A force calculation method for one-time tensioning inclined cable and hanging cable based on influence matrix method

Abstract

The present application relates to the field of bridge construction technology, disclose a kind of once tensioning cable-stayed buckle hanging cable force calculation method based on influence matrix method, comprising: establishing the Midascivil model of arch rib complete construction stage;Extract the overall influence matrix of cable-stayed buckle hanging system structure;Draft initial cable force;Solve the first correction cable force based on correction matrix;Solve the second correction cable force;Solve the n+1 correction cable force;Calculate the arch rib displacement and displacement difference value in slack cable stage;Iterate gradually until the arch rib displacement and target displacement difference value in slack cable stage meet final accuracy.The present application effectively improves the calculation speed and accuracy by solving the other half-span buckle cable force;Based on influence matrix method, the optimization of initial cable force and the correction of influence matrix are increased, which effectively improves the calculation iteration efficiency;Improve the uniformity of buckle cable force;Wide range of application, can be used for symmetric, asymmetric arch rib cable-stayed buckle hanging system calculation.

Description

Technical Field

[0001] This application relates to the field of bridge construction technology, and more specifically, to a method for calculating the tension of a single-tensioning cable-stayed cable based on the influence matrix method. Background Technology

[0002] In modern bridge engineering, arch bridges, with their graceful curves and unique structural forms, have become an important component of urban landscapes and transportation infrastructure. Especially for large bridges spanning wide rivers or deep valleys, arch bridge structures are highly favored due to their excellent load-bearing capacity and economic efficiency. In recent years, the cable-stayed method has been widely applied in the construction of long-span arch bridges. This construction technique uses cables to fasten arch rib segments, utilizing tension to balance the bending moment of the arch ribs, thus achieving structural stability and shape control. Therefore, determining the cable force during construction has a significant impact on the safety of arch rib construction and the final arch shape. Traditional cable force calculation methods, such as the zero-displacement method, zero-bending-moment method, positive-installation iterative method, and fixed-length cable-stayed method, while meeting engineering requirements to some extent, each have limitations. For example, they require multiple adjustments during construction, the calculation process is complex, the overall calculation efficiency is low, and they are difficult to meet the requirements of high-precision construction.

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

[0004] This invention aims to solve the problems existing in the above-mentioned different methods in the construction of cable-stayed arch bridges, and provides a method for calculating the cable force of cable-stayed arch bridges under single tensioning based on the influence matrix method.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

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

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

[0008] Step 3: Determine the initial cable force, input it into the Midascivil model, calculate the arch rib displacement during the cable loosening stage, and solve for the difference between the displacement and the target displacement.

[0009] Step 4: Using MATLAB to set up large-scale constraints based on the displacement difference, solve for the first corrected cable force based on the correction matrix;

[0010] Step 5: Input the first corrected cable force into the Midascivil model, calculate the arch rib displacement during the cable loosening stage again to solve for the difference between it and the target displacement, and then use MATLAB to solve the second corrected cable force over a large range.

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

[0012] Step 7: Input the (n+1)th corrected cable force into the Midascivil model and recalculate the arch rib displacement and displacement difference during the cable loosening stage.

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

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

[0015] In the first step, each sling is subjected to a unit force of 1 kN.

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

[0017]

[0018] In the second step, the influence matrix extracted from Midascivil does not consider the tangential assembly displacement during the construction phase, i.e., it does not consider the displacement influence of installed segments on uninstalled segments. The influence value of the installed arch rib stage on the uninstalled segments can be obtained from the geometric relationships, and then the influence matrix can be corrected:

[0019] The influence matrix of the half-span arch rib structure during the closure stage in the DX and DZ directions was extracted using Midascivil, as follows: Figure 1 Geometric analysis of m11 yields the following relationship:

[0020]

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

[0022]

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

[0024]

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

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

[0027] In the third step, the cable faces are arranged symmetrically by default. Only the displacement of the control point of the half-span arch rib is compared. The initial cable force of the cable is symmetrically input into the model. The following steps up to the eighth step are all carried out in this way.

[0028] In the fourth step, the result obtained by MATLAB is the change value of the cable force ΔT. That is, after knowing the correction matrix m and the difference between the initial cable force displacement and the target displacement ΔS in the third step, the change value of the cable force is solved by the following formula. 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 the problem by limiting the variation of adjacent cable tension to 10% to 15% of the initial cable tension.

[0031] The reason why the displacement difference is not zero in the fifth step is: 1. The limitation of the change value of the cable force; 2. The influence matrix is ​​the influence matrix before the maximum cable loosening, and the influence of the cable loosening construction stage on each control point is not considered; 3. The correction matrix m is not the actual influence matrix calculated by finite element method. It only considers the influence of tangential splicing and cannot consider the dynamic structural stiffness after deformation in each construction stage under different initial cable forces.

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

[0033] In the sixth step, the MATLAB solution is limited to a range of 1% to 5% of the initial cable force variation between adjacent cable tensions.

[0034] Steps four through eight are the process of dynamically correcting the cable force. Essentially, it is based on the dynamic adjustment of the initial cable force to fit the target line shape of the arch rib. Ultimately, the difference between the arch rib displacement and the target displacement in the loosened state can be achieved by tensioning and diagonally pulling the cable force once, which satisfies the final accuracy.

[0035] Steps one through eight describe the symmetrical arrangement of the cable faces of the arch rib. When the cable face arrangement at both ends of one side of the arch rib is different, the following steps need to be completed:

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

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

[0038] In the ninth step, steps six through eight are repeated. When solving for the cable force of the other half span, only the cable force of the half span that has not converged is iterated. That is, the cable force of the half span that has met the requirements in steps one through eight remains unchanged.

[0039] According to the embodiment of this application, a method for calculating the tension of a single-tensioning cable-stayed cable based on the influence matrix method has the following advantages:

[0040] 1. This invention optimizes and adjusts the initial cable force of the cable-stayed cable based on the influence matrix method, which effectively improves the calculation speed and accuracy compared to traditional cable adjustment methods;

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

[0042] 3. Compared with the traditional influence matrix method, the present invention has a wider range of applications and can be used for calculations of symmetrical and asymmetrical arch rib cable-stayed systems;

[0043] 4. This invention achieves a similar trend between the final cable force and the initial cable force by setting large-scale constraints and small-scale constraints, and can effectively optimize the change value of cable force and improve the uniformity of cable force.

[0044] 5. This invention achieves the final accuracy of the tangential displacement of the arch rib during the slack cable stage by only adjusting the tension of the arch rib cable once, thereby improving construction efficiency and avoiding the construction risks caused by adjusting the cable force in subsequent construction stages. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

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

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

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

[0049] Figure 4 This is a schematic diagram of the displacement iteration convergence of the arch rib segment according to an embodiment of this application. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0051] The following describes in detail, through specific embodiments, a method for calculating the force of a single-tensioning cable-stayed cable based on the influence matrix method, as described in the present invention. Figures 1 to 4 As shown, this example is a mid-span, long-span, basket-type steel box girder arch bridge. The total length of the main bridge is 612m, the clear span is 570m, the clear rise is 126.67m, and the clear rise-to-span ratio is 1 / 4.5. The arch ribs are divided into 47 segments, and the arch ribs are installed using a cable hoisting + inclined cable-stayed method. The calculation of the cable force for G4-G23 and G4'-G23' uses a single-tensioning inclined cable-stayed cable force calculation method based on the influence matrix method involved 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 a 1KN cable force into each cable and run it;

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

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

[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 Midascivil model, calculate the arch rib displacement S0 during the cable loosening stage, and solve for the difference ΔS 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: Using the displacement difference and MATLAB to set large-scale constraints, solve for the first corrected cable force based on the correction matrix;

[0061] Constraints:

[0062] objective function min:

[0063] Where: ΔT n This represents the change in the initial cable force during the nth iteration;

[0064] This represents the difference between the initial cable force in the nth iteration and the arch rib displacement during the cable loosening stage, calculated using Midas, and the target displacement.

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

[0066] Step 5: Input the first corrected cable force into the Midascivil model, calculate the arch rib displacement in the loosening stage again to solve for the difference between it and the target displacement, and use MATLAB to solve for the second corrected cable force over a large range.

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

[0068] The 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 Midasciivil model, and recalculate the arch rib displacement and displacement difference during the cable loosening stage;

[0070] Step 8: Iterate step by step until the difference between the arch rib displacement and the target displacement in the slack cable stage meets the final accuracy. At this time, the corrected cable force is the first tension cable force that meets the requirements.

[0071] The results of steps seven and eight are shown in Table 3.

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

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

[0074] Table 1 Calculation of Initial Cable Force for Large-Scale Constraints

[0075]

[0076]

[0077] Table 2 Calculation of Initial Cable Force for Large-Scale Constraints

[0078]

[0079]

[0080] Table 3 Calculation of Initial Cable Force for Small-Scale Constraints

[0081]

[0082]

[0083] Table 4 Final Cable Force During Iteration

[0084]

[0085]

[0086] The above embodiments are only used to illustrate specific implementations of the present invention and are not limited thereto. For those skilled in the art, various similar modifications and transformations can be made based on the concept of the present invention, and these modifications and transformations should all be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the force of a single-tensioned cable-stayed cable based on the influence matrix method, characterized in that, Includes the following steps: Step 1: Establish a Midascivil model of the complete construction phase of the arch rib, input the unit cable force and run it; Step 2: Extract the overall influence matrix of the inclined cable-stayed system structure, and consider the positive influence matrix of the tangential splicing of the arch ribs; Step 3: Determine the initial cable force, input it into the Midascivil model, calculate the arch rib displacement during the cable loosening stage, and solve for the difference between the displacement and the target displacement. Step 4: Using MATLAB to set up large-scale constraints based on the displacement difference, solve for the first corrected cable force based on the correction matrix; Step 5: Input the first corrected cable force into the Midascivil model, calculate the arch rib displacement during the cable loosening stage again to solve for the difference between it and the target displacement, and then use MATLAB to solve the second corrected cable force over a large range. Step 6: When the displacement difference reaches the initial accuracy after the nth iteration, use MATLAB to set small-range constraints to solve the (n+1)th corrected cable force based on the correction matrix; Step 7: Input the (n+1)th corrected cable force into the Midascivil model and recalculate the arch rib displacement and displacement difference during the cable loosening stage. Step 8: Iterate step by step until the difference between the arch rib displacement and the target displacement in the slack cable stage meets the final accuracy. At this time, the corrected cable force is the first tension cable force that meets the requirements. In the third step, the initial cable force of the buckle corresponding to each arch rib segment is obtained by force analysis of each independent arch rib segment, that is, the buckle tension is solved by knowing the angle between the buckle and the vertical direction and the weight 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; by default, the cable planes of the ties are arranged symmetrically, and only the displacement of the control points of the half-span arch rib is compared. The initial cable force of the ties is symmetrically input into the model. The following steps up to the eighth step are all carried out in this way. Steps one through eight describe the symmetrical arrangement of the cable faces of the arch rib. When the cable face arrangements at both ends of one side of the arch rib are different, the following steps need to be completed: Step 9: Extract and correct the influence matrix of the arch rib in the other half span, input the cable force in step 8, and repeat steps 6 to 8 to solve for the cable force of the other half span. In the ninth step, the cable force input in the eighth step is still a symmetrical cable force; In the ninth step, steps six through eight are repeated. When solving for the cable force of the other half span, only the cable force of the half span that has not converged is iterated. That is, the cable force of the half span that has met the requirements in steps one through eight remains unchanged.

2. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described in claim 1, characterized in that, In the first step, the complete construction phase of the finite element analysis model of the arch rib includes arch rib installation, arch rib closure, cable loosening, and arch formation.

3. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described in claim 2, characterized in that, The arch rib installation stage includes: arch rib segments and corresponding fasteners and arch rib cross bracing segments.

4. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described in claim 1, characterized in that, In the first step, each sling is subjected to a unit force of 1 kN.

5. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described 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 installed arch rib segments in each construction stage, i.e., the previous triangular matrix m.

6. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described in claim 1, characterized in that, In the second step, since the influence matrix extracted from Midascivil does not consider the tangential assembly displacement during the construction stage, that is, it does not consider the displacement influence of installed segments on uninstalled segments, the influence value of the installed arch rib stage on the uninstalled segments can be obtained from the geometric relationship, and then the influence matrix is ​​corrected: The influence matrix of the semi-span arch rib structure during the closure stage in the DX and DZ directions was extracted using Midascivil.

7. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described in claim 1, characterized in that, In the fourth step, the result obtained by MATLAB is the change value of the cable force ΔT. That is, after knowing the correction matrix m and the difference between the initial cable force displacement and the target displacement ΔS in the third step, the change value of the cable force is solved by the following formula. The change value is added to the initial value as the initial cable force for subsequent finite element calculations. The MATLAB solution is to limit the change value of the cable force of adjacent cable to 10% to 15% of the initial cable force of the cable.

8. The method for calculating the tension of a single-tensioned cable-stayed cable based on the influence matrix method as described in claim 1, characterized in that, In the sixth step, the MATLAB solution is limited to a range of 1% to 5% of the initial cable force variation between adjacent cable tensions.

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