North-south flat wide steel box girder bridge vertical temperature gradient model

Abstract

The present application relates to a kind of north-south flat wide steel box girder bridge vertical temperature gradient model, the model is composed of vertical positive temperature gradient model and vertical negative temperature gradient model, and both are double broken line form.For the flat wide steel box girder section characteristics and temperature field distribution characteristics, and the probability distribution of temperature representative value at typical position, long-life temperature gradient model suitable for flat wide steel box girder bridge 100 years, 150 years and 200 years design service life is proposed.The temperature gradient model can be used for flat wide steel box girder bridge design calculation analysis, and can provide reference for the revision of relevant design specification.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge engineering, and particularly relates to a north-south flat wide steel box girder bridge vertical temperature gradient model. BACKGROUND

[0002] The temperature action of a bridge structure is divided into uniform temperature rise and fall and gradient temperature action. For a multi-span continuous beam, uniform temperature rise and fall only causes deformation and does not generate secondary stress in the structure. Under the action of nonlinear temperature gradient, the temperature strains at different positions of the same section are inconsistent, and there is mutual constraint between fibers at different positions, which causes temperature self-stress of the section. Research shows that the nonlinear temperature gradient forms are significantly different for different main girder section forms and different bridge site directions, and the generated temperature self-stress also has differences, so it is necessary to construct a vertical temperature gradient load model suitable for different bridge section forms and bridge site directions.

[0003] With the advancement of large-span bridge construction, especially the large-scale application of cable-stayed bridges and suspension bridges, flat steel box girders are the main main girder form adopted, however, there is no vertical temperature gradient load model of flat steel box girders of different bridge site directions in the bridge design specification. Therefore, it is necessary to construct a vertical temperature gradient load model of flat steel box girders by using long-term monitoring data of the temperature field of an actual flat steel box girder and considering the influence of the bridge site direction, so as to support the calculation and analysis of the temperature stress of the main girder. SUMMARY

[0004] The technical problem to be solved by the application is to provide a north-south flat wide steel box girder bridge vertical temperature gradient model, which can be used to calculate the temperature stress of a flat wide steel box girder bridge.

[0005] The technical scheme adopted to solve the above technical problem is that the model is composed of a positive temperature gradient model T P (y) and a negative temperature gradient model T N (y).

[0006] The positive temperature gradient model T P (y) is:

[0007]

[0008] In formula (1), T P1 is a representative value of the positive temperature gradient at the top plate, in ℃, T P2 is a representative value of the positive temperature gradient at a position 0.3 m away from the top plate, in ℃, is an initial value of the positive temperature gradient at the top plate, in ℃, is an initial value of the positive temperature gradient at a position 0.3 m away from the top plate, in ℃, y is the distance from the flat steel box girder section to the bottom plate, h is the height of the flat steel box girder, N dThe design service life of the flat steel box girder bridge is 100 or 150 or 200 years, is F P1 the inverse function of (α), is F P2 the inverse function of (α), F P1 (α) is a distribution function of the initial value of the positive temperature gradient at the top plate, F P2 (α) is a distribution function of the initial value of the positive temperature gradient at a distance of 0.3 m from the top plate, α, a1, μ P1 , σ P1 , μ P2 , σ P2 are intermediate variables.

[0009] The negative temperature gradient model T N (y) is:

[0010]

[0011] In formula (2), T N1 is a representative value of the negative temperature gradient at the top plate, in ℃, T N2 is a representative value of the negative temperature gradient at the bottom plate, in ℃, is an initial value of the negative temperature gradient at the top plate, in ℃, is an initial value of the negative temperature gradient at the bottom plate, in ℃, is the inverse function of F N1 (α) function, is the inverse function of F N2 (α) function, F N1 (α) is a distribution function of the initial value of the negative temperature gradient at the top plate, F N2 (α) is a distribution function of the initial value of the negative temperature gradient at the bottom plate, μ N1 , σ N1 , μ N2 , σ N2 are intermediate variables.

[0012] In the formula (1) of the positive temperature gradient model T P (y) of the application, the value of μ P1 is [11.16, 12.52], the value of σ P1 is [3.3, 4.27], the value of μ P2 is [9.65, 10.32], the value of σ P2 is [1.62, 2.10], in formula (2), the value of μ N1 is [-5.33, -4.91], the value of σ N1 is [1.02, 1.32], the value of μ N2 is [-10.19, -9.88], and the value of σN2 The value of N is [0.75, 0.97].

[0013] In the positive temperature gradient model T P (y) of the application, the N d , mu P1 , sigma P1 , mu P2 , sigma P2 The value of N is: N d is 100 years, mu P1 optimum is 11.84, sigma P1 optimum is 3.76, mu P2 optimum is 9.98, sigma P2 optimum is 1.84.

[0014] In the negative temperature gradient model T N (y) of the application, the N d , mu N1 , sigma N1 , mu N2 , sigma N2 The value of N is: N d is 100 years, mu N1 optimum is -5.12, sigma N1 optimum is 1.16, mu N2 optimum is -10.04, sigma N2 optimum is 0.85.

[0015] The beneficial effects of the application are as follows:

[0016] 1. The application uses the long-term monitoring data of the temperature field of the north-south bridge flat wide steel box girder to construct the temperature gradient load model of the north-south flat wide steel box girder bridge, and the load model considers the influence of the temperature probability distribution characteristics of different positions of the beam height and the cross section.

[0017] 2. The north-south flat wide steel box girder bridge temperature gradient model constructed by the application has the characteristics of simple form and convenient calculation and analysis, and can be used for the long-life design of the north-south flat wide steel box girder bridge with a design service life of 100 years, 150 years and 200 years. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a cross-sectional view of a flat wide steel box girder bridge.

[0019] Figure 2 is a typical position temperature representative value distribution diagram of a flat wide steel box girder bridge vertical positive temperature gradient model.

[0020] Figure 3is a temperature representative value distribution diagram of typical positions of a vertical negative temperature gradient model of a flat wide steel box girder bridge.

[0021] Figure 4 is a vertical temperature measuring point arrangement diagram of a measured temperature field.

[0022] Figure 5 is a temperature history curve of a measuring point.

[0023] Figure 6 is a measured T P1 statistical histogram of a positive temperature difference at a position.

[0024] Figure 7 is a measured T P2 statistical histogram of a positive temperature difference at a position.

[0025] Figure 8 is a measured T N1 statistical histogram of a negative temperature difference at a position.

[0026] Figure 9 is a measured T N2 statistical histogram of a negative temperature difference at a position. DETAILED DESCRIPTION

[0027] The application will be further described in detail below in combination with the drawings and examples, but the application is not limited to the following embodiments.

[0028] Example 1

[0029] This embodiment relates to a vertical temperature gradient model of a flat wide steel box girder bridge in the north-south direction, which is composed of a positive temperature gradient model T P (y) and a negative temperature gradient model T N (y).

[0030] The positive temperature gradient model T P (y) is:

[0031]

[0032] In formula (1), T P1 is a positive temperature gradient representative value at the top plate, in ℃, T P2 is a positive temperature gradient representative value at a position 0.3 m away from the top plate, in ℃, is a positive temperature gradient initial value at the top plate, in ℃, is a positive temperature gradient initial value at a position 0.3 m away from the top plate, in ℃, y is the distance from the flat steel box girder section to the bottom plate, h is the height of the flat steel box girder, N d is the design service life of the flat steel box girder bridge, which is 100 or 150 or 200, in years, is F P1The inverse function of (α), It's F P2 The inverse function of (α), F P1 (α) is the distribution function of the initial value of the positive temperature gradient at the top plate, F P2 (α) is the distribution function of the initial value of the positive temperature gradient at 0.3m from the top plate, α, a1, μ P1 , σ P1 、μ P2 , σ P2 is an intermediate variable.

[0033] The negative temperature gradient model T N (y) is:

[0034]

[0035] In formula (2), T N1 is the representative value of negative temperature gradient at the top plate, in °C, T N2 is the representative value of the negative temperature gradient at the bottom plate, in °C. is the initial value of negative temperature gradient at the top plate, in °C, is the initial value of the negative temperature gradient at the bottom plate, in °C. F N1 (α) is the inverse function of the function, F N2 (α) The inverse function, F N1 (α) is the distribution function of the initial value of the negative temperature gradient at the top plate, F N2 (α) is the distribution function of the initial negative temperature gradient of the bottom plate, μ N1 , σ N1 、μ N2 , σ N2 is an intermediate variable.

[0036] This embodiment takes a flat wide steel box girder bridge in the south as an example. Its three-dimensional structure is as follows: Figure 1 As shown in formula (1), μ P1 is 11.84, σ P1 is 3.76, μ P2 is 9.98, σ P2 =1.84, and the corresponding vertical positive temperature gradient model of the flat wide steel box girder bridge was constructed according to this parameter. The temperature gradient representative values ​​in the vertical positive temperature gradient model corresponding to the design service life of 100 years, 150 years, and 200 years are shown in Table 1. The temperature representative value distribution of the typical position of the vertical positive temperature gradient model constructed according to this parameter is shown in Table 1. Figure 2 shown.

[0037] Table 1 Representative values ​​of temperature gradient in vertical positive temperature gradient model

[0038]

[0039] in formula (2), μ N1 is -5.12, σ N1 is 1.16, μ N2 is -10.04, σ N2 is 0.85, and a vertical negative temperature gradient model of a corresponding flat wide steel box girder bridge is constructed according to the parameters. The representative values of the temperature gradient in the vertical negative temperature gradient model corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 2. The representative value distribution of the temperature at a typical position of the vertical negative temperature gradient model constructed according to the parameters is shown in Figure 3 .

[0040] Table 2 Representative values of temperature gradient in vertical negative temperature gradient model

[0041]

[0042] Example 2

[0043] This example relates to a vertical temperature gradient model of a flat wide steel box girder bridge in the north-south direction, which has the same form as that of Example 1, but different representative values of temperature.

[0044] This example takes a flat wide steel box girder bridge as an example, and the three-dimensional structural form thereof is shown in Figure 1 , in formula (1), μ P1 is 11.16, σ P1 is 3.3, μ P2 is 9.65, σ P2 is 1.62, and a vertical positive temperature gradient model of a corresponding flat wide steel box girder bridge is constructed according to the parameters. The representative values of the temperature gradient in the vertical positive temperature gradient model corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 3. The representative value distribution of the temperature at a typical position of the vertical positive temperature gradient model constructed according to the parameters is shown in Figure 2 .

[0045] Table 3 Representative values of temperature gradient in vertical positive temperature gradient model

[0046]

[0047] in formula (2), μ N1 is -5.33, σ N1 is 1.02, μ N2 is -10.19, σ N2= 0.75, the corresponding vertical negative temperature gradient model of the flat wide steel box girder bridge is constructed according to the parameter. The representative values of the temperature gradient in the vertical negative temperature gradient model corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 4. The representative value distribution of the temperature at the typical position of the vertical negative temperature gradient model constructed according to the parameter is shown in Figure 3 .

[0048] Table 4 Representative values of temperature gradient in vertical negative temperature gradient model

[0049]

[0050] Example 3

[0051] This example relates to the form of the vertical temperature gradient model of the flat wide steel box girder bridge in the north-south direction, which is the same as that in Example 1, but the representative values of the temperature are different.

[0052] This example takes a flat wide steel box girder bridge as an example, and the three-dimensional structure form thereof is shown in Figure 1 . In formula (1), μ P1 = 12.52, σ P1 = 4.27, μ P2 = 10.32, and σ P2 = 2.10. The corresponding vertical positive temperature gradient model of the flat wide steel box girder bridge is constructed according to the parameter. The representative values of the temperature gradient in the vertical positive temperature gradient model corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 5. The representative value distribution of the temperature at the typical position of the vertical positive temperature gradient model constructed according to the parameter is shown in Figure 2 .

[0053] Table 5 Representative values of temperature gradient in vertical positive temperature gradient model

[0054]

[0055] In formula (2), μ N1 = -4.91, σ N1 = 1.32, μ N2 = -9.88, and σ N2 = 0.97. The corresponding vertical negative temperature gradient model of the flat wide steel box girder bridge is constructed according to the parameter. The representative values of the temperature gradient in the vertical negative temperature gradient model corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 6. The representative value distribution of the temperature at the typical position of the vertical negative temperature gradient model constructed according to the parameter is shown in Figure 3 .

[0056] Table 6 Representative values of temperature gradient in vertical negative temperature gradient model

[0057]

[0058] Test 1

[0059] In order to verify the effect of the vertical positive temperature gradient model of the north-south flat wide steel box girder bridge, the inventors arranged the vertical temperature sensors on the Nanjing Yangtze River cable-stayed bridge and conducted long-term temperature field monitoring. The specific construction process is as follows:

[0060] I. Long-term monitoring equipment

[0061] The monitoring equipment is a remote temperature collection instrument DH2002 produced by Donghua in Taizhou, Jiangsu. The temperature measuring point selects a three-wire Pt100 sensor.

[0062] II. Temperature measuring point arrangement

[0063] The temperature measuring points are arranged on the top plate, bottom plate and web of the flat steel box girder bridge. The coordinate system is established with the center of the bottom plate of the flat steel box girder bridge as the coordinate origin. The temperature measuring point arrangement principle on the top plate, transverse plate and bottom plate of the flat steel box girder bridge is that the vertical distance from the transverse plate to the lower surface of the top plate of the flat steel box girder bridge is expressed as 0.00 m, 1.98 m, 2.68 m, 3.20 m, 3.30 m, 3.40 m, 3.45 m and 3.50 m, which are denoted as yc1-yc8. The specific arrangement is shown in Figure 4 The collection interval is 1 minute.

[0064] III. Effect analysis of vertical positive temperature gradient load model

[0065] Taking the positions of T P1 and T P2 in the vertical positive temperature gradient model of the north-south flat wide steel box girder bridge as examples, the temperature history curves of the measuring points are drawn based on the temperature monitoring data, as shown in Figure 5 The temperature difference between the positions of T P1 and T P2 and the average temperature of the lowest position of the box girder section measuring point is calculated, respectively. The probability density histogram is drawn based on the data and the probability density function is fitted, as shown in Figure 6 and Figure 7 The temperature gradient representative values of the positions of T P1 and T P2 are 23.6°C and 16.0°C, respectively, which are obtained by taking the 99% guarantee rate in the probability density function.

[0066] The temperature gradient model corresponding to the design service life of 100 years is constructed by using the vertical temperature gradient model of the north-south flat wide steel box girder bridge. μ P1 is 11.84, σ P1 is 3.76, μ P2 is 9.98, σ P2 is 1.84, and T P1 and TP2 23.8℃ and 16.5℃, which is less different from the measured results, and the test shows that the positive temperature gradient model has good applicability.

[0067] Test 2

[0068] In order to verify the effect of the vertical negative temperature gradient model of the north-south flat wide steel box girder bridge, the inventors arranged the vertical temperature sensors on the flat steel box girder bridge described in embodiment 1 and conducted long-term temperature field monitoring, and the specific construction process is as follows:

[0069] I. Long-term monitoring equipment

[0070] Consistent with test 1.

[0071] II. Temperature measurement point arrangement

[0072] Consistent with test 1.

[0073] III. Effect analysis of vertical negative temperature gradient load model

[0074] Taking the positions of T N1 and T N2 in the vertical negative temperature gradient model of the north-south flat wide steel box girder bridge as an example, the temperature history curves of the measurement points were drawn based on the temperature measured monitoring data, as shown in Figure 5 The temperature difference between the positions of T N1 and T N2 and the highest position of the average temperature of the box girder section measurement points was calculated, the probability density histogram was drawn based on the data, and the probability density function was fitted, as shown in Figure 8 and Figure 9 respectively. The guarantee rate of 1% in the probability density function was valued respectively, and the temperature gradient representative values at the positions of T N1 and T N2 were-5.8℃ and-8.7℃ respectively.

[0075] Using the vertical negative temperature gradient model of the north-south flat wide steel box girder bridge, the temperature gradient model corresponding to the design service life of 100 years was constructed, μ N1 was-5.12, σ N1 was 1.16, μ N2 was-10.04, σ N2 was 0.85, and T N1 and T N2 were-6.0℃ and-8.7℃. The test shows that the negative temperature gradient model has good applicability.

Claims

1. A vertical temperature gradient model for a north-south flat wide steel box girder bridge, characterized by: The model consists of a positive temperature gradient model T P (y) and negative temperature gradient model T N (y) constitute; The positive temperature gradient model T P (y) is: In formula (1), T P1 is the representative value of the positive temperature gradient at the top plate, in °C, T P2 is the representative value of the positive temperature gradient at 0.3m from the top plate, in °C. is the initial value of the positive temperature gradient at the top plate, in °C, is the initial value of the positive temperature gradient at 0.3m from the top plate, in °C, y is the distance from the flat steel box girder section to the bottom plate, h is the height of the flat steel box girder, N d The design service life of the flat steel box girder bridge is 100, 150 or 200, in years. It's F P1 The inverse function of (α), It's F P2 The inverse function of (α), F P1 (α) is the distribution function of the initial value of the positive temperature gradient at the top plate, F P2 (α) is the distribution function of the initial value of the positive temperature gradient at 0.3m from the top plate, α, a1, μ P1 , σ P1 、μ P2 , σ P2 is an intermediate variable; The negative temperature gradient model T N (y) is: In formula (2), T N1 is the representative value of negative temperature gradient at the top plate, in °C, T N2 is the representative value of the negative temperature gradient at the bottom plate, in °C. is the initial value of negative temperature gradient at the top plate, in °C, is the initial value of the negative temperature gradient at the bottom plate, in °C. F N1 (α) is the inverse function of the function, F N2 (α) The inverse function, F N1 (α) is the distribution function of the initial value of the negative temperature gradient at the top plate, F N2 (α) is the distribution function of the initial negative temperature gradient of the bottom plate, μ N1 , σ N1 、μ N2 , σ N2 is an intermediate variable.

2. The vertical temperature gradient model for a north-south flat wide steel box girder bridge according to claim 1 is characterized by: In formula (1), the μ P1 The value of is [11.16,12.52], σ P1 The value of μ is [3.3,4.27], P2 The value of is [9.65,10.32], σ P2 The value of is [1.62, 2.10]. In formula (2), the μ N1 The value of is [-5.33,-4.91], σ N1 The value of μ is [1.02,1.32], N2 The value of is [-10.19,-9.88], σ N2 The value of is [0.75,0.97].

3. The vertical temperature gradient model for a north-south flat wide steel box girder bridge according to claim 1 is characterized by: In formula (1), the N d 、μ P1 , σ P1 、μ P2 , σ P2 The value of is: N d For 100 years, μ P1 is 11.84, σ P1 is 3.76, μ P2 is 9.98, σ P2 It is 1.

84.

4. The vertical temperature gradient model for a north-south flat wide steel box girder bridge according to claim 1 is characterized by: In formula (2), the N d 、μ N1 , σ N1 、μ N2 , σ N2 The value of is: N d For 100 years, μ N1 is -5.12, σ N1 is 1.16, μ N2 is -10.04, σ N2 is 0.85.

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