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CN-122020796-A - Method for judging anti-overturning stability of single-column pier curve girder bridge

CN122020796ACN 122020796 ACN122020796 ACN 122020796ACN-122020796-A

Abstract

The invention relates to a method for judging the anti-overturning stability of a single-pier curved beam bridge, which comprises the following steps of S1, calculating the anti-overturning stability effect of the bridge under the action of constant load according to the basic principle of structural mechanics based on mechanical analysis of displacement of a simple-pier hyperstatic curved beam and counter force of a support, S2, calculating the overturning stability effect of the bridge under the action of live load according to the basic principle of structural mechanics based on mechanical analysis of displacement of the simple-pier hyperstatic curved beam and counter force of the support, S3, calculating the anti-overturning stability coefficient of the bridge according to the calculation results of the constant load anti-overturning stability effect and the live load overturning stability effect, and S4, judging the anti-overturning stability of the bridge according to the standard threshold value based on the calculation results of the anti-overturning stability coefficient of the single-pier curved beam bridge. The method can improve the efficiency of calculating and judging the anti-overturning stability of the single-column pier curve girder bridge, is beneficial to popularization of bridge health monitoring technology, and has the advantages of simplicity, high efficiency and rapidness.

Inventors

  • ZHENG YUGUO
  • Hua Dengwu
  • LIAO YUQI
  • LI XUCHANG

Assignees

  • 湖南科技大学

Dates

Publication Date
20260512
Application Date
20260203

Claims (10)

  1. 1. A method for judging the anti-overturning stability of a single-column pier curve girder bridge is characterized by comprising the following steps: S1, calculating an anti-overturning stabilizing effect of a single-column pier curve beam bridge under a constant load effect according to a basic principle of structural mechanics based on mechanical analysis of displacement of a simple support hyperstatic curve beam and counter force of a support; S2, calculating the overturning instability effect of the single-pier curve beam bridge under the action of live load according to the basic principle of structural mechanics based on mechanical analysis of the displacement of the simple-support hyperstatic curve beam and the counter force of the support; S3, calculating the anti-overturning stability coefficient of the single-pier curved beam bridge according to the calculation results of the constant load anti-overturning stability effect of S1 and the live load overturning instability effect of S2; And S4, judging the anti-overturning stability of the bridge according to the standard threshold value based on the calculation result of the anti-overturning stability coefficient of the single-pier curve bridge in S3.
  2. 2. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 1, wherein in the step S1, the anti-overturning stability effect of the single-pier curved beam bridge under the action of constant load is calculated according to the basic principle of structural mechanics, an upper structural curved beam is expressed by a plane axis of the upper structural curved beam, uniform constant load q 1 required by the action specification is acted on the upper structural curved beam, a basic model M1 of the hyperstatic structure of the single-pier curved beam bridge under the action of the uniform constant load q 1 is established, and based on the basic principle of solution of a hyperstatic structural force method in structural mechanics, a simple hyperstatic curved beam is taken as a basic structure U; Taking a basic structure U as a reference, removing redundant constraint of the basic model M1, replacing the redundant constraint with a corresponding constraint counter force X 1 、X 2 , establishing a basic system Q1 corresponding to the basic model M1 force method solution, wherein the basic system Q1 is equivalent to the basic model M1 based on the basic principle of structural mechanics, and X 1 、X 2 is the basic unknown quantity of the basic model M1 force method solution; based on a displacement analysis result of a simple hyperstatic curve beam in structural mechanics, calculating a related flexibility coefficient and a related free term of a basic model M1 force method solution; establishing a basic equation solved by a basic model M1 force method according to a deformation coordination principle, and solving to obtain a basic unknown quantity X 1 、X 2 ; respectively calculating support counter forces of the potential failure supports A 2 and D 2 of the basic structure U under the action of the constant load q 1 and the redundant constraint force X 1 、X 2 ; Calculating the support counter force of the potential failure supports A 2 and D 2 of the basic model M1 under the action of the constant load q 1 by adopting the superposition principle; based on the pure torsion analysis theory of the curved beam bridge, the anti-overturning stabilizing effect of the single-column pier curved beam bridge under the constant load effect is calculated.
  3. 3. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 2, wherein in the step S1, the correlation compliance coefficients delta 11 、δ 22 、δ 12 and delta 21 solved by a basic model M1 force method are calculated based on the basic principle solved by the hyperstatic structural force method in structural mechanics and the displacement analysis result of a simple hyperstatic curved beam in structural mechanics, wherein delta 11 is a dummy unit load Displacement at position X 1 upon acting at position X 1 of basic structure U, delta 22 being dummy unit load Displacement at position X 2 upon acting at position X 2 of basic structure U, delta 12 being dummy unit load Displacement at position X 1 upon acting at position X 2 of basic structure U, delta 21 being dummy unit load A displacement at position X 2 upon acting at position X 1 of the basic structure U; Based on the basic principle of the solution of the hyperstatic structural force method in structural mechanics and the displacement analysis result of a simple hyperstatic curve beam in structural mechanics, calculating a related free term delta 1p 、Δ 2p 、Δ 1p of the solution of the basic model M1 force method, wherein the displacement is generated by uniformly distributing constant load q 1 acting on a basic structure U at the position X 1 , and the displacement delta 2p is generated by uniformly distributing constant load q 1 acting on the basic structure U at the position X 2 ; the basic equation for establishing a basic model M1 force method solution based on the deformation coordination principle is as follows: Solving a basic equation of a force method of the basic model M1 to obtain basic unknown quantities X 1 、X 2 of the force method of the basic model M1, wherein the basic unknown quantities X 1 、X 2 are respectively: 。
  4. 4. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 2, wherein in the step S1, based on the superposition principle, the support counter force F A21 of the potential failure support A 2 and the support counter force F D21 of the potential failure support D 2 of the basic model M1 under the action of uniform constant load q 1 are calculated as follows: Wherein the method comprises the steps of 、 、 Respectively distributing support counter forces of a potential failure support A 2 of the basic structure U under the actions of constant load q 1 , redundant constraint force X 1 and redundant constraint force X 2 , 、 、 Respectively distributing support counter forces of a potential failure support D 2 of the basic structure U under the actions of constant load q 1 , redundant constraint force X 1 and redundant constraint force X 2 , 、 、 And 、 、 And respectively calculating and determining based on analysis results of the simple hyperstatic curve beam support counter force in structural mechanics.
  5. 5. The method for judging the anti-overturning stability of the single-column pier curved beam bridge according to claim 2, wherein in the step S1, the anti-overturning stability effect G 1 under the constant load effect of the single-column pier curved beam bridge is calculated based on the pure torsion analysis theory of the curved beam bridge and is as follows: Wherein, L 1 is the distance between the support a 1 and a 2 on the left end support line a 1 A 2 , and L 2 is the distance between the support D 1 and D 2 on the right end support line D 1 D 2 .
  6. 6. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 1, wherein in the step S2, according to the basic principle of structural mechanics, the overturning instability effect of the single-pier curved beam bridge under the action of active load is calculated, the upper structural curved beam is expressed by the plane axis of the upper structural curved beam, the active load required by the action specification on the upper structural curved beam comprises a concentrated force P 2 , a concentrated torque T 2 , an even distribution force q 2 and an even distribution torque T 2 , an overstatic basic model M2 of the single-pier curved beam bridge under the action of the active load is established, and based on the basic principle of the overstatic structural force method solving in the structural mechanics, a simply supported overstatic curved beam is taken as a basic structure U; Taking a basic structure U as a reference, removing redundant constraint of the basic model M2, replacing the redundant constraint with a corresponding redundant constraint counter force X 3 、X 4 , establishing a basic system Q2 corresponding to the basic model M2 force method solution, wherein the basic system Q2 is equivalent to the basic model M2 based on the basic principle of structural mechanics, and X 3 、X 4 is the basic unknown quantity of the basic model M2 force method solution; based on a displacement analysis result of a simple hyperstatic curve beam in structural mechanics, calculating a related flexibility coefficient and a related free term of a basic model M2 force method solution; Establishing a basic equation solved by a basic model M2 force method according to a deformation coordination principle, and solving to obtain a basic unknown quantity X 3 、X 4 ; Based on analysis of the support counter force of the simple support hyperstatic curve beam in structural mechanics, the support counter forces of the potential failure supports A 2 and D 2 of the basic structure U under the action of various live loads and redundant constraint forces X 3 、X 4 are calculated respectively; Calculating the support counter force of the support A 2 and the support D 2 which are potentially invalid under the action of live load by adopting the superposition principle; Based on the pure torsion analysis theory of the curved girder bridge, the overturning instability effect of the single-column pier curved girder bridge under the action of live load is calculated.
  7. 7. The method for judging the anti-overturning stability of the single-column pier girder bridge according to claim 6, wherein the method is characterized in that the relative compliance coefficients delta 33 、δ 44 、δ 34 and delta 43 solved by a basic model M2 force method are calculated based on a basic principle solved by the hyperstatic structural force method in structural mechanics and a displacement analysis result of a simple hyperstatic curve girder in the structural mechanics, wherein delta 33 is a dummy unit load Displacement at position X 3 upon acting at position X 3 of basic structure U, delta 44 being dummy unit load Displacement at position X 4 upon acting at position X 4 of basic structure U, delta 34 being dummy unit load Displacement at position X 3 upon acting at position X 4 of basic structure U, delta 43 being dummy unit load A displacement at position X 4 upon acting at position X 3 of the basic structure U; Based on the basic principle and the superposition principle of the hyperstatic structural force method solution in structural mechanics, the related free term delta 3p 、Δ 4p of the basic model M2 force method solution is calculated as follows: Wherein Delta 3p is the displacement of the live load on the basic structure U at the position X 3 , delta 4p is the displacement of the live load on the basic structure U at the position X 4 , 、 、 、 Respectively the displacement of the basic structure U at the position of the redundant constraint force X 3 under the actions of the live load concentrated force P 2 , the concentrated torque T 2 , the uniform distributed force q 2 and the uniform distributed torque T 2 , 、 、 、 Respectively the displacement of the basic structure U at the position of the redundant constraint force X 4 under the actions of the live load concentrated force P 2 , the concentrated torque T 2 , the uniform distributed force q 2 and the uniform distributed torque T 2 , 、 、 、 And 、 、 、 Respectively calculating and determining based on displacement analysis results of the simple statically indeterminate curved beams in structural mechanics; the basic equation for establishing a basic model M2 force method solution based on the deformation coordination principle is as follows: Solving a basic equation of a force method of the basic model M2 to obtain basic unknowns X 3 、X 4 solved by the force method of the basic model M2, wherein the basic unknowns X 3 、X 4 are respectively: 。
  8. 8. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 6, wherein the method is characterized in that based on a superposition principle, the support counter force F A22 of the potential failure support A 2 and the support counter force F D22 of the potential failure support D 2 of the basic model M2 under the action of live load are respectively as follows: Wherein, the 、 、 、 、 、 The support counter forces of the potential failure support A 2 of the basic structure U under the actions of the live load concentrated force P 2 , the concentrated torque T 2 , the uniform distributed force q 2 , the uniform distributed torque T 2 , the redundant constraint forces X 3 and X 4 are respectively, 、 、 、 、 、 The support counter forces of the potential failure support D 2 of the basic structure U under the actions of the live load concentrated force P 2 , the concentrated torque T 2 , the uniform distributed force q 2 , the uniform distributed torque T 2 , the redundant constraint forces X 3 and X 4 are respectively, 、 、 、 、 、 And 、 、 、 、 、 Respectively calculating and determining based on analysis results of the simple hyperstatic curve beam support counter force in structural mechanics; Based on the pure torsion analysis theory of the curve girder bridge, the overturning instability effect G 2 under the action of the live load of the single-column pier curve girder bridge is calculated as follows: 。
  9. 9. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 1, wherein in the step S3, the anti-overturning stability coefficient G 1 /G 2 of the single-pier curved beam bridge is calculated according to the calculation results of the constant load anti-overturning stability effect and the live load overturning instability effect based on the pure torsion analysis theory of the curved beam bridge, and is as follows: 。
  10. 10. The method for judging the anti-overturning stability of the single-pier curved beam bridge according to claim 1, wherein in the step S4, in judging the anti-overturning stability of the bridge according to the standard threshold, based on the calculation result of the anti-overturning stability coefficient of the single-pier curved beam bridge, when the anti-overturning stability coefficient G 1 /G 2 of the single-pier curved beam bridge is more than or equal to 2.5 according to the standard requirement, the bridge can be judged not to be overturned and unstable, and when G 1 /G 2 is less than 2.5, the bridge can be judged to be overturned and unstable.

Description

Method for judging anti-overturning stability of single-column pier curve girder bridge Technical Field The invention relates to a bridge health monitoring technology, in particular to a method for judging the anti-overturning stability of a single-column pier curve girder bridge. Background The upper structure of the single-column pier curved beam bridge usually adopts an integral box beam, the middle pier of the lower structure usually adopts a single-column pier, the structure is light and attractive, the requirement of the line type design of the whole road can be met, the occupied area of the lower structure is smaller, and the use space under the bridge can be increased, so that the single-column pier curved beam bridge is widely applied to urban bridges and highway ramp bridges. The abutment or the side pier top of the single-column pier curved beam bridge is usually provided with double supports, the middle pier top is usually provided with a single support, so that effective torsion resistance constraint is difficult to provide on the cross section, when a passing vehicle deviates from the outer convex side of the curved beam bridge and runs along a bridge deck, the side pier of the bridge is extremely easy to cause the state that the convex side support is pressed and the concave side support is empty, namely the concave side support is a potential failure support, and the whole bridge has a risk of transverse overturning. In recent years, more single pier curved beam bridge transverse overturning accidents occur, and serious direct and indirect economic losses and various adverse effects are caused. Therefore, deep analysis and calculation of the anti-overturning stability of the single-column curved girder bridge are needed, and implementation and popularization of the bridge health monitoring technology are achieved. The classical curve Liang Wanniu coupling calculation method is used for constructing a displacement-load equation of the curve beam by jointly using a stress balance equation, a physical equation and a geometric equation of the structure, and the aim of solving the stress and the displacement of the curve beam is fulfilled by solving the equation. If the method is adopted to analyze and calculate the anti-overturning stability of the single pier curved beam bridge, a simultaneous high-order differential equation set needs to be solved, and the method is very difficult and complicated. Therefore, the classical curve Liang Wanniu coupling calculation method has weak practicability in engineering practice, and is not beneficial to popularization of bridge health monitoring technology. Disclosure of Invention The invention aims to provide a method for judging the anti-overturning stability of a single-column pier curve girder bridge, which is based on mechanical analysis of displacement of a simple hyperstatic curve girder and counter force of a support, and calculates the anti-overturning stability effect of the single-column pier curve girder bridge under the constant load and the overturning instability effect of the single-column pier curve girder bridge under the live load according to the basic principle of structural mechanics, then calculates the anti-overturning stability coefficient of the bridge, and judges the anti-overturning stability of the bridge according to the result of the anti-overturning stability coefficient. Compared with the classical bending-torsion coupling calculation method and the conventional finite element method, the method can improve the efficiency of calculating and judging the anti-overturning stability of the single-column pier curve girder bridge, is beneficial to the popularization of bridge health monitoring technology, and has the advantages of simplicity, high efficiency and rapidness. In order to achieve the above purpose, the present invention provides the following technical solutions: A method for judging the anti-overturning stability of a single-column pier curve girder bridge comprises the following steps: S1, calculating an anti-overturning stabilizing effect of a single-column pier curve beam bridge under a constant load effect according to a basic principle of structural mechanics based on mechanical analysis of displacement of a simple support hyperstatic curve beam and counter force of a support; S2, calculating the overturning instability effect of the single-pier curve beam bridge under the action of live load according to the basic principle of structural mechanics based on mechanical analysis of the displacement of the simple-support hyperstatic curve beam and the counter force of the support; S3, calculating the anti-overturning stability coefficient of the single-pier curved beam bridge according to the calculation results of the constant load anti-overturning stability effect of S1 and the live load overturning instability effect of S2; And S4, judging the anti-overturning stability of the bridge according to the standard t