Method and system for determining reasonable vertical stiffness of long-span new highway bridge

Abstract

Disclosed in the present invention are a method and system for determining reasonable vertical stiffness of a long-span new highway bridge. The method comprises: by means of a finite element model for an initial design scheme of a long-span new highway bridge, calculating a vertical deflection-to-span ratio and a beam end vertical rotation angle of the bridge under the characteristic combination of a permanent load, a live load, a temperature action, and a wind load; performing checking calculation on indicators for driving safety and comfort on the bridge, indicators for the usage of a beam end bearing and an expansion joint, and indicators for a vertical curve of a route after vertical deformation of a main girder; taking the requirements for the driving safety and comfort on the bridge, the requirements for the usage of the beam end bearing and the expansion joint, and the requirements for the vertical curve of the route after the vertical deformation of the main girder as constraints to decrease or increase bridge design parameters in the finite element model; and determining, as the minimum value of the reasonable vertical stiffness of the bridge, the maximum vertical deflection-to-span ratio and the maximum beam end vertical rotation angle in all schemes satisfying the constraints. The present invention can provide a reliable reference for the reasonable design, economy, and safety of long-span new highway bridges.

Description

A method and system for determining reasonable vertical stiffness of newly built long-span highway bridges Technical Field

[0001] The present invention belongs to the technical field of bridge engineering, and more specifically, relates to a method and system for determining the reasonable vertical stiffness of a newly built long-span highway bridge. Background Art

[0002] As bridge spans increase, their inherent stiffness decreases, their damping becomes lower, and their sensitivity to dynamic forces increases. Bridge stiffness can be primarily categorized as vertical and lateral stiffness, often expressed using metrics such as the vertical and lateral deflection-to-span ratios. For example, the "Design Code for Highway Suspension Bridges" (JTGT D65-05-2015) stipulates that "the maximum vertical deflection of the stiffening beam caused by frequently encountered lane loads should not exceed 1 / 250 of the span" and "the maximum lateral displacement of the stiffening beam under wind loads should not exceed 1 / 150 of the span." The explanatory text states that "the limits on the vertical deflection and lateral displacement of the stiffening beam are primarily intended to ensure smooth, comfortable, and safe driving, and are established with reference to statistical data from existing suspension bridges domestically and internationally." Therefore, determining the appropriate stiffness limit is a complex issue involving both engineering safety and economic efficiency: too low a stiffness makes it difficult to ensure structural safety, driving safety, and comfort; too high a stiffness significantly increases construction investment and complexity. Technical issues

[0003] The scope of application of current bridge design specifications is limited. For example, the "Highway Suspension Bridge Design Specification" (JTGT D65-05-2015) applies only to bridges with main spans under 2,000 meters, and the "Highway Cable-Stayed Bridge Design Specification" (JTG3365-01) applies only to the design of new and renovated highway cable-stayed bridges with spans under 1,000 meters. There are no relevant design specifications for cable-stayed and suspension bridges. For suspension bridges with spans exceeding 2,000 meters, cable-stayed bridges with spans exceeding 1,200 meters, and cable-stayed and suspension bridges with spans exceeding 150 meters, the current design specifications are not applicable or lack relevant regulations, resulting in a lack of design basis. Therefore, for these large-span highway bridges, a reasonable vertical stiffness determination method and system suitable for new large-span highway bridges is urgently needed to provide technical support for bridge design. Technical Solutions

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a method and system for determining the reasonable vertical stiffness of a newly built long-span highway bridge, establishes a finite element model of the initial design scheme of a newly built long-span highway bridge, increases or decreases the vertical stiffness of the bridge by increasing or decreasing the cross-sectional area or elastic modulus of the main cables or stays, main beams, and bridge towers in the finite element model, calculates the vertical deflection-span ratio and vertical beam end rotation angle of the bridge under the standard combination of dead load, live load, temperature, and wind load after the vertical stiffness adjustment, and simultaneously performs wind-vehicle-bridge coupled vibration analysis, taking the requirements for driving safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, the requirements for the vertical curve of the line after the vertical deformation of the main beam, etc. as restriction conditions, and the bridge that meets the above requirements will be included. The maximum vertical deflection-span ratio and vertical beam end rotation angle in all schemes with the above-mentioned restriction conditions are used as characterizing indicators of reasonable vertical stiffness of the bridge; this allows designers to ensure that the vertical deflection-span ratio and vertical beam end rotation angle of the final design scheme of a new large-span highway bridge are less than the allowable vertical deflection-span ratio and allowable beam end rotation angle under the standard combination of dead load, live load, temperature and wind load during bridge design; the present invention can solve the problem that the existing highway bridge design specifications for suspension bridges with a span of over 2000 meters, cable-stayed bridges with a span of over 1200 meters, cable-stayed-suspension combined bridges with a span of over 150 meters, etc., have no provisions for vertical stiffness limits and lack a basis for vertical stiffness design, and can provide a reliable reference for the reasonable design, economy and safety of new large-span highway bridges.

[0005] To achieve the above object, one aspect of the present invention provides a method for determining the reasonable vertical stiffness of a newly built long-span highway bridge, comprising the following steps:

[0006] S1: Establish a finite element model for the initial design of a new long-span highway bridge;

[0007] S2: Calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the finite element model, and record the calculation results;

[0008] S3: Perform wind-vehicle-bridge coupled vibration analysis to verify the safety and comfort indicators of driving on the bridge, the use indicators of beam end supports and expansion joints, and the vertical curve indicators of the line after vertical deformation of the main beam;

[0009] S4: Using the requirements for driving safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam as constraints, the cross-sectional area or elastic modulus of the bridge main cables or stays, main beams, and bridge towers in the finite element model is reduced or increased to obtain an updated finite element model, and then the next step is executed;

[0010] S5: Calculate the bridge through the updated finite element model under the action of the standard combination of dead load, live load, temperature, wind load vertical deflection span ratio and beam end vertical rotation; repeat steps S3 ~ S4;

[0011] S6: Determine the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the restriction conditions described in step S4 in step S3 as the minimum value of the reasonable vertical stiffness of the bridge.

[0012] Furthermore, step S3 includes: performing wind-vehicle-bridge coupled vibration analysis, and respectively verifying the driving safety and comfort indicators on the bridge, the use indicators of the beam end supports and expansion joints, and the vertical curve indicators of the line after the vertical deformation of the main beam; at the same time, judging whether this verification is the first verification; if yes, executing steps S4 to S5; otherwise, further judging whether the result of this verification is consistent with the result of the previous verification; if consistent, executing steps S4 to S5; if inconsistent, executing step S6.

[0013] Furthermore, step S4 includes: judging whether the driving safety and comfort index on the bridge, the use index of the beam end support and expansion joint, and the vertical curve index of the line after the vertical deformation of the main beam meet the respective use requirements; if so, reducing the cross-sectional area or elastic modulus of the main cables or cables, main beams, and bridge towers in the finite element model in step S1 by 2% to 5%, and obtaining a finite element model with increased parameters; if not, increasing the cross-sectional area or elastic modulus of the main cables or cables, main beams, and bridge towers in the finite element model in step S1 by 2% to 5%, and obtaining a finite element model with decreased parameters.

[0014] Furthermore, in step S3, the calculation of the on-bridge driving safety and comfort index includes:

[0015] S31: constructing a random traffic flow model based on the survey and prediction analysis results of vehicles passing through the newly built bridge on the large-span highway;

[0016] S32: Establishing a wind-vehicle-bridge coupled vibration equation using the random vehicle flow model;

[0017] S33: Calculate and analyze the vehicle acceleration and the contact force response between the wheels and the bridge deck during the entire process of random vehicle flow passing through the bridge through the wind-vehicle-bridge coupled vibration equation to obtain the roll safety factor, sideslip safety factor and vehicle comfort of driving on the bridge.

[0018] Furthermore, the wind-vehicle-bridge coupled vibration equation in step S32 is expressed by equations (1) and (2):

[0019] (1)

[0020] (2)

[0021] Where, Indicates the quality of the car; Indicates the quality of the bridge; Indicates the damping of the car; represents the damping of the bridge; represents the stiffness matrix of the car; represents the stiffness matrix of the bridge; represents the force vector of the car; represents the force vector of the bridge; represents the displacement of the car; represents the displacement of the bridge; Indicates the speed of the car; Indicates the speed of the bridge; represents the acceleration of the car; represents the acceleration of the bridge; represents the force exerted by the bridge on the car; represents the force exerted by the car on the bridge; the superscript ae represents the wind effect; Indicates the force of wind on the car; Represents the force exerted by the car on the bridge.

[0022] Furthermore, the roll safety factor in step S33 is expressed by formula (3):

[0023] (3)

[0024] Where, RSF represents the roll safety factor; Indicates the vertical contact force between the left wheel and the road; Indicates the vertical contact force between the right wheel and the road surface; Indicates the vehicle's axles, Indicates the total number of axles of the vehicle;

[0025] The sideslip safety factor in step S33 is expressed by formula (4):

[0026] (4)

[0027] Where, represents the sideslip safety factor; Indicates the RMS value of the sideslip resistance of a certain axle; is the lateral adhesion rate between the wheel and the road surface; it can be set to 0.7, 0.5, 0.15, and 0.07 according to road conditions, representing four basic road conditions: dry, wet, snowy, and icy; is the weight of a certain axle of the vehicle, usually the axle with lighter axle weight; is the sideslip resistance of a certain axle; It represents the mean value of the sideslip resistance of a certain axle.

[0028] Furthermore, the vehicle comfort level in step S33 is calculated using equations (8) to (13):

[0029] (8)

[0030] (9)

[0031] (10)

[0032] (11)

[0033] (12)

[0034] (13)

[0035] Where, is the vehicle comfort; f is the frequency; Wx(f) is the frequency weighting function of longitudinal vibration; Wy(f) is the frequency weighting function of lateral vibration; Wz(f) is the frequency weighting function of vertical vibration; awx is the weighted acceleration of longitudinal vibration; awy is the weighted acceleration of lateral vibration; awz is the weighted acceleration of vertical vibration; Gax(f) is the power spectral density function of vehicle longitudinal vibration; Gay(f) is the power spectral density function of vehicle longitudinal vibration; Gaz(f) is the power spectral density function of vehicle longitudinal vibration.

[0036] Furthermore, the safety and comfort indexes of the bridge in step S4 satisfy the requirements, which means that the roll safety factor RSF of the vehicle passing the bridge is greater than 1.2, the sideslip safety factor SSF is greater than 1.0, and the vehicle comfort is greater than 1. Less than 0.315.

[0037] Furthermore, the beam end support and the telescopic device described in step S4 meet the use requirements, which means that under the standard combination of dead load, live load, temperature and wind load of the bridge, the vertical rotation angle of the beam end is less than the limit value of the vertical rotation angle in the current relevant specifications for highway bridge supports; the vertical misalignment of the telescopic device caused by the vertical rotation angle of the beam end meets the relevant vertical misalignment requirements in the current specifications for telescopic devices.

[0038] Another aspect of the present invention provides a system for determining the reasonable vertical stiffness of a newly built long-span highway bridge, which is used to implement the method for determining the reasonable vertical stiffness of a newly built long-span highway bridge, comprising:

[0039] The first main module is used to establish a finite element model for the initial design of a new long-span highway bridge;

[0040] The second main module is used to calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect and wind load through the finite element model, and record the calculation results;

[0041] The third main module is used to perform wind-vehicle-bridge coupled vibration analysis, verifying the safety and comfort indicators of driving on the bridge, the use indicators of beam end supports and expansion joints, and the vertical curve indicators of the line after the vertical deformation of the main beam;

[0042] The fourth main module is used to use the requirements for traffic safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam as constraints. It adjusts or increases the cross-sectional area or elastic modulus of the bridge's main cables or stays, main beams, and bridge towers in the finite element model to obtain an updated finite element model and then proceed to the next step.

[0043] The fifth main module is used to calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the updated finite element model; repeating steps S3 to S4;

[0044] The sixth main module is used to determine the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the restriction conditions described in step S4 in step S3 as the minimum value of the reasonable vertical stiffness of the bridge. Beneficial effects

[0045] The present invention provides a method and system for determining the reasonable vertical stiffness of a newly built long-span highway bridge. The method establishes a finite element model of the initial design scheme of the newly built long-span highway bridge, takes the requirements for driving safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, the requirements for the vertical curve of the line after the vertical deformation of the main beam, etc. as constraint conditions, continuously adjusts the finite element model parameters to adjust the vertical stiffness of the bridge, calculates the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load through the finite element model, and determines the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the constraint conditions as the minimum value of the reasonable vertical stiffness of the bridge; so that designers can During the design process, it can be ensured that the vertical deflection-span ratio and the vertical beam end rotation angle of the final design scheme of a newly built large-span highway bridge are less than the allowable vertical deflection-span ratio and the allowable beam end rotation angle under the standard combination of dead load, live load, temperature effect and wind load, thereby ensuring the safety of the bridge from three aspects: the safety of the bridge structure itself, the safety of drivers and passengers, and the safety of ancillary facilities, so that the process of determining the reasonable stiffness of the bridge can be quantified, analyzed scientifically, and have rules to rely on. The present invention breaks through the limitations of the previous norms that rely on the empirical method of statistical analysis of the stiffness indicators of existing bridges to determine the stiffness standard, and establishes a scientific method for determining the reasonable stiffness for specific bridges. It can provide technical support for the design of super bridge projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] FIG1 is a flow chart of a method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to an embodiment of the present invention;

[0047] FIG2 is a schematic diagram of the main calculation process of a method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to an embodiment of the present invention. Best Mode for Carrying Out the Invention

[0048] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0049] As shown in FIG1 and FIG2, the present invention provides a method for determining the reasonable vertical stiffness of a newly built long-span highway bridge, comprising the following steps:

[0050] S1: Establish a finite element model for the initial design of a new long-span highway bridge;

[0051] S2: Calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the finite element model, and record the calculation results;

[0052] S3: Perform wind-vehicle-bridge coupled vibration analysis to verify the safety and comfort indicators of driving on the bridge, the use indicators of beam end supports and expansion joints, and the vertical curve indicators of the line after vertical deformation of the main beam;

[0053] S4: Using the requirements for driving safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam as constraints, the cross-sectional area or elastic modulus of the bridge main cables or stays, main beams, and bridge towers in the finite element model is reduced or increased to obtain an updated finite element model, and then the next step is executed;

[0054] S5: Calculate the bridge through the updated finite element model under the action of the standard combination of dead load, live load, temperature, wind load vertical deflection span ratio and beam end vertical rotation; repeat steps S3 ~ S4;

[0055] S6: Determine the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the restriction conditions described in step S4 in step S3 as the minimum value of the reasonable vertical stiffness of the bridge.

[0056] Furthermore, the "newly constructed large-span highway bridge" in step S1 refers to a suspension bridge with a span exceeding 2,000 meters, a cable-stayed bridge with a span exceeding 1,200 meters, or a cable-stayed-suspension bridge with a span exceeding 150 meters. The establishment of a finite element model for the initial design of the new long-span highway bridge includes:

[0057] S11: Determine the node positions and element types of the finite element model based on the design drawings of the initial design scheme of the new long-span highway bridge, use cable elements to simulate the main cables or stays, and use beam elements to simulate the bridge towers, piers, and main beams;

[0058] S12: According to the design requirements of the bridge, set the material properties and cross-sectional characteristics of the unit; the material properties include elastic modulus, Poisson's ratio, and density; the cross-sectional characteristics mainly include the geometric shape or cross-sectional area of ​​the cross-section;

[0059] S13: According to the design requirements of the bridge, determine the constraints and boundary conditions between the main components, and adopt fixed constraints at the bottom of the foundation;

[0060] S14: According to the design requirements of the bridge, determine the loads on the finite element model. All units are subject to the dead load caused by their own weight and temperature effects; all units corresponding to structural components above the water surface are subject to wind loads; all units where the main beams are located are subject to live loads, as well as the dead weight loads caused by the bridge deck pavement and railings.

[0061] Furthermore, in step S2, the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature action, and wind load are calculated using the finite element model, including:

[0062] S21: Determine the load combination method under the standard combination according to the bridge design specification;

[0063] S22: Using the finite element model established in step S1, respectively solve the deflection of the mid-span main beam and the vertical rotation angle at the beam end of the bridge under the action of dead load, live load, temperature, and wind load; wherein the deflection of the mid-span main beam and the vertical rotation angle at the beam end under the action of live load adopt the results of the most unfavorable loading position;

[0064] S23: Calculate the vertical deflection-span ratio and vertical rotation of the beam ends of a bridge under the standard combination of dead load, live load, temperature effect, and wind load.

[0065] Furthermore, in step S23, the vertical deflection-span ratio of the bridge is the deflection of the bridge under vertical load, which is calculated by the ratio of the maximum vertical displacement of the bridge to the span of the bridge, and is used to evaluate the vertical safety of the bridge; the vertical rotation angle of the beam end of the bridge is obtained by the rotation angle of the beam end section or the displacement difference of the beam end node, and is used to evaluate the degree of rotation of the beam end of the bridge under load, and then evaluate the safety of the bridge.

[0066] Furthermore, step S3 includes: performing a wind-vehicle-bridge coupled vibration analysis to verify the traffic safety and comfort indicators on the bridge, the use indicators of the beam end supports and expansion joints, and the vertical curve indicators of the line after the vertical deformation of the main beam; and determining whether this verification is the first verification; if so, executing steps S4 to S5; otherwise, further determining whether the verification results are consistent with the previous verification results; if they are consistent, executing steps S4 to S5; if not, executing step S6;

[0067] Furthermore, in step S3, the calculation of the on-bridge driving safety and comfort index includes:

[0068] S31: constructing a random traffic flow model based on the survey and prediction analysis results of vehicles passing through the newly built bridge on the large-span highway;

[0069] S32: Establishing a wind-vehicle-bridge coupled vibration equation using the random vehicle flow model;

[0070] S33: Calculate and analyze the vehicle acceleration and the contact force response between the wheels and the bridge deck during the entire process of random vehicle flow passing through the bridge through the wind-vehicle-bridge coupled vibration equation to obtain the roll safety factor, sideslip safety factor and vehicle comfort of driving on the bridge.

[0071] Furthermore, the wind-vehicle-bridge coupled vibration equation in step S32 is expressed by equations (1) and (2):

[0072] (1)

[0073] (2)

[0074] Where, Indicates the quality of the car; Indicates the quality of the bridge; Indicates the damping of the car; represents the damping of the bridge; represents the stiffness matrix of the car; represents the stiffness matrix of the bridge; represents the force vector of the car; represents the force vector of the bridge; represents the displacement of the car; represents the displacement of the bridge; Indicates the speed of the car; Indicates the speed of the bridge; represents the acceleration of the car; represents the acceleration of the bridge; represents the force exerted by the bridge on the car; represents the force exerted by the car on the bridge; the superscript ae represents the wind effect; Indicates the force of wind on the car; Represents the force exerted by the car on the bridge.

[0075] Furthermore, the roll safety factor in step S33 is used to evaluate the safety of the bridge under the action of lateral force, and is expressed by formula (3):

[0076] (3)

[0077] Where, RSF represents the roll safety factor; Indicates the vertical contact force between the left wheel and the road; Indicates the vertical contact force between the right wheel and the road surface; Indicates the vehicle's axles, Indicates the total number of axles of the vehicle;

[0078] Furthermore, the sideslip safety factor in step S33 is used to evaluate the stability of the bridge under the action of lateral force, and is expressed by formula (4):

[0079] (4)

[0080] (5)

[0081] (6)

[0082] (7)

[0083] Where, represents the sideslip safety factor; Indicates the RMS value of the sideslip resistance of a certain axle; is the lateral adhesion rate between the wheel and the road surface; it can be set to 0.7, 0.5, 0.15, and 0.07 according to road conditions, representing four basic road conditions: dry, wet, snowy, and icy; is the weight of a certain axle of the vehicle, usually the axle with lighter axle weight; It is called sideslip resistance; represents the mean value of the sideslip resistance of a certain axle; T is the calculation time length; Indicates the wheel on the windward side of a certain axle, represents the vertical contact force of the wheel on the leeward side of a certain axle; represents the lateral contact force of the wheel on the windward side of a certain axle, is the lateral contact force of the wheel on the leeward side of a certain axle.

[0084] The vehicle comfort level in step S33 is calculated using equations (8) to (13):

[0085] (8)

[0086] (9)

[0087] (10)

[0088] (11)

[0089] (12)

[0090] (13)

[0091] Where, is the vehicle comfort; f is the frequency; Wx(f) is the frequency weighting function of longitudinal vibration; Wy(f) is the frequency weighting function of lateral vibration; Wz(f) is the frequency weighting function of vertical vibration; awx is the weighted acceleration of longitudinal vibration; awy is the weighted acceleration of lateral vibration; awz is the weighted acceleration of vertical vibration; Gax(f) is the power spectral density function of vehicle longitudinal vibration; Gay(f) is the power spectral density function of vehicle longitudinal vibration; Gaz(f) is the power spectral density function of vehicle longitudinal vibration.

[0092] Furthermore, step S4 includes: judging whether the driving safety and comfort index on the bridge, the use index of the beam end support and expansion joint, and the vertical curve index of the line after the vertical deformation of the main beam meet the respective use requirements; if so, reducing the cross-sectional area or elastic modulus of the main cables or cables, main beams, and bridge towers in the finite element model in step S1 by 2% to 5%, and obtaining a finite element model with increased parameters; if not, increasing the cross-sectional area or elastic modulus of the main cables or cables, main beams, and bridge towers in the finite element model in step S1 by 2% to 5%, and obtaining a finite element model with decreased parameters.

[0093] Furthermore, the safety and comfort indexes of the bridge in step S4 satisfy the requirements, which means that the roll safety factor RSF of the vehicle passing the bridge is greater than 1.2, the sideslip safety factor SSF is greater than 1.0, and the vehicle comfort is greater than 1. less than 0.315; the beam end support and the expansion device described in step S4 meet the use requirements, which means that under the standard combination of dead load, live load, temperature effect and wind load, the vertical rotation angle of the beam end is less than the limit value of its vertical rotation angle in the current relevant specifications for highway bridge supports; the vertical misalignment of the expansion device caused by the vertical rotation angle of the beam end meets the relevant vertical misalignment requirements in the current specifications for expansion devices; the vertical curve of the line after the vertical deformation of the main beam described in step S4 meets the requirements, which means that under the standard combination of dead load, live load, temperature effect and wind load, after considering the vertical displacement of the main beam, the maximum longitudinal slope of the main beam is less than the maximum longitudinal slope requirement of the current "Highway Engineering Technical Standard"; after considering the vertical deformation of the main beam, the sight distance from the viewpoint height of a passenger car (1.2m) and the viewpoint height of a heavy truck (2.0m) on the bridge deck to the height of the top of the obstacle on the road in front of the viewpoint (0.1m) should be greater than the requirements for the parking sight distance in the current "Highway Engineering Technical Standard".

[0094] Furthermore, the present invention uses the vertical deflection-span ratio of the bridge and the vertical rotation angle of the beam end of the bridge as evaluation indicators of the vertical stiffness of the bridge; the maximum values ​​of the vertical deflection-span ratio of the bridge and the vertical rotation angle of the beam end of the bridge are used as the minimum value of the reasonable vertical stiffness of the bridge; in step S6, the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle calculated by the finite element model of the initial design scheme, the finite element model after parameter increase and update, and the finite element model after parameter decrease and update are used as the minimum value of the reasonable vertical stiffness design of the bridge; wherein, the maximum vertical deflection-span ratio is referred to as the allowable vertical deflection-span ratio ; The maximum vertical beam end rotation angle is referred to as the allowable beam end rotation angle; when designing, designers should ensure that the vertical deflection-span ratio and the vertical beam end rotation angle of the final design scheme of the newly built large-span highway bridge under the standard combination of dead load, live load, temperature and wind load are less than the allowable vertical deflection-span ratio and the allowable beam end rotation angle, so that the designed bridge maintains a reasonable vertical stiffness, and thus ensures the safety of the bridge from three aspects: the safety of the bridge structure, the safety of drivers and passengers, and the safety of ancillary facilities; the present invention makes the process of determining the reasonable stiffness of the bridge quantifiable, scientific, reasonable and rule-based.

[0095] Another aspect of the present invention provides a system for determining the reasonable vertical stiffness of a newly built long-span highway bridge, comprising:

[0096] The first main module is used to establish a finite element model for the initial design of a new long-span highway bridge;

[0097] The second main module is used to calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect and wind load through the finite element model, and record the calculation results;

[0098] The third main module is used to perform wind-vehicle-bridge coupled vibration analysis, verifying the safety and comfort indicators of driving on the bridge, the use indicators of beam end supports and expansion joints, and the vertical curve indicators of the line after the vertical deformation of the main beam;

[0099] The fourth main module is used to use the requirements for traffic safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam as constraints. It adjusts or increases the cross-sectional area or elastic modulus of the bridge's main cables or stays, main beams, and bridge towers in the finite element model to obtain an updated finite element model and then proceed to the next step.

[0100] The fifth main module is used to calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the updated finite element model; repeating steps S3 to S4;

[0101] The sixth main module is used to determine the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the restriction conditions described in step S4 in step S3 as the minimum value of the reasonable vertical stiffness of the bridge.

[0102] The present invention provides a method for determining the reasonable vertical stiffness of a newly built long-span highway bridge. A finite element model of an initial design scheme for a newly built long-span highway bridge is established. The vertical stiffness of the bridge is increased or decreased by adjusting the cross-sectional area or elastic modulus of the main cables or stays, main beams, and bridge towers in the finite element model. The vertical deflection-span ratio and vertical beam end rotation angle of the bridge are calculated under the standard combination of dead load, live load, temperature, and wind load. At the same time, a wind-vehicle-bridge coupled vibration analysis is performed. The requirements for driving safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam are used as restrictive conditions. The best solution among all the schemes that meet the above restrictive conditions is selected. The large vertical deflection-span ratio and the vertical beam end rotation angle are used as the minimum values ​​of the reasonable vertical stiffness of the bridge; this allows designers to ensure that the vertical deflection-span ratio and the vertical beam end rotation angle of the final design scheme of the new large-span highway bridge are less than the allowable vertical deflection-span ratio and the allowable beam end rotation angle under the standard combination of dead load, live load, temperature and wind load during bridge design, thereby ensuring the safety of the bridge from three aspects: the safety of the bridge structure, the safety of drivers and passengers, and the safety of ancillary facilities; the present invention can solve the stiffness design problem of the new large-span highway bridge whose main span exceeds the scope of application of the current specifications and whose bridge type is novel and has no design specifications to follow, and can provide a reliable reference for the reasonable design and economic safety of the new large-span highway bridge.

[0103] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining the reasonable vertical stiffness of a newly built long-span highway bridge, characterized by: The steps include: S1: Establish a finite element model for the initial design of a new long-span highway bridge; S2: Calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the finite element model, and record the calculation results; S3: Perform wind-vehicle-bridge coupled vibration analysis to verify the safety and comfort indicators of driving on the bridge, the use indicators of beam end supports and expansion joints, and the vertical curve indicators of the line after vertical deformation of the main beam; S4: Using the requirements for driving safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam as constraints, the cross-sectional area or elastic modulus of the bridge main cables or stays, main beams, and bridge towers in the finite element model is reduced or increased to obtain an updated finite element model, and then the next step is executed; S5: Calculating the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the updated finite element model; Repeat steps S3 to S4; S6: Determine the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the restriction conditions described in step S4 in step S3 as the minimum value of the reasonable vertical stiffness of the bridge.

2. The method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to claim 1, characterized in that: Step S3 includes: performing wind-vehicle-bridge coupled vibration analysis, and verifying the driving safety and comfort indicators on the bridge, the use indicators of the beam end supports and expansion joints, and the vertical curve indicators of the line after the vertical deformation of the main beam; at the same time, judging whether this verification is the first verification; if yes, executing steps S4 to S5; otherwise, further judging whether the results of this verification are consistent with the results of the previous verification; if consistent, executing steps S4 to S5; if inconsistent, executing step S6.

3. The method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to claim 2, characterized in that: Step S4 includes: judging whether the driving safety and comfort index on the bridge, the use index of the beam end support and expansion joint, and the vertical curve index of the line after the vertical deformation of the main beam meet the respective use requirements; if so, reducing the cross-sectional area or elastic modulus of the main cables or cables, main beams, and bridge towers in the finite element model in step S1 by 2% to 5%, and obtaining a finite element model with increased parameters; if not, increasing the cross-sectional area or elastic modulus of the main cables or cables, main beams, and bridge towers in the finite element model in step S1 by 2% to 5%, and obtaining a finite element model with decreased parameters.

4. A method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to any one of claims 1 to 3, characterized in that: In step S3, the calculation of the on-bridge driving safety and comfort index includes: S31: constructing a random traffic flow model based on the survey and prediction analysis results of vehicles passing through the newly built bridge on the large-span highway; S32: Establishing a wind-vehicle-bridge coupled vibration equation using the random vehicle flow model; S33: Calculate and analyze the vehicle acceleration and the contact force response between the wheels and the bridge deck during the entire process of random vehicle flow passing through the bridge through the wind-vehicle-bridge coupled vibration equation to obtain the roll safety factor, sideslip safety factor and vehicle comfort of driving on the bridge.

5. The method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to claim 4 is characterized in that: The wind-vehicle-bridge coupled vibration equation in step S32 is expressed by equations (1) and (2): （1） （2） Where, Indicates the quality of the car; Indicates the quality of the bridge; Indicates the damping of the car; represents the damping of the bridge; represents the stiffness matrix of the car; represents the stiffness matrix of the bridge; represents the force vector of the car; represents the force vector of the bridge; represents the displacement of the car; represents the displacement of the bridge; Indicates the speed of the car; Indicates the speed of the bridge; represents the acceleration of the car; represents the acceleration of the bridge; represents the force exerted by the bridge on the car; represents the force exerted by the car on the bridge; Indicates the force of wind on the car; Represents the force exerted by wind on the bridge.

6. The method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to claim 4 is characterized by: The roll safety factor in step S33 is expressed by formula (3): （3） Where, RSF represents the roll safety factor; Indicates the vertical contact force between the left wheel and the road surface; Indicates the vertical contact force between the right wheel and the road; Indicates the vehicle's axles, Indicates the total number of axles of the vehicle; The sideslip safety factor in step S33 is expressed by formula (4): （4） Where, represents the sideslip safety factor; Indicates the RMS value of the sideslip resistance of a certain axle; is the lateral adhesion rate between the wheel and the road; is the weight of a certain axle of the vehicle, usually the axle with lighter axle weight; is the sideslip resistance of a certain axle; It represents the mean value of the sideslip resistance of a certain axle.

7. The method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to claim 4 is characterized by: The vehicle comfort level in step S33 is calculated using equations (8) to (13): （8） （9） （10） （11） （12） （13） Where, is the vehicle comfort; f is the frequency; Wx(f) is the frequency weighting function of longitudinal vibration; Wy(f) is the frequency weighting function of lateral vibration; Wz(f) is the frequency weighting function of vertical vibration; awx is the weighted acceleration of longitudinal vibration; awy is the weighted acceleration of lateral vibration; awz is the weighted acceleration of vertical vibration; Gax(f) is the power spectral density function of vehicle longitudinal vibration; Gay(f) is the power spectral density function of vehicle longitudinal vibration; Gaz(f) is the power spectral density function of vehicle longitudinal vibration.

8. A method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to any one of claims 1 to 3, 5 or 6, characterized in that: In step S4, the safety and comfort indexes of the bridge driving meet the requirements, which means that the roll safety factor RSF of the vehicle passing the bridge is greater than 1.2, the sideslip safety factor SSF is greater than 1.0, and the vehicle comfort Less than 0.

315.

9. A method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to any one of claims 1 to 3, 5 or 6, characterized in that: The beam end support and expansion device described in step S4 meet the use requirements, which means that under the standard combination of dead load, live load, temperature and wind load of the bridge, the vertical rotation angle of the beam end is less than the limit value of the vertical rotation angle in the current relevant specifications for highway bridge supports; the vertical misalignment of the expansion device caused by the vertical rotation angle of the beam end meets the relevant vertical misalignment requirements in the current specifications for expansion devices.

10. A system for determining the reasonable vertical stiffness of a newly built long-span highway bridge, characterized in that: A method for determining the reasonable vertical stiffness of a newly built long-span highway bridge according to any one of claims 1 to 9, comprising: The first main module is used to establish a finite element model for the initial design of a new long-span highway bridge; The second main module is used to calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect and wind load through the finite element model, and record the calculation results; The third main module is used to perform wind-vehicle-bridge coupled vibration analysis, verifying the safety and comfort indicators of driving on the bridge, the use indicators of beam end supports and expansion joints, and the vertical curve indicators of the line after the vertical deformation of the main beam; The fourth main module is used to use the requirements for traffic safety and comfort on the bridge, the requirements for the use of beam end supports and expansion joints, and the requirements for the vertical curve of the line after the vertical deformation of the main beam as constraints. It adjusts or increases the cross-sectional area or elastic modulus of the bridge's main cables or stays, main beams, and bridge towers in the finite element model to obtain an updated finite element model and then proceed to the next step. The fifth main module is used to calculate the vertical deflection-span ratio and the vertical rotation angle of the beam end of the bridge under the standard combination of dead load, live load, temperature effect, and wind load using the updated finite element model; repeating steps S3 to S4; The sixth main module is used to determine the maximum vertical deflection-span ratio and the maximum vertical beam end rotation angle in each scheme that meets the restriction conditions described in step S4 in step S3 as the minimum value of the reasonable vertical stiffness of the bridge.

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