Method for establishing temperature gradient of double-layer steel truss girder under action of solar radiation

Abstract

The invention discloses a method for establishing a temperature gradient of a double-layer steel truss girder under solar radiation, which comprises the following steps of: S1, calculating a solar elevation angle alpha s (t) and a solar azimuth angle gamma (t) according to the latitude and longitude of a bridge site, an hour angle and a solar declination; projecting the solar ray vector to the cross section of the main beam according to the included angle xi between the axis of the main beam and the east-west direction to obtain a solar incident angle theta (t) in the cross section; s2, respectively deducing solar radiation areas of an upper-layer bridge floor, a lower-layer bridge floor and web members on the basis of a solar incident angle theta (t) and geometric parameters of the bridge; s3, establishing a temperature field formula related to the solar radiation duration, the air temperature, the material attribute, the surface direction and the coating; s4, temperature gradients of the upper-layer bridge floor, the lower-layer bridge floor and the web members are calculated according to the solar radiation area and a temperature field formula, and the most unfavorable temperature gradient and the corresponding moment are determined; according to the scheme, a reliable temperature working condition basis is provided for temperature effect analysis, stress evaluation and structural design of the double-layer steel truss girder.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically to a method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation. Background Technology

[0002] Double-deck steel truss main girders are a typical structural form for modern road-rail bridges due to their excellent load-bearing and spanning capabilities and economic efficiency. The temperature effect of the double-deck steel truss main girder directly impacts its structural safety and long-term service performance. The temperature gradient caused by solar radiation is one of the key factors leading to uneven deformation of the main girder, support misalignment, and even localized stress exceeding limits; especially in east-west oriented bridges, changes in the solar azimuth angle cause more significant vertical and lateral temperature gradients.

[0003] Current bridge specifications often use temperature gradient models for main girders based on simple structures or specific environmental conditions, primarily referencing single structural forms such as highway box girders. However, the double-layer steel truss main girder structure is unique, with its upper and lower layers influencing each other. The general models in the specifications are difficult to accurately adapt and cannot precisely reflect its temperature distribution and gradient characteristics. Furthermore, the specifications oversimplify the consideration of solar radiation, resulting in several shortcomings: the crisscrossing members of the double-layer steel truss main girder mean the specifications do not consider the shading effect of the upper structure on the lower structure, making it impossible to reflect temperature changes in shaded areas; solar altitude angle, azimuth angle, and other solar radiation conditions change over time, while the specifications often use fixed parameters for simulation, failing to reflect actual changes; in addition, the specifications rarely address the impact of seasonal and regional climate differences on temperature gradients. These issues lead to significant discrepancies between the temperature gradient models in the specifications and actual conditions.

[0004] Therefore, this study takes the double-layer steel truss main beam as the research object, considers the effect of solar radiation, derives the functional relationship between temperature gradient and solar radiation parameters, and establishes a temperature gradient model for the double-layer steel truss main beam. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this invention provides a method for establishing a temperature gradient for a double-layer steel truss main beam that takes into account the effects of solar radiation, thus solving the problem that existing bridge temperature gradient specifications are difficult to adapt to double-layer steel truss main beam structures.

[0006] By accurately deriving the time-varying region of solar radiation, the relationship between the structural temperature field and the environment, a temperature gradient model for the upper deck, lower deck and web members of the double-layer steel truss main girder was established. This provides a reference for calculating the temperature effect of the double-layer steel truss main girder structure under solar radiation and provides a basis for relevant specifications for similar main girder temperature gradient models.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation is provided, which includes the following steps: S1: Calculate the solar altitude angle α based on the bridge site's latitude and longitude, hour angle, and solar declination. s ( t ) and solar azimuth c ( t ); and based on the angle between the main beam axis and the east-west direction. x By projecting the vector of sunlight onto the cross section of the main beam, the angle of solar incidence within the cross section can be obtained. i ( t ); S2: Based on solar incidence angle i ( t Based on the bridge's geometric parameters, the solar radiation zones of the upper deck, lower deck, and web members are derived respectively. S3: Establish temperature field formulas related to solar radiation duration, air temperature, material properties, surface orientation, and coatings; S4: Calculate the temperature gradients of the upper bridge deck, lower bridge deck, and web members based on the solar radiation region and temperature field formulas, and determine the most unfavorable temperature gradient and its corresponding time.

[0008] Furthermore, the angle of solar incidence i ( t The formula for calculating ) is:

[0009] The formula for calculating the width of the solar radiation zone on the upper bridge deck is:

[0010] in, B ht This refers to the width of the solar radiation zone on the upper bridge deck. B f The width of the cantilever. B e Excluding the width of the upper bridge deck of the cantilever structure, B dt To reduce the width of the shaded area for the bridge railings, H l This refers to the height of the bridge railings. The formula for calculating the width of the solar radiation zone on the lower bridge deck is:

[0011] in, B hb This refers to the width of the solar radiation zone on the lower bridge deck. B b This refers to the area of ​​solar radiation shielded by the upper bridge deck. HThe height from the upper surface of the upper bridge deck to the upper surface of the lower bridge deck of the double-layer steel truss main beam; The struts include the sun-facing struts, the middle struts, and the shaded struts. The formula for calculating the height of the solar radiation zone of the sun-facing struts is as follows:

[0012] in, H s1 The height of the solar radiation zone on the sun-facing side of the ventral pole. H d1 The height of the shaded area of ​​the sunlit side ventral bar; The formula for calculating the height of the solar radiation zone in the middle section of the strut is:

[0013] in, H s2 This refers to the height of the solar radiation region in the middle section of the trunk. H d2 The height of the shaded area of ​​the middle section of the web; The formula for calculating the height of the solar radiation zone on the shady side of the ventral bar is as follows:

[0014] in, H s3 The height of the solar radiation zone on the ventral side of the pole. H d3 The height of the shaded area on the ventral side of the pole.

[0015] Furthermore, the temperature field formula is:

[0016] in, s The geometric dimensions are the independent variables. t s The independent variable is the cumulative time of solar radiation. T a The ambient temperature near the bridge site. k m The temperature conversion coefficient of solar radiation intensity for materials. k s For surface geometric coefficients, I ( s ( ) represents the intensity of solar radiation. After sunrise, when s If the region is a solar radiation area, then the solar radiation intensity is equal to the direct solar radiation. I d ,when s If it is a shaded area, then the solar radiation intensity I Solar scattered radiation I s ,I d , I s Measurements were taken from a meteorological station near the bridge site. α The solar radiation absorption rate of the material surface. k This is the heating rate coefficient.

[0017] Furthermore, the method for establishing the temperature gradient of the upper bridge deck in step S4 is as follows: Substitute the geometric parameters of the solar radiation range of the upper bridge deck into the input s When 0≤ s ≤ B ht hour, s For the solar radiation area, when B ht ≤ s ≤ 2B f +B e hour, s The area is shaded; Total temperature integral of the solar radiation area and the shaded area of ​​the upper bridge deck T s1 , T s2 They are respectively:

[0018]

[0019] The equivalent temperature of the solar radiation area and the shadow area on the upper bridge deck T e1 , T e2 They are respectively:

[0020]

[0021] The temperature gradient of the upper bridge deck T ht for: .

[0022] Furthermore, by differentiating the temperature gradient of the upper bridge deck and setting it to zero, the cumulative radiation time corresponding to the most unfavorable temperature gradient is obtained as follows: Then the time corresponding to the most unfavorable temperature gradient on the upper bridge deck is t a + t s1 , t aIf the sunrise time is given, then the most unfavorable temperature gradient on the upper bridge deck is: .

[0023] Furthermore, the temperature gradient of the lower bridge deck is calculated using the same method as that used to establish the temperature gradient of the upper bridge deck, thus obtaining the temperature gradient of the lower bridge deck. T hb for:

[0024] in, T e3 , T e4 These are the equivalent temperatures of the solar radiation area and the shaded area of ​​the lower bridge deck, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient on the lower bridge deck is The time corresponding to the most unfavorable temperature gradient on the lower bridge deck is t a + t s2 Then the most unfavorable temperature gradient of the lower bridge deck is: .

[0025] Furthermore, the temperature gradients of the sun-facing side web members, the middle web members, and the shady side web members were calculated according to the method for establishing the temperature gradient of the upper bridge deck. Temperature gradient of sun-facing side bar T f1 for:

[0026] in, T e5 , T e6 These are the equivalent temperatures of the solar radiation region and the shaded region on the sun-facing side of the ventral rod, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient on the sun-facing side bar is The time corresponding to the most unfavorable temperature gradient on the sun-facing side bar is t a + t s3 The most unfavorable temperature gradient on the sun-facing side of the ventral bar is:

[0027] Temperature gradient of the middle web T f2 for:

[0028] in, T e7 ,T e8 These are the equivalent temperatures of the solar radiation region and the shadow region of the mid-section of the basal bar, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient in the middle web is: The time corresponding to the most unfavorable temperature gradient in the middle section of the web is t a + t s4 The most unfavorable temperature gradient for the middle section of the spindle is:

[0029] Temperature gradient on the ventral side of the sun T f3 for:

[0030] in, T e9 , T e10 These are the equivalent temperatures of the solar radiation region and the shaded region on the ventral side of the rod, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient on the ventral side of the rod is The time corresponding to the most unfavorable temperature gradient on the shaded side is t a + t s5 The most unfavorable temperature gradient on the shaded side is: .

[0031] Furthermore, the method for establishing the temperature gradient from the upper bridge deck to the shaded area of ​​the web members is as follows: Based on the temperature field formula and the temperature decay region H w Calculate the temperature decay slope ， The calculation formula is as follows:

[0032] in, T 4( H , t s ( ) represents the temperature of the upper bridge deck. k 1 represents the temperature decay slope of the sun-facing side brace. k 2 represents the slope of temperature decay in the web of the middle section. k 3 represents the temperature decay slope of the ventral bar on the shaded side, and its calculation formulas are as follows: ; ;

[0033] Using the intersection of the upper bridge deck and each web member as the origin, and the width direction as the abscissa and the height direction as the ordinate, the temperature gradient distribution from the upper bridge deck to the shaded areas of the sun-facing web members, the middle web members, and the shaded web members is plotted. T t1 , T t2 , T t3 They are respectively: ; ;

[0034] The cumulative radiation time corresponding to the most unfavorable temperature gradient of the sun-facing ventral rod, the middle ventral rod, and the shaded ventral rod. , , The most unfavorable temperature gradients from the upper bridge deck to the shaded areas of the sun-facing web members, the middle web members, and the shaded web members are as follows: ; ; .

[0035] The beneficial effects of this invention are as follows: 1. This scheme systematically quantifies the shading of the upper bridge deck from the lower bridge deck, the web members, and the railings from the bridge deck, accurately deriving the time-varying regions of solar radiation. This transforms the division of "sunny" and "shaded" regions in temperature field calculations from rough estimation to precise calculation based on geometric optics, fundamentally improving the physical realism of temperature distribution simulation. Simultaneously, this scheme obtains the solar altitude and azimuth angles in real time and projects them onto the main beam section to obtain the solar incidence angle that changes over time. This mechanism ensures that the model can automatically adapt to changes in the solar trajectory throughout the day, from sunrise to sunset, and across different seasons, making the calculation results dynamic, continuous, and more consistent with natural laws.

[0036] 2. The temperature field formula of this scheme is a model that considers multiple parameters such as bridge site latitude and longitude, season, time, material coating, and structural geometry. This model does not require changes to the core algorithm. By simply adjusting the input parameters, it can be applied to double-deck steel truss bridges with different geographical environments, different climate conditions, different coating schemes, and different structural dimensions, thus improving the versatility and accuracy of the model in complex environments.

[0037] 3. This scheme calculates the temperature gradient patterns for the upper bridge deck, lower bridge deck, and web members at different locations (sun-facing side, middle section, and shaded side). This refined output for each part can be directly used as load input conditions for finite element analysis or structural design, accurately assessing the stress state of each component under sunlight. Simultaneously, it determines the most unfavorable moment when the temperature gradient reaches its extreme value for each part and outputs the gradient value at that moment. This provides a controlling load condition for structural safety and fatigue analysis, ensuring the structure's safety reserve under the most demanding temperature conditions.

[0038] 4. This scheme establishes a complete analytical theory and methodology system for the characteristics of double-layer steel truss main beams, effectively filling the gaps and limitations of existing specifications. It provides a reliable temperature condition basis for the temperature effect analysis, stress assessment, and structural design of double-layer steel truss main beams, which helps to avoid structural damage caused by temperature gradients and extend the service life of bridges. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The above and other objects, features, and advantages of the present invention will become clearer through the accompanying drawings. The same reference numerals indicate the same parts in all the drawings. The drawings are not intentionally drawn to scale to actual dimensions; the focus is on illustrating the main points of the invention.

[0040] Figure 1 A flowchart illustrating the method for establishing the temperature gradient of a double-layer steel truss main beam.

[0041] Figure 2 This is a schematic diagram showing the projection of air temperature, main beam parameters, and solar altitude angle within the main beam cross-section.

[0042] Figure 3 This is a schematic diagram of the sunlight effect on the double-layer steel truss main beam at 7 o'clock.

[0043] Figure 4 This is a schematic diagram of the sunlight effect on the double-layer steel truss main beam at 2 PM.

[0044] Figure 5 This is a schematic diagram showing the parameter annotations and temperature gradient mode for the double-layer steel truss main beam.

[0045] Figure 6 This is a schematic diagram comparing the calculated and measured temperature gradients of highway bridge surfaces in summer.

[0046] Figure 7 This is a schematic diagram comparing the calculated and measured temperature gradients of highway bridge surfaces in winter. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0048] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0049] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0050] Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0051] like Figure 1 to Figure 5 As shown, this scheme provides a method for establishing the temperature gradient of a double-layer steel truss main girder under solar radiation. This includes deriving the time-varying regions of solar radiation on the upper deck, lower deck, and web members of the double-layer steel truss main girder based on the bridge site, bridge alignment, and solar radiation conditions; and solving the temperature gradient action mode of the upper deck, lower deck, and web members of the double-layer steel truss main girder based on the time-varying regions of solar radiation and the Fourier heat conduction differential equation. This invention takes a double-layer steel truss Yangtze River railway-highway bridge as an example, and the specific method for establishing the temperature gradient mode of its double-layer steel truss main girder is as follows: S1: Calculate the solar altitude angle based on the latitude and longitude of the bridge site; calculate the angle between the sunlight and the horizontal plane within the cross section of the main beam based on the solar altitude angle and the direction of the main beam.

[0052] Solar declination d Hour angle oh The formulas are as follows:

[0053]

[0054] In the formula, D is the day number. In this embodiment, the calculation is based on the date of the highest summer temperature, August 6, 2024, and the date of the lowest winter temperature, March 38, 2025. Therefore, D is 219 and 39 respectively. Substituting these values, we can obtain... dx =16.4、 d d =-15.9, where in this embodiment the subscript x represents summer and the subscript d represents winter; t The time is local time. In this embodiment, the longitude of the bridge is 118°04′29″-118°29′52″. Since the most unfavorable temperature gradients for each structure of the double-layer steel truss main beam are not at the same time, the time of the highest daily temperature, 14:00, is used for calculation. Substituting this, we can obtain... oh =0.52.

[0055] Solar altitude angle a s ( t ), Sun azimuth c ( t The formulas are as follows:

[0056]

[0057] In the formula, f The bridge site latitude is 31°26′18″-32°03′39″ N. We will use 32° for calculation. f =32° d x =16.4、 d d Substituting -15.9 and ω=0.52, we get... α sx =1.02、 α sd =0.75、 c x =1.18、 c d =0.63.

[0058] The angle between the sun's rays and the horizontal plane within the cross-section of the double-layer steel truss main beam (hereinafter referred to as the solar incidence angle) is the projection angle obtained by projecting the solar altitude angle onto the cross-section of the main beam. The angle between the main beam's orientation and the east-west direction is... x In this embodiment x =0, the projection of the solar altitude angle onto the main beam section plane from a three-dimensional perspective is as follows: Figure 2 As shown; by performing vector decomposition on the solar altitude angle, the vertical component of the solar altitude angle is: sin( a s ( t )) The horizontal projection component of the solar altitude angle within the main beam section is: cos( a s ( t))·cos( c ( t )+ x ) Then we have:

[0059] Simplifying, we get:

[0060] Will α sx =1.02、 α sd =0.75、 c x =1.18、 c d =0.63、 x Substituting =0, we get... i x =1.35、 i d =0.71.

[0061] S2: Solving for the time-varying region of solar radiation: S21: Solve for the time-varying region of solar radiation under the shading effect of the upper bridge deck railing on the double-layer steel truss main beam, i.e. the region affected by the temperature gradient on the upper bridge deck.

[0062] The parameters of the double-layer steel truss main girder bridge deck are as follows: Figure 3 , 4 As shown, the width of the upper bridge deck is... B t for: B t =2 B f + B e = B ht + B dt In the formula, B f The width of the cantilever. B e In this embodiment, the road width is... B f =1.8 m B e =31.0 m; B ht This refers to the width of the solar radiation zone on the upper bridge deck. B dt This represents the width of the shaded area on the upper bridge deck.

[0063] According to the angle of solar incidence i railing height H l The width of the shaded area on the upper bridge deck is... B dt for:

[0064] In the formula, H l =1.6 m, calculate the width B of the solar radiation area on the upper deck of the double-layer steel truss main beam. ht for:

[0065] Will B f =1.8 m B e =31.0 m、 H l =1.6 m i x =1.35、 i d Substituting =0.71, we get B htx =34.2 m、 B htd =34.0 m.

[0066] S22: Solve for the time-varying region of solar radiation on the lower deck of the double-layer steel truss main beam under the shading effect of the upper deck, i.e. the region affected by the temperature gradient of the lower deck.

[0067] According to the angle of solar incidence i Height of the double-layer steel truss main beam H The area illuminated by sunlight B b for:

[0068] The height of the lower bridge deck railing is H l The width of the shadow cast by the railing is:

[0069] Based on geometric relationships, the width B of the solar radiation zone on the lower bridge deck is... hb for:

[0070] Will B f =1.8 m H =15.5 m i x =1.35、 i d Substituting =0.71, we get B hbx =1.32 m、 B hbd =14.94 S23: Solve for the time-varying region of solar radiation in the web members of the double-layer steel truss main beam under the shading effect of the upper bridge deck, i.e. the region of influence of the web member temperature gradient.

[0071] S231: Solar radiation temporal variation region on the sun-facing ventral bar: like Figure 4 As shown, the distance from the centerline of the sun-facing side brace to the end point of the sun-facing side cantilever is... B S1 for:

[0072] The shaded area on the sunlit side of the abdomen. H d1 for:

[0073] The height of the solar radiation zone on the sun-facing side of the ventral pole. H s1 for:

[0074] Will H =15.5 m B f =1.8 m i x =1.35、 i d Substituting =0.71, we get H s1x =7.48 m H s1d =13.9m.

[0075] S232: Time-varying region of solar radiation in the middle section of the belly bar: like Figure 4 As shown, the distance from the centerline of the middle web member to the end point of the cantilever on the sun-facing side is... B S2 for:

[0076] The shaded area of ​​the middle section of the belly rod. H d2 for:

[0077] The height of the solar radiation region of the middle section of the trunk. H s2for:

[0078] Will H 1 = 15.5 m B f =1.8 m B e =31.0 m、 i x =1.35、 i d Substituting =0.71, we get H s2x =0 m、 H s2d =0.63 m.

[0079] S233: Temporally varying region of solar radiation on the shady ventral side of the bar: Depend on Figure 4 It can be seen that the distance from the center line of the ventral pole on the shady side to the end point of the cantilever on the sunny side is... B S3 for:

[0080] The shaded area on the lateral side of the abdomen. H d3 for:

[0081] The height of the solar radiation zone on the ventral side of the pole. H s3 for:

[0082] In the formula, H The height of the web member is shown in this embodiment. H =15.5 m, will H =15.5 m B f =1.8 m B e =31.0m i x =1.35、 i d Substituting =0.71, we get H s3x =0 m、 H s3d =0 m.

[0083] S3: Solve for the magnitude of the temperature gradient within the solar radiation region of each structure.

[0084] Based on the solar radiation region of the double-layer steel truss main girder, formulas related to solar radiation duration, bridge site air temperature, steel materials, and coatings can be established, thus revealing the structural temperature field. T ( t )for:

[0085] in, T a The ambient temperature near the bridge site; k m The solar radiation intensity temperature conversion coefficient of the material varies with the type of material; the value is 0.02 for steel and 0.03 for asphalt. k s This is the surface geometry coefficient; when the surface receiving thermal radiation is a horizontal plane, k s When the heat-radiating surface is vertical, the value is 1.0. k s Take 0.5; I Solar radiation intensity; α The solar radiation absorption rate of the steel surface is mainly affected by the color of the surface coating. The value is 0.8 for dark coatings, 0.6 for medium coatings, and 0.3 for light coatings. k This is the rate of warming, when the weather is sunny. k Take 0.3, when the weather is cloudy. k Take 0.15; t This represents the cumulative time of solar radiation.

[0086] Therefore, the structural temperature field at any time can be obtained. T ( s , t s ),in, s Geometric dimensions are the independent variables. ，t s The cumulative time of solar radiation is the independent variable.

[0087] S31: Temperature gradient mode of the upper deck of the double-layer steel truss main girder: From temperature field T ( s , t s The equivalent temperature of the solar radiation area on the upper bridge deck is then... T e1 for:

[0088] Equivalent temperature of the shaded area of ​​the upper bridge deck T e2 for:

[0089] upper bridge deck temperature gradient T ht for:

[0090] According to temperature data from the meteorological station near the bridge, at 2:00 PM, in summer... T a The value is 37.3 ℃, in winter. T a Value: -3.2℃; Sunrise at 8:00 AM. t s The value is 7 h; the upper deck of the main beam is paved with asphalt. α The value is 0.8, and the lower bridge deck is paved with ballast and concrete pavement. α Value: 0.8; Summer direct solar radiation intensity I ax The summer diffuse radiation intensity is 814 W / m². I sx 254 W / m²; Winter direct solar radiation intensity I ad The winter diffuse radiation intensity is 572 W / m². I sd It is 101 W / m². Also... B ht夏 =34.2 m、 B ht冬 =34.0 m、 B f =1.8 m B e =31 m, substituting the parameters, we get T e1x =48.7 ℃, T e2x =40.8 ℃, T e1d =4.8 ℃, T e2d =-1.8 ℃, then T htx =7.9 ℃ T htd =6.6 ℃; right T ht ( t s Taking the derivative to zero, we can find the time corresponding to the most unfavorable temperature gradient. t When 1 = 14.

[0091] S32: Temperature gradient mode of the lower deck of the double-layer steel truss main girder: From temperature fieldT ( s , t s The equivalent temperature of the solar radiation area on the lower bridge deck is then... T e3 for:

[0092] Equivalent temperature of the shaded area of ​​the lower bridge deck T e4 for:

[0093] The temperature gradient of the lower bridge deck T hb for:

[0094] Will T ax =37.3 ℃ T ad =-3.2 ℃、 t s =7 h、 α =0.8、 I ax =814 W / m² I sx =254 W / m² I ad =572 W / m² I sd =101 W / m² B hb夏 =1.68 m B hb冬 =16.2 m、 B f Substituting = 1.8 m, we get T hbx =7.9℃ T hbd =6.6 ℃; right T hb ( t s Taking the derivative to zero, we can find the time corresponding to the most unfavorable temperature gradient. t When 2=14.

[0095] S33: Temperature gradient mode of web members in double-layer steel truss main beam: S331: Temperature gradient on the sun-facing side brace: From temperature field T ( s , ts Then, the temperature field of the sun-facing web members of the double-layer steel truss main beam, varying along its height, can be assumed to be: T 1( s , t s The equivalent temperature of the solar radiation region on the sun-facing side of the ventral rod is then... T e5 for:

[0096] Equivalent temperature of the shaded area of ​​the sunlit lateral ventral rod T e6 for:

[0097] Temperature gradient on the sun-facing side of the bar T f1 for:

[0098] Will T ax =37.3 ℃ T ad =-3.2 ℃、 t s =7 h、 α =0.8、 I ax =814 W / m² I sx =254 W / m² I ad =572 W / m² I sd =101 W / m² k s =0.5、 H s1x =7.48 m H s1d =13.9 m H =15.5 m, substituting, we get T f1x =4.0 ℃ T f1d =3.3 ℃.

[0099] right T f1 ( t s Taking the derivative to zero, we can find the time corresponding to the most unfavorable temperature gradient. t When 3 = 14.

[0100] S332: Temperature gradient of the web of the middle section: From temperature field T ( s , t s Then, we can assume that the temperature field of the web members in the middle section of the double-layer steel truss main beam varies along the height as follows: T 2( s , t s ), then the equivalent temperature of the solar radiation region in the middle section of the belly bar. T e7 for:

[0101] Equivalent temperature of the shaded area of ​​the middle web rod T e8 for:

[0102] Then the temperature gradient of the web of the middle plate T f2 for:

[0103] Will T ax =37.3 ℃ T ad =-3.2 ℃、 t s =7 h、 α =0.8、 I ax =814 W / m² I sx =254 W / m² I ad =572 W / m² I sd =101 W / m² k s =0.5、 H s1x =7.48 m H s1d =13.9 m H =15.5 m, substituting, we get T f2x =4.0 ℃ T f2d =3.3 ℃.

[0104] right T f2 ( t s Taking the derivative to zero, we can find the time corresponding to the most unfavorable temperature gradient. t When 4 = 14.

[0105] S333: Temperature gradient on the ventral side of the sun-facing side: From temperature field T ( s , t s Then, the temperature field of the double-layer steel truss main beam's shady side web members varying along the height can be assumed to be: T 3( s , t s The equivalent temperature of the solar radiation region on the ventral side of the rod is then calculated. T e9 for:

[0106] Equivalent temperature of the shaded area on the lateral side of the trunk T e10 for:

[0107] Temperature gradient on the ventral side of the shaded side T f3 for:

[0108] Will T ax =37.3 ℃ T ad =-3.2 ℃、 t s =7 h、 α =0.8、 I ax =814 W / m² I sx =254 W / m² I ad =572 W / m² I sd =101 W / m² k s =0.5、 H s1x =7.48 m H s1d =13.9 m H =15.5 m, substituting, we get T f3x =4.0 ℃ T f3d =3.3 ℃.

[0109] right T f3 ( t sTaking the derivative to zero, we can find the time corresponding to the most unfavorable temperature gradient. t 5 = 16.

[0110] S334: Temperature gradient from the upper bridge deck to the shaded area of ​​the web strut: The temperature gradient from the upper bridge deck to the shaded area of ​​the web members is mainly due to the temperature attenuation caused by the heating effect of the web members on the solar radiation area of ​​the upper bridge deck, according to the temperature field. T ( x , y,z The temperature decay region can be set as follows: H w In this embodiment H w =0.8m, then the temperature decay slope k for:

[0111] in, T 4( H , t s ( ) represents the temperature of the upper bridge deck. k 1 represents the temperature decay slope of the sun-facing side brace. k 2 represents the slope of temperature decay in the web of the middle section. k 3 represents the slope of temperature decay on the ventral side of the rod; s = H Substituting j=1 into the equation, we can obtain the slope of temperature decay on the ventral side of the rod. k 1 is:

[0112] Will s = H Substituting j=2 into formula (105), the slope of temperature decay in the web of the middle plate is obtained. k 2 is:

[0113] Will s = H Substituting j=3 into formula (106), the slope of temperature decay in the web of the middle plate is then calculated. k 3 is:

[0114] Using the intersection of the upper bridge deck and each web member as the origin, and the width direction as the ordinate, and the height direction as the ordinate, the temperature gradient distribution from the upper bridge deck to the shaded areas of the sun-facing web members, the middle web members, and the shaded web members is plotted. T t1 , T t2 , T t3 They are respectively: ; ;

[0115] Because the area shaded from the upper bridge deck to the sun-facing side of the bracing is blocked by the railing, the actual effect is that the area shaded from the upper bridge deck to the sun-facing side of the bracing is the area shaded. Therefore, k3=0. T 3(H)-T e10 =0; set k1=k2=10, k3=0, T 1(H)-T e6 = T 2(H)-T e8 =8、 T 3(H)-T e10 Substituting =0, we get... T t1 = T t2 =10 h +8, T t3 =0.

[0116] In summary, the temperature gradient patterns of the upper and lower bridge decks and web members of the double-layer steel truss main girder are as follows: Figure 5 As shown, the calculated and measured values ​​of the temperature gradient model are compared as follows: Figure 6 and Figure 7 As shown.

[0117] Although the specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent; various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims are still within the scope of protection of this patent.

Claims

1. A method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation, characterized in that, Includes the following steps: S1: Calculate the solar altitude angle α based on the bridge site's latitude and longitude, hour angle, and solar declination. s ( t ) and solar azimuth γ ( t ); and based on the angle between the main beam axis and the east-west direction. ξ By projecting the vector of sunlight onto the cross section of the main beam, the angle of solar incidence within the cross section can be obtained. θ ( t ); S2: Based on solar incidence angle θ ( t Based on the bridge's geometric parameters, the solar radiation zones of the upper deck, lower deck, and web members are derived respectively. S3: Establish temperature field formulas related to solar radiation duration, air temperature, material properties, surface orientation, and coatings; S4: Calculate the temperature gradients of the upper bridge deck, lower bridge deck, and web members based on the solar radiation region and temperature field formulas, and determine the most unfavorable temperature gradient and its corresponding time.

2. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 1, characterized in that, The angle of solar incidence θ ( t The formula for calculating ) is: The formula for calculating the width of the solar radiation area on the upper bridge deck is as follows: in, B ht This refers to the width of the solar radiation zone on the upper bridge deck. B f The width of the cantilever. B e Excluding the width of the upper bridge deck of the cantilever structure, B dt To determine the width of the shaded area for the bridge railings, H l This refers to the height of the bridge railings. The formula for calculating the width of the solar radiation area on the lower bridge deck is as follows: in, B hb This refers to the width of the solar radiation zone on the lower bridge deck. B b This refers to the area of ​​solar radiation shielded by the upper bridge deck. H The height from the upper surface of the upper bridge deck to the upper surface of the lower bridge deck of the double-layer steel truss main beam; The struts include sun-facing struts, middle struts, and shaded struts. The formula for calculating the height of the solar radiation zone of the sun-facing struts is as follows: in, H s1 The height of the solar radiation zone on the sun-facing side of the ventral pole. H d1 The height of the shaded area of ​​the sunlit side ventral bar; The formula for calculating the height of the solar radiation region of the middle section of the strut is as follows: in, H s2 This refers to the height of the solar radiation region in the middle section of the trunk. H d2 The height of the shaded area of ​​the middle section of the web; The formula for calculating the height of the solar radiation zone on the shady side of the ventral bar is as follows: in, H s3 The height of the solar radiation zone on the ventral side of the pole. H d3 The height of the shaded area on the ventral side of the pole.

3. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 2, characterized in that, The temperature field formula is: in, s The geometric dimensions are the independent variables. t s The independent variable is the cumulative time of solar radiation. T a The ambient temperature near the bridge site. k m The temperature conversion coefficient of solar radiation intensity for materials. k s For surface geometric coefficients, I ( s ( ) represents the intensity of solar radiation. After sunrise, when s If the region is a solar radiation area, then the solar radiation intensity is equal to the direct solar radiation. I d ,when s If it is a shaded area, then the solar radiation intensity I Solar scattered radiation I s , I d , I s Measurements were taken from a meteorological station near the bridge site. α The solar radiation absorption rate of the material surface. k This is the heating rate coefficient.

4. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 3, characterized in that, The method for establishing the temperature gradient of the upper bridge deck in step S4 is as follows: Substitute the geometric parameters of the solar radiation range of the upper bridge deck into the input s When 0≤ s ≤ B ht hour, s For the solar radiation area, when B ht ≤ s ≤ 2B f +B e hour, s The area is shaded; Total temperature integral of the solar radiation area and the shaded area of ​​the upper bridge deck T s1 , T s2 They are respectively: The equivalent temperature of the solar radiation area and the shadow area on the upper bridge deck T e1 , T e2 They are respectively: The temperature gradient of the upper bridge deck T ht for: 。 5. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 4, characterized in that, Differentiating the temperature gradient over the upper bridge deck and setting it to zero, we obtain the cumulative radiation time corresponding to the most unfavorable temperature gradient. Then the time corresponding to the most unfavorable temperature gradient on the upper bridge deck is t a + t s1 , t a If the sunrise time is given, then the most unfavorable temperature gradient on the upper bridge deck is: 。 6. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 5, characterized in that, The temperature gradient of the lower bridge deck is calculated using the same method as for establishing the temperature gradient of the upper bridge deck. T hb for: in, T e3 , T e4 These are the equivalent temperatures of the solar radiation area and the shaded area of ​​the lower bridge deck, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient on the lower bridge deck is The time corresponding to the most unfavorable temperature gradient on the lower bridge deck is t a + t s2 Then the most unfavorable temperature gradient of the lower bridge deck is: 。 7. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 6, characterized in that, The temperature gradients of the sun-facing side web members, the middle web members, and the shady side web members are calculated according to the method for establishing the temperature gradient of the upper bridge deck. Temperature gradient of sun-facing side bar T f1 for: in, T e5 , T e6 These are the equivalent temperatures of the solar radiation region and the shaded region on the sun-facing side of the ventral rod, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient on the sun-facing side bar is The time corresponding to the most unfavorable temperature gradient on the sun-facing side bar is t a + t s3 The most unfavorable temperature gradient on the sun-facing side of the ventral bar is: Temperature gradient of the middle web T f2 for: in, T e7 , T e8 These are the equivalent temperatures of the solar radiation region and the shadow region of the mid-section of the basal bar, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient in the middle web is: The time corresponding to the most unfavorable temperature gradient in the middle section of the web is t a + t s4 The most unfavorable temperature gradient for the middle section of the spindle is: Temperature gradient on the ventral side of the sun T f3 for: in, T e9 , T e10 These are the equivalent temperatures of the solar radiation region and the shaded region on the ventral side of the rod, respectively. The cumulative radiation time corresponding to the most unfavorable temperature gradient on the ventral side of the rod is The time corresponding to the most unfavorable temperature gradient on the shaded side is t a + t s5 The most unfavorable temperature gradient on the shaded side is: 。 8. The method for establishing the temperature gradient of a double-layer steel truss main beam under solar radiation as described in claim 7, characterized in that, The method for establishing the temperature gradient from the upper bridge deck to the shaded area of ​​the web members is as follows: Based on the temperature field formula and the temperature decay region H w Calculate the temperature decay slope ， The calculation formula is as follows: in, T 4( H , t s ( ) represents the temperature of the upper bridge deck. k 1 represents the temperature decay slope of the sun-facing side brace. k 2 represents the slope of temperature decay in the web of the middle section. k 3 represents the temperature decay slope of the ventral bar on the shaded side, and its calculation formulas are as follows: ； ； Using the intersection of the upper bridge deck and each web member as the origin, and the width direction as the abscissa and the height direction as the ordinate, the temperature gradient distribution from the upper bridge deck to the shaded areas of the sun-facing web members, the middle web members, and the shaded web members is plotted. T t1 , T t2 , T t3 They are respectively: ； ； The cumulative radiation time corresponding to the most unfavorable temperature gradient of the sun-facing ventral rod, the middle ventral rod, and the shaded ventral rod. , , The most unfavorable temperature gradients from the upper bridge deck to the shaded areas of the sun-facing web members, the middle web members, and the shaded web members are as follows: ； ； 。

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