Transverse temperature gradient model of flat wide steel box girder bridge in east-west direction

Abstract

The invention relates to an east-west direction flat wide steel box girder bridge transverse temperature gradient model which is composed of a transverse positive temperature gradient model and a transverse negative temperature gradient model, the positive temperature gradient is in a bifold line form, and the negative temperature gradient is in a four-fold line form. Long-term monitoring of the temperature field of the east-west direction flat steel box girder bridge is carried out according to distribution characteristics of the transverse temperature field of the east-west direction flat steel box girder bridge, probability distribution of a daily temperature difference extreme value at a typical position is analyzed, and a transverse temperature gradient model suitable for designing the east-west direction flat wide steel box girder bridge with the service life of 100 years is provided. The constructed temperature gradient model can be used for calculating transverse temperature deformation and stress of the flat wide steel box girder bridge in the east-west direction, and reference is provided for revision of related 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] The flat steel box girder bridge is a typical closed section with a relatively obvious frame effect. Under the action of uniform heating and cooling and transverse temperature gradient, the flat steel box girder section will produce transverse temperature stress, of which the transverse temperature gradient is the main cause of transverse temperature stress. Existing studies have shown that the transverse temperature gradient of the bridge section is significantly different for different main beam section forms and different bridge positions, and the transverse temperature stress distribution is also quite different. Therefore, it is necessary to arrange temperature sensors according to the temperature field distribution characteristics of the east-west flat steel box girder bridge, use the long-term monitoring data of the transverse temperature field of the flat steel box girder, analyze the probability distribution of the extreme values ​​of the daily temperature difference at different heights, and propose a transverse temperature gradient model for the east-west flat wide steel box girder bridge with a design service life of 100 years, which is used for the calculation and analysis of the transverse temperature stress of the main beam. 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 lateral positive temperature gradient model T HP (x) and the lateral 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, Ν 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 positive 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 lateral negative temperature gradient model T HN (x) is 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 surface, 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 positive 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: d The best is 100, α HP1 The best is 1.64, A HP1 The best value 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 formula (2) of the present invention, N d , α HN1 , A HN1 ,t HN1 , β HN1 , α HN2 , A HN2 ,t HN2 , β HN2 The value of is: 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 value is 0.11, and 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] The present invention uses the long-term monitoring data of the transverse temperature field of the east-west flat wide steel box girder bridge to construct a transverse temperature gradient model of the east-west flat wide steel box girder bridge, which is divided into a positive temperature gradient model and a negative temperature gradient model. The model is simple in form and can calculate the additional stress and deformation of the transverse temperature gradient, which is suitable for the 100-year design of the east-west flat wide steel box girder bridge. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0017] Figure 2 It 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 It 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 It is a layout diagram of the transverse temperature measuring points of the measured temperature field in the present invention.

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

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

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

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

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

[0025] The present invention will be further described in detail below in conjunction with 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 lateral 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, Ν 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 positive 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 lateral negative temperature gradient model T HN (x) is 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 surface, 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 positive 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 values ​​of temperature 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 is 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 values ​​of temperature 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 Embodiment 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 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 3. The temperature representative value distribution of the transverse positive temperature gradient model constructed according to this parameter is shown in Figure 2 shown.

[0043] Table 3 Representative values ​​of temperature 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 is 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 Figure 3 shown.

[0046] Table 4 Representative values ​​of temperature 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 Embodiment 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 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 5. The temperature representative value distribution of the transverse positive temperature gradient model constructed according to this parameter is shown in Table 5. Figure 2 shown.

[0051] Table 5 Representative values ​​of temperature 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 is 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 values ​​of temperature in the lateral negative temperature gradient model

[0055]

[0056] Test 1

[0057] In order to verify the effect of the transverse positive temperature gradient model of the east-west flat wide steel box girder bridge, the inventors arranged 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 acquisition instrument produced in Taizhou, Jiangsu, 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 the 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 taken 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 horizontal distance from the coordinate origin, and are recorded as HT1~HT8. Figure 4 As shown, the acquisition interval is 1 minute.

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

[0063] In the model of positive temperature gradient in the transverse direction 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 HP1 and T HP2 The temperature difference between the position and the position where the average temperature of the box girder section measuring point is the lowest, and a probability density histogram is drawn based on the data and a 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 the 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 transverse positive temperature gradient model of the east-west flat wide steel box girder bridge. 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 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 lateral positive temperature gradient model has good applicability.

[0065] Test 2

[0066] In order to verify the effect of the transverse negative temperature gradient model of the east-west flat wide steel box girder, the inventors arranged 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. Analysis of the effect of the lateral 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 HN1 and T HN2 Taking the location 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 Figure 8 and Fig. 9 As shown. The 1% guarantee rate in the probability density function is taken as the value, and the obtained 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 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 lateral 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, Ν 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 positive 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 lateral negative temperature gradient model T HN (x) is 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 surface, 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 positive 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 of the 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 of the east-west flat wide steel box girder bridge according to claim 1 is characterized by: In formula (1), N d , α HP1 , A HP1 ,t HP1 , β HP1 , α HP2 , A HP2 ,t HP2 , β HP2 The value of is: 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 is 1.

30.

4. The transverse temperature gradient model of the east-west flat wide steel box girder bridge according to claim 1 is characterized by: In formula (2), N d , α HN1 , A HN1 ,t HN1 , β HN1 , α HN2 , A HN2 ,t HN2 , β HN2 The value of is: 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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