Vertical temperature gradient model of double-layer steel truss girder bridge

Abstract

The invention relates to a vertical temperature gradient model of a double-layer steel truss girder bridge, which comprises vertical temperature gradient models of upper and lower layers of bridge floors and a vertical temperature gradient model of a main truss, and the vertical temperature gradient models of the upper and lower layers of bridge floors are composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model. The main truss vertical temperature gradient model is composed of vertical positive and negative temperature gradient models of upper and lower chord members and web members. A double-layer steel truss girder bridge vertical temperature gradient model with the design service life up to 200 years is constructed according to double-layer steel truss girder temperature field distribution characteristics and probability distribution of temperature representative values at typical positions. The overall vertical temperature field distribution type of the double-layer truss girder bridge is disclosed for the first time and can be used for long-life design and evaluation of the double-layer steel truss girder bridge, and the problem that no vertical temperature gradient model of the double-layer steel truss girder bridge exists in steel bridge design specifications is solved.

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 double-layer steel truss bridge. Background Art

[0002] The type of nonlinear vertical temperature gradient significantly affects the magnitude of temperature stress. Under the action of vertical nonlinear temperature gradient, the temperature strains at different positions of the same section of the bridge structure are inconsistent. In addition, there are mutual constraints between fibers at different positions, which leads to temperature self-stress in the section. Studies have shown that the nonlinear temperature gradient forms of different main beam cross-sections are significantly different, 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-sections.

[0003] A double-deck steel truss bridge consists of an upper deck, a lower deck and a main truss. Due to its complex structural system and the direction of the bridge, the nonlinear vertical temperature gradients of the upper deck, lower deck and main truss of the double-deck steel truss bridge are significantly different. Therefore, it is necessary to conduct long-term temperature field monitoring of the main truss and upper and lower deck systems of the double-deck steel truss bridge respectively, and to construct a vertical temperature gradient model of the double-deck steel truss bridge. 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 double-layer steel truss bridge.

[0005] The vertical temperature gradient model of the double-deck steel truss bridge is:

[0006] The model is composed of an upper deck vertical temperature gradient model, a lower deck vertical temperature gradient model and a main truss temperature gradient model; the upper deck vertical temperature gradient model is composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model, the lower deck vertical temperature gradient model is composed of a lower deck vertical positive temperature gradient model and a vertical negative temperature gradient model, and the main truss temperature gradient model is composed of a main truss vertical positive temperature gradient model and a main truss vertical negative temperature gradient model;

[0007] The vertical positive temperature gradient model T of the upper deck of the double-deck steel truss bridge TP (y1) is as shown in formula (1):

[0008]

[0009] In formula (1), T TP1 0.35h from the bottom of the upper bridge deck T The representative value of the positive temperature gradient is T TP2 0.88h from the bottom of the upper bridge deck T The representative value of the positive temperature gradient is T TP3 is the representative value of the positive temperature gradient at the top of the upper bridge deck, 0.35h from the bottom of the upper bridge deck T At the initial value of positive temperature gradient, 0.88h from the bottom of the upper bridge deck T At the initial value of positive temperature gradient, is the initial value of the positive temperature gradient at the top of the upper bridge deck, y1 is the height of any position of the cross section from the upper bridge deck, h T is the upper deck beam height, N d The design service life of a double-deck steel truss bridge is 100 years, 150 years or 200 years. F TP1 (α) is the inverse function of the function, F TP2 (α) is the inverse function of the function, F TP3 (α) The inverse function, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.35h1 from the bottom of the upper bridge deck, F TP2 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.88h1 from the bottom of the upper bridge deck, F TP3 (α) is the distribution function of the initial value of the positive temperature gradient at the top of the upper bridge deck, α, μ TP1 , σ TP1 , μ TP2 , σ TP2 , μ TP3 , σ TP3 is an intermediate variable.

[0010] The vertical negative temperature gradient model T of the upper deck of the double-deck steel truss bridge TN (y1) is shown in formula (2):

[0011]

[0012] In formula (2), T TN1 is the representative value of negative temperature gradient at the bottom of the upper bridge deck, T TN2 is the representative value of negative temperature gradient from the top of the upper bridge deck, is the initial value of the negative temperature gradient from the bottom of the upper bridge deck, is the initial value of the negative temperature gradient at the top of the upper bridge deck, y1 is the distance from any position of the cross section to the top of the upper bridge deck, 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 bottom of the upper bridge deck, F TN2 (α) is the distribution function of the negative temperature gradient from the top of the upper bridge deck, and the guarantee rate μTN1 , σ TN1 , μ TN2 , σ TN2 is an intermediate variable.

[0013] The vertical positive temperature gradient model T of the lower deck of the double-deck steel truss bridge BP (y2) is shown in formula (3):

[0014]

[0015] In formula (3), T BP1 is the distance from the lower bridge deck to the top h B / 2 positive temperature gradient representative value, T BP2 is the representative value of the positive temperature gradient from the top of the lower bridge deck, is the initial value of the positive temperature gradient from the bottom of the lower bridge deck, is the initial value of the positive temperature gradient from the top of the lower deck, h B is the height of the lower deck, y2 is the distance from any position of the cross section to the top of the lower deck, F BP1 (α) is the inverse function of the function, F BP2 (α) The inverse function, F BP1 (α) is the distance from the top of the lower bridge deck h B The distribution function of the positive temperature gradient at the position / 2, F BP2 (α) is the distribution function of the positive temperature gradient at the top of the lower deck, β BP1 , BP1 , μ BP2 , σ BP2 is an intermediate variable.

[0016] The vertical negative temperature gradient model T of the lower deck of the double-deck steel truss bridge BN (y2) is shown in formula (4):

[0017]

[0018] In formula (4), T BN1 is the representative value of negative temperature gradient at the bottom of the lower bridge deck, T BN2 is the representative value of the negative temperature gradient at the top of the lower bridge deck, is the initial value of the negative temperature gradient at the bottom of the lower bridge deck, is the initial value of the negative temperature gradient from the top of the lower deck, y2 is the distance from any position of the cross section to the top of the lower deck, F BN1 (α) is the inverse function of the function, F BN2 (α) The inverse function, FBN1 (α) is the distribution function of the negative temperature gradient at the bottom of the lower bridge deck, F BN2 (α) is the distribution function of the negative temperature gradient at the top of the lower deck, μ BN1 , σ BN1 , μ BN2 , σ BN2 is an intermediate variable.

[0019] The vertical positive temperature gradient model of the main truss of the double-deck steel truss bridge is composed of the vertical positive temperature gradient model T CP (y C ), vertical positive temperature gradient model of lower chord T DP (y D ) and the vertical positive temperature gradient model of the web member T FP (y F ), specifically as shown in formula (5):

[0020]

[0021] In formula (5), T CP1 is the representative value of the positive temperature gradient of the upper chord of the main truss, T DP1 is the representative value of the positive temperature gradient of the lower chord of the main truss, T FP1 is the representative value of the positive temperature gradient of the main truss web, y C is the distance from the bottom plate of the upper chord of the main truss at any position of the cross section, y D is the distance from the bottom plate of the lower chord of the main truss at any position of the cross section, y F h is the distance between the inner wing plate of the main truss web at any position of the cross section, TC is the height of the main truss upper chord, h BC is the height of the lower chord of the main truss, h F is the main truss web height, F CP1 (α) is the inverse function of the function, F DP1 (α) is the inverse function of the function, F FP1 (α) The inverse function, F CP1 (α) is the distribution function of the positive temperature gradient of the upper chord of the main truss, F DP1 (α) is the distribution function of the positive temperature gradient of the lower chord of the main truss, F FP1 (α) is the distribution function of the positive temperature gradient of the main truss web, μ CP1 , σ CP1 , μ DP1 , σ DP1 , μ FP1 , σ FP1 is an intermediate variable.

[0022] The vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge is composed of the vertical negative temperature gradient model T CN (y C ), vertical negative temperature gradient model of lower chord T DN (y D ) and the vertical negative temperature gradient model of the web member T FN (y F ), specifically as shown in formula (6):

[0023]

[0024] In formula (6), T CN1 is the representative value of negative temperature gradient of the upper chord of the main truss, T DN1 is the representative value of negative temperature gradient of the lower chord of the main truss, T FN1 is the representative value of negative temperature gradient of the main truss web, F CN1 (α) is the inverse function of the function, F DN1 (α) is the inverse function of the function, F FN1 (α) The inverse function, F CN1 (α) is the distribution function of the negative temperature gradient of the upper chord of the main truss, F DN1 (α) is the distribution function of the negative temperature gradient of the lower chord of the main truss, F FN1 (α) is the distribution function of the negative temperature gradient of the main truss web, μ CN1 , σ CN1 , μ DN1 , σ DN1 , μ FN1 , σ FN1 is an intermediate variable.

[0025] In formula (1) of the present invention, the μ TP1 The value of is [5.81,8.76], σ TP1 The value of is [5.67,7.78], μ TP2 The value of is [10.17,14.93], σ TP2 The value of is [9.14,12.55], μ TP3 The value of is [6.92,10.23], σ TP3 The value of is [6.35,8.72]; in formula (2), the μ TN1 The value of is [-2.05,-1.50], σ TN1 The value of is [1.06,1.45], μ TN2 The value of is [-2.52,-1.89], σ TN2 The value of is [1.21,1.86]; in formula (3), the βBP1 The value is [0.42, 0.45], λ BP1 The value is [0.46, 0.50], μ BP2 The value is [-1.80,-1.75], σ BP2 The value is [1.50,1.55]; in formula (4), the μ BN1 The value of is [-1.02,-0.93], σ BN1 The value of is [3.32,.3.38], μ BN2 The value of is [-1.73,-1.68], σ BN2 The value of is [1.92,1.96]; in formula (5), the μ CP1 The value of is [3.03,6.04], σ CP1 The value of is [2.46,5.20], μ DP1 The value of is [0.56,2.82], σ DP1 The value of is [1.21,3.41], μ FP1 The value of is [0.45,1.94], σ FP1 The value of is [0.38,2.34]; in formula (6), the μ CN1 The value of is [-2.2,-0.80], σ CN1 The value of is [0.78,2.60], μ DN1 The value of is [-1.60,-0.13], σ DN1 The value of is [0.66,1.58], μ FN1 The value of is [-2.20,-0.02], σ FN1 The value of is [0.52,4.63].

[0026] In the formula (1) of the present invention, the N d , μ TP1 , σ TP1 , μ TP2 , σ TP2 , μ TP3 , σ TP3 The value of is: d For 100 years, μ TP1 The best is 7.29, σ TP1 The best is 6.64, μ TP2 The best value is 12.55, σ TP2 The best is 10.71, μ TP3 The best is 8.57, and the best σ TP3 It is 7.44.

[0027] In formula (2) of the present invention, N d , μTN1 , σ TN1 , μ TN2 , σ TN2 The value of is: d For 100 years, μ TN1 The best is -1.78, σ TN1 The best is 1.24, μ TN2 The best is -2.49, σ TN2 The best is 1.75.

[0028] In the formula (3) of the present invention, the N d , β BP1 , BP1 , μ BP2 , σ BP2 The value of is: d For 100 years, β BP1 The best value is 0.44, λ BP1 The best is 0.48, μ BP2 The best is -1.77, σ BP2 The best is 1.53.

[0029] In the formula (4) of the present invention, the N d , μ BN1 , σ BN1 , μ BN2 , σ BN2 The value of is: d For 100 years, μ BN1 The best is -0.98, σ BN1 The best is 3.35, μ BN2 The best is -1.71, σ BN2 The best is 1.94.

[0030] In formula (5) of the present invention, the μ CP1 The best value is 4.64, σ CP1 The best is 4.61, μ DP1 The best value is 1.91, σ DP1 The best is 2.32, the best μ FP1 is 1.23, σ FP1 The best is 1.38.

[0031] In formula (6) of the present invention, the μ CN1 The best is -1.62, σ CN1 The best value is 1.80, μ DN1 The best is -0.86, σ DN1 The best is 1.31, μ FN1 The best is -1.16, and the best σ FN1 is 2.95.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1. The present invention conducts long-term monitoring of the temperature field of a double-deck steel truss bridge, analyzes the probability distribution characteristics of the daily temperature difference extreme values, obtains the standard values ​​of temperature difference at typical vertical positions of the double-deck steel truss bridge within different design service lives, and constructs a temperature gradient model for double-deck steel truss bridges with a design service life of 100 to 200 years. The model can be used to calculate the vertical additional stress and deformation caused by the temperature gradient of the double-deck steel truss bridge during the operation stage, providing a basis for improving the relevant design specifications in my country. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is the three-dimensional structure diagram of the double-deck steel truss bridge.

[0035] Figure 2 This is the temperature representative value distribution diagram of the vertical positive temperature gradient model on the upper deck of a double-deck steel truss bridge.

[0036] Figure 3 This is the temperature representative value distribution diagram of the vertical negative temperature gradient model on the upper deck of a double-deck steel truss bridge.

[0037] Figure 4 This is the temperature representative value distribution diagram of the vertical positive temperature gradient model of the lower deck of a double-deck steel truss bridge.

[0038] Figure 5 This is the temperature representative value distribution diagram of the vertical negative temperature gradient model of the lower deck of a double-deck steel truss bridge.

[0039] Figure 6 This is the temperature representative value distribution diagram of the vertical positive temperature gradient model of the main truss of a double-deck steel truss bridge.

[0040] Figure 7 This is the temperature representative value distribution diagram of the vertical negative temperature gradient model of the main truss of a double-deck steel truss bridge.

[0041] Figure 8 It is the arrangement diagram of vertical temperature measuring points of the measured temperature field.

[0042] Fig. 9 It is the medium temperature history curve.

[0043] Fig.10 It is the measured T TP1 Histogram of positive temperature difference statistics at locations.

[0044] Fig.11 It is the measured T TP2 Histogram of positive temperature difference statistics at locations.

[0045] Fig.12 It is the measured T TP3 Histogram of positive temperature difference statistics at locations. DETAILED DESCRIPTION

[0046] 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.

[0047] Example 1

[0048] The vertical temperature gradient model of the double-deck steel truss bridge involved in this embodiment is composed of a vertical temperature gradient model of the upper bridge deck, a vertical temperature gradient model of the lower bridge deck and a main truss temperature gradient model; the vertical temperature gradient model of the upper bridge deck is composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model, the vertical temperature gradient model of the lower bridge deck is composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model of the lower bridge deck, and the main truss temperature gradient model is composed of a vertical positive temperature gradient model of the main truss and a vertical negative temperature gradient model of the main truss.

[0049] The vertical positive temperature gradient model T of the upper deck of the double-deck steel truss bridge in this embodiment TP (y1) is shown in formula (4):

[0050]

[0051] In formula (1), T TP1 0.35h from the bottom of the upper bridge deck T The representative value of the positive temperature gradient is T TP2 0.88h from the bottom of the upper bridge deck T The representative value of the positive temperature gradient is T TP3 is the representative value of the positive temperature gradient at the top of the upper bridge deck, 0.35h from the bottom of the upper bridge deck T At the initial value of positive temperature gradient, 0.88h from the bottom of the upper bridge deck T At the initial value of positive temperature gradient, is the initial value of the positive temperature gradient at the top of the upper bridge deck, y1 is the height of any position of the cross section from the upper bridge deck, h T is the upper deck beam height, N d The design service life of a double-deck steel truss bridge is 100 years, 150 years or 200 years. F TP1 (α) is the inverse function of the function, F TP2 (α) is the inverse function of the function, F TP3 (α) The inverse function, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.35h1 from the bottom of the upper bridge deck, F TP2 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.88h1 from the bottom of the upper bridge deck, FTP3 (α) is the distribution function of the initial value of the positive temperature gradient at the top of the upper bridge deck, α, μ TP1 , σ TP1 , μ TP2 , σ TP2 , μ TP3 , σ TP3 is an intermediate variable.

[0052] The vertical negative temperature gradient model T of the upper deck of the double-deck steel truss bridge in this embodiment TN (y1) is shown in formula (2):

[0053]

[0054] In formula (2), T TN1 is the representative value of negative temperature gradient at the bottom of the upper bridge deck, T TN2 is the representative value of negative temperature gradient from the top of the upper bridge deck, is the initial value of the negative temperature gradient from the bottom of the upper bridge deck, is the initial value of the negative temperature gradient at the top of the upper bridge deck, y1 is the distance from any position of the cross section to the top of the upper bridge deck, 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 bottom of the upper bridge deck, F TN2 (α) is the distribution function of the negative temperature gradient from the top of the upper bridge deck, and the guarantee rate μ TN1 , σ TN1 , μ TN2 , σ TN2 is an intermediate variable.

[0055] The vertical positive temperature gradient model T of the lower deck of the double-deck steel truss bridge in this embodiment BP (y2) is shown in formula (3):

[0056]

[0057] In formula (3), T BP1 is the distance from the lower bridge deck to the top h B / 2 positive temperature gradient representative value, T BP2 is the representative value of the positive temperature gradient from the top of the lower bridge deck, is the initial value of the positive temperature gradient from the bottom of the lower bridge deck, is the initial value of the positive temperature gradient from the top of the lower deck, h B is the height of the lower deck, y2 is the distance from any position of the cross section to the top of the lower deck, F BP1(α) is the inverse function of the function, F BP2 (α) The inverse function, F BP1 (α) is the distance from the top of the lower bridge deck h B The distribution function of the positive temperature gradient at the position / 2, F BP2 (α) is the distribution function of the positive temperature gradient at the top of the lower deck, β BP1 , BP1 , μ BP2 , σ BP2 is an intermediate variable.

[0058] The vertical negative temperature gradient model T of the lower deck of the double-deck steel truss bridge in this embodiment BN (y2) is shown in formula (4):

[0059]

[0060] In formula (4), T BN1 is the representative value of negative temperature gradient at the bottom of the lower bridge deck, T BN2 is the representative value of the negative temperature gradient at the top of the lower bridge deck, is the initial value of the negative temperature gradient at the bottom of the lower bridge deck, is the initial value of the negative temperature gradient from the top of the lower deck, y2 is the distance from any position of the cross section to the top of the lower deck, F BN1 (α) is the inverse function of the function, F BN2 (α) The inverse function, F BN1 (α) is the distribution function of the negative temperature gradient at the bottom of the lower bridge deck, F BN2 (α) is the distribution function of the negative temperature gradient at the top of the lower deck, μ BN1 , σ BN1 , μ BN2 , σ BN2 is an intermediate variable.

[0061] The vertical positive temperature gradient model of the main truss of the double-deck steel truss bridge in this embodiment is composed of the vertical positive temperature gradient model T CP (y C ), vertical positive temperature gradient model of lower chord T DP (y D ) and the vertical positive temperature gradient model of the web member T FP (y F ), specifically as shown in formula (5):

[0062]

[0063] In formula (5), T CP1 is the representative value of the positive temperature gradient of the upper chord of the main truss, TDP1 is the representative value of the positive temperature gradient of the lower chord of the main truss, T FP1 is the representative value of the positive temperature gradient of the main truss web, y C is the distance from the bottom plate of the upper chord of the main truss at any position of the cross section, y D is the distance from the bottom plate of the lower chord of the main truss at any position of the cross section, y F h is the distance between the inner wing plate of the main truss web at any position of the cross section, TC is the height of the main truss upper chord, h BC is the height of the lower chord of the main truss, h F is the main truss web height, F CP1 (α) is the inverse function of the function, F DP1 (α) is the inverse function of the function, F FP1 (α) The inverse function, F CP1 (α) is the distribution function of the positive temperature gradient of the upper chord of the main truss, F DP1 (α) is the distribution function of the positive temperature gradient of the lower chord of the main truss, F FP1 (α) is the distribution function of the positive temperature gradient of the main truss web, μ CP1 , σ CP1 , μ DP1 , σ DP1 , μ FP1 , σ FP1 is an intermediate variable.

[0064] The vertical negative temperature gradient model of the main truss of the double-deck steel truss bridge in this embodiment is composed of the vertical negative temperature gradient model T CN (y C ), vertical negative temperature gradient model of lower chord T DN (y D ) and the vertical negative temperature gradient model of the web member T FN (y F ), specifically as shown in formula (6):

[0065]

[0066] In formula (6), T CN1 is the representative value of negative temperature gradient of the upper chord of the main truss, T DN1 is the representative value of negative temperature gradient of the lower chord of the main truss, T FN1 is the representative value of negative temperature gradient of the main truss web, F CN1 (α) is the inverse function of the function, F DN1 (α) is the inverse function of the function, F FN1 (α) The inverse function, FCN1 (α) is the distribution function of the negative temperature gradient of the upper chord of the main truss, F DN1 (α) is the distribution function of the negative temperature gradient of the lower chord of the main truss, F FN1 (α) is the distribution function of the negative temperature gradient of the main truss web, μ CN1 , σ CN1 , μ DN1 , σ DN1 , μ FN1 , σ FN1 is an intermediate variable.

[0067] In this embodiment, a double-deck steel truss bridge in Northwest China is taken as an example. Its three-dimensional structure is as follows: Figure 1 As shown in formula (1), μ TP1 is 7.29, σ TP1 is 6.64, μ TP2 is 12.55, σ TP2 is 10.71, μ TP3 is 8.57, σ TP3 is 7.44. According to this parameter, the corresponding vertical positive temperature gradient model T of the upper deck of the double-deck steel truss bridge is constructed. TP The temperature representative values ​​in the vertical positive temperature gradient model of the upper deck 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 of the upper deck constructed according to this parameter is shown in Figure 2 shown.

[0068] Table 1 Representative values ​​of temperature in the vertical positive temperature gradient model of the upper deck

[0069]

[0070] In formula (2), μ TN1 is -1.78, σ TN1 is 1.24, μ TN2 is -2.49, σ TN2 is 1.75. According to this parameter, the corresponding vertical negative temperature gradient model T of the upper deck of the double-deck steel truss bridge is constructed. TN (y1). The temperature representative values ​​in the upper deck 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 upper deck vertical negative temperature gradient model constructed according to this parameter is shown in Figure 3 shown.

[0071] Table 2 Representative values ​​of temperature in the vertical negative temperature gradient model of the upper deck

[0072]

[0073] In formula (3), βBP1 is 0.44, λ BP1 is 0.48, μ BP2 is -1.77, σ BP2 The corresponding vertical positive temperature gradient model T of the lower deck of the double-deck steel truss bridge constructed according to this parameter is BP (y2). The temperature representative values ​​in the vertical positive temperature gradient model of the lower deck 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 of the lower deck constructed according to this parameter is shown in Figure 4 shown.

[0074] Table 3. Representative temperature values ​​in the vertical positive temperature gradient model of the lower deck

[0075]

[0076] In formula (4), μ BN1 is -0.98, σ BN1 is 3.35, μ BN2 is -1.71, σ BN2 is 1.94. According to this parameter, the corresponding vertical negative temperature gradient model T of the lower deck of the double-deck steel truss bridge is constructed. BN (y2). The temperature representative values ​​in the vertical negative temperature gradient model of the lower deck 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 of the lower deck constructed according to this parameter is shown in Figure 5 shown.

[0077] Table 4. Representative temperature values ​​in the vertical negative temperature gradient model of the lower deck

[0078]

[0079] In formula (5), μ CP1 is 4.64, σ CP1 is 4.61, μ DP1 is 1.91, σ DP1 is 2.32, μ FP1 is 1.23, σ FP1 is 1.38. The corresponding vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge is constructed according to this parameter. The temperature representative values ​​in the vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge 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 of the main truss of the double-layer steel truss bridge constructed according to this parameter is shown in Figure 6 shown.

[0080] Table 5 Representative values ​​of temperature in the vertical positive temperature gradient model of the main truss

[0081]

[0082] In formula (6), μ CN1 is -1.62, σ CN1 is 1.80, μ DN1 is -0.86, σ DN1 is 1.31, μ FN1 is -1.16, σ FN1 is 2.95. The corresponding vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge is constructed according to this parameter. The temperature representative values ​​in the vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge 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 of the main truss of the double-layer steel truss bridge constructed according to this parameter is shown in Figure 7 shown.

[0083] Table 6 Representative temperature values ​​in the vertical negative temperature gradient model of the main truss

[0084]

[0085] Example 2

[0086] The expression of the vertical temperature gradient model of the double-deck steel truss bridge in this embodiment is the same as that in Embodiment 1, but the temperature representative value is different.

[0087] In formula (1), μ TP1 is 5.81, σ TP1 is 5.67, μ TP2 is 10.17, σ TP2 is 9.14, μ TP3 is 6.92, σ TP3 is 6.35. According to this parameter, the corresponding vertical positive temperature gradient model T of the upper deck of the double-deck steel truss bridge is constructed. TP (y1). The temperature representative values ​​in the vertical positive temperature gradient model of the upper deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 7. The temperature representative value distribution of the vertical positive temperature gradient model of the upper deck constructed according to this parameter is shown in Figure 2 shown.

[0088] Table 7 Representative values ​​of temperature in the vertical positive temperature gradient model of the upper deck

[0089]

[0090] In formula (2), μ TN1 is -2.05, σ TN1 is 1.06, μ TN2 is -2.52, σ TN2is 1.21. According to this parameter, the corresponding vertical negative temperature gradient model T of the upper deck of the double-deck steel truss bridge is constructed. TN (y1). The temperature representative values ​​in the vertical negative temperature gradient model of the upper deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 8. The temperature representative value distribution of the vertical negative temperature gradient model of the upper deck constructed according to this parameter is shown in Figure 3 shown.

[0091] Table 8 Representative values ​​of temperature in the vertical negative temperature gradient model of the upper deck

[0092]

[0093] In formula (3), β BP1 is 0.42, λ BP1 is 0.46, μ BP2 is -1.80, σ BP2 is 1.50. The corresponding vertical positive temperature gradient model T of the lower deck of the double-deck steel truss bridge constructed according to this parameter BP (y2). The temperature representative values ​​in the vertical positive temperature gradient model of the lower deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 9. The temperature representative value distribution of the vertical positive temperature gradient model of the lower deck constructed according to this parameter is shown in Figure 4 shown.

[0094] Table 9 Representative values ​​of temperature in the vertical positive temperature gradient model of the lower deck

[0095]

[0096] In formula (4), μ BN1 is -1.02, σ BN1 is 3.32, μ BN2 is -1.73, σ BN2 is 1.92. According to this parameter, the corresponding vertical negative temperature gradient model T of the lower deck of the double-deck steel truss bridge is constructed. BN (y2). The temperature representative values ​​in the vertical negative temperature gradient model of the lower deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 10. The temperature representative value distribution of the vertical negative temperature gradient model of the lower deck constructed according to this parameter is shown in Figure 5 shown.

[0097] Table 10 Temperature representative values ​​in the vertical negative temperature gradient model of the lower deck

[0098]

[0099] In formula (5), μ CP1 is 3.03, σ CP1 is 2.46, μDP1 is 0.56, σ DP1 is 1.21, μ FP1 is 0.45, σ FP1 is 0.38. The corresponding vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge is constructed according to this parameter. The temperature representative values ​​in the vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 11. The temperature representative value distribution of the vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge constructed according to this parameter is shown in Figure 6 shown.

[0100] Table 11 Representative temperature values ​​in the vertical positive temperature gradient model of the main truss

[0101]

[0102] In formula (6), μ CN1 is -2.2, σ CN1 is 0.78, μ DN1 is -1.60, σ DN1 is 0.66, μ FN1 is -2.20, σ FN1 is 0.52. The corresponding vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge is constructed according to this parameter. The temperature representative values ​​in the vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 12. The temperature representative value distribution of the vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge constructed according to this parameter is shown in Figure 7 Shown

[0103] Table 12 Temperature representative values ​​in the vertical negative temperature gradient model of the main truss

[0104]

[0105] Example 3

[0106] The vertical temperature gradient model of the double-deck steel truss bridge involved in this embodiment is the same as that in Embodiment 1, but the temperature representative values ​​are different.

[0107] In formula (1), μ TP1 is 8.76, σ TP1 is 7.78, μ TP2 is 14.93, σ TP2 is 12.55, μ TP3 is 10.23, σ TP3 The temperature representative values ​​in the vertical positive temperature gradient model of the upper deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 13. The temperature representative value distribution of the vertical positive temperature gradient model of the upper deck constructed according to this parameter is shown in Figure 2 shown.

[0108] Table 13 Representative values ​​of temperature in the vertical positive temperature gradient model of the upper deck

[0109]

[0110] In formula (2), μ TN1 is -1.50, σ TN1 is 1.45, μ TN2 is -1.89, σ TN2 is 1.86. According to this parameter, the corresponding vertical negative temperature gradient model T of the upper deck of the double-deck steel truss bridge is constructed. TN The representative temperature values ​​in the vertical negative temperature gradient model of the upper deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 14.

[0111] The temperature representative value distribution of the vertical negative temperature gradient model of the upper bridge deck constructed according to this parameter is as follows: Figure 3 shown.

[0112] Table 14 Representative temperature values ​​in the vertical negative temperature gradient model of the upper bridge deck

[0113]

[0114] In formula (3), β BP1 is 0.45, λ BP1 is 0.50, μ BP2 is -1.75, σ BP2 is 1.55. The corresponding vertical positive temperature gradient model T of the lower deck of the double-deck steel truss bridge constructed according to this parameter BP (y2). The temperature representative values ​​in the vertical positive temperature gradient model of the lower deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 15. The temperature representative value distribution of the vertical positive temperature gradient model of the lower deck constructed according to this parameter is shown in Figure 4 shown.

[0115] Table 15 Temperature representative values ​​in the vertical positive temperature gradient model of the lower deck

[0116]

[0117] In formula (4), μ BN1 is -0.93, σ BN1 is 3.38, μ BN2 is -1.68, σ BN2 is 1.96. According to this parameter, the corresponding vertical negative temperature gradient model T of the lower deck of the double-deck steel truss bridge is constructed. BN(y2). The temperature representative values ​​in the vertical negative temperature gradient model of the lower deck corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 16. The temperature representative value distribution of the vertical negative temperature gradient model of the lower deck constructed according to this parameter is shown in Figure 5 shown.

[0118] Table 16 Temperature representative values ​​in the vertical negative temperature gradient model of the lower deck

[0119]

[0120] In formula (5), μ CP1 is 6.04, σ CP1 is 5.20, μ DP1 is 2.82, σ DP1 is 3.41, μ FP1 is 1.94, σ FP1 is 2.34. The corresponding vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge is constructed according to this parameter. The temperature representative values ​​in the vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 17. The temperature representative value distribution of the vertical positive temperature gradient model of the main truss of the double-layer steel truss bridge constructed according to this parameter is shown in Figure 6 shown.

[0121] Table 17 Temperature representative values ​​in the vertical positive temperature gradient model of the main truss

[0122]

[0123] In formula (6), μ CN1 is -0.80, σ CN1 is 2.60, μ DN1 is -0.13, σ DN1 is 1.58, μ FN1 is -0.02, σ FN1 is 4.63. The corresponding vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge is constructed according to this parameter. The temperature representative values ​​in the vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge corresponding to the design service life of 100 years, 150 years and 200 years are shown in Table 18. The temperature representative value distribution of the vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge constructed according to this parameter is shown in Figure 7 shown.

[0124] Table 18 Temperature representative values ​​in the vertical negative temperature gradient model of the main truss

[0125]

[0126] Test 1

[0127] In order to verify the effect of the vertical temperature gradient model of the double-deck steel truss bridge, the inventors arranged vertical temperature sensors on the Weihe River Bridge in Baqiao District, Xi'an, Shaanxi, and conducted long-term temperature field monitoring. The specific construction process is as follows:

[0128] 1. Long-term monitoring equipment

[0129] The monitoring equipment is the Jingming JM3813 remote temperature acquisition instrument produced in Yangzhou, Jiangsu, and the temperature measurement point uses a three-wire Pt100 sensor.

[0130] 2. Temperature measurement point arrangement

[0131] The temperature measuring points are arranged on the upper deck of the double-deck steel truss bridge, and a coordinate system is established with the bottom center of the upper deck of the double-deck steel truss bridge as the coordinate origin. The arrangement principle of the temperature measuring points on the upper deck of the double-deck steel truss bridge is as follows: the measuring point positions are expressed as 0.00m, 0.56m, 1.06m, 1.36m, 1.46m, 1.56m, 1.61m, 1.65m in vertical distance from the coordinate origin, and are recorded as WT-T1 to WT-T8. Figure 8 As shown, the acquisition interval is 1 minute.

[0132] 3. Analysis of the effect of the vertical positive temperature gradient load model on the upper deck

[0133] In the vertical positive temperature gradient load model of the upper deck of a double-deck steel truss bridge, T TP1 , T TP2 , and T TP3 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 Fig. 9 As shown. Calculate T TP1 , T TP2 , and T TP3 The temperature difference at the lowest position of the average temperature of the measuring point is plotted based on the data and the probability density function is fitted, as shown in the figure. Fig.10 , Fig.11 and Fig.12 As shown. The 99% guarantee rate in the probability density function is taken as the value, and the obtained T TP1 , T TP2 , and T TP3 The representative values ​​of temperature gradients at the locations are 11.9°C, 14.8°C and 20.8°C respectively.

[0134] The vertical positive temperature gradient load model of the upper deck of a double-deck steel truss bridge is used to construct a temperature gradient model corresponding to a design service life of 100 years. TP1 is 7.29, σ TP1 is 6.64, μ TP2 is 12.55, σ TP2 is 10.71, μTP3 is 8.57, σ TP3 is 7.44, and T TP1 , T TP2 , and T TP3 The temperature of the upper deck of a double-deck steel truss bridge is 12.3℃, 15.4℃ and 21.0℃, which are slightly different from the measured results. This test shows that the vertical positive temperature gradient load model for the upper deck of a double-deck steel truss bridge has good applicability.

Claims

1. A vertical temperature gradient model for a double-deck steel truss bridge, characterized by: The model is composed of an upper deck vertical temperature gradient model, a lower deck vertical temperature gradient model and a main truss temperature gradient model; the upper deck vertical temperature gradient model is composed of a vertical positive temperature gradient model and a vertical negative temperature gradient model, the lower deck vertical temperature gradient model is composed of a lower deck vertical positive temperature gradient model and a vertical negative temperature gradient model, and the main truss temperature gradient model is composed of a main truss vertical positive temperature gradient model and a main truss vertical negative temperature gradient model; The vertical positive temperature gradient model T of the upper deck of the double-deck steel truss bridge TP (y1) is as shown in formula (1): In formula (1), T TP1 0.35h from the bottom of the upper bridge deck T The representative value of the positive temperature gradient is T TP2 0.88h from the bottom of the upper bridge deck T The representative value of the positive temperature gradient is T TP3 is the representative value of the positive temperature gradient at the top of the upper bridge deck, 0.35h from the bottom of the upper bridge deck T At the initial value of positive temperature gradient, 0.88h from the bottom of the upper bridge deck T At the initial value of positive temperature gradient, is the initial value of the positive temperature gradient at the top of the upper bridge deck, y1 is the height of any position of the cross section from the upper bridge deck, h T is the upper deck beam height, N d The design service life of a double-deck steel truss bridge is 100 years, 150 years or 200 years. F TP1 (α) is the inverse function of the function, F TP2 (α) is the inverse function of the function, F TP3 (α) The inverse function, F TP1 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.35h1 from the bottom of the upper bridge deck, F TP2 (α) is the distribution function of the initial value of the positive temperature gradient at a distance of 0.88h1 from the bottom of the upper bridge deck, F TP3 (α) is the distribution function of the initial value of the positive temperature gradient at the top of the upper bridge deck, α, μ TP1 , σ TP1 , μ TP2 , σ TP2 , μ TP3 , σ TP3 is an intermediate variable; The vertical negative temperature gradient model T of the upper deck of the double-deck steel truss bridge TN (y1) is shown in formula (2): In formula (2), T TN1 is the representative value of negative temperature gradient at the bottom of the upper bridge deck, T TN2 is the representative value of negative temperature gradient from the top of the upper bridge deck, is the initial value of the negative temperature gradient from the bottom of the upper bridge deck, is the initial value of the negative temperature gradient at the top of the upper bridge deck, y1 is the distance from any position of the cross section to the top of the upper bridge deck, 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 bottom of the upper bridge deck, F TN2 (α) is the distribution function of the negative temperature gradient from the top of the upper bridge deck, and the guarantee rate μ TN1 , σ TN1 , μ TN2 , σ TN2 is an intermediate variable; The vertical positive temperature gradient model T of the lower deck of the double-deck steel truss bridge BP (y2) is shown in formula (3): In formula (3), T BP1 is the distance from the lower bridge deck to the top h B / 2 positive temperature gradient representative value, T BP2 is the representative value of the positive temperature gradient from the top of the lower bridge deck, is the initial value of the positive temperature gradient from the bottom of the lower bridge deck, is the initial value of the positive temperature gradient from the top of the lower deck, h B is the height of the lower deck, y2 is the distance from any position of the cross section to the top of the lower deck, F BP1 (α) is the inverse function of the function, F BP2 (α) The inverse function, F BP1 (α) is the distance from the top of the lower bridge deck h B The distribution function of the positive temperature gradient at the position / 2, F BP2 (α) is the distribution function of the positive temperature gradient at the top of the lower deck, β BP1 , BP1 , μ BP2 , σ BP2 is an intermediate variable; The vertical negative temperature gradient model T of the lower deck of the double-deck steel truss bridge BN (y2) is shown in formula (4): In formula (4), T BN1 is the representative value of negative temperature gradient at the bottom of the lower bridge deck, T BN2 is the representative value of the negative temperature gradient at the top of the lower bridge deck, is the initial value of the negative temperature gradient at the bottom of the lower bridge deck, is the initial value of the negative temperature gradient from the top of the lower deck, y2 is the distance from any position of the cross section to the top of the lower deck, F BN1 (α) is the inverse function of the function, F BN2 (α) The inverse function, F BN1 (α) is the distribution function of the negative temperature gradient at the bottom of the lower bridge deck, F BN2 (α) is the distribution function of the negative temperature gradient at the top of the lower deck, μ BN1 , σ BN1 , μ BN2 , σ BN2 is an intermediate variable; The vertical positive temperature gradient model of the main truss of the double-deck steel truss bridge is composed of the vertical positive temperature gradient model T CP (y C ), vertical positive temperature gradient model of lower chord T DP (y D ) and the vertical positive temperature gradient model of the web member T FP (y F ), specifically: In formula (5), T CP1 is the representative value of the positive temperature gradient of the upper chord of the main truss, T DP1 is the representative value of the positive temperature gradient of the lower chord of the main truss, T FP1 is the representative value of the positive temperature gradient of the main truss web, y C is the distance from the bottom plate of the upper chord of the main truss at any position of the cross section, y D is the distance from the bottom plate of the lower chord of the main truss at any position of the cross section, y F h is the distance between the inner wing plate of the main truss web at any position of the cross section, TC is the height of the main truss upper chord, h BC is the height of the lower chord of the main truss, h F is the main truss web height, F CP1 (α) is the inverse function of the function, F DP1 (α) is the inverse function of the function, F FP1 (α) The inverse function, F CP1 (α) is the distribution function of the positive temperature gradient of the upper chord of the main truss, F DP1 (α) is the distribution function of the positive temperature gradient of the lower chord of the main truss, F FP1 (α) is the distribution function of the positive temperature gradient of the main truss web, μ CP1 , σ CP1 , μ DP1 , σ DP1 , μ FP1 , σ FP1 is an intermediate variable; The vertical negative temperature gradient model of the main truss of the double-layer steel truss bridge is composed of the vertical negative temperature gradient model T CN (y C ), vertical negative temperature gradient model of lower chord T DN (y D ) and the vertical negative temperature gradient model of the web member T FN (y F ), specifically: In formula (6), T CN1 is the representative value of negative temperature gradient of the upper chord of the main truss, T DN1 is the representative value of negative temperature gradient of the lower chord of the main truss, T FN1 is the representative value of negative temperature gradient of the main truss web, F CN1 (α) is the inverse function of the function, F DN1 (α) is the inverse function of the function, F FN1 (α) The inverse function, F CN1 (α) is the distribution function of the negative temperature gradient of the upper chord of the main truss, F DN1 (α) is the distribution function of the negative temperature gradient of the lower chord of the main truss, F FN1 (α) is the distribution function of the negative temperature gradient of the main truss web, μ CN1 , σ CN1 , μ DN1 , σ DN1 , μ FN1 , σ FN1 is an intermediate variable.

2. The vertical temperature gradient model of a double-deck steel truss bridge according to claim 1 is characterized in that: In formula (1), the μ TP1 The value of is [5.81,8.76], σ TP1 The value of is [5.67,7.78], μ TP2 The value of is [10.17,14.93], σ TP2 The value of is [9.14,12.55], μ TP3 The value of is [6.92,10.23], σ TP3 The value of is [6.35,8.72]; in formula (2), the μ TN1 The value of is [-2.05,-1.50], σ TN1 The value of is [1.06,1.45], μ TN2 The value of is [-2.52,-1.89], σ TN2 The value of is [1.21,1.86]; In formula (3), the β BP1 The value is [0.42, 0.45], λ BP1 The value is [0.46, 0.50], μ BP2 The value is [-1.80,-1.75], σ BP2 The value is [1.50,1.55]; In formula (4), the μ BN1 The value of is [-1.02,-0.93], σ BN1 The value of is [3.32,.3.38], μ BN2 The value of is [-1.73,-1.68], σ BN2 The value of is [1.92,1.96]; in formula (5), the μ CP1 The value of is [3.03,6.04], σ CP1 The value of is [2.46,5.20], μ DP1 The value of is [0.56,2.82], σ DP1 The value of is [1.21,3.41], μ FP1 The value of is [0.45,1.94], σ FP1 The value of is [0.38,2.34]; in formula (6), the μ CN1 The value of is [-2.2,-0.80], σ CN1 The value of is [0.78,2.60], μ DN1 The value of is [-1.60,-0.13], σ DN1 The value of is [0.66,1.58], μ FN1 The value of is [-2.20,-0.02], σ FN1 The value of is [0.52,4.63].

3. The vertical temperature gradient model of a double-deck steel truss bridge according to claim 1 is characterized in that: In formula (1), N d , μ TP1 , σ TP1 , μ TP2 , σ TP2 , μ TP3 , σ TP3 The value of is: d For 100 years, μ TP1 is 7.29, σ TP1 is 6.64, μ TP2 is 12.55, σ TP2 is 10.71, μ TP3 is 8.57, σ TP3 It is 7.

44.

4. The vertical temperature gradient model of double-deck steel truss bridge according to claim 1 is characterized in that: In formula (2), N d , μ TN1 , σ TN1 , μ TN2 , σ TN2 The value of is: d For 100 years, μ TN1 is -1.78, σ TN1 is 1.24, μ TN2 is -2.49, σ TN2 is 1.

75.

5. The vertical temperature gradient model of a double-deck steel truss bridge according to claim 1 is characterized in that: In formula (3), N d , β BP1 , BP1 , μ BP2 , σ BP2 The value of is: d For 100 years, β BP1 is 0.44, λ BP1 is 0.48, μ BP2 is -1.77, σ BP2 is 1.

53.

6. The vertical temperature gradient model of a double-deck steel truss bridge according to claim 1 is characterized in that: In formula (4), N d , μ BN1 , σ BN1 , μ BN2 , σ BN2 The value of is: d For 100 years, μ BN1 is -0.98, σ BN1 is 3.35, μ BN2 is -1.71, σ BN2 It is 1.

94.

7. The vertical temperature gradient model of a double-deck steel truss bridge according to claim 1 is characterized in that: In formula (5), the μ CP1 is 4.64, σ CP1 is 4.61, μ DP1 is 1.91, σ DP1 is 2.32, μ FP1 is 1.23, σ FP1 is 1.

38.

8. The vertical temperature gradient model of a double-deck steel truss bridge according to claim 1 is characterized in that: In formula (6), the μ CN1 is -1.62, σ CN1 is 1.80, μ DN1 is -0.86, σ DN1 is 1.31, μ FN1 is -1.16, σ FN1 is 2.95.

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