Temperature fatigue load spectrum and construction method of wingless steel box girder bridge

Abstract

A method for constructing a temperature fatigue load spectrum for wingless steel box girder bridges is presented, comprising six vertical temperature sub-gradients and their occurrence probabilities, and six transverse temperature sub-gradients and their occurrence probabilities. Based on the structural characteristics and temperature field distribution of wingless steel box girder bridges, temperature measuring points are arranged and long-term temperature field monitoring is conducted. Temperature fatigue stress analysis is performed, and a reasonable clustering algorithm is used to propose vertical and transverse temperature fatigue load spectra applicable to wingless steel box girder bridges with design service lives of 100, 150, and 200 years. The provided temperature fatigue load spectra can provide a basis for temperature fatigue damage analysis, solving the problem of the lack of temperature fatigue load spectra for wingless steel box girder bridges in the fatigue resistance design of steel bridges.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically relating to a temperature fatigue load spectrum and construction method for a wingless steel box girder bridge. Background Technology

[0002] Wingless steel box girders are a typical closed-section form. Due to their special cross-sectional shape, the web of the wingless steel box girder is directly exposed to sunlight, resulting in complex transverse and vertical temperature gradients. Under the action of a vertical nonlinear temperature gradient, wingless steel box girders will generate longitudinal temperature fatigue stress. Due to the framing effect of the closed section, the transverse temperature gradient will cause transverse temperature fatigue stress in the wingless steel box girder section. The temperature effects on wingless steel box girders include the cyclical effects of diurnal and seasonal temperature differences, and temperature fatigue can be characterized by a temperature gradient fatigue load spectrum. Therefore, to meet the fatigue resistance design requirements of wingless steel box girder bridges, a vertical and transverse temperature gradient fatigue load spectrum applicable to wingless steel box girder bridges with a design service life of up to 200 years should be proposed. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a temperature fatigue load spectrum and construction method for wingless steel box girder bridges that can be used for long-life design or fatigue life assessment of 150-year or 200-year lifespan.

[0004] The technical solution adopted to solve the above-mentioned technical problems is: a temperature fatigue load spectrum for a wingless 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 consists of 6 vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0005]

[0006] In the formula, T Gi (y) represents the temperature of the i-th vertical temperature sub-gradient at position y, h represents the cross-sectional height of the wingless steel box girder bridge, Gi represents the i-th vertical temperature sub-gradient, and T Gi,1 T Gi,2 T Gi,3 T represents the representative temperature values ​​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, respectively, in the i-th vertical temperature sub-gradient, in °C. G1,1 T G1,2 T G1,3 These are the representative temperature values ​​(T) 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, respectively, in the first vertical temperature sub-gradient. G1,1 The value range is [3.3, 6.2], and the unit is ℃ (T). G1,2 The value range is [4.8, 7.4], and the unit is ℃ (T).G1,3 The value range is [0.3, 3.2], and the unit is ℃ (T). Gi,j N represents the representative temperature value at the j-th typical height in the i-th vertical temperature sub-gradient. d For the design service life, T G1,j P(T) represents the temperature at the j-th typical height in the first vertical temperature sub-gradient. G1 (y)), P(T) G2 (y)), P(T) G3 (y)), P(T) G4 (y)), P(T) G5 (y)), P(T) G6 (y) represents the probability of occurrence of the six vertical temperature sub-gradients within the design service life, and T G1,1 T G2,1 T G3,1 T G4,1 T G5,1 T G6,1 These are the representative temperature values ​​at the top plate of the steel box girder in the six vertical temperature sub-gradients;

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

[0008]

[0009] In the formula, T Hq (x) represents the temperature of the q-th lateral temperature sub-gradient at position x, L is the width of the wingless steel box girder, Hq is the q-th lateral temperature sub-gradient, and T... Hq,1 T Hq,2 T Hq,3 These are the representative temperature values ​​(°C, T) at the sun-facing edge, the position 0.6L from the sun-facing edge, and the shaded edge in the transverse temperature sub-gradient of the q-th wingless steel box girder bridge. H1,1 T H1,2 T H1,3 T represents the representative temperature values ​​at the sunlit side edge, 0.6L from the sunlit side edge, and the shaded side edge in the first transverse temperature subgradient, respectively. H1,1 The value range is [8.6, 11.2], and the unit is ℃ (T). H1,2 The value range is [7.6, 10.1], and the unit is ℃ (T). H1,3 The value range is [8.4, 12.2], and the unit is ℃ (T). Hq,w N represents the representative temperature value at the w-th typical location within the q-th lateral temperature subgradient. d For the design service life, T H1,wP(T) represents the temperature at the w-th typical location in the first transverse temperature subgradient. H1 (x)), P(T) H2 (x)), P(T) H3 (x)), P(T) H4 (x)), P(T) H5 (x)), P(T) H6 (x) represent the probabilities of the occurrence of the six transverse temperature sub-gradients within the design service life, and T represents the probability of these occurrences. H1,1 T H2,1 T H3,1 T H4,1 T H5,1 T H6,1 These represent the temperature values ​​at the sunlit side edges of the six transverse temperature sub-gradients.

[0010] This invention also provides a method for constructing the temperature fatigue load spectrum of a wingless steel box girder bridge, comprising the following steps:

[0011] Step 1: Collect temperature data for the wingless steel box girder bridge.

[0012] m measuring points were arranged on the wingless steel box girder bridge. Temperature values ​​were collected at each measuring point at regular intervals to obtain the measured temperature gradient time history curves at each location. The measured temperature gradient time history curves were then extended to the design service life N using a long short-term memory recurrent neural network. d Temperature history at typical locations is obtained, yielding the daily temperature maxima at each measuring point for each day within the design service life. A daily temperature extreme value matrix Q = [M1, M2, ..., M] is then constructed for the design service life. t ,…,M Nd×365 ],M t Let be the vector of daily temperature maxima at each measuring point on day t. y1 represents the coordinates of the first temperature measuring point. m Let m be the coordinates of the m-th temperature measuring point. This represents the maximum temperature value at the first temperature measurement point on day t. The maximum temperature value at the m-th temperature measurement point on day t;

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

[0014] Step 2.1: Define the number of cluster families as c. l A vector is randomly selected from the daily temperature extreme value matrix Q for the design service life as the first initial cluster center. The Manhattan distance between other vectors in the daily temperature extreme value matrix Q for the design service life and the first initial cluster center is obtained according to the Manhattan distance calculation method. The vector with the largest Manhattan distance to the first initial cluster center is selected 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 daily temperature extreme value matrix Q (excluding 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 1 initial cluster center, and construct c l An initial cluster family;

[0017] Step 3: Divide the vectors in the daily extreme temperature matrix Q for the design service life into cluster families:

[0018] Based on the Manhattan distance calculation method, each vector in the daily extreme temperature matrix Q for the design service life is obtained, along with c. l The Manhattan distance between the initial cluster centers will be used to assign each vector in the annual daily temperature extreme value matrix Q to the initial cluster family corresponding to the initial cluster center with the smallest Manhattan distance.

[0019] Step 4: Update the cluster family:

[0020] The vector obtained by averaging all vector points in each cluster is used as the virtual new cluster center for each cluster. The Manhattan distance D between the virtual new cluster center and the old cluster center of each cluster is calculated. v Manhattan is far from D v ≤ set threshold D th The cluster centers of the cluster families remain unchanged, and Manhattan is far from D. v > Set threshold D th For each cluster family, the virtual new cluster center is used as the new cluster center. Step 3 is repeated to update the cluster families until the Manhattan distance D between the virtual new cluster center and the old cluster center of all cluster families is found. v ≤ set threshold D th This yields the final cluster family;

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

[0022] Let the number of clusters cl be an integer between 2 and 10, and follow steps 2 and 3 to obtain the corresponding number of clusters c. l The final 9 clusters are obtained, and the cluster centers of each final cluster form a cluster center matrix. The sum of squared residuals (RMSE) of the maximum residual temperature of each cluster center matrix is ​​obtained according to the following formula. Plot c l -RMSE two-dimensional line chart, using the elbow rule to determine the optimal number of clusters c. l =6;

[0023]

[0024] In the formula, The vector in the k-th row of the cluster center matrix;

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

[0026] Using the number of cluster families c determined in step 5 l and the corresponding cluster center matrix C end Each cluster is a temperature sub-gradient, and the row vector of the cluster center matrix takes the typical representative value of each temperature sub-gradient. The number of sample points in each cluster divided by the total number is the probability of occurrence of each temperature sub-gradient, thus obtaining the corresponding temperature fatigue load spectrum of the wingless steel box girder bridge.

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

[0028] Preferably, in step 1, the m measuring points are used to construct the vertical temperature fatigue load spectrum. The arrangement method is as follows: one measuring point is arranged on the upper surface of the bottom plate of the wingless steel box girder bridge, and with this measuring point as the origin of the coordinate system, measuring points are arranged on the middle web plate and the top plate along the vertical height direction, for a total of m = 11 measuring points. The position of the measuring points is expressed as the vertical distance from the upper surface of the bottom plate of the wingless steel box girder 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.

[0029] Preferably, in step 1, the m measuring points are used to construct the transverse temperature fatigue load spectrum. The arrangement method is as follows: a measuring point is arranged at the edge of the sunny side of the top plate, and with this measuring point as the origin of the coordinate system, 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 horizontal distances from the origin of the coordinate system as 0.00m, L-10.35m, L-5.35m, and L-15.75m.

[0030] Preferably, the time interval between the temperature values ​​of each measuring point in step 1 is 60 to 1200 seconds.

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

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

[0033] 2. The temperature gradient fatigue load spectrum construction method proposed in this invention applies the Kmeans++ algorithm, which overcomes the difficulty in determining the initial cluster center in the original temperature clustering, improves the accuracy and efficiency of clustering, and constructs the vertical and horizontal temperature gradient fatigue load spectrum of the wingless steel box girder bridge by using long-term temperature field monitoring data, thereby improving the data utilization efficiency.

[0034] 3. This invention helps improve the safety and durability of bridge structures by accurately simulating the temperature fatigue stress process.

[0035] 4. The implementation of this invention provides a basis for temperature fatigue damage analysis, solves the problem of the lack of temperature fatigue load spectrum for wingless steel box girder bridges 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. Attached Figure Description

[0036] Figure 1 This is a three-dimensional structural diagram of the wingless steel box girder of the highway wingless steel box girder bridge in the embodiment.

[0037] Figure 2 This is the vertical temperature sub-gradient mode for a wingless steel box girder bridge.

[0038] Figure 3 The frequencies of the vertical temperature gradients for wingless steel box girder bridges on highways.

[0039] Figure 4 This is a flowchart illustrating the method for constructing the temperature fatigue load spectrum of a wingless steel box girder highway bridge.

[0040] Figure 5 A temperature measurement point layout diagram is used to construct a temperature fatigue load spectrum.

[0041] Figure 6 This is the temperature gradient history curve for a wingless steel box girder bridge.

[0042] Figure 7 To construct the vertical temperature sample clustering results for the 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] Figure 9 This is the transverse temperature gradient mode for a wingless steel box girder bridge.

[0045] Figure 10 The frequencies of the transverse temperature gradients of a wingless steel box girder bridge.

[0046] Figure 11 To construct the lateral temperature sample clustering results for the vertical temperature fatigue load spectrum. Detailed Implementation

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

[0048] Example 1

[0049] This embodiment takes a wingless steel box girder highway bridge with a beam height h of 3.90m under the climatic conditions of South China as an example. Figure 1 .

[0050] This embodiment of the thermal fatigue load spectrum for a wingless steel box girder bridge includes a vertical thermal gradient fatigue load spectrum and a transverse thermal gradient fatigue load spectrum. The vertical thermal gradient fatigue load spectrum consists of six vertical thermal sub-gradients and their probability of occurrence within the design service life, specifically:

[0051]

[0052] In the formula, T Gi (y) represents the temperature of the i-th vertical temperature sub-gradient at position y, h represents the cross-sectional height of the wingless steel box girder bridge, Gi represents the i-th vertical temperature sub-gradient, and T Gi,1 T Gi,2 T Gi,3 T represents the representative temperature values ​​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, respectively, in the i-th vertical temperature sub-gradient, in °C. G1,1 T G1,2 T G1,3 These are the representative temperature values ​​(T) 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, respectively, in the first vertical temperature sub-gradient. G1,1 The value range is [3.3, 6.2], and the unit is ℃ (T). G1,2 The value range is [4.8, 7.4], and the unit is ℃ (T). G1,3 The value range is [0.3, 3.2], and the unit is ℃ (T). Gi,j N represents the representative temperature value at the j-th typical height in the i-th vertical temperature sub-gradient. d For the design service life, T G1,j P(T) represents the temperature at the j-th typical height in the first vertical temperature sub-gradient. G1 (y)), P(T) G2 (y)), P(T) G3 (y)), P(T) G4 (y)), P(T) G5 (y)), P(T) G6 (y) represents the probability of occurrence of the six vertical temperature sub-gradients within the design service life, and T G1,1 TG2,1 T G3,1 T G4,1 T G5,1 T G6,1 These represent the temperature values ​​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 T is 4.7. G1,2 The value of T is 6.8. G1,3 The value is 1.8;

[0053] The vertical temperature fatigue load spectra of the 100-year, 150-year, and 200-year design service life of the wingless steel box girder bridge were obtained from the above model. The linear temperature gradient mode is as follows: Figure 2 As shown in Table 1, where 150 years and 200 years are the long-life design service life, the vertical temperature sub-gradient T of the wingless steel box girder highway bridge is... G1 ~T G6 The probability of occurrence is 21.4%, 17.9%, 10.7%, 21.4%, 21.4%, and 7.2%, respectively. Figure 3 As shown.

[0054] Table 1. Representative values ​​of vertical temperature fatigue load spectrum gradient temperature for wingless steel box girders.

[0055]

[0056] exist Figure 4 The method for constructing the vertical temperature fatigue load spectrum of a wingless steel box girder bridge in this embodiment includes the following steps:

[0057] Step 1: Collect temperature data for the wingless steel box girder bridge

[0058] One measuring point is arranged on the bottom slab of the wingless steel box girder bridge. Using this measuring point as the origin, measuring points are arranged along the vertical direction on the middle web and top slab, for a total of m = 11 measuring points. Figure 5 (a) The measuring points are located at vertical distances from the bottom surface of the wingless steel box girder, denoted as 0.00m, 0.60m, 1.60m, 2.10m, 2.60m, 3.10m, 3.40m, 3.50m, 3.60m, 3.70m, and 3.75m. Temperature values ​​are collected at 2-second intervals at each measuring point to obtain the measured temperature gradient time history curves for each location, as shown below. Figure 6 As shown. The measured temperature gradient time history curve is extended to the design service life N using a long short-term memory recurrent neural network. d Temperature history at typical locations is obtained, yielding the daily temperature maxima at each measuring point for each day within the design service life. A daily temperature extreme value matrix Q = [M1, M2, ..., M] is then constructed for the design service life. t ,…,M Nd×365 ], Mt Let be the vector of daily temperature maxima at each measuring point on day t. y1 represents the coordinates of the first temperature measuring point. m Let m be the coordinates of the m-th temperature measuring point. This represents the maximum temperature value at the first temperature measurement point on day t. The maximum temperature value is the m-th temperature measurement point on day t. In this embodiment, the temperature value acquisition time of the measurement point can also be 1 second or 1800 seconds.

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

[0060] Step 2.1: Define the number of cluster families as c. l A vector is randomly selected from the daily temperature extreme value matrix Q for the design service life as the first initial cluster center. The Manhattan distance between other vectors in the daily temperature extreme value matrix Q for the design service life and the first initial cluster center is obtained according to the Manhattan distance calculation method. The vector with the largest Manhattan distance to the first initial cluster center is selected 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 daily temperature extreme value matrix Q (excluding 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 1 initial cluster center, and construct c l An initial cluster family;

[0063] Step 3: Divide the vectors in the daily extreme temperature matrix Q for the design service life into clusters. Calculate the relationship between each vector in the daily extreme temperature matrix Q for the design service life and c using the Manhattan distance method. l The Manhattan distance between the initial cluster centers will be used to assign each vector in the annual daily temperature extreme value matrix Q to the initial cluster family corresponding to the initial cluster center with the smallest Manhattan distance.

[0064] Step 4: Update the cluster families

[0065] The vector obtained by averaging all vector points in each cluster is used as the virtual new cluster center for each cluster. The Manhattan distance D between the virtual new cluster center and the old cluster center of each cluster is calculated. v Manhattan is far from D v ≤ set threshold D th The cluster centers of the cluster families remain unchanged, and Manhattan is far from D. v> Set threshold D th For each cluster family, the virtual new cluster center is used as the new cluster center. Step 3 is repeated to update the cluster families until the Manhattan distance D between the virtual new cluster center and the old cluster center of all cluster families is found. v ≤ set threshold D th This yields the final cluster family, such as Figure 7 The threshold D in this embodiment th =0.001, the threshold D in this embodiment th It can also be 0.00005, or an interval of 0.01;

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

[0067] Let c be the number of clusters. l The numbers are integers from 2 to 10. Following steps 2 and 3, the number of clusters c is obtained. l The final 9 clusters are obtained, and the cluster centers of each final cluster form a cluster center matrix. The sum of squared residuals (RMSE) of the maximum residual temperature of each cluster center matrix is ​​obtained according to the following formula. Plot c l -RMSE 2D line chart, such as Figure 8 Based on the elbow rule, determine the optimal number of clusters c. l =6;

[0068]

[0069] In the formula, The vector in the k-th row of the cluster center matrix;

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

[0071] Using the number of cluster families c determined in step 5 l and the corresponding cluster center matrix C end Each cluster is a vertical temperature sub-gradient, and the row vector of the cluster center matrix takes the typical representative value of each temperature sub-gradient. The number of sample points in each cluster divided by the total number is the probability of occurrence of each sub-gradient, thus obtaining the vertical temperature fatigue load spectrum of the corresponding wingless steel box girder bridge.

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

[0073]

[0074] In the formula, T Hq(x) represents the temperature of the q-th lateral temperature sub-gradient at position x, L is the width of the wingless steel box girder, Hq is the q-th lateral temperature sub-gradient, and T... Hq,1 T Hq,2 T Hq,3 These are the representative temperature values ​​(°C, T) at the sun-facing edge, the position 0.6L from the sun-facing edge, and the shaded edge in the transverse temperature sub-gradient of the q-th wingless steel box girder bridge. H1,1 T H1,2 T H1,3 T represents the representative temperature values ​​at the sunlit side edge, 0.6L from the sunlit side edge, and the shaded side edge in the first transverse temperature subgradient, respectively. H1,1 The value range is [8.6, 11.2], and the unit is ℃ (T). H1,2 The value range is [7.6, 10.1], and the unit is ℃ (T). H1,3 The value range is [8.4, 12.2], and the unit is ℃ (T). Hq,w N represents the representative temperature value at the w-th typical location within the q-th lateral temperature subgradient. d For the design service life, T H1,w P(T) represents the temperature at the w-th typical location in the first transverse temperature subgradient. H1 (x)), P(T) H2 (x)), P(T) H3 (x)), P(T) H4 (x)), P(T) H5 (x)), P(T) H6 (x) represent the probabilities of the occurrence of the six transverse temperature sub-gradients within the design service life, and T represents the probability of these occurrences. H1,1 T H2,1 T H3,1 T H4,1 T H5,1 T H6,1 These represent the temperature values ​​at the sunlit side edges of the six transverse temperature sub-gradients. In this embodiment, T... H1,1 The temperature was 9.9℃, T H1,2 The temperature was 8.3℃, T H1,3 It is 9.5℃.

[0075] The temperature gradient values ​​of the transverse temperature fatigue load spectrum for the 100-year, 150-year, and 200-year design service life of a wingless steel box girder highway bridge were obtained from the above model. The transverse sub-gradient modes are as follows: Figure 9 As shown in Table 2, the transverse temperature fatigue load spectrum gradient T of a wingless steel box girder highway bridge is... H1 ~T H6 The probability of occurrence is 32.1%, 17.9%, 25.0%, 10.7%, 7.1%, and 7.2%, respectively. Figure 10 .

[0076] Table 2. Representative values ​​of transverse temperature fatigue load spectrum gradient temperature for wingless steel box girders.

[0077]

[0078] A method for constructing the transverse temperature fatigue load spectrum of a wingless steel box girder highway bridge includes the following steps:

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

[0080] Steps 2-6 are similar to the method for constructing the vertical temperature fatigue load spectrum of wingless steel box girder bridges, and the clustering results are as follows: Figure 11 As shown.

Claims

1. A temperature fatigue load spectrum for a wingless steel box girder bridge, characterized in that: The temperature fatigue load spectrum includes a vertical temperature gradient fatigue load spectrum and a horizontal 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 each sub-gradient within the design service life, specifically: In the formula, T Gi (y) represents the temperature of the i-th vertical temperature sub-gradient at position y, h represents the cross-sectional height of the wingless steel box girder bridge, Gi represents the i-th vertical temperature sub-gradient, and T Gi,1 T Gi,2 T Gi,3 These are the representative temperature values ​​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, respectively, in the i-th vertical temperature sub-gradient, in °C and T. G1,1 T G1,2 T G1,3 These are the representative temperature values ​​(T) 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, respectively, in the first vertical temperature sub-gradient. G1,1 The value range is [3.3, 6.2], and the unit is ℃ (T). G1,2 The value range is [4.8, 7.4], and the unit is ℃ (T). G1,3 The value range is [0.3, 3.2], and the unit is ℃ (T). Gi,j N represents the representative temperature value at the j-th typical height in the i-th vertical temperature sub-gradient. d For the design service life, T G1,j P(T) represents the temperature at the j-th typical height in the first vertical temperature sub-gradient. G1 (y)), P(T) G2 (y)), P(T) G3 (y)), P(T) G4 (y)), P(T) G5 (y)), P(T) G6 (y) represents the probability of occurrence of the six vertical temperature sub-gradients within the design service life, and T G1,1 T G2,1 T G3,1 T G4,1 T G5,1 T G6,1 These are the representative temperature values ​​at the top plate of the steel box girder in the six vertical temperature sub-gradients; The transverse temperature gradient fatigue load spectrum consists of six transverse temperature sub-gradients and the probability of occurrence of each sub-gradient within the design service life, specifically: In the formula, T Hq (x) represents the temperature of the q-th lateral temperature sub-gradient at position x, L is the width of the wingless steel box girder, Hq is the q-th lateral temperature sub-gradient, and T... Hq,1 T Hq,2 T Hq,3 These are the representative temperature values ​​(°C, T) at the sun-facing edge, the position 0.6L from the sun-facing edge, and the shaded edge in the transverse temperature sub-gradient of the q-th wingless steel box girder bridge. H1,1 T H1,2 T H1,3 T represents the representative temperature values ​​at the sunlit side edge, 0.6L from the sunlit side edge, and the shaded side edge in the first transverse temperature subgradient, respectively. H1,1 The value range is [8.6, 11.2], and the unit is ℃ (T). H1,2 The value range is [7.6, 10.1], and the unit is ℃ (T). H1,3 The value range is [8.4, 12.2], and the unit is ℃ (T). Hq,w N represents the representative temperature value at the w-th typical location within the q-th lateral temperature subgradient. d For the design service life, T H1,w P(T) represents the temperature at the w-th typical location in the first transverse temperature subgradient. H1 (x)), P(T) H2 (x)), P(T) H3 (x)), P(T) H4 (x)), P(T) H5 (x)), P(T) H6 (x) represent the probabilities of the occurrence of the six transverse temperature sub-gradients within the design service life, and T represents the probability of these occurrences. H1,1 T H2,1 T H3,1 T H4,1 T H5,1 T H6,1 These represent the temperature values ​​at the sunlit side edges of the six transverse temperature sub-gradients.

2. The temperature fatigue load spectrum of the wingless steel box girder bridge according to claim 1, characterized in that, Its construction method includes the following steps: Step 1: Collect temperature data for the wingless steel box girder bridge. m measuring points were arranged on the wingless steel box girder bridge. Temperature values ​​were collected at each measuring point at regular intervals to obtain the measured temperature gradient time history curves at each location. The measured temperature gradient time history curves were then extended to the design service life N using a long short-term memory recurrent neural network. d Temperature history at typical locations is obtained, yielding the daily temperature maxima at each measuring point for each day within the design service life. A daily temperature extreme value matrix Q = [M1, M2, ..., M] is then constructed for the design service life. t ,…,M Nd×365 ],M t Let be the vector of daily temperature maxima at each measuring point on day t. y1 represents the coordinates of the first temperature measuring point. m Let m be the coordinates of the m-th temperature measuring point. This represents the maximum temperature value at the first temperature measurement point on day t. The maximum temperature value at the m-th temperature measurement point on day t; Step 2: Use the Kmeans++ algorithm to determine the initial cluster centers and cluster families: Step 2.1: Define the number of cluster families as c. l A vector is randomly selected from the daily temperature extreme value matrix Q for the design service life as the first initial cluster center. The Manhattan distance between other vectors in the daily temperature extreme value matrix Q for the design service life and the first initial cluster center is obtained according to the Manhattan distance calculation method. The vector with the largest Manhattan distance to the first initial cluster center is selected 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 daily temperature extreme value matrix Q (excluding 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 1 initial cluster center, and construct c l An initial cluster family; Step 3: Divide the vectors in the daily extreme temperature matrix Q for the design service life into cluster families: Based on the Manhattan distance calculation method, each vector in the daily extreme temperature matrix Q for the design service life is obtained, along with c. l The Manhattan distance between the initial cluster centers will be used to assign each vector in the annual daily temperature extreme value matrix Q to the initial cluster family corresponding to the initial cluster center with the smallest Manhattan distance. Step 4: Update the cluster family: The vector obtained by averaging all vector points in each cluster is used as the virtual new cluster center for each cluster. The Manhattan distance D between the virtual new cluster center and the old cluster center of each cluster is calculated. v Manhattan is far from D v ≤ set threshold D th The cluster centers of the cluster families remain unchanged, and Manhattan is far from D. v > Set threshold D th For each cluster family, the virtual new cluster center is used as the new cluster center. Step 3 is repeated to update the cluster families until the Manhattan distance D between the virtual new cluster center and the old cluster center of all cluster families is found. v ≤ set threshold D th This yields the final cluster family; Step 5: Determine the appropriate number of clusters c l : Let c be the number of clusters. l The numbers are integers from 2 to 10. Following steps 2 and 3, the number of clusters c is obtained. l The final 9 clusters are obtained, and the cluster centers of each final cluster form a cluster center matrix. The sum of squared residuals (RMSE) of the maximum residual temperature of each cluster center matrix is ​​obtained according to the following formula. Plot c l -RMSE two-dimensional line chart, using the elbow rule to determine the optimal number of clusters c. l =6; In the formula, The vector in the k-th row of the cluster center matrix; Step 6: Determine the temperature fatigue load spectrum: Using the number of cluster families c determined in step 5 l and the corresponding cluster center matrix C end Each cluster is a temperature sub-gradient, and the row vector of the cluster center matrix takes the typical representative value of each temperature sub-gradient. The number of sample points in each cluster divided by the total number is the probability of occurrence of each temperature sub-gradient, thus obtaining the corresponding temperature fatigue load spectrum of the wingless steel box girder bridge.

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

4. The method for constructing the temperature fatigue load spectrum of a wingless steel box girder bridge according to claim 2, characterized in that, The m measuring points mentioned in step 1 are used to construct the vertical temperature fatigue load spectrum. The arrangement method is as follows: one measuring point is arranged on the upper surface of the bottom plate of the wingless steel box girder bridge, and the measuring point is used as the origin of the coordinate system. Measuring points are arranged along the vertical height direction on the middle web plate and the top plate, for a total of m = 11 measuring points. The position of the measuring points is expressed as the vertical distance from the upper surface of the bottom plate of the wingless steel box girder 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.

5. The method for constructing the temperature fatigue load spectrum of a wingless steel box girder bridge according to claim 2, characterized in that, In step 1, m measuring points are used to construct the transverse temperature fatigue load spectrum. The arrangement method is as follows: a measuring point is arranged at the edge of the sunny side of the top plate, and with this measuring point as the origin of the coordinate system, 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 horizontal distances from the origin of the coordinate system as 0.00m, L-10.35m, L-5.35m, and L-15.75m.

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

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