Calculation method for steel wire internal force redistribution after bridge cable steel wire group is fractured by fire

Abstract

According to the method for calculating the internal force redistribution of the steel wires after the bridge cable steel wire group is fractured by fire, the method that after the bridge cable steel wire group is heated in a fire, part of the steel wires are fractured and quit work, and the stress borne by the remaining steel wires is calculated under the action of stress redistribution is determined. The purposes of determining the mechanical property of a bridge cable steel wire group at high temperature, providing parameter guidance for cable fire-resistant protection design and improving the fire-resistant and fireproof capacity of a bridge are achieved.

Description

Technical Field

[0001] The present invention relates to the field of safety protection of bridge cables, and particularly to a calculation method for the internal force redistribution of steel wires in a bridge cable steel wire group after fire-induced fracture. Background Art

[0002] Under the current technical background, suspension bridges play a role as key urban traffic arteries, carrying heavy traffic flows. With the operation of vehicles on the bridge, the risk of vehicle fires is increasing. Once a vehicle combustion accident occurs, it may not only cause serious casualties, bringing the bridge traffic system to a standstill, but also the main cable, as a very critical element in the bridge structure, which needs to bear huge tensile forces. Once encountering a vehicle fire, the tensile ultimate capacity and elastic modulus of the main cable and the suspenders will be significantly reduced, thereby greatly shortening the service life of the suspension bridge, increasing the complexity of bridge repair work, and the losses will be inestimable.

[0003] How to analyze the internal force redistribution of the cable steel wire group after heat-induced fracture is a technical problem that urgently needs to be solved at the present stage. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a calculation method for the internal force redistribution of steel wires in a bridge cable steel wire group after fire-induced fracture, and clarifies the method for calculating the stress on the remaining steel wires under the action of stress redistribution after some steel wires fracture after the bridge cable steel wire group is heated in a fire. In order to determine the mechanical properties of the bridge cable steel wire group at high temperatures, provide parameter guidance for cable fire protection design, and improve the fire resistance and fire prevention ability of the bridge.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A calculation method for the internal force redistribution of steel wires in a bridge cable steel wire group after fire-induced fracture, characterized by including the following steps:

[0007] S1. Define the material parameters of the cable steel wires at high temperatures;

[0008] S2. Calculate the centroid change and eccentricity;

[0009] S3. Calculate the stress of specific steel wires;

[0010] S4. Establish the stress-strain relationship.

[0011] As a preferred technical solution of the present invention: In step S2, it is necessary to consider the centroid change of the overall steel wire group after the fractured steel wires withdraw from work through a coordinate system to calculate the eccentricity. The specific steps are as follows:

[0012] S21. Determine the coefficient of thermal expansion α(T) and elastic modulus Es(T) of the steel wires at high temperatures

[0013] S211. Determine the coefficient of thermal expansion α(T) of the steel wire at high temperature:

[0014]

[0015] S212. Determine the reduction coefficient K of the steel wire at high temperature y，t :

[0016]

[0017] S213. Determine the modulus of elasticity Es(T) of the steel wire at high temperature:

[0018] Es(T) = E O × k y,T (4)

[0019] where E O is the modulus of elasticity of the steel wire at normal temperature;

[0020] S22. Establish a coordinate system based on the cross-section of the cable steel wire group;

[0021] S23. Analyze the original centroid (x o , y o ) and the change of the centroid at high temperature (x c , y c ) through the coordinate system

[0022]

[0023] where N re is the number of remaining steel wires;

[0024] S24. Calculate the moment of inertia Ι, eccentricity e x of the remaining steel wires, and the eccentricity M, specifically as follows: y as follows:

[0025]

[0026] e x = x c - x o , e y = y c - y o (7)

[0027]

[0028] As a preferred technical solution of the present invention: In step S3, it is necessary to calculate the axial stress σ m , bending stress σ b and the total stress by considering the change of the centroid. The specific steps are as follows:

[0029] S31. Calculate the axial stress σ m and the bending stress σ b :

[0030] Determine that the total number of steel wires is N O , the number of failed steel wires is N fa , the number of remaining steel wires is N re， The cross-sectional area of each steel wire is A, and the total cross-sectional area is A O, The initial total load is F, and the initial stress is σ O , then there is:

[0031] A O = N O ×A(9)

[0032]

[0033] N re = N0 - N fa (11)

[0034]

[0035] S32. Calculate the total stress:

[0036]

[0037] As a preferred technical solution of the present invention: In step S4, it is necessary to consider the thermal expansion strain generated by the coefficient of thermal expansion, so it is necessary to calculate the thermal expansion strain ε th and the mechanical strain ε mech , and the specific steps are as follows:

[0038] S41. Calculate the thermal expansion strain ε th and the mechanical strain ε mech

[0039]

[0040] S42. Calculate the total strain ε

[0041]

[0042] S43. Establish the stress-strain relationship.

[0043] The calculation method for the internal force redistribution of the steel wire group of the bridge cable after fire proposed by the present invention clarifies the method for calculating the stress on the remaining steel wires under the action of stress redistribution after some steel wires break due to heating in the fire of the steel wire group of the bridge cable. In order to achieve the purpose of determining the mechanical properties of the steel wire group of the bridge cable at high temperature, providing parameter guidance for the fire protection design of the cable and improving the fire resistance and fire prevention ability of the bridge.

[0044] The present invention analyzes the stress-strain relationship of steel wires at high temperatures, obtains the stress redistribution results of each section of steel wires at high temperatures, and analyzes through the calculation results to determine the mechanical properties of the steel wire group of the bridge cable at high temperatures, providing parameter guidance for the fire protection design of the cable and improving the fire resistance and fire prevention ability of the bridge.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] 1. The thermal expansion caused by high temperature will change the initial strain state of the steel wire. By combining the coefficient of thermal expansion with the stress-strain relationship, the superposition effect of thermal stress and mechanical stress can be accurately calculated, and the redistribution of additional internal forces caused by the temperature gradient can be revealed.

[0047] 2. By calculating and analyzing the centroid correction and the stress-strain relationship at high temperatures, potential dangerous points can be accurately calculated and identified to guide the fire-resistant reinforcement design. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of establishing a coordinate system according to the cross-section of the cable steel wire group;

[0049] Figure 2 It is a schematic diagram of the centroid change after partial steel wires fail at high temperatures;

[0050] Figure 3 It is a schematic diagram of the eccentricity of the required steel wire. DETAILED DESCRIPTION OF THE INVENTION

[0051] The following further describes the present invention in detail in conjunction with the drawings and specific embodiments:

[0052] The calculation method for the internal force redistribution of the steel wire group of the bridge cable after being broken by fire proposed by the present invention includes the following steps:

[0053] S1. Define the material parameters of the cable steel wires at high temperatures;

[0054] S2. Calculate the centroid change and eccentricity;

[0055] S3. Calculate the stress of specific steel wires;

[0056] S4. Establish the stress-strain relationship.

[0057] The following further describes the present invention in detail in conjunction with formula calculations.

[0058] S21. Determine the coefficient of thermal expansion α(T) and elastic modulus Es(T) of the steel wire at high temperatures;

[0059] S211. Determine the coefficient of thermal expansion of the steel wire at high temperatures;

[0060]

[0061] S212. Determine the high-temperature reduction coefficient of the steel wire;

[0062]

[0063] S213. Determine the elastic modulus of the steel wire at high temperature (E O is the elastic modulus of the steel wire at normal temperature);

[0064] Es(T) = E O × k y,T (3)

[0065] S22. Establish a coordinate system based on the cross-section of the cable steel wire group, as Figure 1 shown. In the figure, A is the original centroid (x o , y o );

[0066] S23. Analyze the change in the centroid of the original shape (x o , y o ) and the centroid at high temperature through the coordinate system, as Figure 2 shown. In the figure, B is the new centroid (x o , y o ), B is the remaining steel wire, and C is the failed steel wire;

[0067] Calculate the centroid coordinates of the remaining steel wire (x c , y c ), (N re is the number of remaining steel wires);

[0068]

[0069] S24. Calculate the moment of inertia Ι, eccentricity e x of the remaining steel wire, e y and the eccentricity M;

[0070] Calculate the moment of inertia Ι of the steel wire;

[0071]

[0072] Calculate the eccentricity e x of the steel wire, e y , as Figure 3 shown;

[0073] e x = x c - x o , e y = y c - y o (7)

[0074] Calculate the eccentricity M;

[0075]

[0076] S31. Calculate the axial stress σ m and the bending stress σ b ;

[0077] Calculate the axial stress σ m ;

[0078] Determine that the total number of steel wires is N O , the number of failed steel wires is N fa , and the number of remaining steel wires is N re， The cross-sectional area of each steel wire is A, and the total cross-sectional area is A O, The initial total load is F, and the initial stress is σ O ;

[0079] A O = N O × A(9)

[0080]

[0081] N re = N0 - N fa (11)

[0082]

[0083] Calculate the bending stress σ b ;

[0084]

[0085] S32. Calculate the total stress

[0086]

[0087] S41. Calculate the thermal expansion strain ε th and the mechanical strain ε mech as well as the total strain ε

[0088] Calculate the thermal expansion strain ε th ;

[0089]

[0090] Calculate the mechanical strain ε mech ;

[0091]

[0092] S42. Calculate the total strain ε;

[0093]

[0094] S43. Establish the stress-strain relationship.

[0095] The calculation method for the internal force redistribution of bridge cable steel wires after fire-induced fracture proposed by the present invention clarifies the method for calculating the stress borne by the remaining steel wires under the action of stress redistribution after some steel wires break after being heated in a fire for the bridge cable steel wire group. The purpose is to determine the mechanical properties of the bridge cable steel wire group at high temperatures, provide parameter guidance for the fire protection design of the cable, and improve the fire resistance and fire prevention ability of the bridge.

[0096] In the above manner, the present invention analyzes the stress-strain relationship of the steel wires at high temperatures, obtains the stress redistribution results of each section of the steel wires at high temperatures, and analyzes through the calculation results to achieve the purpose of determining the mechanical properties of the bridge cable steel wire group at high temperatures, providing parameter guidance for the fire protection design of the cable, and improving the fire resistance and fire prevention ability of the bridge.

[0097] The above is only a preferred embodiment of the present invention, and it is not a limitation of the present invention in any other form. Any modification or equivalent change made according to the technical essence of the present invention still belongs to the scope protected by the present invention.

Claims

1. A calculation method for the internal force redistribution of steel wires in a group of bridge cable wires after fire-induced fracture, characterized in that It includes the following steps: S1. Determine the material parameters of the cable wire at high temperature; S2. Calculate the centroid change and eccentricity; S3. Calculate the stress of specific wires; S4. Establish the stress-strain relationship.

2. The calculation method for the internal force redistribution of steel wires after the fire-induced fracture of a group of bridge cable steel wires according to claim 1, characterized in that, In step S2, it is necessary to consider the centroid change of the overall wire group after the broken wire exits the work through the coordinate system to calculate the eccentricity. The specific steps are as follows: S21. Determine the coefficient of thermal expansion α(T) and elastic modulus Es(T) of the wire at high temperature S211. Determine the coefficient of thermal expansion α(T) of the wire at high temperature: S212. Determine the high-temperature reduction coefficient K of the steel wire y，t : S213. Determine the elastic modulus Es(T) of the wire at high temperature: Es(T) = E O × k y,T (4) Among them, E O is the elastic modulus of the steel wire at room temperature; S22. Establish a coordinate system according to the cross-section of the cable wire group; S23. Analyze the original centroid (x o , y o ) and the centroid change at high temperature (x c , y c ) Among them, N re is the remaining number of steel wires; S24. Calculate the moment of inertia Ι of the remaining steel wire and the wire eccentricity e x , e y and the eccentricity M, specifically as follows: e x = x c - x o , e y = y c - y o (7) 3. The calculation method for the internal force redistribution of steel wires after the fire-induced fracture of a group of bridge cable steel wires according to claim 1, characterized in that, In step S3, it is necessary to calculate the axial stress σ by considering the change in the centroid. m and the bending stress σ b as well as the total stress. The specific steps are as follows: S31. Calculate the axial stress σ m and the bending stress σ b : Determine that the total number of steel wires is N O , the number of failed steel wires is N fa , the number of remaining steel wires is N re， The cross-sectional area of each steel wire is A, and the total cross-sectional area is A O, The initial total load is F, and the initial stress is σ O , then there is: A O = N O × A(9) N re = N0 - N fa (11) S32. Calculate the total stress:

4. The calculation method for the internal force redistribution of steel wires after the fire-induced fracture of a group of bridge cable steel wires according to claim 1, characterized in that In step S4, the thermal expansion strain caused by the coefficient of thermal expansion needs to be considered, so it is necessary to calculate the thermal expansion strain ε th and the mechanical strain ε mech , and the specific steps are as follows: S41. Calculate the thermal expansion strain ε th and the mechanical strain ε mech S42. Calculate the total strain ε S43. Establish the stress-strain relationship.

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