Long-life temperature gradient fatigue load model and construction method for flat steel box girder bridges

Abstract

A long-life temperature gradient fatigue load model and construction method for a flat steel box girder bridge are disclosed. This model includes vertical and horizontal temperature gradient fatigue load models, where the vertical model is a bilinear form and the horizontal model is a trilinear form. In this invention, long-term temperature field monitoring was conducted on the structural characteristics and temperature field distribution features of a flat steel box girder bridge. Using the Latin hypercube sampling method and the fatigue damage equivalence principle, a method for constructing the temperature gradient fatigue load model for the flat steel box girder bridge was proposed. This method constructs a long-life temperature gradient fatigue load model for the flat steel box girder bridge, which can be used for fatigue design and fatigue life assessment of flat steel box girder bridges with a design service life of up to 200 years.

Description

Technical Field

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

[0002] Flat steel box girders are typical closed-section bridges with a small height-to-width ratio. Under solar radiation, they experience not only vertical temperature gradients but also significant transverse temperature gradients. Under the influence of vertical nonlinear temperature gradients, flat steel box girders generate longitudinal temperature stresses, while the closed section exhibits a framing effect, leading to transverse temperature stresses under transverse temperature gradients. With alternating diurnal temperatures, the flat steel box girder cross-section exhibits periodically varying temperature fatigue stresses, contributing to cumulative fatigue damage. Therefore, it is necessary to conduct long-term temperature field monitoring for flat steel box girder bridges. Using the Latin hypercube sampling method and the fatigue damage equivalence principle, 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 should be constructed to provide a technical basis for the fatigue-resistant design and evaluation of flat steel box girder bridges. Summary of the Invention

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

[0004] Another technical problem that this invention aims to solve is to provide a method for constructing a long-life temperature gradient fatigue load model for flat steel box girder bridges.

[0005] The long-life temperature gradient fatigue load model for flat steel box girder bridges 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 equation (1), T + (y) represents the positive temperature gradient model in the vertical temperature gradient fatigue load model, T - (y) represents the negative temperature gradient model in the vertical temperature gradient fatigue load model, where y is the height of the location to be calculated, h is the section height, and T... G1 This represents the temperature at the top plate location, in °C (°C) or T. G2 This represents the temperature at a point 1 / 4 h from the top plate, in °C (°C) and T. G3 This represents the temperature at the bottom plate location, in °C. B is the width of the top plate, b is the width of the bottom plate, and β... TG (B), βTG (b) is an intermediate variable. This represents the initial temperature at the top plate location, in °C. This is the initial temperature value at a point 1 / 4h away from the top plate, in °C. This is the initial temperature value at the base plate location, in °C (N). d The design service life is specified, and the value is 100, 150, or 200, in years.

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

[0010]

[0011] In equation (2), x is the lateral position to be calculated, B is the width of the top plate, and T is the width of the top plate. H1 T represents the temperature at the sunny side of the roof. H2 This represents the temperature at a point 0.2B above the sunlit surface, in °C (°C) and T. H3 This represents the temperature at position 1 / 2B of the top plate, in °C (°C) and T. H4 This represents the temperature at the shaded side of the roof, in °C, β. TH (h) is an intermediate variable. This represents the initial temperature value at the sunny side of the roof, in °C. This represents the initial temperature at a point 0.2B above the sunlit side of the roof, in °C. This is the initial temperature value at position 1 / 2B of the top plate, in °C. This is the initial temperature value at the shaded side of the roof, in °C.

[0012] Further preferred, in formula (1), the... The values ​​of are [12.0, 14.5], and the unit is ℃; the values ​​of b are [10.0, 40.0], and the unit is m; the values ​​of B are [25.0, 50.0], and the unit is m.

[0013] Further preferred, B, b, as described in formula (1) The values ​​are: B = 33.0m, b = 28.5m. It is 13.3℃.

[0014] Further preferred, the formula (2) described The value of is [6.1, 10.0], and the unit is ℃. The value of h is [2.5, 4.5], and the unit is m.

[0015] Further optimization, the h, mentioned in formula (2) The value of h is 3.5m. It is 7.6℃.

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

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

[0018] Temperature sensors were installed on the top slab, bottom slab, and transverse diaphragms of the flat steel box girder bridge to collect temperatures. The collection time interval was set to 1–20 minutes, and the collected vertical temperature was recorded as a representative value in T. A (y), the collected transverse temperature representative value is T A (x).

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

[0020] Using the time interval between data acquisitions as the time interval, plot the measured temperature gradient time history curve and record the vertical temperature gradient time history curve T. A Let (y,t) denote the time history curve T of the transverse temperature gradient. A (x,t).

[0021] The temperature stress history at each location is obtained from the following formula;

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

[0023]

[0024] In the formula, ρ is the influence coefficient of temperature-induced secondary bending moment, and E s Let α be the elastic modulus of steel. s Let y be the coefficient of thermal expansion of steel, A be the cross-sectional area of ​​the flat wide steel box girder bridge, I be the moment of inertia of the cross-section of the flat wide steel box girder bridge, and y be the coefficient of thermal expansion of steel. s y represents the vertical neutral axis position of the flat wide steel box girder bridge section, and b(y) represents the section thickness at the vertical y position of the flat wide steel box girder bridge.

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

[0026]

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

[0028] (3) Temperature stress amplitude cycle count

[0029] The stress amplitude is counted by rainflow counting method to obtain the temperature stress amplitude vector at each location of the cross section.

[0030] 1) For constructing a 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) represents the na-th measured stress amplitude at position y, where na represents the number of elements in vector B1 and is a finite positive integer.

[0033] 2) For constructing a 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) represents the nb-th measured stress amplitude at position x, where nb represents the number of elements in vector B2 and is a finite positive integer.

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

[0037]

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

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

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

[0041] (4) Determine the total number of temperature stress cycles.

[0042] The total number of temperature stress cyclic loading cycles N corresponding to different design service lives is determined by the following formula. fs :

[0043] N fs =δ×N d ×365

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

[0045] (5) Sampling of temperature stress amplitude data

[0046] Determine the number of strata N for stratified sampling La N La Take N d The upper limit of stratified sampling x T Lower limit x B For constructing a vertical temperature gradient fatigue load model, x T Take 2max(B1), x B Taking min(B1) - max(B1), for the construction of the transverse temperature gradient fatigue load model, x T Take 2max(B2), x B Take min(B2)-max(B2) and determine the number of samplings for the p-th layer under the design service life based on the corresponding probability density function f(g).

[0047] 1) For constructing a vertical temperature gradient fatigue load model, the number of samplings for the p-th layer is n. y for:

[0048]

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

[0050] 2) For constructing a fatigue load model with a transverse temperature gradient, the number of samplings for the p-th layer is n. x for:

[0051]

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

[0053] The stress amplitude sampling results were obtained using the uniform sampling method.

[0054] 1) For constructing a 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) represents the ny-th stress amplitude at position y, where ny is the number of elements in the vector and is a finite positive integer.

[0057] 2) For constructing a lateral 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) represents the nx-th stress amplitude at position x, where nx is the number of elements in the vector and is a finite positive integer.

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

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

[0062]

[0063] 2) For constructing a 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 a flat steel box girder bridge is obtained by the following formula.

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

[0068]

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

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

[0071]

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

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

[0074] The equivalent fatigue temperature of a flat steel box girder bridge is constructed according to the following formula:

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

[0076]

[0077] 2) For constructing a fatigue load model with a transverse temperature gradient, the equivalent fatigue temperature T eqx for:

[0078]

[0079] A variable parameter analysis was performed on the flat steel box girder bridge, and the equivalent fatigue temperature was fitted using the least squares method to establish the temperature gradient fatigue load model of equations (1) and (2).

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

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

[0082] 2. The long-life temperature gradient fatigue load model for flat steel box girder bridges constructed in this invention fully considers the influence of the top plate width B, bottom plate width b, and beam height h of the flat steel box girder bridge, and can be used for calculating the temperature fatigue stress history of flat steel box girder bridges. Attached Figure Description

[0083] Figure 1 This represents the temperature distribution in the vertical temperature gradient fatigue load model of a flat steel box girder bridge.

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

[0085] Figure 3 This is a flowchart illustrating the model construction process 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 for a flat steel box girder bridge.

[0088] Figure 6 This is a cross-sectional view of a flat steel box girder bridge. Detailed Implementation

[0089] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0090] Example 1

[0091] This embodiment relates to a long-life temperature gradient fatigue load model for flat steel box girder bridges. The model consists of a vertical temperature gradient fatigue load model and a horizontal 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 as the shaded side. In actual use, the determination is based on the day's light intensity; the side with higher light intensity is the sunny side.

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

[0093]

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

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

[0096]

[0097] In equation (2), x is the lateral position to be calculated, B is the width of the top plate, and T is the width of the top plate. H1 T represents the temperature at the sunny side of the roof. H2 This represents the temperature at a point 0.2B above the sunlit surface, in °C (°C) and T. H3 This represents the temperature at position 1 / 2B of the top plate, in °C (°C) and T. H4 This represents the temperature at the shaded side of the roof, in °C, β. TH (h) is an intermediate variable. This represents the initial temperature value at the sunny side of the roof, in °C. This represents the initial temperature at a point 0.2B above the sunlit side of the roof, in °C. This is the initial temperature value at position 1 / 2B of the top plate, in °C. This is the initial temperature value at the shaded side of the roof, in °C.

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

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

[0100]

[0101] Table 2. Representative Temperature Values ​​of the Lateral 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 above-mentioned flat steel box girder bridge includes the following steps:

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

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

[0106] Temperature sensors were installed on the top slab, bottom slab, and transverse diaphragms of the flat steel box girder bridge to collect temperatures. The collection time interval was set to 1–20 minutes, and the collected vertical temperature was recorded as a representative value in T. A (y), the collected transverse temperature representative value is T A (x).

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

[0108] Using the time interval between data acquisitions as the time interval, plot the measured temperature gradient time history curve and record the vertical temperature gradient time history curve T. A Let (y,t) denote the time history curve T of the transverse temperature gradient. A (x,t), such as Figure 5 As shown.

[0109] The temperature stress history at each location is obtained from the following formula;

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

[0111]

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

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

[0114]

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

[0116] (3) Temperature stress amplitude cycle count

[0117] The stress amplitude is counted by rainflow counting method to obtain the temperature stress amplitude vector at each location of the cross section.

[0118] 1) For constructing a 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) represents the na-th measured stress amplitude at position y, where na represents the number of elements in vector B1 and is a finite positive integer.

[0121] 2) For constructing a 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) represents the nb-th measured stress amplitude at position x, where nb represents the number of elements in vector B2 and is a finite positive integer.

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

[0125]

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

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

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

[0129] (4) Determine the total number of temperature stress cycles.

[0130] The total number of temperature stress cyclic loading cycles N corresponding to different design service lives is determined by the following formula. fs :

[0131] N fs =δ×N d ×365

[0132] In the formula, δ is the stress cycle coefficient, which takes the value of [1.05, 1.3], and is taken as 1.1 in this embodiment.

[0133] (5) Sampling of temperature stress amplitude data

[0134] Determine the number of strata N for stratified sampling La N La Take N d The upper limit of stratified sampling x T Lower limit x B For constructing a vertical temperature gradient fatigue load model, x T Take 2max(B1), x B Taking min(B1) - max(B1), for the construction of the transverse temperature gradient fatigue load model, x T Take 2max(B2), x B Take min(B2)-max(B2) and determine the number of samplings for the p-th layer under the design service life based on the corresponding probability density function f(g).

[0135] 1) For constructing a vertical temperature gradient fatigue load model, the number of samplings for the p-th layer is n. yfor:

[0136]

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

[0138] 2) For constructing a fatigue load model with a transverse temperature gradient, the number of samplings for the p-th layer is n. x for:

[0139]

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

[0141] The stress amplitude sampling results were obtained using the uniform sampling method:

[0142] 1) For constructing a 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) represents the ny-th stress amplitude at position y, where ny is the number of elements in the vector and is a finite positive integer.

[0145] 2) For constructing a lateral 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) represents the nx-th stress amplitude at position x, where 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 constructing a vertical temperature gradient fatigue load model, the final stress amplitude sampling vector A y for:

[0149]

[0150] 2) For constructing a 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 a flat steel box girder bridge is obtained by the following formula.

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

[0155]

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

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

[0158]

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

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

[0161] The equivalent fatigue temperature of a flat steel box girder bridge is constructed according to the following formula:

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

[0163]

[0164] 2) For constructing a fatigue load model with a transverse temperature gradient, the equivalent fatigue temperature T eqx for:

[0165]

[0166] A variable parameter analysis was performed on the flat steel box girder bridge, and the equivalent fatigue temperature was fitted using the least squares method to establish the temperature gradient fatigue load model of equations (1) and (2).

[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 in embodiment 1.

[0169] In this embodiment, formula (1) selects the top plate width B as 25.0m and the bottom plate width b as 10.0m. Equation (2) selects the beam height h as 2.5m. All other parameters are the same as in Example 1. The temperature representative values ​​in the corresponding vertical temperature gradient fatigue load model are distributed as follows: Figure 1 As shown, the distribution of representative temperature values ​​in the corresponding transverse temperature gradient fatigue load model is as follows: Figure 2 As shown.

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

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

[0172]

[0173] Table 4. Representative Temperature Values ​​of the Lateral 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 embodiment 1.

[0177] In this embodiment, the width B of the top plate in formula (1) is 50.0m, and the width b of the bottom plate is 40.0m. In equation (2), the beam height h is selected as 4.5m. All other parameters are the same as in Example 1. The temperature representative values ​​in the corresponding vertical temperature gradient fatigue load model are distributed as follows: Figure 1 As shown, the distribution of representative temperature values ​​in the corresponding transverse temperature gradient fatigue load model is as follows: Figure 2 As shown, the representative temperature values ​​at different altitudes corresponding to 100 years, 150 years, and 200 years are shown in Tables 5 and 6.

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

[0179]

[0180] Table 6. Representative Temperature Values ​​of the Lateral Temperature Gradient Fatigue Load Model

[0181]

[0182] Experiment 1

[0183] To verify the effectiveness of the vertical temperature gradient fatigue load model for flat steel box girder bridges, the model and construction method of Example 1 were used for testing. Sensors were deployed on the Nanjing Yangtze River Bridge for long-term temperature field monitoring. Its cross-sectional shape is as follows: Figure 6 As shown.

[0184] I. Long-term monitoring instruments

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

[0186] II. Arrangement of Temperature Measurement Points

[0187] Temperature measuring points were selected on the top slab, bottom slab, and web of the flat steel box girder bridge. A coordinate system was established with the center of the bottom slab of the flat steel box girder bridge as the origin. The arrangement principle for the temperature measuring points on the top slab, diaphragms, and bottom slab of the flat steel box girder bridge is as follows: the positions of the temperature measuring points on the diaphragms are represented by their vertical distances from the lower surface of the top slab of the flat steel box girder bridge as 0.00m, 1.98m, 2.68m, 3.20m, 3.30m, 3.40m, 3.45m, and 3.50m, denoted as yc1 to yc8. (Specific details are as follows...) Figure 4 As shown, the sampling interval is 1 minute, and its temperature history curve is as follows. Figure 5 As shown.

[0188] III. Effect Analysis 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 is constructed based on the measured temperature monitoring data. The temperature stress amplitude is cyclically counted using the rain flow counting method to obtain the temperature stress amplitude spectrum. Then, the equivalent fatigue stress is calculated based on the measured results, and the result is 21.6 MPa.

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

[0191]

[0192] The equivalent temperature fatigue stress was found to be 21.4 MPa, which is basically consistent with the measured equivalent fatigue stress. This indicates 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 coupled 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 a vertical temperature gradient fatigue load model and a horizontal temperature gradient fatigue load model. The vertical temperature gradient fatigue load model is as follows: In equation (1), T + (y) represents the positive temperature gradient model in the vertical temperature gradient fatigue load model, and T_(y) represents the negative temperature gradient model in the vertical temperature gradient fatigue load model. y is the height of the location to be calculated, h is the section height, and T G1 This represents the temperature at the top plate location, in °C (°C) or T. G2 This represents the temperature at a point 1 / 4 h from the top plate, in °C (°C) and T. G3 This represents the temperature at the bottom plate location, in °C. B is the width of the top plate, b is the width of the bottom plate, and β... TG (B), β TG (b) is an intermediate variable. This represents the initial temperature at the top plate location, in °C. This is the initial temperature value at a point 1 / 4h away from the top plate, in °C. This is the initial temperature value at the base plate location, in °C (N). d The design service life is specified as 100, 150, or 200, with the unit being years. The lateral temperature gradient fatigue load model is as follows: In equation (2), x is the lateral position to be calculated, B is the width of the top plate, and T is the width of the top plate. H1 T represents the temperature at the sunny side of the roof. H2 This represents the temperature at a point 0.2B above the sunlit surface, in °C (°C) and T. H3 This represents the temperature at position 1 / 2B of the top plate, in °C (°C) and T. H4 This represents the temperature at the shaded side of the roof, in °C, β. TH (h) is an intermediate variable. This represents the initial temperature value at the sunny side of the roof, in °C. This represents the initial temperature at a point 0.2B above the sunlit side of the roof, in °C. This is the initial temperature value at position 1 / 2B of the top plate, in °C. This is the initial temperature value at the shaded side of the roof, in °C.

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

3. The long-life temperature gradient fatigue load model for flat steel box girder bridges according to claim 1, characterized in that... The B, b, mentioned in formula (1) The values ​​are: B = 33.0m, b = 28.5m. It is 13.3℃.

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

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

6. A method for constructing a long-life temperature gradient fatigue load model for a flat steel box girder bridge as described in claim 1 comprises the following steps: (1) Long-term monitoring of temperature field of flat steel box girder bridge Temperature sensors were installed on the top slab, bottom slab, and transverse diaphragms of the flat steel box girder bridge to collect temperatures. The collection time interval was set to 1–20 minutes, and the collected vertical temperature was recorded as a representative value in T. A (y), the collected transverse temperature representative value is T A (x); (2) Constructing the temperature stress history of a flat steel box girder bridge Using the time interval between data acquisitions as the time interval, plot the measured temperature gradient time history curve and record the vertical temperature gradient time history curve T. A Let (y,t) denote the time history curve T of the transverse temperature gradient. A (x,t); The temperature stress history at each location is obtained from the following formula; 1) For constructing a vertical temperature gradient fatigue load model, the temperature stress history σ A (y,t): In the formula, ρ is the influence coefficient of temperature-induced secondary bending moment, and E s Let α be the elastic modulus of steel. s Let y be the coefficient of thermal expansion of steel, A be the cross-sectional area of ​​the flat wide steel box girder bridge, I be the moment of inertia of the cross-section of the flat wide steel box girder bridge, and y be the coefficient of thermal expansion of steel. s y represents the vertical neutral axis position of the flat wide steel box girder bridge section, and b(y) represents the section thickness at the vertical y position of the flat wide steel box girder bridge. For constructing a fatigue load model with a transverse temperature gradient, the temperature stress history σ A (x,t): Where x s Let x be the transverse neutral axis position of the flat steel box girder bridge section, and b(x) be the section thickness at position x of the flat steel box girder bridge. (3) Temperature stress amplitude cycle count The stress amplitude vector at each location of the cross section is obtained by counting stress amplitudes using the rainflow counting method. 1) For constructing a 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) represents the nath measured stress amplitude at position y, where na represents the number of elements in vector B1 and is a finite positive integer. 2) For constructing a 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) represents the nb-th measured stress amplitude at position x, where nb represents the number of elements in vector B2 and is a finite positive integer. The temperature stress amplitude vector at each location is fitted with a Weibull function to obtain the corresponding temperature stress amplitude probability density curve f(g); Where: μ is the mean amplitude of temperature stress, and σ is the variance of temperature stress amplitude; For the construction of the vertical temperature gradient fatigue load model, g takes the value of [min(B1)-max(B1),2max(B1)]; For constructing the fatigue load model with transverse temperature gradient, the value of g is [min(B2)-max(B2),2max(B2)]; (4) Determine the total number of temperature stress cycles. The total number of temperature stress cyclic loading cycles N corresponding to different design service lives is determined by the following formula. fs : N fs =δ×N d ×365 In the formula, δ is the stress cycle coefficient, which takes the value [1.05, 1.30]. (5) Sampling of temperature stress amplitude data Determine the number of strata NLa for stratified sampling, where NLa is N d The upper limit of stratified sampling x T Lower limit x B For constructing a vertical temperature gradient fatigue load model, x T Take 2max(B1), x B Taking min(B1) - max(B1), for the construction of the transverse temperature gradient fatigue load model, x T Take 2max(B2), x B Take min(B2)-max(B2) and determine the number of samplings for the p-th layer under the design service life based on the corresponding probability density function f(g); 1) For constructing a vertical temperature gradient fatigue load model, the number of samplings for the p-th layer is n. y for: In the formula, p y The value of is [1, N] La ]; 2) For constructing a fatigue load model with a transverse temperature gradient, the number of samplings for the p-th layer is n. x for: In the formula, p x The value of is [1, N] La ]; The stress amplitude sampling results were obtained using the uniform sampling method: 1) For constructing a vertical temperature gradient fatigue load model, the sampling result vector A py for: A py =(σ1(y),σ2(y),...,σ ny (y)) Where, σ ny (y) represents the ny-th stress amplitude at position y, where ny is the number of elements in the vector and is a finite positive integer. 2) For constructing a lateral temperature gradient fatigue load model, the sampling result vector A px for: A px =(σ1(x),σ2(x),...,σ nx (x)) Where, σ nx (y) represents the nx-th stress amplitude at position x, where 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; 1) For constructing a vertical temperature gradient fatigue load model, the final stress amplitude sampling vector A y for: 2) For constructing a 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 a flat steel box girder bridge is obtained by the following formula. 1) For constructing a vertical temperature gradient fatigue load model, the equivalent temperature stress amplitude Δσ eqy for: Where, Let vector A y The i-th element; 2) For constructing a fatigue load model with a transverse temperature gradient, the equivalent temperature stress amplitude Δσ eqx for: In the formula, Let vector A x The i-th element; (7) Constructing a long-life temperature fatigue load model for a flat steel box girder bridge The equivalent fatigue temperature of a flat steel box girder bridge is constructed according to the following formula: 1) For constructing a vertical temperature gradient fatigue load model, the equivalent fatigue temperature T eqy for: 2) For constructing a fatigue load model with a transverse temperature gradient, the equivalent fatigue temperature T eqx for: A variable parameter analysis was performed on the flat steel box girder bridge, and the equivalent fatigue temperature was fitted using the least squares method to establish the temperature gradient fatigue load model of equations (1) and (2).

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