Method for calculating cable hanging force of one-time tensioning cable-stayed buckle based on influence matrix method

Abstract

The invention relates to the technical field of bridge construction, and discloses a one-time tensioning cable-stayed buckle cable hanging force calculation method based on an influence matrix method, and the method comprises the steps: building a Midascivil model at a complete construction stage of an arch rib; extracting an overall influence matrix of the cable-stayed buckling system structure; initial cable force is prepared; solving a first correction cable force based on the correction matrix; solving a second correction cable force; solving the (n + 1) th correction cable force; arch rib displacement and a displacement difference value in the cable loosening stage are calculated; iterating step by step until the difference value between the arch rib displacement in the cable loosening stage and the target displacement meets the final precision. According to the method, the cable force of the other half-span buckle cable is solved, so that the calculation speed and precision are effectively improved; based on an influence matrix method, optimization of initial cable force and correction of an influence matrix are added, and the calculation iteration efficiency is effectively improved; the uniformity of the cable force of the buckle cable is improved; the method is wide in application range and can be used for calculating symmetric and asymmetric arch rib cable-stayed buckling systems.

Description

Technical Field

[0001] The present application relates to the technical field of bridge construction, and in particular to a method for calculating the force of a single-tensioned inclined cable based on an influence matrix method. Background Art

[0002] In modern bridge engineering, arch bridges have become an important part of urban landscape and transportation infrastructure with their beautiful curves and unique structural forms. Especially for large bridges across wide rivers or deep valleys, arch bridge structures are favored for their good bearing capacity and economy. In recent years, the cable-stayed buckle method has been widely used in the construction of large-span arch bridges. This construction technology uses cable-stayed arch rib segments to balance the bending moment of the arch ribs by tensioning force to achieve structural stability and shape control. Therefore, the determination of the cable force during construction has an important impact on the safety of arch rib construction and the final arch shape. Although traditional cable force calculation methods, such as the zero displacement method, the zero bending moment method, the normal installation iteration method and the fixed length cable method, can meet engineering needs to a certain extent, they each have their own limitations, such as the need for multiple adjustments during the construction phase, the complex calculation process, the low overall calculation efficiency, and the difficulty in meeting the requirements of high-precision construction.

[0003] With the development of computer technology and finite element analysis methods, the calculation methods of cable forces for one-time tensioning based on the unknown load coefficient method and the influence matrix method have been continuously developed. These methods can improve the calculation accuracy and efficiency of cable forces to a certain extent, but they still have their own applicable conditions. For example, the cable adjustment method based on the unknown load coefficient method cannot solve the problem of uniformity of adjacent cable forces, and the traditional cable adjustment method based on the influence matrix cannot consider the change in structural stiffness caused by the displacement of the installed segments during the inclined buckling process. Summary of the invention

[0004] The present invention aims to solve the problems existing in the above-mentioned different methods during the construction process of arch bridge cable-stayed buckle and hanging, and provides a method for calculating the force of a single-tensioned cable-stayed buckle and hanging cable based on an influence matrix method.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] Step 1: Establish the Midascivil model of the complete construction stage of the arch rib, input the unit cable force and run it;

[0007] Step 2: Extract the overall influence matrix of the cable-stayed buckle system structure, and consider the positive influence matrix of the arch rib tangential assembly;

[0008] Step 3: Draft the initial cable force, input it into the Midascivil model, calculate the arch rib displacement during the cable release stage, and solve the difference between it and the target displacement;

[0009] Step 4: Combine the displacement difference and use MATLAB to set large-scale constraints to solve the first correction cable force based on the correction matrix;

[0010] Step 5: Input the first revised cable force into the Midascivil model, calculate the arch rib displacement in the cable-releasing stage again to find the difference between it and the target displacement, and use Matlab to solve the second revised cable force on a large scale again;

[0011] Step 6: When the displacement difference of the nth iteration reaches the initial accuracy, use MATLAB to set small-range constraints to solve the n+1th corrected cable force based on the correction matrix;

[0012] Step 7: Input the (n+1)th corrected cable force into the Midascivil model and calculate the arch rib displacement and displacement difference in the cable-releasing stage again;

[0013] Step 8: Iterate gradually until the difference between the arch rib displacement in the cable-releasing stage and the target displacement meets the final accuracy. At this time, the corrected cable force is the primary cable tension that meets the requirements.

[0014] In the first step, the complete construction phase of the arch rib finite element analysis model includes arch rib installation, arch rib closure, cable loosening and arch formation, wherein the arch rib installation phase includes: arch rib segments and corresponding cables and arch rib cross bracing segments.

[0015] In the first step, a unit cable force of 1 kN is input into each cable.

[0016] In the second step, the influence matrix extracted in Midascivil is the influence matrix of the half-span arch rib structure in the closure stage in the DZ direction. This influence matrix only considers the influence of the displacement of the installed arch rib segments in each construction stage, that is, the previous triangular matrix m:

[0017]

[0018] In the second step, since the influence matrix extracted in Midascivil does not take into account the tangential assembly displacement during the construction phase, that is, the displacement influence of the installed segment on the uninstalled segment is not considered. The geometric relationship can be used to obtain the influence value of the installed arch rib stage on the uninstalled segment, and then the influence matrix is ​​corrected:

[0019] The influence matrix of the half-span arch rib structure at the closure stage in the DX and DZ directions is extracted by Midascivil, as follows: Figure 1 , the geometric analysis of m11 has the following relationship:

[0020]

[0021] Considering the displacement effect of the tangential assembly of the arch rib, the geometric analysis of m12 can reveal the influence of the first arch rib on the second arch rib in the DZ direction:

[0022]

[0023] In the second step, the modified influence matrix m is:

[0024]

[0025] In the third step, the initial cable force corresponding to each section of the arch rib is obtained by solving the force analysis of each independent arch rib segment, that is, the cable tension is solved by knowing the angle between the cable and the vertical direction and the gravity of the arch rib segment.

[0026] In the third step, the gravity G of each independent rib segment includes the sum of the gravity of the current rib segment and the gravity of the cross brace at the corresponding position.

[0027] In the third step, the cables are arranged symmetrically on the surface by default, and only the control point displacements of the half-span arch ribs are compared. The initial cable forces of the cables are input symmetrically into the model, and the following steps until the eighth step are all carried out in this way.

[0028] In the fourth step, the result solved by Matlab is the change value △T of the cable force, that is, after the correction matrix m is known and the difference △S between the initial cable force displacement and the target displacement in the third step is calculated by the following formula, and the change value is added to the initial value as the initial cable force for subsequent finite element calculations.

[0029] [M′][ΔT]=[ΔS]

[0030] In the fourth step, MATLAB solves on a large scale to limit the change in the force of adjacent cables to 10% to 15% of the initial force of the cables.

[0031] In the fifth step, the reasons why the displacement difference is not zero are: 1. The limit of the change value of the cable tension; 2. The influence matrix is ​​the influence matrix before the maximum cable loosening, which fails to consider the impact of the cable loosening construction stage on each control point; 3. The correction matrix m is not the actual influence matrix of the finite element calculation, which only considers the impact of the tangential connection assembly, and cannot consider the dynamic structural stiffness after deformation at each construction stage under different initial cable tensions.

[0032] In the sixth step, according to the standard, the arch rib arch deviation is 1 / 3000 of the arch rib span L. In order to improve the iteration rate and ensure the calculation accuracy, the present invention controls the initial accuracy at L / 6000.

[0033] In the sixth step, MATLAB solves in a small range to limit the change value of the adjacent cable forces to 1% to 5% of the initial cable forces.

[0034] The fourth step to the eighth step are the process of dynamic correction of cable force, which is essentially based on the dynamic adjustment of the initial cable force to fit the target line shape of the arch rib, and finally achieve the difference between the arch rib displacement in the loose cable state and the target displacement to meet the final accuracy by tensioning the inclined cable force once.

[0035] The first step to the eighth step are for the case where the arch rib buckle cable surfaces are arranged symmetrically. When the buckle cable surfaces at both ends of one side of the arch rib are arranged in different forms, the following steps need to be continued:

[0036] Step 9: Extract the influence matrix of the arch rib of the other half span and make corrections, input the cable force of step 8, repeat steps 6 to 8, and solve the cable force of the other half span.

[0037] In the ninth step, the input eighth step cable force is still a symmetrical cable force.

[0038] In the ninth step, steps 6 to 8 are repeated to solve the cable forces of the other half span, and only the cable forces of the half span that have not converged are iteratively calculated, that is, the cable forces of the half span that have been iteratively satisfied in steps 1 to 8 remain unchanged.

[0039] According to a method for calculating the force of a primary tensioned inclined buckle cable based on an influence matrix method in an embodiment of the present application, the beneficial effects are:

[0040] 1. The present invention optimizes and adjusts the initial cable force of the inclined cable hook based on the influence matrix method, which effectively improves the calculation speed and accuracy compared with the traditional cable adjustment method;

[0041] 2. Compared with the traditional influence matrix method, the present invention adds optimization of initial cable force and correction of influence matrix, which effectively improves the iterative efficiency of cable force calculation based on influence matrix method;

[0042] 3. Compared with the traditional influence matrix method, the present invention has a wider application range and can be used for the calculation of symmetrical and asymmetrical arch rib inclined buckle hanging systems;

[0043] 4. The present invention realizes that the trend of the final cable force of the cable is similar to that of the initial cable force by setting large-range constraints and small-range constraints, and can effectively optimize the change value of the cable force and improve the uniformity of the cable force;

[0044] 5. The present invention can achieve that the tangential displacement of the arch rib meets the final accuracy in the cable release stage by only performing one tensioning adjustment on the arch rib cable, thereby improving the construction efficiency and avoiding the construction risks caused by adjusting the cable force in the subsequent construction stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the implementation methods of the present application, the drawings required for use in the implementation methods will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0046] Figure 1 It is a schematic diagram of the overall process according to an embodiment of the present application;

[0047] Figure 2 is a schematic diagram of tangential displacement influence matrix correction according to an embodiment of the present application;

[0048] Figure 3 is a simplified force diagram of an arch rib segment according to an embodiment of the present application;

[0049] Figure 4 It is a schematic diagram of iterative convergence of displacement of arch rib segments according to an embodiment of the present application. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the implementation methods of this application clearer, the technical solutions in the implementation methods of this application will be clearly and completely described below in conjunction with the drawings in the implementation methods of this application. Obviously, the described implementation methods are part of the implementation methods of this application, not all of the implementation methods. Based on the implementation methods in this application, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0051] The following describes in detail a method for calculating the force of a primary tensioned inclined cable based on an influence matrix method of the present invention through a specific embodiment. Figures 1 to 4 As shown, this example is a mid-through large-span steel box arch bridge with a basket handle. The total length of the main bridge is 612m, the clear span is 570m, the clear rise is 126.67m, and the clear rise-span ratio is 1 / 4.5. The arch rib is generally divided into 47 segments, and the arch rib is installed by cable hoisting + inclined buckle hanging method. The calculation of the G4-G23 and G4'-G23' buckle force adopts a one-time tensioned inclined buckle hanging cable force calculation method based on the influence matrix method described in this invention. The specific steps are as follows:

[0052] Step 1: Establish a Midascivil model of the complete construction stage of the arch rib, input 1KN cable force to each cable and run it;

[0053] Step 2: Extract the overall influence matrix of the cable-stayed buckle system structure, and consider the positive influence matrix of the arch rib tangential assembly;

[0054] Step 3: Simplify the calculation of the initial cable force T0 of each section of the arch rib:

[0055] T0=[2589,1194,1194,1036,1041,2308,1086,1118,2514,1026,1045,2365,1134,1179,2685,1269,1291,2987,1443,2086]

[0056] Input the Midas Vil model, calculate the arch rib displacement S0 in the cable-releasing stage, and solve for the difference △S between it and the target displacement X:

[0057] S0=[21,45,85,137,202,280,369,470,580,699,826,960,1099,1242,1386,1532,1676,1818,1958,2069]

[0058] ×

[0059]

[0060] Step 4: Combine the displacement difference and use Matlab to set large-scale constraints to solve the first correction cable force based on the correction matrix;

[0061] Constraints:

[0062] Objective function min:

[0063] Where: ΔT n Indicates the change value of the initial cable force at the nth iteration;

[0064] It represents the difference between the arch rib displacement in the cable-releasing stage calculated by Midas and the target displacement of the initial cable force of the nth iteration;

[0065] δ represents the variation range of adjacent cable forces.

[0066] Step 5: Input the first revised cable force into the Midascii model, calculate the arch rib displacement in the cable-releasing stage again to obtain the difference between it and the target displacement, and use Matlab to solve the second revised cable force in a large range again;

[0067] Step 6: When the displacement difference of the nth iteration reaches the initial accuracy, use Matlab to set small-range constraints to solve the n+1th corrected cable force based on the correction matrix;

[0068] Some results of steps 5 and 6 are shown in Tables 1 and 2.

[0069] Step 7: Input the (n+1)th corrected cable force into the Midascii il model and calculate the arch rib displacement and displacement difference in the cable-releasing stage again;

[0070] Step 8: Iterate gradually until the difference between the arch rib displacement in the cable-releasing stage and the target displacement meets the final accuracy. At this time, the corrected cable force is the primary tensioning force that meets the requirements.

[0071] The results of steps 7 to 8 are shown in Table 3

[0072] Step 9: Extract the influence matrix of the arch rib of the other half span and make corrections, input the cable force of step 8, repeat steps 6 to 8, and solve the cable force of the other half span.

[0073] The results of steps 8 to 9 are shown in Table 4

[0074] Table 1 Calculation of initial cable force for large range constraints Table 1

[0075]

[0076]

[0077] Table 2 Calculation of initial cable force for large range constraints Table 2

[0078]

[0079]

[0080] Table 3 Calculation table of initial cable force for small range constraints

[0081]

[0082]

[0083] Table 4 Final cable force after iteration

[0084]

[0085]

[0086] The above embodiments are only used to illustrate the specific embodiments of the present invention and are not limited thereto. For those skilled in the art, various similar deformations and changes can be made according to the concept of the present invention, and these deformations and changes should be regarded as the protection scope of the present invention.

Claims

1. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method, characterized in that: The following steps are involved: Step 1: Establish the Midascivil model of the complete construction stage of the arch rib, input the unit cable force and run it; Step 2: Extract the overall influence matrix of the cable-stayed buckle system structure, and consider the positive influence matrix of the arch rib tangential assembly; Step 3: Draft the initial cable force, input it into the Midascivil model, calculate the arch rib displacement during the cable release stage, and solve the difference between it and the target displacement; Step 4: Combine the displacement difference and use MATLAB to set large-scale constraints to solve the first correction cable force based on the correction matrix; Step 5: Input the first revised cable force into the Midascivil model, calculate the arch rib displacement in the cable-releasing stage again to find the difference between it and the target displacement, and use Matlab to solve the second revised cable force on a large scale again; Step 6: When the displacement difference of the nth iteration reaches the initial accuracy, use MATLAB to set small-range constraints to solve the n+1th corrected cable force based on the correction matrix; Step 7: Input the (n+1)th corrected cable force into the Midascivil model and calculate the arch rib displacement and displacement difference in the cable-releasing stage again; Step 8: Iterate gradually until the difference between the arch rib displacement in the cable-releasing stage and the target displacement meets the final accuracy. At this time, the corrected cable force is the primary cable tension that meets the requirements.

2. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the first step, the complete construction phase of the arch rib finite element analysis model includes arch rib installation, arch rib closure, cable release and arch completion.

3. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 2, characterized in that: The arch rib installation stage includes: arch rib segments and corresponding cables and arch rib cross bracing segments.

4. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the first step, a unit cable force of 1 kN is input into each cable.

5. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the second step, the influence matrix extracted in Midascivil is the influence matrix of the half-span arch rib structure in the closure stage in the DZ direction. This influence matrix only considers the influence of the displacement of the arch rib segments installed in each construction stage, that is, the previous triangular matrix m.

6. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the second step, since the influence matrix extracted in Midascivil does not take into account the tangential assembly displacement during the construction phase, that is, the displacement influence of the installed segment on the uninstalled segment is not considered, the geometric relationship can be used to obtain the influence value of the installed arch rib stage on the uninstalled segment, and then the influence matrix is ​​corrected: The influence matrix of the half-span arch rib structure at the closure stage in the DX and DZ directions was extracted using Midascivil.

7. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the third step, the initial cable force corresponding to each section of the arch rib is obtained by solving the force analysis of each independent arch rib segment, that is, the cable tension is solved by knowing the angle between the cable and the vertical direction and the gravity of the arch rib segment; The gravity G of each independent arch rib segment includes the sum of the gravity of the current arch rib segment and the gravity of the corresponding cross brace. The cables are arranged symmetrically on the default surface, and only the displacement of the control points of the half-span arch rib is compared. The initial cable force of the cables is input symmetrically into the model. The following steps until the eighth step are all carried out in this way.

8. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the fourth step, the result solved by matlab is the change value △T of the cable force, that is, after the correction matrix m is known and the difference △S between the initial cable force displacement and the target displacement in the third step is calculated by the following formula, and the change value is added to the initial value as the initial cable force for subsequent finite element calculation; matlab solves on a large scale to limit the change value of the adjacent cable force to 10% to 15% of the initial cable force of the cable.

9. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: In the sixth step, MATLAB solves in a small range to limit the change value of the adjacent cable forces to 1% to 5% of the initial cable forces.

10. A method for calculating the force of a primary tensioned inclined cable based on an influence matrix method as claimed in claim 1, characterized in that: The first step to the eighth step are for the case where the arch rib buckle cable surfaces are arranged symmetrically. When the buckle cable surfaces at both ends of one side of the arch rib are arranged in different forms, the following steps need to be continued: Step 9: Extract the influence matrix of the arch rib of the other half span and make corrections, input the cable force of step 8, repeat steps 6 to 8, and solve the cable force of the other half span; In the ninth step, the inputted cable force of the eighth step is still the symmetrical cable force; In the ninth step, steps 6 to 8 are repeated to solve the cable forces of the other half-span, and only the cable forces of the half-span that have not converged are iteratively calculated, that is, the cable forces of the half-span that have been iteratively satisfied in steps 1 to 8 remain unchanged.

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