Vertical temperature gradient model of east-west flat wide steel box girder bridge

Abstract

The invention relates to an east-west 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. A long-term monitoring result of a vertical temperature field of the east-west flat steel box girder is adopted, probability distribution characteristics of temperature representative values at different positions are analyzed, and a vertical temperature gradient model of the east-west flat wide steel box girder bridge suitable for 100-year, 150-year and 200-year designed service life is provided. The temperature gradient model can be used for long-life design of the flat wide steel box girder bridge in the east-west direction.

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 east-west flat wide steel box girder bridge. Background Art

[0002] Bridge structures will form a nonlinear vertical temperature field under the sun. 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, resulting in temperature self-stress in the section. Existing 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] The bridge design specifications have not yet clearly stipulated the standard value of the design temperature gradient of the east-west flat steel box girder bridge. Therefore, it is necessary to carry out long-term temperature monitoring of the east-west flat steel box girder bridge, analyze the probability distribution characteristics of the representative temperature values ​​at different positions, and obtain the temperature gradient model of the east-west flat steel box girder bridge. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a vertical temperature gradient model for an east-west flat wide steel box girder bridge.

[0005] The temperature gradient model of the east-west flat steel box girder bridge mentioned above consists of a vertical positive temperature gradient model and a vertical negative temperature gradient model.

[0006] The vertical positive temperature gradient model T TP (y) is as shown in formula (1):

[0007]

[0008] In formula (1), T TP1 is the representative value of the positive temperature gradient at the top plate, T TP2 is the representative value of the positive temperature gradient at 0.32h from the top plate, is the initial value of the positive temperature gradient at the top plate, is the initial value of the positive temperature gradient at 0.32h from the top plate, y is the distance between the section and the bottom of the steel box beam, h is the beam height, N d is the design service life of the east-west flat steel box girder bridge, with values ​​of 100, 150 and 200, in years. F TP1 (α) is the inverse function of the function, F TP2 (α) The inverse function, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at the top plate, FTP1 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.32h from the top plate, α, λ, k, μ TP2 , σ TP2 is an intermediate variable;

[0009] The vertical negative temperature gradient model T TN (y) is shown in formula (2):

[0010]

[0011] In formula (2), T TN1 is the representative value of negative temperature gradient at the top plate, T TN2 is the representative value of negative temperature gradient at the bottom plate, is the initial value of negative temperature gradient at the top plate, is the initial value of the negative temperature gradient at the bottom plate, h is the position at any height of the cross section, F TN1 (α) is the inverse function of the function, F TN2 (α) The inverse function, F TN1 (α) is the distribution function of the negative temperature gradient at the top plate, F TN2 (α) is the distribution function of the negative temperature gradient at the bottom plate, α, μ TN1 , σ TN1 , μ TN2 , σ TN2 is an intermediate variable.

[0012] In formula (1) of the present invention, the value of λ is [2.71, 2.83], the value of k is [0.63, 0.65], and μ TP2 The value of is [5.11,5.14], σ TP2 The value of is [1.32,1.35].

[0013] In the formula (1) of the present invention, the λ, k, μ TP2 , σ TP2 The values ​​of are: λ is optimally 2.77, k is optimally 0.64, μ TP2 The best is 5.13, σ TP2 The best is 1.33.

[0014] In formula (2) of the present invention, the μ TN1 The value of is [-3.04,-3.01], σ TN1 The value of is [1.36,1.38], μ TN2 The value of is [-1.60,-1.58], σ TN2 The value of is [0.25,0.27].

[0015] In formula (2) of the present invention, the μ TN1 , σ TN1 , μ TN2 , σ TN2 The value of is: TN1 The best is -3.02, σ TN1 The best is 1.37, μ TN2 The best is -1.59, σ TN2 The best value is 0.26.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] The present invention adopts the long-term vertical temperature field monitoring data of a certain east-west flat steel box girder bridge, analyzes the probability distribution characteristics of its vertical temperature gradient, and constructs a vertical temperature gradient model of the east-west flat wide steel box girder bridge. The temperature gradient model can calculate the self-stress, secondary stress and deformation generated by the vertical nonlinear temperature gradient of the east-west flat steel box girder, and can be used for the long-life design of the east-west flat steel box girder bridge with a design service life of 100, 150 and 200 years. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is the three-dimensional structural diagram of the east-west flat steel box girder bridge.

[0019] Figure 2 This is the temperature representative value distribution diagram of the vertical positive temperature gradient model of the east-west flat steel box girder bridge.

[0020] Figure 3 This is the temperature representative value distribution diagram of the vertical negative temperature gradient model of the east-west flat 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.

[0023] Figure 6 It is the measured T TP1 Histogram of positive temperature difference statistics at locations.

[0024] Figure 7 It is the measured T TP2 Histogram of positive temperature difference statistics at locations.

[0025] Figure 8 It is the measured T TN1 Histogram of negative temperature difference statistics at locations.

[0026] Fig. 9 It is the measured T TN2 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 east-west flat wide steel box girder bridge in this embodiment is composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model.

[0030] The vertical positive temperature gradient submodel T Tp (y) is as shown in formula (1):

[0031]

[0032] In formula (1), T TP1 is the representative value of the positive temperature gradient at the top plate, T TP2 is the representative value of the positive temperature gradient at 0.32h from the top plate, is the initial value of the positive temperature gradient at the top plate, is the initial value of the positive temperature gradient at 0.32h from the top plate, y is the distance between the section and the bottom of the steel box beam, h is the beam height, N d is the design service life of the east-west flat steel box girder bridge, with values ​​of 100, 150 and 200, in years. F TP1 (α) is the inverse function of the function, F TP2 (α) The inverse function, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at the top plate, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.32h from the top plate, α, λ, k, μ TP2 , σ TP2 is an intermediate variable.

[0033] The vertical negative temperature gradient model T TN (y) is shown in formula (2):

[0034]

[0035] In formula (2), T TN1 is the representative value of negative temperature gradient at the top plate, T TN2 is the representative value of negative temperature gradient at the bottom plate, is the initial value of negative temperature gradient at the top plate, is the initial value of the negative temperature gradient at the bottom plate, h is the position at any height of the cross section, F TN1 (α) is the inverse function of the function, F TN2 (α) The inverse function, FTN1 (α) is the distribution function of the negative temperature gradient at the top plate, F TN2 (α) is the distribution function of the negative temperature gradient at the bottom plate, α, μ TN1 , σ TN1 , μ TN2 , σ TN2 is an intermediate variable.

[0036] This embodiment takes an east-west flat steel box girder bridge in Dongguan as an example. Its three-dimensional structure is as follows: Figure 1 As shown in formula (1), λ is 2.77, k is 0.64, μ TP2 is 5.13, σ TP2 The vertical positive temperature gradient model temperature representative value is shown in Table 1. The vertical negative temperature gradient model temperature representative value distribution constructed according to this parameter is shown in Figure 2 shown.

[0037] The temperature gradient model can calculate the self-stress, secondary stress and deformation caused by the vertical nonlinear temperature gradient of the east-west flat steel box girder, and can be used for the long-life design of east-west flat steel box girder bridges with design service lives of 100, 150 and 200 years.

[0038] Table 1 Representative values ​​of vertical positive temperature gradient model temperature

[0039]

[0040] In formula (2), μ TN1 is -3.02, σ TN1 is 1.37, μ TN2 is -1.59, σ TN2 is 0.26, the vertical negative temperature gradient model temperature representative value is shown in Table 2, and the vertical negative temperature gradient model temperature representative value distribution constructed according to this parameter is shown in Figure 3 shown.

[0041] Table 2 Representative values ​​of vertical negative temperature gradient model temperature

[0042]

[0043] Example 2

[0044] The expression of the vertical 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.

[0045] In this embodiment, a certain east-west flat steel box girder bridge is taken as an example. In formula (1), λ is 2.71, k is 0.63, μ TP2 is 5.11, σ TP2The vertical positive temperature gradient model temperature representative value is shown in Table 3. The vertical negative temperature gradient model temperature representative value distribution constructed according to this parameter is shown in Figure 2 shown.

[0046] Table 3. Representative values ​​of vertical positive temperature gradient model temperature

[0047]

[0048] In formula (2), μ TN1 is -3.04, σ TN1 is 1.36, μ TN2 is -1.60, σ TN2 is 0.25, the vertical negative temperature gradient model temperature representative values ​​are shown in Table 4, and the vertical negative temperature gradient model temperature representative value distribution constructed according to this parameter is shown in Figure 3 shown.

[0049] Table 4 Representative values ​​of vertical negative temperature gradient model temperature

[0050]

[0051] Example 3

[0052] The expression of the vertical 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.

[0053] In this embodiment, a certain east-west flat steel box girder bridge is taken as an example. In formula (1), λ is 2.83, k is 0.65, μ TP2 is 5.14, σ TP2 The vertical positive temperature gradient model temperature representative value is shown in Table 5. The vertical negative temperature gradient model temperature representative value distribution constructed according to this parameter is shown in Figure 2 shown.

[0054] Table 5 Representative values ​​of vertical positive temperature gradient model temperature

[0055]

[0056] In formula (2), μ TN1 is -3.01, σ TN1 is 1.38, μ TN2 is -1.58, σ TN2 is 0.27, the vertical negative temperature gradient model temperature representative value is shown in Table 6, and the vertical negative temperature gradient model temperature representative value distribution constructed according to this parameter is shown in Figure 3 shown.

[0057] Table 6 Representative values ​​of vertical negative temperature gradient model temperature

[0058]

[0059] Test 1

[0060] In order to verify the effect of the vertical temperature gradient model of the east-west flat wide steel box girder bridge, the inventors arranged vertical 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:

[0061] 1. Long-term monitoring equipment

[0062] 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.

[0063] 2. Temperature measurement point arrangement

[0064] 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, 0.49m, 1.44m, 2.19m, 2.84m, 3.33m, 3.56m and 3.59m in vertical distance from the lower surface of the top plate of the flat steel box girder bridge, as shown in the following figure. Figure 4 As shown, the acquisition interval is 1 minute.

[0065] 3. Analysis of the effect of vertical positive temperature gradient load model

[0066] The vertical positive temperature gradient model T of the east-west flat wide steel box girder bridge is used as the TP1 Neutralize T TP2 Taking the location as an example, a temperature history curve 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 these locations are 16.4°C and 13.8°C, respectively.

[0067] The vertical temperature gradient model of the east-west flat wide steel box girder bridge is used to construct the temperature gradient model corresponding to the 100-year design service life, with λ being 2.77, k being 0.64, and μ TP2 is 5.13, σ TP2 is 1.33, and T TP1 and T TP2The results are 17.9℃ and 15.0℃, which are slightly different from the measured results. This experiment shows that the positive temperature gradient model has good applicability.

[0068] Test 2

[0069] In order to verify the effect of the vertical temperature gradient model of the east-west flat wide steel box girder bridge, the inventors arranged vertical 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:

[0070] 1. Long-term monitoring equipment

[0071] Same as Experiment 1.

[0072] 2. Temperature measurement point arrangement

[0073] Same as Experiment 1.

[0074] 3. Analysis of the effect of vertical negative temperature gradient load model

[0075] In the vertical negative temperature gradient model of the east-west flat wide steel box girder bridge, T TN1 and T TN2 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 TN1 and T TN2 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 TN1 and T TN2 The representative values ​​of temperature gradients at the locations are -10.9°C and -11.2 respectively.

[0076] The vertical negative temperature gradient model of the east-west flat wide steel box girder bridge is used to construct the temperature gradient model corresponding to the 100-year design service life. TN1 is -3.02, σ TN1 is 1.37, μ TN2 is -1.59, σ TN2 is 0.26, and T HN1 and T HN2 The results show that the negative temperature gradient model has good applicability.

Claims

1. A vertical temperature gradient model for an east-west flat wide steel box girder bridge. Features: The temperature gradient model of the east-west flat steel box girder bridge consists of a vertical positive temperature gradient model and a vertical negative temperature gradient model. The vertical positive temperature gradient model T TP (y) is as shown in formula (1): In formula (1), T TP1 is the representative value of the positive temperature gradient at the top plate, T TP2 is the representative value of the positive temperature gradient at 0.32h from the top plate, is the initial value of the positive temperature gradient at the top plate, is the initial value of the positive temperature gradient at 0.32h from the top plate, y is the distance between the section and the bottom of the steel box beam, h is the beam height, N d is the design service life of the east-west flat steel box girder bridge, with values ​​of 100, 150 and 200, in years. F TP1 (α) is the inverse function of the function, F TP2 (α) The inverse function, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at the top plate, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.32h from the top plate, α, λ, k, μ TP2 , σ TP2 is an intermediate variable; The vertical negative temperature gradient model T TN (y) is shown in formula (2): In formula (2), T TN1 is the representative value of negative temperature gradient at the top plate, T TN2 is the representative value of negative temperature gradient at the bottom plate, is the initial value of negative temperature gradient at the top plate, is the initial value of the negative temperature gradient at the bottom plate, h is the position at any height of the cross section, F TN1 (α) is the inverse function of the function, F TN2 (α) The inverse function, F TN1 (α) is the distribution function of the negative temperature gradient at the top plate, F TN2 (α) is the distribution function of the negative temperature gradient at the bottom plate, α, μ TN1 , σ TN1 , μ TN2 , σ TN2 is an intermediate variable.

2. According to the vertical temperature gradient model of the east-west flat wide steel box girder bridge described in claim 1, Features: In formula (1), the value of λ is [2.71, 2.83], the value of k is [0.63, 0.65], and μ TP2 The value of is [5.11,5.14], σ TP2 The value of is [1.32,1.35].

3. According to the vertical temperature gradient model of the east-west flat wide steel box girder bridge described in claim 1, Features: In formula (1), the λ, k, μ TP2 , σ TP2 The values ​​are: λ=2.77,k=0.64,μ TP2 =5.13,σ TP2 =1.

33.

4. According to the vertical temperature gradient model of the east-west flat wide steel box girder bridge described in claim 1, Features: In formula (2), the μ TN1 The value of is [-3.04,-3.01], σ TN1 The value of is [1.36,1.38], μ TN2 The value of is [-1.60,-1.58], σ TN2 The value of is [0.25,0.27].

5. According to the vertical temperature gradient model of the east-west flat wide steel box girder bridge described in claim 1, Features: In formula (2), the μ TN1 , σ TN1 , μ TN2 , σ TN2 The value of is: TN1 =-3.02,σ TN1 =1.37,μ TN2 =-1.59,σ TN2 =0.26.

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