Bridge floor deformation prediction method under temperature influence of highway-railway dual-purpose multi-tower cable-stayed bridge

Abstract

The invention discloses a bridge floor deformation prediction method under temperature influence of a highway-railway dual-purpose multi-tower cable-stayed bridge, which comprises the following steps of: based on a temperature gradient model of a bridge tower, establishing a longitudinal deformation model of the bridge tower at the most unfavorable temperature, and establishing a main beam deformation prediction model caused by deformation of the bridge tower; based on the temperature gradient model of the main beam, establishing a main beam deformation prediction model of the main beam at the most unfavorable temperature; establishing a main beam deformation prediction model of the stay cable at the most unfavorable temperature based on the most unfavorable temperature difference model among the stay cable, the tower and the beam; performing weighted combination on the three girder deformation prediction models according to the combination coefficient to obtain a bridge floor overall deformation prediction model; according to the scheme, the method for establishing the deformation of the bridge floor through the deformation of the main beam caused by the bridge tower, the deformation of the main beam and the deformation of the main beam caused by the stay cable is systematically provided, and reference is provided for simplifying and calculating the temperature effect borne by the same type of bridge structures.

Description

A method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use Technical Field

[0001] This invention relates to the field of bridge deformation prediction technology, specifically to a method for predicting bridge deck deformation under the influence of temperature in a multi-tower cable-stayed bridge for both road and rail use. Background Technology

[0002] Multi-tower cable-stayed bridges have become an important type of bridge for long-span road-rail dual-purpose bridges due to their strong span capacity and economical structure. However, the structural system of multi-tower cable-stayed bridges is relatively flexible and highly sensitive to temperature changes. Solar radiation and periodic changes in ambient temperature can create non-uniform temperature fields in the bridge towers, main beams, and stay cables, causing structural deformation and consequently affecting the bridge deck alignment, driving comfort, and structural safety.

[0003] Currently, the consideration of temperature effects in bridge design is mostly based on the assumption of uniform temperature change or simplified temperature gradient models, which are difficult to accurately reflect the structural response under the complex coupling effects of sunlight and environment. Existing prediction methods often only target a single component (such as considering only the temperature gradient of the main beam) or rely on refined finite element models. Although the latter has higher accuracy, it is complex to model and time-consuming to calculate, which is not convenient for rapid evaluation and routine maintenance in engineering practice.

[0004] Furthermore, temperature-induced bridge deck deformation is the result of the combined effects of temperature deformation in the bridge towers, main beams, and stay cables, and is influenced by various factors such as the bridge's geographical location, orientation, season, and daily variations in solar radiation intensity. Existing standards and methods typically use fixed parameters, which cannot reflect real-time changes in sunlight and environmental conditions, leading to discrepancies between predicted results and actual conditions.

[0005] Therefore, it is necessary to propose a bridge deck temperature deformation prediction method that can comprehensively consider multiple temperature influencing factors, has a clear structural response mechanism, high computational efficiency, and is applicable to different geographical and climatic conditions, so as to make up for the shortcomings of existing technologies. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, this invention provides a method for predicting bridge deck deformation under the influence of temperature in multi-tower cable-stayed bridges used for both road and rail, thus solving the problem that existing bridge deck deformation prediction methods suffer from large deviations in prediction results due to the limited number of factors considered.

[0007] To achieve the above objectives, the technical solution adopted by this invention is as follows: A method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use is provided, comprising the following steps: S1: Establishing temperature gradient models for the bridge towers and main beams under the most unfavorable temperature conditions, and establishing the most unfavorable temperature difference model between the stay cables and the towers / beams; S2: Based on the temperature gradient model of the bridge towers, establishing a longitudinal deformation model of the bridge towers under the most unfavorable temperature, and establishing a prediction model for the main beam deformation caused by the bridge tower deformation; S3: Based on the temperature gradient model of the main beams, establishing a prediction model for the main beam deformation itself under the most unfavorable temperature; S4: Based on the most unfavorable temperature difference model between the stay cables and the towers / beams, establishing a prediction model for the main beam deformation of the stay cables under the most unfavorable temperature; S5: Determining the combination coefficients of the bridge tower-induced main beam deformation, the main beam deformation itself, and the stay cable-induced deformation on the bridge deck deformation according to the season, bridge site latitude and longitude, orientation, and sunshine conditions; S6: Weighting and combining the main beam deformation prediction models obtained in steps S2, S3, and S4 according to the combination coefficients determined in step S5 to obtain an overall bridge deck deformation prediction model.

[0008] Furthermore, in step S1, the temperature gradient model T of the bridge tower under the most unfavorable temperature condition... p (θ,d) is: ;

[0009] Where θ is the bridge alignment influence coefficient, d is the length variable along the longitudinal temperature gradient direction, and k p (θ) is a coefficient related to the bridge site's latitude and longitude, sunshine conditions, temperature, bridge alignment, and bridge materials; Q is the material's heat storage coefficient; I p T0 represents the measured solar radiation intensity of the bridge tower, and T0 represents the ambient temperature.

[0010] Furthermore, in step S1, the temperature gradient model T of the main beam under the most unfavorable temperature condition... g (θ,H g )for: ;

[0011] Among them, H g It is the height variable of the main beam, k g (θ) is a coefficient related to the bridge site's latitude and longitude, sunlight conditions, bridge alignment, and bridge structure and materials. g This is the measured solar radiation intensity of the main beam.

[0012] Furthermore, in step S1, the most unfavorable temperature difference model between the stay cables and the tower / beam is:

[0013] Where T1 is the most unfavorable temperature difference between the stay cable and the bridge tower, and T2 is the most unfavorable temperature difference between the stay cable and the main beam. When the temperature difference is positive, the stay cable elongates; when the temperature difference is negative, the stay cable contracts. In both cases, the main beam deforms symmetrically.

[0014] Furthermore, in step S2, the longitudinal deformation model of the bridge tower under the most unfavorable temperature... for: ; ; Where z is the height variable starting from the ground, D is the cross-sectional width of the bridge tower, and α p Let A be the coefficient of linear expansion of the bridge tower. p K is the influence coefficient. p K is the bending stiffness coefficient of the bridge tower. c n is the tensile stiffness coefficient of the stay cables corresponding to the bridge tower. p E represents the number of tower limbs. p I p Here, H represents the bridge tower stiffness, H is the height of the bridge tower above the crossbeam, and E is the bridge tower height. c A c For the stiffness of the stay cable, l c Let θ be the average length of the stay cable. c The average inclination angle of the cable stays; the negative sign indicates that the direction of the bridge tower displacement is opposite to the direction of direct solar radiation.

[0015] Furthermore, in step S2, the prediction model for the main girder deformation caused by the bridge tower deformation includes the vertical deformation of the main span main girder and the vertical deformation of the side span main girder; the vertical deformation of the main span main girder is antisymmetric about the central tower, and the vertical deformation of the main girder is approximately a sine function waveform, the expression of which is: ; ; The vertical deformation of the side span is approximately equal to half a sine function waveform, and its expression is:

[0016] Among them, L i Let H be the span of the i-th main beam. i Let x be the height of the i-th main beam, and its value ranges from 0 to L. i A g It is a coefficient related to the stiffness of the bridge towers, the stiffness of the main beams, and the stiffness of the stay cables, δ ’ (H i ) is the corner of the middle bridge tower, K g It is the axial stiffness coefficient of the main beam, E g I g Main beam stiffness, δ ’ (H b ) is the corner of the side bridge tower, L b It refers to the side span.

[0017] Furthermore, in step S3, the main beam deformation prediction model under the most unfavorable temperature is as follows:

[0018] Where h0 is the height of the main beam section, α g The coefficient of linear expansion of the main beam, T g It is the temperature gradient model of the main beam.

[0019] Furthermore, in step S4, the prediction model for the main beam deformation of the stay cables under the most unfavorable temperature is as follows:

[0020]

[0021] Where, θ c Let λ be the average angle between the stay cable and the main girder in the longitudinal plane of the bridge, and l be the cable-to-girder stiffness ratio. c It is the average length of the stay cable, α c The coefficient of linear expansion of the cable-stayed bridge is denoted by ; the negative sign indicates downward displacement of the main beam. Under the cooling temperature gradient, the deformation of the main beam has the opposite sign and the same magnitude of change.

[0022] Furthermore, in step S6, the overall deformation prediction model for the bridge deck is as follows:

[0023] The expression for the vertical deformation of the main span main beam is as follows:

[0024] The expression for the vertical deformation of the main beam at the side span is:

[0025] Wherein, η1, η2, and η3 are the combination coefficients of the deformation of the main beam caused by the bridge tower, the deformation of the main beam itself, and the deformation of the main beam caused by the stay cables, respectively, on the bridge deck deformation.

[0026] Furthermore, the general expression for the combination coefficients is:

[0027] ; ; ; ;

[0028] Where i is 1, 2, or 3; φ z φ is the influence coefficient of bridge alignment. s φ is the seasonal influence coefficient. j φw These are the influence coefficients for longitude and latitude, S, respectively. i Let θ be the solar radiation coefficient. z The angle between due north and the longitudinal axis of the bridge, M is the month, ε1 is latitude, ε2 is longitude, and I... t I represents the measured solar radiation intensity at that moment. i The solar radiation intensities corresponding to the temperature gradient models of the bridge tower, the main girder, and the most unfavorable temperature difference models between the stay cables and the tower and girder, namely I1, I2, and I3, are respectively I p I g and I c .

[0029] The beneficial effects of this invention are as follows: 1. This solution takes into account the influence of factors such as the latitude and longitude of the bridge site, sunshine conditions, air temperature, bridge orientation and bridge materials, and systematically proposes a method for establishing the temperature gradient of the bridge tower, the temperature gradient of the main beam, and the temperature difference between the stay cables and the tower and beam, providing a reference for the simplification and calculation of the temperature effects on similar bridge structures.

[0030] 2. This scheme proposes calculation methods for the following models under temperature effects: bridge tower deformation model, bridge tower deformation leading to main beam deformation model, main beam deformation model, and temperature difference between stay cables and towers / beams leading to main beam deformation model. This refined calculation of each component can simultaneously determine the peak deformation of each component under the most unfavorable temperature conditions, providing a more reliable basis for predicting bridge deck deformation and ensuring the safety reserve of the structure under the most demanding temperature conditions.

[0031] 3. This scheme proposes a method for determining the combination coefficients for predicting bridge deck deformation under temperature effects. It considers the influence of bridge site orientation, latitude and longitude, season, and sunshine conditions, making the combination coefficients applicable to different geographical environments and climatic conditions, thus improving the model's versatility and accuracy in complex environments. At the same time, this scheme ensures that the model can adapt to the changes in sunshine conditions from sunrise to sunset throughout the day by acquiring solar radiation intensity in real time, making the calculation results dynamic, continuous, and more in line with natural laws.

[0032] 4. This scheme establishes a complete analytical theory and methodology system for the characteristics of bridge deck deformation under the influence of temperature in multi-tower cable-stayed bridges. It effectively fills the gaps and limitations of existing standards, and provides a reliable basis for the temperature effect analysis, deformation assessment, and structural design of bridge decks in multi-tower cable-stayed bridges. It helps to avoid structural damage caused by temperature gradients and extend the service life of bridges. Attached Figure Description

[0033] 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.

[0034] Figure 1 is a flowchart of the bridge deck deformation prediction method in this scheme.

[0035] Figure 2 is a schematic diagram of the temperature conditions of the bridge tower.

[0036] Figure 3 is a schematic diagram of the temperature conditions of the main beam.

[0037] Figure 4 shows a model for predicting the deformation of the main beam caused by the deformation of the bridge tower.

[0038] Figure 5 shows the prediction model of the main beam deformation under the most unfavorable temperature.

[0039] Figure 6 shows the prediction model of the main beam deformation under the most unfavorable temperature difference for the stay cables.

[0040] Figure 7 shows the prediction model of the main beam deformation under the most unfavorable temperature difference for the stay cables.

[0041] Figure 8 shows the prediction model of the overall deformation of the bridge deck. Detailed Implementation

[0042] 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.

[0043] 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.

[0044] 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.

[0045] Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0046] As shown in Figure 1, the method for predicting bridge deck deformation under temperature influence in this dual-purpose (railway and highway) multi-tower cable-stayed bridge includes the following steps: S1: Establish temperature gradient models for the bridge towers and main beams under the most unfavorable temperature conditions, and establish the most unfavorable temperature difference models between the stay cables and the towers and beams; specifically, this includes: S11: Bridge tower temperature gradient model T p Solving for (θ,d): Based on the measured and simulation analysis results of bridge tower temperature, and considering only the influence of the longitudinal direction, a simplified formula for the most unfavorable temperature gradient of the horizontal section of the bridge tower is proposed:

[0047] In the formula, d is the length variable (m) of the longitudinal bridge along the temperature gradient direction, and k p (θ) is a coefficient (°C / m) related to the bridge site's latitude and longitude, sunlight conditions, temperature, bridge alignment, and bridge materials. p The formula for calculating (θ) is:

[0048] In the formula, I p The measured solar radiation intensity (kW / m²) of the bridge tower 2 ), shaded area I p =0, which is related to the latitude and longitude of the bridge site and the sunshine conditions; T0 is the ambient temperature (°C), Q is defined as the material heat storage coefficient (m / kW), which is 0.28 for steel and 0.10 for concrete; θ is the influence coefficient of bridge orientation, which is the acute angle between the bridge orientation and the due north direction; the temperature gradient model of the bridge tower is shown in Figure 2.

[0049] S12: Main beam temperature gradient model T g (θ,H g Solution of the problem: Based on the measured and simulation analysis results of the main beam temperature, a simplified formula for the most unfavorable temperature gradient of the main beam is proposed as follows:

[0050] In the formula, H g It is the height variable (m) of the main beam, and H is the bottom of the lower flange of the main beam. g =0; k g It is a coefficient (°C / m) related to the bridge site's latitude and longitude, sunlight conditions, bridge alignment, and bridge structure and materials, k g The calculation method is as follows:

[0051] In the formula, I gThe measured solar radiation intensity (kW / m²) of the main beam 2 ), shaded area I p =0, which is related to the latitude and longitude of the bridge site and the sunshine conditions; T0 is the ambient temperature (°C), Q is the material heat storage coefficient (m / kW), which is 28 for steel and 10 for concrete; θ is the bridge orientation influence coefficient, which is the acute angle between the bridge orientation and the due north direction; the temperature gradient model of the main beam is shown in Figure 3.

[0052] S13: Temperature difference T between stay cables and tower / beam c的 Solution: Based on the measured and simulation analysis results of the temperatures of the stay cables, tower, and beams, a simplified formula for the most unfavorable temperature difference is proposed as follows:

[0053] In the formula, T1 is the most unfavorable temperature difference between the stay cable and the bridge tower, and T2 is the most unfavorable temperature difference between the stay cable and the main beam. When the temperature difference is positive, the stay cable elongates; when it is negative, the stay cable contracts. In both cases, the deformation of the main beam is symmetrical.

[0054] S2: Based on the temperature gradient model of the bridge tower, establish a longitudinal deformation model of the bridge tower under the most unfavorable temperature, and establish a prediction model for the main beam deformation caused by the deformation of the bridge tower; specifically including: S21: Establish a longitudinal deformation model of the bridge tower under the most unfavorable temperature: based on the temperature gradient model T of the bridge tower p (θ,d); is used to derive the bridge tower's temperature gradient T p Deformation mode of bridge tower under (θ,d) action By treating the bridge tower as a cantilever beam, the relationship between temperature conditions and the deformation mode of the bridge tower can be derived. Relationship formula:

[0055] In the formula, D is the width of the bridge tower cross-section (m), z is the independent variable of height starting from the ground (m), and α p The linear expansion coefficient of the bridge tower (°C) is given by A. The negative sign indicates that the direction of the bridge tower's displacement is opposite to the direction of direct solar radiation. p To account for the influence coefficients of tower stiffness and the number of tower limbs, the direction of tower displacement is positive to the right in the longitudinal direction of the bridge.

[0056] In the formula, the influence coefficient A p The calculation method is as follows:

[0057] In the formula, K p It is the bending stiffness coefficient of the bridge tower, and its magnitude is the reciprocal of the displacement of the cantilever beam under a unit force.

[0058] Kc It is the tensile stiffness coefficient of the stay cable corresponding to the bridge tower, and its magnitude is the conversion of the axial stiffness of the stay cable into the horizontal constraint stiffness of the main beam:

[0059] Among them, E p I p Bridge tower stiffness (N·m) 2 E c A c For the stiffness of the cable (N), l c Let θ be the average length of the stay cable. c n is the average inclination angle of the cable-stayed bridge. p H represents the number of tower segments, and H represents the height of the bridge tower above the crossbeam.

[0060] right The relational formula is integrated twice, and the boundary conditions are substituted. , The deformation mode of the bridge tower under the action of a temperature gradient is obtained as follows:

[0061] S22: Solving the prediction model for main beam deformation caused by bridge tower deformation: For the vertical deformation of the main beam in the main span: According to the measured results, the vertical deformation of the main beam is antisymmetric about the central tower. Within each main span, the vertical deformation of the main beam is approximately a sine function waveform. The vertical deformation of the main beam in the main span is:

[0062] In the formula, x=0 is located at the left tower of each span, and the value of x ranges from 0 to L. i H i Let δ be the height of the i-th span of the main beam, with upward vertical displacement of the main beam considered positive. ’ (H i ) is the corner of the middle bridge tower, A g It is a coefficient related to the stiffness of the bridge tower, the stiffness of the main girder, and the stiffness of the stay cables. Considering the stiffness factor of the main girder, its calculation method is as follows:

[0063] In the formula, K g It is the axial stiffness coefficient of the main beam, calculated as follows:

[0064] Among them, L i E is the span of the i-th main beam. g I g This refers to the stiffness of the main beam.

[0065] The vertical deformation of the side span main girder is as follows: Since the vertical deformation of the side span is approximately a half-sine function waveform, and is only constrained by the cable force of half of the side bridge tower's stay cables, the vertical deformation of the side span main girder under the action of the temperature gradient is obtained as follows:

[0066] In the formula, δ ’ (H b ) is the corner of the side bridge tower, L b The side span is shown in Figure 4. Under the most unfavorable temperature gradient of the bridge tower, the prediction model of the main beam deformation caused by the deformation of the bridge tower is shown in Figure 4.

[0067] S3: Based on the temperature gradient model of the main beam, establish a prediction model for the deformation of the main beam under the most unfavorable temperature; specifically, this includes: to facilitate obtaining the deformation prediction model of the main beam under the temperature gradient T g (θ,H g The main girder deformation prediction model under the action of temperature gradient simplifies the main girder of the cable-stayed bridge into a multi-span continuous beam structure with vertical supports at the bridge towers, considering only the deformation of the main girder itself under temperature. Based on the actual deformation of the main girder, the deformation model caused by the temperature gradient of the main girder itself is shown in Figure 5.

[0068] Based on the measured deformation results of the main beam, it can be seen that the deformation of each span of the main beam is approximately a half-sine function waveform. Since the span length L of each span is... i The vertical deformation amplitudes of the main beams are different, so they are considered separately. Let the vertical deformation model of each span of the main beam under temperature action be:

[0069] In the formula, x=0 represents the left tower of each span, and w m For the equivalent continuous beam mid-span deflection; L i Let x be the span (m) of the i-th main span, and its value range is 0~L. i The vertical displacement of the main beam is positive when it is upward.

[0070] To solve for the mid-span deflection w of the equivalent continuous beam m The relationship between temperature and vertical deformation of the equivalent continuous beam is obtained as follows:

[0071] In the formula, h0 is the height of the main beam section, and α g The coefficient of linear expansion of the main beam, T g It is the temperature gradient of the main beam, A g These are coefficients that consider the stiffness of the cable-stayed beam and tower; integrate them twice and substitute them into the constraint conditions: The deformation curve of the continuous beam can be obtained by solving the problem. for:

[0072] Let x = 0.5L i Substituting the obtained deflection w m for:

[0073] The vertical deformation of the i-th span main beam under temperature action is obtained as follows: .

[0074] S4: Based on the most unfavorable temperature difference model between the stay cables and the tower / beam, a model for predicting the deformation of the main beam under the most unfavorable temperature is established. Specifically, it includes: to simplify the calculation, only the deformation of the stay cables caused by temperature changes is considered, and the parameters of the stay cables are the same, while the temperature of the main beam and the bridge tower remains unchanged. The vertical deformation at the connection between the bridge tower and the main beam is 0, and it can rotate freely. The model of the deformation of the main beam caused by the most unfavorable temperature difference between the stay cables and the tower / beam is shown in Figures 6 and 7.

[0075] Considering the constraint effect of the bridge towers and stay cables on the deformation of the main beam, and based on the measured data, the deformation mode of the main beam for each span is as follows:

[0076] In the formula, x=0 is located at the left tower of each span, and the value of x ranges from 0 to L. i θ c It is the average angle between the stay cable and the main girder in the longitudinal plane of the bridge. The vertical displacement of the main girder is positive when it is upward. c (i,θ c The peak value of the cable deformation is related to the compressive stiffness of the tower, the inclination angle and tensile stiffness of the cable, and the span and stiffness of the main beam. Its calculation method is as follows:

[0077] In the formula, α c The linear expansion coefficient of the stay cable is λ, and the cable-beam stiffness ratio is defined as follows:

[0078] Among them, l c Given the average length of the stay cables, and combining this with the above formula, the vertical deformation of the main beam caused by the deformation of the stay cables under the action of the temperature gradient is:

[0079] In the formula, the negative sign indicates the downward displacement of the main beam; under the cooling temperature gradient, the deformation of the main beam has only the opposite sign, but the magnitude of change is the same.

[0080] S5: Determine the combination coefficient of bridge deck deformation caused by the bridge towers, the main beam deformation itself, and the deformation caused by the stay cables, based on the season, bridge site latitude and longitude, orientation, and sunlight conditions; specifically, the calculation method for the combination coefficient is as follows:

[0081] In the formula, i represents 1, 2, and 3; η1, η2, and η3 are the combination coefficients of the deformation of the main girder caused by the bridge tower, the deformation of the main girder itself, and the deformation of the main girder caused by the stay cables, respectively, on the bridge deck deformation; φ z This is the bridge alignment influence coefficient, with due north as 0 and clockwise as positive. The angle between due north and the longitudinal bridge axis is defined as θ. z , then φ z The calculation method is as follows:

[0082] φ s This is the seasonal influence coefficient, defined as the month M ranging from 1 to 12, with June being summer. Therefore, φ... s The calculation method is as follows:

[0083] φ j , φ w This is the latitude and longitude influence coefficient. ε1 is defined as latitude, ranging from -60° to 60°; ε2 is longitude, ranging from 0 to 360°. 120° East longitude is the regional centerline. Therefore, φ... j , φ w The calculation formula is:

[0084]

[0085] S i It is the solar radiation coefficient, which is the ratio of the measured solar radiation intensity to the solar radiation intensity at the most unfavorable time for the structure, i.e.:

[0086] In the formula, where I t It is the measured solar radiation intensity at that moment, I i Let I1, I2, and I3 be the solar radiation intensities corresponding to the temperature gradient models of the bridge tower, the main beam, and the most unfavorable temperature difference models between the stay cables and the tower / beam, respectively. p I g and I c .

[0087] S6: Based on the combination coefficients determined in step S5, the main beam deformation prediction models obtained in steps S2, S3, and S4 are weighted and combined to obtain the overall bridge deck deformation prediction model. Specifically, this includes: combining the bridge tower deformation model under the most unfavorable temperature, the main beam deformation model under temperature, the temperature difference between the stay cables and the tower, and the cable beam causing the main beam deformation, and performing linear superposition or weighted combination based on the combination of temperature loads in the actual environment to construct the final comprehensive prediction model of vertical deformation of the main beam under temperature, which is used to predict the bridge deck deformation under specific temperature conditions.

[0088] Based on the asynchronous occurrence of the most unfavorable temperature gradients in each structure, the deformation of the main beam caused by the three temperature gradients is reduced and combined according to the actual situation, resulting in the following prediction model for the overall deformation of the bridge deck:

[0089] In the formula, g p (x,i) represents the prediction model for the main beam deformation caused by the bridge tower deformation, g g (x,i) represents the main beam deformation prediction model under the most unfavorable temperature, and g is the main beam deformation prediction model. c (x,i,θ c This is a model for predicting the deformation of the main beam caused by the temperature difference between the stay cables, the tower, and the cable beam.

[0090] Specifically, the vertical deformation of the main span main beam is as follows:

[0091] The vertical deformation of the side span main beam is as follows:

[0092] Wherein, η1, η2, and η3 are the combination coefficients of the deformation of the main beam caused by the bridge tower, the deformation of the main beam itself, and the deformation of the main beam caused by the stay cables, respectively, on the bridge deck deformation. The overall deformation prediction model of the bridge deck of a multi-tower cable-stayed bridge under temperature action is shown in Figure 8.

[0093] The following scheme takes the Ma'anshan Yangtze River Highway-Railway Bridge as an example and gives a specific process for establishing a bridge deck overall deformation prediction model: S1: Establish temperature gradient models for the bridge tower and main beam under the most unfavorable temperature conditions, and establish the most unfavorable temperature difference model between the stay cables and the tower and beam.

[0094] (1) Bridge tower temperature gradient model Solution: Based on the measured results of the bridge tower, the most unfavorable temperature gradient of the bridge tower can be simplified as follows:

[0095] In the formula, d is the length variable (m) of the longitudinal bridge along the temperature gradient direction, and k pIt is a coefficient (°C / m) related to the bridge site's latitude and longitude, sunlight conditions, temperature, bridge alignment, and bridge materials, k p The calculation method is as follows:

[0096] In the formula, I p The measured direct solar radiation intensity (kW / m²) of the bridge tower 2 ), shaded area I p =0, which is related to the latitude and longitude of the bridge site and the sunshine conditions; T0 is the ambient temperature (°C); Q is defined as the material heat storage coefficient (m / kW), which is 0.28 for steel and 0.10 for concrete; θ is the bridge orientation influence coefficient, which is the acute angle between the bridge orientation and the due north direction.

[0097] Temperature data from the meteorological station near the bridge shows that under the most unfavorable temperature gradient, T0 is 37.3 ℃ in summer and -3.2 ℃ in winter; the bridge tower is a steel-concrete composite tower, and conservatively, Q is taken as 0.28; the summer direct solar radiation intensity I... p 814 W / m 2 Winter solar direct radiation intensity I p It is 572 W / m².

[0098] Set Q=0.28, I p =0.814 kW / m², θ=0, T0=37.3 ℃. Substituting these values, we get:

[0099] Substituting D=16 m, the most unfavorable temperature gradient for the side bridge tower is:

[0100] Substituting D=42.6 m, the most unfavorable temperature gradient for the middle bridge tower is:

[0101] (2) Temperature gradient model of main beam Solution: Based on the measured results of the main beam, the most unfavorable temperature gradient of the main beam can be simplified as follows:

[0102] In the formula, z is the height variable of the main beam (m), and z=0 at the bottom of the lower flange of the main beam; k g It is a coefficient (°C / m) related to the bridge site's latitude and longitude, sunlight conditions, bridge alignment, and bridge structure and materials, k g The calculation method is as follows:

[0103] In the formula, I gThe measured direct solar radiation intensity of the main beam (kW / m²) 2 ), shaded area I p =0, which is related to the latitude and longitude of the bridge site and the sunshine conditions; T0 is the ambient temperature (°C), Q is the material heat storage coefficient (m / kW), which is 28 for steel and 10 for concrete; θ is the bridge orientation influence coefficient, which is the acute angle between the bridge orientation and the due north direction.

[0104] The main beam is a steel structure, and Q is taken as 0.28; the summer direct solar radiation intensity I p 732 W / m 2 Winter solar direct radiation intensity I p It is 467 W / m².

[0105] Set Q=0.28, I p =0.732 kW / m², θ=0, T0=37.3 ℃. Substituting these values, we get:

[0106] Substituting z = 15.5 m, we get:

[0107] (3) The most unfavorable temperature difference model T between the stay cables and the tower and beam c Solution: Based on the measured and simulation analysis results of the most unfavorable temperature difference between the stay cables and the cable-beam, and between the cable-beam and the most unfavorable temperature difference, a simplified formula for the most unfavorable temperature difference between the stay cables and the tower, and between the cable-beam, is proposed as follows:

[0108] In the formula, T1 is the most unfavorable temperature difference between the stay cable and the tower, and T2 is the most unfavorable temperature difference between the stay cable and the cable beam. When the temperature difference is positive, the stay cable elongates; when it is negative, the stay cable contracts. In both cases, the deformation of the main beam is symmetrical.

[0109] In this example, the most unfavorable temperature difference between the stay cable, the tower, and the cable beam is taken as: .

[0110] S2: Based on the temperature gradient model of the bridge tower, establish a longitudinal deformation model of the bridge tower under the most unfavorable temperature, and establish a prediction model of the main beam deformation caused by the deformation of the bridge tower.

[0111] (1) Longitudinal deformation model of bridge tower under the most unfavorable temperature for: ; ; Where z is the height variable starting from the ground, D is the cross-sectional width of the bridge tower, and α p Let A be the coefficient of linear expansion of the bridge tower. p K is the influence coefficient. pK is the bending stiffness coefficient of the bridge tower. c n is the tensile stiffness coefficient of the stay cables corresponding to the bridge tower. p E represents the number of tower limbs. p I p Here, H represents the bridge tower stiffness, H is the height of the bridge tower above the crossbeam, and E is the bridge tower height. c A c For the stiffness of the stay cable, l c Let θ be the average length of the stay cable. c The average inclination angle of the cable stays; the negative sign indicates that the direction of the bridge tower displacement is opposite to the direction of direct solar radiation.

[0112] This example is a three-tower, four-span cable-stayed bridge. All towers are steel-concrete composite towers, with the upper half made of steel and the lower half of concrete. The side towers are double-legged, 308 m high, and have a stiffness of 4.3 × 10⁻⁶ m. 13 N·m 2 The central tower has four legs, a height of 345 m, and a stiffness of 2.2 × 10⁻⁶. 13 N·m 2 The cable pitch d = 0.13 m, the average length on both sides of the central tower is 431.1 m, the average inclination angle is 49.5°, and the stiffness is 9.5 × 10⁻⁶ m. 9 N·m 2 The average length of each side tower is 396.2 m, the average inclination angle is 50.5°, and the stiffness is 6.6 × 10⁻⁶ m. 13 N·m 2 .

[0113] (2) Solve for the bridge tower deformation under the most unfavorable temperature: Let E p I p =2.2×10 13 N·m 2 Substituting H=206.7 m, the stiffness coefficient of the side tower is obtained as follows:

[0114] E p I p =4.3×10 13 N·m 2 Substituting H=292 m, the stiffness coefficient of the middle tower is:

[0115] E c A c =6.6×10 9 N, l c =396.2 m, θ c Substituting 50.5°, we obtain the stiffness of the side tower cable as:

[0116] E c A c =9.5×10 9 N, l c =431.1 m, θ c Substituting 49.5°, we obtain the stiffness of the cable-stayed tower's middle cable as:

[0117] n p Substituting 2 into the equation yields the influence coefficient A of the two tower limbs. p for:

[0118] General n p Substituting 4 into the equation yields the influence coefficient A of the four-tower leg. p for:

[0119] Substituting D=16 and z=308, we obtain the longitudinal displacement of the top of the side tower under the most unfavorable temperature gradient as follows:

[0120] Substituting D=21.3 and z=345, we obtain the longitudinal displacement of the top of the middle tower under the most unfavorable temperature gradient as follows:

[0121] (3) Solving for the deformation of the main beam caused by the deformation of the bridge tower: According to the measured data, the vertical deformation of the main beam is antisymmetric about the middle tower. Within each main span, the vertical deformation of the main beam is approximately a sine function waveform. Let the vertical deformation of the main beam in the main span be:

[0122] In the formula, x=0 is located at the left tower of each span, and the value of x ranges from 0 to L. i； The vertical displacement of the main beam is positive when it is upward, δ ’ (H i ) is the corner of the middle bridge tower, A g It is a coefficient related to the stiffness of the bridge tower, the stiffness of the main girder, and the stiffness of the stay cables. Considering the stiffness factor of the main girder, its calculation method is as follows:

[0123] In the formula, K g It is the axial stiffness coefficient of the main beam, calculated as follows:

[0124] Among them, L i It is the span of the i-th main beam.

[0125] Since the vertical deformation of the side span is approximately a half-sine function waveform, and is only constrained by the cable force of half of the side tower's stay cables, the vertical deformation of the main beam of the side span under the action of the temperature gradient is obtained as follows:

[0126] In this example, the stiffness E of the main span beam is... g I g 5.10×10 16 N·m 2 The main span of the side span is 1120 m, and the stiffness of the main beam is E. g I g 9.09×10 15 N·m 2 The side span is 504 m.

[0127] For the coefficient of the mid-span main girder: E g I g =5.10×10 16 N·m 2 L i Substituting 1120 m, the axial stiffness of the main span beam is:

[0128] Obtain coefficient A g for:

[0129] For the coefficient of the side span main beam: E g I g =9.09×10 15 N·m 2 L i Substituting 504 m, the axial stiffness of the side span main beam is:

[0130] Obtain coefficient A g for:

[0131] L b =504 m, H b Substituting =308 m and D=16 m, we finally obtain the vertical deformation of the side span main beam under the action of temperature gradient:

[0132] L i =1120 m, H i Substituting 345 m and D = 42.6 m, the vertical deformation of the main beam in the mid-span under the action of the temperature gradient is finally obtained as follows:

[0133] S3: Based on the temperature gradient model of the main beam, the deformation prediction model of the main beam under the most unfavorable temperature is as follows:

[0134] Where h0 is the height of the main beam section, α g The coefficient of linear expansion of the main beam, T g It is the temperature gradient model of the main beam.

[0135] Given h0 = 15.5 m, L i Substituting 1120 m, we obtain the vertical deformation of the main span beam:

[0136] For the deformation of the main beam in the side span: Given h0 = 15.5 m, L b Substituting 504 m, we obtain the vertical deformation of the main beam in the side span:

[0137] S4: Based on the most unfavorable temperature difference model between the stay cables and the tower / beam, the prediction model for the main beam deformation of the stay cables under the most unfavorable temperature is as follows:

[0138]

[0139] Where, θ c Let λ be the average angle between the stay cable and the main girder in the longitudinal plane of the bridge, and l be the cable-to-girder stiffness ratio. c It is the average length of the stay cable, α c Here, d is the linear expansion coefficient of the cable-stayed bridge; the negative sign indicates the downward displacement of the main beam. Under the cooling temperature gradient, the deformation of the main beam has the opposite sign and the same magnitude.

[0140] For the vertical deformation of the main beam in the side span: Given d = 0.13 m, E c A c =4.3×10 13 , l c =396.2 m, θ c =50.5 °, E g I g =9.09×10 15 N·m 2 Substituting into the formula, we can obtain the stiffness ratio of the side span cable beam as:

[0141] Given d = 0.13 m, T c =10°, L b=504 m, θ c Substituting 50.5°, we obtain the vertical deformation of the main beam in the side span under the temperature gradient of the cable-stayed cable:

[0142] For the vertical deformation of the mid-span main beam: Given d = 0.13 m, E c A c =8.6×10 13 , l c =431.1 m, θ c =49.5 °, E g I g =5.10×10 16 N·m 2 Substituting these values, we obtain the stiffness ratio of the mid-span cable-stayed beam as:

[0143] Given d = 0.13 m, T c =10°, L i =1120 m, θ c Substituting 49.5° into the equation, the vertical deformation of the main beam in the middle span under the condition of the cable-stayed bridge's temperature gradient is:

[0144] S5: Determine the combination coefficients of the deformation of the main girder caused by the bridge towers, the deformation of the main girder itself, and the deformation caused by the stay cables, based on the season, the latitude and longitude of the bridge site, the orientation, and the sunlight conditions; and perform a weighted combination based on the combination coefficients to obtain the overall bridge deck deformation prediction model, which specifically includes: the vertical deformation of the main girder of the main span is:

[0145] The vertical deformation of the side span main beam is as follows:

[0146] The general expression for the combination coefficients is:

[0147] ; ; ; ;

[0148] Where i is 1, 2, or 3; φ z φ is the influence coefficient of bridge alignment. s φ is the seasonal influence coefficient. j φ w These are the influence coefficients for longitude and latitude, S, respectively.i Let θ be the solar radiation coefficient. z The angle between due north and the longitudinal axis of the bridge, M is the month, ε1 is latitude, ε2 is longitude, and I... t I represents the measured solar radiation intensity at that moment. i The solar radiation intensities corresponding to the temperature gradient models of the bridge tower, the main girder, and the most unfavorable temperature difference models between the stay cables and the tower and girder, namely I1, I2, and I3, are respectively I p I g and I c .

[0149] This example bridge is located at 32°N, 118°E; the bridge runs east-west, and the most unfavorable temperature gradient occurs in August during the summer. The most unfavorable daily temperature gradient occurs at 14:00, at which time the measured solar radiation intensity I... t It is 0.732 kW / m 2 Given I p =0.814、I g =0.732、I c =0.904.

[0150] θ z Substituting 90°, we get: .

[0151] Substituting M=8, we get: .

[0152] Substituting ε1=32° and ε2=118°, we get: , .

[0153] I respectively p =0.814、I g =0.732、I c =0.513 and I t Substituting =0.732, we get: , , .

[0154] Will , , , , , , Substituting the values, we get: , , .

[0155] Substituting the above combination coefficients, we can obtain the following: The vertical deformation of the main span main beam is:

[0156] The vertical deformation of the side span main beam is as follows:

[0157] Substituting x=280, we get the maximum vertical deformation of the main span beam as 4.14 m.

[0158] Substituting x=252, we get the maximum vertical deformation of the side span main beam as 2.7 m.

[0159] In summary, this scheme can determine the vertical deformation at any position of the main beam in the middle span and the main beam in the side span under the most unfavorable temperature gradient, which is the bridge deck deformation prediction model under the influence of temperature.

[0160] 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 predicting bridge deck deformation under the influence of temperature in a multi-tower cable-stayed bridge for both road and rail use, characterized in that, Includes the following steps: S1: Establish temperature gradient models for the bridge tower and main girder under the most unfavorable temperature conditions, and establish the most unfavorable temperature difference model between the stay cables and the tower and girder; S2: Based on the temperature gradient model of the bridge tower, establish a longitudinal deformation model of the bridge tower under the most unfavorable temperature, and establish a prediction model for the deformation of the main girder caused by the deformation of the bridge tower; S3: Based on the temperature gradient model of the main girder, establish a prediction model for the deformation of the main girder itself under the most unfavorable temperature; S4: Based on the most unfavorable temperature difference model between the stay cables and the tower and girder, establish a prediction model for the deformation of the main girder of the stay cables under the most unfavorable temperature; S5: Determine the combination coefficients of the deformation of the main girder caused by the bridge tower, the deformation of the main girder itself, and the deformation caused by the stay cables on the bridge deck deformation according to the season, the latitude and longitude of the bridge site, the orientation, and the sunshine conditions; S6: Based on the combination coefficients determined in step S5, the main beam deformation prediction models obtained in steps S2, S3, and S4 are weighted and combined to obtain the overall bridge deck deformation prediction model.

2. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 1, is characterized in that... In step S1, the temperature gradient model T of the bridge tower under the most unfavorable temperature condition is... p (θ,d) is: ； Where θ is the bridge alignment influence coefficient, d is the length variable along the longitudinal temperature gradient direction, and k p (θ) is a coefficient related to the bridge site's latitude and longitude, sunshine conditions, temperature, bridge alignment, and bridge materials; Q is the material's heat storage coefficient; I p T0 represents the measured solar radiation intensity of the bridge tower, and T0 represents the ambient temperature.

3. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 2, is characterized in that... In step S1, the temperature gradient model T of the main beam under the most unfavorable temperature condition is... g (θ,H g )for: ； Among them, H g It is the height variable of the main beam, k g (θ) is a coefficient related to the bridge site's latitude and longitude, sunlight conditions, bridge alignment, and bridge structure and materials. g This is the measured solar radiation intensity of the main beam.

4. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 3, is characterized in that... In step S1, the most unfavorable temperature difference model between the stay cables and the tower / beam is: Where T1 is the most unfavorable temperature difference between the stay cable and the bridge tower, and T2 is the most unfavorable temperature difference between the stay cable and the main beam. When the temperature difference is positive, the stay cable elongates; when the temperature difference is negative, the stay cable contracts. In both cases, the main beam deforms symmetrically.

5. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 4, is characterized in that... In step S2, the longitudinal deformation model of the bridge tower under the most unfavorable temperature. for: ； ； Where z is the height variable starting from the ground, D is the cross-sectional width of the bridge tower, and α p Let A be the coefficient of linear expansion of the bridge tower. p K is the influence coefficient. p K is the bending stiffness coefficient of the bridge tower. c n is the tensile stiffness coefficient of the stay cables corresponding to the bridge tower. p E represents the number of tower limbs. p I p Here, H represents the bridge tower stiffness, H is the height of the bridge tower above the crossbeam, and E is the bridge tower height. c A c For the stiffness of the stay cable, l c Let θ be the average length of the stay cable. c The average inclination angle of the cable stays; the negative sign indicates that the direction of the bridge tower displacement is opposite to the direction of direct solar radiation.

6. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 5, is characterized in that... In step S2, the prediction model for the main girder deformation caused by the bridge tower deformation includes the vertical deformation of the main span main girder and the vertical deformation of the side span main girder; the vertical deformation of the main span main girder is antisymmetric about the central tower, and the vertical deformation of the main girder is approximately a sine function waveform, the expression of which is: ； ； The vertical deformation of the side span is approximately equal to half a sine function waveform, and its expression is: Among them, L i Let H be the span of the i-th main beam. i Let x be the height of the i-th main beam, and its value ranges from 0 to L. i A g It is a coefficient related to the stiffness of the bridge towers, the stiffness of the main beams, and the stiffness of the stay cables, δ ’ (H i ) is the corner of the middle bridge tower, K g It is the axial stiffness coefficient of the main beam, E g I g Main beam stiffness, δ ’ (H b ) is the corner of the side bridge tower, L b It refers to the side span.

7. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 6, is characterized in that... In step S3, the main beam deformation prediction model under the most unfavorable temperature is as follows: Where h0 is the height of the main beam section, α g The coefficient of linear expansion of the main beam, T g It is the temperature gradient model of the main beam.

8. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 7, is characterized in that... In step S4, the prediction model for the main beam deformation of the stay cables under the most unfavorable temperature is as follows: Where, θ c Let λ be the average angle between the stay cable and the main girder in the longitudinal direction of the bridge, and l be the cable-to-girder stiffness ratio. c It is the average length of the stay cable, α c The coefficient of linear expansion of the cable-stayed bridge is denoted by . The negative sign indicates downward displacement of the main beam. Under the temperature gradient of cooling, the deformation of the main beam has the opposite sign and the same magnitude of change.

9. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 8, is characterized in that... In step S6, the overall deformation prediction model of the bridge deck is as follows: The expression for the vertical deformation of the main span main beam is as follows: The expression for the vertical deformation of the main beam at the side span is: Wherein, η1, η2, and η3 are the combination coefficients of the deformation of the main beam caused by the bridge tower, the deformation of the main beam itself, and the deformation of the main beam caused by the stay cables, respectively, on the bridge deck deformation.

10. The method for predicting bridge deck deformation under temperature influence in a multi-tower cable-stayed bridge for both road and rail use, as described in claim 9, is characterized in that... The general expression for the combination coefficients is: ； ； ； ； Where i is 1, 2, or 3; φ z φ is the influence coefficient of bridge alignment. s φ is the seasonal influence coefficient. j φ w These are the influence coefficients for longitude and latitude, S, respectively. i Let θ be the solar radiation coefficient. z The angle between due north and the longitudinal axis of the bridge, M is the month, ε1 is latitude, ε2 is longitude, and I... t I represents the measured solar radiation intensity at that moment. i The solar radiation intensities corresponding to the temperature gradient models of the bridge tower, the main girder, and the most unfavorable temperature difference models between the stay cables and the tower and girder, namely I1, I2, and I3, are respectively I p I g and I c .

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