Vertical temperature gradient fatigue load spectrum and construction method of composite slab girder bridge

Abstract

A fatigue load spectrum and construction method for vertical temperature gradient of composite plate girder bridges are disclosed, comprising four vertical temperature sub-gradients and their occurrence probabilities. The inventors proposed a simplified calculation formula for temperature stress in composite plate girder bridges, analyzed the distribution characteristics of the vertical temperature field of composite steel plate girders, obtained the temperature sub-gradients of composite plate girder bridges using a noisy density clustering analysis method, calculated the occurrence probability of the sub-gradients using basic principles of mathematical statistics, and proposed a fatigue load spectrum for vertical temperature gradient of composite plate girder bridges with design service lives of 100, 150, and 200 years. The constructed fatigue load spectrum for vertical temperature gradient of composite plate girder bridges can be used for long-life fatigue-resistant design and fatigue damage assessment of composite plate girder bridges.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically relating to a vertical temperature gradient fatigue load spectrum and construction method for composite slab girder bridges. Background Technology

[0002] Composite slab girder bridges typically utilize I-beam cross-section steel beams, resulting in significant vertical temperature gradients. Under solar radiation, periodically varying temperature fatigue stresses occur at key details. Under the coupled cyclic action of temperature loads and vehicle loads, the cumulative fatigue damage at these details significantly increases. Since the temperature effects encompass the cyclical effects of diurnal and seasonal temperature variations, a temperature gradient fatigue load spectrum can be used to characterize various periodic temperature fatigue effects. This study delves into the temperature effects and structural behavior of composite steel plate girders in natural environments, constructing a temperature gradient fatigue load spectrum suitable for composite slab girder bridges with a design service life of up to 200 years. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a vertical temperature gradient fatigue load spectrum for a composite slab girder bridge and a method for constructing it.

[0004] The technical solution adopted to solve the above-mentioned technical problems is as follows: a vertical temperature gradient fatigue load spectrum for composite slab girder bridges, which consists of four vertical temperature sub-gradients and the probability of occurrence of each sub-gradient within its 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, and h represents the height of the composite slab-girder bridge. c h is the height of the composite layer. s The height of the steel plate beam is h = h c +h s Gi is the i-th vertical temperature sub-gradient, and 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 G1,1 T G1,2 T G1,3 T G1,4 These represent the top of the combined layer in the i-th vertical temperature sub-gradient, and the distance h from the top plate, respectively. c Location, 0.5h from the bottom plate s The representative temperature values ​​at the bottom plate of the lower flange and the bottom plate, T G1,1 The value range is [4.1, 5.2], and the unit is ℃ (T). G1,2 The value range is [5.5, 7.4], and the unit is ℃ (T). Gi,jN 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) represents the probability of occurrence of the four vertical temperature sub-gradients within the design service life, and T G1,1 T G2,1 T G3,1 T G4,1 These are the representative temperature values ​​at the top plates of the four vertical temperature sub-gradients.

[0007] A method for constructing the vertical temperature gradient fatigue load spectrum of a composite slab girder bridge includes the following steps:

[0008] Step 1: Collect temperature data for the composite slab girder bridge

[0009] m temperature measuring points are arranged inside the concrete slab, steel top slab, bottom slab, and web of the composite slab girder bridge. Temperature values ​​are collected at regular intervals at each measuring point to obtain the measured temperature gradient time history curves at each location. The measured temperature gradient time history curves are then extended to the design service life N using a long short-term memory recurrent neural network algorithm. 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;

[0010] Step 2: Preprocess the daily temperature extreme value matrix Q for the design service life using a noisy density clustering algorithm.

[0011] Define the initial parameters of the density clustering algorithm, namely the minimum number of points MP and the neighborhood radius r. e In the daily temperature extreme value matrix Q for the design service life, each vector is selected as a high-dimensional coordinate point A. The Euclidean distance between other vectors and this high-dimensional coordinate point A is calculated, and the Euclidean distance is ≤ the neighborhood radius r. e The vector is classified into the neighborhood of the high-dimensional coordinate point A, resulting in N. d ×365 neighborhoods are selected, and neighborhoods containing vectors ≥ minimum number of points MP are selected. Each selected neighborhood is taken as a temporary cluster family T. The high-dimensional coordinate point A of each temporary cluster family T is taken as the core point of the cluster family. All temporary cluster families T constitute a temporary cluster family set R.

[0012] Step 3: Merge temporary clusters to obtain formal clusters:

[0013] Step 3.1: Randomly select a temporary cluster T from the temporary cluster set R. Then, sequentially query other temporary clusters and remove any other temporary clusters whose core points are located in this temporary cluster T from the temporary cluster set R and merge them into this temporary cluster, thus obtaining the formal cluster T. / ;

[0014] Step 3.2: Repeat step 3.1 until all temporary clusters in the temporary cluster set R are taken, resulting in S formal clusters T. / ;

[0015] Step 4: Determine the temperature gradient fatigue load spectrum of the concrete box girder bridge.

[0016] Each formal cluster T / The vertical temperature subgradient T Gi (y), each formal cluster family T / The middle sample points and S formal clusters T / The ratio of all sample points is the probability P(T) of each sub-gradient occurring within the design service life. Gi Thus, the temperature fatigue load spectrum of the concrete box girder bridge was obtained.

[0017] Preferably, in step 2, the minimum number of points MP ≤ 25 and the neighborhood radius r e The value ranges from 2.5 to 7.5.

[0018] Preferably, the Euclidean distance is obtained according to the following formula;

[0019]

[0020] In the formula, d e Euclidean distance. For t A Date y k The maximum temperature at location y k Let t be the location of the kth typical measuring point. A t represents the date of the temporary cluster family, and t represents the date of the extreme daily temperature vectors other than the cluster center.

[0021] Preferably, the arrangement method of the m measuring points in step 1 is as follows: a measuring point is arranged on the bottom plate of the composite slab beam bridge, and with this measuring point as the origin of the coordinate system, measuring points are arranged on the web and top plate along the vertical height direction, for a total of m = 9 measuring points. The positions of the measuring points are expressed as the vertical distances from the lower surface of the bottom plate of the composite slab beam bridge as 0.00m, H-0.96m, H-0.51m, H-0.36m, H-0.26m, H-0.21m, H-0.20m, H-0.12m, and H, where H is the height of the composite steel plate beam.

[0022] Preferably, the time interval between the temperature values ​​of each measuring point in step 1 is 60 to 1200 seconds.

[0023] The beneficial effects of this invention are as follows:

[0024] 1. This invention establishes a vertical temperature gradient fatigue load spectrum for long-life composite slab girder bridges by analyzing measured temperature field data of composite slab girder bridges. This temperature fatigue load spectrum can be used for long-life fatigue-resistant design and fatigue damage assessment of composite slab girder bridges.

[0025] 2. This invention proposes a method for constructing the temperature fatigue load spectrum of composite plate girder bridges using a noisy density clustering algorithm. This method can self-identify and cluster the number of clusters based on the statistical characteristics of temperature data, thereby improving the accuracy and reliability of load spectrum construction.

[0026] 3. The load spectrum constructed in this invention can be directly used for long-life fatigue-resistant design and fatigue damage assessment of composite slab girder bridges, providing a practical tool for bridge design and maintenance.

[0027] 4. This invention extends measured temperature data to the design service life through a long short-term memory recurrent neural network algorithm, effectively processing a large amount of temperature data and improving data processing efficiency. Attached Figure Description

[0028] Figure 1 This is the vertical temperature sub-gradient mode for composite slab girder bridges.

[0029] Figure 2 This is a frequency distribution diagram of the vertical temperature sub-gradients of the composite slab girder bridge.

[0030] Figure 3 This is a flowchart illustrating the construction of the vertical temperature fatigue load spectrum for the composite plate girder bridge of the present invention.

[0031] Figure 4 This is a diagram showing the layout of temperature measuring points for a composite slab beam bridge.

[0032] Figure 5 This is a temperature history curve at a typical location in a composite slab girder bridge.

[0033] Figure 6 The results are from a density clustering algorithm with noise. Detailed Implementation

[0034] 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 these embodiments.

[0035] Example 1

[0036] Taking a composite slab girder bridge in Xi'an with a beam height of 1.40m as an example, the temperature gradient fatigue load spectrum of this bridge consists of four vertical temperature sub-gradients and the probability of occurrence of each sub-gradient within its design service life, specifically:

[0037]

[0038] In the formula, T Gi (y) represents the temperature of the i-th vertical temperature sub-gradient at position y, and h represents the height of the composite slab-girder bridge. c h is the height of the composite layer. s The height of the steel plate beam is h = h c +h s Gi is the i-th vertical temperature sub-gradient, and 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 G1,1 T G1,2 T G1,3 T G1,4 These represent the top of the combined layer in the i-th vertical temperature sub-gradient, and the distance h from the top plate, respectively. c Location, 0.5h from the bottom plate s The representative temperature values ​​at the bottom plate of the lower flange and the bottom plate, T G1,1 The value range is [4.1, 5.2], and the unit is ℃ (T). G1,2 The value range is [5.5, 7.4], 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) represents the probability of occurrence of the four vertical temperature sub-gradients within the design service life, and T G1,1 T G2,1 T G3,1 T G4,1 These are the representative temperature values ​​at the top plates of the four vertical temperature sub-gradients.

[0039] In this embodiment, T G1,1 =4.8℃, T G1,2 =6.9℃. Based on the temperature fatigue load spectrum of the above composite slab girder bridge, the representative temperature values ​​of each sub-gradient at different heights corresponding to the design service life of 100 years, 150 years, and 200 years are shown in Table 1. The vertical temperature sub-gradient is as follows: Figure 1 As shown. Vertical temperature subgradient T G1 ~T G4 The probability of occurrence is 23.6%, 36.1%, 26.1%, and 14.2%, respectively. See details... Figure 2 .

[0040] Table 1. Representative values ​​of vertical temperature fatigue load spectrum gradient temperature for highway composite steel plate girders.

[0041]

[0042] exist Figure 3 The method for constructing the temperature fatigue load spectrum of the composite slab girder bridge in this embodiment includes the following steps:

[0043] Step 1: Long-term temperature data monitoring;

[0044] A measuring point is set up on the bottom slab of the composite slab girder bridge, and using this measuring point as the origin, measuring points are set up along the vertical direction on the web and top slab, for a total of m = 9 measuring points. The positions of the measuring points are expressed as vertical distances from the lower surface of the bottom slab of the composite slab girder bridge as 0.00m, 0.45m, 0.90m, 1.05m, 1.15m, 1.20m, 1.21m, 1.29m, and 1.41m. The arrangement of the measuring points is as follows: Figure 4 As shown, the temperature values ​​of each measuring point are collected every 300 seconds, or every 1 second, or every 1800 seconds.

[0045] The measured temperature gradient time history curves at various locations of the composite slab girder bridge were obtained, as follows: Figure 5 The measured temperature gradient time history curve is extended to the design service life N using a long short-term memory recurrent neural network algorithm, as shown. 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;

[0046] Step 2: Preprocess the daily temperature extreme value matrix Q for the design service life using a noisy density clustering algorithm.

[0047] Define the initial parameters for the noisy density clustering algorithm: the minimum number of points MP and the neighborhood radius r. e Minimum number of points MP≤25, neighborhood radius r e The value is between 2.5 and 7.5. In this embodiment, the minimum number of points MP = 15, and the neighborhood radius r e It is 5;

[0048] In the daily temperature extreme value matrix Q for the design service life, each vector is selected as a high-dimensional coordinate point A. The Euclidean distance between other vectors and this high-dimensional coordinate point A is calculated, and the Euclidean distance d is expressed as... e ≤ Neighborhood radius r e The vector is classified into the neighborhood of the high-dimensional coordinate point A, resulting in N. d ×365 neighborhoods are selected, and neighborhoods containing vectors ≥ minimum number of points MP are selected. Each selected neighborhood is taken as a temporary cluster family T. The high-dimensional coordinate point A of each temporary cluster family T is taken as the core point of the cluster family. All temporary cluster families T constitute a temporary cluster family set R.

[0049] The Euclidean distance is obtained according to the following formula;

[0050]

[0051] In the formula, d e Euclidean distance. For t A Date y k The maximum temperature at location y k Let t be the location of the kth typical measuring point. A t represents the date of the temporary cluster core point, and t represents the date of the daily temperature extreme value vectors other than the cluster center point;

[0052] Step 3: Merge temporary clusters to obtain formal clusters:

[0053] Step 3.1: Randomly select a temporary cluster T from the temporary cluster set R. Then, sequentially query other temporary clusters and remove any other temporary clusters whose core is located in the selected temporary cluster T from the temporary cluster set R and merge them into the selected temporary cluster T to obtain the final cluster T. / ;

[0054] Step 3.2: Repeat step 3.1 until all temporary clusters in the temporary cluster set R are taken, resulting in S formal clusters T. / The cluster analysis results are as follows Figure 6 As shown.

[0055] Step 4: Determine the temperature fatigue load spectrum of the concrete box girder bridge.

[0056] Each formal cluster T / The vertical temperature subgradient T of this model Gi (y), each formal cluster family T / The middle sample points and S formal clusters T / The ratio of all sample points is the probability P(T) of each sub-gradient occurring within the design service life. Gi Thus, the temperature fatigue load spectrum of the concrete box girder bridge was obtained.

Claims

1. A vertical temperature gradient fatigue load spectrum for a composite slab girder bridge, characterized in that: The load spectrum consists of four 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, and h represents the height of the composite slab-girder bridge. c h is the height of the composite layer. s Let h be the height of the steel plate beam, where h = h c +h s Gi is the i-th vertical temperature sub-gradient, and 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 G1,1 T G1,2 T G1,3 T G1,4 These represent the top of the combined layer in the i-th vertical temperature sub-gradient, and the distance h from the top plate, respectively. c Location, 0.5h from the bottom plate s The representative temperature values ​​at the bottom plate of the lower flange and the bottom plate, T G1,1 The value range is [4.1, 5.2], and the unit is ℃ (T). G1,2 The value range is [5.5, 7.4], and the unit is ℃. P(T) G1 (y)), P(T) G2 (y)), P(T) G3 (y)), P(T) G4 (y) represents the probability of occurrence of the four vertical temperature sub-gradients within the design service life, and T G1,1 T G2,1 T G3,1 T G4,1 These are the representative temperature values ​​at the top plates of the four vertical temperature sub-gradients.

2. The method for constructing the vertical temperature gradient fatigue load spectrum of a composite slab girder bridge according to claim 1 includes the following steps: Step 1: Collect temperature data for the composite slab girder bridge m temperature measuring points are arranged inside the concrete slab, steel top slab, bottom slab, and web of the composite slab girder bridge. Temperature values ​​are collected at regular intervals at each measuring point to obtain the measured temperature gradient time history curves at each location. The measured temperature gradient time history curves are then extended to the design service life N using a long short-term memory recurrent neural network algorithm. 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; Step 2: Preprocess the daily temperature extreme value matrix Q for the design service life using a noisy density clustering algorithm. Define the initial parameters of the density clustering algorithm, namely the minimum number of points MP and the neighborhood radius r. e In the daily temperature extreme value matrix Q for the design service life, each vector is selected as a high-dimensional coordinate point A. The Euclidean distance between other vectors and this high-dimensional coordinate point A is calculated, and the Euclidean distance is ≤ the neighborhood radius r. e The vector is classified into the neighborhood of the high-dimensional coordinate point A, resulting in N. d ×365 neighborhoods are selected, and neighborhoods containing vectors ≥ minimum number of points MP are selected. Each selected neighborhood is taken as a temporary cluster family T. The high-dimensional coordinate point A of each temporary cluster family T is taken as the core point of the cluster family. All temporary cluster families T constitute a temporary cluster family set R. Step 3: Merge temporary clusters to obtain formal clusters: Step 3.1: Randomly select a temporary cluster T from the temporary cluster set R. Then, sequentially query other temporary clusters and remove any other temporary clusters whose core points are located in this temporary cluster T from the temporary cluster set R and merge them into this temporary cluster, thus obtaining the formal cluster T. / ; Step 3.2: Repeat step 3.1 until all temporary clusters in the temporary cluster set R are taken, resulting in S formal clusters T. / ; Step 4: Determine the temperature gradient fatigue load spectrum of the concrete box girder bridge. Each formal cluster T / The vertical temperature subgradient T Gi (y), each formal cluster family T / The middle sample points and S formal clusters T / The ratio of all sample points is the probability P(T) of each sub-gradient occurring within the design service life. Gi Thus, the temperature fatigue load spectrum of the concrete box girder bridge was obtained.

3. The method for constructing the vertical temperature gradient fatigue load spectrum of a composite slab girder bridge according to claim 2, characterized in that: In step 2, the minimum number of points MP ≤ 25, and the neighborhood radius r e The value ranges from 2.5 to 7.

5.

4. The method for constructing the vertical temperature gradient fatigue load spectrum of a composite slab girder bridge according to claim 2, characterized in that: The Euclidean distance is obtained according to the following formula; In the formula, d e For Euclidean distance, T Nd (y k ,t A ) for t A Date y k The maximum temperature at location y k Let t be the location of the kth typical measuring point. A t represents the date of the temporary cluster family, and t represents the date of the extreme daily temperature vectors other than the cluster center.

5. The method for constructing the vertical temperature gradient fatigue load spectrum of a composite slab girder bridge according to claim 2, characterized in that, The arrangement method of the m measuring points in step 1 is as follows: a measuring point is arranged on the bottom plate of the composite slab beam bridge, and the measuring point is used as the origin of the coordinate system. Measuring points are arranged on the web and top plate along the vertical height direction, for a total of m = 9 measuring points. The positions of the measuring points are expressed as the vertical distances from the bottom surface of the composite slab beam bridge as 0.00m, H-0.96m, H-0.51m, H-0.36m, H-0.26m, H-0.21m, H-0.20m, H-0.12m, and H, where H is the height of the composite steel plate beam.

6. The method for constructing the vertical temperature gradient fatigue load spectrum of a composite slab 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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