A method and device for evaluating temperature gradient mode distribution of a spatial three-curved steel box girder bridge

Abstract

The application discloses a temperature gradient mode distribution evaluation method for a spatial three-curved steel box girder bridge, which comprises the following steps: step 1, selecting a characteristic surface of a curved section of the spatial three-curved steel box girder bridge and arranging temperature measuring points; step 2, analyzing daily collected temperature data and fitting corresponding temperature gradient functions; step 3, statistically processing correction parameters and exponential parameters in all temperature gradient functions in step 2 to obtain corresponding statistical correction parameters and statistical exponential parameters; and step 4, substituting a daily temperature difference value of a to-be-measured point, a structural feature of a part where the to-be-measured point is located and the statistical correction parameters and the statistical exponential parameters obtained in step 3 into a temperature gradient function where the part is located to fit a temperature gradient distribution mode corresponding to a cross section of the to-be-measured point. The application further discloses a spatial three-curved steel box girder bridge evaluation device. The application is suitable for temperature evaluation tasks of all parts of a girder bridge, thereby providing more comprehensive guidance for subsequent girder bridge design.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge temperature measurement, and particularly relates to a temperature gradient mode distribution evaluation method and device for a spatial three-curved steel box girder bridge. BACKGROUND

[0002] City bridges need to be aesthetically pleasing and have beautiful lines in addition to meeting safety and durability requirements. Curved bridges can greatly improve the utilization of urban space and are very aesthetically pleasing. If designed properly, they can become a fascinating landscape. Steel bridges have the advantages of small self-weight, large carrying capacity, and good seismic performance, and are widely used in city bridges. However, existing city bridges are mostly two-dimensional flat curve bent bridges and vertical curve variable cross-section bridges.

[0003] In addition, temperature action is one of the variable actions of bridges and can be divided into uniform temperature action and gradient temperature action. Domestic and foreign researches usually ignore the longitudinal distribution of gradient temperature action, which can be further divided into transverse temperature gradient action and vertical temperature gradient action. Temperature gradient can cause different degrees of deformation of the fibers of the bridge cross-section, thereby generating self-balancing temperature self-stress in the cross-section. For curved bridges, temperature gradient action can cause serious accidents such as support shedding, bridge creep, and overturning, and cannot be ignored.

[0004] The calculation method of temperature gradient is: heat conduction differential equation, numerical solution, and semi-theoretical and semi-empirical formula. The heat conduction differential equation can give an analytical solution under given initial conditions and boundary conditions, but the calculation is very complex and is rarely used in engineering. Numerical solution is to convert the differential equation into the solution of equation groups by finite difference method or finite element method, and most commercial finite element software can provide solutions. Semi-theoretical and semi-empirical formula is relatively simple to apply and is strongly influenced by regional factors. It is necessary to study the temperature gradient distribution suitable for the bridge for bridges with special structural forms.

[0005] However, the temperature gradient distribution mode in the General Code for Design of Highway Bridges and Culverts (JTG D60-2015) is obtained by referring to the AASHTO specification of the United States, and there is no specific provision for steel box girders. Most current researches refer to the multi-segment broken line distribution mode of vertical temperature gradient for steel box girders in the British BS-5400 specification, and the distribution mode described by a nonlinear function is adopted in the specifications of the Netherlands and other countries.

[0006] Academic Literature Research on Vertical Temperature Gradient Model of Steel Box Girder - Taking a Steel Box Girder of a Viaduct in Wuhan as an Example [J]. Journal of Wuhan University, 2021, 43(02):202-206.DOI:10.19843 / j.cnki.CN42-1779 / TQ.201912003. Taking a variable cross-section continuous steel box girder bridge in Wuhan as the engineering background, this paper studies the vertical temperature gradient model of steel box girder and obtains the temperature change law of exponential function, but does not consider the influence of solar incidence angle on the temperature gradient of the top plate.

[0007] Patent document CN107391823A discloses a method for evaluating the temperature gradient pattern of a highway steel box girder bridge. It statistically analyzes and fits the temperature distribution of the top plate and web to obtain the distribution pattern, but it neglects the temperature gradient pattern of the closed curved panel under special cross-sections. For spatial triple-curved steel box girder bridges, the cross-sectional curve parameters and bridge alignment continuously change along the driving direction, causing the curve parameters and solar incidence angle to affect the temperature gradient pattern of different cross-sections. Existing temperature gradient distribution methods cannot adequately describe the temperature distribution patterns of the top plate, web, and curved panel of the cross-section. Summary of the Invention

[0008] To address the aforementioned issues, this invention provides a method for evaluating the temperature gradient pattern distribution of a spatial three-curved steel box girder bridge. This evaluation method is applicable to temperature evaluation tasks in all parts of the girder bridge, thereby providing more comprehensive guidance for subsequent girder bridge design.

[0009] A method for evaluating the temperature gradient pattern distribution of a spatial three-curved steel box girder bridge, comprising:

[0010] Step 1: Select the standard section, the section with the largest lateral change, and the section with the largest vertical change of the curved section of the spatial three-curved steel box girder bridge as characteristic surfaces, and arrange several temperature measuring points on the top plate, web plate, and curved plate of the section of the spatial three-curved steel box girder bridge. Temperature measuring points are also set at the intersection of the web plate and the top plate.

[0011] Step 2: Analyze the daily temperature data collected to obtain the extreme values ​​of the daily temperature difference at the two ends of the top plate and the center line of the road, the extreme values ​​of the daily temperature difference in the vertical direction of the web plate, and the extreme values ​​of the daily temperature difference at the starting point of the curved bottom plate. Based on the temperature data at the time corresponding to the extreme values ​​of the daily temperature difference, use temperature as the abscissa and the distance between measuring points as the ordinate to fit the corresponding temperature gradient functions respectively.

[0012] Step 3: Perform probability statistics on the correction parameters and exponential parameters in all temperature gradient functions from Step 2 to obtain the corresponding statistical correction parameters and statistical exponential parameters;

[0013] Step 4, the daily temperature difference value corresponding to the to-be-tested point, the structural features of the part where the to-be-tested point is located, and the statistical correction parameter and the statistical index parameter obtained in step 3 are substituted into the temperature gradient function corresponding to the part to obtain the temperature gradient distribution mode corresponding to the cross section of the to-be-tested point by fitting.

[0014] The method provided by the application fits the temperature gradient functions of multiple key parts, obtains corresponding statistical correction parameters and statistical index parameters, and recombines the statistical correction parameters, the statistical index parameters and the temperature gradient functions to obtain the corresponding temperature gradient distribution mode by taking the temperature data and the structural features of the to-be-tested point as inputs.

[0015] Specifically, the arrangement of the temperature measuring points comprises: adopting variable interval arrangement within a preset range from the two ends of the top plate, the top point of the web plate and the starting point of the curved plate, the interval of the variable interval arrangement comprising 0.07 m, 0.15 m, 0.25 m, 0.37 m and 0.5 m, and adopting equal interval arrangement outside the preset range, the interval of the equal interval arrangement being 0.5 m.

[0016] Preferably, in step 2, the temperature data should be collected in summer, sunny, small wind speed and strong sunlight weather, and the collection time interval is 1 h, so as to ensure the reliability of the temperature data.

[0017] Specifically, in step 2, the temperature distribution diagram comprises: a temperature gradient distribution diagram of the two ends of the top plate and the position of the center line of the road, a vertical temperature gradient distribution diagram of the web plate and a temperature gradient distribution diagram of the starting and ending points of the curved bottom plate.

[0018] Specifically, the temperature gradient distribution diagram of the two ends of the top plate and the position of the center line of the road is fitted by using a double exponential function of the solar incident angle correction parameter and the curve long axis index parameter:

[0019]

[0020] In the formula, T 01 is the temperature difference extreme value at the left end of the top plate and the position of the center line of the road, T 02 is the temperature difference extreme value at the right end of the top plate and the position of the center line of the road, f(θ a ) is the correction function of the solar incident angle on the left side of the top plate cross section, g(θ b ) is the correction function of the solar incident angle on the right side of the top plate cross section, μ1 and μ2 are long axis parameters, a1 and a2 are curve long axes, and x is a coordinate value with the center line of the road as the origin.

[0021] In the formula, f(θ a ) and g(θ b ) have the following specific expressions:

[0022]

[0023]

[0024] In the formula, θ a is the solar incidence angle on the left side of the top plate section, θ b is the solar incidence angle on the right side of the top plate section (related to the inclination angle of the section, the bridge azimuth angle, and the solar elevation angle and solar azimuth angle at the time), λ is a correction parameter, h s is the solar elevation angle (related to the bridge latitude, the solar declination angle at the time, and the solar hour angle).

[0025] The temperature gradient distribution diagram of the end point of the curved bottom plate is fitted by a double exponential product function of the long axis short axis exponential parameter:

[0026]

[0027] In the formula, T 03 is the temperature difference extreme value at the start point and end point of the curved plate, η1 is the long axis parameter, η2 is the short axis parameter, a is the long axis of the curve, b is the short axis of the curve, and s is the distance between the temperature measurement point and the start point.

[0028] The temperature gradient distribution of the web vertical is fitted by a single exponential function:

[0029] T=T 04 ·e -cy

[0030] In the formula, T 04 is the temperature difference extreme value of the web vertical, c is the exponential parameter, and y is the distance between the temperature measurement point and the top point of the web.

[0031] Specifically, in step 3, the statistical correction parameter and the statistical exponential parameter are respectively selected as the parameters corresponding to the maximum frequency in each statistical histogram.

[0032] Specifically, in step 4, the structural features of the part where the to-be-measured point is located include the section inclination angle and the azimuth angle.

[0033] The application also provides a spatial three-curved steel box girder bridge evaluation device, which comprises a memory and one or more processors, the memory stores executable code, and the one or more processors execute the executable code to implement the spatial three-curved steel box girder bridge temperature gradient distribution mode evaluation method.

[0034] The daily collected girder bridge temperature data are acquired, the temperature data are analyzed according to the spatial three-curved steel box girder bridge temperature gradient distribution evaluation method, and all the section temperature distribution modes of the girder bridge are output.

[0035] Compared with the prior art, the present application has the beneficial effects:

[0036] The present application is based on measured data, considers the correction parameters of the solar incident angle and the exponential parameters of the long axis and the short axis, fits the temperature collection data of three characteristic sections, obtains the temperature gradient distribution suitable for any section of the whole bridge, and thus provides more comprehensive guidance for the subsequent design of the beam bridge. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The flowchart of the temperature gradient mode distribution evaluation method provided for the present embodiment is shown in the figure;

[0038] Figure 2 The characteristic section view of the beam bridge provided for the present embodiment is shown in the figure;

[0039] Figure 3 The temperature measurement point view of the characteristic section of the beam bridge provided for the present embodiment is shown in the figure;

[0040] Figure 4 The temperature gradient distribution view of the characteristic section provided for the present embodiment is shown in the figure;

[0041] Figure 5 The probability distribution histogram of the daily temperature difference extreme value moment provided for the present embodiment is shown in the figure;

[0042] Figure 6 The roof temperature gradient fitting view provided for the present embodiment is shown in the figure;

[0043] Figure 7 The solar radiation angle relationship view provided for the present embodiment is shown in the figure;

[0044] Figure 8 The probability distribution histogram of the long axis parameter provided for the present embodiment is shown in the figure;

[0045] Figure 9 The curved plate temperature gradient fitting view provided for the present embodiment is shown in the figure;

[0046] Figure 10 The probability distribution histogram of the long axis and the short axis provided for the present embodiment is shown in the figure;

[0047] Figure 11 The web temperature gradient fitting view provided for the present embodiment is shown in the figure;

[0048] Figure 12 The probability distribution histogram of the exponential parameter provided for the present embodiment is shown in the figure. DETAILED DESCRIPTION

[0049] The present application will be further described in detail below in combination with the drawings and embodiments, but the present application is not limited to the following embodiment methods.

[0050] As Figure 1As shown, a method for evaluating the temperature gradient pattern distribution of a spatial three-curved steel box girder bridge includes:

[0051] Step 1, as follows Figure 2 As shown, the standard section of the curved segment of the spatial triple-curved steel box girder bridge is selected. Figure 2 a) The section with the largest lateral change ( Figure 2 (b) and the section with the largest vertical change ( Figure 2 c) is used as the feature surface.

[0052] Within a predetermined range from the two ends of the top slab, the apex of the web, and the starting point of the curved panel, the three-curved steel box girder bridge in this space adopts a variable-spacing arrangement. The spacing of the variable-spacing arrangement includes 0.07m, 0.15m, 0.25m, 0.37m, and 0.5m. Outside the predetermined range, an equal-spacing arrangement is adopted, with an interval of 0.5m. The specific distribution method is as follows: Figure 3 As shown in the figure, the circles represent the set temperature measurement points;

[0053] Step 2: Select a sunny day with low wind speed and strong sunshine between July and mid-August to collect temperature changes throughout the day, with a collection interval of 1 hour.

[0054] Based on the daily temperature data collected, the extreme daily temperature difference values ​​at the two ends of the top plate and the center line of the road, the extreme daily temperature difference values ​​in the vertical direction of the web plate, and the extreme daily temperature difference values ​​at the starting point of the curved bottom plate are obtained. The temperature data of each measuring point at the time when the top plate, web plate, and curved plate reach the extreme daily temperature difference values ​​are found. With temperature as the abscissa and the distance between measuring points as the ordinate, the temperature gradient distribution map of the top plate, web plate, and curved plate is drawn.

[0055] like Figure 4 As shown in the figure, d is the temperature gradient distribution map of the top plate, e is the temperature gradient distribution map of the web plate, and f is the temperature gradient distribution map of the curved plate. The corresponding temperature gradient function is obtained by fitting the temperature gradient distribution map.

[0056] Step 3: Perform statistical analysis on the times corresponding to the extreme daily temperature ranges to obtain a histogram of the probability distribution of the extreme daily temperature range times, such as... Figure 5 As shown, the value corresponding to the maximum frequency is finally taken as the time of the extreme value of the daily temperature difference.

[0057] The temperature gradient distribution of the roof plate was fitted using a bi-exponential sum function that considers the solar incidence angle correction parameter and the major axis exponent parameter, such as... Figure 6 As shown, this is the temperature gradient fitting of the top plate in a standard cross section:

[0058]

[0059] In the formula, T 01 The extreme temperature difference, T, is located at the left end of the roof slab and the center line of the road.02 is the temperature difference extreme value of the right end of the roof and the position of the road center line, f(θ a ) is the correction function of the solar incidence angle of the left side of the roof cross section, g(θ b ) is the correction function of the solar incidence angle of the right side of the roof cross section, μ1 and μ2 are the long axis parameters, a1 and a2 are the long axis of the curve, and x is the coordinate value with the road center line as the origin.

[0060] Wherein, the specific expression of f(θ a ) and g(θ b ) is as follows:

[0061]

[0062]

[0063] In the formula, θ a is the solar incidence angle of the left side of the roof cross section, θ b is the solar incidence angle of the right side of the roof cross section (related to the inclination angle of the cross section, the bridge azimuth angle, and the solar altitude angle and the solar azimuth angle at that time), λ is the correction parameter, h s is the solar altitude angle (related to the bridge latitude, the solar declination angle and the solar hour angle at that time).

[0064] Wherein, the solar radiation angle relationship is shown in Figure 7

[0065] sinh s =sinφsinδ+cosδcosφcosω

[0066] In the formula, φ is the bridge latitude, δ is the solar declination angle, and ω is the solar hour angle.

[0067] The expression of the solar declination angle is:

[0068] In the formula, D is the date sequence number from January 1st in a year, and July 23rd is selected as the daily temperature difference extreme value date.

[0069] The expression of the solar hour angle is:

[0070] ω=(12-t)×15°

[0071]

[0072] Δt=0.165sin2θ N -0.025sinθ N -0.126cosθ N

[0073] θ N ​= 360°(D - 81) / 364

[0074] cos θ = cos α sinh s + sin α cosh s cos(ψ - ψ0)

[0075] where h s is the solar elevation angle, α is the cross-section inclination angle, ψ0 is the bridge azimuth angle, and ψ is the solar azimuth angle.

[0076]

[0077] According to the corrected temperature difference extreme value divided by the daily measured temperature difference extreme value, the corresponding correction function is obtained.

[0078] According to the daily temperature difference extreme value moment and the date, the correction parameter λ in the correction function is least square fitted to obtain the λ value, and the fitting correlation degree is greater than 0.95.

[0079] The roof long axis parameters obtained by fitting are statistically analyzed to obtain the probability distribution histogram of the long axis parameters, as shown in Figure 8 The maximum frequency corresponding value in the histogram is selected as the roof long axis parameter.

[0080] The curved panel is fitted by a double exponential product function considering the long axis and short axis parameters of the curve, as shown in Figure 9 The temperature gradient fitting diagram of the quasi-section curved panel is shown in

[0081]

[0082] where T 03 is the temperature difference extreme value of the curved panel starting and ending point position, η1 is the long axis parameter, η2 is the short axis parameter, a is the long axis of the curve, b is the short axis of the curve, and s is the distance between the temperature measurement point and the starting point.

[0083] The long axis and short axis parameters of the curved panel obtained by fitting are statistically analyzed to obtain the probability distribution histogram of the long axis and short axis parameters, as shown in Figure 10 The maximum frequency corresponding value is selected as the long axis and short axis parameters of the curved panel.

[0084] The web is fitted by a single exponential function for temperature gradient distribution, as shown in Figure 11 The temperature gradient fitting diagram of the standard section web is shown in

[0085] T = T 04 · e -cy

[0086] where T 04 is the vertical temperature difference extreme value of the web, c is the exponential parameter, and y is the distance between the temperature measurement point and the web vertex.

[0087] The statistical analysis of the web index parameters obtained by fitting is performed to obtain the probability distribution histogram of the index parameters, as shown in Figure 12 The value corresponding to the maximum frequency is selected as the web index parameter.

[0088] Step 4. Obtain the temperature gradient distribution mode of each component of the spatial three-curved steel box girder bridge according to the statistical correction parameters and statistical index parameters determined by feature surface fitting.

[0089] The extreme value of the daily temperature difference, the cross-section inclination angle and the azimuth angle obtained by collection are brought into the temperature distribution function of the corresponding part, so that the corresponding temperature gradient distribution mode is obtained.

[0090] The embodiment also provides a spatial three-curved steel box girder bridge evaluation device, which comprises a memory and one or more processors, the memory stores executable code, and the one or more processors execute the executable code to implement the temperature gradient distribution mode evaluation method in the above embodiment, and the specific steps are as follows:

[0091] The girder bridge temperature data collected every day is obtained, the temperature data is analyzed according to the spatial three-curved steel box girder bridge temperature gradient distribution evaluation method, and all cross-section temperature distribution modes of the girder bridge are output.

Claims

1. A method for evaluating temperature gradient pattern distribution of a spatial three-curved steel box girder bridge, characterized in that, The method comprises the following steps: Step 1, selecting the standard section, the maximum transverse variation section and the maximum vertical variation section of the spatial three-curved steel box girder bridge as characteristic surfaces, and arranging a plurality of temperature measuring points on the top plate, web plate and curved plate of the spatial three-curved steel box girder bridge, and arranging temperature measuring points at the intersection of the web plate and the top plate; Step 2, analyzing the daily collected temperature data to obtain the transverse daily temperature difference extreme value of the two ends of the top plate and the position of the road center line, the vertical daily temperature difference extreme value of the web plate and the daily temperature difference extreme value of the starting point of the curved bottom plate, and according to the temperature data corresponding to the daily temperature difference extreme value, taking the temperature as the horizontal coordinate and the measuring point spacing as the vertical coordinate, the corresponding temperature gradient function is fitted to obtain the temperature gradient distribution of the two ends of the top plate and the position of the road center line, the vertical temperature gradient distribution of the web plate and the temperature gradient distribution of the starting and ending points of the curved bottom plate; The temperature gradient distribution of the top plate is fitted by a double exponential sum function considering the correction parameter of the solar incident angle and the long axis index parameter, and the standard cross-section temperature gradient fitting of the top plate is: ; wherein, is the temperature difference extreme value at the left end of the top plate and the position of the road center line, is the temperature difference extreme value at the right end of the top plate and the position of the road center line, is the correction function of the solar incident angle on the left side of the top plate section, is the correction function of the solar incident angle on the right side of the top plate section, and is the long axis parameter, and is the long axis of the curve, is the coordinate value with the road center line as the origin; wherein, and The specific expressions of and are as follows: ; ; wherein, is the solar incident angle on the left side of the top plate section, is the solar incident angle on the right side of the top plate section, is the correction parameter, is the solar elevation angle; the temperature gradient distribution of the curved bottom plate is fitted by a double exponential product function considering the long axis and short axis parameters of the curve, and the temperature gradient fitting of the quasi-cross-section curved plate is: ; wherein, is the temperature difference extreme value at the start and end positions of the curved plate, is the long axis parameter, is the short axis parameter, is the long axis of the curve, is the short axis of the curve, is the distance between the temperature measurement point and the start point; the temperature gradient distribution of the web vertically is fitted by a single exponential function, and the standard cross-section web temperature gradient fitting is: ; wherein, is the temperature difference extreme value of the web vertically, is the exponential parameter, is the distance between the temperature measurement point and the top of the web; step 3, according to the correction parameters and the exponential parameters in all the temperature gradient functions in step 2, the corresponding statistical correction parameters and statistical exponential parameters are obtained; Step 4, substituting the daily temperature difference value of the to-be-measured point, the structural characteristics of the part where the to-be-measured point is located, and the statistical correction parameter and the statistical index parameter obtained in step 3 into the temperature gradient function of the corresponding part to fit the temperature gradient distribution mode corresponding to the to-be-measured point section.

2. The method of claim 1, wherein the temperature gradient pattern distribution of the spatial three-curved steel box girder bridge is evaluated by using a finite element analysis program. In step 1, the arrangement of the temperature measuring points comprises: arranging with variable spacing within a predetermined range from the two ends of the top plate, the top of the web plate and the starting point of the curved plate, the variable spacing comprises 0.07m, 0.15m, 0.25m, 0.37m and 0.5m, and arranging with equal spacing outside the predetermined range, the interval of the equal spacing is 0.5m.

3. The method of claim 1, wherein the temperature gradient pattern distribution of the spatial three-curved steel box girder bridge is evaluated by using a finite element analysis program. In step 2, the temperature data should be collected in the summer sunny, small wind speed and strong sunlight weather, the collection time interval is 1h, and the collection days are not less than 10 days.

4. The method of claim 1, wherein the temperature gradient pattern distribution of the spatial three-curved steel box girder bridge is evaluated by using a finite element analysis program. The temperature gradient distribution diagram of the two ends of the top plate and the position of the road center line is fitted by using a double exponential sum function of the solar incident angle correction parameter and the long axis index parameter; The temperature gradient distribution diagram of the vertical temperature gradient distribution of the web plate is fitted by using a single exponential function; The temperature gradient distribution diagram of the starting and ending points of the curved bottom plate is fitted by using a double exponential product function of the long axis and short axis index parameters.

5. The method of claim 1, wherein the temperature gradient pattern distribution of the spatial three-curved steel box girder bridge is evaluated by using a finite element analysis program. In step 3, the statistical correction parameter and the statistical index parameter are respectively selected as the parameters corresponding to the maximum frequency in each statistical histogram.

6. The method of claim 1, wherein the temperature gradient pattern distribution of the spatial three-curved steel box girder bridge is evaluated by using a finite element analysis program. In step 4, the structural characteristics of the part where the to-be-measured point is located include the section inclination angle and the azimuth angle.

7. A spatial three-curved steel box girder bridge evaluation device, characterized in that, The memory stores executable code, and the one or more processors execute the executable code to implement the spatial three-curved steel box girder bridge temperature gradient mode distribution evaluation method according to any one of claims 1-6, and the specific steps are as follows: obtaining the daily collected girder bridge temperature data, analyzing the temperature data according to the spatial three-curved steel box girder bridge temperature gradient distribution evaluation method, and outputting all section temperature distribution modes of the girder bridge.

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