length difference as the search range, the length of the left-end uniformly distributed force region is adjusted with the second set length difference to obtain the maximum value among all the fixed-length live load response values ​​corresponding to the length of the left-end uniformly distributed force region obtained by adjusting with the second set length difference:

[0078] The length of the uniformly distributed force region at the left end is adjusted by the second set length difference. Each adjustment of the length of the uniformly distributed force region at the left end yields a corresponding fixed-length live load response value. If the current fixed-length live load response value is greater than the previous fixed-length live load response value, the fixed-length live load response value is updated until the entire search range is searched.

[0079] Specifically, a local encrypted search is performed on Lx. Within the range of Lx-2.0 to Lx+2.0 on both sides of Lx where the maximum value occurs, an encrypted search is performed with an interval of 0.25 (or even smaller, such as 0.125), i.e., Lx-2.0+0.25, Lx-2.0+0.5, ..., Lx+2.0-0.25. Each loop will yield a long live load response value. If a value greater than M is found, then M is updated.

[0080] The preset uniformly distributed forces on the left and right ends are both w, and there are four concentrated forces in the middle, Q1=Q2=Q3=Q4=Q. The distance between adjacent concentrated forces in the middle is L1, and the distance between the concentrated forces in the middle and the uniformly distributed forces on the left and right ends is L2. The preset loading position of the first concentrated force on the left end is x, and the length of the uniformly distributed force region on the left end is L. x ;

[0081] Determine whether x - L2 - Lx and x - L2 are less than 0:

[0082] If x-L2-Lx is less than 0 and x-L2 is greater than 0, then the loading range of the uniformly distributed force on the left end is updated to 0 to x-L2; if x-L2 is less than 0, then the loading range of the uniformly distributed force on the left end is set to 0.

[0083] Determine whether x+3*L1+L2 and x+L-Lx-L2 are greater than Z. If x+L-Lx-L2 is greater than Z and x+3*L1+L2 is less than Z, then update the loading range of the uniformly distributed force on the right end to x+3*L1+L2~Z. If x+3*L1+L2 is greater than Z, then set the loading range of the uniformly distributed force on the right end to 0.

[0084] If x+L1 is greater than Z, then the concentrated force Q2 is 0; if x+2*L1 is greater than Z, then the concentrated force Q3 is 0; if x+3*L1 is greater than Z, then the concentrated force Q4 is 0. Z is the length of the moving load track, and L is the length of the fixed-length live load.

[0085] A: Based on the location of the intermediate concentrated force region and the influence line value of the corresponding location, the response value corresponding to the intermediate concentrated force is obtained. Specifically, the segments where the four concentrated force locations x, x+L1, x+2*L1, and x+3*L1 are located are determined, and y1, y2, y3, and y4 are obtained based on the influence line value of the corresponding location. Then, the response value of the intermediate concentrated force is calculated by superimposing these values: Q1*y1 + Q2*y2 + Q3*y3 + Q4*y4.

[0086] B: Based on the location of the uniformly distributed force region on the left end, and in conjunction with the influence line, determine the opposite-sign loading regions within the uniformly distributed force region on the left end, and load the uniformly distributed force region on the left end and the opposite-sign loading regions according to the influence line to obtain the response value corresponding to the uniformly distributed force on the left end.

[0087] C: Based on the location of the uniformly distributed force region on the right end, and in conjunction with the influence line, determine the loading regions with opposite signs within the uniformly distributed force region on the right end, and load the uniformly distributed force region on the right end and the loading regions with opposite signs according to the influence line, to obtain the response value corresponding to the uniformly distributed force on the right end.

[0088] D: The response values ​​corresponding to the concentrated force in the middle, the uniformly distributed force at the left end, and the uniformly distributed force at the right end are superimposed to obtain the response value of the live load of constant length.

[0089] In some optional embodiments, determining the opposite-sign loading area within the left-end uniformly distributed force area based on its location and the influence line, and determining the opposite-sign loading area within the right-end uniformly distributed force area based on its location and the influence line, both include:

[0090] Calculate the ordinates of all points with a vertical coordinate of 0 within either the left or right uniformly distributed force region; based on the ordinates of all points with a vertical coordinate of 0, calculate the distance l between any two adjacent points.dj And calculate the influence line value y at the midpoint of each pair of adjacent points. dj For each pair of adjacent point segments, determine whether it is an area requiring loading of the opposite number zone. If l dj >=l0 and y dj If the value is less than 0, then the segment is a loading area for areas with different numbers, and l0 is the length of the area with different numbers that needs to be loaded.

[0091] In some optional embodiments, the loading of the uniformly distributed force region at the left end based on the influence line, and the loading of the uniformly distributed force region at the right end based on the influence line, include:

[0092] The moving load track is divided into multiple track units; the loading range within the uniformly distributed force region is determined based on the relative relationship between each track unit and the uniformly distributed force region; and the response value of the uniformly distributed force region is obtained based on the loading range within the uniformly distributed force region and the influence line.

[0093] In some optional embodiments, when loading the opposite-sign loading area, the sign of the influence line at the end of the track unit and the end of the uniformly distributed force area is used to determine whether to load. If loading is required, the response value of the opposite-sign loading area is determined in conjunction with the influence line.

[0094] Step A specifically includes:

[0095] Calculate the response values ​​of the four concentrated force loads. Based on the influence line values ​​calculated in step S1, determine the segments containing the four concentrated force positions x, x+L1, x+2*L1, and x+3*L1, and interpolate the influence line values ​​at the corresponding positions to obtain y1, y2, y3, and y4. Then, sum and calculate the concentrated force load effect value Q1*y1 + Q2*y2 + Q3*y3 + Q4*y4. Taking the calculation of y1 as an example, determine the segment containing x from left to right, and find x. i <x<x i+1 x i and x i+1 The corresponding influence line values ​​are y i and y i+1 Then y1 = y i +(y i+1 -y i ) / (x i+1 -x i )*(xx i The other three points are similar.

[0096] Step B specifically includes:

[0097] I) Let x be the positions of the two ends of the uniformly distributed force range on the left. z0 and x z1 Its value is determined based on the length of the uniformly distributed force, the location of the concentrated force, and the distance between the uniformly distributed force and the distributed force.

[0098] II) Determine the areas with opposite loading signs within the track influence line under the uniformly distributed force, and assign an indicator to each segment of each track unit to indicate whether or not to apply loading to these areas. The specific process is as follows: x z0 and x z1 Set the vertical coordinates of all influence lines outside the affected area to 0; calculate the ordinates of all points on the influence line where the vertical coordinate is 0, and label them as x. dj (where j = 1 to m, and m is the total number of zero points); calculate the distance between any two adjacent points, i.e., l dj =x dj+1 -x dj And calculate (x) dj+1 +x dj The influence line value at position ) / 2 is determined segment by segment from left to right (x) dj+1 +x dj Find x in the segment containing ) / 2. i <(x dj+1 +x dj ) / 2 <x i+1 x i and x i+1 The corresponding influence line values ​​are y i and y i+1 The value of the influence line is y. dj =y i +(y i+1 -y i ) / (x i+1 -x i )*((x dj+1 +x dj ) / 2-x i There are a total of m-1 segments; for each of the m-1 segments, determine whether it is a region that needs to be loaded with a different number. If l dj >=l0 and y dj If <0, then the segment is a loading area of ​​the opposite number zone; assign the segment of the track unit covered by the loading area of ​​the opposite number zone to the loading mark of the opposite number zone 1, and load it when considering loading of the opposite number zone, otherwise it is 0; restore the vertical coordinate of the influence line to the original value.

[0099] Ⅲ) Take the first orbital unit, and divide each orbital unit into multiple segments.

[0100] IV) First, for segment 1 of the track unit, calculate the vertical coordinates of the two sides of the segment as x0 and x1, and the vertical coordinates of the influence line as y0 and y1, based on the length of the uniformly distributed force, the location of the concentrated force, and the spacing between the uniformly distributed force and the distributed force.

[0101] V) According to x z0 x z1Based on the relative relationship with x0 and x1, determine the type of this segment. I. When x0 < x z1 <= x1, and x z0 < x0, that is, the left part of the segment is loaded, and it is of type 1; II. When x z1 > x1, and x0 < x z0 < x1, that is, the right part of the segment is loaded, and it is of type 2; III. When x z1 > x1, and x z0 <= x0, that is, the entire segment is loaded, and it is of type 3; IV. When x0 < x z1 <= x1, and x z0 >= x0, that is, the middle part of the segment is loaded, and it is of type 4. After determining the type of the segment, select different calculation methods for the response value according to the type. The calculation methods for the response values of the four types are as follows:

[0102] Type 1: First, calculate the influence line value corresponding to the x z1 point, that is, y z1 = y0 + (y1 - y0) / (x1 - x0)*(x z1 - x0). If y0 > 0 and y z1 < 0, calculate the length from the point where the influence line value between x0 and x z1 is 0 to x0, that is, y0 / (y0 - y z1 )*(x z1 - x0), then the response value is y0 / 2*[y0 / (y0 - y z1 )*(x z1 - x0)]*w; If y0 < 0 and y z1 > 0, calculate the length from the point where the influence line value between x0 and x z1 is 0 to x0, that is, y0 / (y0 - y z1 )*(x z1 - x0), then the response value is y z1 / 2*[x z1 - x0 - y0 / (y0 - y z1 )*(x z1 - x0)]*w; If y0 >= 0 and y z1 >= 0, the influence line length between x0 and x z1 is x z1 - x0, then the response value is (y0 + y z1 ) / 2*(x z1 - x0)*w; If y0 < 0 and y z1 < 0, the response value is 0.

[0103] Type 2: First, calculate the influence line value corresponding to the x z0 point, that is, y z0=y0+(y1-y0) / (x1-x0)*(x z0 -x0). If y1<0 and y z0 If the value is greater than 0, calculate x1 and x2. z0 The influence line between the points with a value of 0 and x z0 The length of y z0 / (y z0 -y1)*(x1-x z0 If ), then the response value is y. z0 / 2*[y z0 / (y z0 -y1)*(x1-x z0 If y1>0 and y z0 If <0, calculate x1 and x. z0 The influence line between the points with a value of 0 and x z0 The length of y z0 / (y z0 -y1)*(x1-x z0 If the response value is y1 / 2*[x1-x], then the response value is y1 / 2*[x1-x]. z0 -y z0 / (y z0 -y1)*(x1-x z0 If y1>=0 and y z0 >=0, x1 and x z0 The length of the influence line between them is x1-x z0 The response value is (y) z0 +y1) / 2*(x1-x z0 )*w; if y1<0 and y z0 If the value is less than 0, the response value is 0.

[0104] Type 3: If y0>0 and y1<0, calculate the length from the point where the influence line value between x0 and x1 is 0 to x0, i.e., y0 / (y0-y1)*(x1-x0), then the response value is y0 / 2*[y0 / (y0-y1)*(x1-x0)]*w; If y0<0 and y1>0, calculate the length from the point where the influence line value between x0 and x1 is 0 to x0, i.e., y0 / (y0-y1)*(x1-x0), then the response value is y1 / 2*[x1-x0-y0 / (y0-y1)*(x1-x0)]*w; If y0>=0 and y1>=0, the influence line length between x0 and x1 is x1-x0, then the response value is (y0+y1) / 2*(x1-x0)*w; If y0<0 and y1<0, then the response value is 0.

[0105] Type 4: First calculate x z1 The influence line value corresponding to the point, i.e., y z1=y0+(y1-y0) / (x1-x0)*(x z1 -x0); then calculate x z0 The influence line value corresponding to the point, i.e., y z0 =y0+(y1-y0) / (x1-x0)*(x z0 -x0). If y z0 >0 and y z1 <0, calculate x z1 and x z0 The influence line between the points with a value of 0 and x z0 The length of y z0 / (y z0 -y z1 )*(x z1 -x z0 If ), then the response value is y. z0 / 2*[y z0 / (y z0 -y z1 )*(x z1 -x z0 )]*w; if y z0 <0 and y z1 If x > 0, calculate x z1 and x z0 The influence line between the points with a value of 0 and x z0 The length of y z0 / (y z0 -y z1 )*(x z1 -x z0 If ), then the response value is y. z1 / 2*[x z1 -x z0 -y z0 / (y z0 -y z1 )*(x z1 -x z0 )]*w; if y z0 >=0 and y z1 If x >= 0, calculate x z1 and x z0 The influence line length between them is x z1 -x z0 The response value is (y) z0 +y z1 ) / 2*(x z1 -x z0 )*w; if y z0 <0 and y z1 If the value is less than 0, the response value is 0.

[0106] VI) Loading in Different Number Zones. Calculate the track unit segments requiring loading in different number zones as determined in step II). Based on the segment type (already determined in step V), select different methods for calculating the response value in different number zones. Segments not requiring loading in different number zones are skipped in this step. The calculation methods for the four types of loading in different number zones are as follows:

[0107] Type 1: If y0 < 0 and y z1 If the value is greater than 0, the response value is y0 / 2*[y0 / (y0-y z1 )*(x z1 -x0)]*w0;If y0>0 and y z1 If the value is less than 0, the response value is y. z1 / 2*[x z1 -x0-y0 / (y0-y z1 )*(x z1 -x0)]*w0;If y0<=0 and y z1 If <= 0, then the response value is (y0 + y z1 ) / 2*(x z1 -x0)*w0; if y0>0 and y z1 If the value is greater than 0, the response value is 0.

[0108] Type 2: If y1>0 and y z0 If the value is less than 0, the response value is y. z0 / 2*[y z0 / (y z0 -y1)*(x1-x z0 If y1 < 0 and y z0 If the value is greater than 0, the response value is y1 / 2*[x1-x]. z0 -y z0 / (y z0 -y1)*(x1-x z0 If y1 <= 0 and y z0 If <= 0, then the response value is (y z0 +y1) / 2*(x1-x z0 )*w0; if y1<0 and y z0 If the value is less than 0, the response value is 0.

[0109] Type 3: If y0 < 0 and y1 > 0, the response value is y0 / 2*[y0 / (y0-y1)*(x1-x0)]*w0; if y0 > 0 and y1 < 0, the response value is y1 / 2*[x1-x0-y0 / (y0-y1)*(x1-x0)]*w0; if y0 <= 0 and y1 <= 0, the response value is (y0+y1) / 2*(x1-x0)*w0; if y0 > 0 and y1 > 0, the response value is 0.

[0110] Type 4: If y z0 <0 and y z1 If the value is greater than 0, then the response value is y. z0 / 2*[y z0 / (y z0 -y z1 )*(x z1 -x z0 )]*w0; if y z0 >0 and y z1 If the value is less than 0, the response value is y. z1 / 2*[x z1 -x z0 -y z0 / (y z0 -y z1 )*(x z1 -x z0 )]*w0; if y z0 <= 0 and y z1 If <= 0, then the response value is (y z0 +y z1 ) / 2*(x z1 -x z0 )*w0; if y z0 >0 and y z1 If the value is greater than 0, the response value is 0.

[0111] VII) Return to IV) and calculate the next segment until all segments of this track unit have been calculated.

[0112] VIII) Return to Ⅲ) and calculate the next orbital unit until all orbital units have been calculated.

[0113] Step C specifically includes:

[0114] I) Let the positions of the two ends of the uniformly distributed force range on the right be x. r0 and x r1 Its value is determined according to step 6.

[0115] II) Determine the areas with opposite loading signs within the track influence line under the uniformly distributed force, and assign an indicator to each segment of each track unit to indicate whether or not to apply loading to these areas. The specific process is as follows: x r0 and x r1 Set the vertical coordinates of all influence lines outside the affected area to 0; calculate the ordinates of all points on the influence line where the vertical coordinate is 0, and label them as x. dj (where j = 1 to m, and m is the total number of zero points); calculate the distance between any two adjacent points, i.e., l dj =x dj+1 -x dj And calculate (x) dj+1 +x dj The influence line value at position ) / 2 is determined segment by segment from left to right (x)dj+1 +x dj Locate x in the segment where ) / 2 is located i <(x dj+1 +x dj ) / 2 < x i+1 , x i and x i+1 The corresponding influence line values are y i and y i+1 , then the influence line value is y dj = y i +(y i+1 -y i ) / (x i+1 -x i )*((x dj+1 +x dj ) / 2 - x i ), a total of m - 1 segments; judge one by one for the m - 1 segments whether they are the areas that need to be loaded in the zone with different signs. If l dj >= l0 and y dj < 0, then this segment is the area to be loaded in the zone with different signs; assign the segments of the track units covered by the area to be loaded in the zone with different signs the identification 1 for loading in the case of considering the loading in the zone with different signs, otherwise 0; restore the vertical coordinates of the influence line to the original values.

[0116] Ⅲ) Take the first track unit and divide the track unit into multiple segments.

[0117] Ⅳ) First, for the 1st segment of this track unit, calculate the vertical coordinates on both sides of this segment as x0 and x1 and the influence line vertical coordinate values y0 and y1 according to the uniform force length, the position where the concentrated force is set, and the spacing between the uniform force and the distributed force.

[0118] Ⅴ) According to the relative relationship between x r0 , x r1 and x0, x1, judge the type of this segment. 1. When x0 < x r1 <= x1, and x r0 < x0, that is, the left part of the segment is loaded, it is type 1; 2. When x r1 > x1, and x0 < x r0 < x1, that is, the right part of the segment is loaded, it is type 2; 3. When x r1 > x1, and x r0 <= x0, that is, the whole segment is loaded, it is type 3; 4. When x0 < x r1 <= x1, and x r0 >= x0, that is, the middle part of the segment is loaded, it is type 4. After judging the type of the segment, select different response value calculation methods according to the type. The response value calculation methods for the four types are as follows:

[0119] Type 1: First calculate x r1 The influence line value corresponding to the point, i.e., y r1 =y0+(y1-y0) / (x1-x0)*(x r1 -x0). If y0>0 and y r1 If <0, calculate x0 and x. r1 The length from the point where the influence line value is 0 to x0, i.e., y0 / (y0-y r1 )*(x r1 -x0), then the response value is y0 / 2*[y0 / (y0-y r1 )*(x r1 -x0)]*w;If y0<0 and y r1 Given x > 0, calculate x0 and x r1 The length from the point where the influence line value is 0 to x0, i.e., y0 / (y0-y r1 )*(x r1 If -x0), then the response value is y. r1 / 2*[x r1 -x0-y0 / (y0-y r1 )*(x r1 -x0)]*w;If y0>=0 and y r1 >=0, x0 and x r1 The length of the influence line between them is x r1 -x0, then the response value is (y0+y r1 ) / 2*(x r1 -x0)*w; if y0<0 and y r1 If the value is less than 0, the response value is 0.

[0120] Type 2: First calculate x r0 The influence line value corresponding to the point, i.e., y r0 =y0+(y1-y0) / (x1-x0)*(x r0 -x0). If y1<0 and y r0 If the value is greater than 0, calculate x1 and x2. r0 The influence line between the points with a value of 0 and x r0 The length of y r0 / (y r0 -y1)*(x1-x r0 If ), then the response value is y. r0 / 2*[y r0 / (y r0 -y1)*(x1-x r0 If y1>0 and y r0 If <0, calculate x1 and x. r0 The influence line between the points with a value of 0 and x r0 The length of y r0 / (y r0 -y1)*(x1-x r0 If the response value is y1 / 2*[x1-x], then the response value is y1 / 2*[x1-x]. r0 -y r0 / (y r0 -y1)*(x1-x r0 If y1>=0 and y r0 >=0, x1 and x r0 The length of the influence line between them is x1-x r0 The response value is (y r0 +y1) / 2*(x1-x r0 )*w; if y1<0 and y r0 If the value is less than 0, the response value is 0.

[0121] Type 3: If y0>0 and y1<0, calculate the length from the point where the influence line value between x0 and x1 is 0 to x0, i.e., y0 / (y0-y1)*(x1-x0), then the response value is y0 / 2*[y0 / (y0-y1)*(x1-x0)]*w; If y0<0 and y1>0, calculate the length from the point where the influence line value between x0 and x1 is 0 to x0, i.e., y0 / (y0-y1)*(x1-x0), then the response value is y1 / 2*[x1-x0-y0 / (y0-y1)*(x1-x0)]*w; If y0>=0 and y1>=0, the influence line length between x0 and x1 is x1-x0, then the response value is (y0+y1) / 2*(x1-x0)*w; If y0<0 and y1<0, then the response value is 0.

[0122] Type 4: First calculate x r1 The influence line value corresponding to the point, i.e., y r1 =y0+(y1-y0) / (x1-x0)*(x r1 -x0); then calculate x r0 The influence line value corresponding to the point, i.e., y r0 =y0+(y1-y0) / (x1-x0)*(x r0 -x0). If y r0 >0 and y r1 <0, calculate x r1 and x r0 The influence line between the points with a value of 0 and x r0 The length of y r0 / (y r0 -y r1 )*(x r1 -x r0 If ), then the response value is y. r0 / 2*[y r0 / (y r0 -yr1 )*(x r1 -x r0 )]*w; if y r0 <0 and y r1 If x > 0, calculate x r1 and x r0 The influence line between the points with a value of 0 and x r0 The length of y r0 / (y r0 -y r1 )*(x r1 -x r0 If ), then the response value is y. r1 / 2*[x r1 -x r0 -y r0 / (y r0 -y r1 )*(x r1 -x r0 )]*w; if y r0 >=0 and y r1 If x >= 0, calculate x r1 and x r0 The influence line length between them is x r1 -x r0 The response value is (y) r0 +y r1 ) / 2*(x r1 -x r0 )*w; if y r0 <0 and y r1 If the value is less than 0, the response value is 0.

[0123] VI) Loading in Different Number Zones. Calculate the segmented units identified in step II) that require loading in different number zones. Based on the segment type (already determined in step V), select different methods for calculating the response value in different number zones. Segments not loaded in different number zones are ignored in this step. The calculation methods for the four types of response values ​​in different number zones are as follows:

[0124] Type 1: If y0 < 0 and y r1 If the value is greater than 0, the response value is y0 / 2*[y0 / (y0-y r1 )*(x r1 -x0)]*w0;If y0>0 and y r1 If the value is less than 0, the response value is y. r1 / 2*[x r1 -x0-y0 / (y0-y r1 )*(x r1 -x0)]*w0;If y0<=0 and y r1 If <= 0, then the response value is (y0 + y r1 ) / 2*(x r1-x0)*w0; if y0>0 and y r1 If the value is greater than 0, the response value is 0.

[0125] Type 2: If y1>0 and y r0 If the value is less than 0, the response value is y. r0 / 2*[y r0 / (y r0 -y1)*(x1-x r0 If y1 < 0 and y r0 If the value is greater than 0, the response value is y1 / 2*[x1-x]. r0 -y r0 / (y r0 -y1)*(x1-x r0 If y1 <= 0 and y r0 If <= 0, then the response value is (y r0 +y1) / 2*(x1-x r0 )*w0; if y1<0 and y r0 If the value is less than 0, the response value is 0.

[0126] Type 3: If y0 < 0 and y1 > 0, the response value is y0 / 2*[y0 / (y0-y1)*(x1-x0)]*w0; if y0 > 0 and y1 < 0, the response value is y1 / 2*[x1-x0-y0 / (y0-y1)*(x1-x0)]*w0; if y0 <= 0 and y1 <= 0, the response value is (y0+y1) / 2*(x1-x0)*w0; if y0 > 0 and y1 > 0, the response value is 0.

[0127] Type 4: If y r0 <0 and y r1 If the value is greater than 0, then the response value is y. r0 / 2*[y r0 / (y r0 -y r1 )*(x r1 -x r0 )]*w0; if y r0 >0 and y r1 If the value is less than 0, the response value is y. r1 / 2*[x r1 -x r0 -y r0 / (y r0 -y r1 )*(x r1 -x r0 )]*w0; if y r0 <= 0 and y r1 If <= 0, then the response value is (y r0 +y r1) / 2*(x r1 -x r0 )*w0; if y r0 >0 and y r1 If the value is greater than 0, the response value is 0.

[0128] VII) Return to IV) and calculate the next segment until all segments of this track unit have been calculated.

[0129] VIII) Return to Ⅲ) and calculate the next orbital unit until all orbital units have been calculated.

[0130] The response values ​​from A to C are summed to obtain the total effect value, and the result is saved to determine the maximum response value for a fixed-length live load.

[0131] S4: The loading form corresponding to the most unfavorable response value is used as a static load case to perform nonlinear analysis of the most unfavorable effect on the bridge.

[0132] The load form that produces the most unfavorable effect value is applied as a static load case to the moving load track, and structural nonlinear calculations are performed. The nonlinear effect value obtained replaces the quasi-linear result of the maximum response value of the fixed-length live load, which is the final true most unfavorable effect value of the ZK live load.

[0133] This solution also provides a fixed-length loading device for live loads on long-span railway bridges, comprising the following steps: influence line acquisition module, parameter setting module, response value solution module, and analysis module.

[0134] The influence line acquisition module is used to load the moving load track on the bridge using a moving unit concentrated force to obtain the influence line of the set parameters; the parameter setting module is used to divide the fixed-length live load into the load of the left end uniform force region, the middle concentrated force region and the right end uniform force region; the response value solving module is used to adjust the setting position of the end of the middle concentrated force region and adjust the length of the left end uniform force region at each setting position, and obtain the response value of the fixed-length live load corresponding to the setting position of the end of the middle concentrated force region and the length of the left end uniform force region according to the influence line; the analysis module is used to perform the most unfavorable effect nonlinear analysis on the bridge as the static load case corresponding to the loading form corresponding to the most unfavorable response value.

[0135] Furthermore, this scheme applies a moving unit concentrated force to the moving load track on the bridge to obtain the influence line of the set parameters. The fixed-length live load is divided into a uniformly distributed force region at the left end, a concentrated force region in the middle, and a uniformly distributed force region at the right end. The setting position of the end of the middle concentrated force region is adjusted, and the length of the uniformly distributed force region at the left end is adjusted at each setting position. Based on the influence line, the response values ​​of the fixed-length live load corresponding to different setting positions of the ends of the middle concentrated force region and different lengths of the uniformly distributed force region at the left end are obtained. The loading form corresponding to the most unfavorable response value is used as a static load case for nonlinear analysis of the most unfavorable effect on the bridge. This method can determine the distribution length of the uniformly distributed force at both ends of the fixed-length live load. Compared with the traditional method of directly specifying the distribution length of the uniformly distributed force at both ends, it can find a more unfavorable length distribution method and calculate the true extreme value of the effect. By using the loading form corresponding to the most unfavorable response value as a static load case for nonlinear analysis of the most unfavorable effect on the bridge, the final true most unfavorable effect value of the fixed-length live load can be obtained.

[0136] Furthermore, when determining whether to load in areas with different numerical values, the loading range of the uniformly distributed force is considered; that is, the loading judgment for areas with different numerical values ​​is nested within the determination of the uniformly distributed force distribution length. Loading is only determined within the influence line area of ​​the uniformly distributed force loading range. Outside the loading range, regardless of whether the influence line segment length of the area with different numerical values ​​is greater than 15m, no loading is performed, which complies with the specifications and actual conditions.

[0137] The load application location, the length of the uniformly distributed force on both sides, and the judgment of the load in the opposite sign area are interconnected, forming three layers: the outer layer determines the load application location on the track, the middle layer is the distribution of the uniformly distributed force length on both sides, and the inner layer handles the load in the opposite sign area. The influence is gradual from the inside to the outside. Multiple factors are considered at the same time and influence each other, so that the most unfavorable extreme value can be obtained.

[0138] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0139] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0140] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for applying a constant load to a live load of a long span railway bridge, characterized in that, The method comprises the following steps: The mobile unit concentrated force is used to load the mobile load track on the bridge to obtain the influence line of the set parameters; The fixed-length live load is divided into a left end uniform force area, a middle concentrated force area and a right end uniform force area; The setting position of the end of the middle concentrated force area is adjusted, and the length of the left end uniform force area is adjusted at each setting position, and the response value of the fixed-length live load corresponding to different setting positions of the end of the middle concentrated force area and different lengths of the left end uniform force area is obtained according to the influence line; The most unfavorable response value is obtained, and the most unfavorable effect nonlinear analysis of the bridge is carried out under the static load working condition of the loading form; When the response value of the fixed-length live load corresponding to the setting position of the end of the middle concentrated force area and the length of the left end uniform force area is obtained according to the influence line: The response value corresponding to the middle concentrated force is obtained according to the setting position of the middle concentrated force area and the influence line value of the corresponding position, which comprises: The segments where the four concentrated force positions x, x+L1, x+2×L1 and x+3×L1 are located are judged, and y1, y2, y3 and y4 are obtained according to the influence line value of the corresponding position, and then the response value of the middle concentrated force is obtained by superimposed calculation Q1×y1+Q2×y2+Q3×y3+Q4×y4; The setting position of the left end uniform force area is combined with the influence line to judge the different sign loading areas in the left end uniform force area, and the response value corresponding to the left end uniform force is obtained by loading the left end uniform force area and the different sign loading areas according to the influence line; The setting position of the right end uniform force area is combined with the influence line to judge the different sign loading areas in the right end uniform force area, and the response value corresponding to the right end uniform force is obtained by loading the right end uniform force area and the different sign loading areas according to the influence line; The response value of the fixed-length live load is obtained by superimposing the response value corresponding to the middle concentrated force, the response value corresponding to the left end uniform force and the response value corresponding to the right end uniform force; When the response value of the fixed-length live load corresponding to the setting position of the end of the middle concentrated force area and the length of the left end uniform force area is obtained according to the influence line: The preset left and right end uniform forces are both w , the middle four concentrated forces are Q1= Q2= Q3= Q4=Q, the distance between adjacent middle concentrated forces is L1, the distance between the middle concentrated force and the left and right end uniform force is L2, the loading position of the first concentrated force at the left end is x, and the length of the left end uniform force region is L x ; Whether x-L2-Lx and x-L2 are less than 0 is judged, If x-L2-Lx is less than 0 and x-L2 is greater than 0, the left end uniform force loading range is updated to 0-x-L2, and if x-L2 is less than 0, the left end uniform force loading range is set to 0; Whether x+3×L1+L2 and x+L-Lx-L2 are greater than Z is judged, if x+L-Lx-L2 is greater than Z and x+3×L1+L2 is less than Z, the right end uniform force loading range is updated to x+3×L1+L2-Z, and if x+3×L1+L2 is greater than Z, the right end uniform force loading range is set to 0; If x+L1 is greater than Z, the concentrated force Q2 is taken as 0, if x+2×L1 is greater than Z, the concentrated force Q3 is taken as 0, if x+3×L1 is greater than Z, the concentrated force Q4 is taken as 0, and Z is the length of the mobile load track and L is the length of the fixed-length live load.

2. The method of claim 1, wherein: The setting position of the end of the intermediate concentrated force area is adjusted, and the length of the left end uniform distribution force area is adjusted at each setting position, according to the influence line, the response value corresponding to the fixed length live load of different setting positions of the end of the intermediate concentrated force area and different lengths of the left end uniform distribution force area is obtained, including: The end of the intermediate concentrated force area is located at the peak value of the influence line; The initial value of the length of the left end uniform distribution force area is set to zero, the length of the left end uniform distribution force area is adjusted by a first set length difference value, the maximum value in the response values corresponding to the fixed length live load of all lengths of the left end uniform distribution force area adjusted by the first set length difference value is obtained, the length of the left end uniform distribution force area corresponding to the maximum value in the response values is taken as the center, the length of the left end uniform distribution force area is adjusted by a second set length difference value in a search range of the first set length difference value, the maximum value in the response values corresponding to the fixed length live load of all lengths of the left end uniform distribution force area adjusted by the second set length difference value is obtained, and the second set length difference value is smaller than the first length difference value; the position of the end of the intermediate concentrated force area is adjusted, and the step is repeated to obtain the maximum response value of the length adjustment of the left end uniform distribution force area corresponding to the fixed length live load at different setting positions of the end of the intermediate concentrated force area.

3. The method of claim 2, wherein, When the position of the end of the intermediate concentrated force area is adjusted, The position of the end of the intermediate concentrated force area is adjusted in a positive direction by a first interval difference value until the maximum response value of the fixed length live load corresponding to the setting position of the end of the intermediate concentrated force area becomes smaller, then the position of the end of the intermediate concentrated force area is adjusted in a reverse direction by half of the first interval difference value, the position of the end of the intermediate concentrated force area is continuously adjusted according to the change of the maximum response value of the fixed length live load, and the maximum response value of the length adjustment of the left end uniform distribution force area corresponding to the fixed length live load at the maximum position of the end of the intermediate concentrated force area is obtained. The position of the end of the intermediate concentrated force area is adjusted in a reverse direction by the first interval difference value until the maximum response value of the fixed length live load corresponding to the setting position of the end of the intermediate concentrated force area becomes smaller, then the position of the end of the intermediate concentrated force area is adjusted in a positive direction by half of the first interval difference value, the position of the end of the intermediate concentrated force area is continuously adjusted according to the change of the maximum response value of the fixed length live load, and the maximum response value of the length adjustment of the left end uniform distribution force area corresponding to the fixed length live load at the maximum position of the end of the intermediate concentrated force area is obtained.

4. The method of claim 2, wherein the method further comprises, When the length of the left end uniform distribution force area is adjusted by the first set length difference value to obtain the maximum value in the response values corresponding to the fixed length live load of all lengths of the left end uniform distribution force area adjusted by the first set length difference value: The length of the left end uniform distribution force area is adjusted by the first set length difference value, and a corresponding response value of the fixed length live load is obtained each time the length of the left end uniform distribution force area is adjusted, if the current response value of the fixed length live load is greater than the previous response value of the fixed length live load, the response value of the fixed length live load is updated until the length of the left end uniform distribution force area increases to a maximum limit value; Centered on the length of the left-end uniformly distributed force region corresponding to the maximum value among the fixed-length live load response values ​​obtained by adjusting with the first set length difference, and with the first set length difference as the search range, the length of the left-end uniformly distributed force region is adjusted with the second set length difference to obtain the maximum value among all the fixed-length live load response values ​​corresponding to the length of the left-end uniformly distributed force region obtained by adjusting with the second set length difference: The length of the uniformly distributed force region at the left end is adjusted by the second set length difference. Each adjustment of the length of the uniformly distributed force region at the left end yields a corresponding fixed-length live load response value. If the current fixed-length live load response value is greater than the previous fixed-length live load response value, the fixed-length live load response value is updated until the entire search range is searched.

5. The method of claim 1, wherein, Based on the location of the uniformly distributed force region on the left and the influence line, the regions with opposite loading signs within the uniformly distributed force region on the left and the regions with opposite loading signs within the uniformly distributed force region on the right, based on the location of the uniformly distributed force region on the right and the influence line, both include: Calculate the ordinates of all points with a vertical coordinate of 0 within the uniformly distributed force region on the left or right end; According to the ordinate of all points with the abscissa 0, the distance between two adjacent points is calculated l dj , and the influence line value y at the position of the midpoint of the corresponding two adjacent points is calculated dj ; For all two two adjacent point section, judge whether it is the area which needs to load the area of different sign, if l dj >= l 0 and y dj <0, the section is the area of different sign loading area, l 0 is the length of different sign area which needs to load.

6. The method of claim 1, wherein, Applying uniformly distributed force to the left-hand side region based on the influence line, and applying uniformly distributed force to the right-hand side region based on the influence line, including: The moving load track is divided into multiple track units; The loading range within the uniformly distributed force region is determined based on the relative relationship between each track unit and the uniformly distributed force region. Based on the loading range within the uniformly distributed force region and in conjunction with the influence line, the response value of the uniformly distributed force region is obtained.

7. A fixed-length loading device for live loads of long-span railway bridges, characterized in that, A fixed-length loading method for implementing live load on long-span railway bridges as described in any one of claims 1-6 includes the following steps: The influence line acquisition module is used to load the moving load track on the bridge using a moving unit concentrated force to acquire the influence line with set parameters. The parameter setting module is used to divide a fixed-length live load into a uniformly distributed force region at the left end, a concentrated force region in the middle, and a uniformly distributed force region at the right end. The response value solving module is used to adjust the setting position of the end of the intermediate concentrated force region and adjust the length of the uniformly distributed force region on the left end at each setting position. Based on the influence line, the response value of the fixed-length live load corresponding to the setting position of the end of the intermediate concentrated force region and the length of the uniformly distributed force region on the left end is obtained. The analysis module is used to perform nonlinear analysis of the most unfavorable effects on the bridge by taking the loading form corresponding to the most unfavorable response value as a static load condition.

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