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 computing method and safety pre-warning method of a large-span steel box girder bridge based on monitored data and temperature stress analysis. The total stress computing method comprises a step 1 of acquiring the strain and the temperature of the bridge by using a health monitoring system; a step 2 of separating temperature strain from the actually measured strain; a step 3of computing the uniform temperature and gradient temperature on the upper cross section of the steel box girder; a step 4 of computing axial restraint stress; a step 5 of computing bending restraint stress; a step 6 of computing temperature self-stress; a step 7 of acquiring geostatic stress from a finite element model; and a step 8 of computing the total stress of the large-span bridge in operation. Compared with a conventional early warning method, the early warning method is clear in early warning index and clear in mechanical model, takes account of the influence of temperature load on the large-span bridge structure, and is applicable to popularization in engineering field.

Description

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

Technical Field

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

Background

The safety early warning of the bridge structure is a complex research subject, which not only relates to professional knowledge in the bridge field, but also relates to multiple disciplines such as system science, management science, decision making and the like, and the early warning problem of the bridge structure can be understood more deeply and comprehensively only by comprehensively applying numerous latest discipline knowledge to the bridge structure safety monitoring field. In recent years, early warning methods based on vibration mode analysis and parameter identification are widely researched, but due to the complex characteristics of bridge structures, the technologies have many problems when applied to large bridge structures. With the push of social informatization and the increasingly wide application of technologies such as computers, networks and the like, particularly the installation and operation of bridge structure health monitoring systems, the research of efficient bridge early warning systems is necessary to improve the safe operation condition of bridge structures.

The structural stress can be used as an early warning index to early warn the operation state of the long-span bridge. Stress is the concentration of internal forces on a cross-section of a structural member and can be used to determine whether a structure has failed due to insufficient strength. The stress of the structure truly reflects the stress condition of the structure under external load. In a long-span bridge early warning system, at present, engineering personnel only act on the vehicle-mounted stress to give an early warning index, and the total stress of the structure is not completely considered. The reason for this is that: under the service state of a large-span bridge, the structural reaction is very complex, and the components for monitoring strain data for a long time are more complex. The strain caused by the vehicle load is easy to extract, and the vehicle load strain is directly multiplied by the elastic modulus to obtain the vehicle-mounted stress, so that engineering personnel are used to use the vehicle load stress as an early warning index. However, the bridge is not only subjected to vehicle loads, but also to temperature loads, particularly on large-span bridges. In this case, the stress calculation of the structure becomes more complicated, rather than simply multiplying the measured strain by the modulus of elasticity. For example, in a daily operation state of the bridge in jiangyin, the strain monitoring value can reach 200 μ, the stress is about 42MPa, 7 months in 2014, a truck static load test is performed on the bridge in jiangyin, and when 52 heavy trucks (corresponding to 17689kN) are loaded in a main beam span, the strain of the main beam reaches 156 μ and the stress reaches 32 MPa. From the data calculation, under the normal operation state of the Jiangyin bridge, the service state of the main beam reaches the static load stage of the truck, which is obviously not right. The long-term monitoring data are interfered by temperature load, and the temperature load is not completely converted into stress when acting on the main beam. That is to say, the traditional stress calculation method can not be directly used for solving long-term monitoring data and can not be used for early warning.

The large-span bridge early warning parameters and models are many, and mainly comprise displacement/deflection early warning, vehicle-mounted stress early warning (fatigue early warning), frequency early warning, energy early warning, a grey system theoretical prediction model, a BP neural network algorithm model, a wavelet packet energy spectrum and the like. The Niyiqing and other people utilize GPS data to perform early warning setting on the bridge; the Limega Xia et al uses the frequency stress of the steel box girder to perform early warning; sunzhong et al discuss a method for realizing a novel detection technology by using a Feed-forward back propagation network (Feed-forward BP network), and perform simulation research on damage early warning on a cable-stayed bridge structure by using a structure natural frequency as a basic input of the network. The wavelet packet energy spectrum, Dingjuliang and other systems illustrate the theoretical basis and essence of the structural damage early warning method based on the wavelet packet energy spectrum, and develop 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 and the like) are easily influenced by environment, particularly temperature change; 2. the traditional early warning parameters are usually macroscopic indexes (such as structural deflection), the macroscopic indexes only reflect the overall condition of the structure, and in fact, the damage of structural regions or members is a direct cause of structural damage and even collapse, and the macroscopic indexes cannot reflect the local characteristics of the structure; 3. the traditional early warning method is complex in theory and not easy to popularize in the engineering field. Compared with the early warning based on structural stress, the method has the advantages that the physical concept and the mechanical model are clearer, and the method is suitable for operation of engineering personnel, but the problems exist when the method is used for early warning of the long-span bridge.

Disclosure of Invention

The invention aims to solve the technical problem of providing a method for solving the total stress of a large-span bridge in a service state and an early warning method taking the total stress as an evaluation index, which have better precision by considering the influence of temperature strain on load strain, aiming at the defects in the prior art.

In order to solve the technical problems, the invention adopts the technical scheme that:

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

Wherein,_lis a steel box girderActual deformation under 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

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;

axial constraint stress calculation

Wherein,for indicating steel box girdersAxial constraint stress;

step five, calculating bending constraint stress

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

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 represents cross-sectional bending stiffness;

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

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

Wherein,θ′_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

Wherein, σ'_MRepresenting rotational constraint stress;

step six, calculating the self-stress of the temperature

g) 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.

Strain sensors and temperature sensors are respectively arranged on the top plate and the bottom plate in the 1/4, 1/2 and 3/4 sections of the steel box girder so as to monitor the strain and the temperature of each section of the steel box girder, 2n strain sensors are arranged on n sections of the bridge girder, wherein the n strain sensors are respectively arranged on the top plate and the bottom plate of the steel box girder, and one temperature sensor is also arranged at each strain sensor position.

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

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 total stress calculated by adopting the structural total stress calculation method is used as an early warning index.

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

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.

Advantageous effects

1. The invention provides a real-time monitoring and early warning method based on structural stress. The method has the advantages that the total stress of the key regions and the components of the structure is calculated by directly utilizing the monitoring data, and the working performance index of the current structure in the operation stage is directly reflected. Meanwhile, the invention greatly reduces the cost of regular manual detection of key areas and areas difficult to detect. The invention is suitable for all bridge types, in particular to long-term monitoring large-span bridges.

2. The temperature stress correlation calculation method provided by the invention can not only obtain the stress size and distribution of the section of the main beam, but also invert the deformation of the bridge structure under the temperature load, thereby greatly improving the high-efficiency utilization rate and deep excavation force of the bridge monitoring data.

Drawings

Fig. 1 is a flow chart of a stress warning method.

FIG. 2 is a reaction at a uniform temperature with an axial confinement structure. Graph a shows uniform temperature acting on a simple-supported structure with axial constraint, graph b shows deformation of a simple-supported structure without axial constraint at uniform temperature, and graph c shows deformation of a simple-supported structure with axial constraint at uniform temperature

FIG. 3 is a reaction at a gradient temperature with a rotation restriction. Graph a shows the effect of gradient temperature on a simple-supported structure with rotational constraint, graph b shows the deformation of a simple-supported structure without rotational constraint at the gradient temperature, and graph c shows the deformation of a simple-supported structure with rotational constraint at the gradient temperature

FIG. 4 is a cross-sectional strain and temperature sensor layout.

Fig. 5 is a temperature strain separation diagram. Graph a shows the measured strain, graph b shows the temperature strain separated from the measured strain by the EEMD technique, graph c shows the vehicle load strain, and graph d shows the change in temperature of the main beam over the day.

Fig. 6 shows the temperature stress at a certain time during the span of the bridge in the river or the south. Graph a shows temperature induced axial constraint stress, graph b shows temperature induced self-constraint stress, and graph c shows total temperature stress

FIG. 7 real-time early warning model. The diagram a shows a cross-middle top plate real-time early warning model, and the diagram b shows a cross-middle bottom plate real-time early warning model

The specific implementation mode is as follows:

the present invention is further illustrated by the following description taken in conjunction with the accompanying drawings and the detailed description, it is to be understood that these examples are given by way of illustration only and not by way of limitation, and that various equivalent modifications of the present invention will become apparent to those skilled in the art after reading the present invention.

1. The axial constraint gradual release concept, fig. 2.

As shown in FIG. 2(a), the simply supported beam is exposed to solar radiation, and the temperature T inside the structure is uniform_AvgAnd the beam end is added with rigidity k_RIs axially constrained. Releasing as shown in FIG. 2(b)Boundary axial constraint, then beam end will be generated_TIs deformed in the axial direction. As shown in FIG. 2(c), there is actual monitoring data to calculate the actual deformation of the structure_lThen the deformation compressed by the boundary constraint can be expressed asThe axial constraint stress generated by the boundary caused by temperature can be calculated through the constrained deformation.

2. Temperature induced axial constraint stress calculation

a) And the strain and the temperature of the bridge are acquired through a health monitoring system. 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_UnBottom plate T_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_LiRepresenting the monitored temperature data of the top and bottom plates of the ith cross-section.

The temperature strain is separated from the measured strain by the eemd (ensemble Empirical Mode composition) technique. Temperature strain of the top plate_TU1,_TU2,…_TUi…_TUnStrain of the base plate_TL1,_TL2,…_TLi…_TLnAnd roof board on-board strain_VU1,_VU2,…_VUi…_VUnFloor vehicle mounted strain_VL1,_VL2,…_VLi…_VLn。

b) And calculating the uniform temperature and the gradient temperature on the upper section of the steel box girder according to the monitoring temperature data. The invention divides the section temperature into uniform temperature and gradient temperature.

Uniform temperature of cross section

T_Avgi＝T_Li(1)

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

temperature gradient of cross section

T_yi＝T_Ui-T_Li(2)

Wherein, T_yiRepresents the gradient temperature of the ith section;

c) axial constraint stress calculation

Uniform temperature induced unconstrained deformation

_T＝αLT_Avgi(3)

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

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(5)

Wherein, formula (5) represents the temperature stress to which the nonlinear gradient temperature is completely converted; formula (6) represents the temperature stress equivalent axial force; formula (7) represents the strain produced under 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; finally, the unconstrained axial deformation generated by the nonlinear temperature gradient can be calculated as;

axial constraint stress calculation

Wherein,the axial restraint stress of the steel box girder is shown.

3. The rotational constraint gradual release concept, fig. 3.

As shown in FIG. 3(a), the simply supported beam is exposed to solar radiation, and the temperature inside the structure is gradient T_yAnd the beam end is added with rigidity k_sIs restricted. If the boundary rotation constraint is released as shown in FIG. 3(b), θ will be generated at the beam end_TThe corner of (2) is deformed. Referring to fig. 3(c), the actual monitoring data can calculate the actual beam end corner deformation θ of the structure_UThen the corner deformation compressed by the boundary constraint may be represented as θ'_R＝θ_T-θ_UAnd the rotation constraint stress generated by the boundary caused by the gradient temperature can be calculated through the compressed rotation deformation.

4. Temperature induced bending constraint stress calculation

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

θ_T＝M_TL/2EI (12)

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 represents cross-sectional bending stiffness;

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

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

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

θ′_R＝θ_T-θ_U(14)

Wherein, theta'_RIndicating a restrained beam end corner; m_sRepresenting the bending moment caused by the boundary constraint, the bending constraint stress caused by the bending moment can be calculated by the formula (12-15)

Wherein, σ'_MRepresenting rotational constraint stress.

The method for early warning the damage of the steel box girder of the long-span bridge based on consideration of the temperature stress influence comprises the following specific steps:

step 1: extracting bridge strain and temperature data

And the strain and the temperature of the bridge are acquired through a health monitoring system. 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_UnBottom plate T_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_LiRepresenting the monitored temperature data of the top and bottom plates of the ith cross-section.

Step 2: processing of monitoring data

The temperature strain is separated from the measured strain by the eemd (ensemble Empirical Mode composition) technique. Temperature strain of the top plate_TU1,_TU2,…_TUi…_TUnStrain of the base plate_TL1,_TL2,…_TLi…_TLnAnd roof board on-board strain_VU1,_VU2,…_VUi…_VUnFloor vehicle mounted strain_VL1,_VL2,…_VLi…_VLn。

And step 3: temperature stress calculation

a) Calculating the axial constraint stress caused by the temperature load by adopting a formula (9)

b) Calculating the bending constraint stress caused by the temperature load by adopting a formula (16)

c) Calculation of self-stress caused by temperature load

d) On-board stress calculation

e)σ′_V＝E_VLi(18)

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

σ′_GThe dead weight stress can be obtained according to a finite element model

And 4, step 4: total stress calculation and early warning

Structural total stress: sigma'_Total＝σ′_N+σ′_M+σ′_V(19)

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

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.

The calculation method comprises the following specific steps:

step 1: arrangement of bridge strain and temperature sensors

Arranging strain sensors and temperature sensors on the inner top plate and the inner bottom plate of the 1/4, 1/2 and 3/4 sections of the steel box girder to monitor the strain and the temperature of each section of the steel box girder; arranging 2n strain sensors on n sections of the bridge, wherein the n strain sensors are respectively arranged on a top plate and a bottom plate of the steel box girder, and a temperature sensor is also arranged at the position of each strain sensor; step 2: processing of monitoring data

a) And the strain and the temperature of the bridge are acquired through a health monitoring system. 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_LiRepresenting the monitored temperature data of the top and bottom plates of the ith cross-section.

b) The measured strain mainly comprises a high-frequency part and a low-frequency part, wherein the high-frequency part is mainly caused by vehicle load, and the low-frequency part is mainly caused by temperature load. The temperature strain is separated from the measured strain by the EEMD technique. Temperature strain of the top plate_TU1,_TU2,…_TUi…_TUnStrain of the base plate_TL1,_TL2,…_TLi…_TLnAnd roof board on-board strain_VU1,_VU2,…_VUi…_VUnFloor vehicle mounted strain_VL1,_VL2,…_VLi…_VLn。

c) And calculating the uniform temperature and the gradient temperature on the upper section of the steel box girder according to the monitoring temperature data. The invention divides the section temperature into uniform temperature and gradient temperature.

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;

d) axial constraint stress calculation

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

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 resulting from the non-linear temperature gradient. The effect of the nonlinear temperature gradient can be equated to a bending moment and an axial force.

σ_RT(y)＝E·α·T_yi

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

axial constraint stress calculation

Wherein,the axial restraint stress of the steel box girder is shown.

e) Bending constraint stress calculation

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

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 represents cross-sectional bending stiffness;

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

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

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

θ′_R＝θ_T-θ_U

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 can be calculated

Wherein, σ'_MRepresenting rotational constraint stress.

f) Temperature self-stress calculation

g) On-board stress calculation

σ′_V＝E_VLi

h) Obtaining dead weight stress sigma 'from finite element model'_G

i) Total stress calculation of large-span bridge during operation

σ′_Total＝σ′_N+σ′_M+σ′_V

And step 3: establishing an early warning model

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

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.

Example (b):

the following takes stress early warning calculation analysis of the suspension bridge of the river-yin bridge under the combined action of vehicle load and temperature as an example, and the specific implementation process of the invention is described as follows:

(1) in the arrangement process of the bridge strain sensors and the temperature sensors, the number, the positions and the parameters of the sensors can be set according to the specific conditions of bridge type, span, bridge deck width, bridge site environment and the like. The steel box girder of the Jiangyin bridge is divided into 8 equal parts, and 72 optical fiber strain sensors and 36 optical fiber thermometers along the bridge direction are arranged on 9 sections. The arrangement of the strain and temperature sensor of the cross section is shown in figure 4; the Jiangyin bridge is a single-span suspension bridge, the support form is a sliding support, and no rotation restriction is caused, so that the boundary rotation restriction condition is not considered in the calculation example.

(2) Data preprocessing and early warning

a) The 3 rd and 7 th strains per section were selectedThe sensor is an analysis object. And the strain and the temperature of the bridge are acquired through a health monitoring system. Strain of the top plateBaseplate strainTemperature T of the top plate_U1,T_U2,…T_Ui…T_UnBottom plate T_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_LiThe average of 2 thermometers of the i-th cross-sectional top and bottom plate is shown. Fig. 5 shows the curves of measured strain, temperature strain, vehicle-mounted strain and temperature across the mid-section.

b) The temperature strain is separated from the measured strain by the EEMD technique. Temperature strain of the top plateBaseplate strainAnd roof board vehicle mounted strain_VU1,_VU2,…_VUi…_VU9Floor vehicle mounted strain_VL1,_VL2,…_VLi…_VL9。

c) And (3) calculating the uniform temperature and the gradient temperature on the upper section of the steel box girder according to the formulas (1) and (2).

d) Axial constraint stress calculation

The unconstrained deformation caused by the uniform temperature is generated,

wherein,_Tα is the axial deformation of the steel box girder at uniform temperatureRepresenting the expansion coefficient of the steel box girder material; l represents the effective span of the bridge structure; the temperature load is distributed unevenly along the span direction of the bridge, so the elongation of each section is different, so that the delta L of the sensors on the first section and the ninth section is 87m, and the delta L of the sensors on the ninth section is 173m, so that the axial deformation of the steel box girder generated by uniform temperature under the unconstrained condition can be calculated.

In fact, the bridge cannot be completely free and unconstrained in the axial direction, and axial constraint stress is generated when a certain axial constraint rigidity exists in the boundary. The deformation under axial restraint is first calculated from the temperature strains of the top and bottom plates,

wherein,_lthe actual deformation of the steel box girder is generated under the axial constraint; likewise, the Δ L of the sensors in the first and ninth cross-sections is 87m, which is determined by the Δ L of the cross-section being 173m,

not only the steel box girder is deformed axially by the uniform temperature, but also the steel box girder is deformed axially by the nonlinear temperature gradient, and the axial direction generated by the nonlinear gradient temperature is represented by the formulas (5), (6), (7) and (8),

likewise, the Δ L of the sensors in the first and ninth cross-sections is 87m, which is determined by the Δ L of the cross-section being 173m,

finally, the axial constraint stress can be calculated according to equation (9).

e) The temperature self-stress can be calculated according to equation (17), the vehicle-mounted stress can be calculated according to equation (18), and the total stress can be calculated according to equation (19). The temperature stress of the cross section at the highest temperature of the midspan section is shown in fig. 6, fig. 6(a) shows the axial constraint stress of the steel box girder of the Jiangyin bridge at uniform temperature, fig. 6(b) shows the self-constraint stress of the steel box girder at gradient temperature, and fig. 6(c) shows the total temperature stress of the steel box girder.

f) The damage early warning under the operation state of the steel box girder adopts a formula (20)

The main beam of the Jiangyin bridge adopts European standard steel S355J2G3, the national standard is replaced by Q345D, the tensile allowable stress 1 is 230MPa, and the axial compression allowable stress is 230 MPa. The approximate constant load of the bridge in the river and the vagina, which is about 60MP, is obtained by using finite elements. In the embodiment, 35% (or calculated according to the current bridge design stress value) of the bearing capacity utilization rate is selected as the early warning value. The results of the examples are shown in FIG. 7. Fig. 7(a) shows the load capacity utilization of the cross ceiling. Wherein the load bearing capacity is negative due to the top plate compressive stress. The spare degree of the cross section bearing capacity is high, and the safety state is good. Fig. 7(b) also shows that the actual stress of the bottom plate is far away from the safety threshold, the margin degree of the bearing capacity is high, and the bridge operation state is good.

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.