CN-122020807-A - Self-adaptive cross section design method for automatically matching arch bridge main arch strength and stability

CN122020807ACN 122020807 ACN122020807 ACN 122020807ACN-122020807-A

Abstract

The invention discloses a section self-adaptive design method for automatically matching the main arch strength and stability of an arch bridge, and relates to the technical field of bridge engineering structural design and optimization. The method comprises the steps of taking arch top section damage as a failure mode of a structure, establishing a main arch strength and stable coupling correlation model, setting constraint conditions, solving the main arch strength and stable coupling correlation model under the constraint conditions, optimizing and solving in solution sets meeting the constraint conditions with the aim of minimizing the main arch material consumption, solving and obtaining size parameters of the width of the box section and the thickness of the concrete slab according to a calculation formula of the area and the moment of inertia of the box section, and determining a final section design scheme of the main arch of the arch bridge based on the size parameters of the width of the box section and the thickness of the concrete slab. The invention can improve the material utilization rate, the structural safety and the design efficiency of the large-span arch bridge, and realize the dual goals of economy and safety.

Inventors

ZHOU JIANTING
LUO CHAO
ZHOU YIN
ZHANG HONG
TANG QIZHI
HUANG BING
MEN PENGFEI
FAN YONGHUI

Assignees

重庆交通大学

Dates

Publication Date: 20260512
Application Date: 20260213

Claims (6)

1. A section self-adaptive design method for automatically matching the main arch strength and stability of an arch bridge is characterized by comprising the following steps: S1, establishing a main arch strength and stable coupling correlation model comprising a nonlinear stability coefficient, a arch cross section height, a design shaft compressive stress and a arch cross section rigidity by taking arch cross section damage as a failure mode of a structure; S2, setting constraint conditions, and solving a main arch strength and stable coupling correlation model under the constraint conditions according to the correlation between the design shaft compressive stress and the design arch cross-section area to obtain a design combination solution set of the arch cross-section area, the arch cross-section rigidity and the arch cross-section height which meet all the constraint conditions; S3, optimizing and solving in a solution set meeting constraint conditions with the aim of minimizing the consumption of the main arch material to obtain an optimal design combination of the arch cross-section area, the arch cross-section rigidity and the arch cross-section height; S4, solving and obtaining the dimension parameters of the width of the box section and the thickness of the concrete slab according to the area of the box section and a moment of inertia calculation formula based on the optimal design combination of the area of the dome section, the rigidity of the dome section and the height of the dome section; S5, determining a final section design scheme of the arch bridge main arch based on the width of the box section and the size parameters of the concrete slab thickness.
2. A cross-section self-adaptive design method for automatically matching arch bridge main arch strength with stability according to claim 1, wherein, In S1, a main arch strength and stable coupling correlation model comprising a nonlinear stability coefficient, a arch crown section height, a design shaft compressive stress and a arch crown section rigidity is established by taking the arch crown section damage as a failure mode of the structure, and specifically comprises the following steps: The arch crown cross-section damage is defined as the local concrete compressive stress reaching the compressive strength design value f c , satisfying the following formula (1): (1) In the formula, In order to design the compressive stress of the shaft, Is a nonlinear bending stress upon failure of the arch bridge, Is a nonlinear stability coefficient; according to the nonlinear bending moment calculation formula, Represented by formula (2): (2) In the formula, H 0 is the arch cross-section height, Is the rigidity of the arch crown section; And (3) combining the formulas (1) and (2) to obtain a main arch strength and stable coupling correlation model: (3) according to the design shaft compressive stress And design dome area Correlation formula (4) between: (4) Substituting formula (4) into formula (3) to obtain formula (5): (5)。
3. A cross-section self-adaptive design method for automatically matching arch bridge main arch strength with stability according to claim 2, wherein, S2, setting constraint conditions, specifically: Stability factor of a kind And (3) with 、、 The formula of the relation between the two is shown as formula (6): (6) wherein E is the elastic modulus of the main arch material, I 0 is the arch cross-sectional moment of inertia, For the main arch span, μ is the main arch span calculated length coefficient: Wherein, the The arch is widened for equal height: in the formula, S=al is the horizontal inclination of the arch axis arch springing, a is the arch curvature, and l is half of the main arch span; for equal width and variable height arches The calculation can be performed as follows; The stability coefficient is larger than the nonlinear stability coefficient As rib rigidity constraint condition (7): (7) according to engineering experience, selecting and setting a vault section height constraint condition (8): (8)。
4. A cross-section self-adaptive design method for automatically matching the main arch strength and stability of an arch bridge according to claim 3, In S3, taking the minimum consumption of the main arch material as a target, and carrying out optimization solution in a solution set meeting constraint conditions to obtain the optimal design combination of the arch crown cross-section area, the arch crown cross-section rigidity and the arch crown cross-section height, wherein the design combination specifically comprises the following steps: s301, input design parameter losing height Span of main arch The magnitude of the vertical concentrated force And position Main arch material volume weight Modulus of elasticity of main arch material And nonlinear stability coefficient ; S302, inputting larger values of the strength f c of the design material and the compressive stress sigma m of the design shaft, and calculating according to the following formula Order the , As the stress iteration coefficient, selecting according to the convergence condition, wherein the initial value of k 1 is 0.9; S303, based on the shortest force transmission path, determining a reasonable bridge formation state of the arch bridge, and calculating to obtain a reasonable arch axis through static balance conditions Hy '' =q (x) Cross-sectional area of dome H is the horizontal counter force of the arch, q (x) is the constant load distribution of the arch, and the design parameters of the arch structure are preliminarily calculated through the step S301; s304, obtaining allowable bending stress according to (1) ; S305, inputting a small value of moment of inertia of the arch crown section I 0 , and calculating according to the following formula: Wherein eta 2 is a nonlinear stability coefficient, and the value of the reference specification is 1.75; s306, obtaining the bending moment of the arch cross section according to a nonlinear bending moment analysis and calculation method The dome section height is calculated according to equation (3): Wherein w s is a nonlinear redundant force coefficient, and the solution is carried out according to the following formula: Wherein epsilon m= σ m /E is the arch crown section compressive strain value, and l is half of the main arch span; in the formula, pi 1-pi 4 are calculation coefficients, and the calculation is carried out according to the following formula: Wherein betas, S is the loading progress coefficient and the horizontal inclination angle of the arch center of the arch axis respectively, 、 S=al, a is the dome curvature.
5. A method for cross-sectional self-adaptive design for automatic matching of arch bridge main arch strength and stability according to claim 4, S4, calculating a formula of the area and the moment of inertia of the box-shaped section, wherein the formula specifically comprises the following steps: After obtaining 、、 And then, according to the area of the box-shaped section and a moment of inertia calculation formula: (9) (10) Where the unknown is the cross-sectional width Thick with concrete slab ; And (3) combining the formula (9) and the formula (10) and adopting numerical solution.
6. A cross-section self-adaptive design method for automatically and stably matching the main arch strength of an arch bridge according to claim 5, S4, solving to obtain the dimension parameters of the width of the box section and the thickness of the concrete slab according to the area of the box section and a moment of inertia calculation formula, wherein the dimension parameters are specifically as follows: s401, at this time, 、、 It is known that the calculation is performed according to the formulas (9) and (10) 、 Order-making ; S402, if Or (b) Repeating steps S302 to S306; S403, if Order in principle , Taking 1.01 as a stress correction coefficient, repeating steps S302 to S306, S401 and S404; S404, if Or (b) , , Taking 1.01 as a rigidity correction coefficient, repeating steps S302 to S306, step S401 and step S404; S405、 the steps S403 and S404 are repeated, ; Ending the operation and outputting the cross-sectional dimension 、、。

Description

Self-adaptive cross section design method for automatically matching arch bridge main arch strength and stability Technical Field The invention relates to the technical field of bridge engineering structure design and optimization, in particular to a section self-adaptive design method for automatically matching the main arch strength and stability of an arch bridge. Background The cross section design of the main arch of the large-span arch bridge is critical to the safety and the economy of the structure, and the unmanageable material distribution not only can cause the waste of materials, but also can become the encumbrance of the structure. Therefore, the main arch section design not only meets the strength requirement of the structure, but also ensures reasonable distribution of the rigidity of the arch rib, and can effectively resist structural stress, deformation and instability under various load actions. The conventional arch bridge section design method adopts an elastic theory and an empirical formula to design, and fails to solve the problem of matching between material strength and structural stability under the influence of strong nonlinearity, so that the accurate section size under the complex load condition and the geometric nonlinearity effect cannot be obtained, but the safety coefficient is simply added into the empirical formula, so that the arch structure is in a bulkiness state, and the further development of the span of the arch bridge is hindered. Meanwhile, the conventional arch bridge section design method adopts an optimization iteration mode, achieves the design targets of strength and stability by repeatedly adjusting the main arch section, has complicated design flow and low design efficiency, cannot ensure the global optimum of the design result, and the final effect depends on the experience of a designer. Therefore, a cross-section self-adaptive design method for automatically matching the main arch strength and stability of the arch bridge is provided to solve the problems existing in the prior art, which is a problem to be solved by those skilled in the art. Disclosure of Invention In view of the above, the invention provides a cross section self-adaptive design method for automatically matching the main arch strength and stability of an arch bridge, which can improve the material utilization rate, the structural safety and the design efficiency of the large-span arch bridge, thereby realizing the dual goals of economy and safety. In order to achieve the above purpose, the present invention adopts the following technical scheme: a section self-adaptive design method for automatically matching the main arch strength and stability of an arch bridge comprises the following steps: S1, establishing a main arch strength and stable coupling correlation model comprising a nonlinear stability coefficient, a arch cross section height, a design shaft compressive stress and a arch cross section rigidity by taking arch cross section damage as a failure mode of a structure; S2, setting constraint conditions, and solving a main arch strength and stable coupling correlation model under the constraint conditions according to the correlation between the design shaft compressive stress and the design arch cross-section area to obtain a design combination solution set of the arch cross-section area, the arch cross-section rigidity and the arch cross-section height which meet all the constraint conditions; S3, optimizing and solving in a solution set meeting constraint conditions with the aim of minimizing the consumption of the main arch material to obtain an optimal design combination of the arch cross-section area, the arch cross-section rigidity and the arch cross-section height; S4, solving and obtaining the dimension parameters of the width of the box section and the thickness of the concrete slab according to the area of the box section and a moment of inertia calculation formula based on the optimal design combination of the area of the dome section, the rigidity of the dome section and the height of the dome section; S5, determining a final section design scheme of the arch bridge main arch based on the width of the box section and the size parameters of the concrete slab thickness. In the above method, optionally, in S1, a failure mode of taking the fracture of the dome section as a structure is used to build a main arch strength and stable coupling correlation model including a nonlinear stability coefficient, a dome section height, a design shaft compressive stress and a dome section stiffness, specifically: The arch crown cross-section damage is defined as the local concrete compressive stress reaching the compressive strength design value f c, satisfying the following formula (1): (1) In the formula, In order to design the compressive stress of the shaft,Is a nonlinear bending stress upon failure of the arch bridge,Is a nonlinear stability coefficient; according to the nonlinear