A method for calculating the safety of a bridge cable after a fire

Abstract

This invention discloses a method for calculating the safety of bridge suspension cables after a fire, belonging to the technical field of calculation, estimation, or counting. The method includes: establishing a material strength model of the cable base material after high-temperature water cooling based on experimental data; establishing a fire numerical simulation model of the bridge suspension cable using FDS software to calculate the time-varying temperature model of each node on the cable surface from ignition to water spray extinguishing; establishing a refined finite element model of the bridge suspension cable including all steel wires using finite element software to calculate the time-varying temperature of each steel wire; based on the strength model of the cable base material, obtaining the remaining strength of each steel wire after water spray extinguishing from the highest temperature of each steel wire; comparing the stress of each steel wire with the remaining strength of the steel wire to obtain the effective number of steel wires and the effective area of ​​the cable cross-section, and then calculating the safety of the suspension cable structure after a fire. This invention enables a reasonable assessment of the safety of bridge suspension cable structures after a vehicle fire on a bridge.

Description

Technical Field

[0001] This invention relates to bridge engineering counting, and in particular discloses a method for calculating the safety of bridge suspension cables after a fire, belonging to the technical field of calculation, estimation or counting. Background Technology

[0002] To meet the engineering requirements of large and super-large spans, cable-stayed bridge structures are increasingly widely used in bridge construction. Compared with concrete, the steel base material of cable-stayed bridges has a lower specific heat capacity and higher thermal conductivity, making it more susceptible to high temperatures during fires. After a fire occurs on a bridge, the cable structure near the fire source is affected by high temperatures, leading to a degradation of the base material's strength and impacting structural safety. Therefore, it is necessary to conduct research on the safety of cable-stayed structures after a fire. Currently, some scholars have conducted experimental and simulation studies on the mechanical properties of cables after a fire. However, most of these studies rely on artificially set heating processes or referencing heating curves from relevant domestic and international standards to study the resistance of cables after high temperatures. This lack of calculation of actual fire temperature changes results in inaccurate data. Furthermore, previous finite element analysis methods treated cables as homogeneous cylinders, but the cable cross-section, composed of parallel steel wires, contains gaps. Considering the entire cross-section as a whole cannot reflect the true residual resistance of the cable cross-section, leading to significant discrepancies between the calculated mechanical properties of cables after high temperatures and the actual situation. This invention aims to propose a method for calculating the safety of bridge cables after a fire to overcome these shortcomings. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing a method for calculating the safety of bridge suspension cables after a fire. This method approximates the finite element model of the temperature field of the bridge suspension cable section during a fire simulation process, thereby achieving the objective of accurately analyzing and evaluating the safety of bridge suspension cables after a fire. This solves the technical problem that the calculated mechanical properties of suspension cables after high temperatures obtained by existing bridge fire safety analysis techniques do not match the actual situation.

[0004] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0005] This application provides a method for calculating the safety of bridge suspension cables after a fire, including:

[0006] S1: Establish a material strength model for bridge cable base material after high-temperature water cooling based on experimental data;

[0007] S2: Establish a numerical simulation model of fire on bridge suspension cables and a time-varying model of the highest surface temperature of the suspension cables from the time of fire ignition to the time of water spraying for fire extinguishing;

[0008] S3: Establish a finite element model to simulate the temperature field of the bridge cable section. Define the time-varying model of the highest temperature on the surface of the cable as the boundary condition of the finite element model. Synchronize the fire numerical simulation model and the finite element model. Simulate the highest temperature experienced by each steel wire during the fire in the finite element model.

[0009] S4: Based on the material strength model of the bridge suspension cable base material after being cooled by water at high temperature, the remaining strength of each steel wire after water spraying is obtained from the highest temperature experienced by each steel wire during the fire.

[0010] S5: By comparing the stress of each steel wire with the remaining strength of the steel wire after water spraying for fire extinguishing, the effective number of steel wires and the effective area of ​​the cable cross-section are obtained, and then the remaining bearing capacity of the bridge cable after the fire is calculated to determine the structural safety of the cable after the fire.

[0011] As a further optimization of the method for calculating the safety of bridge slings after a fire, S2 uses FDS software to establish a fire numerical simulation model of bridge slings, and establishes a time-varying model of the highest surface temperature of the slings from the time of fire ignition to the time of water spraying for fire extinguishing. Specifically, it includes S21 and S22.

[0012] S21: Set the simulation range (i.e., the size of the spatial area to be simulated) and grid size of the software according to the fire impact range and calculation accuracy requirements. Select the combustion reaction model according to the fire combustibles, such as setting the fuel type, energy released per unit mass of oxygen, and calorific value. Set the size and position of structures and obstacles according to the spatial orientation of the site. Establish the combustion model according to formula (1):

[0013] HRR m =at 2 (1)

[0014] In equation (1), HRR m t represents the maximum heat release rate of the fire source, t represents the time required to reach the maximum fire scale from the start of the fire, and a represents the fire growth coefficient, which is 0.002931, 0.01127, 0.04689, and 0.1878 for slow-speed, medium-speed, fast-speed, and ultra-fast-speed fires, respectively.

[0015] The initial conditions for the simulation are set according to meteorological parameters such as temperature, humidity, and air pressure. The ventilation conditions of the four boundaries are determined according to the actual wind direction and wind speed. For example, the upper boundary of the simulated space is set to a free and open ventilation state, and the lower boundary is set to a non-ventilated, sealed, and insulated state.

[0016] S22: A thermocouple is installed at regular intervals on the surface of the cable. The temperature of each node on the cable surface (i.e., the location of the thermocouple) is calculated throughout the entire fire process. By comparing the temperature of each node on the cable surface at each moment, the highest temperature of the cable surface at any moment is extracted. Taking the moment of ignition as the initial time and the time of water spraying for fire extinguishing as the end time, a time-varying curve model T(t)~t of the highest temperature on the cable surface is established.

[0017] As a further optimization of the calculation method for the safety of bridge slings after a fire, S3 is a method that simulates the highest temperature experienced by each steel wire during a fire in the finite element model of the bridge slings, specifically including S31 to S33.

[0018] S31: First, treat the sling as a homogeneous steel bar, establish a refined model of the sling in the finite element software, mesh the sling cross section, and set the thermal parameters (thermal conductivity, specific heat capacity, coefficient of thermal expansion) of the steel wire material as a function of temperature to accurately reflect the heat transfer within the cross section and the final cross section temperature distribution.

[0019] The thermal conductivity varies with temperature as follows:

[0020]

[0021] The coefficient of thermal expansion varies with temperature as follows:

[0022]

[0023] The specific heat capacity changes with temperature as follows:

[0024]

[0025] λ s (T) is the thermal conductivity at temperature T, α s (T) is the coefficient of thermal expansion at temperature T, c s (T) represents the specific heat capacity at temperature T.

[0026] S32: Define the time-varying model of the highest temperature on the cable surface as a thermal boundary condition in the finite element model. Set the simulation duration and number of steps to be the same as the FDS fire model. In the fire numerical simulation model, infinitely approximate the finite element model during the fire process. Through simulation calculation, the time-varying temperature model T of each steel wire during the fire process can be obtained. i (t)~t.

[0027] S33: The time when the fire truck intervenes by spraying water, counting from the start of the fire, is denoted as t. w According to T i (t)~t find 0~t w The highest temperature T experienced by each steel wire of the sling during the fire within a given time period.w,i :

[0028] T w,i =T i (t) max ,0≤t≤t w (5)

[0029] i is the wire number within the cross section. If the sling consists of n parallel wires, then i = 1, 2, 3...n.

[0030] As a further optimization of the method for calculating the safety of bridge suspension cables after a fire, the specific method for calculating the residual strength of each steel wire after water spray extinguishing is as follows:

[0031] The highest temperature T experienced by each steel wire during the fire will be determined based on... w,i Substitute the material strength model f of the sling base material after high temperature water cooling u (T), calculate the residual strength f of each sling after water spraying fire extinguishing. ui .

[0032] As a further optimization of the calculation method for the safety of bridge suspenders after a fire, this method determines the effective number of steel wires and the effective cross-sectional area by comparing the remaining strength of the steel wires with the cross-sectional stress, and evaluates the safety and remaining load-bearing capacity of the suspender structure after a fire. Specifically, this includes:

[0033] S51: Process the daily cable force time history N(t) of the bridge suspenders on a daily basis to obtain the maximum daily cable force N of the suspenders during the monitoring period. d And calculate the maximum daily cable force N of the sling. d The probability density distribution model f(N) d The maximum daily cable force with a guarantee rate of over 95% is taken as the representative value N0 of the cable tension, i.e.:

[0034]

[0035] S52: Take the sum of the cross-sectional areas of all the steel wires in the sling as the initial effective cross-sectional area of ​​the sling, denoted as A0, and the cross-sectional area of ​​the i-th steel wire is denoted as A. i Find the stress S0 at the section of the sling:

[0036]

[0037]

[0038] S53: The residual strength f of each steel wire ui Compared with the full-section stress S0, condition f is satisfied. ui≥ The steel wire of S0 is taken as the effective steel wire, and its quantity is recorded as n1;

[0039] S54: Judge the value of n1. If n1 = n, the remaining bearing capacity after fire is the product of the minimum value of the remaining strengths of these n steel wires and the sum of the cross-sectional areas of the n steel wires, that is:

[0040] N[[ID=--]] u ≥min{f ui , i = 1, 2, 3, … n}A0 (9)

[0041] All steel wires are effective and the sling is in a safe state;

[0042] If n1 = 0, the remaining bearing capacity of the sling after fire is 0, the whole cross-section fails, and the sling is not safe;

[0043] S55: If 0 < n1 < n, the cross-section is partially effective. Deduct the failed steel wires and re-number the remaining effective steel wires. j = 1, 2, 3, …, n1. The effective cross-sectional area of the sling is denoted as A1. Calculate the stress of the sling cross-section as:

[0044]

[0045]

[0046] Compare the remaining strength f uj of each steel wire with the cross-section stress S1. The steel wires that meet the condition f uj≥ ≥ S1 are regarded as effective steel wires, and the number of them is denoted as n2;

[0047] If n2 = n1, the remaining bearing capacity after fire is:

[0048]

[0049] Then these n1 steel wires are all effective and the sling is in a safe state;

[0050] If n2 = 0, the remaining bearing capacity after fire is 0, and all n1 steel wires fail, and the sling is not safe;

[0051] S56: If 0 < n2 < n1, it is necessary to continue the calculation according to the steps of S55 until n k+1 = n k or 0 appears in the k-th calculation result:

[0052] If n k+1 = n k , then the remaining bearing capacity after fire:

[0053] N u ≥min{f um , m = 1, 2, 3, …, n k}A k (13)

[0054]

[0055] This n k All steel wires are effective, and the sling is in a safe state; where m is the effective steel wire number in the k-th calculation, m=1,2,3…,n k ;

[0056] If n k+1 =0, the remaining load-bearing capacity of the sling after the fire is 0, n k All steel wires have failed, making the sling unsafe.

[0057] Specific embodiments of this application are disclosed in detail with reference to the following description and accompanying drawings, indicating how the principles of this application can be adopted. It should be understood that the embodiments of this application are not limited in scope. Within the spirit and scope of the appended claims, embodiments of this application include many changes, modifications, and equivalents.

[0058] Features described and / or shown in one embodiment may be used in the same or similar manner in one or more other embodiments, combined with features in other embodiments, or substituted for features in other embodiments.

[0059] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, whole, step, or component, and does not exclude the presence or addition of one or more other features, wholes, steps, or components.

[0060] The present invention, employing the above-mentioned technical solution, has the following beneficial effects: The present invention simulates and reconstructs the fire scene environment during a fire using an established fire numerical simulation model to obtain the true thermal environment of the sling. A time-varying model of the highest surface temperature of the sling is used as the thermal boundary condition to perform finite element thermal analysis on the sling cross-section, determining the highest temperature experienced by each steel wire during the fire. Based on the material strength model of the sling's parent material after high-temperature water cooling, the remaining resistance of each steel wire after water spray extinguishing is calculated. Finally, the overall post-fire safety of the sling is calculated and evaluated based on the comparison between the remaining resistance of each steel wire and the stress of the sling cross-section. Compared with traditional research methods, this method has a clear approach, is easy to use in engineering and technical fields, more accurately reflects the thermal environment of the sling under fire, makes the temperature field of the sling cross-section and the remaining resistance of each steel wire clearer, and ultimately enables a more scientific assessment of the sling's safety after a fire. Attached Figure Description

[0061] Figure 1 A flowchart illustrating a method for calculating the safety of bridge slings after a fire, provided as an embodiment of this application.

[0062] Figure 2 This is a schematic diagram of the strength model of the sling base material in an embodiment of the present invention.

[0063] Figure 3 This is a schematic diagram of the time-varying model of the surface temperature of the sling in an embodiment of the present invention.

[0064] Figure 4 This is a simulation result of the temperature field distribution of the cable cross section in an embodiment of the present invention.

[0065] Figure 5 This is a schematic diagram of the probability density distribution model of cable force on the bridge suspension cable in an embodiment of the present invention.

[0066] Figure 6 This is a schematic diagram of the cross-sectional structure of the suspension cable in an embodiment of the present invention. Detailed Implementation

[0067] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0068] Please see Figure 1 The present invention provides a method for calculating the safety of bridge suspension cables after a fire, comprising five steps S1 to S5.

[0069] S1: Establish a material strength model for the sling base material after high-temperature water cooling based on experimental data. u (T), where T is the temperature, f u (T) represents the material strength of the sling base material at temperature T.

[0070] S2: Use FDS software to establish a fire numerical simulation model of the bridge suspension cable and calculate the time-varying model of the highest temperature on the cable surface from the time of fire ignition to the time of water spraying extinguishing. This includes steps S21 and S22.

[0071] S21: Set the spatial range and grid size for software simulation calculation according to the fire impact range and calculation accuracy requirements. Select the combustion reaction model according to the combustibles, such as setting the fuel type, energy released per unit mass of oxygen, and calorific value. Set the size and location of structures and obstacles according to the spatial orientation of the site. Establish the combustion model according to formula (1):

[0072] HRR m =at 2 (1)

[0073] In equation (1), HRR mt is the maximum heat release rate of the fire source; t is the time required to reach the maximum fire size from the start of the fire; a is the fire growth coefficient, which is 0.002931, 0.01127, 0.04689, and 0.1878 for slow, medium, fast, and ultra-fast fires, respectively.

[0074] The initial conditions for simulation are set according to meteorological parameters such as temperature, humidity, and air pressure. The ventilation conditions of the four boundaries of the simulation calculation space are determined according to the actual wind direction and wind speed. For example, the upper boundary of the simulation calculation space is set to a free and open ventilation state, and the lower boundary of the simulation calculation space is set to a non-ventilated, sealed, and insulated state.

[0075] S22: A thermocouple is installed at regular intervals on the surface of the cable. The temperature of each node on the cable surface (i.e., the location of the thermocouple) is calculated throughout the entire fire process. By comparing the temperature of each node on the cable surface at each moment, the highest temperature of the cable surface at any moment is extracted. Taking the moment of ignition as the initial time and the time of water spraying for fire extinguishing as the end time, a time-varying curve model T(t)~t of the highest temperature on the cable surface is established.

[0076] S3: Use finite element software to establish a finite element model of the bridge suspension cable, input the time-varying data of the highest surface temperature of the suspension cable into the finite element model of the bridge suspension cable, and calculate the highest temperature experienced by each steel wire during the fire, specifically including steps S31 to S33.

[0077] S31: First, treat the sling as a homogeneous steel bar, establish a finite element model of the sling in the finite element software, mesh the sling cross section, and set the thermal parameters (thermal conductivity, specific heat capacity, coefficient of thermal expansion) of the steel wire material as a function of temperature to accurately reflect the heat transfer situation in the sling cross section and the final cross section temperature distribution.

[0078] The thermal conductivity varies with temperature as follows:

[0079]

[0080] The coefficient of thermal expansion varies with temperature as follows:

[0081]

[0082] The specific heat capacity changes with temperature as follows:

[0083]

[0084] In equations (2) to (4), λ s (T) is the thermal conductivity at temperature T, with units of W / (m·℃); α s (T) is the coefficient of thermal expansion at temperature T, with units of 1 / ℃; c s(T) represents the specific heat capacity at temperature T, expressed in J / (kg·℃).

[0085] S32: Define the time-varying model of the highest surface temperature of the sling as the thermal boundary condition in the finite element model. Set the simulation duration and number of steps of the finite element model to be the same as the fire numerical simulation model. After simulation calculation by the finite element model, the time-varying temperature process model T of each steel wire during the fire can be obtained. i (t)~t.

[0086] S33: The time when the fire truck intervenes by spraying water, counting from the start of the fire, is denoted as t. w According to T i (t)~t find 0~t w The highest temperature T experienced by each steel wire of the sling during the fire within a given time period. w,i :

[0087] T w,i =T i (t) max ,0≤t≤t w (5)

[0088] In equation (5), i is the wire number in the cross section. If the sling is composed of n parallel wires, then i = 1, 2, 3...n.

[0089] S4: Based on the material strength model of the sling base material after being cooled by water at high temperature, the residual strength of each steel wire after water spraying is obtained from the highest temperature experienced by each steel wire during the fire. Specifically, the highest temperature T experienced by each steel wire i during the fire is calculated as follows: w,i Substitute the material strength model f of the sling base material after high temperature water cooling u (T), calculate the residual strength f of each steel wire after water spray extinguishing. ui .

[0090] S5: By comparing the stress of each steel wire with the remaining strength after water spraying for fire extinguishing, the effective number of steel wires and the effective area of ​​the cable cross-section are obtained, and then the safety of the bridge cable after the fire is calculated. This includes steps S51 to S56.

[0091] S51: Process the daily cable force time history N(t) of the bridge suspenders on a daily basis to obtain the maximum daily cable force N of the suspenders during the monitoring period. d And calculate the maximum daily cable force N of the sling. d The probability density distribution model f(N) d The maximum daily cable force with a guarantee rate of over 95% is taken as the representative value N0 of the cable tension, i.e.:

[0092]

[0093] S52: Take the sum of the cross-sectional areas of all the steel wires in the sling as the initial effective area of the sling cross-section, denoted as A0, and the cross-sectional area of the i-th steel wire is denoted as A i , and calculate the stress S0 of the sling cross-section:

[0094]

[0095]

[0096] S53: Compare the remaining strength f of each steel wire after sprinkler fire extinguishing ui with the stress S0 of the sling cross-section. The steel wires that meet the condition f ui≥ ≥ S0 are regarded as effective steel wires, and the number of them is denoted as n1;

[0097] S54: Judge the value of n1. If n1 = n, then the minimum value of the remaining bearing capacity of the sling after fire is taken as the product of the minimum value of the remaining strength of these n steel wires and the sum of the cross-sectional areas of the n steel wires, that is:

[0098] N u ≥ min{f ui , i = 1, 2, 3, … n}A0 (9)

[0099] All the steel wires are effective, and the sling is in a safe state;

[0100] If n1 = 0, then the remaining bearing capacity of the sling after fire is 0, the full cross-section fails, and the sling is not safe;

[0101] S55: If 0 < n1 < n, then the cross-section is partially effective. Deduct the failed steel wires and re-number the remaining effective steel wires, j = 1, 2, 3, …, n1. Denote the effective cross-sectional area of the sling as A1, and calculate the stress of the sling cross-section as:

[0102]

[0103]

[0104] Compare the remaining strength f of each steel wire uj with the stress S1 of the sling cross-section. The steel wires that meet the condition f uj≥ ≥ S1 are regarded as effective steel wires, and the number of them is denoted as n2;

[0105] If n2 = n1, the remaining bearing capacity N of the sling after fire u is:

[0106] N u ≥ min{f uj , j = 1, 2, 3, … n1}A1 (12)

[0107] Then these n1 steel wires are all effective, and the sling is in a safe state;

[0108] If n2 = 0, the remaining bearing capacity of the sling after the fire is 0, all n1 steel wires fail, and the sling is unsafe.

[0109] S56: If 0 < n2 < n1, continue the calculation according to step S55 until n k+1 = n k or 0:

[0110] If n k+1 = n k , the remaining bearing capacity of the sling after the fire:

[0111]

[0112]

[0113] These n k steel wires are all effective, and the sling is in a safe state; where m is the effective steel wire number in the kth calculation, m = 1, 2, 3..., n k ;

[0114] If n k+1 = 0, the remaining bearing capacity of the sling after the fire is 0, and all n k steel wires fail, and the sling is unsafe.

[0115] In a specific application scenario of this application, taking the safety assessment of the sling after a vehicle fire on the Runyang Yangtze River Bridge as an example, the specific implementation process of the present invention is described:

[0116] 1) In this embodiment, experimental research is carried out on the mechanical properties of the sling base material - 1670 - grade steel wire after being cooled by water at high temperature on the Runyang Yangtze River Bridge, and the material strength model of the sling at different temperatures is obtained. As Figure 2 shown, the degree of strength degradation of the sling base material is represented by the ratio f u (T) / f u of the strength after high temperature to the strength at normal temperature.

[0117] 2) Use the fire simulation software FDS to reconstruct the fire scene of a fire accident that occurred on the bridge on March 4, 2017 through simulation. The fire scale is taken as 200 MW, and the fast - type "t 2"Fire, a is taken as 0.04689, according to equation (1), the fire reaches its maximum intensity 43.3 minutes after ignition. The initial ambient temperature is 5℃, the relative humidity is 40%, the maximum visibility is 30.0m, the simulation duration is 5400s (90min), the number of steps is 1000, and the simulation boundaries on all four sides are in a free ventilation state. A thermocouple is installed every 0.5m on the four slings at points 15 and 16. The highest temperature of the slings at any time is calculated to obtain the time-varying model of the highest surface temperature of each sling, such as..." Figure 3 As shown.

[0118] 3) A refined model of the sling is established in the finite element software ABAQUS, and the thermal parameters of the steel wire material are set to vary with temperature as follows:

[0119] The thermal conductivity varies with temperature as follows:

[0120]

[0121] The coefficient of thermal expansion varies with temperature as follows:

[0122]

[0123] The specific heat capacity changes with temperature as follows:

[0124]

[0125] The time-varying model of the highest temperature on the surface of the sling is defined as the thermal boundary condition in the finite element model. The simulation duration of the finite element model is set to 5400s, and the number of steps is 100. After simulation calculation, the time-varying temperature process model T of each steel wire during the fire can be obtained. i (t)~t, the temperature distribution on the cross section of the sling is as follows: Figure 4 As shown.

[0126] (4) Assume that the fire truck arrives at the scene and begins spraying water to extinguish the fire 45 minutes after the fire starts, so let the water cooling intervention time be t. w =45min, the highest temperature T experienced by each steel wire during the fire can be obtained from equation (5). wi , and then according to Figure 2 The strength model of the sling material is used to calculate the remaining strength of the steel wire after water spraying. The highest temperature experienced by each steel wire during the fire and the remaining strength of each steel wire after water spraying are shown in Table 1.

[0127]

[0128]

[0129] Table 1

[0130] (5) Monitor the cable tension on the bridge to obtain the probability density distribution model of the daily maximum cable tension, as shown in the figure. Figure 5 As shown, the cross-sectional structure of the suspension cable is as follows: Figure 6 As shown, the representative value of the cable force N0 = 1200kN is taken from equation (6), and the stress S0 of the cable section is obtained from equations (7) and (8) as 500MPa. The residual strength f of each steel wire is then calculated. ui Compared with the full-section stress S0, condition f is satisfied. ui≥ The number of wires n in S0 s =n=109, from equation (9) we know the remaining bearing capacity of the sling after the fire:

[0131] N u ≥min{f ui ,i=1,2,3,…n}A0=1575MPa×109×0.25π×(5mm) 2 =3369kN. All wires in the entire cross-section of the sling are effective, and the sling is in a safe condition.

[0132] The above descriptions are merely preferred embodiments of this application, and the present invention is not limited to the above embodiments. It is understood that other improvements and variations directly derived or conceived by those skilled in the art without departing from the spirit and concept of the present invention should be considered to be included within the protection scope of the present invention.

Claims

1. A method for calculating the safety of bridge suspension cables after a fire, characterized in that, Includes the following steps: Step 1: Establish a material strength model for the bridge suspension cable base material after it is cooled by water at high temperature based on experimental data; Step 2: Establish a numerical simulation model of fire on bridge suspension cables and a time-varying model of the highest surface temperature of the suspension cables from the time of fire ignition to the time of water spraying for fire extinguishing. Step 3: Establish a finite element model to simulate the temperature field of the bridge cable section, synchronize the fire numerical simulation model and the finite element model, simulate the highest temperature experienced by each steel wire during the fire, and define the time-varying model of the highest temperature on the cable surface from the start of the fire to the water spraying fire extinguishing as the boundary condition of the finite element model. Step 4: Calculate the remaining strength of each steel wire after water spraying extinguishing based on the material strength model of the bridge cable parent material after being cooled by water at high temperature and the highest temperature experienced by each steel wire during the fire. Step 5: Determine the effective number of steel wires and the effective cross-sectional area of ​​the suspenders based on the remaining strength of each steel wire after water spraying fire extinguishing; calculate the remaining load-bearing capacity of the bridge suspenders after the fire; and determine the safety of the bridge suspenders after the fire. Specifically: Step 5-1, initialize the representative value of the sling tension. Step 5-2: Calculate the initial value of the effective number of steel wires in the bridge suspenders and the initial value of the effective area of ​​the suspenders for this iteration. Calculate the stress in the suspender section based on the representative value of the suspender tension and the initial value of the effective area of ​​the suspenders for this iteration. Step 5-3: Wires with a remaining strength greater than or equal to the stress at the cable section after water spraying are recorded as effective wires. Step 5-4: Based on the number of effective steel wires and the initial value of the number of effective steel wires in the bridge suspenders for this iteration, determine the safety of the bridge suspenders after the fire. When the number of effective steel wires equals the initial value of the number of effective steel wires in this iteration, the remaining load-bearing capacity of the bridge suspender after the fire is the product of the minimum remaining strength of the effective steel wires after water spray extinguishing and the sum of the cross-sectional areas of the effective steel wires. All steel wires are effective, and the bridge suspender is in a safe state after the fire. The remaining load-bearing capacity of the bridge suspender after the fire is: ,in, The remaining load-bearing capacity of the bridge suspension cables after the fire. The number of effective steel wires in the k-th calculation. Let m be the remaining strength of the m-th steel wire after water spraying for fire extinguishing. This is the initial value of the effective area of ​​the sling in the k-th calculation. , Let m be the cross-sectional area of ​​the m-th wire. When the number of effective steel wires is zero, the remaining load-bearing capacity of the bridge suspender after a fire is zero, the entire cross-section of the bridge suspender fails, and the bridge suspender is in an unsafe state after a fire. When the number of effective steel wires is between zero and the initial value of the number of effective steel wires in the bridge cable for this iteration, part of the bridge cable section fails. After renumbering the effective steel wires, return to step 5-2.

2. The method for calculating the safety of bridge suspension cables after a fire according to claim 1, characterized in that, The specific method for establishing the fire numerical simulation model of the bridge suspension cables in step 2 is as follows: Set the spatial range and grid size for simulation calculation according to the fire impact range and calculation accuracy requirements; select a combustion reaction model based on the combustibles; set the size and location of structures and obstacles according to the on-site spatial orientation within the fire impact range; and establish a model as shown in the expression... The combustion model shown, where HRR m Let be the maximum heat release rate of the ignition source, and t be the time required for the fire to reach its maximum size from the start of ignition. Fire growth coefficients, representing the fire growth coefficients for slow-moving, medium-moving, fast-moving, and ultra-fast-moving fires. The values ​​were 0.002931, 0.01127, 0.04689, and 0.1878, respectively.

3. The method for calculating the safety of bridge suspension cables after a fire according to claim 2, characterized in that, The specific method for establishing the time-varying model of the highest temperature on the bridge cable surface during the period from fire ignition to water spraying in step 2 is as follows: thermocouples are laid out on the surface of the bridge cable, the temperature at each thermocouple placement position on the bridge cable surface is calculated throughout the entire fire process, the temperature at each thermocouple placement position on the bridge cable surface is compared at each moment, the highest temperature on the bridge cable surface at each moment is extracted, and the time of fire ignition is taken as the initial time and the time of water spraying is taken as the end time to establish the time-varying model of the highest temperature on the bridge cable surface.

4. The method for calculating the safety of bridge suspension cables after a fire according to claim 3, characterized in that, In step 3, during the process of establishing a finite element model simulating the temperature field of the bridge cable section, the variation law of the thermal parameters of the steel wire with temperature is introduced. The variation law of the thermal parameters of the steel wire with temperature includes: the variation law of thermal conductivity with temperature, the variation law of thermal expansion coefficient with temperature, and the variation law of specific heat capacity with temperature.

5. The method for calculating the safety of bridge suspension cables after a fire according to claim 4, characterized in that, The specific method for step 3, simulating the highest temperature experienced by each steel wire during the fire, is as follows: the finite element model is infinitely approximated in the fire simulation process of the fire numerical simulation model, and the time-varying temperature model of each steel wire during the fire process is calculated. The maximum value of the time-varying temperature model of each steel wire during the fire process from the start of the fire to the intervention of the fire truck is the highest temperature experienced by each steel wire during the fire process.

6. The method for calculating the safety of bridge suspension cables after a fire according to claim 4, characterized in that, The thermal conductivity varies with temperature as follows: The coefficient of thermal expansion varies with temperature as follows: The specific heat capacity changes with temperature as follows: ,in, For temperature thermal conductivity at the following values, For temperature The coefficient of thermal expansion at that point, For temperature The specific heat capacity below.

7. The method for calculating the safety of bridge suspension cables after a fire according to claim 5, characterized in that, The specific method for calculating the remaining strength of each steel wire after water spraying in step 4, based on the material strength model of the bridge cable parent material after being cooled by water at high temperature and the highest temperature experienced by each steel wire during the fire, is as follows: Substitute the highest temperature experienced by each steel wire during the fire into the material strength model of the bridge cable parent material after being cooled by water at high temperature.

8. The method for calculating the safety of bridge suspension cables after a fire according to claim 1, characterized in that, The specific method for step 5-1 is to use the maximum daily cable force with a guarantee rate of over 95% as the representative value of the cable tension. ,in, The maximum daily cable force of the sling. Maximum daily cable force The probability density distribution model, where N0 is the representative value of the cable tension. This indicates the probability that the maximum daily cable force is less than or equal to the representative value of the cable tension.

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