A method for setting pre-camber of a long-span bridge
By constructing a vehicle-track-bridge coupled dynamic model and a finite element model, the precamber curves that offset the dynamic load of the train, environmental factors, and concrete shrinkage and creep are calculated and superimposed. This solves the problem that the existing technology fails to fully consider dynamic interaction and time-varying characteristics, and improves the dynamic performance of long-span bridges under complex environments.
Patent Information
- Application Number
- CN202310220536.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-03-09
- Publication Date
- 2026-02-03
- Estimated Expiration
- 2043-03-09
AI Technical Summary
Existing technologies fail to adequately consider the dynamic interaction between trains and bridges, the time-varying characteristics of ambient temperature, and the time-varying characteristics of concrete shrinkage and creep when setting the pre-camber of long-span bridges, resulting in poor dynamic performance of trains crossing bridges under normal environmental conditions.
By constructing a vehicle-track-bridge coupled dynamic model and a finite element model, the precamber curves that offset the dynamic load of the train, environmental factors, and concrete shrinkage and creep are calculated and superimposed to form the final precamber curve, in order to counteract the influence of these factors.
It ensures the full protection of train dynamics performance under long-term service conditions and improves the stability and ride comfort of the bridge in complex environments.
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Figure CN116401737B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the field of rail transit, and particularly relates to a method for setting pre-camber of a large-span bridge. BACKGROUND
[0002] China is vast in territory and populous in population, and the railway has always played a leading role in the national transportation system. Bridge is an important component of high-speed railway. In the high-speed railway built in China, the total length of the bridge is more than 50%, and most of these bridges use prestressed concrete simply supported box girder with a span of 32 m. At the same time, China has geographical and climatic diversity. In the west, there are dry plateaus, towering mountains, deep and large gorges, and turbulent rivers. In the southeast, there are broad rivers and the sea. To cross the broad water area and the mountain gorge, large-span bridges must also be built.
[0003] When the high-speed train runs on the large-span bridge, compared with the conventional 32m simply supported beam bridge, the large-span bridge will produce larger deformation and severe vibration under the action of train load, which has an important influence on the riding comfort of the train running on the bridge. At the same time, under the influence of environmental factors such as high temperature and concrete shrinkage and creep, the large-span bridge will also produce significant vertical deformation, which will further affect the dynamic performance of the high-speed train. At present, in the actual railway engineering construction, a certain pre-camber (i.e. initial deformation) is usually set for the newly built large-span bridge to offset the bridge deformation caused by train load, environmental temperature load and concrete shrinkage and creep as much as possible, so as to ensure the safety and smoothness of the train passing through the large-span bridge and the comfort of the passengers.
[0004] In the prior art, when setting the pre-camber of the high-speed railway large-span bridge, the bridge deformation caused by the train static live load, the bridge deformation caused by the extreme temperature and the extreme value of the concrete shrinkage and creep after a long time of operation are mainly considered. However, the existing pre-camber setting method only considers the influence of the bridge deformation caused by the train static axle load, does not consider the train-large-span bridge dynamic interaction, and cannot evaluate the influence of train speed on the pre-camber. In addition, the environmental temperature and the bridge concrete shrinkage and creep are time-varying quantities, i.e. they change with time. Generally, the environmental temperature curve has an annual periodicity and presents a sine wave characteristic, while the concrete shrinkage and creep deformation presents a non-linear increasing trend with the increase of service time and tends to be stable after a certain period of time. The existing pre-camber setting method only considers the bridge deformation caused by the extreme environmental temperature and shrinkage and creep to set the pre-camber of the large-span bridge, which can only guarantee the train dynamic performance under extreme conditions, but the extreme conditions are small probability events, and the bridge is in a non-extreme condition for a long time. At this time, this design method is not conducive to the train dynamic performance under the regular environmental conditions. SUMMARY
[0005] In view of the problems in the prior art, the present application provides a large-span bridge pre-camber setting method, which aims to fully consider the dynamic interaction of the vehicle-track bridge, the time-varying characteristics and probability distribution of the environmental temperature, and the time-varying characteristics of the concrete shrinkage and creep, so as to fully guarantee the train over-bridge dynamic performance of the high-speed train under long-term service conditions.
[0006] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is to provide a large-span bridge pre-camber setting method, comprising:
[0007] S1: defining a pre-camber design curve, calculating a pre-camber curve of the large-span bridge for offsetting the train dynamic load or various environmental factors based on the pre-camber design curve, comprising:
[0008] S2: constructing a vehicle-track bridge coupled dynamics model, setting a plurality of pre-camber design curves with different amplitudes based on the pre-camber design curve, and taking them as input excitations of the vehicle-track bridge coupled dynamics model, obtaining each dynamics index through simulation calculation of the vehicle-track bridge coupled dynamics model, analyzing each dynamics index, and obtaining a first pre-camber curve for offsetting the train dynamic load;
[0009] S3: establishing a bridge finite element model through a finite element software, then obtaining deformation data of the bridge generated by environmental factors through the finite element model, and obtaining a deformation pre-camber curve of the large-span bridge for offsetting the environmental factors based on the pre-camber design curve;
[0010] S6: superimposing the first pre-camber curve for offsetting the train dynamic load and the deformation pre-camber curve for offsetting the environmental factors to obtain a final pre-camber curve of the large-span bridge for offsetting the train dynamic load and the environmental factors.
[0011] Preferably, the pre-camber curve of the large-span bridge for offsetting the environmental factors calculated by the present application further comprises:
[0012] S4: calculating the bridge shrinkage and creep deformation amplitude within the bridge service life based on the bridge finite element model of S3, finding out the years when the bridge shrinkage and creep deformation tends to be constant, and calculating a third pre-camber curve for offsetting the bridge shrinkage and creep deformation based on the years.
[0013] Preferably, the pre-camber curve of the large-span bridge for offsetting the environmental factors calculated by the present application further comprises:
[0014] S5: obtaining the bridge long-term monitoring temperature data statistics and analysis based on the bridge finite element model of S3, obtaining the range and joint probability distribution of the bridge temperature load, determining the temperature load combination working conditions according to the range of the temperature load, calculating the bridge temperature-induced deformation of each combination working condition, and calculating the bridge temperature-induced deformation of each combination working condition by using the joint probability distribution of the temperature load to obtain a second pre-camber curve for offsetting the bridge temperature-induced deformation;
[0015] Preferably, in S1 of the present application, the formula of the pre-camber design curve is shown as formula (1):
[0016] (1)
[0017] wherein x is the longitudinal coordinate with the bridge midspan as the origin, A is the amplitude of the upward curve, and L is the length of the main span of the long-span bridge.
[0018] Preferably, in S2 of the present application, the dynamic indexes include wheel-rail force, wheel load reduction rate, vehicle body vibration acceleration, track vibration acceleration, bridge displacement, and bridge vibration acceleration.
[0019] Preferably, in S2 of the present application, the first pre-camber curve for offsetting the train dynamic load is specifically obtained by calculating the root mean square values of each dynamic index, analyzing the change rule of the root mean square values with the pre-camber amplitude, determining the upward curve amplitude A1 at which the root mean square value change rule is minimum, taking the amplitude A1 as the pre-camber curve amplitude, and obtaining the first pre-camber curve for offsetting the train dynamic load, and the formula is shown as formula (2):
[0020] (2).
[0021] Preferably, S5 of the present application is specifically:
[0022] S5.1: establishing a full-size long-span bridge finite element model by using a finite element software;
[0023] S5.2: detecting the environmental temperature at the site where the long-span bridge is planned to be built, analyzing the change characteristics of the environmental temperature with time, and obtaining the change range of the environmental temperature;
[0024] S5.3: establishing a two-dimensional temperature field analysis model of the long-span bridge by using the finite element software;
[0025] S5.4: based on the two-dimensional temperature field analysis model, calculating the temperature data of each key position of the long-span bridge box girder and bridge tower under different environmental temperatures and solar radiation conditions, then statistically analyzing the range of the overall temperature change of the bridge and the range of the temperature gradient of the bridge tower structure, and the joint probability distribution of the two kinds of temperature loads;
[0026] S5.5: according to the range of the temperature load, dividing the overall temperature change and the temperature gradient into m and n determined temperature loads respectively according to the parameter interval;
[0027] S5.6: applying the temperature loads determined in step S5.5 to the bridge finite element model to calculate the temperature-induced deformation of the bridge under m×n kinds of combined working conditions;
[0028] S5.7: The weighted average of the temperature-induced deformation of the bridge under m×n combined working conditions is obtained by using the joint probability distribution of the two temperature loads. Curve S is obtained by inverting curve S. Then, curve S' is fitted, with the precamber curve amplitude as the fitting variable. After fitting, the second precamber curve that offsets the temperature-induced deformation of the bridge is obtained, as shown in equation (3):
[0029] (3).
[0030] Preferably, in S5 of the present invention, the construction of the two-dimensional temperature field analysis model specifically includes: the box girder body is modeled using solid elements, and the air inside and outside the box girder is modeled using fluid elements; the radiation effect of the sun and the air outside the box girder on the outer surface of the box girder is converted into an equivalent temperature value and applied to the model in the form of a temperature boundary; by setting the thermal conductivity of the steel beam and the convective heat transfer coefficient between the air inside and outside the box girder and the box girder, the influence of the ambient temperature on the temperature field inside the box girder is simulated.
[0031] Preferably, the third precamber curve obtained in S4 of the present invention to offset the shrinkage and creep deformation of the bridge is specifically as follows:
[0032] S4.1: Based on the bridge finite element model established in S3, set the parameters related to concrete, and then calculate the shrinkage and creep deformation amplitude of the bridge in each year during its service life.
[0033] S4.2: Taking the year of bridge completion as year 0, find the number of years in which the shrinkage and creep deformation of the bridge tends to remain constant, denoted as N;
[0034] S4.3: Let Zi be the amplitude of bridge shrinkage and creep deformation in year i, and let the pre-camber amplitude be the value to offset the shrinkage and creep deformation. Will make Take the minimum value, that is ;
[0035] S4.4: The third precamber curve that offsets the shrinkage and creep deformation of the bridge is obtained, as shown in equation (4):
[0036] (4).
[0037] Preferably, the present invention superimposes the first precamber curve, the second precamber curve, and the third precamber curve to obtain the final precamber curve for large-span bridges to offset the dynamic load of trains and environmental factors, as shown in equation (5):
[0038] (5).
[0039] Compared with the prior art, the technical solution of the present invention has the following advantages / benefits:
[0040] 1. This invention considers the dynamic interaction between the vehicle and the bridge through a first precamber curve, the time-varying characteristics and probability distribution of the bridge's ambient temperature through a second precamber curve, and the time-varying characteristics of concrete shrinkage and creep through a third precamber curve. The amplitudes of these three precamber curves are superimposed to obtain the final precamber curve for large-span bridges that offsets the dynamic load of trains and environmental factors, so as to fully guarantee the dynamic performance of high-speed trains crossing bridges under long-term service conditions.
[0041] 2. This invention establishes a two-dimensional temperature field analysis model for long-span bridges to simulate the influence of ambient temperature on the temperature field inside the box girder, thereby achieving accurate simulation of the temperature field of long-span bridges under complex environmental conditions. Attached Figure Description
[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.
[0043] Figure 1 This is a flowchart of the pre-camber setting process for long-span bridges according to the present invention;
[0044] Figure 2 This is a schematic diagram of the vehicle-track-bridge coupled dynamics model of the present invention;
[0045] Figure 3 This is a schematic diagram showing the root mean square values of various dynamic indices under different pre-camber amplitudes according to the present invention.
[0046] Figure 4 This is a schematic diagram of the finite element model of the long-span bridge of the present invention;
[0047] Figure 5 This is a schematic diagram of the measured ambient temperature at the bridge site over one year, as presented in this invention.
[0048] Figure 6 This is a schematic diagram illustrating the statistical analysis of the measured ambient temperature in this invention.
[0049] Figure 7 This is a statistical diagram illustrating the amplitude of temperature-induced deformation of bridges according to the present invention.
[0050] Figure 8 This is a schematic diagram illustrating the pre-camber used to offset temperature-induced deformation according to the present invention.
[0051] Figure 9 This is a schematic diagram illustrating the pre-camber used to offset temperature-induced deformation according to the present invention.
[0052] Figure 10 This is a schematic diagram of bridge shrinkage and creep deformation during different service periods according to the present invention;
[0053] Figure 11 This is a schematic diagram of the pre-camber of a long-span bridge according to the present invention. Detailed Implementation
[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention are described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of this invention, not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention. Therefore, the detailed description of the embodiments of this invention provided below is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention.
[0055] Example 1: This example 1 constructs a long-span high-speed railway cable-stayed bridge. The bridge is 570m long, with a main span of 300m and a total tower height of 120.6m above the main span tower base. The flowchart of the method for setting the pre-camber of this long-span bridge is shown below. Figure 1 As shown, including
[0056] S1: Define the pre-camber design curve. The formula for the pre-camber design curve is shown in equation (1):
[0057] (1)
[0058] Where x is the longitudinal coordinate with the mid-span of the bridge as the origin, A is the amplitude of the upper arch curve, and L is the length of the main span of the long-span bridge.
[0059] Then, based on the pre-camber design curve, the pre-camber curve for long-span bridges to offset train dynamic loads or various environmental factors is calculated, including:
[0060] S2: As Figure 2 As shown, a vehicle-track-bridge coupled dynamic model is constructed. Based on the pre-camber design curve, pre-camber design curves with different amplitudes (1mm, 2mm, 3mm…40mm) are set and used as input excitations for the vehicle-track-bridge coupled dynamic model. The model obtains various dynamic indices through simulation calculations, including: wheel-rail force, wheel load reduction rate, vehicle vibration acceleration, track vibration acceleration, bridge displacement, and bridge vibration acceleration. The root mean square values of each dynamic index are calculated, and the results are normalized. Typical calculation results are shown below. Figure 3 As shown. The variation law of the root mean square value with the increase of the pre-camber amplitude is analyzed, and the upper camber curve amplitude A1 with the smallest variation law of the root mean square value is determined. Figure 3From this, we can see that A1 should be 18mm; use it as the amplitude of the precamber curve, and obtain the first precamber curve to offset the dynamic load of the train, the formula of which is shown in equation (2):
[0061] (2).
[0062] In this embodiment 1, when constructing the track-bridge coupled dynamic model, the three-dimensional dynamic behavior of high-speed trains, the spatial flexibility of the track and long-span bridge, and the nonlinear contact characteristics of the wheel and rail are fully considered.
[0063] S3: As Figure 4 As shown, a finite element model of the bridge was constructed using finite element software. Based on long-term monitoring temperature data obtained from on-site measurements, the range and joint probability distribution of the bridge temperature load were obtained. Temperature load combinations were determined according to the range of temperature loads, and the temperature-induced deformation of the bridge under each combination was calculated. The joint probability distribution of the temperature loads was used to calculate the temperature-induced deformation of the bridge under each combination, resulting in a second pre-camber curve to offset the temperature-induced deformation of the bridge. Specifically, S3 is:
[0064] S3.1: Establish a full-size, large-span bridge finite element model using finite element software; the software used in this embodiment 1 is ANSYS, but other finite element software that can be used can also be used.
[0065] S3.2: Conduct environmental temperature monitoring at the site where a long-span bridge is planned to be built, analyze the characteristics of environmental temperature changes over time, and obtain the range of environmental temperature changes; the environmental temperature curve of the long-span bridge site in Example 1 is as follows. Figure 5 As shown;
[0066] S3.3: A two-dimensional temperature field analysis model for a long-span bridge is established using finite element software. The specific construction of the two-dimensional temperature field analysis model includes: modeling the box girder body using solid elements, and modeling the air inside and outside the box girder using fluid elements; the radiation from the sun and the air outside the box girder is converted into equivalent temperature values and applied to the model as temperature boundaries; by setting the thermal conductivity of the steel beam and the convective heat transfer coefficient between the air inside and outside the box girder and the box girder itself, the influence of ambient temperature on the temperature field inside the box girder is simulated. This embodiment 1 achieves accurate simulation of the temperature field of a long-span bridge under complex environmental conditions through a two-dimensional temperature field analysis model.
[0067] S3.4: Based on the two-dimensional temperature field analysis model, calculate the temperature data of key locations of the box girder and tower of the long-span bridge under different ambient temperatures and solar radiation conditions, and then statistically analyze the range of overall temperature change of the bridge and the range of temperature gradient of the tower structure, as well as the joint probability distribution of the two temperature loads.
[0068] S3.5: Based on the range of the temperature load, the overall temperature change and temperature gradient are divided into m and n defined temperature loads according to parameter intervals; in this embodiment 1, m and n are 9 and 7 respectively. Due to the random variation of ambient temperature, the frequency distribution of ambient temperature of long-span bridges is as follows: Figure 6 As shown, different temperatures have different probabilities of occurring, which in turn lead to different probabilities of temperature-induced deformation of the bridge.
[0069] S3.6: Apply the temperature load determined in step S3.5 to the bridge finite element model and calculate the temperature-induced deformation of the bridge under m×n combined load conditions; such as Figure 7 As shown.
[0070] S3.7: The temperature-induced deformation of the bridge under m×n combined working conditions is weighted and averaged using the joint probability distribution of the two temperature loads, as shown in formula (6):
[0071] (6)
[0072] Where x represents the longitudinal position of the bridge alignment. This is the bridge alignment after weighted average. For the temperature load probability of the combined working condition of the i-th temperature gradient and the j-th overall temperature change, the corresponding temperature-induced deformation linear shape is given by... express.
[0073] The weighted average yields curve S, such as Figure 8 As shown, inverting curve S yields curve S', as follows: Figure 9 As shown, the curve S' is then fitted, with the fitting variable being the amplitude of the pre-camber curve. After fitting, the second precamber curve that offsets the temperature-induced deformation of the bridge is obtained, as shown in equation (3):
[0074] (3).
[0075] like Figure 9 As shown, the amplitude of the pre-camber curve for offsetting temperature-induced deformation in the long-span bridge in Example 1 is... =9mm.
[0076] S4: Based on the bridge finite element model in S3, calculate the amplitude of bridge shrinkage and creep deformation during the bridge's service life, identify the number of years in which the bridge shrinkage and creep deformation tends to remain constant, and calculate the third precamber curve to offset the bridge shrinkage and creep deformation based on this number of years. Specifically:
[0077] S4.1: Based on the bridge finite element model established in S3, set concrete-related parameters, including: setting time-dependent material properties for the concrete structure in the model, setting the grade strength of different concrete materials, the average annual relative humidity, the theoretical thickness of the components, the cement type coefficient, and the concrete age at the onset of shrinkage; then calculate the shrinkage and creep deformation amplitude of the bridge each year during its service life; such as... Figure 10 As shown.
[0078] S4.2: Taking the year of bridge completion as year 0, find the number of years in which the shrinkage and creep deformation of the bridge tends to remain constant, denoted as N;
[0079] S4.3: Let Zi be the amplitude of bridge shrinkage and creep deformation in year i, and let the pre-camber amplitude be the value to offset the shrinkage and creep deformation. Will make Take the minimum value, that is ;
[0080] S4.4: The third precamber curve that offsets the shrinkage and creep deformation of the bridge is obtained, as shown in equation (4):
[0081] (4).
[0082] In Example 1, the shrinkage and creep of the long-span bridge exhibits non-linear growth; the deformation amplitude in year 30 is -99.21 mm (the negative sign indicates downward deformation), and the increase thereafter is minimal. Therefore, it is assumed that after N=30 years, the bridge shrinkage and creep deformation tends to remain constant. Thus, it can be calculated that... .
[0083] S5: Camber to offset train dynamic load deformation, temperature-induced deformation, and bridge shrinkage and creep deformation, as well as the total bridge camber considering the above factors, as follows: Figure 11 As shown. By superimposing all the precamber curves obtained above for offsetting train dynamic loads and environmental factors, the final precamber curve for offsetting train dynamic loads and environmental factors of long-span bridges is obtained, as shown in Equation (5):
[0084] (5).
[0085] In the formula, A1+A2+A3=107mm, therefore, the total reasonable precamber of the long-span bridge in this embodiment 1 should be designed to be 107mm. This embodiment 1 is the most preferred implementation method. The final precamber curve is obtained by superimposing the first precamber curve that offsets the deformation caused by train dynamic load, the second precamber curve that offsets the deformation caused by temperature, and the third precamber curve that offsets the deformation caused by bridge shrinkage and creep. However, the final precamber curve obtained by superimposing only the first precamber curve and the second precamber curve or the first precamber curve and the third precamber curve still falls within the protection scope of this invention.
[0086] The above are merely preferred embodiments of the present invention. It should be noted that the above preferred embodiments should not be considered as limitations on the present invention, and the scope of protection of the present invention should be determined by the scope defined in the claims. For those skilled in the art, several improvements and modifications can be made without departing from the spirit and scope of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for setting the pre-camber of a long-span bridge, characterized in that, include: S1: Define the pre-camber design curve. Based on the pre-camber design curve, calculate the pre-camber curve of the long-span bridge to offset the dynamic load of trains or various environmental factors. The formula for the pre-camber design curve is shown in equation (1): (1) Where x is the longitudinal coordinate with the mid-span of the bridge as the origin, A is the amplitude of the upper arch curve, and L is the length of the main span of the long-span bridge; S2: Construct a vehicle-rail-bridge coupled dynamic model. Based on the pre-camber design curve, set several pre-camber design curves with different amplitudes and use them as input excitations for the vehicle-rail-bridge coupled dynamic model. The vehicle-rail-bridge coupled dynamic model obtains various dynamic indicators through simulation calculations. Analyze the dynamic indicators to obtain the first pre-camber curve to offset the dynamic load of the train. The dynamic indicators include: wheel-rail force, wheel load reduction rate, vehicle vibration acceleration, track vibration acceleration, bridge displacement, and bridge vibration acceleration. S3: Establish a finite element model of the bridge using finite element software, then obtain deformation data of the bridge caused by environmental factors through the finite element model, and obtain the deformation precamber curve of the long-span bridge to offset environmental factors based on the precamber design curve. S4: Based on the bridge finite element model of S3, calculate the amplitude of bridge shrinkage and creep deformation during the bridge's service life, find the number of years in which the bridge shrinkage and creep deformation tends to remain constant, and calculate the third precamber curve to offset the bridge shrinkage and creep deformation based on this number of years. S5: Based on the bridge finite element model of S3, obtain and analyze the long-term monitoring temperature data of the bridge to obtain the range and joint probability distribution of the bridge temperature load. Determine the temperature load combination conditions according to the range of temperature load, calculate the bridge temperature-induced deformation of each combination condition, and use the joint probability distribution of temperature load to calculate the bridge temperature-induced deformation of each combination condition to obtain the second precamber curve to offset the bridge temperature-induced deformation. S6: The first precamber curve for offsetting train dynamic load and the deformation precamber curve for offsetting environmental factors obtained above are superimposed to obtain the final precamber curve for offsetting train dynamic load and environmental factors of long-span bridges.
2. The method for setting the pre-camber of a long-span bridge according to claim 1, characterized in that, In S2, the first precamber curve to offset the dynamic load of the train is obtained as follows: the root mean square value of each dynamic index is calculated, the variation law of the root mean square value with the increase of the precamber amplitude is analyzed, the upper camber curve amplitude A1 with the smallest variation law of the root mean square value is determined, and it is taken as the precamber curve amplitude, and the first precamber curve to offset the dynamic load of the train is obtained, and its formula is shown in Equation (2): (2)。 3. The method for setting the pre-camber of a long-span bridge according to claim 2, characterized in that, S5 specifically refers to: S5.1: Establish a full-scale, large-span bridge finite element model using finite element software; S5.2: Conduct environmental temperature monitoring at the site where a long-span bridge is planned to be built, analyze the characteristics of environmental temperature changes over time, and obtain the range of environmental temperature changes; S5.3: Establish a two-dimensional temperature field analysis model for long-span bridges using finite element software; S5.4: Based on a two-dimensional temperature field analysis model, calculate the temperature data of key locations of the box girder and tower of a long-span bridge under different ambient temperatures and solar radiation conditions. Then, statistically analyze the range of overall temperature change of the bridge and the range of temperature gradient of the tower structure, as well as the joint probability distribution of the two temperature loads. S5.5: Based on the range of the temperature load, the overall temperature change and temperature gradient are divided into m and n determined temperature loads according to the parameter intervals, respectively. S5.6: Apply the temperature load determined in step S5.5 to the bridge finite element model and calculate the temperature-induced deformation of the bridge under m×n combined working conditions; S5.7: The combined probability distribution of the two temperature loads is used to perform a weighted average of the bridge temperature-induced deformation under m×n combined working conditions to obtain curve S. Curve S' is obtained by inverting curve S. Then curve S' is fitted with the precamber curve amplitude A2 as the fitting variable. After fitting, the second precamber curve that offsets the bridge temperature-induced deformation is obtained, as shown in equation (3): (3)。 4. The method for setting the pre-camber of a long-span bridge according to claim 3, characterized in that, In S5, the construction of the two-dimensional temperature field analysis model specifically includes: the box girder body is modeled using solid elements, and the air inside and outside the box girder is modeled using fluid elements; the radiation effect of the sun and the air outside the box girder on the outer surface of the box girder is converted into an equivalent temperature value and applied to the model in the form of a temperature boundary; by setting the thermal conductivity of the steel beam and the convective heat transfer coefficient between the air inside and outside the box girder and the box girder, the influence of the ambient temperature on the temperature field inside the box girder is simulated.
5. The method for setting the pre-camber of a long-span bridge according to claim 1, characterized in that, The third precamber curve obtained in S4 to offset the shrinkage and creep deformation of the bridge is as follows: S4.1: Based on the bridge finite element model established in S3, set the parameters related to concrete, and then calculate the shrinkage and creep deformation amplitude of the bridge in each year during its service life. S4.2: Taking the year of bridge completion as year 0, find the number of years in which the shrinkage and creep deformation of the bridge tends to remain constant, denoted as N; S4.3: Let the amplitude of bridge shrinkage and creep deformation in year i be Zi, and the pre-camber amplitude A3 to offset the shrinkage and creep deformation will make Take the minimum value, that is ; S4.4: The third precamber curve that offsets the shrinkage and creep deformation of the bridge is obtained, as shown in equation (4): (4)。 6. A method for setting the pre-camber of a long-span bridge according to any one of claims 1-5, characterized in that, The first precamber curve, the second precamber curve, and the third precamber curve are superimposed to obtain the final precamber curve of the long-span bridge to offset the dynamic load of trains and environmental factors, as shown in Equation (5): (5)。
Citation Information
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