CN101723246A

CN101723246A - Method for acquiring stress time-domain values of evaluation points by utilizing operating data of bridge crane

Info

Publication number: CN101723246A
Application number: CN200910227828A
Authority: CN
Inventors: 高崇仁; 王守信; 韩玉习; 何洋洋; 田建涛
Original assignee: Taiyuan University of Science and Technology
Current assignee: Taiyuan University of Science and Technology
Priority date: 2009-12-15
Filing date: 2009-12-15
Publication date: 2010-06-09
Anticipated expiration: 2029-12-15
Also published as: CN101723246B

Abstract

The invention relates to a method for obtaining the stress time domain value of an evaluation point by using the operation data of a bridge crane. The invention mainly solves the technical difficulties existing in the existing bridge cranes, such as small space for collecting data samples, limited number of collected evaluation points and the like. The technical scheme of the present invention is: the method for obtaining the stress time domain value of the evaluation point by utilizing the operating data of the bridge crane, comprising the following steps: 1) using a data recorder to collect real-time operating data such as the lifting capacity of the crane; 2) pre-setting the above data Processing; 3) Establishing the bridge crane structure calculation model; 4) Calculating the internal force of the section at a certain moment; 5) Calculating the stress at the evaluation point at a certain moment; 6) Adding or subtracting the correction value to the stress value obtained above at a certain moment to obtain the correction 7) Repeat the above process to obtain internal forces and corrected stress data corresponding to multiple evaluation points; 8) Organize the calculated structural internal forces and stress data corresponding to multiple moments into stress spectrum data.

Description

The method of obtaining the stress time domain value of the evaluation point by using the operation data of bridge crane

技术领域technical field

本发明涉及一种利用桥式起重机运行数据获取评估点应力时域值的方法，它属于一种利用桥式起重机的批量运行数据经快速计算得到结构评估点的应力时域数据的方法。The invention relates to a method for obtaining stress time-domain values of evaluation points by using bridge crane operation data, which belongs to a method for obtaining stress time-domain data of structural evaluation points through rapid calculation using batch operation data of bridge cranes.

背景技术Background technique

随着科学技术的不断进步和桥式起重机安全性能要求的提高，对其安全运行要求也越来越高，为此，人们从各个方面做了大量的工作，如加强桥式起重机运行的使用管理、增加桥式起重机安全运行的各种限位装置等。但做到这些还不够，由于桥式起重机的主要组成部分--金属结构存在疲劳问题，即使其它方面做到位了，设备结构本身存在问题，也将是设备运行的极大安全隐患。所以，桥式起重机金属结构可靠性评估对于保障桥式起重机安全运行十分重要。With the continuous advancement of science and technology and the improvement of the safety performance requirements of bridge cranes, the requirements for their safe operation are also getting higher and higher. For this reason, people have done a lot of work from various aspects, such as strengthening the use management of bridge cranes. , Add various limit devices for the safe operation of bridge cranes, etc. But it is not enough to do this, because the main component of the bridge crane - the metal structure has fatigue problems, even if other aspects are in place, the problem of the equipment structure itself will be a great safety hazard for the operation of the equipment. Therefore, the reliability evaluation of the metal structure of the bridge crane is very important to ensure the safe operation of the bridge crane.

然而，桥式起重机金属结构可靠性评估的重要依据就是应力-时域数据，即应力谱。而应力-时域数据就是实际的应力数据，其数据量的多少是影响可靠性评估或疲劳寿命预测准确度的根本原因，如果没有一定量的数据作为基础，再好、再先进的可靠性评估或疲劳寿命预测理论都犹如空中楼阁。However, the important basis for the reliability assessment of bridge crane metal structures is the stress-time domain data, that is, the stress spectrum. The stress-time domain data is the actual stress data, and the amount of data is the fundamental reason that affects the accuracy of reliability assessment or fatigue life prediction. If there is no certain amount of data as the basis, no matter how good or advanced the reliability assessment is Or fatigue life prediction theory are like castles in the air.

目前，桥式起重机可靠性评估的数据来源主要是：通过桥式起重机结构上的相应部位贴应变片测量其在外载荷作用下的应力，把这些应力进行加工处理，得到起重机评估结论。其优点是简便易行；缺点是采集数据样本空间小，采集的评估点部位数量有限，若多部位长期采集，成本较高，实际中不可行。At present, the main source of data for the reliability evaluation of bridge cranes is to measure the stress under external loads by attaching strain gauges to the corresponding parts of the bridge crane structure, and process these stresses to obtain the crane evaluation conclusion. The advantage is that it is simple and easy to implement; the disadvantage is that the data sample space is small, and the number of evaluation points collected is limited. If multiple parts are collected for a long time, the cost is high, and it is not feasible in practice.

发明内容Contents of the invention

本发明的目的是解决现有的桥式起重机存在的采集数据样本空间小、采集的评估点部位数量有限等技术难点，并提供一种采集数据样本完整和采集的评估点部位数量多的利用桥式起重机运行数据获取评估点应力时域值的方法。The purpose of the present invention is to solve the technical difficulties existing in the existing bridge cranes such as the small space for collecting data samples and the limited number of collected evaluation points, and to provide a utilization bridge with complete collected data samples and a large number of collected evaluation points. The method of obtaining the time-domain value of the stress of the evaluation point from the operation data of the crane.

本发明为解决上述技术难点而采用的技术方案是：利用桥式起重机运行数据获取评估点应力时域值的方法，其包括下列步骤：The technical scheme adopted by the present invention to solve the above-mentioned technical difficulties is: the method for obtaining the stress time domain value of the evaluation point by using the operating data of the bridge crane, which includes the following steps:

1)使用数据记录仪采集桥式起重机的起重量、起升高度、小车和大车运行位置的实时运行数据，并将采集到的上述实时运行参数存放到存储单元中，以获得桥式起重机较长时间的运行数据；1) Use the data recorder to collect the real-time operation data of the lifting weight, lifting height, trolley and cart running positions of the bridge crane, and store the collected real-time operation parameters in the storage unit to obtain the comparative Long-term running data;

2)对采集的较长时间的实时运行数据进行预处理，并依据速度公式：

求出速度，然后根据求出的两点的速度与加速度公式：

求出加速度，获得各机构的速度和加速度的参数；2) Preprocess the real-time running data collected for a long time, and according to the speed formula:

Find the speed, and then according to the speed and acceleration formulas of the two points obtained:

Calculate the acceleration and obtain the parameters of the speed and acceleration of each mechanism;

3)建立桥式起重机结构计算模型，读入结构模型计算所需参数；3) Establish the structural calculation model of the bridge crane, and read in the parameters required for the calculation of the structural model;

4)计算某时刻桥式起重机上截面的内力，根据评估所需，确定桥式起重机结构评估点的多个截面位置，根据上述建立的计算模型，计算结构上多个计算截面的内力；4) Calculate the internal force of the upper section of the bridge crane at a certain moment, determine the multiple section positions of the structural evaluation point of the bridge crane according to the evaluation requirements, and calculate the internal force of multiple calculation sections on the structure according to the calculation model established above;

5)计算某时刻起重机评估点的应力，由第4)步骤所得的某时刻的多个计算截面的内力，再计算该时刻的多个截面上多个评估点的结构应力数据；5) Calculate the stress of the evaluation point of the crane at a certain moment, and calculate the structural stress data of multiple evaluation points on multiple sections at this moment from the internal forces of multiple calculation sections at a certain moment obtained in step 4);

6)将上述第5)步骤所得的某时刻应力值加上或减去修正值，得到修正后的应力值，修正值的范围为计算值的0％～15％；6) Adding or subtracting the correction value to the stress value at a certain moment obtained in the above step 5) to obtain the corrected stress value, and the range of the correction value is 0% to 15% of the calculated value;

7)重复上述第4)步骤、第5)步骤和第6)步骤过程，得到多个评估点多个时刻所对应内力和修正后的应力数据；7) Repeat the above steps 4), 5) and 6) to obtain internal forces and corrected stress data corresponding to multiple evaluation points at multiple times;

8)将第7)步骤计算得到的桥式起重机的任意点的多个时刻所对应的结构内力、应力数据整理成多个评估点的应力谱数据。8) Arranging the structural internal force and stress data corresponding to multiple moments at any point of the bridge crane calculated in step 7) into stress spectrum data of multiple evaluation points.

所述桥式起重机数据记录仪包括用于监控桥式起重机参数信息的传感器采集装置、微处理单元、数据存储单元和通讯网络接口单元；参数信息的传感器采集装置的信号与微处理单元的信号输入接口连接；微处理单元的数据输出接口连接数据存储单元的输入接口；通讯网络接口单元的输入端连接微处理单元的通讯输出接口。The bridge crane data recorder includes a sensor acquisition device for monitoring the parameter information of the bridge crane, a micro-processing unit, a data storage unit and a communication network interface unit; the signal of the sensor acquisition device for parameter information and the signal input of the micro-processing unit Interface connection; the data output interface of the micro-processing unit is connected to the input interface of the data storage unit; the input end of the communication network interface unit is connected to the communication output interface of the micro-processing unit.

所述参数信息的传感器采集装置由传感器和模数转换芯片构成，传感器的输出端与模数转换芯片的输入端连接。The sensor acquisition device for the parameter information is composed of a sensor and an analog-to-digital conversion chip, and the output terminal of the sensor is connected to the input terminal of the analog-digital conversion chip.

由于本发明采用了上述技术方案，解决了现有的桥式起重机存在的采集数据样本空间小、采集的评估点部位数量有限等技术难点。因此，与背景技术相比，本发明具有采集数据样本大和采集的评估点部位数量多及能快速获得评估点应力时域数据等优点。Since the present invention adopts the above-mentioned technical solution, the technical difficulties existing in the existing bridge cranes such as the small space for collecting data samples and the limited number of collected evaluation points are solved. Therefore, compared with the background technology, the present invention has the advantages of large sample of collected data, large number of collected evaluation points, quick acquisition of stress time-domain data of evaluation points, and the like.

附图说明Description of drawings

图1是本发明的流程框图；Fig. 1 is a block flow diagram of the present invention;

图2是本发明桥式起重机数据记录仪的结构框图；Fig. 2 is the structural block diagram of bridge crane data logger of the present invention;

图3是本发明水平方向的计算简图；Fig. 3 is the calculation diagram of horizontal direction of the present invention;

图4是本发明垂直方向的计算简图；Fig. 4 is the calculation diagram of the vertical direction of the present invention;

图5是本发明主梁中间截面的形状图；Fig. 5 is the shape diagram of the middle section of the girder of the present invention;

图6是本发明弯矩合成应力的应力谱；Fig. 6 is the stress spectrum of the bending moment composite stress of the present invention;

图7是本发明单元e在整体坐标系X-Y和局部坐标系X-Y受力图；Fig. 7 is a force diagram of unit e of the present invention in the global coordinate system X-Y and the local coordinate system X-Y;

图8是本发明固定端力学计算模型图；Fig. 8 is a mechanical calculation model diagram of the fixed end of the present invention;

图9是本发明弯矩、剪力的计算模型图。Fig. 9 is a calculation model diagram of bending moment and shear force of the present invention.

具体实施方式Detailed ways

下面结合附图和实施例对本发明作进一步的详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments.

如图1所示，利用桥式起重机运行数据获取评估点应力时域值的方法，其包括下列步骤：As shown in Figure 1, the method for obtaining the stress time-domain value of the evaluation point by using the operating data of the bridge crane includes the following steps:

2)对采集的较长时间的实时运行数据进行预处理，并依据速度公式：求出速度，然后根据求出的两点的速度与加速度公式：

求出加速度，获得各机构的速度和加速度的参数；2) Preprocess the real-time running data collected for a long time, and according to the speed formula: Find the speed, and then according to the speed and acceleration formulas of the two points obtained:

6)将上述第5)步骤所得的某时刻应力值加上或减去修正值，得到修正后的应力值，修正值的范围为计算值的0％～15％左右；修正值的具体取值根据距梁内隔板的远近等因素选取；6) Add or subtract the correction value to the stress value at a certain moment obtained in the above step 5) to obtain the corrected stress value, and the range of the correction value is about 0% to 15% of the calculated value; the specific value of the correction value Select according to factors such as the distance from the beam inner partition;

如图2所示，所述桥式起重机数据记录仪包括用于监控桥式起重机参数信息的传感器采集装置1、微处理单元(STC89LE516RD)2、数据存储单元3和通讯网络接口单元4；参数信息的传感器采集装置1的信号与微处理单元2的信号输入接口连接；微处理单元2的数据输出接口连接数据存储单元3的输入接口；通讯网络接口单元4的输入端连接微处理单元2的通讯输出接口。所述参数信息的传感器采集装置1由传感器1a和模数转换芯片1b构成，传感器1a的输出端与模数转换芯片1b的输入端连接。As shown in Figure 2, the bridge crane data recorder includes a sensor acquisition device 1 for monitoring the parameter information of the bridge crane, a microprocessing unit (STC89LE516RD) 2, a data storage unit 3 and a communication network interface unit 4; parameter information The signal of the sensor acquisition device 1 is connected to the signal input interface of the microprocessing unit 2; the data output interface of the microprocessing unit 2 is connected to the input interface of the data storage unit 3; Output Interface. The sensor collection device 1 for parameter information is composed of a sensor 1a and an analog-to-digital conversion chip 1b, and the output terminal of the sensor 1a is connected to the input terminal of the analog-to-digital conversion chip 1b.

所述建立桥式起重机结构计算模型是：对于垂直平面的结构(见图4)，垂直方向的结构简化为静定结构和一次超静定结构。对水平平面的结构(见图3)，考虑启、制动工况和支座约束，分为：启动支座对称、启动支座不对称、制动支座对称和制动支座不对称等四种情况。The establishment of the bridge crane structure calculation model is: for the vertical plane structure (see Figure 4), the structure in the vertical direction is simplified to a statically indeterminate structure and a first-order hyperstatically indeterminate structure. For the structure on the horizontal plane (see Figure 3), considering the starting and braking conditions and support constraints, it can be divided into: symmetrical starting support, asymmetric starting support, symmetrical braking support and asymmetrical braking support, etc. Four situations.

所述读入结构模型计算所需参数是：将下列通过桥式起重机工程图纸或者测量桥式起重机的形状尺寸的方法获得的形状参数：主主梁的长度、副主梁的长度、主端梁的长度、副端梁的长度、主小车的轮距、副小车的轮距、主小车的轨距、副小车的轨距、主主梁腹板的厚度、主主梁腹板的高度、主主梁上翼缘板的厚度、主主梁翼缘板的宽度、副主梁腹板的厚度、副主梁腹板的高度、副主梁上翼缘板的厚度、副主梁翼缘板的宽度、主端梁腹板的厚度、主端梁腹板的高度、主端梁上翼缘板的厚度、主端梁翼缘板的宽度、副端梁腹板的厚度、副端梁腹板的高度、副端梁上翼缘板的厚度、副端梁翼缘板的宽度和附加数据：通过使用厂家和生产厂家可以获得该桥式起重机其他数据包括：材料的弹性模量、截面惯性矩和静距、各机构的自重等读入计算机中，确定结构计算所需的模型数据。The parameters required for the calculation of the read-in structure model are: the following shape parameters obtained through the bridge crane engineering drawings or the method of measuring the shape and size of the bridge crane: the length of the main girder, the length of the sub-girder, the main end girder The length of the auxiliary end beam, the wheelbase of the main trolley, the wheelbase of the auxiliary trolley, the gauge of the main trolley, the gauge of the auxiliary trolley, the thickness of the main girder web, the height of the main girder web, the main The thickness of the upper flange plate of the main girder, the width of the flange plate of the main main girder, the thickness of the web of the sub-main girder, the height of the web of the sub-main girder, the thickness of the upper flange plate of the sub-main girder, the width of the flange plate of the sub-main girder, and the web of the main end girder thickness of main end girder web, height of main end girder upper flange plate, main end girder flange plate width, auxiliary end girder web thickness, auxiliary end girder web height, auxiliary end girder upper flange plate thickness, The width and additional data of the flange plate of the auxiliary end girder: other data of the bridge crane can be obtained by using the manufacturer and the manufacturer, including: the elastic modulus of the material, the moment of inertia of the section and the static distance, the self-weight of each mechanism, etc. read into the computer to determine Model data required for structural calculations.

所述读入结构模型计算所需参数包括但不仅限于主主梁、副主梁、主端梁、副端梁结构参数，主小车、副小车和其他一些附加数据等。The parameters required for the calculation of the read-in structural model include but are not limited to the structural parameters of the main main girder, sub-main girder, main end girder, auxiliary end girder, main trolley, auxiliary trolley and other additional data.

所述计算某时刻桥式起重机上截面的内力是：The internal force of the upper section of the bridge crane at a certain moment in the calculation is:

水平平面的计算：根据水平平面的结构是超静定的结构，采用力法和矩阵位移法进行分析，可以计算得到载荷大小任意(不大于额定载荷)作用，作用位置任意时，结构在水平平面的任意截面的内力。Calculation of the horizontal plane: According to the fact that the structure of the horizontal plane is a statically indeterminate structure, the force method and the matrix displacement method can be used for analysis, and it can be calculated that the load is arbitrary (not greater than the rated load), and when the action position is arbitrary, the structure is in the horizontal plane The internal force of any section of .

方法一：力法计算超静定力，然后计算结构的内力。Method 1: The force method calculates the hyperstatic force, and then calculates the internal force of the structure.

对于超静定结构，将原超静定结构中去掉多余联系后所得到的静定结构称为力法的基本结构，所去掉的多余联系，则以相应的多余未知力(也叫单位力)X_i来代替起作用，以下是求解多余未知力(也叫单位力)X_i的力法协调方程：For the statically indeterminate structure, the statically indeterminate structure obtained after removing redundant connections from the original statically indeterminate structure is called the basic structure of the force method. X _i will act instead, the following is the coordination equation of the force method for solving the redundant unknown force (also called unit force) X _i :

$\{\begin{matrix} {δ δ}_{1111} {X x}_{11} + + {δ δ}_{1212} {X x}_{22} + + . . . . . . + + {δ δ}_{11 i i} {X x}_{i i} + + . . . . . . + + {δ δ}_{11 n no} {X x}_{n no} + + {Δ Δ}_{11 p p} = = 00 \\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \\ {δ δ}_{i i 11} {X x}_{11} + + {δ δ}_{i i 22} {X x}_{22} + + . . . . . . + + {δ δ}_{ii i} {X x}_{i i} + + . . . . . . + + {δ δ}_{in in} {X x}_{n no} + + {Δ Δ}_{ip ip} = = 00 \\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \\ {δ δ}_{n no 11} {X x}_{11} + + {δ δ}_{n no 22} {X x}_{22} + + . . . . . . + + {δ δ}_{ni ni} {X x}_{i i} + + . . . . . . + + {δ δ}_{nn n} {X x}_{n no} + + {Δ Δ}_{np np} = = 00 . . \end{matrix} - - - - - - ((11))$

${δ δ}_{ij ij} = = Σ Σ &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{{M m}_{i i} {M m}_{j j}}}{EI EI} ds ds - - - - - - ((22))$

${Δ Δ}_{ip ip} = = Σ Σ &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{{M m}_{i i}} {M m}_{p p}}{EI EI} ds ds - - - - - - ((33))$

将公式(2)、公式(3)计算出来的结果代入公式1，可以求解出超静定力X_i，Substituting the results calculated by formula (2) and formula (3) into formula 1, the indeterminate force X _i can be solved,

M＝M₁X₁+M₂X₂+…+M_iX_i+…+M_nX_n+M_p (4)M＝M ₁ X ₁ +M ₂ X ₂ +...+M _i X _i +...+M _n X _n +M _p (4)

最后通过弯矩合成公式(4)求得结构的内力(弯矩)。Finally, the internal force (bending moment) of the structure is obtained through the bending moment synthesis formula (4).

对弯矩求导数可得到结构的内力(剪力)：Q＝M′The internal force (shear force) of the structure can be obtained by taking the derivative of the bending moment: Q=M'

以上公式(1)、(2)、(3)和(4)中：In the above formulas (1), (2), (3) and (4):

n：超静定次数，n: number of hyperstatic indetermination,

i，j：i＝1，2…，n；j＝1，2…，n；i, j: i=1, 2..., n; j=1, 2..., n;

M_i：在多余未知力X_i＝1作用下结构的弯矩图，(对于不同的结构弯矩图各不一样所以无法写出通式，下同)M _i : the bending moment diagram of the structure under the action of the redundant unknown force X _i = 1, (the bending moment diagram is different for different structures, so the general formula cannot be written, the same below)

M_j：在多余未知力X_j＝1作用下结构的弯矩图，M _j : the bending moment diagram of the structure under the action of the redundant unknown force X _j =1,

M_p：在结构外载荷P作用下的弯矩图，M _p : the bending moment diagram under the external load P of the structure,

δ_ij：多余未知力X_i＝1和多余未知力X_j＝1单独作用在基本结构上，沿X_i方向的位移，δ _ij : the displacement along the direction of X _i when the redundant unknown force X _i = 1 and the redundant unknown force X _j = 1 act on the basic structure alone,

Δ_ip：多余未知力X_i＝1和外载荷P单独作用在基本结构上，沿X_i方向的位移，Δ _ip : the displacement along the direction of _Xi when the redundant unknown force X _i = 1 and the external load P act on the basic structure alone,

E：材料的弹性模量，E: modulus of elasticity of the material,

I：截面的惯性矩，由截面的形状尺寸计算获得。I: Moment of inertia of the section, calculated from the shape and size of the section.

方法二：矩阵位移法计算杆端力，然后计算结构内力Method 2: Matrix displacement method to calculate the rod end force, and then calculate the internal force of the structure

对节点和单元进行编号，选定整体坐标和局部坐标(如图7)Number the nodes and units, select the overall coordinates and local coordinates (as shown in Figure 7)

X-Y为整体坐标系，x-y为局部坐标系，i，j为节点编号，e为节点i，j组成的单元。X-Y is the overall coordinate system, x-y is the local coordinate system, i, j are the node numbers, and e is the unit composed of nodes i, j.

单元unit 节点(始)Node (beginning) 节点(末)Node (end) ee II JJ

计算各个单元的刚度矩阵，如图7Calculate the stiffness matrix of each unit, as shown in Figure 7

${k k}_{ij ij}^{e e} = = [\begin{matrix} \frac{EA EA}{l l} c c + + \frac{1212 EI EI}{{l l}^{33}} {s the s}^{22} & ((\frac{EA EA}{l l} - - \frac{1212 EI EI}{{l l}^{33}})) cs cs & - - \frac{66 EI EI}{{l l}^{22}} s the s & - - \frac{EA EA}{l l} {c c}^{22} - - \frac{1212 EI EI}{{l l}^{33}} {s the s}^{22} & ((- - \frac{EA EA}{l l} + + \frac{1212 EI EI}{{l l}^{33}})) cs cs & - - \frac{66 EI EI}{{l l}^{22}} s the s \\ ((\frac{EA EA}{l l} - - \frac{1212 EI EI}{{l l}^{33}})) cs cs & \frac{EA EA}{l l} {s the s}^{22} + + \frac{1212 EI EI}{{l l}^{33}} {c c}^{22} & \frac{66 EI EI}{{l l}^{22}} c c & ((- - \frac{EA EA}{l l} + + \frac{1212 EI EI}{{l l}^{33}})) cs cs & - - \frac{EA EA}{l l} {s the s}^{22} - - \frac{1212 EI EI}{{l l}^{33}} c c & \frac{66 EI EI}{{l l}^{22}} c c \\ - - \frac{66 EI EI}{{l l}^{22}} s the s & \frac{66 EI EI}{{l l}^{22}} c c & \frac{44 EI EI}{l l} & \frac{66 EI EI}{{l l}^{22}} s the s & - - \frac{66 EI EI}{{l l}^{22}} c c & \frac{22 EI EI}{l l} \\ - - \frac{EA EA}{l l} {c c}^{22} - - \frac{1212 EI EI}{{l l}^{33}} {s the s}^{22} & ((- - \frac{EA EA}{l l} + + \frac{1212 EI EI}{{l l}^{33}})) cs cs & \frac{66 EI EI}{{l l}^{22}} s the s & \frac{EA EA}{l l} {c c}^{22} + + \frac{1212 EI EI}{{l l}^{33}} {s the s}^{22} & ((\frac{EA EA}{l l} - - \frac{1212 EI EI}{{l l}^{33}})) cs cs & \frac{66 EI EI}{{l l}^{22}} s the s \\ ((- - \frac{EA EA}{l l} + + \frac{1212 EI EI}{{l l}^{33}})) cs cs & - - \frac{EA EA}{l l} {s the s}^{22} - - \frac{1212 EI EI}{{l l}^{33}} {c c}^{22} & - - \frac{66 EI EI}{{l l}^{22}} c c & ((\frac{EA EA}{l l} - - \frac{1212 EI EI}{{l l}^{33}})) cs cs & \frac{EA EA}{l l} {s the s}^{22} + + \frac{1212 EI EI}{{l l}^{33}} c c & - - \frac{66 EI EI}{{l l}^{22}} c c \\ - - \frac{66 EI EI}{{l l}^{22}} s the s & \frac{66 EI EI}{{l l}^{22}} c c & \frac{22 EI EI}{l l} & \frac{66 EI EI}{{l l}^{22}} s the s & - - \frac{66 EI EI}{{l l}^{22}} c c & \frac{44 EI EI}{l l} \end{matrix}] - - - - - - ((55))$

其中，in,

c：cosα，c:cosα,

s：sinα，s: sinα,

α：杆件(i，j)在整体坐标X-Y中与X轴的夹角，α: The angle between the member (i, j) and the X axis in the overall coordinate X-Y,

A：该杆件的截面面积，A: The cross-sectional area of the member,

E：该杆件的弹性模量，E: modulus of elasticity of the bar,

l：该杆件的长度，l: the length of the member,

I：该杆件的惯性矩，I: moment of inertia of the member,

i，j：刚架的节点号，i，j＝2，3，…，n，n为节点总数，形成原始刚度矩阵，即总刚度矩阵i, j: the node number of the rigid frame, i, j=2, 3,..., n, n is the total number of nodes, forming the original stiffness matrix, that is, the total stiffness matrix

$K K = = [\begin{matrix} {k k}_{1111}^{e e} & {k k}_{1111}^{e e} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {k k}_{11 j j}^{e e} & \cdot \cdot \cdot \cdot \cdot &Center Dot; & {k k}_{11 n no}^{e e} \\ {k k}_{21 twenty one}^{e e} & {k k}_{22 twenty two}^{e e} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {k k}_{22 j j}^{e e} & \cdot \cdot \cdot \cdot \cdot &Center Dot; & {k k}_{22 n no}^{e e} \\ \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; \\ {k k}_{i i 11}^{e e} & {k k}_{i i 22}^{e e} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {k k}_{ij ij}^{e e} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {k k}_{in in}^{e e} \\ \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & \cdot \cdot \cdot &Center Dot; \cdot \cdot & \cdot \cdot \cdot \cdot \cdot &Center Dot; \\ {k k}_{n no 11}^{e e} & {k k}_{n no 22}^{e e} & \cdot &Center Dot; \cdot \cdot \cdot \cdot & {k k}_{nj nj}^{e e} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {k k}_{nn n}^{e e} \end{matrix}] - - - - - - ((66))$

当i＝j时，即公式(6)里面主对角线上的单元矩阵，是由节点i(或j)的相关单元的刚度矩阵的叠加求得的，即 $k_{ij}^{e} = Σ k_{ij}^{e};$ 当i≠j时，且i，j为相关点时，即为联结它们的单元的相应单元的刚度矩阵；当i≠j时，且i，j为非相关节点时， $k_{ij}^{e} = 0 .$ When i=j, that is, the element matrix on the main diagonal in formula (6), is obtained by the superposition of the stiffness matrix of the relevant element at node i (or j), namely $k_{ij}^{e} = Σ k_{ij}^{e};$ When i≠j, and i, j are related points, it is the stiffness matrix of the corresponding unit connecting their units; when i≠j, and i, j are non-correlated nodes, $k_{ij}^{e} = 0 .$

计算固端力，等效节点载荷及综合节点载荷Calculation of fixed end forces, equivalent nodal loads and combined nodal loads

由于结构上的单元可能有外载荷作用，所以需求出固端力，如图8，Since the structural units may have external loads, the fixed end force is required, as shown in Figure 8,

N_i＝0N _i =0

${Q Q}_{i i} = = \frac{q q \cdot &Center Dot; L L}{22} + + \frac{P P 11 \cdot &Center Dot; {bg bg 11}^{22} \cdot \cdot ((L L + + 22 \cdot \cdot ag ag 11))}{{L L}^{33}} + + \frac{P P 22 \cdot \cdot {bg bg 22}^{22} \cdot &Center Dot; ((L L + + 22 \cdot \cdot ag ag 22))}{{L L}^{33}}$

${M m}_{i i} = = \frac{q q \cdot \cdot {L L}^{22}}{1212} + + \frac{P P 11 \cdot &Center Dot; ag ag 11 \cdot &Center Dot; {bg bg 11}^{22}}{{L L}^{22}} + + \frac{P P 22 \cdot \cdot {ag ag 22 \cdot \cdot bg bg 22}^{22}}{{L L}^{22}}$

N_j＝0N _j =0

${Q Q}_{j j} = = \frac{q q \cdot &Center Dot; L L}{22} + + \frac{P P 11 \cdot \cdot {ag ag 11}^{22} \cdot &Center Dot; ((L L + + 22 \cdot &Center Dot; bg bg 11))}{{L L}^{33}} + + \frac{P P 22 \cdot \cdot {ag ag 22}^{22} \cdot &Center Dot; ((L L + + 22 \cdot &Center Dot; bg bg 22))}{{L L}^{33}}$

${M m}_{j j} = = \frac{q q \cdot &Center Dot; {L L}^{22}}{1212} + + \frac{P P 11 \cdot &Center Dot; bg bg 11 \cdot &Center Dot; {ag ag 11}^{22}}{{L L}^{22}} + + \frac{P P 22 \cdot &Center Dot; {bg bg 22 \cdot &Center Dot; ag ag 22}^{22}}{{L L}^{22}}$

q：单元上产生的均布外载荷，如图8，q: Uniform external load generated on the unit, as shown in Figure 8,

L：改单元的长度，如图8，L: change the length of the unit, as shown in Figure 8,

P1，P2：作用在单元上的集中外载荷，如图8，P1, P2: Concentrated external load acting on the unit, as shown in Figure 8,

引如支撑条件，修改原始刚度方程Citing support conditions, modify the original stiffness equation

其中： $P_{i} = \{\begin{matrix} X_{i} \\ Y_{i} \\ M_{i} \end{matrix}\}$ $Δ_{i} = \{\begin{matrix} u_{i} \\ v_{i} \\ φ_{i} \end{matrix}\}$ in: $P_{i} = \{\begin{matrix} x_{i} \\ Y_{i} \\ m_{i} \end{matrix}\}$ $Δ_{i} = \{\begin{matrix} u_{i} \\ v_{i} \\ φ_{i} \end{matrix}\}$

公式(7)中：P_i表示节点i的外力列向量，X_i，Y_i和M_i分别为作用于节点i沿x，y方向的外力和外力偶，即：以上求出的固端力N_i，Q_i，M_i。In formula (7): P _i represents the external force column vector of node i, Xi _, Y _i and M _i are the external force and external force couple acting on node i along the x and y directions respectively, that is, the fixed end force obtained above N _i , Q _i , M _i .

Δ_i表示节点i的位移列向量，u_i，v_i和φ_i分别为节点i沿结构坐标系x，y轴的线位移和角位移。Δ _i represents the displacement column vector of node i, u _i , v _i and φ _i are the line displacement and angular displacement of node i along the x and y axes of the structural coordinate system, respectively.

P₁，··P_i，··P_n中只包括已知的节点位移，Δ₁，··Δ_i，··Δ_n只包括未知节点位移，此时的刚度矩阵K_修即为从结构的原始刚度矩阵中删去与已知为零的节点位移对应的行和列，称为结构的刚度矩阵，或者称为缩减的总刚。P ₁ ,··P _i ,··P _n only include known node displacements, Δ ₁ ,··Δ _i ,·· _Δn only include unknown node displacements, the stiffness matrix K at this time is _modified from the structure The rows and columns corresponding to the nodal displacements known to be zero are deleted from the original stiffness matrix of , which is called the stiffness matrix of the structure, or the reduced total stiffness.

计算各个单元杆端力。Calculate the rod end force for each element.

通过公式 $P_{ij}^{e} = k_{ij}^{e} Δ_{ij}^{e}$ 求出单元的杆端力，by formula $P_{ij}^{e} = k_{ij}^{e} Δ_{ij}^{e}$ Find the rod end force of the element,

P_ij ^e：为列向量，表示单元e的i，j节点的杆端力，包括轴力，剪力，弯矩，P _ij ^e : is a column vector, indicating the rod end force of node i and j of element e, including axial force, shear force, bending moment,

k_ij ^e：表示单元的e的刚度矩阵，见公式(6)，k _ij ^e : represents the stiffness matrix of e of the element, see formula (6),

Δ_ij ^e：为列向量，表示单元e的i，j节点的位移，已从公式(7)解出。Δ _ij ^e : It is a column vector, representing the displacement of node i and j of unit e, which has been solved from formula (7).

通过计算出来的杆端力计算结构内力，如图9，Calculate the internal force of the structure through the calculated rod end force, as shown in Figure 9,

当0≤x＜a时， $M = - M_{i} - Q_{i} \cdot x + \frac{1}{2} q \cdot x^{2}$ When 0≤x<a, $m = - m_{i} - Q_{i} \cdot x + \frac{1}{2} q &Center Dot; x^{2}$

弯矩：当a≤x＜a+c时， $M = - M_{i} - Q_{i} \cdot x + \frac{1}{2} q \cdot x^{2} + P 1 \cdot (x - a)$ Bending moment: when a≤x<a+c, $m = - m_{i} - Q_{i} &Center Dot; x + \frac{1}{2} q &Center Dot; x^{2} + P 1 \cdot (x - a)$

当a+c≤x≤L时， $M = - M_{i} - Q_{i} \cdot x + \frac{1}{2} q \cdot x^{2} + P 1 \cdot (x - a) + P 2 \cdot (x - a - c)$ When a+c≤x≤L, $m = - m_{i} - Q_{i} \cdot x + \frac{1}{2} q &Center Dot; x^{2} + P 1 &Center Dot; (x - a) + P 2 &Center Dot; (x - a - c)$

当0≤x＜a时，Q＝-Q_i+q·xWhen 0≤x<a, Q＝-Q _i +q·x

剪力：Shear force:

当a≤x＜a+c时，Q＝-Q_i+q·x+P1When a≤x<a+c, Q=-Q _i +q·x+P1

当a+c≤x≤L时，Q＝-Q_i+q·x+P1+P2When a+c≤x≤L, Q＝-Q _i +q·x+P1+P2

其中，M_i，Q_i即为求出的杆端力。Among them, M _i and Q _i are the calculated rod end forces.

垂直平面的计算：把计算模型简化成简支梁(如图4)，Calculation of the vertical plane: Simplify the calculation model into a simply supported beam (as shown in Figure 4),

计算小车的轮压：Pv1＝Pv2＝(吊重+葫芦自重)×9.8×0.5 (8)Calculate the wheel pressure of the trolley: Pv1＝Pv2＝(lifting weight+hoist weight)×9.8×0.5 (8)

根据力的平衡求出支座反力： $R 2 = \frac{Pv 1 \cdot a + Pv 2 \cdot (a + c) + \frac{1}{2} q L^{2}}{L}$ Find the support reaction force from the balance of forces: $R 2 = \frac{PV 1 &Center Dot; a + PV 2 &Center Dot; (a + c) + \frac{1}{2} q L^{2}}{L}$

R1＝Pv1·a+Pv2·(a+c)+qL-R1 (9)R1＝Pv1·a+Pv2·(a+c)+qL-R1 (9)

根据支座反力和小车轮压求出主梁中间截面的内力：Calculate the internal force of the middle section of the main beam according to the reaction force of the support and the pressure of the trolley:

均布载荷与集中载荷叠加后的弯矩：Bending moment after superposition of uniform load and concentrated load:

$M_{v} = - R 1 \cdot \frac{x}{2} + \frac{1}{2} q {(\frac{x}{2})}^{2}$ 当x＝L即主梁中间截面的位置 (10) $m_{v} = - R 1 &Center Dot; \frac{x}{2} + \frac{1}{2} q {(\frac{x}{2})}^{2}$ When x=L is the position of the middle section of the main beam (10)

剪力(剪力是弯矩的导数)：Shear force (shear force is the derivative of bending moment):

${Q Q}_{v v} = = {M m}_{v v}^{' '} = = {((- - R R 11 \cdot &Center Dot; \frac{x x}{22} + + \frac{11}{22} q q {((\frac{x x}{22}))}^{22}))}^{' '} - - - - - - ((1111))$

所述计算某时刻起重机评估点的应力是：由上述步骤所得的某时刻的多个计算截面的内力，再计算该时刻的多个截面上多个评估点的结构应力数据；The calculation of the stress of the evaluation point of the crane at a certain moment is: the internal force of multiple calculation sections at a certain moment obtained by the above steps, and then calculate the structural stress data of multiple evaluation points on multiple sections at this moment;

水平平面的应力计算Stress Calculation in Horizontal Plane

弯矩产生的应力： Stress due to bending moment:

剪力产生的应力：

Stress due to shear force:

垂直平面的应力计算Stress Calculation in Vertical Plane

弯矩产生的应力： Stress due to bending moment:

剪力产生的剪应力： Shear stress due to shear force:

在公式(12)、(13)、(14)和(15)中：M-水平平面的弯矩，Q-水平平面的剪力，M_v-垂直平面的弯矩，Q_v-垂直平面的剪力，S-主梁中间截面静矩，δ-主梁腹板厚度，I_x-主梁中间截面x方向惯性矩，X_c-主梁中间截面x方向的型心，I_y-主梁中间截面x方向惯性矩，Y_c-主梁中间截面x方向的型心。In formulas (12), (13), (14) and (15): M - bending moment in horizontal plane, Q - shear force in horizontal plane, M _v - bending moment in vertical plane, Q _v - bending moment in vertical plane Shear force, S- static moment of main beam middle section, δ- main beam web thickness, I _x - moment of inertia of main beam middle section in x direction, X _c - core of main beam middle section in x direction, I _y - main beam The moment of inertia in the x-direction of the middle section, Y _c - the core of the main beam in the x-direction of the middle section.

应力的合成：Synthesis of Stress:

根据垂直方向，水平方向的弯矩产生的应力代数相加得到合成的弯曲应力，剪力产生的应力代数相加得到合成的剪应力。According to the algebraic addition of the stresses generated by the bending moment in the vertical direction and the horizontal direction to obtain the composite bending stress, the algebraic sum of the stresses generated by the shear force is obtained to obtain the composite shear stress.

弯矩合成：σ_合成＝σ_垂直+σ_水平+σ_修正 (16)Bending moment synthesis: σ _synthesis = σ _vertical + σ _horizontal + σ _correction (16)

剪力合成：τ_合成＝τ_垂直+τ_水平+τ_修正 (17)Shear force synthesis: τ _synthesis = τ _vertical + τ _horizontal + τ _correction (17)

式中：σ_修正、τ_修正为本专利中前述的修正值，修正值的范围为计算值的0％～15％左右，修正值的具体取值根据距梁内隔板的远近等因素选取。In the formula: σ _correction and τ _correction are the aforementioned correction values in this patent, and the range of the correction value is about 0% to 15% of the calculated value. The specific value of the correction value is selected according to factors such as the distance from the beam inner partition.

下面具体实施例：Below specific embodiment:

以一台单主梁桥式起重机为例，计算任意多个截面、任意多个点的内力和应力，为了说明本发明的快速计算方法，只选择跨中截面上所示点的应力计算过程，先计算该截面的内力，再计算得到该点的应力，根据不同时刻所受的外载荷，可以计算出不同时刻的外载荷作用结果。具体形状、截面参数如下：形状参数，截面参数以及其他参数如表：Taking a single main girder bridge crane as an example, calculate the internal force and stress of any number of sections and points. In order to illustrate the fast calculation method of the present invention, only the stress calculation process of the points shown on the mid-span section is selected. First calculate the internal force of the section, and then calculate the stress at this point. According to the external loads at different times, the results of the external loads at different times can be calculated. The specific shape and section parameters are as follows: shape parameters, section parameters and other parameters are shown in the table:

选择计算点：Select calculation point:

主梁的中间截面(如图3，图4中L/2处为主梁的中间截面所在位置，图5即为中间截面)The middle section of the main beam (as shown in Figure 3, the location of the middle section of the main beam at L/2 in Figure 4, and Figure 5 is the middle section)

x′方向惯性矩为：2.5×10⁹mm⁴ The moment of inertia in the x′ direction is: 2.5×10 ⁹ mm ⁴

y′方向的惯性矩为：4.229×10⁹mm⁴ The moment of inertia in the y′ direction is: 4.229×10 ⁹ mm ⁴

形心坐标为：Xc＝330.7mm，Yc＝783.6mmThe centroid coordinates are: Xc＝330.7mm, Yc＝783.6mm

截面面积：39700mm^2Sectional area: 39700mm^2

计算点为：在初始坐标下的(0，0)点(如图5)，在图5中，x-y为初始坐标，其建立是任意的，根据方便程度来确定；x′-y′是以截面形心为原点的坐标轴，实际计算时，Xc，Yc是相对于初始坐标位置值。The calculation point is: the (0,0) point (as shown in Figure 5) under the initial coordinates. In Figure 5, x-y is the initial coordinates, and its establishment is arbitrary and determined according to the degree of convenience; x'-y' is based on The centroid of the section is the coordinate axis of the origin. In actual calculation, Xc and Yc are relative to the initial coordinate position value.

如下表1为吊重与运行数据。Table 1 below shows the hoisting weight and operating data.

第一：计算垂直方向的内力和应力。First: Calculate the internal forces and stresses in the vertical direction.

把计算模型简化成简支梁(如图4)，根据表1(一个时刻)可以看出小车在主梁上的位置a；Simplify the calculation model into a simply supported beam (as shown in Figure 4), and according to Table 1 (one moment), it can be seen that the position a of the trolley on the main beam;

计算小车的轮压：Pv1＝Pv2＝(吊重+葫芦自重)×9.8×0.5Calculate the wheel pressure of the trolley: Pv1 = Pv2 = (lifting weight + hoist weight) × 9.8 × 0.5

＝(10000+3000)×9.8×0.5＝6.37×10⁴N=(10000+3000)×9.8×0.5＝6.37×10 ⁴ N

根据力的平衡求出支座反力： $R 2 = \frac{Pv 1 \cdot a + Pv 2 \cdot (a + c) + \frac{1}{2} q L^{2}}{L} =$ Find the support reaction force from the balance of forces: $R 2 = \frac{PV 1 &Center Dot; a + PV 2 \cdot (a + c) + \frac{1}{2} q L^{2}}{L} =$

$\frac{6.37 6.37 \times \times 1010^{44} \times \times 1010 + + 6.37 6.37 \times \times 1010^{44} \cdot &Center Dot; ((1010 + + 11)) + + \frac{11}{22} \frac{80008000 \times \times 9.8 9.8}{1515} 1515^{22}}{1515} = = 7742277422 N N$

$R R 11 = = Pv PV 11 \cdot &Center Dot; a a + + Pv PV 22 \cdot &Center Dot; ((a a + + c c)) + + qL QUR - - R R 11$

$= = 6.37 6.37 \times \times 1010^{44} \times \times 1010 + + 6.37 6.37 \times \times 1010^{44} \cdot &Center Dot; ((1010 + + 11)) + + \frac{80008000 \times \times 9.8 9.8}{1515} 1515 - - R R 22$

$= = 2515225152 N N$

$M_{v} = - R 1 \cdot \frac{x}{2} + \frac{1}{2} q {(\frac{x}{2})}^{2}$ 其中x＝L即主梁中间截面的位置 $m_{v} = - R 1 &Center Dot; \frac{x}{2} + \frac{1}{2} q {(\frac{x}{2})}^{2}$ Where x=L is the position of the middle section of the main beam

$= = - - 2515225152 \cdot &Center Dot; \frac{1515}{22} + + \frac{11}{22} \frac{80008000 \times \times 9.8 9.8}{1515} {((\frac{1515}{22}))}^{22}$

$= = - - 321775321775 N N \cdot &Center Dot; m m$

剪力：Shear force:

$Q_{v} = M_{v}^{'}$ 剪力是弯矩的导数 $Q_{v} = m_{v}^{'}$ The shear force is the derivative of the bending moment

$= = {((- - R R 11 \cdot &Center Dot; \frac{x x}{22} + + \frac{11}{22} q q {((\frac{x x}{22}))}^{22}))}^{' '} = = - - 2515225152 \times \times \frac{11}{22} + + \frac{11}{22} \times \times \frac{80008000 \times \times 9.8 9.8}{1515} \times \times \frac{7.5 7.5}{22}$

$= = - - 5128751287 N N$

第二，计算出水平方向的内力和应力。Second, the internal forces and stresses in the horizontal direction are calculated.

由于桥式起重机在水平方向要行走所以在水平平面产生惯性力，计算模型如图3，根据表1可以得到大车的加速度为0.12m/s。Because the bridge crane needs to walk in the horizontal direction, inertia force is generated on the horizontal plane. The calculation model is shown in Figure 3. According to Table 1, the acceleration of the cart can be obtained as 0.12m/s.

1、水平方向的惯性载荷为：1. The inertial load in the horizontal direction is:

(其中P1，P2为轮压Pv1，Pv2在水平方向产生的惯性载荷，q为主梁自重在水平方向产生的惯性载荷)(where P1 and P2 are the inertial loads generated by the wheel pressure Pv1 and Pv2 in the horizontal direction, and q is the inertial load generated by the self-weight of the main girder in the horizontal direction)

2、水平方向的结构计算简图为如图32. The structural calculation diagram in the horizontal direction is as shown in Figure 3

根据公式1，2得According to formula 1, 2 get

δ₁₁X₁+Δ_1p＝0δ ₁₁ X ₁ +Δ _1p =0

${δ δ}_{1111} = = Σ Σ &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{{M m}_{11}} \overset{&OverBar; &OverBar;}{{M m}_{11}}}{EI EI} ds ds = = \frac{22}{33} {k k}^{33} + + L L \cdot \cdot {k k}^{22} = = 15.6 15.6 {m m}^{33}$

集中载荷单独作用，根据公式(3)得Concentrated load acting alone, according to formula (3)

${Δ Δ}_{11 p p} = = Σ Σ &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{{M m}_{11}} \overset{&OverBar; &OverBar;}{{M m}_{p p}}}{EI EI} ds ds = = 1092010920 N N \cdot &Center Dot; {m m}^{33}$

${X x}_{11} = = - - \frac{{Δ Δ}_{11 p p}}{{δ δ}_{1111}} = = - - \frac{1092010920}{15.6 15.6} = = - - 700700 N N$

根据公式(4)得跨中截面的弯矩：According to the formula (4), the bending moment of the mid-span section is obtained:

M_p＝M₁X₁+M_p＝-1×700+780×7.5＝5150N·mM _p =M ₁ X ₁ +M _p =-1×700+780×7.5=5150N·m

Q_p＝M′_p＝-780NQ _p = M' _p = -780N

均布载荷单独作用，根据公式3得Uniformly distributed load acts alone, according to formula 3

${Δ Δ}_{11 p p} = = Σ Σ &Integral; &Integral; \frac{\overset{&OverBar; &OverBar;}{{M m}_{11}} \overset{&OverBar; &OverBar;}{{M m}_{p p}}}{EI EI} ds ds = = \frac{11}{22} \times \times 62.27 62.27 \times \times \frac{{7.5 7.5}^{33}}{33} \times \times 1515 \times \times 11 = = 6615066150 N N \cdot &Center Dot; m m$

${X x}_{11} = = - - \frac{{Δ Δ}_{11 p p}}{{δ δ}_{1111}} = = - - \frac{6615066150}{15.6 15.6} = = - - 42404240 N N$

${M m}_{q q} = = \overset{&OverBar; &OverBar;}{{M m}_{11}} {X x}_{11} + + {M m}_{p p} = = - - 11 \times \times 42404240 + + \frac{11}{22} \times \times 62.72 62.72 \times \times {7.5 7.5}^{22} = = - - 24672467 N N \cdot \cdot m m$

Q_q＝M′_q＝-1746NQ _q ＝M′ _q ＝-1746N

集中载荷与均布载荷产生的弯矩，剪力的叠加Superposition of bending moment and shear force generated by concentrated load and uniform load

弯矩：M＝M_p+M_q＝-5150-2467＝-7617N·mBending moment: M＝M _p +M _q ＝-5150-2467＝-7617N·m

剪力：Q＝Q_p+Q_q＝-780-1746＝2526NShear force: Q＝Q _p +Q _q ＝-780-1746＝2526N

第三，计算该点的应力及应力的合成Third, calculate the stress at the point and the resultant stress

垂直方向vertical direction

弯矩产生的正应力：Normal stress due to bending moment:

剪力产生的剪应力：Shear stress due to shear force:

水平方向，根据公式(12)，(13)Horizontal direction, according to formula (12), (13)

弯矩产生的应力：

Stress due to bending moment:

剪力产生的应力：

Stress due to shear force:

弯矩合成：σ_合成＝σ_垂直+σ_水平+σ_修正＝-101-5.596+0.0＝106.596MpaBending moment synthesis: σ _synthesis = σ _vertical + σ _horizontal + σ _correction = -101-5.596+0.0 = 106.596Mpa

剪力合成：τ_合成＝τ_垂直+τ_水平+τ_修正＝-1.4-0.433+0.0＝-1.833MpaShear force synthesis: τ _synthesis = τ _vertical + τ _horizontal + τ _correction = -1.4-0.433 + 0.0 = -1.833Mpa

上述实施例中的σ_修正、τ_修正取值均取为0.0。The values of σ _correction and τ _correction in the above embodiments are both taken as 0.0.

计算结果如表2为计算后的内力，表3为计算后的应力。应力中的修正值此处均取了0.0。The calculation results are shown in Table 2 for the calculated internal force, and Table 3 for the calculated stress. The correction value in stress is taken as 0.0 here.

表1Table 1

吊重 Hoist 起升加速度Lifting acceleration 小车位置trolley position 大车加速度Cart acceleration 10000Kg10000Kg 0m/s² 0m/s ² 10000mm10000mm 0.012m/s0.012m/s

表2Table 2

垂直方向的弯矩Bending moment in the vertical direction 垂直方向剪力Shear force in vertical direction 水平方向弯矩Horizontal Bending Moment 水平方向剪力Horizontal shear force -32115Nm-32115Nm -51287N-51287N -9951Nm-9951Nm -545.8N-545.8N

表3table 3

垂直方向弯曲应力Vertical bending stress 垂直方向剪应力Shear stress in the vertical direction 水平方向弯曲应力Horizontal Bending Stress 水平方向剪应力Horizontal shear stress 弯矩的合成Composition of Bending Moments 剪力的合成Synthesis of shear force -101MPa-101MPa -1.4MPa-1.4MPa -5.596MPa-5.596MPa -0.433MPa-0.433MPa -106.596MPa-106.596MPa -1.833MPa-1.833MPa

第四，同理根据以上的例子过程，可以求出下表4中各时刻外载荷作用下，所求点的不同时刻的应力值，结果详见表5。Fourth, similarly, based on the above example process, the stress values at different moments of the point under the action of external loads at each moment in Table 4 below can be obtained, and the results are shown in Table 5 for details.

表4Table 4

时刻moment 吊重 Hoist 起升加速度Lifting acceleration 小车位置trolley position 大车加速度Cart acceleration 2009-6-3’8:15:152009-6-3'8:15:15 10000Kg10000Kg 0m/s² 0m/s ² 1000mm1000mm 0m/s² 0m/s ² 2009-6-3’8:16:452009-6-3'8:16:45 10000Kg10000Kg 0m/s² 0m/s ² 5000mm5000mm 0m/s² 0m/s ² 2009-6-3’8:17:002009-6-3'8:17:00 10000Kg10000Kg 0m/s² 0m/s ² 7500mm7500mm 0m/s² 0m/s ² 2009-6-3’8:17:302009-6-3'8:17:30 10000Kg10000Kg 0m/s² 0m/s ² 10000mm10000mm 0m/s² 0m/s ² 2009-6-3’8:18:452009-6-3'8:18:45 10000Kg10000Kg 0m/s² 0m/s ² 12000mm12000mm 0m/s² 0m/s ² 2009-6-3’8:19:002009-6-3'8:19:00 10000Kg10000Kg 0m/s² 0m/s ² 10000mm10000mm 0m/s² 0m/s ² 2009-6-3’8:19:152009-6-3'8:19:15 10000Kg10000Kg 0m/s² 0m/s ² 7500mm7500mm 0m/s² 0m/s ² 2009-6-3’8:19:302009-6-3'8:19:30 10000Kg10000Kg 0m/s² 0m/s ² 5000mm5000mm 0m/s² 0m/s ² 2009-6-3’8:19:452009-6-3'8:19:45 10000Kg10000Kg 0m/s² 0m/s ² 1000mm1000mm 0m/s² 0m/s ²

同以上的方法求出这9个时刻的应力得：Calculate the stress at these 9 moments by the same method as above:

表5table 5

时刻moment 垂直方向弯矩Bending moment in vertical direction 垂直方向剪力Shear force in vertical direction 水平方向弯矩Horizontal Bending Moment 水平方向剪力Horizontal shear force 弯矩的合成Composition of Bending Moments 剪力的合成Synthesis of shear force 2009-6-3’8:15:152009-6-3'8:15:15 -83.3MPa-83.3MPa -3.9MPa-3.9MPa 0MPa0MPa 0MPa0MPa -83.3MPa-83.3MPa -3.9MPa-3.9MPa 2009-6-3’8:16:452009-6-3'8:16:45 -152MPa-152MPa -5.4MPa-5.4MPa 0MPa0MPa 0MPa0MPa -152MPa-152MPa -5.4MPa-5.4MPa 2009-6-3’8:17:002009-6-3'8:17:00 -174.3MPa-174.3MPa -4MPa-4MPa 0MPa0MPa 0MPa0MPa -174.3MPa-174.3MPa -4MPa-4MPa 2009-6-3’8:17:302009-6-3'8:17:30 -154MPa-154MPa -2.5MPa-2.5MPa 0MPa0MPa 0MPa0MPa -154MPa-154MPa -2.5MPa-2.5MPa 2009-6-3’8:18:452009-6-3'8:18:45 -116MPa-116MPa -1.33MPa-1.33MPa 0MPa0MPa 0MPa0MPa -116MPa-116MPa -1.33MPa-1.33MPa 2009-6-3’8:19:002009-6-3'8:19:00 -154MPa-154MPa -2.5MPa-2.5MPa 0MPa0MPa 0MPa0MPa -154MPa-154MPa -2.5MPa-2.5MPa 2009-6-3’8:19:152009-6-3'8:19:15 -174.3MPa-174.3MPa -4MPa-4MPa 0MPa0MPa 0MPa0MPa -174.3MPa-174.3MPa -4MPa-4MPa

时刻moment 垂直方向弯矩Bending moment in vertical direction 垂直方向剪力Shear force in vertical direction 水平方向弯矩Horizontal Bending Moment 水平方向剪力Horizontal shear force 弯矩的合成Composition of Bending Moments 剪力的合成Synthesis of shear force 2009-6-3’8:19:302009-6-3'8:19:30 -152MPa-152MPa -5.4MPa-5.4MPa 0MPa0MPa 0MPa0MPa -152MPa-152MPa -5.4MPa-5.4MPa 2009-6-3’8:19:452009-6-3'8:19:45 -83.3MPa-83.3MPa -3.9MPa-3.9MPa 0MPa0MPa 0MPa0MPa -83.3MPa-83.3MPa -3.9MPa-3.9MPa

特别注意，对于大批量载荷数据，可以根据以上方法，快速计算出不同时刻的应力值。另外对于桥式起重机水平平面的内力计算，用第二种方法矩阵位移法也可以解决桥式起重机水平平面超静定刚架的内力计算，用矩阵位移法计算以上的例子可以得出相同的结果。In particular, for large batches of load data, the stress values at different moments can be quickly calculated according to the above method. In addition, for the calculation of the internal force of the horizontal plane of the bridge crane, the second method, the matrix displacement method, can also be used to solve the calculation of the internal force of the statically indeterminate rigid frame of the horizontal plane of the bridge crane, and the above example can be calculated by the matrix displacement method. The same result can be obtained .

第五，根据计算求得的应力数据，绘制出该点的应力时域图。本例中可以按照表5，做出该段时间的弯矩合成产生的弯曲应力时域图，即应力谱，如图6。Fifth, according to the calculated stress data, draw the stress time-domain diagram of the point. In this example, according to Table 5, the time-domain diagram of the bending stress generated by the bending moment synthesis during this period, that is, the stress spectrum, can be made, as shown in Figure 6.

Claims

1. A method utilizing bridge crane operating data to obtain the stress time-domain value of the evaluation point is characterized in that it comprises the following steps:

1) Use the data recorder to collect the real-time operation data of the lifting weight, lifting height, trolley and cart running positions of the bridge crane, and store the collected real-time operation parameters in the storage unit to obtain the comparative Long-term running data;

2) Preprocess the real-time running data collected for a long time, and according to the speed formula:

3) Establish the structural calculation model of the bridge crane, and read in the parameters required for the calculation of the structural model;

4) Calculate the internal force of the upper section of the bridge crane at a certain moment, determine the multiple section positions of the structural evaluation point of the bridge crane according to the evaluation requirements, and calculate the internal force of multiple calculation sections on the structure according to the calculation model established above;

5) Calculate the stress of the evaluation point of the crane at a certain moment, and calculate the structural stress data of multiple evaluation points on multiple sections at this moment from the internal forces of multiple calculation sections at a certain moment obtained in step 4);

6) Adding or subtracting the correction value to the stress value at a certain moment obtained in the above step 5) to obtain the corrected stress value, and the range of the correction value is 0% to 15% of the calculated value;

7) Repeat the above steps 4), 5) and 6) to obtain internal forces and corrected stress data corresponding to multiple evaluation points at multiple times;

8) Arranging the structural internal force and stress data corresponding to multiple moments at any point of the bridge crane calculated in step 7) into stress spectrum data of multiple evaluation points.

2. The method for obtaining the stress time domain value of the evaluation point by using the bridge crane operating data according to claim 1, characterized in that: the bridge crane data recorder includes a sensor acquisition device for monitoring the bridge crane parameter information , a microprocessing unit, a data storage unit and a communication network interface unit; the signal of the sensor acquisition device for parameter information is connected to the signal input interface of the microprocessing unit; the data output interface of the microprocessing unit is connected to the input interface of the data storage unit; the communication network interface The input end of the unit is connected with the communication output interface of the micro-processing unit.

3. The method according to claim 2 utilizing bridge crane operating data to obtain the stress time domain value of the evaluation point, characterized in that: the sensor acquisition device of the parameter information is made of a sensor and an analog-to-digital conversion chip, and the output terminal of the sensor Connect with the input end of the analog-to-digital conversion chip.