CN111721486B - Equal-section continuous beam damage identification method based on support reaction influence line curvature difference - Google Patents

Equal-section continuous beam damage identification method based on support reaction influence line curvature difference Download PDF

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CN111721486B
CN111721486B CN202010573666.1A CN202010573666A CN111721486B CN 111721486 B CN111721486 B CN 111721486B CN 202010573666 A CN202010573666 A CN 202010573666A CN 111721486 B CN111721486 B CN 111721486B
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唐盛华
张佳奇
秦付倩
成鹏
刘宇翔
杨文轩
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Xiangtan University
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Abstract

The invention discloses a method for identifying damage of a constant-section continuous beam based on curvature difference of a support reaction influence line, which comprises the following steps: setting support reaction force measuring points at the supports of the continuous beam, and applying a moving load to obtain support reaction force influence lines of the supports of the continuous beam; the curvature of the support reaction influence line is calculated and further differentiated, and damage positioning is carried out through sudden change of a support reaction influence line curvature differential curve; further, damage degree quantification is carried out through the differential change of the curvature of the continuous beam support reaction influence line. The method does not need information before the continuous beam is damaged, only needs to arrange the measuring points at the support, has less requirement on the number of the measuring points, saves the using amount of a monitoring sensor, can accurately position and quantify the damage of the continuous beam with the equal cross section, and is applied to the damage evaluation of the continuous beam with the equal cross section.

Description

Equal-section continuous beam damage identification method based on support reaction influence line curvature difference
Technical Field
The invention relates to the technical field of damage detection of a constant-section continuous beam structure, in particular to a method for identifying damage of a constant-section continuous beam based on support reaction influence line curvature difference.
Background
With the rapid development of economy in China, the number of bridges in China is rapidly increased at present. The bridge is not only related to traffic, but also closely connected with the economic development of society and the life safety of people. In the service period of the bridge, the bridge structure is damaged by load and environment, so that the state and performance of the bridge need to be detected to judge the health condition of the bridge. At present, the main methods for identifying damage can be divided into two categories, one is a method based on dynamic parameters, and the damage of a structure is judged by using the change conditions of factors such as the natural frequency, the rigidity matrix, the modal shape and the like of the structure; the other type is a method based on static parameters, and usually, a static load is applied to a structure, and factors such as support counter force, displacement on a beam, deflection, strain and the like are measured to identify the position and the damage degree of the damage. The first method has higher requirement on the precision of the instrument and has the influence of uncertain factors such as damping and the like; the second method is less harsh than the first method in terms of use conditions, is more mature in terms of technology and equipment, and has a certain accuracy in measurement results. Therefore, methods based on static parameters have been extensively studied.
Most methods for researching the structure damage identification technology based on the static parameters use information before damage, the information before damage can not be provided for bridges built earlier, the damage identification method based on the curvature difference of the support reaction influence line can realize damage identification without the information before damage, along with the progress of the support reaction sensor technology, the curvature difference of the support reaction influence line is expected to be applied to damage identification of structures, and at present, literature reports related to support reaction damage identification without the information before damage are rarely found.
Disclosure of Invention
In order to solve the technical problems, the invention provides the equal-section continuous beam damage identification method based on the support reaction influence line curvature difference, which is simple in algorithm and low in cost.
The technical scheme for solving the problems is as follows: a method for identifying damage of a constant-section continuous beam based on curvature difference of a support reaction influence line is characterized by comprising the following steps:
(1) setting support reaction force measuring points at the positions of the supports of the continuous beam, applying moving load to the continuous beam and obtaining support reaction force influence lines of the measuring points;
(2) curvature and further difference are solved for the continuous beam support reaction influence line, and damage positioning is carried out through sudden change of a support reaction influence line curvature difference curve;
(3) and identifying the damage position through continuous beam damage positioning, and quantifying the damage degree by using the support reaction force of one of the supports on two sides of the damage span to influence the curvature difference change of the line.
In the method for identifying the damage of the constant-section continuous beam based on the curvature difference of the support reaction influence lines, in the step (1), in order to reduce the loading times of the moving load and the number of corresponding support reaction influence line data in the actual process, the moving load can be loaded at equal intervals, and the support reaction influence lines with less data are obtained by sequentially recording the support reaction values of the measuring points.
In the method for identifying the damage of the constant-section continuous beam based on the curvature difference of the reaction influence line of the support, in the step (2), the curvature X' of the reaction influence line of the support is obtained by calculating the center difference:
Figure BDA0002550543520000021
wherein, subscript i is the node number, X ″, of the mobile load loaded on the nodeiThe curvature of a line is influenced by the reaction force of a support applied to the position of the node i by a moving load, epsilon is the average value of the distance between the node i-1 and the node i and the distance between the node i and the node i +1 (usually, the distances between adjacent nodes are the same), and X isiThe value of the counter force of the support when the moving load acts on the node i.
In the method for identifying the damage of the uniform-section continuous beam based on the curvature difference of the support reaction influence line, in the step (2), the damage positioning index D of the curvature difference of the support reaction influence line is as follows:
Figure BDA0002550543520000034
in the formula, X ″)iThe curvature of a line is influenced by the reaction force of a support acting on the ith node position for moving load, n is the number of nodes, the No. 1 node is located on the support at one end of the continuous beam, the No. n node is located on the support at the other end of the continuous beam, the number of the nodes is continuous, and the number of the nodes is increased from 1 to n in sequence.
According to the method for identifying the damage of the uniform-section continuous beam based on the curvature difference of the support reaction influence line, in the step (3), the position where the damage is located can be judged according to the damage positioning index (the damage of some positions is obvious only through locally amplifying the damage positioning index), the curvature difference index of the support reaction influence line of the support far away from the damage position is insensitive to the damage, and therefore the accuracy of damage positioning and quantification can be improved by selecting the curvature difference of the support reaction influence line of one of two supports spanning the damage.
In the method for identifying the damage of the constant-section continuous beam based on the curvature difference of the reaction influence line of the support, in the step (3), the damage degree is quantified according to the curvature difference change of the reaction influence line of the support, and the damage degree calculation method is divided into the following three types:
for the damage of the left side unit of the structure, the damage degree calculation method comprises the following steps:
Figure BDA0002550543520000032
when the right side unit is damaged, the reverse force influence line values of the support can be calculated according to the damage of the left side unit in a reverse order;
the damage degree calculation method for the structural intermediate unit damage comprises the following steps:
Figure BDA0002550543520000033
for the damage of the units on the two sides of the middle support of the structure, the calculation method of the damage degree of the unit on the left side is as follows:
Figure BDA0002550543520000041
when the right unit is damaged, only the above formula D is neededfAnd DjInterchanging;
subscripts i and i +1 respectively represent the node numbers of left and right nodes of the damaged unit, f represents the node number of an undamaged unit on the left side of the damaged unit, and f<i, j represents the node number of the undamaged cell to the right of the damaged cell, j>i+2；DeDegree of damage, D3The difference value of curvature of the support reaction influence line is 3 nodes Di+1The differential value of curvature of the support reaction influence line of the right node of the damaged unit, DfRepresenting the differential curvature value of the support reaction influence line of the node at the undamaged unit on the left side of the i node, DjRepresenting the curvature difference value of the support reaction influence line of the node at the undamaged unit at the right side of the i +2 node (the curvature difference values of the support reaction influence lines of the same span undamaged unit are the same, namely the same span Df＝Dj)。
In the method for identifying the damage of the constant-section continuous beam based on the curvature difference of the reaction influence line of the support, in the steps (1) and (3), when the moving load is loaded on the continuous beam at equal intervals, the number of nodes of each span is not less than 7 (including two nodes at the support).
The invention has the beneficial effects that: the invention applies moving load to the damaged constant-section continuous beam to obtain the sudden change of the curvature differential curve of the support reaction influence line of each support of the beam for carrying out damage positioning, and simultaneously establishes an explicit expression for calculating the damage degree by the curvature differential value of the support reaction influence line of the structural damage, and the damage degree can be directly calculated by the curvature differential value of the support reaction influence line; and by taking the two-span continuous beam and three-span continuous beam examples and considering various damage working conditions, the application value of the support reaction influence line curvature difference index in the equal-section continuous beam damage identification is verified, and an effective new method is provided for equal-section continuous beam damage positioning and quantification.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention.
FIG. 2 is a model diagram of a two-span continuous beam structure of the invention across an intra-span unit damage.
FIG. 3 is a cross section of the present inventionBasic structure of internal unit damage
Figure BDA0002550543520000051
Moment diagram.
FIG. 4 is a basic structure M of the present invention for cross-intra cell damagePMoment diagram.
FIG. 5 is a model view of a two-span continuous beam structure with damage to the support-side units of the present invention.
FIG. 6 is a basic structure of a damage of a support-side unit in the present invention
Figure BDA0002550543520000052
Moment diagram.
FIG. 7 shows a basic structure M of a damage of a support-side unit in the present inventionPMoment diagram.
FIG. 8 is a schematic view of the arrangement of two-span continuous beam joints according to the present invention.
FIG. 9 is a finite element model diagram of a two-span continuous beam according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of the damage localization indicator D of the working conditions 1# to 3# according to the embodiment of the present invention.
Fig. 11 is a schematic diagram of the damage localization index D under the first working condition two 1# to 3# in the embodiment of the present invention.
FIG. 12 is a finite element model diagram of a two-span and three-span continuous beam according to an embodiment of the present invention.
Fig. 13 is a schematic diagram of the damage localization index D of the second working condition 1# to 4# according to the embodiment of the present invention.
Fig. 14 is a schematic diagram of a 1-unit local damage localization indicator D under the second working condition 1# according to the embodiment of the present invention.
Fig. 15 is a schematic diagram of the damage localization index D under the second working condition two 1# to 4# in the embodiment of the present invention.
FIG. 16 is a schematic diagram of the 1-unit local damage localization indicator D in condition two 2# according to the embodiment of the present invention.
Detailed Description
The present invention is further described with reference to the following drawings and examples, wherein like reference numerals refer to the same or similar elements throughout the different views unless otherwise specified.
As shown in fig. 1, a method for identifying damage to a continuous beam with an equal cross section based on a curvature difference of a support reaction influence line includes the following steps:
1. setting support reaction force measuring points at the positions of the supports of the continuous beam, applying moving load to the continuous beam and obtaining support reaction force influence lines of the measuring points;
2. curvature and further difference are solved for the continuous beam support reaction influence line, and damage positioning is carried out through sudden change of a support reaction influence line curvature difference curve;
3. and identifying the damage position through continuous beam damage positioning, and quantifying the damage degree by using the support reaction force of one of the supports on two sides of the damage span to influence the curvature difference change of the line.
The application step 1:
(1) taking the two-span unequal continuous beam damage in the first span as an example, the structural model is shown in fig. 2, the distance from the load P to the support A is z, and the lengths of the two spans are L respectively1And L2A, B and C are three supports of the two-span continuous beam respectively, the distance between the damaged position and the support A is a, the length of the damaged area is epsilon, the rigidity of the undamaged position is EI, and the rigidity of the damaged area is kEI; in the figure, the numbers and letters below the beams represent node numbers, the node number of a support A is 1, the node number of a support C is n, the node numbers are continuous, wherein the acting position of a load P is at a node m, the node numbers of the left side and the right side of a damaged area are i and i +1 respectively, and the node number of a middle support B is n1(ii) a The load P is transferred from the carrier a to the carrier C, and the carrier reaction force influence line of the carrier B is obtained by multiplying the force method and the graph.
With a simple supported beam as a basic structure, when a load P acts on the beam, a basic equation can be established by a force method as follows:
δ11X+Δ1P＝0 (1)
wherein X is the counter-force of the intermediate support B, delta11N for unit force acting on the support B1Nodal displacement, Δ1PIs n under the action of a load P1Displacement of the node.
To find delta11And Δ1PActing on a unit loadLower bending moment diagram
Figure BDA0002550543520000061
And moment diagram M under load PPAs shown in fig. 3 and 4, respectively. FIG. 3 shows a bending moment diagram
Figure BDA0002550543520000062
The expression in (1) is:
Figure BDA0002550543520000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002550543520000064
represents that unit load acts on the support B, x belongs to [0, L ]1]The distance from the beam support A is a bending moment at the position of x;
Figure BDA0002550543520000065
represents that the unit load acts on the support B, x belongs to the element (L)1,L1+L2]The distance from the beam support A is a bending moment at the position of x; x represents the distance from the beam support a;
in fig. 4, the bending moment when the load P acts on the position away from the support a by the length z is expressed as follows:
Figure BDA0002550543520000071
in the formula, M1(x) The length of the load P acting on the support A is represented as z position, and x belongs to [0, z ]]The distance from the beam support A is a bending moment at the position of x; m2(x) The length of the load P acting on the support A is represented as z position, and x belongs to (z, L)1+L2]The distance from the beam support A is the bending moment at the x position.
And (3) calculating a reaction force influence line of the support B by graph multiplication:
Figure BDA0002550543520000072
when a load P acts on the left side of the damaged area, Δ1PAnd the influence lines of the counter force of the support are respectively as follows:
Figure BDA0002550543520000073
Figure BDA0002550543520000074
when the load P acts on the right side of the damaged area (still within the first span), Δ1PAnd the influence lines of the counter force of the support are respectively as follows:
Figure BDA0002550543520000075
Figure BDA0002550543520000076
in the formula: xl(m)Representing the corresponding middle support counter force X when the load P acts on the m node and is positioned at the left side of the damage arear(m)And the corresponding middle support counter force is shown when the load P acts on the m node and is positioned at the right side of the damage area.
(2) Taking the damage of the two-span unequal continuous beam on the left unit of the first-span middle support as an example, the structural model is as shown in fig. 5, and the distance between the damage position and the support a is a (a is L)1-epsilon), the length of the damaged area is epsilon, the stiffness of the undamaged position is EI and the stiffness of the damaged cell is kEI.
Taking a simple supported beam as a basic structure, when P acts on the beam, a basic equation can be established by a force method as follows:
δ11X+Δ1P＝0 (9)
wherein X is the counter-force of the intermediate support B, delta11N for unit force acting on the support B1Nodal displacement, Δ1PIs a loadN under the action of P1Displacement of the node.
To find delta11And Δ1PDrawing a bending moment diagram under the action of unit load
Figure BDA0002550543520000084
And bending moment diagram M under P loadPAs shown in fig. 6 and 7, respectively; bending moment in FIG. 6
Figure BDA0002550543520000085
The expression in the figure is the same as the above formula (2); the expression of the bending moment when the load P acts on the position z away from the left end support A in FIG. 7 is the same as the above formula (3).
And (3) calculating a reaction force influence line of the support B by graph multiplication:
Figure BDA0002550543520000081
when a load P acts on the left side of the damaged area, Δ1PAnd the influence lines of the counter force of the support are respectively as follows:
Figure BDA0002550543520000082
Figure BDA0002550543520000083
when a load P acts on the right side of the damaged area (acting in the second span), Δ1PAnd the influence lines of the counter force of the support are respectively as follows:
Figure BDA0002550543520000091
Figure BDA0002550543520000092
in the formula: xl(m)Representing the corresponding middle support counter force X when the load P acts on the m node and is positioned at the left side of the damage arear(m)And the corresponding middle support counter force is shown when the load P acts on the m node and is positioned at the right side of the damage area.
The application step 2:
the curvature of each node of the support reaction influence line is solved by adopting a center difference method, and the formula is as follows:
Figure BDA0002550543520000093
wherein i represents a node number, ε represents a length between adjacent nodes, and 1 node and the last node are due to the absence of Xi-1And Xi+1Therefore, the curvature of the two nodes is directly 0, i.e. X ″1＝X″n＝0。
The positioning index D of curvature difference damage of the support reaction influence line is as follows:
Figure BDA0002550543520000094
in the formula, n is the number of nodes, the No. 1 node is located at one end support of the continuous beam, the No. n node is located at the other end support of the continuous beam, the number of the nodes is continuous, and the number of the nodes is increased from 1 to n in sequence. Due to absence of X'0' so there is no D value for node 1.
In order to better understand the distribution rule of the D values on the beam nodes, the following definitions are made for the distribution of the nodes, which are specifically shown in fig. 8; where the numbers and letters below the beams represent the node numbers, increasing from 1 to n, from left to right. i and i +1 represent nodes on both sides of a damaged unit, f represents a node at an undamaged unit on the left side of the node i, j represents a node at an undamaged unit on the right side of the node i +2, and n1Representing the node at the intermediate support.
(1) The specific D value of the inter-span unit damage is different according to the action node of the mobile load P, and can be divided into the following five conditions:
in f node (left side of damage unit), f value range is f ∈ [2, i-1 ]:
Figure BDA0002550543520000101
at inode:
Figure BDA0002550543520000102
at node i + 1:
Figure BDA0002550543520000103
at node i + 2:
Figure BDA0002550543520000104
when j node is positioned (the right side of the damage unit), the value range of j belongs to [ i +3, n ∈ ]1-1]：
Figure BDA0002550543520000105
As can be seen from the above five cases of cross-intra cell damage, the difference in curvature of the nodes at undamaged cells is a constant value, i.e., D at nodes f and j is a constant value, which changes at the damaged locations (i, i +1 and i +2 node locations). Therefore, the damaged cell position can be determined by calculating the value D corresponding to the support reaction force, drawing a graph, and determining the point on the graph where the change has occurred.
(2) The specific D value of the damage of the unit beside the middle support is different according to the action node of the moving load P, and can be divided into the following five conditions:
in f node (left side of damage unit), f value range is f ∈ [2, i-1 ]:
Figure BDA0002550543520000111
at inode:
Figure BDA0002550543520000112
at the i +1 node, (i +1 ═ n)1)：
Figure BDA0002550543520000113
At node i + 2:
Figure BDA0002550543520000114
in the j node (right side of the damage unit), the value range of j belongs to the [ i +3, n ]:
Figure BDA0002550543520000115
from the above five cases of the cell damage beside the support, it can be seen that the curvature difference value at the two-span undamaged cell nodes (f node and j node) is two constant values. When no damage occurs, the curvatures at the i +1 and i +2 nodes are changed due to the influence of the support, and the curvatures at the i node position are not changed; when the damage exists, the value is changed at the nodes of the damaged positions i, i +1 and i +2, so that whether the positions are damaged or not can be judged according to the change number of the curvature difference value, and whether the bulges or the recesses exist in the D value graph or not can be judged. Therefore, the position of the damaged cell can be determined by calculating the value D corresponding to the reaction force of the support, drawing a graph, and determining the point on the graph where the change has occurred.
Application step 3:
after the D value graph is used for judging the damage position, the curvature difference index of the support reaction influence line of one of the supports at the two sides of the damage position is selected for quantifying the damage degree. Because the distance between the support reaction force influence line curvature difference index of other supports and the damage position is far and is not sensitive, the precision of calculating the damage degree is not high.
And (3) carrying out damage quantification according to the change rule of the D value:
(1) when the damage is at the side span cell (taking the left end cell as an example):
when a is 0, D is the 2-node position, since a + e2＝X″2-X″1And X ″)1Is assumed to be zero, so to avoid the influence of the support, D is chosen3. According to equations (20) and (21) there are:
Figure BDA0002550543520000121
after the deformation is carried out by the formula, the damage degree D can be obtainedeThe method comprises the following steps:
Figure BDA0002550543520000122
when the right side unit is damaged, the reverse reaction influence line values of the support can be calculated according to the damage of the left side unit in a reverse order.
(2) When the damage is in the middle cell:
according to the formulae (17), (19) and (21):
Figure BDA0002550543520000123
after the deformation is carried out by the formula, the damage degree D can be obtainedeThe method comprises the following steps:
Figure BDA0002550543520000124
wherein DjAnd DfBoth are equal, so D can also be used in formula (30)fAlternative Dj。
(3) When the damage is to the unit beside the middle support, taking the damage unit on the left side of the middle support as an example:
according to the formulas (24), (26) and (28) are combined:
Figure BDA0002550543520000125
after the deformation is carried out by the formula, the damage degree D can be obtainedeThe method comprises the following steps:
Figure BDA0002550543520000131
when the damage unit is on the right side of the middle support, only D in the above formula, namely formula (32), is neededfAnd DjTwo interchange positions.
In steps 1 and 3, the moving load is loaded on the continuous beam at equal intervals, and the number of nodes per span is not less than 7 (including two nodes at the support).
The first embodiment is as follows: referring to fig. 9, the span of the two-span continuous beam is arranged to be 50+50cm, 5cm is divided into a unit and 21 nodes (in the figure, the numbers in the circle at the upper row are unit numbers, and the numbers at the lower row are node numbers). The cross-section dimension of the plate is b × h ═ 6cm × 3cm, and the elastic modulus of the material is 2.7 × 103MPa, density 1200kg/m3。
In general, damage in an actual bridge structure, such as crack generation, material corrosion or elastic modulus reduction, only causes a large change in the structural rigidity, but has a small influence on the structural quality. Therefore, in the finite element calculation, the damage of the element is simulated by lowering the elastic modulus. And establishing a beam structure model by adopting finite element software. Taking the damage working condition of a single unit of the two-span continuous beam as an example, the damage working condition of the middle-span 5 unit and the damage working condition of the middle support side 10 unit are considered to be respectively damaged, and the damage working condition is shown in table 1.
TABLE 1 two-span continuous beam Single Damage Condition
Figure BDA0002550543520000132
The specific implementation steps are as follows:
step 1: measuring points are arranged at the positions of the supports 1#, 2# and 3#, 1kN moving load is applied to the two-span continuous beam, and a support reaction force influence line measured actually by the beam support is obtained.
Step 2: the curvature difference is obtained for the support reaction force influence line of the support, and the damage location is carried out through the curvature difference curve of the support reaction force influence line, so that the sudden change of the 5, 6 and 7 nodes can be observed from fig. 10, which means that the damage exists nearby, and the 5, 6 and 7 nodes respectively correspond to the theoretical i, i +1 and i +2 nodes, so that the damage is judged to occur on the 5 units between the 5 and 6 nodes, which is the same as the assumed position of the damage. Nodes 11 and 12 on the curve of fig. 10 affect the D index because of being close to the support, but do not affect the damage identification of the nearby unit, for example, fig. 11 (where there is a protrusion (or there are three abrupt points) of the unit damage beside the support), similar to fig. 10 damage location, fig. 11 can also determine 10 unit damage.
And step 3: the damage degree is quantified by the influence line curvature difference value of the optional support 2# for damage localization.
Working condition 1: di+1＝D6If it is-1.27, take Dj-1.184 substituting for formula:
Figure BDA0002550543520000141
working condition 2: di+1＝D11H is-0.8372, take Df＝-1.134，DjSubstituting 1.134 into the following formula:
Figure BDA0002550543520000142
from the top two kinds DeThe value shows that the index can accurately quantify the damage degree, and the identified damage degree is very close to the actual damage degree, so that the damage degree of the index to the single damage of the continuous beam can be accurately identified.
Example two: referring to FIG. 12, the span of the three-span continuous beamThe arrangement is 50+75+50cm, 5cm divides a unit into 36 nodes (in the figure, the numbers in the upper row of circles are unit numbers, and the numbers in the lower row are node numbers). The cross-section dimension of the plate is b × h ═ 6cm × 3cm, and the elastic modulus of the material is 2.7 × 103MPa, density 1200kg/m3. Considering that a plurality of parts are damaged in different degrees at the same time, the damage working condition is shown in table 2.
TABLE 2 cantilever Multi-Damage Condition
Figure BDA0002550543520000143
The specific implementation steps are as follows:
step 1: measuring points are arranged at the positions of the supports 1#, 2#, 3# and 4#, 1kN moving load is applied to the three-span continuous beam, and the actually measured support reaction force influence line of the beam support is obtained.
Step 2: curvature difference is calculated for the support reaction influence lines of all the supports, the specific D value is shown in fig. 13 and fig. 15, damage positioning is carried out through a support reaction influence line curvature difference curve, and by taking the working condition 1 as an example, 10 unit damage can be judged through the first mutation points 10, 11 and 12 nodes in fig. 13, and the result is consistent with the set damage unit result. Other locations may also be determined and verified according to the method. For the side cell damage, such as cell No. 1, since the left point of cell No. 1 belongs to the previous point for which the moving load starting point is not differentiated, the node is not drawn on the figure either, although there are only two abrupt points, but the damage location can also be used. In condition 2, it can be judged from fig. 15 that there is damage at units 1, 10 and 18. In addition, it can be seen from FIG. 13 that the mutation caused by the 1-unit damage is not very obvious, and even cannot be observed on the 4# curve under the two working conditions. The reason for this is that the support 4# is located too far away from the damaged unit, so that the support counter force is not sensitive to the influence of the damaged unit and is difficult to generate obvious mutation points; on the other hand, the points on the curve are changed greatly (compared with the numerical mutation caused by the damage), so that the points mutated due to the damage are covered. For this case, a local D-index map or the like may be taken for the edge cell position. As shown in fig. 14 and 16, the mutation point can be clearly seen by plotting the D value of 2# which is highly sensitive to 1-unit damage, thereby judging 1-unit damage.
And step 3: and 2# support reaction force influence line curvature difference value can be selected for damage positioning to quantify the damage degree.
Working condition 1:
for 1 unit injury D3When the root is equal to-0.858, take Dj-0.9364 substituting for formula:
Figure BDA0002550543520000151
for 10 unit injury Di+1＝D11H is-0.6768, take Df＝-0.9364，DjSubstitution of 1.0248 into the following equation:
Figure BDA0002550543520000161
working condition 2:
for 1 unit injury D3When the root is equal to-0.8, take Dj-0.934 substituting for:
Figure BDA0002550543520000162
for 10 unit injury Di+1＝D110.6736, if Df＝-0.934，DjSubstitution of 1.0248 into the following equation:
Figure BDA0002550543520000163
for 18 unit injury Di+1＝D191.098, get DjSubstitution of 1.0248 into the following equation:
Figure BDA0002550543520000164
from the above two kinds of multi-damage working conditions DeThe value can be known that the index can accurately quantify the damage degree, and the identified damage degree is very close to the actual damage degree, so that the damage degree of the continuous beam multiple damage can be accurately identified by the index.
The above description is only 2 embodiments of the present invention, and all equivalent changes and modifications made according to the claims of the present invention are included in the scope of the present invention.

Claims (4)

1. A method for identifying damage of a constant-section continuous beam based on curvature difference of a support reaction influence line is characterized by comprising the following steps:
(1) setting support reaction force measuring points at the positions of the supports of the continuous beam, applying moving load to the continuous beam and obtaining support reaction force influence lines of the measuring points;
(2) curvature and further difference are solved for the continuous beam support reaction influence line, and damage positioning is carried out through sudden change of a support reaction influence line curvature difference curve;
the curvature X' of the support reaction influence line is obtained by central difference calculation:
Figure FDA0003368598710000011
wherein, subscript i is the node number, X ″, of the mobile load loaded on the nodeiThe curvature of a support reaction influence line for the position of a moving load acting on the node i is shown in the specification, epsilon is the average value of the distance between the node i-1 and the node i and the distance between the node i and the node i +1, and XiThe value of the reaction force of the support when the moving load acts on the i node is shown;
the positioning index D of curvature difference damage of the support reaction influence line is as follows:
Figure FDA0003368598710000012
in the formula, X ″)iSupport reaction shadow acting on ith node position for moving loadThe number of the nodes is continuous and is increased from 1 to n;
(3) identifying a damage position through continuous beam damage positioning, and quantifying the damage degree by using the support reaction of one of the supports at the two sides of the damage span to influence the curvature difference change of the line;
the damage degree is quantified according to the curvature difference change of the support reaction influence line, and the damage degree calculation method is divided into the following three types:
for the damage of the left side unit of the structure, the damage degree calculation method comprises the following steps:
Figure FDA0003368598710000021
when the right side unit is damaged, the reverse force influence line values of the support can be calculated according to the damage of the left side unit in a reverse order;
the damage degree calculation method for the structural intermediate unit damage comprises the following steps:
Figure FDA0003368598710000022
for the damage of the units on the two sides of the middle support of the structure, the calculation method of the damage degree of the unit on the left side is as follows:
Figure FDA0003368598710000023
when the right unit is damaged, only the above formula D is neededfAnd DjInterchanging;
subscripts i and i +1 respectively represent the node numbers of left and right nodes of the damaged unit, f represents the node number of an undamaged unit on the left side of the damaged unit, and f<i, j represents the node number of the undamaged cell to the right of the damaged cell, j>i+2；DeDegree of damage, D3The difference value of curvature of the support reaction influence line is 3 nodes Di+1The differential value of curvature of the support reaction influence line of the right node of the damaged unit, DfRepresenting the differential curvature value of the support reaction influence line of the node at the undamaged unit on the left side of the i node, DjRepresenting the curvature difference value of the support reaction influence line of the node at the undamaged unit at the right side of the i +2 node, wherein the curvature difference values of the support reaction influence lines of the same span undamaged units are the same, namely the same span Df＝Dj。
2. The method for identifying the damage of the constant-section continuous beam based on the curvature difference of the support reaction influence line, which is characterized by comprising the following steps of: in the step (1), in order to reduce the loading times of the moving load and the number of corresponding support reaction force influence line data in the actual process, the moving load can be loaded at equal intervals, and the support reaction force values of the measuring points are recorded in sequence to obtain the support reaction force influence lines with less data.
3. The method for identifying the damage of the constant-section continuous beam based on the curvature difference of the support reaction influence line, which is characterized by comprising the following steps of: in the step (3), the position of the damage can be judged according to the damage positioning index, and the support reaction influence line curvature difference index of the support far away from the damage position is insensitive to the damage, so that the support reaction influence line curvature difference of one of the two supports of the damage span can be selected to improve the accuracy of damage positioning and quantification.
4. The method for identifying the damage of the constant-section continuous beam based on the curvature difference of the support reaction influence line, which is characterized by comprising the following steps of: in the steps (1) and (3), when the moving load is loaded on the continuous beam at equal intervals, the number of nodes of each span is not less than 7, and the number of nodes comprises two nodes at the support.
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