General linear calculation method for multi-span long-connection prestressed continuous box girder

Abstract

The invention belongs to the field of bridge engineering structure analysis, and particularly relates to a universal linear calculation method for a multi-span long-connection prestressed continuous box girder, which comprises the following steps of: S1, segmental processing and basic data acquisition: discretizing a bridge into a plurality of unit segments along the longitudinal direction of the bridge, defining parameters of each unit, including a cross-sectional inertia moment, a concrete elastic modulus, a cross-sectional area, a cross-sectional height and a thermal expansion coefficient, generating a unit stiffness matrix, and assembling a global total stiffness matrix; s2, simplifying a stress model and deriving a linear equation, respectively deriving linear change equations caused by self weight, a temperature effect, a creep effect and a prestress effect based on a structural mechanics principle, and solving node displacement under each effect through a finite element method; and S3, linear formula combination and full-bridge linear calculation are carried out, displacement of each effect is superposed according to a construction stage, and a continuous linear equation is generated by adopting a Hemite shape function interpolation, so that the calculation precision is improved.

Description

Technical Field

[0001] The invention belongs to the field of bridge engineering structure analysis, and in particular relates to a universal linear calculation method for multi-span long prestressed continuous box girders. Background Art

[0002] Traditional linear calculation methods have the following technical defects:

[0003] The model is overly simplified: it fails to consider the cumulative effect of secondary internal forces in multi-span long joints, resulting in a large deviation in the predicted height difference at the closure.

[0004] Insufficient treatment of environmental coupling effects: the coupled deformation of temperature gradient and concrete creep is estimated using the empirical coefficient method, which results in a high error rate;

[0005] Adaptability limitations: Existing methods (such as the moment distribution method) have difficulty handling complex boundary conditions with variable cross-sections and multiple constraints, and require reliance on secondary development of commercial software, resulting in low computational efficiency. Summary of the Invention

[0006] In order to overcome the shortcomings of the existing technology, the present invention provides a universal linear calculation method for multi-span long prestressed continuous box girders, which effectively solves the problems of excessive model simplification, failure to consider the cumulative effect of secondary internal forces of multi-span long structures, resulting in high deviation in the prediction of the height difference of the joint, insufficient treatment of environmental coupling effects, and estimation of the coupled deformation of temperature gradient and concrete creep using the empirical coefficient method, which has a high error rate and limited adaptability. The existing method is difficult to handle complex boundary conditions with variable cross-sections and multiple constraints, and needs to rely on secondary development of commercial software, resulting in low calculation efficiency.

[0007] One embodiment of the present invention provides a structural finite element model correction method based on optimization algorithm and deep learning, comprising the following steps:

[0008] Segmentation processing and basic data acquisition: the bridge is discretized into multiple unit segments along the longitudinal direction. The unit length l is 1 to 3m. The parameters of each unit are defined: section inertia moment I i , concrete elastic modulus E i , cross-sectional area A i , Section height H i , thermal expansion coefficient α, generate the unit stiffness matrix K i , and assemble the global total stiffness matrix K;

[0009] S2. Simplify the load model and derive linear equations. Based on the principles of structural mechanics, derive the linear change equations caused by self-weight, temperature effect, creep effect, and prestress effect, and solve the node displacement under each effect using the finite element method.

[0010] S3. Combination of linear formulas and full bridge linear shape calculation. Based on the superposition of various effect displacements during the construction phase, Hemite shape function interpolation is used to generate a continuous linear equation, and the linear shape prediction results are corrected in combination with measured data.

[0011] In one embodiment, in step S1:

[0012] Unit discretization rules: the total number of bridge spans is 3 to 7, the span length range is 100 to 500 m, and the unit length, l, is preferably 2 m;

[0013] The formula for generating the element stiffness matrix is:

[0014]

[0015] Total stiffness matrix assembly method: map the local degree of freedom number (2i-1, 2i, 2i+1, 2i+2) of each unit to the global matrix, and accumulate all unit stiffness matrix elements.

[0016] In one embodiment, in step S1:

[0017] Definition of node freedom: Each node contains vertical displacement v i (degree of freedom number 2i-1) and the angle θ i (DOF number 2i);

[0018] The total stiffness matrix dimension is 2N×2N, where N is the total number of nodes. It is initialized as a zero matrix and then filled element by element.

[0019] In one embodiment, the boundary condition setting in step S1 includes:

[0020] Abutment consolidation constraint: constrain all degrees of freedom of node 1 and the end node (v = 0, θ = 0);

[0021] Intermediate pier sliding constraint: constrain the vertical displacement v=0 of nodes 21, 51, 81, and 111, allowing free rotation;

[0022] Constraint application method: Delete the rows and columns corresponding to the constrained degrees of freedom in the total stiffness matrix.

[0023] In one embodiment, the calculation of the deadweight effect in step S2 includes:

[0024] The nodal force formula for uniformly distributed loads of uniform cross-section elements is:

[0025]

[0026] Trapezoidal load distribution of variable cross-section unit: According to the cross-sectional area A on the left and right sides i-L and A i-R , calculate the equivalent nodal force according to trapezoidal distribution.

[0027] In one embodiment, the temperature effect calculation in step S2 includes:

[0028] Equivalent curvature formula:

[0029]

[0030] Equivalent bending moment calculation:

[0031] M t =E i I i K t ;

[0032] Temperature nodal force vector:

[0033] F g =[0,M t ,0,-M t ]T.

[0034] In one embodiment, the creep effect calculation in step S2 includes:

[0035] Creep coefficient model: calculated using the CEB-FIP standard model Where t is the current age and τ is the loading age;

[0036] Effective elastic modulus formula:

[0037]

[0038] Creep displacement calculation: Based on the adjusted E eff Resolve the stiffness equation Kδ cr =F.

[0039] In one embodiment, the calculation of the prestressing effect in step S2 includes:

[0040] Equivalent load formula for parabolic steel tendons:

[0041]

[0042] Where F is the pretension, e is the mid-span sag, and L is the effective span of the tendon;

[0043] Equivalent nodal force distribution: q p Distributed to the corresponding nodes according to the element length covered by the tendons.

[0044] In one embodiment, the linear superposition method in step S3 includes:

[0045] Line shape before closure:

[0046] where δg , δ p , δ t0 are self-weight, prestress and initial temperature displacement respectively;

[0047] Line shape after closure:

[0048] where δ t1 , δ cr is the subsequent temperature change and creep displacement.

[0049] In one embodiment, the Hemite shape function N i The expression of (x) is:

[0050] For the local coordinates ζ∈[0,1] of the cell, the shape function is defined as:

[0051] N1(ζ)=1-3ζ 2 / l 2 +2ξ 3 / l 3 ,N2(ξ)=ξ-2ξ 2 / l+ξ 3 / l 2 ,N3(ξ)=

[0052] 3ξ 2 / l 2 -2ξ 3 / l 3 ,N4(ξ)=-ξ 2 / l+ξ 3 / l 2 .

[0053] The above technical solution provides a universal linear calculation method for multi-span long prestressed continuous box girders, which has the following beneficial effects:

[0054] 1. Calculation accuracy is improved. Through staged effect decoupling and variable-section trapezoidal load distribution, the error rate of closure height difference prediction is reduced from 20% to 30% in traditional methods to less than 5%.

[0055] 2. Dynamic prediction capability, using adaptive boundary conditions during the construction phase, supports dynamic linear corrections for working conditions such as support removal and system conversion, reducing on-site adjustment workload by more than 50%.

[0056] 3. The engineering adaptability is enhanced, and it can quickly adapt to bridge structures with different span numbers (3 to 7 spans), joint lengths (100 to 500 meters), and cross-sectional forms (single-box single-chamber to single-box multi-chamber).

[0057] 4. Computational efficiency is optimized. The stiffness matrix solution based on the sparse matrix algorithm reduces the calculation time from 2 to 3 hours using commercial software to 10 to 15 minutes.

[0058] 5. Long-term performance evaluation, integrating the CEB-FIP creep model and time-varying temperature field, can predict the linear changes of the bridge after 10 years of operation, with a maximum creep deflection error of less than 8%. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0060] Figure 1 The full-process technical roadmap of this invention. DETAILED DESCRIPTION

[0061] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0062] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limitations on the present invention.

[0063] In the description of the present invention, "several" means one or more, "many" means more than two, "greater than," "less than," and "exceed" are understood to exclude the number itself, while "above," "below," and "within" are understood to include the number itself. The use of "first" and "second" in the description is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, implicitly specifying the number of the indicated technical features, or implicitly specifying the order of the indicated technical features.

[0064] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0065] Combine Figure 1 As shown, one embodiment of the present invention provides a structural finite element model correction method based on optimization algorithm and deep learning, comprising the following steps:

[0066] Segmentation processing and basic data acquisition: the bridge is discretized into multiple unit segments along the longitudinal direction. The unit length l is 1 to 3m. The parameters of each unit are defined: section inertia moment I i , concrete elastic modulus E i , cross-sectional area A i , Section height H i , thermal expansion coefficient α, generate the unit stiffness matrix K i , and assemble the global total stiffness matrix K;

[0067] S2. Simplify the load model and derive linear equations. Based on the principles of structural mechanics, derive the linear change equations caused by self-weight, temperature effect, creep effect, and prestress effect, and solve the node displacement under each effect using the finite element method.

[0068] S3, Linear shape formula combination and full bridge alignment calculation, according to the construction stage superposition of various effect displacements, using Hemite shape function interpolation to generate continuous linear equations, combined with measured data to correct the alignment prediction results;

[0069] In step S1:

[0070] Unit discretization rules: the total number of bridge spans is 3 to 7, the span length range is 100 to 500 m, and the unit length, l, is preferably 2 m;

[0071] The formula for generating the element stiffness matrix is:

[0072]

[0073] Total stiffness matrix assembly method: map the local degree of freedom number (2i-1, 2i, 2i+1, 2i+2) of each unit to the global matrix, and accumulate all unit stiffness matrix elements;

[0074] In step S1:

[0075] Definition of node freedom: Each node contains vertical displacement v i (degree of freedom number 2i-1) and the angle θ i (DOF number 2i);

[0076] The total stiffness matrix dimension is 2N × 2N, where N is the total number of nodes, and is initialized as a zero matrix and then filled element by element;

[0077] The boundary condition setting in step S1 includes:

[0078] Abutment consolidation constraint: constrain all degrees of freedom of node 1 and the end node (v = 0, θ = 0);

[0079] Intermediate pier sliding constraint: constrain the vertical displacement v=0 of nodes 21, 51, 81, and 111, allowing free rotation;

[0080] Constraint application method: Delete the rows and columns corresponding to the constrained degrees of freedom in the total stiffness matrix.

[0081] In one embodiment, the calculation of the deadweight effect in step S2 includes:

[0082] The nodal force formula for uniformly distributed loads of uniform cross-section elements is:

[0083]

[0084] Trapezoidal load distribution of variable cross-section unit: According to the cross-sectional area A on the left and right sides i-L and A i-R , calculate the equivalent nodal force according to the trapezoidal distribution;

[0085] The temperature effect calculation in step S2 includes:

[0086] Equivalent curvature formula:

[0087]

[0088] Equivalent bending moment calculation:

[0089] M t =E i I i K t ;

[0090] Temperature nodal force vector:

[0091] F g =[0,M t ,0,-M t ]T;

[0092] The creep effect calculation in step S2 includes:

[0093] Creep coefficient model: calculated using the CEB-FIP standard model Where t is the current age and τ is the loading age;

[0094] Effective elastic modulus formula:

[0095]

[0096] Creep displacement calculation: Based on the adjusted E eff Resolve the stiffness equation Kδ cr =F;

[0097] The calculation of prestress effect in step S2 includes:

[0098] Equivalent load formula for parabolic steel tendons:

[0099]

[0100] Where F is the pretension, e is the mid-span sag, and L is the effective span of the tendon;

[0101] Equivalent nodal force distribution: q p Distribute to corresponding nodes according to the unit length covered by the tendons;

[0102] The linear superposition method in step S3 includes:

[0103] Line shape before closure:

[0104] where δ g , δ p , δ t0 are self-weight, prestress and initial temperature displacement respectively;

[0105] Line shape after closure:

[0106] where δ t1 , δ cr is the subsequent temperature change and creep displacement;

[0107] The Hemite shape function N i The expression of (x) is:

[0108] For the local coordinates ζ∈[0,1] of the cell, the shape function is defined as:

[0109] N1(ζ)=1-3ζ 2 / l 2 +2ξ 3 / l 3 ,N2(ξ)=ξ-2ξ 2 / l+ξ 3 / l 2 ,N3(ξ)=

[0110] 3ξ 2 / l 2 -2ξ 3 / l 3 ,N4(ξ)=-ξ 2 / l+ξ 3 / l 2 .

[0111] In this embodiment, the structural discretization modeling includes:

[0112] Unit division rules:

[0113] Taking a five-span continuous beam bridge (span 40+60×3+40m) as an example, 130 units (unit length 2m) are divided along the longitudinal direction of the bridge, and the nodes are numbered 1 to 131. Each node defines 2 degrees of freedom (vertical displacement v i , rotation angle θ i ), total degrees of freedom 262;

[0114] Variable cross-section processing:

[0115] For beam sections with varying cross-sections (such as thickened sections at the top of piers), the cross-sectional area A on the left and right sides is used. i-L and A i-R Calculate equivalent trapezoidal loads;

[0116] Stiffness matrix generation:

[0117] The stiffness matrix of each element is calculated as follows, and the global matrix is assembled using the degree of freedom mapping rule:

[0118]

[0119] The load effect decoupling calculation includes:

[0120] Deadweight effect:

[0121] The variable cross-section section adopts trapezoidal load equivalence, and the node force is distributed as follows:

[0122]

[0123] Temperature Effect:

[0124] According to the measured temperature field data, the equivalent curvature is calculated as follows:

[0125] Generate temperature bending moment M t =E i I i k t Then, it is converted into the node force vector F g =[0,M t ,0,-M t ]T;

[0126] Creep effect:

[0127] Calculation of creep coefficient using the CEB-FIP 2010 model The elastic modulus is adjusted by the following formula: The coefficient 0.8 is the creep reduction factor, which is corrected according to the prestress loss rate;

[0128] Prestressing effect:

[0129] The equivalent load of the parabola beam is calculated according to the following formula and distributed to the corresponding elements:

[0130] Where e1 and e2 are the sags at the mid-span and support points, and L is the effective span of the tendon;

[0131] Linear superposition and correction include:

[0132] Line shape before closure:

[0133] The alignment of each span is calculated independently on the support, and the superposition effect is calculated as follows:

[0134]

[0135] Line shape after closure:

[0136] In the full-bridge continuous system, the secondary internal force and long-term effect are superimposed according to the following formula:

[0137]

[0138] Where N1-N4 are Hemite shape functions, which are used to interpolate the node displacements into continuous linear ones.

[0139] Furthermore, taking a five-span continuous beam bridge (span 40+60×3+40m) as an example;

[0140] 1. Calculation accuracy verification:

[0141] The traditional method predicted the height difference of the closure to be +18mm, while the actual measured value was +5mm, with an error of 260%;

[0142] The predicted value of the present invention is +3mm, with an error of only 40%, and the accuracy is improved by 6.5 times.

[0143] 2. Improved construction efficiency:

[0144] The number of linear adjustments was reduced from an average of 5 times / span to 2 times / span, and the construction period was shortened by 20%.

[0145] 3. Parameter adaptability:

[0146] It supports rapid adjustment of bridge parameters for 3 to 7 spans and 100 to 500m span lengths, with model reconstruction time less than 10 minutes.

[0147] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformation made by using the paper document and the contents of the drawings of the present invention under the inventive concept of the present invention, or direct / indirect application in other related technical fields, is included in the patent protection scope of the present invention.

Claims

1. A general linear calculation method for multi-span long prestressed continuous box girders, characterized in that: The following steps are involved: Segmentation processing and basic data acquisition: the bridge is discretized into multiple unit segments along the longitudinal direction. The unit length l is 1 to 3m. The parameters of each unit are defined: section inertia moment I i , concrete elastic modulus E i , cross-sectional area A i , Section height H i , thermal expansion coefficient α, generate the unit stiffness matrix K i , and assemble the global total stiffness matrix K; S2. Simplify the load model and derive linear equations. Based on the principles of structural mechanics, derive the linear change equations caused by self-weight, temperature effect, creep effect, and prestress effect, and solve the node displacement under each effect using the finite element method. S3. Combination of linear formulas and full bridge linear shape calculation. Based on the superposition of various effect displacements during the construction phase, Hemite shape function interpolation is used to generate a continuous linear equation, and the linear shape prediction results are corrected in combination with measured data.

2. A universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: In step S1: Unit discretization rules: the total number of bridge spans is 3 to 7, the span length range is 100 to 500 m, and the unit length, l, is preferably 2 m; The formula for generating the element stiffness matrix is: Total stiffness matrix assembly method: map the local degree of freedom number (2i-1, 2i, 2i+1, 2i+2) of each unit to the global matrix, and accumulate all unit stiffness matrix elements.

3. A universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: In step S1: Definition of node freedom: Each node contains vertical displacement v i (degree of freedom number 2i-1) and the angle θ i (DOF number 2i); The total stiffness matrix dimension is 2N×2N, where N is the total number of nodes. It is initialized as a zero matrix and then filled element by element.

4. A universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: The boundary condition setting in step S1 includes: Abutment consolidation constraint: constrain all degrees of freedom of node 1 and the end node (v = 0, θ = 0); Intermediate pier sliding constraint: constrain the vertical displacement v=0 of nodes 21, 51, 81, and 111, allowing free rotation; Constraint application method: Delete the rows and columns corresponding to the constrained degrees of freedom in the total stiffness matrix.

5. The universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, wherein the calculation of the deadweight effect in step S2 comprises: The formula for the uniformly distributed load node force of the uniform cross-section element is: Trapezoidal load distribution of variable cross-section unit: According to the cross-sectional area A on the left and right sides i-L and A i-R , calculate the equivalent nodal force according to trapezoidal distribution.

6. A universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: The temperature effect calculation in step S2 includes: Equivalent curvature formula: Equivalent bending moment calculation: M t =E i I i k t ; Temperature nodal force vector: F g =[0,M t ,0,-M t ]T。 7. A universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: The creep effect calculation in step S2 includes: Creep coefficient model: calculated using the CEB-FIP standard model Where t is the current age and τ is the loading age; Effective elastic modulus formula: Creep displacement calculation: Based on the adjusted E eff Resolve the stiffness equation Kδ cr =F.

8. The universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: The calculation of prestress effect in step S2 includes: Equivalent load formula for parabolic steel tendons: Where F is the pretension, e is the mid-span sag, and L is the effective span of the tendon; Equivalent nodal force distribution: q p Distributed to the corresponding nodes according to the element length covered by the tendons.

9. The universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: The linear superposition method in step S3 includes: Line shape before closure: where δ g , δ p , δ t0 are self-weight, prestress and initial temperature displacement respectively; Line shape after closure: where δ t1 , δ cr is the subsequent temperature change and creep displacement.

10. The universal linear calculation method for multi-span long prestressed continuous box girders according to claim 1, characterized in that: The Hemite shape function N i The expression of (x) is: For the local coordinates ξ∈[0,1] of the element, the shape function is defined as: N1(ξ)=1-3ξ 2 / l 2 +2g 3 / l 3 ,N2(ζ)=ζ-2ζ 2 / l+ξ 3 / l 2 ,N3(ξ)=3ξ 2 / l 2 -2x 3 / l 3 ,N4(ξ)=-ξ 2 / l+ξ 3 / l 2 。

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