CN-122020805-A - Large-span arch bridge geometric nonlinear structure response calculation method

CN122020805ACN 122020805 ACN122020805 ACN 122020805ACN-122020805-A

Abstract

The invention discloses a large-span arch bridge geometric nonlinear structure response calculation method, and relates to the technical field of bridge engineering structure analysis. The method comprises the steps of setting a reasonable arch axis, establishing a second-order deflection nonlinear balance equation of a large-span arch bridge, dispersing the reasonable arch axis into a polynomial capable of being solved in a single way, deducing a nonlinear deflection expression and a nonlinear bending moment expression of the large-span arch bridge based on the second-order deflection nonlinear balance equation, solving unknown parameters in the nonlinear deflection expression and the nonlinear bending moment expression based on the principle that the integral of elastic compression quantity and compressive strain along the arch axis arc length is equal, obtaining the nonlinear deflection and the nonlinear bending moment of the large-span arch bridge, verifying the calculation method by adopting a numerical simulation method considering geometric nonlinearity, and analyzing the change rule and the spatial distribution rule of the nonlinear structure response of the large-span arch bridge along with loading process through the numerical simulation. The invention provides reliable basis for evaluating and optimizing the structure safety reserve.

Inventors

LUO CHAO
ZHOU JIANTING
LI KUN
WANG YUANWEI
ZHOU YIN
TANG QIZHI
XIN JINGZHOU
FAN YONGHUI
MEN PENGFEI

Assignees

重庆交通大学
四川川交路桥有限责任公司

Dates

Publication Date: 20260512
Application Date: 20260213

Claims (10)

1. The method for calculating the geometric nonlinear structure response of the large-span arch bridge is characterized by comprising the following steps of: s1, setting a reasonable arch axis, and establishing a second-order deflection nonlinear equilibrium equation of a large-span arch bridge; S2, dispersing a reasonable arch axis into a polynomial capable of being solved in a single way, and deducing a nonlinear deflection expression and a nonlinear bending moment expression of the large-span arch bridge based on a second-order deflection nonlinear equilibrium equation; s3, solving unknown parameters in a nonlinear deflection expression and a nonlinear bending moment expression based on the principle that the integral of the elastic compression quantity and the compressive strain along the arc length of the arch axis is equal to obtain nonlinear deflection and nonlinear bending moment of the large-span arch bridge; S4, verifying the calculation method from the step S1 to the step S3 by adopting a numerical simulation method considering geometric nonlinearity; S5, analyzing the change rule and the space distribution rule of the nonlinear structure response of the large-span arch bridge along with the loading process through numerical simulation.
2. The method of claim 1, wherein the second-order flexural nonlinear equilibrium equation in S1 is established based on a control differential equation of the arch structure, and the total structural bending moment accounting for the second-order effect comprises a structural line elastic bending moment.
3. The method for calculating the geometric nonlinear structure response of a large-span arch bridge according to claim 1, wherein the arch structure corresponding to the reasonable arch axis in the step S1 is a hyperstatic and hingeless arch, the additional bending moment is a bending moment generated by overlapping an additional bending moment of the three-hinged arch with an additional residual force, and the residual force comprises a residual horizontal force and a bending moment.
4. The method for calculating the response of the geometric nonlinear structure of the large-span arch bridge according to claim 1, wherein the nonlinear deflection expression and the nonlinear bending moment expression in the step S2 are composed of cosine terms and high-order polynomials and are functions of the structure loading progress and response space distribution.
5. The method of claim 4, wherein when the reasonable arch axis is parabolic, the nonlinear displacement expression is composed of a cosine curve and a parabolic, and the nonlinear bending moment expression is a cosine curve.
6. The method for calculating the geometric nonlinear structure response of the large-span arch bridge according to claim 1, wherein in the solving process of the unknown parameters in the step S3, the nonlinear change of the redundant horizontal force is considered by combining the change characteristic of the geometric rigidity of the arch rib, and the redundant horizontal force comprises the redundant horizontal force solved according to the linear elasticity theory and the additional redundant force after the nonlinear effect is considered.
7. The method for calculating the geometrical nonlinear structure response of the large-span arch bridge according to claim 1, wherein the numerical simulation in S4 adopts a Newton-Raphson iteration method, and the simulation verification indexes comprise the total deflection and total bending moment of the large-span arch bridge, the calculation error of the total deflection is less than 4.4%, and the calculation error of the total bending moment is less than 5.9%.
8. The method for calculating the geometric nonlinear structural response of the large-span arch bridge according to claim 1, wherein the nonlinear structural response in S5 comprises nonlinear bending moment, the spatial distribution of the nonlinear bending moment is in an M form, two positive bending moment peaks and one negative bending moment peak occur after passing through two bending moment zero points in the half arch range.
9. The method for calculating the geometric nonlinear structure response of the large-span arch bridge according to claim 1, wherein the load of the loading process in the step S5 is set to be 1.75 times of arch rib constant load, and the loading analysis is carried out by dividing the arch rib constant load into 10 stages.
10. The method of claim 1, further comprising correcting the vault bending moment increase coefficient of the variable-height arch, and constructing a correction formula based on the vault bending moment increase coefficient of the variable-height arch and combining the antisymmetric first-order stability coefficient of the arch rib, the constant load lower axle compression stress and the span.

Description

Large-span arch bridge geometric nonlinear structure response calculation method Technical Field The invention relates to the technical field of bridge engineering structure analysis, in particular to a large-span arch bridge geometric nonlinear structure response calculation method. Background The large-span arch bridge is widely applied to the construction of important traffic infrastructures due to the characteristics of strong spanning capability, excellent stress performance, attractive appearance and the like. With the continuous increase of the span, the arch rib axial compressive stress is obviously improved, the geometrical nonlinear effect of the structure is more remarkable, and the stress performance and the safety reserve of the structure are directly affected. The existing nonlinear analysis method of the large-span arch bridge mainly comprises a numerical simulation method and an analysis method. The numerical simulation method (finite element method) can process complex structural forms, but the calculation process is complex, the time consumption is long, the internal rule of nonlinear response is difficult to intuitively reveal, the traditional analysis method is mostly based on a simplified assumption, and the nonlinear change of discrete characteristics and redundant horizontal force of an arch axis is ignored, so that the calculation accuracy is insufficient, and the requirement of the fine design of a large-span arch bridge is difficult to meet. In addition, the existing method lacks systematic research on the distribution rule of nonlinear bending moment and the application range of the bending moment increase coefficient, and cannot provide accurate nonlinear effect evaluation basis for structural design. Therefore, a method for calculating the response of the geometric nonlinear structure of the large-span arch bridge is provided to solve the difficulties existing in the prior art, which is a problem to be solved by the technicians in the field. Disclosure of Invention In view of the above, the present invention provides a method for calculating the geometric nonlinear structure response of a large-span arch bridge, which is used for solving the problems existing in the prior art. In order to achieve the above object, the present invention provides the following technical solutions: a method for calculating the response of a geometric nonlinear structure of a large-span arch bridge comprises the following steps: s1, setting a reasonable arch axis, and establishing a second-order deflection nonlinear equilibrium equation of a large-span arch bridge; S2, dispersing a reasonable arch axis into a polynomial capable of being solved in a single way, and deducing a nonlinear deflection expression and a nonlinear bending moment expression of the large-span arch bridge based on a second-order deflection nonlinear equilibrium equation; s3, solving unknown parameters in a nonlinear deflection expression and a nonlinear bending moment expression based on the principle that the integral of the elastic compression quantity and the compressive strain along the arc length of the arch axis is equal to obtain nonlinear deflection and nonlinear bending moment of the large-span arch bridge; S4, verifying the calculation method from the step S1 to the step S3 by adopting a numerical simulation method considering geometric nonlinearity; S5, analyzing the change rule and the space distribution rule of the nonlinear structure response of the large-span arch bridge along with the loading process through numerical simulation. Optionally, the second-order deflection nonlinear equilibrium equation in S1 is established based on a control differential equation of the arch structure, and the total structural bending moment including the structural line elastic bending moment which accounts for the second-order effect. Optionally, the arch structure corresponding to the reasonable arch axis in the S1 is a hyperstatic and hingeless arch, the additional bending moment is a bending moment generated by overlapping the additional bending moment of the three-hinged arch with the redundant force, and the redundant force comprises redundant horizontal force and bending moment. Optionally, the nonlinear deflection expression and the nonlinear bending moment expression in S2 consist of cosine terms and higher order polynomials, and are functions of structure loading progress and response space distribution. Alternatively, when the reasonable arch axis is parabolic, the nonlinear displacement expression is composed of a cosine curve and parabolic, and the nonlinear bending moment expression is a cosine curve. Optionally, in the solving process of the unknown parameters in S3, the nonlinear change of the redundant horizontal force needs to be considered in combination with the change characteristic of the geometric stiffness of the arch rib, and the redundant horizontal force comprises the redundant horizontal force solved ac