Cable force calculation method for rib division installation of large-span steel truss arch bridge

Abstract

The invention provides a cable force calculation method for rib-dividing installation of a large-span steel truss arch bridge, and relates to the technical field of large-span arch bridges. The technology comprises the following steps: based on an influence matrix principle, establishing an influence matrix reflecting a mutual relation between initial tension and accumulated displacement of a buckle anchor cable in rib-dividing installation; and the initial tension of the buckling anchor cable capable of controlling the inter-rib height difference, the arch rib displacement and the buckling tower displacement at the same time is solved. The cable force calculation method provided by the invention is simple and clear in principle and small in calculation amount, iterative calculation or a complex optimization algorithm is not needed in the solving process, only the influence matrix method is adopted, the calculation principle is simple, and the mechanical concept is clear; according to the method, the inter-rib height difference of rib division installation and the arch rib displacement and buckling tower displacement of the arch rib sections can be controlled at the same time; in addition, the initial tension of the buckle anchor cable can be calculated at the same time, cable force conversion is not needed, and the initial tension of the buckle anchor cable installed in a rib dividing mode can be directly solved.

Description

Technical Field

[0001] The present invention relates to the technical field of long-span arch bridges, and particularly to a cable force calculation method for rib-by-rib installation of long-span steel truss arch bridges. Background Art

[0002] Steel truss arch bridges use steel truss structures as arch ribs. Multiple rib segments are arranged horizontally for the arch ribs to adapt to the development trend of long-span and wide-deck bridges. Cross braces are set between the ribs to strengthen the overall structural stability and the characteristics of collaborative force. Limited by the lifting capacity of the cable hoisting system, each arch rib segment is installed rib by rib. The arch rib is divided into several arch rib segments along the span direction and constructed by the cable-stayed cantilever method. That is, for a single arch rib segment, first use the cable hoisting system to hoist a single rib segment to the predetermined position for installation, and then rely on the cable-stayed fastening system to tension the fastening cable of this rib segment to adjust it to the preset elevation, and synchronously tension the corresponding anchor cable to ensure that the deviation of the fastening tower is within the allowable range. Install the remaining rib segments of this arch rib segment in this process in turn. After the elevation difference between the ribs is within the allowable range, install the cross braces between the ribs, and continue to construct the subsequent arch rib segments according to this rib-by-rib installation process until closure. The following requirements exist during the rib-by-rib installation process: 1. Strictly control the elevation difference between the ribs; the steel structure has strict requirements for the installation accuracy of components. The allowable error of the reserved bolt holes for the connection between the cross brace connecting components and the rib segments is generally 2 mm. Therefore, the elevation difference between the ribs must be strictly controlled before installing the cross braces. Otherwise, once the elevation difference between the ribs exceeds the limit, it will cause the bolt holes of the cross brace connecting components to be misaligned and unable to be installed, and at the same time, it will also affect the lateral deviation of the arch rib. In extreme cases, it may even cause the fastening tower to twist too much and cause an accident, endangering the overall stability of the bridge and construction safety.

[0003] 2. Strictly control the elevation of the arch rib segment after the rib-by-rib installation is completed; in order to ensure that the linear shape after cable loosening to form an arch and the predetermined position of the subsequent arch rib segment installation remain unchanged, it is necessary to ensure that the structural state after the installation of the cross braces between the ribs is the same as the structural state of the integral rib installation of the arch rib segment. That is, at this time, the arch rib segment is at the preset elevation set according to the integral rib installation of the arch rib segment, and the cable force of the fastening anchor cable is the same as the cable force value calculated by the integral rib installation of the arch rib segment.

[0004] The above processes are all completed by the cable-stayed fastening system. However, the cable-stayed fastening system is a complex statically indeterminate structural system integrating multiple components such as arch ribs, fastening cables, fastening towers, and anchor cables, showing a complex interaction mechanism of structural mechanics behavior during the construction process. The first-installed rib segment of each arch rib segment will affect the preset elevation of the later-installed rib segment, and the tension of the fastening anchor cables of the subsequent rib segments will also act on the first-installed rib segment, resulting in changes in its cable force distribution and elevation, causing changes in the cable force and linear shape of the first-installed rib segment. On the other hand, in order to avoid safety hazards such as anchor slip caused by excessive cable adjustment times, the fastening anchor cables must be tensioned by the one-time tensioning method.

[0005] Therefore, during the installation of the split ribs, appropriate initial tension needs to be applied to the tie-down cables of each split rib segment to meet the above two requirements simultaneously after the split rib installation is completed.

[0006] For the calculation of the cable forces during split rib installation, the calculation idea of "first overall then local" is adopted. That is, first, in the way of installing the integral rib of the arch rib segment, the existing mature cable force algorithms (such as: zero displacement method, elastic support method, optimization algorithm, etc.) are used to calculate the cable force for the integral rib installation of the arch rib segment, and then the cable force for split rib installation is calculated. The methods for calculating the cable force for split rib installation in the prior art are: 1. The reverse dismantling method (applicable to double-rib arch bridges) The reverse dismantling method takes the ideal completed state of integral rib installation of each arch rib segment as the starting point for backtracking, and strictly disassembles step by step in the reverse order of the actual operation of split rib construction. Finally, the corresponding initial tension of the tie-down cables and pre-lifting amount parameters of each split rib segment under the split rib installation condition are obtained.

[0007] Different from double-rib arch bridges: The middle arch rib of the multi-rib arch bridge structure system needs to bear half of the cross-brace weight additionally compared with the outer arch ribs. Therefore, when using the initial tension of integral rib installation for the overall installation of the arch rib segment, this uneven stress phenomenon causes the configuration that the elevation of the middle arch rib is lower than that of the two side arch ribs for each arch rib segment, and as the cantilever length increases, the difference in elevation between the ribs shows a gradually increasing trend. Therefore, starting from this state with an initial difference in elevation between the ribs for reverse dismantling, the initial tension of the tie-down cables and pre-lifting amount of each split rib segment during split rib installation obtained cannot control the difference in elevation between the split rib segments, and finally it still returns to the initial state with a difference in elevation between the ribs.

[0008] 2. The stress-free state method (applicable to double-rib arch bridges) The stress-free state method is based on the state after the integral rib installation of the arch rib segment. Taking this as the benchmark, the stress-free cable length is obtained, and then the initial tension of the tie-down cables and pre-lifting amount of each split rib segment during split rib installation are obtained by forward installation with the stress-free cable length. The same as the reverse dismantling method, the stress-free cable length is calculated based on the state with an initial difference in elevation between the ribs, and it still cannot effectively control the difference in elevation between the split rib segments.

[0009] 3. In the calculation of the hoisting cable force for split rib installation published by Liu Shaoping, Li Qiuyuan, Zhang Litao, etc., a method for calculating the cable force for split rib installation is proposed. This method considers the collaborative influence of the cable and the tie-down tower and uses step-by-step interpolation iteration to calculate the initial tension of split rib installation. This method requires multiple iterations and the number of iterations depends on the control accuracy of the difference in elevation between the ribs, and there are problems of cumbersome calculation and low accuracy.

[0010] 4. A method, construction method and system for accurately calculating the pre - lifting value of the arch rib installation section with the publication number CN116756800A, including: establishing a self - weight model of the bare arch rib to obtain the target alignment; establishing an integral installation model of the arch rib, assigning an initial cable - fastening force, and obtaining the pre - lifting value; judging whether the difference between the pre - lifting value and the target alignment is within the allowable error; if not, adjusting the initial cable - fastening force until the pre - lifting value is within the allowable error; if so, outputting the cable - fastening force; establishing a segmented installation model of the arch rib to obtain a displacement influence matrix under the action of the unit cable - fastening force and the cable - anchor force; obtaining the cable - fastening force difference for segmented installation of the arch rib based on the displacement amount obtained with the cable - fastening force as the initial cable force, the displacement influence matrix and the pre - lifting value; obtaining the actual cable - fastening force based on the cable - fastening force difference and the cable - fastening force; and obtaining the actual pre - lifting value based on the actual cable - fastening force. This method calculates the initial tension of the cable for segmented rib installation based on the displacement influence matrix, and then calculates the corresponding initial tension of the cable - anchor according to the horizontal component balance principle of the cable - anchor force to control the deviation of the cable tower. However, this method controls the elevation of the arch rib through the initial tension of the cable, without establishing a direct corresponding relationship between the initial tension of the cable - anchor and the elevation of the arch rib, and ignores the influence of the cable - anchor tension on the elevation of the arch rib.

[0011] 5. A method for calculating the cable - fastening force and pre - lifting amount of the inclined - cable - hung arch rib of a long - span steel arch bridge with the publication number CN117332656A, belonging to the field of bridge construction control. A method for calculating the cable - fastening force and pre - lifting amount of the inclined - cable - hung arch rib of a long - span steel arch bridge, the method includes the following steps: S1. Establishing a finite - element model of the basket - handle arch bridge; S2. Conducting a forward calculation to obtain the influence matrix of the integral rib cable force and displacement; S3. Calculating the integral pre - lifting value of the integral rib model; S4. Judging whether the integral pre - lifting value meets the requirements of the target alignment. If it meets, enter step S5; otherwise, modify the constraint conditions of the objective function, and then transfer to step S3; S5. Obtaining the estimated cable force value and the corresponding displacement array; S6. Judging whether the displacement under the action of the segmented rib cable force meets the error requirements of the current - stage target displacement. If it meets, output the cable force; otherwise, continue the difference iteration according to the obtained displacement and the target displacement. Although the present invention proposes a calculation method based on the current integral pre - lifting value to solve the cable - fastening force of the arch rib and the side cable - wind cable force, and constructs the corresponding influence matrix of the segmented rib cable force assembly, and then obtains the segmented rib cable force within the displacement error range of the arch rib through cyclic iteration. However, this method is limited to calculating the cable - fastening force for segmented rib installation and the side cable - wind cable force, fails to obtain the cable - anchor force, and does not control the displacement of the cable tower. Summary of the Invention

[0012] The present invention provides a method for calculating the cable force for segmented installation of a long - span steel truss arch bridge, aiming to solve at least the technical problems existing in the prior art and being applicable to all types of arch - rib bridges.

[0013] The present invention provides the following technical solutions to achieve the above - mentioned purpose: A cable force calculation method for the segmented rib installation of long-span steel truss arch bridges. Based on the influence matrix principle, an influence matrix reflecting the mutual relationship between the initial tension of the cable-stayed cables for segmented rib installation and the cumulative displacement is established, and the initial tension of the cable-stayed cables that can simultaneously control the height difference between ribs, the rib displacement of the arch rib segment, and the displacement of the cable tower is solved. The calculation method is as follows: Step S1: Under the condition of considering the arch-forming line shape, establish a finite element model for the integral rib installation of the arch rib segment. Taking the arch rib segment as the calculation object, solve the rib displacement and the cable tower displacement during the integral rib installation of this arch rib segment, and use this rib displacement and the cable tower displacement as the adjustment target values for the segmented rib installation of this arch rib segment; Step S2: Based on the finite element model for the integral rib installation of the arch rib segment, under the condition of taking segmented rib installation as the construction method, apply a unit force to each cable-stayed cable of this arch rib segment respectively, extract the displacement influence factor as the element of the influence matrix, and construct the influence matrix; Step S3: Based on the finite element model for the integral rib installation of the arch rib segment, under the condition of taking segmented rib installation as the construction method, apply an initial force to each cable-stayed cable of this arch rib segment respectively, and extract the cumulative initial displacement for installing this arch rib segment. The cumulative initial displacement includes rib displacement and cable tower displacement; Step S4: Based on the rib displacement and the cable tower displacement calculated in S1, extract the average value of the rib displacement as the rib displacement target value for segmented rib installation, and extract the cable tower displacement as the cable tower displacement target value for segmented rib installation; Step S5: Establish a matrix equation and solve the initial tension of each cable-stayed cable for segmented rib installation.

[0014] Furthermore, the step S1 is as follows: S1.1 Establish a finite element model for the integral rib installation of the arch rib segment. Each arch rib segment in the finite element model for the integral rib installation of the arch rib segment includes n segmented rib segments arranged horizontally and n corresponding cable-stayed cables. A displacement measuring point is arranged on each segmented rib segment to monitor the vertical displacement of this segmented rib segment, and n displacement measuring points are arranged at the cable tower top corresponding to the positions of the cable-stayed cables to monitor the horizontal displacement of the cable tower; S1.2 Under the condition of taking the integral rib installation of the arch rib segment as the construction method, adopt the existing cable force calculation method, aiming at approximating the one-time arch-forming line shape with the cable-loosing arch-forming line shape, and calculate the measured point displacement of this arch rib segment during the integral rib installation , ; Equation (1) Where: ( ) is the vertical displacement of the measured point i of the segmented rib segment, ( ) is the horizontal displacement of the measured point i of the cable tower.

[0015] Further, the step S2 includes applying unit forces to all the cable-bracing cables of the arch rib segment, extracting the displacement influence factors under the action of the unit forces as the elements of the influence matrix, and forming the influence matrix. ; Equation (2) Where: , (i = 1~n, j = 1~n) are the vertical displacement influence factor of the measuring point j of the sub-rib segment and the horizontal displacement influence factor of the measuring point j of the cable-bracing tower generated by the unit force of the cable-bracing cable i; similarly , (i = 1~n, j = 1~n) are the vertical displacement influence factor of the measuring point j of the sub-rib segment and the horizontal displacement influence factor of the measuring point j of the cable-bracing tower generated by the unit force of the cable i.

[0016] Further, the step S3 includes applying initial forces to all the cable-bracing cables of the arch rib segment , and extracting the cumulative initial displacements of each measuring point after the installation of the arch rib segment ; ; Equation (3) Where: (i = 1~n) is the cumulative initial vertical displacement of the measuring point i of the sub-rib segment, (i = 1~n) is the cumulative initial horizontal displacement of the measuring point i of the cable-bracing tower.

[0017] Further, the step S4 includes taking the average value of the displacements of the measuring points of the sub-rib segment ( ) as the arch rib displacement target value ( ), taking the displacement value of the measuring point of the cable-bracing tower ( ) as the cable-bracing tower displacement target value ( ); ; Equation (4) Then the displacement target value of each measuring point is: ; Equation (5).

[0018] Further, the step S5 establishes the following matrix equation: ; Equation (6) Where: is the initial tension array of the cable-bracing cables for the installation of the sub-rib, is the unit cable force diagonal matrix; And substituting Equation (2), Equation (3), and Equation (5) into Equation (6), the initial tension of the cable-bracing cables for the installation of the sub-rib is solved.

[0019] Compared with the prior art, the present invention has the following beneficial effects: The principle of the cable force calculation method proposed by the present invention is simple and clear, with a small amount of calculation. During the solution process, there is no need for iterative calculation or complex optimization algorithms. Only the influence matrix method is adopted, and the calculation principle is simple and the mechanical concept is clear. This method can simultaneously control the elevation difference between ribs during the installation of sub-ribs, as well as the displacement of the arch rib segments and the displacement of the cable tower for the arch rib segments. In addition, this method can calculate the initial tension of the cable anchor for buckling simultaneously, without the need for cable force conversion, and can directly solve the initial tension of the cable anchor for buckling during the installation of sub-ribs. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings described below only relate to some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 Schematic diagram of the finite element model for the installation of arch rib segments of the present invention; Figure 2 Schematic diagram of the bridge in the application example of the present invention; Figure 3 For Figure 2 Schematic diagram of the arch rib model of the bridge shown; Figure 4 For Figure 2 Schematic diagram of the layout of the cable anchors for buckling of the bridge shown; Figure 5 For Figure 2 Schematic diagram of the finite element model of the bridge shown; Figure 6 For Figure 2 Calculation model for the installation of sub-rib NS7 of the arch rib on the Anshun bank of the bridge shown; Figure 7 For Figure 6 Schematic diagram of the layout of the measuring points on the cable tower at the top of the cable tower for buckling in A shown; Figure 8 For Figure 6 Schematic diagram of the layout of the measuring points on the arch rib at the buckling point of the arch rib in B shown. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention.

[0023] It should be noted that in the present invention: The terms "comprising", "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices; The terms "upper", "lower", "left", "right", "front", "rear", "top", "bottom", "inner", "outer", "middle", "vertical", "horizontal", "lateral", "longitudinal", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. These terms are mainly used to better describe the present invention and its embodiments, and are not used to limit that the indicated device, element or component must have a specific orientation or be constructed and operated in a specific orientation; The terms "first", "second", etc. are used to distinguish similar objects and do not necessarily describe a specific order or sequence; The terms "installed", "set up", "provided with", "connected", "connected to", "socketed", etc. should be understood in a broad sense; For example, it can be a fixed connection, a detachable connection, or an integral structure; It can be a mechanical connection or an electrical connection; It can be directly connected, or indirectly connected through an intermediate medium, or there can be internal communication between two devices, elements or components. And, in addition to being able to represent the orientation or positional relationship, some terms may also be used to represent other meanings. For example, the term "upper" may also be used to represent a certain attachment relationship or connection relationship in some cases. For those of ordinary skill in the art, the specific meanings of these terms in the present invention can be understood according to specific circumstances.

[0024] Embodiment. A cable force calculation method for rib-by-rib installation of long-span steel truss arch bridges, characterized in that: Based on the influence matrix principle, an influence matrix reflecting the mutual relationship between the initial tension of the cable-stayed cables for rib-by-rib installation and the cumulative displacement is established, and the initial tension of the cable-stayed cables that can simultaneously control the height difference between the ribs, the rib displacement of the arch rib segment and the displacement of the cable tower is solved. The calculation method is as follows: Step S1. Under the condition of considering the arch shape, establish a finite element model for the integral rib installation of the arch rib segment. Taking the arch rib segment as the calculation object, solve the rib displacement and the cable tower displacement during the integral rib installation of the arch rib segment, and use this rib displacement and the cable tower displacement as the adjustment target values for the rib-by-rib installation of this arch rib segment; Step S2. Based on the finite element model for the integral rib installation of the arch rib segment, under the condition of taking rib-by-rib installation as the construction method, apply a unit force to each cable-stayed cable of the arch rib segment respectively, extract the displacement influence factor as an element of the influence matrix, and construct the influence matrix; Step S3: Based on the finite element model of the integral rib installation of the arch rib segment, under the condition that the construction method is the separate rib installation, initial forces are respectively applied to each cable of the arch rib segment, and the cumulative initial displacement of installing this arch rib segment is extracted. Based on the characteristics of matrix calculation, the initial force can take any value, and the finally calculated initial tension of the cable is unique. For the convenience of calculation, the unit force is often taken as the initial force for calculation; Step S4: Based on the arch rib displacement and the cable tower displacement calculated in S1, the average value of the arch rib displacement is extracted as the arch rib displacement target value for the separate rib installation, and the cable tower displacement is extracted as the cable tower displacement target value for the separate rib installation; Step S5: Establish a matrix equation and solve the initial tension of each cable for the separate rib installation.

[0025] The above-mentioned step S1 is as follows: S1.1 Establish a finite element model for the integral rib installation of the arch rib segment. Each arch rib segment in the finite element model of the integral rib installation of the arch rib segment includes n separate rib segments arranged horizontally and n corresponding cables. One displacement measuring point is arranged on each separate rib segment to monitor the vertical displacement of this separate rib segment, and n displacement measuring points are arranged at the corresponding cable positions on the top of the cable tower to monitor the horizontal displacement of the cable tower; S1.2 Under the condition that the construction method is the integral rib installation of the arch rib segment, using the existing cable force calculation method, with the goal of approximating the once-formed arch shape by the cable-loosing arch shape, calculate the measured point displacement of this arch rib segment during the integral rib installation , ; Equation (1) Where: ( ) is the vertical displacement of the measuring point i of the separate rib segment, ( ) is the horizontal displacement of the measuring point i of the cable tower.

[0026] The above-mentioned step S2 includes applying unit forces to all cables of the arch rib segment, extracting the displacement influence factors under the action of the unit forces as the elements of the influence matrix, and forming the influence matrix ; Equation (2) Where: , (i = 1~n, j = 1~n) are the vertical displacement influence factor of the measuring point j of the separate rib segment and the horizontal displacement influence factor of the measuring point j of the cable tower generated by the unit force of the cable i; similarly , (i = 1~n, j = 1~n) are the vertical displacement influence factor of the measuring point j of the separate rib segment and the horizontal displacement influence factor of the measuring point j of the cable tower generated by the unit force of the cable i.

[0027] The above-mentioned step S3 includes applying initial forces to all cables of the arch rib segment , extract the cumulative initial displacements of each measuring point after the installation of the arch rib segment ; ; Equation (3) Where: (i = 1~n) is the cumulative initial vertical displacement of measuring point i of the sub-arch rib segment, (i = 1~n) is the cumulative initial horizontal displacement of measuring point i of the cable tower.

[0028] The said step S4 includes taking the displacements of the measuring points of the sub-arch rib segment ( ) and taking the average value as the arch rib displacement target value ( ), taking the displacement value of the measuring point of the cable tower ( ) as the cable tower displacement target value ( ); ; Equation (4) Then the displacement target values of each measuring point are: ; Equation (5).

[0029] Furthermore, the said step S5 establishes the following matrix equation: ; Equation (6) Where: is the initial tension array of the sub-arch installation cable, is the unit cable force diagonal matrix; and substitute Equation (2), Equation (3), and Equation (5) into Equation (6) to solve for the initial tension of the sub-arch installation cable .

[0030] The problems solved by this application and the calculation idea are as follows: In the existing arch bridge installation project, the arch ribs of large arch bridges are often very large and heavy. If they are manufactured and transported as a whole, huge challenges will be faced. Whether it is road, railway or waterway transportation, they will be restricted by size and weight; therefore, the arch ribs of the arch bridge are divided into several arch rib segments, and the arch rib segments are further divided into several sub-arch rib segments structurally, thereby reducing the pressure of arch rib manufacturing and transportation. During the installation of the arch rib, a cable crane system (the cable crane system includes cable stays, anchor cables and cable towers) is often used to maintain the arch shape of the arch rib by adjusting the cable forces of the cable stays and anchor cables, as Figure 4 , 5 and shown in 6. From the perspective of maintaining the arch shape, whether it is the construction method of installing the whole arch rib segment or the sub-arch installation (installing the whole arch rib segment means regarding all the sub-arch rib segments that make up the arch rib segment as a whole and using the cable crane system for hoisting and installation. In the application example of this application, the Guniuhe River Extra-large Bridge project mentioned has an arch rib segment including four parallel sub-arch rib segments, asFigure 8 as shown; the split rib installation means that each arch rib segment is installed one by one with a single split rib segment first, and after all the split rib installations are completed, the cross braces between the split ribs are installed; the finite element models used in the two construction methods are the same, such as Figure 5 , 6 , 7 and 8, and the difference lies only in the installation method of the arch rib; the integral rib installation and split rib installation of the arch rib segment are common construction methods in the prior art), and the formed arch alignment to be maintained is the same; however, from a mechanical point of view, the two construction methods have different effects on the indeterminate system composed of the arch rib, the cable, the anchor cable and the cable tower, so the cable force value of the integral rib installation of the arch rib segment cannot be applied to the construction process of the split rib installation; therefore, the calculation idea of this application is based on the integral rib installation of the arch rib segment, and first calculates the displacement of the arch rib and the displacement of the cable tower required to maintain the formed arch alignment, and uses this arch rib displacement and cable tower displacement as the target values to control the displacement of each split rib segment and the cable tower during the split rib installation, and then calculates the cable forces required for the anchor cable and the cable by inversion to reach this target value, that is, the initial tension of the cable and anchor cable.

[0031] Application example. This application has been used in the Guniuhe Extra-large Bridge project. Taking the split rib installation of this project as an example, the cable force calculation method used in this application is specifically described; The main bridge of the Guniuhe Extra-large Bridge is a deck steel box truss arch bridge, as Figure 2 shown, the calculated span L = 520m, the calculated rise f = 130m, the calculated rise-span ratio L / f = 1 / 4, and the arch axis coefficient is 1.55. The radial height of the arch crown section of the truss arch is 9.0m, and the radial height of the arch foot section is 14.0m. The truss arch consists of 4 arch ribs in the transverse direction of the bridge, and cross braces are arranged between the arch ribs, as Figure 3 shown.

[0032] Each single arch rib of the bridge is divided into 22 segments, including 10 segments on the Anshun bank, 9 segments on the Panzhou bank, 2 arch foot segments and 1 mid-span closure segment. The arch rib is assembled by cantilever using inclined cable-stayed buckles and the hinge is sealed after the NS3 segment is installed. The Anshun bank is divided into 11 segments for hoisting, and the Panzhou bank is for 10 segments hoisting. The maximum segment lifting weight is 283.3t (arch rib NS1 segment), and the minimum segment lifting weight is 118.0t (arch rib NS11 segment on the Anshun bank). The layout of the inclined cable-stayed buckle system is as Figure 4 shown. The 1#-8# cable and anchor cables on the Anshun bank are anchored to the Anshun bank boundary pier, and the 5# upper arch column is used as an auxiliary tower, and a cable saddle is set on the top of the tower to support the 9#-11# through cables. The 1#-8# cable and anchor cables on the Panzhou bank are anchored to the Panzhou bank boundary pier, and an auxiliary tower is set on the transfer pier, and the 9#-11# cable and anchor cables are anchored to the auxiliary tower anchor box.

[0033] Taking the split rib installation of the arch rib segment NS7 on the Anshun bank as an example, the cable force calculation process of the split rib installation of this application is described: 1) A finite element program is used to establish a calculation model for the integral rib installation of the arch rib segments. According to the construction sequence of first installing 4 arch ribs simultaneously for each arch rib segment and then installing the cross braces, with the goal of approximating the once-formed arch shape by the cable-loosening arch shape, the initial tension of the cable-locking cables at each construction stage is obtained using the existing cable force calculation method. In this model, the arch ribs and cable-locking towers are simulated using beam elements, and the cable-locking cables and anchor cables are simulated using cable elements; the bottom of the transfer pier is fixed and the arch feet are fixed. The calculation model is as shown in Figure 5 shown. The layout of the NS7 measuring points on the arch rib segments on the Anshun bank is as shown in Figure 6 shown. Cable-locking tower measuring points 1-4 are arranged at the top of the cable-locking tower, as shown in Figure 7 shown, for monitoring the horizontal displacement of the cable-locking tower. Arch rib measuring points 1-4 are arranged at each arch rib cable-locking point, as shown in Figure 8 shown, for monitoring the vertical displacement of the rib segments.

[0034] 2) A finite element program is used to establish a calculation model for the rib-by-rib installation of the NS7 arch rib segments on the Anshun bank. The calculation model is as shown in Figure 6 shown. Cable-locking tower measuring points 1-4 are arranged at the top of the cable-locking tower, as shown in Figure 7 shown, for monitoring the horizontal displacement of the cable-locking tower. Arch rib measuring points 1-4 are arranged at each arch rib cable-locking point, as shown in Figure 8 shown, for monitoring the vertical displacement of the rib segments.

[0035] The 4 arch ribs and cross braces of the NS7 arch rib segment are installed in the rib-by-rib construction method of "arch rib 3 → arch rib 2 → arch rib 4 → arch rib 1 → cross brace". A unit force of 100 kN is applied to each cable-locking cable of the NS7 arch rib segment, and the influence factors of this unit force on the displacements of each measuring point after installing all rib segments are extracted to form the influence matrix ,

[0036] The unit force column matrix is:

[0037] The unit force diagonal matrix is:

[0038] 4) Based on the construction method described in step 3), an initial force of 100 kN is applied to each cable-locking cable, and the cumulative initial displacements of each displacement measuring point after installing all rib segments are extracted ;

[0039] The initial force column matrix is:

[0040] 5) Based on the calculation model for the integral rib installation of the arch rib segments described in step 1), the cable-locking cable forces and the displacements of the arch ribs and cable-locking towers of the NS7 arch rib segment on the Anshun bank during integral rib installation are extracted, as shown in Tables 1 and 2;

[0041] As can be seen from Table 1, when installing the integral ribs of this segment, the same initial tension is applied to each tie-down cable. After installing the cross braces, the forces of the tie-down cables increase. Due to the large stiffness of the cross braces between the ribs, the increment of the tie-down cable force only differs by 0.3 kN after installing the cross braces. After installing the cross braces, the resultant forces of the tie-down cables are 5575.0 kN and 4188.8 kN respectively.

[0042] As can be seen from Table 2, since the middle two ribs of each arch rib segment bear half of the cross brace weight more than the outer ribs, after installing the cross braces for each arch rib segment, the middle ribs will be lower than the two side ribs. This height difference between the ribs accumulates to the arch rib segment NS7, and the height difference between the ribs reaches 4.7 mm. After installing the cross braces, the height difference between the ribs increases to 5.0 mm. It can be seen that the state with the initial height difference between the ribs cannot be used as the benchmark for reverse disassembly or calculating the stress-free state quantity.

[0043] As can be obtained from Table 2, when installing all the ribs of the arch rib segment NS7 with integral ribs, the displacements of each measuring point ;

[0044] 6) In order to control the elevation difference between the ribs after the installation of the split ribs of the arch rib segment NS7 and the elevation of this arch rib segment, take the average value of the arch rib displacement in Equation (12) as the target value of the arch rib displacement, and the target value of the buckle tower displacement is the same as Equation (12). Then, after the installation of all the ribs of the arch rib segment NS7 is completed, the target values of the displacements of each measuring point are ,

[0045] 7) Establish a matrix equation and substitute Equations (7), (9), (10), (11), and (13) into the matrix equation;

[0046] Solve to obtain the initial tension of the tie-down cables for split rib installation ;

[0047] Take Equation (14) as the initial tension of the tie-down cables for split rib installation. The forces and displacements of the tie-down cables during the split rib installation of the arch rib segment NS7 are shown in Tables 3 and 4;

[0048] As can be seen from Table 3, when the initial tension is installed by rib-by-rib installation and all rib-by-rib segments of the arch rib segment NS7 are installed (construction stage: installing arch rib 1), the cable forces of each stay cable are basically symmetrically distributed. The cable forces of the middle stay cables (stay cable 2 and stay cable 3) are slightly greater than those of the outer stay cables (stay cable 1 and stay cable 4). This is because after the cross brace of the previous arch rib segment (arch rib segment NS6) is installed, the middle arch rib is lower than the outer arch rib, resulting in the initial installation position of the tangent line of the middle arch rib of the arch rib segment NS7 being lower than that of the outer arch rib. A greater cable force needs to be applied in this stage to make up for the initial elevation difference between the middle arch rib tangents. After the cross brace is installed, the resultant forces of the stay cables are 5566.1 kN and 4203.9 kN respectively, with differences of 1.6‰ and 3.6‰ from the resultant forces of the stay cables in the integral rib installation. It can be seen that the resultant forces of the stay cables in the rib-by-rib installation are almost the same as those in the integral rib installation.

[0049] As can be seen from Table 4, after all rib-by-rib segments are installed (construction stage: installing arch rib 1), the measured points of each arch rib and the buckle tower are at the displacement target values shown in Equation (13), and the elevation difference between the ribs is 0 mm, meeting the elevation difference limit of the arch ribs with the clearance of the bolts for installing the cross brace members < 2 mm. After installing the cross brace, the middle arch rib bears half of the weight of the cross brace more, and is 0.2 mm lower than the outer arch rib.

[0050] The rib-by-rib installation stay cable forces calculated by this method are used to install the rib-by-rib segments of the remaining arch rib segments. After loosening the cables to form an arch, the comparison of the arch rib shapes with the integral rib installation and the one-time arch formation is shown in Table 5. Due to the symmetry of the arch rib structure, only the displacement data of arch rib 1 and arch rib 2 are listed in the table.

[0051]

[0052] As can be obtained from Table 5, after forming the arch, the maximum elevation difference between the ribs obtained by the integral rib installation is 109.5 mm, the maximum elevation difference between the ribs obtained by the rib-by-rib installation is 2 mm, and the maximum elevation difference between the ribs obtained by the one-time arch formation is 1.2 mm. The elevation difference between the ribs in the rib-by-rib installation is much smaller than that in the integral rib installation, and is only 0.8 mm greater than the maximum elevation difference between the ribs in the one-time bridge formation. It can be seen that the cable forces in the rib-by-rib installation can effectively control the elevation difference between the ribs after forming the arch. Comparing the arch rib shapes of arch rib 1 and arch rib 2 after loosening the cables to form an arch, the arch rib shapes obtained by the integral rib installation and the rib-by-rib installation can both approximate the one-time arch formation shape, indicating that the structural states after the installation of each arch rib segment by rib-by-rib installation are basically the same as those in the integral rib installation. Compared with the one-time arch formation shape, the maximum deviations of arch rib 1 in the two installation methods are 11.6 mm and 10.8 mm respectively, and the maximum deviations of arch rib 2 in the two installation methods are -110 mm and 9.6 mm respectively. It shows that the rib-by-rib installation cable forces obtained by the method of this application can better fit the arch formation shape target after loosening the cables to form an arch.

[0053] Obviously, the above are only some embodiments of the present invention, rather than all embodiments. The above embodiments are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any combination, modification, equivalent replacement, improvement and all other embodiments that can be made by those of ordinary skill in the art within the spirit and principle of the present invention should fall within the protection scope of the present invention.

Claims

1. A cable force calculation method for rib installation of a long-span steel truss arch bridge, characterized in that: Based on the influence matrix principle, an influence matrix reflecting the relationship between the initial tension and cumulative displacement of the buckle anchor cable installed in the ribs is established to solve the initial tension of the buckle anchor cable that can simultaneously control the height difference between ribs, the displacement of the arch ribs and the displacement of the buckle tower. The calculation method is as follows: Step S1, under the condition of considering the arch line shape, establish a finite element model for the whole rib installation of the arch rib segment, take the arch rib segment as the calculation object, solve the arch rib displacement and the tower displacement when the whole rib of the arch rib segment is installed, and use the arch rib displacement and the tower displacement as the adjustment target value of the rib installation of the arch rib segment; Step S2, based on the finite element model of whole rib installation of the arch rib segment, under the condition of separate rib installation as the construction method, a unit force is applied to each anchor cable of the arch rib segment, and the displacement influence factor is extracted as an element of the influence matrix to construct the influence matrix; Step S3, based on the finite element model of the whole rib installation of the arch rib segment, under the condition of the construction mode of the split rib installation, the initial force is applied to each anchor cable of the arch rib segment respectively, and the cumulative initial displacement of the installation of the arch rib segment is extracted, and the cumulative initial displacement includes the arch rib displacement and the anchor tower displacement; Step S4, based on the arch rib displacement and tower displacement calculated in S1, extract the average value of the arch rib displacement as the arch rib displacement target value for the rib-separated installation, and extract the tower displacement as the tower displacement target value for the rib-separated installation; Step S5: Establishing a matrix equation ; in: To install the anchor cable initial tension array for the ribs, is the unit cable force diagonal matrix, is the influence matrix, is the displacement target value of each measuring point, is the cumulative initial displacement of each measuring point after the arch rib segment is installed, is the initial force; And solve the initial tension of each buckle anchor cable installed in the ribs.

2. A cable force calculation method for rib installation of a long-span steel truss arch bridge according to claim 1, characterized in that: Described step S1 is as follows: S1.1 Establish a finite element model for the installation of an arch rib segment and a whole rib. In the finite element model for the installation of an arch rib segment and a whole rib, each arch rib segment includes n transversely arranged sub-rib segments and correspondingly arranged n buckle anchor cables. A displacement measuring point is arranged on each sub-rib segment to monitor the vertical displacement of the sub-rib segment. n displacement measuring points are arranged at the top of the buckle tower corresponding to the buckle anchor cable position to monitor the horizontal displacement of the buckle tower. S1.2 Under the condition of the whole rib installation of the arch rib segment as the construction method, the existing cable force calculation method is used, and the goal is to approximate the arch line shape of the loose cable to the primary arch line shape. The displacement of the measuring point of the arch rib segment during the whole rib installation is calculated. , ； in: ( ) is the vertical displacement of the measuring point i of the rib segment, ( ) is the horizontal displacement of the tower measuring point i.

3. The cable force calculation method for rib installation of a long-span steel truss arch bridge according to claim 2 is characterized by: The step S2 includes applying a unit force to all the anchor cables of the arch rib segment, extracting the displacement influence factor under the unit force as an element of the influence matrix, and forming an influence matrix ; ； in: , (i=1~n, j=1~n) is the vertical displacement influence factor of the rib segment measuring point j and the horizontal displacement influence factor of the tower measuring point j caused by the unit force of the cable i; , (i=1~n, j=1~n) is the vertical displacement influence factor of the rib segment measuring point j and the horizontal displacement influence factor of the tower measuring point j caused by the unit force of anchor cable i.

4. The cable force calculation method for rib installation of a long-span steel truss arch bridge according to claim 3 is characterized by: The step S3 includes applying an initial force to all the anchor cables of the arch rib segment. , extract the cumulative initial displacement of each measuring point after the arch rib segment is installed ; ； in: (i=1~n) is the cumulative initial vertical displacement of the measuring point i of the rib segment, (i=1~n) is the cumulative initial horizontal displacement of the tower measuring point i.

5. The cable force calculation method for rib installation of a long-span steel truss arch bridge according to claim 4 is characterized in that: The step S4 includes taking the displacement of the measuring points of the rib segments ( ) is taken as the target value of arch rib displacement ( ), take the displacement value of the tower measuring point ( ) as the target value of the tower displacement ( ); ； Then the displacement target value of each measuring point is for: .

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