Vertical temperature gradient fatigue load model and construction method for steel box girder bridge with wing plates

Abstract

A vertical temperature gradient fatigue load model and construction method for a steel box girder bridge with wing plates, the model specifically being a bilinear type. Long-term temperature field monitoring of a steel box girder bridge with wing plates is performed, and the measured temperature data is extrapolated and analyzed using autoregressive theory to predict the temperature history over a design service life of 100 to 200 years. Combining the damage equivalence principle, a method for constructing a temperature gradient fatigue load model is proposed, and a vertical temperature gradient fatigue load model for a steel box girder bridge with wing plates suitable for a design service life of 100, 150, and 200 years is established. The temperature gradient fatigue load model constructed by the present invention can calculate the temperature fatigue stress history of a steel box girder bridge with wing plates, and can be used for the fatigue resistance design and evaluation of a steel box girder bridge with wing plates.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge engineering, and particularly relates to a vertical temperature gradient fatigue load model and a construction method of a steel box girder bridge with a wing plate. BACKGROUND

[0002] The steel box girder bridge with a wing plate is widely used in engineering. Under the action of solar radiation, the steel box girder bridge with a wing plate generates a nonlinear vertical temperature gradient. The shielding of the wing plate makes the vertical temperature gradient of the steel box girder bridge with a wing plate more significant under the alternating day and night temperature, and further causes a larger temperature fatigue stress of the beam section, resulting in the fatigue cumulative damage of the steel box girder bridge with a wing plate at the details. At present, there is no related report on the temperature gradient fatigue load model of the steel box girder bridge with a wing plate at home and abroad, and there is no related provision in the design specification. Therefore, it is necessary to perform long-term monitoring on the temperature field of the steel box girder bridge with a wing plate, to extrapolate and analyze the measured temperature data by using a reasonable temperature history evolution algorithm, to predict the temperature history in the design service life of 100 years to 200 years, to propose a construction method of the temperature gradient fatigue load model, to establish the vertical temperature gradient fatigue load model of the steel box girder bridge with a wing plate, to calculate the temperature fatigue stress history, and to perform fatigue damage analysis. SUMMARY

[0003] The technical problem to be solved by the application is to overcome the deficiencies of the prior art, and to provide a vertical temperature gradient fatigue load model of a steel box girder bridge with a wing plate.

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

[0005] The vertical temperature gradient fatigue load model of the steel box girder bridge with a wing plate solving the above technical problem is composed of a positive temperature gradient model T + (y) and a negative temperature gradient model T - (y):

[0006]

[0007] In formula (1), y is the height of a position to be calculated, h is the height of a section, T G1 is a representative value of temperature at a top plate position, T G2 is a representative value of temperature at a position of h / 4 away from the top plate of the web, T G3 is a representative value of temperature at a bottom plate position, B is the width of the top plate, b is the width of the bottom plate, k is the number of box chambers, β TG (B) is a coefficient of the top plate, β TG (b) is a coefficient of the web, β TG (h) is a coefficient of the bottom plate, and β TG (k) is an intermediate variable, is an initial value of temperature at the top plate position, and the unit is ℃, T0 is a temperature initial value at a position of a top plate, in unit of ℃, T0 is a temperature initial value at a position of a bottom plate, in unit of ℃, N d N is a design service life, and is 100, 150 or 200 years.

[0008] Further preferably, the h, B, b, k, T0 is [13.8, 15.2] ℃, T0 is [8.9, 9.8] ℃, h is [2.00, 5.00] m, b is [4.00, 17.00] m, B is [7.00, 20.00] m, k is [1, 4], and k is a positive integer.

[0009] Further preferably, the h, B, b, k, T0 is: B is 18.00 m, b is 11.25 m, h is 3.00 m, and k is 3, T0 is 14.5 ℃, T0 is 9.4 ℃.

[0010] The method for constructing the vertical temperature gradient fatigue load model of the steel box girder bridge with wing plates according to the application comprises the following steps:

[0011] (1) Long-term temperature monitoring of the steel box girder bridge with wing plates

[0012] Temperature measuring points are arranged on the top plate, bottom plate and transverse diaphragm of the steel box girder bridge with wing plates, and the temperature is collected, and the time interval for each collection is 1-20 minutes, and the collection interval is denoted as t d , and a temperature gradient time history T A (y, t') of the steel box girder bridge with wing plates is constructed, wherein t' is any time in the temperature history.

[0013] (2) Standardization processing of the original data

[0014] The standard data T A (y, t') of the temperature gradient time history T sta (y, t') is obtained according to the following formula:

[0015]

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

[0017] (3) Construction of an autoregressive prediction model

[0018] The autoregressive prediction model Y(y, t') is obtained according to the following formula:

[0019] Y(y, t') = α1 x T sta (y, t' - n x t d ) + α2 x T sta (y, t' - (n - 1) x t d ) +... + α n x T sta (y, t' - t d ) + c In the formula, α1, α2,..., α n , c are parameters of the temperature prediction model Y(y, t'), n, c are finite positive integers.

[0020] (4) Predicting temperature in design service life

[0021] The temperature Y(y, t' + t d ) at t' + t d at y height is predicted according to the following formula:

[0022] Y(y, t' + t d ) = α1 x T sta (y, t' - (n - 1) x t d ) + α2 x T sta (y, t' - (n - 2) x t d ) +... + α n x T sta (y, t') + c The representative value of temperature at t' + t d is brought back into the autoregressive prediction model and prediction of t' + 2t d is carried out until the prediction of all temperature gradient measuring points in the design service life is completed, and the temperature gradient time history T Y (y, t') in the design service life is obtained.

[0023] (5) Determining equivalent temperature

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

[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 with wing plates, I s is the moment of inertia of the cross section of the steel box girder with wing plates, y s is the neutral axis of the cross section of the steel box girder with wing plates, and b(y) is the cross-sectional thickness at y position of the steel box girder with wing plates.

[0027] Based on the rainflow counting method, the temperature stress time history σY (y,t') are processed to obtain a corresponding temperature stress amplitude vector A within the designed service life:

[0028] A=(Δσ1(y),Δσ2(y),...,Δσ m (y))

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

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

[0031]

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

[0033] The equivalent temperature T eqy is obtained from the equivalent temperature stress Δσ eqy according to formula (3):

[0034]

[0035] (6) Constructing a vertical temperature gradient fatigue load model of a steel box girder bridge with a wing plate

[0036] The least square method is used to fit the equivalent temperature representative value T d of different positions y and different design service lives N eqy , and a vertical temperature gradient fatigue load model T(y) of formula (1) of the steel box girder bridge with a wing plate is obtained, then the positive temperature stress and the negative temperature stress are split according to the time length ratio of 3:1 to obtain a positive temperature gradient model T + (y) and a negative temperature gradient model T - (y).

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

[0038] 1. The present application uses an autoregressive algorithm and a damage equivalent principle to propose a temperature gradient fatigue load model construction method of a steel box girder bridge with a wing plate, which overcomes the deficiency that Latin hypercube sampling cannot be continuously extended for temperature stress, and can provide a reliable vertical temperature gradient fatigue load model for long-life design of a steel box girder.

[0039] 2, the vertical temperature gradient fatigue load model of the steel box girder bridge with wing plate is established by using the long-term temperature monitoring results of the steel box girder bridge with wing plate, which is suitable for the design service life of 100 years, 150 years and 200 years, and the temperature gradient fatigue load model fully considers the influence of the roof width B, the bottom plate width b, the beam height h and the number of chambers k of the steel box girder bridge with wing plate.

[0040] 3, the vertical temperature gradient fatigue load model of the steel box girder bridge with wing plate is established by using the long-term temperature monitoring results of the steel box girder bridge with wing plate, which is suitable for the design service life of 100 years, 150 years and 200 years, and the temperature gradient fatigue load model fully considers the influence of the roof width B, the bottom plate width b, the beam height h and the number of chambers k of the steel box girder bridge with wing plate. DETAILED DESCRIPTION

[0041] Figure 1 The temperature representative value distribution of the vertical temperature gradient fatigue load model of the steel box girder bridge with wing plate.

[0042] Figure 2 The flow chart for constructing the vertical temperature gradient fatigue load model of the steel box girder bridge with wing plate.

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

[0044] Figure 4 The three-dimensional structure diagram of the steel box girder with wing plate.

[0045] Figure 5 The vertical temperature measuring point layout diagram of the steel box girder with wing plate.

[0046] Figure 6 The measured temperature history curve of the steel box girder bridge with wing plate.

[0047] Figure 7 The measured temperature stress amplitude histogram of K-9 measuring point. DETAILED DESCRIPTION

[0048] The present application will be further described in detail below in combination with the drawings and examples, but the present application is not limited to these examples.

[0049] Example 1

[0050] The vertical temperature gradient fatigue load model of the steel box girder bridge with wing plate in this example is composed of the positive temperature gradient model T + (y) and the negative temperature gradient model T - (y) shown in formula (1):

[0051]

[0052] In formula (1), y is the height of the position to be calculated, h is the cross section height, T G1 is the temperature representative value at the roof position, TG2 T is a representative value of temperature at the web distance from the top plate h / 4 G3 T is a representative value of temperature at the bottom plate position, B is the width of the top plate, b is the width of the bottom plate, k is the number of box chambers, β TG (B), β TG (b), β TG (h), β TG (k) is an intermediate variable, T0 is an initial value of temperature at the top plate position, in units of ℃, T0 is an initial value of temperature at the web distance from the top plate h / 4, in units of ℃, T0 is an initial value of temperature at the bottom plate position, in units of ℃, N d N is the design service life, which is 100, 150 or 200 years.

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

[0054] Table 1 Representative values of temperature in the vertical temperature fatigue load model of the steel box girder bridge with wing plates

[0055]

[0056] As shown in Figure 2 , the construction method of the vertical temperature gradient fatigue load model of the steel box girder bridge with wing plates described above specifically includes the following steps:

[0057] (1) Long-term temperature monitoring of the steel box girder bridge with wing plates

[0058] Temperature measuring points are arranged on the top plate, bottom plate and diaphragm of the steel box girder bridge with wing plates, and temperatures are collected, and the time interval for each collection is 1-20 minutes, and the monitoring interval is recorded as t d , and the temperature gradient time history T A (y, t') of the steel box girder bridge with wing plates is constructed; wherein t' is any time in the temperature history.

[0059] (2) Standardization processing of original data

[0060] The temperature gradient time history T A(y, t') is obtained from the standard data T sta (y, t') as follows

[0061]

[0062] wherein E(·) is a mean value of the measured temperature data, and D(·) is a 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') = 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

[0066] wherein α1, α2,..., α n , and c are parameters of the temperature prediction model Y(y, t'), and n and c are finite positive integers.

[0067] (4) Predicting the temperature in the design service life

[0068] The temperature Y(y, t'+t d ) at t'+t d at y height is predicted as follows

[0069] 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 d The temperature value at t'+t d is used to re-input the autoregressive prediction model and to predict t'+2t Y , until the prediction of all temperature gradient measuring points in the design service life is completed, to obtain the temperature gradient time course T Y (y, t') in the design service life, as shown in Figure 3

[0070] (5) Determining the equivalent temperature

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

[0072]

[0073] Where, 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 flanges, I s is the moment of inertia of the steel box girder bridge section with flanges, y s is the neutral axis of the steel box girder bridge with flanges, b(y) is the cross-sectional thickness of the steel box girder bridge with flanges at position y; in this example, E s =2.06×10 5 MPa, α s =1.1×10 -5 ℃ -1 .

[0074] The temperature stress time history σ is analyzed based on the 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=(Δσ1(y),Δσ2(y),...,Δσ m (y))

[0076] Where 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] Use Matlab software to analyze the different positions y and different design service life N d The equivalent temperature representative value T eqyThe least square method is used for fitting to obtain the vertical temperature gradient fatigue load model T(y) of the steel box girder bridge with wing plates of formula (1), then the positive temperature gradient model T + (y) and the negative temperature gradient model T - (y) is obtained according to the time length ratio of positive temperature stress and negative temperature stress of 3:1.

[0084] Example 2

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

[0086] In formula (1) of this embodiment, the beam height h is 2.00 m, the roof width B is 7.00 m, the bottom plate width b is 4.00 m, the number of chambers k of the steel box girder bridge with wing plates is 1, The value of T is 13.8℃, The value of T is 8.9℃, and the remaining parameters are the same as in the example. 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 shown in Figure 1 , wherein the positive temperature gradient model is shown in figure (a), and the negative temperature gradient is shown in figure (b).

[0087] Table 2 Vertical temperature fatigue load model representative value of steel box girder bridge with wing plates

[0088]

[0089] Example 3

[0090] The vertical temperature gradient fatigue load model of the steel box girder bridge with wing plates 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 area as an example, in formula (1), the beam height h is 5.00 m, the roof width B is 20.00 m, the bottom plate width b is 17.00 m, and the number of chambers k of the steel box girder bridge with wing plates is 4, The value of T is 15.2℃, The value of T is 9.8℃, and the remaining parameters are the same as in the example. 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 shown in Figure 1 , wherein the positive temperature gradient model is shown in figure (a), and the negative temperature gradient is shown in figure (b).

[0092] Table 3 Representative value of vertical temperature fatigue load model of steel box girder bridge with wing plate

[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 wing plate, the model and construction method of Example 1 are used to arrange the vertical temperature sensors of Shenyang Houdingxiang Viaduct and conduct long-term temperature field monitoring. The cross section form is shown in Figure 4 .

[0096] I. Long-term monitoring instrument

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

[0098] II. Temperature measurement point arrangement

[0099] Temperature measurement points are arranged on the top plate, web plate and bottom plate of the steel box girder with wing plate. The temperature measurement point positions arranged on the steel webs on both sides are expressed as 0.00 m, 0.90 m, 1.80 m, 2.40 m, 2.70 m, 2.80 m, 2.90 m, 2.95 m, 3.00 m in vertical distance from the lower surface of the steel box girder bottom plate, denoted as K-1 to K-9, wherein h is the height of the steel box girder with wing plate, and the measurement point arrangement is shown in Figure 5 . The continuous temperature acquisition is conducted on these measurement points to obtain one year of effective monitoring data, the acquisition interval is 10 minutes, and the actual temperature history curve is shown in Figure 6 .

[0100] III. Effect analysis of vertical temperature gradient fatigue load model

[0101] Taking the butt weld at the bottom of the steel box girder bridge with wing plate as an example, the temperature stress history is plotted based on the temperature monitoring data, the rain flow counting method is used to count the temperature stress amplitude cycles, the stress amplitude histogram is obtained, and the result is shown in Figure 7 . Then the equivalent fatigue stress is calculated based on the measured results, and the result is 7.8 MPa.

[0102] The temperature stress history is constructed based on the temperature gradient fatigue load model and the temperature stress amplitude is analyzed. Wherein B = 18.00 m, b = 11.25 m, h = 3.00 m, k = 3, N d = 100 years, which is brought into the following formula:

[0103]

[0104] The equivalent temperature fatigue stress σeq (y) is 8.2 MPa, the result is basically consistent with the equivalent fatigue stress of the measured result. It shows that the established fatigue load model of the steel box girder bridge with wing plates under vertical temperature gradient has good applicability.

Claims

1. A vertical temperature gradient fatigue load model for a steel box girder bridge with flanges, characterized by: The model is represented by 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 temperature value at the top plate position, T G2 is the representative temperature value of the web at a distance of h / 4 from the top plate, T G3 is the representative temperature value at the bottom plate position, 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 position, 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 position, in ℃, N d It is the design service life, which can be 100, 150 or 200, in years.

2. The vertical temperature gradient fatigue load model for steel box girder bridges with flanges according to claim 1 is characterized in that: In formula (1), The value 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 for steel box girder bridge with flanges 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, is 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 for each collection is 1 to 20 minutes, and the collection interval is recorded as 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; (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 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 carried out until the prediction of all temperature gradient measuring 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 history: Where, 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 flanges, I s is the moment of inertia of the steel box girder bridge section with flanges, y s is the neutral axis of the steel box girder bridge with flanges, b(y) is the cross-sectional thickness at position y of the steel box girder bridge with flanges; The temperature stress time history σ is analyzed based on the 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)) Where 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 temperature stress amplitude vector A according to formula (2): eqy : Where 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 to obtain the vertical temperature gradient fatigue load model T(y) of the steel box girder bridge with flange plate 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).

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