Thermal fatigue load model for steel box girder bridge without flange

Abstract

A thermal fatigue load model for flangeless steel box girder bridges is constructed. This model consists of a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model, both of which are bilinear. Based on the temperature field and thermal stress distribution characteristics of flangeless steel box girders, a thermal gradient fatigue load model for flangeless steel box girder bridges with a design service life of 100 years was constructed using the Latin hypercube sampling method and the damage equivalence principle. This thermal fatigue load model enables rapid calculation of the thermal fatigue stress history of flangeless steel box girder bridges and can be used for fatigue design and fatigue life assessment of flangeless steel box girder bridges.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a temperature fatigue load model of a flangeless steel box girder bridge. Background Art

[0002] Flanged steel box girder bridges have been used to some extent in engineering. Their temperature field distribution characteristics under solar radiation are quite different from those of steel box girder bridges with flanging plates. The temperature field distribution of the flanged steel box girder cross section is highly nonlinear, resulting in large temperature self-stresses within the cross section. As the temperature alternates between day and night, the steel box girder cross section will experience periodic temperature fatigue stresses, contributing to the cumulative fatigue damage of the structure. Currently, there are few reports on the research of temperature gradient fatigue load models for flanged steel box girder bridges at home and abroad, and there are no relevant provisions in the design specifications. Therefore, it is necessary to establish a temperature gradient fatigue load model for flanged steel box girder bridges based on long-term temperature field monitoring data of flanged steel box girder bridges, using the Latin hypercube sampling method and the damage equivalence principle, to provide a technical basis for their fatigue resistance design and evaluation. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a thermal fatigue load model for a flangeless steel box girder bridge, which can solve the fatigue damage calculation and analysis of the flangeless steel box girder bridge under transverse or vertical temperature loads.

[0004] The model consists of a vertical temperature gradient fatigue load model T G (y) and transverse temperature gradient fatigue load model T H (x) composition;

[0005] The vertical temperature gradient fatigue load model T G (y) is shown in formula (1):

[0006]

[0007] In formula (1), y is the vertical distance from the top plate of the section, p1, p2, β TG (B), β T (b) is the intermediate variable, T G1 is the representative temperature value at the top plate of the steel box girder without flange, in °C, T G2 T is the representative temperature value at a vertical distance of 0.2h from the top plate of the steel box girder without flange, in °C. G3 is the representative value of the temperature at the bottom plate of the steel box girder without flange, in °C, h is the height of the steel box girder without flange, B is the width of the top plate of the steel box girder without flange, b is the width of the bottom plate of the steel box girder without flange, in m. is the initial temperature value at the top plate of the steel box girder without flange, in °C. is the initial temperature value at a vertical distance of 0.2h from the top plate of the steel box girder without flange, in °C. is the initial temperature of the bottom plate of the steel box girder without flange, in ℃, N d is the design service life, the value is 100, the unit is year;

[0008] The transverse temperature gradient fatigue load model T H (x) is as shown in formula (2):

[0009]

[0010] In formula (2), x is the horizontal distance from the positive side of the cross section, p1, p2, p3, β TH (h) is the intermediate variable, T H1 is the representative temperature value at the sunny side of the steel box girder section without flange, in °C, T H2 T is the representative temperature value at the position 0.6L from the sun side of the middle section of the steel box girder, in °C. H3 is the representative temperature value at the position L on the sunny side of the middle section of the steel box girder, L is the width of the steel box girder without flange, in m, h is the height of the steel box girder without flange, in m, is the initial temperature value at the sunny side of the steel box girder section without flange, in °C. is the initial temperature value at the position 0.6L from the sun side of the middle section of the steel box girder, in °C. is the initial temperature value of the steel box girder at the position L on the sunny side of the cross section, in °C, N d It is the design service life, with a value of 100 and the unit is year.

[0011] In the formula (1) of the present invention, the The value is [7.7,8.1], the unit is ℃, The value of is [3.9, 4.3], the unit is ℃, the value of B is [9.0, 25.0], the value of b is [6.0, 22.0], the unit is m, in formula (2), the The value is [11.0,11.4], the unit is ℃, The value of is [4.3,4.7], the unit is ℃, and the value of h is [2.5,5.0], the unit is m.

[0012] In the formula (1) of the present invention, the B, b, The values ​​of are: B is best at 16.5m, b is best at 12.25m, The best temperature is 7.9℃. The best temperature is 4.1℃.

[0013] In the formula (2) of the present invention, the h, The value of is: h is 3.8m, is 11.2℃, It is 4.5℃.

[0014] The beneficial effects of the present invention are as follows:

[0015] 1. Based on the analysis of long-term monitoring data of fatigue temperature field of flangeless steel box girder bridge, the present invention constructs a thermal fatigue load model of flangeless steel box girder bridge, taking into account the influence of section height and top and bottom plate width.

[0016] 2. The thermal fatigue load model for flangeless steel box girder bridges with a design service life of 100 years constructed in the present invention is simple in form, realizes the rapid calculation of the transverse or vertical daily thermal stress amplitude at fatigue details, and can be used for temperature-vehicle coupled fatigue analysis of flangeless steel box girder bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is the temperature representative value distribution diagram in the vertical temperature fatigue load model of the steel box girder without flange.

[0018] Figure 2 This is the temperature representative value distribution diagram in the transverse temperature fatigue load model of the steel box girder without flange.

[0019] Figure 3 This is the cross-section of a steel box girder bridge without flanges.

[0020] Figure 4 Arrangement of temperature measuring points for the section of steel box girder without flange.

[0021] Figure 5 This is the temperature history curve of the steel box girder bridge without flange.

[0022] Figure 6 It is the histogram of vertical stress amplitude in the measured temperature field. DETAILED DESCRIPTION

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and examples, but the present invention is not limited to these examples.

[0024] Example 1

[0025] The thermal fatigue load model of the flangeless steel box girder bridge involved in this embodiment is composed of the vertical temperature gradient fatigue load model T G (y) and transverse temperature gradient fatigue load model T H (x) composition. In this embodiment, the left side of the beam cross section is defined as the sunny side, and the right side of the beam cross section is defined as the shady side. In actual use, the side with higher light intensity is defined as the sunny side based on the light intensity within a day.

[0026] The vertical temperature gradient fatigue load model T G(y) is shown in formula (1):

[0027]

[0028] In formula (1), y is the vertical distance from the top plate of the section, p1, p2, β TG (B), β T (b) is the intermediate variable, T G1 is the representative temperature value at the top plate of the steel box girder without flange, in °C, T G2 T is the representative temperature value at a vertical distance of 0.2h from the top plate of the steel box girder without flange, in °C. G3 is the representative value of the temperature at the bottom plate of the steel box girder without flange, in °C, h is the height of the steel box girder without flange, B is the width of the top plate of the steel box girder without flange, b is the width of the bottom plate of the steel box girder without flange, in m. is the initial temperature value at the top plate of the steel box girder without flange, in °C. is the initial temperature value at a vertical distance of 0.2h from the top plate of the steel box girder without flange, in °C. is the initial temperature of the bottom plate of the steel box girder without flange, in ℃, N d is the design service life, the value is 100, the unit is year;

[0029] The transverse temperature gradient fatigue load model T H (x) is as shown in formula (2):

[0030]

[0031] In formula (2), x is the horizontal distance from the typical position to the side of the cross section, T H1 is the temperature representative value at the side of the steel box girder section without flange, in °C, p1, p2, p3, β TH (h) is the intermediate variable, T H2 T is the representative temperature value at the position 0.6L from the side of the section in the middle of the steel box girder, in °C. H3 is the representative temperature value at the position L from the side of the section in the middle of the steel box girder, L is the half-section width of the steel box girder without flange, h is the height of the steel box girder without flange, the unit is m, is the initial temperature value at the side of the steel box girder section without flange, in °C. is the initial temperature value of the steel box girder at a position 0.6L from the side of the section, in °C. is the initial temperature value of the steel box girder at the position L from the side of the section, in °C, N d It is the design service life, with a value of 100 and the unit is year.

[0032] In the present embodiment, formula (1) is selected 7.9℃, A vertical temperature gradient fatigue load model for a steel box girder bridge without flanges was constructed based on a temperature of 4.1°C, a top plate width B of 16.5m, and a bottom plate width b of 12.25m. The corresponding 100-year representative temperature values ​​for the vertical temperature gradient fatigue load model are shown in Table 1. The distribution of representative temperature values ​​in the vertical temperature fatigue load model constructed based on these parameters is shown.

[0033] like Figure 1 shown.

[0034] Table 1 Representative values ​​of vertical temperature gradient fatigue load model temperature corresponding to the design service life

[0035]

[0036] In formula (2), the beam height h is selected as 3.8m, is 11.2℃, The corresponding transverse temperature gradient fatigue load model of the steel box girder bridge without flange is constructed with a value of 4.5℃. The representative values ​​of the transverse temperature gradient fatigue load model corresponding to 100 years are shown in Table 2. The fatigue temperature distribution at typical positions in the transverse temperature fatigue load model constructed according to this parameter is shown in Figure 2 shown.

[0037] Table 2 Representative values ​​of transverse temperature gradient fatigue load model temperature corresponding to the design service life

[0038]

[0039] Example 2

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

[0041] In formula (1), the top plate width B is selected as 9.0m, is 7.7℃, 3.9℃, bottom plate width b is 6.0m, and other parameters are the same as in Example 1. The corresponding vertical temperature gradient fatigue load model of the steel box girder bridge without flange is constructed. The temperature representative values ​​of the vertical temperature gradient fatigue load model corresponding to 100 years are shown in Table 3. The temperature representative value distribution in the vertical temperature gradient fatigue load model constructed according to the parameters is as follows Figure 1 shown.

[0042] Table 3 Representative values ​​of vertical temperature gradient fatigue load model temperature corresponding to the design service life

[0043]

[0044] In formula (2), select 11.0℃, The temperature of the transverse temperature gradient fatigue load model corresponding to the 100-year corresponding transverse temperature gradient fatigue load model is shown in Table 4. The temperature representative value distribution in the transverse temperature fatigue load model constructed according to the parameters is as follows: Figure 2 shown.

[0045] Table 4 Representative values ​​of transverse temperature gradient fatigue load model temperature corresponding to the design service life

[0046]

[0047] Example 3

[0048] The expression of the temperature fatigue load model of the flangeless steel box girder bridge involved in this embodiment is the same as that in Example 1, but the temperature representative value is different.

[0049] In formula (1), select is 8.1℃, The temperature is 4.3℃, the top plate width B is 25.0m, the bottom plate width b is 22.0m, and the other parameters are the same as those in Example 1. The corresponding vertical temperature gradient fatigue load model of the flangeless steel box girder bridge is constructed. The values ​​of the vertical temperature gradient fatigue load model corresponding to 100 years are shown in Table 5. The temperature representative value distribution in the vertical temperature gradient fatigue load model constructed according to the parameters is as follows Figure 1 shown.

[0050] Table 5 Representative values ​​of vertical temperature gradient fatigue load model temperature corresponding to the design service life

[0051]

[0052] In formula (2), select is 11.4℃, The temperature of the transverse temperature gradient fatigue load model corresponding to 100 years is shown in Table 6. The temperature representative value distribution in the transverse temperature gradient fatigue load model constructed according to the parameters is shown in Table 6. Figure 2 shown.

[0053] Table 6 Representative values ​​of transverse temperature gradient fatigue load model temperature corresponding to design service life

[0054]

[0055] Test 1

[0056] In order to verify the effect of the thermal fatigue load model of the steel box girder bridge without flange, the inventors arranged vertical temperature sensors on the Taiping Waterway Bridge in Dongguan City, Guangdong Province and conducted long-term temperature field monitoring. Figure 3 The specific test process is as follows:

[0057] 1. Long-term monitoring instruments

[0058] The monitoring instrument is a 32-channel DH2002 temperature acquisition module produced in Taizhou, Jiangsu. The temperature acquisition system is a PHM long-term temperature monitoring system produced in Taizhou, Jiangsu. The temperature measurement point uses a three-wire Pt100 sensor.

[0059] 2. Temperature measurement point arrangement

[0060] The temperature measuring points are arranged on the top plate, bottom plate and web of the flangeless steel box girder bridge. The coordinate system is established with the center of the flangeless steel box girder bottom plate as the coordinate origin. A total of 12 measuring points are arranged vertically. The vertical distance from the lower surface of the flangeless steel box girder top plate is expressed as y. The positions of different measuring points are recorded as 0.00m, 0.60m, 1.60m, 2.10m, 2.60m, 3.10m, 3.40m, 3.50m, 3.60m, 3.70m, 3.75m and 3.80m respectively. The measuring point arrangement scheme is as follows: Figure 4 As shown, the acquisition interval is 5 minutes, and the temperature history obtained by monitoring is T te (y,t).

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

[0062] Taking the bottom plate butt weld of a steel box girder bridge without flange as an example, the temperature stress history σ is calculated based on the temperature monitoring data as follows: te (y,t), the temperature history curve is as follows Figure 5 As shown in the figure, the temperature stress amplitude cycle count is performed using the rain flow counting method to obtain the stress amplitude histogram. The results are shown in Figure 6 The equivalent fatigue stress was calculated based on the measured results, and the result was 9.08MPa.

[0063]

[0064] Where σ te (y,t) is the stress history of the steel box girder section, E s is the elastic modulus of steel, α s is the thermal expansion coefficient of steel, A is the cross-sectional area of ​​the steel box girder without flange, I is the moment of inertia of the steel box girder without flange, in this case E s 206GPa, α s 1.1×10 -5 ℃ -1 .

[0065] The vertical temperature gradient fatigue load model is used to construct the temperature stress history and perform temperature stress amplitude analysis. The beam height h is 3.8m, the top plate width B is 16.5m, the bottom plate width is 12.25m, and the design service life N is 2.5m. d For a period of 100 years, the equivalent fatigue stress is calculated as follows:

[0066] σ eq (y) = α × E × T(y)

[0067] Where α is the thermal expansion coefficient of steel and E is the elastic modulus of steel. In this example,

[0068] E s =2.06×10 5 MPa, α s =1.1×10 -5 ℃ -1 .

[0069] The equivalent thermal fatigue stress is 9.10 MPa, which is basically consistent with the measured results, indicating that the thermal fatigue load model of the flangeless steel box girder bridge has a good effect.

Claims

1. A thermal fatigue load model for a flangeless steel box girder bridge, characterized by: The model consists of a vertical temperature gradient fatigue load model T G (y) and transverse temperature gradient fatigue load model T H (x) composition; The vertical temperature gradient fatigue load model T G (y) is shown in formula (1): In formula (1), y is the vertical distance from the top plate of the section, p1, p2, β TG (B), β T (b) is the intermediate variable, T G1 is the representative temperature value at the top plate of the steel box girder without flange, in °C, T G2 T is the representative temperature value at a vertical distance of 0.2h from the top plate of the steel box girder without flange, in °C. G3 is the representative value of the temperature at the bottom plate of the steel box girder without flange, in °C, h is the height of the steel box girder without flange, B is the width of the top plate of the steel box girder without flange, b is the width of the bottom plate of the steel box girder without flange, in m. is the initial temperature value at the top plate of the steel box girder without flange, in °C. is the initial temperature value at a vertical distance of 0.2h from the top plate of the steel box girder without flange, in °C. is the initial temperature of the bottom plate of the steel box girder without flange, in ℃, N d is the design service life, the value is 100, the unit is year; The transverse temperature gradient fatigue load model T H (x) is as shown in formula (2): In formula (2), x is the horizontal distance from the positive side of the cross section, p1, p2, p3, β TH (h) is the intermediate variable, T H1 is the representative temperature value at the sunny side of the steel box girder section without flange, in °C, T H2 T is the representative temperature value at the position 0.6L from the sun side of the middle section of the steel box girder, in °C. H3 is the representative temperature value at the position L on the sunny side of the middle section of the steel box girder, L is the width of the steel box girder without flange, in m, h is the height of the steel box girder without flange, in m, is the initial temperature value at the sunny side of the steel box girder section without flange, in °C. is the initial temperature value at the position 0.6L from the sun side of the middle section of the steel box girder, in °C. is the initial temperature value of the steel box girder at the position L on the sunny side of the cross section, in °C, N d It is the design service life, with a value of 100 and the unit is year.

2. The thermal fatigue load model of the flangeless steel box girder bridge according to claim 1 is characterized in that: In formula (1), The value is [7.7,8.1], the unit is ℃, The value of is [3.9, 4.3], the unit is ℃, the value of B is [9.0, 25.0], the value of b is [6.0, 22.0], the unit is m, in formula (2), the The value is [11.0,11.4], the unit is ℃, The value of is [4.3,4.7], the unit is ℃, and the value of h is [2.5,5.0], the unit is m.

3. The thermal fatigue load model of the flangeless steel box girder bridge according to claim 1 is characterized in that B, b, The values ​​of are: B is 16.5m, b is 12.25m, 7.9℃, It is 4.1℃.

4. The thermal fatigue load model of the flangeless steel box girder bridge according to claim 1 is characterized in that h described in formula (2) The value of is: h is 3.8m, is 11.2℃, It is 4.5℃.

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