Method for calculating lateral action effect of vertical live load on curved lane

Abstract

This application relates to a method for calculating the lateral action effect caused by vertical live load on a curved lane, including: obtaining the lateral action effect caused by vertical live load on the curved lane. n The coordinates of the lane sequence nodes are determined; the lane sequence nodes are fitted to generate a lane fitting curve; the coordinates of the lane sequence nodes are substituted into the lane fitting curve to calculate the lateral centrifugal effect at each lane sequence node; based on the lateral centrifugal effect, the coordinates of the first lane sequence node on the curve are calculated. n This application calculates the lateral effect of vertical live loads on bridges by analyzing the vertical live loads at each lane sequence node. It generates lane fitting curves through lane sequence nodes to accurately capture the curvature changes of curved lanes; it independently calculates the lateral centrifugal effect at each lane sequence node, achieving real-time dynamic binding of centrifugal force and vertical load; and it calculates the vertical live load based on the lateral centrifugal effect, performing coupled calculations to eliminate errors and efficiently and accurately calculate the lateral effect of vertical loading on the bridge.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering analysis technology, specifically to a method for calculating the lateral effect caused by vertical live loads on curved lanes. Background Technology

[0002] In bridge design and analysis, accurately assessing the lateral forces acting on vehicles traveling on curved lanes is crucial for evaluating the safety and structural stability of bridge structures.

[0003] In related technologies, the most unfavorable load state corresponding to the maximum effect of vertical load is used. Then, the vertical load at this point is multiplied by an equivalent fixed lateral centrifugal effect C to obtain the most unfavorable lateral load, which is then applied to the structure to solve for the lateral response of the vertical live load on the curved lane. This method assumes that the location of the most unfavorable vertical load is exactly the same as the location of the most unfavorable lateral centrifugal force. However, in reality, the two may not be synchronized, and the fixed lateral centrifugal effect C cannot reflect the dynamic changes of centrifugal force, which may lead to error accumulation and make it difficult to efficiently and accurately calculate the lateral effect of lane vertical loading on the bridge. Summary of the Invention

[0004] This application provides a method for calculating the lateral effect caused by vertical live load on a curved lane, solving the technical problem that related technologies are unable to efficiently and accurately calculate the lateral effect on the bridge when the lane is vertically loaded.

[0005] This application provides a method for calculating the lateral effect caused by vertical live load on a curved lane, which includes the following steps:

[0006] Get on the curved lane n The coordinates of each lane sequence node;

[0007] Fit the lane sequence nodes to generate a lane fitting curve;

[0008] The coordinates of the lane sequence nodes are substituted into the lane fitting curve to calculate the lateral centrifugal effect at each lane sequence node.

[0009] Based on the lateral centrifugal effect, the first [item] on the curved lane is calculated. n The vertical live load on each lane sequence node is used to obtain the lateral effect caused by the vertical live load.

[0010] In one implementation, the acquisition of curved lanes n The coordinates of the lane sequence nodes include:

[0011] In the finite element model of the bridge structure, the longitudinal row of the main beam nodes is used as the reference axis, and the transverse offset distance is set to determine the actual position of the vehicle live load.

[0012] Based on the node coordinates on the reference axis and the transverse bridge offset distance, calculate the planar coordinates of the lane sequence nodes. , i = 1... n , n This represents the number of nodes in the lane sequence.

[0013] In one implementation, fitting the lane sequence nodes to generate a lane fitting curve includes:

[0014] The lane sequence nodes are initially fitted using a fourth-order polynomial to generate an initial lane curve;

[0015] The initial lane curve is approximated twice using a cubic polynomial to generate a lane fitting curve;

[0016] The lane fitting curve is represented as follows: .

[0017] In one embodiment, the step of substituting the coordinates of the lane sequence nodes into the lane fitting curve to calculate the lateral eccentricity effect at each of the lane sequence nodes includes:

[0018] The coordinates of each lane sequence node are substituted into the lane fitting curve to obtain the curvature at each lane sequence node. k ;

[0019] Based on the curvature k Calculate the lateral centrifugal effect at each lane sequence node. C。

[0020] In one implementation, the curvature k The calculation formula is: ;

[0021] in, , They are respectively y The first and second derivatives.

[0022] In one embodiment, the lateral centrifugal effect C The calculation formula is: ;

[0023] in, V The design speed for the curved lane.

[0024] In one implementation, the calculation of the first curve lane based on the lateral centrifugal effect... n The vertical live load on each lane sequence node is used to obtain the lateral effect caused by the vertical live load, including:

[0025] An influence matrix of corresponding action effects at each of the lane sequence nodes is calculated wherein n represents the i-th lane sequence node, n m represents the i-th lane sequence node, m

[0026] The vertical live load action at the i-th lane sequence node on the curved lane is obtained n

[0027] The live load action force is calculated based on the vertical live load action and the lateral centrifugal effect C

[0028] The influence matrix is multiplied by the live load action force to obtain the live load result of the i-th live load calculation item at the i-th lane sequence node action live load n m

[0029] The live load results of the i-th live load calculation item of all lane sequence nodes at the live load action position are superimposed to obtain the lateral action effect caused by the vertical live load action. m

[0030] In an embodiment, the influence matrix of corresponding action effects at each lane sequence node is calculated by a motorized method influence line

[0031] In an embodiment, the influence matrix is represented as:

[0032]

[0033] wherein, k ij in the formula, F represents the action effect, i and F represents the unit force applied at the lane sequence node. j

[0034] In an embodiment, the calculation formula of the live load action force is:

[0035]

[0036] wherein, is the intersection angle cosine of the projection of the unit coordinate axis at the lane sequence node in the horizontal plane and the axis of the overall coordinate system, y is the intersection angle cosine of the projection of the unit coordinate axis at the lane sequence node in the horizontal plane and the axis of the overall coordinate system, X is the intersection angle cosine of the projection of the unit coordinate axis at the lane sequence node in the horizontal plane and the axis of the overall coordinate system, is the intersection angle cosine of the projection of the unit coordinate axis at the lane sequence node in the horizontal plane and the axis of the overall coordinate system.​​​​​​​​​​​​​​x Projection of the axis on the horizontal plane and the overall coordinate system Y Cosine of the intersection angle of the axes.

[0037] The technical scheme provided by the embodiment of the application brings the beneficial effects including:

[0038] The application provides a calculation method of transverse action effect caused by vertical live load on a curved lane, generates a lane fitting curve through lane sequence nodes, accurately captures the curvature change of the curved lane, and provides a real geometric basis for subsequent centrifugal force calculation, and is especially suitable for complex line shapes (such as S-shaped bends and spiral ramps); the transverse centrifugal effect is independently calculated on each lane sequence node, the fixed transverse centrifugal effect C is replaced, real-time dynamic binding of the centrifugal force and the vertical load is realized, and the actual physical scene is more in line with; and the vertical live load action is calculated based on the transverse centrifugal effect, coupling calculation is performed to synchronously obtain the joint most unfavorable state of the vertical load and the transverse effect, errors possibly caused by the fixed transverse centrifugal effect in the related art are eliminated, the transverse action effect of the lane on the bridge when the lane is vertically loaded is efficiently and accurately calculated, and accurate transverse load data support is provided for bridge structure design and safety evaluation. BRIEF DESCRIPTION OF DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed to be used in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0040] Figure 1 The step flow chart of the calculation method of the transverse action effect caused by the vertical live load on the curved lane in an embodiment of the application.

[0041] Figure 2 The schematic diagram of the lane sequence node and the lane fitting curve in an embodiment of the application.

[0042] Figure 3 The direction schematic diagram of the centrifugal force effect influence matrix in an embodiment of the application.

[0043] In the figure: 1, lane sequence node; 2, lane fitting curve; 3, beam unit. DETAILED DESCRIPTION

[0044] In the following, the technical solutions in the embodiments of the present application will be described clearly and completely in conjunction with the accompanying drawings of the embodiments of the present application, so that those skilled in the art can better understand the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0045] The embodiment of the present application provides a calculation method of a lateral action effect caused by a vertical live load on a curved lane, which can solve the technical problem that the related art cannot efficiently and accurately calculate the lateral action effect of the bridge caused by the vertical loading of the lane.

[0046] As shown in Figure 1 , Fig. 1 is a step flow chart of the calculation method of the lateral action effect caused by the vertical live load on the curved lane according to an embodiment of the present application. Figure 1

[0047] The embodiment of the present application provides a calculation method of a lateral action effect caused by a vertical live load on a curved lane, which includes the following steps:

[0048] Step S1, obtaining coordinates of a plurality of lane sequence nodes on a curved lane; n

[0049] Step S2, fitting the lane sequence nodes to generate a lane fitting curve;

[0050] Step S3, bringing the coordinates of the lane sequence nodes into the lane fitting curve to calculate a lateral centrifugal effect at each lane sequence node;

[0051] Step S4, calculating a vertical live load action on the first lane sequence node on the curved lane based on the lateral centrifugal effect to obtain a lateral action effect caused by the vertical live load action. n

[0052] ​​​The embodiment provides a calculation method of a transverse action effect caused by a vertical live load on a curve lane, lane fitting curves are generated through lane sequence nodes, variation of curvatures of the curve lane is accurately captured, and a real geometric basis is provided for subsequent centrifugal force calculation, and the method is especially suitable for complex line shapes (such as S-shaped bends and spiral ramps); the transverse centrifugal effect is independently calculated on each lane sequence node, a fixed transverse centrifugal effect C is replaced, real-time dynamic binding of the centrifugal force and the vertical load is realized, and the method is more in line with an actual physical scene; and the vertical live load action is calculated based on the transverse centrifugal effect, coupling calculation is performed to synchronously obtain a joint most unfavorable state of the vertical load and the transverse effect, errors possibly caused by the fixed transverse centrifugal effect in related technologies are eliminated, the transverse action effect of the lane vertical loading on the bridge is efficiently and accurately calculated, and accurate transverse load data support is provided for bridge structure design and safety evaluation.

[0053] The following will be described in detail.

[0054] In an embodiment, step S1, coordinates of lane sequence nodes on a curve lane are acquired, and the lane sequence nodes are generated through lane fitting curves. n The coordinates of the lane sequence nodes include:

[0055] Step S11, in the bridge structure finite element model, a main girder node longitudinal column is taken as a reference axis, a transverse bridge offset distance is set to determine an actual action position of the vehicle live load;

[0056] Step S12, plane coordinates of the lane sequence nodes are calculated according to the node coordinates on the reference axis and the transverse bridge offset distance. i = 1... n n The lane sequence nodes are numbered.

[0057] Through the above scheme, the main girder node longitudinal column is an actual structure axis (including real geometric shapes of the bridge, such as pre-camber and construction deformation) in the bridge structure finite element model, rather than an ideal design line; the transverse bridge offset distance is set to determine the actual action position of the vehicle live load (such as lane width and vehicle transverse distribution), and the load is ensured to be applied at a real most unfavorable position of the structure response, so that the geometric matching degree of the load-structure is significantly improved, and calculation errors of bending moment and torque caused by coordinate deviation are avoided.

[0058] Please refer to Figure 2 Figure 2 FIG. 1 is a schematic diagram of lane sequence nodes and lane fitting curves in an embodiment of the present application.

[0059] In an embodiment, step S2, fitting the lane sequence nodes to generate lane fitting curves includes:

[0060] Step S21, a fourth-degree polynomial is used to initially fit the lane sequence nodes to generate an initial lane curve.​​​

[0061] Specifically, the complex lane geometry features (such as S-shaped curves, sudden curvature changes) are captured, and a 4th order polynomial is used to represent the lane fitting curve as follows: An initial fitting is performed on the lane sequence nodes to generate an initial lane curve.

[0062] Step S22, a 3rd order polynomial is used to perform a second approximation on the initial lane curve to generate a lane fitting curve.

[0063] The lane fitting curve is represented as follows: .

[0064] Specifically, a 3rd order polynomial is used to perform a degradation approximation fitting, which is represented as follows: A tolerance value is set to ensure that the maximum deviation of the new curve from the initial lane curve does not exceed the engineering tolerance error. Based on the initial lane curve, a second approximation is performed to generate a lane fitting curve, which is represented as follows: .

[0065] Through the above scheme, since the curved lane often contains complex geometric features such as S-shaped curves, sudden curvature changes, and variable radius sections, a low-order polynomial (such as 2nd order) cannot be flexibly fitted, and a high-order polynomial (such as 5th order or above) is prone to numerical oscillation. The present application first uses a 4th order polynomial to accurately describe the curvature change (such as inflection point, curvature extreme value), while avoiding overfitting and balancing flexibility and stability. Then, a 3rd order polynomial is used to perform a second approximation to improve the calculation efficiency. The lane sequence nodes are fitted by using a polynomial fitting method to filter the construction error and ensure the reliability of the curvature calculation.

[0066] In an embodiment, step S3, the coordinates of the lane sequence nodes are brought into the lane fitting curve to calculate the lateral centrifugal effect at each lane sequence node, including:

[0067] Step S31, the coordinates of each lane sequence node are brought into the lane fitting curve to obtain the curvature k .

[0068] In an embodiment, the curvature k is calculated according to the following formula: ;

[0069] Wherein, , are the first derivative and the second derivative of , respectively.

[0070] Step S32, based on the curvature k , the lateral centrifugal effect C at each lane sequence node is calculated.

[0071] In an embodiment, the lateral centrifugal effectC The calculation formula is: ;

[0072] in, V The design speed for the curved lane.

[0073] Using the above method, the curvature at each lane sequence node is calculated by fitting the lane curve, accurately capturing the curvature gradient; the lateral centrifugal effect at each lane sequence node is calculated in combination with the design speed, replacing the fixed lateral centrifugal effect in related technologies, and realizing real-time dynamic binding of centrifugal force and vertical load.

[0074] In one embodiment, step S4 involves calculating the number of lanes on the curved path based on the lateral centrifugal effect. n The vertical live load on each lane sequence node is used to obtain the lateral effect caused by the vertical live load, including:

[0075] Step S41: Calculate the influence matrix of the corresponding effect at each lane sequence node. ,in n Indicates the first n Lane sequence nodes, m Indicates the first m Live load calculation items;

[0076] Step S42: Obtain the first curve lane. n Vertical live load at each lane sequence node ;

[0077] Step S43, based on vertical live load action and lateral centrifugal effect C Calculate live load force ;

[0078] Step S44: Influence matrix With live load force Multiply to obtain the result at the 1st position. n The live load of the lane sequence node, the first m Live load results for the live load calculation item;

[0079] Step S45: Superimpose calculations on the first node of the sequence of all lanes at the location of the live load. m The live load calculation results are used to obtain the lateral action effect caused by the vertical live load.

[0080] The vertical live load and the transverse centrifugal force are considered synchronously at each lane sequence node to calculate the live load force, real-time load coupling is performed, and decoupling error is avoided; the influence matrix of the corresponding effect at each lane sequence node is calculated to directly map the load to the effect, and complex effects are compatible; the influence matrix and the live load force are multiplied to obtain the effect of each lane sequence node, and finally the effects of all lane sequence nodes are superimposed to realize automatic coverage of the most unfavorable combination, and the spatial distribution of the live load is accurately reflected.

[0081] In an embodiment, the influence matrix of the corresponding effect at each lane sequence node is calculated by a motorized influence line .

[0082] The motorized method (virtual work principle method) is an influence line solving method based on the virtual work principle, which constructs the influence line through virtual displacement (motorization), and is suitable for statically determinate and statically indeterminate structures. The influence line describes the change rule of an effect (such as bending moment, shear force, displacement, etc.) at a specified position when a unit moving load moves along the structure.

[0083] In an embodiment, the influence matrix is expressed as:

[0084] ;

[0085] wherein, k ij In the middle i , the action effect is, for example, the node displacement, the internal force or stress of the element, etc.; j The unit force applied at the lane sequence node, such as , , , , , .

[0086] For example, is the displacement influence matrix of node n , then k 23 represents the displacement value of node n at the lane sequence node under the action of the unit force applied at the lane sequence node n . d y .

[0087] Through the above scheme, the influence matrix is constructed once by the motorized method, which essentially encapsulates the structural response characteristics as a mathematical tool (matrix) in advance, so that the live load effect analysis is transformed from repetitive finite element calculation to efficient linear algebra operation, the calculation efficiency is improved, the matrix supports arbitrary load vector superposition, and is naturally adapted to centrifugal force and multi-lane loading.

[0088] Please refer to Figure 3 , Figure 3 Figure 1 is a schematic diagram of the direction of the centrifugal force effect influence matrix in an embodiment of the present application.

[0089] In an embodiment, the live load force is calculated by the formula:

[0090] ;

[0091] wherein, is the intersection angle cosine of the projection of the unit coordinate axis in the horizontal plane of the lane sequence node and the overall coordinate system y is the intersection angle cosine of the projection of the unit coordinate axis in the horizontal plane of the lane sequence node and the overall coordinate system X is the intersection angle cosine of the projection of the unit coordinate axis in the horizontal plane of the lane sequence node and the overall coordinate system is the intersection angle cosine of the projection of the unit coordinate axis in the horizontal plane of the lane sequence node and the overall coordinate system x is the intersection angle cosine of the projection of the unit coordinate axis in the horizontal plane of the lane sequence node and the overall coordinate system Y is the intersection angle cosine of the projection of the unit coordinate axis in the horizontal plane of the lane sequence node and the overall coordinate system

[0092] Through the above scheme, the live load force (including vertical load and transverse centrifugal force) under the local coordinate system is accurately converted into the overall coordinate system by introducing the direction cosine (cosα and cosβ), which strictly reflects the spatial directionality of the load and is compatible with any complex geometric shape.

[0093] It should be noted that the above-mentioned sequence numbers of the embodiments of the present application are only for description, and do not represent the advantages and disadvantages of the embodiments. The terms "include" and "have" in the specification and claims of the present application and the above-mentioned drawings are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units not listed, or optionally includes other steps or units inherent to the process, method, product or device. The terms "first", "second" and "third" and the like descriptions are used to distinguish different objects, and do not represent the order or limit the types of "first", "second" and "third".

[0094] In the description of the embodiments of the present application, "exemplary", "for example" or "for instance" is used to represent an example, illustration or description. Any embodiment or design scheme described as "exemplary", "for example" or "for instance" in the embodiments of the present application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. On the contrary, the words "exemplary", "for example" or "for instance" are intended to present the relevant concept in a specific way.

[0095] In the description of the embodiments of the present application, unless otherwise specified, " / " means the meaning of or, for example, A / B can mean A or B; "and / or" in the text only describes the relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent: A exists alone, A and B exist together, and B exists alone, in addition, in the description of the embodiments of the present application, "multiple" means two or more than two.

[0096] In some of the processes described in the embodiments of the present application, a plurality of operations or steps are included in a specific order, but it should be understood that these operations or steps can be executed or executed in parallel without the order in which they appear in the embodiments of the present application, and the serial number of the operation is only used to distinguish different operations, and the serial number itself does not represent any execution order. In addition, these processes can include more or fewer operations, and these operations or steps can be executed in sequence or in parallel, and these operations or steps can be combined.

[0097] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation using the content of the specification and drawings of the present application, or directly or indirectly applied to other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for calculating the lateral effect caused by vertical live load on a curved roadway, characterized in that, It includes the following steps: Get on the curved lane n The coordinates of each lane sequence node; Fit the lane sequence nodes to generate a lane fitting curve; The coordinates of the lane sequence nodes are substituted into the lane fitting curve to calculate the lateral centrifugal effect at each lane sequence node. Based on the lateral centrifugal effect and the curved lane at the first n The vertical live load effect on each lane sequence node is calculated to obtain the lateral effect caused by the vertical live load effect; Among them, the first based on the lateral centrifugal effect and the curved lane n The vertical live load effect on each lane sequence node is calculated to obtain the lateral effect caused by the vertical live load effect, including: Calculate the influence matrix of the corresponding effect at each lane sequence node. ,in n Indicates the first n Lane sequence nodes, m Indicates the first m Live load calculation items; Obtain the first curve lane n Vertical live load at each lane sequence node ; Based on the aforementioned vertical live load effect and lateral centrifugal effect C Calculate live load force ; The influence matrix With live load force Multiply to obtain the result at the 1st position. n The live load of the lane sequence node, the first m Live load results for the live load calculation item; The superposition calculation of the first node of the sequence of all lanes at the location of live load application m The live load calculation results are used to obtain the lateral action effect caused by the vertical live load.

2. The calculation method for the lateral effect caused by vertical live load on a curved lane as described in claim 1, characterized in that, The acquisition of curved lanes n The coordinates of the lane sequence nodes include: In the finite element model of the bridge structure, the longitudinal row of the main beam nodes is used as the reference axis, and the transverse offset distance is set to determine the actual position of the vehicle live load. Based on the node coordinates on the reference axis and the transverse bridge offset distance, calculate the planar coordinates of the lane sequence nodes. , i=1......n , n This represents the number of nodes in the lane sequence.

3. The calculation method for the lateral effect caused by vertical live load on a curved lane as described in claim 1, characterized in that, The process of fitting the lane sequence nodes to generate a lane fitting curve includes: The lane sequence nodes are initially fitted using a fourth-order polynomial to generate an initial lane curve; The initial lane curve is approximated twice using a cubic polynomial to generate a lane fitting curve; The lane fitting curve is represented as follows: .

4. The calculation method for the lateral action effect caused by vertical live load on a curved lane as described in claim 3, characterized in that, The step of substituting the coordinates of the lane sequence nodes into the lane fitting curve to calculate the lateral eccentricity effect at each lane sequence node includes: The coordinates of each lane sequence node are substituted into the lane fitting curve to obtain the curvature at each lane sequence node. k ; Based on the curvature k Calculate the lateral centrifugal effect at each lane sequence node. C。 5. The calculation method for the lateral action effect caused by vertical live load on a curved lane as described in claim 4, characterized in that, The curvature k The calculation formula is: ; in, , They are respectively y The first and second derivatives.

6. The calculation method for the lateral action effect caused by vertical live load on a curved lane as described in claim 5, characterized in that, The transverse centrifugal effect C The calculation formula is: ; in, V The design speed for the curved lane.

7. The calculation method for the lateral action effect caused by vertical live load on a curved lane as described in claim 1, characterized in that, The influence matrix of the corresponding effect at each lane sequence node is calculated using the influence line of the maneuvering method. .

8. The calculation method for the lateral action effect caused by vertical live load on a curved lane as described in claim 7, characterized in that, The influence matrix Represented as: ； in, k ij middle i For the effect, j The unit force applied at the node of this lane sequence.

9. The calculation method for the lateral action effect caused by vertical live load on a curved lane as described in claim 1, characterized in that, The live load force The calculation formula is: ； in, The unit coordinates at the lane sequence node y The projection of the axis onto the horizontal plane and the global coordinate system X The cosine of the angle between the axes, The unit coordinates at the lane sequence node x The projection of the axis onto the horizontal plane and the global coordinate system Y The cosine of the angle between the axes.

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