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

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

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CN106092402B
CN106092402B CN201610373912.2A CN201610373912A CN106092402B CN 106092402 B CN106092402 B CN 106092402B CN 201610373912 A CN201610373912 A CN 201610373912A CN 106092402 B CN106092402 B CN 106092402B
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张建
夏琪
刘森林
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Abstract

本发明公开了一种基于监测数据与温度应力分析的大跨钢箱梁桥的总应力计算方法及安全预警方法,其中总应力计算方法包括步骤一、通过健康监测系统采集到的桥梁的应变与温度;步骤二、从实测应变中分离出温度应变;步骤三、计算钢箱梁上截面上的均匀温度和梯度温度;步骤四、轴向约束应力计算;步骤五、弯曲约束应力计算;步骤六、温度自应力计算;步骤七、从有限元模型中获取自重应力;步骤八、大跨桥梁在运营期间总应力计算。相比传统预警方法而言,本发明预警指标明确、力学模型清晰,并考虑了温度荷载对大跨桥梁结构的影响,适合于工程界推广。

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

基于监测数据与温度应力分析的大跨钢箱梁桥的总应力计算 方法及安全预警方法Total stress calculation of long-span steel box girder bridge based on monitoring data and temperature stress analysis Method and safety warning method

技术领域technical field

本发明涉及土木与交通工程的大跨桥梁监测数据预警领域。The invention relates to the field of monitoring data early warning of long-span bridges in civil engineering and traffic engineering.

背景技术Background technique

桥梁结构的安全预警是一个复杂的研究课题,不仅涉及桥梁领域的专业知识,还涉及到系统科学、管理学、决策学等多门学科,只有将众多最新学科知识综合应用到桥梁结构安全监控领域,才能对桥梁结构的预警问题有更加深入和全面的了解。近年来,在振动模态分析和参数识别基础上的预警方法得到了广泛的研究,但是由于桥梁结构复杂的特性,使得这些技术在应用于大型桥梁结构尚有诸多问题。随着社会信息化的推进及计算机、网络等技术应用的日益广泛,特别是桥梁结构健康监测系统的安装运营,研究高效的桥梁预警系统对于提高桥梁结构的安全运营状况十分必要。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.

结构应力可以作为预警指标来对大跨桥梁运营状态进行预警。应力就是结构构件某一截面上内力的集度,可以用于判断结构是否因强度不足而破坏。结构应力真实的反应了结构在外部荷载下的受力情况。在大跨桥梁预警系统中,目前工程人员只是将车载应力作用预警指标,并没有完全考虑结构的总应力。其原因在于:大跨桥梁在服役状态下,其结构反应是非常复杂的,而长期监测应变数据的成份更为复杂。车辆荷载引起的应变是较为容易提取的,将车辆荷载应变直接乘以弹性模量就可以得到车载应力,故工程人员习惯用车辆荷载应力作为预警指标。但是,桥梁并非只受到车辆荷载作用,温度荷载的作用是不容忽视的,特别是在大跨桥梁上。此时,结构的应力计算变得更为复杂,而不是简单的用实测应变去乘以弹性模量。比如,江阴大桥在日常运营状态下,其应变监测值可达200με,换成应力大约为42MPa,2014年7月,江阴大桥进行了卡车静载试验,当主梁跨中加载52辆重型卡车(相当于17689kN)时,主梁应变达到156με,应力达到32MPa。从数据计算上来看,江阴大桥在正常运营状态下,主梁服役状态就达到了卡车静载阶段,显然这是不对的。长期监测数据受到了温度荷载的干扰,并且温度荷载作用在主梁上并没有完全转化为应力。也就是说传统应力计算方法不能直接用来解决长期监测数据的,更不能用来预警。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.

大跨桥梁预警参数和模型很多,主要包括位移/挠度预警、车载应力预警(疲劳预警)、频率预警、能量预警,灰色系统理论预测模型、BP神经网络算法模型、小波包能量谱等等。倪一清等人利用GPS数据对青马大桥进行了预警设定;李兆霞等人利用钢箱梁频率应力进行预警;孙宗光等探讨了应用前馈BP网络(Feed-forward back propagation network)实现新奇检测技术的方法,以结构自振频率作为网络的基本输入,对斜拉桥结构进行了损伤预警的模拟研究。小波包能量谱,丁幼亮等系统的阐述了以小波包能量谱为基础的结构损伤预警方法的理论基础和本质,并开展了Benchemark结构损伤预警的试验研究。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.

这些预警方法具有以下几点不足:1.传统预警参数(比如结构频率等)容易受到环境引起,特别是温度变化的影响;2.传统预警参数往往都是宏观指标(比如结构挠度),宏观指标只反映了结构整体状况,事实上,结构区域或构件的损坏是导致结构破坏甚至垮塌的直接原因,这些宏观指标无法反应结构局部特征;3.传统预警方法理论复杂,不易在工程界推广。相比基于结构应力预警来说,其物理概念、力学模型更加清晰,适合于工程人员操作,但是该方法用于大跨桥梁预警还存在如前面所述的一些问题。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.

发明内容Contents of the invention

本发明所要解决的技术问题是针对上述现有技术存在的不足,而提供考虑温度应变对载荷应变影响的精度更好的一种求解大跨桥梁在服役状态下的总应力的方法和将总应力作为评价指标的预警方法。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.

为解决上述技术问题,本发明采用的技术方案是:In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

一种基于监测数据与温度应力分析的大跨钢箱梁桥的结构总应力计算方法,其特征在于,包括以下步骤: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:

步骤一、通过健康监测系统采集到的桥梁的应变与温度:Step 1. The strain and temperature of the bridge collected by the health monitoring system:

顶板应变εU1U2,…εUi…εUn,底板应变εL1L2,…εLi…εLn,顶板温度TU1,TU2,…TUi…TUn,底板温度TL1,TL2,…TLi…TLn;式中,εUi和εLi分别表示第i截面顶板和底板的监测应变数据;TUi和TLi表示第i个截面顶板和底板的监测温度数据;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;

步骤二、从实测应变中分离出温度应变:Step 2. Separate the temperature strain from the measured strain:

顶板温度应变εTU1TU2,…εTUi…εTUn,底板温度应变εTL1TL2,…εTLi…εTLn,以及顶板车载应变εVU1VU2,…εVUi…εVUn,底板车载应变εVL1VL2,…εVLi…εVLnTop 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 ;

步骤三、计算钢箱梁上截面上的均匀温度和梯度温度:Step 3. Calculate the uniform temperature and gradient temperature on the upper section of the steel box girder:

截面均匀温度Cross section uniform temperature

TAvgi=TLi T Avgi = T Li

其中,TAvgi表示第i截面的均匀温度;Among them, T Avgi represents the uniform temperature of the i-th section;

截面梯度温度section gradient temperature

Tyi=TUi-TLi T yi =T Ui -T Li

其中,Tyi表示第i截面的梯度温度;Among them, T yi represents the gradient temperature of the i-th section;

步骤四、轴向约束应力计算:Step 4. Calculation of axial restraint stress:

均匀温度产生的无约束变形Unconstrained deformation by uniform temperature

δT=αLTAvgi δT = αLT Avgi

其中,δT是钢箱梁在均匀温度下产生的轴向变形;α表示钢箱梁材料的膨胀系数;L表示桥梁结构有效跨径;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;

由实测顶板和底板温度应变计算有轴向约束情况下的变形Deformation under axial constraints is calculated from the measured temperature and strain of the top and bottom plates

其中,δl是钢箱梁在有轴向约束下产生的实际变形;n表示传感器布置了n截面;Δl表示按传感器数目将钢箱梁跨径划分为长度,Δl=L/n;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;

非线性温度梯度产生的无约束轴向变形Unconstrained Axial Deformation Generated by Nonlinear Temperature Gradients

σRT(y)=E·α·Tyi σ RT (y)=E·α·T yi

其中,σRT(y)表示非线性梯度温度完全转化为的温度应力;NTy表示温度应力等效的轴力;表示等效轴力下产生的应变;h0表示截面上表面距离截面中心轴的距离;b(y)表示截面宽度,且随截面高度变化;A表示截面面积;E表示结构材料的弹性模量。最后非线性温度梯度产生的无约束轴向变形可以计算为;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;

轴向约束应力计算Axial restraint stress calculation

其中,表示钢箱梁的轴向约束应力;in, Indicates the axial restraint stress of the steel box girder;

步骤五、弯曲约束应力计算Step 5. Calculation of Bending Constraint Stress

非线性温度梯度产生的无约束弯曲应变及梁端转角Unconstrained Bending Strain and Beam End Angle Caused by Nonlinear Temperature Gradient

θT=MTL/2EIθ T =M T L/2EI

其中,MT表示非线性温度梯度产生的温度应力等效为弯矩;表示等效弯矩产生的应变;θT表示等效弯矩在无约束状态下产生的梁端转角;EI表示截面抗弯刚度;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;

由实测顶板和底板温度应变计算梁端的实际转角Calculate the actual angle of rotation of the beam end from the measured temperature and strain of the top plate and bottom plate

其中,h表示钢箱梁截面高度;Among them, h represents the section height of the steel box girder;

那么,实际被约束的转角以及与边界约束弯矩的关系表示为Then, the relationship between the actually constrained rotation angle and the boundary constraint bending moment is expressed as

θ′R=θTU θ′ R =θ TU

其中,θ′R表示被约束住的梁端转角;Ms表示边界约束引起的转动弯矩,那么转动弯矩引起的弯曲约束应力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

其中,σ′M表示转动约束应力;Among them, σ′ M represents the rotational restraint stress;

步骤六、温度自应力计算Step 6. Calculation of temperature self-stress

g)车载应力计算g) On-board stress calculation

σ′V=EεVLi σ′ V = Eε VLi

步骤七、从有限元模型中获取自重应力σ′GStep 7. Obtain the self-weight stress σ′ G from the finite element model;

步骤八、大跨桥梁在运营期间总应力计算:Step 8. Calculation of the total stress of the long-span bridge during operation:

σ′Total=σ′N+σ′M+σ′V σ′ Total =σ′ N +σ′ M +σ′ V

其中,σ′Total为总应力。Among them, σ′ Total is the total stress.

通过在钢箱梁1/4截面、1/2截面和3/4截面内顶板和底板分别布置应变传感器和温度传感器,用以监测钢箱梁各个截面的应变和温度,在桥梁n个截面上布置2n个应变传感器,其中n应变传感器分别布置于钢箱梁顶板和底板,且每个应变传感器位置处也布置一个温度传感器。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.

通过EEMD技术从实测应变中分离出温度应变。The temperature strain was separated from the measured strain by EEMD technique.

一种基于监测数据与温度应力分析的大跨钢箱梁桥的安全预警方法,其特征在于,采用上述结构总应力计算方法计算的总应力作为预警的指标。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.

钢箱梁运营状态下损伤预警,定义如下公式为预警计算值,The damage early warning of steel box girder under the operating state, the following formula is defined as the early warning calculation value,

其中,SF表示桥梁结构正常状态下的应力预警值,μ表示总应力放大系数;RN表示结构容许应力,或者是设计值应力;预警上下区间则可以根据结构或者关键区域的重要性来设定预警阈值。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.

有益效果Beneficial effect

1.本发明提供了一种基于结构重应力的实时监测预警方法。该方法的优点在于直接利用监测数据进行了结构关键区域和构件的总应力计算,直接反应了当前结构在运营阶段的下工作性能指标。同时本发明大大减小了关键区域以及难于检测区域的定期人工检测成本。本发明适合所有桥型,特别是长期监测的大跨桥梁。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.本发明中提出的温度应力相关计算方法,不仅可以得到主梁截面的应力大小和分布,同时还可以反演桥梁结构在温度荷载下的变形,这大大提高了桥梁监测数据的高效利用率与深层次挖掘力度。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.

附图说明Description of drawings

图1是应力预警方法流程图。Figure 1 is a flowchart of the stress early warning method.

图2是附有轴向约束结构在均匀温度下的反应。图a表示均匀温度作用于含有轴向约束的简支结构,图b表示无轴向约束的简支结构在均匀温度下的变形,图c表示有轴向约束的简支结构在均匀温度下的变形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

图3是附有转动约束结构在梯度温度下的反应。图a表示梯度温度作用于含有转动约束的简支结构,图b表示无转动约束的简支结构在梯度温度下的变形,图c表示有转动约束的简支结构在梯度温度下的变形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

图4是跨中截面应变和温度传感器布置图。Figure 4 is a diagram of the arrangement of strain and temperature sensors in the mid-span section.

图5是温度应变分离图。图a表示实测应变,图b表示利用EEMD技术分从实测应变中分离出的温度应变,图c表示车辆荷载应变,图d表示主梁一天的温度的变化。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.

图6是江阴大桥跨中某一时刻下温度应力。图a表示温度引起的轴向约束应力,图b表示温度引起的自约束应力,图c表示总温度应力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

图7实时预警模型。图a表示跨中顶板实时预警模型,图b表示跨中底板实时预警模型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

具体实施方式:detailed description:

下面结合附图和具体实施例,进一步阐明本发明,应理解这些施例仅用于说明本发明而不用于限制本发明的范围,在阅读了本发明之后,本领域计算人员对本发明的各种等价形式的修改均落雨本申请所附权利要求所限定的范围。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.轴向约束逐步释放理念,如图2。1. The concept of gradual release of axial constraints, as shown in Figure 2.

如图2(a),已简支梁受到太阳辐射,结构内部为均匀温度TAvg,且梁端附加有刚度为kR的轴向约束。如图2(b)释放边界轴向约束,则梁端会产生δT的轴向变形。如图2(c),有实际监测数据可以计算结构实际变形δl,那么被边界约束所压缩的变形可以表示为通过被约束的变形即可计算温度引起的边界产生的轴向约束应力。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.温度引起的轴向约束应力计算2. Calculation of axial restraint stress caused by temperature

a)通过健康监测系统采集到的桥梁的应变与温度。顶板应变εU1U2,…εUi…εUn,底板应变εL1L2,…εLi…εLn,顶板温度TU1,TU2,…TUi…TUn,底板TL1,TL2,…TLi…TLn;式中,εUi和εLi分别表示第i截面顶板和底板的监测应变数据;TUi和TLi表示第i个截面顶板和底板的监测温度数据。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.

通过EEMD(Ensemble Empirical Mode Decomposition)技术从实测应变中分离出温度应变。顶板温度应变εTU1TU2,…εTUi…εTUn,底板应变εTL1TL2,…εTLi…εTLn,以及顶板车载应变εVU1VU2,…εVUi…εVUn,底板车载应变εVL1VL2,…εVLi…εVLnThe 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)根据监测温度数据,计算钢箱梁上截面上的均匀温度和梯度温度。本发明将截面温度分为均匀温度和梯度温度。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.

截面均匀温度Cross section uniform temperature

TAvgi=TLi (1)T Avgi = T Li (1)

其中,TAvgi表示第i截面的均匀温度;Among them, T Avgi represents the uniform temperature of the i-th section;

截面梯度温度section gradient temperature

Tyi=TUi-TLi (2)T yi =T Ui -T Li (2)

其中,Tyi表示第i截面的梯度温度;Among them, T yi represents the gradient temperature of the i-th section;

c)轴向约束应力计算c) Calculation of axial restraint stress

均匀温度产生的无约束变形Unconstrained deformation by uniform temperature

δT=αLTAvgi (3) δT = αLT Avgi ( 3)

其中,δT是钢箱梁在均匀温度下产生的轴向变形;α表示钢箱梁材料的膨胀系数;L表示桥梁结构有效跨径;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;

由实测顶板和底板温度应变计算有轴向约束情况下的变形Deformation under axial constraints is calculated from the measured temperature and strain of the top and bottom plates

其中,δl是钢箱梁在有轴向约束下产生的实际变形;n表示传感器布置了n截面;Δl表示按传感器数目将钢箱梁跨径划分为长度,Δl=L/n;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;

非线性温度梯度产生的无约束轴向变形Unconstrained Axial Deformation Generated by Nonlinear Temperature Gradients

σRT(y)=E·α·Tyi (5)σ RT (y) = E·α·T yi (5)

其中,式(5)表示非线性梯度温度完全转化为的温度应力;式(6)表示温度应力等效的轴力;式(7)表示等效轴力下产生的应变;h0表示截面上表面距离截面中心轴的距离;b(y)表示截面宽度,且随截面高度变化;A表示截面面积;最后非线性温度梯度产生的无约束轴向变形可以计算为;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:

轴向约束应力计算Axial restraint stress calculation

其中,表示钢箱梁的轴向约束应力。in, Indicates the axial restraint stress of the steel box girder.

3.转动约束逐步释放理念,如图3。3. The concept of gradual release of rotation constraints, as shown in Figure 3.

如图3(a),已简支梁受到太阳辐射,结构内部为梯度温度Ty,且梁端附加有刚度为ks的转动约束。如图3(b)释放边界转动约束,则梁端会产生θT的转角变形。如图3(c),有实际监测数据可以计算结构实际梁端转角变形θU,那么被边界约束所压缩的转角变形可以表示为θ′R=θTU,通过被压缩的转动变形即可计算梯度温度引起的边界产生的转动约束应力。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.温度引起的弯曲约束应力计算4. Calculation of bending restraint stress caused by temperature

非线性梯度温度产生的无约束弯曲应变及梁端转角Unconstrained Bending Strain and Beam End Angle Caused by Nonlinear Gradient Temperature

θT=MTL/2EI (12)θ T =M T L/2EI (12)

其中,MT表示非线性温度梯度产生的温度应力等效为弯矩;表示等效弯矩产生的应变;θT表示等效弯矩在无约束状态下产生的梁端转角;EI表示截面抗弯刚度;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;

由实测顶板和底板温度应变计算梁端的实际转角Calculate the actual angle of rotation of the beam end from the measured temperature and strain of the top plate and bottom plate

其中,h表示钢箱梁截面高度;Among them, h represents the section height of the steel box girder;

那么,实际被约束的转角以及与边界约束弯矩的关系可以表示为Then, the relationship between the actual constrained rotation angle and the boundary constraint bending moment can be expressed as

θ′R=θTU (14)θ′ R = θ T - θ U (14)

其中,θ′R表示被约束住的梁端转角;Ms表示边界约束引起的转动弯矩,那么转动弯矩引起的弯曲约束应力可以由式(12-15)计算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)

其中,σ′M表示转动约束应力。Among them, σ′ M represents the rotational restraint stress.

基于考虑温度应力影响的大跨桥梁钢箱梁损伤预警方法,其具体步骤如下: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:

步骤1:提取桥梁应变及温度数据Step 1: Extract bridge strain and temperature data

通过健康监测系统采集到的桥梁的应变与温度。顶板应变εU1U2,…εUi…εUn,底板应变εL1L2,…εLi…εLn,顶板温度TU1,TU2,…TUi…TUn,底板TL1,TL2,…TLi…TLn;式中,εUi和εLi分别表示第i截面顶板和底板的监测应变数据;TUi和TLi表示第i个截面顶板和底板的监测温度数据。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.

步骤2:监测数据的处理Step 2: Processing of monitoring data

通过EEMD(Ensemble Empirical Mode Decomposition)技术从实测应变中分离出温度应变。顶板温度应变εTU1TU2,…εTUi…εTUn,底板应变εTL1TL2,…εTLi…εTLn,以及顶板车载应变εVU1VU2,…εVUi…εVUn,底板车载应变εVL1VL2,…εVLi…εVLnThe 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 .

步骤3:温度应力计算Step 3: Temperature Stress Calculation

a)温度荷载引起的轴向约束应力计算,采用公式(9)a) Calculation of axial restraint stress caused by temperature load, using formula (9)

b)温度荷载引起的弯曲约束应力计算,采用公式(16)b) Calculation of bending restraint stress caused by temperature load, using formula (16)

c)温度荷载引起自应力计算c) Calculation of self-stress caused by temperature load

d)车载应力计算d) On-board stress calculation

e)σ′V=EεVLi (18)e) σ′ V = Eε VLi (18)

f)大跨桥梁自重应力计算f) Calculation of self-weight stress of long-span bridges

σ′G,自重应力可以根据有限元模型获得σ′ G , self-weight stress can be obtained according to the finite element model

步骤4:总应力计算及预警Step 4: Total stress calculation and early warning

结构总应力:σ′Total=σ′N+σ′M+σ′V (19)Total structural stress: σ′ Total = σ′ N + σ′ M + σ′ V (19)

钢箱梁运营状态下损伤预警,定义如下公式为预警计算值,The damage early warning of steel box girder under the operating state, the following formula is defined as the early warning calculation value,

其中,SF表示桥梁结构正常状态下的应力预警值,μ表示总应力放大系数;RN表示结构容许应力,或者是设计值应力;预警上下区间则可以根据结构或者关键区域的重要性来设定预警阈值。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.

本发明计算方法的具体步骤是:The concrete steps of computing method of the present invention are:

步骤1:桥梁应变及温度传感器的布置Step 1: Arrangement of Bridge Strain and Temperature Sensors

在钢箱梁1/4截面、1/2截面、3/4截面内顶板和底板布置应变传感器和温度传感器,用以监测钢箱梁各个截面的应变和温度;在桥梁n个截面上布置2n个应变传感器,其中n应变传感器分别布置于钢箱梁顶板和底板,且每个应变传感器位置处也布置一个温度传感器;步骤2:监测数据的处理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)通过健康监测系统采集到的桥梁的应变与温度。顶板应变εU1U2,…εUi…εUn,底板应变εL1L2,…εLi…εLn,顶板温度TU1,TU2,…TUi…TUn,底板温度TL1,TL2,…TLi…TLn;式中,εUi和εLi分别表示第i截面顶板和底板的监测应变数据;TUi和TLi表示第i个截面顶板和底板的监测温度数据。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)实测应变中主要包含高频部分和低频部分,高频部分主要由车辆荷载引起,低频部分主要由温度荷载引起。通过EEMD技术从实测应变中分离出温度应变。顶板温度应变εTU1TU2,…εTUi…εTUn,底板应变εTL1TL2,…εTLi…εTLn,以及顶板车载应变εVU1VU2,…εVUi…εVUn,底板车载应变εVL1VL2,…εVLi…εVLnb) 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)根据监测温度数据,计算钢箱梁上截面上的均匀温度和梯度温度。本发明将截面温度分为均匀温度和梯度温度。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.

截面均匀温度Cross section uniform temperature

TAvgi=TLi T Avgi =T Li

其中,TAvgi表示第i截面的均匀温度;Among them, T Avgi represents the uniform temperature of the i-th section;

截面梯度温度section gradient temperature

Tyi=TUi-TLi T yi =T Ui -T Li

其中,Tyi表示第i截面的梯度温度;Among them, T yi represents the gradient temperature of the i-th section;

d)轴向约束应力计算d) Calculation of axial restraint stress

均匀温度产生的无约束变形Unconstrained deformation by uniform temperature

δT=αLTAvgi δT = αLT Avgi

其中,δT是钢箱梁在均匀温度下产生的轴向变形;α表示钢箱梁材料的膨胀系数;L表示桥梁结构有效跨径;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;

由实测顶板和底板温度应变计算有轴向约束情况下的变形Deformation under axial constraints is calculated from the measured temperature and strain of the top and bottom plates

其中,δl是钢箱梁在有轴向约束下产生的实际变形;n表示传感器布置了n截面;Δl表示按传感器数目将钢箱梁跨径划分为长度,Δl=L/n;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;

非线性温度梯度产生的无约束轴向变形。非线性温度梯度作用效应可以等价为一个弯矩和一个轴力。Unconstrained axial deformation due to nonlinear temperature gradient. The nonlinear temperature gradient effect can be equivalent to a bending moment and an axial force.

σRT(y)=E·α·Tyi σ RT (y)=E·α·T yi

其中,σRT(y)表示非线性梯度温度完全转化为的温度应力;NTy表示温度应力等效的轴力;表示等效轴力下产生的应变;h0表示截面上表面距离截面中心轴的距离;b(y)表示截面宽度,且随截面高度变化;A表示截面面积;最后非线性温度梯度产生的无约束轴向变形可以计算为;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;

轴向约束应力计算Axial restraint stress calculation

其中,表示钢箱梁的轴向约束应力。in, Indicates the axial restraint stress of the steel box girder.

e)弯曲约束应力计算e) Calculation of bending restraint stress

非线性温度梯度产生的无约束弯曲应变及梁端转角Unconstrained Bending Strain and Beam End Angle Caused by Nonlinear Temperature Gradient

θT=MTL/2EIθ T =M T L/2EI

其中,MT表示非线性温度梯度产生的温度应力等效为弯矩;表示等效弯矩产生的应变;θT表示等效弯矩在无约束状态下产生的梁端转角;EI表示截面抗弯刚度;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;

由实测顶板和底板温度应变计算梁端的实际转角Calculate the actual angle of rotation of the beam end from the measured temperature and strain of the top plate and bottom plate

其中,h表示钢箱梁截面高度;Among them, h represents the section height of the steel box girder;

那么,实际被约束的转角以及与边界约束弯矩的关系可以表示为Then, the relationship between the actual constrained rotation angle and the boundary constraint bending moment can be expressed as

θ′R=θTU θ′ R =θ TU

其中,θ′R表示被约束住的梁端转角;Ms表示边界约束引起的转动弯矩,那么转动弯矩引起的弯曲约束应力可以计算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

其中,σ′M表示转动约束应力。Among them, σ′ M represents the rotational restraint stress.

f)温度自应力计算f) Temperature self-stress calculation

g)车载应力计算g) On-board stress calculation

σ′V=EεVLi σ′ V = Eε VLi

h)从有限元模型中获取自重应力σ′G h) Obtain the self-weight stress σ′ G from the finite element model

i)大跨桥梁在运营期间总应力计算i) Calculation of total stress of long-span bridges during operation

σ′Total=σ′N+σ′M+σ′V σ′ Total =σ′ N +σ′ M +σ′ V

步骤3:建立预警模型Step 3: Build an early warning model

钢箱梁运营状态下损伤预警,定义如下公式为预警计算值,The damage early warning of steel box girder under the operating state, the following formula is defined as the early warning calculation value,

其中,SF表示桥梁结构正常状态下的应力预警值,μ表示总应力放大系数;RN表示结构容许应力,或者是设计值应力;预警上下区间则可以根据结构或者关键区域的重要性来设定预警阈值。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.

实施例:Example:

下面以江阴大桥悬索桥在车辆荷载和温度共同作用下的应力预警计算分析为例,说本发明的具体实施过程: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)在桥梁应变传感器、温度传感器的布置过程中,传感器数量、位置及参数的设置可视桥型、跨径、桥面宽度以及桥址的环境等具体情况而定。江阴大桥钢箱梁共分为8等分,在9个截面共布置了72个顺桥向光纤应变传感器,36个光纤温度计。其跨中截面应变与温度传感器布置如图4;江阴大桥为单跨悬索桥,其支座形式为滑动支座,无转动约束限制,故算例中不考虑边界转动约束情况。(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)数据预处理与预警(2) Data preprocessing and early warning

a)选取每个截面第3个和7个应变传感器作为分析对象。通过健康监测系统采集到的桥梁的应变与温度。顶板应变底板应变顶板温度TU1,TU2,…TUi…TUn,底板TL1,TL2,…TLi…TLn;式中,εUi和εLi分别表示第i截面顶板和底板的监测应变数据;TUi和TLi表示第i个截面顶板和底板的2个温度计的平均值。图5给出了跨中截面实测应变、温度应变、车载应变、温度的曲线。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)通过EEMD技术从实测应变中分离出温度应变。顶板温度应变底板应变以及顶板车载应变εVU1VU2,…εVUi…εVU9,底板车载应变εVL1VL2,…εVLi…εVL9b) 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)根据公式(1)(2),计算钢箱梁上截面上的均匀温度和梯度温度。c) Calculate the uniform temperature and gradient temperature on the upper section of the steel box girder according to formula (1) (2).

d)轴向约束应力计算d) Calculation of axial restraint stress

均匀温度产生的无约束变形,Unconstrained deformation by uniform temperature,

其中,δT是钢箱梁在均匀温度下产生的轴向变形;α表示钢箱梁材料的膨胀系数;L表示桥梁结构有效跨径;温度荷载沿桥梁跨径方向分布是不均匀的,所以每个截面的伸长量是不一样的,所以第一截面和第九截面上的传感器的ΔL为87m,其用截面的ΔL为173m,这样就可以计算出钢箱梁在无约束的情况下均匀温度所产生的轴向变形。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.

事实上,桥梁在轴向上不可能是完全自由无约束状态的,边界存在一定的轴向约束刚度,则就会产生轴向的约束应力。首先由顶板和底板的温度应变计算有轴向约束下的变形,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,

其中,δl是钢箱梁在有轴向约束下产生的实际变形;同样,第一截面和第九截面上的传感器的ΔL为87m,其用截面的ΔL为173m,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,

不仅均匀温度会使钢箱梁产生轴向变形,非线性温度梯度也会使其产生轴向变形,利用公式(5)(6)(7)(8),则非线性梯度温度产生的轴向为,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,

同样,第一截面和第九截面上的传感器的ΔL为87m,其用截面的ΔL为173m,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,

最后,轴向约束应力可根据公式(9)计算。Finally, the axial restraint stress can be calculated according to formula (9).

e)温度自应力可按公式(17)计算,车载应力可按公式(18)计算,总应力可按公式(19)计算。跨中截面在最高温度下截面的温度应力,如图6,图6(a)表示均匀温度下江阴大桥钢箱梁轴向约束应力,图6(b)表示梯度温度下钢箱梁自约束应力,图6(c)表示钢箱梁温度总应力。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)钢箱梁运营状态下损伤预警,采用公式(20)f) Damage early warning of steel box girder in operation state, using formula (20)

江阴大桥主梁采用了欧洲标准钢材S355J2G3,国标代替为Q345D,其拉伸允许应力1为230MPa,轴向压缩许用应力为230MPa。本文已用有限元得到了江阴大桥的近似恒载,约为60MP。本算例选取35%(或根据当前桥梁设计应力值计算)的承载能力利用率作为预警值。算例结果见图7。图7(a)给出了跨中顶板的承载能力利用率。其中承载能力的负是由于顶板压应力导致的。截面承载能力富余程度高,安全状态良好。图7(b)也表明底板实际应力离安全阈值距离较远,承载能力富余程度高,桥梁运营状态良好。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 plateU1,U2,…UiUnStrain of the base plateL1,L2,…LiLnTemperature T of the top plateU1,TU2,…TUi…TUnTemperature T of the soleplateL1,TL2,…TLi…TLn(ii) a In the formula,UiandLirespectively representing monitored strain data of the top plate and the bottom plate of the ith section; t isUiAnd TLi(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 plateTU1,TU2,…TUiTUnTemperature strain of the soleplateTL1,TL2,…TLiTLnAnd roof board on-board strainVU1,VU2,…VUiVUnFloor vehicle mounted strainVL1,VL2,…VLiVLn
Step three, calculating the uniform temperature and the gradient temperature on the upper section of the steel box girder:
uniform temperature of cross section
TAvgi=TLi
Wherein, TAvgiRepresents the uniform temperature of the i-th section;
temperature gradient of cross section
Tyi=TUi-TLi
Wherein, TyiRepresents the gradient temperature of the ith section;
step four, calculating the axial constraint stress:
uniform temperature induced unconstrained deformation
T=αLTAvgi
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
δ l = Σ N = 1 n ϵ T U i + ϵ T L i 2 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
σRT(y)=E·α·Tyi
N T y = ∫ - h 0 / 2 h 0 / 2 σ R T ( y ) · b ( y ) d y
ϵ T N = N T E A
Wherein σRT(y) represents the temperature stress at which the nonlinear gradient temperature is completely converted; n is a radical ofTyAxial 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;
δ T y = Lϵ T N
axial constraint stress calculation
σ ′ N = E ( δ T + δ T y - 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 σ R T ( y ) · b ( y ) · y d y
ϵ T M = M T · y 0 E I
θT=MTL/2EI
Wherein M isTThe temperature stress generated by the nonlinear temperature gradient is equivalent to bending moment;representing the strain generated by the equivalent bending moment; thetaTRepresenting 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
θ U = ( ϵ T U i - ϵ T L i ) L 2 h
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=θTU
θ R ′ = M S L 2 E I
Wherein, theta'RIndicating a restrained beam end corner; msRepresenting the bending moment induced by the boundary constraint, the bending constraint stress induced by the bending moment
σ ′ M = h ( θ T - θ U ) L
Wherein, σ'MRepresenting rotational constraint stress;
step six, calculating the self-stress of the temperature
σ ′ S E ( y ) = Eϵ T N + Eϵ T M - σ R T ( y )
On-board stress calculation
σ′V=EVLi
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,
S F = σ ′ T o t a l ( 1 + μ ) R N - 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; rNRepresenting 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.
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