Transverse temperature gradient model for east-west flat wide steel box girder bridges

Abstract

The present invention relates to a transverse temperature gradient model for an east-west flat wide steel box girder bridge, which consists of a transverse positive temperature gradient model and a transverse negative temperature gradient model, wherein the positive temperature gradient is in the form of a double broken line, and the negative temperature gradient is in the form of a quadrilateral line. Based on the transverse temperature field distribution characteristics of the east-west flat steel box girder, long-term monitoring of the temperature field of the east-west flat steel box girder bridge was carried out, the probability distribution of the extreme values ​​of the daily temperature difference at typical locations was analyzed, and a transverse temperature gradient model for the east-west flat wide steel box girder bridge with a design service life of 100 years was proposed. The constructed temperature gradient model can be used for the calculation of transverse temperature deformation and stress of the east-west flat wide steel box girder bridge, providing a reference for the revision of relevant design specifications.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a transverse temperature gradient model of an east-west flat wide steel box girder bridge. Background Art

[0002] Flat steel box girder bridges are typical closed cross-sections with a pronounced frame effect. Under the effects of uniform heating and cooling and transverse temperature gradients, flat steel box girder cross-sections will generate transverse thermal stresses, with the transverse thermal gradient being the primary cause of these stresses. Previous studies have shown that the transverse thermal gradients and transverse thermal stress distributions vary significantly across different main girder cross-sections and bridge orientations. Therefore, it is necessary to deploy temperature sensors tailored to the temperature field distribution characteristics of east-west flat steel box girder bridges. Using long-term transverse temperature field monitoring data from flat steel box girders, the probability distribution of daily temperature extremes at different heights can be analyzed. A transverse thermal gradient model suitable for east-west flat wide steel box girder bridges with a design life of 100 years can be proposed for the calculation and analysis of transverse thermal stresses in the main girder. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a transverse temperature gradient model for an east-west flat wide steel box girder bridge.

[0004] The above model is composed of the transverse positive temperature gradient model T HP (x) and the transverse negative temperature gradient model T HN (x) composition;

[0005] The transverse positive temperature gradient model T HP (x) is as shown in formula (1):

[0006]

[0007] In formula (1), T HP1 is the representative value of the positive temperature gradient at the sun side, in °C, T HP2 is the representative value of the positive temperature gradient at the shady side, in °C, x is the transverse distance from the east-west flat wide steel box girder bridge section to the sunny side, L is the width of the east-west flat wide steel box girder bridge, N d The design service life of the east-west flat wide steel box girder bridge is 100, in years. F HP1 (α) is the inverse function of the function, F HP2 (α) The inverse function, F HP1 (α) is the distribution function of the representative value of the positive temperature gradient at the sun side, F HP2 (α) is the distribution function of the representative value of the positive temperature gradient at the shadow side, α, α HP1 、AHP1 , t HP1 , β HP1 , α HP2 、A HP2 , t HP2 , β HP2 is an intermediate variable;

[0008] The transverse negative temperature gradient model T HN (x) is as shown in formula (2):

[0009]

[0010] In formula (2), T HN1 is the representative value of the negative temperature gradient at a distance of L / 4 from the sun side, in °C, T HN2 is the representative value of the negative temperature gradient at the position L / 4 from the shadow side, in °C, x is the distance from the east-west flat wide steel box girder bridge section to the sun side, L is the width of the east-west flat wide steel box girder bridge, F HN1 (α) is the inverse function of the function, F HN2 (α) The inverse function, F HN1 (α) is the distribution function of the representative value of the negative temperature gradient at a distance of L / 4 from the sun side, F HN2 (α) is the distribution function of the representative value of the negative temperature gradient at the position L / 4 away from the shadow surface, α HN1 、A HN1 , t HN1 , β HN1 , α HN2 、A HN2 , t HN2 , β HN2 is an intermediate variable.

[0011] In the formula (1) of the present invention, the α HP1 The value of is [1.53,1.74], A HP1 The value of is [0.23,0.38], t HP1 The value of is [7.09,7.71], β HP1 The value of is [4.63,14.37], α HP2 The value of is [1.53,1.77], A HP2 The value of is [0.26,0.43], t HP2 The value of is [3.33,4.13], β HP2 The value of is [0.80,1.80]. In formula (2), the α HN1 The value of is [-0.67,-0.46], A HN1 The value of is [0.24,0.39], tHN1 The value of is [-2.77,-2.71], β HN1 The value of is [0.29, 0.31], α HN2 The value of is [-0.95,-0.87], A HN2 The value of is [0.08,0.14], t HN2 The value of is [-1.46,-1.22], β HN2 The value of is [0.27,0.55].

[0012] In the formula (1) of the present invention, the N d , α HP1 、A HP1 , t HP1 , β HP1 , α HP2 、A HP2 , t HP2 , β HP2 The value of is: N d The best is 100, α HP1 The best is 1.64, A HP1 The best is 0.31, t HP1 The best is 7.40, β HP1 The best is 9.50, α HP2 The best is 1.65, A HP2 The best value is 0.35, t HP2 The best is 3.73, β HP2 The best is 1.30.

[0013] In the formula (2) of the present invention, the N d , α HN1 、A HN1 , t HN1 , β HN1 , α HN2 、A HN2 , t HN2 , β HN2 The value of is: N d The best is 100, α HN1 The best is -0.57, A HN1 The best is 0.32, t HN1 The best is -2.74, β HN1 The best value is 0.30, α HN2 The best is -0.91, A HN2 The best is 0.11, the best t HN2 is -1.34, β HN2 The best is 0.41.

[0014] The beneficial effects of the present invention are as follows:

[0015] This study utilizes long-term transverse temperature field monitoring data from east-west, flat, wide steel box girder bridges to construct a transverse temperature gradient model for these bridges. This model is divided into two types: a positive temperature gradient model and a negative temperature gradient model. This simple model can calculate additional stress and deformation associated with transverse temperature gradients and is suitable for the 100-year design of east-west, flat, wide steel box girder bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a cross-sectional view of an east-west flat wide steel box girder bridge.

[0017] Figure 2 This is the temperature representative value distribution diagram of the positive temperature gradient model of the east-west flat wide steel box girder bridge.

[0018] Figure 3 This is the temperature representative value distribution diagram of the negative temperature gradient model of the east-west flat wide steel box girder bridge.

[0019] Figure 4 This is a diagram showing the arrangement of transverse temperature measuring points in the measured temperature field of the present invention.

[0020] Figure 5 It is the temperature history curve in the present invention.

[0021] Figure 6 is the measured T in the present invention HP1 Histogram of positive temperature difference statistics at locations.

[0022] Figure 7 is the measured T in the present invention HP2 Histogram of positive temperature difference statistics at locations.

[0023] Figure 8 is the measured T in the present invention HN1 Histogram of negative temperature difference statistics at locations.

[0024] Figure 9 is the measured T in the present invention HN2 Histogram of negative temperature difference statistics at locations. DETAILED DESCRIPTION

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and examples, but the present invention is not limited to the following embodiments.

[0026] Example 1

[0027] The transverse temperature gradient model of the east-west flat wide steel box girder bridge in this embodiment is composed of the transverse positive temperature gradient model T HP (x) and the transverse negative temperature gradient model T HN (x) composition; wherein, in this embodiment, the south side of the beam cross section is defined as the positive side, and the north side of the beam cross section is defined as the negative side.

[0028] The transverse positive temperature gradient model T HP (x) is as shown in formula (1):

[0029]

[0030] In formula (1), T HP1 is the representative value of the positive temperature gradient at the sun side, in °C, T HP2 is the representative value of the positive temperature gradient at the shady side, in °C, x is the transverse distance from the east-west flat wide steel box girder bridge section to the sunny side, L is the width of the east-west flat wide steel box girder bridge, N d The design service life of the east-west flat wide steel box girder bridge is in years, and the value is 100. F HP1 (α) is the inverse function of the function, F HP2 (α) The inverse function, F HP1 (α) is the distribution function of the representative value of the positive temperature gradient at the sun side, F HP2 (α) is the distribution function of the representative value of the positive temperature gradient at the shadow side, α, α HP1 、A HP1 , t HP1 , β HP1 , α HP2 、A HP2 , t HP2 , β HP2 is an intermediate variable.

[0031] The transverse negative temperature gradient model T HN (x) is as shown in formula (2):

[0032]

[0033] In formula (2), T HN1 is the representative value of the negative temperature gradient at a distance of L / 4 from the sun side, in °C, T HN2 is the representative value of the negative temperature gradient at the position L / 4 from the shadow side, in °C, x is the distance from the east-west flat wide steel box girder bridge section to the sun side, L is the width of the east-west flat wide steel box girder bridge, F HN1 (α) is the inverse function of the function, F HN2 (α) The inverse function, F HN1 (α) is the distribution function of the representative value of the negative temperature gradient at a distance of L / 4 from the sun side, F HN2 (α) is the distribution function of the representative value of the negative temperature gradient at the position L / 4 away from the shadow surface, α HN1 、A HN1 , t HN1 , βHN1 , α HN2 、A HN2 , t HN2 , β HN2 is an intermediate variable.

[0034] In this embodiment, a flat wide steel box girder bridge in the south is taken as an example. Figure 1 As shown, in formula (1) α HP1 is 1.64, A HP1 is 0.31, t HP1 is 7.40, β HP1 is 9.50, α HP2 is 1.65, A HP2 is 0.35, t HP2 is 3.73, β HP2 =1.30, and the transverse positive temperature gradient model of the east-west flat wide steel box girder bridge is constructed according to this parameter. The temperature representative values ​​in the transverse positive temperature gradient model corresponding to its 100-year design service life are shown in Table 1. The temperature representative value distribution of the transverse positive temperature gradient model constructed according to this parameter is shown in Table 1. Figure 2 shown.

[0035] Table 1 Representative temperature values ​​in the transverse positive temperature gradient model

[0036]

[0037] In formula (2), α HN1 is -0.57, A HN1 is 0.32, t HN1 is -2.74, β HN1 is 0.30, α HN2 is -0.91, A HN2 is 0.11, t HN2 is -1.34, β HN2 =0.41, and the transverse negative temperature gradient model of the east-west flat wide steel box girder bridge was constructed according to this parameter. The temperature representative values ​​in the transverse negative temperature gradient model corresponding to its 100-year design service life are shown in Table 2. The temperature representative value distribution of the transverse negative temperature gradient model constructed according to this parameter is shown in Table 2. Figure 3 shown.

[0038] Table 2 Representative temperature values ​​in the lateral negative temperature gradient model

[0039]

[0040] Example 2

[0041] The expression of the transverse temperature gradient model of the east-west flat wide steel box girder bridge in this embodiment is the same as that in Example 1, but the temperature representative values ​​are different.

[0042] In this embodiment, a certain east-west flat wide steel box girder bridge is taken as an example. In formula (1), α HP1 is 1.53, A HP1 is 0.23, t HP1 is 7.09, β HP1 is 4.63, α HP2 is 1.53, A HP2 is 0.26, t HP2 is 3.33, β HP2 =0.80, and the transverse positive temperature gradient model of the east-west flat wide steel box girder bridge was constructed according to this parameter. The temperature representative values ​​in the transverse positive temperature gradient model corresponding to its 100-year design service life are shown in Table 3. The temperature representative value distribution of the transverse positive temperature gradient model constructed according to this parameter is shown in Table 3. Figure 2 shown.

[0043] Table 3 Representative temperature values ​​in the transverse positive temperature gradient model

[0044]

[0045] In formula (2), α HN1 is -0.67, A HN1 is 0.24, t HN1 is -2.77, β HN1 is 0.29, α HN2 is -0.95, A HN2 is 0.08, t HN2 is -1.46, β HN2 =0.27, and the transverse negative temperature gradient model of the east-west flat wide steel box girder bridge was constructed according to this parameter. The temperature representative values ​​in the transverse negative temperature gradient model corresponding to its 100-year design service life are shown in Table 4. The temperature representative value distribution of the transverse negative temperature gradient model constructed according to this parameter is shown in Table 4. Figure 3 shown.

[0046] Table 4 Representative temperature values ​​in the lateral negative temperature gradient model

[0047]

[0048] Example 3

[0049] The expression of the transverse temperature gradient model of the east-west flat wide steel box girder bridge in this embodiment is the same as that in Example 1, but the temperature representative values ​​are different.

[0050] In this embodiment, a certain east-west flat wide steel box girder bridge is taken as an example. In formula (1), α HP1 is 1.74, A HP1 is 0.38, t HP1 is 7.71, β HP1is 14.37, α HP2 is 1.77, A HP2 is 0.43, t HP2 is 4.13, β HP2 =1.80, and a transverse positive temperature gradient model for an east-west flat wide steel box girder bridge was constructed based on this parameter. The temperature representative values ​​in the transverse positive temperature gradient model corresponding to its 100-year design service life are shown in Table 5. The temperature representative value distribution of the transverse positive temperature gradient model constructed based on this parameter is shown in Table 5. Figure 2 shown.

[0051] Table 5 Representative temperature values ​​in the transverse positive temperature gradient model

[0052]

[0053] In formula (2), α HN1 is -0.46, A HN1 is 0.39, t HN1 is -2.71, β HN1 is 0.31, α HN2 is -0.87, A HN2 is 0.14, t HN2 is -1.22, β HN2 =0.55, and the transverse negative temperature gradient model of the east-west flat wide steel box girder bridge was constructed according to this parameter. The temperature representative values ​​in the transverse negative temperature gradient model corresponding to its 100-year design service life are shown in Table 6. The temperature representative value distribution of the transverse negative temperature gradient model constructed according to this parameter is shown in Table 6. Figure 3 shown.

[0054] Table 6 Representative temperature values ​​in the lateral negative temperature gradient model

[0055]

[0056] Test 1

[0057] To verify the effectiveness of the transverse positive temperature gradient model for an east-west flat wide steel box girder bridge, the inventors deployed transverse temperature sensors on the Shawan Waterway Bridge in Nansha District, Guangzhou City, Guangdong Province, and conducted long-term temperature field monitoring. The specific construction process is as follows:

[0058] 1. Long-term monitoring equipment

[0059] The monitoring equipment is the Donghua DH5921 remote temperature collector produced in Taizhou, Jiangsu Province, and the temperature measurement point uses a three-wire Pt100 sensor.

[0060] 2. Temperature measurement point arrangement

[0061] The flat steel box girder bridge top plate is selected to arrange the temperature measuring points, and a coordinate system is established with the center of the flat steel box girder bridge top plate as the coordinate origin. The arrangement principle of the temperature measuring points on the flat steel box girder bridge top plate is as follows: the positive side edge of the top plate is used as the coordinate origin, and the temperature measuring points are arranged in the width direction of the top plate. The positions of the measuring points are expressed as 0.00m, 4.62m, 8.00m, 19.50m, 20.50m, 32.00m, 35.38m, and 40.00m from the coordinate origin, and are recorded as HT1 to HT8. Figure 4 As shown, the sampling interval is 1 minute.

[0062] 3. Analysis of the effect of the transverse positive temperature gradient load model

[0063] In the model of the positive temperature gradient of the east-west flat wide steel box girder bridge, T HP1 and T HP2 Taking the location as an example, the temperature history curve of the measuring point is drawn based on the actual temperature monitoring data, such as Figure 5 As shown. Calculate T respectively HP1 and T HP2 The temperature difference between the position and the lowest position of the average temperature of the box girder section measuring point is plotted based on the data and the probability density function is fitted, as shown in the figure. Figure 6 and Figure 7 As shown. The 99% guarantee rate in the probability density function is taken as the value, and the obtained T HP1 and T HP2 The representative values ​​of temperature gradient at these locations are 9.8°C and 10.2°C respectively.

[0064] The temperature gradient model corresponding to the 100-year design service life is constructed using the east-west flat wide steel box girder bridge transverse positive temperature gradient model. HP1 is 1.64, A HP1 is 0.31, t HP1 is 7.40, β HP1 is 9.50, α HP2 is 1.65, A HP2 is 0.35, t HP2 is 3.73, β HP2 is 1.30, and T is calculated HP1 and T HP2 The results are 14.7℃ and 11.8℃, which are slightly different from the measured results. This experiment shows that the transverse positive temperature gradient model has good applicability.

[0065] Test 2

[0066] To verify the effectiveness of the transverse negative temperature gradient model for east-west flat wide steel box girders, the inventors deployed transverse temperature sensors on the Shawan Waterway Bridge in Nansha District, Guangzhou City, Guangdong Province, and conducted long-term temperature field monitoring. The specific construction process is as follows:

[0067] 1. Long-term monitoring equipment

[0068] Same as Experiment 1.

[0069] 2. Temperature measurement point arrangement

[0070] Same as Experiment 1.

[0071] 3. Effect Analysis of Transverse Negative Temperature Gradient Load Model

[0072] The T in the transverse negative temperature gradient model of the east-west flat wide steel box girder bridge is HN1 and T HN2 Taking the position as an example, the temperature history curve of the measuring point is drawn based on the actual temperature monitoring data. Calculate T HN1 and T HN2 The temperature difference between the position and the position with the highest average temperature of the box girder section measuring point is plotted based on the data and the probability density function is fitted, as shown in the figure. Figure 8 and Figure 9 As shown. Take the value of 1% guarantee rate in the probability density function respectively, and get T HN1 and T HN2 The representative values ​​of the temperature gradient at the locations are -5.5°C and -5.5°C respectively.

[0073] The temperature gradient model corresponding to the 100-year design service life is constructed using the transverse negative temperature gradient model of the east-west flat wide steel box girder bridge. HN1 is -0.57, A HN1 is 0.32, t HN1 is -2.74, β HN1 is 0.30, α HN2 is -0.91, A HN2 is 0.11, t HN2 is -1.34, β HN2 is 0.41, and T is calculated HN1 and T HN2 The results show that the lateral negative temperature gradient model has good applicability.

Claims

1. A transverse temperature gradient model for an east-west flat wide steel box girder bridge, characterized by: The model consists of a transverse positive temperature gradient model T HP (x) and the transverse negative temperature gradient model T HN (x) composition; The transverse positive temperature gradient model T HP (x) is as shown in formula (1): In formula (1), T HP1 is the representative value of the positive temperature gradient at the sun side, in °C, T HP2 is the representative value of the positive temperature gradient at the shady side, in °C, x is the transverse distance from the east-west flat wide steel box girder bridge section to the sunny side, L is the width of the east-west flat wide steel box girder bridge, N d The design service life of the east-west flat wide steel box girder bridge is 100, in years. F HP1 (α) is the inverse function of the function, F HP2 (α) The inverse function, F HP1 (α) is the distribution function of the representative value of the positive temperature gradient at the sun side, F HP2 (α) is the distribution function of the representative value of the positive temperature gradient at the shadow side, α, α HP1 、A HP1 , t HP1 , β HP1 , α HP2 、A HP2 , t HP2 , β HP2 is an intermediate variable; The transverse negative temperature gradient model T HN (x) is as shown in formula (2): In formula (2), T HN1 is the representative value of the negative temperature gradient at a distance of L / 4 from the sun side, in °C, T HN2 is the representative value of the negative temperature gradient at the position L / 4 from the shadow side, in °C, x is the distance from the east-west flat wide steel box girder bridge section to the sun side, L is the width of the east-west flat wide steel box girder bridge, F HN1 (α) is the inverse function of the function, F HN2 (α) The inverse function, F HN1 (α) is the distribution function of the representative value of the negative temperature gradient at a distance of L / 4 from the sun side, F HN2 (α) is the distribution function of the representative value of the negative temperature gradient at the position L / 4 away from the shadow surface, α HN1 、A HN1 , t HN1 , β HN1 , α HN2 、A HN2 , t HN2 , β HN2 is an intermediate variable.

2. The transverse temperature gradient model for an east-west flat wide steel box girder bridge according to claim 1 is characterized by: In formula (1), the α HP1 The value of is [1.53,1.74], A HP1 The value of is [0.23,0.38], t HP1 The value of is [7.09,7.71], β HP1 The value of is [4.63,14.37], α HP2 The value of is [1.53,1.77], A HP2 The value of is [0.26,0.43], t HP2 The value of is [3.33,4.13], β HP2 The value of is [0.80,1.80]. In formula (2), the α HN1 The value of is [-0.67,-0.46], A HN1 The value of is [0.24,0.39], t HN1 The value of is [-2.77,-2.71], β HN1 The value of is [0.29, 0.31], α HN2 The value of is [-0.95,-0.87], A HN2 The value of is [0.08,0.14], t HN2 The value of is [-1.46,-1.22], β HN2 The value of is [0.27,0.55].

3. The transverse temperature gradient model for an east-west flat wide steel box girder bridge according to claim 1 is characterized by: In formula (1), the N d , α HP1 、A HP1 , t HP1 , β HP1 , α HP2 、A HP2 , t HP2 , β HP2 The value of is: N d is 100, α HP1 is 1.64, A HP1 is 0.31, t HP1 is 7.40, β HP1 is 9.50, α HP2 is 1.65, A HP2 is 0.35, t HP2 is 3.73, β HP2 It is 1.

30.

4. The transverse temperature gradient model for an east-west flat wide steel box girder bridge according to claim 1 is characterized by: In formula (2), the N d , α HN1 、A HN1 , t HN1 , β HN1 , α HN2 、A HN2 , t HN2 , β HN2 The value of is: N d is 100, α HN1 is -0.57, A HN1 is 0.32, t HN1 is -2.74, β HN1 is 0.30, α HN2 is -0.91, A HN2 is 0.11, t HN2 is -1.34, β HN2 It is 0.41.

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