CN116484699A - Method for accurately designing stress-free state line shape and space position of steel truss tied arch bridge - Google Patents
Method for accurately designing stress-free state line shape and space position of steel truss tied arch bridge Download PDFInfo
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Abstract
The invention relates to a method for accurately designing the line shape and the space position of an unstressed state of a steel truss tied arch bridge; belongs to the technical field of civil engineering application. The invention uses the design line of the steel truss tied arch bridge to form an initial unstressed line, calculates the spatial line under the set load, reversely superimposes the difference value between the spatial line and the design line to the initial unstressed line for correction, and develops iterative calculation for a plurality of times until the spatial position of the unstressed line under the load approaches the design line of the bridge infinitely. The method fully considers the characteristics of nonlinear characteristics of the steel truss tied arch bridge, structural system conversion and load classification implementation in the bridge forming process, realizes the accurate calculation of the stress-free line shape and the space position of the bridge, and provides a filling condition for the subsequent accurate design. The method can synchronously acquire the pre-camber of the arch bridge and the spatial position of each node, directly and accurately guide construction and manufacturing of the components, and is also suitable for the arch bridge structure without a horizontal tie rod.
Description
Technical Field
The invention relates to a method for accurately designing the line shape and the space position of an unstressed state of a steel truss tied arch bridge; belongs to the technical field of civil engineering application.
Background
In recent years, along with the continuous development of bridge structural forms in China, the steel truss tied arch bridge is widely applied to bridge construction due to the advantages of light dead weight, high strength and the like. Meanwhile, the development of an accurate design concept ensures the stress rationality of the bridge construction in the whole life stage and is a new trend in recent years. As a high-order hyperstatic structure, the steel truss tied arch bridge has higher requirements on construction control, and the linear control of the bridge is a key problem in the design and construction stages [3-5] . Design specification in ChinaThe bridge span structure is provided with a pre-camber to counteract deflection deformation caused by constant load and 1/2 live load, and a deflection value obtained by applying the constant load and the 1/2 live load to a bridge formation state is generally used as the pre-camber. The problem of obtaining manufacturing (assembling) lines by developing pre-camber setting based on bridge formation lines is a great concern, and the main methods related to pre-camber setting of steel truss bridges currently include a geometric method, a temperature raising and lowering method, a stress-free state arching method and the like.
The geometric method establishes a relationship between the upper chord adjustment value and the pre-camber setting based on the geometric relationship between truss members. Chen Xiaojia and the like are based on a geometric positive sequence assembly method, a segment truss matrix, an internode length matrix and a theoretical pre-camber are used as input parameters, and a factory pre-camber curve is obtained by combining rod manufacturing precision. Feng Pei the influence matrix of the upper chord member adjustment value on the displacement of the lower chord node is established by adopting a geometric method, and the proper upper chord member adjustment value is obtained by solving a multi-element constraint condition equation set. However, the method generally needs repeated trial and error to obtain a linear shape which is well matched with the theoretical pre-camber, and is only suitable for the steel truss bridge with simple structural form. The temperature increasing and decreasing method adjusts the expansion and contraction amount of the rod piece through temperature change, so that the displacement of the control node accords with the theoretical pre-camber. Li Jiali and the like obtain an influence coefficient matrix of temperature load on node displacement, support counter force and rod stress based on a finite element method, and establish a pre-camber optimization model by combining an operation research multi-objective planning theory. The method comprises the steps of forming a constraint multi-element equation set by using the influence vector of the rod member temperature change value on the node pre-camber value or other constraint conditions, and obtaining the ideal pre-camber by combining a least square method. For a large-span hyperstatic structure, the method is easy to generate support counter force and additional rod member stress, and a constraint equation set is generally difficult to solve. The stress-free state method takes the bridge formation line shape as a known quantity, solves the size of each component in the stress-free state, and obtains the stress-free line shape of the structure, wherein the line shape automatically approaches to the target line shape under the action of load. Li Maonong and the like take the relative pre-camber between adjacent sections as input load, and calculate the expansion and contraction amount of the rod piece by a mechanical balance equation under the stress-free state, thereby achieving the aim of pre-setting camber. The essence of the research work is that the truss structure arches, the pre-arching degree is reasonably and reversely overlapped to the design line shape, and the purpose of the research work is to obtain the space line shape and the specific node position of the bridge structure in the unstressed state, so that reference and guidance are provided for segment manufacture. Therefore, obtaining stress-free state information of the bridge structure is a key problem of linear design.
Currently, some researches are attempted to directly obtain the stress-free line shape of the bridge. But starting the communication, namely establishing a staged forming structure linear control equation of the relation between the structural design target state and the unit stress-free state quantity, and processing the control equation by combining the specific geometric construction of the structure, so as to solve the stress-free line shape of the structure. However, the method is mainly suitable for beam bridges, the influence caused by the structural nonlinearity of the large-span arch bridge is not ignored, and particularly, certain deviation exists when the longitudinal pre-deflection quantity set for counteracting the longitudinal deformation generated by the main arch bearing is calculated, so that the stress-free linear deviation has great influence on the stress control at the bridge construction stage and the force distribution in the bridge forming state. Zhu Yongzhan for the first time, an idea of adopting an iterative method to carry out linear design of a bridge is provided for a long-span continuous steel truss bridge, and the method considers structural nonlinearity to a certain extent, but does not consider the specific structure of the truss structure, and cannot directly obtain truss node assembly coordinates.
In general, accurate acquisition of the linear and nodal spatial locations of a steel truss tied arch bridge in an unstressed state is a critical issue closely related to design and construction, and little research is currently done in this regard.
Disclosure of Invention
The method takes the concrete construction process of the steel truss tied arch bridge into consideration for the first time, and proposes taking the designed line shape of the bridge as an initial unstressed line shape, calculating the difference between the line shape and the designed line shape after deformation under a set load, correcting the unstressed line shape, and carrying out iterative calculation until the spatial position of the unstressed line shape after the stress-free line shape is subjected to the set load is infinitely approximate to the designed line shape of the bridge. In particular, the structural system conversion in the actual bridge formation process is considered, and loads are loaded to bridge structural systems in different stages in a grading manner, so that the stress-free line shape and the spatial position of the bridge are accurately extracted.
The invention discloses a method for accurately designing the linear and spatial positions of a steel truss tied arch bridge in an unstressed state, which comprises the following steps:
step one
Obtaining a designed bridge line shape of a main arch structure of the steel truss tied arch bridge, and taking the designed bridge line shape as an initial stress-free line shape;
step two
Taking the design line as an initial stress-free line shape, and calculating a curve of the design line after deformation under the action of a grading load; obtaining a difference delta 1 between the curve and a target line shape (namely a design line shape), and reversely superposing the difference delta 1 to an initial stress-free line shape to form one-time updating; and then taking the updated stress-free line as a reference, repeating the steps to calculate a curve after the deformation under the action of the grading load, comparing and obtaining a difference delta 2 between the curve and the target line, updating again, and the like until delta n meets the criterion requirement, namely taking the updated stress-free line as the stress-free state line of the structure.
In general, the vertical displacement difference vector Y at each node is extracted from Δn n Setting a cutoff condition by specifying its two norms; namely:
R(n)＝||Y n || (1)
when R (n)<10 -4 m, stopping the iteration, wherein R (n) is a criterion.
In the invention, the main arch structure of the steel truss tied arch bridge is designed into a bridge line shape and is provided by a design unit. The bridge formation line shape generally contains the information of the integral line shape of the structure, the space coordinates of the nodes of each rod piece and the like.
The invention relates to a method for accurately designing the linear and spatial positions of an unstressed state of a steel truss tied arch bridge; structural system conversion and load classification during bridging must be performed. The load is divided into N stages, and N is more than or equal to 2.
The main span structure of the steel truss tied arch bridge generally consists of a main arch, a horizontal flexible tie bar and a main girder. The main arch is a main bearing structure, and the horizontal flexible tie bars and the main beams are used for counteracting horizontal thrust generated when the main arch bears the weight, so that deformation is reduced. The structural system fully combines the stress characteristics of the beams and the arches, and effectively improves the integral bearing level of the bridge structure.
Because the structures are not formed synchronously, the steel truss tied arch bridge can undergo structural system conversion during construction. In general, the main arch is first closed to form a structural system consisting of the main arch and the horizontal flexible tie (first stage system), and then the main beam is closed to form a structural system consisting of the main arch, the horizontal flexible tie and the main beam (second stage system). According to different actual construction processes, multiple system conversion can exist, the basic thought of the system conversion method is similar to that of two-stage system conversion, different structural systems correspond to different construction stages, and the load born by the different structural systems is different. Therefore, when the invention carries out the stress-free linear calculation of the steel truss tied arch bridge, the structural system and the stress condition in the construction process are fully considered, and the load step-by-step loading mode is adopted. Taking the two-stage system as an example, only applying a first-stage constant load on the system before the main beams are folded, wherein the specific first-stage constant load is selected according to the general standard for highway bridge and culvert design (JTG D60-2015); and applying a second-stage constant load and a 1/2 active load to the system after the main beams are folded, wherein the concrete of the second-stage constant load and the 1/2 active load is selected according to the general Standard for highway bridge and culvert design (JTG D60-2015). This eliminates the calculation bias caused by the inconsistent stiffness of different structural systems.
When the method is actually applied, before iterative computation is carried out, the designed line shape of the steel truss tied arch bridge is required to be obtained as an initial stress-free line shape, and a finite element computation model is established based on designed physical parameters (various material densities, elastic modulus, shear modulus, poisson ratio and the like) and geometric parameters (various component section sizes, lengths, node space positions and the like). Obtaining a rigidity matrix of a first-stage structural system, and then applying a first-stage constant load corresponding to the first-stage structural system at a corresponding node position; and carrying out matrix calculation by combining the structural system rigidity matrix and the load array to obtain the deformation under the load action and the deformed middle line shape. On the basis, updating a finite element calculation model, obtaining a rigidity matrix of the second-stage structural system, then applying a load corresponding to the second stage (namely, a second-stage constant load plus 1/2 live load), and carrying out matrix operation to solve the deformation and the deformed structural line shape under the action of the second-stage load. And calculating the difference between the deformed structural line shape and the target (design) line shape, and superposing the difference to the initial stress-free line shape for correction, namely completing one-time iterative calculation of the stress-free line shape, and forming one-time update.
The invention relates to a primary constant load mainly referring to the dead weight of a structure, wherein the dead weight of a main girder acts on the corresponding position of a main arch through a suspender. And the second-stage constant load is the dead weight of bridge deck pavement and auxiliary facilities. 1/2 live load, including automobile load, crowd load and non-motor vehicle load, is set according to the specification.
And taking the updated stress-free line shape and node space position information as references, and combining designed physical parameters (various material densities, elastic modulus and the like) and related geometric parameters to build a finite element calculation model. And sequentially acquiring a rigidity matrix and a load array of the first-stage structural system and a rigidity matrix and a load array of the second-stage structural system, calculating deformation and deformed structural line shape, and correcting the stress-free line shape again according to the difference between the deformed structural line shape and the target (design) line shape.
And (3) repeatedly calculating until the deformed structure line shape is very close to the target (design) line shape, and stopping calculating, wherein the stress-free line shape at the moment is the accurate stress-free line shape of the steel truss tied arch bridge structure.
In practical application, the stress-free line shape gradually maintains stable and unchanged along with the increase of iteration times, and meanwhile, the obtained line shape gradually approaches to the design line shape under the action of load. And stopping iterative calculation when the error after repeated iterative calculation is smaller than the allowable value, namely the accuracy meets the requirement, and finally obtaining the stress-free state linear shape of the integral structure, the stress-free length of each component of the structure and the node space position coordinates.
When accuracy judgment is carried out, a difference delta n (n=1, 2 … …) between the linear shape and the target linear shape after the structural deformation obtained by the nth iterative computation is obtained, and a vertical displacement difference vector Y at each node is extracted n The cutoff condition is set by specifying its two norms.
R(n)＝||Y n || (1)
When R (n) is combined with calculation experience<10 -4 And m, stopping iteration. The stress-free line shape adopted in the calculation can be used as the accurate stress-free line shape of the steel truss tied arch bridge, and the coordinates of each node contained in the line shape areIs accurate spatial position information.
Principle and advantages
The basic principle comprises:
finite element modeling and deformation calculation for steel truss tied arch bridge
Carrying out finite element modeling on each rod (such as an upper chord, a lower chord, a web member, a longitudinal beam, a cross beam and a wind brace) of the main arch truss and a horizontal tie rod by adopting a beam column unit and a rod unit respectively, calculating structural deformation under the action of load by considering boundary constraint conditions, and firstly establishing the number, the length, the cross sectional area, the material elastic modulus and the node number of each rod under a local coordinate system;
the beam column unit nodes comprise translational degrees of freedom and rotational degrees of freedom, and a unit model under a local coordinate system is built. Assuming that the displacement array of the units is { delta ] e }＝{u i ,v i ,θ i ,u j ,v j ,θ j } T As shown in fig. 2, wherein: i. j is the node number of two nodes forming the unit; u (u) i 、u j Representing the axial displacement of the node, v i ,、v j Represents the lateral displacement of the node, theta i ,、θ j Representing the angular displacement of the node; the load array is { F ] e }＝{F xi ,F yi ,M i ,F xj ,F yj ,M j } T Wherein: f (F) xi 、F xj Representing the axial load of the joint, F yi ,、F yj Represents the transverse load of the node, M i ,、M j Representing the node bending moment. Assuming that the material is subjected to linear elastic deformation, the beam column unit is small in deformation, the axial displacement and bending deformation of the unit cannot be affected mutually, and the rigidity matrix [ K ] of the beam column unit can be obtained by combining the rigidity matrix of the rod unit with the rigidity matrix of the pure bending beam according to the superposition principle e ]The following are provided:
wherein E is the elastic modulus of the material; a is the cross-sectional area of the rod piece; i is the section coefficient of the rod piece; l is the length of the rod piece unit,
x i 、y i and x j 、y j The coordinate values of two nodes of the units i and j are respectively shown.
Because the directions of the beam column units are different in the overall structure, as shown in fig. 3, the unit stiffness matrix, the displacement array and the load array under the local coordinate system need to be converted into the same coordinate system (overall coordinate system). The cell stiffness matrix under the global coordinate system is recorded as
In [ K ] e ]Is a unit stiffness matrix in a local coordinate system, [ C ]]Is a coordinate transformation matrix, as follows
Wherein θ is the angle between the unit local coordinate system and the unit global coordinate system.
The unit node force arrays and displacement arrays under the whole coordinate system are respectively as follows:
{F e and is the load array of cells in the global coordinate system,as units in an integral coordinate systemA displacement array;
based on this, for all units respectivelyThe total rigidity matrix K is formed by assembling according to 'seating' rule]The total load matrix { F } and the total deformation matrix { delta } while also considering and aggregating the correlation matrices of the horizontal tie bars. Then under the integral coordinate system, the structural overall deformation calculation equation is as follows
[K]{δ}＝{F} (7)
The curve obtained by subtracting the deformation amount from the stress-free line shape of the structure is the deformed line shape, and the difference value between the deformed line shape and the target line shape (design line shape) is delta 1, delta 2, and delta n. And (3) performing accuracy judgment on the difference delta n between the linear shape and the target linear shape after the structure deformation obtained by the nth iteration calculation, and determining an iteration stop condition, thereby obtaining the stress-free state linear shape of the structure and accurate spatial position information of the node.
The main advantages include:
(1) The limited iterative calculation takes the formed bridge line shape as the initial stress-free line shape, and the accurate stress-free line shape and the spatial position of the steel truss tied arch bridge structure can be obtained after a small number of times (generally less than 10 times) of iterative updating.
(2) The limited iterative calculation method fully considers the nonlinear characteristics of the structure, and ensures that the deformed bridge line shape is completely consistent with the bridge line shape.
(3) The limited iterative calculation method can obtain accurate spatial position information of each node of the steel truss and the stress-free length of each unit, and the accurate manufacturing line shape can be directly obtained without arching analysis.
(4) When the stress-free state linear and spatial position information is calculated, the structural system conversion and load grading implementation characteristics in the bridge forming process are considered, so that the calculation process is consistent with the actual bridge forming process.
The method can synchronously acquire the pre-camber of the arch bridge and the spatial position of each node, directly and accurately guide construction and manufacturing of the components, and is also suitable for the arch bridge structure without a horizontal tie rod.
Drawings
FIG. 1 is a flow chart of a staged iterative computation
Fig. 2 is a beam column unit diagram.
FIG. 3 is a schematic diagram of a model of a main girder.
Fig. 4 is a schematic diagram of the staged loading.
FIG. 5 is a schematic diagram of a steel truss tied arch bridge structure.
FIG. 6 is a graph of the deformation of the main arch under a graded load.
Fig. 7 is a general layout of a main bridge.
FIG. 8 is a diagram of a host bridge finite element model.
Fig. 9 is a diagram of a steel truss arch and horizontal tie bar model.
Fig. 10 is a boom number and placement diagram.
FIG. 11 is a comparison of the top chord pre-camber calculation.
FIG. 12 is a graph comparing the pre-camber values of the main span upper chord.
Fig. 13 is a spatial position diagram of an unstressed state.
From fig. 1, it can be seen that the precise design of the stress-free state line shape and the space position is performed based on the bridge formation line shape, and the transformation and load characteristics of the structural system existing in the construction process are considered in the iterative calculation.
It can be seen from fig. 2 that each beam-column unit comprises two nodes, 3 degrees of freedom per node, totaling 6 degrees of freedom.
The relationship between the main girder nodes can be seen from fig. 3.
It can be seen from fig. 4 that at different stages of the construction process, the load on the structure is different.
It can be seen from fig. 5 that there are different structural systems at different stages of the construction process.
From fig. 6 it can be seen that from a stress free line to a bridge line, the overall deformation is a superposition of the amounts of deformation of different structural systems under different loads.
The overall arrangement information of the host bridge can be seen from fig. 7.
Fig. 8 includes 340 beam-column units and 167 nodes.
As can be seen from fig. 9, the rigid truss tied arch bridge is generally composed of main arch, horizontal main beams (rigid tie bars), flexible tie bars, and the like.
The boom number and arrangement position information can be seen from fig. 10.
From fig. 11, it can be seen that the curve obtained by iterative calculation based on the present invention is highly coincident with the calculation result of the existing commercial software, which proves the correctness of the finite element modeling and calculation method.
From fig. 12, it can be seen that the stress-free line shape calculated by the invention according to the different system stage loading iteration is obviously different from the calculation result of the existing one-time loading method.
From fig. 13, it can be seen that the method of the present invention can synchronously obtain the accurate stress-free linear and spatial position information of the steel truss arch structure.
Detailed Description
Example 1
When the stress-free state linear and spatial positions of the steel truss tied arch bridge are designed and calculated, the characteristics of structural system conversion and load grading staged implementation in the bridge construction process are considered, and a stress-free state linear and spatial position accurate design method based on limited iterative calculation is provided; taking the bridge design line shape as an initial stress-free line shape, calculating the difference between the line shape after deformation under a set load and the design line shape, and correcting the initial stress-free line shape; and carrying out iterative calculation until the spatial position of the stress-free line shape after the stress-free line shape is subjected to the set load action approaches the bridge design line shape infinitely. Thereby realizing the accurate extraction of the linear and spatial positions of the stress-free state of the bridge.
The invention discloses a method for accurately designing the linear and spatial positions of a steel truss tied arch bridge in an unstressed state, which comprises the following steps:
step one
Obtaining a designed bridge line shape of a main arch structure of the steel truss tied arch bridge, and taking the designed bridge line shape as an initial stress-free line shape;
step two
Taking the design line as an initial stress-free line shape, and calculating a curve of the design line after deformation under the action of a grading load; obtaining the difference delta 1 between the curve and the target line shape (i.e. design line shape), and inversely adding the difference delta 1 to the initial stress-free line shape to form a curveUpdating for the second time; and then taking the updated stress-free line as a reference, repeating the steps to calculate the curve after the deformation under the action of the grading load, comparing and obtaining a difference delta 2, updating again, and so on until delta n is small enough, namely taking the updated stress-free line as the stress-free state line of the structure. In general, the vertical displacement difference vector Y at each node is extracted from Δn n The cutoff condition is set by specifying its two norms.
The invention relates to a method for accurately designing the linear and spatial positions of an unstressed state of a steel truss tied arch bridge; structural system conversion and load classification during bridging must be performed. The main span structure of the steel truss tied arch bridge generally consists of a main arch, a horizontal flexible tie bar and a main girder. The main arch is a main bearing structure, and the horizontal flexible tie bars and the main beams are used for counteracting horizontal thrust generated when the main arch bears the weight, so that deformation is reduced. The structural system fully combines the stress characteristics of the beams and the arches, and effectively improves the integral bearing level of the bridge structure.
Because the structures are not formed synchronously, the steel truss tied arch bridge can undergo structural system conversion during construction. In general, the main arch is first closed to form a structural system consisting of the main arch and the horizontal flexible tie (first stage system), and then the main beam is closed to form a structural system consisting of the main arch, the horizontal flexible tie and the main beam (second stage system). According to different actual construction processes, multiple system conversion can exist, the basic thought of the system conversion method is similar to that of two-stage system conversion, different structural systems correspond to different construction stages, and the load born by the different structural systems is different. Therefore, when the invention carries out the stress-free linear calculation of the steel truss tied arch bridge, the structural system and the stress condition in the construction process are fully considered, and the load step-by-step loading mode is adopted. Taking the two-stage system as an example, only applying a first-stage constant load on the system before the main beams are folded, wherein the specific first-stage constant load is selected according to the general standard for highway bridge and culvert design (JTG D60-2015); and applying a second-stage constant load and a 1/2 active load to the system after the main beams are folded, wherein the concrete of the second-stage constant load and the 1/2 active load is selected according to the general Standard for highway bridge and culvert design (JTG D60-2015). This eliminates the calculation bias caused by the inconsistent stiffness of different structural systems.
When the method is actually applied, before iterative computation is carried out, the designed line shape of the steel truss tied arch bridge is required to be obtained as an initial stress-free line shape, and a finite element computation model is established based on designed physical parameters (various material densities, elastic modulus, shear modulus, poisson ratio and the like) and geometric parameters (various component section sizes, lengths, node space positions and the like).
Carrying out finite element modeling on each rod (such as an upper chord, a lower chord, a web member, a longitudinal beam, a cross beam and a wind brace) of the main arch truss and a horizontal tie rod by adopting a beam column unit and a rod unit respectively, calculating structural deformation under the action of load by considering boundary constraint conditions, and firstly establishing the number, the length, the cross sectional area, the material elastic modulus and the node number of each rod under a local coordinate system;
the beam column unit nodes comprise translational degrees of freedom and rotational degrees of freedom, and a unit model under a local coordinate system is built. Assuming that the displacement array of the units is { delta ] e }＝{u i ,v i ,θ i ,u j ,v j ,θ j } T As shown in fig. 2, wherein: i. j is the node number of two nodes forming the unit; u (u) i 、u j Representing the axial displacement of the node, v i ,、v j Represents the lateral displacement of the node, theta i ,、θ j Representing the angular displacement of the node; the load array is { F ] e }＝{F xi ,F yi ,M i ,F xj ,F yj ,M j } T Wherein: f (F) xi 、F xj Representing the axial load of the joint, F yi ,、F yj Represents the transverse load of the node, M i ,、M j Representing the node bending moment. Assuming that the material is subjected to linear elastic deformation, the beam column unit is small in deformation, the axial displacement and bending deformation of the unit cannot be affected mutually, and the rigidity matrix [ K ] of the beam column unit can be obtained by combining the rigidity matrix of the rod unit with the rigidity matrix of the pure bending beam according to the superposition principle e ]The following are provided:
wherein E is the elastic modulus of the material; a is the cross-sectional area of the rod piece; i is the section coefficient of the rod piece; l is the length of the rod piece unit,
x i 、y i and x j 、y j The coordinate values of two nodes of the units i and j are respectively shown.
Because the directions of the beam column units are different in the overall structure, as shown in fig. 3, the unit stiffness matrix, the displacement array and the load array under the local coordinate system need to be converted into the same coordinate system (overall coordinate system). The cell stiffness matrix under the global coordinate system is recorded as
In [ K ] e ]Is a unit stiffness matrix in a local coordinate system, [ C ]]Is a coordinate transformation matrix, as follows
Wherein θ is the angle between the unit local coordinate system and the unit global coordinate system.
The unit node force arrays and displacement arrays under the whole coordinate system are respectively as follows:
is a load array of units in an overall coordinate system, < >>A displacement array of units in an overall coordinate system;
based on this, for all units respectivelyThe total rigidity matrix K is formed by assembling according to 'seating' rule]The total load matrix { F } and the total deformation matrix { delta } while also considering and aggregating the correlation matrices of the horizontal tie bars. Then under the integral coordinate system, the structural overall deformation calculation equation is as follows
[K]{δ}＝{F} (7)
And calculating the integral deformation of the steel truss arch bridge structure by considering the characteristics of structural system conversion and load grading implementation in stages in the bridge construction process. Load classification implementation mode, as shown in fig. 4. The two-stage load is applied in stages to the main arch-flexible tie system (first stage system) and the main arch-rigid-flexible tie-bar common combination system (second stage system), as shown in fig. 5.
Firstly, obtaining a rigidity matrix of a first-stage structural system, and then applying first-stage constant load corresponding to the first-stage structural system at a corresponding node position; and carrying out matrix calculation by combining the structural system rigidity matrix and the load array to obtain the deformation under the load action and the deformed middle line shape. On the basis, updating a finite element calculation model, obtaining a rigidity matrix of the second-stage structural system, then applying a load corresponding to the second stage (namely, a second-stage constant load plus 1/2 live load), and carrying out matrix operation to solve the deformation and the deformed structural line shape under the action of the second-stage load. The superposition of the deformation amounts is that the stress-free state line is totally deformed under the load, as shown in fig. 6.
And calculating the difference between the deformed structural line shape and the target (design) line shape, and superposing the difference to the initial stress-free line shape for correction, namely completing one-time iterative calculation of the stress-free line shape, and forming one-time update. And taking the updated stress-free line shape and node space position information as references, and combining designed physical parameters (various material densities, elastic modulus and the like) and related geometric parameters to build a finite element calculation model. And sequentially acquiring a rigidity matrix and a load array of the first-stage structural system and a rigidity matrix and a load array of the second-stage structural system, calculating deformation and deformed structural line shape, and correcting the stress-free line shape again according to the difference between the deformed structural line shape and the target (design) line shape.
And (3) repeatedly calculating until the deformed structure line shape is very close to the target (design) line shape, and stopping calculating, wherein the stress-free line shape at the moment is the accurate stress-free line shape of the steel truss tied arch bridge structure.
In practical application, the stress-free line shape gradually maintains stable and unchanged along with the increase of iteration times, and meanwhile, the obtained line shape gradually approaches to the design line shape under the action of load. And stopping iterative calculation when the error after repeated iterative calculation is smaller than the allowable value, namely the accuracy meets the requirement, and finally obtaining the stress-free state linear shape of the integral structure, the stress-free length of each component of the structure and the node space position coordinates.
When accuracy judgment is carried out, a difference delta n (n=1, 2 … …) between the linear shape and the target linear shape after the structural deformation obtained by the nth iterative computation is obtained, and a vertical displacement difference vector Y at each node is extracted n The cutoff condition is set by specifying its two norms.
R(n)＝||Y n || (1)
When R (n) is combined with calculation experience<10 -4 And m, stopping iteration. The stress-free line shape adopted in the calculation can be used as the accurate stress-free line shape of the steel truss tied arch bridge, and the coordinates of each node contained in the line shape are accurate spatial position information.
Engineering test verification
And (3) researching the correctness and feasibility of the finite iteration algorithm in the unstressed state in the text by combining related design parameters of the twilight level Xiangjiang bridge. The super bridge of Mitsui Xiangjiang is located in Hunan province, is a (70+180+180+70) m four-span continuous middle-bearing Feilin type steel truss tied arch bridge, the total length of the bridge is 500m, the main span is 2 multiplied by 180m, the sagittal height of the main arch is 36m, the sagittal ratio is 1/5, and the main girder adopts a superposed girder structure. The full-bridge transverse bridge adopts a double-sheet steel arch frame, and the transverse distance is 34.1m. The restraint system adopts a four-span continuous supporting system, a fixed support is adopted at the middle pier, and all other piers are provided with unidirectional or multidirectional movable supports. The overall arrangement of the full bridge is shown in fig. 7.
The main span steel arch rib and the main beam of the bridge are constructed by adopting a diagonal-draw buckling cantilever splicing method, and the whole sections of the arch sections are welded and connected on site. The main construction sequence comprises: after the main arch is closed, stretching a first batch of horizontal flexible tie bars, removing a buckling cable system and temporarily consolidating measures; tensioning the second batch and the third batch of flexible tie bars, and closing the main beams; and finally paving the bridge deck. The rigidity of the horizontal tie bars of the steel truss tied arch bridge is greatly different before and after the main beams are folded, the primary constant load before the main beams are folded is borne by the main arch and the flexible tie bars, and the horizontal rigid tie bars do not participate in bearing the primary constant load. Therefore, the stress-free line shape or pre-camber is studied by considering the system conversion and load classification application in the bridge formation process.
Parameters and calculations
And (4) carrying out limited iterative calculation on the stress-free state line shape and the space position of the bridge by combining the design drawing and the parameters of the twilight level Xiangjiang bridge. The main arch, the upper chord members, the lower chord members and the web members of the side span structure are regarded as beam column units, the horizontal tie bars are regarded as rod units, a single-arch three-dimensional finite element model (shown in fig. 8) is built based on a Matlab platform, and corresponding constraints are set. Wherein: the full bridge comprises 340 beam column units and 167 nodes.
The material parameters of the main span and the side span beam column units are elastic modulus 2.06 multiplied by 105Mpa, the material density is 7850kg/m < 3 >, and the related geometric parameters (wherein the section moment of inertia is the section horizontal axis moment of inertia) are calculated and obtained by referring to the design data. 4 bundles are respectively arranged on each side of the horizontal flexible tie rod and are divided into a midspan cable X1 and a through long cable X2; rigid tie bars Z1 and Z2 are disposed across the two spans, respectively, as shown in fig. 9. The main parameters of the flexible tie bar and the rigid tie bar are shown in table 1, and the tensile rigidity of the two are obviously different.
Table 1 horizontal tie parameters
The load involved in the analysis of the stress-free state of the bridge comprises: (1) The primary constant load mainly refers to the self weight of the structure, wherein the self weight of the main girder acts on the corresponding position of the main arch through the suspender. (2) And the second-stage constant load is the dead weight of bridge deck pavement and auxiliary facilities. (3) 1/2 live load, including automobile load, crowd load and non-motor vehicle load, is set according to the specification. In combination with the actual construction process of the steel truss tied arch bridge, in the conversion process from the unstressed state to the bridge forming state, the primary constant load is mainly borne by a main arch-flexible tie rod system, the dead weight of the main arch is equivalently applied to the joints of each beam column unit, and the primary constant load such as the dead weight of the suspender and the main beam is equivalently applied to the joints of the main arch as a suspender force, as shown in fig. 10. The second-stage transverse load equivalent is girder node force (side span) and boom force (main span); when the method is used for single arch calculation, the live load is only half of a specified value, and the influence of the load and rigidity of the transverse connecting rod is ignored. Table 2 shows the composition of the main arch structure section node drawbar forces.
Table 2 rib drawbar force equivalent value unit: kN
And when carrying out iterative calculation, modeling by taking the design line shape as an initial line shape in a stress-free state, and applying a balance load and a 1/2 live load according to the regulations to calculate the integral deformation of the steel truss structure. According to the load step-by-step implementation mode provided by the invention, two stages of loads are applied to the main arch-flexible tie rod system model and the main arch-rigid and flexible tie rod combined model in a step-by-step mode. And comparing and calculating the difference between the structural line shape and the design line shape under the action of the specified load, and superposing the line shape difference to the initial line shape in the stress-free state to realize one-time updating of the integral line shape and the space position of the structure in the stress-free state. Based on the updated stress-free line shape, the model is re-established to calculate the deformation, and the difference between the deformed structure line shape and the design line shape is calculated, so that the stress-free state line shape is updated again. And repeating the calculation to finally obtain the accurate stress-free line shape of the structure.
Test results
It is easy to find that the effect of the method is equivalent to that of the existing method (namely, the method of reversely superposing target lines such as deflection deformation on the basis of bridge line formation) if the method is implemented for only 1 time by aiming at the stress-free linear iterative calculation method of the steel truss tied arch bridge structure. For comparison, once loading calculation is still carried out on the bridge formation system, and the deformation obtained by carrying out 1 calculation based on the method, the deformation after iterative calculation and the deflection deformation calculated based on Midas software are compared as shown in figure 11. The curve obtained based on 1 calculation is highly coincident with the calculation result of the existing commercial software, and the correctness of the finite element modeling and calculation method is proved. On the other hand, the vertical and horizontal deformation of the deformation curve after repeated iterative computation is increased, which indicates the necessity of developing limited iterative computation.
Furthermore, by combining the embodiment model and the limited iterative calculation method, the actual conditions of structural system conversion, load phased implementation and the like existing in the actual bridge forming process are considered, and the stress-free state linear and spatial position calculation is performed. Taking the right main arch as an example, the results of the stress-free linear iterative calculation under two working conditions of primary loading in a bridge formation state and staged loading in different systems are shown in fig. 12, and the stress-free linear relative design linear vertical increment DeltaV and horizontal decrement DeltaH calculated by different methods are compared as shown in table 3.
TABLE 3 results of stress free linear calculation of the main arches on the right side
It can be seen that the calculated steel truss tied-arch bridge is stress free linear (, when the system conversion and the staged load implementation of the bridge formation process are fully considered for the bridge structure V ＝26.9cm，△ H =18.6 cm) and linear (delta) designed according to the existing method V ＝12.5cm，△ H =5.9 cm) deviation is large. The existing design method is insufficient in consideration of pre-camber when the steel truss arch is manufactured into a linear shape, the linear shape is not a true stress-free state linear shape of the structure, and certain influence is exerted on truss segment processing and manufacturing and pre-deflection design of the movable support.
It should be noted that, considering the system conversion and the staged load implementation of the bridge forming process, the present invention can synchronously calculate the positions of the spatial nodes in the stress-free state of the structure, as shown in fig. 13. The method can directly and accurately obtain the spatial position of each node under the manufacturing line shape and the stress-free size of the component, and avoids complex arching calculation in the traditional method.
In the embodiment of the invention, a single-arch three-dimensional finite element model is established based on a Matlab platform by combining design parameters of a twilight level Xiangjiang bridge, and the stress-free linear iterative computation of the bridge is carried out. The result shows that the stress-free state line shape obtained based on one-time calculation is highly consistent with the calculation result of the existing commercial software, and the correctness of the modeling and calculation method is verified. On the other hand, the stress-free linear relative design linear difference calculated based on the two working conditions of the primary loading of the bridge forming state and the hierarchical loading of different systems is obvious, which indicates the necessity and rationality of considering the structural system conversion and the load staged application of the bridge forming process during the stress-free linear design.
Claims (6)
1. The method for accurately designing the non-stress state line shape and the space position of the steel truss tied arch bridge is characterized by comprising the following steps of:
step one
Obtaining a designed bridge line shape of a main arch structure of the steel truss tied arch bridge, and taking the designed bridge line shape as an initial stress-free line shape;
step two
Taking the design line as an initial stress-free line shape, and calculating a curve of the design line after deformation under the action of a grading load; obtaining a difference delta 1 between the curve and the design line shape, and reversely superposing the difference delta 1 to the initial stress-free line shape to form one-time updating; and then taking the updated stress-free line as a reference, repeating the steps to calculate a curve after the deformation under the action of the graded load, comparing and obtaining a difference delta 2 between the curve and the design line, updating again, and the like until delta n meets the criterion requirement, namely taking the updated stress-free line as the stress-free state line of the structure.
2. The method for accurately designing the stress state line shape and the space position of the steel truss tied-arch bridge according to claim 1, which is characterized in that: extracting the vertical displacement difference value vector Y at each node from delta n n Setting a cutoff condition by specifying its two norms; namely:
R(n)＝||Y n || (1)
when R (n)<10 -4 m, stopping the iteration, wherein R (n) is a criterion.
3. The method for accurately designing the stress state line shape and the space position of the steel truss tied-arch bridge according to claim 1, which is characterized in that: the load is divided into N stages, and N is more than or equal to 2.
4. The method for accurately designing the stress state line shape and the space position of the steel truss tied-arch bridge according to claim 1, which is characterized in that: before iterative computation, the design line shape of the steel truss tied arch bridge is required to be obtained as an initial stress-free line shape, and a finite element computation model is established based on the designed physical parameters and geometric parameters; the physical parameters of the design comprise the density, the elastic modulus, the shear modulus and the poisson ratio of various materials; the geometric parameters comprise the cross-sectional size, the length and the node space position of various components.
5. The method for accurately designing the stress state line shape and the space position of the steel truss tied-arch bridge according to claim 1, which is characterized in that: when n=2, the number of the N-type metal wires is,
obtaining a rigidity matrix of a first-stage structural system, and then applying a first-stage constant load corresponding to the first-stage structural system at a corresponding node position; performing matrix calculation by combining the rigidity matrix of the structural system and the load array to obtain deformation under the action of load and deformed middle line shape;
on the basis, updating a finite element calculation model, obtaining a rigidity matrix of a second-stage structural system, and then applying a load corresponding to the second stage, namely: carrying out matrix operation to solve the deformation and the deformed structural line shape under the action of the load of the second stage; and calculating the difference between the deformed structural line shape and the design line shape, and superposing the difference to the initial stress-free line shape to correct, namely completing one-time iterative calculation of the stress-free line shape to form one-time updating.
6. The method for accurately designing the stress state line shape and the space position of the steel truss tied-arch bridge according to claim 1, which is characterized in that: the finite element modeling and deformation calculation process of the steel truss tied arch bridge comprises the following steps:
carrying out finite element modeling on each rod piece and the horizontal tie rod of the main arch truss by adopting a beam column unit and a rod unit respectively, calculating structural deformation under the action of load by considering boundary constraint conditions, and firstly establishing the number, length, cross section area, material elastic modulus and node number of each rod piece under a local coordinate system; each member of the main arch truss comprises an upper chord member, a lower chord member, web members, longitudinal beams, cross beams and wind braces;
the beam column unit nodes comprise translational degrees of freedom and rotational degrees of freedom, and a unit model under a local coordinate system is built; assuming that the displacement array of the units is { delta ] e }＝{u i ,v i ,θ i ,u j ,v j ,θ j } T Wherein: i. j is the node number of two nodes forming the unit; u (u) i 、u j Representing the axial displacement of the node, v i ,、v j Represents the lateral displacement of the node, theta i ,、θ j Representing the angular displacement of the node; the load array is { F ] e }＝{F xi ,F yi ,M i ,F xj ,F yj ,M j } T Wherein: f (F) xi 、F xj Representing the axial load of the joint, F yi ,、F yj Represents the transverse load of the node, M i ,、M j Representing the node bending moment; assuming that the material is elastically deformed linearly, the beam column unit is small in deformation, the axial displacement and bending deformation of the unit cannot be mutually influenced, and the rod unit is arranged according to the superposition principleThe element rigidity matrix is combined with the pure bending beam rigidity matrix to obtain a rigidity matrix [ K ] of the beam column unit e ]The following are provided:
wherein E is the elastic modulus of the material; a is the cross-sectional area of the rod piece; i is the section coefficient of the rod piece; l is the length of the rod piece unit,x i 、y i and x j 、y j Respectively representing coordinate values of two nodes of the units i and j;
because the directions of the beam column units are different in the integral structure, the unit stiffness matrix, the displacement array and the load array under the local coordinate system are required to be converted into the integral coordinate system; the cell stiffness matrix under the global coordinate system is recorded as
In [ K ] e ]Is a unit stiffness matrix in a local coordinate system, [ C ]]Is a coordinate transformation matrix, as follows
Wherein θ is the angle between the unit local coordinate system and the unit global coordinate system.
The unit node force arrays and displacement arrays under the whole coordinate system are respectively as follows:
is a load array of units in an overall coordinate system, < >>A displacement array of units in an overall coordinate system;
based on this, for all units respectivelyThe total rigidity matrix K is formed by assembling according to 'seating' rule]A total load matrix { F } and a total deformation matrix { delta } while also considering and aggregating correlation matrices for horizontal tie bars; then in the global coordinate system, the structural global deformation calculation equation is:
[K]{δ}＝{F} (7)
the curve obtained by subtracting the deformation amount from the stress-free line shape of the structure is the deformed line shape, and the difference value between the deformed line shape and the designed line shape is delta 1, delta 2, delta n; and (3) performing accuracy judgment on the difference delta n between the linear shape and the target linear shape after the structure deformation obtained by the nth iteration calculation, and determining an iteration stop condition, thereby obtaining the stress-free state linear shape of the structure and accurate spatial position information of the node.
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| CN116226972A (en) * | 2023-01-04 | 2023-06-06 | 中铁大桥勘测设计院集团有限公司 | Continuous steel truss girder pre-camber setting method and continuous steel truss girder |
| CN117634233A (en) * | 2023-10-23 | 2024-03-01 | 中交路桥建设有限公司 | Truss arch bridge staged construction intelligent monitoring method based on stress-free state |
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| CN116226972A (en) * | 2023-01-04 | 2023-06-06 | 中铁大桥勘测设计院集团有限公司 | Continuous steel truss girder pre-camber setting method and continuous steel truss girder |
| CN116226972B (en) * | 2023-01-04 | 2024-04-19 | 中铁大桥勘测设计院集团有限公司 | Continuous steel truss girder pre-camber setting method and continuous steel truss girder |
| CN117634233A (en) * | 2023-10-23 | 2024-03-01 | 中交路桥建设有限公司 | Truss arch bridge staged construction intelligent monitoring method based on stress-free state |
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