Vertical temperature gradient fatigue load model of steel box girder bridge with wing plate and construction method

Abstract

The invention discloses a vertical temperature gradient fatigue load model of a steel box girder bridge with a wing plate and a construction method. The model is specifically in a bifold line type. According to the method, temperature field long-term monitoring is conducted on the steel box girder bridge with the wing plate, extrapolation analysis is conducted on actually-measured temperature data through the autoregression theory, the temperature history of the designed service life of 100 years to 200 years is predicted, and a temperature gradient fatigue load model construction method is provided by combining the damage equivalence principle. A vertical temperature gradient fatigue load model of the steel box girder bridge with the wing plate, which is suitable for the designed service life of 100 years, 150 years and 200 years, is established. The temperature gradient fatigue load model constructed by the method can be used for calculating the temperature fatigue stress process of the steel box girder bridge with the wing plate, and can be used for anti-fatigue design and evaluation of the steel box girder bridge with the wing plate.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a vertical temperature gradient fatigue load model and a construction method for a steel box girder bridge with wing plates. Background Art

[0002] Steel box girder bridges with wing plates are widely used in engineering. Under solar radiation, steel box girders with wing plates will produce nonlinear vertical temperature gradients. The shielding of the wing plates makes the vertical temperature gradient of steel box girder bridges with wing plates more significant with the alternation of day and night temperatures, which in turn leads to large temperature fatigue stress in the beam section, resulting in fatigue cumulative damage in the details of steel box girder bridges with wing plates. At present, there are no reports on the temperature gradient fatigue load model of steel box girder bridges with wing plates at home and abroad, and there are no relevant regulations in the design specifications. Therefore, it is necessary to conduct long-term monitoring of the temperature field of steel box girder bridges with wing plates, use a reasonable temperature history evolution algorithm to perform extrapolation analysis on the measured temperature data, predict the temperature history of the design service life of 100 to 200 years, propose a method for constructing a temperature gradient fatigue load model, establish a vertical temperature gradient fatigue load model of steel box girder bridges with wing plates, calculate the temperature fatigue stress history, and conduct fatigue damage analysis. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a vertical temperature gradient fatigue load model for a steel box girder bridge with wing plates.

[0004] Another technical problem provided by the present invention is to provide a construction method for a vertical temperature gradient fatigue load model of a steel box girder bridge with flanges.

[0005] The vertical temperature gradient fatigue load model of the steel box girder bridge with flange plate used to solve the above technical problems is the positive temperature gradient model T shown in formula (1): + (y), negative temperature gradient model T - (y) Composition:

[0006]

[0007] In formula (1), y is the height of the position to be calculated, h is the section height, T G1 is the representative value of the temperature at the top plate, T G2 is the representative value of the temperature at the distance h / 4 from the top plate to the web, T G3 is the representative value of the temperature at the bottom plate, B is the width of the top plate, b is the width of the bottom plate, k is the number of chambers, β TG (B), β TG (b), β TG (h), β TG (k) intermediate variables, is the initial temperature value at the top plate, in °C, is the initial temperature value of the web at a distance of h / 4 from the top plate, in °C. is the initial temperature value at the bottom plate, in °C, N d It is the design service life, and its value is 100, 150 or 200, in years.

[0008] More preferably, the The value of is [13.8,15.2], the unit is ℃, The value of is [8.9,9.8], the unit is ℃, the value of h is [2.00,5.00], the unit is m, the value of b is [4.00,17.00], the unit is m, the value of B is [7.00,20.00], the unit is m, the value of k is [1,4], and k is a positive integer.

[0009] More preferably, h, B, b, k, The values ​​are: B is 18.00m, b is 11.25m, h is 3.00m, k is 3, 14.5℃, It is 9.4℃.

[0010] The method for constructing a vertical temperature gradient fatigue load model of a steel box girder bridge with flanges of the present invention comprises the following steps:

[0011] (1) Long-term temperature monitoring of steel box girder bridges with flanges

[0012] Temperature measuring points are arranged on the top plate, bottom plate and diaphragm of the steel box girder bridge with flange plates to collect temperature. The time interval between each collection is 1 to 20 minutes, and the collection interval is t d , construct the temperature gradient time history T of the steel box girder bridge with flange A (y,t'), where t' is any moment in the temperature history.

[0013] (2) Standardization of raw data

[0014] Temperature gradient time history T A (y, t') is obtained by the following formula to obtain the standard data T sta (y,t'):

[0015]

[0016] Where E(·) is the mean of the measured temperature data, and D(·) is the variance of the measured temperature data.

[0017] (3) Constructing an autoregressive prediction model

[0018] The autoregressive prediction model Y(y,t') is obtained as follows:

[0019] Y(y,t')=α 1 ×T sta (y,t'-n×t d )+α 2 ×T sta (y,t'-(n-1)×t d )+…+α n ×T sta (y,t'-t d )+c, α 1 , α 2 , ..., α n , c are the parameters of the temperature prediction model Y(y,t'), and n and c are finite positive integers.

[0020] (4) Predict the temperature within the design service life

[0021] Predict the y height at t'+t by the following formula d The temperature Y(y,t'+t d ):

[0022] Y(y,t'+t d )=α 1 ×T sta (y,t'-(n-1)×t d )+α 2 ×T sta (y,t'-(n-2)×t d )+…+α n ×T sta (y,t')+c uses t'+t d The temperature representative value is brought back into the autoregressive prediction model and t'+2t d The prediction is performed until the prediction of all temperature gradient measurement points within the design service life is completed, and the temperature gradient time history T within the design service life is obtained. Y (y,t').

[0023] (5) Determine the equivalent temperature

[0024] The temperature gradient time history T within the design service life Y (y, t') is obtained by the following formula to obtain the temperature stress time history:

[0025]

[0026] In the formula, E s is the elastic modulus of steel, α s is the thermal expansion coefficient of steel, A s is the cross-sectional area of ​​the steel box girder bridge with flange, I s is the moment of inertia of the steel box girder bridge section with flange, y sis the neutral axis of the steel box girder bridge with wing plates, and b(y) is the section thickness at position y of the steel box girder bridge with wing plates.

[0027] Temperature stress time history σ based on rain flow counting method Y (y, t') is processed to obtain the temperature stress amplitude vector A corresponding to the design service life:

[0028] A=(Δσ 1 (y),Δσ 2 (y),...,Δσ m (y))

[0029] In the formula, Δσ m (y) is the mth stress amplitude at position y, and m represents the number of elements in the vector, which is a finite positive integer.

[0030] The equivalent temperature stress Δσ is obtained from the above stress amplitude vector A according to formula (2): eqy :

[0031]

[0032] In the formula, A i is the i-th element in the temperature stress amplitude vector A.

[0033] From the equivalent temperature stress Δσ eqy According to formula (3), the equivalent temperature T eqy :

[0034]

[0035] (6) Constructing a vertical temperature gradient fatigue load model for a steel box girder bridge with flanges

[0036] Using Matlab software, the different positions y and different design service life N d The equivalent temperature representative value T eqy The least squares method is used for fitting, and the vertical temperature gradient fatigue load model T(y) of the steel box girder bridge with flange is obtained in formula (1). Then, the positive temperature gradient model T is obtained by splitting the positive temperature stress and negative temperature stress according to the time ratio of 3:1. + (y) and negative temperature gradient model T - (y).

[0037] The beneficial effects of the present invention are as follows:

[0038] 1. The present invention proposes a method for constructing a temperature gradient fatigue load model for a steel box girder bridge with flanges by using an autoregressive algorithm and the damage equivalence principle. This method overcomes the deficiency that Latin hypercube sampling cannot perform continuous extension of temperature stress, and can provide a reliable vertical temperature gradient fatigue load model for the long-life design of steel box girders.

[0039] 2. The present invention uses the long-term temperature monitoring results of steel box girder bridges with wing plates to establish a vertical temperature gradient fatigue load model for steel box girder bridges with wing plates with a design service life of 100 years, 150 years and 200 years. The temperature gradient fatigue load model fully considers the influence of the top plate width B, bottom plate width b, beam height h and number of box chambers k of the steel box girder bridge with wing plates.

[0040] 3. The vertical temperature gradient fatigue load model of the steel box girder bridge with wing plates constructed by the present invention is simple in form and can calculate the stress history of the fatigue details of the steel box girder with wing plates. It is suitable for the long-life fatigue resistance design and evaluation of the steel box girder bridge with wing plates. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is the temperature representative value distribution of the vertical temperature gradient fatigue load model for steel box girder bridge with flanges.

[0042] Figure 2 A flow chart is developed for the vertical temperature gradient fatigue load model of a steel box girder bridge with flanges.

[0043] Figure 3 This is the temperature gradient time history prediction result based on the autoregressive algorithm.

[0044] Figure 4 Schematic diagram of the three-dimensional structure of a steel box girder with flanges.

[0045] Figure 5 This is the layout diagram of vertical temperature measurement points for steel box girder with flange plates.

[0046] Figure 6 This is the measured temperature history curve of the steel box girder bridge with wing plates.

[0047] Figure 7 This is the histogram of the measured temperature stress amplitude at the K-9 measuring point. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to these embodiments.

[0049] Example 1

[0050] The vertical temperature gradient fatigue load model of the steel box girder bridge with flanges involved in this embodiment is a positive temperature gradient model T shown in formula (1): + (y), negative temperature gradient model T - (y) Composition:

[0051]

[0052] In formula (1), y is the height of the position to be calculated, h is the section height, TG1 is the representative value of the temperature at the top plate, T G2 is the representative value of the temperature at the distance h / 4 from the top plate to the web, T G3 is the representative value of the temperature at the bottom plate, B is the width of the top plate, b is the width of the bottom plate, k is the number of chambers, β TG (B), β TG (b), β TG (h), β TG (k) is the intermediate variable, is the initial temperature value at the top plate, in °C, is the initial temperature value of the web at a distance of h / 4 from the top plate, in °C. is the initial temperature value at the bottom plate, in °C, N d It is the design service life, and its value is 100, 150 or 200, in years.

[0053] In the present embodiment (1), the beam height h is selected to be 3.00 m, the top plate width B is selected to be 18.00 m, the bottom plate width b is selected to be 11.25 m, and the number of steel box beam bridge box chambers k with flange plates is selected to be 3. The value of is 14.5℃, The value of is 9.4℃, and the corresponding vertical temperature fatigue load model is constructed. The temperature representative values ​​at different heights corresponding to 100 years, 150 years, and 200 years are shown in Table 1. The temperature representative value distribution in the vertical temperature gradient fatigue load model constructed according to this parameter is as follows Figure 1 As shown, the positive temperature gradient model is shown in Figure (a) and the negative temperature gradient model is shown in Figure (b).

[0054] Table 1 Representative values ​​of vertical temperature fatigue load model temperature for steel box girder bridge with flange

[0055]

[0056] like Figure 2 As shown, the method for constructing the vertical temperature gradient fatigue load model of the steel box girder bridge with flanges specifically includes the following steps:

[0057] (1) Long-term temperature monitoring of steel box girder bridges with flanges

[0058] Temperature measuring points are arranged on the top plate, bottom plate and diaphragm of the steel box girder bridge with flange plates to collect temperature. The time interval for each collection is 1 to 20 minutes, and the monitoring interval is t d , construct the temperature gradient time history T of the steel box girder bridge with flange A (y,t'); where t' is any moment in the temperature history.

[0059] (2) Standardization of raw data

[0060] Temperature gradient time history T A (y, t') is obtained by the following formula to obtain the standard data T sta (y,t'):

[0061]

[0062] Where E(·) is the mean of the measured temperature data, and D(·) is the variance of the measured temperature data.

[0063] (3) Constructing an autoregressive prediction model

[0064] The autoregressive prediction model Y(y,t') is obtained as follows:

[0065] Y(y,t')=α 1 ×T sta (y,t'-n×t d )+α 2 ×T sta (y,t'-(n-1)×t d )+…+α n ×T sta (y,t'-t d )+c

[0066] In the formula, α 1 ,α 2 ,...,α n , c is the parameter of the temperature prediction model Y(y,t'), n and c are finite positive integers.

[0067] (4) Predict the temperature within the design service life

[0068] Predict the y height at t'+t by the following formula d The temperature Y(y,t'+t d ):

[0069] Y(y,t'+t d )=α 1 ×T sta (y,t'-(n-1)×t d )+α 2 ×T sta (y,t'-(n-2)×t d )+…+α n ×T sta (y,t')+c uses t'+t d The temperature value is brought back into the autoregressive prediction model and t'+2t d The prediction is performed until the prediction of all temperature gradient measurement points within the design service life is completed, and the temperature gradient time history T within the design service life is obtained. Y (y,t'), such as Figure 3shown.

[0070] (5) Determine the equivalent temperature

[0071] The temperature gradient time history T within the design service life Y (y, t') is obtained by the following formula to obtain the temperature stress time history

[0072]

[0073] In the formula, E s is the elastic modulus of steel, α s is the thermal expansion coefficient of steel, A s is the cross-sectional area of ​​the steel box girder bridge with flange, I s is the moment of inertia of the steel box girder bridge section with flange, y s is the neutral axis of the steel box girder bridge with flange, b(y) is the section thickness at the y position of the steel box girder bridge with flange; in this example, E s =2.06×10 5 MPa, α s =1.1×10 -5 ℃ -1 .

[0074] Temperature stress time history σ based on rain flow counting method Y (y, t') is processed to obtain the temperature stress amplitude vector A corresponding to the design service life:

[0075] A=(Δσ 1 (y),Δσ 2 (y),...,Δσ m (y))

[0076] In the formula, Δσ m (y) is the mth stress amplitude at position y, and m represents the number of elements in the vector, which is a finite positive integer.

[0077] The equivalent temperature stress Δσ is obtained from the above stress amplitude vector A according to the following formula: eqy :

[0078]

[0079] Where: A i is the i-th element in the temperature stress amplitude vector A.

[0080] From the equivalent temperature stress Δσ eqy The equivalent temperature T is obtained by the following formula eqy :

[0081]

[0082] (6) Constructing a vertical temperature gradient fatigue load model for a steel box girder bridge with flanges

[0083] Using Matlab software, we can analyze the different positions y and different design service life N. d The equivalent temperature representative value T eqy The least squares method is used for fitting, and the vertical temperature gradient fatigue load model T(y) of the steel box girder bridge with flange is obtained in formula (1). Then, the positive temperature gradient model T is obtained by splitting the positive temperature stress and negative temperature stress according to the time ratio of 3:1. + (y) and negative temperature gradient model T - (y).

[0084] Example 2

[0085] The vertical temperature gradient fatigue load model of the steel box girder bridge with flange involved in this embodiment is shown in formula (1), and the construction method is the same as that of Example 1.

[0086] In this embodiment, the formula (1) selects the beam height h as 2.00m, the top plate width B as 7.00m, the bottom plate width b as 4.00m, and the number of steel box girder bridge box chambers k with flange plates as 1. The value of is 13.8℃, The value of is 8.9°C, and the other parameters are the same as those in the embodiment. The corresponding vertical temperature gradient fatigue load model is constructed, and the temperature representative values ​​at different heights corresponding to 100 years, 150 years, and 200 years are shown in Table 2. The temperature representative value distribution in the vertical temperature gradient fatigue load model constructed according to the parameters is as follows Figure 1 As shown, the positive temperature gradient model is shown in Figure (a) and the negative temperature gradient model is shown in Figure (b).

[0087] Table 2 Representative values ​​of vertical temperature fatigue load model for steel box girder bridge with flange

[0088]

[0089] Example 3

[0090] The vertical temperature gradient fatigue load model of the steel box girder bridge with flange involved in this embodiment is shown in formula (1), and the construction method is the same as that of Example 1.

[0091] Taking the climate in Liaoning as an example, in formula (1), the beam height h is selected as 5.00m, the top plate width B is selected as 20.00m, the bottom plate width b is selected as 17.00m, and the number of box chambers k of the steel box girder bridge with flange is selected as 4. The value of is 15.2℃, The value of is 9.8°C, and the other parameters are the same as those in the embodiment. The corresponding vertical temperature gradient fatigue load model is constructed, and the temperature representative values ​​at different heights corresponding to 100 years, 150 years, and 200 years are shown in Table 3. The temperature representative value distribution in the vertical temperature gradient fatigue load model constructed according to the parameters is as follows Figure 1 As shown, the positive temperature gradient model is shown in Figure (a) and the negative temperature gradient model is shown in Figure (b).

[0092] Table 3 Representative values ​​of vertical temperature fatigue load model for steel box girder bridge with flange

[0093]

[0094] Test 1

[0095] In order to verify the effect of the vertical temperature gradient fatigue load model of the steel box girder bridge with flange, the model and construction method of Example 1 were used to arrange vertical temperature sensors on the Shenyang Houdingxiang Viaduct and conduct long-term temperature field monitoring. Figure 4 shown.

[0096] 1. Long-term monitoring instruments

[0097] The monitoring instrument is a 16-channel JM3812 multi-function data acquisition instrument produced in Yangzhou, Jiangsu; the temperature acquisition software is the JMTEST static signal test and analysis software produced in Yangzhou, Jiangsu; the temperature sensor is a three-wire Pt100 sensor.

[0098] 2. Temperature measurement point arrangement

[0099] Temperature measuring points are arranged on the top plate, web plate and bottom plate of the steel box girder with flange plates. The positions of the temperature measuring points arranged on the steel web plates on both sides are expressed as 0.00m, 0.90m, 1.80m, 2.40m, 2.70m, 2.80m, 2.90m, 2.95m, 3.00m in vertical distance from the lower surface of the bottom plate of the steel box girder, recorded as K-1 to K-9, where h is the height of the steel box girder with flange plates. The measuring points are arranged as follows: Figure 5 Continuous temperature collection was performed at these measuring points to obtain effective monitoring data for one year, with a collection interval of 10 minutes. The measured temperature history curve is shown in Figure 6 shown.

[0100] 3. Analysis of the effect of vertical temperature gradient fatigue load model

[0101] Taking the bottom butt weld of a steel box girder bridge with flange as an example, the temperature stress history is plotted based on the temperature measurement monitoring data, and the temperature stress amplitude cycle counting is performed using the rain flow counting method to obtain the stress amplitude histogram. The results are as follows: Figure 7 Then, the equivalent fatigue stress was calculated based on the measured results, and the result was 7.8MPa.

[0102] Based on the temperature gradient fatigue load model, the temperature stress history is constructed and the temperature stress amplitude analysis is performed. Where B = 18.00m, b = 11.25m, h = 3.00m, k = 3, N d =100 years, substitute into the following formula:

[0103]

[0104] The equivalent temperature fatigue stress σ can be obtained eq (y) is 8.2MPa, which is basically consistent with the equivalent fatigue stress of the measured results. This shows that the vertical temperature gradient fatigue load model of the steel box girder bridge with flange plate has good applicability.

Claims

1. A vertical temperature gradient fatigue load model for a steel box girder bridge with flanges, characterized in that: The model is composed of the positive temperature gradient model T shown in formula (1) + (y), negative temperature gradient model T - (y) composition: In formula (1), y is the height of the position to be calculated, h is the section height, T G1 is the representative value of the temperature at the top plate, T G2 is the representative value of the temperature at the distance h / 4 from the top plate to the web, T G3 is the representative value of the temperature at the bottom plate, B is the width of the top plate, b is the width of the bottom plate, k is the number of chambers, β TG (B), β TG (b), β TG (h), β TG (k) intermediate variables, is the initial temperature value at the top plate, in °C, is the initial temperature value of the web at a distance of h / 4 from the top plate, in °C. is the initial temperature value at the bottom plate, in °C, N d It is the design service life, and its value is 100, 150 or 200, in years.

2. The vertical temperature gradient fatigue load model of the steel box girder bridge with flange according to claim 1 is characterized in that: In formula (1), The value of is [13.8,15.2], the unit is ℃, The value of is [8.9,9.8], the unit is ℃, the value of h is [2.00,5.00], the unit is m, the value of b is [4.00,17.00], the unit is m, the value of B is [7.00,20.00], the unit is m, the value of k is [1,4], and k is a positive integer.

3. The vertical temperature gradient fatigue load model of the steel box girder bridge with flange according to claim 1 is characterized in that h, B, b, k, The values ​​are: B is 18.00m, b is 11.25m, h is 3.00m, k is 3, 14.5℃, It is 9.4℃.

4. A method for constructing a vertical temperature gradient fatigue load model for a steel box girder bridge with flanges according to claim 1, characterized in that It consists of the following steps: (1) Long-term temperature monitoring of steel box girder bridges with flanges Temperature measuring points are arranged on the top plate, bottom plate and diaphragm of the steel box girder bridge with flange plates to collect temperature. The time interval between each collection is 1 to 20 minutes, and the collection interval is t d , construct the temperature gradient time history T of the steel box girder bridge with flange A (y, t'), where t' is any time in the temperature history; (2) Standardization of raw data Temperature gradient time history T A (y, t') is obtained by the following formula to obtain the standard data T sta (y,t'): Where, E(·) is the mean of the measured temperature data, and D(·) is the variance of the measured temperature data; (3) Constructing an autoregressive prediction model The autoregressive prediction model Y(y,t') is obtained as follows: Y(y,t')=α1×T sta (y,t'-n×t d )+α2×T sta (y,t'-(n-1)×t d )+…+α n ×T sta (y,t'-t d )+c, where α1, α2, ..., α n , c are the parameters of the temperature prediction model Y(y,t'), n and c are finite positive integers; (4) Predict the temperature within the design service life Predict the y height at t'+t by the following formula d The temperature Y(y,t'+t d ): Y(y,t'+t d )=α1×T sta (y,t'-(n-1)×t d )+α2×T sta (y,t'-(n-2)×t d )+…+α n ×T sta (y,t')+c uses t'+t d The temperature representative value is brought back into the autoregressive prediction model and t'+2t d The prediction is performed until the prediction of all temperature gradient measurement points within the design service life is completed, and the temperature gradient time history T within the design service life is obtained. Y (y,t'); (5) Determine the equivalent temperature The temperature gradient time history T within the design service life Y (y, t') is obtained by the following formula to obtain the temperature stress time history: In the formula, E s is the elastic modulus of steel, α s is the thermal expansion coefficient of steel, A s is the cross-sectional area of ​​the steel box girder bridge with flange, I s is the moment of inertia of the steel box girder bridge section with flange, y s is the neutral axis of the steel box girder bridge with flange, b(y) is the section thickness at position y of the steel box girder bridge with flange; Temperature stress time history σ based on rain flow counting method Y (y, t') is processed to obtain the temperature stress amplitude vector A corresponding to the design service life: A=(Δσ1(y),Δσ2(y),...,Δσ m (y)) In the formula, Δσ m (y) is the mth stress amplitude at position y, where m represents the number of elements in the vector and is a finite positive integer; The equivalent temperature stress Δσ is obtained from the above stress amplitude vector A according to formula (2): eqy : In the formula, A i is the i-th element in the temperature stress amplitude vector A; From the equivalent temperature stress Δσ eqy According to formula (3), the equivalent temperature T eqy : (6) Constructing a vertical temperature gradient fatigue load model for a steel box girder bridge with flanges Using Matlab software, the different positions y and different design service life N d The equivalent temperature representative value T eqy The least squares method is used for fitting, and the vertical temperature gradient fatigue load model T(y) of the steel box girder bridge with flange is obtained in formula (1). Then, the positive temperature gradient model T is obtained by splitting the positive temperature stress and negative temperature stress according to the time ratio of 3:

1. + (y) and negative temperature gradient model T - (y).

Images