Internal force and linear double-control-based arch bridge cable force algorithm and storage medium

Abstract

The invention belongs to the technical field of bridge construction, and particularly discloses an internal force and linear double-control-based arch bridge cable force algorithm and a storage medium, and the algorithm comprises the steps: building a primary falling frame arching model, and obtaining a bending moment target value which is a bare arch bending moment value under the dead load effect; building an arch rib finite element model, and obtaining a cable force-bending moment influence matrix and a constant vector; setting a cable force calculation algorithm model based on a bending moment target value, a cable force-bending moment influence matrix and the constant vector; the initial tensioning force of the buckle cable is solved based on a cable force calculation algorithm model; and inputting the initial tensioning force of the buckle cable into the arch rib finite element model, and calculating to obtain the bending moment and displacement of the arch rib. According to the method, after the influence matrix and the constant vector are extracted from the finite element model, the whole cable adjustment process can be independently completed by the cable force calculation algorithm model, interactive iteration with finite element software is not needed, the cable adjustment process is greatly simplified on the premise that the cable adjustment precision is met, and the cable adjustment efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge construction, and in particular relates to an arch bridge cable force algorithm and a storage medium based on dual control of internal force and linear shape. Background Art

[0002] The cable-stayed, buckled-and-hung method is a common construction method for long-span arch bridges. During the cantilever assembly of the arch ribs, adjusting the cable tension effectively controls the arch rib shape and internal forces. Therefore, determining the appropriate cable tension is a crucial issue in the construction of such arch bridges.

[0003] In related technologies, the calculation method based on the influence matrix method and the difference iteration method, with the arch rib displacement as the target, requires the use of finite element software and cable adjustment program to continuously interact and iterate, and the calculation process is cumbersome and time-consuming. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, the present invention proposes an arch bridge cable tension algorithm and storage medium based on dual control of internal force and linear shape.

[0005] In a first aspect, an algorithm for the tension of arch bridge cables based on dual control of internal force and linear shape is provided, comprising: establishing a one-time arch formation model to obtain a target bending moment value, wherein the target bending moment value is the bending moment value of the bare arch under a constant load; establishing an arch rib finite element model to obtain a cable force-bending moment influence matrix and a constant vector; setting a cable force calculation algorithm model based on the target bending moment value, the cable force-bending moment influence matrix and the constant vector; solving the initial tension of the cables based on the cable force calculation algorithm model; inputting the initial tension of the cables into the arch rib finite element model to calculate the arch rib bending moment and displacement.

[0006] In an optional embodiment, the arch rib finite element model includes a finite element model of the arch rib in the maximum cantilever state, a finite element model of the arch rib in the closed state, and a finite element model of the arch rib in the construction stage. Obtaining the cable force-bending moment influence matrix and the constant vector specifically includes:

[0007] Establishing a finite element model of the arch rib in a maximum cantilever state to obtain a first influence matrix, wherein the first influence matrix is an influence matrix of a unit change in the internal force of the cable on the arch rib bending moment when the cable is tensioned in the maximum cantilever state;

[0008] Establishing a finite element model of the arch rib in a closed state to obtain a second influence matrix, wherein the second influence matrix is an influence matrix of a unit change in the internal force of the cable on the arch rib bending moment when the cable is removed in the closed state;

[0009] Establishing a finite element model of the arch rib construction stage to obtain the constant vector, wherein the constant vector includes the cable dead load internal force and the arch rib dead load bending moment, wherein the cable dead load internal force is the cable dead load internal force caused by the dead load in the maximum cantilever state, and the arch rib dead load bending moment is the bending moment caused by the dead load in the arch rib state with the cables loosened;

[0010] The cable force-bending moment influence matrix includes the first influence matrix and the second influence matrix.

[0011] In an optional embodiment, the cable force calculation algorithm model is set based on the bending moment target value, the cable force-bending moment influence matrix and the constant vector, specifically including: establishing an equilibrium equation of the cable tensioning internal force and the arch rib bending moment based on the cable force-bending moment influence matrix and the arch rib constant load bending moment; establishing a constraint function based on the bending moment target value and the cable constant load internal force; and setting the cable force calculation algorithm model based on the equilibrium equation and the constraint function.

[0012] In an optional embodiment, the calculation formula of the equilibrium equation is as follows: Where, T m is the cable tension internal force, C1 is the first influence matrix; C2 is the second influence matrix, m mg is the arch rib dead load bending moment, m m is the arch rib bending moment, where C1, C2 and m are equal when the structural stiffness and construction process remain unchanged. mg All are fixed values.

[0013] In an optional embodiment, the constraint function includes an arch rib bending moment constraint function, and the calculation formula is as follows: Where, is the target value of the bending moment; ε m is the allowable error of the bending moment at point m of the arch rib;

[0014] The constraint function also includes a cable internal force constraint function, and the calculation formula is as follows:

[0015] Where, T mg is the internal force of the cable No. m under the maximum cantilever state, t lm is the lower limit of the internal force of the mth cable in the maximum cantilever state, t um is the upper limit of the internal force of the mth cable in the maximum cantilever state, where T mg Is a fixed value.

[0016] In an optional embodiment, the initial tensioning force of the cable is solved based on the cable force calculation algorithm model, specifically including: solving the cable tensioning internal force based on the cable force calculation algorithm model, the cable tensioning internal force is the cable internal force caused by the cable tensioning in the maximum cantilever state; adding the cable tensioning internal force and the cable constant load internal force to obtain the comprehensive internal force of the cable; and solving the initial tensioning force of the cable based on the comprehensive internal force of the cable.

[0017] In an optional embodiment, the arch bridge cable tension algorithm based on dual control of internal force and linear shape further includes: solving the stress-free cable length of the cable based on the cable tension calculation algorithm model.

[0018] In an optional embodiment, an objective function is set based on the bending moment target value, and the objective function minimizes the sum of squares of the integrated internal forces of the cable, as shown in the following formula: min:f(T)=∑(T i +T ig ) 2 Where, T i is the cable tensioning internal force, T ig is the internal force of the cable dead load.

[0019] In an optional embodiment, an objective function is set based on the bending moment target value, and the objective function is to minimize the sum of squares of the differences between the actual arch rib bending moment and the bending moment target value, as shown in the following formula:

[0020]

[0021] Where, T i is the cable tension internal force, C1 is the first influence matrix; C2 is the second influence matrix, m ig is the arch rib dead load bending moment, is the target value of the bending moment.

[0022] In a second aspect, a storage medium is also provided, which stores a computer program, and when the computer program is executed by a processor, it implements any one of the arch bridge cable tension algorithms based on dual control of internal force and linear shape.

[0023] The beneficial effects of the present invention are:

[0024] 1. By extracting the influence matrix from the finite element model, the entire cable adjustment process can be completed independently by the cable force calculation algorithm model, without the need for interactive iteration with the finite element software. This greatly simplifies the cable adjustment process and improves the cable adjustment efficiency by more than 2 times.

[0025] 2. By using the actual structural stiffness and influence matrix in the calculation process, and establishing the objective function and constraint function according to the stress state of the arch rib during the actual construction process, the calculation results are true and reliable.

[0026] 3. The internal force and linear shape of the arch ribs in the cable-loose arch state can meet the target requirements, realizing dual control of internal force and linear shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Other features, objects and advantages of the present application will become more apparent upon reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0028] Figure 1 A flowchart of an algorithm for arch bridge cable tension based on dual control of internal force and linear shape provided by one embodiment of the present invention;

[0029] Figure 2a A schematic diagram of the cable-stayed cable construction on the south bank of the bridge, based on an algorithm for arch bridge cable tension based on dual control of internal force and linear shape, provided by one embodiment of the present invention;

[0030] Figure 2b A schematic diagram of the cable-stayed cable-hanging construction on the north bank of the bridge, based on an algorithm for arch bridge cable tension based on dual control of internal force and linear shape, provided by one embodiment of the present invention;

[0031] Figure 3 An arch rib finite element model of an arch bridge cable tension algorithm based on dual control of internal force and linear shape provided in one embodiment of the present invention;

[0032] Figure 4 The arch rib bending moment distribution diagram of the arch bridge cable force calculation based on the dual control of internal force and linear shape provided by one embodiment of the present invention;

[0033] Figure 5 This is another embodiment of the present invention providing an arch rib displacement distribution diagram of an arch bridge cable tension calculation based on dual control of internal force and linear shape. DETAILED DESCRIPTION

[0034] Based on the influence matrix method and the difference iteration method, the calculation process of the arch rib displacement is as follows:

[0035] 1. Establish a finite element model of the arch rib cable-stayed buckle and extract the "cable force-displacement" influence matrix.

[0036] 2. Using the "cable force-displacement" influence matrix, set the objective function (arch rib displacement) and constraint function (cable force value, adjacent cable force difference, etc.), and write the cable adjustment program (module).

[0037] 3. Set the initial cable force and input it into the finite element model to obtain the arch rib displacement, and calculate the difference between this displacement and the target displacement.

[0038] 4. Based on the displacement difference in 3, use the cable adjustment program to calculate the cable force difference, and correct the initial cable force based on the cable force difference.

[0039] 5. Input the corrected initial cable force into the finite element model to obtain a new set of arch rib displacements, and calculate the difference between the new arch rib displacements and the target displacements.

[0040] 6. Repeat steps 4 and 5. After several iterations of difference, a set of initial cable forces is finally obtained, which can make the arch rib displacement meet the target requirements.

[0041] This method has the following three flaws:

[0042] 1. The influence coefficients in the original "cable force-displacement" influence matrix fail to account for the effects of tangential assembly, necessitating a correction to the influence matrix. Because the correction is approximate, for small-span arch bridges with a small number of cables, the calculation results gradually converge after several iterations. However, for large-span arch bridges with a large number of cables, the calculation may converge first and then diverge, making it difficult to achieve high accuracy for the arch rib displacement.

[0043] 2. It requires the use of finite element software and cable adjustment programs for continuous iteration, making the calculation process cumbersome and time-consuming;

[0044] 3. Calculations using displacement as the target state cannot guarantee that the internal forces of the arch ribs meet the requirements. (Under normal circumstances, the arch ribs' bearing capacity during cantilever assembly meets the requirements. However, this does not take into account the loads during bridge operation, such as the main beam dead load and vehicle live loads. Therefore, to ensure that the arch ribs' bearing capacity during operation still meets the requirements, the internal forces of the arch ribs in the cable-released arch state after cantilever assembly are within a certain range, leaving sufficient margin for subsequent loads. Therefore, the internal forces of the arch ribs in the target state are much smaller than the arch rib bearing capacity.)

[0045] This paper proposes an arch bridge cable tension algorithm based on dual control of internal forces and linear shape, which can solve the above problems. The algorithm is based on the influence matrix method and takes the internal forces of the arch rib as the target, and can meet the following requirements:

[0046] 1. No simplification or assumptions are required for the structure. The actual structural stiffness and influence matrix are used in the calculation process. The objective function and constraint function are established according to the stress state of the arch rib during the actual construction process. The calculation results are true and reliable.

[0047] 2. After extracting the influence matrix and constant vector from the finite element model, the entire tuning process can be completed independently by the tuning program without the need for interactive iteration with the finite element software (existing methods usually require 6 to 8 interactive iterations), greatly simplifying the tuning process and improving the tuning efficiency by more than 2 times.

[0048] 3. The internal forces and linear shapes of the arch ribs in the cable-slack arch state can be made to meet target requirements, i.e., dual control of internal forces and linear shapes. (According to the stress-free state theory, when the stress-free state, materials, boundaries, and external loads of a structure are the same, its stress state and displacement are also the same.)

[0049] The following is combined with Figures 1 to 5 The present invention is further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the relevant invention and are not intended to limit the invention. It should also be noted that for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0050] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0051] Please refer to Figure 1 , a flowchart of an arch bridge cable tension algorithm based on dual control of internal force and linear shape is provided for an embodiment of the present invention. The arch bridge cable tension algorithm based on dual control of internal force and linear shape includes the following steps:

[0052] Step S101: Establish a one-time arch-forming model and obtain a target bending moment value. The target bending moment value is the bending moment value of the bare arch under a constant load, that is, the bending moment value of the arch-forming state with the cables loosened under a constant load after the arch rib cantilever is assembled.

[0053] Step S102: Establish an arch rib finite element model and obtain the cable force-bending moment influence matrix and constant vector.

[0054] Step S103: Setting a cable force calculation algorithm model based on the bending moment target value, the cable force-bending moment influence matrix and the constant vector.

[0055] Step S104: Calculate the initial tension of the cable based on the cable force calculation algorithm model.

[0056] Step S105: inputting the initial tensioning force of the cable into the arch rib finite element model to calculate the arch rib bending moment and displacement.

[0057] Based on this embodiment, a single-stage arching model is established during the construction of a cable-stayed, buckled arch bridge. This model simulates the mechanical behavior of the arch bridge after construction is complete, when temporary support structures, such as brackets or cables, are removed and the final arch state is reached. This single-stage arching model can be used to calculate the bending moment at a key point on the arch rib under a constant load, such as the deadweight of the arch rib. This bending moment value is called the target bending moment value and reflects the stress state at the key location of the arch bridge in its ideal arched state.

[0058] A finite element model based on the arch rib was established. Through finite element analysis, the constant vector and the relationship between the cable forces and the arch rib bending moment, known as the cable force-bending moment influence matrix, were calculated. This matrix describes the influence of each cable tension on the arch rib bending moment. The constant vectors are the arch rib bending moment in the untied-cable arching state under dead load and the internal forces in the cables in the maximum cantilever state.

[0059] A cable force calculation algorithm model is established based on the acquired bending moment target value, the cable force-bending moment influence matrix, and the constant vector. This model allows the calculation of the initial cable tension. By adjusting this initial tension, the actual bending moment of the arch rib after construction is as close as possible to the target bending moment value. This model is implemented through program module configuration. Accurately calculating the initial cable tension ensures that the arch rib's stress state remains within a controllable range during construction, preventing structural deformation or damage caused by excessive or insufficient cable tension.

[0060] After determining the initial cable tension, this known condition is input into the previously established finite element model for the arch rib construction phase. Finite element analysis is used to calculate the actual bending moment distribution of the arch rib in the arched state, under the action of this initial cable tension. This bending moment distribution reflects the actual stress state of the arch rib after construction, taking into account the cable tension. The accuracy of the cable force calculation algorithm model can be verified by comparing the calculated arch rib bending moment with the target bending moment. If there is a significant deviation between the actual bending moment and the target bending moment, the cable force calculation algorithm model needs to be adjusted and the initial cable tension must be recalculated until the actual arch rib bending moment is roughly consistent with the target bending moment. This process achieves dual control of internal forces and line shape during arch bridge construction, ensuring the accuracy and safety of arch bridge construction.

[0061] Through the above steps, the cable tension algorithm for arch bridges based on dual control of internal force and linear shape can effectively guide the tensioning operation of the cables during arch bridge construction, ensuring the construction quality and structural safety of the arch bridge.

[0062] Furthermore, based on step S102, the arch rib finite element model includes a finite element model of the arch rib in the maximum cantilever state, a finite element model of the arch rib in the closed state, and a finite element model of the arch rib in the construction stage, and obtaining a cable force-bending moment influence matrix and a constant vector specifically includes the following steps:

[0063] Step S1021: Establish a finite element model of the arch rib in the maximum cantilever state and obtain a first influence matrix, which is the influence matrix of the unit change in the internal force of the cable on the arch rib bending moment when the cable is tensioned in the maximum cantilever state.

[0064] Step S1022: establishing a finite element model of the arch rib in the closed state, and obtaining a second influence matrix, which is an influence matrix of a unit change in the internal force of the cable on the arch rib bending moment when the cable is removed in the closed state;

[0065] Step S1023: Establish a finite element model for the arch rib construction phase and obtain constant vectors. The constant vectors include the cable dead load internal force and the arch rib dead load bending moment. The cable dead load internal force is the cable dead load internal force caused by the dead load in the maximum cantilever state, and the arch rib dead load bending moment is the bending moment caused by the dead load in the arch rib state.

[0066] The cable force-bending moment influence matrix includes a first influence matrix and a second influence matrix.

[0067] In this embodiment, the maximum cantilever state refers to the portion of the arch bridge construction process where the arch ribs are not yet fully closed and are supported only by the cables. At this point, the stress state of the arch ribs differs significantly from the final arch state, necessitating a separate finite element model for analysis. The influence matrix obtained from the maximum cantilever state finite element model is the first influence matrix, which describes the effect of a unit change in internal force on the arch rib bending moment when the cables are tensioned in the maximum cantilever state.

[0068] The closed state refers to the state during arch bridge construction when the arch ribs are fully closed but the cables have not yet been removed. At this point, the arch ribs are stressed close to their final arched state, but are still constrained by the cables. The influence matrix obtained from the closed-state finite element model is the second influence matrix, which describes the effect of a unit change in internal force on the arch rib bending moment when the cables are removed in the closed state. By combining these two influence matrices, the effect of the cable tensioning internal force on the arch rib bending moment can be fully described.

[0069] Through the above steps, the cable force-bending moment influence matrix can be obtained from the arch rib finite element model.

[0070] The finite element model of the arch rib construction phase allows for the determination of the dead load internal forces and bending moments of the arch ribs. In the maximum cantilever state, the arch ribs have not yet fully closed, and the cables bear the weight of the arch ribs and part of the construction load. Finite element analysis allows for the calculation of the internal forces of the cables under dead loads, i.e., the dead load internal forces of the cables. This reflects the initial stress state generated by dead loads such as dead weight during construction. In the arch state, after the arch bridge is constructed, the cables are removed and the arch ribs form their final arch structure. At this point, the arch ribs are subjected to dead loads, such as dead weight, and the finite element model is used to calculate the dead load bending moments at key points on the arch ribs.

[0071] Based on the dead-load internal forces and arch rib bending moments obtained from the finite element model during the arch rib construction phase, combined with the target bending moment value and the cable force-bending moment influence matrix, a cable force calculation algorithm model can be accurately set up. This can effectively guide the tensioning operation of the cables during arch bridge construction, ensuring that the internal forces and linear shapes of the arch ribs are always in a controllable state during construction, thereby improving the quality and safety of arch bridge construction.

[0072] Furthermore, step S103 sets a cable force calculation algorithm model based on the bending moment target value, the cable force-bending moment influence matrix, and the constant vector, specifically including the following steps:

[0073] Step S1031: Establishing the equilibrium equation of the cable tensioning internal force and the arch rib bending moment based on the cable force-bending moment influence matrix and the arch rib dead load bending moment.

[0074] Step S1032: Establish a constraint function based on the bending moment target value and the internal force of the cable dead load.

[0075] Step S1033: Setting a cable force calculation algorithm model based on the equilibrium equation and constraint function.

[0076] The cable force-bending moment influence matrix describes the quantitative impact of each cable tension on the arch rib bending moment, reflecting the incremental bending moment caused by a unit cable tension at key points on the arch rib. The equilibrium equation is a mathematical relationship between the cable tension internal force and the arch rib bending moment, indicating that the actual arch rib bending moment is composed of the dead load bending moment and the incremental bending moment caused by the cable tension. By establishing the equilibrium equation, the influence of the cable tension on the arch rib bending moment can be quantitatively described. Constraint functions are used to limit the range of cable tension values, ensuring the operability of the calculation results in actual construction, and ensuring the rationality of the cable tension and the accuracy of the arch rib bending moment. The goal of the cable force calculation algorithm model is to make the actual arch rib bending moment as close as possible to the target bending moment value.

[0077] This model uses mathematical optimization methods to comprehensively consider the impact of cable tension on arch rib bending moment, as well as the actual constraints during construction. By solving this model, the optimal cable tension can be obtained, thereby achieving precise control of the arch rib bending moment.

[0078] Furthermore, the influence matrix method uses the structural influence matrix to describe the effect of changes in the control vector on the response vector. For the calculation of cable-stayed arch bridges during construction, the "cable force-bending moment" influence matrix from the finite element model is extracted to establish an equilibrium equation for the internal force of the cantilever cable and the bending moment of the arch rib when the cables are loose and arched. The equation for this equilibrium equation is as follows:

[0079]

[0080] Where, T m is the cable tensioning internal force, which does not include the cable tensioning internal force caused by dead loads such as the arch rib self-weight, and T m Can be negative. C1 is the first influence matrix; C2 is the second influence matrix, m mg is the arch rib dead load bending moment, m m is the arch rib bending moment, is the bending moment at the mth point of the arch rib under the combined action of dead load and cable force in the state of arch formation with loose cables. Among them, when the structural stiffness and construction process remain unchanged, C1, C2 and m mg All are fixed values.

[0081] The constraint function includes the arch rib bending moment constraint function, and the calculation formula is as follows:

[0082]

[0083] Where, is the target value of the bending moment; ε m is the allowable error of the bending moment at point m of the arch rib.

[0084] The constraint function also includes the cable internal force constraint function, and the calculation formula is as follows:

[0085] Where, T mg is the internal force of the cable No. m under the maximum cantilever state, t lm is the lower limit of the internal force of the mth cable in the maximum cantilever state, t um is the upper limit of the internal force of the mth cable in the maximum cantilever state, where T mg Is a fixed value.

[0086] In step S104, the initial tension of the cable is calculated based on the cable force calculation algorithm model, which specifically includes the following steps:

[0087] Step S1041: solving the cable tensioning internal force based on the cable force calculation algorithm model, where the cable tensioning internal force is the cable internal force caused by the cable tensioning in the maximum cantilever state.

[0088] Step S1042: Add the tensioning internal force of the cable and the dead load internal force of the cable to obtain the comprehensive internal force of the cable.

[0089] Step S1043: Calculate the initial tension of the cable based on the comprehensive internal force of the cable.

[0090] Among them, the internal force of cable tensioning refers to the internal stress of the cable caused by cable tensioning when the cable is in the maximum cantilever state during the construction of the arch bridge, that is, the part where the arch ribs have not been fully closed and are only supported by the cables.

[0091] In this embodiment, a cable force calculation algorithm model is used to calculate the tensioning internal forces of the cables in the maximum cantilever state. At this point, the arch ribs of the arch bridge have not yet fully closed and rely solely on the cables for support, placing the cables in a critical stress state. In this state, the tensioning internal forces of the cables are the internal stresses caused by the cable tensioning operation. This internal force reflects the stress distribution within the cables during the tensioning process. The deadweight of the cables generates a certain internal force along their length, which acts together with the tensioning internal force on the cables. By adding these two forces, the comprehensive internal force of the cables can be obtained. The comprehensive internal force represents the total internal force experienced by the cables during actual construction and provides a more comprehensive reflection of the stresses on the cables. The initial tensioning force is the tensioning force required to be applied to the cables during the initial construction phase. It directly affects the stress state and stability of the cables during subsequent construction. By accurately calculating the initial tensioning force, it is possible to ensure that the cables can safely and stably support the arch ribs in the maximum cantilever state, thereby effectively ensuring the smooth progress of arch bridge construction.

[0092] Initially, a set of cable tensioning internal forces is assumed. The actual bending moment of the arch rib is calculated using equilibrium equations. The cable tensioning force is then adjusted based on the objective function and constraint function, gradually reducing the objective function until the constraints are met and the error is within the allowable range. The resulting cable tensioning force is a crucial parameter in arch bridge construction. Accurately calculating the cable tensioning force effectively controls the internal forces and alignment of the arch rib, ensuring the quality and safety of arch bridge construction.

[0093] The stress-free cable length of the cable is calculated based on the cable force calculation algorithm model. This refers to the natural length of the cable when not subjected to any external forces. Accurate calculation of the stress-free cable length ensures the tension of the cable and the construction accuracy of the arch bridge, thereby ensuring the quality and safety of the arch bridge.

[0094] When solving T m After that, combined with T mg The unstressed cable length and initial tension of the cable are then calculated. By inputting the initial tension into the construction-stage finite element model, the arch rib bending moment and displacement in the arched state with the cables loosened are calculated, completing the cable adjustment. Furthermore, the constraint functions of this cable adjustment program can be further expanded, such as limiting the difference between adjacent cable forces. Furthermore, the objective function can be adjusted based on actual needs, such as minimizing the sum of the squares of the difference between the actual and target arch rib bending moments.

[0095] The objective function is set based on the bending moment target value. The objective function minimizes the sum of the squares of the comprehensive internal forces of the cables, as shown in the following formula:

[0096] min:f(T)=∑(T i +T ig ) 2 .

[0097] Where, T i is the cable tensioning internal force, T ig is the internal force of the cable with constant load of cable No. i in the maximum cantilever state.

[0098] The objective function can also be to minimize the sum of the squares of the differences between the actual arch rib bending moment and the target bending moment, as shown in the following formula:

[0099]

[0100] Where, T i is the cable tension internal force, C1 is the first influence matrix; C2 is the second influence matrix, m ig is the arch rib dead load bending moment, is the target value of the bending moment.

[0101] The present invention also proposes a storage medium storing a computer program, which, when executed by a processor, implements any one of the arch bridge cable tension algorithms for dual control of internal force and linear shape.

[0102] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAMbus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM). The various embodiments in this specification are described in a progressive manner, and similar parts between the various embodiments can be referenced to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the embodiments of the apparatus, device, and non-volatile computer storage medium, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referenced to the partial description of the method embodiments.

[0103] The calculation scheme of this invention was applied to a large-scale bridge. This bridge is a mid-through steel box arch bridge with a total main bridge length of 612 meters, a clear span of 570 meters, a clear rise of 126.67 meters, a clear rise-to-span ratio of 1 / 4.5, and a multiple parabola-shaped arch axis. The standard cross-section of the arch ribs is a chamfered steel box with a width of 5.5 meters and a gradual height change from 12 meters at the arch foot to 8 meters at the arch crown. Two straight crossbeams and 10 straight steel box cross braces are installed between the two arch ribs.

[0104] The single arch rib is divided into 47 hoisting segments, with 23 cantilever segments on each of the south and north banks, and one arch crown closure segment. Segments G1 to G3 at the arch foot are installed using brackets. Each segment G4 to G23 is equipped with a pair of cables for cantilever assembly, totaling 40 pairs of cables for the single arch rib. The steel box arch is constructed of Q420qD steel, and the cables are Φ15.24 steel strands (fy = 1860 MPa).

[0105] Due to the site's topographical limitations, the cable towers are arranged asymmetrically. The north bank cable towers are 62.5m away from the arch foot, while the south bank cable towers are 66.5m away from the arch foot. The different cable lengths and inclinations on both sides result in different cable forces. The cable-stayed cable system is as follows: Figure 2a and Figure 2b As shown, Figure 2a and Figure 2b It can form a complete bridge.

[0106] In the finite element analysis software, the arch ribs and cables were modeled using beam elements and truss elements, respectively. Only the cable forces were studied, ignoring the effects of the pylons and back cables. The connection between the cables and pylons was simplified to a fixed end, and the arch foot was fully consolidated during the arch rib construction process. The target arch rib bending moment was the arch rib under the action of its own weight. The finite element model is shown below. Figure 3 shown.

[0107] like Figure 4 As shown in the figure, the arch rib bending moment distribution can be calculated using the cable force calculation algorithm model, where the arch rib displacement distribution is as follows: Figure 5 As shown in the figure, the rib bending moment calculated by the proposed method is essentially consistent with the target bending moment. Although the proposed method does not control the rib displacement during the calculation process, the calculation example shows that when the rib bending moment is essentially consistent, the deviation between the rib displacement and the target displacement is very small, approximately 1 cm. Therefore, it can be concluded that the proposed method can ensure that both the rib bending moment and displacement meet the requirements.

[0108] The above description is merely a preferred embodiment of the present application and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention herein is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also encompasses other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features having similar functions disclosed in this application.

Claims

1. An algorithm for calculating the cable tension of an arch bridge based on dual control of internal force and linear shape, characterized in that: include: Establish a one-time arch-drop model to obtain a target bending moment value, which is a bare arch bending moment value under a constant load; Establish an arch rib finite element model and obtain the cable force-bending moment influence matrix and constant vector; Setting a cable force calculation algorithm model based on the bending moment target value, the cable force-bending moment influence matrix and the constant vector; Solve the initial tensioning force of the cable based on the cable force calculation algorithm model; The initial tensioning force of the cable is input into the arch rib finite element model to calculate the arch rib bending moment and displacement.

2. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to claim 1 is characterized in that: The arch rib finite element model includes a finite element model of the arch rib in the maximum cantilever state, a finite element model of the arch rib in the closed state, and a finite element model of the arch rib in the construction stage. The cable force-bending moment influence matrix and the constant vector are obtained, specifically including: Establishing a finite element model of the arch rib in a maximum cantilever state to obtain a first influence matrix, wherein the first influence matrix is an influence matrix of a unit change in the internal force of the cable on the arch rib bending moment when the cable is tensioned in the maximum cantilever state; Establishing a finite element model of the arch rib in a closed state to obtain a second influence matrix, wherein the second influence matrix is an influence matrix of a unit change in the internal force of the cable on the arch rib bending moment when the cable is removed in the closed state; Establishing a finite element model of the arch rib construction stage to obtain the constant vector, wherein the constant vector includes the cable dead load internal force and the arch rib dead load bending moment, wherein the cable dead load internal force is the cable dead load internal force caused by the dead load in the maximum cantilever state, and the arch rib dead load bending moment is the bending moment caused by the dead load in the arching state with the cables loosened; The cable force-bending moment influence matrix includes the first influence matrix and the second influence matrix.

3. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to claim 2 is characterized in that: The cable force calculation algorithm model is set based on the bending moment target value, the cable force-bending moment influence matrix, and the constant vector, specifically including: Establishing an equilibrium equation between the cable tensioning internal force and the arch rib bending moment based on the cable force-bending moment influence matrix and the arch rib dead load bending moment; Establishing a constraint function based on the bending moment target value and the dead load internal force of the cable; The cable force calculation algorithm model is set based on the equilibrium equation and the constraint function.

4. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to claim 3 is characterized in that: The calculation formula of the equilibrium equation is as follows: Where, T m is the cable tension internal force, C1 is the first influence matrix; C2 is the second influence matrix, m mg is the arch rib dead load bending moment, m m is the arch rib bending moment, where C1, C2 and m are equal when the structural stiffness and construction process remain unchanged. mg All are fixed values.

5. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to claim 3 is characterized in that: The constraint function includes the arch rib bending moment constraint function, and the calculation formula is as follows: Where, is the target value of the bending moment; ε m is the allowable error of the bending moment at point m of the arch rib; The constraint function also includes a cable internal force constraint function, and the calculation formula is as follows: Where, T mg is the internal force of the cable No. m under the maximum cantilever state, tl m is the lower limit of the internal force of the mth cable in the maximum cantilever state, t um is the upper limit of the internal force of the mth cable in the maximum cantilever state, where T mg Is a fixed value.

6. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to any one of claims 2 to 5, characterized in that: Solving the initial tension of the cable based on the cable force calculation algorithm model specifically includes: Solving the cable tensioning internal force based on the cable force calculation algorithm model, wherein the cable tensioning internal force is the cable tensioning internal force caused by the cable tensioning in the maximum cantilever state; Adding the tensioning internal force of the cable and the dead load internal force of the cable to obtain the comprehensive internal force of the cable; The initial tensioning force of the cable is obtained based on the comprehensive internal force of the cable.

7. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to claim 6 is characterized in that: Also includes: An objective function is set based on the bending moment target value, and the objective function minimizes the sum of squares of the comprehensive internal forces of the cable, as shown in the following formula: min:f(T)=∑(T i +T ig ) 2 , Where, T i is the cable tensioning internal force, T ig To find out the constant load internal force.

8. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to claim 6 is characterized in that: An objective function is set based on the bending moment target value. The objective function is to minimize the sum of the squares of the differences between the actual arch rib bending moment and the bending moment target value, as shown in the following formula: Where, T i is the cable tension internal force, C1 is the first influence matrix; C2 is the second influence matrix, m ig is the arch rib dead load bending moment, is the target value of the bending moment.

9. The arch bridge cable tension algorithm based on dual control of internal force and linear shape according to any one of claims 1 to 5, characterized in that: Also includes: The stress-free cable length of the buckle cable is solved based on the cable force calculation algorithm model.

10. A storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the arch bridge cable tension algorithm based on dual control of internal force and linear shape according to any one of claims 1 to 9 is implemented.

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