CN106092402B - Total stress computing method and safety pre-warning method of large-span steel box girder bridge based on monitored data and temperature stress analysis - Google Patents

Abstract

The invention discloses a total stress calculation method and a safety warning method of a long-span steel box girder bridge based on monitoring data and temperature stress analysis, wherein the total stress calculation method includes step 1, the strain and Temperature; step 2, separate the temperature strain from the measured strain; step 3, calculate the uniform temperature and gradient temperature on the upper section of the steel box girder; step 4, calculate the axial restraint stress; step 5, calculate the bending restraint stress; step 6 1. Temperature self-stress calculation; step 7, obtaining self-weight stress from the finite element model; step 8, calculating the total stress of the long-span bridge during operation. Compared with the traditional early warning method, the present invention has clear early warning indicators and a clear mechanical model, and considers the influence of temperature load on long-span bridge structures, and is suitable for popularization in engineering circles.

Description

Total stress calculation of long-span steel box girder bridge based on monitoring data and temperature stress analysis Method and safety warning method

technical field

The invention relates to the field of monitoring data early warning of long-span bridges in civil engineering and traffic engineering.

Background technique

The safety early warning of bridge structures is a complex research topic, which not only involves professional knowledge in the field of bridges, but also involves many disciplines such as system science, management science, and decision science. In order to have a more in-depth and comprehensive understanding of the early warning problems of bridge structures. In recent years, early warning methods based on vibration modal analysis and parameter identification have been widely studied, but due to the complex characteristics of bridge structures, there are still many problems in applying these technologies to large bridge structures. With the advancement of social informatization and the increasingly widespread application of computer and network technologies, especially the installation and operation of bridge structure health monitoring systems, it is necessary to study efficient bridge early warning systems to improve the safe operation of bridge structures.

Structural stress can be used as an early warning indicator to warn the operation status of long-span bridges. Stress is the concentration of internal force on a certain section of a structural member, which can be used to judge whether the structure is damaged due to insufficient strength. Structural stress truly reflects the stress of the structure under external loads. In the early-warning system of long-span bridges, engineers currently only use the vehicle-mounted stress as an early-warning indicator, and do not fully consider the total stress of the structure. The reason is that the structural response of long-span bridges is very complex when they are in service, and the components of long-term monitoring strain data are even more complex. The strain caused by the vehicle load is relatively easy to extract. The vehicle stress can be obtained by directly multiplying the vehicle load strain by the elastic modulus. Therefore, engineers are accustomed to using the vehicle load stress as an early warning indicator. However, bridges are not only affected by vehicle loads, and the effect of temperature loads cannot be ignored, especially on long-span bridges. At this time, the stress calculation of the structure becomes more complicated, rather than simply multiplying the measured strain by the elastic modulus. For example, under the daily operation status of the Jiangyin Bridge, the strain monitoring value can reach 200με, and the stress is about 42MPa. In July 2014, the Jiangyin Bridge underwent a truck static load test. When 52 heavy trucks (equivalent to At 17689kN), the strain of the main beam reaches 156με, and the stress reaches 32MPa. From the point of view of data calculation, under the normal operation state of Jiangyin Bridge, the service state of the main girder has reached the static load stage of trucks, which is obviously wrong. The long-term monitoring data is disturbed by the temperature load, and the temperature load is not completely converted into stress on the main beam. That is to say, traditional stress calculation methods cannot be directly used to solve long-term monitoring data, let alone early warning.

There are many early warning parameters and models for long-span bridges, mainly including displacement/deflection early warning, vehicle stress early warning (fatigue early warning), frequency early warning, energy early warning, gray system theory prediction model, BP neural network algorithm model, wavelet packet energy spectrum, etc. Ni Yiqing and others used GPS data to set early warning for Qingma Bridge; Li Zhaoxia and others used the frequency stress of steel box girder for early warning; Sun Zongguang and others discussed the application of feed-forward back propagation network (Feed-forward back propagation network) to realize novel detection technology Using the method of structure natural vibration frequency as the basic input of the network, the simulation research of damage early warning of cable-stayed bridge structure is carried out. The wavelet packet energy spectrum, Ding Youliang and others systematically expounded the theoretical basis and essence of the structural damage early warning method based on the wavelet packet energy spectrum, and carried out the experimental research of the Benchemark structural damage early warning.

These early warning methods have the following disadvantages: 1. Traditional early warning parameters (such as structural frequency, etc.) are easily affected by the environment, especially temperature changes; 2. Traditional early warning parameters are often macro indicators (such as structural deflection), macro indicators It only reflects the overall condition of the structure. In fact, the damage of structural areas or components is the direct cause of structural damage or even collapse. These macro indicators cannot reflect the local characteristics of the structure; 3. The theory of traditional early warning methods is complex and difficult to promote in the engineering field. Compared with early warning based on structural stress, its physical concept and mechanical model are clearer, and it is suitable for engineering personnel to operate. However, there are still some problems in this method for early warning of long-span bridges as mentioned above.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for solving the total stress of long-span bridges in service state and to calculate the total stress Early warning method as an evaluation index.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A method for calculating the total structural stress of a long-span steel box girder bridge based on monitoring data and temperature stress analysis, characterized in that it includes the following steps:

Step 1. The strain and temperature of the bridge collected by the health monitoring system:

Top plate strain ε _U1 , ε _U2 ,…ε _Ui …ε _Un , bottom plate strain ε _L1 , ε _L2 ,…ε _Li …ε _Ln , top plate temperature T _U1 , T _U2 ,…T _Ui …T _Un , bottom plate temperature T _L1 , T _L2 ,...T _Li ...T _Ln ; where, ε _Ui and ε _Li respectively represent the monitored strain data of the i-th section top plate and bottom plate; T _Ui and T _Li represent the monitored temperature data of the i-th section top plate and bottom plate;

Step 2. Separate the temperature strain from the measured strain:

Top plate temperature strain ε _TU1 , ε _TU2 , … ε _TUi … ε _TUn , bottom plate temperature strain ε _TL1 , ε _TL2 , … ε _TLi … ε _TLn , and top plate vehicle strain ε _VU1 , ε _VU2 , … ε _VUi … ε _VUn , bottom plate On-vehicle strain ε _VL1 , ε _VL2 , ... ε _VLi ... ε _VLn ;

Step 3. Calculate the uniform temperature and gradient temperature on the upper section of the steel box girder:

Cross section uniform temperature

T _Avgi = T _Li

Among them, T _Avgi represents the uniform temperature of the i-th section;

section gradient temperature

T _yi =T _Ui -T _Li

Among them, T _yi represents the gradient temperature of the i-th section;

Step 4. Calculation of axial restraint stress:

Unconstrained deformation by uniform temperature

_δT = αLT _Avgi

Among them, _δT is the axial deformation of the steel box girder at uniform temperature; α is the expansion coefficient of the steel box girder material; L is the effective span of the bridge structure;

Deformation under axial constraints is calculated from the measured temperature and strain of the top and bottom plates

Among them, δ _l is the actual deformation of the steel box girder under axial constraints; n means that the sensors are arranged in n sections; Δl means that the span of the steel box girder is divided into lengths according to the number of sensors, Δl = L/n;

Unconstrained Axial Deformation Generated by Nonlinear Temperature Gradients

σ _RT (y)=E·α·T _yi

Among them, σ _RT (y) represents the temperature stress that the nonlinear gradient temperature is completely transformed into; N _Ty represents the equivalent axial force of the temperature stress; Indicates the strain generated under the equivalent axial force; h ₀ indicates the distance between the upper surface of the section and the central axis of the section; b(y) indicates the width of the section, which varies with the height of the section; A indicates the area of the section; E indicates the elastic modulus of the structural material . Finally, the unconstrained axial deformation produced by the nonlinear temperature gradient can be calculated as;

Axial restraint stress calculation

in, Indicates the axial restraint stress of the steel box girder;

Step 5. Calculation of Bending Constraint Stress

Unconstrained Bending Strain and Beam End Angle Caused by Nonlinear Temperature Gradient

θ _T =M _T L/2EI

Among them, M _T indicates that the temperature stress generated by the nonlinear temperature gradient is equivalent to the bending moment; Indicates the strain produced by the equivalent bending moment; θ _T indicates the beam end rotation angle produced by the equivalent bending moment in an unconstrained state; EI indicates the section bending stiffness;

Calculate the actual angle of rotation of the beam end from the measured temperature and strain of the top plate and bottom plate

Among them, h represents the section height of the steel box girder;

Then, the relationship between the actually constrained rotation angle and the boundary constraint bending moment is expressed as

θ′ _R ＝θ _T -θ _U

Among them, θ′ _R represents the restrained beam end rotation angle; M _s represents the rotational bending moment caused by the boundary constraints, then the bending restraint stress caused by the rotational bending moment

Among them, σ′ _M represents the rotational restraint stress;

Step 6. Calculation of temperature self-stress

g) On-board stress calculation

σ′ _V = Eε _VLi

Step 7. Obtain the self-weight stress σ′ _G from the finite element model;

Step 8. Calculation of the total stress of the long-span bridge during operation:

σ′ _Total ＝σ′ _N +σ′ _M +σ′ _V

Among them, σ′ _Total is the total stress.

By arranging strain sensors and temperature sensors on the top plate and bottom plate in the 1/4 section, 1/2 section and 3/4 section of the steel box girder respectively, it is used to monitor the strain and temperature of each section of the steel box girder. On n sections of the bridge Arrange 2n strain sensors, where n strain sensors are respectively arranged on the top plate and bottom plate of the steel box girder, and a temperature sensor is also arranged at each strain sensor position.

The temperature strain was separated from the measured strain by EEMD technique.

A safety early warning method for long-span steel box girder bridges based on monitoring data and temperature stress analysis, characterized in that the total stress calculated by the above structural total stress calculation method is used as an early warning index.

The damage early warning of steel box girder under the operating state, the following formula is defined as the early warning calculation value,

Among them, SF represents the stress warning value under the normal state of the bridge structure, μ represents the total stress amplification factor; R _N represents the structural allowable stress, or the design value stress; the upper and lower warning intervals can be set according to the importance of the structure or key areas Early warning threshold.

Beneficial effect

1. The present invention provides a real-time monitoring and early warning method based on structural heavy stress. The advantage of this method is that it directly uses the monitoring data to calculate the total stress of the key areas and components of the structure, which directly reflects the performance indicators of the current structure in the operation stage. At the same time, the invention greatly reduces the regular manual inspection cost of key areas and areas that are difficult to detect. The invention is suitable for all bridge types, especially for long-term monitoring long-span bridges.

2. The temperature-stress correlation calculation method proposed in the present invention can not only obtain the stress magnitude and distribution of the main beam section, but also can invert the deformation of the bridge structure under temperature load, which greatly improves the efficient utilization of bridge monitoring data With deep digging power.

Description of drawings

Figure 1 is a flowchart of the stress early warning method.

Figure 2 is the response of the structure with axial confinement at uniform temperature. Figure a shows the uniform temperature acting on a simply supported structure with axial constraints, figure b shows the deformation of a simply supported structure without axial constraints at a uniform temperature, and figure c shows the deformation of a simply supported structure with axial constraints at a uniform temperature out of shape

Figure 3 is the response of the structure with rotational constraints at gradient temperatures. Figure a shows that the gradient temperature acts on a simply supported structure with rotational constraints, Figure b shows the deformation of a simply supported structure without rotational constraints at a gradient temperature, Figure c shows the deformation of a simply supported structure with rotational constraints under a gradient temperature

Figure 4 is a diagram of the arrangement of strain and temperature sensors in the mid-span section.

Figure 5 is a temperature-strain separation diagram. Figure a shows the measured strain, picture b shows the temperature strain separated from the measured strain using EEMD technology, picture c shows the vehicle load strain, and picture d shows the temperature change of the main beam in a day.

Figure 6 shows the temperature stress at a certain moment in the middle span of the Jiangyin Bridge. Figure a shows the axial restraint stress caused by temperature, picture b shows the self-confined stress caused by temperature, and picture c shows the total temperature stress

Figure 7 Real-time early warning model. Figure a shows the real-time early warning model of the mid-span roof, and figure b shows the real-time early warning model of the mid-span bottom plate

detailed description:

Below in conjunction with accompanying drawing and specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art calculate various aspects of the present invention Modifications in equivalent forms all fall within the scope defined by the appended claims of this application.

1. The concept of gradual release of axial constraints, as shown in Figure 2.

As shown in Figure 2(a), the simply supported beam is subjected to solar radiation, the internal temperature of the structure is T _Avg , and an axial constraint with stiffness k _R is attached to the beam end. As shown in Figure 2(b), if the boundary axial constraint is released, the beam end will produce an axial deformation of _δT . As shown in Figure 2(c), the actual monitoring data can be used to calculate the actual deformation δ _l of the structure, then the deformation compressed by the boundary constraints can be expressed as The temperature-induced axial restraint stress at the boundary can be calculated from the constrained deformation.

2. Calculation of axial restraint stress caused by temperature

a) The strain and temperature of the bridge collected by the health monitoring system. Top plate strain ε _U1 , ε _U2 ,…ε _Ui …ε _Un , bottom plate strain ε _L1 , ε _L2 ,…ε _Li …ε _Ln , top plate temperature T _U1 , T _U2 ,…T _Ui …T _Un , bottom plate T _L1 , T _L2 ,...T _Li ...T _Ln ; where ε _Ui and ε _Li represent the monitored strain data of the top and bottom plates of the i-th section, respectively; T _Ui and T _Li represent the monitored temperature data of the top and bottom plates of the i-th section.

The temperature strain is separated from the measured strain by EEMD (Ensemble Empirical Mode Decomposition) technology. Top plate temperature strain ε _TU1 , ε _TU2 , ... ε _TUi ... ε _TUn , bottom plate strain ε _TL1 , ε _TL2 , ... ε _TLi ... ε _TLn , and top plate on-board strain ε _VU1 , ε _VU2 , ... ε _VUi ... ε _VUn , bottom plate on-board strain Strain ε _VL1 , ε _VL2 , ... ε _VLi ... ε _VLn .

b) Calculate the uniform temperature and gradient temperature on the upper section of the steel box girder according to the monitored temperature data. The present invention divides the section temperature into uniform temperature and gradient temperature.

Cross section uniform temperature

T _Avgi = T _Li (1)

Among them, T _Avgi represents the uniform temperature of the i-th section;

section gradient temperature

T _yi =T _Ui -T _Li (2)

Among them, T _yi represents the gradient temperature of the i-th section;

c) Calculation of axial restraint stress

Unconstrained deformation by uniform temperature

_{δT = αLT Avgi (} 3)

Among them, _δT is the axial deformation of the steel box girder at uniform temperature; α is the expansion coefficient of the steel box girder material; L is the effective span of the bridge structure;

Deformation under axial constraints is calculated from the measured temperature and strain of the top and bottom plates

Among them, δ _l is the actual deformation of the steel box girder under axial constraints; n means that the sensors are arranged in n sections; Δl means that the span of the steel box girder is divided into lengths according to the number of sensors, Δl = L/n;

Unconstrained Axial Deformation Generated by Nonlinear Temperature Gradients

σ _RT (y) = E·α·T _yi (5)

Among them, formula (5) represents the temperature stress that the nonlinear gradient temperature is completely transformed into; formula (6) represents the equivalent axial force of the temperature stress; formula (7) represents the strain generated under the equivalent axial force; h ₀ represents the The distance between the surface and the central axis of the section; b(y) represents the width of the section and changes with the height of the section; A represents the area of the section; finally, the unconstrained axial deformation generated by the nonlinear temperature gradient can be calculated as:

Axial restraint stress calculation

in, Indicates the axial restraint stress of the steel box girder.

3. The concept of gradual release of rotation constraints, as shown in Figure 3.

As shown in Fig. 3(a), the simply supported beam is subjected to solar radiation, the interior of the structure is a gradient temperature T _y , and the beam end is attached with a rotation constraint with a stiffness of k _s . As shown in Figure 3(b), if the boundary rotation constraint is released, the beam end will produce a rotation angle deformation of θ _T. As shown in Figure 3(c), the actual monitoring data can be used to calculate the actual beam end rotational deformation θ _U , then the rotational deformation compressed by the boundary constraints can be expressed as θ′ _R = θ _T - θ _U , through the compressed rotational deformation The rotational confinement stress generated by the boundary caused by the gradient temperature can be calculated.

4. Calculation of bending restraint stress caused by temperature

Unconstrained Bending Strain and Beam End Angle Caused by Nonlinear Gradient Temperature

θ _T =M _T L/2EI (12)

Among them, M _T indicates that the temperature stress generated by the nonlinear temperature gradient is equivalent to the bending moment; Indicates the strain produced by the equivalent bending moment; θ _T indicates the beam end rotation angle produced by the equivalent bending moment in an unconstrained state; EI indicates the section bending stiffness;

Calculate the actual angle of rotation of the beam end from the measured temperature and strain of the top plate and bottom plate

Among them, h represents the section height of the steel box girder;

Then, the relationship between the actual constrained rotation angle and the boundary constraint bending moment can be expressed as

θ′ _R = θ _T - θ _U (14)

Among them, θ′ _R represents the restrained beam end rotation angle; M _s represents the rotational bending moment caused by the boundary constraint, then the bending restraint stress caused by the rotational bending moment can be calculated by formula (12-15)

Among them, σ′ _M represents the rotational restraint stress.

Based on the early warning method of steel box girder damage of long-span bridges considering the influence of temperature stress, the specific steps are as follows:

Step 1: Extract bridge strain and temperature data

The strain and temperature of the bridge collected by the health monitoring system. Top plate strain ε _U1 , ε _U2 ,…ε _Ui …ε _Un , bottom plate strain ε _L1 , ε _L2 ,…ε _Li …ε _Ln , top plate temperature T _U1 , T _U2 ,…T _Ui …T _Un , bottom plate T _L1 , T _L2 ,...T _Li ...T _Ln ; where ε _Ui and ε _Li represent the monitored strain data of the top and bottom plates of the i-th section, respectively; T _Ui and T _Li represent the monitored temperature data of the top and bottom plates of the i-th section.

Step 2: Processing of monitoring data

The temperature strain is separated from the measured strain by EEMD (Ensemble Empirical Mode Decomposition) technology. Top plate temperature strain ε _TU1 , ε _TU2 , ... ε _TUi ... ε _TUn , bottom plate strain ε _TL1 , ε _TL2 , ... ε _TLi ... ε _TLn , and top plate on-board strain ε _VU1 , ε _VU2 , ... ε _VUi ... ε _VUn , bottom plate on-board strain Strain ε _VL1 , ε _VL2 , ... ε _VLi ... ε _VLn .

Step 3: Temperature Stress Calculation

a) Calculation of axial restraint stress caused by temperature load, using formula (9)

b) Calculation of bending restraint stress caused by temperature load, using formula (16)

c) Calculation of self-stress caused by temperature load

d) On-board stress calculation

e) σ′ _V = Eε _VLi (18)

f) Calculation of self-weight stress of long-span bridges

σ′ _G , self-weight stress can be obtained according to the finite element model

Step 4: Total stress calculation and early warning

Total structural stress: σ′ _Total = σ′ _N + σ′ _M + σ′ _V (19)

The damage early warning of steel box girder under the operating state, the following formula is defined as the early warning calculation value,

Among them, SF represents the stress warning value under the normal state of the bridge structure, μ represents the total stress amplification factor; R _N represents the structural allowable stress, or the design value stress; the upper and lower warning intervals can be set according to the importance of the structure or key areas Early warning threshold.

The concrete steps of computing method of the present invention are:

Step 1: Arrangement of Bridge Strain and Temperature Sensors

Arrange strain sensors and temperature sensors on the 1/4 section, 1/2 section, and 3/4 section of the steel box girder on the top and bottom plates to monitor the strain and temperature of each section of the steel box girder; arrange 2n on n sections of the bridge Strain sensors, where n strain sensors are respectively arranged on the top and bottom plates of the steel box girder, and a temperature sensor is also arranged at each strain sensor position; Step 2: Processing of monitoring data

a) The strain and temperature of the bridge collected by the health monitoring system. Top plate strain ε _U1 , ε _U2 ,…ε _Ui …ε _Un , bottom plate strain ε _L1 , ε _L2 ,…ε _Li …ε _Ln , top plate temperature T _U1 , T _U2 ,…T _Ui …T _Un , bottom plate temperature T _L1 , T _L2 ,...T _Li ...T _Ln ; where ε _Ui and ε _Li represent the monitored strain data of the i-th section roof and bottom plate respectively; T _Ui and T _Li represent the monitored temperature data of the i-th section top and bottom plate.

b) The measured strain mainly includes high-frequency part and low-frequency part, the high-frequency part is mainly caused by vehicle load, and the low-frequency part is mainly caused by temperature load. The temperature strain was separated from the measured strain by EEMD technique. Top plate temperature strain ε _TU1 , ε _TU2 , ... ε _TUi ... ε _TUn , bottom plate strain ε _TL1 , ε _TL2 , ... ε _TLi ... ε _TLn , and top plate on-board strain ε _VU1 , ε _VU2 , ... ε _VUi ... ε _VUn , bottom plate on-board strain Strain ε _VL1 , ε _VL2 , ... ε _VLi ... ε _VLn .

c) Calculate the uniform temperature and gradient temperature on the upper section of the steel box girder according to the monitored temperature data. The present invention divides the section temperature into uniform temperature and gradient temperature.

Cross section uniform temperature

T _Avgi =T _Li

Among them, T _Avgi represents the uniform temperature of the i-th section;

section gradient temperature

T _yi =T _Ui -T _Li

Among them, T _yi represents the gradient temperature of the i-th section;

d) Calculation of axial restraint stress

Unconstrained deformation by uniform temperature

_δT = αLT _Avgi

Among them, _δT is the axial deformation of the steel box girder at uniform temperature; α is the expansion coefficient of the steel box girder material; L is the effective span of the bridge structure;

Deformation under axial constraints is calculated from the measured temperature and strain of the top and bottom plates

Among them, δ _l is the actual deformation of the steel box girder under axial constraints; n means that the sensors are arranged in n sections; Δl means that the span of the steel box girder is divided into lengths according to the number of sensors, Δl = L/n;

Unconstrained axial deformation due to nonlinear temperature gradient. The nonlinear temperature gradient effect can be equivalent to a bending moment and an axial force.

σ _RT (y)=E·α·T _yi

Among them, σ _RT (y) represents the temperature stress that the nonlinear gradient temperature is completely transformed into; N _Ty represents the equivalent axial force of the temperature stress; Indicates the strain generated under the equivalent axial force; h ₀ indicates the distance between the upper surface of the section and the central axis of the section; b(y) indicates the width of the section, which varies with the height of the section; A indicates the area of the section; Constrained axial deformation can be calculated as;

Axial restraint stress calculation

in, Indicates the axial restraint stress of the steel box girder.

e) Calculation of bending restraint stress

Unconstrained Bending Strain and Beam End Angle Caused by Nonlinear Temperature Gradient

θ _T =M _T L/2EI

Among them, M _T indicates that the temperature stress generated by the nonlinear temperature gradient is equivalent to the bending moment; Indicates the strain produced by the equivalent bending moment; θ _T indicates the beam end rotation angle produced by the equivalent bending moment in an unconstrained state; EI indicates the section bending stiffness;

Calculate the actual angle of rotation of the beam end from the measured temperature and strain of the top plate and bottom plate

Among them, h represents the section height of the steel box girder;

Then, the relationship between the actual constrained rotation angle and the boundary constraint bending moment can be expressed as

θ′ _R ＝θ _T -θ _U

Among them, θ′ _R represents the restrained beam end rotation angle; M _s represents the rotational bending moment caused by the boundary constraint, then the bending restraint stress caused by the rotational bending moment can be calculated

Among them, σ′ _M represents the rotational restraint stress.

f) Temperature self-stress calculation

g) On-board stress calculation

σ′ _V = Eε _VLi

h) Obtain the self-weight stress σ′ _G from the finite element model

i) Calculation of total stress of long-span bridges during operation

σ′ _Total ＝σ′ _N +σ′ _M +σ′ _V

Step 3: Build an early warning model

The damage early warning of steel box girder under the operating state, the following formula is defined as the early warning calculation value,

Among them, SF represents the stress warning value under the normal state of the bridge structure, μ represents the total stress amplification factor; R _N represents the structural allowable stress, or the design value stress; the upper and lower warning intervals can be set according to the importance of the structure or key areas Early warning threshold.

Example:

Take the stress early-warning calculation analysis of the Jiangyin Bridge suspension bridge as an example under the joint action of vehicle load and temperature below to say the specific implementation process of the present invention:

(1) During the arrangement of bridge strain sensors and temperature sensors, the number, position and parameters of the sensors can be set according to the specific conditions of the bridge type, span, bridge deck width and bridge site environment. The steel box girder of the Jiangyin Bridge is divided into 8 equal parts. A total of 72 fiber optic strain sensors along the bridge direction and 36 fiber optic thermometers are arranged in 9 sections. The layout of the strain and temperature sensors in the mid-span section is shown in Figure 4; Jiangyin Bridge is a single-span suspension bridge, and its support is a sliding support without rotation constraints, so the boundary rotation constraints are not considered in the calculation example.

(2) Data preprocessing and early warning

a) Select the third and seventh strain sensors of each section as the analysis objects. The strain and temperature of the bridge collected by the health monitoring system. roof strain base plate strain Top plate temperature T _U1 , T _U2 ,…T _Ui …T _Un , bottom plate T _L1 , T _L2 ,…T _Li …T _Ln ; where ε _Ui and ε _Li represent the monitoring strain data of the i-th section top plate and bottom plate respectively; T _Ui and T _Li represent the average value of the 2 thermometers on the top and bottom plates of the i-th section. Figure 5 shows the measured strain, temperature strain, on-board strain, and temperature curves of the mid-span section.

b) Separation of temperature strain from measured strain by EEMD technique. Roof temperature strain base plate strain And the vehicle-mounted strains ε _VU1 , ε _VU2 , ...ε _VUi ...ε _VU9 on the top plate, and the vehicle-mounted strains ε _VL1 , ε _VL2 , ...ε _VLi ...ε _VL9 on the bottom plate.

c) Calculate the uniform temperature and gradient temperature on the upper section of the steel box girder according to formula (1) (2).

d) Calculation of axial restraint stress

Unconstrained deformation by uniform temperature,

Among them, _δT is the axial deformation of the steel box girder at uniform temperature; α is the expansion coefficient of the steel box girder material; L is the effective span of the bridge structure; the distribution of temperature load along the span direction of the bridge is uneven, so The elongation of each section is different, so the ΔL of the sensor on the first section and the ninth section is 87m, and the ΔL of the used section is 173m, so that it can be calculated that the steel box girder is unconstrained Axial deformation due to uniform temperature.

In fact, the bridge cannot be completely free and unconstrained in the axial direction. If there is a certain axial restraint stiffness at the boundary, axial restraint stress will be generated. First, the deformation under axial constraints is calculated from the temperature strains of the top and bottom plates,

Among them, δ _l is the actual deformation of the steel box girder under axial constraints; similarly, the ΔL of the sensors on the first and ninth sections is 87m, and the ΔL of the used section is 173m,

Not only the uniform temperature will cause axial deformation of the steel box girder, but also the nonlinear temperature gradient will cause axial deformation. Using the formula (5)(6)(7)(8), the axial deformation caused by the nonlinear gradient temperature for,

Similarly, the ΔL of the sensors on the first section and the ninth section is 87m, and the ΔL of the used section is 173m,

Finally, the axial restraint stress can be calculated according to formula (9).

e) The temperature self-stress can be calculated according to formula (17), the vehicle-mounted stress can be calculated according to formula (18), and the total stress can be calculated according to formula (19). The temperature stress of the mid-span section at the highest temperature is shown in Figure 6. Figure 6(a) shows the axial restraint stress of Jiangyin Bridge steel box girder at uniform temperature, and Figure 6(b) shows the self-constraint stress of steel box girder at gradient temperature , Figure 6(c) shows the total temperature stress of the steel box girder.

f) Damage early warning of steel box girder in operation state, using formula (20)

The main girder of Jiangyin Bridge adopts the European standard steel S355J2G3, and the national standard is replaced by Q345D. The allowable tensile stress 1 is 230MPa, and the axial compressive allowable stress is 230MPa. In this paper, the approximate dead load of Jiangyin Bridge has been obtained by using finite elements, which is about 60MP. In this calculation example, 35% (or calculated according to the current bridge design stress value) bearing capacity utilization rate is selected as the early warning value. The results of the calculation example are shown in Figure 7. Figure 7(a) shows the load-carrying capacity utilization of the mid-span roof. The negative bearing capacity is caused by the compressive stress of the roof. The bearing capacity of the section is high, and the safety status is good. Figure 7(b) also shows that the actual stress of the floor is far away from the safety threshold, the bearing capacity is high, and the bridge is in good condition.

Claims (5)

1. A structural total stress calculation method of a long-span steel box girder bridge based on monitoring data and temperature stress analysis is characterized by comprising the following steps:

step one, strain and temperature of the bridge collected by a health monitoring system are as follows:

strain of the top plate_U1,_U2,…_Ui…_UnStrain of the base plate_L1,_L2,…_Li…_LnTemperature T of the top plate_U1,T_U2,…T_Ui…T_UnTemperature T of the soleplate_L1,T_L2,…T_Li…T_Ln(ii) a In the formula,_Uiand_Lirespectively representing monitored strain data of the top plate and the bottom plate of the ith section; t is_UiAnd T_Li(ii) monitored temperature data representative of the ith cross-sectional top and bottom plates;

step two, separating temperature strain from the measured strain:

temperature strain of the top plate_TU1,_TU2,…_TUi…_TUnTemperature strain of the soleplate_TL1,_TL2,…_TLi…_TLnAnd roof board on-board strain_VU1,_VU2,…_VUi…_VUnFloor vehicle mounted strain_VL1,_VL2,…_VLi…_VLn；

Step three, calculating the uniform temperature and the gradient temperature on the upper section of the steel box girder:

uniform temperature of cross section

T_Avgi＝T_Li

Wherein, T_AvgiRepresents the uniform temperature of the i-th section;

temperature gradient of cross section

T_yi＝T_Ui-T_Li

Wherein, T_yiRepresents the gradient temperature of the ith section;

step four, calculating the axial constraint stress:

uniform temperature induced unconstrained deformation

_T＝αLT_Avgi

Wherein,_Tα represents the expansion coefficient of the steel box girder material, L represents the effective span of the bridge structure;

calculating the deformation under axial constraint by actually measured temperature strain of the top plate and the bottom plate

${\mathrm{\δ}}_l={\mathrm{\Σ}}_{N=1}^n\frac{{\mathrm{\ϵ}}_{TUi}+{\mathrm{\ϵ}}_{TLi}}{2}\mathrm{\Δ}l$

Wherein,_lthe actual deformation of the steel box girder is generated under the axial constraint; n denotes a sensor arrangement n cross-sections; the length of the span of the steel box girder is divided into the length according to the number of the sensors, and the length is L/n;

unconstrained axial deformation by nonlinear temperature gradient

σ_RT(y)＝E·α·T_yi

$N_{Ty}={\∫}_{-h_0/2}^{h_0/2}{\mathrm{\σ}}_{RT}\left(y\right)\·b\left(y\right)dy$

${\mathrm{\ϵ}}_T^N=\frac{N_T}{EA}$

Wherein σ_RT(y) represents the temperature stress at which the nonlinear gradient temperature is completely converted; n is a radical of_TyAxial force representing temperature stress equivalent;representing the strain generated under the equivalent axial force; h is₀Represents the distance of the upper surface of the cross section from the central axis of the cross section; b (y) represents the cross-sectional width and varies with the cross-sectional height; a represents a cross-sectional area; e represents the modulus of elasticity of the structural material;

finally, the unconstrained axial deformation generated by the nonlinear temperature gradient can be calculated as;

${\mathrm{\δ}}_{Ty}={\mathrm{L\ϵ}}_T^N$

axial constraint stress calculation

${{\mathrm{\σ}}^{\′}}_N=\frac{E({\mathrm{\δ}}_T+{\mathrm{\δ}}_{Ty}-{\mathrm{\δ}}_l)}{L}$

Wherein, σ'_NRepresenting the axial constraint stress of the steel box girder;

step five, calculating bending constraint stress

Unconstrained bending strain and beam-end corner generated by nonlinear temperature gradient

$M_T={\∫}_{-h_0/2}^{h_0/2}{\mathrm{\σ}}_{RT}\left(y\right)\·b\left(y\right)\·ydy$

${\mathrm{\ϵ}}_T^M=\frac{M_T\·y_0}{EI}$

θ_T＝M_TL/2EI

Wherein M is_TThe temperature stress generated by the nonlinear temperature gradient is equivalent to bending moment;representing the strain generated by the equivalent bending moment; theta_TRepresenting the beam end corner generated by the equivalent bending moment in an unconstrained state; EI means cross-section bending rigidityDegree;

calculating the actual corner of the beam end by actually measuring the temperature strain of the top plate and the bottom plate

${\mathrm{\θ}}_U=\frac{({\mathrm{\ϵ}}_{TUi}-{\mathrm{\ϵ}}_{TLi})L}{2h}$

Wherein h represents the section height of the steel box girder;

the actually constrained corner and the relationship to the boundary-constrained bending moment are then expressed as

θ′_R＝θ_T-θ_U

${\mathrm{\θ}}_R^{\′}=\frac{M_{S}L}{2EI}$

Wherein, theta'_RIndicating a restrained beam end corner; m_sRepresenting the bending moment induced by the boundary constraint, the bending constraint stress induced by the bending moment

${{\mathrm{\σ}}^{\′}}_M=\frac{h({\mathrm{\θ}}_T-{\mathrm{\θ}}_U)}{L}$

Wherein, σ'_MRepresenting rotational constraint stress;

step six, calculating the self-stress of the temperature

${{\mathrm{\σ}}^{\′}}_{SE}\left(y\right)={\mathrm{E\ϵ}}_T^N+{\mathrm{E\ϵ}}_T^M-{\mathrm{\σ}}_{RT}\left(y\right)$

On-board stress calculation

σ′_V＝E_VLi

Step seven, obtaining dead weight stress sigma 'from the finite element model'_G；

Step eight, calculating the total stress of the large-span bridge during operation:

σ′_Total＝σ′_N+σ′_M+σ′_V

wherein, σ'_TotalIs the total stress.

2. The structural total stress calculation method of claim 1, wherein strain sensors and temperature sensors are arranged on the top plate and the bottom plate of the 1/4 section, 1/2 section and 3/4 section of the steel box girder to monitor the strain and temperature of each section of the steel box girder.

3. Method for calculating the total structural stress according to claim 1, characterized in that the temperature strain is separated from the measured strain by the EEMD technique.

4. A safety early warning method of a long-span steel box girder bridge based on monitoring data and temperature stress analysis is characterized in that the total stress calculated by the structural total stress calculation method according to any one of claims 1 to 3 is used as an early warning index.

5. The safety precaution method according to claim 4, characterized in that the damage precaution of the steel box girder in the operating state is defined as the precaution calculated value by the following formula,

$SF=\frac{{{\mathrm{\σ}}^{\′}}_{Total}(1+\mathrm{\μ})}{R_N-{{\mathrm{\σ}}^{\′}}_G}$

wherein SF represents a stress early warning value under a normal state of the bridge structure, and mu represents a total stress amplification coefficient; r_NRepresenting structural allowable stress, or design value stress; the early warning upper and lower intervals can set early warning threshold values according to the structure or the importance of the key area.