Vertical temperature gradient model of south-north flat wide steel box girder bridge

Abstract

The invention relates to a south-north flat wide steel box girder bridge vertical temperature gradient model which is composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model which are both in a bifold line form. According to section characteristics and temperature field distribution characteristics of the flat wide steel box girder and probability distribution of temperature representative values at typical positions, a long-life temperature gradient model suitable for 100-year, 150-year and 200-year design service life of the flat wide steel box girder bridge is provided. The temperature gradient model can be used for design, calculation and analysis of the flat wide steel box girder bridge, and reference can be provided for 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 vertical temperature gradient model of a north-south flat wide steel box girder bridge. Background Art

[0002] The temperature effects on bridge structures are divided into uniform temperature rise and fall and gradient temperature effects. For multi-span continuous beams, uniform temperature rise and fall will only cause deformation, but will not generate secondary stress inside the structure. Under the action of nonlinear temperature gradient, the temperature strains at different positions of the same section are inconsistent, and there are mutual constraints between fibers at different positions, which will cause temperature self-stress of the section. Studies have shown that the nonlinear temperature gradient forms are significantly different for different main beam cross-section forms and different bridge positions, and the temperature self-stress generated is also different. Therefore, it is necessary to construct a vertical temperature gradient load model suitable for different bridge cross-section forms and bridge positions.

[0003] With the advancement of long-span bridge construction, especially the large-scale application of cable-stayed bridges and suspension bridges, flat steel box girders are the main girder form used. However, there is no vertical temperature gradient load model for flat steel box girders with different bridge positions in the bridge design specifications. Therefore, it is necessary to use the long-term monitoring data of the temperature field of flat steel box girders of real bridges, and consider the influence of the bridge position to construct a vertical temperature gradient load model for flat steel box girders to support the calculation and analysis of the temperature stress of the main girder. Summary of the invention

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

[0005] The technical solution adopted to solve the above technical problems is that the model is composed of a positive temperature gradient model T P (y) and negative temperature gradient model T N (y) constitute;

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

[0007]

[0008] 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 dThe design service life of the flat steel box girder bridge is 100, 150 or 200, in years. Yes F P1 The inverse function of (α), Yes 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 a distance of 0.3 m from the top plate, α, a1, μ P1 , σ P1 , μ P2 , σ P2 is an intermediate variable.

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

[0010]

[0011] 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 negative temperature gradient at the top plate, F N2 (α) is the distribution function of the initial value gradient of the negative temperature of the bottom plate, μ N1 , σ N1 , μ N2 , σ N2 is an intermediate variable.

[0012] In the positive temperature gradient model T of the present invention P In the formula (1) of (y), the μ P1 The value of is [11.16,12.52], σ P1 The value of is [3.3,4.27], μ 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 is [1.02,1.32], μ N2 The value of is [-10.19,-9.88], σN2 The value of is [0.75,0.97].

[0013] In the positive temperature gradient model T of the present invention P In the formula (1) of (y), N d , μ P1 , σ P1 , μ P2 , σ P2 The value of is: d For 100 years, μ P1 The best value is 11.84, σ P1 The best is 3.76, μ P2 The best is 9.98, σ P2 The best is 1.84.

[0014] In the negative temperature gradient model T of the present invention N In the formula (2) of (y), the N d , μ N1 , σ N1 , μ N2 , σ N2 The value of is: d For 100 years, μ N1 The best is -5.12, σ N1 The best is 1.16, μ N2 The best is -10.04, σ N2 The best value is 0.85.

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

[0016] 1. The present invention utilizes the long-term monitoring data of the temperature field of the flat wide steel box main beam of the north-south bridge to construct a temperature gradient load model for the north-south flat wide steel box beam bridge. The constructed load model takes into account the influence of the beam height and the temperature probability distribution characteristics at different cross-sectional positions.

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

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

[0019] Figure 2 It is the distribution diagram of representative temperature values ​​at typical locations of the vertical positive temperature gradient model of a flat wide steel box girder bridge.

[0020] Figure 3It is the distribution diagram of representative temperature values ​​at typical locations of the vertical negative temperature gradient model of a flat wide steel box girder bridge.

[0021] Figure 4 It is the arrangement diagram of vertical temperature measuring points of the measured temperature field.

[0022] Figure 5 It is the temperature history curve at the measuring point.

[0023] Figure 6 It is the measured T P1 Histogram of positive temperature difference statistics at locations.

[0024] Figure 7 It is the measured T P2 Histogram of positive temperature difference statistics at locations.

[0025] Figure 8 It is the measured T N1 Histogram of negative temperature difference statistics at locations.

[0026] Fig. 9 It is the measured T N2 Histogram of negative temperature difference statistics at locations. DETAILED DESCRIPTION

[0027] 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.

[0028] Example 1

[0029] The vertical temperature gradient model of the north-south flat wide steel box girder bridge involved in this embodiment is composed of the positive temperature gradient model T P (y) and negative temperature gradient model T N (y) composition.

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

[0031]

[0032] 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. Yes F P1The inverse function of (α), Yes 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 a distance of 0.3 m 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 negative temperature gradient at the top plate, F N2 (α) is the distribution function of the initial value gradient of the negative temperature 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 is constructed according to this parameter. The representative values ​​of 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 1. The distribution of representative values ​​of temperature at typical positions in the vertical positive temperature gradient model constructed according to this parameter is shown in 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 =0.85, and the corresponding vertical negative temperature gradient model of the flat wide steel box girder bridge is constructed according to this parameter. The representative values ​​of 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 distribution diagram of the representative values ​​of temperature at typical locations in the vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

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

[0041]

[0042] Example 2

[0043] The vertical temperature gradient model form of the north-south flat wide steel box girder bridge involved in this embodiment is the same as that of Embodiment 1, but the temperature representative values ​​are different.

[0044] This embodiment takes a flat wide steel box girder bridge as an example, and its three-dimensional structure is as follows: Figure 1 As shown in formula (1), μ P1 is 11.16, σ P1 is 3.3, μ P2 is 9.65, σ P2 is 1.62, and the corresponding vertical positive temperature gradient model of the flat wide steel box girder bridge is constructed according to this parameter. The representative values ​​of 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 distribution of representative values ​​of temperature at typical positions in the vertical positive temperature gradient model constructed according to this parameter is shown in Figure 2 shown.

[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, and the corresponding vertical negative temperature gradient model of the flat wide steel box girder bridge is constructed according to this parameter. The representative values ​​of 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 distribution diagram of the representative values ​​of temperature at typical locations in the vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

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

[0049]

[0050] Example 3

[0051] The vertical temperature gradient model of the north-south flat wide steel box girder bridge in this embodiment is the same as that in Embodiment 1, but the temperature representative values ​​are different.

[0052] This embodiment takes a flat wide steel box girder bridge as an example, and its three-dimensional structure is as follows: Figure 1 As shown in formula (1), μ P1 is 12.52, σ P1 is 4.27, μ P2 is 10.32, σ P2 =2.10, and the corresponding vertical positive temperature gradient model of the flat wide steel box girder bridge is constructed according to this parameter. The representative values ​​of 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 distribution of representative values ​​of temperature at typical positions in the vertical positive temperature gradient model constructed according to this parameter is shown in Figure 2 shown.

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

[0054]

[0055] In formula (2), μ N1 is -4.91, σ N1 is 1.32, μ N2 is -9.88, σ N2 =0.97, and the corresponding vertical negative temperature gradient model of the flat wide steel box girder bridge is constructed according to this parameter. The representative values ​​of 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 distribution diagram of the representative values ​​of temperature at typical positions in the vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

[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 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] 1. Long-term monitoring equipment

[0061] The monitoring equipment is the Donghua DH2002 remote temperature acquisition instrument produced in Taizhou, Jiangsu, and the temperature measurement point uses a three-wire Pt100 sensor.

[0062] 2. Temperature measurement point arrangement

[0063] The top plate, bottom plate and web of the flat steel box girder bridge are selected to arrange temperature measuring points, and a 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 points are arranged on the top plate, diaphragm plate and bottom plate of the flat steel box girder bridge according to the following arrangement principle: the positions of the temperature measuring points arranged on the diaphragm are expressed as 0.00m, 1.98m, 2.68m, 3.20m, 3.30m, 3.40m, 3.45m and 3.50m in vertical distance from the lower surface of the top plate of the flat steel box girder bridge, and are recorded as yc1 to yc8. Figure 4 As shown, the acquisition interval is 1 minute.

[0064] 3. Analysis of the effect of vertical positive temperature gradient load model

[0065] In the vertical positive temperature gradient model of the north-south flat wide steel box girder bridge, T P1 and T P2 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 P1 and T P2 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 P1 and T P2 The representative values ​​of temperature gradients at the locations are 23.6°C and 16.0°C, respectively.

[0066] The vertical temperature gradient model of the north-south flat wide steel box girder bridge is used to construct the temperature gradient model corresponding to the 100-year design service life. P1 is 11.84, σ P1 is 3.76, μ P2 is 9.98, σ P2 is 1.84, and T P1 and TP2 The results are 23.8℃ and 16.5℃, which are slightly different from the measured results. This experiment 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 inventor arranged vertical temperature sensors on the flat steel box girder bridge described in Example 1 and performed long-term temperature field monitoring. The specific construction process is as follows:

[0069] 1. Long-term monitoring equipment

[0070] Same as Experiment 1.

[0071] 2. Temperature measurement point arrangement

[0072] Same as Experiment 1.

[0073] 3. Analysis of the effect of vertical negative temperature gradient load model

[0074] In the vertical negative temperature gradient model of a north-south flat wide steel box girder bridge, T N1 and T N2 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 N1 and T N2 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 N1 and T N2 The representative values ​​of temperature gradient at the locations are -5.8℃ and -8.7℃ respectively.

[0075] The vertical negative temperature gradient model of the north-south flat wide steel box girder bridge is used to construct the temperature gradient model corresponding to the 100-year design service life. N1 is -5.12, σ N1 is 1.16, μ N2 is -10.04, σ N2 is 0.85, and T N1 and T N2 The results show 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. Yes F P1 The inverse function of (α), Yes 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 a distance of 0.3 m 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 negative temperature gradient at the top plate, F N2 (α) is the distribution function of the initial value gradient of the negative temperature of the bottom plate, μ N1 , σ N1 , μ N2 , σ N2 is an intermediate variable.

2. The vertical temperature gradient model of the 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 is [3.3,4.27], μ 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 is [1.02,1.32], μ 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 of the north-south flat wide steel box girder bridge according to claim 1 is characterized by: In formula (1), N d , μ P1 , σ P1 , μ P2 , σ P2 The value of is: d For 100 years, μ P1 is 11.84, σ P1 is 3.76, μ P2 is 9.98, σ P2 is 1.

84.

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

Images