Flat steel box girder bridge long-life temperature gradient fatigue load model and construction method

Abstract

The invention discloses a long-life temperature gradient fatigue load model of a flat steel box girder bridge and a construction method, the long-life temperature gradient fatigue load model of the flat steel box girder bridge comprises a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model, the transverse temperature gradient fatigue load model is in a three-broken-line form. According to the method, temperature field long-term monitoring is carried out according to structural characteristics and temperature field distribution characteristics of a certain flat steel box girder bridge, a Latin hypercube sampling method and a fatigue damage equivalence principle are adopted, and the construction method of the temperature gradient fatigue load model of the flat steel box girder bridge is provided. A long-life temperature gradient fatigue load model of the flat steel box girder bridge is constructed, and the constructed temperature gradient fatigue load model can be used for designing anti-fatigue design and fatigue life evaluation of the flat steel box girder bridge with the service life of 200 years.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and specifically relates to a long-life temperature gradient fatigue load model and a construction method for a flat steel box girder bridge. Background Art

[0002] Flat steel box girder is a typical closed section with a small aspect ratio. Under solar radiation, not only vertical temperature gradient of the section is generated, but also significant transverse temperature gradient. Flat steel box girder will produce longitudinal temperature stress under the action of vertical nonlinear temperature gradient. There is a frame effect in the closed section, and transverse temperature stress will be generated under the action of transverse temperature gradient. With the alternation of day and night temperature, the flat steel box girder section will have periodic temperature fatigue stress, which contributes to the cumulative fatigue damage of the structure. Therefore, it is necessary to carry out long-term monitoring of the temperature field for flat steel box girder bridges, and use the Latin hypercube sampling method and fatigue damage equivalence principle to construct a long-life transverse and vertical temperature gradient fatigue load model for flat steel box girder bridges with a design service life of 200 years, so as to provide a technical basis for the fatigue design and evaluation of flat steel box girder bridges. Summary of the invention

[0003] A technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a reasonably designed long-life temperature gradient fatigue load model for flat steel box girder bridges;

[0004] Another technical problem to be solved by the present invention is to provide a construction method for a long-life temperature gradient fatigue load model of a flat steel box girder bridge.

[0005] The long-life temperature gradient fatigue load model of the flat steel box girder bridge used to solve the above technical problems consists of a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model.

[0006] The vertical temperature gradient fatigue load model is as follows:

[0007]

[0008] In formula (1), T + (y) is the positive temperature gradient model in the vertical temperature gradient fatigue load model, T - (y) is the negative temperature gradient model in the vertical temperature gradient fatigue load model, y is the height of the position to be calculated, h is the section height, T G1 is the representative value of the temperature at the top plate, in °C, T G2 It is the representative value of the temperature at the position where the web is 1 / 4h away from the top plate, in °C, T G3 is the representative value of the temperature at the bottom plate, in °C, B is the width of the top plate, b is the width of the bottom plate, β TG (B), βTG (b) is the intermediate variable, is the initial temperature value at the top plate, in °C, is the initial temperature value of the web at a distance of 1 / 4h from the top plate, in °C. is the initial temperature value at the bottom plate, in °C, N d It is the design service life, and its value is 100, 150 or 200, in years.

[0009] The transverse temperature gradient fatigue load model is as follows:

[0010]

[0011] In formula (2), x is the lateral position to be calculated, B is the width of the top plate, and T H1 is the representative value of the temperature at the sunny side of the top plate, T H2 It is the representative value of the temperature at the top plate 0.2B away from the sun side, in °C, T H3 It is the representative value of the temperature at the 1 / 2B position of the top plate, in °C, T H4 is the representative value of the temperature at the shadow side of the top plate, in °C, β TH (h) is the intermediate variable, is the initial temperature value at the sunny side of the top plate, in °C. is the initial temperature value of the top plate at 0.2B from the sun side, in °C. is the initial temperature value at the top plate 1 / 2B position, in °C, It is the initial temperature value at the shady side of the top plate, in °C.

[0012] Further preferably, in formula (1), The value of is [12.0,14.5], the unit is ℃, the value of b is [10.0,40.0], the unit is m; the value of B is [25.0,50.0], the unit is m.

[0013] More preferably, B, b, The values ​​of are: B is 33.0m, b is 28.5m, It is 13.3℃.

[0014] More preferably, the The value of is [6.1,10.0], the unit is ℃, and the value of h is [2.5,4.5], the unit is m.

[0015] More preferably, h, The value of is: h is 3.5m, It is 7.6℃.

[0016] The method for constructing a long-life temperature gradient fatigue load model of a flat steel box girder bridge of the present invention comprises the following steps:

[0017] (1) Long-term monitoring of temperature field of flat steel box girder bridge

[0018] Temperature sensors are arranged on the top plate, bottom plate and diaphragm of the flat steel box girder bridge to collect temperature. The collection time interval is set to 1 to 20 minutes. The representative value of the collected vertical temperature is recorded as T A (y), the representative value of the horizontal temperature collected is T A (x).

[0019] (2) Constructing the thermal stress history of a flat steel box girder bridge

[0020] The time interval of the measured temperature gradient is used as the time interval, and the vertical temperature gradient time curve is recorded as T A (y, t), record the transverse temperature gradient time history curve T A (x,t).

[0021] The temperature stress history at each position is obtained by the following formula:

[0022] 1) For the vertical temperature gradient fatigue load model, the temperature stress history σ A (y,t):

[0023]

[0024] Where ρ is the temperature secondary bending moment influence coefficient, 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 flat wide steel box girder bridge, I is the moment of inertia of the flat wide steel box girder bridge section, y s is the vertical neutral axis position of the flat wide steel box girder bridge section, and b(y) is the section thickness of the flat wide steel box girder bridge at the vertical y position.

[0025] For constructing the transverse temperature gradient fatigue load model, the temperature stress history σ A (x,t):

[0026]

[0027] In the formula, x s is the transverse neutral axis position of the flat steel box girder bridge section, and b(x) is the section thickness of the flat steel box girder bridge at position x.

[0028] (3) Temperature stress amplitude cycle count

[0029] The stress amplitude is counted by rain flow counting method, and the temperature stress amplitude vector at each position of the cross section is obtained.

[0030] 1) For the construction of vertical temperature gradient fatigue load model, the temperature stress amplitude vector B1 is:

[0031] B1=(Δσ1(y),Δσ2(y),…,Δσ na (y))

[0032] In the formula, Δσ na (y) is the nath measured stress amplitude at the y position, na represents the number of elements in the vector B1 and is a finite positive integer.

[0033] 2) For the construction of transverse temperature gradient fatigue load model, the temperature stress amplitude vector B2 is:

[0034] B2=(Δσ1(x),Δσ2(x),…,Δσ nb (x)

[0035] In the formula, Δσ nb (x) is the nbth measured stress amplitude at position x, and nb represents the number of elements in vector B2, which is a finite positive integer.

[0036] The temperature stress amplitude vector at each position is fitted with a Weibull function to obtain the corresponding temperature stress amplitude probability density curve f(g);

[0037]

[0038] Where μ is the mean value of the temperature stress amplitude, and σ is the variance of the temperature stress amplitude.

[0039] For the construction of vertical temperature gradient fatigue load model, the value of g is [min(B1)-max(B1),2max(B1)].

[0040] For constructing the transverse temperature gradient fatigue load model, the value of g is [min(B2)-max(B2),2max(B2)].

[0041] (4) Determine the total number of total temperature stress cycle loading

[0042] Determine the total number of total temperature stress cycle loading N corresponding to different design service life according to the following formula fs :

[0043] N fs =δ×N d ×365

[0044] Where δ is the stress cycle coefficient, which takes the value of [1.05,1.30].

[0045] (5) Temperature stress amplitude data sampling

[0046] Determine the number of layers N for stratified sampling La , N La Take N d , the upper limit x of stratified sampling T , lower limit x B , for constructing vertical temperature gradient fatigue load model, x T Take 2max(B1), x B Take min(B1)-max(B1), for the construction of transverse temperature gradient fatigue load model, x T Take 2max(B2), x B Take min(B2)-max(B2) and determine the number of sampling times for the pth layer under the design service life according to the corresponding probability density function f(g).

[0047] 1) For constructing the vertical temperature gradient fatigue load model, the number of sampling times n for the pth layer is y for:

[0048]

[0049] In the formula, p y The value of is [1,N La ].

[0050] 2) For the construction of the transverse temperature gradient fatigue load model, the number of sampling times n for the pth layer is x for:

[0051]

[0052] In the formula, p x The value of is [1,N La ].

[0053] The stress amplitude sampling results are obtained according to the uniform sampling method.

[0054] 1) For constructing the vertical temperature gradient fatigue load model, the sampling result vector A py for:

[0055] A py =(σ1(y),σ2(y),...,σ ny (y))

[0056] In the formula, σ ny (y) is the nyth stress amplitude at position y, and ny is the number of elements in the vector, which is a finite positive integer.

[0057] 2) For the construction of the transverse temperature gradient fatigue load model, the sampling result vector A px for:

[0058] A px=(σ1(x),σ2(x),...,σ nx (x)

[0059] In the formula, σ nx (y) is the nxth stress amplitude at the x position, and nx is the number of elements in the vector, which is a finite positive integer.

[0060] The final stress amplitude sampling vector is obtained according to the following formula;

[0061] 1) For the construction of vertical temperature gradient fatigue load model, the final stress amplitude sampling vector A y for:

[0062]

[0063] 2) For the construction of the transverse temperature gradient fatigue load model, the final stress amplitude sampling vector A x for:

[0064]

[0065] (6) Determine the equivalent temperature stress amplitude

[0066] The equivalent temperature stress amplitude of the flat steel box girder bridge is obtained as follows:

[0067] 1) For the vertical temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqy for:

[0068]

[0069] In the formula, A yi is the vector A y The i-th element in ;

[0070] 2) For the construction of transverse temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqx for:

[0071]

[0072] In the formula, A xi is the vector A x The i-th element in .

[0073] (7) Constructing a long-life temperature fatigue load model for flat steel box girder bridges

[0074] The equivalent fatigue temperature of a flat steel box girder bridge is constructed as follows:

[0075] 1) For the vertical temperature gradient fatigue load model, the equivalent fatigue temperature T eqy for:

[0076]

[0077] 2) For the construction of transverse temperature gradient fatigue load model, the equivalent fatigue temperature T eqx for:

[0078]

[0079] A variable parameter analysis is carried out on the flat steel box girder bridge, and the equivalent fatigue temperature is fitted to the results using the least square method. The temperature gradient fatigue load models of formula (1) and formula (2) are established.

[0080] The beneficial effects of the present invention are as follows:

[0081] The invention proposes a method for constructing a long-life temperature gradient fatigue load model for a flat steel box girder bridge. The method mainly utilizes the Latin hypercube sampling method and the damage equivalence principle, and can use the measured temperature field data of the flat steel box girder bridge to construct vertical and transverse temperature gradient fatigue load models.

[0082] 2. The long-life temperature gradient fatigue load model of the flat steel box girder bridge constructed by the present invention fully considers the influence of the top plate width B, the bottom plate width b and the beam height h of the flat steel box girder bridge, and can be used for the calculation of the temperature fatigue stress history of the flat steel box girder bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 shows the distribution of representative temperature values ​​in the vertical temperature gradient fatigue load model of a flat steel box girder bridge.

[0084] Figure 2 This is the distribution of representative temperature values ​​in the transverse temperature gradient fatigue load model for flat steel box girder bridges.

[0085] Figure 3 A flow chart was constructed for the model of the present invention.

[0086] Figure 4 Arrangement of temperature measuring points for flat steel box girder bridge.

[0087] Figure 5 This is the temperature history curve of the flat steel box girder bridge.

[0088] Figure 6 This is the cross-section diagram of a flat steel box girder bridge. DETAILED DESCRIPTION

[0089] 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.

[0090] Example 1

[0091] The long-life temperature gradient fatigue load model of the flat steel box girder bridge involved in this embodiment is composed of a vertical temperature gradient fatigue load model and a transverse temperature gradient fatigue load model. In this embodiment, the left side of the beam section is defined as the sunny side, and the right side of the beam section is defined as the shaded side. In actual use, it is judged based on the light intensity within a day, and the side with high light intensity is the sunny side.

[0092] The vertical temperature gradient fatigue load model is as follows:

[0093]

[0094] In formula (1), T + (y) is the positive temperature gradient model in the vertical temperature gradient fatigue load model, T - (y) is the negative temperature gradient model in the vertical temperature gradient fatigue load model, y is the height of the position to be calculated, h is the section height, T G1 is the representative value of the temperature at the top plate, in °C, T G2 It is the representative value of the temperature at the position where the web is 1 / 4h away from the top plate, in °C, T G3 is the representative value of the temperature at the bottom plate, in °C, B is the width of the top plate, b is the width of the bottom plate, β TG (B), β TG (b) is the intermediate variable, is the initial temperature value at the top plate, in °C, is the initial temperature value of the web at a distance of 1 / 4h from the top plate, in °C. is the initial temperature value at the bottom plate, in °C, N d It is the design service life, and its value is 100, 150 or 200, in years.

[0095] The transverse temperature fatigue load model T H (x) are as follows:

[0096]

[0097] In formula (2), x is the lateral position to be calculated, B is the width of the top plate, and T H1 is the representative value of the temperature at the sunny side of the top plate, T H2 It is the representative value of the temperature at the top plate 0.2B away from the sun side, in °C, T H3 It is the representative value of the temperature at the 1 / 2B position of the top plate, in °C, T H4 is the representative value of the temperature at the shady side of the top plate, in °C, β TH (h) is the intermediate variable, is the initial temperature value at the sunny side of the top plate, in °C. is the initial temperature value of the top plate at 0.2B from the sun side, in °C. is the initial temperature value at the top plate 1 / 2B position, in °C, It is the initial temperature value at the shady side of the top plate, in °C.

[0098] In the present embodiment (1), the top plate width B is selected as 33.0 m, the bottom plate width b is selected as 28.5 m, In formula (2), the beam height h is selected as 3.5m. The temperature representative value distribution in the corresponding vertical temperature fatigue load model is shown in Figure 1, and the temperature representative value distribution in the corresponding transverse temperature fatigue load model is shown in Figure 2 The representative values ​​of temperature at different altitudes corresponding to 100, 150 and 200 years are shown in Tables 1 and 2.

[0099] Table 1 Representative values ​​of temperature for vertical temperature gradient fatigue load model

[0100]

[0101] Table 2 Representative values ​​of temperature for transverse temperature gradient fatigue load model

[0102]

[0103] like Figure 3 As shown, the method for constructing the vertical temperature gradient fatigue load model of the flat steel box girder bridge comprises the following steps:

[0104] The construction method of the long-life temperature gradient fatigue load model for flat steel box girder bridges consists of the following steps:

[0105] (1) Long-term monitoring of temperature field of flat steel box girder bridge

[0106] Temperature sensors are arranged on the top plate, bottom plate and diaphragm of the flat steel box girder bridge to collect temperature. The collection time interval is set to 1 to 20 minutes. The representative value of the collected vertical temperature is recorded as T A (y), the representative value of the horizontal temperature collected is T A (x).

[0107] (2) Constructing the thermal stress history of a flat steel box girder bridge

[0108] The time interval of the measured temperature gradient is used as the time interval, and the vertical temperature gradient time curve is recorded as T A (y, t), record the transverse temperature gradient time history curve T A (x,t), such as Figure 5 shown.

[0109] The temperature stress history at each position is obtained by the following formula:

[0110] 1) For the vertical temperature gradient fatigue load model, the temperature stress history σ A (y,t):

[0111]

[0112] Where ρ is the temperature secondary bending moment influence coefficient, 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 flat wide steel box girder bridge, I is the moment of inertia of the flat wide steel box girder bridge section, y s is the vertical neutral axis position of the flat wide steel box girder bridge section, b(y) is the cross-sectional thickness of the flat wide steel box girder bridge at the vertical y position. In this embodiment, E s =2.06×10 5 MPa, α s =1.1×10 -5 ℃ -1 .

[0113] For constructing the transverse temperature gradient fatigue load model, the temperature stress history σ A (x,t):

[0114]

[0115] In the formula, x s is the transverse neutral axis position of the flat steel box girder bridge section, and b(x) is the section thickness of the flat steel box girder bridge at position x.

[0116] (3) Temperature stress amplitude cycle count

[0117] The stress amplitude is counted by rain flow counting method, and the temperature stress amplitude vector at each position of the cross section is obtained.

[0118] 1) For the construction of vertical temperature gradient fatigue load model, the temperature stress amplitude vector B1 is:

[0119] B1=(Δσ1(y),Δσ2(y),…,Δσ na (y))

[0120] In the formula, Δσ na (y) is the nath measured stress amplitude at the y position, na represents the number of elements in the vector B1 and is a finite positive integer.

[0121] 2) For the construction of transverse temperature gradient fatigue load model, the temperature stress amplitude vector B2 is:

[0122] B2=(Δσ1(x),Δσ2(x),…,Δσ nb (x))

[0123] In the formula, Δσ nb (x) is the nbth measured stress amplitude at position x, and nb represents the number of elements in vector B2, which is a finite positive integer.

[0124] The temperature stress amplitude vector at each position is fitted with a Weibull function to obtain the corresponding temperature stress amplitude probability density curve f(g);

[0125]

[0126] Where: μ is the mean value of the temperature stress amplitude, σ is the variance of the temperature stress amplitude.

[0127] For the construction of vertical temperature gradient fatigue load model, the value of g is [min(B1)-max(B1),2max(B1)];

[0128] For the construction of the transverse temperature gradient fatigue load model, the value of g is [min(B2)-max(B2),2max(B2)];

[0129] (4) Determine the total number of total temperature stress cycle loading

[0130] Determine the total number of total temperature stress cycle loading N corresponding to different design service life according to the following formula fs :

[0131] N fs =δ×N d ×365

[0132] Wherein, δ is the stress cycle coefficient, which takes a value of [1.05, 1.3], and is 1.1 in this embodiment.

[0133] (5) Temperature stress amplitude data sampling

[0134] Determine the number of layers N for stratified sampling La , N La Take N d , the upper limit x of stratified sampling T , lower limit x B , for constructing vertical temperature gradient fatigue load model, x T Take 2max(B1), x B Take min(B1)-max(B1), for the construction of transverse temperature gradient fatigue load model, x T Take 2max(B2), x B Take min(B2)-max(B2) and determine the number of sampling times for the pth layer under the design service life according to the corresponding probability density function f(g).

[0135] 1) For constructing the vertical temperature gradient fatigue load model, the number of sampling times n for the pth layer is yfor:

[0136]

[0137] In the formula, p y The value of is [1,N La ].

[0138] 2) For the construction of the transverse temperature gradient fatigue load model, the number of sampling times n for the pth layer is x for:

[0139]

[0140] In the formula, p x The value of is [1,N La ].

[0141] According to the uniform sampling method, the stress amplitude sampling results are obtained:

[0142] 1) For constructing the vertical temperature gradient fatigue load model, the sampling result vector A py for:

[0143] A py =(σ1(y),σ2(y),...,σ ny (y))

[0144] In the formula, σ ny (y) is the nyth stress amplitude at position y, and ny is the number of elements in the vector, which is a finite positive integer.

[0145] 2) For the construction of the transverse temperature gradient fatigue load model, the sampling result vector A px for:

[0146] A px =(σ1(x),σ2(x),...,σ nx (x))

[0147] In the formula, σ nx (x) is the nxth stress amplitude at the x position, nx is the number of elements in the vector, and is a finite positive integer; the final stress amplitude sampling vector is obtained according to the following formula:

[0148] 1) For the construction of vertical temperature gradient fatigue load model, the final stress amplitude sampling vector A y for:

[0149]

[0150] 2) For the construction of the transverse temperature gradient fatigue load model, the final stress amplitude sampling vector A x for:

[0151]

[0152] (6) Determine the equivalent temperature stress amplitude

[0153] The equivalent temperature stress amplitude of the flat steel box girder bridge is obtained as follows:

[0154] 1) For the vertical temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqy for:

[0155]

[0156] In the formula, A yi is the vector A y The i-th element in .

[0157] 2) For the construction of transverse temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqx for:

[0158]

[0159] In the formula, A xi is the vector A x The i-th element in .

[0160] (7) Constructing a long-life temperature fatigue load model for flat steel box girder bridges

[0161] The equivalent fatigue temperature of a flat steel box girder bridge is constructed as follows:

[0162] 1) For the vertical temperature gradient fatigue load model, the equivalent fatigue temperature T eqy for:

[0163]

[0164] 2) For the construction of transverse temperature gradient fatigue load model, the equivalent fatigue temperature T eqx for:

[0165]

[0166] A variable parameter analysis is carried out on the flat steel box girder bridge, and the equivalent fatigue temperature is fitted to the results using the least square method. The temperature gradient fatigue load models of formula (1) and formula (2) are established.

[0167] Example 2

[0168] The long-life temperature gradient fatigue load model of the flat steel box girder bridge involved in this embodiment is shown in equations (1) and (2), and the construction method is the same as that of Example 1.

[0169] In this embodiment (1), the top plate width B is selected as 25.0m, the bottom plate width b is selected as 10.0m, Formula (2) selects the beam height h as 2.5m, The remaining parameters are the same as those in Example 1. The temperature representative value distribution in the corresponding vertical temperature gradient fatigue load model is shown in FIG1 , and the temperature representative value distribution in the corresponding transverse temperature gradient fatigue load model is shown in FIG1 . Figure 2 shown.

[0170] The representative values ​​of temperature at different altitudes corresponding to 100, 150 and 200 years are shown in Tables 3 and 4.

[0171] Table 3 Representative values ​​of temperature for vertical temperature gradient fatigue load model

[0172]

[0173] Table 4 Representative values ​​of temperature for transverse temperature gradient fatigue load model

[0174]

[0175] Example 3

[0176] The long-life temperature gradient fatigue load model of the flat steel box girder bridge in this embodiment is shown in equations (1) and (2), and the construction method is the same as that in Example 1.

[0177] In the present embodiment, the top plate width B is 50.0 m, the bottom plate width b is 40.0 m, and T G 0 1=14.5℃, in formula (2), the beam height h is selected as 4.5m, T H 0 1=10.0℃, and the other parameters are the same as those in Example 1. The temperature representative value distribution in the corresponding vertical temperature gradient fatigue load model is shown in FIG1 , and the temperature representative value distribution in the corresponding transverse temperature gradient fatigue load model is shown in FIG2 . Figure 2 The representative values ​​of temperature at different altitudes corresponding to 100, 150 and 200 years are shown in Tables 5 and 6.

[0178] Table 5 Representative values ​​of temperature for vertical temperature gradient fatigue load model

[0179]

[0180] Table 6 Representative values ​​of temperature for transverse temperature gradient fatigue load model

[0181]

[0182] Test 1

[0183] In order to verify the effect of the vertical temperature gradient fatigue load model of the flat steel box girder bridge, the model and construction method of Example 1 were used to conduct experiments, and sensors were arranged on the Nanjing Yangtze River Bridge for long-term temperature field monitoring. Figure 6 shown.

[0184] 1. Long-term monitoring instruments

[0185] The monitoring instrument is a 32-channel DH2002 temperature acquisition device produced in Taizhou, Jiangsu. The temperature acquisition software is the PHM long-term health monitoring software produced in Taizhou, Jiangsu. The temperature sensor is a three-wire Pt100 sensor.

[0186] 2. Temperature measurement point arrangement

[0187] The top plate, bottom plate and web of the flat steel box girder bridge are selected to arrange temperature measuring points, and a coordinate system is established with the center of the bottom plate of the flat steel box girder bridge as the coordinate origin. The temperature measuring points are arranged on the top plate, diaphragm and bottom plate of the flat steel box girder bridge according to the following arrangement principle: the positions of the temperature measuring points arranged on the diaphragm are expressed as 0.00m, 1.98m, 2.68m, 3.20m, 3.30m, 3.40m, 3.45m and 3.50m in vertical distance from the lower surface of the top plate of the flat steel box girder bridge, and are recorded as yc1~yc8. Figure 4 As shown, the sampling interval is 1 minute, and the temperature history curve is as follows Figure 5 shown.

[0188] 3. Analysis of the effect of vertical temperature gradient fatigue load model

[0189] Taking the butt weld of the bottom plate of a flat steel box girder bridge as an example, the temperature stress history was constructed based on the temperature monitoring data. The temperature stress amplitude was cycle counted using the rain flow counting method to obtain the temperature stress amplitude spectrum. Then, the equivalent fatigue stress was calculated based on the measured results, and the result was 21.6MPa.

[0190] Based on the vertical temperature gradient fatigue load model of flat steel box girder bridge, the temperature stress history is constructed and the temperature stress amplitude analysis is performed. Where B = 33.0m, b = 28.5m, N d =100 years of design service life, substitute into the following formula:

[0191]

[0192] The equivalent temperature fatigue stress is 21.4MPa, which is basically consistent with the equivalent fatigue stress of the measured results. This shows that the established temperature fatigue load model for flat steel box girder bridges has good applicability and can be used for vertical temperature or temperature-vehicle coupling fatigue damage assessment of flat steel box girder bridges.

Claims

1. A long-life temperature gradient fatigue load model for a flat steel box girder bridge, characterized in that: The model consists of vertical temperature gradient fatigue load model and transverse temperature gradient fatigue load model; The vertical temperature gradient fatigue load model is as follows: In formula (1), T + (y) is the positive temperature gradient model in the vertical temperature gradient fatigue load model, T - (y) is the negative temperature gradient model in the vertical temperature gradient fatigue load model, y is the height of the position to be calculated, h is the section height, T G1 is the representative value of the temperature at the top plate, in °C, T G2 It is the representative value of the temperature at the position where the web is 1 / 4h away from the top plate, in °C, T G3 is the representative value of the temperature at the bottom plate, in °C, B is the width of the top plate, b is the width of the bottom plate, β TG (B), β TG (b) is the intermediate variable, is the initial temperature value at the top plate, in °C, is the initial temperature value of the web at a distance of 1 / 4h from the top plate, in °C. is the initial temperature value at the bottom plate, in °C, N d The design service life is 100, 150 or 200 years; The transverse temperature gradient fatigue load model is as follows: In formula (2), x is the lateral position to be calculated, B is the width of the top plate, and T H1 is the representative value of the temperature at the sunny side of the top plate, T H2 It is the representative value of the temperature at the top plate 0.2B away from the sun side, in °C, T H3 It is the representative value of the temperature at the 1 / 2B position of the top plate, in °C, T H4 is the representative value of the temperature at the shady side of the top plate, in °C, β TH (h) is the intermediate variable, is the initial temperature value at the sunny side of the top plate, in °C. is the initial temperature value of the top plate at 0.2B from the sun side, in °C. is the initial temperature value at the top plate 1 / 2B position, in °C, is the initial temperature of the shady side of the top plate, in °C.

2. The long-life temperature gradient fatigue load model of the flat steel box girder bridge according to claim 1 is characterized in that: In formula (1), The value of is [12.0,14.5], the unit is ℃, the value of b is [10.0,40.0], the unit is m; the value of B is [25.0,50.0], the unit is m.

3. The long-life temperature gradient fatigue load model of the flat steel box girder bridge according to claim 1 is characterized in that B, b, The values ​​of are: B is 33.0m, b is 28.5m, It is 13.3℃.

4. The long-life temperature gradient fatigue load model for flat steel box girder bridge according to claim 1 is characterized in that: In formula (2), The value of is [6.1,10.0], the unit is ℃, and the value of h is [2.5,4.5], the unit is m.

5. The long-life temperature gradient fatigue load model for flat steel box girder bridge according to claim 1 is characterized in that h described in formula (2) The value of is: h is 3.5m, It is 7.6℃.

6. A method for constructing a long-life temperature gradient fatigue load model of a flat steel box girder bridge according to claim 1, comprising the following steps: (1) Long-term monitoring of temperature field of flat steel box girder bridge Temperature sensors are arranged on the top plate, bottom plate and diaphragm of the flat steel box girder bridge to collect temperature. The collection time interval is set to 1 to 20 minutes. The representative value of the collected vertical temperature is recorded as T A (y), the representative value of the transverse temperature collected is T A (x); (2) Constructing the thermal stress history of a flat steel box girder bridge The time interval of the measured temperature gradient is used as the time interval, and the vertical temperature gradient time curve is recorded as T A (y, t), record the transverse temperature gradient time history curve T A (x,t); The temperature stress history at each position is obtained by the following formula: 1) For the vertical temperature gradient fatigue load model, the temperature stress history σ A (y,t): Where ρ is the temperature secondary bending moment influence coefficient, 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 flat wide steel box girder bridge, I is the moment of inertia of the flat wide steel box girder bridge section, y s is the vertical neutral axis position of the flat wide steel box girder bridge section, b(y) is the section thickness at the vertical y position of the flat wide steel box girder bridge; For constructing the transverse temperature gradient fatigue load model, the temperature stress history σ A (x,t): In the formula, x s is the position of the transverse neutral axis of the flat steel box girder bridge section, b(x) is the section thickness at the x position of the flat steel box girder bridge; (3) Temperature stress amplitude cycle count The stress amplitude is counted by rain flow counting method to obtain the temperature stress amplitude vector at each position of the cross section; 1) For the construction of vertical temperature gradient fatigue load model, the temperature stress amplitude vector B1 is: B1=(Δσ1(y),Δσ2(y),…,Δσ na (y)) In the formula, Δσ na (y) is the nth measured stress amplitude at position y, na represents the number of elements in vector B1 and is a finite positive integer; 2) For the construction of transverse temperature gradient fatigue load model, the temperature stress amplitude vector B2 is: B2=(Δσ1(x),Δσ2(x),…,Δσ nb (x)) In the formula, Δσ nb (x) is the nbth measured stress amplitude at position x, nb represents the number of elements in vector B2 and is a finite positive integer; The temperature stress amplitude vector at each position is fitted with a Weibull function to obtain the corresponding temperature stress amplitude probability density curve f(g); Where: μ is the mean value of temperature stress amplitude, σ is the variance of temperature stress amplitude; For the construction of vertical temperature gradient fatigue load model, the value of g is [min(B1)-max(B1),2max(B1)]; For constructing the transverse temperature gradient fatigue load model, the value of g is [min(B2)-max(B2),2max(B2)]; (4) Determine the total number of total temperature stress cycle loading Determine the total number of total temperature stress cycle loading N corresponding to different design service life according to the following formula fs : N fs =δ×N d ×365 Where, δ is the stress cycle coefficient, and its value is [1.05, 1.30]; (5) Temperature stress amplitude data sampling Determine the number of layers NLa for stratified sampling, where NLa is N d , the upper limit x of stratified sampling T , lower limit x B , for constructing vertical temperature gradient fatigue load model, x T Take 2max(B1), x B Take min(B1)-max(B1), for the construction of transverse temperature gradient fatigue load model, x T Take 2max(B2), x B Take min(B2)-max(B2) and determine the number of sampling times of the pth layer under the design service life according to the corresponding probability density function f(g); 1) For constructing the vertical temperature gradient fatigue load model, the number of sampling times n for the pth layer is y for: In the formula, p y The value of is [1,N La ]; 2) For the construction of the transverse temperature gradient fatigue load model, the number of sampling times n for the pth layer is x for: In the formula, p x The value of is [1,N La ]; The stress amplitude sampling results are obtained according to the uniform sampling method: 1) For constructing the vertical temperature gradient fatigue load model, the sampling result vector A py for: A py =(σ1(y),σ2(y),...,σ ny (y)) In the formula, σ ny (y) is the nyth stress amplitude at position y, ny is the number of elements in the vector, which is a finite positive integer; 2) For the construction of the transverse temperature gradient fatigue load model, the sampling result vector A px for: A px =(σ1(x),σ2(x),...,σ nx (x)) In the formula, σ nx (y) is the nxth stress amplitude at the x position, nx is the number of elements in the vector, which is a finite positive integer; The final stress amplitude sampling vector is obtained according to the following formula; 1) For the construction of vertical temperature gradient fatigue load model, the final stress amplitude sampling vector A y for: 2) For the construction of the transverse temperature gradient fatigue load model, the final stress amplitude sampling vector A x for: (6) Determine the equivalent temperature stress amplitude The equivalent temperature stress amplitude of the flat steel box girder bridge is obtained as follows: 1) For the vertical temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqy for: In the formula, is the vector A y The i-th element in ; 2) For the construction of transverse temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqx for: In the formula, is the vector A x The i-th element in ; (7) Constructing a long-life temperature fatigue load model for flat steel box girder bridges The equivalent fatigue temperature of a flat steel box girder bridge is constructed as follows: 1) For the vertical temperature gradient fatigue load model, the equivalent fatigue temperature T eqy for: 2) For the construction of transverse temperature gradient fatigue load model, the equivalent fatigue temperature T eqx for: A variable parameter analysis is carried out on the flat steel box girder bridge, and the equivalent fatigue temperature is fitted to the results using the least square method. The temperature gradient fatigue load models of formula (1) and formula (2) are established.

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