CN116362071A - High-speed railway tied-arch bridge suspender force inversion method based on beam deformation - Google Patents
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Abstract
The invention discloses a high-speed railway tied-arch bridge suspender force inversion method based on beam deformation, which comprises the following steps: obtaining linear relation between deflection change and temperature and cable force according to deflection change of each point of the main beam, and solving linear related parameters corresponding to deflection and temperature caused by uniform temperature load and deflection and cable force caused by two cable forces respectively through a finite element model to form an influence coefficient matrix of cable force on deflection and an influence coefficient matrix of temperature on deflection; based on the obtained full-bridge expression and the corresponding influence coefficient matrix, the sling force is inverted in real time by combining the actually measured line shape and the temperature field parameters, and the full-bridge sling force evaluation is realized.
Description
Technical Field
The invention relates to a high-speed railway tied-arch bridge suspender force inversion method based on beam deformation, and belongs to the technical field of railway monitoring.
Background
For the tied-arch bridge which is operated for more than 10 years, the suspenders bear load for a long time and are exposed to the atmosphere, wire breakage damage can occur due to fatigue, corrosion and the like, the whole short suspenders can be broken, serious bridge accidents are caused, and the monitoring of the cable force of the suspenders is very necessary. At present, a correction frequency spectrum method is mainly adopted, such as boom cable force identification is carried out according to a string tensioning theory, but the correction frequency spectrum method is not applicable to short booms of 3-5 m, the booms of 5-20 m can be used only by carrying out a series of complex correction, and moreover, based on cost control, a cable sensor cannot cover a full bridge, so that the condition of missing abnormal boom monitoring exists. Under the conditions of saving cost and ensuring the recognition precision of the boom cable force, the full-bridge cable force recognition is realized, and the method has good practicability and economy.
Disclosure of Invention
The invention aims to provide a high-speed railway tied-arch bridge suspender force inversion method based on beam deformation, which aims to solve the defects that a cable sensor in the prior art cannot cover a full bridge and missing abnormal suspender monitoring exists.
A high-speed railway tied-arch bridge suspender force inversion method based on beam deformation comprises the following steps:
obtaining linear relation between deflection change and temperature and cable force according to deflection change of each point of the main beam, and solving linear related parameters corresponding to deflection and temperature caused by uniform temperature load and deflection and cable force caused by two cable forces respectively through a finite element model to form an influence coefficient matrix of cable force on deflection and an influence coefficient matrix of temperature on deflection;
based on the obtained full-bridge expression and the corresponding influence coefficient matrix, the sling force is inverted in real time by combining the actually measured line shape and the temperature field parameters, and the full-bridge sling force evaluation is realized.
Further, the deflection change of each point of the main beam comprises:
the deflection data acquisition point is a connection point A of each inhaul cable and the main beam 1 、A 2 Two inhaul cables are respectively marked as C 1 、C 2 ；
The equivalent cable forces of the two cables are F respectively 1 And F 2 The method comprises the steps of carrying out a first treatment on the surface of the The deflection change of the main beam in the equivalent structure can be divided into four parts, and the first part is the main beam dead weight G g Induced deflection, the second part is deflection caused by uniform temperature load T, and the third part is cable force F 1 Induced deflection, fourth part is cable force F 2 The deflection caused.
Further, the girder deflection expression is:
wherein,,
representing the A on the main beam i Total deflection of the points>
Representing the A on the main beam i The deflection of the point caused by its own weight,
representing the A on the main beam i Deflection of the spot caused by a uniform temperature T +.>
Representing the A on the main beam i From cable force F of point 1 Deflection caused by->
Representing the A on the main beam i From cable force F of point 2 Induced deflection, i=1, 2.
Further, the expression that the deflection change is in linear relation with temperature and cable force is as follows:
wherein,,
representing the main girder A caused by the uniform temperature T=1 ℃ of the bridge system i Deflection change of point->
Represents F 1 On main beam a caused by =1kn i Deflection change of point->
Represents F 2 On main beam a caused by =1kn i Deflection change of point, i=1, 2.
Further, the cable force expression is:
further, the influence coefficient matrix of the temperature on deflection and the influence coefficient matrix of the cable force on deflection are as follows:
obtaining a plurality of common nodes of the bridge, wherein N is adopted respectively 1 ,N 2 ,N 3 ,…,N 20 The function expression is shown as a formula (4);
because the forces in the horizontal directions of the two sling forces are not equal, a proportionality coefficient m exists between the two sling forces, as shown in the formula (5);
wherein alpha is i I=1, 2,3, …,40 is the horizontal angle between the sling and the main beam.
The combination of the formula (4) and the formula (5) can be expanded into a plurality of rope force resultant forces N 1 ,N 2 ,N 3 ,…,N 20 As shown in the formula (6):
wherein X is an influence coefficient matrix of temperature on deflection, and K is an influence coefficient matrix of cable force on deflection.
Further, the calculation method of the sling force is as follows:
and calculating the resultant force of rope force, decomposing the resultant force to two component forces, and obtaining rope force of each sling respectively through the included angle between every two slings on the same node and the specific gravity coefficient m between the rope force of every two slings, wherein the formula is shown as formula (7).
Wherein X is an influence coefficient matrix of temperature on deflection, and K is an influence coefficient matrix of cable force on deflection.
Further, the method for solving the linear related parameters of deflection and temperature caused by uniform temperature load and deflection and cable force caused by two cable forces respectively through the finite element model comprises the following steps:
applying dead weight load G to the structure g And a temperature load T a After operation analysis, A is obtained 1 ,A 2 ,A 3 ,…,A 20 Total deflection value of each point
Then the sling units in the finite element model are all deleted, and dead weight load and temperature load T are applied a After operation analysis, the deflection of each point in the ropeless structure, which is generated by the dead weight of the main beam, is obtained
And deflection caused by temperature load +.>
Meanwhile, the +.A can be calculated by the formula (8)>
The temperature load is applied to the sling unit, and the sling force F can be obtained after operation analysis 1 A is a 1 Deflection of points caused by the cable force
In the model, A 1 Initial deflection of point 0, C 1 When the initial cable force of the sling is 0, when the sling changes the unit cable force, the sling causes A 1 Point deflection Change value +.>
Can be calculated according to formula (9),>
the same applies to the calculation method of (2); when the influence coefficient of the cable force of the rest slings on the deflection of the main beam is calculated, a single cable is neededReplacing slings in the finite element model with corresponding slings, and calculating according to the method;
will total static deflection
Is mainly divided into two parts, one part is just the deflection caused by the temperature field +.>
Part is the deflection caused by the cable force only +.>
And the deflection of each point on the girder caused by dead weight and the deflection of other points are recorded as a constant c i I=1, 2,3, …,20; and (3) establishing a deflection linear superposition equation, as shown in a formula (10):
further obtaining a calculation formula of the resultant force of the cable force:
compared with the prior art, the invention has the beneficial effects that: the analysis method for inverting the full-bridge cable force based on deflection and temperature has the advantages that the coincidence degree of the inverted cable force and the actually-measured cable force is high, the precision is higher than that of the traditional cable force measurement method, and the requirement of cable force periodic monitoring is met. When the sling pressure ring is damaged after being in service for a long time and is difficult to carry out later maintenance, the cable force can be inverted by adopting the method, so that the cable force monitoring can be continuously carried out instead of the original equipment; and the cable force verification can be realized by only arranging a plurality of sling pressure rings, so that the full-bridge cable force monitoring can be realized, and the equipment funds and other project cost can be effectively reduced.
Drawings
FIG. 1 is a diagram of equivalent stress of a sling;
FIG. 2a is the main beam dead weight G g Deflection caused;
FIG. 2b is deflection caused by a uniform temperature load T;
FIG. 2c is a cable force F 1 Deflection caused;
FIG. 2d is a cable force F 2 Deflection caused;
FIG. 3 is a finite element model of a bridge without ropes;
fig. 4 is a bridge single cable finite element model.
Detailed Description
The invention is further described in connection with the following detailed description, in order to make the technical means, the creation characteristics, the achievement of the purpose and the effect of the invention easy to understand.
As shown in the figure, the invention discloses a high-speed railway tied-arch bridge suspender force inversion method based on beam deformation, which comprises the following steps:
obtaining linear relation between deflection change and temperature and cable force according to deflection change of each point of the main beam, and solving linear related parameters corresponding to deflection and temperature caused by uniform temperature load and deflection and cable force caused by two cable forces respectively through a finite element model to form an influence coefficient matrix of cable force on deflection and an influence coefficient matrix of temperature on deflection;
based on the obtained full-bridge expression and the corresponding influence coefficient matrix, the sling force is inverted in real time by combining the actually measured line shape and the temperature field parameters, and the full-bridge sling force evaluation is realized.
In this embodiment, for the above steps, the following is specific:
the slings of the tied arch bridge are mainly subjected to axial tension, and the direction of the internal force is determined after the position of the slings is determined, so that the slings can be equivalent to a pair of axial forces, and the same is true of the stay cables of the cable-stayed bridge, and the cable-stayed bridge is represented by a simple cable-stayed bridge structure, as shown in fig. 1.
The structure consists of a main girder, a bridge tower and two inhaul cables. Before cable equivalence, the cable force can be regarded as a function of linear change along with the system temperature field, and after cable force equivalence, the static deflection can be further regarded as a function of linear change along with the cable force and the system temperature field. Therefore, quantitative assessment of cable damage by the main girder static deflection abnormal change can be converted into detection of cable force abnormal change according to the main girder static deflection abnormal change, and quantitative assessment of cable damage is realized by the cable force abnormal change.
The following will describe how to build a mathematical model between the girder deflection and the cable force: the structure shown in figure 1 is under the action of uniform temperature field T and gravity load, and the gravity load of main beam is G g Representing that the deflection data acquisition point is a connection point A of each inhaul cable and the main beam 1 、A 2 Two inhaul cables are respectively marked as C 1 、C 2 . The equivalent cable forces of the two cables are F respectively 1 And F 2 . The deflection change of the main beam in the equivalent structure can be divided into four parts, and the first part is the main beam dead weight G g Induced deflection, the second part is deflection caused by uniform temperature load T, and the third part is cable force F 1 Induced deflection, fourth part is cable force F 2 The induced deflections are shown in FIGS. 2 (a) - (d), respectively.
Thus, the main beam deflection can be calculated as a superposition of equation (1):
wherein,,
representing the A on the main beam i Total deflection of the points>
Representing the A on the main beam i The deflection of the point caused by its own weight,
representing the A on the main beam i Deflection of the spot caused by a uniform temperature T +.>
Representing on the main beamA i From cable force F of point 1 Deflection caused by->
Representing the A on the main beam i From cable force F of point 2 Induced deflection, i=1, 2.
And because the deflection change of each point of the main beam caused by one sling is in a linear relation with the cable force of the sling, and the deflection change of each point of the main beam caused by temperature is in a linear relation with the temperature. Therefore, the formula (1) can be rewritten as follows:
wherein,,
representing the main girder A caused by the uniform temperature T=1 ℃ of the bridge system i Deflection change of point->
Represents F 1 On main beam a caused by =1kn i Deflection change of point->
Represents F 2 On main beam a caused by =1kn i Deflection change of point, i=1, 2. The cable force can be further solved from equation (7-2) as follows:
respectively adopting N for 20 common nodes 1 ,N 2 ,N 3 ,…,N 20 The functional expression is shown as a formula (4). Since the forces in the horizontal direction of the two sling forces are not equal, a proportionality coefficient m exists between the two sling forces as shown in the formula (5).
Referring to the calculation process, the combination of the formula (4) and the formula (5) can be expanded into 20 cable force resultant forces N 1 ,N 2 ,N 3 ,…,N 20 As shown in the formula (6):
wherein X is an influence coefficient matrix of temperature on deflection, and K is an influence coefficient matrix of cable force on deflection.
After the resultant force of the rope forces is calculated, the resultant force is decomposed into two component forces (namely rope force of the slings), and the rope force of each sling can be respectively calculated through the included angle between every two slings on the same node and the specific gravity coefficient m between every two slings of the rope force, wherein the formula is shown in the formula (7).
Wherein X is an influence coefficient matrix of temperature on deflection, K is an influence coefficient matrix of cable force on deflection, and the concrete calculation method is as follows:
(1) in the model, a dead weight load G is applied to the structure g And a temperature load T a After operation analysis, A is obtained 1 ,A 2 ,A 3 ,…,A 20 Total deflection value of each point
Then the sling units in the finite element model are all deleted, and dead weight load is appliedAnd a temperature load T a After operation analysis, the deflection of each point in the ropeless structure, which is generated by the dead weight of the main beam, is obtained
And deflection caused by temperature load +.>
Meanwhile, the +.A can be calculated by the formula (8)>
(2) The calculation model of the deflection change value of each point of the main beam caused by the rope force of each sling change unit is shown in figure 3, and the calculation method is shown as C in the figure 1 Sling and A 1 Dots are illustrated as examples. In the single rope model, a temperature load is applied to a sling unit, and the sling force F can be obtained after operation analysis 1 A is a 1 Deflection of points caused by the cable force
In the model, A 1 Initial deflection of point 0, C 1 When the initial cable force of the sling is 0, when the sling changes the unit cable force, the sling causes A 1 Point deflection Change value +.>
Can be calculated according to formula (9),>
the same applies to the calculation method of (2).
When the influence coefficient of the cable force of the rest slings on the deflection of the main beam is calculated, the slings in the single cable finite element model are replaced by corresponding slings, and then the calculation is carried out according to the method.
Will total static deflection
Is mainly divided into two parts, one part is just the deflection caused by the temperature field +.>
Part is the deflection caused by the cable force only +.>
And the deflection of each point on the girder caused by dead weight and other possible deflection of the point are recorded as a constant c i I=1, 2,3, …,20. And (3) establishing a deflection linear superposition equation, as shown in a formula (10):
further obtaining a calculation formula of the resultant force of the cable force:
wherein K and X are represented by the formulas (6 b) and (6 c).
One embodiment is specifically:
the section selects the measured data of the temperature, the deflection of the main beam and the cable force for 1 day to carry out inversion calculation, and compares the measured data with the measured value of the cable force of the following 5 days to verify the feasibility of the cable force inversion method.
The deflection and cable force data are all calculated by adopting an average value per second, the sampling frequency is 0.2Hz, 5 data are obtained per second, the average value is obtained, each deflection monitoring point and cable force monitoring point are respectively provided with 86400 data, and the data correspond to 1 day of data. In order to fully consider the change characteristics of the whole temperature rise and fall and the space distribution difference of the temperature field, a principal component analysis method is adopted to extract principal components from the temperature field monitoring data to replace the original temperature field, so that the deflection caused by the temperature field
Through-type (12)And (3) performing calculation:
wherein P is 1 ,P 2 ,P 3 ,…,P M M temperature main components extracted from the actually measured temperature field; omega 1 ,ω 2 ,ω 3 ,…,ω M For the contribution rate of the principal component of each temperature field to the original temperature field, then equation (13) can be rewritten as:
according to the method (13), 20 cable force resultant forces in the real bridge are calculated, and besides clear deflection data and temperature field data, a constant c corresponding to each monitoring point is needed i The estimation can be obtained from formulas (7) and (13):
accordingly, the specific estimation method of the constant term is divided into 3 steps (estimation is performed by using 11 days of data):
(1) Because only 5 deflection sensors are arranged at the upper and lower sides of the bridge respectively, unknown deflection data is obtained by adopting a fitting interpolation method in order to obtain deflection values of 20 points of the full bridge. According to the structural characteristics of the bridge, the deflection line shape of the main beam is a smooth curve, so that the measured deflection data of the upstream and the downstream are fitted through the smooth curve respectively, the shape of the main beam line is approximately obtained, and the deflection value of the position point where the sensor is not installed is obtained through an interpolation method, thus obtaining
(2) Only 10 cable force sensors are arranged at the upper and lower sides of the bridge respectively, and in order to obtain 20 cable force combined force values of the full bridge, unknown cable force data still need to be obtained by adopting a fitting interpolation method. And (3) applying a temperature load to the bridge finite element model, extracting the cable force of the upstream sling and fitting by using a smooth curve. And fitting the change curves of the upstream and downstream cable forces along the forward bridge direction respectively through smooth curves, and obtaining the cable force value of the sling without the sensor by an interpolation method.
(3) Extracting temperature main components of the monitoring data of 24 temperature sensors of the full bridge by adopting a main component analysis method, taking the first two temperature main components to calculate the deflection change of the main beam caused by temperature, wherein the first temperature is P 1 Second temperature principal component P 2 The contribution rates of the main components of the two temperature fields to the original temperature field exceed 95%, so that the first main component and the second main component can be used for calculating instead of the actually measured temperature field. Will calculate the P 1 、P 2 And (1) and (2), and carrying the data into the formula (14) to obtain a constant term c 1 ,c 2 ,c 3 ,…,c 20 . Monitoring the obtained main girder deflection and sling cable force to obtain time sequence data, so c i (i=1, 2,3, …, 20) is also time-series data, c i Fluctuation over time is small, so take c i The average of all moments is taken as the final estimation value.
C is calculated to obtain 1 ,c 2 ,c 3 ,…,c 20 And (3) inverting the sling force value by the equation (13). Firstly, respectively performing smooth curve fitting on the deflection of the main beam measured at the upstream and the downstream, and obtaining the total deflection of each point through the difference value
And the calculated constant term c 1 ,c 2 ,c 3 ,…,c 20 Temperature principal component P 1 、P 2 And (5) carrying out the calculation to obtain 20 cable force resultant force inversion values by taking the cable force inversion values into the formula (13).
And establishing a mathematical model of the girder deflection and the sling cable force according to the structural mechanics superposition principle and the correlative mathematical relationship between the girder deflection, the temperature load and the cable force. According to the mathematical model, a sling force inversion method based on girder deflection change is provided. The full-bridge cable-hanging static cable force and the dynamic cable force are inverted through the deflection of each point of the main beam, so that a good inversion effect is obtained, full-bridge cable force evaluation can be realized, sensors are not required to be installed on all slings to obtain cable force, and the cost of manpower and material resources is effectively reduced.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (8)
1. The method for inverting the boom force of the high-speed railway tied-arch bridge based on beam deformation is characterized by comprising the following steps of:
obtaining linear relation between deflection change and temperature and cable force according to deflection change of each point of the main beam, and solving linear related parameters corresponding to deflection and temperature caused by uniform temperature load and deflection and cable force caused by two cable forces respectively through a finite element model to form an influence coefficient matrix of cable force on deflection and an influence coefficient matrix of temperature on deflection;
based on the obtained full-bridge expression and the corresponding influence coefficient matrix, the sling force is inverted in real time by combining the actually measured line shape and the temperature field parameters, and the full-bridge sling force evaluation is realized.
2. The method for inverting the boom force of the high-speed railway tied-arch bridge based on beam deformation according to claim 1, wherein the deflection change of each point of the main beam comprises:
the deflection data acquisition point is a connection point A of each inhaul cable and the main beam 1 、A 2 Two inhaul cables are respectively marked as C 1 、C 2 ；
The equivalent cable forces of the two cables are F respectively 1 And F 2 The method comprises the steps of carrying out a first treatment on the surface of the The deflection change of the main beam in the equivalent structure can be divided into four parts, and the first part is the main beam dead weight G g Induced deflection, the second part is deflection caused by uniform temperature load T, and the third part is cable force F 1 Induced deflection, fourth part is cable force F 2 The deflection caused.
3. The beam deformation-based high-speed railway tied-arch bridge suspender force inversion method as claimed in claim 2 wherein the main beam deflection expression is:
wherein,,
representing the A on the main beam i Total deflection of the points>
Representing the A on the main beam i Deflection of the point caused by its own weight->
Representing the A on the main beam i Deflection of the spot caused by a uniform temperature T +.>
Representing the A on the main beam i From cable force F of point 1 Deflection caused by->
Representing the A on the main beam i From cable force F of point 2 Induced deflection, i=1, 2.
4. The inversion method of the boom force of the high-speed railway tied-arch bridge based on beam deformation according to claim 1, wherein the expression of the linear relation between deflection change and temperature and cable force is:
wherein,,
representing the main girder A caused by the uniform temperature T=1 ℃ of the bridge system i Deflection change of point->
Represents F 1 On main beam a caused by =1kn i Deflection change of point->
Represents F 2 On main beam a caused by =1kn i Deflection change of point, i=1, 2.
5. The beam deformation-based high-speed railway tied-arch bridge boom force inversion method according to claim 1, wherein the cable force expression is:
6. the beam deformation-based high-speed railway tied-arch bridge suspender force inversion method as claimed in claim 1, wherein the temperature-to-deflection influence coefficient matrix and the cable force-to-deflection influence coefficient matrix are as follows:
obtaining a plurality of common nodes of the bridge, wherein N is adopted respectively 1 ，N 2 ，N 3 ，...，N 20 The function expression is shown as a formula (4);
because the forces in the horizontal directions of the two sling forces are not equal, a proportionality coefficient m exists between the two sling forces, as shown in the formula (5);
wherein alpha is i I=1, 2, 3..40 is the horizontal angle of sling to main beam.
The combination of the formula (4) and the formula (5) can be expanded into a plurality of rope force resultant forces N 1 ，N 2 ，N 3 ，...，N 20 As shown in the formula (6):
wherein X is an influence coefficient matrix of temperature on deflection, and K is an influence coefficient matrix of cable force on deflection.
7. The inversion method of the boom force of the high-speed railway tied-arch bridge based on beam deformation according to claim 1, wherein the calculation method of the sling force is as follows:
and calculating the resultant force of rope force, decomposing the resultant force to two component forces, and obtaining rope force of each sling respectively through the included angle between every two slings on the same node and the specific gravity coefficient m between the rope force of every two slings, wherein the formula is shown as formula (7).
Wherein X is an influence coefficient matrix of temperature on deflection, and K is an influence coefficient matrix of cable force on deflection.
8. The beam deformation-based high-speed railway tied-arch bridge suspender force inversion method as claimed in claim 1, wherein the method for solving linear related parameters of deflection and temperature caused by uniform temperature load and deflection and cable force caused by two cable forces respectively through a finite element model comprises the following steps:
applying dead weight load G to the structure g And a temperature load T a After operation analysis, A is obtained 1 ，A 2 ，A 3 ，...，A 20 Total deflection value of each point
Then the sling units in the finite element model are all deleted, and dead weight load and temperature load T are applied a After operation analysis, the deflection of each point in the ropeless structure, which is generated by the dead weight of the main beam, is obtained
And deflection caused by temperature load +.>
Meanwhile, the +.A can be calculated by the formula (8)>
The temperature load is applied to the sling unit, and the sling force F can be obtained after operation analysis 1 A is a 1 Deflection of points caused by the cable force
In the model, A 1 Initial deflection of point 0, C 1 The initial cable force of the sling is 0, when the sling changes the unit cable forceInduced A 1 Point deflection Change value +.>
Can be calculated according to formula (9),>
the same applies to the calculation method of (2); when the influence coefficient of the cable force of the rest slings on the deflection of the main beam is calculated, the slings in the single cable finite element model are replaced by corresponding slings, and then the calculation is carried out according to the method;
will total static deflection
Is mainly divided into two parts, one part is deflection D caused by temperature field only Ai,Tem Part is the deflection caused by the cable force only +.>
And the deflection of each point on the girder caused by dead weight and the deflection of other points are recorded as a constant c i I=1, 2,3, …,20; and (3) establishing a deflection linear superposition equation, as shown in a formula (10):
further obtaining a calculation formula of the resultant force of the cable force:
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| CN117401580B (en) * | 2023-12-12 | 2024-04-05 | 河南卫华重型机械股份有限公司 | Crane girder deformation soft detection method |
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