A method for measuring cable force of a cable under boundary conditions of upper end ear plate and lower end nut

Abstract

This invention specifically relates to a method for measuring cable force under boundary conditions of an upper lug plate and a lower nut, comprising the following steps: S1, establishing a model of the cable; S2, determining the relationship curve between cable force and frequency; S3, obtaining the measured frequencies f of the cable at each order. i S4, the measured frequencies f of each order i Substituting the values ​​into the graph, we obtain the measured cable forces F at each order. i m Calculate the cable force F at each order of measurement. i m The average and discrete values; S5, if the discrete value is less than 15 and the measured cable force F of each order is... i m If the difference between the maximum and minimum values ​​is less than or equal to 10 kN, then the cable force F measured at each stage will be... i m Compare with the field measurements; if the discrete value is greater than or equal to 15 or the measured cable force F at each order is... i m If the difference between the maximum and minimum values ​​is greater than 10kN, then modify the bending stiffness and repeat S2-S4; S6, if the cable force F measured at each stage... i m If the difference between the measured value and the field measurement value is less than or equal to 20kN, then the cable force F at each stage of measurement is... i m To measure the cable force, if the measured cable force F at each stage... i m If the difference between the measured value and the field measurement is greater than 20kN, modify the boundary conditions and repeat S2-S5.

Description

Technical Field

[0001] This invention relates to the field of cable force testing, and specifically to a method for measuring cable force under boundary conditions of upper lug plate and lower nut. Background Technology

[0002] In an era of rapid economic development, national infrastructure construction has expanded continuously, resulting in the construction of numerous long-span bridges, including suspension bridges, cable-stayed bridges, and arch bridges. Among these bridge structures, the cables, as the primary load-bearing components, significantly influence the distribution of internal forces and the linear deformation of the main girder. Therefore, accurate measurement of cable forces is crucial during bridge construction and subsequent operation and maintenance.

[0003] like Figure 20 As shown, the cable includes ear plate 5, pin 6, fork ear 7, upper anchor head 8, cable body 9, waterproof cover 10, shock absorber ring 11, cable guide 12, lower anchor head 13, and nut 14, wherein the end where the ear plate is located is the upper end, and the end where the nut is located is the lower end.

[0004] Currently, the main technical methods for measuring cable force based on the frequency method are analytical methods and finite element methods. Although existing technical methods for measuring cable force in bridges take into account the effects of sag, bending stiffness, and boundary conditions, they are difficult to apply to the measurement of cable force under the boundary conditions of the upper end ear plate and the lower end nut of complex irregular arch bridges. Summary of the Invention

[0005] To address the technical problems existing in the prior art, the purpose of this invention is to provide a method for measuring cable force under boundary conditions of the upper end lug plate and the lower end nut. This measurement method can identify the bending stiffness and boundary conditions of cables under the boundary conditions of the upper end lug plate and the lower end nut of complex irregular arch bridges based on the finite element method and spline fitting technology, thus solving the problem of cable force measurement and ensuring the accuracy of cable force measurement.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: 1. A method for measuring cable force under boundary conditions of upper end ear plate and lower end nut, characterized by comprising the following steps:

[0007] S1. Establish a model of the cable and set m different bending stiffnesses according to the actual construction process, m = 1, 2, 3... Substitute one of the bending stiffnesses into the model, set the first boundary condition as the upper end of the cable is hinged and the lower end is fixed, and the second boundary condition as both ends of the cable are fixed.

[0008] S2. Input one of the bending stiffness values ​​and the first boundary condition into the model;

[0009] S3. Determine the relationship curve between cable force and frequency using the finite element method and spline fitting technique;

[0010] S4. Obtain the time-domain signal of the cable and get the measured frequencies f of the cable. i Where i is the order, i = 1, 2, 3...;

[0011] S5. Using the spline interpolation principle, the measured frequencies f of each order are... i Substituting the force-frequency relationship curve into the graph, we obtain the values ​​of each measured frequency f. i Corresponding measured cable forces F of each order i m m = 1, 2, 3…, i is the order, i = 1, 2, 3…, calculate the cable force F for each order. i m The average and discrete values;

[0012] S6. If the discrete value is less than 15 and the cable force F of each order is measured i m If the difference between the maximum and minimum values ​​is less than or equal to 10 kN, then the cable force F measured at each stage will be... i m Compare with the on-site measurements.

[0013] If the discrete value is greater than or equal to 15 or the cable force F of each order is measured i m The difference between the maximum and minimum values ​​is greater than 10kN. For another bending stiffness, repeat S3-S5.

[0014] S7. If the cable force F is measured at each stage i m If the difference between the measured value and the field measurement value is less than or equal to 20kN, then the cable force F at each stage of measurement is... i m To measure the cable force,

[0015] If the cable force F is measured at each stage i m If the difference between the measured value and the field value is greater than 20kN, then the second boundary condition replaces the first boundary condition, and S3-S6 are repeated.

[0016] Furthermore, the field frequency of the cable is acquired using an accelerometer, and the time-domain signal is obtained under natural environmental excitation. The time-domain signal is analyzed to obtain a spectrum, and the measured frequencies f of each order are obtained from the spectrum. i .

[0017] Furthermore, in step S1, the bending stiffness ranges from 0.02EI. max ~0.2EI max EI max The maximum bending stiffness of the cable's entire cross-section is given by a value of 0.02EI. max .

[0018] In general, the present invention has the following advantages: (1) Based on the finite element method and spline fitting technology, the bending stiffness and boundary conditions of the cable under the boundary conditions of the upper end ear plate and the lower end nut of the complex irregular arch bridge are identified, the cable force measurement problem is solved, and the cable force accuracy is ensured.

[0019] (2) By adjusting the bending stiffness of the cable under the boundary conditions of upper hinge and lower fixed and both fixed, and by comparing the two calculation results with the actual tension value of the cable device on site, the parameters such as cable boundary conditions and bending stiffness can be accurately identified at the same time.

[0020] (3) Correctly obtain the relationship curve between cable force and frequency. Based on the finite element method, the free vibration analysis of the structure can accurately identify the actual parameters during cable tensioning and obtain the relationship curve between cable force and frequency, thus improving the accuracy of cable force measurement. Attached Figure Description

[0021] Figure 1 This is a flowchart of the measurement method.

[0022] Figure 2 This is a structural diagram of the bridge in this invention.

[0023] Figure 3 This is a force-frequency relationship diagram of cable No. 12 of the present invention under the boundary condition of upper end hinge and lower end fixed.

[0024] Figure 4 This is a force-frequency relationship diagram of cable No. 19 of the present invention under the boundary condition of upper end hinge and lower end fixed.

[0025] Figure 5 This is a force-frequency relationship diagram of cable No. 21 of the present invention under the condition that the upper end is hinged and the lower end is fixed.

[0026] Figure 6 This is a force-frequency relationship diagram of cable No. 23 of the present invention under the boundary condition of upper end hinge and lower end fixed.

[0027] Figure 7 This is a diagram showing the bending stiffness of cable No. 12 under the condition of upper end hinge and lower end fixed boundary.

[0028] Figure 8 This is a diagram showing the bending stiffness of cable No. 19 of this invention under the condition of upper end hinge and lower end fixed boundary.

[0029] Figure 9 This is a diagram showing the bending stiffness of cable No. 21 of this invention under the condition of upper end hinge and lower end fixed boundary.

[0030] Figure 10 This is a diagram showing the bending stiffness of cable No. 23 of this invention under the condition of upper end hinge and lower end fixed boundary.

[0031] Figure 11 This is a diagram showing the force-frequency relationship of cable No. 12 of the present invention under the condition that both ends are fixed.

[0032] Figure 12 This is a diagram showing the force-frequency relationship of cable No. 19 of this invention under the condition that both ends are fixed.

[0033] Figure 13 This is a diagram showing the force-frequency relationship of cable No. 21 of this invention under the condition that both ends are fixed.

[0034] Figure 14 This is a diagram showing the force-frequency relationship of cable No. 23 of this invention under the condition that both ends are fixed.

[0035] Figure 15 This is a diagram showing the bending stiffness identification of cable No. 12 during the tensioning process under the condition of fixed boundaries at both ends.

[0036] Figure 16 This is a diagram showing the bending stiffness identification of cable No. 19 during the tensioning process under the condition of fixed boundaries at both ends.

[0037] Figure 17 This is a diagram showing the bending stiffness identification of cable No. 21 of this invention during the tensioning process under the condition of fixed boundary at both ends.

[0038] Figure 18 This is a diagram showing the bending stiffness identification of cable No. 23 of this invention during the tensioning process under the condition of fixed boundaries at both ends.

[0039] Figure 19 This is a comparison chart of the cable force values ​​of the present invention.

[0040] Figure 20 This is a schematic diagram of the cable structure of the present invention.

[0041] Among them: 1 is cable No. 12, 2 is cable No. 19, 3 is cable No. 21, 4 is cable No. 23, 5 is ear plate, 6 is pin, 7 is fork ear, 8 is upper anchor head, 9 is cable body, 10 is waterproof cover, 11 is shock absorber ring, 12 is cable guide tube, 13 is lower anchor head, and 14 is nut. Detailed Implementation

[0042] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0043] A method for measuring cable force under boundary conditions of upper end lug plate and lower end nut, such as Figure 1 As shown, it includes the following steps:

[0044] S1. Establish the model of the cable, set the first boundary condition as the upper end of the cable is hinged and the lower end is fixed, and the second boundary condition as both ends of the cable are fixed. Set m different sizes of bending stiffness according to the actual construction process, m=1,2,3…;

[0045] S2. Input one of the bending stiffness values ​​and the first boundary condition into the model;

[0046] S3. The relationship curve between cable force and frequency was determined by finite element method and spline fitting technology. For details, please refer to Xu Yufeng. Research on Construction Control Theory and Core Technology and Software Development of Long-Span Prestressed Concrete Cable-Stayed Bridges [D]. South China University of Technology, 2004.

[0047] S4. Obtain the measured frequencies f of the cable under this bending stiffness condition. i Where i is the order, i = 1, 2, 3..., i.e., the first natural frequency, the second natural frequency, the third natural frequency... the i-th natural frequency of the structure. Several accelerometers are installed on the cables, located at the lower end and on the surface of the cables. These accelerometers can collect on-site frequencies and acquire time-domain signals under natural environmental excitation. Analyzing the time-domain signals yields a spectrum, from which the measured frequencies f of the cables are obtained. i ;

[0048] S5. The measured frequencies f of each order i Substituting the relationship between cable force and frequency, we obtain the corresponding measured cable forces F for each order. i m This refers to the measured cable forces at the first, second, third, ..., i-th natural frequencies of the structure, respectively, where m is the selected m-th bending stiffness (m = 1, 2, 3...), and i is the order (i = 1, 2, 3...). The measured cable forces F at each order are then calculated. i m In this embodiment, the average and discrete values ​​of the cable force are obtained by using spline interpolation. A spline function is introduced and interpolated into the curves showing the relationship between the measured frequency and the cable force at each order. i m Plot the measured cable forces F at each order. i m A line graph of the order can be analyzed by whether the line graph is a horizontal straight line;

[0049] S6. If the discrete value is less than 15 and the cable force F of each order is measured i m If the difference between the maximum and minimum values ​​is less than or equal to 10 kN, then the cable force F measured at each stage will be... i m In this embodiment, the measured cable force F at each stage is compared with the field measurement value.i m When the line graph of the order approximates a horizontal straight line (i.e., the difference between the maximum and minimum values ​​is less than or equal to 10 kN), the next step can be performed.

[0050] If the discrete value is greater than or equal to 15 or the cable force F of each order is measured i m If the difference between the maximum and minimum values ​​is greater than 10kN, in this embodiment, the line graph of the measured cable force and the order is not a horizontal straight line. Then, another bending stiffness is input, and S3-S5 are repeated.

[0051] S7. If the cable force F is measured at each stage i m Similar to the field measurement values, i.e., the cable force F at each stage of measurement. i m If the difference between the measured value and the field measurement value is less than or equal to 20kN, then the cable force F at each stage of measurement is... i m To measure the cable force, the cable force F at each stage is calculated. i m The average value is the average cable force value, and the measured cable force F for each order is... i m The corresponding boundary conditions are the actual boundary conditions.

[0052] If the cable force F is measured at each stage i m The difference between the measured value and the field measurement value is greater than 20kN, that is, the cable force F at each stage of measurement is greater than 20kN. i m If the difference between the measured value and the actual value is large, the boundary conditions of the cable will be reset to the second boundary conditions, and S3-S6 will be repeated. In this embodiment, an oil pressure gauge will be set up on site to display the tension value, which initially represents the cable tension, i.e., the measured value on site.

[0053] In this embodiment, the bending stiffness ranges from 0.02EI. max ~0.2EI max EI max The maximum bending stiffness of the cable's entire cross-section is given by a value of 0.02EI. max .

[0054] like Figure 2 As shown, taking the cable tension measurement of Haixin Bridge as an example, four cables evenly distributed within the length range of the bridge's cables—cable 1 (No. 12), cable 2 (No. 19), cable 3 (No. 21), and cable 4 (No. 23)—were selected as the verification objects.

[0055] The cable parameters are shown in Table 1:

[0056]

[0057] Note: The bending stiffness in Table 1 is calculated based on the entire cross section of the cable, and it is the maximum bending stiffness.

[0058] Table 1 Cable Parameters

[0059] like Figure 3-6 As shown. In step S3, by combining the finite element method and spline fitting technique, the relationship between the cable force and frequency of the four cables under the boundary condition of upper hinge and lower fixed end can be obtained.

[0060] As shown in Table 2, in step S4, the measured frequencies of each order were obtained for the four cables. Among them, cable number 23 (4) is a short cable, and the first three measured frequencies were obtained:

[0061]

[0062] Table 2 Measured frequencies of the cable at various stages during the tensioning process.

[0063] In step S3, the equation solution is related to the cable parameters, and the accuracy of these parameters determines the correctness of the cable force measurement. This embodiment identifies parameters by changing a single variable under the condition of an upper hinge and a fixed lower boundary. First, based on the site conditions, all parameters except the cable bending stiffness are based on the design parameters. Second, the upper and lower limits of the cable bending stiffness are roughly determined, and values ​​are taken in reasonable increments. For example, starting from 0.02EI... max Take up to 0.2EI max The difference in bending stiffness between two adjacent elements is 0.02EI. max The measured force-frequency-bending stiffness relationship of the four cables is shown in the following diagram. Figure 7-10 As shown.

[0064] Based on the uniqueness of the cable, by Figure 7-10 It can be seen that the bending stiffness of the four cables is 0.12EI. max The cable force was calculated based on the actual bending stiffness under the condition of upper hinge and lower fixed boundary. The cable force and the actual tension of the hydraulic jack (i.e., the field measurement value) are shown in Table 3.

[0065]

[0066]

[0067] Table 3 Cable Stress Values

[0068] Because the calculated cable force value under the boundary condition of upper hinge and lower fixed end differs significantly from the actual cable tension value, the cable boundary conditions were modified to be fixed at both ends. The cable parameters and measured frequencies are shown in Table 1-2. The relationship between cable force and frequency after modifying the boundary conditions is as follows: Figure 11-14 As shown.

[0069] The cable force calculation method based on the condition of upper end hinge and lower end fixed boundary is used to obtain the cable bending stiffness identification result under the condition of fixed boundary at both ends, as follows: Figure 15-18 As shown.

[0070] Based on the uniqueness of the cable force, by Figure 7-10 It can be seen that the bending stiffness identification result of the four cables is 0.12EI. max .

[0071] The cable force is calculated based on the actual bending stiffness under the condition of fixed boundary at both ends. The cable force and the actual tension of the hydraulic jack are shown in Table 4 below.

[0072]

[0073] Table 4 Cable Stress Values

[0074] A comprehensive comparison of the calculated cable force values ​​under the boundary conditions of fixed ends, hinged upper end, and fixed lower end, and the actual tension values ​​of the hydraulic jacks in the on-site tensioning equipment, yields the following results: Figure 19 As shown.

[0075] Based on the comparison results, the boundary condition for the upper end lug plate and lower end nut of the cable in this case is that both ends are fixed, and the bending stiffness of the cable is taken as 0.12EI. max Subsequent cable tension values ​​can be calculated using these identified parameters, and the calculation results are reliable.

[0076] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for measuring cable force under boundary conditions of upper end ear plate and lower end nut, characterized in that, Includes the following steps: S1. Establish a model of the cable and set m different bending stiffnesses according to the actual construction process, m = 1, 2, 3... Set the first boundary condition as the upper end of the cable is hinged and the lower end is fixed, and the second boundary condition as both ends of the cable are fixed. S2. Input one of the bending stiffness values ​​and the first boundary condition into the model; S3. Determine the relationship curve between cable force and frequency using the finite element method and spline fitting technique; S4. Obtain the time-domain signal of the cable and get the measured frequencies f of the cable. i Where i is the order, i = 1, 2, 3...; S5. Using spline interpolation, the measured frequencies f of each order are... i Substituting the force-frequency relationship curve into the graph, we obtain the values ​​of each measured frequency f. i Corresponding measured cable forces F of each order i m m = 1, 2, 3…, i is the order, i = 1, 2, 3…, calculate the cable force F for each order. i m The average and discrete values; S6. If the discrete value is less than 15 and the cable force F of each order is measured i m If the difference between the maximum and minimum values ​​is less than or equal to 10 kN, then the cable force F measured at each stage will be... i m Compare with the on-site measurements. If the discrete value is greater than or equal to 15 or the cable force F of each order is measured i m If the difference between the maximum and minimum values ​​is greater than 10kN, input another bending stiffness and repeat S3-S5. S7. If the cable force F is measured at each stage i m If the difference between the measured value and the field measurement value is less than or equal to 20kN, then the cable force F at each stage of measurement is... i m To measure the cable force, If the cable force F is measured at each stage i m If the difference between the measured value and the field value is greater than 20kN, then the second boundary condition replaces the first boundary condition, and S3-S6 are repeated.

2. The method for measuring cable force under boundary conditions of upper end ear plate and lower end nut according to claim 1, characterized in that, The field frequency of the cable is acquired using an accelerometer, and the time-domain signal is obtained under natural environmental excitation. The spectrum of the time-domain signal is analyzed, and the measured frequencies f of each order are obtained from the spectrum. i .

3. The method for measuring cable force under boundary conditions of upper end ear plate and lower end nut according to claim 1, characterized in that, In step S1, the bending stiffness ranges from 0.02EI. max ~0.2EI max EI max The maximum bending stiffness of the cable's entire cross-section is given by a value of 0.02EI. max .

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