Wing-plate-free steel box girder bridge temperature fatigue load spectrum and construction method

Abstract

The invention discloses a temperature fatigue load spectrum of a wing-plate-free steel box girder bridge and a construction method. The temperature fatigue load spectrum comprises six vertical temperature sub-gradients and occurrence probabilities thereof and six transverse temperature sub-gradients and occurrence probabilities thereof. Temperature measuring point arrangement and long-term temperature field monitoring are carried out according to structural characteristics and temperature field distribution characteristics of the wing-plate-free steel box girder, temperature fatigue stress analysis is carried out, and vertical and transverse temperature fatigue load spectrums of the wing-plate-free steel box girder bridge suitable for 100-year, 150-year and 200-year design service life are provided by adopting a reasonable clustering algorithm. The provided temperature fatigue load spectrum can provide a basis for temperature fatigue damage analysis, and the problem that a wing-plate-free steel box girder bridge temperature fatigue load spectrum is lacked in steel bridge anti-fatigue design is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a thermal fatigue load spectrum and a construction method of a flangeless steel box girder bridge. Background Art

[0002] The flangeless steel box girder is a typical closed section form. Due to its special section form, the web of the flangeless steel box girder will be directly exposed to the sun, resulting in a more complex transverse and vertical temperature gradient. The flangeless steel box girder will produce longitudinal temperature fatigue stress under the action of vertical nonlinear temperature gradient. Due to the frame effect of the closed section, the transverse temperature gradient will cause transverse temperature fatigue stress in the flangeless steel box girder section. The temperature action of the flangeless steel box girder includes the cyclic action of daily temperature difference and seasonal temperature difference, and the temperature fatigue action can be characterized in the form of temperature gradient fatigue load spectrum. Therefore, in order to meet the anti-fatigue design requirements of flangeless steel box girder bridges, vertical and transverse temperature gradient fatigue load spectra suitable for flangeless steel box girder bridges with a design service life of 200 years should be proposed. Summary of the invention

[0003] The technology to be solved by the present invention is to provide a thermal fatigue load spectrum and construction method for a flangeless steel box girder bridge that can be used for 150-year or 200-year long-life design or fatigue life assessment.

[0004] The technical solution adopted to solve the above technical problems is: a temperature fatigue load spectrum of a flangeless steel box girder bridge, which includes a vertical temperature gradient fatigue load spectrum and a transverse temperature gradient fatigue load spectrum; the vertical temperature gradient fatigue load spectrum is composed of 6 vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0005]

[0006] Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, h is the cross-sectional height of the steel box girder bridge without flange plate, Gi is the ith vertical temperature sub-gradient, T Gi,1 、T Gi,2 、T Gi,3 are the representative values ​​of the temperature at the top plate of the steel box girder, at the height of 0.86h, and at the bottom plate of the steel box girder in the i-th vertical temperature sub-gradient, in °C. G1,1 、T G1,2 、T G1,3 are the representative values ​​of the temperature at the top plate of the steel box girder, at a height of 0.86h, and at the bottom plate of the steel box girder in the first vertical temperature sub-gradient, T G1,1 The value range is [3.3,6.2], the unit is ℃, T G1,2 The value range is [4.8,7.4], the unit is ℃, TG1,3 The value range is [0.3,3.2], the unit is ℃, T Gi,j is the temperature representative value at the jth typical height in the ith vertical temperature sub-gradient, N d is the design service life, T G1,j is the temperature representative value at the jth typical height in the first vertical temperature sub-gradient, P(T G1 (y))、P(T G2 (y))、P(T G3 (y))、P(T G4 (y))、P(T G5 (y))、P(T G6 (y)) are the occurrence probabilities of the six vertical temperature sub-gradients within the design service life, T G1,1 、T G2,1 、T G3,1 、T G4,1 、T G5,1 、T G6,1 They are the representative values ​​of the temperature at the top plate of the steel box girder in the six vertical temperature sub-gradients;

[0007] The transverse temperature gradient fatigue load spectrum is composed of six transverse temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0008]

[0009] Where, T Hq (x) is the temperature of the qth transverse temperature sub-gradient at position x, L is the width of the steel box girder without flange, Hq is the qth transverse temperature sub-gradient, T Hq,1 、T Hq,2 、T Hq,3 are the representative values ​​of the temperature at the edge of the sunny side, the position 0.6L near the sunny side, and the edge of the shady side in the transverse temperature sub-gradient of the qth flangeless steel box girder bridge, in °C, T H1,1 、T H1,2 、T H1,3 are the representative values ​​of the temperature at the edge of the sun side, the position close to 0.6L on the sun side, and the edge of the sun side in the first transverse temperature sub-gradient, T H1,1 The value range is [8.6,11.2], the unit is ℃, T H1,2 The value range is [7.6,10.1], the unit is ℃, T H1,3 The value range is [8.4,12.2], the unit is ℃, T Hq,w is the temperature representative value at the wth typical position in the qth transverse temperature sub-gradient, N d is the design service life, T H1,wis the temperature representative value at the wth typical position in the first transverse temperature sub-gradient, P(T H1 (x))、P(T H2 (x))、P(T H3 (x))、P(T H4 (x))、P(T H5 (x))、P(T H6 (x)) are the occurrence probabilities of the six transverse temperature sub-gradients within the design service life, T H1,1 、T H2,1 、T H3,1 、T H4,1 、T H5,1 、T H6,1 They are the representative values ​​of temperature at the edges of the positive side of the six lateral temperature sub-gradients.

[0010] The present invention also provides a method for constructing a thermal fatigue load spectrum of a flangeless steel box girder bridge, comprising the following steps:

[0011] Step 1: Collect temperature data of steel box girder bridge without flange:

[0012] A total of m measuring points are arranged on the flangeless steel box girder bridge. The temperature values ​​of each measuring point are collected at regular intervals to obtain the measured temperature gradient time history curve at each position. The measured temperature gradient time history curve is extended to the design service life N through the long short memory recurrent neural network. d The temperature history at typical locations is used to obtain the maximum daily temperature at each measuring point every day within the design service life, and the design service life daily temperature extreme value matrix Q = [M1, M2, …, M t ,…,M Nd×365 ],M t is the daily temperature maximum vector of each measuring point on the tth day, y1 is the position coordinate of the first temperature measurement point, y m is the position coordinate of the mth temperature measurement point, is the maximum temperature value of the first temperature measurement point on the tth day, is the maximum temperature value of the mth temperature measurement point on the tth day;

[0013] Step 2: Use Kmeans++ algorithm to determine the initial cluster centers and cluster families:

[0014] Step 2.1: Define the number of clusters as c l , randomly select a vector from the design service life daily temperature extreme value matrix Q as the first initial cluster center, obtain the Manhattan distance between other vectors in the design service life daily temperature extreme value matrix Q and the first initial cluster center according to the Manhattan distance calculation method, and select the vector with the largest Manhattan distance to the first initial cluster center as the second initial cluster center;

[0015] Step 2.2, according to the Manhattan distance calculation method, calculate the sum of the Manhattan distances between each vector in the design service life daily temperature extreme value matrix Q except the determined initial cluster center and all the determined initial cluster centers, and select the vector with the largest sum of Manhattan distances as the next initial cluster center;

[0016] Step 2.3, repeat step 2.2 until c is selected l Initial cluster centers and construct c l Initial clusters;

[0017] Step 3: Divide the vectors in the daily temperature extreme value matrix Q of the design service life into clusters:

[0018] According to the Manhattan distance calculation method, each vector in the daily temperature extreme value matrix Q of the design service life is obtained from the distance between c l The Manhattan distance of the initial clustering centers is used to divide each vector in the daily temperature extreme value matrix Q of the design service life into the initial clustering group corresponding to the initial clustering center with the smallest Manhattan distance;

[0019] Step 4: Update the clustering family:

[0020] The vector obtained by averaging all vector points in each cluster family is used as the virtual new cluster center of each cluster family, and the Manhattan distance D between the virtual new cluster center of each cluster family and its old cluster center is calculated. v , Manhattan distance D v ≤ set threshold D th The cluster center of the cluster family remains unchanged, and the Manhattan distance D v > Set threshold D th The virtual new cluster center is used as the new cluster center, and step 3 is repeated to update the cluster center until the Manhattan distance D between the virtual new cluster center and its old cluster center of all cluster centers is v ≤ set threshold D th , get the final cluster family;

[0021] Step 5: Determine the number of reasonable clusters c l :

[0022] Let the number of clusters cl be an integer from 2 to 10, and follow steps 2 and 3 to get the corresponding number of clusters c. l The 9 final clustering families are obtained. The cluster centers of each final clustering family constitute the cluster center matrix. The residual square sum RMSE of the maximum residual daily temperature is obtained according to the following formula for each cluster center matrix. l -RMSE two-dimensional line chart, based on the elbow rule, determine the optimal number of clusters c l =6;

[0023]

[0024] In the formula, is the kth row vector in the cluster center matrix;

[0025] Step 6: Determine the temperature fatigue load spectrum:

[0026] Use the number of clusters c determined in step 5 l And the corresponding cluster center matrix C end , each cluster family is a temperature sub-gradient, the row vector of the cluster center matrix is ​​the typical representative value of each temperature sub-gradient, and the number of sample points in each cluster family divided by the total number is the occurrence probability of each temperature sub-gradient, thereby obtaining the corresponding temperature fatigue load spectrum of the flangeless steel box girder bridge.

[0027] Preferably, the threshold D th The value range is [0.00005,0.01].

[0028] Preferably, the m measuring points in step 1 are used to construct a vertical temperature fatigue load spectrum, and the arrangement method is: one measuring point is arranged on the upper surface of the bottom plate of the flangeless steel box girder bridge, and the measuring point is used as the coordinate origin, and measuring points are arranged on the middle web and the top plate along the vertical height direction, and a total of m=11 measuring points are arranged. The positions of the measuring points are expressed as 0.00m, h-3.15m, h-2.15m, h-1.65m, h-1.15m, h-0.65m, h-0.35m, h-0.25m, h-0.15m, h-0.05m, h-0.

[0029] Preferably, the m measuring points in step 1 are used to construct the transverse temperature fatigue load spectrum, and the arrangement method is: a measuring point is arranged at the edge of the positive side of the top plate, and the measuring point is used as the coordinate origin, and a total of m=4 measuring points are arranged along the width direction of the top plate, and the positions of the measuring points are expressed as 0.00m, L-10.35m, L-5.35m, and L-15.75m in terms of the horizontal distance from the coordinate origin.

[0030] Preferably, the temperature values ​​of each measuring point in step 1 are collected at intervals of 60 to 1200 seconds.

[0031] The beneficial effects of the present invention are as follows:

[0032] 1. The temperature fatigue load spectrum constructed by the present invention takes into account the influence of transverse and vertical temperature gradients, and can be used to simulate the temperature fatigue stress history of flangeless steel box girders, providing a technical basis for improving the anti-fatigue design system of steel bridges. The proposed temperature gradient fatigue load spectrum is suitable for design service lives of 100, 150 and 200 years, meeting the needs of long-life design.

[0033] 2. The temperature gradient fatigue load spectrum construction method proposed in the present invention applies the Kmeans++ algorithm, which overcomes the difficulty in determining the initial clustering center during the original temperature clustering, improves the accuracy and efficiency of clustering, and uses the long-term monitoring data of the temperature field to construct the vertical and transverse temperature gradient fatigue load spectra of the flangeless steel box girder bridge, thereby improving the utilization efficiency of the data.

[0034] 3. The present invention helps to improve the safety and durability of bridge structures by accurately simulating the temperature fatigue stress history.

[0035] 4. The implementation of the present invention provides a basis for temperature fatigue damage analysis, solves the problem of lack of temperature fatigue load spectrum of flangeless steel box girder bridge in the fatigue resistance design of steel bridges, and helps to promote the development of bridge engineering technology, especially in steel bridge design and evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the three-dimensional structure of the flangeless steel box girder of the highway flangeless steel box girder bridge in the embodiment.

[0037] Figure 2 It is the vertical temperature sub-gradient model of the steel box girder bridge without flange.

[0038] Figure 3 is the frequency of each vertical temperature sub-gradient of the highway steel box girder bridge without flange.

[0039] Figure 4 It is a flow chart of the method for constructing the thermal fatigue load spectrum of a highway steel box girder bridge without flange.

[0040] Figure 5 Arrangement of temperature measurement points for constructing the temperature fatigue load spectrum.

[0041] Figure 6 This is the temperature gradient history curve of the steel box girder bridge without flange.

[0042] Figure 7 Clustering results of vertical temperature samples for constructing vertical temperature fatigue load spectrum.

[0043] Figure 8 Error analysis diagram of vertical temperature sample clustering results for constructing vertical temperature fatigue load spectrum.

[0044] Fig. 9 This is the transverse temperature sub-gradient model of the steel box girder bridge without flange.

[0045] Fig.10 is the frequency of each transverse temperature sub-gradient of the steel box girder bridge without flange.

[0046] Fig.11 Clustering results of transverse temperature samples for constructing vertical temperature fatigue load spectrum. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0048] Example 1

[0049] This embodiment takes a highway steel box girder bridge without flange plates with a beam height h of 3.90 m under the climate conditions of South China as an example. Figure 1 .

[0050] The thermal fatigue load spectrum of the highway wingless steel box girder bridge wing in this embodiment includes a vertical temperature gradient fatigue load spectrum and a transverse temperature gradient fatigue load spectrum. The vertical temperature gradient fatigue load spectrum consists of 6 vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0051]

[0052] Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, h is the cross-sectional height of the steel box girder bridge without flange plate, Gi is the ith vertical temperature sub-gradient, T Gi,1 、T Gi,2 、T Gi,3 are the representative values ​​of the temperature at the top plate of the steel box girder, at the height of 0.86h, and at the bottom plate of the steel box girder in the i-th vertical temperature sub-gradient, in °C. G1,1 、T G1,2 、T G1,3 are the representative values ​​of the temperature at the top plate of the steel box girder, at a height of 0.86h, and at the bottom plate of the steel box girder in the first vertical temperature sub-gradient, T G1,1 The value range is [3.3,6.2], the unit is ℃, T G1,2 The value range is [4.8,7.4], the unit is ℃, T G1,3 The value range is [0.3,3.2], the unit is ℃, T Gi,j is the temperature representative value at the jth typical height in the ith vertical temperature sub-gradient, N d is the design service life, T G1,j is the temperature representative value at the jth typical height in the first vertical temperature sub-gradient, P(T G1 (y))、P(T G2 (y))、P(T G3 (y))、P(T G4 (y))、P(T G5 (y))、P(T G6 (y)) are the occurrence probabilities of the six vertical temperature sub-gradients within the design service life, T G1,1 、TG2,1 、T G3,1 、T G4,1 、T G5,1 、T G6,1 are the representative values ​​of the temperature at the top plate of the steel box girder in the six vertical temperature sub-gradients; in this embodiment, T G1,2 The value of is 4.7, T G1,2 The value of is 6.8, T G1,3 The value of is 1.8;

[0053] The vertical temperature fatigue load spectra of the highway steel box girder bridge with no flange plate of 100, 150 and 200 years of design service life are obtained from the above model. The linear temperature gradient mode is as follows: Figure 2 As shown in Table 1, 150 years and 200 years are long-life design service life, and the vertical temperature sub-gradient T of the highway flangeless steel box girder bridge is G1 ~T G6 The probability of occurrence is 21.4%, 17.9%, 10.7%, 21.4%, 21.4%, 7.2%, such as Figure 3 shown.

[0054] Table 1 Representative values ​​of vertical temperature fatigue load spectrum gradient temperature of steel box girder without flange

[0055]

[0056] exist Figure 4 In the present embodiment, the method for constructing the vertical temperature fatigue load spectrum of the highway flangeless steel box girder bridge comprises the following steps:

[0057] Step 1: Collect temperature data of steel box girder bridge without flange

[0058] Arrange one measuring point on the bottom plate of the steel box girder bridge without flange plates, and use this measuring point as the coordinate origin. Arrange measuring points on the middle web plate and the top plate along the vertical height direction. Arrange m = 11 measuring points in total. Figure 5 (a), the measuring point positions are expressed as 0.00m, 0.60m, 1.60m, 2.10m, 2.60m, 3.10m, 3.40m, 3.50m, 3.60m, 3.70m, 3.75m from the bottom surface of the flangeless steel box girder. The temperature value of each measuring point is collected at an interval of 2 seconds to obtain the measured temperature gradient time history curve at each position, such as Figure 6 The measured temperature gradient time history curve is extended to the design service life N through the long short-term memory recurrent neural network. d The temperature history at typical locations is used to obtain the maximum daily temperature at each measuring point every day within the design service life, and the design service life daily temperature extreme value matrix Q = [M1, M2, …, M t ,…,M Nd×365 ],Mt is the daily temperature maximum vector of each measuring point on the tth day, y1 is the position coordinate of the first temperature measurement point, y m is the position coordinate of the mth temperature measurement point, is the maximum temperature value of the first temperature measurement point on the tth day, is the maximum temperature value of the mth temperature measuring point on the tth day; the acquisition time of the temperature value of the measuring point in this embodiment can also be 1 second interval or 1800 seconds interval;

[0059] Step 2: Use Kmeans++ algorithm to determine the initial cluster centers and cluster families:

[0060] Step 2.1: Define the number of clusters as c l , randomly select a vector from the design service life daily temperature extreme value matrix Q as the first initial cluster center, obtain the Manhattan distance between other vectors in the design service life daily temperature extreme value matrix Q and the first initial cluster center according to the Manhattan distance calculation method, and select the vector with the largest Manhattan distance to the first initial cluster center as the second initial cluster center;

[0061] Step 2.2, according to the Manhattan distance calculation method, calculate the sum of the Manhattan distances between each vector in the design service life daily temperature extreme value matrix Q except the determined initial cluster center and all the determined initial cluster centers, and select the vector with the largest sum of Manhattan distances as the next initial cluster center;

[0062] Step 2.3, repeat step 2.2 until c is selected l Initial cluster centers and construct c l Initial clusters;

[0063] Step 3: Divide the vectors in the design service life daily temperature extreme value matrix Q into clusters. According to the Manhattan distance calculation method, the distance between each vector in the design service life daily temperature extreme value matrix Q and c is obtained. l The Manhattan distance of the initial clustering centers is used to divide each vector in the daily temperature extreme value matrix Q of the design service life into the initial clustering group corresponding to the initial clustering center with the smallest Manhattan distance;

[0064] Step 4: Update the clustering family

[0065] The vector obtained by averaging all vector points in each cluster family is used as the virtual new cluster center of each cluster family, and the Manhattan distance D between the virtual new cluster center of each cluster family and its old cluster center is calculated. v , Manhattan distance D v ≤ set threshold D th The cluster center of the cluster family remains unchanged, and the Manhattan distance D v> Set threshold D th The virtual new cluster center is used as the new cluster center, and step 3 is repeated to update the cluster center until the Manhattan distance D between the virtual new cluster center and its old cluster center of all cluster centers is v ≤ set threshold D th , and get the final cluster family, such as Figure 7 ; The threshold value D in this embodiment th =0.001, the threshold value D in this embodiment th It can also be 0.00005, or the interval can be 0.01;

[0066] Step 5: Determine the number of reasonable clusters c l :

[0067] Let the number of clusters c l are integers from 2 to 10 respectively. Follow steps 2 and 3 to get the corresponding number of clusters c. l The 9 final clustering families are obtained. The cluster centers of each final clustering family constitute the cluster center matrix. The residual square sum RMSE of the maximum residual daily temperature is obtained according to the following formula for each cluster center matrix. l -RMSE two-dimensional line chart, such as Figure 8 , according to the elbow rule, determine the optimal number of clusters c l =6;

[0068]

[0069] In the formula, is the kth row vector in the cluster center matrix;

[0070] Step 6: Determine the vertical temperature gradient fatigue load spectrum of the highway flangeless steel box girder bridge

[0071] Use the number of clusters c determined in step 5 l And the corresponding cluster center matrix C end , each cluster family is a vertical temperature sub-gradient, the row vector of the cluster center matrix is ​​the typical representative value of each temperature sub-gradient, and the number of sample points in each cluster family divided by the total number is the occurrence probability of each sub-gradient, thereby obtaining the corresponding vertical temperature fatigue load spectrum of the flangeless steel box girder bridge.

[0072] The transverse temperature gradient fatigue load spectrum is composed of six transverse temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0073]

[0074] Where, T Hq(x) is the temperature of the qth transverse temperature sub-gradient at position x, L is the width of the steel box girder without flange, Hq is the qth transverse temperature sub-gradient, T Hq,1 、T Hq,2 、T Hq,3 are the representative values ​​of the temperature at the edge of the sunny side, the position 0.6L near the sunny side, and the edge of the shady side in the transverse temperature sub-gradient of the qth flangeless steel box girder bridge, in °C, T H1,1 、T H1,2 、T H1,3 are the representative values ​​of the temperature at the edge of the sun side, the position close to 0.6L on the sun side, and the edge of the sun side in the first transverse temperature sub-gradient, T H1,1 The value range is [8.6,11.2], the unit is ℃, T H1,2 The value range is [7.6,10.1], the unit is ℃, T H1,3 The value range is [8.4,12.2], the unit is ℃, T Hq,w is the temperature representative value at the wth typical position in the qth transverse temperature sub-gradient, N d is the design service life, T H1,w is the temperature representative value at the wth typical position in the first transverse temperature sub-gradient, P(T H1 (x))、P(T H2 (x))、P(T H3 (x))、P(T H4 (x))、P(T H5 (x))、P(T H6 (x)) are the occurrence probabilities of the six transverse temperature sub-gradients within the design service life, T H1,1 、T H2,1 、T H3,1 、T H4,1 、T H5,1 、T H6,1 are the representative values ​​of the temperature at the edge of the positive side of the six transverse temperature sub-gradients. In this embodiment, T H1,1 9.9℃, T H1,2 8.3℃, T H1,3 It is 9.5℃.

[0075] The above model is used to obtain the temperature gradient values ​​of the transverse temperature fatigue load spectrum of the highway flangeless steel box girder bridge with a design service life of 100 years, 150 years, and 200 years. The transverse sub-gradient mode is as follows: Fig. 9 As shown in Table 2, the gradient T of the transverse temperature fatigue load spectrum of the highway steel box girder bridge without flange is H1 ~T H6 The probability of occurrence is 32.1%, 17.9%, 25.0%, 10.7%, 7.1%, and 7.2%. Fig.10 .

[0076] Table 2 Representative values ​​of gradient temperature of transverse temperature fatigue load spectrum of steel box girder without flange

[0077]

[0078] The method for constructing the transverse temperature fatigue load spectrum of a highway flangeless steel box girder bridge comprises the following steps:

[0079] Step 1: Arrange a measuring point at the edge of the positive side of the roof, and use this measuring point as the coordinate origin. Arrange m = 4 measuring points along the width direction of the roof. The positions of the measuring points are expressed as 0.00m, 5.40m, 10.40m, and 15.75m in horizontal distance from the coordinate origin. Figure 5 (b).

[0080] Steps 2 to 6 are similar to the vertical temperature fatigue load spectrum construction method of the flangeless steel box girder bridge. The clustering results are as follows: Fig.11 shown.

Claims

1. A thermal fatigue load spectrum for a flangeless steel box girder bridge, characterized in that: The temperature fatigue load spectrum includes a vertical temperature gradient fatigue load spectrum and a transverse temperature gradient fatigue load spectrum; the vertical temperature gradient fatigue load spectrum is composed of 6 vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically: Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, h is the cross-sectional height of the steel box girder bridge without flange plate, Gi is the ith vertical temperature sub-gradient, T Gi,1 , T Gi,2 , T Gi,3 are the representative values ​​of the temperature at the top plate of the steel box girder, at the height of 0.86h, and at the bottom plate of the steel box girder in the i-th vertical temperature sub-gradient, in °C. G1,1 , T G1,2 , T G1,3 are the representative values ​​of the temperature at the top plate of the steel box girder, at a height of 0.86h, and at the bottom plate of the steel box girder in the first vertical temperature sub-gradient, T G1,1 The value range is [3.3,6.2], the unit is ℃, T G1,2 The value range is [4.8,7.4], the unit is ℃, T G1,3 The value range is [0.3,3.2], the unit is ℃, T Gi,j is the temperature representative value at the jth typical height in the ith vertical temperature sub-gradient, N d is the design service life, T G1,j is the temperature representative value at the jth typical height in the first vertical temperature sub-gradient, P(T G1 (y))、P(T G2 (y))、P(T G3 (y))、P(T G4 (y))、P(T G5 (y))、P(T G6 (y)) are the occurrence probabilities of the six vertical temperature sub-gradients within the design service life, T G1,1 , T G2,1 , T G3,1 , T G4,1 , T G5,1 , T G6,1 They are the representative values ​​of the temperature at the top plate of the steel box girder in the six vertical temperature sub-gradients; The transverse temperature gradient fatigue load spectrum is composed of six transverse temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically: Where, T Hq (x) is the temperature of the qth transverse temperature sub-gradient at position x, L is the width of the steel box girder without flange, Hq is the qth transverse temperature sub-gradient, T Hq,1 , T Hq,2 , T Hq,3 are the representative values ​​of the temperature at the edge of the sunny side, the position 0.6L near the sunny side, and the edge of the shady side in the transverse temperature sub-gradient of the qth flangeless steel box girder bridge, in °C, T H1,1 , T H1,2 , T H1,3 are the representative values ​​of the temperature at the edge of the sun side, the position close to 0.6L on the sun side, and the edge of the sun side in the first transverse temperature sub-gradient, T H1,1 The value range is [8.6,11.2], the unit is ℃, T H1,2 The value range is [7.6,10.1], the unit is ℃, T H1,3 The value range is [8.4,12.2], the unit is ℃, T Hq,w is the temperature representative value at the wth typical position in the qth transverse temperature sub-gradient, N d is the design service life, T H1,w is the temperature representative value at the wth typical position in the first transverse temperature sub-gradient, P(T H1 (x))、P(T H2 (x))、P(T H3 (x))、P(T H4 (x))、P(T H5 (x))、P(T H6 (x)) are the occurrence probabilities of the six transverse temperature sub-gradients within the design service life, T H1,1 , T H2,1 , T H3,1 , T H4,1 , T H5,1 , T H6,1 They are the representative values ​​of temperature at the edges of the positive side of the six lateral temperature sub-gradients.

2. The thermal fatigue load spectrum of the flangeless steel box girder bridge according to claim 1 is characterized in that: The construction method includes the following steps: Step 1: Collect temperature data of steel box girder bridge without flange: A total of m measuring points are arranged on the flangeless steel box girder bridge. The temperature values ​​of each measuring point are collected at regular intervals to obtain the measured temperature gradient time history curve at each position. The measured temperature gradient time history curve is extended to the design service life N through the long short memory recurrent neural network. d The temperature history at typical locations is used to obtain the maximum daily temperature at each measuring point every day within the design service life, and the design service life daily temperature extreme value matrix Q = [M1, M2, …, M t ,…,M Nd×365 ],M t is the daily temperature maximum vector of each measuring point on the tth day, y1 is the position coordinate of the first temperature measurement point, y m is the position coordinate of the mth temperature measurement point, is the maximum temperature value of the first temperature measurement point on the tth day, is the maximum temperature value of the mth temperature measurement point on the tth day; Step 2: Use Kmeans++ algorithm to determine the initial cluster centers and cluster families: Step 2.1: Define the number of clusters as c l , randomly select a vector from the design service life daily temperature extreme value matrix Q as the first initial cluster center, obtain the Manhattan distance between other vectors in the design service life daily temperature extreme value matrix Q and the first initial cluster center according to the Manhattan distance calculation method, and select the vector with the largest Manhattan distance to the first initial cluster center as the second initial cluster center; Step 2.2, according to the Manhattan distance calculation method, calculate the sum of the Manhattan distances between each vector in the design service life daily temperature extreme value matrix Q except the determined initial cluster center and all the determined initial cluster centers, and select the vector with the largest sum of Manhattan distances as the next initial cluster center; Step 2.3, repeat step 2.2 until c is selected l Initial cluster centers and construct c l Initial clusters; Step 3: Divide the vectors in the daily temperature extreme value matrix Q of the design service life into clusters: According to the Manhattan distance calculation method, each vector in the daily temperature extreme value matrix Q of the design service life is obtained from the distance between c l The Manhattan distance of the initial clustering centers is used to divide each vector in the daily temperature extreme value matrix Q of the design service life into the initial clustering group corresponding to the initial clustering center with the smallest Manhattan distance; Step 4: Update the clustering family: The vector obtained by averaging all vector points in each cluster family is used as the virtual new cluster center of each cluster family, and the Manhattan distance D between the virtual new cluster center of each cluster family and its old cluster center is calculated. v , Manhattan distance D v ≤ set threshold D th The cluster center of the cluster family remains unchanged, and the Manhattan distance D v > Set threshold D th The virtual new cluster center is used as the new cluster center, and step 3 is repeated to update the cluster center until the Manhattan distance D between the virtual new cluster center and its old cluster center of all cluster centers is v ≤ set threshold D th , get the final clustering family; Step 5: Determine the number of reasonable clusters c l : Let the number of clusters c l are integers from 2 to 10 respectively. Follow steps 2 and 3 to get the corresponding number of clusters c. l The 9 final clustering families are obtained. The cluster centers of each final clustering family constitute the cluster center matrix. The residual square sum RMSE of the maximum residual daily temperature is obtained according to the following formula for each cluster center matrix. l -RMSE two-dimensional line chart, based on the elbow rule, determine the optimal number of clusters c l =6; In the formula, is the kth row vector in the cluster center matrix; Step 6: Determine the temperature fatigue load spectrum: Use the number of clusters c determined in step 5 l And the corresponding cluster center matrix C end , each cluster family is a temperature sub-gradient, the row vector of the cluster center matrix is ​​the typical representative value of each temperature sub-gradient, and the number of sample points in each cluster family divided by the total number is the occurrence probability of each temperature sub-gradient, thereby obtaining the corresponding temperature fatigue load spectrum of the flangeless steel box girder bridge.

3. The method for constructing the thermal fatigue load spectrum of the flangeless steel box girder bridge according to claim 2 is characterized by: The threshold D th The value range is [0.00005,0.01].

4. The method for constructing the thermal fatigue load spectrum of the flangeless steel box girder bridge according to claim 2 is characterized in that: The m measuring points described in step 1 are used to construct a vertical temperature fatigue load spectrum. The arrangement method is: arrange one measuring point on the upper surface of the bottom plate of the flangeless steel box girder bridge, and take the measuring point as the coordinate origin, arrange measuring points on the middle web and the top plate along the vertical height direction, and arrange m=11 measuring points in total. The positions of the measuring points are expressed as 0.00m, h-3.15m, h-2.15m, h-1.65m, h-1.15m, h-0.65m, h-0.35m, h-0.25m, h-0.15m, h-0.05m, and h from the vertical distance from the upper surface of the bottom plate of the flangeless steel box girder.

5. The method for constructing the thermal fatigue load spectrum of the flangeless steel box girder bridge according to claim 2 is characterized in that: In step 1, the m measuring points are used to construct the transverse temperature fatigue load spectrum, and the arrangement method is: a measuring point is arranged at the edge of the positive side of the top plate, and the measuring point is used as the coordinate origin, and a total of m=4 measuring points are arranged along the width direction of the top plate. The positions of the measuring points are expressed as 0.00m, L-10.35m, L-5.35m, and L-15.75m in terms of the horizontal distance from the coordinate origin.

6. The method for constructing the thermal fatigue load spectrum of the flangeless steel box girder bridge according to claim 2 is characterized in that: In step 1, the temperature values ​​of each measuring point are collected at intervals of 60 to 1200 seconds.

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