Arch bridge temperature effect calculation method

Abstract

The invention relates to the technical field of arch bridge construction, operation and maintenance, in particular to an arch bridge temperature effect calculation method which comprises the following steps: S1, acquiring spatial and temporal distribution characteristics of a typical section temperature field of an arch rib, including an average temperature time domain change rule, a vertical temperature difference time domain evolution characteristic and a transverse temperature difference time domain evolution characteristic; s2, on the basis of an average temperature time domain change rule, a structural closure control temperature is combined, and a design value of long-term temperature increasing and decreasing is calculated; on the basis of vertical temperature difference time domain evolution characteristics, locking the most unfavorable time period of the vertical temperature difference, and fitting a vertical temperature difference mode of a typical section; and on the basis of the transverse temperature difference time domain evolution characteristics, locking the most unfavorable time period of the transverse temperature difference, and fitting the transverse temperature difference mode of the typical cross section. According to the method, the defect that subsequent structural design and operation maintenance are lack of accurate and quantitative theoretical support and technical basis due to the fact that an existing bridge design specification does not clearly stipulate an arch bridge temperature calculation method can be overcome.

Description

Technical Field

[0001] This invention relates to the field of arch bridge construction and maintenance technology, and in particular to a method for calculating the effects of temperature on arch bridges. Background Technology

[0002] As the construction of transportation infrastructure continues to advance into the western mountainous areas, long-span concrete arch bridges have become one of the main structural forms for railway bridge construction in these areas due to their superior load-bearing performance, high construction economy, and good landscape coordination. However, the special environment of the mountains brings special temperature and lighting conditions, which cause the arch ribs to be subjected to special temperature effects. In order to avoid irregular deformation of the arch ribs under temperature effects and adverse effects on the bridge deck track alignment, thereby reducing the safety and comfort of train operation, it is of paramount importance to accurately and quantitatively characterize the temperature effect of the arch ribs of arch bridges.

[0003] However, the significant increase in the span of an arch bridge implies an increase in structural dimensions. The structural temperature field is closely related to the structural form and dimensions of the arch bridge. On the one hand, it determines the range and depth of heating; on the other hand, it significantly affects the processes of energy transfer, dissipation, and atmospheric temperature conduction. Furthermore, the structural form of an arch bridge results in a different effect on solar radiation shielding compared to traditional continuous beam bridges. Therefore, the current "Railway Bridge and Culvert Design Code" and "General Highway Bridge and Culvert Design Code" do not explicitly specify the temperature measurement methods and design approaches for large-span reinforced concrete arch bridges and steel truss arch bridges. Existing technologies often only use system heating and cooling to simulate the temporal distribution of structural temperature when designing arch bridge structures, neglecting to consider the spatial non-uniform distribution characteristics. This leads to inaccurate predictions of structural temperature effects, introducing uncertainties for subsequent alignment control, internal force control, and component durability. Therefore, it is urgent to develop a temperature effect calculation method applicable to arch bridges to meet the requirements of subsequent structural design and operation maintenance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing bridge design specifications, which do not clearly stipulate the method for calculating the temperature of arch bridges, resulting in a lack of accurate and quantitative theoretical support and technical basis for subsequent structural design and operation and maintenance. This invention provides a method for calculating the temperature effect of arch bridges.

[0005] In a first aspect, the present invention provides a method for calculating the effect of temperature on an arch bridge, comprising the following steps: S1. Obtain the spatiotemporal distribution characteristics of the temperature field of a typical cross section of the arch rib. The spatiotemporal distribution characteristics of the temperature field include the time-domain variation law of the average temperature, the time-domain evolution characteristics of the vertical temperature difference, and the time-domain evolution characteristics of the transverse temperature difference. S2. Based on the time-domain variation law of average temperature, combined with the temperature control of structural closure, calculate the design values ​​for long-term temperature rise and fall. Based on the temporal evolution characteristics of vertical temperature difference, the most unfavorable period of vertical temperature difference is identified, and the vertical temperature difference pattern of a typical cross section under the most unfavorable period is fitted. Based on the temporal evolution characteristics of transverse temperature difference, the most unfavorable period of transverse temperature difference is identified, and the transverse temperature difference pattern of a typical cross section under the most unfavorable period is fitted.

[0006] Preferably, S1 includes the following steps: The typical cross section was divided into several zones, and the temperature of each zone was monitored. The average temperature of the typical cross section was calculated using the area weighting method. The average temperature of the typical cross section was continuously monitored to obtain the time-domain variation law of the average temperature.

[0007] Preferably, S1 includes the following steps: Several measuring points are arranged on the top and bottom plates of the arch rib at positions corresponding to typical sections, with the measuring points spaced apart along the transverse direction of the bridge. By continuously monitoring the temperature difference between the center measuring point of the top plate and the center measuring point of the bottom plate, the time-domain evolution characteristics of the vertical temperature difference are obtained; by continuously monitoring the temperature difference between the center measuring point and the edge measuring point, the time-domain evolution characteristics of the lateral temperature difference are obtained.

[0008] Preferably, in S2: The most unfavorable periods for vertical temperature difference include the most unfavorable positive vertical temperature difference and the most unfavorable negative vertical temperature difference; the most unfavorable positive vertical temperature difference is the period when the temperature at the center measuring point of the top plate is greater than the temperature at the center measuring point of the bottom plate and the difference is the largest; the most unfavorable negative vertical temperature difference is the period when the temperature at the center measuring point of the bottom plate is greater than the temperature at the center measuring point of the top plate and the difference is the largest. The vertical temperature difference pattern includes a positive vertical temperature difference pattern and a negative vertical temperature difference pattern. The positive vertical temperature difference pattern is obtained by fitting the time-domain evolution characteristics of the vertical temperature difference during the most unfavorable period of positive vertical temperature difference; the negative vertical temperature difference pattern is obtained by fitting the time-domain evolution characteristics of the vertical temperature difference during the most unfavorable period of negative vertical temperature difference.

[0009] Preferably, in S2: The most unfavorable periods for transverse temperature differences include the most unfavorable positive transverse temperature difference and the most unfavorable negative transverse temperature difference. The most unfavorable positive lateral temperature difference is the period when the temperature at the center measuring point is greater than the temperature at the edge measuring points and the difference is the largest; the most unfavorable negative lateral temperature difference is the period when the temperature at the edge measuring points is greater than the temperature at the center measuring point and the difference is the largest. The transverse temperature difference pattern includes a transverse positive temperature difference pattern and a transverse negative temperature difference pattern. The transverse positive temperature difference pattern is obtained by fitting the transverse temperature difference time-domain evolution characteristics during the most unfavorable transverse positive temperature difference period; the transverse negative temperature difference pattern is obtained by fitting the transverse temperature difference time-domain evolution characteristics during the most unfavorable transverse negative temperature difference period.

[0010] Preferably, the method further includes the following steps: S3. Use interpolation or piecewise fitting to fit the vertical and horizontal temperature difference patterns of the arch rib structure between typical cross sections.

[0011] Preferably, in S2, any one of the following distribution functions—exponential, parabolic, and broken line—is used to fit the vertical or horizontal temperature difference pattern.

[0012] Preferably, the exponential distribution function takes the following form:

[0013] In the formula, This represents the temperature difference at the calculation point; α represents the maximum temperature difference along the vertical or horizontal direction of the arch rib; e represents the natural logarithm; α represents the temperature difference decay coefficient; k represents the vertical or horizontal component of the distance from the calculation point to the reference point.

[0014] Preferably, the typical cross-section of the arch rib includes at least one of the arch foot, quarter span, and crown.

[0015] Preferably, the spatiotemporal distribution characteristics of the temperature field of a typical cross-section of the arch rib have an annual cycle.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a method for calculating the temperature effect on arch bridges. Addressing the technical challenge of unclear spatial distribution characteristics of the temperature field in the arch ribs due to the obstruction caused by the bridge deck system, this method constructs a temperature effect calculation system by combining global and local analytical perspectives. This method fills the gap in the current bridge design specifications regarding the value of the temperature effect on the arch ribs of arch bridges, and achieves accurate quantification of the temperature effect during the operation period, providing theoretical support and technical basis for the scientific setting of the temperature effect threshold during the operation phase. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a typical cross-sectional distribution of the method for calculating the temperature effect on an arch bridge according to the present invention; Figure 2 This is a schematic diagram of the measuring point distribution for a method for calculating the temperature effect on an arch bridge according to the present invention. Figure 1 ; Figure 3 This is a schematic diagram of the measuring point distribution for a method for calculating the temperature effect on an arch bridge according to the present invention. Figure 2 ; Figure 4 This is a schematic diagram of the partitioning of a method for calculating the temperature effect on an arch bridge according to the present invention; Figure 5 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 1 ; Figure 6 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 2 ; Figure 7 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 3 ; Figure 8 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 4 ; Figure 9 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 5 ; Figure 10 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 6 ; Figure 11 This is a schematic diagram of the time-domain variation of the average temperature of a typical cross-section. Figure 7 ; Figure 12 This is a schematic diagram illustrating the time-domain variation of the vertical positive temperature difference in a typical cross-section; Figure 13 This is a schematic diagram illustrating the time-domain variation of the vertical negative temperature difference in a typical cross-section; Figure 14 This is a schematic diagram illustrating the time-domain variation of the transverse positive temperature difference in a typical cross-section top plate. Figure 15 This is a schematic diagram illustrating the time-domain variation of the transverse negative temperature difference in a typical cross-section top plate. Figure 16 This is a schematic diagram illustrating the time-domain variation of the transverse positive temperature difference of a typical cross-section base plate; Figure 17 This is a schematic diagram illustrating the time-domain variation of the transverse negative temperature difference of a typical cross-section base plate. Figure 18 This is a schematic diagram of the spatial and temporal distribution of vertical temperature in a typical cross-section during the period of most unfavorable vertical positive temperature difference; Figure 19 This is a schematic diagram of the fitting results for the vertical positive temperature difference mode of a typical cross section; Figure 20 This is a schematic diagram of the spatial and temporal distribution of vertical temperature in a typical cross-section during the period of most unfavorable vertical negative temperature difference; Figure 21 This is a schematic diagram of the fitting results for the vertical negative temperature difference mode of a typical cross section; Figure 22 This is a schematic diagram of the spatiotemporal distribution of transverse temperature in a typical cross section during the period of most unfavorable transverse positive temperature difference; Figure 23 This is a schematic diagram of the spatiotemporal distribution of transverse temperature in a typical cross section during the period of most unfavorable transverse negative temperature difference; icon: 1- Typical cross-section; 2- Temperature sensor; 3- Zone. Detailed Implementation

[0018] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0019] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," and "outer" to indicate orientation or positional relationships in the description of specific embodiments of the present invention is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is typically placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0020] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," and "parallel" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, or parallel, but rather that it can be slightly tilted or have a deviation. For example, "horizontal" merely means that its direction is more horizontal relative to "vertical," not that the structure must be completely horizontal, but that it can be slightly tilted. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," or "parallel" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the present invention.

[0021] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0022] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as 2, 3, 4, 5, 6, 7, 8, or 9, and can even exceed nine.

[0023] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0024] Example 1 like Figures 1 to 23 As shown, a method for calculating the temperature effect on an arch bridge includes the following steps: S1. Based on the global perspective of the arch bridge, select several typical sections 1 along the length of the arch bridge to obtain the spatiotemporal distribution characteristics of the temperature field of each typical section 1, so as to quantitatively characterize the long-term temperature field variation range of the arch rib as a whole; the spatiotemporal distribution characteristics of the temperature field include the time-domain variation law of the average temperature, the time-domain evolution characteristics of the vertical temperature difference, and the time-domain evolution characteristics of the lateral temperature difference.

[0025] S2. Based on the time-domain variation law of average temperature, define the long-term temperature field fluctuation range of the arch rib as a whole, and calculate the design values ​​of long-term temperature rise and fall in combination with the temperature control of structural closure.

[0026] Based on the local scale of the arch bridge, the temperature difference patterns of typical sections 1 of the arch ribs of the quantitative structural member under the most unfavorable time period are as follows: Based on the temporal evolution characteristics of vertical temperature difference, the most unfavorable period of vertical temperature difference is identified, including the identification of the maximum vertical temperature difference, the occurrence period of the maximum vertical temperature difference, and the vertical spatiotemporal distribution characteristics of temperature during the corresponding period; and the vertical temperature difference pattern of typical section 1 is fitted based on the temporal evolution characteristics data of vertical temperature difference during the most unfavorable period.

[0027] Based on the temporal evolution characteristics of transverse temperature difference, the most unfavorable period of transverse temperature difference is identified, including the identification of the maximum transverse temperature difference, the period in which the maximum transverse temperature difference occurs, and the transverse spatiotemporal distribution characteristics of temperature under the corresponding period; the transverse temperature difference pattern of typical section 1 is fitted according to the transverse temperature difference temporal evolution characteristic data under the most unfavorable period.

[0028] After analyzing the structural form of arch bridges, the inventors of this invention discovered that the temperature calculation methods in current bridge design codes are difficult to apply to arch bridges, mainly in the following three aspects: 1. In a long-span, upper-bearing arch bridge, the bridge deck system is separated from the arch ribs. The distance is greatest at the arch foot and smallest at the arch crown. The shielding effect of the bridge deck system on solar radiation has a significant longitudinal difference on the arch ribs.

[0029] 2. The arch rib has no cantilever plates on both sides, and the webs on both sides are directly exposed to solar radiation. In contrast, the box girder of a continuous beam bridge has long cantilever plates on both sides, and the webs are less exposed to direct solar radiation.

[0030] 3. Railway long-span concrete arch bridges mostly adopt the upper-bearing structure system. The degree of solar radiation shading of the bridge deck structure varies greatly along the arch axis. The shading is weakest at the arch foot and strongest at the arch crown, resulting in a non-uniform temperature field along the longitudinal direction of the arch rib and inside its cross section.

[0031] Therefore, this implementation proposes a method for calculating the temperature effect on arch bridges. Addressing the technical challenge of unclear spatial distribution characteristics of the temperature field in the arch ribs due to the obstruction caused by the bridge deck system, this method constructs a temperature effect calculation system using a combined global and local analysis perspective. This system fully reflects the non-uniformity of the temperature field along the longitudinal, transverse, and height directions of the arch bridge. This method fills the gap in current bridge design specifications regarding the determination of temperature effects on the arch ribs of arch bridges, achieving precise quantification of the temperature effect during operation. It provides theoretical support and technical basis for the scientific setting of temperature effect thresholds during the operation phase, and is particularly suitable for long-span, upper-bearing concrete arch bridges.

[0032] In optional implementations, the spatiotemporal distribution characteristics of the temperature field at a typical cross section 1 of the arch rib in S1 can be obtained by means including but not limited to on-site measurement or refined finite element simulation.

[0033] In an optional implementation, the typical section 1 of the arch rib in S1 includes at least one of the arch foot, quarter arch span, and arch crown.

[0034] In optional implementations, the specific form of the spatiotemporal distribution characteristics of the temperature field in S1 includes, but is not limited to, data tables, function expressions, curves, or scatter plots, as long as they can quantitatively characterize the long-term temperature field variation range of the entire arch rib. For example... Figures 5 to 11 As shown, a scatter plot was used to record the changes in the average temperature, vertical temperature difference, and horizontal temperature difference of each typical section 1 over time.

[0035] In an optional implementation, obtaining the spatiotemporal distribution characteristics of the temperature field at a typical cross section 1 of the arch rib in S1 includes the following steps: The typical cross section 1 is divided into several zones 3. At least one temperature sensor 2 is set in each zone 3 to monitor the temperature of each zone 3. The average temperature of the typical cross section 1 is calculated by using the area weighting method, that is, multiplying the temperature value measured by each temperature sensor 2 by the area of ​​its zone 3, summing the results, and then dividing by the total area of ​​the typical cross section 1 to obtain the average temperature of the typical cross section 1 for each time period. The average temperature of the typical cross section 1 is continuously monitored to obtain the time-domain variation law of the average temperature.

[0036] Due to different heating conditions, the temperature distribution within a single typical cross section 1 is uneven. Therefore, in this embodiment, temperature readings at different locations on the typical cross section 1 are first obtained by multiple temperature sensors 2 located in different partitions 3, and then area-weighted calculations are performed to obtain the average temperature. This allows for a more accurate and objective reflection of the true average temperature distribution of the entire typical cross section 1, avoiding errors caused by uneven arrangement of temperature sensors 2 or local temperature anomalies.

[0037] In an optional implementation, the average temperature of typical section 1 is calculated in S1 according to the following formula:

[0038] In the formula, The average temperature of a typical section 1 of the arch rib. This represents the temperature detected by the i-th temperature sensor 2. This represents the area of ​​partition 3 surrounding the i-th temperature sensor 2, where i is the number of the temperature sensor 2, i=1, 2, 3...; and When the unit is taken as degrees Celsius, The unit is square centimeters.

[0039] This embodiment provides a specific formula for calculating the average temperature of a typical section 1.

[0040] In an optional implementation, S1 includes the following steps: Several measuring points are arranged on the top and bottom plates of the arch rib at positions corresponding to typical section 1. The measuring points are distributed at intervals along the transverse direction of the bridge. A temperature sensor 2 is set at each measuring point to obtain the temperature at the corresponding measuring point. The temperature difference between the center measuring point of the top plate and the center measuring point of the bottom plate is continuously monitored to obtain the time-domain evolution characteristics of the vertical temperature difference. The temperature difference between the center measuring point and the edge measuring point is continuously monitored to obtain the time-domain evolution characteristics of the transverse temperature difference.

[0041] In an optional implementation, the layout of measuring points can follow the principle of minimum density, that is, taking the center of the thickness of each arch rib plate as the reference, and arranging measuring points in a staggered manner at intervals of 10~30cm towards the top edge of the top plate, the outer edge of the web plate and the bottom edge of the bottom plate.

[0042] In an optional implementation, the spatiotemporal distribution characteristics of the temperature field at a typical cross-section 1 of the arch rib are based on an annual cycle. That is, the monitoring of the average temperature, vertical temperature difference, and lateral temperature difference of the arch rib in S1 is maintained for at least one year. This can fully reflect the impact of seasonal changes in environmental factors such as air temperature, sunshine, wind force, and rainfall on the temperature field, and avoid deviations in the fitting results of the temperature difference pattern due to short-term monitoring. The sampling period of the spatiotemporal distribution characteristics of the temperature field at a typical cross-section 1 of the arch rib is determined according to the actual accuracy requirements. For example, for cases with high accuracy requirements, the sampling period of the temperature sensor 2 can be set to once every ten minutes. For cases with low accuracy requirements, the sampling period of the temperature sensor 2 can be appropriately extended.

[0043] In an optional implementation, in S2, the most unfavorable period of vertical temperature difference includes the most unfavorable positive vertical temperature difference and the most unfavorable negative vertical temperature difference; the most unfavorable positive vertical temperature difference is the period when the temperature at the center measuring point of the top plate is greater than the temperature at the center measuring point of the bottom plate and the difference is the largest; the most unfavorable negative vertical temperature difference is the period when the temperature at the center measuring point of the bottom plate is greater than the temperature at the center measuring point of the top plate and the difference is the largest.

[0044] The vertical temperature difference pattern includes a positive vertical temperature difference pattern and a negative vertical temperature difference pattern. The positive vertical temperature difference pattern is obtained by fitting the time-domain evolution characteristics of the vertical temperature difference during the most unfavorable period of positive vertical temperature difference; the negative vertical temperature difference pattern is obtained by fitting the time-domain evolution characteristics of the vertical temperature difference during the most unfavorable period of negative vertical temperature difference.

[0045] When the temperature difference between the center measuring point of the top plate and the center measuring point of the bottom plate reverses, the arch rib exhibits different structural deformation and stress distribution patterns. Therefore, this embodiment classifies the vertical temperature difference of the arch bridge into positive and negative vertical temperature differences based on the sign of the temperature difference between the center measuring points of the top plate and the bottom plate. It then fits the positive and negative vertical temperature difference patterns to accurately match the different structural deformation and stress distribution patterns under the two conditions, enabling the fitting results of this embodiment to more accurately reflect the actual working conditions of the arch bridge.

[0046] In an optional implementation, in S2: The most unfavorable periods for transverse temperature differences include the most unfavorable positive transverse temperature difference and the most unfavorable negative transverse temperature difference. The most unfavorable positive lateral temperature difference is the period when the temperature at the center measuring point is greater than the temperature at the edge measuring point, and the difference is the largest; for example, the period when the temperature at the center measuring point of the top plate is greater than the temperature at the edge measuring point of the top plate, or the period when the temperature at the center measuring point of the bottom plate is greater than the temperature at the edge measuring point of the bottom plate. The most unfavorable negative lateral temperature difference is the period when the temperature at the edge measuring point is greater than the temperature at the center measuring point, and the difference is the largest; for example, the period when the temperature at the center measuring point of the top plate is less than the temperature at the edge measuring point of the top plate, or the period when the temperature at the center measuring point of the bottom plate is less than the temperature at the edge measuring point of the bottom plate.

[0047] The transverse temperature difference pattern includes a transverse positive temperature difference pattern and a transverse negative temperature difference pattern. The transverse positive temperature difference pattern is obtained by fitting the transverse temperature difference time-domain evolution characteristics during the most unfavorable transverse positive temperature difference period; the transverse negative temperature difference pattern is obtained by fitting the transverse temperature difference time-domain evolution characteristics during the most unfavorable transverse negative temperature difference period.

[0048] When the temperature difference between the center measuring point and the edge measuring point reverses, the arch rib exhibits different structural deformation and stress distribution patterns. Therefore, this embodiment divides the transverse temperature difference of the arch bridge into transverse positive temperature difference and transverse negative temperature difference based on the sign of the temperature difference between the center measuring point and the edge measuring point. It then fits transverse positive temperature difference patterns and transverse negative temperature difference patterns to accurately match the different structural deformation and stress distribution patterns under the two conditions. This allows the fitting results of this embodiment to more accurately reflect the actual working conditions of the arch bridge.

[0049] In an optional implementation, in S2, depending on the number of measuring points and the size of the sample data, any one of the exponential distribution function, parabolic distribution function, and piecewise linear distribution function can be used to fit the vertical temperature difference pattern or the horizontal temperature difference pattern; for example, when the data volume is small, a piecewise linear distribution function can be used, while when the data volume is large, an exponential distribution function or a parabolic distribution function can be used to obtain a better fitting effect.

[0050] In an optional implementation, the exponential distribution function takes the following form:

[0051] In the formula, This represents the temperature difference at the calculation point; α represents the maximum temperature difference along the vertical or horizontal direction of the arch rib; e represents the natural logarithm; α represents the temperature difference decay coefficient; k represents the vertical or horizontal component of the distance from the calculation point to the reference point. When k represents the vertical component of the distance from the calculation point to the reference point, k can be denoted as y; when k represents the horizontal component of the distance from the calculation point to the reference point, k can be denoted as z.

[0052] In an optional implementation, the following steps are also included: S3. Use interpolation or piecewise fitting to fit the vertical and horizontal temperature difference patterns of the arch rib structure between typical sections 1.

[0053] This embodiment utilizes the continuity of spatial variation of the temperature field and fits the temperature difference pattern of the arch rib structure between typical cross sections 1 based on the data of typical cross section 1. This can reduce the use of temperature sensor 2, thereby reducing the implementation cost of this embodiment.

[0054] The following is a specific example of this embodiment, using an existing arch bridge as an example; the arch bridge is as follows: Figure 1As shown, the bridge is 687.80m long and designed for a speed of 350km / h. The main bridge is a 1-340m upper-bearing reinforced concrete arch bridge with a rise of 74m. The approach bridges and the span arrangement on the arch are as follows: 2-65m T-beams + (30.40m + 2-29.60m + 29.60m)m prestressed concrete continuous beams + (4-29.60m)m prestressed concrete continuous beams + (29.60m + 2-29.60m + 30.40m)m prestressed concrete continuous beams + (44m + 72m + 44m)m prestressed concrete continuous beams. The main beams on the arch are a three-span, 12-span prestressed concrete continuous beam structure. Each span of 4 continuous beams uses C50 concrete. The arch columns are C40 concrete portal frame piers.

[0055] This arch bridge is a double-ribbed basket arch bridge with an upper support. Due to the unique terrain conditions in the mountainous area, uneven solar radiation and temperature differences can cause uncertain deformation of the two arch ribs, which directly affects the bridge deck track alignment and consequently the safety and comfort of train operation. To ensure operational safety and comfort, and to provide a scientific basis for future maintenance and management decisions (such as determining the optimal timing for alignment adjustments and the amount of track adjustment), this example specifically adopts the following steps: SA. Select several typical cross-sections 1, and implement on-site temperature monitoring using a box-type arch rib single box as the basic unit, including the following steps: SA1. To fully reflect the temperature distribution of the box-section arch rib under sunlight at different locations and heights along the longitudinal direction of the bridge, seven temperature test sections were arranged along the longitudinal direction of the arch rib: arch foot, quarter-span, No. 4 column, arch crown, No. 8 column, three-quarters of the arch span, and arch foot. Figure 1 As shown; and the arrangement of temperature sensor 2 is as follows. Figure 2 and Figure 3 As shown.

[0056] SA2. Conduct continuous temperature monitoring for one year, with data sampling intervals set at once every ten minutes.

[0057] SA3. The daily average temperature of each typical section 1 is calculated using the area-weighted method. This involves multiplying the temperature value measured by each temperature sensor 2 by the area of ​​its corresponding zone 3, summing the results, and then dividing by the total area of ​​that typical section 1 to obtain the average temperature of typical section 1 for each time period. Subsequently, a system is established... Figures 5 to 11 The annual time series of daily average temperature of each typical section 1 shown can be analyzed to show that the temperature of each typical section 1 fluctuates between 7℃ and 35℃ with the changing seasons. Combined with the closure temperature of the arch bridge structure being 20℃, the long-term temperature rise and fall values ​​are +15℃ and -13℃, respectively.

[0058] SB, plot the distribution of vertical positive and negative temperature differences over time for each typical section 1, with an annual cycle. For example... Figure 12and Figure 13 The image shows the interannual distribution of vertical positive and negative temperature differences over time for a typical section 1. Based on this, analysis reveals that the most unfavorable vertical positive and negative temperature differences for section 1 occur from July to September and from December to January, respectively. September 5th and January 24th are identified as the periods of the most unfavorable vertical positive and negative temperature differences, respectively. From the temporal evolution characteristics of the vertical temperature difference, we can obtain... Figure 18 and Figure 20 The vertical temperature spatiotemporal distribution data shown are used to establish the corresponding vertical positive temperature difference pattern and vertical negative temperature difference pattern for the corresponding time period using an exponential distribution function fitting, as follows: Vertical positive temperature difference mode:

[0059] Vertical negative temperature difference mode:

[0060] In the formula, represents the temperature difference at the calculation point; e represents the natural logarithm; y represents the vertical component of the distance from the calculation point to the reference point, which is the top surface of typical section 1.

[0061] like Figure 19 and Figure 21 As shown, the fitting results of this example have a good matching effect with the measured values, which can meet the accuracy requirements of subsequent structural design and operation and maintenance.

[0062] Similarly, the vertical positive temperature difference mode and the vertical negative temperature difference mode of other typical sections 1 can be obtained in turn.

[0063] SC, plot the distribution of transverse positive and negative temperature differences over time for each typical section 1, with an annual cycle. For example... Figures 14 to 17 The image shows the interannual distribution of the positive and negative transverse temperature differences over time for a typical section 1. Based on this, it can be analyzed that the most unfavorable positive and negative transverse temperature differences for section 1 occur from July to September and from December to January, respectively. September 5th and January 24th are identified as the periods of the most unfavorable positive and negative transverse temperature differences, respectively. From the temporal evolution characteristics of the transverse temperature differences, the following can be obtained: Figure 22 and Figure 23 The spatiotemporal distribution data of horizontal temperature shown are used to establish the horizontal positive temperature difference pattern and the horizontal negative temperature difference pattern for the corresponding time period using a piecewise linear distribution function, as follows: Lateral positive temperature difference mode:

[0064] Lateral negative temperature difference mode:

[0065] In the formula, represents the temperature difference at the calculation point; z represents the lateral component of the distance from the calculation point to the reference point, which is the center point of the top or bottom plate of the arch rib.

[0066] Similarly, the transverse positive temperature difference mode and transverse negative temperature difference mode of other typical cross-sections 1 can be obtained in turn.

[0067] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the effect of temperature on an arch bridge, characterized in that, Includes the following steps: S1. Obtain the spatiotemporal distribution characteristics of the temperature field of the typical cross section of the arch rib. The spatiotemporal distribution characteristics of the temperature field include the time-domain variation law of the average temperature, the time-domain evolution characteristics of the vertical temperature difference, and the time-domain evolution characteristics of the transverse temperature difference. S2. Based on the time-domain variation law of average temperature, combined with the temperature control of structural closure, calculate the design values ​​for long-term temperature rise and fall. Based on the temporal evolution characteristics of vertical temperature difference, the most unfavorable period of vertical temperature difference is locked, and the vertical temperature difference pattern of typical cross section (1) under the most unfavorable period is fitted. Based on the temporal evolution characteristics of transverse temperature difference, the most unfavorable period of transverse temperature difference is locked, and the transverse temperature difference pattern of typical cross section (1) under the most unfavorable period is fitted.

2. The method for calculating the temperature effect on an arch bridge according to claim 1, characterized in that, S1 includes the following steps: The typical section (1) is divided into several partitions (3), and the temperature of each partition (3) is monitored. The average temperature of the typical section (1) is calculated by the area weighting method. The average temperature of the typical section (1) is continuously monitored to obtain the time-domain variation law of the average temperature.

3. The method for calculating the temperature effect on an arch bridge according to claim 1, characterized in that, S1 includes the following steps: Several measuring points are arranged on the top and bottom plates of the arch rib at positions corresponding to the typical section (1), with the measuring points distributed at intervals along the transverse direction of the bridge. By continuously monitoring the temperature difference between the center measuring point of the top plate and the center measuring point of the bottom plate, the time-domain evolution characteristics of the vertical temperature difference are obtained; by continuously monitoring the temperature difference between the center measuring point and the edge measuring point, the time-domain evolution characteristics of the lateral temperature difference are obtained.

4. The method for calculating the temperature effect on an arch bridge according to claim 3, characterized in that, In S2: The most unfavorable periods for vertical temperature difference include the most unfavorable positive vertical temperature difference and the most unfavorable negative vertical temperature difference; the most unfavorable positive vertical temperature difference is the period when the temperature at the center measuring point of the top plate is greater than the temperature at the center measuring point of the bottom plate and the difference is the largest; the most unfavorable negative vertical temperature difference is the period when the temperature at the center measuring point of the bottom plate is greater than the temperature at the center measuring point of the top plate and the difference is the largest. The vertical temperature difference pattern includes a positive vertical temperature difference pattern and a negative vertical temperature difference pattern. The positive vertical temperature difference pattern is obtained by fitting the time-domain evolution characteristics of the vertical temperature difference during the most unfavorable period of positive vertical temperature difference. The vertical negative temperature difference model is obtained by fitting the time-domain evolution characteristics of the vertical temperature difference during the most unfavorable vertical negative temperature difference period.

5. The method for calculating the temperature effect on an arch bridge according to claim 3, characterized in that, In S2: The most unfavorable periods for transverse temperature difference include the most unfavorable positive transverse temperature difference and the most unfavorable negative transverse temperature difference; the most unfavorable positive transverse temperature difference is the period when the temperature at the center measuring point is greater than the temperature at the edge measuring point and the difference is the largest; the most unfavorable negative transverse temperature difference is the period when the temperature at the edge measuring point is greater than the temperature at the center measuring point and the difference is the largest. The transverse temperature difference pattern includes a transverse positive temperature difference pattern and a transverse negative temperature difference pattern. The transverse positive temperature difference pattern is obtained by fitting the transverse temperature difference time-domain evolution characteristics during the most unfavorable transverse positive temperature difference period. The lateral negative temperature difference model is obtained by fitting the temporal evolution characteristics of the lateral temperature difference during the most unfavorable lateral negative temperature difference period.

6. A method for calculating the temperature effect on an arch bridge according to any one of claims 1 to 5, characterized in that, It also includes the following steps: S3. Use interpolation or piecewise fitting to fit the vertical and horizontal temperature difference patterns of the arch rib structure between typical sections (1).

7. A method for calculating the temperature effect on an arch bridge according to any one of claims 1 to 5, characterized in that, S2 uses any one of the following distribution functions—exponential, parabolic, and broken line—to fit the vertical or horizontal temperature difference pattern.

8. The method for calculating the temperature effect on an arch bridge according to claim 7, characterized in that, The exponential distribution function takes the following form: In the formula, This represents the temperature difference at the calculation point; α represents the maximum temperature difference along the vertical or horizontal direction of the arch rib; e represents the natural logarithm; α represents the temperature difference decay coefficient; k represents the vertical or horizontal component of the distance from the calculation point to the reference point.

9. A method for calculating the temperature effect on an arch bridge according to any one of claims 1 to 5, characterized in that, A typical cross section of an arch rib (1) includes at least one of the arch foot, quarter span, and crown.

10. A method for calculating the temperature effect on an arch bridge according to any one of claims 1 to 5, characterized in that, Typical cross section of arch rib (1) The spatiotemporal distribution characteristics of temperature field with a period of one year.

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