Long-life concrete box girder bridge temperature gradient fatigue load model

Abstract

A long-life concrete box girder bridge temperature gradient fatigue load model comprises a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model, the vertical temperature gradient fatigue load model is in a double-broken-line form, and the transverse temperature gradient fatigue load model is in a three-broken-line form. Temperature sensors are arranged according to the distribution characteristics of the temperature field of the concrete box girder, long-term monitoring data of the temperature field of the concrete box girder bridge are obtained, and a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model of the concrete box girder bridge are constructed by using a Latin hypercube method and a damage equivalence principle. The built temperature fatigue load model has the characteristics of simple form and high engineering applicability, and can be used for anti-fatigue design and fatigue life evaluation of 100-year, 150-year and 200-year long-life design service life of the concrete box girder bridge.

Description

Technical Field

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

[0002] The thermal conductivity of concrete box girders is different from that of steel structure bridges, resulting in a significant difference in the vertical and transverse temperature gradient distribution form from that of steel structure box girders. At the same time, the wall thickness of concrete box girders is relatively large, and there is a temperature gradient distributed along the wall thickness. The relevant specifications stipulate the vertical temperature gradient model of concrete, but lack a temperature fatigue load model. Existing studies have shown that the coupled cyclic effect of temperature load and vehicle load will significantly increase the cumulative fatigue damage of details, and the fatigue damage under the action of temperature and vehicle alone cannot be simply superimposed. Therefore, it is necessary to carry out long-term and refined temperature field monitoring of concrete box girder bridges, study the temperature fatigue effect of concrete box girder bridges, construct a temperature gradient fatigue load model for concrete box girder bridges with a design service life of 200 years, calculate the temperature fatigue stress history, and couple it with the vehicle fatigue stress sequence to conduct fatigue damage analysis. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a temperature gradient fatigue load model for a long-life concrete box girder bridge.

[0004] The technical solution adopted to solve the above technical problems is:

[0005] The temperature gradient fatigue load model of the long-life concrete box girder bridge is composed of the vertical temperature fatigue load model T G (y) and transverse temperature fatigue load model T H (x) composition;

[0006] The vertical temperature gradient fatigue load model T G (y) is as shown in formula (1):

[0007]

[0008] In formula (1), y is the vertical distance from the section to the bottom plate, T G1 is the representative value of the temperature at the top plate of the concrete box girder, in °C, T G2 is the representative value of the temperature at a vertical distance of 1 / 6h from the top plate of the concrete box beam, in °C, T G3 is the representative value of the temperature at the bottom plate of the concrete box beam, in °C, h is the height of the concrete box beam, B is the width of the top plate of the concrete box beam, in m, b is the width of the bottom plate of the concrete box beam, in m, β TG (B), β TG (b) is the intermediate variable, is the initial temperature value at the top plate of the concrete box girder, in °C. is the initial temperature value at a vertical distance of 1 / 6h from the top plate of the concrete box beam, in °C. is the initial temperature of the bottom plate of the concrete box beam, in °C, N d It is the design service life, which can be 100, 150 or 200, in years.

[0009] The transverse temperature gradient fatigue load model T H (x) is shown in formula (2):

[0010]

[0011] In formula (2), x is the horizontal distance from the typical position to the positive side of the cross section, T H1 is the representative value of the temperature on the positive side of the concrete box girder section, in °C, T H2 It is the representative value of the temperature at the position 1 / 2B from the sun side in the concrete box girder, in °C, T H3 It is the representative value of the temperature at the position 2 / 3B from the sun side in the concrete box girder, in °C, T H4 is the representative value of the temperature at the position B on the sunny side of the concrete box girder, in °C, B is the width of the top plate of the concrete box girder section, h is the height of the concrete box girder, in m, β TH (h) is the intermediate variable, is the initial temperature of the positive side of the concrete box girder section, in °C, is the initial temperature value of the concrete box girder at the position 1 / 2B from the sun side, in °C. is the initial temperature value of the concrete box girder at the position 2 / 3B from the sun side, in °C. It is the initial temperature value at position B on the sunny side of the concrete box girder, in ℃.

[0012] In the formula (1) and formula (2) of the present invention, The value of is [9.9,10.9], The value of is [4.8,5.8], the value of B is [7.0,16.0], the value of b is [4.0,10.0], The value of is [3.6,4.0], and the value of h is [2.5,8.0].

[0013] In the formula (1) of the present invention, B, b, The best value of is: B is 12.0m, b is 6.0m, The best temperature is 10.4℃. The best temperature is 5.3℃.

[0014] In the formula (2) of the present invention, h, The value of h is preferably .4m, The best temperature is 8℃.

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

[0016] 1. The present invention constructs a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model for concrete box girder bridges through a refined analysis of the long-term monitoring data of the temperature field of concrete box girder bridges. The model fully considers the influence of the height, top plate width, bottom plate width and design service life of the concrete box girder bridge.

[0017] 2. The temperature gradient fatigue load model of the long-life concrete box girder bridge constructed by the present invention is simple in form and has strong engineering applicability. It can be used for fatigue resistance design and evaluation of long-life design service lives of 100, 150 and 200 years. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is the temperature representative value distribution diagram of the vertical temperature fatigue load model of the concrete box girder.

[0019] Figure 2 This is the temperature representative value distribution diagram of the transverse temperature fatigue load model of the concrete box girder.

[0020] Figure 3 It is the cross-section diagram of the concrete box girder bridge and the actual measurement point layout.

[0021] Figure 4 This is the measured temperature history curve of the concrete box girder bridge.

[0022] Figure 5 This is the histogram of the measured temperature stress amplitude of the concrete box girder bridge. DETAILED DESCRIPTION

[0023] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0024] Example 1

[0025] The temperature gradient fatigue load model of the long-life concrete box girder bridge involved in this embodiment is composed of the vertical temperature fatigue load model T G (y) and transverse temperature fatigue load model T H (x) composition; in this embodiment, the left side of the beam cross section is defined as the positive side, and the right side of the beam cross section is defined as the negative side. In actual use, it is determined based on the light intensity, and the side with higher light intensity is the positive side;

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

[0027]

[0028] In formula (1), y is the vertical distance from the section to the bottom plate, T G1 is the representative value of the temperature at the top plate of the concrete box girder, in °C, T G2 is the representative value of the temperature at a vertical distance of 1 / 6h from the top plate of the concrete box beam, in °C, T G3 is the representative value of the temperature at the bottom plate of the concrete box beam, in °C, h is the height of the concrete box beam, B is the width of the top plate of the concrete box beam, in m, b is the width of the bottom plate of the concrete box beam, in m, β TG (B), β TG (b) is the intermediate variable, is the initial temperature value at the top plate of the concrete box girder, in °C. is the initial temperature value at a vertical distance of 1 / 6h from the top plate of the concrete box beam, in °C. is the initial temperature of the bottom plate of the concrete box beam, in °C; N d is the design service life, which is 100, 150 or 200, in years;

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

[0030]

[0031] In formula (2), x is the horizontal distance from the typical position to the positive side of the cross section, T H1 is the representative value of the temperature on the positive side of the concrete box girder section, in °C, T H2 It is the representative value of the temperature at the position 1 / 2B from the sun side in the concrete box girder, in °C, T H3 It is the representative value of the temperature at the position 2 / 3B from the sun side in the concrete box girder, in °C, T H4 is the representative value of the temperature at the position B on the sunny side of the concrete box girder, in °C, B is the width of the top plate of the concrete box girder section, h is the height of the concrete box girder, in m, β TH (h) is the intermediate variable, is the initial temperature of the positive side of the concrete box girder section, in °C. is the initial temperature value of the concrete box girder at the position 1 / 2B from the sun side, in °C. is the initial temperature value of the concrete box girder at the position 2 / 3B from the sun side, in °C. It is the initial temperature value at position B on the sunny side of the concrete box girder, in ℃.

[0032] In the embodiment (1), a concrete box beam with a beam height h of 4.4 m, a top plate width B of 12.0 m, and a bottom plate width b of 6.0 m is selected. The corresponding vertical temperature gradient fatigue load model of long-life concrete box girder bridge is constructed. The temperature representative values ​​of the vertical temperature gradient fatigue load model corresponding to 100 years, 150 years, and 200 years are shown in Table 1. The temperature representative value distribution of the vertical temperature gradient fatigue load model constructed according to the parameters is shown in Figure 1 shown.

[0033] Table 1 Representative values ​​of temperature for vertical temperature gradient fatigue load model of concrete box girder bridge

[0034]

[0035] In formula (2), the beam height h is selected as 4.4m. The corresponding transverse temperature fatigue load model of long-life concrete box girder bridge is constructed. The temperature representative values ​​of the transverse temperature fatigue load model corresponding to 100 years, 150 years, and 200 years are shown in Table 2. The distribution of temperature representative values ​​in the transverse temperature fatigue load model constructed according to the parameters is shown in Figure 2 shown.

[0036] Table 2 Representative values ​​of temperature for the fatigue load model of the transverse temperature gradient of concrete box beams

[0037]

[0038] Example 2

[0039] The expression of the temperature gradient fatigue load model of the long-life concrete box girder bridge involved in this embodiment is the same as that in Embodiment 1, but the temperature representative value is different.

[0040] In the embodiment (1), a concrete box beam with a beam height h of 2.5 m, a top plate width B of 7.0 m, and a bottom plate width b of 4.0 m is selected. The remaining parameters are the same as those in Example 1. A corresponding vertical temperature fatigue load model for a long-life concrete box girder bridge is constructed. The temperature representative values ​​of the vertical temperature fatigue load model corresponding to 100 years, 150 years, and 200 years are shown in Table 3. The temperature representative value distribution in the vertical temperature fatigue load model constructed according to the parameters is as follows: Figure 1 shown.

[0041] Table 3 Representative values ​​of temperature in the vertical temperature fatigue load model of concrete box girder bridge

[0042]

[0043] In formula (2), the beam height h is selected as 2.5m. The remaining parameters are the same as those in Example 1. The corresponding transverse temperature fatigue load model of the long-life concrete box girder bridge is constructed. The values ​​of the transverse temperature fatigue load model corresponding to 100 years, 150 years, and 200 years are shown in Table 4. The temperature representative value distribution of the transverse temperature fatigue load model constructed according to the parameters is as follows: Figure 2 shown.

[0044] Table 4 Representative values ​​of temperature in the transverse temperature fatigue load model of concrete box girder

[0045]

[0046] Example 3

[0047] The expression of the temperature gradient fatigue load model of the long-life concrete box girder bridge involved in this embodiment is the same as that in Embodiment 1, but the temperature representative value is different.

[0048] In the embodiment (1), a concrete box beam with a beam height h of 8.0 m, a top plate width B of 16.0 m, and a bottom plate width b of 10.0 m is selected. In formula (2), The remaining parameters are the same as those in Example 1. The corresponding vertical temperature fatigue load model of the long-life concrete box girder bridge is constructed. The temperature representative values ​​of the vertical temperature fatigue load model corresponding to 100 years, 150 years, and 200 years are shown in Table 5. The temperature representative values ​​of the vertical temperature fatigue load model constructed according to the parameters are distributed as follows: Figure 1 shown.

[0049] Table 5 Representative values ​​of temperature for vertical temperature fatigue load model of concrete box girder bridge

[0050]

[0051] In formula (2), the beam height h is selected as 8.0m. The remaining parameters are the same as those in Example 1. The corresponding transverse temperature fatigue load model of the long-life concrete box girder bridge is constructed. The temperature representative values ​​of the transverse temperature fatigue load model corresponding to 100 years, 150 years, and 200 years are shown in Table 6. The temperature representative value distribution in the transverse temperature fatigue load model constructed according to the parameters is as follows: Figure 2 shown.

[0052] Table 6 Representative values ​​of temperature for transverse temperature fatigue load model of concrete box girder

[0053]

[0054] Test 1

[0055] In order to verify the effect of the temperature gradient fatigue load model of the long-life concrete box girder bridge, the inventors used the temperature fatigue load model of the long-life concrete box girder bridge in Example 1 to compare and analyze the long-term monitoring results of the vertical temperature field of the Lintong Railway Concrete Box Girder Bridge. The specific process is as follows:

[0056] 1. Long-term monitoring instruments

[0057] The monitoring instrument is a 16-channel JM3812 temperature collector produced in Yangzhou, Jiangsu; the remote transmission system is JM1813; and the temperature measurement point uses a three-wire Pt100 sensor.

[0058] 2. Temperature measurement point arrangement

[0059] Temperature measuring points are arranged on the web and top and bottom plates of the concrete box girder bridge. The measuring points are arranged as follows: Figure 3 The positions of the temperature sensors in the web arrangement shown in the figure are represented by the vertical distance from the lower surface of the concrete box girder top plate as 0.00m, 0.02m, 0.40m, 0.70m, 1.10m, 2.41m, 3.72m, and 4.22m. The collection interval is 10 minutes, and the obtained temperature history curve is as follows Figure 4 shown.

[0060] 3. Analysis of the effect of vertical temperature gradient fatigue load model

[0061] Taking the concrete box girder bridge top plate as an example, at this time y = 4.42m, the temperature stress history is constructed based on the temperature measurement monitoring data, and the temperature stress amplitude cycle counting is performed using the rain flow counting method to obtain the stress amplitude histogram. The results are as follows: Figure 5 As shown in Figure 2, the equivalent fatigue stress calculation is performed and the result is 22.6MPa.

[0062] Based on the temperature fatigue load model, the temperature stress history is constructed and the temperature stress amplitude analysis is performed. The beam height h is 4.4m, the top plate width B is 12m, and the design service life N is d For 100 years, the fatigue temperature T G Substitute (y) into the following formula:

[0063] σ eq (y) = α × E × T G (y)

[0064] In the formula, σ eq (y) is the equivalent fatigue stress at position y, α is the thermal expansion coefficient of the material, which is 1.1×10 -5 ℃ -1 , E is the elastic modulus of the material, which is 206GPa.

[0065] The equivalent temperature fatigue stress is 23.7MPa, which is basically consistent with the measured equivalent fatigue stress. This shows that the vertical temperature fatigue load model of concrete box girder bridge has good applicability and can be used for vertical temperature and temperature-vehicle coupling fatigue damage assessment of concrete box girder bridge.

Claims

1. A temperature gradient fatigue load model for a long-life concrete box girder bridge, characterized in that: 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 as shown in formula (1): In formula (1), y is the vertical distance from the section to the bottom plate, T G1 is the representative value of the temperature at the top plate of the concrete box girder, in °C, T G2 is the representative value of the temperature at a vertical distance of 1 / 6h from the top plate of the concrete box beam, in °C, T G3 is the representative value of the temperature at the bottom plate of the concrete box beam, in °C, h is the height of the concrete box beam, B is the width of the top plate of the concrete box beam, in m, b is the width of the bottom plate of the concrete box beam, in m, β TG (B), β TG (b) is the intermediate variable, is the initial temperature value at the top plate of the concrete box girder, in °C. is the initial temperature value at a vertical distance of 1 / 6h from the top plate of the concrete box beam, in °C. is the initial temperature of the bottom plate of the concrete box beam, in °C, N d is the design service life, which is 100, 150 or 200, in years; The transverse temperature gradient fatigue load model T H (x) is shown in formula (2): In formula (2), x is the horizontal distance from the typical position to the positive side of the cross section, T H1 is the representative value of the temperature on the positive side of the concrete box girder section, in °C, T H2 It is the representative value of the temperature at the position 1 / 2B from the sun side in the concrete box girder, in °C, T H3 It is the representative value of the temperature at the position 2 / 3B from the sun side in the concrete box girder, in °C, T H4 is the representative value of the temperature at the position B on the sunny side of the concrete box girder, in °C, B is the width of the top plate of the concrete box girder section, h is the height of the concrete box girder, in m, β TH (h) is the intermediate variable, is the initial temperature of the positive side of the concrete box girder section, in °C, is the initial temperature value of the concrete box girder at the position 1 / 2B from the sun side, in °C. is the initial temperature value of the concrete box girder at the position 2 / 3B from the sun side, in °C. It is the initial temperature value at position B on the sunny side of the concrete box girder, in ℃.

2. The temperature gradient fatigue load model of the long-life concrete box girder bridge according to claim 1 is characterized in that: In formula (1) and formula (2), The value of is [9.9,10.9], The value of is [4.8,5.8], the value of B is [7.0,16.0], the value of b is [4.0,10.0], The value of is [3.6,4.0], and the value of h is [2.5,8.0].

3. The temperature gradient fatigue load model of the long-life concrete box girder bridge according to claim 1 is characterized in that: In formula (1), B, b, The values ​​of are: B is 12.0m, b is 6.0m, 10.4℃, It is 5.3℃.

4. The temperature gradient fatigue load model of the long-life concrete box girder bridge according to claim 1 is characterized in that: In formula (2), the h, The value of is: h is 4.4m, It is 3.8℃.

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