CN117349939A - Steel pipe concrete arch bridge construction cable force determination method based on arch rib linear difference iteration - Google Patents
Steel pipe concrete arch bridge construction cable force determination method based on arch rib linear difference iteration Download PDFInfo
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Abstract
The invention discloses a steel pipe concrete arch bridge construction cable force determining method based on arch rib linear difference iteration, which comprises the steps of firstly, calculating and disassembling a steel pipe concrete arch bridge in a staged construction process into static calculation of key working conditions; combining a basic principle of a stress-free state method with an unknown load coefficient method, preliminarily setting a target control value of working conditions such as arch bridge cable body unit tensioning and the like, and simultaneously establishing a structural statics balance condition; by taking reference to the thought of 'forward iteration' in the determination of reasonable construction state of the cable-stayed bridge, the main arch rib cable-loosening simulation line shape gradually approaches to the target line shape through repeated iteration of manually set control target positions.
Description
Technical Field
The invention relates to the field of steel tube concrete arch bridge construction, in particular to a steel tube concrete arch bridge construction cable force determination method based on arch rib linear difference iteration.
Background
The steel pipe concrete arch bridge has the advantages of reasonable stress, high structural rigidity, strong spanning capability and the like, and is widely applied to mountain bridge construction by combining a construction process of a cable-stayed buckling hanging method. At present, the span of the large-span steel pipe concrete arch bridge breaks through 575m, and the span of the reinforced steel pipe concrete arch bridge taking steel pipe concrete as a strong stiffness framework breaks through 600m.
Along with the continuous breakthrough of the span of the arch bridge, the number of cantilever sections of the arch rib and the number of cable units are correspondingly increased, the steel pipe concrete arch bridge comprises a main arch rib, the main arch rib comprises a plurality of arch rib sections, the construction content of each stage comprises the steps of installing a follow-up arch rib section on a preceding arch rib section, and the cable units are fixed on the arch rib sections when the arch rib sections are installed and used for lifting the arch rib sections to target positions; in construction, in order to support the cable body unit, buckling towers are usually arranged at two sides of a river channel, steel anchor boxes are arranged on the buckling towers, the cable body unit comprises buckling cables and back cables, the buckling cables are connected between arch rib sections and the buckling towers and used for providing lifting tension for the arch rib sections, and the back cables are connected at fixed positions of the buckling towers and the bank sides of the river channel and used for providing balanced supporting tension for the buckling towers; in order to protect the structure of the buckling tower, the buckling rope and the back rope are usually fixed on a steel anchor box.
When the steel pipe concrete arch bridge is suspended and spliced, the arch rib, the buckling tower and the cable body unit are in a coupling stress state, the cable force of the cable body unit is required to be frequently adjusted, the structural form is difficult to adjust and control, the construction technology, the safety risk and the like are difficult to build a large-span steel pipe concrete arch bridge in a mountain area, and how to quickly and accurately calculate the cable force of the cable body unit of the arch bridge becomes the key of the safety control and high-quality construction of the arch bridge structure.
When the large-span steel pipe concrete arch bridge is constructed by adopting a cable-stayed buckling method, the steel pipe concrete arch bridge comprises a plurality of arch rib sections, the arch rib sections are constructed in a staged mode according to the sections of the arch rib sections, and finally the arch is formed into an arch shape in a section-by-section mode, but the arch formed by the staged construction is always inconsistent with the arch shape formed by the arch rib once falling frame (namely, the manually set target line shape), and the aim of adjusting the cable force of the cable body unit is to ensure the closing of the arch rib line shape, the tower deflection, the structural stress and the like in the construction process as much as possible.
The common construction mode for the diagonal buckling method is to stretch each arch rib section in sequence, the cable body units used for stretching are not removed before the arch ribs are closed, and the arch ribs are removed uniformly after being closed.
The cable force calculation method commonly used for carding and summarizing the current steel tube concrete arch bridge can be roughly divided into three types according to actual control effects: process adjustment, optimal result, optimal process, controllable result and optimal whole process; the first method can not realize one-time tensioning of the cable body unit, and the cable force needs to be frequently adjusted during site construction, but the arch rib cable loosening and arch forming simulation line shape is good; the second method is opposite to the first method, and focuses on optimization of arch rib line shape in the construction process, namely, uniformity of construction line shape and cable force is guaranteed by sacrificing arch line shape forming precision; the third method optimizes construction cable force by constructing a mathematical model under the constraint condition of the whole process, and has certain requirements on mathematical work bottoms and programming capacity of users, so that the construction cable force is difficult to popularize in engineering in a large scale.
Therefore, the existing arch bridge construction cable force calculation method is either excessively dependent on cable adjusting experience of engineering personnel, or a large amount of influence matrixes are required to be extracted and assembled, or a mathematical means is required to be utilized to self-program an optimization program to solve construction cable force, so that the arch bridge construction cable force calculation method in the prior art is complicated, the difficulty is high, and the calculation method which depends on cable adjusting experience of engineering personnel also has the technical problems of low precision and high error rate.
In addition, in the actual construction process, a novel construction method also appears, namely, each arch rib section is tensioned in sequence, a cable body unit for tensioning is partially dismantled according to different construction stages in the arch rib cantilever assembling process before the arch ribs are closed, the dismantled cable body unit is applied to the tensioning of the subsequent arch rib section or other purposes, and the number of steel anchor boxes is not required to be increased too much, so that the resource utilization rate is improved and the construction cost is saved.
The above cable force calculation methods are not suitable for the novel construction method, and the cable force of each cable body unit in the novel construction method process is difficult to accurately calculate, so that the cable force is frequently adjusted in the construction process, the construction difficulty is increased, and the construction efficiency is reduced.
Disclosure of Invention
The invention aims to provide a steel pipe concrete arch bridge construction cable force determining method based on arch rib linear difference iteration, which aims to solve the technical problems that in the prior art, arch bridge construction cable force calculating methods are complicated, difficulty is high, and the calculating method which depends on cable adjusting experience of engineering personnel is low in precision and high in error rate.
In order to solve the technical problems, the invention adopts the following technical scheme:
the invention discloses a steel pipe concrete arch bridge construction cable force determining method based on arch rib linear difference iteration, wherein the steel pipe concrete arch bridge comprises a main arch rib, the main arch rib comprises a plurality of arch rib sections, the construction content of each stage comprises the steps of installing a follow-up arch rib section on a preceding arch rib section, and cable body units are fixed on the arch rib sections when the arch rib sections are installed and used for lifting the arch rib sections to target positions; the method comprises the following steps:
s1, collecting construction drawing and design scheme information, establishing a staged arching finite element model of a steel pipe concrete arch bridge, and correcting physical parameters of model materials to enable the model materials to be consistent with real structural parameters and performance indexes;
s2, setting initial control target positions of arch rib sections, performing initial arch forming process simulation calculation on a staged arch forming finite element model of the established steel pipe concrete arch bridge, lifting each arch rib section to the control target positions through cable body units before arch rib closure through simulation calculation, obtaining an initial simulated loose cable arch forming simulated line shape after arch rib closure, and then comparing the initial simulated cable forming line shape with a target line shape to obtain height difference values of each arch rib section in the target line shape and each arch rib section in the initial loose cable arch forming simulated line shape; specifically, the initial control target position of the arch rib section is the design position of the arch rib section according to the related construction drawing and design scheme;
S3, judging whether the difference value between the target linear shape and the arch-forming simulation linear shape of the loose cable is smaller than a preset threshold value, if so, stopping calculation, and executing the step S5; otherwise, executing the step S4;
s4, accumulating the height difference value of each arch rib section obtained by the previous calculation and the value of the control target position set by the previous calculation, and performing iterative arch forming process simulation calculation on the staged arch forming finite element model of the steel pipe concrete arch bridge as a new control target position, lifting each arch rib section to the cable force value of the control target position through the cable body unit before closing the arch rib by simulation calculation, and obtaining the height difference value of each arch rib section in the target line shape and each arch rib section in the arch forming simulation line shape of the loose cable after closing the newly simulated arch rib; then, returning to the step S3;
s5, extracting the cable force value results of each cable body unit in the simulation calculation of the last arch forming process, and giving the cable force value results to a staged arch forming finite element model of the steel pipe concrete arch bridge; and then, applying an unclosed mating force to each cable body unit, carrying out structural normal assembly analysis, extracting the internal force result of each cable body unit stretching stage unit, and taking the internal force result of each cable body unit stretching stage unit as a steel pipe concrete arch bridge cable body unit stretching field instruction value.
Preferably, in step S1, the steel pipe concrete arch bridge includes buckling towers arranged at two sides of the river channel, a front wind-resistant cable is arranged between the buckling towers at two sides, and rear wind-resistant cables are respectively arranged at one sides of the buckling towers at two sides, which are far away from each other;
the main arch rib comprises two main arch half spans, namely a first side main arch half span and a second side main arch half span, each main arch half span is provided with N arch rib sections, and the two main arch half spans are connected through a closure section;
each arch rib section is connected with the buckling tower on one side where the arch rib section is located through a pair of cable units, each pair of cable units comprises a buckling cable and a back cable, the buckling cable is connected between the arch rib section and the buckling tower and used for providing lifting tension for the arch rib section, and the back cable is connected at the fixed position of the buckling tower and the bank of the river and used for providing balanced supporting tension for the buckling tower.
Preferably, in step S1, during construction, the cable body units are sequentially installed on each arch rib section according to the sequence of staged construction from two sides to the middle of the main arch, and the cable body units of each arch rib section are maintained to be connected during the assembly process of the arch rib cantilever and before the closure of the arch rib.
Preferably, in step S1, during construction, the cable body units are sequentially installed on each arch rib section according to the sequence of staged construction from two sides to the middle of the main arch, and simultaneously, during construction, before installing the subsequent arch rib sections, during assembling the arch rib cantilever and before closing the arch rib, the cable body units on part of the arch rib sections in the non-terminal arch rib sections are removed.
Preferably, in step S1, the staged arching finite element model of the steel pipe concrete arch bridge includes an initial model and an i-th stage model; the initial model is a static model of a connecting structure between the buckling tower and the front/rear wind-resistant cable, the ith stage model comprises a connecting structure between the buckling tower and the front/rear wind-resistant cable, and also comprises an ith arch rib section, a corresponding cable body unit structure, an arch rib section with a mounted preamble of the corresponding cable body unit structure and a corresponding cable body unit structure, i epsilon {1,2,3,..N }, wherein N represents the number of arch rib sections contained in the main arch half span.
Preferably, in step S1, in the staged arching finite element model of the steel pipe concrete arch bridge, according to the construction drawing and the design scheme information, the design positions corresponding to the 1 st to N-1 st vertical displacements of the cantilever ends of the arch rib segments and the design positions corresponding to the displacement of the cantilever ends of the nth arch rib segments around the transverse bridge to the corner are marked.
The invention has the following beneficial effects: when carrying out calculation and analysis on the construction cable force of the steel pipe concrete arch bridge, the proper iteration mode and iteration times can be flexibly selected while the line shape of the main arch rib process, the tower deviation and the arch loosening simulation line shape are considered, and the comprehensive optimization of the final construction cable force scheme is realized on the basis of ensuring one-time tensioning of the cable body unit; the method can solve the technical problems that the existing arch bridge construction cable force calculation method excessively depends on cable adjusting experience of engineering personnel, or a large amount of influence matrixes are required to be extracted and assembled, or the construction cable force is required to be solved by utilizing a mathematical means self-programming optimization program, so that the arch bridge construction cable force calculation method in the prior art is complicated, the difficulty is high, and the calculation method depending on the cable adjusting experience of the engineering personnel is low in precision and high in error rate.
Drawings
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings, in which:
FIG. 1 is a schematic view of the general arrangement of cantilever beams according to the present invention.
Fig. 2 is a DZ displacement cloud chart of a model of a tensioning first inhaul cable construction stage in the practical verification of the unclosed mating force.
Fig. 3 is a DZ displacement cloud chart of a model in a construction stage of tensioning a second inhaul cable in practical verification of the unclosed mating force.
Fig. 4 is a DZ displacement cloud chart of a first cable tension stage in the unknown load coefficient method of the present invention.
Fig. 5 is a DZ displacement cloud chart of a first cable tension stage in the unknown load coefficient method of the present invention.
Fig. 6 is a schematic illustration of an arch bridge elevation arrangement in an embodiment of the invention.
Fig. 7 is a schematic structural diagram of a cable hoisting and diagonal buckling system in an embodiment of the invention.
Fig. 8 is an enlarged view of the structure of the region C in fig. 7.
FIG. 9 is a finite element model of a structure in an embodiment of the invention.
FIG. 10 is a graph showing the difference between the arch displacement of the loose rope and the falling frame displacement in an iterative manner in the embodiment of the invention.
FIG. 11 is a graph showing the difference between the arch displacement and the first falling displacement of the two loose cables in an iterative manner in an embodiment of the present invention.
FIG. 12 is a graph showing the variation of the cumulative vertical displacement of the cantilever end of an arch rib in an iterative manner in accordance with an embodiment of the present invention.
FIG. 13 is a graph showing the variation of the vertical accumulated displacement of the cantilever ends of two arch ribs in an iterative manner in an embodiment of the invention.
Fig. 14 is a graph showing horizontal displacement change of the vertical bridge of the tower top in different iteration modes according to an embodiment of the present invention.
Fig. 15 is a diagram showing an initial tension change of each cable unit in an iterative manner in accordance with an embodiment of the present invention.
Fig. 16 is a diagram showing initial tension changes of each cable body unit in an iterative manner in an embodiment of the present invention.
Reference numerals illustrate: 100. a first main beam segment; 101. a first cable; 102. a second main beam section; 103. a second guy cable; 200. steel pipe concrete arch bridge; 201. a main tower; 202. buckling a tower; 203. a front wind-resistant cable; 204. a rear wind-resistant cable; 205. a first cable unit group; 206. a second cable unit group; 207. a third cable unit group; 208. a fourth cable body unit group; 209. a fifth cable unit group; 210. rib segments; 211. a cable hoist system; 212. segment number one pair; 213. segment pair number two; 214. segment number three pair; 215. segment number four pair; 216. a segment number five pair; 217. a closure section; 218. a main rope; 219. a traction cable; 220. and (5) lifting ropes.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures. In the description of the present invention, it should be noted that, directions or positional relationships indicated by terms such as "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., are directions or positional relationships based on those shown in the drawings, or are directions or positional relationships conventionally put in use of the inventive product, are merely for convenience of describing the present invention and simplifying the description, and are not indicative or implying that the apparatus or element to be referred to must have a specific direction, be constructed and operated in a specific direction, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," "third," and the like are used merely to distinguish between descriptions and should not be construed as indicating or implying relative importance. Furthermore, the terms "horizontal," "vertical," and the like do not denote a requirement that the component be absolutely horizontal or overhang, but rather may be slightly inclined. As "horizontal" merely means that its direction is more horizontal than "vertical", and does not mean that the structure must be perfectly horizontal, but may be slightly inclined. In the description of the present invention, it should also be noted that, unless explicitly specified and limited otherwise, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
The method can be applied to the field of steel tube concrete arch bridges, and solves the technical problems that in the prior art, all arch bridge construction cable force calculation methods are complicated, the difficulty is high, and the calculation method which depends on cable adjustment experience of engineering personnel is low in precision and high in error rate.
Based on the technical problems solved by the invention, the invention discloses a steel pipe concrete arch bridge construction cable force determining method based on arch rib linear difference iteration, wherein the steel pipe concrete arch bridge comprises a main arch rib, the main arch rib comprises a plurality of arch rib sections, the construction content of each stage comprises that a follow-up arch rib section is arranged on a preceding arch rib section, and cable body units are fixed on the arch rib sections when the arch rib sections are arranged, and are used for lifting the arch rib sections to target positions;
the method is characterized by comprising the following steps of:
s1, collecting construction drawing and design scheme information, establishing a staged arching finite element model of a steel pipe concrete arch bridge, and correcting physical parameters of model materials to enable the model materials to be consistent with real structural parameters and performance indexes;
s2, setting initial control target positions of arch rib sections, performing initial arch forming process simulation calculation on a staged arch forming finite element model of the established steel pipe concrete arch bridge, lifting each arch rib section to the control target positions through cable body units before arch rib closure through simulation calculation, obtaining an initial simulated loose cable arch forming simulated line shape after arch rib closure, and then comparing the initial simulated cable forming line shape with a target line shape to obtain height difference values of each arch rib section in the target line shape and each arch rib section in the initial loose cable arch forming simulated line shape; specifically, the initial control target position of the arch rib section is the design position of the arch rib section according to the related construction drawing and design scheme;
S3, judging whether the difference value between the target linear shape and the arch-forming simulation linear shape of the loose cable is smaller than a preset threshold value, if so, stopping calculation, and executing the step S5; otherwise, executing the step S4;
s4, accumulating the height difference value of each arch rib section obtained by the previous calculation and the value of the control target position set by the previous calculation, and performing iterative arch forming process simulation calculation on the staged arch forming finite element model of the steel pipe concrete arch bridge as a new control target position, lifting each arch rib section to the cable force value of the control target position through the cable body unit before closing the arch rib by simulation calculation, and obtaining the height difference value of each arch rib section in the target line shape and each arch rib section in the arch forming simulation line shape of the loose cable after closing the newly simulated arch rib; then, returning to the step S3;
s5, extracting the cable force value results of each cable body unit in the simulation calculation of the last arch forming process, and giving the cable force value results to a staged arch forming finite element model of the steel pipe concrete arch bridge; and then, applying an unclosed mating force to each cable body unit, carrying out structural normal assembly analysis, extracting the internal force result of each cable body unit stretching stage unit, and taking the internal force result of each cable body unit stretching stage unit as a steel pipe concrete arch bridge cable body unit stretching field instruction value.
The general design idea of the invention is as follows: when the steel pipe concrete arch bridge is constructed by cable-stayed buckling, the arch rib, the buckling tower and the temporary cable body are coupled and stressed, so that the arch rib line shape control difficulty is high, and the construction cable force is complex in calculation; in view of the above, a construction cable force calculation method based on linear difference iteration is provided by fusing the principle of a stress-free state method and the idea of normal loading iteration; firstly, adopting an unclosed cooperation method, and calculating and disassembling a steel pipe concrete arch bridge in a staged construction process into static calculation of key working conditions; combining a basic principle of a stress-free state method with an unknown load coefficient method, preliminarily setting a target control value of working conditions such as arch bridge cable body unit tensioning and the like, and simultaneously establishing a structural statics balance condition; by means of the thought of 'forward iteration' in determining reasonable construction state of the cable-stayed bridge, the main arch rib loose cable arch simulated linear gradually approaches the target linear through repeated iteration of artificially set control target positions.
Specifically, in step S1, the steel pipe concrete arch bridge includes buckling towers arranged at two sides of a river channel, front wind-resistant cables are arranged between the buckling towers at two sides, and rear wind-resistant cables are respectively arranged at one sides of the buckling towers at two sides, which are far away from each other;
the main arch rib comprises two main arch half spans, namely a first side main arch half span and a second side main arch half span, each main arch half span is provided with N arch rib sections, and the two main arch half spans are connected through a closure section;
Each arch rib section is connected with the buckling tower on one side where the arch rib section is located through a pair of cable units, each pair of cable units comprises a buckling cable and a back cable, the buckling cable is connected between the arch rib section and the buckling tower and used for providing lifting tension for the arch rib section, and the back cable is connected at the fixed position of the buckling tower and the bank of the river and used for providing balanced supporting tension for the buckling tower.
In actual construction, the arch rib segments are often hoisted by adopting a cable hoist system, such as tower cranes, automobile cranes and the like, which are common hoisting modes.
Specifically, step S1 combines the basic principle of the stress-free state method with the unknown load coefficient method to establish the structural statics balance condition equation. In the prior art, three important conclusions of the stress-free state method: (1) as long as the stress-free state quantity of the component unit is certain, the final stress state of the structure is uniquely determined no matter how the structure is formed; (2) once the load borne by the structure is determined, the stress-free length adjustment of the cable body and the cable force change have a mapping relation; (3) the final stress state of the staged forming structure can be mutually independent through the stress-free state quantity of the active control unit. Essentially, the stress-free state method establishes a direct link between the process state and the process state, and the process state and the bridge formation state of the bridge construction in stages.
The basic principle of the stress-free state method shows that if the stress-free state quantity of the component units is not controlled, the stress state of the arch bridge structure after a series of construction processes is inconsistent with the static state stress of the structure under the working condition. In order to simplify the calculation and analysis of the construction process of the large-span arch bridge structure, the equivalent conditions of an arch bridge structure staged construction model and a static model under corresponding working conditions are established by applying an unclosed mating force to a member unit, so that the calculation of the stress state analysis of the construction process of the arch bridge structure can be converted into the static calculation under the corresponding working conditions of the structure.
Specifically, in step S1, during construction of the steel pipe concrete arch bridge, the cable units are sequentially installed on each arch rib section according to the sequence of staged construction from two sides to the middle of the main arch, and the cable units of each arch rib section are maintained to be connected during the assembly process of the arch rib cantilever and before the closure of the arch rib.
In another case, in step S1, during construction, the cable units are sequentially installed on each arch rib section according to the sequence of staged construction from two sides to the middle of the main arch, and simultaneously, during construction, before installing the subsequent arch rib section, during the assembly process of the arch rib cantilever and before closing the arch rib, the cable units on part of the arch rib sections in the non-terminal arch rib sections are removed.
Specifically, in step S1, the staged arching finite element model of the steel pipe concrete arch bridge is disassembled into each stage according to key working conditions such as wind-resistant cable tensioning, buckling/back cable tensioning and the like, and the stages comprise an initial model and an ith stage model; the initial model is a static model of a connecting structure between the buckling tower and the front/rear wind-resistant cable, the ith stage model comprises a connecting structure between the buckling tower and the front/rear wind-resistant cable, and also comprises an ith arch rib section, a corresponding cable body unit structure, an arch rib section with a mounted preamble of the corresponding cable body unit structure and a corresponding cable body unit structure, i epsilon {1,2,3,..N }, wherein N represents the number of arch rib sections contained in the main arch half span.
Specifically, in the staged arching finite element model of the steel pipe concrete arch bridge, the design positions corresponding to the vertical displacement of the cantilever ends of the 1 st to N-1 st arch rib sections and the design positions corresponding to the displacement of the cantilever ends of the N th arch rib sections around the transverse bridge to the corner are marked according to the construction drawing and the design scheme information.
Specifically, in step S2, performing initial arch forming process simulation calculation on the staged arch forming finite element model of the established steel pipe concrete arch bridge includes the following steps:
s2.1, aiming at an initial model, determining the tower top deviation h under the working condition of hoisting the heaviest arch rib section d Calculating a front wind resistance cable force value to control the tower top tower deflection to be-h d 2, establishing an initial structure statics balance condition equation, and solving the equation to determine a rear wind resistance cable force value;
s2.2, giving the front wind resistance value and the rear wind resistance value obtained by solving to a model of a 1 st stage, taking the control target position as the longitudinal displacement of the appointed position of the buckling tower body and the vertical displacement of the cantilever end of the 1 st arch rib section as constraint conditions, establishing a 1 st structural statics balance condition equation corresponding to the 1 st stage, and solving the cable force value of the cable body unit of the 1 st stage based on the 1 st structural statics balance condition equation;
the vertical displacement control target position of the cantilever end of the 1 st arch rib section is the corresponding design position, and when the vertical displacement of the cantilever end of the 1 st arch rib section reaches the vertical position height of the corresponding design position, the vertical displacement value of the cantilever end of the 1 st arch rib section is zero; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h 1 h d 2h, where h 1 The distance between the connection point of the 1 st pair of cable units and the buckling tower and the height of the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s2.3, let i=2, then execute step S2.4;
S2.4, giving a cable body unit cable force value in the i-1 stage to an i-stage model, taking a control target position as a specified position longitudinal displacement of a buckling tower body and a cantilever end vertical displacement of an i arch rib section as constraint conditions, establishing an i-stage structure statics balance condition equation corresponding to the i-stage, and solving the cable body unit cable force value in the i-stage based on the i-stage structure statics balance condition equation;
the vertical displacement control target position of the cantilever end of the ith arch rib section is the corresponding design position, and when the vertical displacement of the cantilever end of the ith arch rib section reaches the vertical position height of the corresponding design position, the vertical displacement value of the cantilever end of the ith arch rib section is zero; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h i h d 2h, where h i The height of the connection point of the ith pair of cable body units and the buckling tower from the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s2.5, judging whether i is equal to N-1; if yes, the obtained cable body unit cable force value in the N-1 stage is used for calculating the cable body unit cable force value in the N stage model, and the step S2.6 is executed; otherwise, let i add 1 by oneself, return to step S2.4;
S2.6, aiming at an N-stage model of the first side main arch half-span structure, selecting longitudinal displacement of a designated position of a buckling tower body and angular displacement of an arch rib cantilever end around a transverse bridge as constraint conditions, establishing a structural statics balance condition equation aiming at the first side main arch half-span structure, and solving a cable body unit cable force value of the N-stage of the first side main arch half-span structure;
the cantilever end of the N-th arch rib section of the first side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th stage of the first side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero displacement value; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h N h d 2h, where h N The distance between the connection point of the N pair of cable units and the buckling tower is the height of the buckling tower bottom, h is the height of the buckling tower, h d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s2.7, aiming at an N-stage model of the second side main arch half-span structure, selecting angular displacement of an arch rib cantilever end around a transverse bridge and vertical displacement of an arch rib cantilever end of the current first side main arch half-span as constraint conditions, establishing a structural statics balance condition equation aiming at the second side main arch half-span and solving a cable body unit cable force value of the N-stage of the second side main arch half-span;
The cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero value; the vertical displacement control target position of the cantilever end of the Nth arch rib section of the second side main arch half span is that the vertical displacement of the cantilever end of the Nth arch rib of the second side main arch half span relative to the cantilever end of the Nth arch rib of the current first side main arch half span is zero;
s2.8, after calculation of cable force values of cable body units of all arch rib sections is completed, simulating that the closure section is connected with two main arch half spans, and the arch rib after each arch rib section is loosened is closed into an arch state, so as to obtain a loose cable arch simulation line shape after the arch rib is closed.
Specifically, in step S4, the simulation calculation of the arching process for iterating the phased arching finite element model of the steel tube concrete arch bridge includes the following steps:
s4.1, judging whether the stage 1 carries out iterative arching process simulation calculation or not; if not, jumping to execute the step S4.2; if yes, giving the front wind resistance cable force value and the rear wind resistance cable force value to a 1 st stage model, taking the control target position as the longitudinal displacement of the appointed position of the buckling tower body and the vertical displacement of the cantilever end of the 1 st arch rib section as constraint conditions, establishing a 1 st structural statics balance condition equation corresponding to the 1 st stage, and solving the cable force value of the cable body unit in the 1 st stage based on the 1 st structural statics balance condition equation;
The height difference value of the 1 st arch rib section obtained by previous calculation of the cantilever end vertical displacement control target position of the 1 st arch rib section is accumulated with the value of the vertical displacement control target position of the 1 st arch rib section set by previous calculation; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h 1 h d 2h, where h 1 The distance between the connection point of the 1 st pair of cable units and the buckling tower and the height of the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s4.2, let i=2, then execute step S4.3;
s4.3, judging whether iterative arching process simulation calculation is carried out in the ith stage; if not, jumping to execute the step S4.5; if so, giving the cable body unit cable force value of the i-1 stage to the i stage model, taking the control target position as the specified position longitudinal displacement of the buckling tower body and the cantilever end vertical displacement of the i arch rib section as constraint conditions, establishing an i structure statics balance condition equation corresponding to the i stage, and solving the cable body unit cable force value of the i stage based on the i structure statics balance condition equation; then, step S4.4 is performed;
wherein the ith arch rib segment cantilever Accumulating the height difference value of the ith arch rib section obtained by the previous calculation of the end vertical displacement control target position and the value of the vertical displacement control target position of the ith arch rib section set by the previous calculation; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h i h d 2h, where h 1 The height of the connection point of the ith pair of cable body units and the buckling tower from the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s4.4, judging whether i is equal to N-1; if yes, the obtained cable body unit cable force value in the N-1 stage is used for calculating the cable body unit cable force value in the N stage model, and the step S4.5 is executed; otherwise, let i add 1 by oneself, return to step S4.3;
s4.5, judging whether iterative arching process simulation calculation is carried out in the N stage; if not, jumping to execute the step S4.7; if so, selecting longitudinal displacement of a designated position of a buckling tower body and angular displacement of an arch rib cantilever end around a transverse bridge as constraint conditions according to an N-th stage model of the first side main arch half-span structure, establishing a structural statics balance condition equation aiming at the first side main arch half-span structure, and solving a cable body unit cable force value of the N-th stage of the first side main arch half-span structure; then, step S4.6 is performed;
The cantilever end of the N-th arch rib section of the first side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th stage of the first side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero displacement value; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h N h d 2h, where h N The distance between the connection point of the N pair of cable units and the buckling tower is the height of the buckling tower bottom, h is the height of the buckling tower, h d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s4.6, aiming at an N-stage model of the second side main arch half-span structure, selecting angular displacement of an arch rib cantilever end around a transverse bridge and vertical displacement of an arch rib cantilever end of the current first side main arch half-span as constraint conditions, establishing a structural statics balance condition equation aiming at the second side main arch half-span and solving a cable body unit cable force value of the N-stage of the second side main arch half-span; then, step S4.7 is performed;
the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero value; the vertical displacement control target position of the cantilever end of the Nth arch rib section of the second side main arch half span is that the vertical displacement of the cantilever end of the Nth arch rib of the second side main arch half span relative to the cantilever end of the Nth arch rib of the current first side main arch half span is zero;
S4.7, the simulated closure section is connected with the two main arch half spans, and the arch rib after the arch rib sections are loosened is closed into an arch state, so that the loosened arch rope after the arch rib closure is shaped like an arch.
In step S4, it is first determined whether to perform iterative arch forming process simulation calculation in each of the 1 st to N th stages, because in the actual iterative arch forming process simulation calculation, only a part of the arch rib segments may be selected to be updated as required, and thus, it is determined whether to update the corresponding stage according to the condition of selecting the arch rib segments to be updated.
For example, in step S4, in one implementation manner of updating the value of the new control target position in the simulation calculation of the arching process of each iteration, the first iteration is to update the 1 st to N-1 st arch rib segment cantilever end vertical displacement control target positions, the subsequent iteration process is to update the 2 nd to N-1 st arch rib segment cantilever end vertical displacement control target positions in turn, and the last iteration is to update only the N-2 nd and N-1 th arch rib segment cantilever end vertical displacements, where N represents the number of arch rib segments included in the main arch half span.
The iterative mode is selected because the closer to the arch rib sections on two sides of the main arch rib, the larger the pulling force required for pulling the arch rib sections to the target position is, the larger the error in calculation is, the calculation complexity can be reduced when the previous control target position is not updated, and meanwhile, the final arching shape and the target shape can be realized within the error range.
For another example, in step S4, another implementation manner of updating the value of the new control target position in the simulation calculation of the arching process in each iteration is to update the 2 nd to N-1 th arch rib segment cantilever end vertical displacement control target positions in each iteration process, where N represents the number of arch rib segments included in the main arch half span.
The iteration mode is selected by updating each control target position every time, so that the final arching line shape and the target line shape can be realized within an error range, the accuracy of an iteration calculation result can be further improved, and the calculation error is further reduced.
Specifically, in step S5, the unclosed mating force refers to that in the previous stage of installing the cable unit, the two end nodes of the cable body have been displaced, and in order to install the cable unit, the two end nodes of the displaced cable need to be reset, and then the required force is the unclosed mating force.
Specifically, the non-closed fitting force may be calculated by the static model described in step S1, where the method for calculating the non-closed fitting force is: firstly, the difference between the deformed length L' of the cable body unit and the deformed length L (namely the length of the nodes at two ends of the cable in modeling) is calculated, and then the additional initial tension delta T of the corresponding cable body unit is calculated according to the difference, wherein delta T is calculated according to the formula (1):
Wherein, deltaT is the additional initial tension of the cable body unit, E, A is the elastic modulus and the cross-sectional area of the cable body respectively, L is the length of the cable body unit before deformation, and L' is the length of the cable body unit after deformation.
In the subsequent calculation, the initial tension T calculated in the initial balance state analysis is overlapped to serve as the control tension in the construction stage to carry out the arch bridge structure forward installation analysis.
The steel pipe concrete arch bridge construction cable force determining method based on arch rib linear difference iteration has the following technical effects: when the calculation and analysis of the construction cable force of the steel pipe concrete arch bridge are carried out, the proper iteration mode and iteration times can be flexibly selected while the line shape of the main arch rib process, the tower deviation and the arch loosening simulation line shape are considered, the comprehensive optimization of the final construction cable force scheme is realized on the basis of ensuring one-time tensioning of the cable body units, and the technical problems that the traditional calculation method of the construction cable force of the arch bridge excessively depends on the cable adjusting experience of engineering personnel, or a large number of influence matrixes are required to be extracted and assembled, or the construction cable force is required to be solved by utilizing a mathematical means self-programming optimization program can be solved.
The feasibility of static force calculation for calculating and disassembling the steel pipe concrete arch bridge into key working conditions in the staged construction process by adopting a method for calculating the unclosed mating force, and the feasibility of initially setting the target control values of the working conditions such as tensioning/dismantling of the arch bridge cable body units and the like by adopting a stress-free state method and an unknown load coefficient method and establishing structural statics balance conditions are elaborated.
(1) And (5) verifying the practicality of the unclosed mating force.
Before describing the concept of non-closed mating force, it is necessary to clarify both the in-vivo and in-vitro force concepts; internal forces refer to forces that interact between parts of the interior of an object, which when an object is subjected to external forces, generate internal forces, including tension, pressure, shear forces, etc., according to their structural and stiffness characteristics, as a result of the internal mechanical balance of the object, which are transmitted and balanced to maintain the stability of the object; external forces refer to forces acting on the exterior of an object, from the external environment, other objects or systems, which may be gravity, pressure, tension, shear forces, etc., that act on the surface or boundary of an object, causing the object to be forced or deformed by contact or action with the object.
Generally, when static analysis of arch bridge structure is performed, midas/Civil software applies initial tension of the cable unit in the form of "internal force" by default, as if a temperature load is applied to the unit, and the final tension and initial tension of the cable unit are often unequal.
When the construction stage analysis is carried out, if the initial tension of the cable body unit is applied in the form of 'external force', the initial tension input in the model is equal to the cable force after tensioning.
Taking a cantilever beam with two inhaul cables as an example, the practicality of calculating the construction cable force by adopting an unclosed cooperation force method is verified. The cantilever beam is 20m long, C50 concrete is adopted, the section is rectangular, and the height H and the width B are 1m; the inhaul cable adopts a steel strand, and the diameter D is 0.01m; the weight coefficient of the cantilever beam is 10, the initial pulling force of the inhaul cable is 100kN, and the overall arrangement of the cantilever beam is shown in fig. 1. The construction process comprises the following steps: (1) mounting a first main girder segment 100; (2) tensioning the first guy cable 101; (3) installing a second main beam segment 102; (4) tensioning the second cable 103.
And (3) establishing a structure by adopting Midas/Civil to construct a finite element model (namely an initial model) in a staged manner, and independently storing a first cable tensioning and a second cable tensioning construction stage into two static models. And extracting the vertical displacement DZ displacement of the cantilever end at the point A after the first girder segment is installed to be 109.7mm, calculating the matching force required for tensioning the first cable to be 336.1kN by adopting the method (1), applying the matching force to the first cable, extracting the vertical displacement DZ displacement of the cantilever end at the point A of the initial model after tensioning the first cable and the model at the construction stage of tensioning the first cable, wherein the two displacements are 72.2mm below, and the cloud chart of the vertical displacement DZ displacement of the cantilever end is shown in fig. 2. And extracting the vertical displacement DZ displacement of the cantilever end at the point B after the second girder segment is installed to be-1315.9 mm, calculating the required matching force of the second inhaul cable to be 4030.7kN, applying the matching force to the second inhaul cable, extracting the vertical displacement DZ displacement of the cantilever end at the point B of the initial model after tensioning the second inhaul cable and the model in the construction stage of tensioning the second inhaul cable, wherein the two displacements are-380.7 mm, and the cloud chart of the vertical displacement DZ displacement of the cantilever end is shown in fig. 3.
The Midas/Civil software is one of Midas series software products, is general finite element analysis software, is commonly used in the engineering and building fields, and is particularly used for designing, analyzing and managing various Civil engineering projects, such as roads, bridges, water resource management, sewage treatment and the like, and is commonly used in the prior art.
In summary, the conclusion can be reached as follows: (1) the coordination force required by the inhaul cable is calculated, and the coordination force is applied to the inhaul cable when the inhaul cable is tensioned, so that the structure construction stress state in stages is consistent with the structure stress state in the static model under the corresponding working condition; (2) based on the method of unclosed mating force, the analysis and calculation of the stress state of the arch bridge structure in stages construction can be simplified into static calculation under the corresponding working condition of the structure; (3) in essence, the method of non-closed mating force is equivalent to the method of non-stress state, and the non-closed mating force of the structure is considered to be equivalent to the mode of activating the inhaul cable in a non-stress cable length manner when the inhaul cable is tensioned; (4) the Midas/Civil software can automatically calculate the unoccluded coupling force required by the inhaul cable, and can greatly simplify the analysis and calculation workload in the arch bridge structure construction process.
(2) Unknown load coefficient method
In the process of constructing a steel pipe concrete arch bridge by a cable-stayed buckling method, the arch rib process line shape is often required to be controlled and cannot be far away from the design line shape. Therefore, the process of solving the cable body unit force is equivalent to the process of solving the unknown load under the condition of meeting a certain set target or constraint condition, and the process can be exactly solved by using the unknown load coefficient method, and the basic principle and the specific operation method of the process are still described by adopting the above algorithm.
Referring to fig. 1, in order to control the accumulated displacement of the points a and B to be zero when the first cable and the second cable are tensioned respectively, based on the method of non-closed fitting force, the following static balance conditions may be established only for the first cable tensioning construction stage model and the second cable tensioning construction stage model:
in the formula (2), U A1 、U Aw Respectively representing the vertical displacement of the point A caused by the unit force and the dead weight of the first inhaul cable in the first inhaul cable tensioning construction stage model; u (U) B1 、U B2 、U Bw Respectively representing the B point vertical displacement caused by the unit force of the first inhaul cable, the unit force of the second inhaul cable and the dead weight in the construction stage model of tensioning the second inhaul cable; t (T) 1 、T 2 Respectively represent the first to be solvedA cable force and a second cable force. T (T) 1 、T 2 The expression is as follows:
in formula (3), U A1 、U Aw Respectively representing the vertical displacement of the point A caused by the unit force and the dead weight of the first inhaul cable in the first inhaul cable tensioning construction stage model; u (U) B1 、U B2 、U Bw Respectively representing the B point vertical displacement caused by the unit force of the first inhaul cable, the unit force of the second inhaul cable and the dead weight in the construction stage model of tensioning the second inhaul cable; t (T) 1 、T 2 The first cable force and the second cable force to be solved are represented respectively.
The unknown load coefficient function of Midas/Civil software is adopted to calculate T 1 939.7kN, T 2 When 1538.3kN is reached, the displacement between the point A in the first cable construction stage model and the point B in the second cable construction stage model is zero, and the calculated unclosed matching force is applied to the first cable and the second cable, so that the control target that the accumulated displacement of the point A and the point B in the construction process is zero during the tensioning of the first cable and the second cable can be realized. Fig. 4 and 5 are referred to as a cloud chart of vertical displacement DZ displacement of the cantilever ends of the two inhaul cables in the tensioning stage.
The method for determining the construction cable force of the steel pipe concrete arch bridge based on arch rib linear difference iteration is suitable for a conventional construction method, namely, each arch rib section is sequentially tensioned, a cable body unit for tensioning is not dismounted in the construction process, and the cable body unit is dismounted uniformly after the construction is finished.
The method for determining the construction cable force of the steel pipe concrete arch bridge based on arch rib linear difference iteration disclosed by the invention is also suitable for an improved construction method, namely, each arch rib section is sequentially tensioned, a cable body unit for tensioning is partially dismantled according to different construction stages in the construction process, and the dismantled cable body unit is applied to the tensioning of the subsequent arch rib section, so that the resource utilization rate is improved and the construction cost is saved.
Therefore, in order to further illustrate the arch rib linear difference iteration-based steel tube concrete arch bridge construction cable force determination method, the invention discloses the following examples.
In this embodiment, referring to fig. 6 to 16, taking a steel pipe concrete arch bridge with a net span of 140m as an example, adopting Midas/Civil software to build a structure to construct a finite element model in stages, combining with the basic principle of a stress-free state method, referring to the concept of "normal loading iteration" in the reasonable construction state calculation of the cable-stayed bridge, building the mechanical balance condition of the arch bridge structure under key working conditions such as tensioning of the cable body unit, and implementing the steel pipe concrete arch bridge construction cable force determination method based on arch rib linear difference iteration through repeated iteration artificial set control target positions, so that one-time tensioning of the arch bridge cable body unit is realized while taking both a process and a result into consideration. The Midas/Civil software is one of Midas series software products, is general finite element analysis software, is commonly used in the engineering and building fields, and is particularly used for designing, analyzing and managing various Civil engineering projects, such as roads, bridges, water resource management, sewage treatment and the like, and is commonly used in the prior art.
Specifically, the supporting engineering in this embodiment is an upper-bearing steel pipe concrete arch bridge, the bridge span combination is 2×20m+152m+25m, the whole length is 217m, the bridge deck is 12m wide, and the arch bridge elevation arrangement is shown in fig. 6. The main arch rib is a two-limb dumbbell-shaped steel tube concrete structure, the net span is 140m, the calculated sagittal span ratio is 1/5.957, and the arch axis coefficient is 1.5. The middle distance of the double arch ribs is 7m, the truss height of the arch ribs is 2.9m, the diameter of the upper chord tube and the lower chord tube is 1.2m, C50 concrete is filled in, and the maximum weight of the arch rib sections is 12t. I-shaped cross braces are adopted among the arch ribs, the standard longitudinal spacing is 8m, and the diameter of a cross brace steel pipe is 0.61m.
Specifically, the bridge is constructed by adopting a cable-stayed buckling method, and a cable hanging system 211 referring to fig. 7 and 8 comprises a main tower 201 and a buckling tower 202, wherein the main tower 201 and the buckling tower 202 are integrally arranged, two main towers 201 and two buckling towers 202 are respectively arranged on two sides of a main arch rib 210 of a steel pipe concrete arch bridge 200 to be installed;
the buckling tower 202 is provided with a buckling rope and a back rope, and the buckling rope and the back rope adopt 4 buckling ropes respectivelyφ s 15.2mm prestressed steel strands, wherein a front wind-resistant cable 203 and a rear wind-resistant cable 204 are arranged on the main tower 201, and the front wind-resistant cable and the rear wind-resistant cable respectively adopt 10 and 12 phi s 15.2mm prestressed steel strand;
the main arch rib comprises two main arch half spans, namely a small mileage side main arch half span and a large mileage side main arch half span (also can be called as a first side main arch half span and a second side main arch half span), 5 pairs of arch rib sections and one closure section are arranged in the main arch rib, each pair of arch rib sections are respectively distributed in the small mileage side main arch half span and the large mileage side main arch half span and correspond to each other in position, each arch rib section in each pair of arch rib sections comprises two arch rib sections which are arranged in parallel, please refer to fig. 6 to 9, the 5 pairs of arch rib sections are numbered, namely a first section pair 212, a second section pair 213, a third section pair 214, a fourth section pair 215 and a fifth section pair 216, and 22 arch rib sections are arranged in the whole bridge, and finally, two parallel arch ribs can be formed and are fixedly connected through connecting pieces.
Specifically, each segment pair is correspondingly provided with a cable body unit group, which is a first cable body unit group 205, a second cable body unit group 206, a third cable body unit group 207, a fourth cable body unit group 208 and a fifth cable body unit group 209, each cable body unit group is internally provided with symmetrically arranged cable body units, the symmetrically arranged cable body units are respectively arranged on the buckling towers 202 of the main arch half-span side of the small mileage side and the main arch half-span side of the large mileage side, each cable body unit comprises two buckling cables and two back cables, the two buckling cables are respectively arranged on the arch rib sections, and the buckling cables and the back cables are connected at the buckling towers 202.
The main arch half span side of the small mileage side and the main arch half span side of the large mileage side are coordinate axes which are perpendicular to the central line of the main arch rib elevation and are arranged by taking any point on the central line of the main arch rib elevation as an origin of a coordinate system, the main arch half span facing the negative direction of the coordinate axes is the main arch half span side of the small mileage side, and the main arch half span facing the positive direction of the coordinate axes is the main arch half span side of the large mileage side.
Specifically, the first cable body unit group 205 includes an L1 buckle cable, an L1 back cable, an R1 buckle cable, and an R1 back cable, where the L1 buckle cable and the L1 back cable are installed on a steel anchor box of the buckle tower 202 disposed on the small mileage side, and the R1 buckle cable and the R1 back cable are installed on a steel anchor box of the buckle tower 202 disposed on the large mileage side; each L1 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, each L1 back rope comprises two back ropes which are respectively arranged on a steel anchor box of the buckling tower 202 arranged on the small mileage side, each R1 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, and each R1 back rope comprises two back ropes which are respectively arranged on the steel anchor box of the buckling tower 202 arranged on the large mileage side.
Similarly, the second cable body unit group 206 includes an L2 buckle cable, an L2 back cable, an R2 buckle cable, and an R2 back cable, where the L2 buckle cable and the L2 back cable are installed on the steel anchor box of the buckle tower 202 disposed on the small mileage side, and the R2 buckle cable and the R2 back cable are installed on the steel anchor box of the buckle tower 202 disposed on the large mileage side; each L2 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, each L2 back rope comprises two back ropes which are respectively arranged on a steel anchor box of the buckling tower 202 arranged on the small mileage side, each R2 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, and each R2 back rope comprises two back ropes which are respectively arranged on the steel anchor box of the buckling tower 202 arranged on the large mileage side.
The third cable body unit group 207 comprises an L3 buckling cable, an L3 back cable, an R3 buckling cable and an R3 back cable, wherein the L3 buckling cable and the L3 back cable are installed on a steel anchor box of the buckling tower 202 arranged on the small mileage side, and the R3 buckling cable and the R3 back cable are installed on a steel anchor box of the buckling tower 202 arranged on the large mileage side; each L3 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, each L3 back rope comprises two back ropes which are respectively arranged on a steel anchor box of the buckling tower 202 arranged on the small mileage side, each R3 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, and each R3 back rope comprises two back ropes which are respectively arranged on the steel anchor box of the buckling tower 202 arranged on the large mileage side.
The fourth cable body unit group 208 comprises an L4 buckling cable, an L4 back cable, an R4 buckling cable and an R4 back cable, wherein the L4 buckling cable and the L4 back cable are installed on a steel anchor box of the buckling tower 202 arranged on the small mileage side, and the R4 buckling cable and the R4 back cable are installed on a steel anchor box of the buckling tower 202 arranged on the large mileage side; each L4 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, each L4 back rope comprises two back ropes which are respectively arranged on a steel anchor box of the buckling tower 202 arranged on the small mileage side, each R4 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, and each R4 back rope comprises two back ropes which are respectively arranged on the steel anchor box of the buckling tower 202 arranged on the large mileage side.
The fifth cable unit group 209 comprises an L5 buckle cable, an L5 back cable, an R5 buckle cable, and an R5 back cable, wherein the L53 buckle cable and the L5 back cable are mounted on a steel anchor box of the buckle tower 202 arranged on the small mileage side, and the R5 buckle cable and the R5 back cable are mounted on a steel anchor box of the buckle tower 202 arranged on the large mileage side; each L5 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, each L5 back rope comprises two back ropes which are respectively arranged on a steel anchor box of the buckling tower 202 arranged on the small mileage side, each R5 buckling rope comprises two buckling ropes which are respectively connected with two parallel arch rib sections in the arch rib section, and each R5 back rope comprises two back ropes which are respectively arranged on the steel anchor box of the buckling tower 202 arranged on the large mileage side.
The main arch rib 210 is installed by the following steps:
(1) installing a temporary buckling tower 202 and tensioning an anti-wind cable;
(2) sequentially installing segment pairs from one arch rib to three arch ribs and tensioning corresponding cable body unit groups, namely a first cable body unit group 205;
(3) removing the first cable unit set 205;
(4) installing a fourth segment pair 215 of the arch rib and a fourth cable body unit group 208 of the tensioning cable;
(5) removing the third cable body unit group 207;
(6) installing a fifth segment pair 216 of the arch rib and a fifth cable body unit group 209 of the tensioning cable;
(7) installing closure section 217;
(8) and removing the residual cable body units.
In actual construction, the arch rib segments are often hoisted by adopting a cable hoist system, such as tower cranes, automobile cranes and the like, which are common hoisting modes.
In this embodiment, closure segment 217 is hoisted by main cable 218, hauling cable 219 and hoisting cable 220, wherein one ends of main cable 218, hauling cable 219 and hoisting cable 220 are mounted on main tower 201, the other ends are connected with closure segment 217, hauling cable 219 is used for hauling closure segment 217 to the design position, and hoisting cable 220 is used for hoisting closure segment 217.
Specifically, in the embodiment, the stress conditions of the back cable and the wind resistance cable are considered at the same time, and the structural forward assembly analysis is carried out by a cable force calculation method based on linear difference iteration. The control target position in the present embodiment considers these parameters: the designated position longitudinal displacement DX of the buckling tower body of the buckling tower, the vertical displacement DZ of the cantilever end of the arch rib and the angular displacement RY of the cantilever end of the arch rib around the transverse bridge.
According to the steel pipe concrete arch bridge construction cable force determination method based on arch rib linear difference iteration disclosed by the invention, firstly, a finite element model is established by relying on engineering and software Midas/Civil, space beam unit simulation is adopted for arch ribs and buckling towers, truss unit simulation is adopted for cable body units and wind resistance cables, fixed constraint is adopted for buckling tower bottoms, anchorage and arch feet, rigid connection in elastic connection is adopted for arch rib cross braces and arch ribs, buckling cables and arch ribs, connection relation between a steel anchor box and a buckling tower is adopted for simulation, and the main arch rib volume weight is corrected to be 89.11kN/m based on the principle of equal weight 3 . See fig. 9 for a constructed finite element model.
Specifically, the method for determining the construction cable force of the steel pipe concrete arch bridge based on arch rib linear difference iteration adopted by the embodiment comprises the following steps:
and D1, collecting construction drawing and special scheme information, establishing a finite element model of the computing object in stages, and correcting physical parameters of model materials to enable the model materials to be consistent with real structural parameters and performance indexes.
And D2, disassembling the cable into various stages according to key working conditions such as wind-resistant cable stretching, buckling/back cable stretching/dismantling and the like, wherein the stages comprise an initial model and an ith stage model.
The initial model is a static model of a connecting structure between the buckling tower and the front/rear wind-resistant cable, the ith stage model comprises an ith arch rib section, a corresponding cable body unit structure, arch rib sections and corresponding cable body unit structures, which are arranged in advance, besides the connecting structure between the buckling tower and the front/rear wind-resistant cable, and the ith arch rib section is arranged, wherein i is {1,2,3,4,5}, and the number of arch rib sections is contained in the total of 5 main arch half spans; in the staged arching finite element model of the steel pipe concrete arch bridge, the design positions corresponding to the vertical displacement of the cantilever ends of the 1 st to N-1 st arch rib sections and the design positions corresponding to the displacement of the cantilever ends of the Nth arch rib sections around the transverse bridge to the corner are marked according to the construction drawing and the design scheme information.
Setting an initial control target position of each arch rib section, performing initial arch forming process simulation calculation on the staged arch forming finite element model of the built steel pipe concrete arch bridge, lifting each arch rib section to the control target position through a cable body unit before arch rib closure through simulation calculation, obtaining an initial simulated loose cable arch forming simulated line shape after arch rib closure, and then comparing the initial simulated cable forming line shape with a target line shape to obtain a height difference value of each arch rib section in the target line shape and each arch rib section in the initial loose cable arch forming simulated line shape; specifically, the initial control target position of the arch rib section is the design position of the arch rib section according to the related construction drawing and design scheme;
d4, aiming at an initial model, firstly determining the tower top deviation h under the working condition of hoisting the heaviest arch rib section d Calculating a front wind resistance cable force value to control the tower top tower deflection to be-h d / 2 For the purpose, an initial structure statics balance condition equation is established, and a post-wind resistance cable force value can be determined by solving the equation.
The front wind resistance cable force value and the rear wind resistance cable force value which are obtained through solving are given to a 1 st stage model, longitudinal displacement of a control target position which is a specified position of a buckling tower body and vertical displacement of a cantilever end of a 1 st arch rib section are taken as constraint conditions, a 1 st structural statics balance condition equation corresponding to the 1 st stage is established, and the cable force value of a cable body unit in the 1 st stage is solved based on the 1 st structural statics balance condition equation;
The vertical displacement control target position of the cantilever end of the 1 st arch rib section is the corresponding design position, and when the vertical displacement of the cantilever end of the 1 st arch rib section reaches the vertical position height of the corresponding design position, the vertical displacement value of the cantilever end of the 1 st arch rib section is zero; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h 1 h d 2h, where h 1 The distance between the connection point of the 1 st pair of cable units and the buckling tower and the height of the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of the section of the heaviest arch rib for hoisting.
D6, let i=2, then execute step D7;
d7, giving the cable body unit cable force value in the i-1 stage to an i-stage model, taking the control target position as a specified position longitudinal displacement of the buckling tower body and the vertical displacement of the cantilever end of the i arch rib section as constraint conditions, establishing an i-stage structural statics balance condition equation corresponding to the i-stage, and solving the cable body unit cable force value in the i-stage based on the i-stage structural statics balance condition equation;
the vertical displacement control target position of the cantilever end of the ith arch rib section is the corresponding design position, and when the vertical displacement of the cantilever end of the ith arch rib section reaches the vertical position height of the corresponding design position, the vertical displacement value of the cantilever end of the ith arch rib section is zero; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h i h d 2h, where h i The height of the connection point of the ith pair of cable body units and the buckling tower from the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of the section of the heaviest arch rib for hoisting.
D8, judging whether i is equal to N-1; if yes, the obtained cable body unit cable force value in the N-1 stage is used for calculating the cable body unit cable force value in the N stage model, and the step D9 is executed; otherwise, let i add 1, return to step D7.
D9, selecting longitudinal displacement of a designated position of a buckling tower body and angular displacement of an arch rib cantilever end around a transverse bridge as constraint conditions aiming at an N-th stage model of a first side main arch half-span structure (a small mileage side main arch half-span), establishing a structural statics balance condition equation aiming at the first side main arch half-span and solving a cable body unit cable force value of the N-th stage of the first side main arch half-span structure;
the cantilever end of the N-th arch rib section of the first side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th stage of the first side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero displacement value; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h N h d 2h, where h N The distance between the connection point of the N pair of cable units and the buckling tower is the height of the buckling tower bottom, h is the height of the buckling tower, h d The tower top is deviated under the working condition of the section of the heaviest arch rib for hoisting.
D10, aiming at an N-stage model of a second side main arch half-span structure (a large mileage side main arch half-span), selecting arch rib cantilever end rotation angle displacement around a transverse bridge and current arch rib cantilever end vertical displacement of a first side main arch half-span as constraint conditions, establishing a structural statics balance condition equation aiming at the second side main arch half-span and solving a cable body unit cable force value of the N-stage of the second side main arch half-span;
the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero value; the vertical displacement control target position of the nth arch rib section cantilever end of the second side main arch half span is that the vertical displacement of the nth arch rib cantilever end of the second side main arch half span relative to the nth arch rib cantilever end of the current first side main arch half span is zero.
D11, after the calculation of the cable force values of the cable body units of all arch rib sections is completed, simulating that the closure section is connected with two main arch half spans, and closing the arch ribs of each arch rib section after the cable loosening is in an arch state, so as to obtain an arch simulated line shape of the loose cable after the arch rib closing;
d12, judging whether the difference value between the target linear shape and the arch-forming simulation linear shape of the loose cable is smaller than a preset threshold value, if so, stopping calculation, and executing the step D14; otherwise, executing the step D13;
d13, accumulating the height difference value of each arch rib section obtained by the previous calculation and the value of the control target position set by the previous calculation, and performing iterative arch forming process simulation calculation on the staged arch forming finite element model of the steel pipe concrete arch bridge as a new control target position, lifting each arch rib section to the cable force value of the control target position through the cable body unit before closing the arch rib by simulation calculation, and obtaining the height difference value of each arch rib section in the target line shape and each arch rib section in the arch forming simulation line shape of the loose cable after closing the newly simulated arch rib; then, returning to the step D12;
d14, extracting the cable force value results of each cable body unit in the simulation calculation of the last arch forming process, and giving the cable force value results to a staged arch forming finite element model of the steel pipe concrete arch bridge; and then, applying an unclosed mating force to each cable body unit, carrying out structural normal assembly analysis, extracting the internal force result of each cable body unit stretching stage unit, and taking the internal force result of each cable body unit stretching stage unit as a steel pipe concrete arch bridge cable body unit stretching field instruction value.
Specifically, in step D4, the front wind resistance cable force value is calculated according to the breaking force of the steel strand divided by the safety coefficient, the value of the safety coefficient is determined according to the relevant design standard of the concrete filled steel tube bridge, and the specific calculation formula is shown in formula (4):
T i ＝L×N p /α (4)
in the formula (4), L is the number of the front wind-resistant cable steel strands and N p The yield force of a single steel strand is the safety coefficient, and the value range is 2-3.
Specifically, in step D4, the equation of the initial structural statics equilibrium condition is shown in formula (5):
in formula (5): h 0 、H 0 ' respectively represents the front wind resistance cable and the rear resistanceLongitudinal displacement of the tower top caused by the action of the unit force of the wind cable; t (T) 0 、T 0 ' represents the front and rear wind-resistant cable forces to be solved, respectively; h is a 0 Representing the longitudinal displacement of the column top caused by the constant load of the structure.
Specifically, in step D5, the 1 st structural hydrostatic equilibrium condition equation is shown in formula (6):
in formula (6): h 1 、H 1 ' respectively represents the longitudinal displacement of the designated position of the buckling tower body caused by the unit forces of the 1# buckling cable and the 1# back cable; v (V) 1 、V 1 ' respectively represents the vertical displacement of the cantilever end of the arch rib caused by the unit forces of the 1# buckling rope and the 1# back rope; h is a 1 、v 1 Respectively representing the longitudinal displacement of the appointed position of the buckling tower body and the vertical displacement of the cantilever end of the arch rib, which are caused by the action of the structural constant load (also comprising wind resistance cable force); t (T) 1 、T 1 ' represents the 1# buckle force and the 1# back force to be solved, respectively; c (C) 1h 、C 1v Respectively representing control target values of the longitudinal displacement of the designated position of the tower body of the buckling tower and the vertical displacement of the cantilever end of the 1 st arch rib section;
when the tension of the cable body unit in the 1 st stage and the gravity of the 1 st arch rib section reach force balance, the control target position of the vertical displacement of the cantilever end of the 1 st arch rib section is the reference position;
the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h 1 h d 2h, where h 1 The distance between the connection point of the 1 st pair of cable units and the buckling tower and the height of the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of the section of the heaviest arch rib for hoisting.
The cable force determination method adopted in the embodiment is suitable for a construction mode of removing part of cable body units in the construction process besides a construction mode of not removing cables in the construction process. Specifically, unlike the conventional process of constructing the steel pipe concrete arch bridge 200 by the cable-stayed buckling method, in order to save the cost of the back cable anchorage, in the cable-stayed buckling system of the bridge of this embodiment, the spatial positions of the first cable unit group 205 and the fourth cable unit group 208, and the third cable unit group 207 and the fifth cable unit group 209 are the same. Thus, the cable first cable body unit set 205 is removed prior to tensioning the cable fourth cable body unit set 208; the third cable unit set 207 is removed prior to tensioning the fifth cable unit set 209.
Specifically, in step D13, the simulation calculation of the arching process for iterating the staged arching finite element model of the steel tube concrete arch bridge is shown in the above steps S4.1 to S4.8, and will not be described herein.
Specifically, in step D13, arch rib-buckling cable and back cable-buckling tower coupling stress effects are considered, so as to perform arch bridge structure construction cable body unit force calculation in two iterative modes.
In the first iteration mode, namely in the step D13, in the simulation calculation of the arching process of each iteration, one implementation mode of updating the value of the new control target position is that the 1 st to N-1 st arch rib section cantilever end vertical displacement control target positions are updated in the first iteration, the 2 nd to N-1 st arch rib section cantilever end vertical displacement control target positions are sequentially updated in the subsequent iteration process, and only the N-2 nd and N-1 th arch rib section cantilever end vertical displacements are updated in the last iteration, wherein N represents the number of arch rib sections contained in the main arch half span.
The iteration specific to this embodiment is that, when iteration is first, the vertical displacement control target positions of the cantilever ends of the segments 1-4 of the arch rib are updated, the intermediate iteration process updates the segment control target positions of the segments 2-4 of the arch rib, and when iteration is last, only the segment control target positions of the segments 3, 4 of the arch rib are updated; (2) the position of the specified steel anchor box is controlled to be smaller than |h by the longitudinal bridge horizontal displacement control target position i h d 2h (value 7.0 mm), where h i H respectively represents the height of the steel anchor box from the bottom of the buckling tower and the height of the buckling tower; (3) and setting the iteration ending condition to be that the difference value between the target linear shape and the arch-forming simulation linear shape of the loose cable is smaller than 10.0mm.
The iterative mode is selected because the closer to the arch rib sections on two sides of the main arch rib, the larger the pulling force required for pulling the arch rib sections to the target position is, the larger the error in calculation is, the calculation complexity can be reduced when the previous control target position is not updated, and meanwhile, the final arching shape and the target shape can be realized within the error range.
In the second iteration mode, that is, in the step D13, in the simulation calculation of the arching process of each iteration, one implementation mode of updating the value of the new control target position is to update the 2 nd to N-1 nd arch rib segment cantilever end vertical displacement control target positions in each iteration process, where N represents the number of arch rib segments included in the main arch half span.
The iteration specific to this embodiment is, (1) the whole iteration process updates the control target positions of the segments 2-4 of the arch rib; (2) the position of the specified steel anchor box is controlled to be smaller than |h by the longitudinal bridge horizontal displacement control target position i h d 2h (value 7.0 mm), where h i H respectively represents the height of the steel anchor box from the bottom of the buckling tower and the height of the buckling tower; (3) and setting the iteration ending condition to be that the difference value between the target linear shape and the arch-forming simulation linear shape of the loose cable is smaller than 10.0mm. The iteration mode is selected by updating each control target position every time, so that the final arching line shape and the target line shape can be realized within an error range, the accuracy of an iteration calculation result can be further improved, and the calculation error is further reduced.
Referring to fig. 10 and 11, as can be seen from fig. 10 and 11, the difference between the arch-forming vertical displacement of the main arch rib loose cable and the primary falling frame displacement varies in two iteration modes with different iteration times:
(1) after 6 iterative calculations, the difference between the arch-forming displacement of the main arch rib loose cable and the primary falling frame displacement is minus 10.4mm, and the difference is within 5% from the set iteration ending condition threshold value of 10.0mm;
(2) adopting a second iteration mode, and after 5 times of iteration calculation, the difference between the arch-forming displacement of the main arch rib loose cable and the primary falling frame displacement is minus 9.4mm and is smaller than the threshold value of the iteration ending condition by 10.0mm; (3) by adopting the iteration mode II, the loose cable arching simulation line shape can be more quickly approximate to the design target line shape, and the iteration effect is better overall.
Referring to fig. 13 and 14, as can be seen from fig. 13 and 14, the change of the vertical accumulated displacement of the cantilever end of the main arch rib in the whole construction process under two iteration modes and different iteration times: (1) considering the coupling stress effect of the arch rib, the temporary rope and the buckling tower, the integral line shape of the arch rib has the upward lifting change trend along with the increase of iteration times; (2) after 6 iterative calculations, the maximum accumulated displacement value of the cantilever end of the No. 4 segment of the arch rib is 118.2mm in the stage of stretching the fourth cable body unit group of the main arch half span side of the small mileage side, the accumulated displacement change of the third cable body unit group cable of the main arch half span side of the small mileage side is 23.5mm, and the third cable body unit group cable of the main arch half span side of the small mileage side can lead the arch rib to generate vertical displacement of-94.7 mm, compared with the simulation mode shown in fig. 12, the integral linear change of the arch rib construction process is larger; (3) after 5 times of iterative computation, the accumulated displacement of the cantilever end of the No. 4 segment of the arch rib at the stage of stretching the fourth cable body unit group at the half-span side of the main arch at the small mileage side is 98.2mm, which is reduced by 20.0mm compared with the first iterative computation; the third cable body unit group cable arch rib at the main arch half-span side of the cable disassembly small mileage side generates vertical displacement of-87.9 mm, which is less than 6.8mm in comparison with the first iteration mode, and the integral linear change of the arch rib construction process is smaller than the first iteration mode; (4) and the construction cable body unit force can be calculated by adopting an iteration mode and requiring fewer iteration times, and the linear control overall of the main arch rib construction process is good.
Referring to fig. 14, as can be seen from fig. 14, the change of the horizontal accumulated displacement of the vertical bridge at the top of the buckling tower in the whole construction process in the last iteration of the two iteration modes: (1) in the stage of tensioning the wind-resistant cable, the horizontal accumulated displacement of the buckling tower tops of the first side main arch half span and the second side main arch half span is-9.8 mm/11.2mm, and the buckling tower is deformed to the midspan side in consideration of hoisting of arch rib sections in the construction of a cable-stayed buckling hanging method, so that the overall deformation of the buckling tower is small, and a pre-deflection value of the buckling tower tops far away from the midspan direction is set by tensioning the wind-resistant cable; (2) in the stage of stretching a first cable body unit group at the half span side of the main arch at the small mileage side to a fourth cable body unit group at the half span side of the main arch at the small mileage side, the horizontal accumulated displacement of the buckle top at the small mileage side is 6.4-7.7 mm, the horizontal accumulated displacement of the buckle top at the large mileage side is-8.1-10.2 mm, and the longitudinal horizontal accumulated displacement value of the buckle top is not greatly changed, because the same tower deviation control target position is set during iterative calculation, and the influence of the first cable body unit group at the half span side of the main arch at the small mileage side on the tower deviation is small; (3) in the third cable body unit cable assembling stage of the main arch half-span side of the small mileage side, the buckling tower is deformed more towards the midspan side due to the fact that the cantilever ends of the arch ribs of the small mileage side generate vertical displacement of-94.7 mm/87.9 mm; (4) in the stage of stretching the fifth cable body unit group at the half span side of the main arch at the small mileage side, the small mileage side is provided with a given tower deflection control target position, so that the horizontal accumulated displacement of the buckling tower top is reduced; before the arch rib closure section is installed, the cantilever end of the arch rib at the large mileage side does not control the deflection of the buckling tower, so that the maximum horizontal accumulated displacement of the buckling tower top reaches-13.7 mm; (5) in the arch loosening stage, as the rest cable units are removed, arch rib deformation does not influence buckling tower deformation any more, and the horizontal accumulated displacement of the top of the small/large mileage side buckling tower is changed to 6.1mm/-9.4mm; (6) the horizontal accumulated displacement of the longitudinal bridge at the top of the buckling tower in the whole construction process is far smaller than the h/400 limit value specified in the technical Specification for highway bridge and culvert construction (JTG/T3650-2020).
Considering that the deviation of the large mileage side buckling tower is large in the whole construction process, only the initial tension results of the large mileage side cable units under the different iteration times of two iteration modes are extracted, and the initial tension change of each cable unit is as follows from fig. 15 and 16, and fig. 15 and 16 show that: (1) with the increase of the iteration times, the initial tension of the cable body units of the second cable body unit group at the main arch half-span side at the large mileage side to the fourth cable body unit group at the main arch half-span side at the large mileage side is gradually increased; (2) adopting an iteration mode I, wherein the first cable body unit group cable body unit at the half span side of the main arch at the large mileage side is 99.4kN (100.6 kN) before iteration, and is 354.8kN (318.6 kN) after iteration; adopting a second iteration mode, wherein the first cable body unit force of the first cable body unit group at the main arch half-span side of the large mileage side in the whole iteration process is unchanged; (3) the primary pulling force of the buckling rope of the fifth rope body unit group at the half span side of the main arch at the large mileage side is gradually reduced, the primary pulling force of the back rope of the fifth rope body unit group at the half span side of the main arch at the large mileage side is 481.1kN at maximum before iteration, and fluctuation exists in the whole iteration process; (4) comparing fig. 12, fig. 13, fig. 15 and fig. 16, it can be known that the initial tension change rule of each cable unit is identical to the arch rib linear change rule; (5) after the iteration is completed in two iteration modes, the difference of the cable body unit forces of the first cable body unit group on the main arch half-span side of the large mileage side is larger, the difference of the cable body unit forces of the other cable body units is smaller, and the maximum difference is only 40.1kN; (6) if the main arch rib loose cable arch simulation line shape is certain with the threshold value set by the design target line shape, the proper iteration mode and the iteration times can be flexibly selected while the main arch rib line shape change and the buckling tower deviation are considered in the iteration process.
To sum up, in this embodiment, taking a steel pipe concrete arch bridge with a net span of 140m as an example, the structural forward installation calculation analysis under the mode of simultaneously considering the back cable and the wind cable is performed, and the method has the following technical effects:
(1) As the iterative calculation times increase, the main arch rib loose cable arch forming simulation line gradually approaches to one-time falling frame arch forming target line;
(2) By adopting the iteration mode II, the linear simulation of the loose cable arching can be more quickly approximate to the designed target linear, the linear change of the main arch rib construction process is smaller in the iteration process, and the horizontal accumulated displacement of the longitudinal bridge at the top of the buckling tower in the whole construction process is far smaller than the standard limit value;
(3) When carrying out calculation and analysis on the construction cable force of the steel pipe concrete arch bridge, the proper iteration mode and iteration times can be flexibly selected while the line shape of the main arch rib process, the tower deviation and the arch loosening simulation line shape are considered, and the comprehensive optimization of the final construction cable force scheme is realized on the basis of ensuring one-time tensioning of the cable body unit;
(4) The embodiment defines the evolution characteristics of the key effect parameters of the structure in the iterative computation process, the method has certain advancement, and the double control of the process and the result of the structure can be realized only by a plurality of iterative computation.
It will be understood that the invention has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments by those skilled in the art without departing from the spirit and scope of the invention. Modifications may be made to the features and embodiments of the invention in light of the teachings of the invention to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. The described embodiments of the invention are some, but not all, embodiments of the invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all other embodiments falling within the scope of the invention as defined by the appended claims, as interpreted according to the breadth to which they are fairly set forth in the claims.
Claims (10)
1. The construction content of each stage comprises that a subsequent arch rib section is arranged on a preceding arch rib section, and when the arch rib section is arranged, a cable body unit is fixed on the arch rib section and used for lifting the arch rib section to a target position; the method is characterized by comprising the following steps of:
s1, collecting construction drawing and design scheme information, establishing a staged arching finite element model of a steel pipe concrete arch bridge, and correcting physical parameters of model materials to enable the model materials to be consistent with real structural parameters and performance indexes;
s2, setting initial control target positions of arch rib sections, performing initial arch forming process simulation calculation on a staged arch forming finite element model of the established steel pipe concrete arch bridge, lifting each arch rib section to the control target positions through cable body units before arch rib closure through simulation calculation, obtaining an initial simulated loose cable arch forming simulated line shape after arch rib closure, and then comparing the initial simulated cable forming line shape with a target line shape to obtain height difference values of each arch rib section in the target line shape and each arch rib section in the initial loose cable arch forming simulated line shape;
S3, judging whether the difference value between the target linear shape and the arch-forming simulation linear shape of the loose cable is smaller than a preset threshold value, if so, stopping calculation, and executing the step S5; otherwise, executing the step S4;
s4, accumulating the height difference value of each arch rib section obtained by the previous calculation and the value of the control target position set by the previous calculation, and performing iterative arch forming process simulation calculation on the staged arch forming finite element model of the steel pipe concrete arch bridge as a new control target position, lifting each arch rib section to the cable force value of the control target position through the cable body unit before closing the arch rib by simulation calculation, and obtaining the height difference value of each arch rib section in the target line shape and each arch rib section in the arch forming simulation line shape of the loose cable after closing the newly simulated arch rib; then, returning to the step S3;
s5, extracting the cable force value results of each cable body unit in the simulation calculation of the last arch forming process, and giving the cable force value results to a staged arch forming finite element model of the steel pipe concrete arch bridge; and then, applying an unclosed mating force to each cable body unit, carrying out structural normal assembly analysis, extracting the internal force result of each cable body unit stretching stage unit, and taking the internal force result of each cable body unit stretching stage unit as a steel pipe concrete arch bridge cable body unit stretching field instruction value.
2. The arch rib linear difference iteration-based steel tube concrete arch bridge construction cable force determination method according to claim 1, wherein in the step S1, the steel tube concrete arch bridge comprises buckling towers arranged at two sides of a river channel, front wind resistance cables are arranged between the buckling towers at two sides, and rear wind resistance cables are respectively arranged at one sides of the buckling towers at two sides far away from each other;
the main arch rib comprises two main arch half spans, namely a first side main arch half span and a second side main arch half span, each main arch half span is provided with N arch rib sections, and the two main arch half spans are connected through a closure section;
each arch rib section is connected with the buckling tower on one side where the arch rib section is located through a pair of cable units, each pair of cable units comprises a buckling cable and a back cable, the buckling cable is connected between the arch rib section and the buckling tower and used for providing lifting tension for the arch rib section, and the back cable is connected at the fixed position of the buckling tower and the bank of the river and used for providing balanced supporting tension for the buckling tower.
3. The method for determining the construction cable force of the steel tube concrete arch bridge based on the arch rib linear difference iteration according to claim 2, wherein in the step S1, cable units are sequentially installed on each arch rib section according to the sequence of the staged construction from two sides to the middle of a main arch during the construction of the steel tube concrete arch bridge, and the cable units of each arch rib section are maintained to be connected during the assembly process of an arch rib cantilever and before the closure of the arch rib.
4. The method for determining the construction cable force of the steel tube concrete arch bridge based on the arch rib linear difference iteration according to claim 2, wherein in the step S1, cable units are sequentially installed on each arch rib section according to the sequence of the construction from two sides of a main arch to the middle in a staged manner during the construction, and meanwhile, before the installation of the subsequent arch rib sections, the cable units on part of arch rib sections in the non-terminal arch rib sections are removed during the assembly of arch rib cantilevers and before the closure of the arch ribs during the construction.
5. The arch rib linear difference iteration-based steel tube concrete arch bridge construction cable force determination method according to claim 2, wherein in step S1, the steel tube concrete arch bridge is formed into an arch finite element model in stages, and the arch finite element model comprises an initial model and an i-th stage model;
the initial model is a static model of a connecting structure between the buckling tower and the front/rear wind-resistant cable, the ith stage model comprises a connecting structure between the buckling tower and the front/rear wind-resistant cable, and also comprises an ith arch rib section, a corresponding cable body unit structure, an arch rib section with a mounted preamble of the corresponding cable body unit structure and a corresponding cable body unit structure, i epsilon {1,2,3,..N }, wherein N represents the number of arch rib sections contained in the main arch half span.
6. The method for determining the construction cable force of the steel pipe concrete arch bridge based on the arch rib linear difference iteration of claim 5, wherein in the step S1, in the staged arch forming finite element model of the steel pipe concrete arch bridge, the design positions corresponding to the vertical displacement of the cantilever ends of the 1 st to N-1 st arch rib sections and the design positions corresponding to the displacement of the cantilever ends of the N th arch rib sections around the transverse bridge to the corner are marked according to the construction drawing and the design scheme information.
7. The arch rib linear difference iteration-based steel tube concrete arch bridge construction cable force determining method according to claim 6, wherein in step S2, the initial arch forming process simulation calculation of the staged arch forming finite element model of the established steel tube concrete arch bridge comprises the following steps:
s2.1, aiming at an initial model, determining the tower top deviation h under the working condition of hoisting the heaviest arch rib section d Calculating a front wind resistance cable force value to control the tower top tower deflection to be-h d 2, establishing an initial structure statics balance condition equation, and solving the equation to determine a rear wind resistance cable force value;
s2.2, giving the front wind resistance value and the rear wind resistance value obtained by solving to a model of a 1 st stage, taking the control target position as the longitudinal displacement of the appointed position of the buckling tower body and the vertical displacement of the cantilever end of the 1 st arch rib section as constraint conditions, establishing a 1 st structural statics balance condition equation corresponding to the 1 st stage, and solving the cable force value of the cable body unit of the 1 st stage based on the 1 st structural statics balance condition equation;
The vertical displacement control target position of the cantilever end of the 1 st arch rib section is the corresponding design position, and when the vertical displacement of the cantilever end of the 1 st arch rib section reaches the vertical position height of the corresponding design position, the vertical displacement value of the cantilever end of the 1 st arch rib section is zero; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h 1 h d 2h, where h 1 The distance between the connection point of the 1 st pair of cable units and the buckling tower and the height of the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s2.3, let i=2, then execute step S2.4;
s2.4, giving a cable body unit cable force value in the i-1 stage to an i-stage model, taking a control target position as a specified position longitudinal displacement of a buckling tower body and a cantilever end vertical displacement of an i arch rib section as constraint conditions, establishing an i-stage structure statics balance condition equation corresponding to the i-stage, and solving the cable body unit cable force value in the i-stage based on the i-stage structure statics balance condition equation;
the vertical displacement control target position of the cantilever end of the ith arch rib section is the corresponding design position, and when the vertical displacement of the cantilever end of the ith arch rib section reaches the vertical position height of the corresponding design position, the vertical displacement value of the cantilever end of the ith arch rib section is zero; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h i h d 2h, where h i The height of the connection point of the ith pair of cable body units and the buckling tower from the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s2.5, judging whether i is equal to N-1; if yes, the obtained cable body unit cable force value in the N-1 stage is used for calculating the cable body unit cable force value in the N stage model, and the step S2.6 is executed; otherwise, let i add 1 by oneself, return to step S2.4;
s2.6, aiming at an N-stage model of the first side main arch half-span structure, selecting longitudinal displacement of a designated position of a buckling tower body and angular displacement of an arch rib cantilever end around a transverse bridge as constraint conditions, establishing a structural statics balance condition equation aiming at the first side main arch half-span structure, and solving a cable body unit cable force value of the N-stage of the first side main arch half-span structure;
the cantilever end of the N-th arch rib section of the first side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th stage of the first side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero displacement value; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h N h d 2h, where h N The distance between the connection point of the N pair of cable units and the buckling tower is the height of the buckling tower bottom, h is the height of the buckling tower, h d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s2.7, aiming at an N-stage model of the second side main arch half-span structure, selecting angular displacement of an arch rib cantilever end around a transverse bridge and vertical displacement of an arch rib cantilever end of the current first side main arch half-span as constraint conditions, establishing a structural statics balance condition equation aiming at the second side main arch half-span and solving a cable body unit cable force value of the N-stage of the second side main arch half-span;
the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero value; the vertical displacement control target position of the cantilever end of the Nth arch rib section of the second side main arch half span is that the vertical displacement of the cantilever end of the Nth arch rib of the second side main arch half span relative to the cantilever end of the Nth arch rib of the current first side main arch half span is zero;
s2.8, after calculation of cable force values of cable body units of all arch rib sections is completed, simulating that the closure section is connected with two main arch half spans, and the arch rib after each arch rib section is loosened is closed into an arch state, so as to obtain a loose cable arch simulation line shape after the arch rib is closed.
8. The arch rib linear difference iteration-based steel tube concrete arch bridge construction cable force determination method according to claim 7, wherein in step S4, the arch forming process simulation calculation for iterating the staged arch forming finite element model of the steel tube concrete arch bridge comprises the following steps:
s4.1, judging whether the stage 1 carries out iterative arching process simulation calculation or not; if not, jumping to execute the step S4.2; if yes, giving the front wind resistance cable force value and the rear wind resistance cable force value to a 1 st stage model, taking the control target position as the longitudinal displacement of the appointed position of the buckling tower body and the vertical displacement of the cantilever end of the 1 st arch rib section as constraint conditions, establishing a 1 st structural statics balance condition equation corresponding to the 1 st stage, and solving the cable force value of the cable body unit in the 1 st stage based on the 1 st structural statics balance condition equation;
the height difference value of the 1 st arch rib section obtained by previous calculation of the cantilever end vertical displacement control target position of the 1 st arch rib section is accumulated with the value of the vertical displacement control target position of the 1 st arch rib section set by previous calculation; designated position of tower body of buckling tower is verticalThe directional displacement control target position is smaller than |h 1 h d 2h, where h 1 The distance between the connection point of the 1 st pair of cable units and the buckling tower and the height of the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s4.2, let i=2, then execute step S4.3;
s4.3, judging whether iterative arching process simulation calculation is carried out in the ith stage; if not, jumping to execute the step S4.5; if so, giving the cable body unit cable force value of the i-1 stage to the i stage model, taking the control target position as the specified position longitudinal displacement of the buckling tower body and the cantilever end vertical displacement of the i arch rib section as constraint conditions, establishing an i structure statics balance condition equation corresponding to the i stage, and solving the cable body unit cable force value of the i stage based on the i structure statics balance condition equation; then, step S4.4 is performed;
the height difference value of the ith arch rib section obtained by previous calculation of the cantilever end vertical displacement control target position of the ith arch rib section is accumulated with the value of the vertical displacement control target position of the ith arch rib section set by previous calculation; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h i h d 2h, where h i The height of the connection point of the ith pair of cable body units and the buckling tower from the buckling tower bottom is h, and h is the buckling tower height d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s4.4, judging whether i is equal to N-1; if yes, the obtained cable body unit cable force value in the N-1 stage is used for calculating the cable body unit cable force value in the N stage model, and the step S4.5 is executed; otherwise, let i add 1 by oneself, return to step S4.3;
s4.5, judging whether iterative arching process simulation calculation is carried out in the N stage; if not, jumping to execute the step S4.7; if so, selecting longitudinal displacement of a designated position of a buckling tower body and angular displacement of an arch rib cantilever end around a transverse bridge as constraint conditions according to an N-th stage model of the first side main arch half-span structure, establishing a structural statics balance condition equation aiming at the first side main arch half-span structure, and solving a cable body unit cable force value of the N-th stage of the first side main arch half-span structure; then, step S4.6 is performed;
the cantilever end of the N-th arch rib section of the first side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th stage of the first side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero displacement value; the longitudinal displacement control target position of the designated position of the buckling tower body is smaller than |h N h d 2h, where h N The distance between the connection point of the N pair of cable units and the buckling tower is the height of the buckling tower bottom, h is the height of the buckling tower, h d The tower top is deviated under the working condition of hoisting the heaviest arch rib section;
s4.6, aiming at an N-stage model of the second side main arch half-span structure, selecting angular displacement of an arch rib cantilever end around a transverse bridge and vertical displacement of an arch rib cantilever end of the current first side main arch half-span as constraint conditions, establishing a structural statics balance condition equation aiming at the second side main arch half-span and solving a cable body unit cable force value of the N-stage of the second side main arch half-span; then, step S4.7 is performed;
the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to control the target position to be the corresponding design position, and when the cantilever end of the N-th arch rib section of the second side main arch semi-span is moved around the transverse bridge to the corner to reach the corner around the transverse bridge of the corresponding design position, the cantilever end of the N-th arch rib section is moved around the transverse bridge to the corner to have a zero value; the vertical displacement control target position of the cantilever end of the Nth arch rib section of the second side main arch half span is that the vertical displacement of the cantilever end of the Nth arch rib of the second side main arch half span relative to the cantilever end of the Nth arch rib of the current first side main arch half span is zero;
S4.7, the simulated closure section is connected with the two main arch half spans, and the arch rib after the arch rib sections are loosened is closed into an arch state, so that the loosened arch rope after the arch rib closure is shaped like an arch.
9. The arch rib linear difference iteration-based steel pipe concrete arch bridge construction cable force determination method according to claim 1, wherein in the step S4, in an implementation manner of updating a new control target position value in simulation calculation of an arch forming process of each iteration, the 1 st to N-1 st arch rib segment cantilever end vertical displacement control target positions are updated when the first iteration is performed, the 2 nd to N-1 st arch rib segment cantilever end vertical displacement control target positions are sequentially updated in a subsequent iteration process, and only the N-2 nd and N-1 th arch rib segment cantilever end vertical displacements are updated when the last iteration is performed, wherein N represents the number of arch rib segments included in a main arch half span.
10. The arch rib linear difference iteration-based steel tube concrete arch bridge construction cable force determination method according to claim 1, wherein in step S4, one implementation way of updating the value of the new control target position in the simulation calculation of each iteration arch forming process is to update the 2 nd to N-1 st arch rib segment cantilever end vertical displacement control target position in each iteration process,
N represents the number of rib segments comprised by the main arch half-span.
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