Vertical temperature gradient model of asymmetric wing-plate-free steel box girder bridge

Abstract

An asymmetric wing-plate-free steel box girder bridge vertical temperature gradient model is composed of an asymmetric wing-plate-free steel box girder bridge vertical positive temperature gradient model and an asymmetric wing-plate-free steel box girder bridge vertical negative temperature gradient model, the positive temperature gradient is in a three-fold-line form, and the negative temperature gradient is in a double-fold-line form. According to section characteristics and temperature field distribution characteristics of the asymmetric wing-plate-free steel box girder, long-term monitoring of a vertical temperature field is carried out, and statistical analysis and least square fitting are carried out on a vertical daily extreme temperature difference by utilizing long-term monitoring data of the temperature field; a vertical temperature gradient model suitable for 100-year, 150-year and 200-year design service life of the asymmetric wing-plate-free steel box girder bridge is constructed, and the vertical temperature gradient model can be used for calculating stress and deformation generated by the vertical temperature gradient in the operation stage of the asymmetric wing-plate-free steel box girder bridge.

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 an asymmetric flangeless steel box girder bridge. Background Art

[0002] Asymmetric steel box girder bridges without flanges have been used in engineering to a certain extent. Their cross-sectional structure has a great influence on the surrounding flow field. Under solar radiation, the vertical temperature field distribution of asymmetric steel box girder bridges without flanges is quite different from that of steel box girder bridges with flanges. The vertical temperature field distribution of the steel box girder without flanges is highly nonlinear, and the temperature self-stress is large. The vertical temperature gradient model of steel box girder without flanges has not been specified in the current specifications. Therefore, it is necessary to carry out long-term vertical temperature field monitoring based on the cross-sectional characteristics and temperature field distribution characteristics of asymmetric steel box girder without flanges, conduct statistical analysis of the vertical daily extreme temperature difference and fit the temperature field distribution, construct a vertical temperature gradient model suitable for asymmetric steel box girder bridges without flanges with a design service life of 100, 150 and 200 years, and calculate the stress and deformation caused by the vertical temperature gradient of asymmetric steel box girder bridges without flanges during the operation stage. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a vertical temperature gradient model of an asymmetric steel box girder bridge without flanges, which can be used for calculating the vertical temperature gradient model of an asymmetric steel box girder bridge without flanges.

[0004] The vertical temperature gradient model of the asymmetric flangeless steel box girder bridge is composed of the vertical positive temperature gradient model T P (y) and vertical negative temperature gradient model T N (y) composition.

[0005] The vertical positive temperature gradient model T P (y) is as shown in formula (1):

[0006]

[0007] 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, T P3 is the representative value of the positive temperature gradient at a distance of 0.5 m from the bottom 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. is the initial value of the positive temperature gradient at 0.5m from the bottom plate, in °C, y is the distance between any position of the steel box girder section without flange and the bottom plate, h is the height of the steel box girder without flange, N dIt is the design service life of the steel box girder bridge without flange, the value range is 100, 150 or 200, the unit is year. F P1 (α) is the inverse function of the function, F P2 (α) is the inverse function of the function, F P3 (α) The inverse function, 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, F P3 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.5 m from the bottom plate, and α, β1, β2, β3, γ1, γ2, γ3, and z are intermediate variables.

[0008] The vertical negative temperature gradient model T N (y) is shown in formula (2):

[0009]

[0010] 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 negative temperature gradient 1m away from the top plate, in °C. is the initial value of negative temperature gradient at the top plate, in °C, is the initial value of negative temperature gradient 1m away from the top 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 of the negative temperature gradient at a distance of 1 m from the top plate, F N3 (α) is the distribution function of the initial value of the negative temperature gradient at 2m from the top plate, μ N1 , σ N1 , μ N2 , σ N2 is an intermediate variable.

[0011] In formula (1) of the present invention, the value of β1 is [0.78, 1.88], the value of γ1 is [3.45, 10.16], the value of β2 is [1.12, 2.75], the value of γ2 is [2.05, 5.83], the value of β3 is [9.76, 23.73], and the value of γ3 is [0.06, 0.16]. In formula (2), the value of μ N1 The value of is [-0.35,0.13], σN1 The value of is [0.54,0.88], μ N2 The value of is [0.3,0.59], σ N2 The value of is [0.32,0.53].

[0012] In the formula (1) of the present invention, the N d , the values ​​of β1, γ1, β2, γ2, β3 and γ3 are: Ν d For 100 years, the optimal β1 is 1.21, the optimal γ1 is 5.92, the optimal β2 is 1.75, the optimal γ2 is 3.45, the optimal β3 is 15.85, and the optimal γ3 is 0.10.

[0013] In formula (2) of the present invention, N d , μ N1 , σ N1 , μ N2 , σ N2 The value of is: d For 100 years, μ N1 The best is -0.11, and the best σ N1 is 0.69, μ N2 The best value is 0.44, σ N2 The best value is 0.41.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] The vertical temperature gradient model of an asymmetric flangeless steel box girder bridge proposed in the present invention is simple in form and is constructed using long-term monitoring data of the measured temperature field. It takes into account the influence of the beam height and the temperature probability distribution characteristics at different cross-sectional positions, and can be used to calculate the vertical temperature gradient model of an asymmetric flangeless steel box girder bridge during the operation stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is the cross section of an asymmetric steel box girder bridge without flanges.

[0017] Figure 2 It is the temperature representative value distribution of the vertical positive temperature gradient model of an asymmetric steel box girder bridge without flange.

[0018] Figure 3 It is the temperature representative value distribution of the vertical negative temperature gradient model of an asymmetric steel box girder bridge without flange.

[0019] Figure 4 It is the arrangement of vertical temperature measuring points for the measured temperature field of an asymmetric flangeless steel box girder bridge.

[0020] Figure 5 It is the temperature history curve of the measuring point of the asymmetric flangeless steel box girder bridge.

[0021] Figure 6 It is the measured T P1 Histogram of positive temperature difference statistics at locations.

[0022] Figure 7 It is the measured T P2 Histogram of positive temperature difference statistics at locations.

[0023] Figure 8 It is the measured T P3 Histogram of positive temperature difference statistics at locations. DETAILED DESCRIPTION

[0024] 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.

[0025] Example 1

[0026] The vertical temperature gradient model of the asymmetric flangeless steel box girder bridge involved in this embodiment is composed of a vertical positive temperature gradient model T P (y), vertical negative temperature gradient model T N (y) constitute;

[0027] The vertical positive temperature gradient model T P (y) is as shown in formula (1):

[0028]

[0029] 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, T P3 is the representative value of the positive temperature gradient at a distance of 0.5 m from the bottom 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. is the initial value of the positive temperature gradient at 0.5m from the bottom plate, in °C, y is the distance between any position of the steel box girder section without flange and the bottom plate, h is the height of the steel box girder without flange, N d It is the design service life of the steel box girder bridge without flange, in years, with a range of 100, 150 or 200. F P1 (α) is the inverse function of the function, F P2 (α) is the inverse function of the function, F P3 (α) The inverse function, 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, F P3 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.5 m from the bottom plate, and α, β1, β2, β3, γ1, γ2, γ3, and z are intermediate variables;

[0030] The vertical negative temperature gradient model T N (y) is shown in formula (2):

[0031]

[0032] 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 negative temperature gradient 1m away from the top plate, in °C. is the initial value of negative temperature gradient at the top plate, in °C, is the initial value of negative temperature gradient 1m away from the top 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 of the negative temperature gradient at a distance of 1 m from the top plate, F N3 (α) is the distribution function of the initial value of the negative temperature gradient at 2m from the top plate, μ N1 , σ N1 , μ N2 , σ N2 is an intermediate variable.

[0033] This embodiment takes an asymmetric steel box girder bridge without flanges in Dongguan as an example. Figure 1 As shown in formula (1), β1 is 1.21, γ1 is 5.92, β2 is 1.75, γ2 is 3.45, β3 is 15.85, and γ3 is 0.10. The temperature 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 vertical positive temperature gradient model constructed according to the parameters is shown in Figure 2 shown.

[0034] Table 1 Representative values ​​of temperature in the vertical positive temperature gradient model

[0035]

[0036] In formula (2), μ N1 is -0.11, σ N1 is 0.69, μ N2 is 0.44, σN2 =0.41, and the corresponding vertical temperature gradient model of the asymmetric flangeless steel box girder bridge is constructed according to this parameter. The temperature representative values ​​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 temperature representative value distribution of the vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

[0037] Table 2 Representative values ​​of temperature in the vertical negative temperature gradient model

[0038]

[0039] Example 2

[0040] The expression of the vertical temperature gradient model of the asymmetric flangeless steel box girder bridge in this embodiment is the same as that in Embodiment 1, but the temperature representative value is different.

[0041] This embodiment takes an asymmetric flangeless steel box girder bridge in the south as an example. In formula (1), β1 is 0.78, γ1 is 3.45, β2 is 1.12, γ2 is 2.05, β3 is 9.76, and γ3 is 0.06. The corresponding vertical temperature gradient model of the asymmetric flangeless steel box girder bridge is constructed according to the parameters. The temperature 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 3. The temperature representative value distribution of the vertical positive temperature gradient model constructed according to the parameters is shown in Table 3. Figure 2 shown.

[0042] Table 3 Representative values ​​of temperature in the vertical positive temperature gradient model

[0043]

[0044] In formula (2), μ N1 is -0.35, σ N1 is 0.54, μ N2 is 0.3, σ N2 The value of is 0.32, and the corresponding vertical temperature gradient model of the asymmetric flangeless steel box girder bridge is constructed according to this parameter. The temperature representative values ​​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 temperature representative value distribution of the vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

[0045] Table 4 Representative values ​​of temperature in the vertical negative temperature gradient model

[0046]

[0047] Example 3

[0048] The expression of the vertical temperature gradient model of the asymmetric flangeless steel box girder bridge in this embodiment is the same as that in Embodiment 1, but the temperature representative value is different.

[0049] This embodiment takes an asymmetric flangeless steel box girder bridge in the south as an example. In formula (1), β1 is 1.88, γ1 is 10.16, β2 is 2.75, γ2 is 5.83, β3 is 23.73, and γ3 is 0.16. The vertical temperature gradient model of the asymmetric flangeless steel box girder bridge is constructed according to the parameters. The medium representative values ​​of 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 temperature representative value distribution of the vertical positive temperature gradient model constructed according to the parameters is shown in Table 5. Figure 2 shown.

[0050] Table 5 Representative values ​​of temperature in the vertical positive temperature gradient model

[0051]

[0052] In formula (2), μ N1 is 0.13, σ N1 is 0.88, μ N2 is 0.59, σ N2 =0.53, and the corresponding vertical temperature gradient model of the asymmetric steel box girder bridge without flange is constructed according to this parameter. The temperature representative values ​​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 temperature representative value distribution of the vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

[0053] Table 6 Representative values ​​of temperature in the vertical negative temperature gradient model

[0054]

[0055] Test 1

[0056] In order to verify the effect of the vertical temperature gradient model of the asymmetric flangeless steel box girder bridge, the inventors arranged vertical temperature sensors on the Taiping Waterway Bridge in Dongguan, Guangdong, and conducted long-term temperature field monitoring. The specific construction process is as follows:

[0057] 1. Long-term monitoring equipment

[0058] 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.

[0059] 2. Temperature measurement point arrangement

[0060] The top plate, bottom plate and web of the flangeless steel box girder are selected to arrange temperature measuring points, and a coordinate system is established with the center of the bottom plate of the flangeless steel box girder as the coordinate origin. The temperature measuring points are arranged on the top plate, diaphragm plate and bottom plate of the flangeless steel box girder bridge. The arrangement principle is: 0.00m, 0.60m, 1.60m, 2.10m, 2.60m, 3.10m, 3.40m, 3.50m, 3.60m, 3.70m, 3.75m, 3.80m. The measuring point arrangement scheme is as follows: Figure 4 As shown, denoted as MT1 to MT12. Figure 4 As shown, the acquisition interval is 2 minutes.

[0061] 3. Analysis of the effect of vertical positive temperature gradient load model

[0062] In the vertical positive temperature gradient model of an asymmetric steel box girder bridge without flange, 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 , Figure 7 and Figure 8 As shown. The 99% guarantee rate in the probability density function is taken as the value, and the obtained T P1 、T P2 and T P3 The representative values ​​of temperature gradients at the locations are 14.3°C, 11.1°C and 6.8°C respectively.

[0063] The vertical temperature gradient model of the asymmetric flangeless steel box girder bridge is used to construct the temperature gradient model corresponding to the design service life of 100 years. β1 is 1.21, γ1 is 5.92, β2 is 1.75, γ2 is 3.45, β3 is 15.85, and γ3 is 0.10. The T P1 、T P2 and T P3 They are 14.6℃, 12.3℃ and 7.1℃ respectively, which are slightly different from the measured results. The test shows that the vertical temperature gradient model of asymmetric flangeless steel box girder bridge has good applicability.

Claims

1. A vertical temperature gradient model for an asymmetric flangeless steel box girder bridge, characterized in that: The temperature gradient model consists of a vertical positive temperature gradient model T P (y) and vertical negative temperature gradient model T N (y) constitute; The vertical positive temperature gradient model T P (y) is as shown in formula (1): 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, T P3 is the representative value of the positive temperature gradient at a distance of 0.5 m from the bottom 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. is the initial value of the positive temperature gradient at 0.5m from the bottom plate, in °C, y is the distance between any position of the steel box girder section without flange and the bottom plate, h is the height of the steel box girder without flange, N d It is the design service life of the steel box girder bridge without flange, the value range is 100, 150 or 200, the unit is year. F P1 (α) is the inverse function of the function, F P2 (α) is the inverse function of the function, F P3 (α) The inverse function, 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, F P3 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.5 m from the bottom plate, and α, β1, β2, β3, γ1, γ2, γ3, and z are intermediate variables; The vertical negative temperature gradient model T N (y) is shown in formula (2): 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 negative temperature gradient 1m away from the top plate, in °C. is the initial value of negative temperature gradient at the top plate, in °C, is the initial value of negative temperature gradient 1m away from the top 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 of the negative temperature gradient at a distance of 1 m from the top plate, F N3 (α) is the distribution function of the initial value of the negative temperature gradient at 2m from the top plate, μ N1 , σ N1 , μ N2 , σ N2 is an intermediate variable.

2. The vertical temperature gradient model of an asymmetric flangeless steel box girder bridge according to claim 1 is characterized in that: In formula (1), the value of β1 is [0.78, 1.88], the value of γ1 is [3.45, 10.16], the value of β2 is [1.12, 2.75], the value of γ2 is [2.05, 5.83], the value of β3 is [9.76, 23.73], and the value of γ3 is [0.06, 0.16]. In formula (2), μ N1 The value of is [-0.35,0.13], σ N1 The value of is [0.54,0.88], μ N2 The value of is [0.3,0.59], σ N2 The value of is [0.32,0.53].

3. The vertical temperature gradient model of an asymmetric flangeless steel box girder bridge according to claim 1 is characterized in that: In formula (1), N d , the values ​​of β1, γ1, β2, γ2, β3 and γ3 are: Ν d For 100 years, β1 is 1.21, γ1 is 5.92, β2 is 1.75, γ2 is 3.45, β3 is 15.85, and γ3 is 0.

10.

4. The vertical temperature gradient model of an asymmetric flangeless 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 -0.11, σ N1 is 0.69, μ N2 is 0.44, σ N2 It is 0.41.

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