A cable force calculation method for split-rib installation of a large-span steel truss arch bridge

Abstract

The application provides a cable force calculation method for split-rib installation of a large-span steel truss arch bridge, relates to the technical field of large-span arch bridges, and comprises the following steps: based on the influence matrix principle, an influence matrix reflecting the mutual relationship between the initial tension of the split-rib installation anchoring cable and the cumulative displacement is established, and the initial tension of the anchoring cable capable of simultaneously controlling the height difference between ribs, the displacement of the arch rib and the displacement of the anchoring tower is solved. The cable force calculation method has simple and clear principles, small calculation amount, and does not need iterative calculation or a complex optimization algorithm in the solving process, only uses the influence matrix method, has simple calculation principles and clear mechanical concepts; the method can simultaneously control the height difference between ribs in split-rib installation and the displacement of the arch rib and the displacement of the anchoring tower of the arch rib segment; in addition, the method can simultaneously calculate the initial tension of the anchoring cable, does not need to convert the cable force, and can directly solve the initial tension of the split-rib installation anchoring cable.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of long-span arch bridges, and particularly relates to a cable force calculation method for split-rib installation of a long-span steel truss arch bridge. BACKGROUND

[0002] The steel truss arch bridge adopts a steel truss structure as an arch rib, a plurality of split-rib segments are arranged transversely on the arch rib to adapt to the development trend of long-span and wide bridge decks, and cross braces are arranged between the ribs to strengthen the overall structural stability and collaborative force characteristics. Due to the lifting carrying capacity of the cable hoisting system, each arch rib segment is installed in a split-rib manner, the arch rib is divided into a plurality of arch rib segments along the span direction, and a cable-stayed cantilever method is used for construction, that is, for a single arch rib segment, the single split-rib segment is first hoisted to the predetermined position by the cable hoisting system for installation, then the segment is adjusted to the preset elevation by tensioning the segment cable of the cable-stayed system, and the corresponding anchor cable is simultaneously tensioned to ensure that the offset of the tower is within the allowable range, and the process is repeated for the remaining split-rib segments of the arch rib segment, and the cross braces between the ribs are installed when the height difference between the ribs is within the allowable range, and the subsequent arch rib segments are continuously installed according to the split-rib installation process until the closure.

[0003] 1. Strictly control the height difference between the ribs; the installation accuracy of the steel structure for the member is strictly required, the allowable error of the reserved bolt hole position of the cross brace connecting member and the split-rib segment is generally 2 mm, so the height difference between the ribs must be strictly controlled before the cross brace is installed. Otherwise, if the height difference between the ribs exceeds the limit value, the bolt hole of the cross brace connecting member will be misaligned and cannot be installed, and the transverse offset of the arch rib will also be affected, and in the extreme case, the tower will be twisted too much and an accident will occur, which will endanger the overall stability of the bridge and the safety of the construction.

[0004] 2. Strictly control the elevation of the arch rib segment after the split-rib installation is completed; in order to ensure that the arch line shape is formed and the predetermined position of the subsequent arch rib segment installation is unchanged, the structure state after the installation of the cross brace between the ribs must be consistent with the structure state of the arch rib segment installed as a whole. That is, at this time, the arch rib segment is at the preset elevation set according to the installation of the arch rib segment as a whole, and the cable force is consistent with the cable force value calculated for the installation of the arch rib segment as a whole.

[0005] The foregoing processes are completed by the cable-stayed system, however, the cable-stayed system is a complex statically indeterminate structure system integrating the arch rib, the cable, the tower and the anchor cable, and presents a complex structural mechanics behavior interaction mechanism during the construction process. The split-rib segment installed first in each arch rib segment will affect the preset elevation of the split-rib segment installed later, and the tensioning of the cable of the subsequent split-rib segment will also react on the split-rib segment installed first, causing the change of the cable force distribution and the elevation, and causing the change of the cable force and the line shape of the split-rib segment installed first. On the other hand, in order to avoid too many times of cable adjustment and cause safety hazards such as anchor sliding, the cable must be tensioned once.

[0006] Therefore, in the process of sub-rib installation, the proper initial tension needs to be applied to the anchor cable of each sub-rib segment so that the above two requirements are met after the completion of the sub-rib installation.

[0007] The calculation of the sub-rib installation cable force adopts the calculation idea of "first overall and then local", that is, the existing mature cable force algorithm (such as zero displacement method, elastic support method, optimization algorithm, etc.) is used to calculate the overall installation cable force of the arch rib segment first, and then the sub-rib installation cable force is calculated. The existing technology has the following methods for calculating the sub-rib installation cable force:

[0008] 1. Reverse disassembly method (suitable for double-rib arch bridges)

[0009] The reverse disassembly method takes the ideal overall installation completion state of each arch rib segment as the starting point for backtracking, and strictly follows the reverse order of the actual operation of the sub-rib construction to gradually disassemble, finally obtaining the initial tension and pre-lifting amount parameters of the anchor cable of each sub-rib segment under the sub-rib installation condition.

[0010] Unlike double-rib arch bridges, the middle arch rib of a multi-rib arch bridge structure system needs to additionally bear half of the weight of the cross brace compared to the outer arch ribs. Therefore, when the overall installation initial tension is used for the overall installation of the arch rib segment, the uneven force causes the middle arch rib to have a lower elevation than the two side arch ribs, and as the cantilever length increases, the rib-to-rib elevation difference gradually increases. Therefore, taking this initial rib-to-rib elevation difference as the starting point for reverse disassembly, the initial tension and pre-lifting amount of the anchor cable of each sub-rib segment under the sub-rib installation condition cannot control the rib-to-rib elevation difference of the sub-rib segment, and eventually returns to the initial state with rib-to-rib elevation difference.

[0011] 2. Stress-free state method (suitable for double-rib arch bridges)

[0012] The stress-free state method is based on the state after the overall installation of the arch rib segment is completed, and the stress-free cable length is obtained based on this state. Then, the initial tension and pre-lifting amount of the anchor cable of each sub-rib segment under the sub-rib installation condition are obtained by positive installation of the stress-free cable length. Like the reverse disassembly method, the stress-free cable length is also calculated based on the initial rib-to-rib elevation difference, and the rib-to-rib elevation difference of the sub-rib segment cannot be effectively controlled.

[0013] 3. In the calculation of the hoisting cable force for the sub-rib installation of a large-span three-rib steel truss arch, a method for calculating the sub-rib installation cable force is proposed by Liu Shaoping, Li Qiuyuan, and Zhang Litao. This method considers the collaborative influence of the anchor cable and the anchor tower and uses stepwise interpolation iteration to calculate the sub-rib installation initial tension. This method requires multiple iterations and the number of iterations depends on the rib-to-rib elevation difference control accuracy, which has the problems of complicated calculation and low precision.

[0014] 4、Publication No. CN116756800A, a method for accurately calculating the pre-lifting value of the installation segment of the arch rib, a construction method and a system, comprising: establishing a naked arch self-weight model of the arch rib to obtain a target alignment; establishing an entire segment installation model of the arch rib, assigning an initial cable force, and obtaining a pre-lifting value; determining whether the difference between the pre-lifting value and the target alignment is within the allowable error; if not, adjusting the initial cable force until the pre-lifting value is within the allowable error; if yes, outputting the cable force; establishing a segmented installation model of the arch rib to obtain a displacement influence matrix under the action of the unit cable force and the anchor cable force; based on the cable force as the initial cable force, obtaining the displacement amount, the displacement influence matrix and the pre-lifting value, and obtaining the segmented installation cable force difference of the arch rib; based on the cable force difference and the cable force, obtaining the actual cable force; and based on the actual cable force, obtaining the actual pre-lifting value. The method calculates the initial tension of the segmented rib installation cable based on the displacement influence matrix, and then calculates the corresponding anchor cable initial tension for controlling the tower displacement by using the horizontal component force balance principle of the cable and anchor cable force. However, this method controls the elevation of the arch rib by the initial tension of the cable, does not establish a direct correspondence between the initial tension of the anchor cable and the elevation of the arch rib, and ignores the influence of the anchor cable tension on the elevation of the arch rib.

[0015] 5、Publication No. CN117332656A, a method for calculating the cable force and pre-lifting amount of the arch rib of a large-span steel arch bridge, belongs to the field of bridge construction control. The method comprises the following steps: S1, establishing a finite element model of a basket handle arch bridge; S2, performing forward calculation to obtain the influence matrix of the entire rib cable force and displacement; S3, calculating the entire rib pre-lifting value of the entire rib model; S4, determining whether the entire rib pre-lifting value meets the target alignment requirements; if yes, entering step S5; otherwise, modifying the constraint conditions of the target function, and then turning to step S3; S5, obtaining the estimated cable force value and the corresponding displacement column array; S6, determining whether the displacement under the action of the segmented rib cable force meets the error requirements of the current stage target displacement; if yes, outputting the cable force; otherwise, continuing the difference iteration of the obtained displacement and the target displacement. Although the present application proposes a calculation method based on the current entire rib pre-lifting value to solve the arch rib cable force and side cable wind cable force, and constructs the corresponding segmented rib cable force assembly influence matrix, and then obtains the segmented rib cable force that meets the displacement error range of the arch rib through cyclic iteration. However, this method is limited to calculating the segmented rib installation cable force and side cable wind cable force, and cannot obtain the anchor cable force, and does not control the tower displacement. SUMMARY

[0016] The present application provides a cable force calculation method for segmented rib installation of a large-span steel truss arch bridge, which aims to at least solve the technical problems existing in the prior art and is applicable to all types of arch rib bridges.

[0017] The present application provides the following technical solutions to achieve the above-mentioned purposes:

[0018] A cable force calculation method for split-rib installation of large-span steel truss arch bridge, based on influence matrix principle, establishes an influence matrix reflecting the mutual relationship between the initial tension of the split-rib installation anchor cable and the cumulative displacement, and solves the initial tension of the anchor cable which can simultaneously control the height difference between the ribs, the arch rib displacement of the arch rib segment and the displacement of the anchor tower. The calculation method is as follows:

[0019] Step S1, under the condition of considering the arch line shape, a finite element model of arch rib segment whole rib installation is established, taking the arch rib segment as the calculation object, the arch rib displacement and the anchor tower displacement of the arch rib segment whole rib installation are solved, and the arch rib displacement and the anchor tower displacement are taken as the adjustment target value of the arch rib segment split-rib installation;

[0020] Step S2, based on the finite element model of arch rib segment whole rib installation, under the condition of split-rib installation as the construction method, unit force is applied to each anchor cable of the arch rib segment, and the displacement influence factor is extracted as the element of the influence matrix to construct the influence matrix;

[0021] Step S3, based on the finite element model of arch rib segment whole rib installation, under the condition of split-rib installation as the construction method, initial force is applied to each anchor cable of the arch rib segment, and the cumulative initial displacement of installing the arch rib segment is extracted, which includes the arch rib displacement and the anchor tower displacement;

[0022] Step S4, based on the arch rib displacement and the anchor tower displacement calculated in S1, the average value of the arch rib displacement is extracted as the arch rib displacement target value of the split-rib installation, and the anchor tower displacement is extracted as the anchor tower displacement target value of the split-rib installation;

[0023] Step S5, the matrix equation is established, and the initial tension of each anchor cable of the split-rib installation is solved.

[0024] Further, the step S1 is as follows:

[0025] S1.1, a finite element model of arch rib segment whole rib installation is established, each arch rib segment in the finite element model of arch rib segment whole rib installation includes n split-rib segments arranged transversely and n anchor cables arranged correspondingly, and each split-rib segment is arranged with a displacement measuring point for monitoring the vertical displacement of the split-rib segment, and the top of the anchor tower is arranged with n displacement measuring points corresponding to the anchor cable position for monitoring the horizontal displacement of the anchor tower;

[0026] S1.2, under the condition of arch rib segment whole rib installation as the construction method, the existing cable force calculation method is adopted to approximate the first arch line shape by loosening the cable to approach the arch line shape, and the measuring point displacement of the arch rib segment in the whole rib installation is calculated , ; formula (1)

[0027] Wherein: ( vertical displacement of the measuring point i of the segment, horizontal displacement of the measuring point i of the segment.

[0028] Further, the step S2 comprises applying unit force to all the anchor cables of the segment, and extracting the displacement influence factors under the unit force as elements of the influence matrix to form the influence matrix Formula (2)

[0029] (i=1~n, j=1~n) are vertical displacement influence factors of the measuring point j of the segment and horizontal displacement influence factors of the measuring point j of the segment caused by the unit force of the anchor cable i; similarly (i=1~n, j=1~n) are vertical displacement influence factors of the measuring point j of the segment and horizontal displacement influence factors of the measuring point j of the segment caused by the unit force of the anchor cable i.

[0030] Further, the step S3 comprises applying initial force to all the anchor cables of the segment, and extracting the cumulative initial displacement of each measuring point of the segment after installation; Formula (3)

[0031] (i=1~n) is the cumulative initial vertical displacement of the measuring point i of the segment,

[0032] Further, the step S4 comprises taking the average value of the segment measuring point displacement as the arch rib displacement target value , and taking the segment measuring point displacement value as the segment displacement target value ;

[0033] Then, the displacement target value of each measuring point is:

[0034] Further, the step S5 establishes the matrix equation as follows:

[0035] is the initial tension column array of the segment anchor cable,​​​​​​​​​​​​​​​​ Unit cable force diagonal matrix;

[0036] And formula (2), formula (3), formula (5) are substituted into formula (6), and the initial tension of the split rib installation buckle anchor cable is solved .

[0037] Compared with the prior art, the application has the beneficial effects as follows:

[0038] The cable force calculation method has simple and clear principle, small calculation amount, and does not need iterative calculation or complex optimization algorithm in the solving process, only uses the influence matrix method, has simple calculation principle and clear mechanical concept.

[0039] The method can simultaneously control the inter-rib height difference of the split rib installation and the arch rib displacement and the buckle tower displacement of the arch rib segment;

[0040] In addition, the method can simultaneously calculate the initial tension of the buckle anchor cable, does not need to convert the cable force, and can directly solve the initial tension of the split rib installation buckle anchor cable. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings described below relate to only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor under the premise of the drawings.

[0042] Figure 1 It is an installation finite element model schematic diagram of the arch rib segment of the present application;

[0043] Figure 2 It is a schematic diagram of the bridge in the application example of the present application;

[0044] Figure 3 It is an arch rib model schematic diagram of the bridge shown in the figure; Figure 2

[0045] It is a buckle anchor cable arrangement schematic diagram of the bridge shown in the figure; Figure 4 Figure 2 It is a finite element model schematic diagram of the bridge shown in the figure;

[0046] Figure 5 Figure 2 It is an Anshun bank arch rib segment NS7 split rib installation calculation model of the bridge shown in the figure;

[0047] Figure 6 It is an Anshun bank arch rib segment NS7 split rib installation calculation model of the bridge shown in the figure; Figure 2

[0048] It is an Anshun bank arch rib segment NS7 split rib installation calculation model of the bridge shown in the figure; Figure 7 Figure 6 ​​​The A shown in the figure is a schematic diagram of the arrangement of the measuring points of the tower top of the middle buckle tower.

[0049] Figure 8 For Figure 6 The B shown in the figure is a schematic diagram of the arrangement of the measuring points of the middle buckle rib. DETAILED DESCRIPTION

[0050] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application.

[0051] It should be noted that in the present application: the terms "comprising" and "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 does not have to be limited to those steps or units clearly listed, but can include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices; the orientations or positional relationships indicated by the terms "up", "down", "left", "right", "front", "back", "top", "bottom", "inner", "outer", "middle", "vertical", "horizontal", "lateral", "longitudinal" and the like are based on the orientations or positional relationships shown in the drawings, and these terms are mainly used to better describe the present application and its embodiments, and are not used to limit the indicated devices, elements or components to have a specific orientation, or to be constructed and operated in a specific orientation; the terms "first", "second" and the like are used to distinguish similar objects, and do not necessarily describe a specific order or sequence; the terms "mounting", "setting", "provided with", "connecting", "connected", "sleeved" and the like should be interpreted broadly; for example, it can be fixedly connected, detachably connected, or integrally constructed; it can be mechanically connected, or electrically connected; it can be directly connected, or indirectly connected through an intermediate medium, or it can be the internal communication between two devices, elements or components. In addition, in addition to being used to indicate the orientation or positional relationship, some terms can also be used to indicate other meanings, for example, the term "up" can also be used to indicate a certain dependent relationship or connection relationship in some cases. Those skilled in the art can understand the specific meaning of these terms in the present application according to the specific situation.

[0052] Embodiment. A cable force calculation method for split-rib installation of a large-span steel truss arch bridge, characterized by: based on the influence matrix principle, an influence matrix reflecting the mutual relationship between the initial tension of the split-rib installation anchor cable and the cumulative displacement is established, and the initial tension of the anchor cable which can simultaneously control the height difference between the ribs, the displacement amount of the arch rib segment of the arch rib and the displacement amount of the buckle tower is solved. The calculation method is as follows:

[0053] Step S1, under the condition of considering the arch line shape, an arch rib segment whole rib installation finite element model is established, the arch rib segment is taken as a calculation object, the arch rib displacement and the tower displacement of the arch rib segment during the whole rib installation are solved, and the arch rib displacement and the tower displacement are taken as adjustment target values of the arch rib segment during the partial rib installation;

[0054] Step S2, based on the arch rib segment whole rib installation finite element model, under the condition of the partial rib installation as a construction method, a unit force is respectively applied to each anchor cable of the arch rib segment, a displacement influence factor is extracted as an element of an influence matrix, and the influence matrix is constructed;

[0055] Step S3, based on the arch rib segment whole rib installation finite element model, under the condition of the partial rib installation as a construction method, an initial force is respectively applied to each anchor cable of the arch rib segment, and a cumulative initial displacement of the arch rib segment during the installation is extracted; based on the characteristics of matrix calculation, the initial force can be any value, and the initial force is unique after the final calculation, and for the convenience of calculation, a unit force is usually taken as the initial force for calculation;

[0056] Step S4, based on the arch rib displacement and the tower displacement calculated in S1, an average value of the arch rib displacement is extracted as an arch rib displacement target value during the partial rib installation, and the tower displacement is extracted as a tower displacement target value during the partial rib installation;

[0057] Step S5, a matrix equation is established, and the initial tension of each anchor cable during the partial rib installation is solved.

[0058] The step S1 is as follows:

[0059] S1.1, an arch rib segment whole rib installation finite element model is established, each arch rib segment in the arch rib segment whole rib installation finite element model includes n partial rib segments arranged transversely and n anchor cables arranged correspondingly, one displacement measuring point is arranged on each partial rib segment, for monitoring the vertical displacement of the partial rib segment, and n displacement measuring points are arranged on the top of the tower corresponding to the anchor cable position, for monitoring the horizontal displacement of the tower;

[0060] S1.2, under the condition of the arch rib segment whole rib installation as a construction method, an existing cable force calculation method is adopted, a loose cable arch line shape is taken as a target to approximate a once arch line shape, and the measuring point displacement of the arch rib segment during the whole rib installation is calculated , ; Formula (1)

[0061] Wherein, ( ) is the vertical displacement of the measuring point i of the partial rib segment, ( ) is the horizontal displacement of the measuring point i of the tower.

[0062] The step S2 comprises applying unit force to all the buckle anchor cables of the arch rib segment, extracting displacement influence factors under unit force as elements of the influence matrix to form the influence matrix . Formula (2)

[0063] Wherein: 、 (i=1~n, j=1~n) are vertical displacement influence factors of the sub-rib segment measuring point j and horizontal displacement influence factors of the buckle tower measuring point j caused by unit force of the buckle cable i; similarly 、 (i=1~n, j=1~n) are vertical displacement influence factors of the sub-rib segment measuring point j and horizontal displacement influence factors of the buckle tower measuring point j caused by unit force of the anchor cable i.

[0064] The step S3 comprises applying initial force to all the buckle anchor cables of the arch rib segment , and extracting cumulative initial displacements of each measuring point of the arch rib segment after installation . ; Formula (3)

[0065] Wherein: (i=1~n) is the cumulative initial vertical displacement of the sub-rib segment measuring point i, (i=1~n) is the cumulative initial horizontal displacement of the buckle tower measuring point i.

[0066] The step S4 comprises taking the average value of the sub-rib segment measuring point displacement ( ) as the arch rib displacement target value ( ), and taking the buckle tower measuring point displacement value ( ) as the buckle tower displacement target value ( ). ; Formula (4)

[0067] Then, the displacement target value of each measuring point is: ; Formula (5).

[0068] Further, the step S5 establishes a matrix equation as follows: ; Formula (6)

[0069] Wherein: is the initial tension column array of the buckle anchor cable of the sub-rib, is the unit cable force diagonal matrix; and formula (2), formula (3), formula (5) are substituted into formula (6) to obtain the initial tension of the buckle anchor cable of the sub-rib .

[0070] The problems and calculation ideas solved by the present application are as follows: in the existing arch bridge installation engineering, the arch rib of a large arch bridge is often very large and heavy, and if it is manufactured and transported as a whole, it will face great challenges, whether it is highway, railway or waterway transportation, it will be limited by size and weight; therefore, the arch rib of the arch bridge is divided into several arch rib segments, and the arch rib segments are further divided into several sub-rib segments in structure, thereby reducing the pressure of arch rib manufacturing and transportation. In the installation process of the arch rib, a cable crane system (the cable crane system includes a buckle cable, an anchor cable and a buckle tower) is often used to maintain the arch rib in an arch line shape by adjusting the cable force of the buckle anchor cable, as shown in Figs. Figure 4 、 5 and 6, from the perspective of maintaining the arch line shape, whether the construction method of arch rib segment whole rib installation or sub-rib installation is adopted (the arch rib segment whole rib installation refers to regarding all sub-rib segments constituting the arch rib segment as a whole, and installing and transporting by the cable crane system, the Guniuhe super major bridge project mentioned in the application example is an arch rib segment containing four parallel arranged sub-rib segments, as shown in Fig. Figure 8 ; and the sub-rib installation refers to a construction method of installing each sub-rib segment one by one, and then installing the transverse support between the sub-rib segments after all the sub-rib segments are installed; the finite element models used in the two construction methods are the same, as shown in Figs. Figure 5 、 6 , 7 and 8, the difference is only in the installation method of the arch rib; the arch rib segment whole rib installation and the sub-rib installation are the construction methods commonly used in the prior art, the arch line shape to be maintained is the same; but from the mechanical point of view, the two construction methods have different influences on the statically indeterminate system composed of the arch rib, the buckle cable, the anchor cable and the buckle tower, so the cable force value of the arch rib segment whole rib installation cannot be applied in the construction process of the sub-rib installation; therefore, the calculation idea of the present application is to take the arch rib segment whole rib installation as the condition, to calculate the arch rib displacement and the buckle tower displacement required to maintain the arch line shape first, to take the arch rib displacement and the buckle tower displacement as the target value of controlling the displacement of each sub-rib segment and the buckle tower in the sub-rib installation, and then to calculate the cable force required by the anchor cable and the buckle cable to reach the target value, that is, the initial tension of the buckle anchor cable.

[0071] Application example. The present application has been used in the Guniuhe super major bridge project, and the cable force calculation method used in the present application is specifically explained by taking the sub-rib installation of the project as an example;

[0072] The main bridge of the Guniuhe super major bridge is a deck type steel box truss arch bridge, as shown in Fig. Figure 2 , the calculation span L=520m, the calculation sag f=130m, the calculation sag / span ratio L / f=1 / 4, and the arch axis coefficient is 1.55. The radial height of the truss arch top section is 9.0m, and the radial height of the arch foot section is 14.0m. The truss arch transverse bridge is composed of four arch ribs, and transverse supports are arranged between the arch ribs, as shown in Fig. Figure 3 .

[0073] The bridge single-pier arch rib arch truss is divided into 22 segments, 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 cable-stayed and hanging cantilever, and the hinge is sealed after the installation of the NS3 segment. The Anshun bank is hoisted in 11 segments, and the Panzhou bank is hoisted in 10 segments. The maximum hoisting weight of the segment is 283.3t (the arch rib NS1 segment), and the minimum hoisting weight of the segment is 118.0t (the Anshun bank arch rib NS11 segment). The cable-stayed and hanging system is arranged as shown in Figure 4 The 1#-8# anchor cables on the Anshun bank are anchored to the Anshun bank boundary pier, and the 5# arch upper column is used as an auxiliary tower, and a cable saddle is arranged at the top of the tower for supporting the 9#-11# through cables. The 1#-8# anchor cables on the Panzhou bank are anchored to the Panzhou bank boundary pier, and an auxiliary tower is arranged on the boundary pier, and the 9#-11# anchor cables are anchored to the auxiliary tower anchor box.

[0074] The calculation process of the cable force of the segmental rib installation is described by taking the installation of the Anshun bank arch rib segment NS7 as an example.

[0075] 1) A finite element program is used to establish an arch rib segment whole rib installation calculation model, and the whole rib construction sequence is that each arch rib segment is installed with 4 arch ribs at the same time, and then the cross brace is installed, the initial tension of each construction stage anchor cable is obtained by using the existing cable force calculation method, and the target is to approach the initial arch line shape by loosening the cable. In the model, the arch rib and the anchor tower are simulated by beam elements, and the anchor cable and the cable are simulated by cable elements; the pier bottom is fixed, and the arch foot is fixed. The calculation model is shown in Figure 5 The measurement point arrangement of the Anshun bank arch rib segment NS7 is shown in Figure 6 The anchor tower measurement points 1-4 are arranged on the top of the anchor tower, as shown in Figure 7 The arch rib measurement points 1-4 are arranged at each arch rib anchor point, as shown in Figure 8 The arch rib measurement points 1-4 are arranged at each arch rib anchor point, as shown in

[0076] 2) A finite element program is used to establish an Anshun bank arch rib segment NS7 segmental rib installation calculation model, and the calculation model is shown in Figure 6 The anchor tower measurement points 1-4 are arranged on the top of the anchor tower, as shown in Figure 7 The arch rib measurement points 1-4 are arranged at each arch rib anchor point, as shown in Figure 8 The arch rib measurement points 1-4 are arranged at each arch rib anchor point, as shown in

[0077] The arch rib segment NS7 is installed in the segmental rib construction mode of "arch rib 3→ arch rib 2→ arch rib 4→ arch rib 1→ cross brace". A unit force of 100kN is applied to each anchor cable of the arch rib segment NS7, the influence factor of the unit force on the displacement of each measurement point after the installation of all segmental ribs is extracted, and an influence matrix ,

[0078] Unit force matrix is:

[0079] Unit force diagonal matrix is:

[0080] 4) Based on the construction method described in step 3), an initial force of 100 kN is applied to each anchor cable, and the cumulative initial displacement of each displacement measuring point after installation of all the rib segments is extracted ;

[0081] Initial force matrix is:

[0082] 5) Based on the arch rib segment whole rib installation calculation model described in step 1), the anchor cable force and arch rib and anchor tower displacement of the arch rib segment NS7 during whole rib installation are extracted, as shown in Table 1 and Table 2;

[0083] As can be seen from Table 1, during the whole rib installation of this segment, each anchor cable applies the same initial tension, and the anchor cable force increases after the installation of the cross brace. Due to the large stiffness of the inter-rib cross brace, the anchor cable force increment after the installation of the cross brace only differs by 0.3 kN. After the installation of the cross brace, the anchor cable force is 5575.0 kN and 4188.8 kN, respectively.

[0084] As can be seen from Table 2, due to the fact that the middle two arch ribs of each arch rib segment bear half of the cross brace weight compared to the outer arch ribs, after the installation of the cross brace for each arch rib segment, the middle arch ribs will be lower than the two side arch ribs. This inter-rib height difference accumulates to the arch rib segment NS7, and the inter-rib height difference reaches 4.7 mm, and increases to 5.0 mm after the installation of the cross brace. It can be seen that the inverse dismantling or calculation of the unstressed state cannot be performed based on this state with the initial inter-rib height difference.

[0085] As can be seen from Table 2, during the whole rib installation of the arch rib segment NS7, the displacement of each measuring point ;

[0086] 6) In order to control the inter-rib elevation difference of the arch rib segment NS7 after the completion of the rib installation and the elevation of this arch rib segment, the average value of the arch rib displacement of formula (12) is taken as the target value of the arch rib displacement, and the target value of the anchor tower displacement is the same as formula (12). Then, the displacement target values of each measuring point of the arch rib segment NS7 after the installation of all the arch ribs are ,

[0087] 7) The matrix equation is established, and formula (7), formula (9), formula (10), formula (11), and formula (13) are substituted into the matrix equation;

[0088] Solving score rib installation buckle anchor initial tension ;

[0089] Equation (14) is taken as the initial tension of the buckle anchor installed by the sub-rib, and the force and displacement of the buckle anchor during the installation of the arch rib segment NS7 are shown in Tables 3 and 4.

[0090] As shown in Table 3, the initial tension of the sub-rib installation is used for sub-rib installation, and after the installation of all sub-rib segments of the arch rib segment NS7 is completed (construction stage: installation of arch rib 1), the forces of each buckle anchor are basically symmetrically distributed, and the forces of the middle buckle anchors (buckle anchors 2 and 3) are slightly greater than those of the outer buckle anchors (buckle anchors 1 and 4). This is because after the installation of the cross brace of the previous arch rib segment (arch rib segment NS6), the middle arch rib is lower than the outer arch rib, resulting in that the initial installation position of the tangent of the middle arch rib of the arch rib segment NS7 is lower than that of the outer arch rib, and a greater force needs to be applied to compensate for the initial rib height difference of the tangent installation of the middle arch rib. After the installation of the cross brace, the resultant forces of the buckle anchors are 5566.1 kN and 4203.9 kN, respectively, which are 1.6‰ and 3.6‰ different from the resultant forces of the buckle anchors installed by the whole rib, respectively. It can be seen that the resultant forces of the buckle anchors installed by the sub-rib are almost the same as the resultant forces of the buckle anchors installed by the whole rib.

[0091] As shown in Table 4, after the installation of all sub-rib segments is completed (construction stage: installation of arch rib 1), each arch rib and buckle tower measuring point is located at the displacement target value shown in equation (13), and the rib height difference is 0 mm, which satisfies the arch rib height difference limit value of bolt clearance <2 mm for the installation of the cross brace member. After the installation of the cross brace, the middle arch rib bears half of the weight of the cross brace, which is 0.2 mm lower than the outer arch rib.

[0092] The sub-rib segment of the remaining arch rib segment installed by the buckle anchor force calculated by the method is installed, and the loose cable becomes an arch, which is compared with the whole rib installation and one-time arch rib linear shape as 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.

[0093]

[0094] From Table 5, it can be seen that the maximum inter-rib height difference obtained by installing the whole rib is 109.5 mm, the maximum inter-rib height difference obtained by installing the divided rib is 2 mm, and the maximum inter-rib height difference obtained by once arching is 1.2 mm. The inter-rib height difference obtained by installing the divided rib is far less than that obtained by installing the whole rib, and only 0.8 mm greater than the maximum inter-rib height difference obtained by once arching. It can be seen that the cable force of the divided rib installation can effectively control the inter-rib height difference after arching. Comparing the loose cable arching line shape of arch rib 1 and arch rib 2, the loose cable arching line shapes obtained by installing the whole rib and installing the divided rib can both approximate the once arching line shape, indicating that the structural state of each arch rib segment after installing the divided rib is basically consistent with the structural state of the whole rib installation. Compared with the once arching line shape, the maximum deviations of arch rib 1 obtained by the two installation methods are 11.6 mm and 10.8 mm, respectively, and the maximum deviations of arch rib 2 obtained by the two installation methods are -110 mm and 9.6 mm, respectively. It is shown that the cable force of the divided rib installation obtained by the method can better match the arching line shape target after the loose cable arching.

[0095] Obviously, the above only describes some embodiments of the present application, but not all embodiments. The above embodiments are not intended to limit the present application, and the present application can have various changes and variations for those skilled in the art. Any combination, modification, equivalent replacement, improvement and other embodiments made by those skilled in the art within the spirit and principle of the present application should be within the protection scope of the present application.

Claims

1. A cable force calculation method for split-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 of the split-rib installation anchor cable and the cumulative displacement is established to solve the initial tension of the anchor cable that can simultaneously control the height difference between ribs, the displacement of the arch rib and the displacement of the anchor tower. Step S1, under the condition of considering the arch line shape, a finite element model of the arch rib segment whole-rib installation is established, the arch rib segment is taken as the calculation object, the displacement of the arch rib and the displacement of the anchor tower during the whole-rib installation of the arch rib segment are solved, and the displacement of the arch rib and the displacement of the anchor tower are taken as the adjustment target values of the split-rib installation of the arch rib segment; S1.1, a finite element model of the arch rib segment whole-rib installation is established, each arch rib segment in the finite element model of the arch rib segment whole-rib installation includes n split-rib segments arranged transversely and n anchor cables arranged correspondingly, a displacement measuring point is arranged on each split-rib segment for monitoring the vertical displacement of the split-rib segment, and n displacement measuring points are arranged on the anchor cable at the top of the anchor tower for monitoring the horizontal displacement of the anchor tower; S1.2 under the condition of the installation method of the whole rib with the arch rib segment, using the existing cable force calculation method, approximating the primary arch line shape with the loose cable as the target, calculating the displacement of the measuring point of the arch rib segment when the whole rib is installed , ； wherein: (0.5 < a < 1.5) is the vertical displacement of the measurement point of the rib segment, i (0.5 < a < 1.5) is the horizontal displacement of the measurement point of the tower segment; and i ​​ Step S2, based on the arch rib segment whole rib installation finite element model, under the condition of sub-rib installation as the construction method, unit force is respectively applied to each buckle anchor cable of the arch rib segment, the displacement influence factor is extracted as the element of the influence matrix, and the influence matrix is constructed; the step S2 includes applying unit force to all buckle anchor cables of the arch rib segment, extracting the displacement influence factor under the action of the unit force as the element of the influence matrix, and forming the influence matrix ; ； wherein: , (i = 1 ~ n, j = 1 ~ n) are the vertical displacement influence factors of the sub-rib segment measuring point j and the horizontal displacement influence factors of the tower measuring point j generated by the unit force of the buckle cable i; similarly , (i = 1 ~ n, j = 1 ~ n) are the vertical displacement influence factors of the sub-rib segment measuring point j and the horizontal displacement influence factors of the tower measuring point j generated by the unit force of the anchor cable i; Step S3, based on the finite element model of the arch rib segment whole-rib installation, under the condition of the split-rib installation as the construction method, an initial force is applied to each anchor cable of the arch rib segment, and the cumulative initial displacement of the installation of the arch rib segment is extracted, the cumulative initial displacement includes the displacement of the arch rib and the displacement of the anchor tower; Step S4, based on the displacement of the arch rib and the displacement of the anchor tower calculated in S1, the average value of the displacement of the arch rib is extracted as the target value of the displacement of the arch rib during the split-rib installation, and the displacement of the anchor tower is extracted as the target value of the displacement of the anchor tower during the split-rib installation; Step S5, establishing matrix equation ; wherein: is the initial tension array of the segmental rib installation buckle anchor cable, is a unit cable force diagonal matrix, is an influence matrix, is a displacement target value of each measuring point, is the cumulative initial displacement of each measuring point after the installation of the arch rib segment, is an initial force; and the initial tension of each buckle anchor cable of the segmental rib installation is solved.

2. The cable force calculation method for split-rib installation of long-span steel truss arch bridges according to claim 1, characterized in that: The step S3 includes applying initial force to all the buckle anchor cables of the arch rib segment , extracting the cumulative initial displacement of each measuring point of the arch rib segment after installation ; ； Wherein: =1~n) is the initial vertical displacement of the measuring point of the sub-rib segment, i =1~n) is the initial horizontal displacement of the measuring point of the sub-rib segment, i =1~n) is the initial vertical displacement of the measuring point of the sub-rib segment, =1~n) is the initial horizontal displacement of the measuring point of the sub-rib segment, i =1~n) is the initial vertical displacement of the measuring point of the sub-rib segment, i =1~n) is the initial horizontal displacement of the measuring point of the sub-rib segment, 3. The cable force calculation method for split-rib installation of long-span steel truss arch bridges according to claim 2, characterized in that: The step S4 comprises taking the average value of the displacement of the segment measurement points of the rib as the displacement target value of the arch rib ( ) , and taking the displacement value of the segment measurement points of the tower as the displacement target value of the tower ( ) , the displacement value of the segment measurement points of the tower ( ) as the displacement target value of the tower ( ) ； Then the displacement target value of each measuring point is is: 。

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