Railway steel box girder bridge vertical temperature gradient fatigue load model and construction method

Abstract

The invention discloses a vertical temperature gradient fatigue load model of a railway steel box girder bridge and a construction method, and the model is composed of a positive temperature gradient model and a negative temperature gradient model which are in a three-fold line type and are shown in a formula (1). According to the method, long-term monitoring data of a temperature field of the railway steel box girder is analyzed, and the construction method of the vertical temperature gradient fatigue load model of the railway steel box girder bridge is provided by utilizing a Monte Carlo sampling method and a damage equivalence principle. The constructed vertical temperature gradient fatigue load model is constructed by utilizing long-term temperature field measured data, the influence of the top plate width B, the bottom plate width b, the steel box girder height h and the design service life Nd of the railway steel box girder bridge is considered, and the method can be used for the anti-fatigue design of the railway steel box girder bridge with the design service life of 100 years, 150 years and 200 years.

Description

Technical Field

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

[0002] Affected by factors such as solar radiation and the direction of the bridge, the bridge structure will be subjected to complex time-varying nonlinear temperature gradients under normal use. This temperature effect will cause periodic temperature fatigue stress in the bridge structure, which will cause fatigue damage. Railway steel box girders have the structural characteristics of high height and short wing plates, and the temperature field distribution pattern is significantly different from that of highway steel box girder bridges. Therefore, in order to meet the anti-fatigue design requirements of railway steel box girder bridges, the vertical temperature gradient fatigue load model construction method should be proposed based on the temperature gradient variation law of railway steel box girder bridges, using long-term temperature field measured data, and adopting reasonable sampling methods and damage equivalence principles. The vertical temperature gradient fatigue load model of railway steel box girder bridges is constructed. 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 vertical temperature gradient fatigue load model for a railway steel box girder bridge.

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

[0005] The vertical temperature gradient fatigue load model of the railway steel box girder bridge is as shown in formula (1). + (y), Negative temperature fatigue load model T - (y)Composition:

[0006]

[0007] In formula (1), y is the height of the position to be calculated, h is the section height, the unit is m, T 1 is the representative value of the temperature at the top plate of the railway steel box girder, T 2 is the representative value of the temperature of the railway steel box girder web at 0.6m from the top plate, in °C, T 3 is the representative value of the temperature of the railway steel box girder web at 1 / 2h from the top plate, in °C, T 4 is the representative value of the temperature at the bottom plate of the railway steel box girder, in °C, T 1 0 is the initial temperature of the top plate of the railway steel box girder, in °C, T 2 0 is the initial temperature of the railway steel box girder web at a distance of 0.6 m from the top plate, in °C, T 3 0is the initial temperature of the railway steel box girder web at 1 / 2h from the top plate, in °C, T 4 0 is the initial temperature value at the bottom plate of the railway steel box girder, in ℃, B is the width of the top plate of the railway steel box girder, in m, b is the width of the bottom plate of the railway steel box girder, in m, a 1 、b 1 , β T (B), β T (h), β T (b) is the intermediate variable, N d It is the design service life in years.

[0008] In formula (1), the T 1 0 The value is [17.0,19.2], the unit is ℃, T 2 0 The value of is [21.0, 24.0], the unit is ℃, the value of h is [3.0, 8.0], the unit is m, the value of b is [5.0, 12.0], the unit is m, and the value of B is [7.0, 15.0], the unit is m.

[0009] In formula (1), h, B, b, T 1 0 , T 2 0 The values ​​of are: h is best at 4.8m, B is best at 7.5m, b is best at 5.8m, T 1 0 The best temperature is 18.0℃, T 2 0 The best temperature is 23.0℃.

[0010] The method for constructing the vertical temperature gradient fatigue load model of the railway steel box girder bridge is composed of the following steps:

[0011] (1) Determine the temperature stress amplitude vector

[0012] Temperature sensors are arranged on the top plate, bottom plate and diaphragm of the railway steel box girder bridge to collect temperature. The collection time interval is set to 1 to 20 minutes, and the collected temperature gradient time history is T A (y, t), y is the coordinate of the vertical measuring point, and the temperature stress history σ is obtained by using the temperature stress formula of steel box girder bridge. A (y,t):

[0013]

[0014] In the formula, ρ is the temperature secondary bending moment influence coefficient, E s is the elastic modulus of steel, α sis the thermal expansion coefficient of steel, A is the cross-sectional area of ​​railway steel box girder bridge, I is the moment of inertia of the railway steel box girder bridge section, y s is the neutral axis of the railway steel box girder bridge section, and b(y) is the section thickness at position y of the railway steel box girder bridge.

[0015] The stress cycles are counted using the rain flow counting method to obtain the temperature stress amplitude vector A:

[0016] A=(σ 1 (y),σ 2 (y),...,σ n (y))

[0017] In the formula, σ n (y) is the nth stress amplitude at position y, and n is the number of elements in vector A.

[0018] (2) Fitting the temperature stress amplitude vector

[0019] Based on the Weibull function, the probability function is fitted to the temperature stress amplitude vector A, and the probability density curve f(v) at the y position is obtained:

[0020]

[0021] Where μ is the mean value of the temperature stress amplitude, σ is the variance of the temperature stress amplitude, and v is taken as [0,2max(A)].

[0022] Choose a distribution g(v) and define parameter k so that k×g(v) is greater than f z (v), where g(v) is:

[0023]

[0024] (3) Temperature stress amplitude sampling

[0025] Take the sample point v 0 , and perform a single uniform sampling in the range [0, k×g(v)] to obtain the sampling value μ 0 , if μ 0 <f z (v), then the sample point v 0 is accepted, otherwise it will not be accepted and the step will be repeated; finally, all the accepted sample points constitute the temperature stress amplitude vector C of the design service life:

[0026] C=(Δσ 1 (y),Δσ 2 (y),...,Δσ Nfs (y))

[0027] In the formula, Δσ Nfs (y) is the Nth position at yfs stress amplitude, the number of elements N in the vector is determined by the following formula fs :

[0028] N fs =δ×N d ×365

[0029] Where δ is the coefficient of stress cycle increase caused by sudden temperature change in a short period of time, and the value of δ is [1.05,1.20].

[0030] (4) Determine the equivalent fatigue temperature value

[0031] The equivalent temperature stress amplitude Δσ of railway steel box girder bridge section can be determined by the following formula: eqy :

[0032]

[0033] In the formula, C i is the i-th element in vector C.

[0034] (5) Constructing the temperature fatigue load model

[0035] The equivalent fatigue temperature value T is obtained by the following formula eqy ;

[0036]

[0037] Using Matlab software, we can analyze the different positions y and different design service life N. d The equivalent temperature value T eqy The least squares method is used for fitting and the vertical temperature gradient fatigue load model of railway steel box girder bridge is established as shown in formula (1).

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] 1. The vertical temperature gradient fatigue load model construction method proposed by the present invention using the Monte Carlo sampling method and the damage equivalence principle is highly efficient and easy to implement.

[0040] 2. The present invention utilizes the long-term measured data of the temperature field of railway steel box girders to construct a vertical temperature gradient fatigue load model suitable for the fatigue resistance design and evaluation of railway steel box girder bridges. The constructed vertical temperature gradient fatigue load model takes into account the influence of beam height, top plate width, bottom plate width and design service life. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is the temperature representative value distribution diagram of the vertical temperature gradient fatigue load model of the railway steel box girder bridge.

[0042] Figure 2A flow chart is constructed for the vertical temperature gradient fatigue load model for railway steel box girder bridges.

[0043] Figure 3 This is the layout diagram of the temperature measurement points for railway steel box girders.

[0044] Figure 4 This is the temperature history curve of railway steel box girder bridge.

[0045] Figure 5 It is the histogram of temperature stress amplitude of railway steel box girder bridge. DETAILED DESCRIPTION

[0046] The present invention is further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to these embodiments.

[0047] Example 1

[0048] The vertical temperature gradient fatigue load model of the railway steel box girder bridge involved in this embodiment is as shown in formula (1) by the positive temperature fatigue load model T + (y), negative temperature fatigue load model T-(y) consists of:

[0049]

[0050] In formula (1), y is the height of the position to be calculated, h is the section height, the unit is m, T 1 is the representative value of the temperature at the top plate of the railway steel box girder, T 2 is the representative value of the temperature of the railway steel box girder web at 0.6m from the top plate, in °C, T 3 is the representative value of the temperature of the railway steel box girder web at 1 / 2h from the top plate, in °C, T 4 is the representative value of the temperature at the bottom plate of the railway steel box girder, in °C, T 1 0 is the initial temperature of the top plate of the railway steel box girder, in °C, T 2 0 is the initial temperature of the railway steel box girder web at a distance of 0.6 m from the top plate, in °C, T 3 0 is the initial temperature of the railway steel box girder web at 1 / 2h from the top plate, in °C, T 4 0 is the initial temperature value at the bottom plate of the railway steel box girder, in ℃, B is the width of the top plate of the railway steel box girder, in m, b is the width of the bottom plate of the railway steel box girder, in m, a 1 、b 1 , β T (B), β T (h), β T (b) is the intermediate variable, N d It is the design service life in years.

[0051] In the present embodiment, the beam height h is selected as 4.8 m, the top plate width B is selected as 7.5 m, the bottom plate width b is selected as 5.8 m, and T 1 0 The value of T is 18.0℃, 2 0 The value of is 23.0℃, and the corresponding vertical temperature gradient fatigue load model is constructed. The temperature representative values ​​at different heights 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 this parameter is shown in Figure 1 shown.

[0052] Table 1 Representative values ​​of temperature for vertical temperature gradient fatigue load model of railway steel box girder bridge

[0053]

[0054] like Figure 2 As shown, the method for constructing the vertical temperature gradient fatigue load model of the railway steel box girder bridge is composed of the following steps:

[0055] (1) Determine the temperature stress amplitude vector

[0056] Temperature sensors are arranged on the top plate, bottom plate and diaphragm of the railway steel box girder bridge to collect temperature. The collection time interval is set to 1 minute to 20 minutes. The collected temperature gradient time history is T A (y, t), y is the coordinate of the vertical measuring point, and the temperature stress history σ is obtained by using the temperature stress formula of steel box girder bridge. A (y,t):

[0057]

[0058] 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 ​​railway steel box girder bridge, I is the moment of inertia of the railway steel box girder bridge section, y s is the neutral axis of the railway steel box girder bridge section, b(y) is the section thickness at the y position of the railway steel box girder bridge;

[0059] The stress cycles are counted using the rain flow counting method to obtain the temperature stress amplitude vector A:

[0060] A=(σ 1 (y),σ 2 (y),...,σ n (y))

[0061] In the formula, σ n(y) is the nth stress amplitude at position y, and n is the number of elements in vector A;

[0062] (2) Fitting the temperature stress amplitude vector

[0063] Based on the Weibull function, the probability function is fitted to the temperature stress amplitude vector A, and the probability density curve f(v) at the y position is obtained:

[0064]

[0065] Where, μ is the mean value of the temperature stress amplitude, σ is the variance of the temperature stress amplitude;

[0066] Choose a distribution g(v) and define parameter k so that k×g(v) is greater than f z (v), where g(v) is:

[0067]

[0068] (3) Temperature stress amplitude sampling

[0069] Take the sample point v 0 , and perform a single uniform sampling in the range [0, k×g(v)] to obtain the sampling value μ 0 , if μ 0 <f z (v), then the sample point v 0 is accepted, otherwise it will not be accepted and the step will be repeated; finally, all the accepted sample points constitute the temperature stress amplitude vector C of the design service life:

[0070] C=(Δσ 1 (y),Δσ 2 (y),...,Δσ Nfs (y))

[0071] In the formula, Δσ Nfs (y) is the Nfsth stress amplitude at position y, where Nfs is the number of elements in the vector;

[0072] N fs Determine by the following formula:

[0073] N fs =δ×N d ×365

[0074] Wherein, δ is the coefficient of stress cycle increase caused by temperature mutation in a short period of time, and its value is [1.05, 1.20]. In this embodiment, δ is 1.1;

[0075] (4) Determine the equivalent fatigue temperature value

[0076] The equivalent temperature stress amplitude Δσ of railway steel box girder bridge section can be determined by the following formula: eqy :

[0077]

[0078] In the formula, C i is the i-th element in vector C;

[0079] (5) Constructing the temperature fatigue load model

[0080] The equivalent fatigue temperature value T is obtained by the following formula eqy :

[0081]

[0082] Using Matlab software, the d The equivalent temperature value T eqy The least squares method is used for fitting and the vertical temperature gradient fatigue load model of railway steel box girder bridge is constructed as formula (1).

[0083] Example 2

[0084] The vertical temperature gradient fatigue load model of the railway steel box girder bridge involved in this embodiment is shown in formula (1).

[0085] In the present embodiment, the beam height h is selected as 3.0 m, the top plate width B is selected as 7.0 m, the bottom plate width b is selected as 5.0 m, and T 1 0 The value of T is 17.0℃, 2 0 The value of is 21.0°C, and the other parameters are the same as those in Example 1. The corresponding vertical temperature fatigue load model is constructed, and the temperature representative values ​​corresponding to 100 years, 150 years, and 200 years are shown in Table 2. The temperature representative value distribution of the vertical temperature gradient fatigue load model constructed according to the parameters is as follows: Figure 1 shown.

[0086] Table 2 Representative values ​​of temperature for vertical temperature gradient fatigue load model of railway steel box girder bridge

[0087]

[0088] The method for constructing the vertical temperature gradient fatigue load model of the railway steel box girder bridge is composed of the following steps:

[0089] (1) Determine the temperature stress amplitude vector

[0090] This step is the same as in Example 1.

[0091] (2) Fitting the temperature stress amplitude vector

[0092] This step is the same as in Example 1.

[0093] (3) Temperature stress amplitude sampling

[0094] Take the sample point v 0 , and perform a single uniform sampling in the range [0, k×g(v)] to obtain the sampling value μ 0 , if μ 0 <f z (v), then the sample point v 0 is accepted, otherwise it will not be accepted and the step will be repeated; finally, all the accepted sample points constitute the temperature stress amplitude vector C of the design service life:

[0095] C=(Δσ 1 (y),Δσ 2 (y),...,Δσ Nfs (y))

[0096] In the formula, Δσ Nfs (y) is the Nfsth stress amplitude at position y, and the number of elements Nfs in the vector is determined by the following formula:

[0097] N fs =δ×N d ×365

[0098] Wherein, δ is the coefficient of stress cycle increase caused by sudden temperature change in a short period of time, and the value of δ is [1.05, 1.20]. In this embodiment, the value of δ is 1.05.

[0099] The other steps are the same as those in Example 1. A vertical temperature gradient fatigue load model of a railway steel box girder bridge of formula (1) is constructed.

[0100] Example 3

[0101] The vertical temperature gradient fatigue load model of the railway steel box girder bridge involved in this embodiment is shown in formula (1).

[0102] In the present embodiment, the beam height h is selected as 8.0 m, the top plate width B is selected as 15.0 m, the bottom plate width b is selected as 12.0 m, and T 1 0 The value of T is 19.2℃, 2 0 The value of is 24.0°C, and the other parameters are the same as those in Example 1. The corresponding vertical temperature fatigue load model is constructed, and the temperature representative values ​​corresponding to 100 years, 150 years, and 200 years are shown in Table 3. The temperature representative value distribution of the vertical temperature gradient fatigue load model constructed according to the parameters is as follows: Figure 1 shown.

[0103] Table 3 Representative values ​​of temperature for vertical temperature gradient fatigue load model of railway steel box girder bridge

[0104]

[0105] The method for constructing the vertical temperature gradient fatigue load model of the railway steel box girder bridge is composed of the following steps:

[0106] (1) Determine the temperature stress amplitude vector

[0107] This step is the same as in Example 1.

[0108] (2) Fitting the temperature stress amplitude vector

[0109] This step is the same as in Example 1.

[0110] (3) Temperature stress amplitude sampling

[0111] Take the sample point v 0 , and perform a single uniform sampling in the range [0, k×g(v)] to obtain the sampling value μ 0 , if μ 0 <f z (v), then the sample point v 0 is accepted, otherwise it will not be accepted and the step will be repeated; finally, all the accepted sample points constitute the temperature stress amplitude vector C of the design service life:

[0112] C=(Δσ 1 (y),Δσ 2 (y),...,Δσ Nfs (y))

[0113] In the formula, Δσ Nfs (y) is the Nth position at y fs stress amplitude, the number of elements N in the vector is determined by the following formula fs :

[0114] N fs =δ×N d ×365

[0115] Wherein, δ is the coefficient of stress cycle increase caused by sudden temperature change in a short period of time, and the value of δ is [1.05, 1.20]. In this embodiment, the value of δ is 1.20.

[0116] The other steps are the same as those in Example 1. A vertical temperature gradient fatigue load model of a railway steel box girder bridge of formula (1) is constructed.

[0117] Test 1

[0118] In order to verify the effect of the vertical temperature gradient fatigue load model of the railway steel box girder bridge, vertical temperature sensors were arranged on the Lintong high-speed railway steel box girder bridge and long-term temperature field monitoring was performed, and the measured results were compared with the calculated results of the vertical temperature gradient fatigue load model of the railway steel box girder bridge using Example 1;

[0119] 1. Long-term monitoring instruments

[0120] The monitoring instrument is a 16-channel JM3812 multifunctional data acquisition instrument produced in Yangzhou, Jiangsu; the temperature acquisition software is the JMTEST static signal test and analysis software produced in Yangzhou, Jiangsu; the temperature sensor is a three-wire Pt100 sensor;

[0121] 2. Temperature measurement point arrangement

[0122] The top plate, bottom plate and web of the railway steel box girder bridge are selected to arrange temperature measuring points. The coordinate system is established with the center of the railway steel box girder bottom plate as the coordinate origin. A total of 8 measuring points are arranged vertically. The vertical distance from the lower surface of the railway steel box girder bottom plate is expressed as y. The positions of different measuring points are recorded as 0.0m, 0.6m, 2.4m, 3.4m, 4.3m, 4.5m, 4.7m, and 4.8m, respectively, and recorded as P 1 ~P 8 Where h represents any height; y = 0.0m means the measuring point is arranged on the bottom plate of the steel box girder, y = 4.8m means the measuring point is arranged on the top plate of the steel box girder, y = 0.6m, 2.4m, 3.4m, 4.3m, 4.5m, 4.7m means the measuring point is arranged on the web of the steel box girder respectively. The specific measuring point arrangement diagram is as follows Figure 3 The temperature collected at different height points is recorded as T te (y). From 2014 to 2020, continuous temperature collection was carried out at these measuring points to obtain effective monitoring data for nearly 6 years. The collection interval was 5 minutes, and the obtained temperature history curve was as follows: Figure 4 shown.

[0123] 3. Analysis of the effect of vertical temperature gradient fatigue load model

[0124] 1. Calculate the stress history curve σ at different heights according to the simplified formula of temperature stress obtained by transformation te (y, t), the stress history calculation formula is:

[0125]

[0126] Where: te (y,t) is the stress history of the steel box girder section, E s is the elastic modulus of steel, α s is the thermal expansion coefficient of steel, A is the cross-sectional area of ​​railway steel box girder, I is the moment of inertia of the railway steel box girder section, in this example, E s 206GPa, αs 1.1×10 -5 ℃ -1 .

[0127] Taking the bottom plate butt weld of railway steel box girder bridge as an example, at this time y = 0, the temperature stress history is drawn 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 temperature stress amplitude histogram. The results are as follows: Figure 5 The equivalent fatigue stress of the measured results was calculated and the result was 24.43MPa.

[0128] Based on the vertical temperature gradient fatigue load model of railway steel box girder bridge, the temperature stress history is constructed and the temperature stress amplitude analysis is performed. Where B = 7.5m, b = 5.8m, h = 4.8m, N d =100 years of design service life, substitute into the following formula:

[0129]

[0130] The equivalent temperature fatigue stress is 24.9MPa. The result is basically consistent with the measured equivalent fatigue stress, indicating that the vertical temperature fatigue load model of railway steel box girder bridge has good applicability.

Claims

1. A vertical temperature gradient fatigue load model for railway steel box girder bridge, characterized by: The model is shown in formula (1) by the positive temperature fatigue load model T + (y), Negative temperature fatigue load model T - (y)Composition: In formula (1), y is the height of the position to be calculated, h is the section height, in m, T1 is the representative temperature value at the top plate of the railway steel box girder, T2 is the representative temperature value at the web of the railway steel box girder 0.6 m away from the top plate, in °C, T3 is the representative temperature value at the web of the railway steel box girder 1 / 2 h away from the top plate, in °C, T4 is the representative temperature value at the bottom plate of the railway steel box girder, in °C, T1 0 is the initial temperature value at the top plate of the railway steel box girder, in °C. is the initial temperature of the railway steel box girder web at a distance of 0.6m from the top plate, in °C. is the initial temperature of the railway steel box girder web at 1 / 2h from the top plate, in °C. is the initial temperature of the bottom plate of the railway steel box girder, in °C, B is the width of the top plate of the railway steel box girder, in m, b is the width of the bottom plate of the railway steel box girder, in m, a1, b1, β T (B), β T (h), β T (b) is the intermediate variable, N d It is the design service life in years.

2. The vertical temperature gradient fatigue load model for railway steel box girder bridge according to claim 1 is characterized in that: In formula (1), the T1 0 The value is [17.0,19.2], the unit is ℃, The value of is [21.0, 24.0], the unit is ℃, the value of h is [3.0, 8.0], the unit is m, the value of b is [5.0, 12.0], the unit is m, and the value of B is [7.0, 15.0], the unit is m.

3. The vertical temperature gradient fatigue load model for railway steel box girder bridge according to claim 1 is characterized in that In formula (1), h, B, b, T1 0 , The values ​​are: h is 4.8m, B is 7.5m, b is 5.8m, T1 0 18.0℃, It is 23.0℃.

4. A method for constructing a vertical temperature gradient fatigue load model for a railway steel box girder bridge according to claim 1, characterized in that It consists of the following steps: (1) Determine the temperature stress amplitude vector Temperature sensors are arranged on the top plate, bottom plate and diaphragm of the railway steel box girder bridge to collect temperature. The collection time interval is set to 1 to 20 minutes, and the collected temperature gradient time history is T A (y, t), y is the coordinate of the vertical measuring point, and the temperature stress history σ is obtained by using the temperature stress formula of steel box girder bridge. 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 ​​railway steel box girder bridge, I is the moment of inertia of the railway steel box girder bridge section, y s is the neutral axis of the railway steel box girder bridge section, b(y) is the section thickness at the y position of the railway steel box girder bridge; The stress cycles are counted using the rain flow counting method to obtain the temperature stress amplitude vector A: A=(σ1(y),σ2(y),...,σ n (y)) In the formula, σ n (y) is the nth stress amplitude at position y, and n is the number of elements in vector A; (2) Fitting the temperature stress amplitude vector Based on the Weibull function, the probability function is fitted to the temperature stress amplitude vector A, and the probability density curve f(v) at the y position is obtained: Where, μ is the mean value of the temperature stress amplitude, σ is the variance of the temperature stress amplitude, and v is [0,2max(A)]; Choose a distribution g(v) and define parameter k so that k×g(v) is greater than f z (v), where g(v) is: (3) Temperature stress amplitude sampling Take the sample point v0 and perform a single uniform sampling in the range [0, k×g(v)] to obtain the sample value μ0. If μ0 <f z (v), the sample point v0 is accepted, otherwise it will not be accepted and the step will be repeated; finally, all the accepted sample points constitute the temperature stress amplitude vector C of the design service life: C=(Δσ1(y),Δσ2(y),...,Δσ Nfs (y)) In the formula, Δσ Nfs (y) is the Nth position at y fs stress amplitude, the number of elements N in the vector is determined by the following formula fs : N fs =δ×N d ×365 Where δ is the coefficient of stress cycle increase caused by temperature mutation in a short period of time, and its value is [1.05,1.20]; (4) Determine the equivalent fatigue temperature value The equivalent temperature stress amplitude Δσ of railway steel box girder bridge section can be determined by the following formula: eqy : In the formula, C i is the i-th element in vector C; (5) Constructing the temperature fatigue load model The equivalent fatigue temperature value T is obtained by the following formula eqy ; Using Matlab software, we can analyze the different positions y and different design service life N. d The equivalent temperature value T eqy The least squares method is used for fitting and the vertical temperature gradient fatigue load model of railway steel box girder bridge is established as shown in formula (1).

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